LMFDB - Embedded newform 383.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [383,2,Mod(1,383)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(383, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("383.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	383.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$3.05827039742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.539970 q^{2} +2.48089 q^{3} -1.70843 q^{4} +2.73147 q^{5} +1.33961 q^{6} +1.35462 q^{7} -2.00244 q^{8} +3.15479 q^{9} +1.47491 q^{10} -4.30500 q^{11} -4.23842 q^{12} +5.54722 q^{13} +0.731456 q^{14} +6.77647 q^{15} +2.33560 q^{16} -5.42078 q^{17} +1.70350 q^{18} -3.09802 q^{19} -4.66654 q^{20} +3.36066 q^{21} -2.32457 q^{22} +1.64916 q^{23} -4.96783 q^{24} +2.46095 q^{25} +2.99534 q^{26} +0.384027 q^{27} -2.31428 q^{28} +4.85413 q^{29} +3.65910 q^{30} -6.13774 q^{31} +5.26604 q^{32} -10.6802 q^{33} -2.92706 q^{34} +3.70011 q^{35} -5.38975 q^{36} +10.9948 q^{37} -1.67284 q^{38} +13.7620 q^{39} -5.46962 q^{40} -8.10516 q^{41} +1.81466 q^{42} -4.50158 q^{43} +7.35479 q^{44} +8.61724 q^{45} +0.890496 q^{46} -3.65706 q^{47} +5.79436 q^{48} -5.16500 q^{49} +1.32884 q^{50} -13.4483 q^{51} -9.47705 q^{52} -3.35241 q^{53} +0.207363 q^{54} -11.7590 q^{55} -2.71255 q^{56} -7.68583 q^{57} +2.62109 q^{58} +7.79764 q^{59} -11.5771 q^{60} +10.3211 q^{61} -3.31420 q^{62} +4.27355 q^{63} -1.82770 q^{64} +15.1521 q^{65} -5.76699 q^{66} -14.9913 q^{67} +9.26103 q^{68} +4.09137 q^{69} +1.99795 q^{70} -1.79839 q^{71} -6.31730 q^{72} +3.93808 q^{73} +5.93686 q^{74} +6.10532 q^{75} +5.29275 q^{76} -5.83164 q^{77} +7.43109 q^{78} +5.41776 q^{79} +6.37964 q^{80} -8.51166 q^{81} -4.37655 q^{82} +2.79742 q^{83} -5.74146 q^{84} -14.8067 q^{85} -2.43072 q^{86} +12.0426 q^{87} +8.62051 q^{88} -3.32724 q^{89} +4.65305 q^{90} +7.51439 q^{91} -2.81747 q^{92} -15.2270 q^{93} -1.97471 q^{94} -8.46215 q^{95} +13.0645 q^{96} +6.40340 q^{97} -2.78895 q^{98} -13.5814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) $ 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * 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 $

$2$	0.539970	0.381817	0.190908	−	0.981608i	$-0.438857\pi$
$2$	0.539970	0.381817	0.190908	+	0.981608i	$0.438857\pi$
$3$	2.48089	1.43234	0.716170	−	0.697926i	$-0.245893\pi$
$3$	2.48089	1.43234	0.716170	+	0.697926i	$0.245893\pi$
$4$	−1.70843	−0.854216
$5$	2.73147	1.22155	0.610776	−	0.791803i	$-0.290858\pi$
$5$	2.73147	1.22155	0.610776	+	0.791803i	$0.290858\pi$
$6$	1.33961	0.546892
$7$	1.35462	0.511999	0.256000	−	0.966677i	$-0.417595\pi$
$7$	1.35462	0.511999	0.256000	+	0.966677i	$0.417595\pi$
$8$	−2.00244	−0.707971
$9$	3.15479	1.05160
$10$	1.47491	0.466409
$11$	−4.30500	−1.29800	−0.649002	−	0.760786i	$-0.724814\pi$
$11$	−4.30500	−1.29800	−0.649002	+	0.760786i	$0.724814\pi$
$12$	−4.23842	−1.22353
$13$	5.54722	1.53852	0.769262	−	0.638934i	$-0.220624\pi$
$13$	5.54722	1.53852	0.769262	+	0.638934i	$0.220624\pi$
$14$	0.731456	0.195490
$15$	6.77647	1.74968
$16$	2.33560	0.583901
$17$	−5.42078	−1.31473	−0.657366	−	0.753571i	$-0.728330\pi$
$17$	−5.42078	−1.31473	−0.657366	+	0.753571i	$0.728330\pi$
$18$	1.70350	0.401518
$19$	−3.09802	−0.710734	−0.355367	−	0.934727i	$-0.615644\pi$
$19$	−3.09802	−0.710734	−0.355367	+	0.934727i	$0.615644\pi$
$20$	−4.66654	−1.04347
$21$	3.36066	0.733357
$22$	−2.32457	−0.495600
$23$	1.64916	0.343873	0.171936	−	0.985108i	$-0.444998\pi$
$23$	1.64916	0.343873	0.171936	+	0.985108i	$0.444998\pi$
$24$	−4.96783	−1.01405
$25$	2.46095	0.492189
$26$	2.99534	0.587434
$27$	0.384027	0.0739061
$28$	−2.31428	−0.437358
$29$	4.85413	0.901390	0.450695	−	0.892678i	$-0.351176\pi$
$29$	4.85413	0.901390	0.450695	+	0.892678i	$0.351176\pi$
$30$	3.65910	0.668056
$31$	−6.13774	−1.10237	−0.551185	−	0.834383i	$-0.685824\pi$
$31$	−6.13774	−1.10237	−0.551185	+	0.834383i	$0.685824\pi$
$32$	5.26604	0.930914
$33$	−10.6802	−1.85918
$34$	−2.92706	−0.501987
$35$	3.70011	0.625433
$36$	−5.38975	−0.898292
$37$	10.9948	1.80753	0.903766	−	0.428028i	$-0.140791\pi$
$37$	10.9948	1.80753	0.903766	+	0.428028i	$0.140791\pi$
$38$	−1.67284	−0.271370
$39$	13.7620	2.20369
$40$	−5.46962	−0.864823
$41$	−8.10516	−1.26581	−0.632906	−	0.774228i	$-0.718138\pi$
$41$	−8.10516	−1.26581	−0.632906	+	0.774228i	$0.718138\pi$
$42$	1.81466	0.280008
$43$	−4.50158	−0.686485	−0.343243	−	0.939247i	$-0.611525\pi$
$43$	−4.50158	−0.686485	−0.343243	+	0.939247i	$0.611525\pi$
$44$	7.35479	1.10878
$45$	8.61724	1.28458
$46$	0.890496	0.131296
$47$	−3.65706	−0.533438	−0.266719	−	0.963774i	$-0.585939\pi$
$47$	−3.65706	−0.533438	−0.266719	+	0.963774i	$0.585939\pi$
$48$	5.79436	0.836345
$49$	−5.16500	−0.737857
$50$	1.32884	0.187926
$51$	−13.4483	−1.88314
$52$	−9.47705	−1.31423
$53$	−3.35241	−0.460489	−0.230244	−	0.973133i	$-0.573953\pi$
$53$	−3.35241	−0.460489	−0.230244	+	0.973133i	$0.573953\pi$
$54$	0.207363	0.0282186
$55$	−11.7590	−1.58558
$56$	−2.71255	−0.362480
$57$	−7.68583	−1.01801
$58$	2.62109	0.344166
$59$	7.79764	1.01517	0.507583	−	0.861603i	$-0.330539\pi$
$59$	7.79764	1.01517	0.507583	+	0.861603i	$0.330539\pi$
$60$	−11.5771	−1.49460
$61$	10.3211	1.32148	0.660742	−	0.750613i	$-0.270242\pi$
$61$	10.3211	1.32148	0.660742	+	0.750613i	$0.270242\pi$
$62$	−3.31420	−0.420903
$63$	4.27355	0.538417
$64$	−1.82770	−0.228462
$65$	15.1521	1.87939
$66$	−5.76699	−0.709868
$67$	−14.9913	−1.83147	−0.915737	−	0.401777i	$-0.868393\pi$
$67$	−14.9913	−1.83147	−0.915737	+	0.401777i	$0.868393\pi$
$68$	9.26103	1.12307
$69$	4.09137	0.492543
$70$	1.99795	0.238801
$71$	−1.79839	−0.213429	−0.106715	−	0.994290i	$-0.534033\pi$
$71$	−1.79839	−0.213429	−0.106715	+	0.994290i	$0.534033\pi$
$72$	−6.31730	−0.744501
$73$	3.93808	0.460917	0.230458	−	0.973082i	$-0.425977\pi$
$73$	3.93808	0.460917	0.230458	+	0.973082i	$0.425977\pi$
$74$	5.93686	0.690146
$75$	6.10532	0.704982
$76$	5.29275	0.607120
$77$	−5.83164	−0.664577
$78$	7.43109	0.841405
$79$	5.41776	0.609546	0.304773	−	0.952425i	$-0.401419\pi$
$79$	5.41776	0.609546	0.304773	+	0.952425i	$0.401419\pi$
$80$	6.37964	0.713265
$81$	−8.51166	−0.945739
$82$	−4.37655	−0.483309
$83$	2.79742	0.307056	0.153528	−	0.988144i	$-0.450936\pi$
$83$	2.79742	0.307056	0.153528	+	0.988144i	$0.450936\pi$
$84$	−5.74146	−0.626445
$85$	−14.8067	−1.60601
$86$	−2.43072	−0.262112
$87$	12.0426	1.29110
$88$	8.62051	0.918950
$89$	−3.32724	−0.352687	−0.176343	−	0.984329i	$-0.556427\pi$
$89$	−3.32724	−0.352687	−0.176343	+	0.984329i	$0.556427\pi$
$90$	4.65305	0.490475
$91$	7.51439	0.787722
$92$	−2.81747	−0.293742
$93$	−15.2270	−1.57897
$94$	−1.97471	−0.203675
$95$	−8.46215	−0.868198
$96$	13.0645	1.33339
$97$	6.40340	0.650167	0.325083	−	0.945685i	$-0.394608\pi$
$97$	6.40340	0.650167	0.325083	+	0.945685i	$0.394608\pi$
$98$	−2.78895	−0.281726
$99$	−13.5814	−1.36498
$100$	−4.20436	−0.420436
$101$	−18.0138	−1.79244	−0.896219	−	0.443612i	$-0.853697\pi$
$101$	−18.0138	−1.79244	−0.896219	+	0.443612i	$0.853697\pi$
$102$	−7.26171	−0.719016
$103$	−5.49753	−0.541688	−0.270844	−	0.962623i	$-0.587303\pi$
$103$	−5.49753	−0.541688	−0.270844	+	0.962623i	$0.587303\pi$
$104$	−11.1080	−1.08923
$105$	9.17956	0.895833
$106$	−1.81020	−0.175822
$107$	11.4265	1.10464	0.552322	−	0.833631i	$-0.313742\pi$
$107$	11.4265	1.10464	0.552322	+	0.833631i	$0.313742\pi$
$108$	−0.656084	−0.0631318
$109$	8.82483	0.845265	0.422633	−	0.906301i	$-0.361106\pi$
$109$	8.82483	0.845265	0.422633	+	0.906301i	$0.361106\pi$
$110$	−6.34950	−0.605401
$111$	27.2768	2.58900
$112$	3.16386	0.298957
$113$	−12.6481	−1.18983	−0.594917	−	0.803787i	$-0.702815\pi$
$113$	−12.6481	−1.18983	−0.594917	+	0.803787i	$0.702815\pi$
$114$	−4.15012	−0.388694
$115$	4.50463	0.420059
$116$	−8.29296	−0.769982
$117$	17.5004	1.61791
$118$	4.21049	0.387607
$119$	−7.34311	−0.673142
$120$	−13.5695	−1.23872
$121$	7.53299	0.684817
$122$	5.57310	0.504565
$123$	−20.1080	−1.81307
$124$	10.4859	0.941662
$125$	−6.93536	−0.620317
$126$	2.30759	0.205577
$127$	−9.10939	−0.808327	−0.404164	−	0.914687i	$-0.632437\pi$
$127$	−9.10939	−0.808327	−0.404164	+	0.914687i	$0.632437\pi$
$128$	−11.5190	−1.01814
$129$	−11.1679	−0.983280
$130$	8.18168	0.717581
$131$	9.44118	0.824880	0.412440	−	0.910985i	$-0.364677\pi$
$131$	9.44118	0.824880	0.412440	+	0.910985i	$0.364677\pi$
$132$	18.2464	1.58815
$133$	−4.19664	−0.363895
$134$	−8.09484	−0.699288
$135$	1.04896	0.0902801
$136$	10.8548	0.930792
$137$	15.4680	1.32152	0.660760	−	0.750598i	$-0.270234\pi$
$137$	15.4680	1.32152	0.660760	+	0.750598i	$0.270234\pi$
$138$	2.20922	0.188061
$139$	21.0357	1.78422	0.892112	−	0.451814i	$-0.149223\pi$
$139$	21.0357	1.78422	0.892112	+	0.451814i	$0.149223\pi$
$140$	−6.32139	−0.534255
$141$	−9.07276	−0.764064
$142$	−0.971077	−0.0814909
$143$	−23.8808	−1.99701
$144$	7.36835	0.614029
$145$	13.2589	1.10109
$146$	2.12644	0.175986
$147$	−12.8138	−1.05686
$148$	−18.7838	−1.54402
$149$	5.71337	0.468057	0.234029	−	0.972230i	$-0.424809\pi$
$149$	5.71337	0.468057	0.234029	+	0.972230i	$0.424809\pi$
$150$	3.29669	0.269174
$151$	14.3726	1.16962	0.584812	−	0.811169i	$-0.301168\pi$
$151$	14.3726	1.16962	0.584812	+	0.811169i	$0.301168\pi$
$152$	6.20360	0.503179
$153$	−17.1014	−1.38257
$154$	−3.14891	−0.253747
$155$	−16.7651	−1.34660
$156$	−23.5115	−1.88243
$157$	−15.3958	−1.22872	−0.614359	−	0.789027i	$-0.710585\pi$
$157$	−15.3958	−1.22872	−0.614359	+	0.789027i	$0.710585\pi$
$158$	2.92543	0.232735
$159$	−8.31694	−0.659577
$160$	14.3841	1.13716
$161$	2.23398	0.176063
$162$	−4.59604	−0.361099
$163$	−1.76284	−0.138076	−0.0690381	−	0.997614i	$-0.521993\pi$
$163$	−1.76284	−0.138076	−0.0690381	+	0.997614i	$0.521993\pi$
$164$	13.8471	1.08128
$165$	−29.1727	−2.27109
$166$	1.51052	0.117239
$167$	−6.42239	−0.496980	−0.248490	−	0.968634i	$-0.579934\pi$
$167$	−6.42239	−0.496980	−0.248490	+	0.968634i	$0.579934\pi$
$168$	−6.72954	−0.519195
$169$	17.7717	1.36705
$170$	−7.99519	−0.613203
$171$	−9.77361	−0.747406
$172$	7.69065	0.586406
$173$	12.7475	0.969171	0.484586	−	0.874744i	$-0.338970\pi$
$173$	12.7475	0.969171	0.484586	+	0.874744i	$0.338970\pi$
$174$	6.50262	0.492963
$175$	3.33365	0.252000
$176$	−10.0548	−0.757906
$177$	19.3450	1.45406
$178$	−1.79661	−0.134662
$179$	2.68522	0.200703	0.100351	−	0.994952i	$-0.468003\pi$
$179$	2.68522	0.200703	0.100351	+	0.994952i	$0.468003\pi$
$180$	−14.7220	−1.09731
$181$	23.9469	1.77996	0.889979	−	0.456001i	$-0.150719\pi$
$181$	23.9469	1.77996	0.889979	+	0.456001i	$0.150719\pi$
$182$	4.05755	0.300766
$183$	25.6055	1.89281
$184$	−3.30234	−0.243452
$185$	30.0320	2.20799
$186$	−8.22214	−0.602877
$187$	23.3364	1.70653
$188$	6.24784	0.455671
$189$	0.520212	0.0378398
$190$	−4.56931	−0.331493
$191$	4.81947	0.348724	0.174362	−	0.984682i	$-0.444214\pi$
$191$	4.81947	0.348724	0.174362	+	0.984682i	$0.444214\pi$
$192$	−4.53431	−0.327236
$193$	18.6941	1.34563	0.672815	−	0.739811i	$-0.265085\pi$
$193$	18.6941	1.34563	0.672815	+	0.739811i	$0.265085\pi$
$194$	3.45765	0.248245
$195$	37.5906	2.69192
$196$	8.82405	0.630289
$197$	15.7481	1.12200	0.561002	−	0.827814i	$-0.310416\pi$
$197$	15.7481	1.12200	0.561002	+	0.827814i	$0.310416\pi$
$198$	−7.33354	−0.521172
$199$	8.78805	0.622969	0.311484	−	0.950251i	$-0.399174\pi$
$199$	8.78805	0.622969	0.311484	+	0.950251i	$0.399174\pi$
$200$	−4.92790	−0.348455
$201$	−37.1916	−2.62329
$202$	−9.72691	−0.684383
$203$	6.57552	0.461511
$204$	22.9756	1.60861
$205$	−22.1390	−1.54626
$206$	−2.96851	−0.206826
$207$	5.20275	0.361616
$208$	12.9561	0.898345
$209$	13.3369	0.922536
$210$	4.95669	0.342044
$211$	13.9226	0.958475	0.479237	−	0.877685i	$-0.340913\pi$
$211$	13.9226	0.958475	0.479237	+	0.877685i	$0.340913\pi$
$212$	5.72736	0.393357
$213$	−4.46160	−0.305704
$214$	6.16999	0.421772
$215$	−12.2960	−0.838577
$216$	−0.768993	−0.0523233
$217$	−8.31431	−0.564412
$218$	4.76515	0.322736
$219$	9.76992	0.660190
$220$	20.0894	1.35443
$221$	−30.0703	−2.02275
$222$	14.7287	0.988524
$223$	15.2357	1.02026	0.510128	−	0.860099i	$-0.329598\pi$
$223$	15.2357	1.02026	0.510128	+	0.860099i	$0.329598\pi$
$224$	7.13350	0.476627
$225$	7.76378	0.517585
$226$	−6.82961	−0.454299
$227$	−16.5841	−1.10073	−0.550363	−	0.834925i	$-0.685511\pi$
$227$	−16.5841	−1.10073	−0.550363	+	0.834925i	$0.685511\pi$
$228$	13.1307	0.869602
$229$	19.0304	1.25757	0.628783	−	0.777581i	$-0.283553\pi$
$229$	19.0304	1.25757	0.628783	+	0.777581i	$0.283553\pi$
$230$	2.43237	0.160385
$231$	−14.4676	−0.951901
$232$	−9.72013	−0.638158
$233$	−10.1471	−0.664758	−0.332379	−	0.943146i	$-0.607851\pi$
$233$	−10.1471	−0.664758	−0.332379	+	0.943146i	$0.607851\pi$
$234$	9.44967	0.617744
$235$	−9.98917	−0.651622
$236$	−13.3217	−0.867171
$237$	13.4408	0.873077
$238$	−3.96506	−0.257017
$239$	13.5022	0.873382	0.436691	−	0.899611i	$-0.356150\pi$
$239$	13.5022	0.873382	0.436691	+	0.899611i	$0.356150\pi$
$240$	15.8272	1.02164
$241$	−11.5583	−0.744537	−0.372268	−	0.928125i	$-0.621420\pi$
$241$	−11.5583	−0.744537	−0.372268	+	0.928125i	$0.621420\pi$
$242$	4.06759	0.261475
$243$	−22.2685	−1.42853
$244$	−17.6329	−1.12883
$245$	−14.1081	−0.901331
$246$	−10.8577	−0.692262
$247$	−17.1854	−1.09348
$248$	12.2905	0.780446
$249$	6.94007	0.439809
$250$	−3.74489	−0.236848
$251$	4.61960	0.291587	0.145793	−	0.989315i	$-0.453427\pi$
$251$	4.61960	0.291587	0.145793	+	0.989315i	$0.453427\pi$
$252$	−7.30108	−0.459925
$253$	−7.09961	−0.446349
$254$	−4.91880	−0.308633
$255$	−36.7338	−2.30036
$256$	−2.56452	−0.160283
$257$	−19.3079	−1.20439	−0.602196	−	0.798348i	$-0.705708\pi$
$257$	−19.3079	−1.20439	−0.602196	+	0.798348i	$0.705708\pi$
$258$	−6.03034	−0.375433
$259$	14.8938	0.925454
$260$	−25.8863	−1.60540
$261$	15.3138	0.947900
$262$	5.09796	0.314953
$263$	−10.0777	−0.621418	−0.310709	−	0.950505i	$-0.600566\pi$
$263$	−10.0777	−0.621418	−0.310709	+	0.950505i	$0.600566\pi$
$264$	21.3865	1.31625
$265$	−9.15701	−0.562511
$266$	−2.26606	−0.138941
$267$	−8.25451	−0.505168
$268$	25.6116	1.56448
$269$	24.2492	1.47850	0.739250	−	0.673431i	$-0.235180\pi$
$269$	24.2492	1.47850	0.739250	+	0.673431i	$0.235180\pi$
$270$	0.566408	0.0344705
$271$	−19.6610	−1.19432	−0.597159	−	0.802123i	$-0.703704\pi$
$271$	−19.6610	−1.19432	−0.597159	+	0.802123i	$0.703704\pi$
$272$	−12.6608	−0.767673
$273$	18.6423	1.12829
$274$	8.35226	0.504578
$275$	−10.5944	−0.638864
$276$	−6.98983	−0.420738
$277$	31.9027	1.91685	0.958423	−	0.285353i	$-0.0921108\pi$
$277$	31.9027	1.91685	0.958423	+	0.285353i	$0.0921108\pi$
$278$	11.3587	0.681247
$279$	−19.3633	−1.15925
$280$	−7.40927	−0.442789
$281$	−18.4310	−1.09950	−0.549752	−	0.835328i	$-0.685278\pi$
$281$	−18.4310	−1.09950	−0.549752	+	0.835328i	$0.685278\pi$
$282$	−4.89902	−0.291732
$283$	−9.31764	−0.553876	−0.276938	−	0.960888i	$-0.589320\pi$
$283$	−9.31764	−0.553876	−0.276938	+	0.960888i	$0.589320\pi$
$284$	3.07242	0.182315
$285$	−20.9936	−1.24355
$286$	−12.8949	−0.762492
$287$	−10.9794	−0.648095
$288$	16.6133	0.978947
$289$	12.3849	0.728522
$290$	7.15944	0.420417
$291$	15.8861	0.931260
$292$	−6.72793	−0.393723
$293$	22.8134	1.33277	0.666387	−	0.745606i	$-0.267840\pi$
$293$	22.8134	1.33277	0.666387	+	0.745606i	$0.267840\pi$
$294$	−6.91906	−0.403528
$295$	21.2990	1.24008
$296$	−22.0164	−1.27968
$297$	−1.65324	−0.0959305
$298$	3.08505	0.178712
$299$	9.14824	0.529057
$300$	−10.4305	−0.602207
$301$	−6.09794	−0.351480
$302$	7.76078	0.446582
$303$	−44.6901	−2.56738
$304$	−7.23574	−0.414998
$305$	28.1919	1.61426
$306$	−9.23428	−0.527889
$307$	−0.269272	−0.0153682	−0.00768409	−	0.999970i	$-0.502446\pi$
$307$	−0.269272	−0.0153682	−0.00768409	+	0.999970i	$0.502446\pi$
$308$	9.96296	0.567692
$309$	−13.6388	−0.775881
$310$	−9.05264	−0.514155
$311$	17.8358	1.01138	0.505688	−	0.862717i	$-0.331239\pi$
$311$	17.8358	1.01138	0.505688	+	0.862717i	$0.331239\pi$
$312$	−27.5577	−1.56015
$313$	−28.0566	−1.58585	−0.792925	−	0.609319i	$-0.791443\pi$
$313$	−28.0566	−1.58585	−0.792925	+	0.609319i	$0.791443\pi$
$314$	−8.31327	−0.469145
$315$	11.6731	0.657705
$316$	−9.25587	−0.520684
$317$	−3.77260	−0.211890	−0.105945	−	0.994372i	$-0.533787\pi$
$317$	−3.77260	−0.211890	−0.105945	+	0.994372i	$0.533787\pi$
$318$	−4.49090	−0.251837
$319$	−20.8970	−1.17001
$320$	−4.99231	−0.279078
$321$	28.3479	1.58223
$322$	1.20629	0.0672237
$323$	16.7937	0.934425
$324$	14.5416	0.807866
$325$	13.6514	0.757244
$326$	−0.951880	−0.0527198
$327$	21.8934	1.21071
$328$	16.2301	0.896158
$329$	−4.95394	−0.273120
$330$	−15.7524	−0.867140
$331$	−18.4890	−1.01625	−0.508124	−	0.861284i	$-0.669661\pi$
$331$	−18.4890	−1.01625	−0.508124	+	0.861284i	$0.669661\pi$
$332$	−4.77919	−0.262292
$333$	34.6863	1.90080
$334$	−3.46790	−0.189755
$335$	−40.9482	−2.23724
$336$	7.84917	0.428208
$337$	3.24765	0.176911	0.0884555	−	0.996080i	$-0.471807\pi$
$337$	3.24765	0.176911	0.0884555	+	0.996080i	$0.471807\pi$
$338$	9.59619	0.521964
$339$	−31.3785	−1.70425
$340$	25.2963	1.37188
$341$	26.4229	1.43088
$342$	−5.27746	−0.285372
$343$	−16.4790	−0.889781
$344$	9.01417	0.486011
$345$	11.1755	0.601667
$346$	6.88325	0.370046
$347$	−16.5021	−0.885880	−0.442940	−	0.896551i	$-0.646065\pi$
$347$	−16.5021	−0.885880	−0.442940	+	0.896551i	$0.646065\pi$
$348$	−20.5739	−1.10288
$349$	−14.2112	−0.760707	−0.380354	−	0.924841i	$-0.624198\pi$
$349$	−14.2112	−0.760707	−0.380354	+	0.924841i	$0.624198\pi$
$350$	1.80007	0.0962180
$351$	2.13029	0.113706
$352$	−22.6703	−1.20833
$353$	−15.3811	−0.818651	−0.409326	−	0.912388i	$-0.634236\pi$
$353$	−15.3811	−0.818651	−0.409326	+	0.912388i	$0.634236\pi$
$354$	10.4458	0.555186
$355$	−4.91225	−0.260715
$356$	5.68437	0.301271
$357$	−18.2174	−0.964168
$358$	1.44994	0.0766317
$359$	−1.83336	−0.0967611	−0.0483805	−	0.998829i	$-0.515406\pi$
$359$	−1.83336	−0.0967611	−0.0483805	+	0.998829i	$0.515406\pi$
$360$	−17.2555	−0.909446
$361$	−9.40229	−0.494858
$362$	12.9306	0.679618
$363$	18.6885	0.980891
$364$	−12.8378	−0.672885
$365$	10.7567	0.563034
$366$	13.8262	0.722708
$367$	−15.2837	−0.797805	−0.398902	−	0.916993i	$-0.630609\pi$
$367$	−15.2837	−0.797805	−0.398902	+	0.916993i	$0.630609\pi$
$368$	3.85178	0.200788
$369$	−25.5701	−1.33113
$370$	16.2164	0.843049
$371$	−4.54125	−0.235770
$372$	26.0143	1.34878
$373$	6.84654	0.354500	0.177250	−	0.984166i	$-0.443280\pi$
$373$	6.84654	0.354500	0.177250	+	0.984166i	$0.443280\pi$
$374$	12.6010	0.651582
$375$	−17.2058	−0.888506
$376$	7.32306	0.377658
$377$	26.9270	1.38681
$378$	0.280899	0.0144479
$379$	17.4822	0.898000	0.449000	−	0.893532i	$-0.351780\pi$
$379$	17.4822	0.898000	0.449000	+	0.893532i	$0.351780\pi$
$380$	14.4570	0.741629
$381$	−22.5993	−1.15780
$382$	2.60237	0.133149
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−28.5773	−1.45833
$385$	−15.9290	−0.811816
$386$	10.0943	0.513784
$387$	−14.2016	−0.721906
$388$	−10.9398	−0.555383
$389$	−2.45177	−0.124310	−0.0621549	−	0.998067i	$-0.519797\pi$
$389$	−2.45177	−0.124310	−0.0621549	+	0.998067i	$0.519797\pi$
$390$	20.2978	1.02782
$391$	−8.93972	−0.452101
$392$	10.3426	0.522381
$393$	23.4225	1.18151
$394$	8.50350	0.428400
$395$	14.7985	0.744592
$396$	23.2029	1.16599
$397$	19.5293	0.980146	0.490073	−	0.871681i	$-0.336970\pi$
$397$	19.5293	0.980146	0.490073	+	0.871681i	$0.336970\pi$
$398$	4.74529	0.237860
$399$	−10.4114	−0.521221
$400$	5.74779	0.287390
$401$	6.94861	0.346997	0.173499	−	0.984834i	$-0.444493\pi$
$401$	6.94861	0.346997	0.173499	+	0.984834i	$0.444493\pi$
$402$	−20.0824	−1.00162
$403$	−34.0474	−1.69602
$404$	30.7753	1.53113
$405$	−23.2494	−1.15527
$406$	3.55059	0.176213
$407$	−47.3325	−2.34618
$408$	26.9295	1.33321
$409$	16.3598	0.808939	0.404470	−	0.914551i	$-0.367456\pi$
$409$	16.3598	0.808939	0.404470	+	0.914551i	$0.367456\pi$
$410$	−11.9544	−0.590386
$411$	38.3743	1.89287
$412$	9.39216	0.462719
$413$	10.5629	0.519764
$414$	2.80933	0.138071
$415$	7.64106	0.375085
$416$	29.2119	1.43223
$417$	52.1872	2.55562
$418$	7.20156	0.352240
$419$	−35.5721	−1.73781	−0.868906	−	0.494977i	$-0.835176\pi$
$419$	−35.5721	−1.73781	−0.868906	+	0.494977i	$0.835176\pi$
$420$	−15.6827	−0.765235
$421$	−19.9670	−0.973133	−0.486567	−	0.873643i	$-0.661751\pi$
$421$	−19.9670	−0.973133	−0.486567	+	0.873643i	$0.661751\pi$
$422$	7.51782	0.365962
$423$	−11.5373	−0.560962
$424$	6.71301	0.326013
$425$	−13.3402	−0.647097
$426$	−2.40913	−0.116723
$427$	13.9812	0.676598
$428$	−19.5215	−0.943605
$429$	−59.2455	−2.86040
$430$	−6.63945	−0.320183
$431$	−31.6695	−1.52546	−0.762732	−	0.646715i	$-0.776142\pi$
$431$	−31.6695	−1.52546	−0.762732	+	0.646715i	$0.776142\pi$
$432$	0.896935	0.0431538
$433$	25.9453	1.24685	0.623426	−	0.781883i	$-0.285740\pi$
$433$	25.9453	1.24685	0.623426	+	0.781883i	$0.285740\pi$
$434$	−4.48948	−0.215502
$435$	32.8939	1.57714
$436$	−15.0766	−0.722039
$437$	−5.10912	−0.244402
$438$	5.27547	0.252072
$439$	−0.721438	−0.0344324	−0.0172162	−	0.999852i	$-0.505480\pi$
$439$	−0.721438	−0.0344324	−0.0172162	+	0.999852i	$0.505480\pi$
$440$	23.5467	1.12254
$441$	−16.2945	−0.775929
$442$	−16.2371	−0.772319
$443$	−24.0001	−1.14028	−0.570139	−	0.821548i	$-0.693111\pi$
$443$	−24.0001	−1.14028	−0.570139	+	0.821548i	$0.693111\pi$
$444$	−46.6006	−2.21156
$445$	−9.08827	−0.430825
$446$	8.22681	0.389551
$447$	14.1742	0.670417
$448$	−2.47584	−0.116972
$449$	−2.52659	−0.119237	−0.0596185	−	0.998221i	$-0.518988\pi$
$449$	−2.52659	−0.119237	−0.0596185	+	0.998221i	$0.518988\pi$
$450$	4.19221	0.197623
$451$	34.8927	1.64303
$452$	21.6084	1.01638
$453$	35.6568	1.67530
$454$	−8.95494	−0.420276
$455$	20.5254	0.962244
$456$	15.3904	0.720723
$457$	−6.40528	−0.299627	−0.149813	−	0.988714i	$-0.547867\pi$
$457$	−6.40528	−0.299627	−0.149813	+	0.988714i	$0.547867\pi$
$458$	10.2759	0.480160
$459$	−2.08173	−0.0971667
$460$	−7.69585	−0.358821
$461$	−27.2474	−1.26904	−0.634518	−	0.772908i	$-0.718801\pi$
$461$	−27.2474	−1.26904	−0.634518	+	0.772908i	$0.718801\pi$
$462$	−7.81210	−0.363452
$463$	−29.8580	−1.38762	−0.693809	−	0.720159i	$-0.744069\pi$
$463$	−29.8580	−1.38762	−0.693809	+	0.720159i	$0.744069\pi$
$464$	11.3373	0.526322
$465$	−41.5922	−1.92879
$466$	−5.47913	−0.253816
$467$	−27.1904	−1.25822	−0.629111	−	0.777315i	$-0.716581\pi$
$467$	−27.1904	−1.25822	−0.629111	+	0.777315i	$0.716581\pi$
$468$	−29.8982	−1.38204
$469$	−20.3075	−0.937713
$470$	−5.39386	−0.248800
$471$	−38.1952	−1.75994
$472$	−15.6143	−0.718708
$473$	19.3793	0.891061
$474$	7.25766	0.333355
$475$	−7.62405	−0.349815
$476$	12.5452	0.575008
$477$	−10.5762	−0.484249
$478$	7.29077	0.333472
$479$	−31.9144	−1.45820	−0.729102	−	0.684405i	$-0.760062\pi$
$479$	−31.9144	−1.45820	−0.729102	+	0.684405i	$0.760062\pi$
$480$	35.6852	1.62880
$481$	60.9905	2.78093
$482$	−6.24115	−0.284277
$483$	5.54226	0.252182
$484$	−12.8696	−0.584981
$485$	17.4907	0.794213
$486$	−12.0243	−0.545435
$487$	2.25580	0.102220	0.0511100	−	0.998693i	$-0.483724\pi$
$487$	2.25580	0.102220	0.0511100	+	0.998693i	$0.483724\pi$
$488$	−20.6675	−0.935572
$489$	−4.37340	−0.197772
$490$	−7.61793	−0.344143
$491$	−33.5872	−1.51577	−0.757884	−	0.652389i	$-0.773767\pi$
$491$	−33.5872	−1.51577	−0.757884	+	0.652389i	$0.773767\pi$
$492$	34.3531	1.54876
$493$	−26.3132	−1.18509
$494$	−9.27960	−0.417509
$495$	−37.0972	−1.66739
$496$	−14.3353	−0.643675
$497$	−2.43614	−0.109276
$498$	3.74743	0.167926
$499$	15.3567	0.687460	0.343730	−	0.939069i	$-0.388309\pi$
$499$	15.3567	0.687460	0.343730	+	0.939069i	$0.388309\pi$
$500$	11.8486	0.529885
$501$	−15.9332	−0.711844
$502$	2.49445	0.111333
$503$	16.3889	0.730747	0.365373	−	0.930861i	$-0.380941\pi$
$503$	16.3889	0.730747	0.365373	+	0.930861i	$0.380941\pi$
$504$	−8.55755	−0.381184
$505$	−49.2042	−2.18956
$506$	−3.83358	−0.170423
$507$	44.0895	1.95809
$508$	15.5628	0.690486
$509$	41.0905	1.82131	0.910653	−	0.413171i	$-0.135579\pi$
$509$	41.0905	1.82131	0.910653	+	0.413171i	$0.135579\pi$
$510$	−19.8352	−0.878315
$511$	5.33461	0.235989
$512$	21.6532	0.956946
$513$	−1.18972	−0.0525275
$514$	−10.4257	−0.459857
$515$	−15.0164	−0.661700
$516$	19.0796	0.839933
$517$	15.7436	0.692405
$518$	8.04220	0.353354
$519$	31.6250	1.38818
$520$	−30.3412	−1.33055
$521$	−35.8082	−1.56879	−0.784393	−	0.620264i	$-0.787025\pi$
$521$	−35.8082	−1.56879	−0.784393	+	0.620264i	$0.787025\pi$
$522$	8.26900	0.361924
$523$	−12.8860	−0.563467	−0.281734	−	0.959493i	$-0.590909\pi$
$523$	−12.8860	−0.563467	−0.281734	+	0.959493i	$0.590909\pi$
$524$	−16.1296	−0.704625
$525$	8.27041	0.360950
$526$	−5.44166	−0.237268
$527$	33.2713	1.44932
$528$	−24.9447	−1.08558
$529$	−20.2803	−0.881751
$530$	−4.94452	−0.214776
$531$	24.5999	1.06755
$532$	7.16968	0.310845
$533$	−44.9611	−1.94748
$534$	−4.45719	−0.192881
$535$	31.2113	1.34938
$536$	30.0192	1.29663
$537$	6.66173	0.287475
$538$	13.0939	0.564516
$539$	22.2353	0.957742
$540$	−1.79208	−0.0771187
$541$	−0.426739	−0.0183469	−0.00917347	−	0.999958i	$-0.502920\pi$
$541$	−0.426739	−0.0183469	−0.00917347	+	0.999958i	$0.502920\pi$
$542$	−10.6163	−0.456011
$543$	59.4095	2.54951
$544$	−28.5461	−1.22390
$545$	24.1048	1.03254
$546$	10.0663	0.430799
$547$	39.6287	1.69440	0.847201	−	0.531273i	$-0.178286\pi$
$547$	39.6287	1.69440	0.847201	+	0.531273i	$0.178286\pi$
$548$	−26.4260	−1.12886
$549$	32.5610	1.38967
$550$	−5.72064	−0.243929
$551$	−15.0382	−0.640648
$552$	−8.19274	−0.348706
$553$	7.33902	0.312087
$554$	17.2265	0.731884
$555$	74.5059	3.16260
$556$	−35.9381	−1.52411
$557$	−5.49023	−0.232628	−0.116314	−	0.993212i	$-0.537108\pi$
$557$	−5.49023	−0.232628	−0.116314	+	0.993212i	$0.537108\pi$
$558$	−10.4556	−0.442621
$559$	−24.9713	−1.05617
$560$	8.64200	0.365191
$561$	57.8950	2.44433
$562$	−9.95222	−0.419809
$563$	34.7674	1.46527	0.732635	−	0.680622i	$-0.238290\pi$
$563$	34.7674	1.46527	0.732635	+	0.680622i	$0.238290\pi$
$564$	15.5002	0.652676
$565$	−34.5480	−1.45344
$566$	−5.03125	−0.211479
$567$	−11.5301	−0.484218
$568$	3.60117	0.151102
$569$	5.33205	0.223531	0.111766	−	0.993735i	$-0.464349\pi$
$569$	5.33205	0.223531	0.111766	+	0.993735i	$0.464349\pi$
$570$	−11.3359	−0.474810
$571$	4.52883	0.189525	0.0947627	−	0.995500i	$-0.469791\pi$
$571$	4.52883	0.189525	0.0947627	+	0.995500i	$0.469791\pi$
$572$	40.7987	1.70588
$573$	11.9565	0.499492
$574$	−5.92856	−0.247454
$575$	4.05848	0.169251
$576$	−5.76601	−0.240250
$577$	16.2747	0.677524	0.338762	−	0.940872i	$-0.389992\pi$
$577$	16.2747	0.677524	0.338762	+	0.940872i	$0.389992\pi$
$578$	6.68746	0.278162
$579$	46.3779	1.92740
$580$	−22.6520	−0.940573
$581$	3.78944	0.157212
$582$	8.57803	0.355571
$583$	14.4321	0.597717
$584$	−7.88578	−0.326316
$585$	47.8017	1.97636
$586$	12.3186	0.508875
$587$	−3.98036	−0.164287	−0.0821436	−	0.996621i	$-0.526177\pi$
$587$	−3.98036	−0.164287	−0.0821436	+	0.996621i	$0.526177\pi$
$588$	21.8915	0.902788
$589$	19.0148	0.783492
$590$	11.5009	0.473483
$591$	39.0692	1.60709
$592$	25.6795	1.05542
$593$	3.50713	0.144021	0.0720103	−	0.997404i	$-0.477059\pi$
$593$	3.50713	0.144021	0.0720103	+	0.997404i	$0.477059\pi$
$594$	−0.892698	−0.0366279
$595$	−20.0575	−0.822278
$596$	−9.76090	−0.399822
$597$	21.8022	0.892303
$598$	4.93978	0.202003
$599$	−5.73453	−0.234306	−0.117153	−	0.993114i	$-0.537377\pi$
$599$	−5.73453	−0.234306	−0.117153	+	0.993114i	$0.537377\pi$
$600$	−12.2256	−0.499107
$601$	33.1801	1.35344	0.676721	−	0.736239i	$-0.263400\pi$
$601$	33.1801	1.35344	0.676721	+	0.736239i	$0.263400\pi$
$602$	−3.29271	−0.134201
$603$	−47.2944	−1.92598
$604$	−24.5546	−0.999112
$605$	20.5761	0.836539
$606$	−24.1314	−0.980269
$607$	−16.1721	−0.656404	−0.328202	−	0.944608i	$-0.606443\pi$
$607$	−16.1721	−0.656404	−0.328202	+	0.944608i	$0.606443\pi$
$608$	−16.3143	−0.661632
$609$	16.3131	0.661041
$610$	15.2228	0.616352
$611$	−20.2866	−0.820706
$612$	29.2167	1.18101
$613$	28.0274	1.13202	0.566008	−	0.824400i	$-0.308487\pi$
$613$	28.0274	1.13202	0.566008	+	0.824400i	$0.308487\pi$
$614$	−0.145399	−0.00586783
$615$	−54.9244	−2.21476
$616$	11.6775	0.470501
$617$	−41.1738	−1.65760	−0.828798	−	0.559548i	$-0.810975\pi$
$617$	−41.1738	−1.65760	−0.828798	+	0.559548i	$0.810975\pi$
$618$	−7.36452	−0.296245
$619$	−13.9142	−0.559257	−0.279629	−	0.960108i	$-0.590211\pi$
$619$	−13.9142	−0.559257	−0.279629	+	0.960108i	$0.590211\pi$
$620$	28.6420	1.15029
$621$	0.633321	0.0254143
$622$	9.63081	0.386160
$623$	−4.50716	−0.180575
$624$	32.1426	1.28674
$625$	−31.2485	−1.24994
$626$	−15.1497	−0.605505
$627$	33.0874	1.32139
$628$	26.3027	1.04959
$629$	−59.6003	−2.37642
$630$	6.30313	0.251123
$631$	−27.6205	−1.09955	−0.549777	−	0.835311i	$-0.685287\pi$
$631$	−27.6205	−1.09955	−0.549777	+	0.835311i	$0.685287\pi$
$632$	−10.8488	−0.431541
$633$	34.5405	1.37286
$634$	−2.03709	−0.0809032
$635$	−24.8820	−0.987414
$636$	14.2089	0.563421
$637$	−28.6514	−1.13521
$638$	−11.2838	−0.446729
$639$	−5.67355	−0.224442
$640$	−31.4638	−1.24372
$641$	9.35059	0.369326	0.184663	−	0.982802i	$-0.440881\pi$
$641$	9.35059	0.369326	0.184663	+	0.982802i	$0.440881\pi$
$642$	15.3070	0.604121
$643$	38.5809	1.52148	0.760742	−	0.649055i	$-0.224835\pi$
$643$	38.5809	1.52148	0.760742	+	0.649055i	$0.224835\pi$
$644$	−3.81661	−0.150396
$645$	−30.5049	−1.20113
$646$	9.06809	0.356779
$647$	35.0047	1.37618	0.688089	−	0.725626i	$-0.258450\pi$
$647$	35.0047	1.37618	0.688089	+	0.725626i	$0.258450\pi$
$648$	17.0441	0.669556
$649$	−33.5688	−1.31769
$650$	7.37136	0.289129
$651$	−20.6269	−0.808430
$652$	3.01169	0.117947
$653$	40.0726	1.56816	0.784081	−	0.620658i	$-0.213135\pi$
$653$	40.0726	1.56816	0.784081	+	0.620658i	$0.213135\pi$
$654$	11.8218	0.462268
$655$	25.7883	1.00763
$656$	−18.9304	−0.739109
$657$	12.4238	0.484699
$658$	−2.67498	−0.104282
$659$	−22.5703	−0.879214	−0.439607	−	0.898190i	$-0.644882\pi$
$659$	−22.5703	−0.879214	−0.439607	+	0.898190i	$0.644882\pi$
$660$	49.8395	1.94000
$661$	24.4543	0.951160	0.475580	−	0.879672i	$-0.342238\pi$
$661$	24.4543	0.951160	0.475580	+	0.879672i	$0.342238\pi$
$662$	−9.98351	−0.388020
$663$	−74.6009	−2.89726
$664$	−5.60167	−0.217387
$665$	−11.4630	−0.444517
$666$	18.7296	0.725756
$667$	8.00523	0.309964
$668$	10.9722	0.424528
$669$	37.7980	1.46135
$670$	−22.1108	−0.854216
$671$	−44.4324	−1.71529
$672$	17.6974	0.682692
$673$	46.9363	1.80926	0.904630	−	0.426197i	$-0.140147\pi$
$673$	46.9363	1.80926	0.904630	+	0.426197i	$0.140147\pi$
$674$	1.75364	0.0675476
$675$	0.945070	0.0363758
$676$	−30.3617	−1.16776
$677$	2.16566	0.0832330	0.0416165	−	0.999134i	$-0.486749\pi$
$677$	2.16566	0.0832330	0.0416165	+	0.999134i	$0.486749\pi$
$678$	−16.9435	−0.650710
$679$	8.67419	0.332885
$680$	29.6496	1.13701
$681$	−41.1433	−1.57662
$682$	14.2676	0.546335
$683$	−11.7699	−0.450364	−0.225182	−	0.974317i	$-0.572298\pi$
$683$	−11.7699	−0.450364	−0.225182	+	0.974317i	$0.572298\pi$
$684$	16.6975	0.638446
$685$	42.2504	1.61430
$686$	−8.89816	−0.339733
$687$	47.2123	1.80126
$688$	−10.5139	−0.400839
$689$	−18.5966	−0.708473
$690$	6.03442	0.229727
$691$	2.10859	0.0802147	0.0401074	−	0.999195i	$-0.487230\pi$
$691$	2.10859	0.0802147	0.0401074	+	0.999195i	$0.487230\pi$
$692$	−21.7782	−0.827882
$693$	−18.3976	−0.698868
$694$	−8.91066	−0.338244
$695$	57.4584	2.17952
$696$	−24.1145	−0.914059
$697$	43.9363	1.66421
$698$	−7.67362	−0.290451
$699$	−25.1738	−0.952160
$700$	−5.69532	−0.215263
$701$	−9.83263	−0.371373	−0.185687	−	0.982609i	$-0.559451\pi$
$701$	−9.83263	−0.371373	−0.185687	+	0.982609i	$0.559451\pi$
$702$	1.15029	0.0434149
$703$	−34.0620	−1.28467
$704$	7.86823	0.296545
$705$	−24.7820	−0.933344
$706$	−8.30532	−0.312575
$707$	−24.4019	−0.917727
$708$	−33.0497	−1.24208
$709$	−24.1121	−0.905549	−0.452774	−	0.891625i	$-0.649566\pi$
$709$	−24.1121	−0.905549	−0.452774	+	0.891625i	$0.649566\pi$
$710$	−2.65247	−0.0995454
$711$	17.0919	0.640997
$712$	6.66261	0.249692
$713$	−10.1221	−0.379075
$714$	−9.83687	−0.368136
$715$	−65.2297	−2.43945
$716$	−4.58752	−0.171444
$717$	33.4973	1.25098
$718$	−0.989961	−0.0369450
$719$	13.4949	0.503276	0.251638	−	0.967821i	$-0.419031\pi$
$719$	13.4949	0.503276	0.251638	+	0.967821i	$0.419031\pi$
$720$	20.1264	0.750068
$721$	−7.44708	−0.277344
$722$	−5.07696	−0.188945
$723$	−28.6749	−1.06643
$724$	−40.9116	−1.52047
$725$	11.9458	0.443654
$726$	10.0912	0.374521
$727$	−21.5643	−0.799776	−0.399888	−	0.916564i	$-0.630951\pi$
$727$	−21.5643	−0.799776	−0.399888	+	0.916564i	$0.630951\pi$
$728$	−15.0471	−0.557684
$729$	−29.7107	−1.10040
$730$	5.80833	0.214976
$731$	24.4021	0.902544
$732$	−43.7453	−1.61687
$733$	−38.9418	−1.43835	−0.719175	−	0.694829i	$-0.755480\pi$
$733$	−38.9418	−1.43835	−0.719175	+	0.694829i	$0.755480\pi$
$734$	−8.25277	−0.304615
$735$	−35.0005	−1.29101
$736$	8.68453	0.320116
$737$	64.5373	2.37726
$738$	−13.8071	−0.508246
$739$	−13.0039	−0.478356	−0.239178	−	0.970976i	$-0.576878\pi$
$739$	−13.0039	−0.478356	−0.239178	+	0.970976i	$0.576878\pi$
$740$	−51.3076	−1.88610
$741$	−42.6350	−1.56624
$742$	−2.45214	−0.0900209
$743$	25.8102	0.946883	0.473442	−	0.880825i	$-0.343012\pi$
$743$	25.8102	0.946883	0.473442	+	0.880825i	$0.343012\pi$
$744$	30.4913	1.11786
$745$	15.6059	0.571756
$746$	3.69693	0.135354
$747$	8.82527	0.322900
$748$	−39.8687	−1.45774
$749$	15.4786	0.565577
$750$	−9.29064	−0.339246
$751$	46.2279	1.68688	0.843441	−	0.537222i	$-0.180526\pi$
$751$	46.2279	1.68688	0.843441	+	0.537222i	$0.180526\pi$
$752$	−8.54145	−0.311475
$753$	11.4607	0.417652
$754$	14.5398	0.529507
$755$	39.2583	1.42876
$756$	−0.888746	−0.0323234
$757$	−19.1363	−0.695520	−0.347760	−	0.937584i	$-0.613058\pi$
$757$	−19.1363	−0.695520	−0.347760	+	0.937584i	$0.613058\pi$
$758$	9.43987	0.342871
$759$	−17.6133	−0.639323
$760$	16.9450	0.614659
$761$	−32.1134	−1.16411	−0.582054	−	0.813150i	$-0.697751\pi$
$761$	−32.1134	−1.16411	−0.582054	+	0.813150i	$0.697751\pi$
$762$	−12.2030	−0.442067
$763$	11.9543	0.432775
$764$	−8.23373	−0.297886
$765$	−46.7121	−1.68888
$766$	0.539970	0.0195099
$767$	43.2552	1.56186
$768$	−6.36228	−0.229579
$769$	16.6496	0.600398	0.300199	−	0.953877i	$-0.402947\pi$
$769$	16.6496	0.600398	0.300199	+	0.953877i	$0.402947\pi$
$770$	−8.60118	−0.309965
$771$	−47.9006	−1.72510
$772$	−31.9376	−1.14946
$773$	17.3562	0.624258	0.312129	−	0.950040i	$-0.398958\pi$
$773$	17.3562	0.624258	0.312129	+	0.950040i	$0.398958\pi$
$774$	−7.66843	−0.275636
$775$	−15.1046	−0.542574
$776$	−12.8225	−0.460299
$777$	36.9498	1.32557
$778$	−1.32388	−0.0474636
$779$	25.1099	0.899656
$780$	−64.2210	−2.29948
$781$	7.74205	0.277032
$782$	−4.82718	−0.172620
$783$	1.86412	0.0666182
$784$	−12.0634	−0.430835
$785$	−42.0532	−1.50094
$786$	12.6475	0.451120
$787$	13.5810	0.484109	0.242055	−	0.970263i	$-0.422179\pi$
$787$	13.5810	0.484109	0.242055	+	0.970263i	$0.422179\pi$
$788$	−26.9045	−0.958434
$789$	−25.0016	−0.890081
$790$	7.99073	0.284298
$791$	−17.1334	−0.609194
$792$	27.1959	0.966366
$793$	57.2536	2.03313
$794$	10.5452	0.374236
$795$	−22.7175	−0.805707
$796$	−15.0138	−0.532150
$797$	5.18177	0.183548	0.0917738	−	0.995780i	$-0.470746\pi$
$797$	5.18177	0.183548	0.0917738	+	0.995780i	$0.470746\pi$
$798$	−5.62184	−0.199011
$799$	19.8241	0.701328
$800$	12.9594	0.458186
$801$	−10.4968	−0.370885
$802$	3.75205	0.132489
$803$	−16.9534	−0.598273
$804$	63.5394	2.24086
$805$	6.10207	0.215070
$806$	−18.3846	−0.647570
$807$	60.1595	2.11771
$808$	36.0716	1.26899
$809$	−29.9242	−1.05208	−0.526040	−	0.850460i	$-0.676324\pi$
$809$	−29.9242	−1.05208	−0.526040	+	0.850460i	$0.676324\pi$
$810$	−12.5540	−0.441101
$811$	16.4093	0.576207	0.288104	−	0.957599i	$-0.406975\pi$
$811$	16.4093	0.576207	0.288104	+	0.957599i	$0.406975\pi$
$812$	−11.2338	−0.394230
$813$	−48.7766	−1.71067
$814$	−25.5582	−0.895813
$815$	−4.81514	−0.168667
$816$	−31.4100	−1.09957
$817$	13.9460	0.487908
$818$	8.83380	0.308867
$819$	23.7064	0.828367
$820$	37.8230	1.32084
$821$	54.2340	1.89278	0.946390	−	0.323027i	$-0.104701\pi$
$821$	54.2340	1.89278	0.946390	+	0.323027i	$0.104701\pi$
$822$	20.7210	0.722728
$823$	13.3010	0.463645	0.231822	−	0.972758i	$-0.425531\pi$
$823$	13.3010	0.463645	0.231822	+	0.972758i	$0.425531\pi$
$824$	11.0085	0.383499
$825$	−26.2834	−0.915070
$826$	5.70363	0.198455
$827$	1.11572	0.0387974	0.0193987	−	0.999812i	$-0.493825\pi$
$827$	1.11572	0.0387974	0.0193987	+	0.999812i	$0.493825\pi$
$828$	−8.88855	−0.308898
$829$	−44.8448	−1.55752	−0.778762	−	0.627319i	$-0.784152\pi$
$829$	−44.8448	−1.55752	−0.778762	+	0.627319i	$0.784152\pi$
$830$	4.12595	0.143214
$831$	79.1469	2.74557
$832$	−10.1386	−0.351494
$833$	27.9983	0.970085
$834$	28.1795	0.975777
$835$	−17.5426	−0.607087
$836$	−22.7853	−0.788045
$837$	−2.35706	−0.0814718
$838$	−19.2079	−0.663526
$839$	−9.45493	−0.326420	−0.163210	−	0.986591i	$-0.552185\pi$
$839$	−9.45493	−0.326420	−0.163210	+	0.986591i	$0.552185\pi$
$840$	−18.3816	−0.634224
$841$	−5.43738	−0.187496
$842$	−10.7816	−0.371559
$843$	−45.7253	−1.57486
$844$	−23.7859	−0.818744
$845$	48.5429	1.66993
$846$	−6.22979	−0.214185
$847$	10.2043	0.350626
$848$	−7.82990	−0.268880
$849$	−23.1160	−0.793339
$850$	−7.20334	−0.247072
$851$	18.1321	0.621561
$852$	7.62233	0.261137
$853$	−5.37961	−0.184194	−0.0920972	−	0.995750i	$-0.529357\pi$
$853$	−5.37961	−0.184194	−0.0920972	+	0.995750i	$0.529357\pi$
$854$	7.54944	0.258337
$855$	−26.6963	−0.912996
$856$	−22.8810	−0.782056
$857$	23.4497	0.801026	0.400513	−	0.916291i	$-0.368832\pi$
$857$	23.4497	0.801026	0.400513	+	0.916291i	$0.368832\pi$
$858$	−31.9908	−1.09215
$859$	−54.4080	−1.85638	−0.928189	−	0.372108i	$-0.878635\pi$
$859$	−54.4080	−1.85638	−0.928189	+	0.372108i	$0.878635\pi$
$860$	21.0068	0.716326
$861$	−27.2387	−0.928292
$862$	−17.1006	−0.582448
$863$	−38.8938	−1.32396	−0.661981	−	0.749521i	$-0.730284\pi$
$863$	−38.8938	−1.32396	−0.661981	+	0.749521i	$0.730284\pi$
$864$	2.02230	0.0688002
$865$	34.8193	1.18389
$866$	14.0097	0.476069
$867$	30.7254	1.04349
$868$	14.2044	0.482130
$869$	−23.3234	−0.791193
$870$	17.7617	0.602179
$871$	−83.1599	−2.81777
$872$	−17.6712	−0.598423
$873$	20.2014	0.683714
$874$	−2.75877	−0.0933168
$875$	−9.39479	−0.317602
$876$	−16.6912	−0.563945
$877$	−4.45544	−0.150450	−0.0752248	−	0.997167i	$-0.523967\pi$
$877$	−4.45544	−0.150450	−0.0752248	+	0.997167i	$0.523967\pi$
$878$	−0.389555	−0.0131469
$879$	56.5975	1.90899
$880$	−27.4643	−0.925822
$881$	−47.1137	−1.58730	−0.793650	−	0.608375i	$-0.791822\pi$
$881$	−47.1137	−1.58730	−0.793650	+	0.608375i	$0.791822\pi$
$882$	−8.79855	−0.296263
$883$	16.6598	0.560646	0.280323	−	0.959906i	$-0.409558\pi$
$883$	16.6598	0.560646	0.280323	+	0.959906i	$0.409558\pi$
$884$	51.3730	1.72786
$885$	52.8405	1.77621
$886$	−12.9593	−0.435377
$887$	−45.3101	−1.52137	−0.760683	−	0.649124i	$-0.775136\pi$
$887$	−45.3101	−1.52137	−0.760683	+	0.649124i	$0.775136\pi$
$888$	−54.6203	−1.83294
$889$	−12.3398	−0.413863
$890$	−4.90740	−0.164496
$891$	36.6426	1.22757
$892$	−26.0291	−0.871519
$893$	11.3296	0.379132
$894$	7.65366	0.255977
$895$	7.33461	0.245169
$896$	−15.6039	−0.521289
$897$	22.6957	0.757789
$898$	−1.36428	−0.0455267
$899$	−29.7934	−0.993666
$900$	−13.2639	−0.442129
$901$	18.1727	0.605420
$902$	18.8410	0.627337
$903$	−15.1283	−0.503438
$904$	25.3271	0.842368
$905$	65.4103	2.17431
$906$	19.2536	0.639658
$907$	−15.9304	−0.528960	−0.264480	−	0.964391i	$-0.585200\pi$
$907$	−15.9304	−0.528960	−0.264480	+	0.964391i	$0.585200\pi$
$908$	28.3328	0.940258
$909$	−56.8298	−1.88492
$910$	11.0831	0.367401
$911$	−7.16283	−0.237315	−0.118658	−	0.992935i	$-0.537859\pi$
$911$	−7.16283	−0.237315	−0.118658	+	0.992935i	$0.537859\pi$
$912$	−17.9510	−0.594418
$913$	−12.0429	−0.398560
$914$	−3.45866	−0.114402
$915$	69.9408	2.31217
$916$	−32.5122	−1.07423
$917$	12.7892	0.422338
$918$	−1.12407	−0.0370999
$919$	33.0856	1.09139	0.545696	−	0.837983i	$-0.316265\pi$
$919$	33.0856	1.09139	0.545696	+	0.837983i	$0.316265\pi$
$920$	−9.02026	−0.297389
$921$	−0.668034	−0.0220125
$922$	−14.7128	−0.484539
$923$	−9.97606	−0.328366
$924$	24.7170	0.813129
$925$	27.0576	0.889647
$926$	−16.1224	−0.529816
$927$	−17.3436	−0.569638
$928$	25.5621	0.839117
$929$	−4.13741	−0.135744	−0.0678720	−	0.997694i	$-0.521621\pi$
$929$	−4.13741	−0.135744	−0.0678720	+	0.997694i	$0.521621\pi$
$930$	−22.4586	−0.736445
$931$	16.0013	0.524420
$932$	17.3356	0.567847
$933$	44.2486	1.44863
$934$	−14.6820	−0.480410
$935$	63.7429	2.08461
$936$	−35.0435	−1.14543
$937$	−36.4951	−1.19224	−0.596122	−	0.802894i	$-0.703292\pi$
$937$	−36.4951	−1.19224	−0.596122	+	0.802894i	$0.703292\pi$
$938$	−10.9655	−0.358035
$939$	−69.6051	−2.27148
$940$	17.0658	0.556626
$941$	54.2568	1.76872	0.884360	−	0.466806i	$-0.154595\pi$
$941$	54.2568	1.76872	0.884360	+	0.466806i	$0.154595\pi$
$942$	−20.6243	−0.671975
$943$	−13.3667	−0.435279
$944$	18.2122	0.592756
$945$	1.42094	0.0462233
$946$	10.4642	0.340222
$947$	−42.3195	−1.37520	−0.687600	−	0.726089i	$-0.741336\pi$
$947$	−42.3195	−1.37520	−0.687600	+	0.726089i	$0.741336\pi$
$948$	−22.9628	−0.745796
$949$	21.8454	0.709131
$950$	−4.11676	−0.133565
$951$	−9.35938	−0.303499
$952$	14.7042	0.476565
$953$	0.450629	0.0145973	0.00729864	−	0.999973i	$-0.497677\pi$
$953$	0.450629	0.0145973	0.00729864	+	0.999973i	$0.497677\pi$
$954$	−5.71081	−0.184894
$955$	13.1642	0.425985
$956$	−23.0675	−0.746057
$957$	−51.8431	−1.67585
$958$	−17.2328	−0.556767
$959$	20.9533	0.676617
$960$	−12.3853	−0.399735
$961$	6.67181	0.215220
$962$	32.9331	1.06181
$963$	36.0484	1.16164
$964$	19.7466	0.635995
$965$	51.0624	1.64376
$966$	2.99266	0.0962872
$967$	48.1547	1.54855	0.774275	−	0.632850i	$-0.218115\pi$
$967$	48.1547	1.54855	0.774275	+	0.632850i	$0.218115\pi$
$968$	−15.0844	−0.484830
$969$	41.6632	1.33841
$970$	9.44447	0.303244
$971$	30.1454	0.967413	0.483706	−	0.875230i	$-0.339290\pi$
$971$	30.1454	0.967413	0.483706	+	0.875230i	$0.339290\pi$
$972$	38.0443	1.22027
$973$	28.4954	0.913521
$974$	1.21807	0.0390293
$975$	33.8676	1.08463
$976$	24.1060	0.771615
$977$	−37.5821	−1.20236	−0.601179	−	0.799114i	$-0.705302\pi$
$977$	−37.5821	−1.20236	−0.601179	+	0.799114i	$0.705302\pi$
$978$	−2.36151	−0.0755127
$979$	14.3238	0.457789
$980$	24.1027	0.769931
$981$	27.8405	0.888879
$982$	−18.1361	−0.578746
$983$	29.4214	0.938395	0.469198	−	0.883093i	$-0.344543\pi$
$983$	29.4214	0.938395	0.469198	+	0.883093i	$0.344543\pi$
$984$	40.2651	1.28360
$985$	43.0155	1.37059
$986$	−14.2084	−0.452486
$987$	−12.2902	−0.391200
$988$	29.3601	0.934068
$989$	−7.42382	−0.236064
$990$	−20.0314	−0.636639
$991$	−41.5670	−1.32042	−0.660209	−	0.751082i	$-0.729532\pi$
$991$	−41.5670	−1.32042	−0.660209	+	0.751082i	$0.729532\pi$
$992$	−32.3216	−1.02621
$993$	−45.8691	−1.45561
$994$	−1.31544	−0.0417233
$995$	24.0043	0.760989
$996$	−11.8566	−0.375692
$997$	−11.1707	−0.353780	−0.176890	−	0.984231i	$-0.556604\pi$
$997$	−11.1707	−0.353780	−0.176890	+	0.984231i	$0.556604\pi$
$998$	8.29216	0.262484
$999$	4.22230	0.133588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	383.2.a.c.1.14	✓	24
3.2	odd	2		3447.2.a.j.1.11		24
4.3	odd	2		6128.2.a.p.1.6		24
5.4	even	2		9575.2.a.e.1.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
383.2.a.c.1.14	✓	24	1.1	even	1	trivial
3447.2.a.j.1.11		24	3.2	odd	2
6128.2.a.p.1.6		24	4.3	odd	2
9575.2.a.e.1.11		24	5.4	even	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	383.a (trivial)

\(f(q)\)	\(=\)	\(q+0.539970 q^{2} +2.48089 q^{3} -1.70843 q^{4} +2.73147 q^{5} +1.33961 q^{6} +1.35462 q^{7} -2.00244 q^{8} +3.15479 q^{9} +1.47491 q^{10} -4.30500 q^{11} -4.23842 q^{12} +5.54722 q^{13} +0.731456 q^{14} +6.77647 q^{15} +2.33560 q^{16} -5.42078 q^{17} +1.70350 q^{18} -3.09802 q^{19} -4.66654 q^{20} +3.36066 q^{21} -2.32457 q^{22} +1.64916 q^{23} -4.96783 q^{24} +2.46095 q^{25} +2.99534 q^{26} +0.384027 q^{27} -2.31428 q^{28} +4.85413 q^{29} +3.65910 q^{30} -6.13774 q^{31} +5.26604 q^{32} -10.6802 q^{33} -2.92706 q^{34} +3.70011 q^{35} -5.38975 q^{36} +10.9948 q^{37} -1.67284 q^{38} +13.7620 q^{39} -5.46962 q^{40} -8.10516 q^{41} +1.81466 q^{42} -4.50158 q^{43} +7.35479 q^{44} +8.61724 q^{45} +0.890496 q^{46} -3.65706 q^{47} +5.79436 q^{48} -5.16500 q^{49} +1.32884 q^{50} -13.4483 q^{51} -9.47705 q^{52} -3.35241 q^{53} +0.207363 q^{54} -11.7590 q^{55} -2.71255 q^{56} -7.68583 q^{57} +2.62109 q^{58} +7.79764 q^{59} -11.5771 q^{60} +10.3211 q^{61} -3.31420 q^{62} +4.27355 q^{63} -1.82770 q^{64} +15.1521 q^{65} -5.76699 q^{66} -14.9913 q^{67} +9.26103 q^{68} +4.09137 q^{69} +1.99795 q^{70} -1.79839 q^{71} -6.31730 q^{72} +3.93808 q^{73} +5.93686 q^{74} +6.10532 q^{75} +5.29275 q^{76} -5.83164 q^{77} +7.43109 q^{78} +5.41776 q^{79} +6.37964 q^{80} -8.51166 q^{81} -4.37655 q^{82} +2.79742 q^{83} -5.74146 q^{84} -14.8067 q^{85} -2.43072 q^{86} +12.0426 q^{87} +8.62051 q^{88} -3.32724 q^{89} +4.65305 q^{90} +7.51439 q^{91} -2.81747 q^{92} -15.2270 q^{93} -1.97471 q^{94} -8.46215 q^{95} +13.0645 q^{96} +6.40340 q^{97} -2.78895 q^{98} -13.5814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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