LMFDB - Embedded newform 2401.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.68909 q^{2} -5.32877 q^{3} +13.9876 q^{4} +6.47646 q^{5} +24.9871 q^{6} -28.0763 q^{8} +1.39583 q^{9} +O(q^{10})$	\(q-4.68909 q^{2} -5.32877 q^{3} +13.9876 q^{4} +6.47646 q^{5} +24.9871 q^{6} -28.0763 q^{8} +1.39583 q^{9} -30.3687 q^{10} +21.1431 q^{11} -74.5367 q^{12} +31.8477 q^{13} -34.5116 q^{15} +19.7519 q^{16} +42.0569 q^{17} -6.54519 q^{18} +117.528 q^{19} +90.5900 q^{20} -99.1421 q^{22} -130.889 q^{23} +149.613 q^{24} -83.0555 q^{25} -149.337 q^{26} +136.439 q^{27} -278.949 q^{29} +161.828 q^{30} +199.380 q^{31} +131.992 q^{32} -112.667 q^{33} -197.209 q^{34} +19.5243 q^{36} +300.750 q^{37} -551.102 q^{38} -169.709 q^{39} -181.835 q^{40} +208.784 q^{41} -111.138 q^{43} +295.741 q^{44} +9.04005 q^{45} +613.751 q^{46} -323.111 q^{47} -105.253 q^{48} +389.455 q^{50} -224.112 q^{51} +445.472 q^{52} -100.799 q^{53} -639.774 q^{54} +136.933 q^{55} -626.283 q^{57} +1308.02 q^{58} +249.310 q^{59} -482.734 q^{60} -591.293 q^{61} -934.913 q^{62} -776.939 q^{64} +206.260 q^{65} +528.306 q^{66} +709.040 q^{67} +588.275 q^{68} +697.478 q^{69} -136.416 q^{71} -39.1899 q^{72} -658.930 q^{73} -1410.25 q^{74} +442.584 q^{75} +1643.94 q^{76} +795.782 q^{78} -1138.84 q^{79} +127.922 q^{80} -764.739 q^{81} -979.009 q^{82} -1333.31 q^{83} +272.380 q^{85} +521.135 q^{86} +1486.45 q^{87} -593.622 q^{88} -615.037 q^{89} -42.3896 q^{90} -1830.82 q^{92} -1062.45 q^{93} +1515.10 q^{94} +761.168 q^{95} -703.357 q^{96} +220.142 q^{97} +29.5123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.68909	−1.65784	−0.828922	−	0.559364i	$-0.811045\pi$
$2$	−4.68909	−1.65784	−0.828922	+	0.559364i	$0.811045\pi$
$3$	−5.32877	−1.02552	−0.512762	−	0.858531i	$-0.671377\pi$
$3$	−5.32877	−1.02552	−0.512762	+	0.858531i	$0.671377\pi$
$4$	13.9876	1.74845
$5$	6.47646	0.579272	0.289636	−	0.957137i	$-0.406466\pi$
$5$	6.47646	0.579272	0.289636	+	0.957137i	$0.406466\pi$
$6$	24.9871	1.70016
$7$	0	0
$7$	0	0
$8$	−28.0763	−1.24081
$9$	1.39583	0.0516975
$10$	−30.3687	−0.960343
$11$	21.1431	0.579536	0.289768	−	0.957097i	$-0.406422\pi$
$11$	21.1431	0.579536	0.289768	+	0.957097i	$0.406422\pi$
$12$	−74.5367	−1.79307
$13$	31.8477	0.679458	0.339729	−	0.940523i	$-0.389665\pi$
$13$	31.8477	0.679458	0.339729	+	0.940523i	$0.389665\pi$
$14$	0	0
$15$	−34.5116	−0.594057
$16$	19.7519	0.308623
$17$	42.0569	0.600018	0.300009	−	0.953936i	$-0.403010\pi$
$17$	42.0569	0.600018	0.300009	+	0.953936i	$0.403010\pi$
$18$	−6.54519	−0.0857065
$19$	117.528	1.41910	0.709549	−	0.704656i	$-0.248899\pi$
$19$	117.528	1.41910	0.709549	+	0.704656i	$0.248899\pi$
$20$	90.5900	1.01283
$21$	0	0
$22$	−99.1421	−0.960781
$23$	−130.889	−1.18662	−0.593310	−	0.804974i	$-0.702179\pi$
$23$	−130.889	−1.18662	−0.593310	+	0.804974i	$0.702179\pi$
$24$	149.613	1.27248
$25$	−83.0555	−0.664444
$26$	−149.337	−1.12644
$27$	136.439	0.972506
$28$	0	0
$29$	−278.949	−1.78619	−0.893094	−	0.449869i	$-0.851471\pi$
$29$	−278.949	−1.78619	−0.893094	+	0.449869i	$0.851471\pi$
$30$	161.828	0.984853
$31$	199.380	1.15515	0.577577	−	0.816336i	$-0.303998\pi$
$31$	199.380	1.15515	0.577577	+	0.816336i	$0.303998\pi$
$32$	131.992	0.729162
$33$	−112.667	−0.594328
$34$	−197.209	−0.994736
$35$	0	0
$36$	19.5243	0.0903905
$37$	300.750	1.33630	0.668150	−	0.744027i	$-0.267087\pi$
$37$	300.750	1.33630	0.668150	+	0.744027i	$0.267087\pi$
$38$	−551.102	−2.35265
$39$	−169.709	−0.696800
$40$	−181.835	−0.718767
$41$	208.784	0.795284	0.397642	−	0.917541i	$-0.369829\pi$
$41$	208.784	0.795284	0.397642	+	0.917541i	$0.369829\pi$
$42$	0	0
$43$	−111.138	−0.394147	−0.197074	−	0.980389i	$-0.563144\pi$
$43$	−111.138	−0.394147	−0.197074	+	0.980389i	$0.563144\pi$
$44$	295.741	1.01329
$45$	9.04005	0.0299469
$46$	613.751	1.96723
$47$	−323.111	−1.00278	−0.501390	−	0.865222i	$-0.667178\pi$
$47$	−323.111	−1.00278	−0.501390	+	0.865222i	$0.667178\pi$
$48$	−105.253	−0.316500
$49$	0	0
$50$	389.455	1.10155
$51$	−224.112	−0.615332
$52$	445.472	1.18800
$53$	−100.799	−0.261240	−0.130620	−	0.991432i	$-0.541697\pi$
$53$	−100.799	−0.261240	−0.130620	+	0.991432i	$0.541697\pi$
$54$	−639.774	−1.61226
$55$	136.933	0.335709
$56$	0	0
$57$	−626.283	−1.45532
$58$	1308.02	2.96122
$59$	249.310	0.550125	0.275062	−	0.961426i	$-0.411301\pi$
$59$	249.310	0.550125	0.275062	+	0.961426i	$0.411301\pi$
$60$	−482.734	−1.03868
$61$	−591.293	−1.24110	−0.620552	−	0.784165i	$-0.713091\pi$
$61$	−591.293	−1.24110	−0.620552	+	0.784165i	$0.713091\pi$
$62$	−934.913	−1.91506
$63$	0	0
$64$	−776.939	−1.51746
$65$	206.260	0.393591
$66$	528.306	0.985303
$67$	709.040	1.29288	0.646440	−	0.762965i	$-0.276257\pi$
$67$	709.040	1.29288	0.646440	+	0.762965i	$0.276257\pi$
$68$	588.275	1.04910
$69$	697.478	1.21691
$70$	0	0
$71$	−136.416	−0.228023	−0.114011	−	0.993479i	$-0.536370\pi$
$71$	−136.416	−0.228023	−0.114011	+	0.993479i	$0.536370\pi$
$72$	−39.1899	−0.0641469
$73$	−658.930	−1.05646	−0.528232	−	0.849100i	$-0.677145\pi$
$73$	−658.930	−1.05646	−0.528232	+	0.849100i	$0.677145\pi$
$74$	−1410.25	−2.21538
$75$	442.584	0.681403
$76$	1643.94	2.48122
$77$	0	0
$78$	795.782	1.15519
$79$	−1138.84	−1.62189	−0.810943	−	0.585125i	$-0.801045\pi$
$79$	−1138.84	−1.62189	−0.810943	+	0.585125i	$0.801045\pi$
$80$	127.922	0.178777
$81$	−764.739	−1.04902
$82$	−979.009	−1.31846
$83$	−1333.31	−1.76325	−0.881626	−	0.471948i	$-0.843551\pi$
$83$	−1333.31	−1.76325	−0.881626	+	0.471948i	$0.843551\pi$
$84$	0	0
$85$	272.380	0.347573
$86$	521.135	0.653435
$87$	1486.45	1.83178
$88$	−593.622	−0.719095
$89$	−615.037	−0.732514	−0.366257	−	0.930514i	$-0.619361\pi$
$89$	−615.037	−0.732514	−0.366257	+	0.930514i	$0.619361\pi$
$90$	−42.3896	−0.0496473
$91$	0	0
$92$	−1830.82	−2.07474
$93$	−1062.45	−1.18464
$94$	1515.10	1.66245
$95$	761.168	0.822044
$96$	−703.357	−0.747772
$97$	220.142	0.230433	0.115216	−	0.993340i	$-0.463244\pi$
$97$	220.142	0.230433	0.115216	+	0.993340i	$0.463244\pi$
$98$	0	0
$99$	29.5123	0.0299606
$100$	−1161.75	−1.16175
$101$	284.557	0.280341	0.140171	−	0.990127i	$-0.455235\pi$
$101$	284.557	0.280341	0.140171	+	0.990127i	$0.455235\pi$
$102$	1050.88	1.02013
$103$	−995.906	−0.952714	−0.476357	−	0.879252i	$-0.658043\pi$
$103$	−995.906	−0.952714	−0.476357	+	0.879252i	$0.658043\pi$
$104$	−894.167	−0.843080
$105$	0	0
$106$	472.654	0.433096
$107$	619.130	0.559379	0.279690	−	0.960090i	$-0.409768\pi$
$107$	619.130	0.559379	0.279690	+	0.960090i	$0.409768\pi$
$108$	1908.45	1.70038
$109$	−762.594	−0.670122	−0.335061	−	0.942196i	$-0.608757\pi$
$109$	−762.594	−0.670122	−0.335061	+	0.942196i	$0.608757\pi$
$110$	−642.090	−0.556553
$111$	−1602.63	−1.37041
$112$	0	0
$113$	−884.002	−0.735929	−0.367964	−	0.929840i	$-0.619945\pi$
$113$	−884.002	−0.735929	−0.367964	+	0.929840i	$0.619945\pi$
$114$	2936.70	2.41269
$115$	−847.697	−0.687375
$116$	−3901.82	−3.12306
$117$	44.4541	0.0351263
$118$	−1169.04	−0.912022
$119$	0	0
$120$	968.959	0.737112
$121$	−883.968	−0.664138
$122$	2772.63	2.05756
$123$	−1112.56	−0.815582
$124$	2788.85	2.01973
$125$	−1347.46	−0.964166
$126$	0	0
$127$	955.879	0.667879	0.333939	−	0.942595i	$-0.391622\pi$
$127$	955.879	0.667879	0.333939	+	0.942595i	$0.391622\pi$
$128$	2587.20	1.78655
$129$	592.228	0.404207
$130$	−967.173	−0.652513
$131$	3.25308	0.00216964	0.00108482	−	0.999999i	$-0.499655\pi$
$131$	3.25308	0.00216964	0.00108482	+	0.999999i	$0.499655\pi$
$132$	−1575.94	−1.03915
$133$	0	0
$134$	−3324.75	−2.14339
$135$	883.640	0.563345
$136$	−1180.80	−0.744509
$137$	2146.59	1.33865	0.669327	−	0.742968i	$-0.266582\pi$
$137$	2146.59	1.33865	0.669327	+	0.742968i	$0.266582\pi$
$138$	−3270.54	−2.01744
$139$	−1895.33	−1.15654	−0.578272	−	0.815844i	$-0.696273\pi$
$139$	−1895.33	−1.15654	−0.578272	+	0.815844i	$0.696273\pi$
$140$	0	0
$141$	1721.79	1.02837
$142$	639.668	0.378027
$143$	673.360	0.393771
$144$	27.5703	0.0159551
$145$	−1806.60	−1.03469
$146$	3089.78	1.75145
$147$	0	0
$148$	4206.77	2.33645
$149$	2826.97	1.55432	0.777161	−	0.629301i	$-0.216659\pi$
$149$	2826.97	1.55432	0.777161	+	0.629301i	$0.216659\pi$
$150$	−2075.32	−1.12966
$151$	2919.02	1.57315	0.786577	−	0.617492i	$-0.211851\pi$
$151$	2919.02	1.57315	0.786577	+	0.617492i	$0.211851\pi$
$152$	−3299.77	−1.76083
$153$	58.7045	0.0310194
$154$	0	0
$155$	1291.28	0.669148
$156$	−2373.82	−1.21832
$157$	934.198	0.474886	0.237443	−	0.971401i	$-0.423691\pi$
$157$	934.198	0.474886	0.237443	+	0.971401i	$0.423691\pi$
$158$	5340.10	2.68883
$159$	537.133	0.267908
$160$	854.843	0.422383
$161$	0	0
$162$	3585.93	1.73912
$163$	−2324.46	−1.11697	−0.558483	−	0.829516i	$-0.688617\pi$
$163$	−2324.46	−1.11697	−0.558483	+	0.829516i	$0.688617\pi$
$164$	2920.39	1.39051
$165$	−729.683	−0.344277
$166$	6252.02	2.92320
$167$	−41.2259	−0.0191027	−0.00955137	−	0.999954i	$-0.503040\pi$
$167$	−41.2259	−0.0191027	−0.00955137	+	0.999954i	$0.503040\pi$
$168$	0	0
$169$	−1182.72	−0.538336
$170$	−1277.21	−0.576223
$171$	164.050	0.0733639
$172$	−1554.55	−0.689146
$173$	84.8534	0.0372907	0.0186453	−	0.999826i	$-0.494065\pi$
$173$	84.8534	0.0372907	0.0186453	+	0.999826i	$0.494065\pi$
$174$	−6970.12	−3.03680
$175$	0	0
$176$	417.617	0.178858
$177$	−1328.52	−0.564166
$178$	2883.96	1.21439
$179$	1545.26	0.645243	0.322622	−	0.946528i	$-0.395436\pi$
$179$	1545.26	0.645243	0.322622	+	0.946528i	$0.395436\pi$
$180$	126.449	0.0523606
$181$	2331.86	0.957602	0.478801	−	0.877924i	$-0.341072\pi$
$181$	2331.86	0.957602	0.478801	+	0.877924i	$0.341072\pi$
$182$	0	0
$183$	3150.87	1.27278
$184$	3674.88	1.47237
$185$	1947.80	0.774080
$186$	4981.94	1.96394
$187$	889.216	0.347732
$188$	−4519.55	−1.75331
$189$	0	0
$190$	−3569.19	−1.36282
$191$	2475.43	0.937780	0.468890	−	0.883257i	$-0.344654\pi$
$191$	2475.43	0.937780	0.468890	+	0.883257i	$0.344654\pi$
$192$	4140.13	1.55619
$193$	3661.19	1.36548	0.682741	−	0.730660i	$-0.260788\pi$
$193$	3661.19	1.36548	0.682741	+	0.730660i	$0.260788\pi$
$194$	−1032.26	−0.382022
$195$	−1099.11	−0.403637
$196$	0	0
$197$	−796.734	−0.288147	−0.144073	−	0.989567i	$-0.546020\pi$
$197$	−796.734	−0.288147	−0.144073	+	0.989567i	$0.546020\pi$
$198$	−138.386	−0.0496700
$199$	1572.16	0.560038	0.280019	−	0.959994i	$-0.409659\pi$
$199$	1572.16	0.560038	0.280019	+	0.959994i	$0.409659\pi$
$200$	2331.90	0.824450
$201$	−3778.31	−1.32588
$202$	−1334.31	−0.464762
$203$	0	0
$204$	−3134.78	−1.07588
$205$	1352.18	0.460686
$206$	4669.89	1.57945
$207$	−182.699	−0.0613453
$208$	629.052	0.209697
$209$	2484.92	0.822419
$210$	0	0
$211$	−362.314	−0.118212	−0.0591059	−	0.998252i	$-0.518825\pi$
$211$	−362.314	−0.118212	−0.0591059	+	0.998252i	$0.518825\pi$
$212$	−1409.93	−0.456765
$213$	726.931	0.233843
$214$	−2903.16	−0.927364
$215$	−719.778	−0.228319
$216$	−3830.70	−1.20670
$217$	0	0
$218$	3575.87	1.11096
$219$	3511.29	1.08343
$220$	1915.36	0.586970
$221$	1339.42	0.407687
$222$	7514.89	2.27192
$223$	3125.00	0.938411	0.469206	−	0.883089i	$-0.344540\pi$
$223$	3125.00	0.938411	0.469206	+	0.883089i	$0.344540\pi$
$224$	0	0
$225$	−115.932	−0.0343501
$226$	4145.17	1.22006
$227$	3237.14	0.946505	0.473253	−	0.880927i	$-0.343080\pi$
$227$	3237.14	0.946505	0.473253	+	0.880927i	$0.343080\pi$
$228$	−8760.18	−2.54455
$229$	−748.859	−0.216096	−0.108048	−	0.994146i	$-0.534460\pi$
$229$	−748.859	−0.216096	−0.108048	+	0.994146i	$0.534460\pi$
$230$	3974.93	1.13956
$231$	0	0
$232$	7831.86	2.21632
$233$	−4682.57	−1.31659	−0.658295	−	0.752760i	$-0.728722\pi$
$233$	−4682.57	−1.31659	−0.658295	+	0.752760i	$0.728722\pi$
$234$	−208.449	−0.0582340
$235$	−2092.62	−0.580882
$236$	3487.24	0.961865
$237$	6068.60	1.66328
$238$	0	0
$239$	−4483.39	−1.21342	−0.606708	−	0.794925i	$-0.707510\pi$
$239$	−4483.39	−1.21342	−0.606708	+	0.794925i	$0.707510\pi$
$240$	−681.669	−0.183340
$241$	3064.85	0.819189	0.409595	−	0.912268i	$-0.365670\pi$
$241$	3064.85	0.819189	0.409595	+	0.912268i	$0.365670\pi$
$242$	4145.01	1.10104
$243$	391.274	0.103293
$244$	−8270.77	−2.17001
$245$	0	0
$246$	5216.92	1.35211
$247$	3743.01	0.964219
$248$	−5597.87	−1.43333
$249$	7104.92	1.80826
$250$	6318.38	1.59844
$251$	−7317.96	−1.84026	−0.920130	−	0.391612i	$-0.871918\pi$
$251$	−7317.96	−1.84026	−0.920130	+	0.391612i	$0.871918\pi$
$252$	0	0
$253$	−2767.40	−0.687688
$254$	−4482.21	−1.10724
$255$	−1451.45	−0.356445
$256$	−5916.11	−1.44436
$257$	5477.60	1.32951	0.664754	−	0.747062i	$-0.268536\pi$
$257$	5477.60	1.32951	0.664754	+	0.747062i	$0.268536\pi$
$258$	−2777.01	−0.670113
$259$	0	0
$260$	2885.08	0.688174
$261$	−389.366	−0.0923416
$262$	−15.2540	−0.00359693
$263$	−659.163	−0.154547	−0.0772733	−	0.997010i	$-0.524621\pi$
$263$	−659.163	−0.154547	−0.0772733	+	0.997010i	$0.524621\pi$
$264$	3163.28	0.737448
$265$	−652.817	−0.151329
$266$	0	0
$267$	3277.39	0.751210
$268$	9917.75	2.26053
$269$	−5502.97	−1.24729	−0.623647	−	0.781706i	$-0.714350\pi$
$269$	−5502.97	−1.24729	−0.623647	+	0.781706i	$0.714350\pi$
$270$	−4143.47	−0.933939
$271$	1662.99	0.372766	0.186383	−	0.982477i	$-0.440323\pi$
$271$	1662.99	0.372766	0.186383	+	0.982477i	$0.440323\pi$
$272$	830.704	0.185180
$273$	0	0
$274$	−10065.6	−2.21928
$275$	−1756.05	−0.385069
$276$	9756.03	2.12770
$277$	−2638.10	−0.572232	−0.286116	−	0.958195i	$-0.592364\pi$
$277$	−2638.10	−0.572232	−0.286116	+	0.958195i	$0.592364\pi$
$278$	8887.37	1.91737
$279$	278.302	0.0597186
$280$	0	0
$281$	2783.26	0.590873	0.295436	−	0.955362i	$-0.404535\pi$
$281$	2783.26	0.590873	0.295436	+	0.955362i	$0.404535\pi$
$282$	−8073.62	−1.70488
$283$	−510.143	−0.107155	−0.0535775	−	0.998564i	$-0.517062\pi$
$283$	−510.143	−0.107155	−0.0535775	+	0.998564i	$0.517062\pi$
$284$	−1908.13	−0.398686
$285$	−4056.09	−0.843025
$286$	−3157.45	−0.652810
$287$	0	0
$288$	184.239	0.0376958
$289$	−3144.21	−0.639979
$290$	8471.31	1.71535
$291$	−1173.08	−0.236314
$292$	−9216.84	−1.84717
$293$	−9366.69	−1.86760	−0.933802	−	0.357791i	$-0.883530\pi$
$293$	−9366.69	−1.86760	−0.933802	+	0.357791i	$0.883530\pi$
$294$	0	0
$295$	1614.64	0.318672
$296$	−8443.97	−1.65809
$297$	2884.74	0.563602
$298$	−13255.9	−2.57683
$299$	−4168.51	−0.806258
$300$	6190.68	1.19140
$301$	0	0
$302$	−13687.5	−2.60805
$303$	−1516.34	−0.287496
$304$	2321.41	0.437967
$305$	−3829.49	−0.718937
$306$	−275.271	−0.0514254
$307$	7202.58	1.33900	0.669500	−	0.742812i	$-0.266509\pi$
$307$	7202.58	1.33900	0.669500	+	0.742812i	$0.266509\pi$
$308$	0	0
$309$	5306.96	0.977030
$310$	−6054.92	−1.10934
$311$	−6872.43	−1.25305	−0.626527	−	0.779400i	$-0.715524\pi$
$311$	−6872.43	−1.25305	−0.626527	+	0.779400i	$0.715524\pi$
$312$	4764.81	0.864597
$313$	7268.37	1.31256	0.656282	−	0.754515i	$-0.272128\pi$
$313$	7268.37	1.31256	0.656282	+	0.754515i	$0.272128\pi$
$314$	−4380.54	−0.787287
$315$	0	0
$316$	−15929.6	−2.83578
$317$	1514.87	0.268403	0.134201	−	0.990954i	$-0.457153\pi$
$317$	1514.87	0.268403	0.134201	+	0.990954i	$0.457153\pi$
$318$	−2518.66	−0.444150
$319$	−5897.85	−1.03516
$320$	−5031.81	−0.879022
$321$	−3299.21	−0.573656
$322$	0	0
$323$	4942.89	0.851485
$324$	−10696.9	−1.83417
$325$	−2645.13	−0.451462
$326$	10899.6	1.85176
$327$	4063.69	0.687225
$328$	−5861.90	−0.986797
$329$	0	0
$330$	3421.55	0.570758
$331$	−11387.3	−1.89095	−0.945474	−	0.325697i	$-0.894401\pi$
$331$	−11387.3	−1.89095	−0.945474	+	0.325697i	$0.894401\pi$
$332$	−18649.8	−3.08296
$333$	419.797	0.0690834
$334$	193.312	0.0316694
$335$	4592.06	0.748929
$336$	0	0
$337$	1299.77	0.210099	0.105049	−	0.994467i	$-0.466500\pi$
$337$	1299.77	0.210099	0.105049	+	0.994467i	$0.466500\pi$
$338$	5545.91	0.892478
$339$	4710.65	0.754712
$340$	3809.94	0.607714
$341$	4215.53	0.669453
$342$	−769.246	−0.121626
$343$	0	0
$344$	3120.34	0.489062
$345$	4517.18	0.704919
$346$	−397.886	−0.0618222
$347$	3713.81	0.574546	0.287273	−	0.957849i	$-0.407251\pi$
$347$	3713.81	0.574546	0.287273	+	0.957849i	$0.407251\pi$
$348$	20791.9	3.20277
$349$	6606.70	1.01332	0.506659	−	0.862146i	$-0.330880\pi$
$349$	6606.70	1.01332	0.506659	+	0.862146i	$0.330880\pi$
$350$	0	0
$351$	4345.26	0.660777
$352$	2790.73	0.422575
$353$	−2368.60	−0.357133	−0.178566	−	0.983928i	$-0.557146\pi$
$353$	−2368.60	−0.357133	−0.178566	+	0.983928i	$0.557146\pi$
$354$	6229.53	0.935299
$355$	−883.494	−0.132087
$356$	−8602.88	−1.28076
$357$	0	0
$358$	−7245.89	−1.06971
$359$	−3546.84	−0.521435	−0.260718	−	0.965415i	$-0.583959\pi$
$359$	−3546.84	−0.521435	−0.260718	+	0.965415i	$0.583959\pi$
$360$	−253.812	−0.0371585
$361$	6953.94	1.01384
$362$	−10934.3	−1.58755
$363$	4710.46	0.681089
$364$	0	0
$365$	−4267.53	−0.611980
$366$	−14774.7	−2.11007
$367$	9249.16	1.31554	0.657769	−	0.753220i	$-0.271500\pi$
$367$	9249.16	1.31554	0.657769	+	0.753220i	$0.271500\pi$
$368$	−2585.31	−0.366218
$369$	291.428	0.0411142
$370$	−9133.40	−1.28330
$371$	0	0
$372$	−14861.1	−2.07128
$373$	5510.48	0.764938	0.382469	−	0.923968i	$-0.375074\pi$
$373$	5510.48	0.764938	0.382469	+	0.923968i	$0.375074\pi$
$374$	−4169.61	−0.576486
$375$	7180.32	0.988774
$376$	9071.78	1.24426
$377$	−8883.87	−1.21364
$378$	0	0
$379$	−4513.10	−0.611668	−0.305834	−	0.952085i	$-0.598935\pi$
$379$	−4513.10	−0.611668	−0.305834	+	0.952085i	$0.598935\pi$
$380$	10646.9	1.43730
$381$	−5093.66	−0.684925
$382$	−11607.5	−1.55469
$383$	1137.44	0.151751	0.0758754	−	0.997117i	$-0.475825\pi$
$383$	1137.44	0.151751	0.0758754	+	0.997117i	$0.475825\pi$
$384$	−13786.6	−1.83215
$385$	0	0
$386$	−17167.7	−2.26376
$387$	−155.130	−0.0203764
$388$	3079.25	0.402900
$389$	2157.42	0.281196	0.140598	−	0.990067i	$-0.455097\pi$
$389$	2157.42	0.281196	0.140598	+	0.990067i	$0.455097\pi$
$390$	5153.85	0.669167
$391$	−5504.79	−0.711993
$392$	0	0
$393$	−17.3349	−0.00222502
$394$	3735.96	0.477703
$395$	−7375.62	−0.939513
$396$	412.806	0.0523845
$397$	−903.215	−0.114184	−0.0570920	−	0.998369i	$-0.518183\pi$
$397$	−903.215	−0.114184	−0.0570920	+	0.998369i	$0.518183\pi$
$398$	−7372.01	−0.928456
$399$	0	0
$400$	−1640.50	−0.205063
$401$	−9226.94	−1.14906	−0.574528	−	0.818485i	$-0.694814\pi$
$401$	−9226.94	−1.14906	−0.574528	+	0.818485i	$0.694814\pi$
$402$	17716.9	2.19810
$403$	6349.80	0.784879
$404$	3980.26	0.490162
$405$	−4952.80	−0.607671
$406$	0	0
$407$	6358.81	0.774433
$408$	6292.24	0.763511
$409$	−4970.07	−0.600866	−0.300433	−	0.953803i	$-0.597131\pi$
$409$	−4970.07	−0.600866	−0.300433	+	0.953803i	$0.597131\pi$
$410$	−6340.51	−0.763745
$411$	−11438.7	−1.37282
$412$	−13930.3	−1.66577
$413$	0	0
$414$	856.693	0.101701
$415$	−8635.13	−1.02140
$416$	4203.65	0.495435
$417$	10099.8	1.18606
$418$	−11652.0	−1.36344
$419$	4834.76	0.563707	0.281854	−	0.959457i	$-0.409051\pi$
$419$	4834.76	0.563707	0.281854	+	0.959457i	$0.409051\pi$
$420$	0	0
$421$	−3414.21	−0.395245	−0.197623	−	0.980278i	$-0.563322\pi$
$421$	−3414.21	−0.395245	−0.197623	+	0.980278i	$0.563322\pi$
$422$	1698.92	0.195977
$423$	−451.009	−0.0518412
$424$	2830.05	0.324150
$425$	−3493.06	−0.398678
$426$	−3408.65	−0.387675
$427$	0	0
$428$	8660.14	0.978046
$429$	−3588.18	−0.403821
$430$	3375.11	0.378517
$431$	3049.01	0.340755	0.170378	−	0.985379i	$-0.445501\pi$
$431$	3049.01	0.340755	0.170378	+	0.985379i	$0.445501\pi$
$432$	2694.92	0.300138
$433$	12636.4	1.40247	0.701233	−	0.712933i	$-0.252633\pi$
$433$	12636.4	1.40247	0.701233	+	0.712933i	$0.252633\pi$
$434$	0	0
$435$	9626.96	1.06110
$436$	−10666.9	−1.17167
$437$	−15383.2	−1.68393
$438$	−16464.8	−1.79616
$439$	−7744.03	−0.841919	−0.420960	−	0.907079i	$-0.638307\pi$
$439$	−7744.03	−0.841919	−0.420960	+	0.907079i	$0.638307\pi$
$440$	−3844.57	−0.416551
$441$	0	0
$442$	−6280.65	−0.675882
$443$	−2284.35	−0.244995	−0.122497	−	0.992469i	$-0.539090\pi$
$443$	−2284.35	−0.244995	−0.122497	+	0.992469i	$0.539090\pi$
$444$	−22416.9	−2.39608
$445$	−3983.26	−0.424325
$446$	−14653.4	−1.55574
$447$	−15064.3	−1.59399
$448$	0	0
$449$	4567.81	0.480107	0.240054	−	0.970760i	$-0.422835\pi$
$449$	4567.81	0.480107	0.240054	+	0.970760i	$0.422835\pi$
$450$	543.614	0.0569472
$451$	4414.36	0.460896
$452$	−12365.1	−1.28673
$453$	−15554.8	−1.61331
$454$	−15179.3	−1.56916
$455$	0	0
$456$	17583.7	1.80578
$457$	−818.511	−0.0837819	−0.0418910	−	0.999122i	$-0.513338\pi$
$457$	−818.511	−0.0837819	−0.0418910	+	0.999122i	$0.513338\pi$
$458$	3511.47	0.358254
$459$	5738.20	0.583521
$460$	−11857.2	−1.20184
$461$	−389.420	−0.0393430	−0.0196715	−	0.999806i	$-0.506262\pi$
$461$	−389.420	−0.0393430	−0.0196715	+	0.999806i	$0.506262\pi$
$462$	0	0
$463$	11594.1	1.16376	0.581882	−	0.813274i	$-0.302317\pi$
$463$	11594.1	1.16376	0.581882	+	0.813274i	$0.302317\pi$
$464$	−5509.77	−0.551260
$465$	−6880.93	−0.686227
$466$	21957.0	2.18270
$467$	−17719.5	−1.75580	−0.877902	−	0.478840i	$-0.841057\pi$
$467$	−17719.5	−1.75580	−0.877902	+	0.478840i	$0.841057\pi$
$468$	621.805	0.0614166
$469$	0	0
$470$	9812.47	0.963012
$471$	−4978.13	−0.487007
$472$	−6999.71	−0.682601
$473$	−2349.80	−0.228423
$474$	−28456.2	−2.75746
$475$	−9761.39	−0.942912
$476$	0	0
$477$	−140.698	−0.0135055
$478$	21023.0	2.01166
$479$	−6074.21	−0.579411	−0.289705	−	0.957116i	$-0.593557\pi$
$479$	−6074.21	−0.579411	−0.289705	+	0.957116i	$0.593557\pi$
$480$	−4555.26	−0.433163
$481$	9578.21	0.907960
$482$	−14371.4	−1.35809
$483$	0	0
$484$	−12364.6	−1.16121
$485$	1425.74	0.133483
$486$	−1834.72	−0.171244
$487$	−15197.0	−1.41405	−0.707026	−	0.707187i	$-0.749964\pi$
$487$	−15197.0	−1.41405	−0.707026	+	0.707187i	$0.749964\pi$
$488$	16601.4	1.53998
$489$	12386.5	1.14548
$490$	0	0
$491$	−5569.88	−0.511946	−0.255973	−	0.966684i	$-0.582396\pi$
$491$	−5569.88	−0.511946	−0.255973	+	0.966684i	$0.582396\pi$
$492$	−15562.1	−1.42600
$493$	−11731.7	−1.07175
$494$	−17551.3	−1.59852
$495$	191.135	0.0173553
$496$	3938.14	0.356507
$497$	0	0
$498$	−33315.6	−2.99781
$499$	13146.9	1.17943	0.589716	−	0.807611i	$-0.299240\pi$
$499$	13146.9	1.17943	0.589716	+	0.807611i	$0.299240\pi$
$500$	−18847.7	−1.68579
$501$	219.684	0.0195903
$502$	34314.6	3.05087
$503$	6555.64	0.581116	0.290558	−	0.956857i	$-0.406159\pi$
$503$	6555.64	0.581116	0.290558	+	0.956857i	$0.406159\pi$
$504$	0	0
$505$	1842.92	0.162394
$506$	12976.6	1.14008
$507$	6302.47	0.552076
$508$	13370.4	1.16775
$509$	−21829.4	−1.90093	−0.950464	−	0.310836i	$-0.899391\pi$
$509$	−21829.4	−1.90093	−0.950464	+	0.310836i	$0.899391\pi$
$510$	6805.99	0.590930
$511$	0	0
$512$	7043.59	0.607979
$513$	16035.4	1.38008
$514$	−25685.0	−2.20412
$515$	−6449.94	−0.551880
$516$	8283.84	0.706736
$517$	−6831.59	−0.581147
$518$	0	0
$519$	−452.165	−0.0382425
$520$	−5791.03	−0.488372
$521$	−10320.1	−0.867818	−0.433909	−	0.900957i	$-0.642866\pi$
$521$	−10320.1	−0.867818	−0.433909	+	0.900957i	$0.642866\pi$
$522$	1825.77	0.153088
$523$	−6261.51	−0.523512	−0.261756	−	0.965134i	$-0.584302\pi$
$523$	−6261.51	−0.523512	−0.261756	+	0.965134i	$0.584302\pi$
$524$	45.5028	0.00379351
$525$	0	0
$526$	3090.88	0.256214
$527$	8385.32	0.693113
$528$	−2225.39	−0.183423
$529$	4964.92	0.408065
$530$	3061.12	0.250880
$531$	347.995	0.0284401
$532$	0	0
$533$	6649.30	0.540362
$534$	−15368.0	−1.24539
$535$	4009.77	0.324033
$536$	−19907.2	−1.60422
$537$	−8234.37	−0.661712
$538$	25803.9	2.06782
$539$	0	0
$540$	12360.0	0.984980
$541$	7179.23	0.570535	0.285267	−	0.958448i	$-0.407918\pi$
$541$	7179.23	0.570535	0.285267	+	0.958448i	$0.407918\pi$
$542$	−7797.92	−0.617988
$543$	−12426.0	−0.982042
$544$	5551.19	0.437510
$545$	−4938.91	−0.388183
$546$	0	0
$547$	4273.44	0.334039	0.167019	−	0.985954i	$-0.446586\pi$
$547$	4273.44	0.334039	0.167019	+	0.985954i	$0.446586\pi$
$548$	30025.6	2.34057
$549$	−825.347	−0.0641620
$550$	8234.30	0.638385
$551$	−32784.4	−2.53478
$552$	−19582.6	−1.50995
$553$	0	0
$554$	12370.3	0.948672
$555$	−10379.4	−0.793837
$556$	−26511.1	−2.02216
$557$	−8559.41	−0.651120	−0.325560	−	0.945521i	$-0.605553\pi$
$557$	−8559.41	−0.651120	−0.325560	+	0.945521i	$0.605553\pi$
$558$	−1304.98	−0.0990041
$559$	−3539.48	−0.267807
$560$	0	0
$561$	−4738.43	−0.356607
$562$	−13051.0	−0.979575
$563$	−20029.3	−1.49935	−0.749675	−	0.661806i	$-0.769790\pi$
$563$	−20029.3	−1.49935	−0.749675	+	0.661806i	$0.769790\pi$
$564$	24083.6	1.79806
$565$	−5725.20	−0.426303
$566$	2392.11	0.177646
$567$	0	0
$568$	3830.07	0.282933
$569$	11839.1	0.872271	0.436136	−	0.899881i	$-0.356347\pi$
$569$	11839.1	0.872271	0.436136	+	0.899881i	$0.356347\pi$
$570$	19019.4	1.39760
$571$	−10201.9	−0.747702	−0.373851	−	0.927489i	$-0.621963\pi$
$571$	−10201.9	−0.747702	−0.373851	+	0.927489i	$0.621963\pi$
$572$	9418.68	0.688488
$573$	−13191.0	−0.961715
$574$	0	0
$575$	10871.1	0.788442
$576$	−1084.48	−0.0784489
$577$	2169.83	0.156553	0.0782767	−	0.996932i	$-0.475058\pi$
$577$	2169.83	0.156553	0.0782767	+	0.996932i	$0.475058\pi$
$578$	14743.5	1.06098
$579$	−19509.7	−1.40033
$580$	−25270.0	−1.80910
$581$	0	0
$582$	5500.70	0.391772
$583$	−2131.20	−0.151398
$584$	18500.4	1.31087
$585$	287.905	0.0203477
$586$	43921.3	3.09620
$587$	8900.38	0.625823	0.312911	−	0.949782i	$-0.398696\pi$
$587$	8900.38	0.625823	0.312911	+	0.949782i	$0.398696\pi$
$588$	0	0
$589$	23432.9	1.63928
$590$	−7571.21	−0.528308
$591$	4245.62	0.295501
$592$	5940.39	0.412413
$593$	−293.447	−0.0203211	−0.0101606	−	0.999948i	$-0.503234\pi$
$593$	−293.447	−0.0203211	−0.0101606	+	0.999948i	$0.503234\pi$
$594$	−13526.8	−0.934365
$595$	0	0
$596$	39542.4	2.71765
$597$	−8377.69	−0.574332
$598$	19546.5	1.33665
$599$	−14532.8	−0.991310	−0.495655	−	0.868519i	$-0.665072\pi$
$599$	−14532.8	−0.991310	−0.495655	+	0.868519i	$0.665072\pi$
$600$	−12426.1	−0.845492
$601$	−4059.10	−0.275498	−0.137749	−	0.990467i	$-0.543987\pi$
$601$	−4059.10	−0.275498	−0.137749	+	0.990467i	$0.543987\pi$
$602$	0	0
$603$	989.701	0.0668387
$604$	40830.0	2.75058
$605$	−5724.98	−0.384716
$606$	7110.25	0.476624
$607$	−2172.84	−0.145293	−0.0726466	−	0.997358i	$-0.523145\pi$
$607$	−2172.84	−0.145293	−0.0726466	+	0.997358i	$0.523145\pi$
$608$	15512.9	1.03475
$609$	0	0
$610$	17956.8	1.19189
$611$	−10290.3	−0.681347
$612$	821.134	0.0542359
$613$	−12544.8	−0.826554	−0.413277	−	0.910605i	$-0.635616\pi$
$613$	−12544.8	−0.826554	−0.413277	+	0.910605i	$0.635616\pi$
$614$	−33773.6	−2.21985
$615$	−7205.48	−0.472444
$616$	0	0
$617$	2709.14	0.176768	0.0883841	−	0.996086i	$-0.471830\pi$
$617$	2709.14	0.176768	0.0883841	+	0.996086i	$0.471830\pi$
$618$	−24884.8	−1.61976
$619$	−15311.0	−0.994185	−0.497092	−	0.867698i	$-0.665599\pi$
$619$	−15311.0	−0.994185	−0.497092	+	0.867698i	$0.665599\pi$
$620$	18061.9	1.16997
$621$	−17858.3	−1.15399
$622$	32225.5	2.07737
$623$	0	0
$624$	−3352.08	−0.215049
$625$	1655.16	0.105930
$626$	−34082.1	−2.17603
$627$	−13241.6	−0.843410
$628$	13067.2	0.830314
$629$	12648.6	0.801803
$630$	0	0
$631$	−23857.7	−1.50517	−0.752583	−	0.658497i	$-0.771192\pi$
$631$	−23857.7	−1.50517	−0.752583	+	0.658497i	$0.771192\pi$
$632$	31974.3	2.01245
$633$	1930.69	0.121229
$634$	−7103.37	−0.444970
$635$	6190.71	0.386883
$636$	7513.19	0.468423
$637$	0	0
$638$	27655.6	1.71614
$639$	−190.414	−0.0117882
$640$	16755.9	1.03490
$641$	8715.48	0.537037	0.268518	−	0.963275i	$-0.413466\pi$
$641$	8715.48	0.537037	0.268518	+	0.963275i	$0.413466\pi$
$642$	15470.3	0.951033
$643$	21538.5	1.32099	0.660493	−	0.750832i	$-0.270347\pi$
$643$	21538.5	1.32099	0.660493	+	0.750832i	$0.270347\pi$
$644$	0	0
$645$	3835.54	0.234146
$646$	−23177.6	−1.41163
$647$	−30452.0	−1.85037	−0.925187	−	0.379512i	$-0.876092\pi$
$647$	−30452.0	−1.85037	−0.925187	+	0.379512i	$0.876092\pi$
$648$	21471.1	1.30164
$649$	5271.19	0.318817
$650$	12403.2	0.748454
$651$	0	0
$652$	−32513.6	−1.95296
$653$	−7177.73	−0.430147	−0.215074	−	0.976598i	$-0.568999\pi$
$653$	−7177.73	−0.430147	−0.215074	+	0.976598i	$0.568999\pi$
$654$	−19055.0	−1.13931
$655$	21.0684	0.00125681
$656$	4123.89	0.245443
$657$	−919.757	−0.0546166
$658$	0	0
$659$	−13228.9	−0.781979	−0.390989	−	0.920395i	$-0.627867\pi$
$659$	−13228.9	−0.781979	−0.390989	+	0.920395i	$0.627867\pi$
$660$	−10206.5	−0.601951
$661$	19538.0	1.14968	0.574841	−	0.818265i	$-0.305064\pi$
$661$	19538.0	1.14968	0.574841	+	0.818265i	$0.305064\pi$
$662$	53396.2	3.13490
$663$	−7137.45	−0.418093
$664$	37434.5	2.18786
$665$	0	0
$666$	−1968.47	−0.114529
$667$	36511.3	2.11953
$668$	−576.651	−0.0334001
$669$	−16652.4	−0.962362
$670$	−21532.6	−1.24161
$671$	−12501.8	−0.719265
$672$	0	0
$673$	16106.1	0.922506	0.461253	−	0.887269i	$-0.347400\pi$
$673$	16106.1	0.922506	0.461253	+	0.887269i	$0.347400\pi$
$674$	−6094.76	−0.348311
$675$	−11332.0	−0.646176
$676$	−16543.5	−0.941253
$677$	32970.9	1.87175	0.935875	−	0.352333i	$-0.114612\pi$
$677$	32970.9	1.87175	0.935875	+	0.352333i	$0.114612\pi$
$678$	−22088.7	−1.25119
$679$	0	0
$680$	−7647.43	−0.431273
$681$	−17250.0	−0.970663
$682$	−19767.0	−1.10985
$683$	−25187.3	−1.41108	−0.705538	−	0.708672i	$-0.749295\pi$
$683$	−25187.3	−1.41108	−0.705538	+	0.708672i	$0.749295\pi$
$684$	2294.67	0.128273
$685$	13902.3	0.775445
$686$	0	0
$687$	3990.50	0.221611
$688$	−2195.18	−0.121643
$689$	−3210.20	−0.177502
$690$	−21181.5	−1.16865
$691$	−5325.02	−0.293160	−0.146580	−	0.989199i	$-0.546827\pi$
$691$	−5325.02	−0.293160	−0.146580	+	0.989199i	$0.546827\pi$
$692$	1186.89	0.0652008
$693$	0	0
$694$	−17414.4	−0.952509
$695$	−12275.0	−0.669953
$696$	−41734.2	−2.27289
$697$	8780.83	0.477185
$698$	−30979.4	−1.67993
$699$	24952.4	1.35019
$700$	0	0
$701$	−12582.0	−0.677909	−0.338954	−	0.940803i	$-0.610073\pi$
$701$	−12582.0	−0.677909	−0.338954	+	0.940803i	$0.610073\pi$
$702$	−20375.3	−1.09547
$703$	35346.7	1.89634
$704$	−16426.9	−0.879423
$705$	11151.1	0.595708
$706$	11106.6	0.592071
$707$	0	0
$708$	−18582.7	−0.986415
$709$	32781.9	1.73646	0.868229	−	0.496164i	$-0.165258\pi$
$709$	32781.9	1.73646	0.868229	+	0.496164i	$0.165258\pi$
$710$	4142.78	0.218980
$711$	−1589.62	−0.0838475
$712$	17268.0	0.908911
$713$	−26096.7	−1.37073
$714$	0	0
$715$	4360.99	0.228100
$716$	21614.5	1.12817
$717$	23891.0	1.24439
$718$	16631.5	0.864459
$719$	27245.1	1.41317	0.706587	−	0.707626i	$-0.250234\pi$
$719$	27245.1	1.41317	0.706587	+	0.707626i	$0.250234\pi$
$720$	178.558	0.00924232
$721$	0	0
$722$	−32607.7	−1.68079
$723$	−16331.9	−0.840097
$724$	32617.1	1.67432
$725$	23168.2	1.18682
$726$	−22087.8	−1.12914
$727$	36340.4	1.85391	0.926954	−	0.375176i	$-0.122418\pi$
$727$	36340.4	1.85391	0.926954	+	0.375176i	$0.122418\pi$
$728$	0	0
$729$	18562.9	0.943095
$730$	20010.9	1.01457
$731$	−4674.11	−0.236496
$732$	44073.1	2.22539
$733$	−28092.5	−1.41558	−0.707791	−	0.706422i	$-0.750308\pi$
$733$	−28092.5	−1.41558	−0.707791	+	0.706422i	$0.750308\pi$
$734$	−43370.2	−2.18096
$735$	0	0
$736$	−17276.3	−0.865237
$737$	14991.3	0.749271
$738$	−1366.53	−0.0681610
$739$	2555.89	0.127226	0.0636128	−	0.997975i	$-0.479738\pi$
$739$	2555.89	0.127226	0.0636128	+	0.997975i	$0.479738\pi$
$740$	27245.0	1.35344
$741$	−19945.7	−0.988828
$742$	0	0
$743$	−27444.6	−1.35511	−0.677554	−	0.735473i	$-0.736960\pi$
$743$	−27444.6	−1.35511	−0.677554	+	0.735473i	$0.736960\pi$
$744$	29829.8	1.46991
$745$	18308.7	0.900375
$746$	−25839.1	−1.26815
$747$	−1861.08	−0.0911558
$748$	12438.0	0.607991
$749$	0	0
$750$	−33669.2	−1.63923
$751$	−24064.3	−1.16927	−0.584634	−	0.811297i	$-0.698762\pi$
$751$	−24064.3	−1.16927	−0.584634	+	0.811297i	$0.698762\pi$
$752$	−6382.06	−0.309481
$753$	38995.7	1.88723
$754$	41657.3	2.01203
$755$	18904.9	0.911284
$756$	0	0
$757$	22786.9	1.09406	0.547032	−	0.837112i	$-0.315758\pi$
$757$	22786.9	1.09406	0.547032	+	0.837112i	$0.315758\pi$
$758$	21162.3	1.01405
$759$	14746.9	0.705240
$760$	−21370.8	−1.02000
$761$	3330.23	0.158634	0.0793171	−	0.996849i	$-0.474726\pi$
$761$	3330.23	0.158634	0.0793171	+	0.996849i	$0.474726\pi$
$762$	23884.7	1.13550
$763$	0	0
$764$	34625.3	1.63966
$765$	380.197	0.0179687
$766$	−5333.57	−0.251579
$767$	7939.94	0.373787
$768$	31525.6	1.48123
$769$	6199.52	0.290716	0.145358	−	0.989379i	$-0.453567\pi$
$769$	6199.52	0.290716	0.145358	+	0.989379i	$0.453567\pi$
$770$	0	0
$771$	−29188.9	−1.36344
$772$	51211.2	2.38748
$773$	−21143.6	−0.983809	−0.491904	−	0.870649i	$-0.663699\pi$
$773$	−21143.6	−0.983809	−0.491904	+	0.870649i	$0.663699\pi$
$774$	727.417	0.0337810
$775$	−16559.6	−0.767535
$776$	−6180.77	−0.285924
$777$	0	0
$778$	−10116.3	−0.466180
$779$	24538.1	1.12859
$780$	−15373.9	−0.705738
$781$	−2884.27	−0.132147
$782$	25812.5	1.18037
$783$	−38059.4	−1.73708
$784$	0	0
$785$	6050.29	0.275088
$786$	81.2851	0.00368873
$787$	−16818.1	−0.761754	−0.380877	−	0.924626i	$-0.624378\pi$
$787$	−16818.1	−0.761754	−0.380877	+	0.924626i	$0.624378\pi$
$788$	−11144.4	−0.503810
$789$	3512.53	0.158491
$790$	34584.9	1.55757
$791$	0	0
$792$	−828.598	−0.0371754
$793$	−18831.3	−0.843279
$794$	4235.26	0.189299
$795$	3478.71	0.155192
$796$	21990.7	0.979197
$797$	−13922.5	−0.618771	−0.309386	−	0.950937i	$-0.600123\pi$
$797$	−13922.5	−0.618771	−0.309386	+	0.950937i	$0.600123\pi$
$798$	0	0
$799$	−13589.1	−0.601685
$800$	−10962.7	−0.484487
$801$	−858.488	−0.0378692
$802$	43266.0	1.90496
$803$	−13931.9	−0.612259
$804$	−52849.5	−2.31823
$805$	0	0
$806$	−29774.8	−1.30121
$807$	29324.1	1.27913
$808$	−7989.32	−0.347850
$809$	−40562.2	−1.76278	−0.881392	−	0.472386i	$-0.843393\pi$
$809$	−40562.2	−1.76278	−0.881392	+	0.472386i	$0.843393\pi$
$810$	23224.1	1.00742
$811$	−20852.8	−0.902888	−0.451444	−	0.892300i	$-0.649091\pi$
$811$	−20852.8	−0.902888	−0.451444	+	0.892300i	$0.649091\pi$
$812$	0	0
$813$	−8861.71	−0.382280
$814$	−29817.0	−1.28389
$815$	−15054.2	−0.647027
$816$	−4426.63	−0.189906
$817$	−13061.8	−0.559334
$818$	23305.1	0.996143
$819$	0	0
$820$	18913.8	0.805485
$821$	−16344.6	−0.694801	−0.347400	−	0.937717i	$-0.612936\pi$
$821$	−16344.6	−0.694801	−0.347400	+	0.937717i	$0.612936\pi$
$822$	53637.1	2.27592
$823$	−23574.1	−0.998470	−0.499235	−	0.866467i	$-0.666386\pi$
$823$	−23574.1	−0.998470	−0.499235	+	0.866467i	$0.666386\pi$
$824$	27961.4	1.18214
$825$	9357.62	0.394897
$826$	0	0
$827$	7285.14	0.306323	0.153162	−	0.988201i	$-0.451055\pi$
$827$	7285.14	0.306323	0.153162	+	0.988201i	$0.451055\pi$
$828$	−2555.52	−0.107259
$829$	−40854.2	−1.71161	−0.855805	−	0.517299i	$-0.826937\pi$
$829$	−40854.2	−1.71161	−0.855805	+	0.517299i	$0.826937\pi$
$830$	40490.9	1.69333
$831$	14057.9	0.586837
$832$	−24743.7	−1.03105
$833$	0	0
$834$	−47358.8	−1.96631
$835$	−266.998	−0.0110657
$836$	34758.0	1.43796
$837$	27203.2	1.12339
$838$	−22670.6	−0.934539
$839$	−28359.2	−1.16695	−0.583473	−	0.812132i	$-0.698307\pi$
$839$	−28359.2	−1.16695	−0.583473	+	0.812132i	$0.698307\pi$
$840$	0	0
$841$	53423.4	2.19047
$842$	16009.5	0.655255
$843$	−14831.3	−0.605954
$844$	−5067.89	−0.206687
$845$	−7659.86	−0.311843
$846$	2114.83	0.0859447
$847$	0	0
$848$	−1990.96	−0.0806249
$849$	2718.44	0.109890
$850$	16379.3	0.660947
$851$	−39364.9	−1.58568
$852$	10168.0	0.408862
$853$	7006.23	0.281230	0.140615	−	0.990064i	$-0.455092\pi$
$853$	7006.23	0.281230	0.140615	+	0.990064i	$0.455092\pi$
$854$	0	0
$855$	1062.46	0.0424976
$856$	−17382.9	−0.694084
$857$	−9047.85	−0.360640	−0.180320	−	0.983608i	$-0.557713\pi$
$857$	−9047.85	−0.360640	−0.180320	+	0.983608i	$0.557713\pi$
$858$	16825.3	0.669472
$859$	19885.3	0.789844	0.394922	−	0.918715i	$-0.370772\pi$
$859$	19885.3	0.789844	0.394922	+	0.918715i	$0.370772\pi$
$860$	−10068.0	−0.399203
$861$	0	0
$862$	−14297.1	−0.564919
$863$	10935.0	0.431323	0.215662	−	0.976468i	$-0.430809\pi$
$863$	10935.0	0.431323	0.215662	+	0.976468i	$0.430809\pi$
$864$	18008.9	0.709114
$865$	549.550	0.0216014
$866$	−59253.3	−2.32507
$867$	16754.8	0.656313
$868$	0	0
$869$	−24078.5	−0.939941
$870$	−45141.7	−1.75913
$871$	22581.3	0.878459
$872$	21410.9	0.831495
$873$	307.281	0.0119128
$874$	72133.1	2.79169
$875$	0	0
$876$	49114.5	1.89432
$877$	17050.4	0.656499	0.328249	−	0.944591i	$-0.393541\pi$
$877$	17050.4	0.656499	0.328249	+	0.944591i	$0.393541\pi$
$878$	36312.5	1.39577
$879$	49913.0	1.91527
$880$	2704.68	0.103608
$881$	−31656.1	−1.21058	−0.605289	−	0.796006i	$-0.706943\pi$
$881$	−31656.1	−1.21058	−0.605289	+	0.796006i	$0.706943\pi$
$882$	0	0
$883$	−18707.4	−0.712971	−0.356486	−	0.934301i	$-0.616025\pi$
$883$	−18707.4	−0.712971	−0.356486	+	0.934301i	$0.616025\pi$
$884$	18735.2	0.712820
$885$	−8604.07	−0.326805
$886$	10711.5	0.406163
$887$	−44483.5	−1.68389	−0.841945	−	0.539564i	$-0.818589\pi$
$887$	−44483.5	−1.68389	−0.841945	+	0.539564i	$0.818589\pi$
$888$	44996.0	1.70041
$889$	0	0
$890$	18677.9	0.703464
$891$	−16169.0	−0.607948
$892$	43711.3	1.64076
$893$	−37974.8	−1.42304
$894$	70637.7	2.64259
$895$	10007.8	0.373771
$896$	0	0
$897$	22213.1	0.826837
$898$	−21418.9	−0.795943
$899$	−55616.9	−2.06332
$900$	−1621.60	−0.0600594
$901$	−4239.28	−0.156749
$902$	−20699.3	−0.764093
$903$	0	0
$904$	24819.6	0.913148
$905$	15102.2	0.554712
$906$	72937.9	2.67461
$907$	−36164.5	−1.32395	−0.661975	−	0.749526i	$-0.730281\pi$
$907$	−36164.5	−1.32395	−0.661975	+	0.749526i	$0.730281\pi$
$908$	45279.8	1.65492
$909$	397.194	0.0144929
$910$	0	0
$911$	8535.76	0.310431	0.155215	−	0.987881i	$-0.450393\pi$
$911$	8535.76	0.310431	0.155215	+	0.987881i	$0.450393\pi$
$912$	−12370.3	−0.449145
$913$	−28190.4	−1.02187
$914$	3838.08	0.138897
$915$	20406.5	0.737286
$916$	−10474.7	−0.377833
$917$	0	0
$918$	−26906.9	−0.967387
$919$	−46033.4	−1.65234	−0.826171	−	0.563419i	$-0.809486\pi$
$919$	−46033.4	−1.65234	−0.826171	+	0.563419i	$0.809486\pi$
$920$	23800.2	0.852902
$921$	−38380.9	−1.37317
$922$	1826.03	0.0652246
$923$	−4344.54	−0.154932
$924$	0	0
$925$	−24979.0	−0.887896
$926$	−54365.7	−1.92934
$927$	−1390.12	−0.0492529
$928$	−36819.1	−1.30242
$929$	−196.409	−0.00693647	−0.00346824	−	0.999994i	$-0.501104\pi$
$929$	−196.409	−0.00693647	−0.00346824	+	0.999994i	$0.501104\pi$
$930$	32265.3	1.13766
$931$	0	0
$932$	−65497.9	−2.30199
$933$	36621.6	1.28504
$934$	83088.4	2.91085
$935$	5758.96	0.201431
$936$	−1248.11	−0.0435851
$937$	−8063.86	−0.281147	−0.140574	−	0.990070i	$-0.544895\pi$
$937$	−8063.86	−0.281147	−0.140574	+	0.990070i	$0.544895\pi$
$938$	0	0
$939$	−38731.5	−1.34607
$940$	−29270.6	−1.01564
$941$	36860.9	1.27697	0.638487	−	0.769633i	$-0.279561\pi$
$941$	36860.9	1.27697	0.638487	+	0.769633i	$0.279561\pi$
$942$	23342.9	0.807381
$943$	−27327.6	−0.943699
$944$	4924.34	0.169781
$945$	0	0
$946$	11018.4	0.378689
$947$	−7621.08	−0.261512	−0.130756	−	0.991415i	$-0.541740\pi$
$947$	−7621.08	−0.261512	−0.130756	+	0.991415i	$0.541740\pi$
$948$	84885.0	2.90816
$949$	−20985.4	−0.717824
$950$	45772.0	1.56320
$951$	−8072.41	−0.275253
$952$	0	0
$953$	7182.10	0.244125	0.122062	−	0.992522i	$-0.461049\pi$
$953$	7182.10	0.244125	0.122062	+	0.992522i	$0.461049\pi$
$954$	659.746	0.0223900
$955$	16032.0	0.543229
$956$	−62711.8	−2.12160
$957$	31428.3	1.06158
$958$	28482.5	0.960573
$959$	0	0
$960$	26813.4	0.901457
$961$	9961.50	0.334379
$962$	−44913.1	−1.50526
$963$	864.203	0.0289185
$964$	42869.9	1.43231
$965$	23711.5	0.790986
$966$	0	0
$967$	−14977.0	−0.498064	−0.249032	−	0.968495i	$-0.580112\pi$
$967$	−14977.0	−0.498064	−0.249032	+	0.968495i	$0.580112\pi$
$968$	24818.6	0.824070
$969$	−26339.5	−0.873217
$970$	−6685.41	−0.221295
$971$	−6694.69	−0.221259	−0.110630	−	0.993862i	$-0.535287\pi$
$971$	−6694.69	−0.221259	−0.110630	+	0.993862i	$0.535287\pi$
$972$	5472.98	0.180603
$973$	0	0
$974$	71260.3	2.34428
$975$	14095.3	0.462985
$976$	−11679.2	−0.383034
$977$	30265.5	0.991075	0.495537	−	0.868587i	$-0.334971\pi$
$977$	30265.5	0.991075	0.495537	+	0.868587i	$0.334971\pi$
$978$	−58081.5	−1.89902
$979$	−13003.8	−0.424518
$980$	0	0
$981$	−1064.45	−0.0346436
$982$	26117.7	0.848726
$983$	19845.2	0.643910	0.321955	−	0.946755i	$-0.395660\pi$
$983$	19845.2	0.643910	0.321955	+	0.946755i	$0.395660\pi$
$984$	31236.8	1.01198
$985$	−5160.01	−0.166915
$986$	55011.2	1.77679
$987$	0	0
$988$	52355.7	1.68589
$989$	14546.7	0.467703
$990$	−896.250	−0.0287724
$991$	47771.3	1.53129	0.765643	−	0.643266i	$-0.222421\pi$
$991$	47771.3	1.53129	0.765643	+	0.643266i	$0.222421\pi$
$992$	26316.7	0.842293
$993$	60680.5	1.93921
$994$	0	0
$995$	10182.0	0.324414
$996$	99380.6	3.16164
$997$	10136.1	0.321979	0.160990	−	0.986956i	$-0.448531\pi$
$997$	10136.1	0.321979	0.160990	+	0.986956i	$0.448531\pi$
$998$	−61647.0	−1.95531
$999$	41034.0	1.29956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.4		39
7.6	odd	2		2401.4.a.d.1.4		39
49.6	odd	14		49.4.e.a.36.12	yes	78
49.41	odd	14		49.4.e.a.15.12	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.12	✓	78	49.41	odd	14
49.4.e.a.36.12	yes	78	49.6	odd	14
2401.4.a.c.1.4		39	1.1	even	1	trivial
2401.4.a.d.1.4		39	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-4.68909 q^{2} -5.32877 q^{3} +13.9876 q^{4} +6.47646 q^{5} +24.9871 q^{6} -28.0763 q^{8} +1.39583 q^{9} +O(q^{10})\)	\(q-4.68909 q^{2} -5.32877 q^{3} +13.9876 q^{4} +6.47646 q^{5} +24.9871 q^{6} -28.0763 q^{8} +1.39583 q^{9} -30.3687 q^{10} +21.1431 q^{11} -74.5367 q^{12} +31.8477 q^{13} -34.5116 q^{15} +19.7519 q^{16} +42.0569 q^{17} -6.54519 q^{18} +117.528 q^{19} +90.5900 q^{20} -99.1421 q^{22} -130.889 q^{23} +149.613 q^{24} -83.0555 q^{25} -149.337 q^{26} +136.439 q^{27} -278.949 q^{29} +161.828 q^{30} +199.380 q^{31} +131.992 q^{32} -112.667 q^{33} -197.209 q^{34} +19.5243 q^{36} +300.750 q^{37} -551.102 q^{38} -169.709 q^{39} -181.835 q^{40} +208.784 q^{41} -111.138 q^{43} +295.741 q^{44} +9.04005 q^{45} +613.751 q^{46} -323.111 q^{47} -105.253 q^{48} +389.455 q^{50} -224.112 q^{51} +445.472 q^{52} -100.799 q^{53} -639.774 q^{54} +136.933 q^{55} -626.283 q^{57} +1308.02 q^{58} +249.310 q^{59} -482.734 q^{60} -591.293 q^{61} -934.913 q^{62} -776.939 q^{64} +206.260 q^{65} +528.306 q^{66} +709.040 q^{67} +588.275 q^{68} +697.478 q^{69} -136.416 q^{71} -39.1899 q^{72} -658.930 q^{73} -1410.25 q^{74} +442.584 q^{75} +1643.94 q^{76} +795.782 q^{78} -1138.84 q^{79} +127.922 q^{80} -764.739 q^{81} -979.009 q^{82} -1333.31 q^{83} +272.380 q^{85} +521.135 q^{86} +1486.45 q^{87} -593.622 q^{88} -615.037 q^{89} -42.3896 q^{90} -1830.82 q^{92} -1062.45 q^{93} +1515.10 q^{94} +761.168 q^{95} -703.357 q^{96} +220.142 q^{97} +29.5123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

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