LMFDB - Embedded newform 1859.4.a.g.1.4

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.17505$ of defining polynomial
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)

$f(q)$	$=$	$q-3.17505 q^{2} -0.600459 q^{3} +2.08094 q^{4} +12.4679 q^{5} +1.90649 q^{6} +10.6254 q^{7} +18.7933 q^{8} -26.6394 q^{9} +O(q^{10})$	\(q-3.17505 q^{2} -0.600459 q^{3} +2.08094 q^{4} +12.4679 q^{5} +1.90649 q^{6} +10.6254 q^{7} +18.7933 q^{8} -26.6394 q^{9} -39.5863 q^{10} +11.0000 q^{11} -1.24952 q^{12} -33.7362 q^{14} -7.48648 q^{15} -76.3172 q^{16} -62.9942 q^{17} +84.5816 q^{18} +140.455 q^{19} +25.9449 q^{20} -6.38012 q^{21} -34.9255 q^{22} +69.2931 q^{23} -11.2846 q^{24} +30.4490 q^{25} +32.2083 q^{27} +22.1108 q^{28} -138.264 q^{29} +23.7699 q^{30} -168.325 q^{31} +91.9643 q^{32} -6.60505 q^{33} +200.010 q^{34} +132.477 q^{35} -55.4350 q^{36} +236.618 q^{37} -445.953 q^{38} +234.314 q^{40} +207.596 q^{41} +20.2572 q^{42} -301.808 q^{43} +22.8903 q^{44} -332.138 q^{45} -220.009 q^{46} -343.732 q^{47} +45.8254 q^{48} -230.101 q^{49} -96.6770 q^{50} +37.8254 q^{51} +306.658 q^{53} -102.263 q^{54} +137.147 q^{55} +199.686 q^{56} -84.3378 q^{57} +438.995 q^{58} -266.382 q^{59} -15.5789 q^{60} -733.894 q^{61} +534.441 q^{62} -283.055 q^{63} +318.546 q^{64} +20.9714 q^{66} -180.668 q^{67} -131.087 q^{68} -41.6076 q^{69} -420.620 q^{70} -218.447 q^{71} -500.644 q^{72} -817.244 q^{73} -751.273 q^{74} -18.2834 q^{75} +292.279 q^{76} +116.879 q^{77} -289.899 q^{79} -951.517 q^{80} +699.925 q^{81} -659.128 q^{82} -971.055 q^{83} -13.2766 q^{84} -785.406 q^{85} +958.254 q^{86} +83.0219 q^{87} +206.727 q^{88} +1405.74 q^{89} +1054.56 q^{90} +144.194 q^{92} +101.072 q^{93} +1091.36 q^{94} +1751.19 q^{95} -55.2208 q^{96} +1720.37 q^{97} +730.582 q^{98} -293.034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * 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 $

$2$	−3.17505	−1.12255	−0.561275	−	0.827630i	$-0.689689\pi$
$2$	−3.17505	−1.12255	−0.561275	+	0.827630i	$0.689689\pi$
$3$	−0.600459	−0.115558	−0.0577792	−	0.998329i	$-0.518402\pi$
$3$	−0.600459	−0.115558	−0.0577792	+	0.998329i	$0.518402\pi$
$4$	2.08094	0.260117
$5$	12.4679	1.11516	0.557582	−	0.830122i	$-0.311729\pi$
$5$	12.4679	1.11516	0.557582	+	0.830122i	$0.311729\pi$
$6$	1.90649	0.129720
$7$	10.6254	0.573717	0.286859	−	0.957973i	$-0.407389\pi$
$7$	10.6254	0.573717	0.286859	+	0.957973i	$0.407389\pi$
$8$	18.7933	0.830555
$9$	−26.6394	−0.986646
$10$	−39.5863	−1.25183
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−1.24952	−0.0300587
$13$	0	0
$13$	0	0
$14$	−33.7362	−0.644026
$15$	−7.48648	−0.128867
$16$	−76.3172	−1.19246
$17$	−62.9942	−0.898725	−0.449363	−	0.893349i	$-0.648349\pi$
$17$	−62.9942	−0.898725	−0.449363	+	0.893349i	$0.648349\pi$
$18$	84.5816	1.10756
$19$	140.455	1.69593	0.847966	−	0.530051i	$-0.177827\pi$
$19$	140.455	1.69593	0.847966	+	0.530051i	$0.177827\pi$
$20$	25.9449	0.290073
$21$	−6.38012	−0.0662979
$22$	−34.9255	−0.338461
$23$	69.2931	0.628200	0.314100	−	0.949390i	$-0.398297\pi$
$23$	69.2931	0.628200	0.314100	+	0.949390i	$0.398297\pi$
$24$	−11.2846	−0.0959776
$25$	30.4490	0.243592
$26$	0	0
$27$	32.2083	0.229574
$28$	22.1108	0.149234
$29$	−138.264	−0.885344	−0.442672	−	0.896684i	$-0.645969\pi$
$29$	−138.264	−0.885344	−0.442672	+	0.896684i	$0.645969\pi$
$30$	23.7699	0.144659
$31$	−168.325	−0.975229	−0.487614	−	0.873059i	$-0.662133\pi$
$31$	−168.325	−0.975229	−0.487614	+	0.873059i	$0.662133\pi$
$32$	91.9643	0.508036
$33$	−6.60505	−0.0348422
$34$	200.010	1.00886
$35$	132.477	0.639789
$36$	−55.4350	−0.256643
$37$	236.618	1.05134	0.525672	−	0.850687i	$-0.323814\pi$
$37$	236.618	1.05134	0.525672	+	0.850687i	$0.323814\pi$
$38$	−445.953	−1.90377
$39$	0	0
$40$	234.314	0.926206
$41$	207.596	0.790758	0.395379	−	0.918518i	$-0.370613\pi$
$41$	207.596	0.790758	0.395379	+	0.918518i	$0.370613\pi$
$42$	20.2572	0.0744226
$43$	−301.808	−1.07035	−0.535177	−	0.844740i	$-0.679755\pi$
$43$	−301.808	−1.07035	−0.535177	+	0.844740i	$0.679755\pi$
$44$	22.8903	0.0784282
$45$	−332.138	−1.10027
$46$	−220.009	−0.705186
$47$	−343.732	−1.06677	−0.533387	−	0.845871i	$-0.679081\pi$
$47$	−343.732	−1.06677	−0.533387	+	0.845871i	$0.679081\pi$
$48$	45.8254	0.137798
$49$	−230.101	−0.670848
$50$	−96.6770	−0.273444
$51$	37.8254	0.103855
$52$	0	0
$53$	306.658	0.794769	0.397384	−	0.917652i	$-0.369918\pi$
$53$	306.658	0.794769	0.397384	+	0.917652i	$0.369918\pi$
$54$	−102.263	−0.257708
$55$	137.147	0.336235
$56$	199.686	0.476504
$57$	−84.3378	−0.195979
$58$	438.995	0.993843
$59$	−266.382	−0.587796	−0.293898	−	0.955837i	$-0.594953\pi$
$59$	−266.382	−0.587796	−0.293898	+	0.955837i	$0.594953\pi$
$60$	−15.5789	−0.0335204
$61$	−733.894	−1.54042	−0.770209	−	0.637792i	$-0.779848\pi$
$61$	−733.894	−1.54042	−0.770209	+	0.637792i	$0.779848\pi$
$62$	534.441	1.09474
$63$	−283.055	−0.566056
$64$	318.546	0.622161
$65$	0	0
$66$	20.9714	0.0391121
$67$	−180.668	−0.329435	−0.164718	−	0.986341i	$-0.552671\pi$
$67$	−180.668	−0.329435	−0.164718	+	0.986341i	$0.552671\pi$
$68$	−131.087	−0.233774
$69$	−41.6076	−0.0725938
$70$	−420.620	−0.718195
$71$	−218.447	−0.365139	−0.182570	−	0.983193i	$-0.558442\pi$
$71$	−218.447	−0.365139	−0.182570	+	0.983193i	$0.558442\pi$
$72$	−500.644	−0.819464
$73$	−817.244	−1.31029	−0.655145	−	0.755503i	$-0.727393\pi$
$73$	−817.244	−1.31029	−0.655145	+	0.755503i	$0.727393\pi$
$74$	−751.273	−1.18019
$75$	−18.2834	−0.0281491
$76$	292.279	0.441141
$77$	116.879	0.172982
$78$	0	0
$79$	−289.899	−0.412863	−0.206432	−	0.978461i	$-0.566185\pi$
$79$	−289.899	−0.412863	−0.206432	+	0.978461i	$0.566185\pi$
$80$	−951.517	−1.32978
$81$	699.925	0.960117
$82$	−659.128	−0.887665
$83$	−971.055	−1.28418	−0.642091	−	0.766628i	$-0.721933\pi$
$83$	−971.055	−1.28418	−0.642091	+	0.766628i	$0.721933\pi$
$84$	−13.2766	−0.0172452
$85$	−785.406	−1.00223
$86$	958.254	1.20153
$87$	83.0219	0.102309
$88$	206.727	0.250422
$89$	1405.74	1.67424	0.837122	−	0.547016i	$-0.184236\pi$
$89$	1405.74	1.67424	0.837122	+	0.547016i	$0.184236\pi$
$90$	1054.56	1.23511
$91$	0	0
$92$	144.194	0.163405
$93$	101.072	0.112696
$94$	1091.36	1.19751
$95$	1751.19	1.89124
$96$	−55.2208	−0.0587078
$97$	1720.37	1.80080	0.900399	−	0.435066i	$-0.143275\pi$
$97$	1720.37	1.80080	0.900399	+	0.435066i	$0.143275\pi$
$98$	730.582	0.753060
$99$	−293.034	−0.297485
$100$	63.3624	0.0633624
$101$	−1711.22	−1.68587	−0.842936	−	0.538014i	$-0.819175\pi$
$101$	−1711.22	−1.68587	−0.842936	+	0.538014i	$0.819175\pi$
$102$	−120.098	−0.116583
$103$	−755.128	−0.722378	−0.361189	−	0.932493i	$-0.617629\pi$
$103$	−755.128	−0.722378	−0.361189	+	0.932493i	$0.617629\pi$
$104$	0	0
$105$	−79.5468	−0.0739330
$106$	−973.655	−0.892167
$107$	250.109	0.225971	0.112986	−	0.993597i	$-0.463959\pi$
$107$	250.109	0.225971	0.112986	+	0.993597i	$0.463959\pi$
$108$	67.0234	0.0597160
$109$	−290.883	−0.255611	−0.127805	−	0.991799i	$-0.540793\pi$
$109$	−290.883	−0.255611	−0.127805	+	0.991799i	$0.540793\pi$
$110$	−435.449	−0.377440
$111$	−142.079	−0.121492
$112$	−810.900	−0.684133
$113$	361.698	0.301113	0.150556	−	0.988601i	$-0.451894\pi$
$113$	361.698	0.301113	0.150556	+	0.988601i	$0.451894\pi$
$114$	267.777	0.219996
$115$	863.940	0.700546
$116$	−287.719	−0.230293
$117$	0	0
$118$	845.775	0.659830
$119$	−669.338	−0.515614
$120$	−140.696	−0.107031
$121$	121.000	0.0909091
$122$	2330.15	1.72919
$123$	−124.653	−0.0913787
$124$	−350.274	−0.253674
$125$	−1178.85	−0.843519
$126$	898.712	0.635426
$127$	553.305	0.386597	0.193299	−	0.981140i	$-0.438081\pi$
$127$	553.305	0.386597	0.193299	+	0.981140i	$0.438081\pi$
$128$	−1747.11	−1.20644
$129$	181.223	0.123688
$130$	0	0
$131$	1473.00	0.982420	0.491210	−	0.871041i	$-0.336555\pi$
$131$	1473.00	0.982420	0.491210	+	0.871041i	$0.336555\pi$
$132$	−13.7447	−0.00906304
$133$	1492.40	0.972985
$134$	573.631	0.369807
$135$	401.570	0.256012
$136$	−1183.87	−0.746441
$137$	−1390.89	−0.867384	−0.433692	−	0.901061i	$-0.642789\pi$
$137$	−1390.89	−0.867384	−0.433692	+	0.901061i	$0.642789\pi$
$138$	132.106	0.0814901
$139$	1886.90	1.15140	0.575702	−	0.817660i	$-0.304729\pi$
$139$	1886.90	1.15140	0.575702	+	0.817660i	$0.304729\pi$
$140$	275.675	0.166420
$141$	206.397	0.123275
$142$	693.580	0.409887
$143$	0	0
$144$	2033.05	1.17653
$145$	−1723.86	−0.987305
$146$	2594.79	1.47087
$147$	138.166	0.0775222
$148$	492.386	0.273472
$149$	2331.13	1.28170	0.640850	−	0.767666i	$-0.278582\pi$
$149$	2331.13	1.28170	0.640850	+	0.767666i	$0.278582\pi$
$150$	58.0506	0.0315987
$151$	2342.83	1.26263	0.631313	−	0.775528i	$-0.282516\pi$
$151$	2342.83	1.26263	0.631313	+	0.775528i	$0.282516\pi$
$152$	2639.62	1.40856
$153$	1678.13	0.886724
$154$	−371.098	−0.194181
$155$	−2098.66	−1.08754
$156$	0	0
$157$	2276.13	1.15704	0.578518	−	0.815670i	$-0.303631\pi$
$157$	2276.13	1.15704	0.578518	+	0.815670i	$0.303631\pi$
$158$	920.444	0.463459
$159$	−184.136	−0.0918422
$160$	1146.60	0.566543
$161$	736.266	0.360409
$162$	−2222.30	−1.07778
$163$	1016.82	0.488609	0.244305	−	0.969699i	$-0.421440\pi$
$163$	1016.82	0.488609	0.244305	+	0.969699i	$0.421440\pi$
$164$	431.994	0.205690
$165$	−82.3512	−0.0388548
$166$	3083.15	1.44156
$167$	−2071.03	−0.959648	−0.479824	−	0.877365i	$-0.659299\pi$
$167$	−2071.03	−0.959648	−0.479824	+	0.877365i	$0.659299\pi$
$168$	−119.904	−0.0550640
$169$	0	0
$170$	2493.70	1.12505
$171$	−3741.66	−1.67328
$172$	−628.042	−0.278417
$173$	−1980.96	−0.870575	−0.435288	−	0.900291i	$-0.643353\pi$
$173$	−1980.96	−0.870575	−0.435288	+	0.900291i	$0.643353\pi$
$174$	−263.599	−0.114847
$175$	323.533	0.139753
$176$	−839.489	−0.359539
$177$	159.951	0.0679248
$178$	−4463.28	−1.87942
$179$	−3440.83	−1.43676	−0.718380	−	0.695651i	$-0.755116\pi$
$179$	−3440.83	−1.43676	−0.718380	+	0.695651i	$0.755116\pi$
$180$	−691.159	−0.286200
$181$	−2545.54	−1.04535	−0.522676	−	0.852532i	$-0.675066\pi$
$181$	−2545.54	−1.04535	−0.522676	+	0.852532i	$0.675066\pi$
$182$	0	0
$183$	440.673	0.178008
$184$	1302.25	0.521755
$185$	2950.13	1.17242
$186$	−320.910	−0.126507
$187$	−692.936	−0.270976
$188$	−715.283	−0.277486
$189$	342.226	0.131710
$190$	−5560.11	−2.12301
$191$	−1700.45	−0.644191	−0.322096	−	0.946707i	$-0.604387\pi$
$191$	−1700.45	−0.644191	−0.322096	+	0.946707i	$0.604387\pi$
$192$	−191.274	−0.0718960
$193$	3538.34	1.31966	0.659832	−	0.751413i	$-0.270627\pi$
$193$	3538.34	1.31966	0.659832	+	0.751413i	$0.270627\pi$
$194$	−5462.27	−2.02148
$195$	0	0
$196$	−478.825	−0.174499
$197$	−2590.46	−0.936867	−0.468434	−	0.883499i	$-0.655181\pi$
$197$	−2590.46	−0.936867	−0.468434	+	0.883499i	$0.655181\pi$
$198$	930.397	0.333942
$199$	−4681.28	−1.66757	−0.833786	−	0.552087i	$-0.813832\pi$
$199$	−4681.28	−1.66757	−0.833786	+	0.552087i	$0.813832\pi$
$200$	572.238	0.202317
$201$	108.484	0.0380690
$202$	5433.22	1.89247
$203$	−1469.11	−0.507937
$204$	78.7123	0.0270145
$205$	2588.29	0.881825
$206$	2397.57	0.810905
$207$	−1845.93	−0.619811
$208$	0	0
$209$	1545.01	0.511343
$210$	252.565	0.0829935
$211$	4948.59	1.61457	0.807286	−	0.590160i	$-0.200936\pi$
$211$	4948.59	1.61457	0.807286	+	0.590160i	$0.200936\pi$
$212$	638.136	0.206733
$213$	131.169	0.0421949
$214$	−794.108	−0.253664
$215$	−3762.91	−1.19362
$216$	605.301	0.190674
$217$	−1788.52	−0.559506
$218$	923.568	0.286935
$219$	490.722	0.151415
$220$	285.394	0.0874604
$221$	0	0
$222$	451.109	0.136380
$223$	141.065	0.0423606	0.0211803	−	0.999776i	$-0.493258\pi$
$223$	141.065	0.0423606	0.0211803	+	0.999776i	$0.493258\pi$
$224$	977.157	0.291469
$225$	−811.144	−0.240339
$226$	−1148.41	−0.338014
$227$	−1870.17	−0.546818	−0.273409	−	0.961898i	$-0.588151\pi$
$227$	−1870.17	−0.546818	−0.273409	+	0.961898i	$0.588151\pi$
$228$	−175.501	−0.0509775
$229$	3641.42	1.05079	0.525397	−	0.850857i	$-0.323917\pi$
$229$	3641.42	1.05079	0.525397	+	0.850857i	$0.323917\pi$
$230$	−2743.05	−0.786398
$231$	−70.1813	−0.0199896
$232$	−2598.44	−0.735327
$233$	520.689	0.146401	0.0732006	−	0.997317i	$-0.476679\pi$
$233$	520.689	0.146401	0.0732006	+	0.997317i	$0.476679\pi$
$234$	0	0
$235$	−4285.62	−1.18963
$236$	−554.323	−0.152896
$237$	174.073	0.0477098
$238$	2125.18	0.578802
$239$	−1128.38	−0.305392	−0.152696	−	0.988273i	$-0.548796\pi$
$239$	−1128.38	−0.305392	−0.152696	+	0.988273i	$0.548796\pi$
$240$	571.347	0.153668
$241$	−317.382	−0.0848314	−0.0424157	−	0.999100i	$-0.513505\pi$
$241$	−317.382	−0.0848314	−0.0424157	+	0.999100i	$0.513505\pi$
$242$	−384.181	−0.102050
$243$	−1289.90	−0.340523
$244$	−1527.19	−0.400689
$245$	−2868.88	−0.748106
$246$	395.779	0.102577
$247$	0	0
$248$	−3163.39	−0.809981
$249$	583.079	0.148398
$250$	3742.92	0.946892
$251$	3603.60	0.906204	0.453102	−	0.891459i	$-0.350317\pi$
$251$	3603.60	0.906204	0.453102	+	0.891459i	$0.350317\pi$
$252$	−589.019	−0.147241
$253$	762.224	0.189409
$254$	−1756.77	−0.433975
$255$	471.604	0.115816
$256$	2998.80	0.732130
$257$	−4545.48	−1.10326	−0.551632	−	0.834087i	$-0.685995\pi$
$257$	−4545.48	−1.10326	−0.551632	+	0.834087i	$0.685995\pi$
$258$	−575.393	−0.138846
$259$	2514.16	0.603174
$260$	0	0
$261$	3683.28	0.873522
$262$	−4676.86	−1.10281
$263$	1247.98	0.292599	0.146299	−	0.989240i	$-0.453264\pi$
$263$	1247.98	0.292599	0.146299	+	0.989240i	$0.453264\pi$
$264$	−124.131	−0.0289383
$265$	3823.39	0.886298
$266$	−4738.43	−1.09222
$267$	−844.087	−0.193473
$268$	−375.959	−0.0856917
$269$	−4206.71	−0.953486	−0.476743	−	0.879043i	$-0.658183\pi$
$269$	−4206.71	−0.953486	−0.476743	+	0.879043i	$0.658183\pi$
$270$	−1275.01	−0.287387
$271$	−6741.39	−1.51111	−0.755554	−	0.655086i	$-0.772632\pi$
$271$	−6741.39	−1.51111	−0.755554	+	0.655086i	$0.772632\pi$
$272$	4807.54	1.07169
$273$	0	0
$274$	4416.14	0.973682
$275$	334.939	0.0734457
$276$	−86.5828	−0.0188829
$277$	627.466	0.136104	0.0680519	−	0.997682i	$-0.478322\pi$
$277$	627.466	0.136104	0.0680519	+	0.997682i	$0.478322\pi$
$278$	−5991.02	−1.29251
$279$	4484.09	0.962206
$280$	2489.67	0.531380
$281$	8848.01	1.87839	0.939195	−	0.343383i	$-0.111573\pi$
$281$	8848.01	1.87839	0.939195	+	0.343383i	$0.111573\pi$
$282$	−655.320	−0.138382
$283$	−8304.85	−1.74442	−0.872212	−	0.489128i	$-0.837315\pi$
$283$	−8304.85	−1.74442	−0.872212	+	0.489128i	$0.837315\pi$
$284$	−454.574	−0.0949789
$285$	−1051.52	−0.218549
$286$	0	0
$287$	2205.79	0.453672
$288$	−2449.88	−0.501251
$289$	−944.736	−0.192293
$290$	5473.35	1.10830
$291$	−1033.01	−0.208097
$292$	−1700.63	−0.340829
$293$	−1448.89	−0.288891	−0.144446	−	0.989513i	$-0.546140\pi$
$293$	−1448.89	−0.288891	−0.144446	+	0.989513i	$0.546140\pi$
$294$	−438.685	−0.0870225
$295$	−3321.23	−0.655489
$296$	4446.83	0.873199
$297$	354.291	0.0692191
$298$	−7401.44	−1.43877
$299$	0	0
$300$	−38.0465	−0.00732206
$301$	−3206.83	−0.614081
$302$	−7438.59	−1.41736
$303$	1027.52	0.194817
$304$	−10719.2	−2.02232
$305$	−9150.13	−1.71782
$306$	−5328.14	−0.995391
$307$	−3135.48	−0.582904	−0.291452	−	0.956585i	$-0.594138\pi$
$307$	−3135.48	−0.582904	−0.291452	+	0.956585i	$0.594138\pi$
$308$	243.218	0.0449956
$309$	453.423	0.0834769
$310$	6663.36	1.22082
$311$	−6381.54	−1.16355	−0.581775	−	0.813350i	$-0.697642\pi$
$311$	−6381.54	−1.16355	−0.581775	+	0.813350i	$0.697642\pi$
$312$	0	0
$313$	−895.167	−0.161654	−0.0808272	−	0.996728i	$-0.525756\pi$
$313$	−895.167	−0.161654	−0.0808272	+	0.996728i	$0.525756\pi$
$314$	−7226.81	−1.29883
$315$	−3529.10	−0.631246
$316$	−603.261	−0.107393
$317$	1411.07	0.250011	0.125005	−	0.992156i	$-0.460105\pi$
$317$	1411.07	0.250011	0.125005	+	0.992156i	$0.460105\pi$
$318$	584.640	0.103097
$319$	−1520.90	−0.266941
$320$	3971.61	0.693812
$321$	−150.180	−0.0261129
$322$	−2337.68	−0.404577
$323$	−8847.87	−1.52418
$324$	1456.50	0.249743
$325$	0	0
$326$	−3228.44	−0.548488
$327$	174.663	0.0295380
$328$	3901.42	0.656768
$329$	−3652.28	−0.612027
$330$	261.469	0.0436164
$331$	−358.291	−0.0594968	−0.0297484	−	0.999557i	$-0.509471\pi$
$331$	−358.291	−0.0594968	−0.0297484	+	0.999557i	$0.509471\pi$
$332$	−2020.70	−0.334038
$333$	−6303.37	−1.03730
$334$	6575.63	1.07725
$335$	−2252.56	−0.367375
$336$	486.913	0.0790573
$337$	583.989	0.0943973	0.0471986	−	0.998886i	$-0.484971\pi$
$337$	583.989	0.0943973	0.0471986	+	0.998886i	$0.484971\pi$
$338$	0	0
$339$	−217.185	−0.0347961
$340$	−1634.38	−0.260696
$341$	−1851.58	−0.294043
$342$	11879.9	1.87834
$343$	−6089.42	−0.958595
$344$	−5671.97	−0.888989
$345$	−518.761	−0.0809540
$346$	6289.64	0.977264
$347$	2653.34	0.410486	0.205243	−	0.978711i	$-0.434202\pi$
$347$	2653.34	0.410486	0.205243	+	0.978711i	$0.434202\pi$
$348$	172.763	0.0266123
$349$	−2697.04	−0.413665	−0.206833	−	0.978376i	$-0.566316\pi$
$349$	−2697.04	−0.413665	−0.206833	+	0.978376i	$0.566316\pi$
$350$	−1027.23	−0.156880
$351$	0	0
$352$	1011.61	0.153179
$353$	−439.546	−0.0662739	−0.0331370	−	0.999451i	$-0.510550\pi$
$353$	−439.546	−0.0662739	−0.0331370	+	0.999451i	$0.510550\pi$
$354$	−507.853	−0.0762489
$355$	−2723.58	−0.407190
$356$	2925.25	0.435499
$357$	401.910	0.0595836
$358$	10924.8	1.61283
$359$	4427.30	0.650874	0.325437	−	0.945564i	$-0.394489\pi$
$359$	4427.30	0.650874	0.325437	+	0.945564i	$0.394489\pi$
$360$	−6241.98	−0.913837
$361$	12868.7	1.87618
$362$	8082.22	1.17346
$363$	−72.6556	−0.0105053
$364$	0	0
$365$	−10189.3	−1.46119
$366$	−1399.16	−0.199823
$367$	−10299.4	−1.46491	−0.732455	−	0.680816i	$-0.761625\pi$
$367$	−10299.4	−1.46491	−0.732455	+	0.680816i	$0.761625\pi$
$368$	−5288.25	−0.749101
$369$	−5530.25	−0.780198
$370$	−9366.81	−1.31610
$371$	3258.36	0.455973
$372$	210.325	0.0293141
$373$	−7178.91	−0.996541	−0.498270	−	0.867022i	$-0.666031\pi$
$373$	−7178.91	−0.996541	−0.498270	+	0.867022i	$0.666031\pi$
$374$	2200.10	0.304184
$375$	707.854	0.0974758
$376$	−6459.86	−0.886015
$377$	0	0
$378$	−1086.58	−0.147851
$379$	−4214.23	−0.571163	−0.285581	−	0.958354i	$-0.592187\pi$
$379$	−4214.23	−0.571163	−0.285581	+	0.958354i	$0.592187\pi$
$380$	3644.11	0.491944
$381$	−332.237	−0.0446746
$382$	5399.03	0.723137
$383$	6506.29	0.868031	0.434015	−	0.900905i	$-0.357096\pi$
$383$	6506.29	0.868031	0.434015	+	0.900905i	$0.357096\pi$
$384$	1049.07	0.139415
$385$	1457.24	0.192904
$386$	−11234.4	−1.48139
$387$	8039.99	1.05606
$388$	3579.98	0.468418
$389$	−10872.8	−1.41715	−0.708577	−	0.705633i	$-0.750663\pi$
$389$	−10872.8	−1.41715	−0.708577	+	0.705633i	$0.750663\pi$
$390$	0	0
$391$	−4365.06	−0.564579
$392$	−4324.36	−0.557177
$393$	−884.479	−0.113527
$394$	8224.85	1.05168
$395$	−3614.44	−0.460410
$396$	−609.785	−0.0773809
$397$	−9020.48	−1.14037	−0.570183	−	0.821518i	$-0.693128\pi$
$397$	−9020.48	−1.14037	−0.570183	+	0.821518i	$0.693128\pi$
$398$	14863.3	1.87193
$399$	−896.122	−0.112437
$400$	−2323.78	−0.290473
$401$	−607.247	−0.0756221	−0.0378111	−	0.999285i	$-0.512039\pi$
$401$	−607.247	−0.0756221	−0.0378111	+	0.999285i	$0.512039\pi$
$402$	−344.442	−0.0427344
$403$	0	0
$404$	−3560.95	−0.438524
$405$	8726.61	1.07069
$406$	4664.50	0.570185
$407$	2602.80	0.316992
$408$	710.865	0.0862575
$409$	−14792.5	−1.78836	−0.894181	−	0.447707i	$-0.852241\pi$
$409$	−14792.5	−1.78836	−0.894181	+	0.447707i	$0.852241\pi$
$410$	−8217.96	−0.989892
$411$	835.172	0.100234
$412$	−1571.37	−0.187903
$413$	−2830.41	−0.337229
$414$	5860.91	0.695769
$415$	−12107.0	−1.43208
$416$	0	0
$417$	−1133.01	−0.133054
$418$	−4905.48	−0.574007
$419$	−8676.69	−1.01166	−0.505828	−	0.862634i	$-0.668813\pi$
$419$	−8676.69	−1.01166	−0.505828	+	0.862634i	$0.668813\pi$
$420$	−165.532	−0.0192312
$421$	9185.80	1.06339	0.531697	−	0.846935i	$-0.321555\pi$
$421$	9185.80	1.06339	0.531697	+	0.846935i	$0.321555\pi$
$422$	−15712.0	−1.81244
$423$	9156.82	1.05253
$424$	5763.12	0.660099
$425$	−1918.11	−0.218922
$426$	−416.467	−0.0473659
$427$	−7797.91	−0.883764
$428$	520.460	0.0587790
$429$	0	0
$430$	11947.4	1.33990
$431$	12680.2	1.41713	0.708565	−	0.705646i	$-0.249343\pi$
$431$	12680.2	1.41713	0.708565	+	0.705646i	$0.249343\pi$
$432$	−2458.05	−0.273757
$433$	−713.344	−0.0791712	−0.0395856	−	0.999216i	$-0.512604\pi$
$433$	−713.344	−0.0791712	−0.0395856	+	0.999216i	$0.512604\pi$
$434$	5678.64	0.628073
$435$	1035.11	0.114091
$436$	−605.309	−0.0664886
$437$	9732.59	1.06538
$438$	−1558.07	−0.169971
$439$	−14808.1	−1.60992	−0.804958	−	0.593332i	$-0.797812\pi$
$439$	−14808.1	−1.60992	−0.804958	+	0.593332i	$0.797812\pi$
$440$	2577.45	0.279262
$441$	6129.76	0.661890
$442$	0	0
$443$	2373.33	0.254538	0.127269	−	0.991868i	$-0.459379\pi$
$443$	2373.33	0.254538	0.127269	+	0.991868i	$0.459379\pi$
$444$	−295.658	−0.0316020
$445$	17526.6	1.86706
$446$	−447.888	−0.0475519
$447$	−1399.75	−0.148111
$448$	3384.68	0.356945
$449$	6893.13	0.724515	0.362257	−	0.932078i	$-0.382006\pi$
$449$	6893.13	0.724515	0.362257	+	0.932078i	$0.382006\pi$
$450$	2575.42	0.269792
$451$	2283.56	0.238423
$452$	752.671	0.0783245
$453$	−1406.77	−0.145907
$454$	5937.89	0.613830
$455$	0	0
$456$	−1584.99	−0.162772
$457$	−494.530	−0.0506196	−0.0253098	−	0.999680i	$-0.508057\pi$
$457$	−494.530	−0.0506196	−0.0253098	+	0.999680i	$0.508057\pi$
$458$	−11561.7	−1.17957
$459$	−2028.93	−0.206324
$460$	1797.80	0.182224
$461$	8827.06	0.891794	0.445897	−	0.895084i	$-0.352885\pi$
$461$	8827.06	0.891794	0.445897	+	0.895084i	$0.352885\pi$
$462$	222.829	0.0224393
$463$	−16787.9	−1.68510	−0.842551	−	0.538617i	$-0.818947\pi$
$463$	−16787.9	−1.68510	−0.842551	+	0.538617i	$0.818947\pi$
$464$	10551.9	1.05573
$465$	1260.16	0.125674
$466$	−1653.21	−0.164343
$467$	−7114.94	−0.705011	−0.352506	−	0.935810i	$-0.614670\pi$
$467$	−7114.94	−0.705011	−0.352506	+	0.935810i	$0.614670\pi$
$468$	0	0
$469$	−1919.67	−0.189003
$470$	13607.0	1.33542
$471$	−1366.72	−0.133705
$472$	−5006.20	−0.488197
$473$	−3319.88	−0.322724
$474$	−552.689	−0.0535566
$475$	4276.73	0.413115
$476$	−1392.85	−0.134120
$477$	−8169.20	−0.784156
$478$	3582.65	0.342817
$479$	−18089.7	−1.72555	−0.862775	−	0.505588i	$-0.831276\pi$
$479$	−18089.7	−1.72555	−0.862775	+	0.505588i	$0.831276\pi$
$480$	−688.488	−0.0654688
$481$	0	0
$482$	1007.70	0.0952275
$483$	−442.098	−0.0416483
$484$	251.793	0.0236470
$485$	21449.5	2.00819
$486$	4095.50	0.382254
$487$	−8829.17	−0.821536	−0.410768	−	0.911740i	$-0.634739\pi$
$487$	−8829.17	−0.821536	−0.410768	+	0.911740i	$0.634739\pi$
$488$	−13792.3	−1.27940
$489$	−610.557	−0.0564629
$490$	9108.83	0.839786
$491$	15260.5	1.40264	0.701321	−	0.712845i	$-0.252594\pi$
$491$	15260.5	1.40264	0.701321	+	0.712845i	$0.252594\pi$
$492$	−259.395	−0.0237692
$493$	8709.83	0.795681
$494$	0	0
$495$	−3653.52	−0.331745
$496$	12846.1	1.16292
$497$	−2321.09	−0.209487
$498$	−1851.30	−0.166584
$499$	6698.24	0.600911	0.300455	−	0.953796i	$-0.402861\pi$
$499$	6698.24	0.600911	0.300455	+	0.953796i	$0.402861\pi$
$500$	−2453.12	−0.219414
$501$	1243.57	0.110895
$502$	−11441.6	−1.01726
$503$	1941.27	0.172082	0.0860409	−	0.996292i	$-0.472578\pi$
$503$	1941.27	0.172082	0.0860409	+	0.996292i	$0.472578\pi$
$504$	−5319.54	−0.470141
$505$	−21335.4	−1.88002
$506$	−2420.10	−0.212621
$507$	0	0
$508$	1151.39	0.100561
$509$	7599.74	0.661793	0.330896	−	0.943667i	$-0.392649\pi$
$509$	7599.74	0.661793	0.330896	+	0.943667i	$0.392649\pi$
$510$	−1497.37	−0.130009
$511$	−8683.54	−0.751737
$512$	4455.57	0.384590
$513$	4523.83	0.389341
$514$	14432.1	1.23847
$515$	−9414.87	−0.805571
$516$	377.114	0.0321735
$517$	−3781.05	−0.321645
$518$	−7982.57	−0.677093
$519$	1189.49	0.100602
$520$	0	0
$521$	−7464.85	−0.627718	−0.313859	−	0.949470i	$-0.601622\pi$
$521$	−7464.85	−0.627718	−0.313859	+	0.949470i	$0.601622\pi$
$522$	−11694.6	−0.980571
$523$	17020.9	1.42308	0.711542	−	0.702643i	$-0.247997\pi$
$523$	17020.9	1.42308	0.711542	+	0.702643i	$0.247997\pi$
$524$	3065.23	0.255544
$525$	−194.268	−0.0161496
$526$	−3962.38	−0.328456
$527$	10603.5	0.876463
$528$	504.079	0.0415478
$529$	−7365.47	−0.605365
$530$	−12139.4	−0.994913
$531$	7096.26	0.579947
$532$	3105.58	0.253090
$533$	0	0
$534$	2680.02	0.217183
$535$	3118.34	0.251995
$536$	−3395.36	−0.273614
$537$	2066.08	0.166030
$538$	13356.5	1.07034
$539$	−2531.11	−0.202268
$540$	835.642	0.0665932
$541$	−9247.23	−0.734879	−0.367440	−	0.930047i	$-0.619766\pi$
$541$	−9247.23	−0.734879	−0.367440	+	0.930047i	$0.619766\pi$
$542$	21404.3	1.69629
$543$	1528.49	0.120799
$544$	−5793.21	−0.456584
$545$	−3626.71	−0.285048
$546$	0	0
$547$	3661.21	0.286183	0.143092	−	0.989709i	$-0.454296\pi$
$547$	3661.21	0.286183	0.143092	+	0.989709i	$0.454296\pi$
$548$	−2894.35	−0.225621
$549$	19550.5	1.51985
$550$	−1063.45	−0.0824464
$551$	−19419.9	−1.50148
$552$	−781.946	−0.0602932
$553$	−3080.29	−0.236867
$554$	−1992.24	−0.152783
$555$	−1771.43	−0.135483
$556$	3926.53	0.299500
$557$	−16803.9	−1.27828	−0.639142	−	0.769089i	$-0.720710\pi$
$557$	−16803.9	−1.27828	−0.639142	+	0.769089i	$0.720710\pi$
$558$	−14237.2	−1.08012
$559$	0	0
$560$	−10110.2	−0.762921
$561$	416.080	0.0313135
$562$	−28092.9	−2.10859
$563$	13085.7	0.979571	0.489785	−	0.871843i	$-0.337075\pi$
$563$	13085.7	0.979571	0.489785	+	0.871843i	$0.337075\pi$
$564$	429.498	0.0320659
$565$	4509.63	0.335790
$566$	26368.3	1.95820
$567$	7436.98	0.550836
$568$	−4105.35	−0.303268
$569$	−20152.0	−1.48474	−0.742368	−	0.669992i	$-0.766298\pi$
$569$	−20152.0	−1.48474	−0.742368	+	0.669992i	$0.766298\pi$
$570$	3338.62	0.245332
$571$	8555.61	0.627042	0.313521	−	0.949581i	$-0.398491\pi$
$571$	8555.61	0.627042	0.313521	+	0.949581i	$0.398491\pi$
$572$	0	0
$573$	1021.05	0.0744417
$574$	−7003.50	−0.509269
$575$	2109.90	0.153024
$576$	−8485.90	−0.613853
$577$	−13753.6	−0.992323	−0.496161	−	0.868230i	$-0.665258\pi$
$577$	−13753.6	−0.992323	−0.496161	+	0.868230i	$0.665258\pi$
$578$	2999.58	0.215858
$579$	−2124.63	−0.152498
$580$	−3587.25	−0.256815
$581$	−10317.8	−0.736758
$582$	3279.87	0.233599
$583$	3373.24	0.239632
$584$	−15358.7	−1.08827
$585$	0	0
$586$	4600.30	0.324295
$587$	−8182.82	−0.575368	−0.287684	−	0.957725i	$-0.592885\pi$
$587$	−8182.82	−0.575368	−0.287684	+	0.957725i	$0.592885\pi$
$588$	287.515	0.0201648
$589$	−23642.2	−1.65392
$590$	10545.1	0.735819
$591$	1555.47	0.108263
$592$	−18058.0	−1.25368
$593$	3774.00	0.261349	0.130674	−	0.991425i	$-0.458286\pi$
$593$	3774.00	0.261349	0.130674	+	0.991425i	$0.458286\pi$
$594$	−1124.89	−0.0777018
$595$	−8345.25	−0.574995
$596$	4850.92	0.333392
$597$	2810.92	0.192702
$598$	0	0
$599$	−3293.48	−0.224654	−0.112327	−	0.993671i	$-0.535830\pi$
$599$	−3293.48	−0.224654	−0.112327	+	0.993671i	$0.535830\pi$
$600$	−343.605	−0.0233794
$601$	−12195.7	−0.827740	−0.413870	−	0.910336i	$-0.635823\pi$
$601$	−12195.7	−0.827740	−0.413870	+	0.910336i	$0.635823\pi$
$602$	10181.8	0.689336
$603$	4812.91	0.325036
$604$	4875.27	0.328430
$605$	1508.62	0.101379
$606$	−3262.43	−0.218691
$607$	−153.122	−0.0102389	−0.00511947	−	0.999987i	$-0.501630\pi$
$607$	−153.122	−0.0102389	−0.00511947	+	0.999987i	$0.501630\pi$
$608$	12916.9	0.861594
$609$	882.140	0.0586964
$610$	29052.1	1.92834
$611$	0	0
$612$	3492.08	0.230652
$613$	−17683.7	−1.16515	−0.582577	−	0.812775i	$-0.697956\pi$
$613$	−17683.7	−1.16515	−0.582577	+	0.812775i	$0.697956\pi$
$614$	9955.31	0.654338
$615$	−1554.16	−0.101902
$616$	2196.55	0.143671
$617$	4930.92	0.321737	0.160868	−	0.986976i	$-0.448571\pi$
$617$	4930.92	0.321737	0.160868	+	0.986976i	$0.448571\pi$
$618$	−1439.64	−0.0937069
$619$	22061.4	1.43251	0.716254	−	0.697839i	$-0.245855\pi$
$619$	22061.4	1.43251	0.716254	+	0.697839i	$0.245855\pi$
$620$	−4367.19	−0.282888
$621$	2231.81	0.144218
$622$	20261.7	1.30614
$623$	14936.5	0.960543
$624$	0	0
$625$	−18504.0	−1.18425
$626$	2842.20	0.181465
$627$	−927.716	−0.0590899
$628$	4736.47	0.300965
$629$	−14905.5	−0.944869
$630$	11205.1	0.708604
$631$	−30547.7	−1.92724	−0.963618	−	0.267283i	$-0.913874\pi$
$631$	−30547.7	−1.92724	−0.963618	+	0.267283i	$0.913874\pi$
$632$	−5448.16	−0.342906
$633$	−2971.42	−0.186577
$634$	−4480.21	−0.280649
$635$	6898.56	0.431120
$636$	−383.175	−0.0238897
$637$	0	0
$638$	4828.95	0.299655
$639$	5819.31	0.360263
$640$	−21782.9	−1.34538
$641$	−13540.0	−0.834321	−0.417160	−	0.908833i	$-0.636975\pi$
$641$	−13540.0	−0.834321	−0.417160	+	0.908833i	$0.636975\pi$
$642$	476.829	0.0293130
$643$	3224.64	0.197772	0.0988861	−	0.995099i	$-0.468472\pi$
$643$	3224.64	0.197772	0.0988861	+	0.995099i	$0.468472\pi$
$644$	1532.12	0.0937486
$645$	2259.48	0.137933
$646$	28092.4	1.71096
$647$	−5934.82	−0.360621	−0.180310	−	0.983610i	$-0.557710\pi$
$647$	−5934.82	−0.360621	−0.180310	+	0.983610i	$0.557710\pi$
$648$	13153.9	0.797430
$649$	−2930.20	−0.177227
$650$	0	0
$651$	1073.93	0.0646556
$652$	2115.93	0.127095
$653$	13383.6	0.802055	0.401028	−	0.916066i	$-0.368653\pi$
$653$	13383.6	0.802055	0.401028	+	0.916066i	$0.368653\pi$
$654$	−554.565	−0.0331578
$655$	18365.3	1.09556
$656$	−15843.2	−0.942944
$657$	21770.9	1.29279
$658$	11596.2	0.687031
$659$	22121.9	1.30766	0.653829	−	0.756642i	$-0.273162\pi$
$659$	22121.9	1.30766	0.653829	+	0.756642i	$0.273162\pi$
$660$	−171.368	−0.0101068
$661$	24670.9	1.45172	0.725861	−	0.687841i	$-0.241441\pi$
$661$	24670.9	1.45172	0.725861	+	0.687841i	$0.241441\pi$
$662$	1137.59	0.0667881
$663$	0	0
$664$	−18249.4	−1.06658
$665$	18607.1	1.08504
$666$	20013.5	1.16443
$667$	−9580.74	−0.556173
$668$	−4309.68	−0.249621
$669$	−84.7038	−0.00489512
$670$	7151.99	0.412396
$671$	−8072.83	−0.464453
$672$	−586.743	−0.0336817
$673$	−6709.79	−0.384314	−0.192157	−	0.981364i	$-0.561548\pi$
$673$	−6709.79	−0.384314	−0.192157	+	0.981364i	$0.561548\pi$
$674$	−1854.19	−0.105966
$675$	980.710	0.0559223
$676$	0	0
$677$	−3713.77	−0.210830	−0.105415	−	0.994428i	$-0.533617\pi$
$677$	−3713.77	−0.210830	−0.105415	+	0.994428i	$0.533617\pi$
$678$	689.573	0.0390603
$679$	18279.6	1.03315
$680$	−14760.4	−0.832404
$681$	1122.96	0.0631894
$682$	5878.85	0.330077
$683$	−12021.6	−0.673488	−0.336744	−	0.941596i	$-0.609326\pi$
$683$	−12021.6	−0.673488	−0.336744	+	0.941596i	$0.609326\pi$
$684$	−7786.15	−0.435250
$685$	−17341.5	−0.967276
$686$	19334.2	1.07607
$687$	−2186.52	−0.121428
$688$	23033.1	1.27635
$689$	0	0
$690$	1647.09	0.0908749
$691$	−10210.5	−0.562121	−0.281060	−	0.959690i	$-0.590686\pi$
$691$	−10210.5	−0.562121	−0.281060	+	0.959690i	$0.590686\pi$
$692$	−4122.25	−0.226451
$693$	−3113.60	−0.170672
$694$	−8424.47	−0.460790
$695$	23525.8	1.28401
$696$	1560.26	0.0849733
$697$	−13077.3	−0.710674
$698$	8563.23	0.464360
$699$	−312.653	−0.0169179
$700$	673.250	0.0363521
$701$	19676.4	1.06015	0.530076	−	0.847950i	$-0.322163\pi$
$701$	19676.4	1.06015	0.530076	+	0.847950i	$0.322163\pi$
$702$	0	0
$703$	33234.3	1.78301
$704$	3504.01	0.187589
$705$	2573.34	0.137472
$706$	1395.58	0.0743958
$707$	−18182.4	−0.967214
$708$	332.849	0.0176684
$709$	4472.68	0.236918	0.118459	−	0.992959i	$-0.462205\pi$
$709$	4472.68	0.236918	0.118459	+	0.992959i	$0.462205\pi$
$710$	8647.50	0.457091
$711$	7722.75	0.407350
$712$	26418.5	1.39055
$713$	−11663.8	−0.612639
$714$	−1276.08	−0.0668855
$715$	0	0
$716$	−7160.15	−0.373726
$717$	677.544	0.0352906
$718$	−14056.9	−0.730639
$719$	−12341.2	−0.640121	−0.320061	−	0.947397i	$-0.603703\pi$
$719$	−12341.2	−0.640121	−0.320061	+	0.947397i	$0.603703\pi$
$720$	25347.9	1.31203
$721$	−8023.53	−0.414441
$722$	−40858.9	−2.10611
$723$	190.575	0.00980299
$724$	−5297.11	−0.271914
$725$	−4210.00	−0.215663
$726$	230.685	0.0117927
$727$	−11805.3	−0.602248	−0.301124	−	0.953585i	$-0.597362\pi$
$727$	−11805.3	−0.602248	−0.301124	+	0.953585i	$0.597362\pi$
$728$	0	0
$729$	−18123.5	−0.920767
$730$	32351.6	1.64026
$731$	19012.1	0.961955
$732$	917.013	0.0463030
$733$	−14972.2	−0.754448	−0.377224	−	0.926122i	$-0.623121\pi$
$733$	−14972.2	−0.754448	−0.377224	+	0.926122i	$0.623121\pi$
$734$	32700.9	1.64443
$735$	1722.65	0.0864500
$736$	6372.49	0.319148
$737$	−1987.35	−0.0993285
$738$	17558.8	0.875811
$739$	19331.6	0.962281	0.481141	−	0.876643i	$-0.340223\pi$
$739$	19331.6	0.962281	0.481141	+	0.876643i	$0.340223\pi$
$740$	6139.03	0.304967
$741$	0	0
$742$	−10345.5	−0.511852
$743$	35774.8	1.76642	0.883211	−	0.468977i	$-0.155377\pi$
$743$	35774.8	1.76642	0.883211	+	0.468977i	$0.155377\pi$
$744$	1899.49	0.0936002
$745$	29064.3	1.42931
$746$	22793.4	1.11867
$747$	25868.4	1.26703
$748$	−1441.95	−0.0704854
$749$	2657.50	0.129644
$750$	−2247.47	−0.109421
$751$	14454.8	0.702347	0.351174	−	0.936310i	$-0.385783\pi$
$751$	14454.8	0.702347	0.351174	+	0.936310i	$0.385783\pi$
$752$	26232.6	1.27208
$753$	−2163.82	−0.104720
$754$	0	0
$755$	29210.2	1.40804
$756$	712.150	0.0342601
$757$	−25002.3	−1.20043	−0.600215	−	0.799839i	$-0.704918\pi$
$757$	−25002.3	−1.20043	−0.600215	+	0.799839i	$0.704918\pi$
$758$	13380.4	0.641158
$759$	−457.684	−0.0218879
$760$	32910.6	1.57078
$761$	36019.9	1.71579	0.857897	−	0.513822i	$-0.171771\pi$
$761$	36019.9	1.71579	0.857897	+	0.513822i	$0.171771\pi$
$762$	1054.87	0.0501494
$763$	−3090.75	−0.146648
$764$	−3538.54	−0.167565
$765$	20922.8	0.988843
$766$	−20657.8	−0.974407
$767$	0	0
$768$	−1800.66	−0.0846037
$769$	−11963.0	−0.560986	−0.280493	−	0.959856i	$-0.590498\pi$
$769$	−11963.0	−0.560986	−0.280493	+	0.959856i	$0.590498\pi$
$770$	−4626.82	−0.216544
$771$	2729.37	0.127492
$772$	7363.06	0.343267
$773$	−9003.56	−0.418933	−0.209467	−	0.977816i	$-0.567173\pi$
$773$	−9003.56	−0.418933	−0.209467	+	0.977816i	$0.567173\pi$
$774$	−25527.4	−1.18548
$775$	−5125.33	−0.237558
$776$	32331.5	1.49566
$777$	−1509.65	−0.0697019
$778$	34521.7	1.59083
$779$	29158.0	1.34107
$780$	0	0
$781$	−2402.92	−0.110094
$782$	13859.3	0.633768
$783$	−4453.25	−0.203252
$784$	17560.7	0.799957
$785$	28378.6	1.29029
$786$	2808.26	0.127439
$787$	2322.23	0.105182	0.0525912	−	0.998616i	$-0.483252\pi$
$787$	2322.23	0.105182	0.0525912	+	0.998616i	$0.483252\pi$
$788$	−5390.59	−0.243695
$789$	−749.358	−0.0338122
$790$	11476.0	0.516833
$791$	3843.19	0.172754
$792$	−5507.08	−0.247078
$793$	0	0
$794$	28640.5	1.28012
$795$	−2295.79	−0.102419
$796$	−9741.44	−0.433764
$797$	−9108.50	−0.404818	−0.202409	−	0.979301i	$-0.564877\pi$
$797$	−9108.50	−0.404818	−0.202409	+	0.979301i	$0.564877\pi$
$798$	2845.23	0.126216
$799$	21653.1	0.958737
$800$	2800.22	0.123753
$801$	−37448.0	−1.65189
$802$	1928.04	0.0848896
$803$	−8989.69	−0.395068
$804$	225.748	0.00990240
$805$	9179.71	0.401916
$806$	0	0
$807$	2525.96	0.110183
$808$	−32159.6	−1.40021
$809$	−20587.8	−0.894719	−0.447359	−	0.894354i	$-0.647636\pi$
$809$	−20587.8	−0.894719	−0.447359	+	0.894354i	$0.647636\pi$
$810$	−27707.4	−1.20190
$811$	−36898.8	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$811$	−36898.8	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$812$	−3057.12	−0.132123
$813$	4047.93	0.174621
$814$	−8264.00	−0.355839
$815$	12677.6	0.544879
$816$	−2886.73	−0.123843
$817$	−42390.5	−1.81525
$818$	46966.8	2.00752
$819$	0	0
$820$	5386.07	0.229378
$821$	26017.3	1.10598	0.552991	−	0.833187i	$-0.313486\pi$
$821$	26017.3	1.10598	0.552991	+	0.833187i	$0.313486\pi$
$822$	−2651.71	−0.112517
$823$	−42783.6	−1.81208	−0.906041	−	0.423190i	$-0.860910\pi$
$823$	−42783.6	−1.81208	−0.906041	+	0.423190i	$0.860910\pi$
$824$	−14191.4	−0.599975
$825$	−201.117	−0.00848727
$826$	8986.70	0.378556
$827$	8366.69	0.351800	0.175900	−	0.984408i	$-0.443716\pi$
$827$	8366.69	0.351800	0.175900	+	0.984408i	$0.443716\pi$
$828$	−3841.26	−0.161223
$829$	30518.2	1.27858	0.639289	−	0.768967i	$-0.279229\pi$
$829$	30518.2	1.27858	0.639289	+	0.768967i	$0.279229\pi$
$830$	38440.4	1.60758
$831$	−376.768	−0.0157279
$832$	0	0
$833$	14495.0	0.602908
$834$	3597.36	0.149360
$835$	−25821.4	−1.07017
$836$	3215.07	0.133009
$837$	−5421.47	−0.223887
$838$	27548.9	1.13563
$839$	−40913.5	−1.68354	−0.841771	−	0.539835i	$-0.818487\pi$
$839$	−40913.5	−1.68354	−0.841771	+	0.539835i	$0.818487\pi$
$840$	−1494.95	−0.0614055
$841$	−5272.06	−0.216165
$842$	−29165.4	−1.19371
$843$	−5312.87	−0.217064
$844$	10297.7	0.419978
$845$	0	0
$846$	−29073.3	−1.18152
$847$	1285.67	0.0521561
$848$	−23403.3	−0.947727
$849$	4986.72	0.201583
$850$	6090.09	0.245751
$851$	16396.0	0.660454
$852$	272.953	0.0109756
$853$	−42770.2	−1.71679	−0.858396	−	0.512988i	$-0.828539\pi$
$853$	−42770.2	−1.71679	−0.858396	+	0.512988i	$0.828539\pi$
$854$	24758.8	0.992069
$855$	−46650.7	−1.86599
$856$	4700.37	0.187682
$857$	36034.8	1.43632	0.718160	−	0.695878i	$-0.244984\pi$
$857$	36034.8	1.43632	0.718160	+	0.695878i	$0.244984\pi$
$858$	0	0
$859$	35219.1	1.39890	0.699452	−	0.714679i	$-0.253427\pi$
$859$	35219.1	1.39890	0.699452	+	0.714679i	$0.253427\pi$
$860$	−7830.38	−0.310481
$861$	−1324.49	−0.0524256
$862$	−40260.2	−1.59080
$863$	9065.72	0.357591	0.178795	−	0.983886i	$-0.442780\pi$
$863$	9065.72	0.357591	0.178795	+	0.983886i	$0.442780\pi$
$864$	2962.01	0.116632
$865$	−24698.4	−0.970835
$866$	2264.90	0.0888735
$867$	567.275	0.0222211
$868$	−3721.80	−0.145537
$869$	−3188.89	−0.124483
$870$	−3286.53	−0.128073
$871$	0	0
$872$	−5466.66	−0.212299
$873$	−45829.8	−1.77675
$874$	−30901.4	−1.19595
$875$	−12525.8	−0.483942
$876$	1021.16	0.0393856
$877$	43800.2	1.68646	0.843232	−	0.537549i	$-0.180650\pi$
$877$	43800.2	1.68646	0.843232	+	0.537549i	$0.180650\pi$
$878$	47016.5	1.80721
$879$	870.000	0.0333838
$880$	−10466.7	−0.400945
$881$	−28864.1	−1.10381	−0.551905	−	0.833907i	$-0.686099\pi$
$881$	−28864.1	−1.10381	−0.551905	+	0.833907i	$0.686099\pi$
$882$	−19462.3	−0.743004
$883$	35808.9	1.36474	0.682369	−	0.731008i	$-0.260950\pi$
$883$	35808.9	1.36474	0.682369	+	0.731008i	$0.260950\pi$
$884$	0	0
$885$	1994.26	0.0757473
$886$	−7535.44	−0.285731
$887$	−10226.5	−0.387117	−0.193558	−	0.981089i	$-0.562003\pi$
$887$	−10226.5	−0.387117	−0.193558	+	0.981089i	$0.562003\pi$
$888$	−2670.14	−0.100905
$889$	5879.08	0.221798
$890$	−55647.8	−2.09586
$891$	7699.18	0.289486
$892$	293.547	0.0110187
$893$	−48279.0	−1.80918
$894$	4444.26	0.166262
$895$	−42900.0	−1.60222
$896$	−18563.8	−0.692157
$897$	0	0
$898$	−21886.0	−0.813303
$899$	23273.3	0.863413
$900$	−1687.94	−0.0625163
$901$	−19317.7	−0.714279
$902$	−7250.41	−0.267641
$903$	1925.57	0.0709622
$904$	6797.51	0.250091
$905$	−31737.6	−1.16574
$906$	4466.57	0.163788
$907$	24472.6	0.895921	0.447961	−	0.894053i	$-0.352150\pi$
$907$	24472.6	0.895921	0.447961	+	0.894053i	$0.352150\pi$
$908$	−3891.71	−0.142237
$909$	45586.0	1.66336
$910$	0	0
$911$	16334.0	0.594038	0.297019	−	0.954872i	$-0.404007\pi$
$911$	16334.0	0.594038	0.297019	+	0.954872i	$0.404007\pi$
$912$	6436.42	0.233697
$913$	−10681.6	−0.387196
$914$	1570.16	0.0568230
$915$	5494.28	0.198508
$916$	7577.56	0.273329
$917$	15651.3	0.563631
$918$	6441.97	0.231608
$919$	−16363.0	−0.587338	−0.293669	−	0.955907i	$-0.594876\pi$
$919$	−16363.0	−0.587338	−0.293669	+	0.955907i	$0.594876\pi$
$920$	16236.3	0.581842
$921$	1882.73	0.0673594
$922$	−28026.3	−1.00108
$923$	0	0
$924$	−146.043	−0.00519962
$925$	7204.77	0.256099
$926$	53302.6	1.89161
$927$	20116.2	0.712732
$928$	−12715.3	−0.449786
$929$	30435.9	1.07489	0.537444	−	0.843300i	$-0.319390\pi$
$929$	30435.9	1.07489	0.537444	+	0.843300i	$0.319390\pi$
$930$	−4001.08	−0.141076
$931$	−32318.9	−1.13771
$932$	1083.52	0.0380814
$933$	3831.85	0.134458
$934$	22590.3	0.791410
$935$	−8639.47	−0.302183
$936$	0	0
$937$	−6898.43	−0.240514	−0.120257	−	0.992743i	$-0.538372\pi$
$937$	−6898.43	−0.240514	−0.120257	+	0.992743i	$0.538372\pi$
$938$	6095.06	0.212165
$939$	537.511	0.0186805
$940$	−8918.09	−0.309443
$941$	−2825.01	−0.0978668	−0.0489334	−	0.998802i	$-0.515582\pi$
$941$	−2825.01	−0.0978668	−0.0489334	+	0.998802i	$0.515582\pi$
$942$	4339.41	0.150091
$943$	14385.0	0.496754
$944$	20329.5	0.700921
$945$	4266.84	0.146879
$946$	10540.8	0.362274
$947$	37405.2	1.28353	0.641766	−	0.766900i	$-0.278202\pi$
$947$	37405.2	1.28353	0.641766	+	0.766900i	$0.278202\pi$
$948$	362.234	0.0124101
$949$	0	0
$950$	−13578.8	−0.463742
$951$	−847.288	−0.0288908
$952$	−12579.1	−0.428246
$953$	43831.7	1.48987	0.744936	−	0.667136i	$-0.232480\pi$
$953$	43831.7	1.48987	0.744936	+	0.667136i	$0.232480\pi$
$954$	25937.6	0.880253
$955$	−21201.1	−0.718379
$956$	−2348.08	−0.0794376
$957$	913.241	0.0308473
$958$	57435.6	1.93702
$959$	−14778.7	−0.497634
$960$	−2384.79	−0.0801758
$961$	−1457.64	−0.0489288
$962$	0	0
$963$	−6662.76	−0.222954
$964$	−660.452	−0.0220661
$965$	44115.7	1.47164
$966$	1403.68	0.0467523
$967$	−28908.3	−0.961352	−0.480676	−	0.876898i	$-0.659609\pi$
$967$	−28908.3	−0.961352	−0.480676	+	0.876898i	$0.659609\pi$
$968$	2273.99	0.0755050
$969$	5312.79	0.176131
$970$	−68103.1	−2.25429
$971$	−4021.04	−0.132895	−0.0664477	−	0.997790i	$-0.521167\pi$
$971$	−4021.04	−0.132895	−0.0664477	+	0.997790i	$0.521167\pi$
$972$	−2684.20	−0.0885759
$973$	20049.1	0.660581
$974$	28033.0	0.922214
$975$	0	0
$976$	56008.7	1.83688
$977$	32966.5	1.07952	0.539760	−	0.841819i	$-0.318515\pi$
$977$	32966.5	1.07952	0.539760	+	0.841819i	$0.318515\pi$
$978$	1938.55	0.0633824
$979$	15463.1	0.504804
$980$	−5969.96	−0.194595
$981$	7748.97	0.252197
$982$	−48452.9	−1.57454
$983$	20732.5	0.672699	0.336350	−	0.941737i	$-0.390808\pi$
$983$	20732.5	0.672699	0.336350	+	0.941737i	$0.390808\pi$
$984$	−2342.64	−0.0758951
$985$	−32297.7	−1.04476
$986$	−27654.1	−0.893191
$987$	2193.05	0.0707249
$988$	0	0
$989$	−20913.2	−0.672397
$990$	11600.1	0.372400
$991$	34338.8	1.10071	0.550357	−	0.834930i	$-0.314492\pi$
$991$	34338.8	1.10071	0.550357	+	0.834930i	$0.314492\pi$
$992$	−15479.9	−0.495451
$993$	215.139	0.00687536
$994$	7369.56	0.235159
$995$	−58365.8	−1.85962
$996$	1213.35	0.0386009
$997$	−1792.04	−0.0569253	−0.0284626	−	0.999595i	$-0.509061\pi$
$997$	−1792.04	−0.0569253	−0.0284626	+	0.999595i	$0.509061\pi$
$998$	−21267.2	−0.674552
$999$	7621.05	0.241361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.4		17
13.3	even	3		143.4.e.b.100.14	✓	34
13.9	even	3		143.4.e.b.133.14	yes	34
13.12	even	2		1859.4.a.h.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.14	✓	34	13.3	even	3
143.4.e.b.133.14	yes	34	13.9	even	3
1859.4.a.g.1.4		17	1.1	even	1	trivial
1859.4.a.h.1.14		17	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)

\(f(q)\)	\(=\)	\(q-3.17505 q^{2} -0.600459 q^{3} +2.08094 q^{4} +12.4679 q^{5} +1.90649 q^{6} +10.6254 q^{7} +18.7933 q^{8} -26.6394 q^{9} +O(q^{10})\)	\(q-3.17505 q^{2} -0.600459 q^{3} +2.08094 q^{4} +12.4679 q^{5} +1.90649 q^{6} +10.6254 q^{7} +18.7933 q^{8} -26.6394 q^{9} -39.5863 q^{10} +11.0000 q^{11} -1.24952 q^{12} -33.7362 q^{14} -7.48648 q^{15} -76.3172 q^{16} -62.9942 q^{17} +84.5816 q^{18} +140.455 q^{19} +25.9449 q^{20} -6.38012 q^{21} -34.9255 q^{22} +69.2931 q^{23} -11.2846 q^{24} +30.4490 q^{25} +32.2083 q^{27} +22.1108 q^{28} -138.264 q^{29} +23.7699 q^{30} -168.325 q^{31} +91.9643 q^{32} -6.60505 q^{33} +200.010 q^{34} +132.477 q^{35} -55.4350 q^{36} +236.618 q^{37} -445.953 q^{38} +234.314 q^{40} +207.596 q^{41} +20.2572 q^{42} -301.808 q^{43} +22.8903 q^{44} -332.138 q^{45} -220.009 q^{46} -343.732 q^{47} +45.8254 q^{48} -230.101 q^{49} -96.6770 q^{50} +37.8254 q^{51} +306.658 q^{53} -102.263 q^{54} +137.147 q^{55} +199.686 q^{56} -84.3378 q^{57} +438.995 q^{58} -266.382 q^{59} -15.5789 q^{60} -733.894 q^{61} +534.441 q^{62} -283.055 q^{63} +318.546 q^{64} +20.9714 q^{66} -180.668 q^{67} -131.087 q^{68} -41.6076 q^{69} -420.620 q^{70} -218.447 q^{71} -500.644 q^{72} -817.244 q^{73} -751.273 q^{74} -18.2834 q^{75} +292.279 q^{76} +116.879 q^{77} -289.899 q^{79} -951.517 q^{80} +699.925 q^{81} -659.128 q^{82} -971.055 q^{83} -13.2766 q^{84} -785.406 q^{85} +958.254 q^{86} +83.0219 q^{87} +206.727 q^{88} +1405.74 q^{89} +1054.56 q^{90} +144.194 q^{92} +101.072 q^{93} +1091.36 q^{94} +1751.19 q^{95} -55.2208 q^{96} +1720.37 q^{97} +730.582 q^{98} -293.034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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