LMFDB - Embedded newform 4767.2.a.g.1.8

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			1.8
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)

$f(q)$	$=$	\(q-1.66837 q^{2} -1.00000 q^{3} +0.783461 q^{4} +3.62303 q^{5} +1.66837 q^{6} +1.00000 q^{7} +2.02964 q^{8} +1.00000 q^{9} -6.04455 q^{10} -1.55311 q^{11} -0.783461 q^{12} +5.76612 q^{13} -1.66837 q^{14} -3.62303 q^{15} -4.95311 q^{16} +4.02549 q^{17} -1.66837 q^{18} -3.81253 q^{19} +2.83850 q^{20} -1.00000 q^{21} +2.59117 q^{22} +4.52801 q^{23} -2.02964 q^{24} +8.12631 q^{25} -9.62002 q^{26} -1.00000 q^{27} +0.783461 q^{28} +0.231853 q^{29} +6.04455 q^{30} +5.76137 q^{31} +4.20435 q^{32} +1.55311 q^{33} -6.71601 q^{34} +3.62303 q^{35} +0.783461 q^{36} -5.74729 q^{37} +6.36072 q^{38} -5.76612 q^{39} +7.35343 q^{40} +6.56181 q^{41} +1.66837 q^{42} -4.05042 q^{43} -1.21680 q^{44} +3.62303 q^{45} -7.55439 q^{46} -4.05857 q^{47} +4.95311 q^{48} +1.00000 q^{49} -13.5577 q^{50} -4.02549 q^{51} +4.51753 q^{52} -8.83161 q^{53} +1.66837 q^{54} -5.62697 q^{55} +2.02964 q^{56} +3.81253 q^{57} -0.386817 q^{58} +0.709258 q^{59} -2.83850 q^{60} +12.1514 q^{61} -9.61209 q^{62} +1.00000 q^{63} +2.89181 q^{64} +20.8908 q^{65} -2.59117 q^{66} +6.36873 q^{67} +3.15381 q^{68} -4.52801 q^{69} -6.04455 q^{70} +16.6181 q^{71} +2.02964 q^{72} +0.636147 q^{73} +9.58861 q^{74} -8.12631 q^{75} -2.98697 q^{76} -1.55311 q^{77} +9.62002 q^{78} +2.87290 q^{79} -17.9452 q^{80} +1.00000 q^{81} -10.9475 q^{82} +6.19721 q^{83} -0.783461 q^{84} +14.5844 q^{85} +6.75761 q^{86} -0.231853 q^{87} -3.15226 q^{88} +15.8733 q^{89} -6.04455 q^{90} +5.76612 q^{91} +3.54752 q^{92} -5.76137 q^{93} +6.77121 q^{94} -13.8129 q^{95} -4.20435 q^{96} +9.40322 q^{97} -1.66837 q^{98} -1.55311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.66837	−1.17972	−0.589858	−	0.807507i	$-0.700816\pi$
$2$	−1.66837	−1.17972	−0.589858	+	0.807507i	$0.700816\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.783461	0.391730
$5$	3.62303	1.62027	0.810133	−	0.586246i	$-0.199395\pi$
$5$	3.62303	1.62027	0.810133	+	0.586246i	$0.199395\pi$
$6$	1.66837	0.681109
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.02964	0.717586
$9$	1.00000	0.333333
$10$	−6.04455	−1.91145
$11$	−1.55311	−0.468282	−0.234141	−	0.972203i	$-0.575228\pi$
$11$	−1.55311	−0.468282	−0.234141	+	0.972203i	$0.575228\pi$
$12$	−0.783461	−0.226166
$13$	5.76612	1.59923	0.799616	−	0.600511i	$-0.205036\pi$
$13$	5.76612	1.59923	0.799616	+	0.600511i	$0.205036\pi$
$14$	−1.66837	−0.445891
$15$	−3.62303	−0.935461
$16$	−4.95311	−1.23828
$17$	4.02549	0.976325	0.488162	−	0.872753i	$-0.337667\pi$
$17$	4.02549	0.976325	0.488162	+	0.872753i	$0.337667\pi$
$18$	−1.66837	−0.393239
$19$	−3.81253	−0.874655	−0.437327	−	0.899302i	$-0.644075\pi$
$19$	−3.81253	−0.874655	−0.437327	+	0.899302i	$0.644075\pi$
$20$	2.83850	0.634708
$21$	−1.00000	−0.218218
$22$	2.59117	0.552440
$23$	4.52801	0.944155	0.472077	−	0.881557i	$-0.343504\pi$
$23$	4.52801	0.944155	0.472077	+	0.881557i	$0.343504\pi$
$24$	−2.02964	−0.414298
$25$	8.12631	1.62526
$26$	−9.62002	−1.88664
$27$	−1.00000	−0.192450
$28$	0.783461	0.148060
$29$	0.231853	0.0430541	0.0215270	−	0.999768i	$-0.493147\pi$
$29$	0.231853	0.0430541	0.0215270	+	0.999768i	$0.493147\pi$
$30$	6.04455	1.10358
$31$	5.76137	1.03477	0.517386	−	0.855752i	$-0.326905\pi$
$31$	5.76137	1.03477	0.517386	+	0.855752i	$0.326905\pi$
$32$	4.20435	0.743231
$33$	1.55311	0.270363
$34$	−6.71601	−1.15179
$35$	3.62303	0.612403
$36$	0.783461	0.130577
$37$	−5.74729	−0.944849	−0.472424	−	0.881371i	$-0.656621\pi$
$37$	−5.74729	−0.944849	−0.472424	+	0.881371i	$0.656621\pi$
$38$	6.36072	1.03184
$39$	−5.76612	−0.923317
$40$	7.35343	1.16268
$41$	6.56181	1.02478	0.512391	−	0.858752i	$-0.328760\pi$
$41$	6.56181	1.02478	0.512391	+	0.858752i	$0.328760\pi$
$42$	1.66837	0.257435
$43$	−4.05042	−0.617684	−0.308842	−	0.951113i	$-0.599941\pi$
$43$	−4.05042	−0.617684	−0.308842	+	0.951113i	$0.599941\pi$
$44$	−1.21680	−0.183440
$45$	3.62303	0.540089
$46$	−7.55439	−1.11383
$47$	−4.05857	−0.592004	−0.296002	−	0.955187i	$-0.595653\pi$
$47$	−4.05857	−0.592004	−0.296002	+	0.955187i	$0.595653\pi$
$48$	4.95311	0.714920
$49$	1.00000	0.142857
$50$	−13.5577	−1.91735
$51$	−4.02549	−0.563681
$52$	4.51753	0.626468
$53$	−8.83161	−1.21311	−0.606557	−	0.795040i	$-0.707450\pi$
$53$	−8.83161	−1.21311	−0.606557	+	0.795040i	$0.707450\pi$
$54$	1.66837	0.227036
$55$	−5.62697	−0.758741
$56$	2.02964	0.271222
$57$	3.81253	0.504982
$58$	−0.386817	−0.0507916
$59$	0.709258	0.0923376	0.0461688	−	0.998934i	$-0.485299\pi$
$59$	0.709258	0.0923376	0.0461688	+	0.998934i	$0.485299\pi$
$60$	−2.83850	−0.366449
$61$	12.1514	1.55583	0.777913	−	0.628371i	$-0.216278\pi$
$61$	12.1514	1.55583	0.777913	+	0.628371i	$0.216278\pi$
$62$	−9.61209	−1.22074
$63$	1.00000	0.125988
$64$	2.89181	0.361476
$65$	20.8908	2.59118
$66$	−2.59117	−0.318951
$67$	6.36873	0.778064	0.389032	−	0.921224i	$-0.372810\pi$
$67$	6.36873	0.778064	0.389032	+	0.921224i	$0.372810\pi$
$68$	3.15381	0.382456
$69$	−4.52801	−0.545108
$70$	−6.04455	−0.722462
$71$	16.6181	1.97220	0.986102	−	0.166142i	$-0.0531310\pi$
$71$	16.6181	1.97220	0.986102	+	0.166142i	$0.0531310\pi$
$72$	2.02964	0.239195
$73$	0.636147	0.0744554	0.0372277	−	0.999307i	$-0.488147\pi$
$73$	0.636147	0.0744554	0.0372277	+	0.999307i	$0.488147\pi$
$74$	9.58861	1.11465
$75$	−8.12631	−0.938346
$76$	−2.98697	−0.342629
$77$	−1.55311	−0.176994
$78$	9.62002	1.08925
$79$	2.87290	0.323227	0.161613	−	0.986854i	$-0.448330\pi$
$79$	2.87290	0.323227	0.161613	+	0.986854i	$0.448330\pi$
$80$	−17.9452	−2.00634
$81$	1.00000	0.111111
$82$	−10.9475	−1.20895
$83$	6.19721	0.680232	0.340116	−	0.940383i	$-0.389534\pi$
$83$	6.19721	0.680232	0.340116	+	0.940383i	$0.389534\pi$
$84$	−0.783461	−0.0854826
$85$	14.5844	1.58191
$86$	6.75761	0.728692
$87$	−0.231853	−0.0248573
$88$	−3.15226	−0.336032
$89$	15.8733	1.68256	0.841282	−	0.540597i	$-0.181802\pi$
$89$	15.8733	1.68256	0.841282	+	0.540597i	$0.181802\pi$
$90$	−6.04455	−0.637151
$91$	5.76612	0.604453
$92$	3.54752	0.369854
$93$	−5.76137	−0.597426
$94$	6.77121	0.698396
$95$	−13.8129	−1.41717
$96$	−4.20435	−0.429105
$97$	9.40322	0.954752	0.477376	−	0.878699i	$-0.341588\pi$
$97$	9.40322	0.954752	0.477376	+	0.878699i	$0.341588\pi$
$98$	−1.66837	−0.168531
$99$	−1.55311	−0.156094
$100$	6.36665	0.636665
$101$	6.93091	0.689651	0.344826	−	0.938667i	$-0.387938\pi$
$101$	6.93091	0.689651	0.344826	+	0.938667i	$0.387938\pi$
$102$	6.71601	0.664984
$103$	−15.2460	−1.50224	−0.751119	−	0.660167i	$-0.770485\pi$
$103$	−15.2460	−1.50224	−0.751119	+	0.660167i	$0.770485\pi$
$104$	11.7031	1.14759
$105$	−3.62303	−0.353571
$106$	14.7344	1.43113
$107$	−9.98708	−0.965488	−0.482744	−	0.875762i	$-0.660360\pi$
$107$	−9.98708	−0.965488	−0.482744	+	0.875762i	$0.660360\pi$
$108$	−0.783461	−0.0753886
$109$	−15.3367	−1.46899	−0.734493	−	0.678617i	$-0.762580\pi$
$109$	−15.3367	−1.46899	−0.734493	+	0.678617i	$0.762580\pi$
$110$	9.38788	0.895099
$111$	5.74729	0.545509
$112$	−4.95311	−0.468025
$113$	−17.6956	−1.66467	−0.832333	−	0.554275i	$-0.812995\pi$
$113$	−17.6956	−1.66467	−0.832333	+	0.554275i	$0.812995\pi$
$114$	−6.36072	−0.595736
$115$	16.4051	1.52978
$116$	0.181648	0.0168656
$117$	5.76612	0.533078
$118$	−1.18331	−0.108932
$119$	4.02549	0.369016
$120$	−7.35343	−0.671273
$121$	−8.58783	−0.780712
$122$	−20.2730	−1.83543
$123$	−6.56181	−0.591658
$124$	4.51380	0.405352
$125$	11.3267	1.01309
$126$	−1.66837	−0.148630
$127$	20.3929	1.80958	0.904789	−	0.425860i	$-0.140028\pi$
$127$	20.3929	1.80958	0.904789	+	0.425860i	$0.140028\pi$
$128$	−13.2333	−1.16967
$129$	4.05042	0.356620
$130$	−34.8536	−3.05686
$131$	−15.8074	−1.38110	−0.690548	−	0.723287i	$-0.742630\pi$
$131$	−15.8074	−1.38110	−0.690548	+	0.723287i	$0.742630\pi$
$132$	1.21680	0.105909
$133$	−3.81253	−0.330589
$134$	−10.6254	−0.917895
$135$	−3.62303	−0.311820
$136$	8.17029	0.700596
$137$	9.49883	0.811539	0.405770	−	0.913975i	$-0.367003\pi$
$137$	9.49883	0.811539	0.405770	+	0.913975i	$0.367003\pi$
$138$	7.55439	0.643073
$139$	−6.57503	−0.557687	−0.278843	−	0.960337i	$-0.589951\pi$
$139$	−6.57503	−0.557687	−0.278843	+	0.960337i	$0.589951\pi$
$140$	2.83850	0.239897
$141$	4.05857	0.341794
$142$	−27.7251	−2.32664
$143$	−8.95544	−0.748891
$144$	−4.95311	−0.412759
$145$	0.840010	0.0697591
$146$	−1.06133	−0.0878362
$147$	−1.00000	−0.0824786
$148$	−4.50278	−0.370126
$149$	−18.2360	−1.49395	−0.746977	−	0.664850i	$-0.768496\pi$
$149$	−18.2360	−1.49395	−0.746977	+	0.664850i	$0.768496\pi$
$150$	13.5577	1.10698
$151$	−11.9222	−0.970215	−0.485108	−	0.874454i	$-0.661220\pi$
$151$	−11.9222	−0.970215	−0.485108	+	0.874454i	$0.661220\pi$
$152$	−7.73806	−0.627640
$153$	4.02549	0.325442
$154$	2.59117	0.208803
$155$	20.8736	1.67661
$156$	−4.51753	−0.361692
$157$	8.91593	0.711569	0.355784	−	0.934568i	$-0.384214\pi$
$157$	8.91593	0.711569	0.355784	+	0.934568i	$0.384214\pi$
$158$	−4.79306	−0.381316
$159$	8.83161	0.700392
$160$	15.2325	1.20423
$161$	4.52801	0.356857
$162$	−1.66837	−0.131080
$163$	−13.8308	−1.08331	−0.541656	−	0.840600i	$-0.682203\pi$
$163$	−13.8308	−1.08331	−0.541656	+	0.840600i	$0.682203\pi$
$164$	5.14092	0.401438
$165$	5.62697	0.438059
$166$	−10.3392	−0.802481
$167$	−10.9306	−0.845836	−0.422918	−	0.906168i	$-0.638994\pi$
$167$	−10.9306	−0.845836	−0.422918	+	0.906168i	$0.638994\pi$
$168$	−2.02964	−0.156590
$169$	20.2481	1.55755
$170$	−24.3323	−1.86620
$171$	−3.81253	−0.291552
$172$	−3.17335	−0.241966
$173$	3.74622	0.284820	0.142410	−	0.989808i	$-0.454515\pi$
$173$	3.74622	0.284820	0.142410	+	0.989808i	$0.454515\pi$
$174$	0.386817	0.0293245
$175$	8.12631	0.614291
$176$	7.69275	0.579863
$177$	−0.709258	−0.0533111
$178$	−26.4825	−1.98495
$179$	−20.7284	−1.54931	−0.774656	−	0.632383i	$-0.782077\pi$
$179$	−20.7284	−1.54931	−0.774656	+	0.632383i	$0.782077\pi$
$180$	2.83850	0.211569
$181$	−19.4073	−1.44253	−0.721266	−	0.692658i	$-0.756439\pi$
$181$	−19.4073	−1.44253	−0.721266	+	0.692658i	$0.756439\pi$
$182$	−9.62002	−0.713083
$183$	−12.1514	−0.898257
$184$	9.19022	0.677512
$185$	−20.8226	−1.53091
$186$	9.61209	0.704793
$187$	−6.25205	−0.457195
$188$	−3.17973	−0.231906
$189$	−1.00000	−0.0727393
$190$	23.0450	1.67186
$191$	−9.18747	−0.664782	−0.332391	−	0.943142i	$-0.607855\pi$
$191$	−9.18747	−0.664782	−0.332391	+	0.943142i	$0.607855\pi$
$192$	−2.89181	−0.208698
$193$	21.7611	1.56640	0.783198	−	0.621773i	$-0.213587\pi$
$193$	21.7611	1.56640	0.783198	+	0.621773i	$0.213587\pi$
$194$	−15.6881	−1.12634
$195$	−20.8908	−1.49602
$196$	0.783461	0.0559615
$197$	10.4454	0.744207	0.372103	−	0.928191i	$-0.378637\pi$
$197$	10.4454	0.744207	0.372103	+	0.928191i	$0.378637\pi$
$198$	2.59117	0.184147
$199$	16.1117	1.14213	0.571064	−	0.820905i	$-0.306531\pi$
$199$	16.1117	1.14213	0.571064	+	0.820905i	$0.306531\pi$
$200$	16.4935	1.16626
$201$	−6.36873	−0.449215
$202$	−11.5633	−0.813593
$203$	0.231853	0.0162729
$204$	−3.15381	−0.220811
$205$	23.7736	1.66042
$206$	25.4361	1.77221
$207$	4.52801	0.314718
$208$	−28.5602	−1.98029
$209$	5.92130	0.409585
$210$	6.04455	0.417114
$211$	−11.7685	−0.810180	−0.405090	−	0.914277i	$-0.632760\pi$
$211$	−11.7685	−0.810180	−0.405090	+	0.914277i	$0.632760\pi$
$212$	−6.91922	−0.475214
$213$	−16.6181	−1.13865
$214$	16.6622	1.13900
$215$	−14.6748	−1.00081
$216$	−2.02964	−0.138099
$217$	5.76137	0.391107
$218$	25.5872	1.73299
$219$	−0.636147	−0.0429868
$220$	−4.40851	−0.297222
$221$	23.2114	1.56137
$222$	−9.58861	−0.643546
$223$	16.4412	1.10098	0.550491	−	0.834841i	$-0.314441\pi$
$223$	16.4412	1.10098	0.550491	+	0.834841i	$0.314441\pi$
$224$	4.20435	0.280915
$225$	8.12631	0.541754
$226$	29.5229	1.96383
$227$	−1.00000	−0.0663723
$227$	−1.00000	−0.0663723
$228$	2.98697	0.197817
$229$	24.2066	1.59962	0.799808	−	0.600255i	$-0.204934\pi$
$229$	24.2066	1.59962	0.799808	+	0.600255i	$0.204934\pi$
$230$	−27.3698	−1.80471
$231$	1.55311	0.102187
$232$	0.470578	0.0308950
$233$	−17.6159	−1.15405	−0.577027	−	0.816725i	$-0.695787\pi$
$233$	−17.6159	−1.15405	−0.577027	+	0.816725i	$0.695787\pi$
$234$	−9.62002	−0.628880
$235$	−14.7043	−0.959204
$236$	0.555676	0.0361714
$237$	−2.87290	−0.186615
$238$	−6.71601	−0.435334
$239$	−2.39752	−0.155083	−0.0775414	−	0.996989i	$-0.524707\pi$
$239$	−2.39752	−0.155083	−0.0775414	+	0.996989i	$0.524707\pi$
$240$	17.9452	1.15836
$241$	30.3512	1.95509	0.977546	−	0.210723i	$-0.0675819\pi$
$241$	30.3512	1.95509	0.977546	+	0.210723i	$0.0675819\pi$
$242$	14.3277	0.921019
$243$	−1.00000	−0.0641500
$244$	9.52014	0.609465
$245$	3.62303	0.231467
$246$	10.9475	0.697989
$247$	−21.9835	−1.39878
$248$	11.6935	0.742537
$249$	−6.19721	−0.392732
$250$	−18.8971	−1.19516
$251$	19.6038	1.23738	0.618691	−	0.785635i	$-0.287663\pi$
$251$	19.6038	1.23738	0.618691	+	0.785635i	$0.287663\pi$
$252$	0.783461	0.0493534
$253$	−7.03251	−0.442130
$254$	−34.0229	−2.13479
$255$	−14.5844	−0.913314
$256$	16.2944	1.01840
$257$	−8.75027	−0.545827	−0.272913	−	0.962039i	$-0.587987\pi$
$257$	−8.75027	−0.545827	−0.272913	+	0.962039i	$0.587987\pi$
$258$	−6.75761	−0.420710
$259$	−5.74729	−0.357119
$260$	16.3671	1.01505
$261$	0.231853	0.0143514
$262$	26.3725	1.62930
$263$	−14.5412	−0.896647	−0.448323	−	0.893871i	$-0.647979\pi$
$263$	−14.5412	−0.896647	−0.448323	+	0.893871i	$0.647979\pi$
$264$	3.15226	0.194008
$265$	−31.9971	−1.96557
$266$	6.36072	0.390001
$267$	−15.8733	−0.971428
$268$	4.98965	0.304791
$269$	−28.5216	−1.73899	−0.869497	−	0.493937i	$-0.835557\pi$
$269$	−28.5216	−1.73899	−0.869497	+	0.493937i	$0.835557\pi$
$270$	6.04455	0.367860
$271$	11.6579	0.708169	0.354085	−	0.935213i	$-0.384792\pi$
$271$	11.6579	0.708169	0.354085	+	0.935213i	$0.384792\pi$
$272$	−19.9387	−1.20896
$273$	−5.76612	−0.348981
$274$	−15.8476	−0.957386
$275$	−12.6211	−0.761081
$276$	−3.54752	−0.213535
$277$	−17.8048	−1.06979	−0.534894	−	0.844919i	$-0.679649\pi$
$277$	−17.8048	−1.06979	−0.534894	+	0.844919i	$0.679649\pi$
$278$	10.9696	0.657912
$279$	5.76137	0.344924
$280$	7.35343	0.439452
$281$	22.2993	1.33027	0.665133	−	0.746725i	$-0.268375\pi$
$281$	22.2993	1.33027	0.665133	+	0.746725i	$0.268375\pi$
$282$	−6.77121	−0.403219
$283$	−4.36001	−0.259176	−0.129588	−	0.991568i	$-0.541365\pi$
$283$	−4.36001	−0.259176	−0.129588	+	0.991568i	$0.541365\pi$
$284$	13.0196	0.772572
$285$	13.8129	0.818206
$286$	14.9410	0.883479
$287$	6.56181	0.387331
$288$	4.20435	0.247744
$289$	−0.795434	−0.0467903
$290$	−1.40145	−0.0822959
$291$	−9.40322	−0.551227
$292$	0.498396	0.0291664
$293$	−29.9225	−1.74809	−0.874045	−	0.485845i	$-0.838512\pi$
$293$	−29.9225	−1.74809	−0.874045	+	0.485845i	$0.838512\pi$
$294$	1.66837	0.0973014
$295$	2.56966	0.149611
$296$	−11.6649	−0.678010
$297$	1.55311	0.0901209
$298$	30.4245	1.76244
$299$	26.1090	1.50992
$300$	−6.36665	−0.367579
$301$	−4.05042	−0.233463
$302$	19.8907	1.14458
$303$	−6.93091	−0.398170
$304$	18.8839	1.08307
$305$	44.0248	2.52085
$306$	−6.71601	−0.383929
$307$	28.4143	1.62169	0.810845	−	0.585262i	$-0.199008\pi$
$307$	28.4143	1.62169	0.810845	+	0.585262i	$0.199008\pi$
$308$	−1.21680	−0.0693339
$309$	15.2460	0.867317
$310$	−34.8249	−1.97792
$311$	−34.4140	−1.95144	−0.975718	−	0.219028i	$-0.929711\pi$
$311$	−34.4140	−1.95144	−0.975718	+	0.219028i	$0.929711\pi$
$312$	−11.7031	−0.662559
$313$	17.5107	0.989763	0.494881	−	0.868961i	$-0.335212\pi$
$313$	17.5107	0.989763	0.494881	+	0.868961i	$0.335212\pi$
$314$	−14.8751	−0.839449
$315$	3.62303	0.204134
$316$	2.25081	0.126618
$317$	−3.92038	−0.220190	−0.110095	−	0.993921i	$-0.535116\pi$
$317$	−3.92038	−0.220190	−0.110095	+	0.993921i	$0.535116\pi$
$318$	−14.7344	−0.826264
$319$	−0.360095	−0.0201614
$320$	10.4771	0.585688
$321$	9.98708	0.557425
$322$	−7.55439	−0.420990
$323$	−15.3473	−0.853947
$324$	0.783461	0.0435256
$325$	46.8573	2.59917
$326$	23.0749	1.27800
$327$	15.3367	0.848119
$328$	13.3181	0.735369
$329$	−4.05857	−0.223756
$330$	−9.38788	−0.516786
$331$	−22.1304	−1.21640	−0.608198	−	0.793785i	$-0.708107\pi$
$331$	−22.1304	−1.21640	−0.608198	+	0.793785i	$0.708107\pi$
$332$	4.85527	0.266468
$333$	−5.74729	−0.314950
$334$	18.2363	0.997846
$335$	23.0741	1.26067
$336$	4.95311	0.270214
$337$	16.7306	0.911374	0.455687	−	0.890140i	$-0.349394\pi$
$337$	16.7306	0.911374	0.455687	+	0.890140i	$0.349394\pi$
$338$	−33.7813	−1.83746
$339$	17.6956	0.961096
$340$	11.4263	0.619681
$341$	−8.94806	−0.484565
$342$	6.36072	0.343948
$343$	1.00000	0.0539949
$344$	−8.22089	−0.443241
$345$	−16.4051	−0.883220
$346$	−6.25008	−0.336006
$347$	6.01078	0.322675	0.161338	−	0.986899i	$-0.448419\pi$
$347$	6.01078	0.322675	0.161338	+	0.986899i	$0.448419\pi$
$348$	−0.181648	−0.00973736
$349$	−23.6460	−1.26574	−0.632870	−	0.774258i	$-0.718123\pi$
$349$	−23.6460	−1.26574	−0.632870	+	0.774258i	$0.718123\pi$
$350$	−13.5577	−0.724690
$351$	−5.76612	−0.307772
$352$	−6.52984	−0.348041
$353$	16.4845	0.877379	0.438690	−	0.898639i	$-0.355443\pi$
$353$	16.4845	0.877379	0.438690	+	0.898639i	$0.355443\pi$
$354$	1.18331	0.0628920
$355$	60.2077	3.19549
$356$	12.4361	0.659111
$357$	−4.02549	−0.213051
$358$	34.5826	1.82775
$359$	14.8673	0.784664	0.392332	−	0.919824i	$-0.371668\pi$
$359$	14.8673	0.784664	0.392332	+	0.919824i	$0.371668\pi$
$360$	7.35343	0.387560
$361$	−4.46459	−0.234979
$362$	32.3785	1.70178
$363$	8.58783	0.450744
$364$	4.51753	0.236783
$365$	2.30478	0.120638
$366$	20.2730	1.05969
$367$	33.4289	1.74498	0.872488	−	0.488635i	$-0.162505\pi$
$367$	33.4289	1.74498	0.872488	+	0.488635i	$0.162505\pi$
$368$	−22.4277	−1.16913
$369$	6.56181	0.341594
$370$	34.7398	1.80604
$371$	−8.83161	−0.458514
$372$	−4.51380	−0.234030
$373$	−2.97643	−0.154113	−0.0770567	−	0.997027i	$-0.524552\pi$
$373$	−2.97643	−0.154113	−0.0770567	+	0.997027i	$0.524552\pi$
$374$	10.4307	0.539360
$375$	−11.3267	−0.584909
$376$	−8.23744	−0.424813
$377$	1.33689	0.0688535
$378$	1.66837	0.0858117
$379$	−1.78355	−0.0916150	−0.0458075	−	0.998950i	$-0.514586\pi$
$379$	−1.78355	−0.0916150	−0.0458075	+	0.998950i	$0.514586\pi$
$380$	−10.8219	−0.555150
$381$	−20.3929	−1.04476
$382$	15.3281	0.784254
$383$	−17.0108	−0.869212	−0.434606	−	0.900621i	$-0.643112\pi$
$383$	−17.0108	−0.869212	−0.434606	+	0.900621i	$0.643112\pi$
$384$	13.2333	0.675309
$385$	−5.62697	−0.286777
$386$	−36.3055	−1.84790
$387$	−4.05042	−0.205895
$388$	7.36706	0.374006
$389$	−16.8950	−0.856612	−0.428306	−	0.903634i	$-0.640889\pi$
$389$	−16.8950	−0.856612	−0.428306	+	0.903634i	$0.640889\pi$
$390$	34.8536	1.76488
$391$	18.2274	0.921801
$392$	2.02964	0.102512
$393$	15.8074	0.797376
$394$	−17.4269	−0.877953
$395$	10.4086	0.523713
$396$	−1.21680	−0.0611467
$397$	31.3846	1.57515	0.787575	−	0.616219i	$-0.211336\pi$
$397$	31.3846	1.57515	0.787575	+	0.616219i	$0.211336\pi$
$398$	−26.8803	−1.34739
$399$	3.81253	0.190865
$400$	−40.2505	−2.01253
$401$	27.2652	1.36156	0.680780	−	0.732488i	$-0.261641\pi$
$401$	27.2652	1.36156	0.680780	+	0.732488i	$0.261641\pi$
$402$	10.6254	0.529947
$403$	33.2207	1.65484
$404$	5.43010	0.270157
$405$	3.62303	0.180030
$406$	−0.386817	−0.0191974
$407$	8.92620	0.442455
$408$	−8.17029	−0.404490
$409$	19.2371	0.951215	0.475608	−	0.879657i	$-0.342228\pi$
$409$	19.2371	0.951215	0.475608	+	0.879657i	$0.342228\pi$
$410$	−39.6632	−1.95882
$411$	−9.49883	−0.468543
$412$	−11.9447	−0.588472
$413$	0.709258	0.0349003
$414$	−7.55439	−0.371278
$415$	22.4527	1.10216
$416$	24.2428	1.18860
$417$	6.57503	0.321981
$418$	−9.87892	−0.483194
$419$	29.7182	1.45183	0.725914	−	0.687786i	$-0.241417\pi$
$419$	29.7182	1.45183	0.725914	+	0.687786i	$0.241417\pi$
$420$	−2.83850	−0.138505
$421$	5.34168	0.260337	0.130169	−	0.991492i	$-0.458448\pi$
$421$	5.34168	0.260337	0.130169	+	0.991492i	$0.458448\pi$
$422$	19.6343	0.955782
$423$	−4.05857	−0.197335
$424$	−17.9250	−0.870513
$425$	32.7124	1.58678
$426$	27.7251	1.34329
$427$	12.1514	0.588047
$428$	−7.82449	−0.378211
$429$	8.95544	0.432373
$430$	24.4830	1.18067
$431$	−23.3525	−1.12485	−0.562426	−	0.826847i	$-0.690132\pi$
$431$	−23.3525	−1.12485	−0.562426	+	0.826847i	$0.690132\pi$
$432$	4.95311	0.238307
$433$	27.0077	1.29791	0.648953	−	0.760828i	$-0.275207\pi$
$433$	27.0077	1.29791	0.648953	+	0.760828i	$0.275207\pi$
$434$	−9.61209	−0.461395
$435$	−0.840010	−0.0402754
$436$	−12.0157	−0.575446
$437$	−17.2632	−0.825810
$438$	1.06133	0.0507123
$439$	17.5089	0.835654	0.417827	−	0.908527i	$-0.362792\pi$
$439$	17.5089	0.835654	0.417827	+	0.908527i	$0.362792\pi$
$440$	−11.4207	−0.544462
$441$	1.00000	0.0476190
$442$	−38.7253	−1.84197
$443$	−35.0550	−1.66551	−0.832756	−	0.553640i	$-0.813238\pi$
$443$	−35.0550	−1.66551	−0.832756	+	0.553640i	$0.813238\pi$
$444$	4.50278	0.213692
$445$	57.5093	2.72620
$446$	−27.4299	−1.29885
$447$	18.2360	0.862535
$448$	2.89181	0.136625
$449$	30.1024	1.42062	0.710311	−	0.703888i	$-0.248554\pi$
$449$	30.1024	1.42062	0.710311	+	0.703888i	$0.248554\pi$
$450$	−13.5577	−0.639116
$451$	−10.1912	−0.479887
$452$	−13.8638	−0.652101
$453$	11.9222	0.560154
$454$	1.66837	0.0783005
$455$	20.8908	0.979375
$456$	7.73806	0.362368
$457$	−9.31357	−0.435670	−0.217835	−	0.975986i	$-0.569900\pi$
$457$	−9.31357	−0.435670	−0.217835	+	0.975986i	$0.569900\pi$
$458$	−40.3856	−1.88709
$459$	−4.02549	−0.187894
$460$	12.8527	0.599262
$461$	16.6791	0.776825	0.388412	−	0.921486i	$-0.373024\pi$
$461$	16.6791	0.776825	0.388412	+	0.921486i	$0.373024\pi$
$462$	−2.59117	−0.120552
$463$	−22.8075	−1.05995	−0.529976	−	0.848012i	$-0.677799\pi$
$463$	−22.8075	−1.05995	−0.529976	+	0.848012i	$0.677799\pi$
$464$	−1.14840	−0.0533129
$465$	−20.8736	−0.967989
$466$	29.3898	1.36146
$467$	−26.9195	−1.24569	−0.622843	−	0.782347i	$-0.714023\pi$
$467$	−26.9195	−1.24569	−0.622843	+	0.782347i	$0.714023\pi$
$468$	4.51753	0.208823
$469$	6.36873	0.294081
$470$	24.5322	1.13159
$471$	−8.91593	−0.410824
$472$	1.43954	0.0662601
$473$	6.29077	0.289250
$474$	4.79306	0.220153
$475$	−30.9818	−1.42154
$476$	3.15381	0.144555
$477$	−8.83161	−0.404372
$478$	3.99996	0.182954
$479$	5.32505	0.243308	0.121654	−	0.992573i	$-0.461180\pi$
$479$	5.32505	0.243308	0.121654	+	0.992573i	$0.461180\pi$
$480$	−15.2325	−0.695263
$481$	−33.1395	−1.51103
$482$	−50.6370	−2.30645
$483$	−4.52801	−0.206031
$484$	−6.72823	−0.305829
$485$	34.0681	1.54695
$486$	1.66837	0.0756788
$487$	−28.5646	−1.29438	−0.647192	−	0.762327i	$-0.724057\pi$
$487$	−28.5646	−1.29438	−0.647192	+	0.762327i	$0.724057\pi$
$488$	24.6629	1.11644
$489$	13.8308	0.625451
$490$	−6.04455	−0.273065
$491$	9.57255	0.432003	0.216001	−	0.976393i	$-0.430698\pi$
$491$	9.57255	0.432003	0.216001	+	0.976393i	$0.430698\pi$
$492$	−5.14092	−0.231771
$493$	0.933323	0.0420348
$494$	36.6766	1.65016
$495$	−5.62697	−0.252914
$496$	−28.5367	−1.28133
$497$	16.6181	0.745423
$498$	10.3392	0.463313
$499$	28.3713	1.27007	0.635037	−	0.772482i	$-0.280985\pi$
$499$	28.3713	1.27007	0.635037	+	0.772482i	$0.280985\pi$
$500$	8.87403	0.396859
$501$	10.9306	0.488344
$502$	−32.7064	−1.45976
$503$	−24.9537	−1.11263	−0.556314	−	0.830972i	$-0.687785\pi$
$503$	−24.9537	−1.11263	−0.556314	+	0.830972i	$0.687785\pi$
$504$	2.02964	0.0904073
$505$	25.1109	1.11742
$506$	11.7328	0.521588
$507$	−20.2481	−0.899249
$508$	15.9770	0.708867
$509$	40.5062	1.79541	0.897703	−	0.440602i	$-0.145235\pi$
$509$	40.5062	1.79541	0.897703	+	0.440602i	$0.145235\pi$
$510$	24.3323	1.07745
$511$	0.636147	0.0281415
$512$	−0.718557	−0.0317560
$513$	3.81253	0.168327
$514$	14.5987	0.643921
$515$	−55.2368	−2.43402
$516$	3.17335	0.139699
$517$	6.30343	0.277225
$518$	9.58861	0.421299
$519$	−3.74622	−0.164441
$520$	42.4007	1.85940
$521$	−11.1658	−0.489181	−0.244591	−	0.969626i	$-0.578654\pi$
$521$	−11.1658	−0.489181	−0.244591	+	0.969626i	$0.578654\pi$
$522$	−0.386817	−0.0169305
$523$	8.53789	0.373336	0.186668	−	0.982423i	$-0.440231\pi$
$523$	8.53789	0.373336	0.186668	+	0.982423i	$0.440231\pi$
$524$	−12.3844	−0.541017
$525$	−8.12631	−0.354661
$526$	24.2601	1.05779
$527$	23.1923	1.01027
$528$	−7.69275	−0.334784
$529$	−2.49716	−0.108572
$530$	53.3831	2.31881
$531$	0.709258	0.0307792
$532$	−2.98697	−0.129502
$533$	37.8362	1.63887
$534$	26.4825	1.14601
$535$	−36.1835	−1.56435
$536$	12.9262	0.558327
$537$	20.7284	0.894496
$538$	47.5847	2.05152
$539$	−1.55311	−0.0668974
$540$	−2.83850	−0.122150
$541$	−38.3960	−1.65078	−0.825388	−	0.564567i	$-0.809043\pi$
$541$	−38.3960	−1.65078	−0.825388	+	0.564567i	$0.809043\pi$
$542$	−19.4498	−0.835439
$543$	19.4073	0.832846
$544$	16.9246	0.725635
$545$	−55.5651	−2.38015
$546$	9.62002	0.411699
$547$	8.26349	0.353321	0.176661	−	0.984272i	$-0.443471\pi$
$547$	8.26349	0.353321	0.176661	+	0.984272i	$0.443471\pi$
$548$	7.44196	0.317905
$549$	12.1514	0.518609
$550$	21.0567	0.897859
$551$	−0.883948	−0.0376575
$552$	−9.19022	−0.391162
$553$	2.87290	0.122168
$554$	29.7051	1.26205
$555$	20.8226	0.883869
$556$	−5.15128	−0.218463
$557$	11.9348	0.505695	0.252847	−	0.967506i	$-0.418633\pi$
$557$	11.9348	0.505695	0.252847	+	0.967506i	$0.418633\pi$
$558$	−9.61209	−0.406912
$559$	−23.3552	−0.987820
$560$	−17.9452	−0.758325
$561$	6.25205	0.263962
$562$	−37.2035	−1.56934
$563$	−6.17373	−0.260192	−0.130096	−	0.991501i	$-0.541528\pi$
$563$	−6.17373	−0.260192	−0.130096	+	0.991501i	$0.541528\pi$
$564$	3.17973	0.133891
$565$	−64.1118	−2.69720
$566$	7.27411	0.305754
$567$	1.00000	0.0419961
$568$	33.7287	1.41522
$569$	−2.90390	−0.121738	−0.0608689	−	0.998146i	$-0.519387\pi$
$569$	−2.90390	−0.121738	−0.0608689	+	0.998146i	$0.519387\pi$
$570$	−23.0450	−0.965251
$571$	7.31841	0.306266	0.153133	−	0.988206i	$-0.451064\pi$
$571$	7.31841	0.306266	0.153133	+	0.988206i	$0.451064\pi$
$572$	−7.01624	−0.293364
$573$	9.18747	0.383812
$574$	−10.9475	−0.456941
$575$	36.7960	1.53450
$576$	2.89181	0.120492
$577$	10.7624	0.448043	0.224022	−	0.974584i	$-0.428081\pi$
$577$	10.7624	0.448043	0.224022	+	0.974584i	$0.428081\pi$
$578$	1.32708	0.0551992
$579$	−21.7611	−0.904359
$580$	0.658115	0.0273268
$581$	6.19721	0.257104
$582$	15.6881	0.650291
$583$	13.7165	0.568079
$584$	1.29115	0.0534281
$585$	20.8908	0.863728
$586$	49.9218	2.06225
$587$	−2.73295	−0.112801	−0.0564005	−	0.998408i	$-0.517962\pi$
$587$	−2.73295	−0.112801	−0.0564005	+	0.998408i	$0.517962\pi$
$588$	−0.783461	−0.0323094
$589$	−21.9654	−0.905068
$590$	−4.28715	−0.176499
$591$	−10.4454	−0.429668
$592$	28.4670	1.16999
$593$	9.85793	0.404816	0.202408	−	0.979301i	$-0.435123\pi$
$593$	9.85793	0.404816	0.202408	+	0.979301i	$0.435123\pi$
$594$	−2.59117	−0.106317
$595$	14.5844	0.597904
$596$	−14.2872	−0.585227
$597$	−16.1117	−0.659408
$598$	−43.5595	−1.78128
$599$	−30.9205	−1.26338	−0.631689	−	0.775222i	$-0.717638\pi$
$599$	−30.9205	−1.26338	−0.631689	+	0.775222i	$0.717638\pi$
$600$	−16.4935	−0.673343
$601$	27.2819	1.11285	0.556426	−	0.830897i	$-0.312172\pi$
$601$	27.2819	1.11285	0.556426	+	0.830897i	$0.312172\pi$
$602$	6.75761	0.275420
$603$	6.36873	0.259355
$604$	−9.34058	−0.380063
$605$	−31.1139	−1.26496
$606$	11.5633	0.469728
$607$	25.6092	1.03945	0.519723	−	0.854335i	$-0.326035\pi$
$607$	25.6092	1.03945	0.519723	+	0.854335i	$0.326035\pi$
$608$	−16.0292	−0.650071
$609$	−0.231853	−0.00939517
$610$	−73.4497	−2.97389
$611$	−23.4022	−0.946752
$612$	3.15381	0.127485
$613$	−0.630638	−0.0254712	−0.0127356	−	0.999919i	$-0.504054\pi$
$613$	−0.630638	−0.0254712	−0.0127356	+	0.999919i	$0.504054\pi$
$614$	−47.4056	−1.91313
$615$	−23.7736	−0.958644
$616$	−3.15226	−0.127008
$617$	26.9039	1.08311	0.541556	−	0.840665i	$-0.317836\pi$
$617$	26.9039	1.08311	0.541556	+	0.840665i	$0.317836\pi$
$618$	−25.4361	−1.02319
$619$	−24.6918	−0.992446	−0.496223	−	0.868195i	$-0.665280\pi$
$619$	−24.6918	−0.992446	−0.496223	+	0.868195i	$0.665280\pi$
$620$	16.3536	0.656777
$621$	−4.52801	−0.181703
$622$	57.4153	2.30214
$623$	15.8733	0.635949
$624$	28.5602	1.14332
$625$	0.405380	0.0162152
$626$	−29.2143	−1.16764
$627$	−5.92130	−0.236474
$628$	6.98528	0.278743
$629$	−23.1357	−0.922479
$630$	−6.04455	−0.240821
$631$	28.4766	1.13363	0.566817	−	0.823843i	$-0.308175\pi$
$631$	28.4766	1.13363	0.566817	+	0.823843i	$0.308175\pi$
$632$	5.83095	0.231943
$633$	11.7685	0.467758
$634$	6.54065	0.259762
$635$	73.8840	2.93200
$636$	6.91922	0.274365
$637$	5.76612	0.228462
$638$	0.600772	0.0237848
$639$	16.6181	0.657401
$640$	−47.9446	−1.89518
$641$	−6.38759	−0.252295	−0.126147	−	0.992012i	$-0.540261\pi$
$641$	−6.38759	−0.252295	−0.126147	+	0.992012i	$0.540261\pi$
$642$	−16.6622	−0.657603
$643$	−10.2841	−0.405564	−0.202782	−	0.979224i	$-0.564998\pi$
$643$	−10.2841	−0.405564	−0.202782	+	0.979224i	$0.564998\pi$
$644$	3.54752	0.139792
$645$	14.6748	0.577819
$646$	25.6050	1.00742
$647$	36.4749	1.43398	0.716988	−	0.697086i	$-0.245520\pi$
$647$	36.4749	1.43398	0.716988	+	0.697086i	$0.245520\pi$
$648$	2.02964	0.0797317
$649$	−1.10156	−0.0432400
$650$	−78.1753	−3.06629
$651$	−5.76137	−0.225806
$652$	−10.8359	−0.424366
$653$	37.9792	1.48624	0.743120	−	0.669158i	$-0.233345\pi$
$653$	37.9792	1.48624	0.743120	+	0.669158i	$0.233345\pi$
$654$	−25.5872	−1.00054
$655$	−57.2704	−2.23774
$656$	−32.5014	−1.26897
$657$	0.636147	0.0248185
$658$	6.77121	0.263969
$659$	−14.9491	−0.582333	−0.291167	−	0.956672i	$-0.594043\pi$
$659$	−14.9491	−0.582333	−0.291167	+	0.956672i	$0.594043\pi$
$660$	4.40851	0.171601
$661$	14.9419	0.581174	0.290587	−	0.956849i	$-0.406149\pi$
$661$	14.9419	0.581174	0.290587	+	0.956849i	$0.406149\pi$
$662$	36.9217	1.43500
$663$	−23.2114	−0.901458
$664$	12.5781	0.488125
$665$	−13.8129	−0.535641
$666$	9.58861	0.371551
$667$	1.04983	0.0406497
$668$	−8.56370	−0.331340
$669$	−16.4412	−0.635652
$670$	−38.4961	−1.48723
$671$	−18.8725	−0.728565
$672$	−4.20435	−0.162186
$673$	−13.8003	−0.531962	−0.265981	−	0.963978i	$-0.585696\pi$
$673$	−13.8003	−0.531962	−0.265981	+	0.963978i	$0.585696\pi$
$674$	−27.9129	−1.07516
$675$	−8.12631	−0.312782
$676$	15.8636	0.610138
$677$	25.0718	0.963587	0.481793	−	0.876285i	$-0.339986\pi$
$677$	25.0718	0.963587	0.481793	+	0.876285i	$0.339986\pi$
$678$	−29.5229	−1.13382
$679$	9.40322	0.360862
$680$	29.6012	1.13515
$681$	1.00000	0.0383201
$682$	14.9287	0.571649
$683$	16.0738	0.615048	0.307524	−	0.951540i	$-0.400500\pi$
$683$	16.0738	0.615048	0.307524	+	0.951540i	$0.400500\pi$
$684$	−2.98697	−0.114210
$685$	34.4145	1.31491
$686$	−1.66837	−0.0636987
$687$	−24.2066	−0.923539
$688$	20.0622	0.764864
$689$	−50.9241	−1.94005
$690$	27.3698	1.04195
$691$	−30.2127	−1.14935	−0.574673	−	0.818383i	$-0.694871\pi$
$691$	−30.2127	−1.14935	−0.574673	+	0.818383i	$0.694871\pi$
$692$	2.93501	0.111572
$693$	−1.55311	−0.0589979
$694$	−10.0282	−0.380665
$695$	−23.8215	−0.903601
$696$	−0.470578	−0.0178372
$697$	26.4145	1.00052
$698$	39.4503	1.49321
$699$	17.6159	0.666294
$700$	6.36665	0.240637
$701$	−27.4489	−1.03673	−0.518365	−	0.855159i	$-0.673459\pi$
$701$	−27.4489	−1.03673	−0.518365	+	0.855159i	$0.673459\pi$
$702$	9.62002	0.363084
$703$	21.9117	0.826417
$704$	−4.49131	−0.169273
$705$	14.7043	0.553796
$706$	−27.5022	−1.03506
$707$	6.93091	0.260664
$708$	−0.555676	−0.0208836
$709$	32.3245	1.21397	0.606986	−	0.794713i	$-0.292378\pi$
$709$	32.3245	1.21397	0.606986	+	0.794713i	$0.292378\pi$
$710$	−100.449	−3.76978
$711$	2.87290	0.107742
$712$	32.2170	1.20738
$713$	26.0875	0.976985
$714$	6.71601	0.251340
$715$	−32.4458	−1.21340
$716$	−16.2399	−0.606913
$717$	2.39752	0.0895371
$718$	−24.8041	−0.925681
$719$	−16.3930	−0.611354	−0.305677	−	0.952135i	$-0.598883\pi$
$719$	−16.3930	−0.611354	−0.305677	+	0.952135i	$0.598883\pi$
$720$	−17.9452	−0.668780
$721$	−15.2460	−0.567792
$722$	7.44860	0.277208
$723$	−30.3512	−1.12877
$724$	−15.2048	−0.565084
$725$	1.88411	0.0699742
$726$	−14.3277	−0.531751
$727$	11.1181	0.412346	0.206173	−	0.978516i	$-0.433899\pi$
$727$	11.1181	0.412346	0.206173	+	0.978516i	$0.433899\pi$
$728$	11.7031	0.433747
$729$	1.00000	0.0370370
$730$	−3.84522	−0.142318
$731$	−16.3049	−0.603060
$732$	−9.52014	−0.351875
$733$	−4.24615	−0.156835	−0.0784176	−	0.996921i	$-0.524987\pi$
$733$	−4.24615	−0.156835	−0.0784176	+	0.996921i	$0.524987\pi$
$734$	−55.7719	−2.05858
$735$	−3.62303	−0.133637
$736$	19.0373	0.701725
$737$	−9.89137	−0.364353
$738$	−10.9475	−0.402984
$739$	−13.4932	−0.496354	−0.248177	−	0.968715i	$-0.579832\pi$
$739$	−13.4932	−0.496354	−0.248177	+	0.968715i	$0.579832\pi$
$740$	−16.3137	−0.599703
$741$	21.9835	0.807584
$742$	14.7344	0.540917
$743$	32.9523	1.20890	0.604452	−	0.796642i	$-0.293392\pi$
$743$	32.9523	1.20890	0.604452	+	0.796642i	$0.293392\pi$
$744$	−11.6935	−0.428704
$745$	−66.0696	−2.42060
$746$	4.96578	0.181810
$747$	6.19721	0.226744
$748$	−4.89823	−0.179097
$749$	−9.98708	−0.364920
$750$	18.8971	0.690026
$751$	48.1661	1.75761	0.878804	−	0.477184i	$-0.158342\pi$
$751$	48.1661	1.75761	0.878804	+	0.477184i	$0.158342\pi$
$752$	20.1026	0.733065
$753$	−19.6038	−0.714403
$754$	−2.23043	−0.0812276
$755$	−43.1944	−1.57201
$756$	−0.783461	−0.0284942
$757$	0.335144	0.0121810	0.00609051	−	0.999981i	$-0.498061\pi$
$757$	0.335144	0.0121810	0.00609051	+	0.999981i	$0.498061\pi$
$758$	2.97563	0.108080
$759$	7.03251	0.255264
$760$	−28.0352	−1.01694
$761$	−32.3557	−1.17289	−0.586446	−	0.809988i	$-0.699473\pi$
$761$	−32.3557	−1.17289	−0.586446	+	0.809988i	$0.699473\pi$
$762$	34.0229	1.23252
$763$	−15.3367	−0.555224
$764$	−7.19802	−0.260415
$765$	14.5844	0.527302
$766$	28.3804	1.02542
$767$	4.08966	0.147669
$768$	−16.2944	−0.587975
$769$	−15.0459	−0.542569	−0.271284	−	0.962499i	$-0.587448\pi$
$769$	−15.0459	−0.542569	−0.271284	+	0.962499i	$0.587448\pi$
$770$	9.38788	0.338316
$771$	8.75027	0.315133
$772$	17.0489	0.613605
$773$	−13.2889	−0.477967	−0.238984	−	0.971024i	$-0.576814\pi$
$773$	−13.2889	−0.477967	−0.238984	+	0.971024i	$0.576814\pi$
$774$	6.75761	0.242897
$775$	46.8187	1.68178
$776$	19.0851	0.685116
$777$	5.74729	0.206183
$778$	28.1872	1.01056
$779$	−25.0171	−0.896331
$780$	−16.3671	−0.586037
$781$	−25.8098	−0.923547
$782$	−30.4101	−1.08746
$783$	−0.231853	−0.00828576
$784$	−4.95311	−0.176897
$785$	32.3026	1.15293
$786$	−26.3725	−0.940677
$787$	29.9311	1.06693	0.533464	−	0.845823i	$-0.320890\pi$
$787$	29.9311	1.06693	0.533464	+	0.845823i	$0.320890\pi$
$788$	8.18359	0.291528
$789$	14.5412	0.517679
$790$	−17.3654	−0.617833
$791$	−17.6956	−0.629185
$792$	−3.15226	−0.112011
$793$	70.0664	2.48813
$794$	−52.3612	−1.85823
$795$	31.9971	1.13482
$796$	12.6229	0.447406
$797$	−20.5276	−0.727126	−0.363563	−	0.931570i	$-0.618440\pi$
$797$	−20.5276	−0.727126	−0.363563	+	0.931570i	$0.618440\pi$
$798$	−6.36072	−0.225167
$799$	−16.3377	−0.577988
$800$	34.1658	1.20795
$801$	15.8733	0.560854
$802$	−45.4885	−1.60625
$803$	−0.988009	−0.0348661
$804$	−4.98965	−0.175971
$805$	16.4051	0.578203
$806$	−55.4244	−1.95224
$807$	28.5216	1.00401
$808$	14.0672	0.494884
$809$	−33.8324	−1.18948	−0.594742	−	0.803917i	$-0.702746\pi$
$809$	−33.8324	−1.18948	−0.594742	+	0.803917i	$0.702746\pi$
$810$	−6.04455	−0.212384
$811$	−37.3889	−1.31290	−0.656451	−	0.754369i	$-0.727943\pi$
$811$	−37.3889	−1.31290	−0.656451	+	0.754369i	$0.727943\pi$
$812$	0.181648	0.00637460
$813$	−11.6579	−0.408862
$814$	−14.8922	−0.521972
$815$	−50.1094	−1.75525
$816$	19.9387	0.697994
$817$	15.4424	0.540260
$818$	−32.0947	−1.12216
$819$	5.76612	0.201484
$820$	18.6257	0.650437
$821$	−13.5911	−0.474332	−0.237166	−	0.971469i	$-0.576219\pi$
$821$	−13.5911	−0.474332	−0.237166	+	0.971469i	$0.576219\pi$
$822$	15.8476	0.552747
$823$	2.38065	0.0829843	0.0414922	−	0.999139i	$-0.486789\pi$
$823$	2.38065	0.0829843	0.0414922	+	0.999139i	$0.486789\pi$
$824$	−30.9440	−1.07798
$825$	12.6211	0.439410
$826$	−1.18331	−0.0411725
$827$	−12.4974	−0.434578	−0.217289	−	0.976107i	$-0.569721\pi$
$827$	−12.4974	−0.434578	−0.217289	+	0.976107i	$0.569721\pi$
$828$	3.54752	0.123285
$829$	45.5222	1.58105	0.790525	−	0.612430i	$-0.209808\pi$
$829$	45.5222	1.58105	0.790525	+	0.612430i	$0.209808\pi$
$830$	−37.4593	−1.30023
$831$	17.8048	0.617643
$832$	16.6745	0.578085
$833$	4.02549	0.139475
$834$	−10.9696	−0.379846
$835$	−39.6019	−1.37048
$836$	4.63911	0.160447
$837$	−5.76137	−0.199142
$838$	−49.5809	−1.71275
$839$	−30.3796	−1.04882	−0.524409	−	0.851466i	$-0.675714\pi$
$839$	−30.3796	−1.04882	−0.524409	+	0.851466i	$0.675714\pi$
$840$	−7.35343	−0.253717
$841$	−28.9462	−0.998146
$842$	−8.91190	−0.307124
$843$	−22.2993	−0.768029
$844$	−9.22019	−0.317372
$845$	73.3593	2.52364
$846$	6.77121	0.232799
$847$	−8.58783	−0.295081
$848$	43.7439	1.50217
$849$	4.36001	0.149635
$850$	−54.5764	−1.87195
$851$	−26.0238	−0.892083
$852$	−13.0196	−0.446045
$853$	19.4387	0.665569	0.332784	−	0.943003i	$-0.392012\pi$
$853$	19.4387	0.665569	0.332784	+	0.943003i	$0.392012\pi$
$854$	−20.2730	−0.693729
$855$	−13.8129	−0.472391
$856$	−20.2702	−0.692820
$857$	−4.72322	−0.161342	−0.0806711	−	0.996741i	$-0.525706\pi$
$857$	−4.72322	−0.161342	−0.0806711	+	0.996741i	$0.525706\pi$
$858$	−14.9410	−0.510077
$859$	−4.57910	−0.156237	−0.0781185	−	0.996944i	$-0.524891\pi$
$859$	−4.57910	−0.156237	−0.0781185	+	0.996944i	$0.524891\pi$
$860$	−11.4971	−0.392049
$861$	−6.56181	−0.223626
$862$	38.9607	1.32701
$863$	26.2851	0.894755	0.447377	−	0.894345i	$-0.352358\pi$
$863$	26.2851	0.894755	0.447377	+	0.894345i	$0.352358\pi$
$864$	−4.20435	−0.143035
$865$	13.5726	0.461483
$866$	−45.0588	−1.53116
$867$	0.795434	0.0270144
$868$	4.51380	0.153209
$869$	−4.46195	−0.151361
$870$	1.40145	0.0475136
$871$	36.7228	1.24431
$872$	−31.1279	−1.05412
$873$	9.40322	0.318251
$874$	28.8014	0.974221
$875$	11.3267	0.382913
$876$	−0.498396	−0.0168393
$877$	−27.6912	−0.935066	−0.467533	−	0.883976i	$-0.654857\pi$
$877$	−27.6912	−0.935066	−0.467533	+	0.883976i	$0.654857\pi$
$878$	−29.2113	−0.985835
$879$	29.9225	1.00926
$880$	27.8710	0.939532
$881$	−32.1347	−1.08265	−0.541323	−	0.840815i	$-0.682076\pi$
$881$	−32.1347	−1.08265	−0.541323	+	0.840815i	$0.682076\pi$
$882$	−1.66837	−0.0561770
$883$	17.4521	0.587311	0.293655	−	0.955911i	$-0.405128\pi$
$883$	17.4521	0.587311	0.293655	+	0.955911i	$0.405128\pi$
$884$	18.1853	0.611636
$885$	−2.56966	−0.0863782
$886$	58.4847	1.96483
$887$	18.6112	0.624902	0.312451	−	0.949934i	$-0.398850\pi$
$887$	18.6112	0.624902	0.312451	+	0.949934i	$0.398850\pi$
$888$	11.6649	0.391449
$889$	20.3929	0.683956
$890$	−95.9468	−3.21614
$891$	−1.55311	−0.0520313
$892$	12.8810	0.431288
$893$	15.4734	0.517799
$894$	−30.4245	−1.01755
$895$	−75.0995	−2.51030
$896$	−13.2333	−0.442094
$897$	−26.1090	−0.871754
$898$	−50.2220	−1.67593
$899$	1.33579	0.0445512
$900$	6.36665	0.212222
$901$	−35.5515	−1.18439
$902$	17.0028	0.566130
$903$	4.05042	0.134790
$904$	−35.9158	−1.19454
$905$	−70.3131	−2.33729
$906$	−19.8907	−0.660823
$907$	−0.509175	−0.0169069	−0.00845344	−	0.999964i	$-0.502691\pi$
$907$	−0.509175	−0.0169069	−0.00845344	+	0.999964i	$0.502691\pi$
$908$	−0.783461	−0.0260001
$909$	6.93091	0.229884
$910$	−34.8536	−1.15538
$911$	13.0788	0.433321	0.216660	−	0.976247i	$-0.430484\pi$
$911$	13.0788	0.433321	0.216660	+	0.976247i	$0.430484\pi$
$912$	−18.8839	−0.625308
$913$	−9.62498	−0.318540
$914$	15.5385	0.513967
$915$	−44.0248	−1.45542
$916$	18.9649	0.626619
$917$	−15.8074	−0.522005
$918$	6.71601	0.221661
$919$	12.0563	0.397700	0.198850	−	0.980030i	$-0.436279\pi$
$919$	12.0563	0.397700	0.198850	+	0.980030i	$0.436279\pi$
$920$	33.2964	1.09775
$921$	−28.4143	−0.936283
$922$	−27.8270	−0.916432
$923$	95.8218	3.15401
$924$	1.21680	0.0400299
$925$	−46.7043	−1.53563
$926$	38.0513	1.25044
$927$	−15.2460	−0.500746
$928$	0.974792	0.0319991
$929$	−31.4697	−1.03249	−0.516244	−	0.856442i	$-0.672670\pi$
$929$	−31.4697	−1.03249	−0.516244	+	0.856442i	$0.672670\pi$
$930$	34.8249	1.14195
$931$	−3.81253	−0.124951
$932$	−13.8013	−0.452078
$933$	34.4140	1.12666
$934$	44.9117	1.46956
$935$	−22.6513	−0.740777
$936$	11.7031	0.382529
$937$	−5.61312	−0.183373	−0.0916864	−	0.995788i	$-0.529226\pi$
$937$	−5.61312	−0.183373	−0.0916864	+	0.995788i	$0.529226\pi$
$938$	−10.6254	−0.346932
$939$	−17.5107	−0.571440
$940$	−11.5203	−0.375749
$941$	−34.3491	−1.11975	−0.559875	−	0.828577i	$-0.689151\pi$
$941$	−34.3491	−1.11975	−0.559875	+	0.828577i	$0.689151\pi$
$942$	14.8751	0.484656
$943$	29.7119	0.967553
$944$	−3.51303	−0.114340
$945$	−3.62303	−0.117857
$946$	−10.4953	−0.341233
$947$	−6.67661	−0.216961	−0.108480	−	0.994099i	$-0.534598\pi$
$947$	−6.67661	−0.216961	−0.108480	+	0.994099i	$0.534598\pi$
$948$	−2.25081	−0.0731028
$949$	3.66810	0.119071
$950$	51.6892	1.67702
$951$	3.92038	0.127127
$952$	8.17029	0.264801
$953$	−41.7141	−1.35125	−0.675627	−	0.737244i	$-0.736127\pi$
$953$	−41.7141	−1.35125	−0.675627	+	0.737244i	$0.736127\pi$
$954$	14.7344	0.477044
$955$	−33.2864	−1.07712
$956$	−1.87837	−0.0607507
$957$	0.360095	0.0116402
$958$	−8.88415	−0.287034
$959$	9.49883	0.306733
$960$	−10.4771	−0.338147
$961$	2.19333	0.0707527
$962$	55.2890	1.78259
$963$	−9.98708	−0.321829
$964$	23.7790	0.765869
$965$	78.8409	2.53798
$966$	7.55439	0.243059
$967$	−23.7614	−0.764114	−0.382057	−	0.924139i	$-0.624784\pi$
$967$	−23.7614	−0.764114	−0.382057	+	0.924139i	$0.624784\pi$
$968$	−17.4302	−0.560228
$969$	15.3473	0.493027
$970$	−56.8382	−1.82497
$971$	53.1009	1.70409	0.852045	−	0.523468i	$-0.175362\pi$
$971$	53.1009	1.70409	0.852045	+	0.523468i	$0.175362\pi$
$972$	−0.783461	−0.0251295
$973$	−6.57503	−0.210786
$974$	47.6563	1.52701
$975$	−46.8573	−1.50063
$976$	−60.1872	−1.92655
$977$	−14.9913	−0.479614	−0.239807	−	0.970821i	$-0.577084\pi$
$977$	−14.9913	−0.479614	−0.239807	+	0.970821i	$0.577084\pi$
$978$	−23.0749	−0.737854
$979$	−24.6530	−0.787914
$980$	2.83850	0.0906725
$981$	−15.3367	−0.489662
$982$	−15.9706	−0.509641
$983$	55.0024	1.75430	0.877152	−	0.480213i	$-0.159441\pi$
$983$	55.0024	1.75430	0.877152	+	0.480213i	$0.159441\pi$
$984$	−13.3181	−0.424566
$985$	37.8441	1.20581
$986$	−1.55713	−0.0495891
$987$	4.05857	0.129186
$988$	−17.2232	−0.547943
$989$	−18.3403	−0.583189
$990$	9.38788	0.298366
$991$	−21.1160	−0.670773	−0.335387	−	0.942081i	$-0.608867\pi$
$991$	−21.1160	−0.670773	−0.335387	+	0.942081i	$0.608867\pi$
$992$	24.2228	0.769074
$993$	22.1304	0.702287
$994$	−27.7251	−0.879388
$995$	58.3731	1.85055
$996$	−4.85527	−0.153845
$997$	4.59981	0.145677	0.0728387	−	0.997344i	$-0.476794\pi$
$997$	4.59981	0.145677	0.0728387	+	0.997344i	$0.476794\pi$
$998$	−47.3339	−1.49833
$999$	5.74729	0.181836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4767.2.a.g.1.8	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4767.2.a.g.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.66837 q^{2} -1.00000 q^{3} +0.783461 q^{4} +3.62303 q^{5} +1.66837 q^{6} +1.00000 q^{7} +2.02964 q^{8} +1.00000 q^{9} -6.04455 q^{10} -1.55311 q^{11} -0.783461 q^{12} +5.76612 q^{13} -1.66837 q^{14} -3.62303 q^{15} -4.95311 q^{16} +4.02549 q^{17} -1.66837 q^{18} -3.81253 q^{19} +2.83850 q^{20} -1.00000 q^{21} +2.59117 q^{22} +4.52801 q^{23} -2.02964 q^{24} +8.12631 q^{25} -9.62002 q^{26} -1.00000 q^{27} +0.783461 q^{28} +0.231853 q^{29} +6.04455 q^{30} +5.76137 q^{31} +4.20435 q^{32} +1.55311 q^{33} -6.71601 q^{34} +3.62303 q^{35} +0.783461 q^{36} -5.74729 q^{37} +6.36072 q^{38} -5.76612 q^{39} +7.35343 q^{40} +6.56181 q^{41} +1.66837 q^{42} -4.05042 q^{43} -1.21680 q^{44} +3.62303 q^{45} -7.55439 q^{46} -4.05857 q^{47} +4.95311 q^{48} +1.00000 q^{49} -13.5577 q^{50} -4.02549 q^{51} +4.51753 q^{52} -8.83161 q^{53} +1.66837 q^{54} -5.62697 q^{55} +2.02964 q^{56} +3.81253 q^{57} -0.386817 q^{58} +0.709258 q^{59} -2.83850 q^{60} +12.1514 q^{61} -9.61209 q^{62} +1.00000 q^{63} +2.89181 q^{64} +20.8908 q^{65} -2.59117 q^{66} +6.36873 q^{67} +3.15381 q^{68} -4.52801 q^{69} -6.04455 q^{70} +16.6181 q^{71} +2.02964 q^{72} +0.636147 q^{73} +9.58861 q^{74} -8.12631 q^{75} -2.98697 q^{76} -1.55311 q^{77} +9.62002 q^{78} +2.87290 q^{79} -17.9452 q^{80} +1.00000 q^{81} -10.9475 q^{82} +6.19721 q^{83} -0.783461 q^{84} +14.5844 q^{85} +6.75761 q^{86} -0.231853 q^{87} -3.15226 q^{88} +15.8733 q^{89} -6.04455 q^{90} +5.76612 q^{91} +3.54752 q^{92} -5.76137 q^{93} +6.77121 q^{94} -13.8129 q^{95} -4.20435 q^{96} +9.40322 q^{97} -1.66837 q^{98} -1.55311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) \) 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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