LMFDB - Embedded newform 8018.2.a.h.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.58821 q^{3} +1.00000 q^{4} +4.43977 q^{5} -1.58821 q^{6} +2.05481 q^{7} -1.00000 q^{8} -0.477577 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.58821 q^{3} +1.00000 q^{4} +4.43977 q^{5} -1.58821 q^{6} +2.05481 q^{7} -1.00000 q^{8} -0.477577 q^{9} -4.43977 q^{10} -2.29898 q^{11} +1.58821 q^{12} +1.35690 q^{13} -2.05481 q^{14} +7.05131 q^{15} +1.00000 q^{16} -5.61423 q^{17} +0.477577 q^{18} -1.00000 q^{19} +4.43977 q^{20} +3.26348 q^{21} +2.29898 q^{22} +6.75495 q^{23} -1.58821 q^{24} +14.7116 q^{25} -1.35690 q^{26} -5.52314 q^{27} +2.05481 q^{28} +5.14682 q^{29} -7.05131 q^{30} -4.55085 q^{31} -1.00000 q^{32} -3.65128 q^{33} +5.61423 q^{34} +9.12290 q^{35} -0.477577 q^{36} +2.78120 q^{37} +1.00000 q^{38} +2.15505 q^{39} -4.43977 q^{40} +6.16701 q^{41} -3.26348 q^{42} +1.84953 q^{43} -2.29898 q^{44} -2.12033 q^{45} -6.75495 q^{46} +9.53619 q^{47} +1.58821 q^{48} -2.77775 q^{49} -14.7116 q^{50} -8.91660 q^{51} +1.35690 q^{52} +4.52921 q^{53} +5.52314 q^{54} -10.2070 q^{55} -2.05481 q^{56} -1.58821 q^{57} -5.14682 q^{58} +5.82027 q^{59} +7.05131 q^{60} -4.55498 q^{61} +4.55085 q^{62} -0.981330 q^{63} +1.00000 q^{64} +6.02433 q^{65} +3.65128 q^{66} +0.756021 q^{67} -5.61423 q^{68} +10.7283 q^{69} -9.12290 q^{70} +6.75575 q^{71} +0.477577 q^{72} +4.44621 q^{73} -2.78120 q^{74} +23.3651 q^{75} -1.00000 q^{76} -4.72398 q^{77} -2.15505 q^{78} +10.7397 q^{79} +4.43977 q^{80} -7.33919 q^{81} -6.16701 q^{82} -17.2935 q^{83} +3.26348 q^{84} -24.9259 q^{85} -1.84953 q^{86} +8.17425 q^{87} +2.29898 q^{88} -6.04620 q^{89} +2.12033 q^{90} +2.78818 q^{91} +6.75495 q^{92} -7.22772 q^{93} -9.53619 q^{94} -4.43977 q^{95} -1.58821 q^{96} +2.42152 q^{97} +2.77775 q^{98} +1.09794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.58821	0.916956	0.458478	−	0.888706i	$-0.348395\pi$
$3$	1.58821	0.916956	0.458478	+	0.888706i	$0.348395\pi$
$4$	1.00000	0.500000
$5$	4.43977	1.98553	0.992764	−	0.120086i	$-0.0383170\pi$
$5$	4.43977	1.98553	0.992764	+	0.120086i	$0.0383170\pi$
$6$	−1.58821	−0.648386
$7$	2.05481	0.776646	0.388323	−	0.921523i	$-0.373055\pi$
$7$	2.05481	0.776646	0.388323	+	0.921523i	$0.373055\pi$
$8$	−1.00000	−0.353553
$9$	−0.477577	−0.159192
$10$	−4.43977	−1.40398
$11$	−2.29898	−0.693170	−0.346585	−	0.938019i	$-0.612659\pi$
$11$	−2.29898	−0.693170	−0.346585	+	0.938019i	$0.612659\pi$
$12$	1.58821	0.458478
$13$	1.35690	0.376337	0.188168	−	0.982137i	$-0.439745\pi$
$13$	1.35690	0.376337	0.188168	+	0.982137i	$0.439745\pi$
$14$	−2.05481	−0.549172
$15$	7.05131	1.82064
$16$	1.00000	0.250000
$17$	−5.61423	−1.36165	−0.680825	−	0.732446i	$-0.738379\pi$
$17$	−5.61423	−1.36165	−0.680825	+	0.732446i	$0.738379\pi$
$18$	0.477577	0.112566
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.43977	0.992764
$21$	3.26348	0.712150
$22$	2.29898	0.490145
$23$	6.75495	1.40850	0.704252	−	0.709950i	$-0.251283\pi$
$23$	6.75495	1.40850	0.704252	+	0.709950i	$0.251283\pi$
$24$	−1.58821	−0.324193
$25$	14.7116	2.94232
$26$	−1.35690	−0.266110
$27$	−5.52314	−1.06293
$28$	2.05481	0.388323
$29$	5.14682	0.955741	0.477870	−	0.878430i	$-0.341409\pi$
$29$	5.14682	0.955741	0.477870	+	0.878430i	$0.341409\pi$
$30$	−7.05131	−1.28739
$31$	−4.55085	−0.817356	−0.408678	−	0.912679i	$-0.634010\pi$
$31$	−4.55085	−0.817356	−0.408678	+	0.912679i	$0.634010\pi$
$32$	−1.00000	−0.176777
$33$	−3.65128	−0.635606
$34$	5.61423	0.962833
$35$	9.12290	1.54205
$36$	−0.477577	−0.0795961
$37$	2.78120	0.457227	0.228613	−	0.973517i	$-0.426581\pi$
$37$	2.78120	0.457227	0.228613	+	0.973517i	$0.426581\pi$
$38$	1.00000	0.162221
$39$	2.15505	0.345084
$40$	−4.43977	−0.701990
$41$	6.16701	0.963125	0.481563	−	0.876412i	$-0.340069\pi$
$41$	6.16701	0.963125	0.481563	+	0.876412i	$0.340069\pi$
$42$	−3.26348	−0.503566
$43$	1.84953	0.282051	0.141025	−	0.990006i	$-0.454960\pi$
$43$	1.84953	0.282051	0.141025	+	0.990006i	$0.454960\pi$
$44$	−2.29898	−0.346585
$45$	−2.12033	−0.316080
$46$	−6.75495	−0.995963
$47$	9.53619	1.39100	0.695498	−	0.718528i	$-0.255184\pi$
$47$	9.53619	1.39100	0.695498	+	0.718528i	$0.255184\pi$
$48$	1.58821	0.229239
$49$	−2.77775	−0.396821
$50$	−14.7116	−2.08053
$51$	−8.91660	−1.24857
$52$	1.35690	0.188168
$53$	4.52921	0.622134	0.311067	−	0.950388i	$-0.399314\pi$
$53$	4.52921	0.622134	0.311067	+	0.950388i	$0.399314\pi$
$54$	5.52314	0.751604
$55$	−10.2070	−1.37631
$56$	−2.05481	−0.274586
$57$	−1.58821	−0.210364
$58$	−5.14682	−0.675811
$59$	5.82027	0.757735	0.378868	−	0.925451i	$-0.376314\pi$
$59$	5.82027	0.757735	0.378868	+	0.925451i	$0.376314\pi$
$60$	7.05131	0.910320
$61$	−4.55498	−0.583206	−0.291603	−	0.956539i	$-0.594189\pi$
$61$	−4.55498	−0.583206	−0.291603	+	0.956539i	$0.594189\pi$
$62$	4.55085	0.577958
$63$	−0.981330	−0.123636
$64$	1.00000	0.125000
$65$	6.02433	0.747227
$66$	3.65128	0.449441
$67$	0.756021	0.0923627	0.0461814	−	0.998933i	$-0.485295\pi$
$67$	0.756021	0.0923627	0.0461814	+	0.998933i	$0.485295\pi$
$68$	−5.61423	−0.680825
$69$	10.7283	1.29154
$70$	−9.12290	−1.09039
$71$	6.75575	0.801760	0.400880	−	0.916131i	$-0.368704\pi$
$71$	6.75575	0.801760	0.400880	+	0.916131i	$0.368704\pi$
$72$	0.477577	0.0562829
$73$	4.44621	0.520389	0.260195	−	0.965556i	$-0.416213\pi$
$73$	4.44621	0.520389	0.260195	+	0.965556i	$0.416213\pi$
$74$	−2.78120	−0.323308
$75$	23.3651	2.69798
$76$	−1.00000	−0.114708
$77$	−4.72398	−0.538348
$78$	−2.15505	−0.244011
$79$	10.7397	1.20831	0.604155	−	0.796867i	$-0.293511\pi$
$79$	10.7397	1.20831	0.604155	+	0.796867i	$0.293511\pi$
$80$	4.43977	0.496382
$81$	−7.33919	−0.815466
$82$	−6.16701	−0.681032
$83$	−17.2935	−1.89821	−0.949106	−	0.314956i	$-0.898010\pi$
$83$	−17.2935	−1.89821	−0.949106	+	0.314956i	$0.898010\pi$
$84$	3.26348	0.356075
$85$	−24.9259	−2.70359
$86$	−1.84953	−0.199440
$87$	8.17425	0.876372
$88$	2.29898	0.245073
$89$	−6.04620	−0.640896	−0.320448	−	0.947266i	$-0.603833\pi$
$89$	−6.04620	−0.640896	−0.320448	+	0.947266i	$0.603833\pi$
$90$	2.12033	0.223503
$91$	2.78818	0.292280
$92$	6.75495	0.704252
$93$	−7.22772	−0.749480
$94$	−9.53619	−0.983583
$95$	−4.43977	−0.455511
$96$	−1.58821	−0.162096
$97$	2.42152	0.245868	0.122934	−	0.992415i	$-0.460770\pi$
$97$	2.42152	0.245868	0.122934	+	0.992415i	$0.460770\pi$
$98$	2.77775	0.280595
$99$	1.09794	0.110347
$100$	14.7116	1.47116
$101$	8.95487	0.891042	0.445521	−	0.895271i	$-0.353018\pi$
$101$	8.95487	0.891042	0.445521	+	0.895271i	$0.353018\pi$
$102$	8.91660	0.882875
$103$	−2.04613	−0.201611	−0.100805	−	0.994906i	$-0.532142\pi$
$103$	−2.04613	−0.201611	−0.100805	+	0.994906i	$0.532142\pi$
$104$	−1.35690	−0.133055
$105$	14.4891	1.41399
$106$	−4.52921	−0.439915
$107$	−18.9633	−1.83325	−0.916625	−	0.399749i	$-0.869097\pi$
$107$	−18.9633	−1.83325	−0.916625	+	0.399749i	$0.869097\pi$
$108$	−5.52314	−0.531464
$109$	−19.6342	−1.88061	−0.940306	−	0.340330i	$-0.889461\pi$
$109$	−19.6342	−1.88061	−0.940306	+	0.340330i	$0.889461\pi$
$110$	10.2070	0.973197
$111$	4.41714	0.419257
$112$	2.05481	0.194161
$113$	9.66587	0.909288	0.454644	−	0.890673i	$-0.349766\pi$
$113$	9.66587	0.909288	0.454644	+	0.890673i	$0.349766\pi$
$114$	1.58821	0.148750
$115$	29.9904	2.79662
$116$	5.14682	0.477870
$117$	−0.648024	−0.0599098
$118$	−5.82027	−0.535800
$119$	−11.5362	−1.05752
$120$	−7.05131	−0.643694
$121$	−5.71467	−0.519515
$122$	4.55498	0.412389
$123$	9.79453	0.883143
$124$	−4.55085	−0.408678
$125$	43.1173	3.85652
$126$	0.981330	0.0874238
$127$	16.5167	1.46562	0.732808	−	0.680435i	$-0.238209\pi$
$127$	16.5167	1.46562	0.732808	+	0.680435i	$0.238209\pi$
$128$	−1.00000	−0.0883883
$129$	2.93745	0.258628
$130$	−6.02433	−0.528369
$131$	−0.350625	−0.0306342	−0.0153171	−	0.999883i	$-0.504876\pi$
$131$	−0.350625	−0.0306342	−0.0153171	+	0.999883i	$0.504876\pi$
$132$	−3.65128	−0.317803
$133$	−2.05481	−0.178175
$134$	−0.756021	−0.0653103
$135$	−24.5215	−2.11047
$136$	5.61423	0.481416
$137$	−3.05966	−0.261404	−0.130702	−	0.991422i	$-0.541723\pi$
$137$	−3.05966	−0.261404	−0.130702	+	0.991422i	$0.541723\pi$
$138$	−10.7283	−0.913254
$139$	15.9057	1.34910	0.674550	−	0.738229i	$-0.264338\pi$
$139$	15.9057	1.34910	0.674550	+	0.738229i	$0.264338\pi$
$140$	9.12290	0.771026
$141$	15.1455	1.27548
$142$	−6.75575	−0.566930
$143$	−3.11949	−0.260865
$144$	−0.477577	−0.0397980
$145$	22.8507	1.89765
$146$	−4.44621	−0.367971
$147$	−4.41166	−0.363867
$148$	2.78120	0.228613
$149$	−4.44775	−0.364374	−0.182187	−	0.983264i	$-0.558318\pi$
$149$	−4.44775	−0.364374	−0.182187	+	0.983264i	$0.558318\pi$
$150$	−23.3651	−1.90776
$151$	24.4752	1.99176	0.995880	−	0.0906781i	$-0.0289035\pi$
$151$	24.4752	1.99176	0.995880	+	0.0906781i	$0.0289035\pi$
$152$	1.00000	0.0811107
$153$	2.68122	0.216764
$154$	4.72398	0.380669
$155$	−20.2047	−1.62288
$156$	2.15505	0.172542
$157$	−7.38221	−0.589164	−0.294582	−	0.955626i	$-0.595180\pi$
$157$	−7.38221	−0.589164	−0.294582	+	0.955626i	$0.595180\pi$
$158$	−10.7397	−0.854404
$159$	7.19335	0.570470
$160$	−4.43977	−0.350995
$161$	13.8801	1.09391
$162$	7.33919	0.576621
$163$	18.6256	1.45887	0.729436	−	0.684049i	$-0.239783\pi$
$163$	18.6256	1.45887	0.729436	+	0.684049i	$0.239783\pi$
$164$	6.16701	0.481563
$165$	−16.2109	−1.26201
$166$	17.2935	1.34224
$167$	15.7031	1.21514	0.607569	−	0.794267i	$-0.292145\pi$
$167$	15.7031	1.21514	0.607569	+	0.794267i	$0.292145\pi$
$168$	−3.26348	−0.251783
$169$	−11.1588	−0.858371
$170$	24.9259	1.91173
$171$	0.477577	0.0365212
$172$	1.84953	0.141025
$173$	0.0855464	0.00650397	0.00325199	−	0.999995i	$-0.498965\pi$
$173$	0.0855464	0.00650397	0.00325199	+	0.999995i	$0.498965\pi$
$174$	−8.17425	−0.619689
$175$	30.2295	2.28514
$176$	−2.29898	−0.173292
$177$	9.24384	0.694810
$178$	6.04620	0.453182
$179$	−26.1770	−1.95656	−0.978280	−	0.207287i	$-0.933537\pi$
$179$	−26.1770	−1.95656	−0.978280	+	0.207287i	$0.933537\pi$
$180$	−2.12033	−0.158040
$181$	14.8185	1.10145	0.550727	−	0.834685i	$-0.314351\pi$
$181$	14.8185	1.10145	0.550727	+	0.834685i	$0.314351\pi$
$182$	−2.78818	−0.206673
$183$	−7.23428	−0.534774
$184$	−6.75495	−0.497981
$185$	12.3479	0.907836
$186$	7.22772	0.529962
$187$	12.9070	0.943855
$188$	9.53619	0.695498
$189$	−11.3490	−0.825519
$190$	4.43977	0.322095
$191$	7.93251	0.573977	0.286988	−	0.957934i	$-0.407346\pi$
$191$	7.93251	0.573977	0.286988	+	0.957934i	$0.407346\pi$
$192$	1.58821	0.114619
$193$	12.6200	0.908405	0.454202	−	0.890898i	$-0.349924\pi$
$193$	12.6200	0.908405	0.454202	+	0.890898i	$0.349924\pi$
$194$	−2.42152	−0.173855
$195$	9.56793	0.685174
$196$	−2.77775	−0.198411
$197$	−18.0255	−1.28426	−0.642130	−	0.766596i	$-0.721949\pi$
$197$	−18.0255	−1.28426	−0.642130	+	0.766596i	$0.721949\pi$
$198$	−1.09794	−0.0780273
$199$	16.1148	1.14235	0.571174	−	0.820829i	$-0.306488\pi$
$199$	16.1148	1.14235	0.571174	+	0.820829i	$0.306488\pi$
$200$	−14.7116	−1.04027
$201$	1.20072	0.0846925
$202$	−8.95487	−0.630062
$203$	10.5757	0.742272
$204$	−8.91660	−0.624287
$205$	27.3801	1.91231
$206$	2.04613	0.142560
$207$	−3.22600	−0.224223
$208$	1.35690	0.0940842
$209$	2.29898	0.159024
$210$	−14.4891	−0.999844
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	4.52921	0.311067
$213$	10.7296	0.735178
$214$	18.9633	1.29630
$215$	8.21149	0.560019
$216$	5.52314	0.375802
$217$	−9.35114	−0.634796
$218$	19.6342	1.32979
$219$	7.06153	0.477174
$220$	−10.2070	−0.688154
$221$	−7.61795	−0.512439
$222$	−4.41714	−0.296459
$223$	4.89471	0.327774	0.163887	−	0.986479i	$-0.447597\pi$
$223$	4.89471	0.327774	0.163887	+	0.986479i	$0.447597\pi$
$224$	−2.05481	−0.137293
$225$	−7.02591	−0.468394
$226$	−9.66587	−0.642964
$227$	−5.39640	−0.358171	−0.179086	−	0.983833i	$-0.557314\pi$
$227$	−5.39640	−0.358171	−0.179086	+	0.983833i	$0.557314\pi$
$228$	−1.58821	−0.105182
$229$	−12.0150	−0.793974	−0.396987	−	0.917824i	$-0.629944\pi$
$229$	−12.0150	−0.793974	−0.396987	+	0.917824i	$0.629944\pi$
$230$	−29.9904	−1.97751
$231$	−7.50269	−0.493641
$232$	−5.14682	−0.337905
$233$	15.2206	0.997133	0.498566	−	0.866852i	$-0.333860\pi$
$233$	15.2206	0.997133	0.498566	+	0.866852i	$0.333860\pi$
$234$	0.648024	0.0423627
$235$	42.3385	2.76186
$236$	5.82027	0.378868
$237$	17.0569	1.10797
$238$	11.5362	0.747780
$239$	−16.0011	−1.03502	−0.517512	−	0.855676i	$-0.673142\pi$
$239$	−16.0011	−1.03502	−0.517512	+	0.855676i	$0.673142\pi$
$240$	7.05131	0.455160
$241$	−11.6318	−0.749273	−0.374636	−	0.927172i	$-0.622232\pi$
$241$	−11.6318	−0.749273	−0.374636	+	0.927172i	$0.622232\pi$
$242$	5.71467	0.367353
$243$	4.91320	0.315182
$244$	−4.55498	−0.291603
$245$	−12.3326	−0.787899
$246$	−9.79453	−0.624476
$247$	−1.35690	−0.0863375
$248$	4.55085	0.288979
$249$	−27.4658	−1.74058
$250$	−43.1173	−2.72697
$251$	15.4096	0.972644	0.486322	−	0.873780i	$-0.338338\pi$
$251$	15.4096	0.972644	0.486322	+	0.873780i	$0.338338\pi$
$252$	−0.981330	−0.0618180
$253$	−15.5295	−0.976332
$254$	−16.5167	−1.03635
$255$	−39.5877	−2.47908
$256$	1.00000	0.0625000
$257$	−13.9633	−0.871007	−0.435503	−	0.900187i	$-0.643430\pi$
$257$	−13.9633	−0.871007	−0.435503	+	0.900187i	$0.643430\pi$
$258$	−2.93745	−0.182878
$259$	5.71484	0.355103
$260$	6.02433	0.373613
$261$	−2.45800	−0.152146
$262$	0.350625	0.0216617
$263$	−16.2507	−1.00206	−0.501030	−	0.865430i	$-0.667045\pi$
$263$	−16.2507	−1.00206	−0.501030	+	0.865430i	$0.667045\pi$
$264$	3.65128	0.224721
$265$	20.1087	1.23526
$266$	2.05481	0.125989
$267$	−9.60266	−0.587673
$268$	0.756021	0.0461814
$269$	10.9794	0.669423	0.334711	−	0.942321i	$-0.391361\pi$
$269$	10.9794	0.669423	0.334711	+	0.942321i	$0.391361\pi$
$270$	24.5215	1.49233
$271$	−7.25337	−0.440611	−0.220305	−	0.975431i	$-0.570705\pi$
$271$	−7.25337	−0.440611	−0.220305	+	0.975431i	$0.570705\pi$
$272$	−5.61423	−0.340413
$273$	4.42822	0.268008
$274$	3.05966	0.184841
$275$	−33.8217	−2.03953
$276$	10.7283	0.645768
$277$	−29.3998	−1.76646	−0.883231	−	0.468938i	$-0.844637\pi$
$277$	−29.3998	−1.76646	−0.883231	+	0.468938i	$0.844637\pi$
$278$	−15.9057	−0.953958
$279$	2.17338	0.130117
$280$	−9.12290	−0.545197
$281$	16.0111	0.955142	0.477571	−	0.878593i	$-0.341517\pi$
$281$	16.0111	0.955142	0.477571	+	0.878593i	$0.341517\pi$
$282$	−15.1455	−0.901902
$283$	0.397567	0.0236329	0.0118165	−	0.999930i	$-0.496239\pi$
$283$	0.397567	0.0236329	0.0118165	+	0.999930i	$0.496239\pi$
$284$	6.75575	0.400880
$285$	−7.05131	−0.417684
$286$	3.11949	0.184460
$287$	12.6720	0.748007
$288$	0.477577	0.0281415
$289$	14.5196	0.854093
$290$	−22.8507	−1.34184
$291$	3.84589	0.225450
$292$	4.44621	0.260195
$293$	−0.00299746	−0.000175114 0	−8.75568e−5	−	1.00000i	$-0.500028\pi$
$293$	−0.00299746	−0.000175114 0	−8.75568e−5		1.00000i	$0.500028\pi$
$294$	4.41166	0.257293
$295$	25.8407	1.50450
$296$	−2.78120	−0.161654
$297$	12.6976	0.736790
$298$	4.44775	0.257651
$299$	9.16579	0.530072
$300$	23.3651	1.34899
$301$	3.80043	0.219053
$302$	−24.4752	−1.40839
$303$	14.2222	0.817046
$304$	−1.00000	−0.0573539
$305$	−20.2231	−1.15797
$306$	−2.68122	−0.153275
$307$	−15.2122	−0.868207	−0.434104	−	0.900863i	$-0.642935\pi$
$307$	−15.2122	−0.868207	−0.434104	+	0.900863i	$0.642935\pi$
$308$	−4.72398	−0.269174
$309$	−3.24969	−0.184868
$310$	20.2047	1.14755
$311$	11.5586	0.655428	0.327714	−	0.944777i	$-0.393722\pi$
$311$	11.5586	0.655428	0.327714	+	0.944777i	$0.393722\pi$
$312$	−2.15505	−0.122006
$313$	−12.3937	−0.700536	−0.350268	−	0.936650i	$-0.613909\pi$
$313$	−12.3937	−0.700536	−0.350268	+	0.936650i	$0.613909\pi$
$314$	7.38221	0.416602
$315$	−4.35688	−0.245483
$316$	10.7397	0.604155
$317$	0.829297	0.0465779	0.0232890	−	0.999729i	$-0.492586\pi$
$317$	0.829297	0.0465779	0.0232890	+	0.999729i	$0.492586\pi$
$318$	−7.19335	−0.403383
$319$	−11.8325	−0.662491
$320$	4.43977	0.248191
$321$	−30.1177	−1.68101
$322$	−13.8801	−0.773510
$323$	5.61423	0.312384
$324$	−7.33919	−0.407733
$325$	19.9622	1.10730
$326$	−18.6256	−1.03158
$327$	−31.1833	−1.72444
$328$	−6.16701	−0.340516
$329$	19.5951	1.08031
$330$	16.2109	0.892378
$331$	3.31406	0.182157	0.0910787	−	0.995844i	$-0.470969\pi$
$331$	3.31406	0.182157	0.0910787	+	0.995844i	$0.470969\pi$
$332$	−17.2935	−0.949106
$333$	−1.32824	−0.0727869
$334$	−15.7031	−0.859233
$335$	3.35656	0.183389
$336$	3.26348	0.178037
$337$	3.56784	0.194353	0.0971764	−	0.995267i	$-0.469019\pi$
$337$	3.56784	0.194353	0.0971764	+	0.995267i	$0.469019\pi$
$338$	11.1588	0.606960
$339$	15.3515	0.833777
$340$	−24.9259	−1.35180
$341$	10.4623	0.566567
$342$	−0.477577	−0.0258244
$343$	−20.0914	−1.08484
$344$	−1.84953	−0.0997199
$345$	47.6312	2.56438
$346$	−0.0855464	−0.00459900
$347$	−19.7879	−1.06227	−0.531135	−	0.847287i	$-0.678234\pi$
$347$	−19.7879	−1.06227	−0.531135	+	0.847287i	$0.678234\pi$
$348$	8.17425	0.438186
$349$	−6.03306	−0.322942	−0.161471	−	0.986877i	$-0.551624\pi$
$349$	−6.03306	−0.322942	−0.161471	+	0.986877i	$0.551624\pi$
$350$	−30.2295	−1.61584
$351$	−7.49435	−0.400019
$352$	2.29898	0.122536
$353$	19.1308	1.01823	0.509116	−	0.860698i	$-0.329972\pi$
$353$	19.1308	1.01823	0.509116	+	0.860698i	$0.329972\pi$
$354$	−9.24384	−0.491305
$355$	29.9940	1.59192
$356$	−6.04620	−0.320448
$357$	−18.3219	−0.969700
$358$	26.1770	1.38350
$359$	−4.88352	−0.257743	−0.128871	−	0.991661i	$-0.541135\pi$
$359$	−4.88352	−0.257743	−0.128871	+	0.991661i	$0.541135\pi$
$360$	2.12033	0.111751
$361$	1.00000	0.0526316
$362$	−14.8185	−0.778846
$363$	−9.07612	−0.476373
$364$	2.78818	0.146140
$365$	19.7402	1.03325
$366$	7.23428	0.378142
$367$	29.6182	1.54606	0.773029	−	0.634371i	$-0.218741\pi$
$367$	29.6182	1.54606	0.773029	+	0.634371i	$0.218741\pi$
$368$	6.75495	0.352126
$369$	−2.94522	−0.153322
$370$	−12.3479	−0.641937
$371$	9.30667	0.483178
$372$	−7.22772	−0.374740
$373$	4.09713	0.212141	0.106071	−	0.994359i	$-0.466173\pi$
$373$	4.09713	0.212141	0.106071	+	0.994359i	$0.466173\pi$
$374$	−12.9070	−0.667407
$375$	68.4794	3.53626
$376$	−9.53619	−0.491791
$377$	6.98373	0.359680
$378$	11.3490	0.583730
$379$	−21.2299	−1.09051	−0.545253	−	0.838272i	$-0.683566\pi$
$379$	−21.2299	−1.09051	−0.545253	+	0.838272i	$0.683566\pi$
$380$	−4.43977	−0.227756
$381$	26.2320	1.34391
$382$	−7.93251	−0.405863
$383$	−31.4928	−1.60921	−0.804603	−	0.593813i	$-0.797622\pi$
$383$	−31.4928	−1.60921	−0.804603	+	0.593813i	$0.797622\pi$
$384$	−1.58821	−0.0810482
$385$	−20.9734	−1.06890
$386$	−12.6200	−0.642339
$387$	−0.883292	−0.0449002
$388$	2.42152	0.122934
$389$	−31.3251	−1.58825	−0.794123	−	0.607758i	$-0.792069\pi$
$389$	−31.3251	−1.58825	−0.794123	+	0.607758i	$0.792069\pi$
$390$	−9.56793	−0.484491
$391$	−37.9238	−1.91789
$392$	2.77775	0.140297
$393$	−0.556868	−0.0280903
$394$	18.0255	0.908109
$395$	47.6818	2.39913
$396$	1.09794	0.0551736
$397$	−4.69693	−0.235732	−0.117866	−	0.993030i	$-0.537605\pi$
$397$	−4.69693	−0.235732	−0.117866	+	0.993030i	$0.537605\pi$
$398$	−16.1148	−0.807762
$399$	−3.26348	−0.163378
$400$	14.7116	0.735579
$401$	17.8115	0.889462	0.444731	−	0.895664i	$-0.353299\pi$
$401$	17.8115	0.889462	0.444731	+	0.895664i	$0.353299\pi$
$402$	−1.20072	−0.0598866
$403$	−6.17505	−0.307601
$404$	8.95487	0.445521
$405$	−32.5843	−1.61913
$406$	−10.5757	−0.524866
$407$	−6.39394	−0.316936
$408$	8.91660	0.441437
$409$	19.1183	0.945338	0.472669	−	0.881240i	$-0.343291\pi$
$409$	19.1183	0.945338	0.472669	+	0.881240i	$0.343291\pi$
$410$	−27.3801	−1.35221
$411$	−4.85939	−0.239696
$412$	−2.04613	−0.100805
$413$	11.9596	0.588492
$414$	3.22600	0.158549
$415$	−76.7794	−3.76895
$416$	−1.35690	−0.0665275
$417$	25.2616	1.23707
$418$	−2.29898	−0.112447
$419$	−18.7083	−0.913959	−0.456980	−	0.889477i	$-0.651069\pi$
$419$	−18.7083	−0.913959	−0.456980	+	0.889477i	$0.651069\pi$
$420$	14.4891	0.706996
$421$	−5.02578	−0.244942	−0.122471	−	0.992472i	$-0.539082\pi$
$421$	−5.02578	−0.244942	−0.122471	+	0.992472i	$0.539082\pi$
$422$	−1.00000	−0.0486792
$423$	−4.55426	−0.221436
$424$	−4.52921	−0.219958
$425$	−82.5942	−4.00641
$426$	−10.7296	−0.519849
$427$	−9.35963	−0.452944
$428$	−18.9633	−0.916625
$429$	−4.95442	−0.239202
$430$	−8.21149	−0.395993
$431$	0.543242	0.0261670	0.0130835	−	0.999914i	$-0.495835\pi$
$431$	0.543242	0.0261670	0.0130835	+	0.999914i	$0.495835\pi$
$432$	−5.52314	−0.265732
$433$	2.92708	0.140667	0.0703333	−	0.997524i	$-0.477594\pi$
$433$	2.92708	0.140667	0.0703333	+	0.997524i	$0.477594\pi$
$434$	9.35114	0.448869
$435$	36.2918	1.74006
$436$	−19.6342	−0.940306
$437$	−6.75495	−0.323133
$438$	−7.06153	−0.337413
$439$	−19.7472	−0.942484	−0.471242	−	0.882004i	$-0.656194\pi$
$439$	−19.7472	−0.942484	−0.471242	+	0.882004i	$0.656194\pi$
$440$	10.2070	0.486598
$441$	1.32659	0.0631708
$442$	7.61795	0.362349
$443$	−27.9849	−1.32960	−0.664801	−	0.747020i	$-0.731484\pi$
$443$	−27.9849	−1.32960	−0.664801	+	0.747020i	$0.731484\pi$
$444$	4.41714	0.209628
$445$	−26.8438	−1.27252
$446$	−4.89471	−0.231771
$447$	−7.06398	−0.334115
$448$	2.05481	0.0970807
$449$	27.3337	1.28996	0.644978	−	0.764202i	$-0.276867\pi$
$449$	27.3337	1.28996	0.644978	+	0.764202i	$0.276867\pi$
$450$	7.02591	0.331205
$451$	−14.1779	−0.667609
$452$	9.66587	0.454644
$453$	38.8718	1.82636
$454$	5.39640	0.253265
$455$	12.3789	0.580330
$456$	1.58821	0.0743749
$457$	−22.4523	−1.05027	−0.525137	−	0.851018i	$-0.675986\pi$
$457$	−22.4523	−1.05027	−0.525137	+	0.851018i	$0.675986\pi$
$458$	12.0150	0.561424
$459$	31.0082	1.44734
$460$	29.9904	1.39831
$461$	−1.39180	−0.0648225	−0.0324113	−	0.999475i	$-0.510319\pi$
$461$	−1.39180	−0.0648225	−0.0324113	+	0.999475i	$0.510319\pi$
$462$	7.50269	0.349057
$463$	−37.3455	−1.73559	−0.867795	−	0.496922i	$-0.834464\pi$
$463$	−37.3455	−1.73559	−0.867795	+	0.496922i	$0.834464\pi$
$464$	5.14682	0.238935
$465$	−32.0894	−1.48811
$466$	−15.2206	−0.705079
$467$	−22.4553	−1.03911	−0.519553	−	0.854438i	$-0.673901\pi$
$467$	−22.4553	−1.03911	−0.519553	+	0.854438i	$0.673901\pi$
$468$	−0.648024	−0.0299549
$469$	1.55348	0.0717331
$470$	−42.3385	−1.95293
$471$	−11.7245	−0.540238
$472$	−5.82027	−0.267900
$473$	−4.25204	−0.195509
$474$	−17.0569	−0.783451
$475$	−14.7116	−0.675014
$476$	−11.5362	−0.528760
$477$	−2.16304	−0.0990389
$478$	16.0011	0.731873
$479$	−37.2851	−1.70360	−0.851800	−	0.523867i	$-0.824489\pi$
$479$	−37.2851	−1.70360	−0.851800	+	0.523867i	$0.824489\pi$
$480$	−7.05131	−0.321847
$481$	3.77381	0.172071
$482$	11.6318	0.529816
$483$	22.0446	1.00307
$484$	−5.71467	−0.259758
$485$	10.7510	0.488177
$486$	−4.91320	−0.222867
$487$	18.7377	0.849088	0.424544	−	0.905407i	$-0.360434\pi$
$487$	18.7377	0.849088	0.424544	+	0.905407i	$0.360434\pi$
$488$	4.55498	0.206194
$489$	29.5815	1.33772
$490$	12.3326	0.557129
$491$	−12.2678	−0.553638	−0.276819	−	0.960922i	$-0.589280\pi$
$491$	−12.2678	−0.553638	−0.276819	+	0.960922i	$0.589280\pi$
$492$	9.79453	0.441572
$493$	−28.8954	−1.30139
$494$	1.35690	0.0610499
$495$	4.87461	0.219097
$496$	−4.55085	−0.204339
$497$	13.8818	0.622683
$498$	27.4658	1.23077
$499$	−17.0649	−0.763931	−0.381965	−	0.924177i	$-0.624753\pi$
$499$	−17.0649	−0.763931	−0.381965	+	0.924177i	$0.624753\pi$
$500$	43.1173	1.92826
$501$	24.9398	1.11423
$502$	−15.4096	−0.687763
$503$	33.3399	1.48655	0.743277	−	0.668983i	$-0.233270\pi$
$503$	33.3399	1.48655	0.743277	+	0.668983i	$0.233270\pi$
$504$	0.981330	0.0437119
$505$	39.7576	1.76919
$506$	15.5295	0.690371
$507$	−17.7226	−0.787088
$508$	16.5167	0.732808
$509$	3.41676	0.151445	0.0757226	−	0.997129i	$-0.475874\pi$
$509$	3.41676	0.151445	0.0757226	+	0.997129i	$0.475874\pi$
$510$	39.5877	1.75297
$511$	9.13612	0.404158
$512$	−1.00000	−0.0441942
$513$	5.52314	0.243852
$514$	13.9633	0.615895
$515$	−9.08434	−0.400304
$516$	2.93745	0.129314
$517$	−21.9235	−0.964197
$518$	−5.71484	−0.251096
$519$	0.135866	0.00596386
$520$	−6.02433	−0.264184
$521$	−35.6208	−1.56058	−0.780288	−	0.625421i	$-0.784927\pi$
$521$	−35.6208	−1.56058	−0.780288	+	0.625421i	$0.784927\pi$
$522$	2.45800	0.107584
$523$	−26.4603	−1.15703	−0.578515	−	0.815672i	$-0.696367\pi$
$523$	−26.4603	−1.15703	−0.578515	+	0.815672i	$0.696367\pi$
$524$	−0.350625	−0.0153171
$525$	48.0110	2.09537
$526$	16.2507	0.708564
$527$	25.5495	1.11295
$528$	−3.65128	−0.158902
$529$	22.6293	0.983883
$530$	−20.1087	−0.873464
$531$	−2.77963	−0.120626
$532$	−2.05481	−0.0890874
$533$	8.36802	0.362459
$534$	9.60266	0.415548
$535$	−84.1926	−3.63997
$536$	−0.756021	−0.0326551
$537$	−41.5747	−1.79408
$538$	−10.9794	−0.473353
$539$	6.38600	0.275065
$540$	−24.5215	−1.05524
$541$	8.96807	0.385567	0.192784	−	0.981241i	$-0.438248\pi$
$541$	8.96807	0.385567	0.192784	+	0.981241i	$0.438248\pi$
$542$	7.25337	0.311559
$543$	23.5350	1.00998
$544$	5.61423	0.240708
$545$	−87.1712	−3.73401
$546$	−4.42822	−0.189510
$547$	−24.7487	−1.05818	−0.529089	−	0.848566i	$-0.677466\pi$
$547$	−24.7487	−1.05818	−0.529089	+	0.848566i	$0.677466\pi$
$548$	−3.05966	−0.130702
$549$	2.17535	0.0928418
$550$	33.8217	1.44216
$551$	−5.14682	−0.219262
$552$	−10.7283	−0.456627
$553$	22.0680	0.938429
$554$	29.3998	1.24908
$555$	19.6111	0.832445
$556$	15.9057	0.674550
$557$	−34.2572	−1.45153	−0.725763	−	0.687945i	$-0.758513\pi$
$557$	−34.2572	−1.45153	−0.725763	+	0.687945i	$0.758513\pi$
$558$	−2.17338	−0.0920064
$559$	2.50963	0.106146
$560$	9.12290	0.385513
$561$	20.4991	0.865474
$562$	−16.0111	−0.675388
$563$	46.8437	1.97423	0.987114	−	0.160018i	$-0.0511553\pi$
$563$	46.8437	1.97423	0.987114	+	0.160018i	$0.0511553\pi$
$564$	15.1455	0.637741
$565$	42.9143	1.80542
$566$	−0.397567	−0.0167110
$567$	−15.0807	−0.633328
$568$	−6.75575	−0.283465
$569$	−4.47624	−0.187654	−0.0938268	−	0.995589i	$-0.529910\pi$
$569$	−4.47624	−0.187654	−0.0938268	+	0.995589i	$0.529910\pi$
$570$	7.05131	0.295347
$571$	27.9874	1.17124	0.585619	−	0.810586i	$-0.300852\pi$
$571$	27.9874	1.17124	0.585619	+	0.810586i	$0.300852\pi$
$572$	−3.11949	−0.130433
$573$	12.5985	0.526311
$574$	−12.6720	−0.528921
$575$	99.3760	4.14427
$576$	−0.477577	−0.0198990
$577$	21.5121	0.895562	0.447781	−	0.894143i	$-0.352214\pi$
$577$	21.5121	0.895562	0.447781	+	0.894143i	$0.352214\pi$
$578$	−14.5196	−0.603935
$579$	20.0432	0.832967
$580$	22.8507	0.948825
$581$	−35.5350	−1.47424
$582$	−3.84589	−0.159417
$583$	−10.4126	−0.431245
$584$	−4.44621	−0.183985
$585$	−2.87708	−0.118953
$586$	0.00299746	0.000123824 0
$587$	24.0267	0.991688	0.495844	−	0.868412i	$-0.334859\pi$
$587$	24.0267	0.991688	0.495844	+	0.868412i	$0.334859\pi$
$588$	−4.41166	−0.181934
$589$	4.55085	0.187514
$590$	−25.8407	−1.06384
$591$	−28.6283	−1.17761
$592$	2.78120	0.114307
$593$	38.8719	1.59628	0.798139	−	0.602474i	$-0.205818\pi$
$593$	38.8719	1.59628	0.798139	+	0.602474i	$0.205818\pi$
$594$	−12.6976	−0.520989
$595$	−51.2181	−2.09974
$596$	−4.44775	−0.182187
$597$	25.5937	1.04748
$598$	−9.16579	−0.374817
$599$	5.55475	0.226961	0.113480	−	0.993540i	$-0.463800\pi$
$599$	5.55475	0.226961	0.113480	+	0.993540i	$0.463800\pi$
$600$	−23.3651	−0.953878
$601$	31.8609	1.29963	0.649817	−	0.760091i	$-0.274846\pi$
$601$	31.8609	1.29963	0.649817	+	0.760091i	$0.274846\pi$
$602$	−3.80043	−0.154894
$603$	−0.361058	−0.0147034
$604$	24.4752	0.995880
$605$	−25.3718	−1.03151
$606$	−14.2222	−0.577739
$607$	4.24013	0.172102	0.0860509	−	0.996291i	$-0.472575\pi$
$607$	4.24013	0.172102	0.0860509	+	0.996291i	$0.472575\pi$
$608$	1.00000	0.0405554
$609$	16.7966	0.680631
$610$	20.2231	0.818809
$611$	12.9397	0.523483
$612$	2.68122	0.108382
$613$	−42.7421	−1.72634	−0.863169	−	0.504915i	$-0.831524\pi$
$613$	−42.7421	−1.72634	−0.863169	+	0.504915i	$0.831524\pi$
$614$	15.2122	0.613915
$615$	43.4855	1.75350
$616$	4.72398	0.190335
$617$	7.44251	0.299624	0.149812	−	0.988714i	$-0.452133\pi$
$617$	7.44251	0.299624	0.149812	+	0.988714i	$0.452133\pi$
$618$	3.24969	0.130722
$619$	33.5753	1.34950	0.674752	−	0.738045i	$-0.264251\pi$
$619$	33.5753	1.34950	0.674752	+	0.738045i	$0.264251\pi$
$620$	−20.2047	−0.811442
$621$	−37.3085	−1.49714
$622$	−11.5586	−0.463458
$623$	−12.4238	−0.497749
$624$	2.15505	0.0862710
$625$	117.873	4.71492
$626$	12.3937	0.495354
$627$	3.65128	0.145818
$628$	−7.38221	−0.294582
$629$	−15.6143	−0.622583
$630$	4.35688	0.173582
$631$	24.9466	0.993107	0.496553	−	0.868006i	$-0.334599\pi$
$631$	24.9466	0.993107	0.496553	+	0.868006i	$0.334599\pi$
$632$	−10.7397	−0.427202
$633$	1.58821	0.0631258
$634$	−0.829297	−0.0329356
$635$	73.3302	2.91002
$636$	7.19335	0.285235
$637$	−3.76913	−0.149338
$638$	11.8325	0.468452
$639$	−3.22639	−0.127634
$640$	−4.43977	−0.175497
$641$	−22.4457	−0.886552	−0.443276	−	0.896385i	$-0.646184\pi$
$641$	−22.4457	−0.886552	−0.443276	+	0.896385i	$0.646184\pi$
$642$	30.1177	1.18865
$643$	16.5588	0.653014	0.326507	−	0.945195i	$-0.394128\pi$
$643$	16.5588	0.653014	0.326507	+	0.945195i	$0.394128\pi$
$644$	13.8801	0.546954
$645$	13.0416	0.513513
$646$	−5.61423	−0.220889
$647$	4.49817	0.176841	0.0884206	−	0.996083i	$-0.471818\pi$
$647$	4.49817	0.176841	0.0884206	+	0.996083i	$0.471818\pi$
$648$	7.33919	0.288311
$649$	−13.3807	−0.525239
$650$	−19.9622	−0.782981
$651$	−14.8516	−0.582080
$652$	18.6256	0.729436
$653$	−44.9916	−1.76066	−0.880329	−	0.474364i	$-0.842678\pi$
$653$	−44.9916	−1.76066	−0.880329	+	0.474364i	$0.842678\pi$
$654$	31.1833	1.21936
$655$	−1.55670	−0.0608251
$656$	6.16701	0.240781
$657$	−2.12341	−0.0828419
$658$	−19.5951	−0.763895
$659$	4.82766	0.188059	0.0940294	−	0.995569i	$-0.470025\pi$
$659$	4.82766	0.188059	0.0940294	+	0.995569i	$0.470025\pi$
$660$	−16.2109	−0.631007
$661$	−28.2558	−1.09902	−0.549511	−	0.835486i	$-0.685186\pi$
$661$	−28.2558	−1.09902	−0.549511	+	0.835486i	$0.685186\pi$
$662$	−3.31406	−0.128805
$663$	−12.0989	−0.469884
$664$	17.2935	0.671119
$665$	−9.12290	−0.353771
$666$	1.32824	0.0514681
$667$	34.7665	1.34616
$668$	15.7031	0.607569
$669$	7.77385	0.300554
$670$	−3.35656	−0.129675
$671$	10.4718	0.404261
$672$	−3.26348	−0.125892
$673$	−19.3626	−0.746375	−0.373187	−	0.927756i	$-0.621735\pi$
$673$	−19.3626	−0.746375	−0.373187	+	0.927756i	$0.621735\pi$
$674$	−3.56784	−0.137428
$675$	−81.2541	−3.12747
$676$	−11.1588	−0.429185
$677$	−42.9427	−1.65042	−0.825211	−	0.564824i	$-0.808944\pi$
$677$	−42.9427	−1.65042	−0.825211	+	0.564824i	$0.808944\pi$
$678$	−15.3515	−0.589569
$679$	4.97576	0.190952
$680$	24.9259	0.955865
$681$	−8.57063	−0.328427
$682$	−10.4623	−0.400623
$683$	−1.31743	−0.0504100	−0.0252050	−	0.999682i	$-0.508024\pi$
$683$	−1.31743	−0.0504100	−0.0252050	+	0.999682i	$0.508024\pi$
$684$	0.477577	0.0182606
$685$	−13.5842	−0.519025
$686$	20.0914	0.767094
$687$	−19.0824	−0.728039
$688$	1.84953	0.0705126
$689$	6.14568	0.234132
$690$	−47.6312	−1.81329
$691$	−15.2384	−0.579697	−0.289848	−	0.957073i	$-0.593605\pi$
$691$	−15.2384	−0.579697	−0.289848	+	0.957073i	$0.593605\pi$
$692$	0.0855464	0.00325199
$693$	2.25606	0.0857007
$694$	19.7879	0.751138
$695$	70.6175	2.67868
$696$	−8.17425	−0.309844
$697$	−34.6230	−1.31144
$698$	6.03306	0.228355
$699$	24.1735	0.914327
$700$	30.2295	1.14257
$701$	20.3890	0.770080	0.385040	−	0.922900i	$-0.374188\pi$
$701$	20.3890	0.770080	0.385040	+	0.922900i	$0.374188\pi$
$702$	7.49435	0.282856
$703$	−2.78120	−0.104895
$704$	−2.29898	−0.0866462
$705$	67.2426	2.53250
$706$	−19.1308	−0.719999
$707$	18.4006	0.692024
$708$	9.24384	0.347405
$709$	−17.7204	−0.665503	−0.332752	−	0.943014i	$-0.607977\pi$
$709$	−17.7204	−0.665503	−0.332752	+	0.943014i	$0.607977\pi$
$710$	−29.9940	−1.12565
$711$	−5.12903	−0.192354
$712$	6.04620	0.226591
$713$	−30.7407	−1.15125
$714$	18.3219	0.685681
$715$	−13.8498	−0.517955
$716$	−26.1770	−0.978280
$717$	−25.4132	−0.949072
$718$	4.88352	0.182252
$719$	−2.39760	−0.0894152	−0.0447076	−	0.999000i	$-0.514236\pi$
$719$	−2.39760	−0.0894152	−0.0447076	+	0.999000i	$0.514236\pi$
$720$	−2.12033	−0.0790201
$721$	−4.20440	−0.156580
$722$	−1.00000	−0.0372161
$723$	−18.4739	−0.687050
$724$	14.8185	0.550727
$725$	75.7179	2.81209
$726$	9.07612	0.336846
$727$	35.4984	1.31656	0.658281	−	0.752772i	$-0.271284\pi$
$727$	35.4984	1.31656	0.658281	+	0.752772i	$0.271284\pi$
$728$	−2.78818	−0.103337
$729$	29.8208	1.10447
$730$	−19.7402	−0.730616
$731$	−10.3837	−0.384054
$732$	−7.23428	−0.267387
$733$	−47.5100	−1.75482	−0.877410	−	0.479741i	$-0.840731\pi$
$733$	−47.5100	−1.75482	−0.877410	+	0.479741i	$0.840731\pi$
$734$	−29.6182	−1.09323
$735$	−19.5868	−0.722469
$736$	−6.75495	−0.248991
$737$	−1.73808	−0.0640231
$738$	2.94522	0.108415
$739$	46.8101	1.72194	0.860969	−	0.508657i	$-0.169858\pi$
$739$	46.8101	1.72194	0.860969	+	0.508657i	$0.169858\pi$
$740$	12.3479	0.453918
$741$	−2.15505	−0.0791677
$742$	−9.30667	−0.341659
$743$	−53.6166	−1.96700	−0.983500	−	0.180907i	$-0.942097\pi$
$743$	−53.6166	−1.96700	−0.983500	+	0.180907i	$0.942097\pi$
$744$	7.22772	0.264981
$745$	−19.7470	−0.723474
$746$	−4.09713	−0.150007
$747$	8.25899	0.302181
$748$	12.9070	0.471928
$749$	−38.9660	−1.42379
$750$	−68.4794	−2.50051
$751$	38.7589	1.41433	0.707166	−	0.707048i	$-0.249973\pi$
$751$	38.7589	1.41433	0.707166	+	0.707048i	$0.249973\pi$
$752$	9.53619	0.347749
$753$	24.4737	0.891871
$754$	−6.98373	−0.254332
$755$	108.664	3.95469
$756$	−11.3490	−0.412759
$757$	−9.68450	−0.351989	−0.175995	−	0.984391i	$-0.556314\pi$
$757$	−9.68450	−0.351989	−0.175995	+	0.984391i	$0.556314\pi$
$758$	21.2299	0.771104
$759$	−24.6642	−0.895254
$760$	4.43977	0.161048
$761$	−22.5689	−0.818121	−0.409061	−	0.912507i	$-0.634144\pi$
$761$	−22.5689	−0.818121	−0.409061	+	0.912507i	$0.634144\pi$
$762$	−26.2320	−0.950285
$763$	−40.3445	−1.46057
$764$	7.93251	0.286988
$765$	11.9040	0.430391
$766$	31.4928	1.13788
$767$	7.89753	0.285163
$768$	1.58821	0.0573097
$769$	19.3387	0.697370	0.348685	−	0.937240i	$-0.386628\pi$
$769$	19.3387	0.697370	0.348685	+	0.937240i	$0.386628\pi$
$770$	20.9734	0.755829
$771$	−22.1767	−0.798675
$772$	12.6200	0.454202
$773$	8.38766	0.301683	0.150842	−	0.988558i	$-0.451802\pi$
$773$	8.38766	0.301683	0.150842	+	0.988558i	$0.451802\pi$
$774$	0.883292	0.0317493
$775$	−66.9502	−2.40492
$776$	−2.42152	−0.0869274
$777$	9.07640	0.325614
$778$	31.3251	1.12306
$779$	−6.16701	−0.220956
$780$	9.56793	0.342587
$781$	−15.5314	−0.555756
$782$	37.9238	1.35615
$783$	−28.4266	−1.01588
$784$	−2.77775	−0.0992053
$785$	−32.7753	−1.16980
$786$	0.556868	0.0198628
$787$	−2.76669	−0.0986217	−0.0493108	−	0.998783i	$-0.515702\pi$
$787$	−2.76669	−0.0986217	−0.0493108	+	0.998783i	$0.515702\pi$
$788$	−18.0255	−0.642130
$789$	−25.8096	−0.918845
$790$	−47.6818	−1.69644
$791$	19.8615	0.706195
$792$	−1.09794	−0.0390136
$793$	−6.18066	−0.219482
$794$	4.69693	0.166688
$795$	31.9368	1.13268
$796$	16.1148	0.571174
$797$	6.66271	0.236005	0.118003	−	0.993013i	$-0.462351\pi$
$797$	6.66271	0.236005	0.118003	+	0.993013i	$0.462351\pi$
$798$	3.26348	0.115526
$799$	−53.5384	−1.89405
$800$	−14.7116	−0.520133
$801$	2.88752	0.102026
$802$	−17.8115	−0.628945
$803$	−10.2218	−0.360718
$804$	1.20072	0.0423463
$805$	61.6247	2.17199
$806$	6.17505	0.217507
$807$	17.4376	0.613831
$808$	−8.95487	−0.315031
$809$	−0.489271	−0.0172018	−0.00860092	−	0.999963i	$-0.502738\pi$
$809$	−0.489271	−0.0172018	−0.00860092	+	0.999963i	$0.502738\pi$
$810$	32.5843	1.14490
$811$	−6.62317	−0.232571	−0.116285	−	0.993216i	$-0.537099\pi$
$811$	−6.62317	−0.232571	−0.116285	+	0.993216i	$0.537099\pi$
$812$	10.5757	0.371136
$813$	−11.5199	−0.404020
$814$	6.39394	0.224107
$815$	82.6936	2.89663
$816$	−8.91660	−0.312143
$817$	−1.84953	−0.0647068
$818$	−19.1183	−0.668455
$819$	−1.33157	−0.0465287
$820$	27.3801	0.956156
$821$	−36.8516	−1.28613	−0.643065	−	0.765812i	$-0.722338\pi$
$821$	−36.8516	−1.28613	−0.643065	+	0.765812i	$0.722338\pi$
$822$	4.85939	0.169491
$823$	35.1319	1.22462	0.612310	−	0.790618i	$-0.290241\pi$
$823$	35.1319	1.22462	0.612310	+	0.790618i	$0.290241\pi$
$824$	2.04613	0.0712802
$825$	−53.7161	−1.87016
$826$	−11.9596	−0.416127
$827$	−2.43861	−0.0847989	−0.0423995	−	0.999101i	$-0.513500\pi$
$827$	−2.43861	−0.0847989	−0.0423995	+	0.999101i	$0.513500\pi$
$828$	−3.22600	−0.112111
$829$	14.0476	0.487892	0.243946	−	0.969789i	$-0.421558\pi$
$829$	14.0476	0.487892	0.243946	+	0.969789i	$0.421558\pi$
$830$	76.7794	2.66505
$831$	−46.6931	−1.61977
$832$	1.35690	0.0470421
$833$	15.5949	0.540332
$834$	−25.2616	−0.874737
$835$	69.7180	2.41269
$836$	2.29898	0.0795120
$837$	25.1349	0.868791
$838$	18.7083	0.646267
$839$	−17.1815	−0.593170	−0.296585	−	0.955006i	$-0.595848\pi$
$839$	−17.1815	−0.593170	−0.296585	+	0.955006i	$0.595848\pi$
$840$	−14.4891	−0.499922
$841$	−2.51023	−0.0865597
$842$	5.02578	0.173200
$843$	25.4291	0.875823
$844$	1.00000	0.0344214
$845$	−49.5426	−1.70432
$846$	4.55426	0.156579
$847$	−11.7426	−0.403479
$848$	4.52921	0.155534
$849$	0.631422	0.0216703
$850$	82.5942	2.83296
$851$	18.7869	0.644005
$852$	10.7296	0.367589
$853$	−18.8357	−0.644923	−0.322461	−	0.946583i	$-0.604510\pi$
$853$	−18.8357	−0.644923	−0.322461	+	0.946583i	$0.604510\pi$
$854$	9.35963	0.320280
$855$	2.12033	0.0725138
$856$	18.9633	0.648151
$857$	3.19189	0.109033	0.0545164	−	0.998513i	$-0.482638\pi$
$857$	3.19189	0.109033	0.0545164	+	0.998513i	$0.482638\pi$
$858$	4.95442	0.169141
$859$	−1.10551	−0.0377195	−0.0188597	−	0.999822i	$-0.506004\pi$
$859$	−1.10551	−0.0377195	−0.0188597	+	0.999822i	$0.506004\pi$
$860$	8.21149	0.280009
$861$	20.1259	0.685889
$862$	−0.543242	−0.0185029
$863$	28.6063	0.973770	0.486885	−	0.873466i	$-0.338133\pi$
$863$	28.6063	0.973770	0.486885	+	0.873466i	$0.338133\pi$
$864$	5.52314	0.187901
$865$	0.379807	0.0129138
$866$	−2.92708	−0.0994663
$867$	23.0602	0.783166
$868$	−9.35114	−0.317398
$869$	−24.6904	−0.837564
$870$	−36.2918	−1.23041
$871$	1.02585	0.0347595
$872$	19.6342	0.664897
$873$	−1.15646	−0.0391402
$874$	6.75495	0.228489
$875$	88.5978	2.99515
$876$	7.06153	0.238587
$877$	−38.5189	−1.30069	−0.650346	−	0.759638i	$-0.725376\pi$
$877$	−38.5189	−1.30069	−0.650346	+	0.759638i	$0.725376\pi$
$878$	19.7472	0.666437
$879$	−0.00476061	−0.000160571 0
$880$	−10.2070	−0.344077
$881$	−32.3018	−1.08828	−0.544138	−	0.838996i	$-0.683143\pi$
$881$	−32.3018	−1.08828	−0.544138	+	0.838996i	$0.683143\pi$
$882$	−1.32659	−0.0446685
$883$	−35.3751	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$883$	−35.3751	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$884$	−7.61795	−0.256220
$885$	41.0406	1.37956
$886$	27.9849	0.940171
$887$	−23.2660	−0.781196	−0.390598	−	0.920561i	$-0.627732\pi$
$887$	−23.2660	−0.781196	−0.390598	+	0.920561i	$0.627732\pi$
$888$	−4.41714	−0.148230
$889$	33.9386	1.13826
$890$	26.8438	0.899805
$891$	16.8727	0.565256
$892$	4.89471	0.163887
$893$	−9.53619	−0.319116
$894$	7.06398	0.236255
$895$	−116.220	−3.88480
$896$	−2.05481	−0.0686464
$897$	14.5572	0.486052
$898$	−27.3337	−0.912136
$899$	−23.4224	−0.781181
$900$	−7.02591	−0.234197
$901$	−25.4280	−0.847130
$902$	14.1779	0.472071
$903$	6.03590	0.200862
$904$	−9.66587	−0.321482
$905$	65.7910	2.18697
$906$	−38.8718	−1.29143
$907$	56.4850	1.87555	0.937776	−	0.347241i	$-0.112881\pi$
$907$	56.4850	1.87555	0.937776	+	0.347241i	$0.112881\pi$
$908$	−5.39640	−0.179086
$909$	−4.27663	−0.141847
$910$	−12.3789	−0.410356
$911$	−21.2183	−0.702993	−0.351496	−	0.936189i	$-0.614327\pi$
$911$	−21.2183	−0.702993	−0.351496	+	0.936189i	$0.614327\pi$
$912$	−1.58821	−0.0525910
$913$	39.7576	1.31578
$914$	22.4523	0.742655
$915$	−32.1186	−1.06181
$916$	−12.0150	−0.396987
$917$	−0.720468	−0.0237920
$918$	−31.0082	−1.02342
$919$	24.2283	0.799216	0.399608	−	0.916686i	$-0.369146\pi$
$919$	24.2283	0.799216	0.399608	+	0.916686i	$0.369146\pi$
$920$	−29.9904	−0.988755
$921$	−24.1603	−0.796108
$922$	1.39180	0.0458365
$923$	9.16688	0.301732
$924$	−7.50269	−0.246820
$925$	40.9159	1.34531
$926$	37.3455	1.22725
$927$	0.977182	0.0320949
$928$	−5.14682	−0.168953
$929$	−17.5250	−0.574978	−0.287489	−	0.957784i	$-0.592820\pi$
$929$	−17.5250	−0.574978	−0.287489	+	0.957784i	$0.592820\pi$
$930$	32.0894	1.05225
$931$	2.77775	0.0910370
$932$	15.2206	0.498566
$933$	18.3575	0.600998
$934$	22.4553	0.734758
$935$	57.3043	1.87405
$936$	0.648024	0.0211813
$937$	9.54683	0.311881	0.155941	−	0.987766i	$-0.450159\pi$
$937$	9.54683	0.311881	0.155941	+	0.987766i	$0.450159\pi$
$938$	−1.55348	−0.0507230
$939$	−19.6839	−0.642360
$940$	42.3385	1.38093
$941$	35.2834	1.15021	0.575103	−	0.818081i	$-0.304962\pi$
$941$	35.2834	1.15021	0.575103	+	0.818081i	$0.304962\pi$
$942$	11.7245	0.382006
$943$	41.6578	1.35657
$944$	5.82027	0.189434
$945$	−50.3870	−1.63909
$946$	4.25204	0.138246
$947$	−45.5210	−1.47923	−0.739617	−	0.673028i	$-0.764993\pi$
$947$	−45.5210	−1.47923	−0.739617	+	0.673028i	$0.764993\pi$
$948$	17.0569	0.553983
$949$	6.03306	0.195842
$950$	14.7116	0.477307
$951$	1.31710	0.0427099
$952$	11.5362	0.373890
$953$	−20.9316	−0.678040	−0.339020	−	0.940779i	$-0.610095\pi$
$953$	−20.9316	−0.678040	−0.339020	+	0.940779i	$0.610095\pi$
$954$	2.16304	0.0700311
$955$	35.2186	1.13965
$956$	−16.0011	−0.517512
$957$	−18.7925	−0.607475
$958$	37.2851	1.20463
$959$	−6.28702	−0.203018
$960$	7.05131	0.227580
$961$	−10.2898	−0.331928
$962$	−3.77381	−0.121673
$963$	9.05642	0.291839
$964$	−11.6318	−0.374636
$965$	56.0298	1.80366
$966$	−22.0446	−0.709275
$967$	−15.1977	−0.488724	−0.244362	−	0.969684i	$-0.578579\pi$
$967$	−15.1977	−0.488724	−0.244362	+	0.969684i	$0.578579\pi$
$968$	5.71467	0.183676
$969$	8.91660	0.286442
$970$	−10.7510	−0.345193
$971$	−35.7305	−1.14665	−0.573324	−	0.819329i	$-0.694346\pi$
$971$	−35.7305	−1.14665	−0.573324	+	0.819329i	$0.694346\pi$
$972$	4.91320	0.157591
$973$	32.6831	1.04777
$974$	−18.7377	−0.600396
$975$	31.7042	1.01535
$976$	−4.55498	−0.145801
$977$	31.1196	0.995605	0.497803	−	0.867290i	$-0.334140\pi$
$977$	31.1196	0.995605	0.497803	+	0.867290i	$0.334140\pi$
$978$	−29.5815	−0.945912
$979$	13.9001	0.444250
$980$	−12.3326	−0.393950
$981$	9.37682	0.299379
$982$	12.2678	0.391481
$983$	−6.12208	−0.195264	−0.0976320	−	0.995223i	$-0.531127\pi$
$983$	−6.12208	−0.195264	−0.0976320	+	0.995223i	$0.531127\pi$
$984$	−9.79453	−0.312238
$985$	−80.0289	−2.54993
$986$	28.8954	0.920218
$987$	31.1212	0.990598
$988$	−1.35690	−0.0431688
$989$	12.4935	0.397269
$990$	−4.87461	−0.154925
$991$	59.1191	1.87798	0.938990	−	0.343943i	$-0.111763\pi$
$991$	59.1191	1.87798	0.938990	+	0.343943i	$0.111763\pi$
$992$	4.55085	0.144490
$993$	5.26344	0.167030
$994$	−13.8818	−0.440304
$995$	71.5460	2.26816
$996$	−27.4658	−0.870288
$997$	−50.1823	−1.58929	−0.794645	−	0.607075i	$-0.792343\pi$
$997$	−50.1823	−1.58929	−0.794645	+	0.607075i	$0.792343\pi$
$998$	17.0649	0.540180
$999$	−15.3609	−0.485999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.30	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.30	✓	41	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.58821 q^{3} +1.00000 q^{4} +4.43977 q^{5} -1.58821 q^{6} +2.05481 q^{7} -1.00000 q^{8} -0.477577 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.58821 q^{3} +1.00000 q^{4} +4.43977 q^{5} -1.58821 q^{6} +2.05481 q^{7} -1.00000 q^{8} -0.477577 q^{9} -4.43977 q^{10} -2.29898 q^{11} +1.58821 q^{12} +1.35690 q^{13} -2.05481 q^{14} +7.05131 q^{15} +1.00000 q^{16} -5.61423 q^{17} +0.477577 q^{18} -1.00000 q^{19} +4.43977 q^{20} +3.26348 q^{21} +2.29898 q^{22} +6.75495 q^{23} -1.58821 q^{24} +14.7116 q^{25} -1.35690 q^{26} -5.52314 q^{27} +2.05481 q^{28} +5.14682 q^{29} -7.05131 q^{30} -4.55085 q^{31} -1.00000 q^{32} -3.65128 q^{33} +5.61423 q^{34} +9.12290 q^{35} -0.477577 q^{36} +2.78120 q^{37} +1.00000 q^{38} +2.15505 q^{39} -4.43977 q^{40} +6.16701 q^{41} -3.26348 q^{42} +1.84953 q^{43} -2.29898 q^{44} -2.12033 q^{45} -6.75495 q^{46} +9.53619 q^{47} +1.58821 q^{48} -2.77775 q^{49} -14.7116 q^{50} -8.91660 q^{51} +1.35690 q^{52} +4.52921 q^{53} +5.52314 q^{54} -10.2070 q^{55} -2.05481 q^{56} -1.58821 q^{57} -5.14682 q^{58} +5.82027 q^{59} +7.05131 q^{60} -4.55498 q^{61} +4.55085 q^{62} -0.981330 q^{63} +1.00000 q^{64} +6.02433 q^{65} +3.65128 q^{66} +0.756021 q^{67} -5.61423 q^{68} +10.7283 q^{69} -9.12290 q^{70} +6.75575 q^{71} +0.477577 q^{72} +4.44621 q^{73} -2.78120 q^{74} +23.3651 q^{75} -1.00000 q^{76} -4.72398 q^{77} -2.15505 q^{78} +10.7397 q^{79} +4.43977 q^{80} -7.33919 q^{81} -6.16701 q^{82} -17.2935 q^{83} +3.26348 q^{84} -24.9259 q^{85} -1.84953 q^{86} +8.17425 q^{87} +2.29898 q^{88} -6.04620 q^{89} +2.12033 q^{90} +2.78818 q^{91} +6.75495 q^{92} -7.22772 q^{93} -9.53619 q^{94} -4.43977 q^{95} -1.58821 q^{96} +2.42152 q^{97} +2.77775 q^{98} +1.09794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more