LMFDB - Embedded newform 4767.2.a.g.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4767,2,Mod(1,4767)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4767.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 4767 = 3 \cdot 7 \cdot 227 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4767.a (trivial)

Newform invariants

comment:select newform

sage:traces = [35,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$38.0646866435$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4767.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.858119 q^{2} -1.00000 q^{3} -1.26363 q^{4} -3.59592 q^{5} +0.858119 q^{6} +1.00000 q^{7} +2.80058 q^{8} +1.00000 q^{9} +3.08573 q^{10} -6.36982 q^{11} +1.26363 q^{12} +5.24936 q^{13} -0.858119 q^{14} +3.59592 q^{15} +0.124027 q^{16} +5.50648 q^{17} -0.858119 q^{18} -2.56012 q^{19} +4.54392 q^{20} -1.00000 q^{21} +5.46606 q^{22} -3.17274 q^{23} -2.80058 q^{24} +7.93067 q^{25} -4.50458 q^{26} -1.00000 q^{27} -1.26363 q^{28} -8.19228 q^{29} -3.08573 q^{30} -0.845913 q^{31} -5.70760 q^{32} +6.36982 q^{33} -4.72521 q^{34} -3.59592 q^{35} -1.26363 q^{36} -1.86570 q^{37} +2.19689 q^{38} -5.24936 q^{39} -10.0707 q^{40} +12.3860 q^{41} +0.858119 q^{42} +3.25218 q^{43} +8.04910 q^{44} -3.59592 q^{45} +2.72259 q^{46} +0.370523 q^{47} -0.124027 q^{48} +1.00000 q^{49} -6.80546 q^{50} -5.50648 q^{51} -6.63326 q^{52} -4.98085 q^{53} +0.858119 q^{54} +22.9054 q^{55} +2.80058 q^{56} +2.56012 q^{57} +7.02996 q^{58} -14.3700 q^{59} -4.54392 q^{60} +8.91417 q^{61} +0.725894 q^{62} +1.00000 q^{63} +4.64975 q^{64} -18.8763 q^{65} -5.46606 q^{66} -10.2434 q^{67} -6.95816 q^{68} +3.17274 q^{69} +3.08573 q^{70} -4.13821 q^{71} +2.80058 q^{72} -0.948252 q^{73} +1.60099 q^{74} -7.93067 q^{75} +3.23505 q^{76} -6.36982 q^{77} +4.50458 q^{78} -15.7242 q^{79} -0.445992 q^{80} +1.00000 q^{81} -10.6286 q^{82} -10.8144 q^{83} +1.26363 q^{84} -19.8009 q^{85} -2.79076 q^{86} +8.19228 q^{87} -17.8392 q^{88} +0.302857 q^{89} +3.08573 q^{90} +5.24936 q^{91} +4.00917 q^{92} +0.845913 q^{93} -0.317953 q^{94} +9.20601 q^{95} +5.70760 q^{96} -14.3858 q^{97} -0.858119 q^{98} -6.36982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) $ 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.858119	−0.606782	−0.303391	−	0.952866i	$-0.598119\pi$
$2$	−0.858119	−0.606782	−0.303391	+	0.952866i	$0.598119\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.26363	−0.631816
$5$	−3.59592	−1.60815	−0.804073	−	0.594531i	$-0.797338\pi$
$5$	−3.59592	−1.60815	−0.804073	+	0.594531i	$0.797338\pi$
$6$	0.858119	0.350326
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.80058	0.990156
$9$	1.00000	0.333333
$10$	3.08573	0.975794
$11$	−6.36982	−1.92057	−0.960286	−	0.279017i	$-0.909991\pi$
$11$	−6.36982	−1.92057	−0.960286	+	0.279017i	$0.909991\pi$
$12$	1.26363	0.364779
$13$	5.24936	1.45591	0.727955	−	0.685625i	$-0.240471\pi$
$13$	5.24936	1.45591	0.727955	+	0.685625i	$0.240471\pi$
$14$	−0.858119	−0.229342
$15$	3.59592	0.928464
$16$	0.124027	0.0310068
$17$	5.50648	1.33552	0.667758	−	0.744378i	$-0.267254\pi$
$17$	5.50648	1.33552	0.667758	+	0.744378i	$0.267254\pi$
$18$	−0.858119	−0.202261
$19$	−2.56012	−0.587333	−0.293666	−	0.955908i	$-0.594875\pi$
$19$	−2.56012	−0.587333	−0.293666	+	0.955908i	$0.594875\pi$
$20$	4.54392	1.01605
$21$	−1.00000	−0.218218
$22$	5.46606	1.16537
$23$	−3.17274	−0.661562	−0.330781	−	0.943708i	$-0.607312\pi$
$23$	−3.17274	−0.661562	−0.330781	+	0.943708i	$0.607312\pi$
$24$	−2.80058	−0.571667
$25$	7.93067	1.58613
$26$	−4.50458	−0.883420
$27$	−1.00000	−0.192450
$28$	−1.26363	−0.238804
$29$	−8.19228	−1.52127	−0.760634	−	0.649180i	$-0.775112\pi$
$29$	−8.19228	−1.52127	−0.760634	+	0.649180i	$0.775112\pi$
$30$	−3.08573	−0.563375
$31$	−0.845913	−0.151930	−0.0759652	−	0.997110i	$-0.524204\pi$
$31$	−0.845913	−0.151930	−0.0759652	+	0.997110i	$0.524204\pi$
$32$	−5.70760	−1.00897
$33$	6.36982	1.10884
$34$	−4.72521	−0.810368
$35$	−3.59592	−0.607822
$36$	−1.26363	−0.210605
$37$	−1.86570	−0.306719	−0.153359	−	0.988170i	$-0.549009\pi$
$37$	−1.86570	−0.306719	−0.153359	+	0.988170i	$0.549009\pi$
$38$	2.19689	0.356383
$39$	−5.24936	−0.840570
$40$	−10.0707	−1.59232
$41$	12.3860	1.93436	0.967181	−	0.254088i	$-0.0817754\pi$
$41$	12.3860	1.93436	0.967181	+	0.254088i	$0.0817754\pi$
$42$	0.858119	0.132411
$43$	3.25218	0.495953	0.247976	−	0.968766i	$-0.420235\pi$
$43$	3.25218	0.495953	0.247976	+	0.968766i	$0.420235\pi$
$44$	8.04910	1.21345
$45$	−3.59592	−0.536049
$46$	2.72259	0.401424
$47$	0.370523	0.0540463	0.0270232	−	0.999635i	$-0.491397\pi$
$47$	0.370523	0.0540463	0.0270232	+	0.999635i	$0.491397\pi$
$48$	−0.124027	−0.0179018
$49$	1.00000	0.142857
$50$	−6.80546	−0.962437
$51$	−5.50648	−0.771061
$52$	−6.63326	−0.919867
$53$	−4.98085	−0.684172	−0.342086	−	0.939669i	$-0.611133\pi$
$53$	−4.98085	−0.684172	−0.342086	+	0.939669i	$0.611133\pi$
$54$	0.858119	0.116775
$55$	22.9054	3.08856
$56$	2.80058	0.374244
$57$	2.56012	0.339097
$58$	7.02996	0.923078
$59$	−14.3700	−1.87081	−0.935406	−	0.353575i	$-0.884966\pi$
$59$	−14.3700	−1.87081	−0.935406	+	0.353575i	$0.884966\pi$
$60$	−4.54392	−0.586618
$61$	8.91417	1.14134	0.570671	−	0.821179i	$-0.306683\pi$
$61$	8.91417	1.14134	0.570671	+	0.821179i	$0.306683\pi$
$62$	0.725894	0.0921886
$63$	1.00000	0.125988
$64$	4.64975	0.581218
$65$	−18.8763	−2.34132
$66$	−5.46606	−0.672826
$67$	−10.2434	−1.25144	−0.625718	−	0.780049i	$-0.715194\pi$
$67$	−10.2434	−1.25144	−0.625718	+	0.780049i	$0.715194\pi$
$68$	−6.95816	−0.843801
$69$	3.17274	0.381953
$70$	3.08573	0.368815
$71$	−4.13821	−0.491116	−0.245558	−	0.969382i	$-0.578971\pi$
$71$	−4.13821	−0.491116	−0.245558	+	0.969382i	$0.578971\pi$
$72$	2.80058	0.330052
$73$	−0.948252	−0.110985	−0.0554923	−	0.998459i	$-0.517673\pi$
$73$	−0.948252	−0.110985	−0.0554923	+	0.998459i	$0.517673\pi$
$74$	1.60099	0.186111
$75$	−7.93067	−0.915755
$76$	3.23505	0.371086
$77$	−6.36982	−0.725908
$78$	4.50458	0.510043
$79$	−15.7242	−1.76911	−0.884555	−	0.466437i	$-0.845538\pi$
$79$	−15.7242	−1.76911	−0.884555	+	0.466437i	$0.845538\pi$
$80$	−0.445992	−0.0498635
$81$	1.00000	0.111111
$82$	−10.6286	−1.17374
$83$	−10.8144	−1.18703	−0.593515	−	0.804823i	$-0.702260\pi$
$83$	−10.8144	−1.18703	−0.593515	+	0.804823i	$0.702260\pi$
$84$	1.26363	0.137873
$85$	−19.8009	−2.14771
$86$	−2.79076	−0.300935
$87$	8.19228	0.878305
$88$	−17.8392	−1.90167
$89$	0.302857	0.0321027	0.0160514	−	0.999871i	$-0.494890\pi$
$89$	0.302857	0.0321027	0.0160514	+	0.999871i	$0.494890\pi$
$90$	3.08573	0.325265
$91$	5.24936	0.550282
$92$	4.00917	0.417985
$93$	0.845913	0.0877170
$94$	−0.317953	−0.0327943
$95$	9.20601	0.944517
$96$	5.70760	0.582529
$97$	−14.3858	−1.46065	−0.730327	−	0.683098i	$-0.760632\pi$
$97$	−14.3858	−1.46065	−0.730327	+	0.683098i	$0.760632\pi$
$98$	−0.858119	−0.0866831
$99$	−6.36982	−0.640191
$100$	−10.0214	−1.00214
$101$	−17.6642	−1.75766	−0.878828	−	0.477138i	$-0.841674\pi$
$101$	−17.6642	−1.75766	−0.878828	+	0.477138i	$0.841674\pi$
$102$	4.72521	0.467866
$103$	−2.06602	−0.203571	−0.101785	−	0.994806i	$-0.532455\pi$
$103$	−2.06602	−0.203571	−0.101785	+	0.994806i	$0.532455\pi$
$104$	14.7013	1.44158
$105$	3.59592	0.350926
$106$	4.27416	0.415143
$107$	5.63536	0.544791	0.272396	−	0.962185i	$-0.412184\pi$
$107$	5.63536	0.544791	0.272396	+	0.962185i	$0.412184\pi$
$108$	1.26363	0.121593
$109$	11.2571	1.07824	0.539119	−	0.842230i	$-0.318757\pi$
$109$	11.2571	1.07824	0.539119	+	0.842230i	$0.318757\pi$
$110$	−19.6555	−1.87408
$111$	1.86570	0.177084
$112$	0.124027	0.0117195
$113$	−0.509211	−0.0479026	−0.0239513	−	0.999713i	$-0.507625\pi$
$113$	−0.509211	−0.0479026	−0.0239513	+	0.999713i	$0.507625\pi$
$114$	−2.19689	−0.205758
$115$	11.4089	1.06389
$116$	10.3520	0.961162
$117$	5.24936	0.485304
$118$	12.3312	1.13518
$119$	5.50648	0.504778
$120$	10.0707	0.919324
$121$	29.5746	2.68860
$122$	−7.64942	−0.692546
$123$	−12.3860	−1.11680
$124$	1.06892	0.0959920
$125$	−10.5385	−0.942589
$126$	−0.858119	−0.0764473
$127$	−12.2757	−1.08929	−0.544647	−	0.838665i	$-0.683336\pi$
$127$	−12.2757	−1.08929	−0.544647	+	0.838665i	$0.683336\pi$
$128$	7.42516	0.656298
$129$	−3.25218	−0.286338
$130$	16.1981	1.42067
$131$	−8.84530	−0.772818	−0.386409	−	0.922328i	$-0.626285\pi$
$131$	−8.84530	−0.772818	−0.386409	+	0.922328i	$0.626285\pi$
$132$	−8.04910	−0.700584
$133$	−2.56012	−0.221991
$134$	8.79010	0.759349
$135$	3.59592	0.309488
$136$	15.4214	1.32237
$137$	19.9387	1.70348	0.851741	−	0.523964i	$-0.175547\pi$
$137$	19.9387	1.70348	0.851741	+	0.523964i	$0.175547\pi$
$138$	−2.72259	−0.231762
$139$	19.1611	1.62522	0.812612	−	0.582806i	$-0.198045\pi$
$139$	19.1611	1.62522	0.812612	+	0.582806i	$0.198045\pi$
$140$	4.54392	0.384032
$141$	−0.370523	−0.0312037
$142$	3.55108	0.298000
$143$	−33.4375	−2.79618
$144$	0.124027	0.0103356
$145$	29.4588	2.44642
$146$	0.813714	0.0673434
$147$	−1.00000	−0.0824786
$148$	2.35755	0.193790
$149$	4.94804	0.405359	0.202679	−	0.979245i	$-0.435035\pi$
$149$	4.94804	0.405359	0.202679	+	0.979245i	$0.435035\pi$
$150$	6.80546	0.555663
$151$	−9.32633	−0.758966	−0.379483	−	0.925199i	$-0.623898\pi$
$151$	−9.32633	−0.758966	−0.379483	+	0.925199i	$0.623898\pi$
$152$	−7.16984	−0.581551
$153$	5.50648	0.445172
$154$	5.46606	0.440468
$155$	3.04184	0.244326
$156$	6.63326	0.531086
$157$	−17.8217	−1.42232	−0.711162	−	0.703029i	$-0.751831\pi$
$157$	−17.8217	−1.42232	−0.711162	+	0.703029i	$0.751831\pi$
$158$	13.4932	1.07346
$159$	4.98085	0.395007
$160$	20.5241	1.62257
$161$	−3.17274	−0.250047
$162$	−0.858119	−0.0674202
$163$	−11.9029	−0.932308	−0.466154	−	0.884704i	$-0.654361\pi$
$163$	−11.9029	−0.932308	−0.466154	+	0.884704i	$0.654361\pi$
$164$	−15.6513	−1.22216
$165$	−22.9054	−1.78318
$166$	9.28001	0.720269
$167$	11.7249	0.907298	0.453649	−	0.891181i	$-0.350122\pi$
$167$	11.7249	0.907298	0.453649	+	0.891181i	$0.350122\pi$
$168$	−2.80058	−0.216070
$169$	14.5558	1.11968
$170$	16.9915	1.30319
$171$	−2.56012	−0.195778
$172$	−4.10955	−0.313351
$173$	1.43439	0.109055	0.0545273	−	0.998512i	$-0.482635\pi$
$173$	1.43439	0.109055	0.0545273	+	0.998512i	$0.482635\pi$
$174$	−7.02996	−0.532940
$175$	7.93067	0.599502
$176$	−0.790030	−0.0595508
$177$	14.3700	1.08011
$178$	−0.259887	−0.0194794
$179$	−2.95643	−0.220974	−0.110487	−	0.993878i	$-0.535241\pi$
$179$	−2.95643	−0.220974	−0.110487	+	0.993878i	$0.535241\pi$
$180$	4.54392	0.338684
$181$	12.0629	0.896625	0.448312	−	0.893877i	$-0.352025\pi$
$181$	12.0629	0.896625	0.448312	+	0.893877i	$0.352025\pi$
$182$	−4.50458	−0.333901
$183$	−8.91417	−0.658954
$184$	−8.88553	−0.655050
$185$	6.70891	0.493249
$186$	−0.725894	−0.0532251
$187$	−35.0753	−2.56496
$188$	−0.468205	−0.0341473
$189$	−1.00000	−0.0727393
$190$	−7.89986	−0.573116
$191$	−4.31775	−0.312421	−0.156211	−	0.987724i	$-0.549928\pi$
$191$	−4.31775	−0.312421	−0.156211	+	0.987724i	$0.549928\pi$
$192$	−4.64975	−0.335567
$193$	7.47287	0.537909	0.268954	−	0.963153i	$-0.413322\pi$
$193$	7.47287	0.537909	0.268954	+	0.963153i	$0.413322\pi$
$194$	12.3447	0.886298
$195$	18.8763	1.35176
$196$	−1.26363	−0.0902594
$197$	9.80925	0.698880	0.349440	−	0.936959i	$-0.386372\pi$
$197$	9.80925	0.698880	0.349440	+	0.936959i	$0.386372\pi$
$198$	5.46606	0.388456
$199$	16.3031	1.15569	0.577847	−	0.816145i	$-0.303893\pi$
$199$	16.3031	1.15569	0.577847	+	0.816145i	$0.303893\pi$
$200$	22.2105	1.57052
$201$	10.2434	0.722517
$202$	15.1580	1.06651
$203$	−8.19228	−0.574986
$204$	6.95816	0.487169
$205$	−44.5390	−3.11074
$206$	1.77289	0.123523
$207$	−3.17274	−0.220521
$208$	0.651063	0.0451431
$209$	16.3075	1.12801
$210$	−3.08573	−0.212936
$211$	18.3928	1.26621	0.633106	−	0.774065i	$-0.281780\pi$
$211$	18.3928	1.26621	0.633106	+	0.774065i	$0.281780\pi$
$212$	6.29396	0.432271
$213$	4.13821	0.283546
$214$	−4.83581	−0.330569
$215$	−11.6946	−0.797564
$216$	−2.80058	−0.190556
$217$	−0.845913	−0.0574243
$218$	−9.65997	−0.654255
$219$	0.948252	0.0640770
$220$	−28.9440	−1.95140
$221$	28.9055	1.94439
$222$	−1.60099	−0.107451
$223$	−20.1971	−1.35250	−0.676249	−	0.736673i	$-0.736396\pi$
$223$	−20.1971	−1.35250	−0.676249	+	0.736673i	$0.736396\pi$
$224$	−5.70760	−0.381355
$225$	7.93067	0.528711
$226$	0.436964	0.0290664
$227$	−1.00000	−0.0663723
$227$	−1.00000	−0.0663723
$228$	−3.23505	−0.214247
$229$	10.0676	0.665285	0.332642	−	0.943053i	$-0.392060\pi$
$229$	10.0676	0.665285	0.332642	+	0.943053i	$0.392060\pi$
$230$	−9.79022	−0.645548
$231$	6.36982	0.419103
$232$	−22.9432	−1.50629
$233$	12.9857	0.850724	0.425362	−	0.905023i	$-0.360147\pi$
$233$	12.9857	0.850724	0.425362	+	0.905023i	$0.360147\pi$
$234$	−4.50458	−0.294473
$235$	−1.33237	−0.0869144
$236$	18.1584	1.18201
$237$	15.7242	1.02140
$238$	−4.72521	−0.306290
$239$	−16.0344	−1.03718	−0.518589	−	0.855024i	$-0.673543\pi$
$239$	−16.0344	−1.03718	−0.518589	+	0.855024i	$0.673543\pi$
$240$	0.445992	0.0287887
$241$	23.1859	1.49354	0.746768	−	0.665085i	$-0.231605\pi$
$241$	23.1859	1.49354	0.746768	+	0.665085i	$0.231605\pi$
$242$	−25.3785	−1.63139
$243$	−1.00000	−0.0641500
$244$	−11.2642	−0.721118
$245$	−3.59592	−0.229735
$246$	10.6286	0.677657
$247$	−13.4390	−0.855104
$248$	−2.36905	−0.150435
$249$	10.8144	0.685332
$250$	9.04326	0.571946
$251$	18.9770	1.19782	0.598909	−	0.800817i	$-0.295601\pi$
$251$	18.9770	1.19782	0.598909	+	0.800817i	$0.295601\pi$
$252$	−1.26363	−0.0796013
$253$	20.2098	1.27058
$254$	10.5340	0.660964
$255$	19.8009	1.23998
$256$	−15.6712	−0.979448
$257$	16.3061	1.01715	0.508574	−	0.861018i	$-0.330173\pi$
$257$	16.3061	1.01715	0.508574	+	0.861018i	$0.330173\pi$
$258$	2.79076	0.173745
$259$	−1.86570	−0.115929
$260$	23.8527	1.47928
$261$	−8.19228	−0.507090
$262$	7.59033	0.468932
$263$	24.4644	1.50854	0.754269	−	0.656566i	$-0.227992\pi$
$263$	24.4644	1.50854	0.754269	+	0.656566i	$0.227992\pi$
$264$	17.8392	1.09793
$265$	17.9108	1.10025
$266$	2.19689	0.134700
$267$	−0.302857	−0.0185345
$268$	12.9439	0.790677
$269$	−12.1876	−0.743093	−0.371547	−	0.928414i	$-0.621172\pi$
$269$	−12.1876	−0.743093	−0.371547	+	0.928414i	$0.621172\pi$
$270$	−3.08573	−0.187792
$271$	−20.5377	−1.24758	−0.623789	−	0.781593i	$-0.714407\pi$
$271$	−20.5377	−1.24758	−0.623789	+	0.781593i	$0.714407\pi$
$272$	0.682953	0.0414101
$273$	−5.24936	−0.317706
$274$	−17.1098	−1.03364
$275$	−50.5169	−3.04628
$276$	−4.00917	−0.241324
$277$	−3.47993	−0.209089	−0.104544	−	0.994520i	$-0.533338\pi$
$277$	−3.47993	−0.209089	−0.104544	+	0.994520i	$0.533338\pi$
$278$	−16.4425	−0.986156
$279$	−0.845913	−0.0506435
$280$	−10.0707	−0.601839
$281$	0.634486	0.0378503	0.0189251	−	0.999821i	$-0.493976\pi$
$281$	0.634486	0.0378503	0.0189251	+	0.999821i	$0.493976\pi$
$282$	0.317953	0.0189338
$283$	7.54092	0.448261	0.224130	−	0.974559i	$-0.428046\pi$
$283$	7.54092	0.448261	0.224130	+	0.974559i	$0.428046\pi$
$284$	5.22918	0.310295
$285$	−9.20601	−0.545317
$286$	28.6933	1.69667
$287$	12.3860	0.731120
$288$	−5.70760	−0.336324
$289$	13.3213	0.783606
$290$	−25.2792	−1.48444
$291$	14.3858	0.843309
$292$	1.19824	0.0701218
$293$	18.0394	1.05387	0.526937	−	0.849905i	$-0.323340\pi$
$293$	18.0394	1.05387	0.526937	+	0.849905i	$0.323340\pi$
$294$	0.858119	0.0500465
$295$	51.6734	3.00854
$296$	−5.22504	−0.303700
$297$	6.36982	0.369614
$298$	−4.24601	−0.245964
$299$	−16.6549	−0.963175
$300$	10.0214	0.578588
$301$	3.25218	0.187452
$302$	8.00310	0.460527
$303$	17.6642	1.01478
$304$	−0.317525	−0.0182113
$305$	−32.0547	−1.83545
$306$	−4.72521	−0.270123
$307$	−6.69835	−0.382295	−0.191147	−	0.981561i	$-0.561221\pi$
$307$	−6.69835	−0.382295	−0.191147	+	0.981561i	$0.561221\pi$
$308$	8.04910	0.458640
$309$	2.06602	0.117532
$310$	−2.61026	−0.148253
$311$	12.5116	0.709470	0.354735	−	0.934967i	$-0.384571\pi$
$311$	12.5116	0.709470	0.354735	+	0.934967i	$0.384571\pi$
$312$	−14.7013	−0.832296
$313$	−33.7758	−1.90912	−0.954562	−	0.298013i	$-0.903676\pi$
$313$	−33.7758	−1.90912	−0.954562	+	0.298013i	$0.903676\pi$
$314$	15.2931	0.863040
$315$	−3.59592	−0.202607
$316$	19.8696	1.11775
$317$	−13.0600	−0.733523	−0.366762	−	0.930315i	$-0.619534\pi$
$317$	−13.0600	−0.733523	−0.366762	+	0.930315i	$0.619534\pi$
$318$	−4.27416	−0.239683
$319$	52.1833	2.92171
$320$	−16.7201	−0.934684
$321$	−5.63536	−0.314535
$322$	2.72259	0.151724
$323$	−14.0973	−0.784393
$324$	−1.26363	−0.0702017
$325$	41.6309	2.30927
$326$	10.2141	0.565708
$327$	−11.2571	−0.622521
$328$	34.6879	1.91532
$329$	0.370523	0.0204276
$330$	19.6555	1.08200
$331$	2.88649	0.158656	0.0793279	−	0.996849i	$-0.474723\pi$
$331$	2.88649	0.158656	0.0793279	+	0.996849i	$0.474723\pi$
$332$	13.6654	0.749984
$333$	−1.86570	−0.102240
$334$	−10.0613	−0.550532
$335$	36.8347	2.01249
$336$	−0.124027	−0.00676624
$337$	28.1439	1.53310	0.766548	−	0.642187i	$-0.221973\pi$
$337$	28.1439	1.53310	0.766548	+	0.642187i	$0.221973\pi$
$338$	−12.4906	−0.679399
$339$	0.509211	0.0276566
$340$	25.0210	1.35695
$341$	5.38831	0.291793
$342$	2.19689	0.118794
$343$	1.00000	0.0539949
$344$	9.10800	0.491070
$345$	−11.4089	−0.614236
$346$	−1.23088	−0.0661723
$347$	−0.178187	−0.00956559	−0.00478279	−	0.999989i	$-0.501522\pi$
$347$	−0.178187	−0.00956559	−0.00478279	+	0.999989i	$0.501522\pi$
$348$	−10.3520	−0.554927
$349$	−8.99653	−0.481573	−0.240787	−	0.970578i	$-0.577405\pi$
$349$	−8.99653	−0.481573	−0.240787	+	0.970578i	$0.577405\pi$
$350$	−6.80546	−0.363767
$351$	−5.24936	−0.280190
$352$	36.3564	1.93780
$353$	−15.2438	−0.811347	−0.405673	−	0.914018i	$-0.632963\pi$
$353$	−15.2438	−0.811347	−0.405673	+	0.914018i	$0.632963\pi$
$354$	−12.3312	−0.655394
$355$	14.8807	0.789786
$356$	−0.382699	−0.0202830
$357$	−5.50648	−0.291434
$358$	2.53697	0.134083
$359$	2.83983	0.149880	0.0749401	−	0.997188i	$-0.476123\pi$
$359$	2.83983	0.149880	0.0749401	+	0.997188i	$0.476123\pi$
$360$	−10.0707	−0.530772
$361$	−12.4458	−0.655040
$362$	−10.3514	−0.544056
$363$	−29.5746	−1.55226
$364$	−6.63326	−0.347677
$365$	3.40984	0.178479
$366$	7.64942	0.399842
$367$	2.38991	0.124753	0.0623763	−	0.998053i	$-0.480132\pi$
$367$	2.38991	0.124753	0.0623763	+	0.998053i	$0.480132\pi$
$368$	−0.393506	−0.0205129
$369$	12.3860	0.644787
$370$	−5.75704	−0.299294
$371$	−4.98085	−0.258593
$372$	−1.06892	−0.0554210
$373$	8.02396	0.415465	0.207733	−	0.978186i	$-0.433392\pi$
$373$	8.02396	0.415465	0.207733	+	0.978186i	$0.433392\pi$
$374$	30.0988	1.55637
$375$	10.5385	0.544204
$376$	1.03768	0.0535143
$377$	−43.0042	−2.21483
$378$	0.858119	0.0441369
$379$	11.5658	0.594096	0.297048	−	0.954863i	$-0.403998\pi$
$379$	11.5658	0.594096	0.297048	+	0.954863i	$0.403998\pi$
$380$	−11.6330	−0.596761
$381$	12.2757	0.628904
$382$	3.70514	0.189572
$383$	−34.0916	−1.74200	−0.871000	−	0.491283i	$-0.836528\pi$
$383$	−34.0916	−1.74200	−0.871000	+	0.491283i	$0.836528\pi$
$384$	−7.42516	−0.378914
$385$	22.9054	1.16737
$386$	−6.41261	−0.326393
$387$	3.25218	0.165318
$388$	18.1783	0.922864
$389$	16.1876	0.820745	0.410373	−	0.911918i	$-0.365399\pi$
$389$	16.1876	0.820745	0.410373	+	0.911918i	$0.365399\pi$
$390$	−16.1981	−0.820223
$391$	−17.4706	−0.883527
$392$	2.80058	0.141451
$393$	8.84530	0.446187
$394$	−8.41750	−0.424068
$395$	56.5430	2.84499
$396$	8.04910	0.404483
$397$	20.4509	1.02640	0.513201	−	0.858269i	$-0.328460\pi$
$397$	20.4509	1.02640	0.513201	+	0.858269i	$0.328460\pi$
$398$	−13.9900	−0.701255
$399$	2.56012	0.128167
$400$	0.983618	0.0491809
$401$	−19.6918	−0.983359	−0.491680	−	0.870776i	$-0.663617\pi$
$401$	−19.6918	−0.983359	−0.491680	+	0.870776i	$0.663617\pi$
$402$	−8.79010	−0.438410
$403$	−4.44050	−0.221197
$404$	22.3211	1.11051
$405$	−3.59592	−0.178683
$406$	7.02996	0.348891
$407$	11.8842	0.589076
$408$	−15.4214	−0.763471
$409$	−16.8029	−0.830852	−0.415426	−	0.909627i	$-0.636367\pi$
$409$	−16.8029	−0.830852	−0.415426	+	0.909627i	$0.636367\pi$
$410$	38.2197	1.88754
$411$	−19.9387	−0.983505
$412$	2.61068	0.128619
$413$	−14.3700	−0.707101
$414$	2.72259	0.133808
$415$	38.8876	1.90892
$416$	−29.9612	−1.46897
$417$	−19.1611	−0.938323
$418$	−13.9938	−0.684459
$419$	−17.0909	−0.834944	−0.417472	−	0.908690i	$-0.637084\pi$
$419$	−17.0909	−0.834944	−0.417472	+	0.908690i	$0.637084\pi$
$420$	−4.54392	−0.221721
$421$	−14.1586	−0.690047	−0.345024	−	0.938594i	$-0.612129\pi$
$421$	−14.1586	−0.690047	−0.345024	+	0.938594i	$0.612129\pi$
$422$	−15.7832	−0.768315
$423$	0.370523	0.0180154
$424$	−13.9493	−0.677438
$425$	43.6701	2.11831
$426$	−3.55108	−0.172050
$427$	8.91417	0.431387
$428$	−7.12102	−0.344208
$429$	33.4375	1.61438
$430$	10.0353	0.483947
$431$	33.0440	1.59167	0.795837	−	0.605511i	$-0.207031\pi$
$431$	33.0440	1.59167	0.795837	+	0.605511i	$0.207031\pi$
$432$	−0.124027	−0.00596726
$433$	−18.9572	−0.911025	−0.455512	−	0.890229i	$-0.650544\pi$
$433$	−18.9572	−0.911025	−0.455512	+	0.890229i	$0.650544\pi$
$434$	0.725894	0.0348440
$435$	−29.4588	−1.41244
$436$	−14.2249	−0.681248
$437$	8.12261	0.388557
$438$	−0.813714	−0.0388807
$439$	34.6634	1.65439	0.827196	−	0.561914i	$-0.189935\pi$
$439$	34.6634	1.65439	0.827196	+	0.561914i	$0.189935\pi$
$440$	64.1485	3.05816
$441$	1.00000	0.0476190
$442$	−24.8044	−1.17982
$443$	26.9689	1.28133	0.640665	−	0.767821i	$-0.278659\pi$
$443$	26.9689	1.28133	0.640665	+	0.767821i	$0.278659\pi$
$444$	−2.35755	−0.111885
$445$	−1.08905	−0.0516259
$446$	17.3315	0.820672
$447$	−4.94804	−0.234034
$448$	4.64975	0.219680
$449$	−14.1238	−0.666544	−0.333272	−	0.942831i	$-0.608153\pi$
$449$	−14.1238	−0.666544	−0.333272	+	0.942831i	$0.608153\pi$
$450$	−6.80546	−0.320812
$451$	−78.8963	−3.71508
$452$	0.643455	0.0302656
$453$	9.32633	0.438189
$454$	0.858119	0.0402735
$455$	−18.8763	−0.884935
$456$	7.16984	0.335759
$457$	0.734288	0.0343485	0.0171743	−	0.999853i	$-0.494533\pi$
$457$	0.734288	0.0343485	0.0171743	+	0.999853i	$0.494533\pi$
$458$	−8.63919	−0.403683
$459$	−5.50648	−0.257020
$460$	−14.4167	−0.672181
$461$	−14.0614	−0.654903	−0.327451	−	0.944868i	$-0.606190\pi$
$461$	−14.0614	−0.654903	−0.327451	+	0.944868i	$0.606190\pi$
$462$	−5.46606	−0.254304
$463$	32.2080	1.49683	0.748416	−	0.663229i	$-0.230814\pi$
$463$	32.2080	1.49683	0.748416	+	0.663229i	$0.230814\pi$
$464$	−1.01607	−0.0471697
$465$	−3.04184	−0.141062
$466$	−11.1433	−0.516204
$467$	−27.4513	−1.27029	−0.635147	−	0.772392i	$-0.719060\pi$
$467$	−27.4513	−1.27029	−0.635147	+	0.772392i	$0.719060\pi$
$468$	−6.63326	−0.306622
$469$	−10.2434	−0.472998
$470$	1.14333	0.0527381
$471$	17.8217	0.821179
$472$	−40.2444	−1.85240
$473$	−20.7158	−0.952513
$474$	−13.4932	−0.619764
$475$	−20.3035	−0.931588
$476$	−6.95816	−0.318927
$477$	−4.98085	−0.228057
$478$	13.7594	0.629341
$479$	25.9579	1.18605	0.593023	−	0.805186i	$-0.297934\pi$
$479$	25.9579	1.18605	0.593023	+	0.805186i	$0.297934\pi$
$480$	−20.5241	−0.936792
$481$	−9.79372	−0.446555
$482$	−19.8963	−0.906250
$483$	3.17274	0.144365
$484$	−37.3714	−1.69870
$485$	51.7301	2.34894
$486$	0.858119	0.0389251
$487$	−3.06321	−0.138807	−0.0694037	−	0.997589i	$-0.522110\pi$
$487$	−3.06321	−0.138807	−0.0694037	+	0.997589i	$0.522110\pi$
$488$	24.9649	1.13011
$489$	11.9029	0.538268
$490$	3.08573	0.139399
$491$	10.9237	0.492981	0.246491	−	0.969145i	$-0.420723\pi$
$491$	10.9237	0.492981	0.246491	+	0.969145i	$0.420723\pi$
$492$	15.6513	0.705615
$493$	−45.1106	−2.03168
$494$	11.5323	0.518862
$495$	22.9054	1.02952
$496$	−0.104916	−0.00471087
$497$	−4.13821	−0.185624
$498$	−9.28001	−0.415847
$499$	22.8497	1.02289	0.511447	−	0.859315i	$-0.329110\pi$
$499$	22.8497	1.02289	0.511447	+	0.859315i	$0.329110\pi$
$500$	13.3167	0.595542
$501$	−11.7249	−0.523829
$502$	−16.2845	−0.726814
$503$	−15.8780	−0.707963	−0.353981	−	0.935252i	$-0.615172\pi$
$503$	−15.8780	−0.707963	−0.353981	+	0.935252i	$0.615172\pi$
$504$	2.80058	0.124748
$505$	63.5192	2.82657
$506$	−17.3424	−0.770964
$507$	−14.5558	−0.646445
$508$	15.5120	0.688233
$509$	−20.6645	−0.915936	−0.457968	−	0.888969i	$-0.651423\pi$
$509$	−20.6645	−0.915936	−0.457968	+	0.888969i	$0.651423\pi$
$510$	−16.9915	−0.752397
$511$	−0.948252	−0.0419482
$512$	−1.40259	−0.0619865
$513$	2.56012	0.113032
$514$	−13.9926	−0.617187
$515$	7.42923	0.327371
$516$	4.10955	0.180913
$517$	−2.36016	−0.103800
$518$	1.60099	0.0703435
$519$	−1.43439	−0.0629627
$520$	−52.8647	−2.31827
$521$	5.80196	0.254189	0.127094	−	0.991891i	$-0.459435\pi$
$521$	5.80196	0.254189	0.127094	+	0.991891i	$0.459435\pi$
$522$	7.02996	0.307693
$523$	23.1217	1.01104	0.505521	−	0.862814i	$-0.331300\pi$
$523$	23.1217	1.01104	0.505521	+	0.862814i	$0.331300\pi$
$524$	11.1772	0.488278
$525$	−7.93067	−0.346123
$526$	−20.9933	−0.915353
$527$	−4.65800	−0.202906
$528$	0.790030	0.0343817
$529$	−12.9337	−0.562336
$530$	−15.3696	−0.667611
$531$	−14.3700	−0.623604
$532$	3.23505	0.140257
$533$	65.0184	2.81626
$534$	0.259887	0.0112464
$535$	−20.2643	−0.876104
$536$	−28.6876	−1.23912
$537$	2.95643	0.127579
$538$	10.4584	0.450896
$539$	−6.36982	−0.274367
$540$	−4.54392	−0.195539
$541$	26.4987	1.13927	0.569635	−	0.821898i	$-0.307085\pi$
$541$	26.4987	1.13927	0.569635	+	0.821898i	$0.307085\pi$
$542$	17.6238	0.757008
$543$	−12.0629	−0.517667
$544$	−31.4288	−1.34750
$545$	−40.4798	−1.73396
$546$	4.50458	0.192778
$547$	−25.9856	−1.11106	−0.555531	−	0.831496i	$-0.687485\pi$
$547$	−25.9856	−1.11106	−0.555531	+	0.831496i	$0.687485\pi$
$548$	−25.1952	−1.07629
$549$	8.91417	0.380448
$550$	43.3495	1.84843
$551$	20.9733	0.893491
$552$	8.88553	0.378193
$553$	−15.7242	−0.668660
$554$	2.98620	0.126871
$555$	−6.70891	−0.284777
$556$	−24.2126	−1.02684
$557$	−23.1885	−0.982529	−0.491264	−	0.871010i	$-0.663465\pi$
$557$	−23.1885	−0.982529	−0.491264	+	0.871010i	$0.663465\pi$
$558$	0.725894	0.0307295
$559$	17.0719	0.722063
$560$	−0.445992	−0.0188466
$561$	35.0753	1.48088
$562$	−0.544465	−0.0229668
$563$	36.7706	1.54970	0.774848	−	0.632148i	$-0.217826\pi$
$563$	36.7706	1.54970	0.774848	+	0.632148i	$0.217826\pi$
$564$	0.468205	0.0197150
$565$	1.83109	0.0770343
$566$	−6.47100	−0.271997
$567$	1.00000	0.0419961
$568$	−11.5894	−0.486281
$569$	6.33929	0.265757	0.132878	−	0.991132i	$-0.457578\pi$
$569$	6.33929	0.265757	0.132878	+	0.991132i	$0.457578\pi$
$570$	7.89986	0.330889
$571$	−17.4718	−0.731174	−0.365587	−	0.930777i	$-0.619132\pi$
$571$	−17.4718	−0.731174	−0.365587	+	0.930777i	$0.619132\pi$
$572$	42.2526	1.76667
$573$	4.31775	0.180376
$574$	−10.6286	−0.443630
$575$	−25.1620	−1.04933
$576$	4.64975	0.193739
$577$	28.8297	1.20020	0.600098	−	0.799926i	$-0.295128\pi$
$577$	28.8297	1.20020	0.600098	+	0.799926i	$0.295128\pi$
$578$	−11.4313	−0.475478
$579$	−7.47287	−0.310562
$580$	−37.2251	−1.54569
$581$	−10.8144	−0.448655
$582$	−12.3447	−0.511705
$583$	31.7271	1.31400
$584$	−2.65566	−0.109892
$585$	−18.8763	−0.780439
$586$	−15.4800	−0.639471
$587$	29.1005	1.20111	0.600554	−	0.799584i	$-0.294947\pi$
$587$	29.1005	1.20111	0.600554	+	0.799584i	$0.294947\pi$
$588$	1.26363	0.0521113
$589$	2.16564	0.0892337
$590$	−44.3419	−1.82553
$591$	−9.80925	−0.403498
$592$	−0.231397	−0.00951037
$593$	−8.55688	−0.351389	−0.175694	−	0.984445i	$-0.556217\pi$
$593$	−8.55688	−0.351389	−0.175694	+	0.984445i	$0.556217\pi$
$594$	−5.46606	−0.224275
$595$	−19.8009	−0.811757
$596$	−6.25249	−0.256112
$597$	−16.3031	−0.667241
$598$	14.2919	0.584437
$599$	15.6349	0.638823	0.319412	−	0.947616i	$-0.396515\pi$
$599$	15.6349	0.638823	0.319412	+	0.947616i	$0.396515\pi$
$600$	−22.2105	−0.906740
$601$	10.3561	0.422433	0.211216	−	0.977439i	$-0.432258\pi$
$601$	10.3561	0.422433	0.211216	+	0.977439i	$0.432258\pi$
$602$	−2.79076	−0.113743
$603$	−10.2434	−0.417145
$604$	11.7850	0.479527
$605$	−106.348	−4.32366
$606$	−15.1580	−0.615752
$607$	38.7606	1.57324	0.786621	−	0.617436i	$-0.211829\pi$
$607$	38.7606	1.57324	0.786621	+	0.617436i	$0.211829\pi$
$608$	14.6122	0.592601
$609$	8.19228	0.331968
$610$	27.5067	1.11372
$611$	1.94501	0.0786866
$612$	−6.95816	−0.281267
$613$	−3.92855	−0.158673	−0.0793363	−	0.996848i	$-0.525280\pi$
$613$	−3.92855	−0.158673	−0.0793363	+	0.996848i	$0.525280\pi$
$614$	5.74798	0.231970
$615$	44.5390	1.79598
$616$	−17.8392	−0.718762
$617$	14.3173	0.576391	0.288196	−	0.957572i	$-0.406945\pi$
$617$	14.3173	0.576391	0.288196	+	0.957572i	$0.406945\pi$
$618$	−1.77289	−0.0713160
$619$	28.2618	1.13594	0.567968	−	0.823050i	$-0.307730\pi$
$619$	28.2618	1.13594	0.567968	+	0.823050i	$0.307730\pi$
$620$	−3.84376	−0.154369
$621$	3.17274	0.127318
$622$	−10.7365	−0.430493
$623$	0.302857	0.0121337
$624$	−0.651063	−0.0260634
$625$	−1.75784	−0.0703134
$626$	28.9837	1.15842
$627$	−16.3075	−0.651260
$628$	22.5200	0.898646
$629$	−10.2734	−0.409628
$630$	3.08573	0.122938
$631$	23.9782	0.954559	0.477279	−	0.878752i	$-0.341623\pi$
$631$	23.9782	0.954559	0.477279	+	0.878752i	$0.341623\pi$
$632$	−44.0369	−1.75169
$633$	−18.3928	−0.731048
$634$	11.2070	0.445089
$635$	44.1426	1.75174
$636$	−6.29396	−0.249572
$637$	5.24936	0.207987
$638$	−44.7795	−1.77284
$639$	−4.13821	−0.163705
$640$	−26.7003	−1.05542
$641$	33.3309	1.31649	0.658246	−	0.752803i	$-0.271299\pi$
$641$	33.3309	1.31649	0.658246	+	0.752803i	$0.271299\pi$
$642$	4.83581	0.190854
$643$	−5.44038	−0.214548	−0.107274	−	0.994230i	$-0.534212\pi$
$643$	−5.44038	−0.214548	−0.107274	+	0.994230i	$0.534212\pi$
$644$	4.00917	0.157984
$645$	11.6946	0.460474
$646$	12.0971	0.475955
$647$	−44.8436	−1.76298	−0.881491	−	0.472200i	$-0.843460\pi$
$647$	−44.8436	−1.76298	−0.881491	+	0.472200i	$0.843460\pi$
$648$	2.80058	0.110017
$649$	91.5342	3.59303
$650$	−35.7243	−1.40122
$651$	0.845913	0.0331539
$652$	15.0409	0.589047
$653$	−28.7870	−1.12652	−0.563262	−	0.826279i	$-0.690454\pi$
$653$	−28.7870	−1.12652	−0.563262	+	0.826279i	$0.690454\pi$
$654$	9.65997	0.377735
$655$	31.8070	1.24280
$656$	1.53620	0.0599784
$657$	−0.948252	−0.0369949
$658$	−0.317953	−0.0123951
$659$	4.33009	0.168676	0.0843382	−	0.996437i	$-0.473122\pi$
$659$	4.33009	0.168676	0.0843382	+	0.996437i	$0.473122\pi$
$660$	28.9440	1.12664
$661$	−0.750752	−0.0292009	−0.0146004	−	0.999893i	$-0.504648\pi$
$661$	−0.750752	−0.0292009	−0.0146004	+	0.999893i	$0.504648\pi$
$662$	−2.47695	−0.0962695
$663$	−28.9055	−1.12260
$664$	−30.2865	−1.17535
$665$	9.20601	0.356994
$666$	1.60099	0.0620371
$667$	25.9920	1.00641
$668$	−14.8159	−0.573245
$669$	20.1971	0.780865
$670$	−31.6085	−1.22114
$671$	−56.7816	−2.19203
$672$	5.70760	0.220175
$673$	−41.0075	−1.58072	−0.790361	−	0.612641i	$-0.790107\pi$
$673$	−41.0075	−1.58072	−0.790361	+	0.612641i	$0.790107\pi$
$674$	−24.1508	−0.930255
$675$	−7.93067	−0.305252
$676$	−18.3931	−0.707429
$677$	−46.3125	−1.77993	−0.889967	−	0.456024i	$-0.849273\pi$
$677$	−46.3125	−1.77993	−0.889967	+	0.456024i	$0.849273\pi$
$678$	−0.436964	−0.0167815
$679$	−14.3858	−0.552075
$680$	−55.4540	−2.12656
$681$	1.00000	0.0383201
$682$	−4.62381	−0.177055
$683$	14.3392	0.548674	0.274337	−	0.961634i	$-0.411542\pi$
$683$	14.3392	0.548674	0.274337	+	0.961634i	$0.411542\pi$
$684$	3.23505	0.123695
$685$	−71.6982	−2.73945
$686$	−0.858119	−0.0327631
$687$	−10.0676	−0.384102
$688$	0.403358	0.0153779
$689$	−26.1463	−0.996094
$690$	9.79022	0.372707
$691$	8.89038	0.338206	0.169103	−	0.985598i	$-0.445913\pi$
$691$	8.89038	0.338206	0.169103	+	0.985598i	$0.445913\pi$
$692$	−1.81254	−0.0689024
$693$	−6.36982	−0.241969
$694$	0.152906	0.00580423
$695$	−68.9019	−2.61360
$696$	22.9432	0.869659
$697$	68.2030	2.58337
$698$	7.72010	0.292210
$699$	−12.9857	−0.491166
$700$	−10.0214	−0.378775
$701$	39.1656	1.47927	0.739633	−	0.673011i	$-0.234999\pi$
$701$	39.1656	1.47927	0.739633	+	0.673011i	$0.234999\pi$
$702$	4.50458	0.170014
$703$	4.77642	0.180146
$704$	−29.6180	−1.11627
$705$	1.33237	0.0501801
$706$	13.0810	0.492311
$707$	−17.6642	−0.664332
$708$	−18.1584	−0.682433
$709$	−13.8617	−0.520586	−0.260293	−	0.965530i	$-0.583819\pi$
$709$	−13.8617	−0.520586	−0.260293	+	0.965530i	$0.583819\pi$
$710$	−12.7694	−0.479228
$711$	−15.7242	−0.589703
$712$	0.848176	0.0317867
$713$	2.68386	0.100511
$714$	4.72521	0.176837
$715$	120.239	4.49667
$716$	3.73584	0.139615
$717$	16.0344	0.598815
$718$	−2.43691	−0.0909446
$719$	−23.0610	−0.860031	−0.430016	−	0.902821i	$-0.641492\pi$
$719$	−23.0610	−0.860031	−0.430016	+	0.902821i	$0.641492\pi$
$720$	−0.445992	−0.0166212
$721$	−2.06602	−0.0769424
$722$	10.6799	0.397467
$723$	−23.1859	−0.862293
$724$	−15.2430	−0.566502
$725$	−64.9703	−2.41294
$726$	25.3785	0.941885
$727$	−3.35089	−0.124278	−0.0621388	−	0.998068i	$-0.519792\pi$
$727$	−3.35089	−0.124278	−0.0621388	+	0.998068i	$0.519792\pi$
$728$	14.7013	0.544866
$729$	1.00000	0.0370370
$730$	−2.92605	−0.108298
$731$	17.9080	0.662353
$732$	11.2642	0.416338
$733$	−32.0853	−1.18510	−0.592549	−	0.805534i	$-0.701878\pi$
$733$	−32.0853	−1.18510	−0.592549	+	0.805534i	$0.701878\pi$
$734$	−2.05083	−0.0756976
$735$	3.59592	0.132638
$736$	18.1087	0.667497
$737$	65.2489	2.40347
$738$	−10.6286	−0.391245
$739$	15.4100	0.566866	0.283433	−	0.958992i	$-0.408527\pi$
$739$	15.4100	0.566866	0.283433	+	0.958992i	$0.408527\pi$
$740$	−8.47758	−0.311642
$741$	13.4390	0.493695
$742$	4.27416	0.156909
$743$	40.0262	1.46842	0.734210	−	0.678923i	$-0.237553\pi$
$743$	40.0262	1.46842	0.734210	+	0.678923i	$0.237553\pi$
$744$	2.36905	0.0868536
$745$	−17.7928	−0.651876
$746$	−6.88552	−0.252097
$747$	−10.8144	−0.395677
$748$	44.3222	1.62058
$749$	5.63536	0.205912
$750$	−9.04326	−0.330213
$751$	21.0935	0.769712	0.384856	−	0.922977i	$-0.374251\pi$
$751$	21.0935	0.769712	0.384856	+	0.922977i	$0.374251\pi$
$752$	0.0459549	0.00167580
$753$	−18.9770	−0.691560
$754$	36.9028	1.34392
$755$	33.5368	1.22053
$756$	1.26363	0.0459578
$757$	−35.6810	−1.29685	−0.648424	−	0.761279i	$-0.724572\pi$
$757$	−35.6810	−1.29685	−0.648424	+	0.761279i	$0.724572\pi$
$758$	−9.92484	−0.360486
$759$	−20.2098	−0.733568
$760$	25.7822	0.935219
$761$	−20.3509	−0.737721	−0.368860	−	0.929485i	$-0.620252\pi$
$761$	−20.3509	−0.737721	−0.368860	+	0.929485i	$0.620252\pi$
$762$	−10.5340	−0.381608
$763$	11.2571	0.407536
$764$	5.45604	0.197393
$765$	−19.8009	−0.715902
$766$	29.2547	1.05701
$767$	−75.4332	−2.72374
$768$	15.6712	0.565485
$769$	−31.9317	−1.15149	−0.575744	−	0.817630i	$-0.695287\pi$
$769$	−31.9317	−1.15149	−0.575744	+	0.817630i	$0.695287\pi$
$770$	−19.6555	−0.708337
$771$	−16.3061	−0.587251
$772$	−9.44295	−0.339859
$773$	−1.49574	−0.0537980	−0.0268990	−	0.999638i	$-0.508563\pi$
$773$	−1.49574	−0.0537980	−0.0268990	+	0.999638i	$0.508563\pi$
$774$	−2.79076	−0.100312
$775$	−6.70865	−0.240982
$776$	−40.2886	−1.44628
$777$	1.86570	0.0669315
$778$	−13.8909	−0.498013
$779$	−31.7096	−1.13611
$780$	−23.8527	−0.854063
$781$	26.3597	0.943223
$782$	14.9919	0.536108
$783$	8.19228	0.292768
$784$	0.124027	0.00442954
$785$	64.0853	2.28730
$786$	−7.59033	−0.270738
$787$	20.9446	0.746595	0.373298	−	0.927712i	$-0.378227\pi$
$787$	20.9446	0.746595	0.373298	+	0.927712i	$0.378227\pi$
$788$	−12.3953	−0.441563
$789$	−24.4644	−0.870954
$790$	−48.5206	−1.72629
$791$	−0.509211	−0.0181055
$792$	−17.8392	−0.633889
$793$	46.7937	1.66169
$794$	−17.5493	−0.622802
$795$	−17.9108	−0.635229
$796$	−20.6011	−0.730186
$797$	−18.2914	−0.647915	−0.323957	−	0.946072i	$-0.605013\pi$
$797$	−18.2914	−0.647915	−0.323957	+	0.946072i	$0.605013\pi$
$798$	−2.19689	−0.0777691
$799$	2.04028	0.0721798
$800$	−45.2651	−1.60036
$801$	0.302857	0.0107009
$802$	16.8979	0.596685
$803$	6.04020	0.213154
$804$	−12.9439	−0.456498
$805$	11.4089	0.402112
$806$	3.81048	0.134218
$807$	12.1876	0.429025
$808$	−49.4702	−1.74035
$809$	−21.6360	−0.760682	−0.380341	−	0.924846i	$-0.624193\pi$
$809$	−21.6360	−0.760682	−0.380341	+	0.924846i	$0.624193\pi$
$810$	3.08573	0.108422
$811$	−11.2153	−0.393823	−0.196912	−	0.980421i	$-0.563091\pi$
$811$	−11.2153	−0.393823	−0.196912	+	0.980421i	$0.563091\pi$
$812$	10.3520	0.363285
$813$	20.5377	0.720289
$814$	−10.1980	−0.357440
$815$	42.8020	1.49929
$816$	−0.682953	−0.0239081
$817$	−8.32598	−0.291289
$818$	14.4189	0.504146
$819$	5.24936	0.183427
$820$	56.2808	1.96541
$821$	10.5172	0.367052	0.183526	−	0.983015i	$-0.441249\pi$
$821$	10.5172	0.367052	0.183526	+	0.983015i	$0.441249\pi$
$822$	17.1098	0.596773
$823$	6.05346	0.211010	0.105505	−	0.994419i	$-0.466354\pi$
$823$	6.05346	0.211010	0.105505	+	0.994419i	$0.466354\pi$
$824$	−5.78605	−0.201567
$825$	50.5169	1.75877
$826$	12.3312	0.429056
$827$	−20.6206	−0.717047	−0.358524	−	0.933521i	$-0.616720\pi$
$827$	−20.6206	−0.717047	−0.358524	+	0.933521i	$0.616720\pi$
$828$	4.00917	0.139328
$829$	13.7155	0.476357	0.238179	−	0.971221i	$-0.423450\pi$
$829$	13.7155	0.476357	0.238179	+	0.971221i	$0.423450\pi$
$830$	−33.3702	−1.15830
$831$	3.47993	0.120717
$832$	24.4082	0.846202
$833$	5.50648	0.190788
$834$	16.4425	0.569357
$835$	−42.1617	−1.45907
$836$	−20.6067	−0.712698
$837$	0.845913	0.0292390
$838$	14.6660	0.506629
$839$	−16.2868	−0.562282	−0.281141	−	0.959667i	$-0.590713\pi$
$839$	−16.2868	−0.562282	−0.281141	+	0.959667i	$0.590713\pi$
$840$	10.0707	0.347472
$841$	38.1135	1.31426
$842$	12.1498	0.418708
$843$	−0.634486	−0.0218529
$844$	−23.2417	−0.800013
$845$	−52.3415	−1.80060
$846$	−0.317953	−0.0109314
$847$	29.5746	1.01619
$848$	−0.617761	−0.0212140
$849$	−7.54092	−0.258804
$850$	−37.4741	−1.28535
$851$	5.91937	0.202914
$852$	−5.22918	−0.179149
$853$	29.2972	1.00312	0.501559	−	0.865123i	$-0.332760\pi$
$853$	29.2972	1.00312	0.501559	+	0.865123i	$0.332760\pi$
$854$	−7.64942	−0.261758
$855$	9.20601	0.314839
$856$	15.7823	0.539428
$857$	2.04384	0.0698164	0.0349082	−	0.999391i	$-0.488886\pi$
$857$	2.04384	0.0698164	0.0349082	+	0.999391i	$0.488886\pi$
$858$	−28.6933	−0.979574
$859$	47.7055	1.62769	0.813846	−	0.581081i	$-0.197370\pi$
$859$	47.7055	1.62769	0.813846	+	0.581081i	$0.197370\pi$
$860$	14.7776	0.503914
$861$	−12.3860	−0.422112
$862$	−28.3557	−0.965799
$863$	56.9590	1.93891	0.969454	−	0.245272i	$-0.0788774\pi$
$863$	56.9590	1.93891	0.969454	+	0.245272i	$0.0788774\pi$
$864$	5.70760	0.194176
$865$	−5.15795	−0.175376
$866$	16.2675	0.552793
$867$	−13.3213	−0.452415
$868$	1.06892	0.0362816
$869$	100.160	3.39770
$870$	25.2792	0.857045
$871$	−53.7715	−1.82198
$872$	31.5266	1.06762
$873$	−14.3858	−0.486885
$874$	−6.97017	−0.235769
$875$	−10.5385	−0.356265
$876$	−1.19824	−0.0404848
$877$	42.4335	1.43288	0.716439	−	0.697650i	$-0.245771\pi$
$877$	42.4335	1.43288	0.716439	+	0.697650i	$0.245771\pi$
$878$	−29.7453	−1.00385
$879$	−18.0394	−0.608454
$880$	2.84089	0.0957664
$881$	25.3379	0.853657	0.426828	−	0.904333i	$-0.359631\pi$
$881$	25.3379	0.853657	0.426828	+	0.904333i	$0.359631\pi$
$882$	−0.858119	−0.0288944
$883$	16.0388	0.539749	0.269875	−	0.962895i	$-0.413018\pi$
$883$	16.0388	0.539749	0.269875	+	0.962895i	$0.413018\pi$
$884$	−36.5259	−1.22850
$885$	−51.6734	−1.73698
$886$	−23.1425	−0.777487
$887$	38.3214	1.28671	0.643353	−	0.765569i	$-0.277543\pi$
$887$	38.3214	1.28671	0.643353	+	0.765569i	$0.277543\pi$
$888$	5.22504	0.175341
$889$	−12.2757	−0.411714
$890$	0.934534	0.0313257
$891$	−6.36982	−0.213397
$892$	25.5217	0.854530
$893$	−0.948585	−0.0317432
$894$	4.24601	0.142008
$895$	10.6311	0.355358
$896$	7.42516	0.248057
$897$	16.6549	0.556089
$898$	12.1199	0.404447
$899$	6.92995	0.231127
$900$	−10.0214	−0.334048
$901$	−27.4269	−0.913724
$902$	67.7024	2.25424
$903$	−3.25218	−0.108226
$904$	−1.42609	−0.0474310
$905$	−43.3771	−1.44190
$906$	−8.00310	−0.265885
$907$	16.8323	0.558906	0.279453	−	0.960159i	$-0.409847\pi$
$907$	16.8323	0.558906	0.279453	+	0.960159i	$0.409847\pi$
$908$	1.26363	0.0419351
$909$	−17.6642	−0.585886
$910$	16.1981	0.536962
$911$	−49.4625	−1.63877	−0.819383	−	0.573247i	$-0.805683\pi$
$911$	−49.4625	−1.63877	−0.819383	+	0.573247i	$0.805683\pi$
$912$	0.317525	0.0105143
$913$	68.8855	2.27978
$914$	−0.630107	−0.0208421
$915$	32.0547	1.05969
$916$	−12.7217	−0.420337
$917$	−8.84530	−0.292098
$918$	4.72521	0.155955
$919$	17.8441	0.588623	0.294311	−	0.955710i	$-0.404910\pi$
$919$	17.8441	0.588623	0.294311	+	0.955710i	$0.404910\pi$
$920$	31.9517	1.05342
$921$	6.69835	0.220718
$922$	12.0663	0.397383
$923$	−21.7230	−0.715021
$924$	−8.04910	−0.264796
$925$	−14.7962	−0.486497
$926$	−27.6383	−0.908251
$927$	−2.06602	−0.0678569
$928$	46.7583	1.53492
$929$	36.7677	1.20631	0.603154	−	0.797625i	$-0.293910\pi$
$929$	36.7677	1.20631	0.603154	+	0.797625i	$0.293910\pi$
$930$	2.61026	0.0855938
$931$	−2.56012	−0.0839047
$932$	−16.4092	−0.537501
$933$	−12.5116	−0.409612
$934$	23.5565	0.770791
$935$	126.128	4.12483
$936$	14.7013	0.480526
$937$	−0.818637	−0.0267437	−0.0133718	−	0.999911i	$-0.504257\pi$
$937$	−0.818637	−0.0267437	−0.0133718	+	0.999911i	$0.504257\pi$
$938$	8.79010	0.287007
$939$	33.7758	1.10223
$940$	1.68363	0.0549139
$941$	−12.6648	−0.412860	−0.206430	−	0.978461i	$-0.566185\pi$
$941$	−12.6648	−0.412860	−0.206430	+	0.978461i	$0.566185\pi$
$942$	−15.2931	−0.498276
$943$	−39.2974	−1.27970
$944$	−1.78227	−0.0580079
$945$	3.59592	0.116975
$946$	17.7766	0.577967
$947$	−40.6386	−1.32058	−0.660289	−	0.751011i	$-0.729566\pi$
$947$	−40.6386	−1.32058	−0.660289	+	0.751011i	$0.729566\pi$
$948$	−19.8696	−0.645334
$949$	−4.97772	−0.161584
$950$	17.4228	0.565271
$951$	13.0600	0.423500
$952$	15.4214	0.499809
$953$	54.6442	1.77010	0.885049	−	0.465498i	$-0.154125\pi$
$953$	54.6442	1.77010	0.885049	+	0.465498i	$0.154125\pi$
$954$	4.27416	0.138381
$955$	15.5263	0.502419
$956$	20.2616	0.655305
$957$	−52.1833	−1.68685
$958$	−22.2750	−0.719671
$959$	19.9387	0.643855
$960$	16.7201	0.539640
$961$	−30.2844	−0.976917
$962$	8.40418	0.270962
$963$	5.63536	0.181597
$964$	−29.2984	−0.943639
$965$	−26.8719	−0.865036
$966$	−2.72259	−0.0875979
$967$	−36.1505	−1.16252	−0.581261	−	0.813717i	$-0.697441\pi$
$967$	−36.1505	−1.16252	−0.581261	+	0.813717i	$0.697441\pi$
$968$	82.8261	2.66213
$969$	14.0973	0.452869
$970$	−44.3906	−1.42530
$971$	−5.60797	−0.179968	−0.0899842	−	0.995943i	$-0.528682\pi$
$971$	−5.60797	−0.179968	−0.0899842	+	0.995943i	$0.528682\pi$
$972$	1.26363	0.0405310
$973$	19.1611	0.614277
$974$	2.62860	0.0842258
$975$	−41.6309	−1.33326
$976$	1.10560	0.0353894
$977$	24.8392	0.794677	0.397338	−	0.917672i	$-0.369934\pi$
$977$	24.8392	0.794677	0.397338	+	0.917672i	$0.369934\pi$
$978$	−10.2141	−0.326611
$979$	−1.92914	−0.0616556
$980$	4.54392	0.145150
$981$	11.2571	0.359413
$982$	−9.37387	−0.299132
$983$	1.54871	0.0493961	0.0246980	−	0.999695i	$-0.492138\pi$
$983$	1.54871	0.0493961	0.0246980	+	0.999695i	$0.492138\pi$
$984$	−34.6879	−1.10581
$985$	−35.2733	−1.12390
$986$	38.7103	1.23279
$987$	−0.370523	−0.0117939
$988$	16.9820	0.540268
$989$	−10.3183	−0.328103
$990$	−19.6555	−0.624694
$991$	26.5102	0.842123	0.421061	−	0.907032i	$-0.361658\pi$
$991$	26.5102	0.842123	0.421061	+	0.907032i	$0.361658\pi$
$992$	4.82813	0.153293
$993$	−2.88649	−0.0916000
$994$	3.55108	0.112633
$995$	−58.6246	−1.85853
$996$	−13.6654	−0.433004
$997$	32.8474	1.04029	0.520143	−	0.854079i	$-0.325878\pi$
$997$	32.8474	1.04029	0.520143	+	0.854079i	$0.325878\pi$
$998$	−19.6078	−0.620674
$999$	1.86570	0.0590281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4767.2.a.g.1.12	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4767.2.a.g.1.12	✓	35	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 4767 = 3 \cdot 7 \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4767.a (trivial)

\(f(q)\)	\(=\)	\(q-0.858119 q^{2} -1.00000 q^{3} -1.26363 q^{4} -3.59592 q^{5} +0.858119 q^{6} +1.00000 q^{7} +2.80058 q^{8} +1.00000 q^{9} +3.08573 q^{10} -6.36982 q^{11} +1.26363 q^{12} +5.24936 q^{13} -0.858119 q^{14} +3.59592 q^{15} +0.124027 q^{16} +5.50648 q^{17} -0.858119 q^{18} -2.56012 q^{19} +4.54392 q^{20} -1.00000 q^{21} +5.46606 q^{22} -3.17274 q^{23} -2.80058 q^{24} +7.93067 q^{25} -4.50458 q^{26} -1.00000 q^{27} -1.26363 q^{28} -8.19228 q^{29} -3.08573 q^{30} -0.845913 q^{31} -5.70760 q^{32} +6.36982 q^{33} -4.72521 q^{34} -3.59592 q^{35} -1.26363 q^{36} -1.86570 q^{37} +2.19689 q^{38} -5.24936 q^{39} -10.0707 q^{40} +12.3860 q^{41} +0.858119 q^{42} +3.25218 q^{43} +8.04910 q^{44} -3.59592 q^{45} +2.72259 q^{46} +0.370523 q^{47} -0.124027 q^{48} +1.00000 q^{49} -6.80546 q^{50} -5.50648 q^{51} -6.63326 q^{52} -4.98085 q^{53} +0.858119 q^{54} +22.9054 q^{55} +2.80058 q^{56} +2.56012 q^{57} +7.02996 q^{58} -14.3700 q^{59} -4.54392 q^{60} +8.91417 q^{61} +0.725894 q^{62} +1.00000 q^{63} +4.64975 q^{64} -18.8763 q^{65} -5.46606 q^{66} -10.2434 q^{67} -6.95816 q^{68} +3.17274 q^{69} +3.08573 q^{70} -4.13821 q^{71} +2.80058 q^{72} -0.948252 q^{73} +1.60099 q^{74} -7.93067 q^{75} +3.23505 q^{76} -6.36982 q^{77} +4.50458 q^{78} -15.7242 q^{79} -0.445992 q^{80} +1.00000 q^{81} -10.6286 q^{82} -10.8144 q^{83} +1.26363 q^{84} -19.8009 q^{85} -2.79076 q^{86} +8.19228 q^{87} -17.8392 q^{88} +0.302857 q^{89} +3.08573 q^{90} +5.24936 q^{91} +4.00917 q^{92} +0.845913 q^{93} -0.317953 q^{94} +9.20601 q^{95} +5.70760 q^{96} -14.3858 q^{97} -0.858119 q^{98} -6.36982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) \) 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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