LMFDB - Embedded newform 1859.4.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.79202 q^{2} +1.78265 q^{3} +6.37944 q^{4} -15.2422 q^{5} -6.75985 q^{6} +7.73177 q^{7} +6.14519 q^{8} -23.8222 q^{9} +O(q^{10})$	\(q-3.79202 q^{2} +1.78265 q^{3} +6.37944 q^{4} -15.2422 q^{5} -6.75985 q^{6} +7.73177 q^{7} +6.14519 q^{8} -23.8222 q^{9} +57.7988 q^{10} +11.0000 q^{11} +11.3723 q^{12} -29.3190 q^{14} -27.1715 q^{15} -74.3383 q^{16} -52.0194 q^{17} +90.3342 q^{18} +23.0313 q^{19} -97.2367 q^{20} +13.7830 q^{21} -41.7123 q^{22} +90.8697 q^{23} +10.9547 q^{24} +107.325 q^{25} -90.5982 q^{27} +49.3244 q^{28} -22.7579 q^{29} +103.035 q^{30} +108.149 q^{31} +232.731 q^{32} +19.6092 q^{33} +197.259 q^{34} -117.849 q^{35} -151.972 q^{36} -250.562 q^{37} -87.3352 q^{38} -93.6662 q^{40} +153.536 q^{41} -52.2656 q^{42} +140.488 q^{43} +70.1739 q^{44} +363.102 q^{45} -344.580 q^{46} +202.124 q^{47} -132.519 q^{48} -283.220 q^{49} -406.978 q^{50} -92.7325 q^{51} -342.040 q^{53} +343.550 q^{54} -167.664 q^{55} +47.5132 q^{56} +41.0568 q^{57} +86.2986 q^{58} +446.964 q^{59} -173.339 q^{60} -345.870 q^{61} -410.104 q^{62} -184.187 q^{63} -287.815 q^{64} -74.3584 q^{66} +544.015 q^{67} -331.855 q^{68} +161.989 q^{69} +446.887 q^{70} +535.901 q^{71} -146.392 q^{72} +663.221 q^{73} +950.137 q^{74} +191.322 q^{75} +146.927 q^{76} +85.0494 q^{77} -86.8666 q^{79} +1133.08 q^{80} +481.693 q^{81} -582.214 q^{82} -623.931 q^{83} +87.9281 q^{84} +792.891 q^{85} -532.732 q^{86} -40.5694 q^{87} +67.5971 q^{88} +90.2394 q^{89} -1376.89 q^{90} +579.698 q^{92} +192.792 q^{93} -766.458 q^{94} -351.048 q^{95} +414.878 q^{96} +824.870 q^{97} +1073.98 q^{98} -262.044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * 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 $

$2$	−3.79202	−1.34068	−0.670341	−	0.742053i	$-0.733852\pi$
$2$	−3.79202	−1.34068	−0.670341	+	0.742053i	$0.733852\pi$
$3$	1.78265	0.343071	0.171536	−	0.985178i	$-0.445127\pi$
$3$	1.78265	0.343071	0.171536	+	0.985178i	$0.445127\pi$
$4$	6.37944	0.797430
$5$	−15.2422	−1.36330	−0.681652	−	0.731677i	$-0.738738\pi$
$5$	−15.2422	−1.36330	−0.681652	+	0.731677i	$0.738738\pi$
$6$	−6.75985	−0.459950
$7$	7.73177	0.417476	0.208738	−	0.977972i	$-0.433064\pi$
$7$	7.73177	0.417476	0.208738	+	0.977972i	$0.433064\pi$
$8$	6.14519	0.271582
$9$	−23.8222	−0.882302
$10$	57.7988	1.82776
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	11.3723	0.273575
$13$	0	0
$13$	0	0
$14$	−29.3190	−0.559703
$15$	−27.1715	−0.467710
$16$	−74.3383	−1.16154
$17$	−52.0194	−0.742151	−0.371075	−	0.928603i	$-0.621011\pi$
$17$	−52.0194	−0.742151	−0.371075	+	0.928603i	$0.621011\pi$
$18$	90.3342	1.18289
$19$	23.0313	0.278092	0.139046	−	0.990286i	$-0.455596\pi$
$19$	23.0313	0.278092	0.139046	+	0.990286i	$0.455596\pi$
$20$	−97.2367	−1.08714
$21$	13.7830	0.143224
$22$	−41.7123	−0.404231
$23$	90.8697	0.823810	0.411905	−	0.911227i	$-0.364863\pi$
$23$	90.8697	0.823810	0.411905	+	0.911227i	$0.364863\pi$
$24$	10.9547	0.0931719
$25$	107.325	0.858597
$26$	0	0
$27$	−90.5982	−0.645764
$28$	49.3244	0.332908
$29$	−22.7579	−0.145726	−0.0728628	−	0.997342i	$-0.523214\pi$
$29$	−22.7579	−0.145726	−0.0728628	+	0.997342i	$0.523214\pi$
$30$	103.035	0.627051
$31$	108.149	0.626585	0.313293	−	0.949657i	$-0.398568\pi$
$31$	108.149	0.626585	0.313293	+	0.949657i	$0.398568\pi$
$32$	232.731	1.28567
$33$	19.6092	0.103440
$34$	197.259	0.994989
$35$	−117.849	−0.569147
$36$	−151.972	−0.703574
$37$	−250.562	−1.11330	−0.556650	−	0.830747i	$-0.687914\pi$
$37$	−250.562	−1.11330	−0.556650	+	0.830747i	$0.687914\pi$
$38$	−87.3352	−0.372833
$39$	0	0
$40$	−93.6662	−0.370248
$41$	153.536	0.584838	0.292419	−	0.956290i	$-0.405540\pi$
$41$	153.536	0.584838	0.292419	+	0.956290i	$0.405540\pi$
$42$	−52.2656	−0.192018
$43$	140.488	0.498236	0.249118	−	0.968473i	$-0.419859\pi$
$43$	140.488	0.498236	0.249118	+	0.968473i	$0.419859\pi$
$44$	70.1739	0.240434
$45$	363.102	1.20285
$46$	−344.580	−1.10447
$47$	202.124	0.627293	0.313647	−	0.949540i	$-0.398449\pi$
$47$	202.124	0.627293	0.313647	+	0.949540i	$0.398449\pi$
$48$	−132.519	−0.398489
$49$	−283.220	−0.825714
$50$	−406.978	−1.15111
$51$	−92.7325	−0.254611
$52$	0	0
$53$	−342.040	−0.886467	−0.443234	−	0.896406i	$-0.646169\pi$
$53$	−342.040	−0.886467	−0.443234	+	0.896406i	$0.646169\pi$
$54$	343.550	0.865764
$55$	−167.664	−0.411052
$56$	47.5132	0.113379
$57$	41.0568	0.0954053
$58$	86.2986	0.195372
$59$	446.964	0.986268	0.493134	−	0.869953i	$-0.335851\pi$
$59$	446.964	0.986268	0.493134	+	0.869953i	$0.335851\pi$
$60$	−173.339	−0.372966
$61$	−345.870	−0.725968	−0.362984	−	0.931795i	$-0.618242\pi$
$61$	−345.870	−0.725968	−0.362984	+	0.931795i	$0.618242\pi$
$62$	−410.104	−0.840052
$63$	−184.187	−0.368340
$64$	−287.815	−0.562139
$65$	0	0
$66$	−74.3584	−0.138680
$67$	544.015	0.991970	0.495985	−	0.868331i	$-0.334807\pi$
$67$	544.015	0.991970	0.495985	+	0.868331i	$0.334807\pi$
$68$	−331.855	−0.591814
$69$	161.989	0.282626
$70$	446.887	0.763045
$71$	535.901	0.895771	0.447886	−	0.894091i	$-0.352177\pi$
$71$	535.901	0.895771	0.447886	+	0.894091i	$0.352177\pi$
$72$	−146.392	−0.239617
$73$	663.221	1.06335	0.531673	−	0.846950i	$-0.321564\pi$
$73$	663.221	1.06335	0.531673	+	0.846950i	$0.321564\pi$
$74$	950.137	1.49258
$75$	191.322	0.294560
$76$	146.927	0.221759
$77$	85.0494	0.125874
$78$	0	0
$79$	−86.8666	−0.123712	−0.0618561	−	0.998085i	$-0.519702\pi$
$79$	−86.8666	−0.123712	−0.0618561	+	0.998085i	$0.519702\pi$
$80$	1133.08	1.58353
$81$	481.693	0.660759
$82$	−582.214	−0.784082
$83$	−623.931	−0.825124	−0.412562	−	0.910930i	$-0.635366\pi$
$83$	−623.931	−0.825124	−0.412562	+	0.910930i	$0.635366\pi$
$84$	87.9281	0.114211
$85$	792.891	1.01178
$86$	−532.732	−0.667977
$87$	−40.5694	−0.0499942
$88$	67.5971	0.0818849
$89$	90.2394	0.107476	0.0537379	−	0.998555i	$-0.482886\pi$
$89$	90.2394	0.107476	0.0537379	+	0.998555i	$0.482886\pi$
$90$	−1376.89	−1.61263
$91$	0	0
$92$	579.698	0.656931
$93$	192.792	0.214963
$94$	−766.458	−0.841001
$95$	−351.048	−0.379123
$96$	414.878	0.441076
$97$	824.870	0.863432	0.431716	−	0.902010i	$-0.357908\pi$
$97$	824.870	0.863432	0.431716	+	0.902010i	$0.357908\pi$
$98$	1073.98	1.10702
$99$	−262.044	−0.266024
$100$	684.672	0.684672
$101$	737.803	0.726873	0.363437	−	0.931619i	$-0.381603\pi$
$101$	737.803	0.726873	0.363437	+	0.931619i	$0.381603\pi$
$102$	351.644	0.341352
$103$	−618.656	−0.591825	−0.295913	−	0.955215i	$-0.595624\pi$
$103$	−618.656	−0.591825	−0.295913	+	0.955215i	$0.595624\pi$
$104$	0	0
$105$	−210.084	−0.195258
$106$	1297.02	1.18847
$107$	852.103	0.769868	0.384934	−	0.922944i	$-0.374224\pi$
$107$	852.103	0.769868	0.384934	+	0.922944i	$0.374224\pi$
$108$	−577.966	−0.514952
$109$	−1905.47	−1.67441	−0.837206	−	0.546888i	$-0.815812\pi$
$109$	−1905.47	−1.67441	−0.837206	+	0.546888i	$0.815812\pi$
$110$	635.787	0.551090
$111$	−446.664	−0.381941
$112$	−574.766	−0.484913
$113$	2274.69	1.89367	0.946834	−	0.321721i	$-0.104261\pi$
$113$	2274.69	1.89367	0.946834	+	0.321721i	$0.104261\pi$
$114$	−155.688	−0.127908
$115$	−1385.05	−1.12310
$116$	−145.183	−0.116206
$117$	0	0
$118$	−1694.90	−1.32227
$119$	−402.202	−0.309830
$120$	−166.974	−0.127022
$121$	121.000	0.0909091
$122$	1311.55	0.973293
$123$	273.702	0.200641
$124$	689.931	0.499658
$125$	269.411	0.192775
$126$	698.443	0.493827
$127$	2285.61	1.59697	0.798484	−	0.602016i	$-0.205636\pi$
$127$	2285.61	1.59697	0.798484	+	0.602016i	$0.205636\pi$
$128$	−770.446	−0.532019
$129$	250.440	0.170931
$130$	0	0
$131$	−2268.87	−1.51322	−0.756610	−	0.653866i	$-0.773146\pi$
$131$	−2268.87	−1.51322	−0.756610	+	0.653866i	$0.773146\pi$
$132$	125.096	0.0824861
$133$	178.073	0.116097
$134$	−2062.92	−1.32992
$135$	1380.92	0.880372
$136$	−319.669	−0.201555
$137$	743.599	0.463722	0.231861	−	0.972749i	$-0.425519\pi$
$137$	743.599	0.463722	0.231861	+	0.972749i	$0.425519\pi$
$138$	−614.266	−0.378911
$139$	−2432.62	−1.48440	−0.742201	−	0.670178i	$-0.766218\pi$
$139$	−2432.62	−1.48440	−0.742201	+	0.670178i	$0.766218\pi$
$140$	−751.812	−0.453855
$141$	360.316	0.215206
$142$	−2032.15	−1.20094
$143$	0	0
$144$	1770.90	1.02482
$145$	346.881	0.198668
$146$	−2514.95	−1.42561
$147$	−504.882	−0.283279
$148$	−1598.45	−0.887780
$149$	992.161	0.545510	0.272755	−	0.962084i	$-0.412065\pi$
$149$	992.161	0.545510	0.272755	+	0.962084i	$0.412065\pi$
$150$	−725.499	−0.394912
$151$	1557.02	0.839130	0.419565	−	0.907725i	$-0.362183\pi$
$151$	1557.02	0.839130	0.419565	+	0.907725i	$0.362183\pi$
$152$	141.532	0.0755246
$153$	1239.22	0.654801
$154$	−322.510	−0.168757
$155$	−1648.43	−0.854226
$156$	0	0
$157$	−2616.71	−1.33017	−0.665084	−	0.746768i	$-0.731604\pi$
$157$	−2616.71	−1.33017	−0.665084	+	0.746768i	$0.731604\pi$
$158$	329.400	0.165859
$159$	−609.737	−0.304121
$160$	−3547.33	−1.75276
$161$	702.583	0.343921
$162$	−1826.59	−0.885868
$163$	−1673.53	−0.804178	−0.402089	−	0.915601i	$-0.631716\pi$
$163$	−1673.53	−0.804178	−0.402089	+	0.915601i	$0.631716\pi$
$164$	979.477	0.466368
$165$	−298.887	−0.141020
$166$	2365.96	1.10623
$167$	−644.831	−0.298793	−0.149397	−	0.988777i	$-0.547733\pi$
$167$	−644.831	−0.298793	−0.149397	+	0.988777i	$0.547733\pi$
$168$	84.6994	0.0388970
$169$	0	0
$170$	−3006.66	−1.35647
$171$	−548.655	−0.245361
$172$	896.233	0.397309
$173$	−4035.68	−1.77357	−0.886784	−	0.462184i	$-0.847066\pi$
$173$	−4035.68	−1.77357	−0.886784	+	0.462184i	$0.847066\pi$
$174$	153.840	0.0670264
$175$	829.809	0.358444
$176$	−817.721	−0.350216
$177$	796.781	0.338360
$178$	−342.190	−0.144091
$179$	3034.17	1.26695	0.633477	−	0.773762i	$-0.281627\pi$
$179$	3034.17	1.26695	0.633477	+	0.773762i	$0.281627\pi$
$180$	2316.39	0.959186
$181$	1812.06	0.744138	0.372069	−	0.928205i	$-0.378648\pi$
$181$	1812.06	0.744138	0.372069	+	0.928205i	$0.378648\pi$
$182$	0	0
$183$	−616.565	−0.249059
$184$	558.412	0.223732
$185$	3819.11	1.51777
$186$	−731.072	−0.288198
$187$	−572.214	−0.223767
$188$	1289.44	0.500223
$189$	−700.484	−0.269591
$190$	1331.18	0.508284
$191$	4421.53	1.67503	0.837515	−	0.546415i	$-0.184008\pi$
$191$	4421.53	1.67503	0.837515	+	0.546415i	$0.184008\pi$
$192$	−513.074	−0.192854
$193$	−2104.87	−0.785037	−0.392518	−	0.919744i	$-0.628396\pi$
$193$	−2104.87	−0.785037	−0.392518	+	0.919744i	$0.628396\pi$
$194$	−3127.93	−1.15759
$195$	0	0
$196$	−1806.78	−0.658449
$197$	1145.36	0.414232	0.207116	−	0.978316i	$-0.433592\pi$
$197$	1145.36	0.414232	0.207116	+	0.978316i	$0.433592\pi$
$198$	993.676	0.356654
$199$	−608.906	−0.216906	−0.108453	−	0.994102i	$-0.534590\pi$
$199$	−608.906	−0.216906	−0.108453	+	0.994102i	$0.534590\pi$
$200$	659.531	0.233179
$201$	969.789	0.340317
$202$	−2797.77	−0.974506
$203$	−175.959	−0.0608369
$204$	−591.582	−0.203034
$205$	−2340.23	−0.797312
$206$	2345.96	0.793450
$207$	−2164.71	−0.726850
$208$	0	0
$209$	253.344	0.0838478
$210$	796.643	0.261779
$211$	3379.66	1.10268	0.551339	−	0.834281i	$-0.314117\pi$
$211$	3379.66	1.10268	0.551339	+	0.834281i	$0.314117\pi$
$212$	−2182.02	−0.706896
$213$	955.324	0.307313
$214$	−3231.19	−1.03215
$215$	−2141.34	−0.679247
$216$	−556.743	−0.175378
$217$	836.183	0.261584
$218$	7225.58	2.24485
$219$	1182.29	0.364803
$220$	−1069.60	−0.327785
$221$	0	0
$222$	1693.76	0.512062
$223$	−1521.19	−0.456799	−0.228400	−	0.973567i	$-0.573349\pi$
$223$	−1521.19	−0.456799	−0.228400	+	0.973567i	$0.573349\pi$
$224$	1799.42	0.536736
$225$	−2556.70	−0.757542
$226$	−8625.67	−2.53881
$227$	2187.74	0.639673	0.319836	−	0.947473i	$-0.396372\pi$
$227$	2187.74	0.639673	0.319836	+	0.947473i	$0.396372\pi$
$228$	261.919	0.0760791
$229$	−6392.88	−1.84478	−0.922388	−	0.386266i	$-0.873765\pi$
$229$	−6392.88	−1.84478	−0.922388	+	0.386266i	$0.873765\pi$
$230$	5252.16	1.50573
$231$	151.613	0.0431837
$232$	−139.852	−0.0395764
$233$	−2101.69	−0.590928	−0.295464	−	0.955354i	$-0.595474\pi$
$233$	−2101.69	−0.590928	−0.295464	+	0.955354i	$0.595474\pi$
$234$	0	0
$235$	−3080.81	−0.855191
$236$	2851.38	0.786480
$237$	−154.853	−0.0424421
$238$	1525.16	0.415384
$239$	347.424	0.0940293	0.0470147	−	0.998894i	$-0.485029\pi$
$239$	347.424	0.0940293	0.0470147	+	0.998894i	$0.485029\pi$
$240$	2019.88	0.543262
$241$	4007.93	1.07126	0.535629	−	0.844453i	$-0.320074\pi$
$241$	4007.93	1.07126	0.535629	+	0.844453i	$0.320074\pi$
$242$	−458.835	−0.121880
$243$	3304.84	0.872451
$244$	−2206.46	−0.578909
$245$	4316.89	1.12570
$246$	−1037.88	−0.268996
$247$	0	0
$248$	664.597	0.170169
$249$	−1112.25	−0.283076
$250$	−1021.61	−0.258450
$251$	2943.70	0.740258	0.370129	−	0.928980i	$-0.379313\pi$
$251$	2943.70	0.740258	0.370129	+	0.928980i	$0.379313\pi$
$252$	−1175.01	−0.293726
$253$	999.567	0.248388
$254$	−8667.08	−2.14103
$255$	1413.45	0.347112
$256$	5224.07	1.27541
$257$	−1986.94	−0.482265	−0.241132	−	0.970492i	$-0.577519\pi$
$257$	−1986.94	−0.482265	−0.241132	+	0.970492i	$0.577519\pi$
$258$	−949.676	−0.229164
$259$	−1937.29	−0.464777
$260$	0	0
$261$	542.143	0.128574
$262$	8603.60	2.02875
$263$	981.453	0.230110	0.115055	−	0.993359i	$-0.463296\pi$
$263$	981.453	0.230110	0.115055	+	0.993359i	$0.463296\pi$
$264$	120.502	0.0280924
$265$	5213.44	1.20852
$266$	−675.256	−0.155649
$267$	160.865	0.0368719
$268$	3470.51	0.791027
$269$	1906.21	0.432058	0.216029	−	0.976387i	$-0.430689\pi$
$269$	1906.21	0.432058	0.216029	+	0.976387i	$0.430689\pi$
$270$	−5236.46	−1.18030
$271$	1365.89	0.306169	0.153085	−	0.988213i	$-0.451079\pi$
$271$	1365.89	0.306169	0.153085	+	0.988213i	$0.451079\pi$
$272$	3867.03	0.862034
$273$	0	0
$274$	−2819.74	−0.621704
$275$	1180.57	0.258877
$276$	1033.40	0.225374
$277$	7904.26	1.71452	0.857258	−	0.514887i	$-0.172166\pi$
$277$	7904.26	1.71452	0.857258	+	0.514887i	$0.172166\pi$
$278$	9224.54	1.99011
$279$	−2576.34	−0.552838
$280$	−724.206	−0.154570
$281$	−7155.53	−1.51909	−0.759543	−	0.650457i	$-0.774577\pi$
$281$	−7155.53	−1.51909	−0.759543	+	0.650457i	$0.774577\pi$
$282$	−1366.33	−0.288523
$283$	−8385.41	−1.76135	−0.880673	−	0.473724i	$-0.842909\pi$
$283$	−8385.41	−1.76135	−0.880673	+	0.473724i	$0.842909\pi$
$284$	3418.75	0.714315
$285$	−625.795	−0.130066
$286$	0	0
$287$	1187.11	0.244156
$288$	−5544.15	−1.13435
$289$	−2206.98	−0.449212
$290$	−1315.38	−0.266351
$291$	1470.46	0.296219
$292$	4230.98	0.847944
$293$	−4535.90	−0.904402	−0.452201	−	0.891916i	$-0.649361\pi$
$293$	−4535.90	−0.904402	−0.452201	+	0.891916i	$0.649361\pi$
$294$	1914.52	0.379787
$295$	−6812.72	−1.34458
$296$	−1539.75	−0.302352
$297$	−996.580	−0.194705
$298$	−3762.30	−0.731356
$299$	0	0
$300$	1220.53	0.234891
$301$	1086.22	0.208002
$302$	−5904.26	−1.12501
$303$	1315.25	0.249369
$304$	−1712.11	−0.323013
$305$	5271.81	0.989715
$306$	−4699.13	−0.877881
$307$	139.229	0.0258834	0.0129417	−	0.999916i	$-0.495880\pi$
$307$	139.229	0.0258834	0.0129417	+	0.999916i	$0.495880\pi$
$308$	542.568	0.100376
$309$	−1102.85	−0.203038
$310$	6250.88	1.14525
$311$	−4772.43	−0.870160	−0.435080	−	0.900392i	$-0.643280\pi$
$311$	−4772.43	−0.870160	−0.435080	+	0.900392i	$0.643280\pi$
$312$	0	0
$313$	−6634.44	−1.19809	−0.599043	−	0.800717i	$-0.704452\pi$
$313$	−6634.44	−1.19809	−0.599043	+	0.800717i	$0.704452\pi$
$314$	9922.64	1.78333
$315$	2807.42	0.502160
$316$	−554.161	−0.0986518
$317$	−7518.48	−1.33211	−0.666057	−	0.745901i	$-0.732019\pi$
$317$	−7518.48	−1.33211	−0.666057	+	0.745901i	$0.732019\pi$
$318$	2312.14	0.407730
$319$	−250.337	−0.0439379
$320$	4386.93	0.766366
$321$	1519.00	0.264120
$322$	−2664.21	−0.461089
$323$	−1198.07	−0.206386
$324$	3072.94	0.526909
$325$	0	0
$326$	6346.07	1.07815
$327$	−3396.79	−0.574442
$328$	943.511	0.158831
$329$	1562.77	0.261880
$330$	1133.39	0.189063
$331$	−3447.09	−0.572415	−0.286207	−	0.958168i	$-0.592395\pi$
$331$	−3447.09	−0.572415	−0.286207	+	0.958168i	$0.592395\pi$
$332$	−3980.33	−0.657979
$333$	5968.92	0.982267
$334$	2445.21	0.400587
$335$	−8291.98	−1.35236
$336$	−1024.61	−0.166360
$337$	−5640.83	−0.911796	−0.455898	−	0.890032i	$-0.650682\pi$
$337$	−5640.83	−0.911796	−0.455898	+	0.890032i	$0.650682\pi$
$338$	0	0
$339$	4054.97	0.649663
$340$	5058.20	0.806822
$341$	1189.64	0.188923
$342$	2080.51	0.328951
$343$	−4841.79	−0.762192
$344$	863.323	0.135312
$345$	−2469.07	−0.385305
$346$	15303.4	2.37779
$347$	−12177.5	−1.88393	−0.941964	−	0.335715i	$-0.891022\pi$
$347$	−12177.5	−1.88393	−0.941964	+	0.335715i	$0.891022\pi$
$348$	−258.810	−0.0398669
$349$	5197.21	0.797135	0.398567	−	0.917139i	$-0.369507\pi$
$349$	5197.21	0.797135	0.398567	+	0.917139i	$0.369507\pi$
$350$	−3146.66	−0.480560
$351$	0	0
$352$	2560.04	0.387644
$353$	−6008.89	−0.906008	−0.453004	−	0.891508i	$-0.649648\pi$
$353$	−6008.89	−0.906008	−0.453004	+	0.891508i	$0.649648\pi$
$354$	−3021.41	−0.453634
$355$	−8168.31	−1.22121
$356$	575.677	0.0857045
$357$	−716.986	−0.106294
$358$	−11505.7	−1.69858
$359$	1179.25	0.173367	0.0866834	−	0.996236i	$-0.472373\pi$
$359$	1179.25	0.173367	0.0866834	+	0.996236i	$0.472373\pi$
$360$	2231.33	0.326671
$361$	−6328.56	−0.922665
$362$	−6871.36	−0.997653
$363$	215.701	0.0311883
$364$	0	0
$365$	−10109.0	−1.44966
$366$	2338.03	0.333909
$367$	−12240.1	−1.74096	−0.870478	−	0.492208i	$-0.836190\pi$
$367$	−12240.1	−1.74096	−0.870478	+	0.492208i	$0.836190\pi$
$368$	−6755.09	−0.956885
$369$	−3657.57	−0.516004
$370$	−14482.2	−2.03484
$371$	−2644.57	−0.370079
$372$	1229.91	0.171418
$373$	−6058.31	−0.840985	−0.420493	−	0.907296i	$-0.638143\pi$
$373$	−6058.31	−0.840985	−0.420493	+	0.907296i	$0.638143\pi$
$374$	2169.85	0.300000
$375$	480.266	0.0661355
$376$	1242.09	0.170361
$377$	0	0
$378$	2656.25	0.361436
$379$	−10184.7	−1.38035	−0.690177	−	0.723641i	$-0.742467\pi$
$379$	−10184.7	−1.38035	−0.690177	+	0.723641i	$0.742467\pi$
$380$	−2239.49	−0.302325
$381$	4074.44	0.547874
$382$	−16766.5	−2.24568
$383$	2516.38	0.335720	0.167860	−	0.985811i	$-0.446314\pi$
$383$	2516.38	0.335720	0.167860	+	0.985811i	$0.446314\pi$
$384$	−1373.44	−0.182520
$385$	−1296.34	−0.171604
$386$	7981.73	1.05249
$387$	−3346.72	−0.439595
$388$	5262.21	0.688527
$389$	5280.96	0.688317	0.344159	−	0.938912i	$-0.388164\pi$
$389$	5280.96	0.688317	0.344159	+	0.938912i	$0.388164\pi$
$390$	0	0
$391$	−4726.99	−0.611392
$392$	−1740.44	−0.224249
$393$	−4044.60	−0.519143
$394$	−4343.24	−0.555354
$395$	1324.04	0.168657
$396$	−1671.69	−0.212136
$397$	−8740.31	−1.10495	−0.552473	−	0.833531i	$-0.686316\pi$
$397$	−8740.31	−1.10495	−0.552473	+	0.833531i	$0.686316\pi$
$398$	2308.99	0.290802
$399$	317.441	0.0398294
$400$	−7978.33	−0.997291
$401$	8259.89	1.02863	0.514314	−	0.857602i	$-0.328047\pi$
$401$	8259.89	1.02863	0.514314	+	0.857602i	$0.328047\pi$
$402$	−3677.46	−0.456256
$403$	0	0
$404$	4706.77	0.579631
$405$	−7342.07	−0.900815
$406$	667.241	0.0815630
$407$	−2756.18	−0.335673
$408$	−569.859	−0.0691476
$409$	8637.50	1.04425	0.522123	−	0.852870i	$-0.325140\pi$
$409$	8637.50	1.04425	0.522123	+	0.852870i	$0.325140\pi$
$410$	8874.22	1.06894
$411$	1325.58	0.159090
$412$	−3946.68	−0.471939
$413$	3455.83	0.411743
$414$	8208.64	0.974475
$415$	9510.08	1.12489
$416$	0	0
$417$	−4336.51	−0.509256
$418$	−960.687	−0.112413
$419$	1732.54	0.202005	0.101003	−	0.994886i	$-0.467795\pi$
$419$	1732.54	0.202005	0.101003	+	0.994886i	$0.467795\pi$
$420$	−1340.22	−0.155705
$421$	4257.84	0.492909	0.246454	−	0.969154i	$-0.420734\pi$
$421$	4257.84	0.492909	0.246454	+	0.969154i	$0.420734\pi$
$422$	−12815.7	−1.47834
$423$	−4815.02	−0.553462
$424$	−2101.90	−0.240748
$425$	−5582.97	−0.637209
$426$	−3622.61	−0.412010
$427$	−2674.18	−0.303075
$428$	5435.94	0.613916
$429$	0	0
$430$	8120.01	0.910655
$431$	−5502.16	−0.614918	−0.307459	−	0.951561i	$-0.599479\pi$
$431$	−5502.16	−0.614918	−0.307459	+	0.951561i	$0.599479\pi$
$432$	6734.91	0.750077
$433$	9165.87	1.01728	0.508642	−	0.860978i	$-0.330148\pi$
$433$	9165.87	1.01728	0.508642	+	0.860978i	$0.330148\pi$
$434$	−3170.83	−0.350702
$435$	618.367	0.0681573
$436$	−12155.8	−1.33523
$437$	2092.85	0.229095
$438$	−4483.28	−0.489085
$439$	−13566.2	−1.47489	−0.737445	−	0.675407i	$-0.763968\pi$
$439$	−13566.2	−1.47489	−0.737445	+	0.675407i	$0.763968\pi$
$440$	−1030.33	−0.111634
$441$	6746.91	0.728529
$442$	0	0
$443$	−13603.0	−1.45892	−0.729458	−	0.684025i	$-0.760228\pi$
$443$	−13603.0	−1.45892	−0.729458	+	0.684025i	$0.760228\pi$
$444$	−2849.47	−0.304572
$445$	−1375.45	−0.146522
$446$	5768.38	0.612423
$447$	1768.68	0.187149
$448$	−2225.32	−0.234679
$449$	2030.96	0.213467	0.106734	−	0.994288i	$-0.465961\pi$
$449$	2030.96	0.213467	0.106734	+	0.994288i	$0.465961\pi$
$450$	9695.09	1.01562
$451$	1688.90	0.176335
$452$	14511.2	1.51007
$453$	2775.63	0.287881
$454$	−8295.98	−0.857598
$455$	0	0
$456$	252.302	0.0259103
$457$	−1178.15	−0.120594	−0.0602970	−	0.998180i	$-0.519205\pi$
$457$	−1178.15	−0.120594	−0.0602970	+	0.998180i	$0.519205\pi$
$458$	24242.0	2.47326
$459$	4712.86	0.479254
$460$	−8835.87	−0.895597
$461$	2627.39	0.265444	0.132722	−	0.991153i	$-0.457628\pi$
$461$	2627.39	0.265444	0.132722	+	0.991153i	$0.457628\pi$
$462$	−574.922	−0.0578956
$463$	−4284.84	−0.430094	−0.215047	−	0.976604i	$-0.568990\pi$
$463$	−4284.84	−0.430094	−0.215047	+	0.976604i	$0.568990\pi$
$464$	1691.78	0.169265
$465$	−2938.57	−0.293060
$466$	7969.65	0.792247
$467$	2334.12	0.231285	0.115643	−	0.993291i	$-0.463107\pi$
$467$	2334.12	0.231285	0.115643	+	0.993291i	$0.463107\pi$
$468$	0	0
$469$	4206.20	0.414124
$470$	11682.5	1.14654
$471$	−4664.69	−0.456343
$472$	2746.68	0.267852
$473$	1545.36	0.150224
$474$	587.206	0.0569014
$475$	2471.83	0.238769
$476$	−2565.83	−0.247068
$477$	8148.12	0.782132
$478$	−1317.44	−0.126063
$479$	−19780.0	−1.88679	−0.943396	−	0.331669i	$-0.892388\pi$
$479$	−19780.0	−1.88679	−0.943396	+	0.331669i	$0.892388\pi$
$480$	−6323.65	−0.601321
$481$	0	0
$482$	−15198.2	−1.43622
$483$	1252.46	0.117990
$484$	771.913	0.0724937
$485$	−12572.8	−1.17712
$486$	−12532.0	−1.16968
$487$	−15829.4	−1.47289	−0.736446	−	0.676496i	$-0.763498\pi$
$487$	−15829.4	−1.47289	−0.736446	+	0.676496i	$0.763498\pi$
$488$	−2125.43	−0.197160
$489$	−2983.32	−0.275890
$490$	−16369.8	−1.50920
$491$	4065.47	0.373670	0.186835	−	0.982391i	$-0.440177\pi$
$491$	4065.47	0.373670	0.186835	+	0.982391i	$0.440177\pi$
$492$	1746.07	0.159997
$493$	1183.85	0.108150
$494$	0	0
$495$	3994.12	0.362672
$496$	−8039.61	−0.727801
$497$	4143.46	0.373963
$498$	4217.68	0.379516
$499$	−1624.33	−0.145722	−0.0728609	−	0.997342i	$-0.523213\pi$
$499$	−1624.33	−0.145722	−0.0728609	+	0.997342i	$0.523213\pi$
$500$	1718.69	0.153724
$501$	−1149.51	−0.102507
$502$	−11162.6	−0.992451
$503$	9339.50	0.827888	0.413944	−	0.910302i	$-0.364151\pi$
$503$	9339.50	0.827888	0.413944	+	0.910302i	$0.364151\pi$
$504$	−1131.87	−0.100034
$505$	−11245.7	−0.990949
$506$	−3790.38	−0.333010
$507$	0	0
$508$	14580.9	1.27347
$509$	2020.59	0.175955	0.0879775	−	0.996122i	$-0.471960\pi$
$509$	2020.59	0.175955	0.0879775	+	0.996122i	$0.471960\pi$
$510$	−5359.82	−0.465367
$511$	5127.87	0.443921
$512$	−13646.2	−1.17790
$513$	−2086.59	−0.179582
$514$	7534.53	0.646564
$515$	9429.68	0.806838
$516$	1597.67	0.136305
$517$	2223.36	0.189136
$518$	7346.24	0.623118
$519$	−7194.21	−0.608460
$520$	0	0
$521$	−581.973	−0.0489380	−0.0244690	−	0.999701i	$-0.507790\pi$
$521$	−581.973	−0.0489380	−0.0244690	+	0.999701i	$0.507790\pi$
$522$	−2055.82	−0.172377
$523$	−20783.3	−1.73765	−0.868826	−	0.495118i	$-0.835125\pi$
$523$	−20783.3	−1.73765	−0.868826	+	0.495118i	$0.835125\pi$
$524$	−14474.1	−1.20669
$525$	1479.26	0.122972
$526$	−3721.69	−0.308505
$527$	−5625.85	−0.465021
$528$	−1457.71	−0.120149
$529$	−3909.70	−0.321336
$530$	−19769.5	−1.62025
$531$	−10647.7	−0.870186
$532$	1136.00	0.0925790
$533$	0	0
$534$	−610.005	−0.0494335
$535$	−12987.9	−1.04956
$536$	3343.08	0.269401
$537$	5408.87	0.434655
$538$	−7228.38	−0.579252
$539$	−3115.42	−0.248962
$540$	8809.47	0.702036
$541$	3407.95	0.270830	0.135415	−	0.990789i	$-0.456763\pi$
$541$	3407.95	0.270830	0.135415	+	0.990789i	$0.456763\pi$
$542$	−5179.49	−0.410476
$543$	3230.26	0.255292
$544$	−12106.5	−0.954160
$545$	29043.5	2.28273
$546$	0	0
$547$	−4526.36	−0.353808	−0.176904	−	0.984228i	$-0.556608\pi$
$547$	−4526.36	−0.353808	−0.176904	+	0.984228i	$0.556608\pi$
$548$	4743.75	0.369786
$549$	8239.36	0.640523
$550$	−4476.75	−0.347072
$551$	−524.144	−0.0405251
$552$	995.453	0.0767560
$553$	−671.633	−0.0516469
$554$	−29973.1	−2.29862
$555$	6808.15	0.520702
$556$	−15518.7	−1.18371
$557$	20100.5	1.52906	0.764529	−	0.644590i	$-0.222972\pi$
$557$	20100.5	1.52906	0.764529	+	0.644590i	$0.222972\pi$
$558$	9769.56	0.741180
$559$	0	0
$560$	8760.70	0.661084
$561$	−1020.06	−0.0767680
$562$	27133.9	2.03661
$563$	−5118.56	−0.383165	−0.191582	−	0.981477i	$-0.561362\pi$
$563$	−5118.56	−0.383165	−0.191582	+	0.981477i	$0.561362\pi$
$564$	2298.62	0.171612
$565$	−34671.2	−2.58165
$566$	31797.7	2.36141
$567$	3724.34	0.275851
$568$	3293.21	0.243275
$569$	−7930.55	−0.584299	−0.292150	−	0.956373i	$-0.594370\pi$
$569$	−7930.55	−0.584299	−0.292150	+	0.956373i	$0.594370\pi$
$570$	2373.03	0.174378
$571$	−11926.5	−0.874093	−0.437047	−	0.899439i	$-0.643975\pi$
$571$	−11926.5	−0.874093	−0.437047	+	0.899439i	$0.643975\pi$
$572$	0	0
$573$	7882.04	0.574655
$574$	−4501.54	−0.327336
$575$	9752.56	0.707321
$576$	6856.37	0.495976
$577$	6695.61	0.483088	0.241544	−	0.970390i	$-0.422346\pi$
$577$	6695.61	0.483088	0.241544	+	0.970390i	$0.422346\pi$
$578$	8368.91	0.602251
$579$	−3752.25	−0.269324
$580$	2212.91	0.158424
$581$	−4824.09	−0.344470
$582$	−5576.00	−0.397135
$583$	−3762.44	−0.267280
$584$	4075.62	0.288785
$585$	0	0
$586$	17200.2	1.21252
$587$	17240.6	1.21226	0.606128	−	0.795367i	$-0.292722\pi$
$587$	17240.6	1.21226	0.606128	+	0.795367i	$0.292722\pi$
$588$	−3220.87	−0.225895
$589$	2490.81	0.174248
$590$	25834.0	1.80266
$591$	2041.78	0.142111
$592$	18626.3	1.29314
$593$	−7312.38	−0.506380	−0.253190	−	0.967417i	$-0.581480\pi$
$593$	−7312.38	−0.506380	−0.253190	+	0.967417i	$0.581480\pi$
$594$	3779.05	0.261038
$595$	6130.45	0.422393
$596$	6329.43	0.435006
$597$	−1085.47	−0.0744141
$598$	0	0
$599$	2440.17	0.166448	0.0832242	−	0.996531i	$-0.473478\pi$
$599$	2440.17	0.166448	0.0832242	+	0.996531i	$0.473478\pi$
$600$	1175.71	0.0799971
$601$	14575.9	0.989293	0.494647	−	0.869094i	$-0.335297\pi$
$601$	14575.9	0.989293	0.494647	+	0.869094i	$0.335297\pi$
$602$	−4118.96	−0.278864
$603$	−12959.6	−0.875217
$604$	9932.93	0.669148
$605$	−1844.31	−0.123937
$606$	−4987.44	−0.334325
$607$	3200.73	0.214026	0.107013	−	0.994258i	$-0.465871\pi$
$607$	3200.73	0.214026	0.107013	+	0.994258i	$0.465871\pi$
$608$	5360.09	0.357534
$609$	−313.673	−0.0208714
$610$	−19990.8	−1.32689
$611$	0	0
$612$	7905.50	0.522158
$613$	−11170.3	−0.735995	−0.367997	−	0.929827i	$-0.619956\pi$
$613$	−11170.3	−0.735995	−0.367997	+	0.929827i	$0.619956\pi$
$614$	−527.958	−0.0347014
$615$	−4171.82	−0.273535
$616$	522.645	0.0341850
$617$	9418.66	0.614556	0.307278	−	0.951620i	$-0.400582\pi$
$617$	9418.66	0.614556	0.307278	+	0.951620i	$0.400582\pi$
$618$	4182.02	0.272210
$619$	−14606.4	−0.948436	−0.474218	−	0.880407i	$-0.657269\pi$
$619$	−14606.4	−0.948436	−0.474218	+	0.880407i	$0.657269\pi$
$620$	−10516.1	−0.681186
$621$	−8232.63	−0.531987
$622$	18097.2	1.16661
$623$	697.710	0.0448686
$624$	0	0
$625$	−17522.0	−1.12141
$626$	25158.0	1.60625
$627$	451.624	0.0287658
$628$	−16693.2	−1.06072
$629$	13034.1	0.826237
$630$	−10645.8	−0.673237
$631$	−13626.5	−0.859685	−0.429842	−	0.902904i	$-0.641431\pi$
$631$	−13626.5	−0.859685	−0.429842	+	0.902904i	$0.641431\pi$
$632$	−533.812	−0.0335979
$633$	6024.75	0.378297
$634$	28510.3	1.78594
$635$	−34837.7	−2.17715
$636$	−3889.78	−0.242516
$637$	0	0
$638$	949.284	0.0589068
$639$	−12766.3	−0.790341
$640$	11743.3	0.725304
$641$	−8560.30	−0.527475	−0.263738	−	0.964594i	$-0.584955\pi$
$641$	−8560.30	−0.527475	−0.263738	+	0.964594i	$0.584955\pi$
$642$	−5760.09	−0.354101
$643$	−4289.98	−0.263111	−0.131555	−	0.991309i	$-0.541997\pi$
$643$	−4289.98	−0.263111	−0.131555	+	0.991309i	$0.541997\pi$
$644$	4482.09	0.274253
$645$	−3817.26	−0.233030
$646$	4543.13	0.276698
$647$	15030.5	0.913308	0.456654	−	0.889644i	$-0.349048\pi$
$647$	15030.5	0.913308	0.456654	+	0.889644i	$0.349048\pi$
$648$	2960.10	0.179450
$649$	4916.61	0.297371
$650$	0	0
$651$	1490.62	0.0897421
$652$	−10676.2	−0.641276
$653$	−21685.7	−1.29958	−0.649791	−	0.760113i	$-0.725143\pi$
$653$	−21685.7	−1.29958	−0.649791	+	0.760113i	$0.725143\pi$
$654$	12880.7	0.770145
$655$	34582.5	2.06298
$656$	−11413.6	−0.679310
$657$	−15799.4	−0.938192
$658$	−5926.07	−0.351098
$659$	2670.84	0.157878	0.0789388	−	0.996879i	$-0.474847\pi$
$659$	2670.84	0.157878	0.0789388	+	0.996879i	$0.474847\pi$
$660$	−1906.73	−0.112454
$661$	−6827.82	−0.401772	−0.200886	−	0.979615i	$-0.564382\pi$
$661$	−6827.82	−0.401772	−0.200886	+	0.979615i	$0.564382\pi$
$662$	13071.5	0.767427
$663$	0	0
$664$	−3834.17	−0.224089
$665$	−2714.22	−0.158275
$666$	−22634.3	−1.31691
$667$	−2068.01	−0.120050
$668$	−4113.66	−0.238267
$669$	−2711.75	−0.156715
$670$	31443.4	1.81308
$671$	−3804.57	−0.218888
$672$	3207.74	0.184139
$673$	31304.6	1.79302	0.896510	−	0.443024i	$-0.146094\pi$
$673$	31304.6	1.79302	0.896510	+	0.443024i	$0.146094\pi$
$674$	21390.1	1.22243
$675$	−9723.42	−0.554451
$676$	0	0
$677$	−9189.19	−0.521668	−0.260834	−	0.965384i	$-0.583997\pi$
$677$	−9189.19	−0.521668	−0.260834	+	0.965384i	$0.583997\pi$
$678$	−15376.6	−0.870993
$679$	6377.70	0.360462
$680$	4872.46	0.274780
$681$	3899.99	0.219453
$682$	−4511.14	−0.253285
$683$	−17198.3	−0.963505	−0.481752	−	0.876307i	$-0.659999\pi$
$683$	−17198.3	−0.963505	−0.481752	+	0.876307i	$0.659999\pi$
$684$	−3500.11	−0.195658
$685$	−11334.1	−0.632194
$686$	18360.2	1.02186
$687$	−11396.3	−0.632889
$688$	−10443.6	−0.578719
$689$	0	0
$690$	9362.76	0.516571
$691$	−32780.5	−1.80467	−0.902336	−	0.431033i	$-0.858149\pi$
$691$	−32780.5	−1.80467	−0.902336	+	0.431033i	$0.858149\pi$
$692$	−25745.4	−1.41430
$693$	−2026.06	−0.111059
$694$	46177.4	2.52575
$695$	37078.4	2.02369
$696$	−249.307	−0.0135775
$697$	−7986.88	−0.434038
$698$	−19707.9	−1.06871
$699$	−3746.58	−0.202730
$700$	5293.72	0.285834
$701$	15938.2	0.858742	0.429371	−	0.903128i	$-0.358735\pi$
$701$	15938.2	0.858742	0.429371	+	0.903128i	$0.358735\pi$
$702$	0	0
$703$	−5770.76	−0.309600
$704$	−3165.96	−0.169491
$705$	−5492.01	−0.293392
$706$	22785.8	1.21467
$707$	5704.52	0.303452
$708$	5083.02	0.269819
$709$	−28374.5	−1.50300	−0.751500	−	0.659733i	$-0.770669\pi$
$709$	−28374.5	−1.50300	−0.751500	+	0.659733i	$0.770669\pi$
$710$	30974.4	1.63725
$711$	2069.35	0.109151
$712$	554.538	0.0291885
$713$	9827.47	0.516187
$714$	2718.83	0.142506
$715$	0	0
$716$	19356.3	1.01031
$717$	619.336	0.0322588
$718$	−4471.76	−0.232430
$719$	−4008.81	−0.207933	−0.103966	−	0.994581i	$-0.533153\pi$
$719$	−4008.81	−0.207933	−0.103966	+	0.994581i	$0.533153\pi$
$720$	−26992.4	−1.39715
$721$	−4783.31	−0.247073
$722$	23998.0	1.23700
$723$	7144.74	0.367518
$724$	11559.9	0.593398
$725$	−2442.49	−0.125120
$726$	−817.942	−0.0418136
$727$	12935.3	0.659896	0.329948	−	0.943999i	$-0.392969\pi$
$727$	12935.3	0.659896	0.329948	+	0.943999i	$0.392969\pi$
$728$	0	0
$729$	−7114.34	−0.361446
$730$	38333.4	1.94354
$731$	−7308.09	−0.369767
$732$	−3933.34	−0.198607
$733$	38201.0	1.92495	0.962473	−	0.271379i	$-0.0874797\pi$
$733$	38201.0	1.92495	0.962473	+	0.271379i	$0.0874797\pi$
$734$	46414.9	2.33407
$735$	7695.51	0.386195
$736$	21148.2	1.05915
$737$	5984.16	0.299090
$738$	13869.6	0.691797
$739$	−11127.9	−0.553920	−0.276960	−	0.960881i	$-0.589327\pi$
$739$	−11127.9	−0.553920	−0.276960	+	0.960881i	$0.589327\pi$
$740$	24363.8	1.21031
$741$	0	0
$742$	10028.3	0.496159
$743$	10127.1	0.500038	0.250019	−	0.968241i	$-0.419563\pi$
$743$	10127.1	0.500038	0.250019	+	0.968241i	$0.419563\pi$
$744$	1184.74	0.0583801
$745$	−15122.7	−0.743696
$746$	22973.3	1.12749
$747$	14863.4	0.728009
$748$	−3650.41	−0.178439
$749$	6588.26	0.321402
$750$	−1821.18	−0.0886667
$751$	36539.1	1.77540	0.887702	−	0.460418i	$-0.152300\pi$
$751$	36539.1	1.77540	0.887702	+	0.460418i	$0.152300\pi$
$752$	−15025.5	−0.728623
$753$	5247.59	0.253961
$754$	0	0
$755$	−23732.4	−1.14399
$756$	−4468.70	−0.214980
$757$	8129.43	0.390316	0.195158	−	0.980772i	$-0.437478\pi$
$757$	8129.43	0.390316	0.195158	+	0.980772i	$0.437478\pi$
$758$	38620.7	1.85062
$759$	1781.88	0.0852149
$760$	−2157.25	−0.102963
$761$	29242.5	1.39296	0.696478	−	0.717579i	$-0.254750\pi$
$761$	29242.5	1.39296	0.696478	+	0.717579i	$0.254750\pi$
$762$	−15450.4	−0.734525
$763$	−14732.6	−0.699027
$764$	28206.9	1.33572
$765$	−18888.4	−0.892693
$766$	−9542.16	−0.450095
$767$	0	0
$768$	9312.69	0.437556
$769$	−10834.1	−0.508046	−0.254023	−	0.967198i	$-0.581754\pi$
$769$	−10834.1	−0.508046	−0.254023	+	0.967198i	$0.581754\pi$
$770$	4915.75	0.230067
$771$	−3542.02	−0.165451
$772$	−13427.9	−0.626012
$773$	38173.4	1.77620	0.888100	−	0.459650i	$-0.152025\pi$
$773$	38173.4	1.77620	0.888100	+	0.459650i	$0.152025\pi$
$774$	12690.8	0.589357
$775$	11607.1	0.537984
$776$	5068.98	0.234492
$777$	−3453.51	−0.159451
$778$	−20025.5	−0.922815
$779$	3536.14	0.162639
$780$	0	0
$781$	5894.91	0.270085
$782$	17924.9	0.819682
$783$	2061.83	0.0941043
$784$	21054.1	0.959095
$785$	39884.5	1.81342
$786$	15337.2	0.696006
$787$	33123.5	1.50028	0.750142	−	0.661276i	$-0.229985\pi$
$787$	33123.5	1.50028	0.750142	+	0.661276i	$0.229985\pi$
$788$	7306.77	0.330321
$789$	1749.59	0.0789442
$790$	−5020.79	−0.226116
$791$	17587.4	0.790562
$792$	−1610.31	−0.0722473
$793$	0	0
$794$	33143.5	1.48138
$795$	9293.74	0.414610
$796$	−3884.48	−0.172967
$797$	4565.11	0.202892	0.101446	−	0.994841i	$-0.467653\pi$
$797$	4565.11	0.202892	0.101446	+	0.994841i	$0.467653\pi$
$798$	−1203.74	−0.0533986
$799$	−10514.4	−0.465546
$800$	24977.8	1.10387
$801$	−2149.70	−0.0948262
$802$	−31321.7	−1.37906
$803$	7295.43	0.320611
$804$	6186.71	0.271379
$805$	−10708.9	−0.468869
$806$	0	0
$807$	3398.10	0.148227
$808$	4533.94	0.197405
$809$	−41059.4	−1.78439	−0.892195	−	0.451651i	$-0.850835\pi$
$809$	−41059.4	−1.78439	−0.892195	+	0.451651i	$0.850835\pi$
$810$	27841.3	1.20771
$811$	−14798.8	−0.640758	−0.320379	−	0.947289i	$-0.603810\pi$
$811$	−14798.8	−0.640758	−0.320379	+	0.947289i	$0.603810\pi$
$812$	−1122.52	−0.0485132
$813$	2434.90	0.105038
$814$	10451.5	0.450031
$815$	25508.3	1.09634
$816$	6893.57	0.295739
$817$	3235.61	0.138555
$818$	−32753.6	−1.40000
$819$	0	0
$820$	−14929.4	−0.635801
$821$	34422.4	1.46328	0.731638	−	0.681693i	$-0.238756\pi$
$821$	34422.4	1.46328	0.731638	+	0.681693i	$0.238756\pi$
$822$	−5026.62	−0.213289
$823$	27464.6	1.16325	0.581626	−	0.813457i	$-0.302417\pi$
$823$	27464.6	1.16325	0.581626	+	0.813457i	$0.302417\pi$
$824$	−3801.76	−0.160729
$825$	2104.55	0.0888132
$826$	−13104.6	−0.552017
$827$	31221.5	1.31279	0.656396	−	0.754416i	$-0.272080\pi$
$827$	31221.5	1.31279	0.656396	+	0.754416i	$0.272080\pi$
$828$	−13809.7	−0.579612
$829$	31629.7	1.32514	0.662572	−	0.748998i	$-0.269465\pi$
$829$	31629.7	1.32514	0.662572	+	0.748998i	$0.269465\pi$
$830$	−36062.4	−1.50813
$831$	14090.5	0.588201
$832$	0	0
$833$	14732.9	0.612804
$834$	16444.1	0.682750
$835$	9828.64	0.407346
$836$	1616.20	0.0668628
$837$	−9798.11	−0.404626
$838$	−6569.83	−0.270825
$839$	−21976.4	−0.904304	−0.452152	−	0.891941i	$-0.649344\pi$
$839$	−21976.4	−0.904304	−0.452152	+	0.891941i	$0.649344\pi$
$840$	−1291.01	−0.0530285
$841$	−23871.1	−0.978764
$842$	−16145.8	−0.660834
$843$	−12755.8	−0.521155
$844$	21560.3	0.879309
$845$	0	0
$846$	18258.7	0.742017
$847$	935.544	0.0379524
$848$	25426.6	1.02966
$849$	−14948.3	−0.604267
$850$	21170.7	0.854295
$851$	−22768.5	−0.917149
$852$	6094.44	0.245061
$853$	−16729.0	−0.671501	−0.335750	−	0.941951i	$-0.608990\pi$
$853$	−16729.0	−0.671501	−0.335750	+	0.941951i	$0.608990\pi$
$854$	10140.6	0.406327
$855$	8362.71	0.334501
$856$	5236.34	0.209082
$857$	47300.4	1.88536	0.942679	−	0.333700i	$-0.108297\pi$
$857$	47300.4	1.88536	0.942679	+	0.333700i	$0.108297\pi$
$858$	0	0
$859$	48682.9	1.93369	0.966845	−	0.255365i	$-0.0821957\pi$
$859$	48682.9	1.93369	0.966845	+	0.255365i	$0.0821957\pi$
$860$	−13660.6	−0.541653
$861$	2116.20	0.0837629
$862$	20864.3	0.824410
$863$	−41919.8	−1.65350	−0.826748	−	0.562572i	$-0.809812\pi$
$863$	−41919.8	−1.65350	−0.826748	+	0.562572i	$0.809812\pi$
$864$	−21085.0	−0.830238
$865$	61512.7	2.41791
$866$	−34757.2	−1.36385
$867$	−3934.27	−0.154112
$868$	5334.38	0.208595
$869$	−955.533	−0.0373006
$870$	−2344.86	−0.0913774
$871$	0	0
$872$	−11709.5	−0.454739
$873$	−19650.2	−0.761807
$874$	−7936.12	−0.307143
$875$	2083.02	0.0804789
$876$	7542.36	0.290905
$877$	41056.0	1.58080	0.790401	−	0.612590i	$-0.209872\pi$
$877$	41056.0	1.58080	0.790401	+	0.612590i	$0.209872\pi$
$878$	51443.2	1.97736
$879$	−8085.92	−0.310274
$880$	12463.9	0.477451
$881$	−7309.40	−0.279523	−0.139762	−	0.990185i	$-0.544634\pi$
$881$	−7309.40	−0.279523	−0.139762	+	0.990185i	$0.544634\pi$
$882$	−25584.4	−0.976726
$883$	−41702.6	−1.58936	−0.794679	−	0.607029i	$-0.792361\pi$
$883$	−41702.6	−1.58936	−0.794679	+	0.607029i	$0.792361\pi$
$884$	0	0
$885$	−12144.7	−0.461288
$886$	51583.1	1.95594
$887$	−3955.92	−0.149748	−0.0748742	−	0.997193i	$-0.523856\pi$
$887$	−3955.92	−0.149748	−0.0748742	+	0.997193i	$0.523856\pi$
$888$	−2744.84	−0.103728
$889$	17671.8	0.666696
$890$	5215.73	0.196440
$891$	5298.63	0.199226
$892$	−9704.33	−0.364266
$893$	4655.17	0.174445
$894$	−6706.86	−0.250907
$895$	−46247.5	−1.72724
$896$	−5956.91	−0.222105
$897$	0	0
$898$	−7701.43	−0.286192
$899$	−2461.25	−0.0913095
$900$	−16310.4	−0.604087
$901$	17792.7	0.657893
$902$	−6404.35	−0.236410
$903$	1936.35	0.0713595
$904$	13978.4	0.514286
$905$	−27619.7	−1.01449
$906$	−10525.2	−0.385958
$907$	36152.3	1.32350	0.661752	−	0.749723i	$-0.269813\pi$
$907$	36152.3	1.32350	0.661752	+	0.749723i	$0.269813\pi$
$908$	13956.6	0.510094
$909$	−17576.1	−0.641322
$910$	0	0
$911$	−35153.5	−1.27847	−0.639236	−	0.769010i	$-0.720749\pi$
$911$	−35153.5	−1.27847	−0.639236	+	0.769010i	$0.720749\pi$
$912$	−3052.09	−0.110817
$913$	−6863.24	−0.248784
$914$	4467.57	0.161678
$915$	9397.80	0.339543
$916$	−40783.0	−1.47108
$917$	−17542.4	−0.631734
$918$	−17871.3	−0.642528
$919$	40670.8	1.45986	0.729928	−	0.683524i	$-0.239554\pi$
$919$	40670.8	1.45986	0.729928	+	0.683524i	$0.239554\pi$
$920$	−8511.42	−0.305014
$921$	248.196	0.00887984
$922$	−9963.13	−0.355877
$923$	0	0
$924$	967.209	0.0344360
$925$	−26891.5	−0.955877
$926$	16248.2	0.576619
$927$	14737.7	0.522169
$928$	−5296.47	−0.187355
$929$	27841.2	0.983250	0.491625	−	0.870807i	$-0.336403\pi$
$929$	27841.2	0.983250	0.491625	+	0.870807i	$0.336403\pi$
$930$	11143.1	0.392901
$931$	−6522.92	−0.229624
$932$	−13407.6	−0.471224
$933$	−8507.58	−0.298527
$934$	−8851.04	−0.310080
$935$	8721.80	0.305062
$936$	0	0
$937$	−28093.8	−0.979494	−0.489747	−	0.871865i	$-0.662911\pi$
$937$	−28093.8	−0.979494	−0.489747	+	0.871865i	$0.662911\pi$
$938$	−15950.0	−0.555209
$939$	−11826.9	−0.411029
$940$	−19653.9	−0.681955
$941$	7281.12	0.252240	0.126120	−	0.992015i	$-0.459748\pi$
$941$	7281.12	0.252240	0.126120	+	0.992015i	$0.459748\pi$
$942$	17688.6	0.611811
$943$	13951.8	0.481796
$944$	−33226.6	−1.14558
$945$	10676.9	0.367535
$946$	−5860.06	−0.201403
$947$	12067.1	0.414074	0.207037	−	0.978333i	$-0.433618\pi$
$947$	12067.1	0.414074	0.207037	+	0.978333i	$0.433618\pi$
$948$	−987.875	−0.0338446
$949$	0	0
$950$	−9373.22	−0.320113
$951$	−13402.8	−0.457010
$952$	−2471.61	−0.0841442
$953$	−2988.84	−0.101593	−0.0507965	−	0.998709i	$-0.516176\pi$
$953$	−2988.84	−0.101593	−0.0507965	+	0.998709i	$0.516176\pi$
$954$	−30897.9	−1.04859
$955$	−67393.8	−2.28357
$956$	2216.37	0.0749818
$957$	−446.264	−0.0150738
$958$	75006.4	2.52959
$959$	5749.33	0.193593
$960$	7820.37	0.262918
$961$	−18094.8	−0.607391
$962$	0	0
$963$	−20298.9	−0.679256
$964$	25568.4	0.854254
$965$	32082.9	1.07024
$966$	−4749.36	−0.158187
$967$	−32465.5	−1.07965	−0.539825	−	0.841777i	$-0.681510\pi$
$967$	−32465.5	−1.07965	−0.539825	+	0.841777i	$0.681510\pi$
$968$	743.568	0.0246892
$969$	−2135.75	−0.0708051
$970$	47676.5	1.57814
$971$	−47570.8	−1.57221	−0.786107	−	0.618090i	$-0.787907\pi$
$971$	−47570.8	−1.57221	−0.786107	+	0.618090i	$0.787907\pi$
$972$	21083.0	0.695719
$973$	−18808.4	−0.619702
$974$	60025.5	1.97468
$975$	0	0
$976$	25711.3	0.843238
$977$	2432.41	0.0796518	0.0398259	−	0.999207i	$-0.487320\pi$
$977$	2432.41	0.0796518	0.0398259	+	0.999207i	$0.487320\pi$
$978$	11312.8	0.369882
$979$	992.633	0.0324052
$980$	27539.4	0.897666
$981$	45392.4	1.47734
$982$	−15416.4	−0.500973
$983$	−36245.9	−1.17606	−0.588029	−	0.808840i	$-0.700096\pi$
$983$	−36245.9	−1.17606	−0.588029	+	0.808840i	$0.700096\pi$
$984$	1681.95	0.0544905
$985$	−17457.8	−0.564724
$986$	−4489.20	−0.144995
$987$	2785.88	0.0898435
$988$	0	0
$989$	12766.1	0.410452
$990$	−15145.8	−0.486228
$991$	−35000.5	−1.12192	−0.560962	−	0.827841i	$-0.689569\pi$
$991$	−35000.5	−1.12192	−0.560962	+	0.827841i	$0.689569\pi$
$992$	25169.6	0.805581
$993$	−6144.96	−0.196379
$994$	−15712.1	−0.501366
$995$	9281.07	0.295708
$996$	−7095.54	−0.225734
$997$	−38157.6	−1.21210	−0.606050	−	0.795426i	$-0.707247\pi$
$997$	−38157.6	−1.21210	−0.606050	+	0.795426i	$0.707247\pi$
$998$	6159.51	0.195367
$999$	22700.4	0.718929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.n.1.9	✓	39
13.12	even	2		1859.4.a.o.1.31	yes	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.9	✓	39	1.1	even	1	trivial
1859.4.a.o.1.31	yes	39	13.12	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-3.79202 q^{2} +1.78265 q^{3} +6.37944 q^{4} -15.2422 q^{5} -6.75985 q^{6} +7.73177 q^{7} +6.14519 q^{8} -23.8222 q^{9} +O(q^{10})\)	\(q-3.79202 q^{2} +1.78265 q^{3} +6.37944 q^{4} -15.2422 q^{5} -6.75985 q^{6} +7.73177 q^{7} +6.14519 q^{8} -23.8222 q^{9} +57.7988 q^{10} +11.0000 q^{11} +11.3723 q^{12} -29.3190 q^{14} -27.1715 q^{15} -74.3383 q^{16} -52.0194 q^{17} +90.3342 q^{18} +23.0313 q^{19} -97.2367 q^{20} +13.7830 q^{21} -41.7123 q^{22} +90.8697 q^{23} +10.9547 q^{24} +107.325 q^{25} -90.5982 q^{27} +49.3244 q^{28} -22.7579 q^{29} +103.035 q^{30} +108.149 q^{31} +232.731 q^{32} +19.6092 q^{33} +197.259 q^{34} -117.849 q^{35} -151.972 q^{36} -250.562 q^{37} -87.3352 q^{38} -93.6662 q^{40} +153.536 q^{41} -52.2656 q^{42} +140.488 q^{43} +70.1739 q^{44} +363.102 q^{45} -344.580 q^{46} +202.124 q^{47} -132.519 q^{48} -283.220 q^{49} -406.978 q^{50} -92.7325 q^{51} -342.040 q^{53} +343.550 q^{54} -167.664 q^{55} +47.5132 q^{56} +41.0568 q^{57} +86.2986 q^{58} +446.964 q^{59} -173.339 q^{60} -345.870 q^{61} -410.104 q^{62} -184.187 q^{63} -287.815 q^{64} -74.3584 q^{66} +544.015 q^{67} -331.855 q^{68} +161.989 q^{69} +446.887 q^{70} +535.901 q^{71} -146.392 q^{72} +663.221 q^{73} +950.137 q^{74} +191.322 q^{75} +146.927 q^{76} +85.0494 q^{77} -86.8666 q^{79} +1133.08 q^{80} +481.693 q^{81} -582.214 q^{82} -623.931 q^{83} +87.9281 q^{84} +792.891 q^{85} -532.732 q^{86} -40.5694 q^{87} +67.5971 q^{88} +90.2394 q^{89} -1376.89 q^{90} +579.698 q^{92} +192.792 q^{93} -766.458 q^{94} -351.048 q^{95} +414.878 q^{96} +824.870 q^{97} +1073.98 q^{98} -262.044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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