LMFDB - Embedded newform 2057.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2057,4,Mod(1,2057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2057, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2057.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2057 = 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2057.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:	$121.366928882$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.2636.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 14x - 4 $ x^3 - 14*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.287410$ of defining polynomial
Character	$\chi$	$=$	2057.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} +35.6419 q^{6} -26.1222 q^{7} -27.1912 q^{8} +31.2167 q^{9} +O(q^{10})$	\(q-4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} +35.6419 q^{6} -26.1222 q^{7} -27.1912 q^{8} +31.2167 q^{9} +55.6696 q^{10} -105.453 q^{12} +20.0515 q^{13} +122.024 q^{14} +90.9296 q^{15} +16.4506 q^{16} +17.0000 q^{17} -145.822 q^{18} -57.3466 q^{19} -164.709 q^{20} +199.312 q^{21} +77.0438 q^{23} +207.469 q^{24} +17.0243 q^{25} -93.6662 q^{26} -32.1732 q^{27} -361.033 q^{28} +286.162 q^{29} -424.758 q^{30} -8.54816 q^{31} +140.684 q^{32} -79.4119 q^{34} +311.309 q^{35} +431.443 q^{36} +357.982 q^{37} +267.882 q^{38} -152.992 q^{39} +324.049 q^{40} -194.467 q^{41} -931.044 q^{42} +74.2619 q^{43} -372.021 q^{45} -359.894 q^{46} +23.6130 q^{47} -125.518 q^{48} +339.369 q^{49} -79.5255 q^{50} -129.710 q^{51} +277.130 q^{52} +104.330 q^{53} +150.290 q^{54} +710.295 q^{56} +437.553 q^{57} -1336.75 q^{58} +249.363 q^{59} +1256.73 q^{60} +370.384 q^{61} +39.9309 q^{62} -815.448 q^{63} -788.781 q^{64} -238.961 q^{65} +939.650 q^{67} +234.956 q^{68} -587.843 q^{69} -1454.21 q^{70} -520.197 q^{71} -848.820 q^{72} -348.741 q^{73} -1672.24 q^{74} -129.895 q^{75} -792.583 q^{76} +714.672 q^{78} +953.827 q^{79} -196.049 q^{80} -597.369 q^{81} +908.412 q^{82} +1414.28 q^{83} +2754.68 q^{84} -202.596 q^{85} -346.899 q^{86} -2183.41 q^{87} -486.132 q^{89} +1737.82 q^{90} -523.788 q^{91} +1064.82 q^{92} +65.2223 q^{93} -110.303 q^{94} +683.422 q^{95} -1073.42 q^{96} -685.281 q^{97} -1585.29 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) $ 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} + 56 q^{10} + 22 q^{12} - 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} + 51 q^{17} + 103 q^{18} - 80 q^{19} - 168 q^{20} + 192 q^{21} + 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} - 476 q^{28} + 456 q^{29} - 400 q^{30} + 230 q^{31} + 71 q^{32} - 17 q^{34} + 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} - 556 q^{43} - 384 q^{45} + 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} - 547 q^{50} + 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} + 684 q^{56} + 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 1008 q^{67} + 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} + 927 q^{72} - 838 q^{73} - 836 q^{74} - 1548 q^{75} + 908 q^{76} + 1308 q^{78} + 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} + 2396 q^{83} + 2040 q^{84} - 136 q^{85} - 1264 q^{86} - 1428 q^{87} - 170 q^{89} + 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} + 472 q^{95} - 678 q^{96} - 270 q^{97} - 2857 q^{98}+O(q^{100}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 + 56 * q^10 + 22 * q^12 - 30 * q^13 + 92 * q^14 + 108 * q^15 + 137 * q^16 + 51 * q^17 + 103 * q^18 - 80 * q^19 - 168 * q^20 + 192 * q^21 + 142 * q^23 + 666 * q^24 - 223 * q^25 + 26 * q^26 - 20 * q^27 - 476 * q^28 + 456 * q^29 - 400 * q^30 + 230 * q^31 + 71 * q^32 - 17 * q^34 + 332 * q^35 + 1313 * q^36 + 356 * q^37 + 724 * q^38 - 268 * q^39 + 424 * q^40 + 294 * q^41 - 1128 * q^42 - 556 * q^43 - 384 * q^45 + 704 * q^46 + 640 * q^47 + 774 * q^48 - 269 * q^49 - 547 * q^50 + 68 * q^51 + 774 * q^52 + 302 * q^53 + 1100 * q^54 + 684 * q^56 + 720 * q^57 - 1304 * q^58 + 636 * q^59 + 1328 * q^60 + 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 - 408 * q^65 + 1008 * q^67 + 425 * q^68 + 576 * q^69 - 1504 * q^70 - 402 * q^71 + 927 * q^72 - 838 * q^73 - 836 * q^74 - 1548 * q^75 + 908 * q^76 + 1308 * q^78 + 594 * q^79 - 40 * q^80 - 505 * q^81 + 358 * q^82 + 2396 * q^83 + 2040 * q^84 - 136 * q^85 - 1264 * q^86 - 1428 * q^87 - 170 * q^89 + 2008 * q^90 - 1016 * q^91 + 4896 * q^92 + 632 * q^93 + 2016 * q^94 + 472 * q^95 - 678 * q^96 - 270 * q^97 - 2857 * q^98

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 $

$2$	−4.67129	−1.65155	−0.825775	−	0.564000i	$-0.809262\pi$
$2$	−4.67129	−1.65155	−0.825775	+	0.564000i	$0.809262\pi$
$3$	−7.62999	−1.46839	−0.734196	−	0.678938i	$-0.762441\pi$
$3$	−7.62999	−1.46839	−0.734196	+	0.678938i	$0.762441\pi$
$4$	13.8209	1.72762
$5$	−11.9174	−1.06592	−0.532962	−	0.846139i	$-0.678921\pi$
$5$	−11.9174	−1.06592	−0.532962	+	0.846139i	$0.678921\pi$
$6$	35.6419	2.42512
$7$	−26.1222	−1.41047	−0.705233	−	0.708975i	$-0.749158\pi$
$7$	−26.1222	−1.41047	−0.705233	+	0.708975i	$0.749158\pi$
$8$	−27.1912	−1.20169
$9$	31.2167	1.15617
$10$	55.6696	1.76043
$11$	0	0
$11$	0	0
$12$	−105.453	−2.53682
$13$	20.0515	0.427790	0.213895	−	0.976857i	$-0.431385\pi$
$13$	20.0515	0.427790	0.213895	+	0.976857i	$0.431385\pi$
$14$	122.024	2.32945
$15$	90.9296	1.56519
$16$	16.4506	0.257041
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−145.822	−1.90948
$19$	−57.3466	−0.692432	−0.346216	−	0.938155i	$-0.612534\pi$
$19$	−57.3466	−0.692432	−0.346216	+	0.938155i	$0.612534\pi$
$20$	−164.709	−1.84151
$21$	199.312	2.07112
$22$	0	0
$23$	77.0438	0.698467	0.349233	−	0.937036i	$-0.386442\pi$
$23$	77.0438	0.698467	0.349233	+	0.937036i	$0.386442\pi$
$24$	207.469	1.76456
$25$	17.0243	0.136195
$26$	−93.6662	−0.706517
$27$	−32.1732	−0.229323
$28$	−361.033	−2.43674
$29$	286.162	1.83238	0.916190	−	0.400744i	$-0.131248\pi$
$29$	286.162	1.83238	0.916190	+	0.400744i	$0.131248\pi$
$30$	−424.758	−2.58500
$31$	−8.54816	−0.0495256	−0.0247628	−	0.999693i	$-0.507883\pi$
$31$	−8.54816	−0.0495256	−0.0247628	+	0.999693i	$0.507883\pi$
$32$	140.684	0.777178
$33$	0	0
$34$	−79.4119	−0.400560
$35$	311.309	1.50345
$36$	431.443	1.99742
$37$	357.982	1.59059	0.795296	−	0.606221i	$-0.207315\pi$
$37$	357.982	1.59059	0.795296	+	0.606221i	$0.207315\pi$
$38$	267.882	1.14359
$39$	−152.992	−0.628164
$40$	324.049	1.28091
$41$	−194.467	−0.740748	−0.370374	−	0.928883i	$-0.620770\pi$
$41$	−194.467	−0.740748	−0.370374	+	0.928883i	$0.620770\pi$
$42$	−931.044	−3.42055
$43$	74.2619	0.263368	0.131684	−	0.991292i	$-0.457962\pi$
$43$	74.2619	0.263368	0.131684	+	0.991292i	$0.457962\pi$
$44$	0	0
$45$	−372.021	−1.23239
$46$	−359.894	−1.15355
$47$	23.6130	0.0732831	0.0366416	−	0.999328i	$-0.488334\pi$
$47$	23.6130	0.0732831	0.0366416	+	0.999328i	$0.488334\pi$
$48$	−125.518	−0.377437
$49$	339.369	0.989415
$50$	−79.5255	−0.224932
$51$	−129.710	−0.356137
$52$	277.130	0.739058
$53$	104.330	0.270393	0.135197	−	0.990819i	$-0.456833\pi$
$53$	104.330	0.270393	0.135197	+	0.990819i	$0.456833\pi$
$54$	150.290	0.378739
$55$	0	0
$56$	710.295	1.69495
$57$	437.553	1.01676
$58$	−1336.75	−3.02627
$59$	249.363	0.550243	0.275122	−	0.961409i	$-0.411282\pi$
$59$	249.363	0.550243	0.275122	+	0.961409i	$0.411282\pi$
$60$	1256.73	2.70405
$61$	370.384	0.777424	0.388712	−	0.921359i	$-0.372920\pi$
$61$	370.384	0.777424	0.388712	+	0.921359i	$0.372920\pi$
$62$	39.9309	0.0817940
$63$	−815.448	−1.63074
$64$	−788.781	−1.54059
$65$	−238.961	−0.455992
$66$	0	0
$67$	939.650	1.71338	0.856691	−	0.515830i	$-0.172517\pi$
$67$	939.650	1.71338	0.856691	+	0.515830i	$0.172517\pi$
$68$	234.956	0.419008
$69$	−587.843	−1.02562
$70$	−1454.21	−2.48302
$71$	−520.197	−0.869522	−0.434761	−	0.900546i	$-0.643167\pi$
$71$	−520.197	−0.869522	−0.434761	+	0.900546i	$0.643167\pi$
$72$	−848.820	−1.38937
$73$	−348.741	−0.559137	−0.279568	−	0.960126i	$-0.590191\pi$
$73$	−348.741	−0.559137	−0.279568	+	0.960126i	$0.590191\pi$
$74$	−1672.24	−2.62694
$75$	−129.895	−0.199987
$76$	−792.583	−1.19626
$77$	0	0
$78$	714.672	1.03744
$79$	953.827	1.35840	0.679202	−	0.733951i	$-0.262326\pi$
$79$	953.827	1.35840	0.679202	+	0.733951i	$0.262326\pi$
$80$	−196.049	−0.273986
$81$	−597.369	−0.819437
$82$	908.412	1.22338
$83$	1414.28	1.87033	0.935166	−	0.354211i	$-0.115250\pi$
$83$	1414.28	1.87033	0.935166	+	0.354211i	$0.115250\pi$
$84$	2754.68	3.57809
$85$	−202.596	−0.258525
$86$	−346.899	−0.434966
$87$	−2183.41	−2.69065
$88$	0	0
$89$	−486.132	−0.578987	−0.289493	−	0.957180i	$-0.593487\pi$
$89$	−486.132	−0.578987	−0.289493	+	0.957180i	$0.593487\pi$
$90$	1737.82	2.03536
$91$	−523.788	−0.603384
$92$	1064.82	1.20668
$93$	65.2223	0.0727230
$94$	−110.303	−0.121031
$95$	683.422	0.738080
$96$	−1073.42	−1.14120
$97$	−685.281	−0.717317	−0.358659	−	0.933469i	$-0.616766\pi$
$97$	−685.281	−0.717317	−0.358659	+	0.933469i	$0.616766\pi$
$98$	−1585.29	−1.63407
$99$	0	0
$100$	235.292	0.235292
$101$	−864.755	−0.851944	−0.425972	−	0.904736i	$-0.640068\pi$
$101$	−864.755	−0.851944	−0.425972	+	0.904736i	$0.640068\pi$
$102$	605.912	0.588178
$103$	1880.91	1.79933	0.899665	−	0.436580i	$-0.143810\pi$
$103$	1880.91	1.79933	0.899665	+	0.436580i	$0.143810\pi$
$104$	−545.224	−0.514073
$105$	−2375.28	−2.20765
$106$	−487.355	−0.446567
$107$	32.8149	0.0296480	0.0148240	−	0.999890i	$-0.495281\pi$
$107$	32.8149	0.0296480	0.0148240	+	0.999890i	$0.495281\pi$
$108$	−444.663	−0.396183
$109$	−528.727	−0.464613	−0.232307	−	0.972643i	$-0.574627\pi$
$109$	−528.727	−0.464613	−0.232307	+	0.972643i	$0.574627\pi$
$110$	0	0
$111$	−2731.40	−2.33561
$112$	−429.727	−0.362548
$113$	414.691	0.345229	0.172614	−	0.984989i	$-0.444779\pi$
$113$	414.691	0.345229	0.172614	+	0.984989i	$0.444779\pi$
$114$	−2043.94	−1.67923
$115$	−918.161	−0.744513
$116$	3955.03	3.16565
$117$	625.940	0.494600
$118$	−1164.85	−0.908754
$119$	−444.077	−0.342088
$120$	−2472.49	−1.88088
$121$	0	0
$122$	−1730.17	−1.28395
$123$	1483.78	1.08771
$124$	−118.143	−0.0855613
$125$	1286.79	0.920751
$126$	3809.19	2.69325
$127$	−596.093	−0.416494	−0.208247	−	0.978076i	$-0.566776\pi$
$127$	−596.093	−0.416494	−0.208247	+	0.978076i	$0.566776\pi$
$128$	2559.15	1.76718
$129$	−566.617	−0.386728
$130$	1116.26	0.753094
$131$	−121.819	−0.0812472	−0.0406236	−	0.999175i	$-0.512934\pi$
$131$	−121.819	−0.0812472	−0.0406236	+	0.999175i	$0.512934\pi$
$132$	0	0
$133$	1498.02	0.976652
$134$	−4389.38	−2.82973
$135$	383.420	0.244441
$136$	−462.251	−0.291454
$137$	−897.365	−0.559614	−0.279807	−	0.960056i	$-0.590270\pi$
$137$	−897.365	−0.559614	−0.279807	+	0.960056i	$0.590270\pi$
$138$	2745.98	1.69387
$139$	2113.61	1.28974	0.644871	−	0.764292i	$-0.276911\pi$
$139$	2113.61	1.28974	0.644871	+	0.764292i	$0.276911\pi$
$140$	4302.57	2.59738
$141$	−180.167	−0.107608
$142$	2429.99	1.43606
$143$	0	0
$144$	513.534	0.297184
$145$	−3410.31	−1.95318
$146$	1629.07	0.923442
$147$	−2589.38	−1.45285
$148$	4947.65	2.74793
$149$	−2580.76	−1.41895	−0.709476	−	0.704729i	$-0.751068\pi$
$149$	−2580.76	−1.41895	−0.709476	+	0.704729i	$0.751068\pi$
$150$	606.778	0.330288
$151$	−1342.77	−0.723662	−0.361831	−	0.932244i	$-0.617848\pi$
$151$	−1342.77	−0.723662	−0.361831	+	0.932244i	$0.617848\pi$
$152$	1559.32	0.832091
$153$	530.683	0.280413
$154$	0	0
$155$	101.872	0.0527906
$156$	−2114.50	−1.08523
$157$	−2495.82	−1.26871	−0.634357	−	0.773041i	$-0.718735\pi$
$157$	−2495.82	−1.26871	−0.634357	+	0.773041i	$0.718735\pi$
$158$	−4455.60	−2.24347
$159$	−796.036	−0.397043
$160$	−1676.59	−0.828413
$161$	−2012.55	−0.985164
$162$	2790.48	1.35334
$163$	1961.58	0.942595	0.471297	−	0.881974i	$-0.343786\pi$
$163$	1961.58	0.942595	0.471297	+	0.881974i	$0.343786\pi$
$164$	−2687.72	−1.27973
$165$	0	0
$166$	−6606.51	−3.08894
$167$	−2179.24	−1.00979	−0.504894	−	0.863182i	$-0.668468\pi$
$167$	−2179.24	−1.00979	−0.504894	+	0.863182i	$0.668468\pi$
$168$	−5419.54	−2.48885
$169$	−1794.94	−0.816995
$170$	946.383	0.426966
$171$	−1790.17	−0.800571
$172$	1026.37	0.454999
$173$	−3111.45	−1.36739	−0.683697	−	0.729766i	$-0.739629\pi$
$173$	−3111.45	−1.36739	−0.683697	+	0.729766i	$0.739629\pi$
$174$	10199.4	4.44374
$175$	−444.713	−0.192098
$176$	0	0
$177$	−1902.64	−0.807972
$178$	2270.86	0.956226
$179$	810.106	0.338269	0.169135	−	0.985593i	$-0.445903\pi$
$179$	810.106	0.338269	0.169135	+	0.985593i	$0.445903\pi$
$180$	−5141.68	−2.12910
$181$	−3356.23	−1.37827	−0.689134	−	0.724634i	$-0.742009\pi$
$181$	−3356.23	−1.37827	−0.689134	+	0.724634i	$0.742009\pi$
$182$	2446.77	0.996519
$183$	−2826.03	−1.14156
$184$	−2094.92	−0.839343
$185$	−4266.22	−1.69545
$186$	−304.672	−0.120106
$187$	0	0
$188$	326.353	0.126605
$189$	840.434	0.323453
$190$	−3192.46	−1.21898
$191$	1338.41	0.507038	0.253519	−	0.967330i	$-0.418412\pi$
$191$	1338.41	0.507038	0.253519	+	0.967330i	$0.418412\pi$
$192$	6018.39	2.26219
$193$	227.465	0.0848358	0.0424179	−	0.999100i	$-0.486494\pi$
$193$	227.465	0.0848358	0.0424179	+	0.999100i	$0.486494\pi$
$194$	3201.15	1.18468
$195$	1823.27	0.669575
$196$	4690.40	1.70933
$197$	−815.549	−0.294952	−0.147476	−	0.989066i	$-0.547115\pi$
$197$	−815.549	−0.294952	−0.147476	+	0.989066i	$0.547115\pi$
$198$	0	0
$199$	1866.90	0.665030	0.332515	−	0.943098i	$-0.392103\pi$
$199$	1866.90	0.665030	0.332515	+	0.943098i	$0.392103\pi$
$200$	−462.912	−0.163664
$201$	−7169.52	−2.51591
$202$	4039.52	1.40703
$203$	−7475.19	−2.58451
$204$	−1792.71	−0.615268
$205$	2317.54	0.789581
$206$	−8786.25	−2.97168
$207$	2405.05	0.807549
$208$	329.859	0.109960
$209$	0	0
$210$	11095.6	3.64605
$211$	1102.88	0.359836	0.179918	−	0.983682i	$-0.442417\pi$
$211$	1102.88	0.359836	0.179918	+	0.983682i	$0.442417\pi$
$212$	1441.94	0.467135
$213$	3969.10	1.27680
$214$	−153.288	−0.0489651
$215$	−885.008	−0.280731
$216$	874.828	0.275576
$217$	223.297	0.0698542
$218$	2469.84	0.767332
$219$	2660.89	0.821032
$220$	0	0
$221$	340.875	0.103754
$222$	12759.2	3.85738
$223$	−568.848	−0.170820	−0.0854100	−	0.996346i	$-0.527220\pi$
$223$	−568.848	−0.170820	−0.0854100	+	0.996346i	$0.527220\pi$
$224$	−3674.98	−1.09618
$225$	531.442	0.157464
$226$	−1937.14	−0.570163
$227$	−2106.99	−0.616061	−0.308030	−	0.951377i	$-0.599670\pi$
$227$	−2106.99	−0.616061	−0.308030	+	0.951377i	$0.599670\pi$
$228$	6047.39	1.75657
$229$	4336.30	1.25131	0.625656	−	0.780099i	$-0.284831\pi$
$229$	4336.30	1.25131	0.625656	+	0.780099i	$0.284831\pi$
$230$	4289.00	1.22960
$231$	0	0
$232$	−7781.11	−2.20196
$233$	4517.39	1.27014	0.635072	−	0.772453i	$-0.280970\pi$
$233$	4517.39	1.27014	0.635072	+	0.772453i	$0.280970\pi$
$234$	−2923.95	−0.816856
$235$	−281.405	−0.0781143
$236$	3446.43	0.950609
$237$	−7277.69	−1.99467
$238$	2074.41	0.564976
$239$	−5300.88	−1.43467	−0.717333	−	0.696731i	$-0.754637\pi$
$239$	−5300.88	−1.43467	−0.717333	+	0.696731i	$0.754637\pi$
$240$	1495.85	0.402319
$241$	1368.82	0.365864	0.182932	−	0.983126i	$-0.441441\pi$
$241$	1368.82	0.365864	0.182932	+	0.983126i	$0.441441\pi$
$242$	0	0
$243$	5426.60	1.43258
$244$	5119.05	1.34309
$245$	−4044.40	−1.05464
$246$	−6931.17	−1.79640
$247$	−1149.88	−0.296216
$248$	232.435	0.0595146
$249$	−10790.9	−2.74638
$250$	−6010.96	−1.52067
$251$	−5547.63	−1.39507	−0.697536	−	0.716549i	$-0.745720\pi$
$251$	−5547.63	−1.39507	−0.697536	+	0.716549i	$0.745720\pi$
$252$	−11270.3	−2.81730
$253$	0	0
$254$	2784.52	0.687860
$255$	1545.80	0.379615
$256$	−5644.28	−1.37800
$257$	−193.949	−0.0470748	−0.0235374	−	0.999723i	$-0.507493\pi$
$257$	−193.949	−0.0470748	−0.0235374	+	0.999723i	$0.507493\pi$
$258$	2646.83	0.638700
$259$	−9351.29	−2.24348
$260$	−3302.67	−0.787780
$261$	8933.04	2.11855
$262$	569.052	0.134184
$263$	1345.63	0.315494	0.157747	−	0.987480i	$-0.449577\pi$
$263$	1345.63	0.315494	0.157747	+	0.987480i	$0.449577\pi$
$264$	0	0
$265$	−1243.34	−0.288218
$266$	−6997.67	−1.61299
$267$	3709.18	0.850180
$268$	12986.8	2.96007
$269$	−3083.04	−0.698797	−0.349398	−	0.936974i	$-0.613614\pi$
$269$	−3083.04	−0.698797	−0.349398	+	0.936974i	$0.613614\pi$
$270$	−1791.07	−0.403707
$271$	422.163	0.0946294	0.0473147	−	0.998880i	$-0.484934\pi$
$271$	422.163	0.0946294	0.0473147	+	0.998880i	$0.484934\pi$
$272$	279.661	0.0623416
$273$	3996.50	0.886004
$274$	4191.85	0.924230
$275$	0	0
$276$	−8124.54	−1.77188
$277$	8260.00	1.79168	0.895840	−	0.444377i	$-0.146575\pi$
$277$	8260.00	1.79168	0.895840	+	0.444377i	$0.146575\pi$
$278$	−9873.28	−2.13007
$279$	−266.845	−0.0572602
$280$	−8464.86	−1.80669
$281$	−3321.91	−0.705226	−0.352613	−	0.935769i	$-0.614707\pi$
$281$	−3321.91	−0.705226	−0.352613	+	0.935769i	$0.614707\pi$
$282$	841.611	0.177721
$283$	7954.43	1.67082	0.835409	−	0.549629i	$-0.185231\pi$
$283$	7954.43	1.67082	0.835409	+	0.549629i	$0.185231\pi$
$284$	−7189.61	−1.50220
$285$	−5214.50	−1.08379
$286$	0	0
$287$	5079.91	1.04480
$288$	4391.69	0.898552
$289$	289.000	0.0588235
$290$	15930.5	3.22577
$291$	5228.69	1.05330
$292$	−4819.92	−0.965974
$293$	1171.99	0.233681	0.116841	−	0.993151i	$-0.462723\pi$
$293$	1171.99	0.233681	0.116841	+	0.993151i	$0.462723\pi$
$294$	12095.8	2.39945
$295$	−2971.76	−0.586517
$296$	−9733.98	−1.91141
$297$	0	0
$298$	12055.5	2.34347
$299$	1544.84	0.298798
$300$	−1795.27	−0.345500
$301$	−1939.88	−0.371472
$302$	6272.46	1.19516
$303$	6598.07	1.25099
$304$	−943.387	−0.177983
$305$	−4414.01	−0.828675
$306$	−2478.98	−0.463116
$307$	−865.763	−0.160950	−0.0804751	−	0.996757i	$-0.525644\pi$
$307$	−865.763	−0.160950	−0.0804751	+	0.996757i	$0.525644\pi$
$308$	0	0
$309$	−14351.3	−2.64212
$310$	−475.872	−0.0871862
$311$	6994.83	1.27537	0.637685	−	0.770297i	$-0.279892\pi$
$311$	6994.83	1.27537	0.637685	+	0.770297i	$0.279892\pi$
$312$	4160.05	0.754861
$313$	3442.33	0.621635	0.310818	−	0.950470i	$-0.399397\pi$
$313$	3442.33	0.621635	0.310818	+	0.950470i	$0.399397\pi$
$314$	11658.7	2.09534
$315$	9718.02	1.73825
$316$	13182.8	2.34680
$317$	2066.15	0.366078	0.183039	−	0.983106i	$-0.441407\pi$
$317$	2066.15	0.366078	0.183039	+	0.983106i	$0.441407\pi$
$318$	3718.52	0.655736
$319$	0	0
$320$	9400.22	1.64215
$321$	−250.377	−0.0435349
$322$	9401.21	1.62705
$323$	−974.892	−0.167939
$324$	−8256.20	−1.41567
$325$	341.362	0.0582627
$326$	−9163.11	−1.55674
$327$	4034.18	0.682234
$328$	5287.80	0.890152
$329$	−616.823	−0.103363
$330$	0	0
$331$	9027.44	1.49907	0.749536	−	0.661964i	$-0.230277\pi$
$331$	9027.44	1.49907	0.749536	+	0.661964i	$0.230277\pi$
$332$	19546.7	3.23121
$333$	11175.0	1.83900
$334$	10179.8	1.66771
$335$	−11198.2	−1.82633
$336$	3278.81	0.532362
$337$	−204.309	−0.0330250	−0.0165125	−	0.999864i	$-0.505256\pi$
$337$	−204.309	−0.0330250	−0.0165125	+	0.999864i	$0.505256\pi$
$338$	8384.67	1.34931
$339$	−3164.09	−0.506931
$340$	−2800.06	−0.446631
$341$	0	0
$342$	8362.39	1.32218
$343$	94.8397	0.0149296
$344$	−2019.27	−0.316488
$345$	7005.56	1.09324
$346$	14534.5	2.25832
$347$	−143.063	−0.0221326	−0.0110663	−	0.999939i	$-0.503523\pi$
$347$	−143.063	−0.0221326	−0.0110663	+	0.999939i	$0.503523\pi$
$348$	−30176.8	−4.64841
$349$	3998.42	0.613268	0.306634	−	0.951828i	$-0.400797\pi$
$349$	3998.42	0.613268	0.306634	+	0.951828i	$0.400797\pi$
$350$	2077.38	0.317259
$351$	−645.119	−0.0981024
$352$	0	0
$353$	−5809.57	−0.875956	−0.437978	−	0.898986i	$-0.644305\pi$
$353$	−5809.57	−0.875956	−0.437978	+	0.898986i	$0.644305\pi$
$354$	8887.77	1.33441
$355$	6199.39	0.926844
$356$	−6718.79	−1.00027
$357$	3388.30	0.502320
$358$	−3784.24	−0.558668
$359$	4895.37	0.719687	0.359844	−	0.933013i	$-0.382830\pi$
$359$	4895.37	0.719687	0.359844	+	0.933013i	$0.382830\pi$
$360$	10115.7	1.48096
$361$	−3570.37	−0.520538
$362$	15677.9	2.27628
$363$	0	0
$364$	−7239.24	−1.04242
$365$	4156.08	0.595998
$366$	13201.2	1.88535
$367$	528.151	0.0751206	0.0375603	−	0.999294i	$-0.488041\pi$
$367$	528.151	0.0751206	0.0375603	+	0.999294i	$0.488041\pi$
$368$	1267.42	0.179535
$369$	−6070.62	−0.856433
$370$	19928.7	2.80012
$371$	−2725.33	−0.381380
$372$	901.433	0.125637
$373$	10113.5	1.40390	0.701950	−	0.712226i	$-0.252313\pi$
$373$	10113.5	1.40390	0.701950	+	0.712226i	$0.252313\pi$
$374$	0	0
$375$	−9818.18	−1.35202
$376$	−642.066	−0.0880639
$377$	5737.98	0.783875
$378$	−3925.91	−0.534198
$379$	729.385	0.0988548	0.0494274	−	0.998778i	$-0.484260\pi$
$379$	729.385	0.0988548	0.0494274	+	0.998778i	$0.484260\pi$
$380$	9445.52	1.27512
$381$	4548.18	0.611576
$382$	−6252.12	−0.837399
$383$	−1608.08	−0.214540	−0.107270	−	0.994230i	$-0.534211\pi$
$383$	−1608.08	−0.214540	−0.107270	+	0.994230i	$0.534211\pi$
$384$	−19526.3	−2.59491
$385$	0	0
$386$	−1062.56	−0.140111
$387$	2318.21	0.304499
$388$	−9471.22	−1.23925
$389$	9824.09	1.28047	0.640233	−	0.768181i	$-0.278838\pi$
$389$	9824.09	1.28047	0.640233	+	0.768181i	$0.278838\pi$
$390$	−8517.02	−1.10584
$391$	1309.74	0.169403
$392$	−9227.87	−1.18897
$393$	929.478	0.119303
$394$	3809.66	0.487127
$395$	−11367.1	−1.44796
$396$	0	0
$397$	2876.88	0.363694	0.181847	−	0.983327i	$-0.441792\pi$
$397$	2876.88	0.363694	0.181847	+	0.983327i	$0.441792\pi$
$398$	−8720.82	−1.09833
$399$	−11429.9	−1.43411
$400$	280.061	0.0350076
$401$	−6515.91	−0.811444	−0.405722	−	0.913996i	$-0.632980\pi$
$401$	−6515.91	−0.811444	−0.405722	+	0.913996i	$0.632980\pi$
$402$	33490.9	4.15516
$403$	−171.403	−0.0211866
$404$	−11951.7	−1.47183
$405$	7119.09	0.873457
$406$	34918.8	4.26845
$407$	0	0
$408$	3526.97	0.427968
$409$	8870.10	1.07237	0.536183	−	0.844101i	$-0.319866\pi$
$409$	8870.10	1.07237	0.536183	+	0.844101i	$0.319866\pi$
$410$	−10825.9	−1.30403
$411$	6846.89	0.821732
$412$	25995.9	3.10855
$413$	−6513.92	−0.776099
$414$	−11234.7	−1.33371
$415$	−16854.5	−1.99363
$416$	2820.93	0.332469
$417$	−16126.8	−1.89385
$418$	0	0
$419$	−1009.53	−0.117706	−0.0588531	−	0.998267i	$-0.518744\pi$
$419$	−1009.53	−0.117706	−0.0588531	+	0.998267i	$0.518744\pi$
$420$	−32828.6	−3.81398
$421$	−3253.60	−0.376652	−0.188326	−	0.982107i	$-0.560306\pi$
$421$	−3253.60	−0.376652	−0.188326	+	0.982107i	$0.560306\pi$
$422$	−5151.87	−0.594287
$423$	737.119	0.0847280
$424$	−2836.86	−0.324930
$425$	289.413	0.0330320
$426$	−18540.8	−2.10870
$427$	−9675.25	−1.09653
$428$	453.532	0.0512203
$429$	0	0
$430$	4134.13	0.463640
$431$	2352.51	0.262915	0.131457	−	0.991322i	$-0.458034\pi$
$431$	2352.51	0.262915	0.131457	+	0.991322i	$0.458034\pi$
$432$	−529.269	−0.0589455
$433$	−5860.51	−0.650434	−0.325217	−	0.945639i	$-0.605437\pi$
$433$	−5860.51	−0.650434	−0.325217	+	0.945639i	$0.605437\pi$
$434$	−1043.08	−0.115368
$435$	26020.6	2.86803
$436$	−7307.50	−0.802674
$437$	−4418.20	−0.483641
$438$	−12429.8	−1.35597
$439$	−2894.17	−0.314650	−0.157325	−	0.987547i	$-0.550287\pi$
$439$	−2894.17	−0.314650	−0.157325	+	0.987547i	$0.550287\pi$
$440$	0	0
$441$	10594.0	1.14394
$442$	−1592.32	−0.171356
$443$	−8256.85	−0.885541	−0.442771	−	0.896635i	$-0.646004\pi$
$443$	−8256.85	−0.885541	−0.442771	+	0.896635i	$0.646004\pi$
$444$	−37750.5	−4.03504
$445$	5793.42	0.617156
$446$	2657.25	0.282118
$447$	19691.1	2.08358
$448$	20604.7	2.17295
$449$	15487.1	1.62779	0.813897	−	0.581009i	$-0.197342\pi$
$449$	15487.1	1.62779	0.813897	+	0.581009i	$0.197342\pi$
$450$	−2482.52	−0.260060
$451$	0	0
$452$	5731.42	0.596423
$453$	10245.3	1.06262
$454$	9842.35	1.01745
$455$	6242.19	0.643162
$456$	−11897.6	−1.22184
$457$	16055.6	1.64343	0.821716	−	0.569897i	$-0.193017\pi$
$457$	16055.6	1.64343	0.821716	+	0.569897i	$0.193017\pi$
$458$	−20256.1	−2.06661
$459$	−546.944	−0.0556191
$460$	−12689.8	−1.28623
$461$	−14064.0	−1.42088	−0.710440	−	0.703758i	$-0.751504\pi$
$461$	−14064.0	−1.42088	−0.710440	+	0.703758i	$0.751504\pi$
$462$	0	0
$463$	−8071.30	−0.810162	−0.405081	−	0.914281i	$-0.632757\pi$
$463$	−8071.30	−0.810162	−0.405081	+	0.914281i	$0.632757\pi$
$464$	4707.55	0.470997
$465$	−777.280	−0.0775172
$466$	−21102.0	−2.09771
$467$	8582.41	0.850421	0.425211	−	0.905094i	$-0.360200\pi$
$467$	8582.41	0.850421	0.425211	+	0.905094i	$0.360200\pi$
$468$	8651.07	0.854479
$469$	−24545.7	−2.41667
$470$	1314.53	0.129010
$471$	19043.1	1.86297
$472$	−6780.49	−0.661224
$473$	0	0
$474$	33996.2	3.29429
$475$	−976.286	−0.0943054
$476$	−6137.56	−0.590997
$477$	3256.84	0.312621
$478$	24761.9	2.36942
$479$	6320.96	0.602948	0.301474	−	0.953474i	$-0.402521\pi$
$479$	6320.96	0.602948	0.301474	+	0.953474i	$0.402521\pi$
$480$	12792.4	1.21643
$481$	7178.07	0.680441
$482$	−6394.13	−0.604242
$483$	15355.8	1.44661
$484$	0	0
$485$	8166.77	0.764606
$486$	−25349.2	−2.36597
$487$	7336.47	0.682643	0.341321	−	0.939947i	$-0.389126\pi$
$487$	7336.47	0.682643	0.341321	+	0.939947i	$0.389126\pi$
$488$	−10071.2	−0.934225
$489$	−14966.8	−1.38410
$490$	18892.6	1.74179
$491$	−6672.53	−0.613294	−0.306647	−	0.951823i	$-0.599207\pi$
$491$	−6672.53	−0.613294	−0.306647	+	0.951823i	$0.599207\pi$
$492$	20507.2	1.87914
$493$	4864.76	0.444417
$494$	5371.43	0.489215
$495$	0	0
$496$	−140.623	−0.0127301
$497$	13588.7	1.22643
$498$	50407.6	4.53578
$499$	17920.9	1.60772	0.803858	−	0.594821i	$-0.202777\pi$
$499$	17920.9	1.60772	0.803858	+	0.594821i	$0.202777\pi$
$500$	17784.6	1.59070
$501$	16627.6	1.48276
$502$	25914.6	2.30403
$503$	11325.3	1.00392	0.501959	−	0.864891i	$-0.332613\pi$
$503$	11325.3	1.00392	0.501959	+	0.864891i	$0.332613\pi$
$504$	22173.0	1.95965
$505$	10305.6	0.908108
$506$	0	0
$507$	13695.4	1.19967
$508$	−8238.56	−0.719541
$509$	−8313.78	−0.723972	−0.361986	−	0.932184i	$-0.617901\pi$
$509$	−8313.78	−0.723972	−0.361986	+	0.932184i	$0.617901\pi$
$510$	−7220.89	−0.626953
$511$	9109.87	0.788644
$512$	5892.85	0.508651
$513$	1845.02	0.158791
$514$	905.993	0.0777464
$515$	−22415.5	−1.91795
$516$	−7831.17	−0.668117
$517$	0	0
$518$	43682.6	3.70521
$519$	23740.3	2.00787
$520$	6497.65	0.547963
$521$	5121.64	0.430677	0.215339	−	0.976539i	$-0.430914\pi$
$521$	5121.64	0.430677	0.215339	+	0.976539i	$0.430914\pi$
$522$	−41728.8	−3.49889
$523$	−13378.5	−1.11855	−0.559275	−	0.828982i	$-0.688920\pi$
$523$	−13378.5	−1.11855	−0.559275	+	0.828982i	$0.688920\pi$
$524$	−1683.65	−0.140364
$525$	3393.15	0.282075
$526$	−6285.81	−0.521054
$527$	−145.319	−0.0120117
$528$	0	0
$529$	−6231.26	−0.512144
$530$	5808.01	0.476007
$531$	7784.29	0.636176
$532$	20704.0	1.68728
$533$	−3899.35	−0.316885
$534$	−17326.6	−1.40411
$535$	−391.068	−0.0316025
$536$	−25550.2	−2.05896
$537$	−6181.10	−0.496712
$538$	14401.8	1.15410
$539$	0	0
$540$	5299.23	0.422301
$541$	−9906.81	−0.787296	−0.393648	−	0.919261i	$-0.628787\pi$
$541$	−9906.81	−0.787296	−0.393648	+	0.919261i	$0.628787\pi$
$542$	−1972.04	−0.156285
$543$	25608.0	2.02384
$544$	2391.63	0.188493
$545$	6301.05	0.495243
$546$	−18668.8	−1.46328
$547$	−16399.6	−1.28189	−0.640947	−	0.767585i	$-0.721458\pi$
$547$	−16399.6	−1.28189	−0.640947	+	0.767585i	$0.721458\pi$
$548$	−12402.4	−0.966798
$549$	11562.2	0.898836
$550$	0	0
$551$	−16410.4	−1.26880
$552$	15984.2	1.23248
$553$	−24916.1	−1.91598
$554$	−38584.8	−2.95905
$555$	32551.2	2.48959
$556$	29212.0	2.22818
$557$	−22044.3	−1.67692	−0.838461	−	0.544962i	$-0.816544\pi$
$557$	−22044.3	−1.67692	−0.838461	+	0.544962i	$0.816544\pi$
$558$	1246.51	0.0945681
$559$	1489.06	0.112666
$560$	5121.22	0.386448
$561$	0	0
$562$	15517.6	1.16472
$563$	−12048.8	−0.901947	−0.450973	−	0.892537i	$-0.648923\pi$
$563$	−12048.8	−0.901947	−0.450973	+	0.892537i	$0.648923\pi$
$564$	−2490.07	−0.185906
$565$	−4942.04	−0.367988
$566$	−37157.4	−2.75944
$567$	15604.6	1.15579
$568$	14144.8	1.04490
$569$	23785.4	1.75243	0.876217	−	0.481916i	$-0.160059\pi$
$569$	23785.4	1.75243	0.876217	+	0.481916i	$0.160059\pi$
$570$	24358.4	1.78993
$571$	10878.3	0.797271	0.398635	−	0.917110i	$-0.369484\pi$
$571$	10878.3	0.797271	0.398635	+	0.917110i	$0.369484\pi$
$572$	0	0
$573$	−10212.1	−0.744531
$574$	−23729.7	−1.72554
$575$	1311.62	0.0951274
$576$	−24623.1	−1.78119
$577$	6315.86	0.455689	0.227845	−	0.973698i	$-0.426832\pi$
$577$	6315.86	0.455689	0.227845	+	0.973698i	$0.426832\pi$
$578$	−1350.00	−0.0971500
$579$	−1735.56	−0.124572
$580$	−47133.7	−3.37434
$581$	−36944.1	−2.63804
$582$	−24424.7	−1.73958
$583$	0	0
$584$	9482.69	0.671912
$585$	−7459.58	−0.527206
$586$	−5474.72	−0.385936
$587$	18192.1	1.27916	0.639581	−	0.768724i	$-0.279108\pi$
$587$	18192.1	1.27916	0.639581	+	0.768724i	$0.279108\pi$
$588$	−35787.7	−2.50996
$589$	490.207	0.0342931
$590$	13882.0	0.968663
$591$	6222.63	0.433104
$592$	5889.03	0.408848
$593$	9828.72	0.680636	0.340318	−	0.940310i	$-0.389465\pi$
$593$	9828.72	0.680636	0.340318	+	0.940310i	$0.389465\pi$
$594$	0	0
$595$	5292.25	0.364640
$596$	−35668.5	−2.45140
$597$	−14244.4	−0.976524
$598$	−7216.40	−0.493479
$599$	4662.57	0.318043	0.159021	−	0.987275i	$-0.449166\pi$
$599$	4662.57	0.318043	0.159021	+	0.987275i	$0.449166\pi$
$600$	3532.01	0.240323
$601$	−21658.6	−1.47000	−0.735001	−	0.678066i	$-0.762818\pi$
$601$	−21658.6	−1.47000	−0.735001	+	0.678066i	$0.762818\pi$
$602$	9061.76	0.613504
$603$	29332.8	1.98097
$604$	−18558.3	−1.25021
$605$	0	0
$606$	−30821.5	−2.06607
$607$	−25764.7	−1.72283	−0.861415	−	0.507902i	$-0.830421\pi$
$607$	−25764.7	−1.72283	−0.861415	+	0.507902i	$0.830421\pi$
$608$	−8067.76	−0.538143
$609$	57035.6	3.79507
$610$	20619.1	1.36860
$611$	473.475	0.0313498
$612$	7334.54	0.484446
$613$	−16018.1	−1.05541	−0.527705	−	0.849428i	$-0.676947\pi$
$613$	−16018.1	−1.05541	−0.527705	+	0.849428i	$0.676947\pi$
$614$	4044.23	0.265817
$615$	−17682.8	−1.15941
$616$	0	0
$617$	22250.3	1.45180	0.725902	−	0.687798i	$-0.241422\pi$
$617$	22250.3	1.45180	0.725902	+	0.687798i	$0.241422\pi$
$618$	67038.9	4.36360
$619$	−3765.95	−0.244534	−0.122267	−	0.992497i	$-0.539016\pi$
$619$	−3765.95	−0.244534	−0.122267	+	0.992497i	$0.539016\pi$
$620$	1407.96	0.0912018
$621$	−2478.74	−0.160175
$622$	−32674.9	−2.10634
$623$	12698.8	0.816642
$624$	−2516.82	−0.161464
$625$	−17463.2	−1.11765
$626$	−16080.1	−1.02666
$627$	0	0
$628$	−34494.5	−2.19185
$629$	6085.70	0.385775
$630$	−45395.7	−2.87080
$631$	−20806.5	−1.31267	−0.656334	−	0.754470i	$-0.727894\pi$
$631$	−20806.5	−1.31267	−0.656334	+	0.754470i	$0.727894\pi$
$632$	−25935.7	−1.63239
$633$	−8414.96	−0.528380
$634$	−9651.60	−0.604596
$635$	7103.88	0.443951
$636$	−11002.0	−0.685937
$637$	6804.85	0.423262
$638$	0	0
$639$	−16238.8	−1.00532
$640$	−30498.4	−1.88368
$641$	2439.58	0.150324	0.0751620	−	0.997171i	$-0.476053\pi$
$641$	2439.58	0.150324	0.0751620	+	0.997171i	$0.476053\pi$
$642$	1169.58	0.0719000
$643$	−19320.1	−1.18493	−0.592466	−	0.805595i	$-0.701846\pi$
$643$	−19320.1	−1.18493	−0.592466	+	0.805595i	$0.701846\pi$
$644$	−27815.4	−1.70199
$645$	6752.60	0.412222
$646$	4554.00	0.277360
$647$	−14067.1	−0.854766	−0.427383	−	0.904071i	$-0.640564\pi$
$647$	−14067.1	−0.854766	−0.427383	+	0.904071i	$0.640564\pi$
$648$	16243.2	0.984712
$649$	0	0
$650$	−1594.60	−0.0962238
$651$	−1703.75	−0.102573
$652$	27110.9	1.62844
$653$	15893.7	0.952478	0.476239	−	0.879316i	$-0.342000\pi$
$653$	15893.7	0.952478	0.476239	+	0.879316i	$0.342000\pi$
$654$	−18844.8	−1.12674
$655$	1451.77	0.0866033
$656$	−3199.11	−0.190403
$657$	−10886.5	−0.646459
$658$	2881.36	0.170710
$659$	9653.54	0.570635	0.285318	−	0.958433i	$-0.407901\pi$
$659$	9653.54	0.570635	0.285318	+	0.958433i	$0.407901\pi$
$660$	0	0
$661$	5389.06	0.317111	0.158555	−	0.987350i	$-0.449316\pi$
$661$	5389.06	0.317111	0.158555	+	0.987350i	$0.449316\pi$
$662$	−42169.7	−2.47579
$663$	−2600.87	−0.152352
$664$	−38456.0	−2.24757
$665$	−17852.5	−1.04104
$666$	−52201.7	−3.03720
$667$	22047.0	1.27986
$668$	−30119.1	−1.74453
$669$	4340.30	0.250831
$670$	52309.9	3.01628
$671$	0	0
$672$	28040.1	1.60963
$673$	3032.18	0.173673	0.0868366	−	0.996223i	$-0.472324\pi$
$673$	3032.18	0.173673	0.0868366	+	0.996223i	$0.472324\pi$
$674$	954.386	0.0545424
$675$	−547.726	−0.0312326
$676$	−24807.7	−1.41145
$677$	22029.2	1.25059	0.625295	−	0.780388i	$-0.284979\pi$
$677$	22029.2	1.25059	0.625295	+	0.780388i	$0.284979\pi$
$678$	14780.4	0.837222
$679$	17901.1	1.01175
$680$	5508.83	0.310667
$681$	16076.3	0.904618
$682$	0	0
$683$	−9040.72	−0.506491	−0.253246	−	0.967402i	$-0.581498\pi$
$683$	−9040.72	−0.506491	−0.253246	+	0.967402i	$0.581498\pi$
$684$	−24741.8	−1.38308
$685$	10694.3	0.596506
$686$	−443.023	−0.0246570
$687$	−33085.9	−1.83742
$688$	1221.65	0.0676964
$689$	2091.97	0.115672
$690$	−32725.0	−1.80553
$691$	−22863.5	−1.25871	−0.629355	−	0.777118i	$-0.716681\pi$
$691$	−22863.5	−1.25871	−0.629355	+	0.777118i	$0.716681\pi$
$692$	−43003.1	−2.36233
$693$	0	0
$694$	668.288	0.0365531
$695$	−25188.7	−1.37477
$696$	59369.7	3.23334
$697$	−3305.94	−0.179658
$698$	−18677.8	−1.01284
$699$	−34467.6	−1.86507
$700$	−6146.34	−0.331871
$701$	−1753.00	−0.0944507	−0.0472253	−	0.998884i	$-0.515038\pi$
$701$	−1753.00	−0.0944507	−0.0472253	+	0.998884i	$0.515038\pi$
$702$	3013.54	0.162021
$703$	−20529.1	−1.10138
$704$	0	0
$705$	2147.12	0.114702
$706$	27138.2	1.44668
$707$	22589.3	1.20164
$708$	−26296.2	−1.39587
$709$	11547.0	0.611645	0.305823	−	0.952089i	$-0.401069\pi$
$709$	11547.0	0.611645	0.305823	+	0.952089i	$0.401069\pi$
$710$	−28959.2	−1.53073
$711$	29775.3	1.57055
$712$	13218.5	0.695765
$713$	−658.582	−0.0345920
$714$	−15827.7	−0.829606
$715$	0	0
$716$	11196.4	0.584399
$717$	40445.6	2.10665
$718$	−22867.7	−1.18860
$719$	−10289.8	−0.533720	−0.266860	−	0.963735i	$-0.585986\pi$
$719$	−10289.8	−0.533720	−0.266860	+	0.963735i	$0.585986\pi$
$720$	−6119.99	−0.316776
$721$	−49133.4	−2.53790
$722$	16678.2	0.859695
$723$	−10444.0	−0.537231
$724$	−46386.2	−2.38112
$725$	4871.72	0.249560
$726$	0	0
$727$	2950.10	0.150499	0.0752497	−	0.997165i	$-0.476025\pi$
$727$	2950.10	0.150499	0.0752497	+	0.997165i	$0.476025\pi$
$728$	14242.5	0.725083
$729$	−25275.9	−1.28415
$730$	−19414.2	−0.984320
$731$	1262.45	0.0638762
$732$	−39058.3	−1.97218
$733$	−24348.2	−1.22691	−0.613453	−	0.789731i	$-0.710220\pi$
$733$	−24348.2	−1.22691	−0.613453	+	0.789731i	$0.710220\pi$
$734$	−2467.15	−0.124065
$735$	30858.7	1.54863
$736$	10838.8	0.542833
$737$	0	0
$738$	28357.6	1.41444
$739$	29233.5	1.45517	0.727585	−	0.686017i	$-0.240642\pi$
$739$	29233.5	1.45517	0.727585	+	0.686017i	$0.240642\pi$
$740$	−58963.1	−2.92909
$741$	8773.59	0.434961
$742$	12730.8	0.629868
$743$	−15340.6	−0.757457	−0.378729	−	0.925508i	$-0.623639\pi$
$743$	−15340.6	−0.757457	−0.378729	+	0.925508i	$0.623639\pi$
$744$	−1773.47	−0.0873908
$745$	30755.9	1.51250
$746$	−47242.9	−2.31861
$747$	44149.2	2.16243
$748$	0	0
$749$	−857.197	−0.0418175
$750$	45863.5	2.23293
$751$	39862.6	1.93689	0.968446	−	0.249223i	$-0.0801752\pi$
$751$	39862.6	1.93689	0.968446	+	0.249223i	$0.0801752\pi$
$752$	388.448	0.0188368
$753$	42328.3	2.04851
$754$	−26803.7	−1.29461
$755$	16002.3	0.771369
$756$	11615.6	0.558802
$757$	26375.1	1.26634	0.633169	−	0.774013i	$-0.281754\pi$
$757$	26375.1	1.26634	0.633169	+	0.774013i	$0.281754\pi$
$758$	−3407.17	−0.163264
$759$	0	0
$760$	−18583.1	−0.886946
$761$	−7848.63	−0.373867	−0.186933	−	0.982373i	$-0.559855\pi$
$761$	−7848.63	−0.373867	−0.186933	+	0.982373i	$0.559855\pi$
$762$	−21245.9	−1.01005
$763$	13811.5	0.655322
$764$	18498.1	0.875967
$765$	−6324.37	−0.298899
$766$	7511.78	0.354323
$767$	5000.10	0.235389
$768$	43065.8	2.02344
$769$	−31818.9	−1.49209	−0.746046	−	0.665895i	$-0.768050\pi$
$769$	−31818.9	−1.49209	−0.746046	+	0.665895i	$0.768050\pi$
$770$	0	0
$771$	1479.83	0.0691242
$772$	3143.78	0.146564
$773$	−29559.8	−1.37541	−0.687706	−	0.725990i	$-0.741382\pi$
$773$	−29559.8	−1.37541	−0.687706	+	0.725990i	$0.741382\pi$
$774$	−10829.0	−0.502896
$775$	−145.527	−0.00674512
$776$	18633.6	0.861996
$777$	71350.2	3.29430
$778$	−45891.2	−2.11475
$779$	11152.0	0.512917
$780$	25199.3	1.15677
$781$	0	0
$782$	−6118.19	−0.279778
$783$	−9206.75	−0.420208
$784$	5582.84	0.254320
$785$	29743.6	1.35235
$786$	−4341.86	−0.197034
$787$	28038.7	1.26998	0.634989	−	0.772521i	$-0.281005\pi$
$787$	28038.7	1.26998	0.634989	+	0.772521i	$0.281005\pi$
$788$	−11271.6	−0.509563
$789$	−10267.1	−0.463269
$790$	53099.2	2.39137
$791$	−10832.6	−0.486934
$792$	0	0
$793$	7426.75	0.332574
$794$	−13438.7	−0.600659
$795$	9486.68	0.423217
$796$	25802.3	1.14892
$797$	5320.45	0.236462	0.118231	−	0.992986i	$-0.462278\pi$
$797$	5320.45	0.236462	0.118231	+	0.992986i	$0.462278\pi$
$798$	53392.2	2.36850
$799$	401.421	0.0177738
$800$	2395.05	0.105847
$801$	−15175.4	−0.669409
$802$	30437.7	1.34014
$803$	0	0
$804$	−99089.4	−4.34653
$805$	23984.4	1.05011
$806$	800.673	0.0349907
$807$	23523.6	1.02611
$808$	23513.8	1.02378
$809$	−30934.0	−1.34435	−0.672177	−	0.740390i	$-0.734641\pi$
$809$	−30934.0	−1.34435	−0.672177	+	0.740390i	$0.734641\pi$
$810$	−33255.3	−1.44256
$811$	40364.5	1.74771	0.873854	−	0.486189i	$-0.161613\pi$
$811$	40364.5	1.74771	0.873854	+	0.486189i	$0.161613\pi$
$812$	−103314.	−4.46504
$813$	−3221.10	−0.138953
$814$	0	0
$815$	−23376.9	−1.00473
$816$	−2133.81	−0.0915419
$817$	−4258.66	−0.182364
$818$	−41434.8	−1.77107
$819$	−16350.9	−0.697616
$820$	32030.6	1.36409
$821$	−19799.7	−0.841672	−0.420836	−	0.907137i	$-0.638263\pi$
$821$	−19799.7	−0.841672	−0.420836	+	0.907137i	$0.638263\pi$
$822$	−31983.8	−1.35713
$823$	18756.4	0.794419	0.397210	−	0.917728i	$-0.369979\pi$
$823$	18756.4	0.794419	0.397210	+	0.917728i	$0.369979\pi$
$824$	−51144.1	−2.16225
$825$	0	0
$826$	30428.4	1.28177
$827$	−20958.0	−0.881234	−0.440617	−	0.897695i	$-0.645240\pi$
$827$	−20958.0	−0.881234	−0.440617	+	0.897695i	$0.645240\pi$
$828$	33240.0	1.39513
$829$	−31320.3	−1.31218	−0.656091	−	0.754682i	$-0.727791\pi$
$829$	−31320.3	−1.31218	−0.656091	+	0.754682i	$0.727791\pi$
$830$	78732.4	3.29258
$831$	−63023.7	−2.63089
$832$	−15816.2	−0.659049
$833$	5769.28	0.239968
$834$	75333.0	3.12778
$835$	25970.8	1.07636
$836$	0	0
$837$	275.021	0.0113574
$838$	4715.82	0.194398
$839$	−30290.6	−1.24642	−0.623212	−	0.782053i	$-0.714173\pi$
$839$	−30290.6	−1.24642	−0.623212	+	0.782053i	$0.714173\pi$
$840$	64586.8	2.65292
$841$	57499.9	2.35762
$842$	15198.5	0.622060
$843$	25346.1	1.03555
$844$	15242.8	0.621659
$845$	21391.0	0.870855
$846$	−3443.29	−0.139933
$847$	0	0
$848$	1716.29	0.0695021
$849$	−60692.2	−2.45342
$850$	−1351.93	−0.0545540
$851$	27580.3	1.11098
$852$	54856.6	2.20582
$853$	21111.8	0.847425	0.423712	−	0.905797i	$-0.360727\pi$
$853$	21111.8	0.847425	0.423712	+	0.905797i	$0.360727\pi$
$854$	45195.9	1.81097
$855$	21334.2	0.853348
$856$	−892.277	−0.0356278
$857$	39983.0	1.59369	0.796845	−	0.604184i	$-0.206501\pi$
$857$	39983.0	1.59369	0.796845	+	0.604184i	$0.206501\pi$
$858$	0	0
$859$	−39503.3	−1.56907	−0.784537	−	0.620082i	$-0.787099\pi$
$859$	−39503.3	−1.56907	−0.784537	+	0.620082i	$0.787099\pi$
$860$	−12231.6	−0.484995
$861$	−38759.6	−1.53418
$862$	−10989.2	−0.434217
$863$	26019.9	1.02634	0.513168	−	0.858288i	$-0.328472\pi$
$863$	26019.9	1.02634	0.513168	+	0.858288i	$0.328472\pi$
$864$	−4526.26	−0.178225
$865$	37080.4	1.45754
$866$	27376.1	1.07422
$867$	−2205.07	−0.0863760
$868$	3086.17	0.120681
$869$	0	0
$870$	−121550.	−4.73669
$871$	18841.4	0.732968
$872$	14376.7	0.558323
$873$	−21392.2	−0.829343
$874$	20638.7	0.798757
$875$	−33613.8	−1.29869
$876$	36775.9	1.41843
$877$	−15038.3	−0.579027	−0.289514	−	0.957174i	$-0.593494\pi$
$877$	−15038.3	−0.579027	−0.289514	+	0.957174i	$0.593494\pi$
$878$	13519.5	0.519660
$879$	−8942.30	−0.343136
$880$	0	0
$881$	−18334.3	−0.701133	−0.350567	−	0.936538i	$-0.614011\pi$
$881$	−18334.3	−0.701133	−0.350567	+	0.936538i	$0.614011\pi$
$882$	−49487.5	−1.88927
$883$	26659.5	1.01604	0.508020	−	0.861345i	$-0.330378\pi$
$883$	26659.5	1.01604	0.508020	+	0.861345i	$0.330378\pi$
$884$	4711.21	0.179248
$885$	22674.5	0.861237
$886$	38570.1	1.46251
$887$	−11473.7	−0.434327	−0.217163	−	0.976135i	$-0.569680\pi$
$887$	−11473.7	−0.434327	−0.217163	+	0.976135i	$0.569680\pi$
$888$	74270.1	2.80669
$889$	15571.3	0.587450
$890$	−27062.7	−1.01926
$891$	0	0
$892$	−7862.01	−0.295111
$893$	−1354.12	−0.0507436
$894$	−91983.0	−3.44113
$895$	−9654.36	−0.360569
$896$	−66850.7	−2.49255
$897$	−11787.1	−0.438752
$898$	−72344.6	−2.68838
$899$	−2446.16	−0.0907498
$900$	7345.03	0.272038
$901$	1773.61	0.0655799
$902$	0	0
$903$	14801.3	0.545466
$904$	−11276.0	−0.414860
$905$	39997.5	1.46913
$906$	−47858.8	−1.75497
$907$	−20361.6	−0.745421	−0.372710	−	0.927948i	$-0.621571\pi$
$907$	−20361.6	−0.745421	−0.372710	+	0.927948i	$0.621571\pi$
$908$	−29120.5	−1.06432
$909$	−26994.8	−0.984995
$910$	−29159.1	−1.06221
$911$	−19261.9	−0.700523	−0.350262	−	0.936652i	$-0.613907\pi$
$911$	−19261.9	−0.700523	−0.350262	+	0.936652i	$0.613907\pi$
$912$	7198.03	0.261349
$913$	0	0
$914$	−75000.3	−2.71421
$915$	33678.9	1.21682
$916$	59931.7	2.16179
$917$	3182.18	0.114596
$918$	2554.93	0.0918577
$919$	21191.8	0.760666	0.380333	−	0.924850i	$-0.375809\pi$
$919$	21191.8	0.760666	0.380333	+	0.924850i	$0.375809\pi$
$920$	24965.9	0.894677
$921$	6605.76	0.236338
$922$	65697.0	2.34665
$923$	−10430.7	−0.371973
$924$	0	0
$925$	6094.40	0.216630
$926$	37703.4	1.33802
$927$	58715.6	2.08034
$928$	40258.5	1.42409
$929$	40815.0	1.44144	0.720719	−	0.693227i	$-0.243812\pi$
$929$	40815.0	1.44144	0.720719	+	0.693227i	$0.243812\pi$
$930$	3630.90	0.128024
$931$	−19461.7	−0.685102
$932$	62434.5	2.19432
$933$	−53370.4	−1.87274
$934$	−40090.9	−1.40451
$935$	0	0
$936$	−17020.1	−0.594358
$937$	38439.1	1.34018	0.670092	−	0.742278i	$-0.266255\pi$
$937$	38439.1	1.34018	0.670092	+	0.742278i	$0.266255\pi$
$938$	114660.	3.99124
$939$	−26264.9	−0.912804
$940$	−3889.28	−0.134951
$941$	2244.08	0.0777415	0.0388708	−	0.999244i	$-0.487624\pi$
$941$	2244.08	0.0777415	0.0388708	+	0.999244i	$0.487624\pi$
$942$	−88955.6	−3.07678
$943$	−14982.5	−0.517388
$944$	4102.18	0.141435
$945$	−10015.8	−0.344776
$946$	0	0
$947$	−42289.0	−1.45112	−0.725559	−	0.688160i	$-0.758419\pi$
$947$	−42289.0	−1.45112	−0.725559	+	0.688160i	$0.758419\pi$
$948$	−100584.	−3.44602
$949$	−6992.76	−0.239193
$950$	4560.51	0.155750
$951$	−15764.7	−0.537546
$952$	12075.0	0.411085
$953$	−37426.2	−1.27214	−0.636072	−	0.771629i	$-0.719442\pi$
$953$	−37426.2	−1.27214	−0.636072	+	0.771629i	$0.719442\pi$
$954$	−15213.6	−0.516309
$955$	−15950.4	−0.540464
$956$	−73263.0	−2.47855
$957$	0	0
$958$	−29527.0	−0.995799
$959$	23441.2	0.789317
$960$	−71723.5	−2.41132
$961$	−29717.9	−0.997547
$962$	−33530.8	−1.12378
$963$	1024.37	0.0342782
$964$	18918.3	0.632072
$965$	−2710.80	−0.0904286
$966$	−71731.1	−2.38914
$967$	−1088.56	−0.0362003	−0.0181001	−	0.999836i	$-0.505762\pi$
$967$	−1088.56	−0.0362003	−0.0181001	+	0.999836i	$0.505762\pi$
$968$	0	0
$969$	7438.41	0.246601
$970$	−38149.3	−1.26278
$971$	39506.5	1.30569	0.652845	−	0.757491i	$-0.273575\pi$
$971$	39506.5	1.30569	0.652845	+	0.757491i	$0.273575\pi$
$972$	75000.6	2.47494
$973$	−55212.1	−1.81914
$974$	−34270.8	−1.12742
$975$	−2604.59	−0.0855525
$976$	6093.05	0.199830
$977$	−43326.8	−1.41878	−0.709389	−	0.704817i	$-0.751029\pi$
$977$	−43326.8	−1.41878	−0.709389	+	0.704817i	$0.751029\pi$
$978$	69914.4	2.28591
$979$	0	0
$980$	−55897.3	−1.82202
$981$	−16505.1	−0.537174
$982$	31169.3	1.01288
$983$	10664.1	0.346014	0.173007	−	0.984921i	$-0.444652\pi$
$983$	10664.1	0.346014	0.173007	+	0.984921i	$0.444652\pi$
$984$	−40345.9	−1.30709
$985$	9719.22	0.314396
$986$	−22724.7	−0.733977
$987$	4706.35	0.151778
$988$	−15892.4	−0.511747
$989$	5721.42	0.183954
$990$	0	0
$991$	15461.4	0.495609	0.247804	−	0.968810i	$-0.420291\pi$
$991$	15461.4	0.495609	0.247804	+	0.968810i	$0.420291\pi$
$992$	−1202.59	−0.0384902
$993$	−68879.2	−2.20122
$994$	−63476.7	−2.02551
$995$	−22248.6	−0.708871
$996$	−149141.	−4.74469
$997$	−46061.1	−1.46316	−0.731579	−	0.681756i	$-0.761216\pi$
$997$	−46061.1	−1.46316	−0.731579	+	0.681756i	$0.761216\pi$
$998$	−83713.7	−2.65522
$999$	−11517.4	−0.364760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.4.a.e.1.1		3
11.10	odd	2		17.4.a.b.1.3	✓	3
33.32	even	2		153.4.a.g.1.1		3
44.43	even	2		272.4.a.h.1.3		3
55.32	even	4		425.4.b.f.324.5		6
55.43	even	4		425.4.b.f.324.2		6
55.54	odd	2		425.4.a.g.1.1		3
77.76	even	2		833.4.a.d.1.3		3
88.21	odd	2		1088.4.a.v.1.3		3
88.43	even	2		1088.4.a.x.1.1		3
132.131	odd	2		2448.4.a.bi.1.3		3
187.21	odd	4		289.4.b.b.288.2		6
187.98	odd	4		289.4.b.b.288.1		6
187.186	odd	2		289.4.a.b.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.3	✓	3	11.10	odd	2
153.4.a.g.1.1		3	33.32	even	2
272.4.a.h.1.3		3	44.43	even	2
289.4.a.b.1.3		3	187.186	odd	2
289.4.b.b.288.1		6	187.98	odd	4
289.4.b.b.288.2		6	187.21	odd	4
425.4.a.g.1.1		3	55.54	odd	2
425.4.b.f.324.2		6	55.43	even	4
425.4.b.f.324.5		6	55.32	even	4
833.4.a.d.1.3		3	77.76	even	2
1088.4.a.v.1.3		3	88.21	odd	2
1088.4.a.x.1.1		3	88.43	even	2
2057.4.a.e.1.1		3	1.1	even	1	trivial
2448.4.a.bi.1.3		3	132.131	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:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.a (trivial)

\(f(q)\)	\(=\)	\(q-4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} +35.6419 q^{6} -26.1222 q^{7} -27.1912 q^{8} +31.2167 q^{9} +O(q^{10})\)	\(q-4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} +35.6419 q^{6} -26.1222 q^{7} -27.1912 q^{8} +31.2167 q^{9} +55.6696 q^{10} -105.453 q^{12} +20.0515 q^{13} +122.024 q^{14} +90.9296 q^{15} +16.4506 q^{16} +17.0000 q^{17} -145.822 q^{18} -57.3466 q^{19} -164.709 q^{20} +199.312 q^{21} +77.0438 q^{23} +207.469 q^{24} +17.0243 q^{25} -93.6662 q^{26} -32.1732 q^{27} -361.033 q^{28} +286.162 q^{29} -424.758 q^{30} -8.54816 q^{31} +140.684 q^{32} -79.4119 q^{34} +311.309 q^{35} +431.443 q^{36} +357.982 q^{37} +267.882 q^{38} -152.992 q^{39} +324.049 q^{40} -194.467 q^{41} -931.044 q^{42} +74.2619 q^{43} -372.021 q^{45} -359.894 q^{46} +23.6130 q^{47} -125.518 q^{48} +339.369 q^{49} -79.5255 q^{50} -129.710 q^{51} +277.130 q^{52} +104.330 q^{53} +150.290 q^{54} +710.295 q^{56} +437.553 q^{57} -1336.75 q^{58} +249.363 q^{59} +1256.73 q^{60} +370.384 q^{61} +39.9309 q^{62} -815.448 q^{63} -788.781 q^{64} -238.961 q^{65} +939.650 q^{67} +234.956 q^{68} -587.843 q^{69} -1454.21 q^{70} -520.197 q^{71} -848.820 q^{72} -348.741 q^{73} -1672.24 q^{74} -129.895 q^{75} -792.583 q^{76} +714.672 q^{78} +953.827 q^{79} -196.049 q^{80} -597.369 q^{81} +908.412 q^{82} +1414.28 q^{83} +2754.68 q^{84} -202.596 q^{85} -346.899 q^{86} -2183.41 q^{87} -486.132 q^{89} +1737.82 q^{90} -523.788 q^{91} +1064.82 q^{92} +65.2223 q^{93} -110.303 q^{94} +683.422 q^{95} -1073.42 q^{96} -685.281 q^{97} -1585.29 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} + 56 q^{10} + 22 q^{12} - 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} + 51 q^{17} + 103 q^{18} - 80 q^{19} - 168 q^{20} + 192 q^{21} + 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} - 476 q^{28} + 456 q^{29} - 400 q^{30} + 230 q^{31} + 71 q^{32} - 17 q^{34} + 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} - 556 q^{43} - 384 q^{45} + 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} - 547 q^{50} + 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} + 684 q^{56} + 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 1008 q^{67} + 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} + 927 q^{72} - 838 q^{73} - 836 q^{74} - 1548 q^{75} + 908 q^{76} + 1308 q^{78} + 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} + 2396 q^{83} + 2040 q^{84} - 136 q^{85} - 1264 q^{86} - 1428 q^{87} - 170 q^{89} + 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} + 472 q^{95} - 678 q^{96} - 270 q^{97} - 2857 q^{98}+O(q^{100}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 + 56 * q^10 + 22 * q^12 - 30 * q^13 + 92 * q^14 + 108 * q^15 + 137 * q^16 + 51 * q^17 + 103 * q^18 - 80 * q^19 - 168 * q^20 + 192 * q^21 + 142 * q^23 + 666 * q^24 - 223 * q^25 + 26 * q^26 - 20 * q^27 - 476 * q^28 + 456 * q^29 - 400 * q^30 + 230 * q^31 + 71 * q^32 - 17 * q^34 + 332 * q^35 + 1313 * q^36 + 356 * q^37 + 724 * q^38 - 268 * q^39 + 424 * q^40 + 294 * q^41 - 1128 * q^42 - 556 * q^43 - 384 * q^45 + 704 * q^46 + 640 * q^47 + 774 * q^48 - 269 * q^49 - 547 * q^50 + 68 * q^51 + 774 * q^52 + 302 * q^53 + 1100 * q^54 + 684 * q^56 + 720 * q^57 - 1304 * q^58 + 636 * q^59 + 1328 * q^60 + 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 - 408 * q^65 + 1008 * q^67 + 425 * q^68 + 576 * q^69 - 1504 * q^70 - 402 * q^71 + 927 * q^72 - 838 * q^73 - 836 * q^74 - 1548 * q^75 + 908 * q^76 + 1308 * q^78 + 594 * q^79 - 40 * q^80 - 505 * q^81 + 358 * q^82 + 2396 * q^83 + 2040 * q^84 - 136 * q^85 - 1264 * q^86 - 1428 * q^87 - 170 * q^89 + 2008 * q^90 - 1016 * q^91 + 4896 * q^92 + 632 * q^93 + 2016 * q^94 + 472 * q^95 - 678 * q^96 - 270 * q^97 - 2857 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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