LMFDB - Embedded newform 1859.4.a.o.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.00172 q^{2} -3.02985 q^{3} -6.99655 q^{4} +20.0383 q^{5} +3.03507 q^{6} -1.63570 q^{7} +15.0224 q^{8} -17.8200 q^{9} +O(q^{10})$	\(q-1.00172 q^{2} -3.02985 q^{3} -6.99655 q^{4} +20.0383 q^{5} +3.03507 q^{6} -1.63570 q^{7} +15.0224 q^{8} -17.8200 q^{9} -20.0728 q^{10} -11.0000 q^{11} +21.1985 q^{12} +1.63852 q^{14} -60.7131 q^{15} +40.9241 q^{16} -84.4929 q^{17} +17.8507 q^{18} +92.6768 q^{19} -140.199 q^{20} +4.95594 q^{21} +11.0189 q^{22} +18.2236 q^{23} -45.5156 q^{24} +276.534 q^{25} +135.798 q^{27} +11.4443 q^{28} +81.2112 q^{29} +60.8177 q^{30} -129.176 q^{31} -161.174 q^{32} +33.3284 q^{33} +84.6384 q^{34} -32.7767 q^{35} +124.679 q^{36} -305.194 q^{37} -92.8365 q^{38} +301.023 q^{40} +271.091 q^{41} -4.96447 q^{42} +7.78387 q^{43} +76.9621 q^{44} -357.083 q^{45} -18.2550 q^{46} -249.334 q^{47} -123.994 q^{48} -340.324 q^{49} -277.010 q^{50} +256.001 q^{51} +284.077 q^{53} -136.032 q^{54} -220.421 q^{55} -24.5722 q^{56} -280.797 q^{57} -81.3511 q^{58} -571.555 q^{59} +424.782 q^{60} -435.539 q^{61} +129.399 q^{62} +29.1482 q^{63} -165.942 q^{64} -33.3858 q^{66} -465.254 q^{67} +591.159 q^{68} -55.2148 q^{69} +32.8332 q^{70} +667.783 q^{71} -267.699 q^{72} +661.401 q^{73} +305.720 q^{74} -837.855 q^{75} -648.418 q^{76} +17.9927 q^{77} +857.861 q^{79} +820.050 q^{80} +69.6926 q^{81} -271.558 q^{82} +97.4502 q^{83} -34.6745 q^{84} -1693.09 q^{85} -7.79728 q^{86} -246.058 q^{87} -165.246 q^{88} -563.060 q^{89} +357.698 q^{90} -127.502 q^{92} +391.385 q^{93} +249.763 q^{94} +1857.09 q^{95} +488.332 q^{96} +1769.40 q^{97} +340.911 q^{98} +196.020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.00172	−0.354162	−0.177081	−	0.984196i	$-0.556666\pi$
$2$	−1.00172	−0.354162	−0.177081	+	0.984196i	$0.556666\pi$
$3$	−3.02985	−0.583095	−0.291548	−	0.956556i	$-0.594170\pi$
$3$	−3.02985	−0.583095	−0.291548	+	0.956556i	$0.594170\pi$
$4$	−6.99655	−0.874569
$5$	20.0383	1.79228	0.896140	−	0.443771i	$-0.146360\pi$
$5$	20.0383	1.79228	0.896140	+	0.443771i	$0.146360\pi$
$6$	3.03507	0.206510
$7$	−1.63570	−0.0883197	−0.0441598	−	0.999024i	$-0.514061\pi$
$7$	−1.63570	−0.0883197	−0.0441598	+	0.999024i	$0.514061\pi$
$8$	15.0224	0.663902
$9$	−17.8200	−0.660000
$10$	−20.0728	−0.634758
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	21.1985	0.509957
$13$	0	0
$13$	0	0
$14$	1.63852	0.0312795
$15$	−60.7131	−1.04507
$16$	40.9241	0.639440
$17$	−84.4929	−1.20544	−0.602721	−	0.797952i	$-0.705917\pi$
$17$	−84.4929	−1.20544	−0.602721	+	0.797952i	$0.705917\pi$
$18$	17.8507	0.233747
$19$	92.6768	1.11903	0.559514	−	0.828821i	$-0.310988\pi$
$19$	92.6768	1.11903	0.559514	+	0.828821i	$0.310988\pi$
$20$	−140.199	−1.56747
$21$	4.95594	0.0514988
$22$	11.0189	0.106784
$23$	18.2236	0.165212	0.0826062	−	0.996582i	$-0.473676\pi$
$23$	18.2236	0.165212	0.0826062	+	0.996582i	$0.473676\pi$
$24$	−45.5156	−0.387118
$25$	276.534	2.21227
$26$	0	0
$27$	135.798	0.967938
$28$	11.4443	0.0772417
$29$	81.2112	0.520018	0.260009	−	0.965606i	$-0.416274\pi$
$29$	81.2112	0.520018	0.260009	+	0.965606i	$0.416274\pi$
$30$	60.8177	0.370124
$31$	−129.176	−0.748411	−0.374205	−	0.927346i	$-0.622084\pi$
$31$	−129.176	−0.748411	−0.374205	+	0.927346i	$0.622084\pi$
$32$	−161.174	−0.890367
$33$	33.3284	0.175810
$34$	84.6384	0.426923
$35$	−32.7767	−0.158294
$36$	124.679	0.577216
$37$	−305.194	−1.35604	−0.678022	−	0.735042i	$-0.737163\pi$
$37$	−305.194	−1.35604	−0.678022	+	0.735042i	$0.737163\pi$
$38$	−92.8365	−0.396317
$39$	0	0
$40$	301.023	1.18990
$41$	271.091	1.03262	0.516308	−	0.856403i	$-0.327306\pi$
$41$	271.091	1.03262	0.516308	+	0.856403i	$0.327306\pi$
$42$	−4.96447	−0.0182389
$43$	7.78387	0.0276053	0.0138027	−	0.999905i	$-0.495606\pi$
$43$	7.78387	0.0276053	0.0138027	+	0.999905i	$0.495606\pi$
$44$	76.9621	0.263692
$45$	−357.083	−1.18291
$46$	−18.2550	−0.0585120
$47$	−249.334	−0.773809	−0.386905	−	0.922120i	$-0.626456\pi$
$47$	−249.334	−0.773809	−0.386905	+	0.922120i	$0.626456\pi$
$48$	−123.994	−0.372854
$49$	−340.324	−0.992200
$50$	−277.010	−0.783502
$51$	256.001	0.702888
$52$	0	0
$53$	284.077	0.736244	0.368122	−	0.929777i	$-0.380001\pi$
$53$	284.077	0.736244	0.368122	+	0.929777i	$0.380001\pi$
$54$	−136.032	−0.342807
$55$	−220.421	−0.540393
$56$	−24.5722	−0.0586356
$57$	−280.797	−0.652499
$58$	−81.3511	−0.184171
$59$	−571.555	−1.26119	−0.630594	−	0.776113i	$-0.717189\pi$
$59$	−571.555	−1.26119	−0.630594	+	0.776113i	$0.717189\pi$
$60$	424.782	0.913986
$61$	−435.539	−0.914182	−0.457091	−	0.889420i	$-0.651109\pi$
$61$	−435.539	−0.914182	−0.457091	+	0.889420i	$0.651109\pi$
$62$	129.399	0.265059
$63$	29.1482	0.0582910
$64$	−165.942	−0.324105
$65$	0	0
$66$	−33.3858	−0.0622652
$67$	−465.254	−0.848355	−0.424178	−	0.905579i	$-0.639437\pi$
$67$	−465.254	−0.848355	−0.424178	+	0.905579i	$0.639437\pi$
$68$	591.159	1.05424
$69$	−55.2148	−0.0963345
$70$	32.8332	0.0560617
$71$	667.783	1.11621	0.558107	−	0.829769i	$-0.311528\pi$
$71$	667.783	1.11621	0.558107	+	0.829769i	$0.311528\pi$
$72$	−267.699	−0.438175
$73$	661.401	1.06043	0.530213	−	0.847864i	$-0.322112\pi$
$73$	661.401	1.06043	0.530213	+	0.847864i	$0.322112\pi$
$74$	305.720	0.480260
$75$	−837.855	−1.28996
$76$	−648.418	−0.978667
$77$	17.9927	0.0266294
$78$	0	0
$79$	857.861	1.22173	0.610867	−	0.791734i	$-0.290821\pi$
$79$	857.861	1.22173	0.610867	+	0.791734i	$0.290821\pi$
$80$	820.050	1.14606
$81$	69.6926	0.0956003
$82$	−271.558	−0.365714
$83$	97.4502	0.128874	0.0644370	−	0.997922i	$-0.479475\pi$
$83$	97.4502	0.128874	0.0644370	+	0.997922i	$0.479475\pi$
$84$	−34.6745	−0.0450392
$85$	−1693.09	−2.16049
$86$	−7.79728	−0.00977677
$87$	−246.058	−0.303220
$88$	−165.246	−0.200174
$89$	−563.060	−0.670610	−0.335305	−	0.942110i	$-0.608839\pi$
$89$	−563.060	−0.670610	−0.335305	+	0.942110i	$0.608839\pi$
$90$	357.698	0.418941
$91$	0	0
$92$	−127.502	−0.144490
$93$	391.385	0.436395
$94$	249.763	0.274054
$95$	1857.09	2.00561
$96$	488.332	0.519169
$97$	1769.40	1.85211	0.926057	−	0.377383i	$-0.123176\pi$
$97$	1769.40	1.85211	0.926057	+	0.377383i	$0.123176\pi$
$98$	340.911	0.351400
$99$	196.020	0.198998
$100$	−1934.78	−1.93478
$101$	1910.72	1.88241	0.941206	−	0.337834i	$-0.109694\pi$
$101$	1910.72	1.88241	0.941206	+	0.337834i	$0.109694\pi$
$102$	−256.442	−0.248936
$103$	−173.361	−0.165843	−0.0829213	−	0.996556i	$-0.526425\pi$
$103$	−173.361	−0.165843	−0.0829213	+	0.996556i	$0.526425\pi$
$104$	0	0
$105$	99.3086	0.0923002
$106$	−284.566	−0.260750
$107$	−183.648	−0.165924	−0.0829622	−	0.996553i	$-0.526438\pi$
$107$	−183.648	−0.165924	−0.0829622	+	0.996553i	$0.526438\pi$
$108$	−950.117	−0.846528
$109$	−1816.06	−1.59585	−0.797924	−	0.602759i	$-0.794068\pi$
$109$	−1816.06	−1.59585	−0.797924	+	0.602759i	$0.794068\pi$
$110$	220.801	0.191387
$111$	924.693	0.790702
$112$	−66.9398	−0.0564751
$113$	454.390	0.378278	0.189139	−	0.981950i	$-0.439430\pi$
$113$	454.390	0.378278	0.189139	+	0.981950i	$0.439430\pi$
$114$	281.281	0.231091
$115$	365.170	0.296107
$116$	−568.198	−0.454792
$117$	0	0
$118$	572.539	0.446665
$119$	138.205	0.106464
$120$	−912.055	−0.693824
$121$	121.000	0.0909091
$122$	436.290	0.323769
$123$	−821.364	−0.602113
$124$	903.788	0.654537
$125$	3036.47	2.17272
$126$	−29.1985	−0.0206445
$127$	907.682	0.634203	0.317101	−	0.948392i	$-0.397290\pi$
$127$	907.682	0.634203	0.317101	+	0.948392i	$0.397290\pi$
$128$	1455.62	1.00515
$129$	−23.5840	−0.0160965
$130$	0	0
$131$	−2610.19	−1.74087	−0.870433	−	0.492286i	$-0.836161\pi$
$131$	−2610.19	−1.74087	−0.870433	+	0.492286i	$0.836161\pi$
$132$	−233.184	−0.153758
$133$	−151.592	−0.0988321
$134$	466.055	0.300456
$135$	2721.16	1.73482
$136$	−1269.28	−0.800296
$137$	−592.070	−0.369226	−0.184613	−	0.982811i	$-0.559103\pi$
$137$	−592.070	−0.369226	−0.184613	+	0.982811i	$0.559103\pi$
$138$	55.3099	0.0341181
$139$	−2140.58	−1.30620	−0.653098	−	0.757273i	$-0.726531\pi$
$139$	−2140.58	−1.30620	−0.653098	+	0.757273i	$0.726531\pi$
$140$	229.324	0.138439
$141$	755.443	0.451204
$142$	−668.933	−0.395321
$143$	0	0
$144$	−729.268	−0.422030
$145$	1627.33	0.932019
$146$	−662.541	−0.375563
$147$	1031.13	0.578547
$148$	2135.31	1.18595
$149$	−3149.39	−1.73160	−0.865798	−	0.500393i	$-0.833189\pi$
$149$	−3149.39	−1.73160	−0.865798	+	0.500393i	$0.833189\pi$
$150$	839.299	0.456856
$151$	2988.63	1.61067	0.805334	−	0.592821i	$-0.201986\pi$
$151$	2988.63	1.61067	0.805334	+	0.592821i	$0.201986\pi$
$152$	1392.23	0.742924
$153$	1505.66	0.795592
$154$	−18.0237	−0.00943113
$155$	−2588.47	−1.34136
$156$	0	0
$157$	−2726.51	−1.38598	−0.692991	−	0.720946i	$-0.743707\pi$
$157$	−2726.51	−1.38598	−0.692991	+	0.720946i	$0.743707\pi$
$158$	−859.339	−0.432692
$159$	−860.710	−0.429300
$160$	−3229.65	−1.59579
$161$	−29.8084	−0.0145915
$162$	−69.8127	−0.0338580
$163$	−245.768	−0.118098	−0.0590491	−	0.998255i	$-0.518807\pi$
$163$	−245.768	−0.118098	−0.0590491	+	0.998255i	$0.518807\pi$
$164$	−1896.70	−0.903094
$165$	667.844	0.315100
$166$	−97.6181	−0.0456424
$167$	−364.269	−0.168790	−0.0843952	−	0.996432i	$-0.526896\pi$
$167$	−364.269	−0.168790	−0.0843952	+	0.996432i	$0.526896\pi$
$168$	74.4500	0.0341901
$169$	0	0
$170$	1696.01	0.765165
$171$	−1651.50	−0.738558
$172$	−54.4603	−0.0241428
$173$	−1274.83	−0.560253	−0.280126	−	0.959963i	$-0.590376\pi$
$173$	−1274.83	−0.560253	−0.280126	+	0.959963i	$0.590376\pi$
$174$	246.482	0.107389
$175$	−452.327	−0.195387
$176$	−450.166	−0.192798
$177$	1731.73	0.735392
$178$	564.030	0.237505
$179$	1307.13	0.545808	0.272904	−	0.962041i	$-0.412016\pi$
$179$	1307.13	0.545808	0.272904	+	0.962041i	$0.412016\pi$
$180$	2498.35	1.03453
$181$	−2406.15	−0.988109	−0.494054	−	0.869431i	$-0.664486\pi$
$181$	−2406.15	−0.988109	−0.494054	+	0.869431i	$0.664486\pi$
$182$	0	0
$183$	1319.62	0.533055
$184$	273.762	0.109685
$185$	−6115.57	−2.43041
$186$	−392.059	−0.154555
$187$	929.421	0.363455
$188$	1744.47	0.676749
$189$	−222.125	−0.0854880
$190$	−1860.28	−0.710312
$191$	1569.73	0.594667	0.297334	−	0.954774i	$-0.403903\pi$
$191$	1569.73	0.594667	0.297334	+	0.954774i	$0.403903\pi$
$192$	502.779	0.188984
$193$	881.164	0.328640	0.164320	−	0.986407i	$-0.447457\pi$
$193$	881.164	0.328640	0.164320	+	0.986407i	$0.447457\pi$
$194$	−1772.45	−0.655949
$195$	0	0
$196$	2381.10	0.867747
$197$	−236.296	−0.0854590	−0.0427295	−	0.999087i	$-0.513605\pi$
$197$	−236.296	−0.0854590	−0.0427295	+	0.999087i	$0.513605\pi$
$198$	−196.358	−0.0704775
$199$	3763.82	1.34075	0.670377	−	0.742021i	$-0.266132\pi$
$199$	3763.82	1.34075	0.670377	+	0.742021i	$0.266132\pi$
$200$	4154.19	1.46873
$201$	1409.65	0.494672
$202$	−1914.01	−0.666680
$203$	−132.837	−0.0459279
$204$	−1791.12	−0.614724
$205$	5432.20	1.85074
$206$	173.660	0.0587353
$207$	−324.745	−0.109040
$208$	0	0
$209$	−1019.44	−0.337399
$210$	−99.4796	−0.0326893
$211$	−3382.24	−1.10352	−0.551760	−	0.834003i	$-0.686044\pi$
$211$	−3382.24	−1.10352	−0.551760	+	0.834003i	$0.686044\pi$
$212$	−1987.56	−0.643896
$213$	−2023.28	−0.650859
$214$	183.964	0.0587642
$215$	155.976	0.0494765
$216$	2040.01	0.642616
$217$	211.294	0.0660994
$218$	1819.19	0.565189
$219$	−2003.95	−0.618330
$220$	1542.19	0.472611
$221$	0	0
$222$	−926.286	−0.280037
$223$	−1938.06	−0.581984	−0.290992	−	0.956725i	$-0.593985\pi$
$223$	−1938.06	−0.581984	−0.290992	+	0.956725i	$0.593985\pi$
$224$	263.632	0.0786370
$225$	−4927.83	−1.46010
$226$	−455.173	−0.133972
$227$	2624.64	0.767416	0.383708	−	0.923455i	$-0.374647\pi$
$227$	2624.64	0.767416	0.383708	+	0.923455i	$0.374647\pi$
$228$	1964.61	0.570656
$229$	−2963.84	−0.855266	−0.427633	−	0.903952i	$-0.640652\pi$
$229$	−2963.84	−0.855266	−0.427633	+	0.903952i	$0.640652\pi$
$230$	−365.799	−0.104870
$231$	−54.5153	−0.0155275
$232$	1219.99	0.345241
$233$	876.240	0.246371	0.123185	−	0.992384i	$-0.460689\pi$
$233$	876.240	0.246371	0.123185	+	0.992384i	$0.460689\pi$
$234$	0	0
$235$	−4996.22	−1.38688
$236$	3998.91	1.10300
$237$	−2599.19	−0.712387
$238$	−138.443	−0.0377057
$239$	−4770.96	−1.29125	−0.645623	−	0.763656i	$-0.723402\pi$
$239$	−4770.96	−1.29125	−0.645623	+	0.763656i	$0.723402\pi$
$240$	−2484.63	−0.668259
$241$	−1676.39	−0.448073	−0.224037	−	0.974581i	$-0.571924\pi$
$241$	−1676.39	−0.448073	−0.224037	+	0.974581i	$0.571924\pi$
$242$	−121.208	−0.0321966
$243$	−3877.70	−1.02368
$244$	3047.27	0.799515
$245$	−6819.52	−1.77830
$246$	822.779	0.213246
$247$	0	0
$248$	−1940.53	−0.496871
$249$	−295.260	−0.0751458
$250$	−3041.70	−0.769497
$251$	838.879	0.210954	0.105477	−	0.994422i	$-0.466363\pi$
$251$	838.879	0.210954	0.105477	+	0.994422i	$0.466363\pi$
$252$	−203.937	−0.0509795
$253$	−200.460	−0.0498134
$254$	−909.246	−0.224611
$255$	5129.82	1.25977
$256$	−130.591	−0.0318825
$257$	−5107.47	−1.23967	−0.619835	−	0.784732i	$-0.712800\pi$
$257$	−5107.47	−1.23967	−0.619835	+	0.784732i	$0.712800\pi$
$258$	23.6246	0.00570079
$259$	499.207	0.119765
$260$	0	0
$261$	−1447.18	−0.343212
$262$	2614.69	0.616550
$263$	−6863.06	−1.60910	−0.804552	−	0.593882i	$-0.797595\pi$
$263$	−6863.06	−1.60910	−0.804552	+	0.593882i	$0.797595\pi$
$264$	500.671	0.116720
$265$	5692.41	1.31956
$266$	151.853	0.0350026
$267$	1705.99	0.391029
$268$	3255.17	0.741945
$269$	−3000.82	−0.680161	−0.340081	−	0.940396i	$-0.610454\pi$
$269$	−3000.82	−0.680161	−0.340081	+	0.940396i	$0.610454\pi$
$270$	−2725.85	−0.614407
$271$	−7142.42	−1.60100	−0.800500	−	0.599333i	$-0.795432\pi$
$271$	−7142.42	−1.60100	−0.800500	+	0.599333i	$0.795432\pi$
$272$	−3457.80	−0.770808
$273$	0	0
$274$	593.090	0.130766
$275$	−3041.87	−0.667024
$276$	386.313	0.0842512
$277$	−4733.24	−1.02669	−0.513345	−	0.858183i	$-0.671594\pi$
$277$	−4733.24	−1.02669	−0.513345	+	0.858183i	$0.671594\pi$
$278$	2144.26	0.462606
$279$	2301.92	0.493951
$280$	−492.384	−0.105091
$281$	288.433	0.0612329	0.0306165	−	0.999531i	$-0.490253\pi$
$281$	288.433	0.0612329	0.0306165	+	0.999531i	$0.490253\pi$
$282$	−756.745	−0.159800
$283$	1412.91	0.296781	0.148390	−	0.988929i	$-0.452591\pi$
$283$	1412.91	0.296781	0.148390	+	0.988929i	$0.452591\pi$
$284$	−4672.18	−0.976207
$285$	−5626.69	−1.16946
$286$	0	0
$287$	−443.424	−0.0912003
$288$	2872.12	0.587643
$289$	2226.04	0.453092
$290$	−1630.14	−0.330086
$291$	−5361.01	−1.07996
$292$	−4627.53	−0.927416
$293$	−8536.23	−1.70202	−0.851010	−	0.525149i	$-0.824009\pi$
$293$	−8536.23	−1.70202	−0.851010	+	0.525149i	$0.824009\pi$
$294$	−1032.91	−0.204900
$295$	−11453.0	−2.26040
$296$	−4584.75	−0.900280
$297$	−1493.78	−0.291844
$298$	3154.81	0.613267
$299$	0	0
$300$	5862.10	1.12816
$301$	−12.7321	−0.00243809
$302$	−2993.77	−0.570438
$303$	−5789.19	−1.09762
$304$	3792.72	0.715551
$305$	−8727.47	−1.63847
$306$	−1508.26	−0.281769
$307$	−906.163	−0.168461	−0.0842304	−	0.996446i	$-0.526843\pi$
$307$	−906.163	−0.168461	−0.0842304	+	0.996446i	$0.526843\pi$
$308$	−125.887	−0.0232892
$309$	525.259	0.0967021
$310$	2592.93	0.475060
$311$	−5558.80	−1.01354	−0.506769	−	0.862082i	$-0.669160\pi$
$311$	−5558.80	−1.01354	−0.506769	+	0.862082i	$0.669160\pi$
$312$	0	0
$313$	−3329.89	−0.601331	−0.300666	−	0.953730i	$-0.597209\pi$
$313$	−3329.89	−0.601331	−0.300666	+	0.953730i	$0.597209\pi$
$314$	2731.21	0.490863
$315$	584.081	0.104474
$316$	−6002.07	−1.06849
$317$	1971.36	0.349283	0.174642	−	0.984632i	$-0.444123\pi$
$317$	1971.36	0.349283	0.174642	+	0.984632i	$0.444123\pi$
$318$	862.193	0.152042
$319$	−893.323	−0.156791
$320$	−3325.19	−0.580887
$321$	556.426	0.0967497
$322$	29.8598	0.00516776
$323$	−7830.53	−1.34892
$324$	−487.608	−0.0836091
$325$	0	0
$326$	246.191	0.0418260
$327$	5502.40	0.930531
$328$	4072.43	0.685556
$329$	407.836	0.0683426
$330$	−668.994	−0.111597
$331$	10144.5	1.68456	0.842281	−	0.539039i	$-0.181213\pi$
$331$	10144.5	1.68456	0.842281	+	0.539039i	$0.181213\pi$
$332$	−681.815	−0.112709
$333$	5438.56	0.894989
$334$	364.896	0.0597792
$335$	−9322.90	−1.52049
$336$	202.818	0.0329304
$337$	9040.66	1.46135	0.730677	−	0.682723i	$-0.239204\pi$
$337$	9040.66	1.46135	0.730677	+	0.682723i	$0.239204\pi$
$338$	0	0
$339$	−1376.73	−0.220572
$340$	11845.8	1.88950
$341$	1420.94	0.225654
$342$	1654.35	0.261570
$343$	1117.72	0.175950
$344$	116.932	0.0183272
$345$	−1106.41	−0.172658
$346$	1277.03	0.198420
$347$	11358.7	1.75726	0.878628	−	0.477506i	$-0.158459\pi$
$347$	11358.7	1.75726	0.878628	+	0.477506i	$0.158459\pi$
$348$	1721.56	0.265187
$349$	−8127.02	−1.24650	−0.623252	−	0.782021i	$-0.714189\pi$
$349$	−8127.02	−1.24650	−0.623252	+	0.782021i	$0.714189\pi$
$350$	453.106	0.0691987
$351$	0	0
$352$	1772.91	0.268456
$353$	−11542.8	−1.74040	−0.870198	−	0.492703i	$-0.836009\pi$
$353$	−11542.8	−1.74040	−0.870198	+	0.492703i	$0.836009\pi$
$354$	−1734.71	−0.260448
$355$	13381.2	2.00057
$356$	3939.48	0.586494
$357$	−418.741	−0.0620788
$358$	−1309.38	−0.193305
$359$	−4209.31	−0.618827	−0.309413	−	0.950928i	$-0.600133\pi$
$359$	−4209.31	−0.618827	−0.309413	+	0.950928i	$0.600133\pi$
$360$	−5364.23	−0.785333
$361$	1729.99	0.252222
$362$	2410.29	0.349951
$363$	−366.612	−0.0530086
$364$	0	0
$365$	13253.4	1.90058
$366$	−1321.89	−0.188788
$367$	−8274.02	−1.17684	−0.588420	−	0.808555i	$-0.700250\pi$
$367$	−8274.02	−1.17684	−0.588420	+	0.808555i	$0.700250\pi$
$368$	745.786	0.105643
$369$	−4830.84	−0.681527
$370$	6126.11	0.860760
$371$	−464.665	−0.0650248
$372$	−2738.34	−0.381657
$373$	7566.42	1.05033	0.525167	−	0.850999i	$-0.324003\pi$
$373$	7566.42	1.05033	0.525167	+	0.850999i	$0.324003\pi$
$374$	−931.022	−0.128722
$375$	−9200.06	−1.26690
$376$	−3745.58	−0.513733
$377$	0	0
$378$	222.508	0.0302766
$379$	6903.01	0.935577	0.467788	−	0.883840i	$-0.345051\pi$
$379$	6903.01	0.935577	0.467788	+	0.883840i	$0.345051\pi$
$380$	−12993.2	−1.75404
$381$	−2750.14	−0.369801
$382$	−1572.43	−0.210609
$383$	−14461.4	−1.92936	−0.964679	−	0.263427i	$-0.915147\pi$
$383$	−14461.4	−1.92936	−0.964679	+	0.263427i	$0.915147\pi$
$384$	−4410.30	−0.586100
$385$	360.544	0.0477273
$386$	−882.682	−0.116392
$387$	−138.709	−0.0182195
$388$	−12379.7	−1.61980
$389$	−401.350	−0.0523118	−0.0261559	−	0.999658i	$-0.508327\pi$
$389$	−401.350	−0.0523118	−0.0261559	+	0.999658i	$0.508327\pi$
$390$	0	0
$391$	−1539.76	−0.199154
$392$	−5112.49	−0.658723
$393$	7908.49	1.01509
$394$	236.703	0.0302664
$395$	17190.1	2.18969
$396$	−1371.46	−0.174037
$397$	−14097.6	−1.78221	−0.891105	−	0.453798i	$-0.850069\pi$
$397$	−14097.6	−1.78221	−0.891105	+	0.453798i	$0.850069\pi$
$398$	−3770.30	−0.474845
$399$	459.300	0.0576285
$400$	11316.9	1.41461
$401$	−2963.36	−0.369035	−0.184517	−	0.982829i	$-0.559072\pi$
$401$	−2963.36	−0.369035	−0.184517	+	0.982829i	$0.559072\pi$
$402$	−1412.08	−0.175194
$403$	0	0
$404$	−13368.4	−1.64630
$405$	1396.52	0.171343
$406$	133.066	0.0162659
$407$	3357.14	0.408863
$408$	3845.74	0.466649
$409$	13357.0	1.61482	0.807412	−	0.589989i	$-0.200868\pi$
$409$	13357.0	1.61482	0.807412	+	0.589989i	$0.200868\pi$
$410$	−5441.55	−0.655461
$411$	1793.89	0.215294
$412$	1212.93	0.145041
$413$	934.894	0.111388
$414$	325.304	0.0386179
$415$	1952.74	0.230978
$416$	0	0
$417$	6485.62	0.761636
$418$	1021.20	0.119494
$419$	8701.21	1.01452	0.507258	−	0.861794i	$-0.330659\pi$
$419$	8701.21	1.01452	0.507258	+	0.861794i	$0.330659\pi$
$420$	−694.818	−0.0807229
$421$	1258.88	0.145734	0.0728669	−	0.997342i	$-0.476785\pi$
$421$	1258.88	0.145734	0.0728669	+	0.997342i	$0.476785\pi$
$422$	3388.06	0.390825
$423$	4443.12	0.510714
$424$	4267.51	0.488794
$425$	−23365.1	−2.66676
$426$	2026.77	0.230510
$427$	712.413	0.0807403
$428$	1284.90	0.145112
$429$	0	0
$430$	−156.244	−0.0175227
$431$	−14537.8	−1.62474	−0.812368	−	0.583145i	$-0.801822\pi$
$431$	−14537.8	−1.62474	−0.812368	+	0.583145i	$0.801822\pi$
$432$	5557.41	0.618938
$433$	8021.26	0.890247	0.445124	−	0.895469i	$-0.353160\pi$
$433$	8021.26	0.890247	0.445124	+	0.895469i	$0.353160\pi$
$434$	−211.658	−0.0234099
$435$	−4930.58	−0.543456
$436$	12706.2	1.39568
$437$	1688.91	0.184877
$438$	2007.40	0.218989
$439$	1797.77	0.195451	0.0977256	−	0.995213i	$-0.468843\pi$
$439$	1797.77	0.195451	0.0977256	+	0.995213i	$0.468843\pi$
$440$	−3311.25	−0.358768
$441$	6064.58	0.654852
$442$	0	0
$443$	5962.03	0.639424	0.319712	−	0.947515i	$-0.396414\pi$
$443$	5962.03	0.639424	0.319712	+	0.947515i	$0.396414\pi$
$444$	−6469.66	−0.691524
$445$	−11282.8	−1.20192
$446$	1941.40	0.206117
$447$	9542.18	1.00969
$448$	271.432	0.0286249
$449$	−1948.38	−0.204788	−0.102394	−	0.994744i	$-0.532650\pi$
$449$	−1948.38	−0.204788	−0.102394	+	0.994744i	$0.532650\pi$
$450$	4936.32	0.517112
$451$	−2982.00	−0.311345
$452$	−3179.16	−0.330830
$453$	−9055.09	−0.939173
$454$	−2629.16	−0.271790
$455$	0	0
$456$	−4218.24	−0.433196
$457$	−2294.54	−0.234866	−0.117433	−	0.993081i	$-0.537467\pi$
$457$	−2294.54	−0.234866	−0.117433	+	0.993081i	$0.537467\pi$
$458$	2968.94	0.302903
$459$	−11474.0	−1.16679
$460$	−2554.93	−0.258966
$461$	−12178.9	−1.23043	−0.615214	−	0.788360i	$-0.710930\pi$
$461$	−12178.9	−1.23043	−0.615214	+	0.788360i	$0.710930\pi$
$462$	54.6092	0.00549924
$463$	8917.03	0.895053	0.447526	−	0.894271i	$-0.352305\pi$
$463$	8917.03	0.895053	0.447526	+	0.894271i	$0.352305\pi$
$464$	3323.50	0.332521
$465$	7842.68	0.782141
$466$	−877.750	−0.0872553
$467$	−7731.56	−0.766111	−0.383055	−	0.923725i	$-0.625128\pi$
$467$	−7731.56	−0.766111	−0.383055	+	0.923725i	$0.625128\pi$
$468$	0	0
$469$	761.017	0.0749265
$470$	5004.83	0.491182
$471$	8260.92	0.808159
$472$	−8586.11	−0.837305
$473$	−85.6226	−0.00832332
$474$	2603.67	0.252301
$475$	25628.2	2.47559
$476$	−966.960	−0.0931104
$477$	−5062.25	−0.485921
$478$	4779.18	0.457311
$479$	14368.4	1.37058	0.685290	−	0.728271i	$-0.259676\pi$
$479$	14368.4	1.37058	0.685290	+	0.728271i	$0.259676\pi$
$480$	9785.35	0.930496
$481$	0	0
$482$	1679.28	0.158691
$483$	90.3151	0.00850824
$484$	−846.583	−0.0795063
$485$	35455.7	3.31951
$486$	3884.38	0.362550
$487$	1952.24	0.181652	0.0908259	−	0.995867i	$-0.471049\pi$
$487$	1952.24	0.181652	0.0908259	+	0.995867i	$0.471049\pi$
$488$	−6542.84	−0.606927
$489$	744.640	0.0688625
$490$	6831.27	0.629807
$491$	−3502.34	−0.321911	−0.160956	−	0.986962i	$-0.551458\pi$
$491$	−3502.34	−0.321911	−0.160956	+	0.986962i	$0.551458\pi$
$492$	5746.72	0.526589
$493$	−6861.76	−0.626853
$494$	0	0
$495$	3927.91	0.356659
$496$	−5286.43	−0.478564
$497$	−1092.29	−0.0985837
$498$	295.768	0.0266138
$499$	−7396.20	−0.663526	−0.331763	−	0.943363i	$-0.607643\pi$
$499$	−7396.20	−0.663526	−0.331763	+	0.943363i	$0.607643\pi$
$500$	−21244.8	−1.90020
$501$	1103.68	0.0984208
$502$	−840.324	−0.0747121
$503$	9402.97	0.833515	0.416757	−	0.909018i	$-0.363166\pi$
$503$	9402.97	0.833515	0.416757	+	0.909018i	$0.363166\pi$
$504$	437.876	0.0386995
$505$	38287.5	3.37381
$506$	200.805	0.0176420
$507$	0	0
$508$	−6350.64	−0.554654
$509$	−8185.59	−0.712810	−0.356405	−	0.934332i	$-0.615998\pi$
$509$	−8185.59	−0.712810	−0.356405	+	0.934332i	$0.615998\pi$
$510$	−5138.66	−0.446164
$511$	−1081.86	−0.0936566
$512$	−11514.1	−0.993862
$513$	12585.3	1.08315
$514$	5116.27	0.439044
$515$	−3473.87	−0.297237
$516$	165.006	0.0140775
$517$	2742.67	0.233312
$518$	−500.067	−0.0424164
$519$	3862.55	0.326681
$520$	0	0
$521$	−3936.28	−0.331001	−0.165500	−	0.986210i	$-0.552924\pi$
$521$	−3936.28	−0.331001	−0.165500	+	0.986210i	$0.552924\pi$
$522$	1449.68	0.121553
$523$	−22370.2	−1.87033	−0.935164	−	0.354216i	$-0.884748\pi$
$523$	−22370.2	−1.87033	−0.935164	+	0.354216i	$0.884748\pi$
$524$	18262.3	1.52251
$525$	1370.48	0.113929
$526$	6874.88	0.569884
$527$	10914.5	0.902166
$528$	1363.93	0.112420
$529$	−11834.9	−0.972705
$530$	−5702.22	−0.467337
$531$	10185.1	0.832384
$532$	1060.62	0.0864355
$533$	0	0
$534$	−1708.93	−0.138488
$535$	−3679.99	−0.297383
$536$	−6989.22	−0.563225
$537$	−3960.41	−0.318258
$538$	3005.99	0.240888
$539$	3743.57	0.299159
$540$	−19038.7	−1.51722
$541$	621.112	0.0493599	0.0246799	−	0.999695i	$-0.492143\pi$
$541$	621.112	0.0493599	0.0246799	+	0.999695i	$0.492143\pi$
$542$	7154.72	0.567014
$543$	7290.28	0.576161
$544$	13618.0	1.07329
$545$	−36390.8	−2.86021
$546$	0	0
$547$	11904.8	0.930555	0.465278	−	0.885165i	$-0.345954\pi$
$547$	11904.8	0.930555	0.465278	+	0.885165i	$0.345954\pi$
$548$	4142.45	0.322914
$549$	7761.31	0.603360
$550$	3047.11	0.236235
$551$	7526.39	0.581915
$552$	−829.458	−0.0639567
$553$	−1403.21	−0.107903
$554$	4741.39	0.363615
$555$	18529.3	1.41716
$556$	14976.6	1.14236
$557$	−17396.6	−1.32337	−0.661687	−	0.749780i	$-0.730159\pi$
$557$	−17396.6	−1.32337	−0.661687	+	0.749780i	$0.730159\pi$
$558$	−2305.89	−0.174939
$559$	0	0
$560$	−1341.36	−0.101219
$561$	−2816.01	−0.211929
$562$	−288.930	−0.0216864
$563$	−11164.6	−0.835760	−0.417880	−	0.908502i	$-0.637227\pi$
$563$	−11164.6	−0.835760	−0.417880	+	0.908502i	$0.637227\pi$
$564$	−5285.50	−0.394609
$565$	9105.20	0.677980
$566$	−1415.35	−0.105109
$567$	−113.996	−0.00844339
$568$	10031.7	0.741057
$569$	−8693.90	−0.640540	−0.320270	−	0.947326i	$-0.603774\pi$
$569$	−8693.90	−0.640540	−0.320270	+	0.947326i	$0.603774\pi$
$570$	5636.39	0.414179
$571$	−24800.4	−1.81763	−0.908813	−	0.417203i	$-0.863011\pi$
$571$	−24800.4	−1.81763	−0.908813	+	0.417203i	$0.863011\pi$
$572$	0	0
$573$	−4756.04	−0.346748
$574$	444.188	0.0322997
$575$	5039.44	0.365494
$576$	2957.08	0.213909
$577$	−15508.8	−1.11896	−0.559481	−	0.828843i	$-0.688999\pi$
$577$	−15508.8	−1.11896	−0.559481	+	0.828843i	$0.688999\pi$
$578$	−2229.88	−0.160468
$579$	−2669.80	−0.191629
$580$	−11385.7	−0.815115
$581$	−159.400	−0.0113821
$582$	5370.25	0.382481
$583$	−3124.84	−0.221986
$584$	9935.82	0.704019
$585$	0	0
$586$	8550.94	0.602792
$587$	22011.4	1.54771	0.773856	−	0.633362i	$-0.218325\pi$
$587$	22011.4	1.54771	0.773856	+	0.633362i	$0.218325\pi$
$588$	−7214.37	−0.505979
$589$	−11971.6	−0.837492
$590$	11472.7	0.800549
$591$	715.943	0.0498307
$592$	−12489.8	−0.867108
$593$	−28259.5	−1.95696	−0.978480	−	0.206343i	$-0.933844\pi$
$593$	−28259.5	−1.95696	−0.978480	+	0.206343i	$0.933844\pi$
$594$	1496.35	0.103360
$595$	2769.40	0.190814
$596$	22034.9	1.51440
$597$	−11403.8	−0.781787
$598$	0	0
$599$	−14235.8	−0.971048	−0.485524	−	0.874223i	$-0.661371\pi$
$599$	−14235.8	−0.971048	−0.485524	+	0.874223i	$0.661371\pi$
$600$	−12586.6	−0.856409
$601$	25756.7	1.74815	0.874075	−	0.485792i	$-0.161469\pi$
$601$	25756.7	1.74815	0.874075	+	0.485792i	$0.161469\pi$
$602$	12.7540	0.000863482 0
$603$	8290.82	0.559915
$604$	−20910.1	−1.40864
$605$	2424.63	0.162935
$606$	5799.16	0.388738
$607$	−27336.0	−1.82790	−0.913950	−	0.405827i	$-0.866983\pi$
$607$	−27336.0	−1.82790	−0.913950	+	0.405827i	$0.866983\pi$
$608$	−14937.1	−0.996346
$609$	402.477	0.0267803
$610$	8742.50	0.580285
$611$	0	0
$612$	−10534.4	−0.695800
$613$	−3021.15	−0.199059	−0.0995294	−	0.995035i	$-0.531734\pi$
$613$	−3021.15	−0.199059	−0.0995294	+	0.995035i	$0.531734\pi$
$614$	907.724	0.0596625
$615$	−16458.7	−1.07916
$616$	270.294	0.0176793
$617$	4104.43	0.267809	0.133905	−	0.990994i	$-0.457248\pi$
$617$	4104.43	0.267809	0.133905	+	0.990994i	$0.457248\pi$
$618$	−526.164	−0.0342482
$619$	3479.46	0.225931	0.112966	−	0.993599i	$-0.463965\pi$
$619$	3479.46	0.225931	0.112966	+	0.993599i	$0.463965\pi$
$620$	18110.4	1.17311
$621$	2474.73	0.159915
$622$	5568.37	0.358957
$623$	920.999	0.0592280
$624$	0	0
$625$	26279.1	1.68186
$626$	3335.63	0.212969
$627$	3088.77	0.196736
$628$	19076.2	1.21214
$629$	25786.7	1.63463
$630$	−585.087	−0.0370007
$631$	10446.5	0.659065	0.329532	−	0.944144i	$-0.393109\pi$
$631$	10446.5	0.659065	0.329532	+	0.944144i	$0.393109\pi$
$632$	12887.1	0.811111
$633$	10247.7	0.643457
$634$	−1974.76	−0.123703
$635$	18188.4	1.13667
$636$	6022.00	0.375453
$637$	0	0
$638$	894.862	0.0555296
$639$	−11899.9	−0.736702
$640$	29168.1	1.80152
$641$	5299.89	0.326573	0.163286	−	0.986579i	$-0.447791\pi$
$641$	5299.89	0.326573	0.163286	+	0.986579i	$0.447791\pi$
$642$	−557.384	−0.0342651
$643$	2049.48	0.125698	0.0628490	−	0.998023i	$-0.479981\pi$
$643$	2049.48	0.125698	0.0628490	+	0.998023i	$0.479981\pi$
$644$	208.556	0.0127613
$645$	−472.583	−0.0288495
$646$	7844.02	0.477738
$647$	−26975.8	−1.63915	−0.819573	−	0.572975i	$-0.805789\pi$
$647$	−26975.8	−1.63915	−0.819573	+	0.572975i	$0.805789\pi$
$648$	1046.95	0.0634692
$649$	6287.10	0.380262
$650$	0	0
$651$	−640.189	−0.0385422
$652$	1719.53	0.103285
$653$	13947.5	0.835849	0.417924	−	0.908482i	$-0.362758\pi$
$653$	13947.5	0.835849	0.417924	+	0.908482i	$0.362758\pi$
$654$	−5511.88	−0.329559
$655$	−52303.8	−3.12012
$656$	11094.2	0.660296
$657$	−11786.2	−0.699882
$658$	−408.538	−0.0242044
$659$	−8235.84	−0.486833	−0.243416	−	0.969922i	$-0.578268\pi$
$659$	−8235.84	−0.486833	−0.243416	+	0.969922i	$0.578268\pi$
$660$	−4672.60	−0.275577
$661$	−22575.2	−1.32840	−0.664199	−	0.747555i	$-0.731227\pi$
$661$	−22575.2	−1.32840	−0.664199	+	0.747555i	$0.731227\pi$
$662$	−10161.9	−0.596608
$663$	0	0
$664$	1463.93	0.0855597
$665$	−3037.64	−0.177135
$666$	−5447.93	−0.316972
$667$	1479.96	0.0859135
$668$	2548.63	0.147619
$669$	5872.05	0.339352
$670$	9338.96	0.538501
$671$	4790.93	0.275636
$672$	−798.767	−0.0458528
$673$	−7301.04	−0.418179	−0.209090	−	0.977896i	$-0.567050\pi$
$673$	−7301.04	−0.418179	−0.209090	+	0.977896i	$0.567050\pi$
$674$	−9056.24	−0.517557
$675$	37552.7	2.14134
$676$	0	0
$677$	−20890.4	−1.18594	−0.592970	−	0.805224i	$-0.702045\pi$
$677$	−20890.4	−1.18594	−0.592970	+	0.805224i	$0.702045\pi$
$678$	1379.11	0.0781183
$679$	−2894.21	−0.163578
$680$	−25434.3	−1.43435
$681$	−7952.26	−0.447476
$682$	−1423.39	−0.0799183
$683$	31298.8	1.75346	0.876731	−	0.480981i	$-0.159720\pi$
$683$	31298.8	1.75346	0.876731	+	0.480981i	$0.159720\pi$
$684$	11554.8	0.645920
$685$	−11864.1	−0.661757
$686$	−1119.64	−0.0623150
$687$	8979.99	0.498702
$688$	318.548	0.0176520
$689$	0	0
$690$	1108.32	0.0611491
$691$	26459.2	1.45667	0.728333	−	0.685223i	$-0.240295\pi$
$691$	26459.2	1.45667	0.728333	+	0.685223i	$0.240295\pi$
$692$	8919.43	0.489980
$693$	−320.631	−0.0175754
$694$	−11378.3	−0.622354
$695$	−42893.5	−2.34107
$696$	−3696.37	−0.201308
$697$	−22905.2	−1.24476
$698$	8141.02	0.441465
$699$	−2654.88	−0.143658
$700$	3164.73	0.170879
$701$	−16335.1	−0.880126	−0.440063	−	0.897967i	$-0.645044\pi$
$701$	−16335.1	−0.880126	−0.440063	+	0.897967i	$0.645044\pi$
$702$	0	0
$703$	−28284.4	−1.51745
$704$	1825.36	0.0977214
$705$	15137.8	0.808684
$706$	11562.7	0.616383
$707$	−3125.37	−0.166254
$708$	−12116.1	−0.643151
$709$	−4127.95	−0.218658	−0.109329	−	0.994006i	$-0.534870\pi$
$709$	−4127.95	−0.218658	−0.109329	+	0.994006i	$0.534870\pi$
$710$	−13404.3	−0.708527
$711$	−15287.1	−0.806344
$712$	−8458.51	−0.445219
$713$	−2354.06	−0.123647
$714$	419.463	0.0219860
$715$	0	0
$716$	−9145.42	−0.477347
$717$	14455.3	0.752919
$718$	4216.56	0.219165
$719$	37238.0	1.93149	0.965745	−	0.259493i	$-0.0835554\pi$
$719$	37238.0	1.93149	0.965745	+	0.259493i	$0.0835554\pi$
$720$	−14613.3	−0.756397
$721$	283.568	0.0146472
$722$	−1732.97	−0.0893276
$723$	5079.21	0.261269
$724$	16834.8	0.864169
$725$	22457.6	1.15042
$726$	367.244	0.0187737
$727$	23770.0	1.21263	0.606315	−	0.795225i	$-0.292647\pi$
$727$	23770.0	1.21263	0.606315	+	0.795225i	$0.292647\pi$
$728$	0	0
$729$	9867.16	0.501304
$730$	−13276.2	−0.673115
$731$	−657.682	−0.0332767
$732$	−9232.79	−0.466193
$733$	8549.33	0.430800	0.215400	−	0.976526i	$-0.430894\pi$
$733$	8549.33	0.430800	0.215400	+	0.976526i	$0.430894\pi$
$734$	8288.28	0.416793
$735$	20662.1	1.03692
$736$	−2937.17	−0.147100
$737$	5117.79	0.255789
$738$	4839.16	0.241371
$739$	−8267.88	−0.411554	−0.205777	−	0.978599i	$-0.565972\pi$
$739$	−8267.88	−0.411554	−0.205777	+	0.978599i	$0.565972\pi$
$740$	42787.9	2.12556
$741$	0	0
$742$	465.466	0.0230294
$743$	31636.7	1.56210	0.781049	−	0.624470i	$-0.214685\pi$
$743$	31636.7	1.56210	0.781049	+	0.624470i	$0.214685\pi$
$744$	5879.53	0.289723
$745$	−63108.4	−3.10351
$746$	−7579.45	−0.371989
$747$	−1736.56	−0.0850569
$748$	−6502.74	−0.317866
$749$	300.394	0.0146544
$750$	9215.91	0.448690
$751$	6497.44	0.315706	0.157853	−	0.987463i	$-0.449543\pi$
$751$	6497.44	0.315706	0.157853	+	0.987463i	$0.449543\pi$
$752$	−10203.8	−0.494804
$753$	−2541.68	−0.123006
$754$	0	0
$755$	59887.0	2.88677
$756$	1554.11	0.0747651
$757$	−15696.4	−0.753628	−0.376814	−	0.926289i	$-0.622980\pi$
$757$	−15696.4	−0.753628	−0.376814	+	0.926289i	$0.622980\pi$
$758$	−6914.90	−0.331346
$759$	607.363	0.0290460
$760$	27897.9	1.33153
$761$	16609.4	0.791184	0.395592	−	0.918426i	$-0.370539\pi$
$761$	16609.4	0.791184	0.395592	+	0.918426i	$0.370539\pi$
$762$	2754.88	0.130969
$763$	2970.54	0.140945
$764$	−10982.7	−0.520078
$765$	30170.9	1.42592
$766$	14486.3	0.683306
$767$	0	0
$768$	395.670	0.0185905
$769$	19517.6	0.915246	0.457623	−	0.889146i	$-0.348701\pi$
$769$	19517.6	0.915246	0.457623	+	0.889146i	$0.348701\pi$
$770$	−361.165	−0.0169032
$771$	15474.9	0.722845
$772$	−6165.11	−0.287419
$773$	31686.7	1.47437	0.737187	−	0.675689i	$-0.236154\pi$
$773$	31686.7	1.47437	0.737187	+	0.675689i	$0.236154\pi$
$774$	138.948	0.00645267
$775$	−35721.5	−1.65569
$776$	26580.6	1.22962
$777$	−1512.52	−0.0698346
$778$	402.042	0.0185269
$779$	25123.8	1.15553
$780$	0	0
$781$	−7345.61	−0.336551
$782$	1542.42	0.0705329
$783$	11028.3	0.503346
$784$	−13927.5	−0.634452
$785$	−54634.6	−2.48407
$786$	−7922.12	−0.359507
$787$	6521.68	0.295391	0.147696	−	0.989033i	$-0.452814\pi$
$787$	6521.68	0.295391	0.147696	+	0.989033i	$0.452814\pi$
$788$	1653.26	0.0747398
$789$	20794.1	0.938261
$790$	−17219.7	−0.775505
$791$	−743.247	−0.0334094
$792$	2944.69	0.132115
$793$	0	0
$794$	14121.9	0.631192
$795$	−17247.2	−0.769426
$796$	−26333.7	−1.17258
$797$	−28373.4	−1.26103	−0.630513	−	0.776179i	$-0.717155\pi$
$797$	−28373.4	−1.26103	−0.630513	+	0.776179i	$0.717155\pi$
$798$	−460.092	−0.0204099
$799$	21066.9	0.932783
$800$	−44569.9	−1.96973
$801$	10033.7	0.442602
$802$	2968.46	0.130698
$803$	−7275.41	−0.319731
$804$	−9862.69	−0.432625
$805$	−597.310	−0.0261521
$806$	0	0
$807$	9092.04	0.396599
$808$	28703.5	1.24974
$809$	37765.4	1.64124	0.820618	−	0.571477i	$-0.193629\pi$
$809$	37765.4	1.64124	0.820618	+	0.571477i	$0.193629\pi$
$810$	−1398.93	−0.0606831
$811$	−27377.0	−1.18537	−0.592687	−	0.805433i	$-0.701933\pi$
$811$	−27377.0	−1.18537	−0.592687	+	0.805433i	$0.701933\pi$
$812$	929.404	0.0401671
$813$	21640.5	0.933535
$814$	−3362.92	−0.144804
$815$	−4924.77	−0.211665
$816$	10476.6	0.449454
$817$	721.385	0.0308911
$818$	−13380.0	−0.571910
$819$	0	0
$820$	−38006.6	−1.61860
$821$	−26304.2	−1.11818	−0.559088	−	0.829109i	$-0.688848\pi$
$821$	−26304.2	−1.11818	−0.559088	+	0.829109i	$0.688848\pi$
$822$	−1796.98	−0.0762490
$823$	−2676.21	−0.113350	−0.0566748	−	0.998393i	$-0.518050\pi$
$823$	−2676.21	−0.113350	−0.0566748	+	0.998393i	$0.518050\pi$
$824$	−2604.30	−0.110103
$825$	9216.41	0.388938
$826$	−936.504	−0.0394493
$827$	−2660.69	−0.111876	−0.0559379	−	0.998434i	$-0.517815\pi$
$827$	−2660.69	−0.111876	−0.0559379	+	0.998434i	$0.517815\pi$
$828$	2272.09	0.0953632
$829$	−15982.9	−0.669612	−0.334806	−	0.942287i	$-0.608671\pi$
$829$	−15982.9	−0.669612	−0.334806	+	0.942287i	$0.608671\pi$
$830$	−1956.10	−0.0818039
$831$	14341.0	0.598657
$832$	0	0
$833$	28755.0	1.19604
$834$	−6496.80	−0.269743
$835$	−7299.33	−0.302520
$836$	7132.60	0.295079
$837$	−17541.9	−0.724415
$838$	−8716.20	−0.359303
$839$	7924.62	0.326089	0.163044	−	0.986619i	$-0.447869\pi$
$839$	7924.62	0.326089	0.163044	+	0.986619i	$0.447869\pi$
$840$	1491.85	0.0612783
$841$	−17793.7	−0.729581
$842$	−1261.05	−0.0516134
$843$	−873.908	−0.0357046
$844$	23664.0	0.965104
$845$	0	0
$846$	−4450.78	−0.180876
$847$	−197.920	−0.00802906
$848$	11625.6	0.470784
$849$	−4280.92	−0.173051
$850$	23405.4	0.944467
$851$	−5561.74	−0.224035
$852$	14156.0	0.569221
$853$	−2910.13	−0.116812	−0.0584061	−	0.998293i	$-0.518602\pi$
$853$	−2910.13	−0.116812	−0.0584061	+	0.998293i	$0.518602\pi$
$854$	−713.641	−0.0285952
$855$	−33093.3	−1.32370
$856$	−2758.83	−0.110158
$857$	−7335.57	−0.292390	−0.146195	−	0.989256i	$-0.546703\pi$
$857$	−7335.57	−0.292390	−0.146195	+	0.989256i	$0.546703\pi$
$858$	0	0
$859$	17581.9	0.698354	0.349177	−	0.937057i	$-0.386461\pi$
$859$	17581.9	0.698354	0.349177	+	0.937057i	$0.386461\pi$
$860$	−1091.29	−0.0432706
$861$	1343.51	0.0531784
$862$	14562.8	0.575420
$863$	−16472.7	−0.649752	−0.324876	−	0.945757i	$-0.605322\pi$
$863$	−16472.7	−0.649752	−0.324876	+	0.945757i	$0.605322\pi$
$864$	−21887.1	−0.861820
$865$	−25545.5	−1.00413
$866$	−8035.08	−0.315292
$867$	−6744.58	−0.264196
$868$	−1478.33	−0.0578085
$869$	−9436.47	−0.368366
$870$	4939.07	0.192472
$871$	0	0
$872$	−27281.6	−1.05949
$873$	−31530.7	−1.22240
$874$	−1691.82	−0.0654766
$875$	−4966.77	−0.191894
$876$	14020.7	0.540772
$877$	−20429.3	−0.786600	−0.393300	−	0.919410i	$-0.628667\pi$
$877$	−20429.3	−0.786600	−0.393300	+	0.919410i	$0.628667\pi$
$878$	−1800.87	−0.0692215
$879$	25863.5	0.992440
$880$	−9020.55	−0.345549
$881$	−17203.3	−0.657882	−0.328941	−	0.944351i	$-0.606692\pi$
$881$	−17203.3	−0.657882	−0.328941	+	0.944351i	$0.606692\pi$
$882$	−6075.03	−0.231924
$883$	39790.5	1.51649	0.758243	−	0.651972i	$-0.226058\pi$
$883$	39790.5	1.51649	0.758243	+	0.651972i	$0.226058\pi$
$884$	0	0
$885$	34700.8	1.31803
$886$	−5972.30	−0.226460
$887$	34067.1	1.28958	0.644792	−	0.764358i	$-0.276944\pi$
$887$	34067.1	1.28958	0.644792	+	0.764358i	$0.276944\pi$
$888$	13891.1	0.524949
$889$	−1484.70	−0.0560126
$890$	11302.2	0.425675
$891$	−766.619	−0.0288246
$892$	13559.8	0.508985
$893$	−23107.4	−0.865914
$894$	−9558.61	−0.357593
$895$	26192.7	0.978241
$896$	−2380.96	−0.0887748
$897$	0	0
$898$	1951.74	0.0725282
$899$	−10490.6	−0.389187
$900$	34477.8	1.27696
$901$	−24002.5	−0.887500
$902$	2987.13	0.110267
$903$	38.5764	0.00142164
$904$	6826.02	0.251139
$905$	−48215.2	−1.77097
$906$	9070.69	0.332620
$907$	−42829.9	−1.56796	−0.783981	−	0.620784i	$-0.786814\pi$
$907$	−42829.9	−1.56796	−0.783981	+	0.620784i	$0.786814\pi$
$908$	−18363.4	−0.671158
$909$	−34049.0	−1.24239
$910$	0	0
$911$	9120.00	0.331678	0.165839	−	0.986153i	$-0.446967\pi$
$911$	9120.00	0.331678	0.165839	+	0.986153i	$0.446967\pi$
$912$	−11491.4	−0.417234
$913$	−1071.95	−0.0388570
$914$	2298.49	0.0831808
$915$	26442.9	0.955384
$916$	20736.7	0.747989
$917$	4269.50	0.153753
$918$	11493.7	0.413235
$919$	47662.3	1.71081	0.855405	−	0.517959i	$-0.173308\pi$
$919$	47662.3	1.71081	0.855405	+	0.517959i	$0.173308\pi$
$920$	5485.73	0.196586
$921$	2745.54	0.0982287
$922$	12199.9	0.435771
$923$	0	0
$924$	381.419	0.0135798
$925$	−84396.4	−2.99993
$926$	−8932.39	−0.316994
$927$	3089.30	0.109456
$928$	−13089.1	−0.463008
$929$	−8233.02	−0.290761	−0.145380	−	0.989376i	$-0.546441\pi$
$929$	−8233.02	−0.290761	−0.145380	+	0.989376i	$0.546441\pi$
$930$	−7856.19	−0.277005
$931$	−31540.2	−1.11030
$932$	−6130.66	−0.215468
$933$	16842.3	0.590989
$934$	7744.88	0.271328
$935$	18624.0	0.651413
$936$	0	0
$937$	−48421.1	−1.68821	−0.844103	−	0.536181i	$-0.819866\pi$
$937$	−48421.1	−1.68821	−0.844103	+	0.536181i	$0.819866\pi$
$938$	−762.328	−0.0265361
$939$	10089.1	0.350633
$940$	34956.3	1.21292
$941$	1470.90	0.0509565	0.0254783	−	0.999675i	$-0.491889\pi$
$941$	1470.90	0.0509565	0.0254783	+	0.999675i	$0.491889\pi$
$942$	−8275.15	−0.286220
$943$	4940.25	0.170601
$944$	−23390.4	−0.806454
$945$	−4451.01	−0.153218
$946$	85.7701	0.00294781
$947$	21669.7	0.743582	0.371791	−	0.928316i	$-0.378744\pi$
$947$	21669.7	0.743582	0.371791	+	0.928316i	$0.378744\pi$
$948$	18185.4	0.623031
$949$	0	0
$950$	−25672.4	−0.876760
$951$	−5972.93	−0.203665
$952$	2076.17	0.0706819
$953$	42919.2	1.45886	0.729428	−	0.684058i	$-0.239787\pi$
$953$	42919.2	1.45886	0.729428	+	0.684058i	$0.239787\pi$
$954$	5070.97	0.172095
$955$	31454.7	1.06581
$956$	33380.3	1.12928
$957$	2706.64	0.0914243
$958$	−14393.1	−0.485408
$959$	968.452	0.0326099
$960$	10074.8	0.338712
$961$	−13104.5	−0.439881
$962$	0	0
$963$	3272.61	0.109510
$964$	11728.9	0.391871
$965$	17657.0	0.589016
$966$	−90.4707	−0.00301330
$967$	4509.17	0.149954	0.0749769	−	0.997185i	$-0.476112\pi$
$967$	4509.17	0.149954	0.0749769	+	0.997185i	$0.476112\pi$
$968$	1817.71	0.0603547
$969$	23725.3	0.786551
$970$	−35516.8	−1.17565
$971$	−42310.9	−1.39837	−0.699187	−	0.714938i	$-0.746455\pi$
$971$	−42310.9	−1.39837	−0.699187	+	0.714938i	$0.746455\pi$
$972$	27130.5	0.895280
$973$	3501.35	0.115363
$974$	−1955.60	−0.0643343
$975$	0	0
$976$	−17824.1	−0.584564
$977$	35226.9	1.15354	0.576769	−	0.816907i	$-0.304313\pi$
$977$	35226.9	1.15354	0.576769	+	0.816907i	$0.304313\pi$
$978$	−745.922	−0.0243885
$979$	6193.66	0.202196
$980$	47713.2	1.55525
$981$	32362.3	1.05326
$982$	3508.37	0.114009
$983$	37433.0	1.21458	0.607288	−	0.794482i	$-0.292258\pi$
$983$	37433.0	1.21458	0.607288	+	0.794482i	$0.292258\pi$
$984$	−12338.9	−0.399744
$985$	−4734.98	−0.153166
$986$	6873.58	0.222008
$987$	−1235.68	−0.0398502
$988$	0	0
$989$	141.850	0.00456074
$990$	−3934.67	−0.126315
$991$	28606.5	0.916969	0.458485	−	0.888702i	$-0.348392\pi$
$991$	28606.5	0.916969	0.458485	+	0.888702i	$0.348392\pi$
$992$	20819.8	0.666361
$993$	−30736.2	−0.982259
$994$	1094.18	0.0349147
$995$	75420.5	2.40301
$996$	2065.80	0.0657202
$997$	19590.8	0.622315	0.311157	−	0.950358i	$-0.399283\pi$
$997$	19590.8	0.622315	0.311157	+	0.950358i	$0.399283\pi$
$998$	7408.94	0.234996
$999$	−41444.7	−1.31257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.18	yes	39
13.12	even	2		1859.4.a.n.1.22	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.22	✓	39	13.12	even	2
1859.4.a.o.1.18	yes	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00172 q^{2} -3.02985 q^{3} -6.99655 q^{4} +20.0383 q^{5} +3.03507 q^{6} -1.63570 q^{7} +15.0224 q^{8} -17.8200 q^{9} +O(q^{10})\)	\(q-1.00172 q^{2} -3.02985 q^{3} -6.99655 q^{4} +20.0383 q^{5} +3.03507 q^{6} -1.63570 q^{7} +15.0224 q^{8} -17.8200 q^{9} -20.0728 q^{10} -11.0000 q^{11} +21.1985 q^{12} +1.63852 q^{14} -60.7131 q^{15} +40.9241 q^{16} -84.4929 q^{17} +17.8507 q^{18} +92.6768 q^{19} -140.199 q^{20} +4.95594 q^{21} +11.0189 q^{22} +18.2236 q^{23} -45.5156 q^{24} +276.534 q^{25} +135.798 q^{27} +11.4443 q^{28} +81.2112 q^{29} +60.8177 q^{30} -129.176 q^{31} -161.174 q^{32} +33.3284 q^{33} +84.6384 q^{34} -32.7767 q^{35} +124.679 q^{36} -305.194 q^{37} -92.8365 q^{38} +301.023 q^{40} +271.091 q^{41} -4.96447 q^{42} +7.78387 q^{43} +76.9621 q^{44} -357.083 q^{45} -18.2550 q^{46} -249.334 q^{47} -123.994 q^{48} -340.324 q^{49} -277.010 q^{50} +256.001 q^{51} +284.077 q^{53} -136.032 q^{54} -220.421 q^{55} -24.5722 q^{56} -280.797 q^{57} -81.3511 q^{58} -571.555 q^{59} +424.782 q^{60} -435.539 q^{61} +129.399 q^{62} +29.1482 q^{63} -165.942 q^{64} -33.3858 q^{66} -465.254 q^{67} +591.159 q^{68} -55.2148 q^{69} +32.8332 q^{70} +667.783 q^{71} -267.699 q^{72} +661.401 q^{73} +305.720 q^{74} -837.855 q^{75} -648.418 q^{76} +17.9927 q^{77} +857.861 q^{79} +820.050 q^{80} +69.6926 q^{81} -271.558 q^{82} +97.4502 q^{83} -34.6745 q^{84} -1693.09 q^{85} -7.79728 q^{86} -246.058 q^{87} -165.246 q^{88} -563.060 q^{89} +357.698 q^{90} -127.502 q^{92} +391.385 q^{93} +249.763 q^{94} +1857.09 q^{95} +488.332 q^{96} +1769.40 q^{97} +340.911 q^{98} +196.020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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