LMFDB - Embedded newform 1859.4.a.o.1.35

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			1.35
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)

$f(q)$	$=$	$q+4.48614 q^{2} -3.10130 q^{3} +12.1255 q^{4} +9.82658 q^{5} -13.9129 q^{6} +8.62268 q^{7} +18.5074 q^{8} -17.3819 q^{9} +O(q^{10})$	\(q+4.48614 q^{2} -3.10130 q^{3} +12.1255 q^{4} +9.82658 q^{5} -13.9129 q^{6} +8.62268 q^{7} +18.5074 q^{8} -17.3819 q^{9} +44.0834 q^{10} -11.0000 q^{11} -37.6047 q^{12} +38.6826 q^{14} -30.4752 q^{15} -13.9768 q^{16} -17.7873 q^{17} -77.9778 q^{18} -11.7877 q^{19} +119.152 q^{20} -26.7415 q^{21} -49.3476 q^{22} -22.8008 q^{23} -57.3971 q^{24} -28.4384 q^{25} +137.642 q^{27} +104.554 q^{28} -239.754 q^{29} -136.716 q^{30} -120.891 q^{31} -210.761 q^{32} +34.1143 q^{33} -79.7965 q^{34} +84.7314 q^{35} -210.764 q^{36} +52.2922 q^{37} -52.8812 q^{38} +181.865 q^{40} -146.753 q^{41} -119.966 q^{42} -84.3225 q^{43} -133.380 q^{44} -170.805 q^{45} -102.288 q^{46} +102.330 q^{47} +43.3463 q^{48} -268.649 q^{49} -127.579 q^{50} +55.1639 q^{51} +267.134 q^{53} +617.480 q^{54} -108.092 q^{55} +159.584 q^{56} +36.5571 q^{57} -1075.57 q^{58} +36.8180 q^{59} -369.526 q^{60} +557.242 q^{61} -542.334 q^{62} -149.879 q^{63} -833.691 q^{64} +153.042 q^{66} +324.683 q^{67} -215.680 q^{68} +70.7123 q^{69} +380.117 q^{70} -1040.72 q^{71} -321.695 q^{72} -243.683 q^{73} +234.590 q^{74} +88.1959 q^{75} -142.931 q^{76} -94.8495 q^{77} -667.959 q^{79} -137.344 q^{80} +42.4440 q^{81} -658.355 q^{82} +41.4217 q^{83} -324.253 q^{84} -174.789 q^{85} -378.283 q^{86} +743.549 q^{87} -203.582 q^{88} -2.12074 q^{89} -766.255 q^{90} -276.471 q^{92} +374.919 q^{93} +459.066 q^{94} -115.833 q^{95} +653.634 q^{96} -188.443 q^{97} -1205.20 q^{98} +191.201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.48614	1.58609	0.793045	−	0.609163i	$-0.208494\pi$
$2$	4.48614	1.58609	0.793045	+	0.609163i	$0.208494\pi$
$3$	−3.10130	−0.596846	−0.298423	−	0.954434i	$-0.596461\pi$
$3$	−3.10130	−0.596846	−0.298423	+	0.954434i	$0.596461\pi$
$4$	12.1255	1.51568
$5$	9.82658	0.878916	0.439458	−	0.898263i	$-0.355171\pi$
$5$	9.82658	0.878916	0.439458	+	0.898263i	$0.355171\pi$
$6$	−13.9129	−0.946651
$7$	8.62268	0.465581	0.232790	−	0.972527i	$-0.425214\pi$
$7$	8.62268	0.465581	0.232790	+	0.972527i	$0.425214\pi$
$8$	18.5074	0.817920
$9$	−17.3819	−0.643775
$10$	44.0834	1.39404
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−37.6047	−0.904629
$13$	0	0
$13$	0	0
$14$	38.6826	0.738453
$15$	−30.4752	−0.524577
$16$	−13.9768	−0.218388
$17$	−17.7873	−0.253768	−0.126884	−	0.991918i	$-0.540498\pi$
$17$	−17.7873	−0.253768	−0.126884	+	0.991918i	$0.540498\pi$
$18$	−77.9778	−1.02109
$19$	−11.7877	−0.142330	−0.0711652	−	0.997465i	$-0.522672\pi$
$19$	−11.7877	−0.142330	−0.0711652	+	0.997465i	$0.522672\pi$
$20$	119.152	1.33216
$21$	−26.7415	−0.277880
$22$	−49.3476	−0.478224
$23$	−22.8008	−0.206709	−0.103354	−	0.994645i	$-0.532958\pi$
$23$	−22.8008	−0.206709	−0.103354	+	0.994645i	$0.532958\pi$
$24$	−57.3971	−0.488172
$25$	−28.4384	−0.227507
$26$	0	0
$27$	137.642	0.981080
$28$	104.554	0.705673
$29$	−239.754	−1.53521	−0.767607	−	0.640921i	$-0.778553\pi$
$29$	−239.754	−1.53521	−0.767607	+	0.640921i	$0.778553\pi$
$30$	−136.716	−0.832027
$31$	−120.891	−0.700409	−0.350204	−	0.936673i	$-0.613888\pi$
$31$	−120.891	−0.700409	−0.350204	+	0.936673i	$0.613888\pi$
$32$	−210.761	−1.16430
$33$	34.1143	0.179956
$34$	−79.7965	−0.402500
$35$	84.7314	0.409206
$36$	−210.764	−0.975760
$37$	52.2922	0.232345	0.116173	−	0.993229i	$-0.462937\pi$
$37$	52.2922	0.232345	0.116173	+	0.993229i	$0.462937\pi$
$38$	−52.8812	−0.225749
$39$	0	0
$40$	181.865	0.718883
$41$	−146.753	−0.558999	−0.279500	−	0.960146i	$-0.590169\pi$
$41$	−146.753	−0.558999	−0.279500	+	0.960146i	$0.590169\pi$
$42$	−119.966	−0.440743
$43$	−84.3225	−0.299048	−0.149524	−	0.988758i	$-0.547774\pi$
$43$	−84.3225	−0.299048	−0.149524	+	0.988758i	$0.547774\pi$
$44$	−133.380	−0.456996
$45$	−170.805	−0.565824
$46$	−102.288	−0.327859
$47$	102.330	0.317581	0.158791	−	0.987312i	$-0.449240\pi$
$47$	102.330	0.317581	0.158791	+	0.987312i	$0.449240\pi$
$48$	43.3463	0.130344
$49$	−268.649	−0.783234
$50$	−127.579	−0.360847
$51$	55.1639	0.151461
$52$	0	0
$53$	267.134	0.692332	0.346166	−	0.938173i	$-0.387483\pi$
$53$	267.134	0.692332	0.346166	+	0.938173i	$0.387483\pi$
$54$	617.480	1.55608
$55$	−108.092	−0.265003
$56$	159.584	0.380808
$57$	36.5571	0.0849493
$58$	−1075.57	−2.43499
$59$	36.8180	0.0812422	0.0406211	−	0.999175i	$-0.487066\pi$
$59$	36.8180	0.0812422	0.0406211	+	0.999175i	$0.487066\pi$
$60$	−369.526	−0.795093
$61$	557.242	1.16963	0.584816	−	0.811166i	$-0.301167\pi$
$61$	557.242	1.16963	0.584816	+	0.811166i	$0.301167\pi$
$62$	−542.334	−1.11091
$63$	−149.879	−0.299730
$64$	−833.691	−1.62830
$65$	0	0
$66$	153.042	0.285426
$67$	324.683	0.592035	0.296017	−	0.955183i	$-0.404341\pi$
$67$	324.683	0.592035	0.296017	+	0.955183i	$0.404341\pi$
$68$	−215.680	−0.384632
$69$	70.7123	0.123373
$70$	380.117	0.649038
$71$	−1040.72	−1.73960	−0.869798	−	0.493408i	$-0.835751\pi$
$71$	−1040.72	−1.73960	−0.869798	+	0.493408i	$0.835751\pi$
$72$	−321.695	−0.526557
$73$	−243.683	−0.390698	−0.195349	−	0.980734i	$-0.562584\pi$
$73$	−243.683	−0.390698	−0.195349	+	0.980734i	$0.562584\pi$
$74$	234.590	0.368521
$75$	88.1959	0.135786
$76$	−142.931	−0.215728
$77$	−94.8495	−0.140378
$78$	0	0
$79$	−667.959	−0.951282	−0.475641	−	0.879639i	$-0.657784\pi$
$79$	−667.959	−0.951282	−0.475641	+	0.879639i	$0.657784\pi$
$80$	−137.344	−0.191944
$81$	42.4440	0.0582222
$82$	−658.355	−0.886624
$83$	41.4217	0.0547786	0.0273893	−	0.999625i	$-0.491281\pi$
$83$	41.4217	0.0547786	0.0273893	+	0.999625i	$0.491281\pi$
$84$	−324.253	−0.421178
$85$	−174.789	−0.223041
$86$	−378.283	−0.474317
$87$	743.549	0.916285
$88$	−203.582	−0.246612
$89$	−2.12074	−0.00252583	−0.00126291	−	0.999999i	$-0.500402\pi$
$89$	−2.12074	−0.00252583	−0.00126291	+	0.999999i	$0.500402\pi$
$90$	−766.255	−0.897449
$91$	0	0
$92$	−276.471	−0.313305
$93$	374.919	0.418036
$94$	459.066	0.503713
$95$	−115.833	−0.125096
$96$	653.634	0.694909
$97$	−188.443	−0.197253	−0.0986263	−	0.995125i	$-0.531445\pi$
$97$	−188.443	−0.197253	−0.0986263	+	0.995125i	$0.531445\pi$
$98$	−1205.20	−1.24228
$99$	191.201	0.194106
$100$	−344.828	−0.344828
$101$	541.932	0.533903	0.266952	−	0.963710i	$-0.413984\pi$
$101$	541.932	0.533903	0.266952	+	0.963710i	$0.413984\pi$
$102$	247.473	0.240230
$103$	−316.122	−0.302412	−0.151206	−	0.988502i	$-0.548316\pi$
$103$	−316.122	−0.302412	−0.151206	+	0.988502i	$0.548316\pi$
$104$	0	0
$105$	−262.778	−0.244233
$106$	1198.40	1.09810
$107$	−1591.19	−1.43763	−0.718815	−	0.695201i	$-0.755315\pi$
$107$	−1591.19	−1.43763	−0.718815	+	0.695201i	$0.755315\pi$
$108$	1668.97	1.48701
$109$	−686.532	−0.603283	−0.301642	−	0.953421i	$-0.597535\pi$
$109$	−686.532	−0.603283	−0.301642	+	0.953421i	$0.597535\pi$
$110$	−484.918	−0.420319
$111$	−162.174	−0.138674
$112$	−120.517	−0.101677
$113$	1811.61	1.50816	0.754079	−	0.656783i	$-0.228083\pi$
$113$	1811.61	1.50816	0.754079	+	0.656783i	$0.228083\pi$
$114$	164.000	0.134737
$115$	−224.054	−0.181680
$116$	−2907.13	−2.32690
$117$	0	0
$118$	165.171	0.128857
$119$	−153.374	−0.118150
$120$	−564.017	−0.429062
$121$	121.000	0.0909091
$122$	2499.87	1.85514
$123$	455.125	0.333636
$124$	−1465.86	−1.06160
$125$	−1507.77	−1.07888
$126$	−672.378	−0.475398
$127$	−1389.49	−0.970847	−0.485424	−	0.874279i	$-0.661335\pi$
$127$	−1389.49	−0.970847	−0.485424	+	0.874279i	$0.661335\pi$
$128$	−2053.96	−1.41833
$129$	261.510	0.178486
$130$	0	0
$131$	1900.69	1.26766	0.633832	−	0.773471i	$-0.281481\pi$
$131$	1900.69	1.26766	0.633832	+	0.773471i	$0.281481\pi$
$132$	413.652	0.272756
$133$	−101.641	−0.0662663
$134$	1456.57	0.939021
$135$	1352.55	0.862287
$136$	−329.198	−0.207562
$137$	−1077.33	−0.671846	−0.335923	−	0.941889i	$-0.609048\pi$
$137$	−1077.33	−0.671846	−0.335923	+	0.941889i	$0.609048\pi$
$138$	317.225	0.195681
$139$	845.480	0.515919	0.257959	−	0.966156i	$-0.416950\pi$
$139$	845.480	0.515919	0.257959	+	0.966156i	$0.416950\pi$
$140$	1027.41	0.620227
$141$	−317.355	−0.189547
$142$	−4668.84	−2.75916
$143$	0	0
$144$	242.944	0.140593
$145$	−2355.96	−1.34932
$146$	−1093.20	−0.619682
$147$	833.163	0.467470
$148$	634.067	0.352162
$149$	1157.84	0.636603	0.318302	−	0.947989i	$-0.396888\pi$
$149$	1157.84	0.636603	0.318302	+	0.947989i	$0.396888\pi$
$150$	395.659	0.215370
$151$	−1016.13	−0.547624	−0.273812	−	0.961783i	$-0.588285\pi$
$151$	−1016.13	−0.547624	−0.273812	+	0.961783i	$0.588285\pi$
$152$	−218.160	−0.116415
$153$	309.178	0.163370
$154$	−425.508	−0.222652
$155$	−1187.95	−0.615600
$156$	0	0
$157$	3691.34	1.87644	0.938221	−	0.346037i	$-0.112473\pi$
$157$	3691.34	1.87644	0.938221	+	0.346037i	$0.112473\pi$
$158$	−2996.56	−1.50882
$159$	−828.461	−0.413215
$160$	−2071.06	−1.02332
$161$	−196.604	−0.0962397
$162$	190.410	0.0923457
$163$	−615.854	−0.295935	−0.147968	−	0.988992i	$-0.547273\pi$
$163$	−615.854	−0.295935	−0.147968	+	0.988992i	$0.547273\pi$
$164$	−1779.45	−0.847266
$165$	335.227	0.158166
$166$	185.824	0.0868839
$167$	−3629.77	−1.68191	−0.840957	−	0.541101i	$-0.818008\pi$
$167$	−3629.77	−1.68191	−0.840957	+	0.541101i	$0.818008\pi$
$168$	−494.917	−0.227284
$169$	0	0
$170$	−784.126	−0.353763
$171$	204.893	0.0916288
$172$	−1022.45	−0.453262
$173$	1090.73	0.479347	0.239674	−	0.970854i	$-0.422960\pi$
$173$	1090.73	0.479347	0.239674	+	0.970854i	$0.422960\pi$
$174$	3335.67	1.45331
$175$	−245.215	−0.105923
$176$	153.745	0.0658463
$177$	−114.184	−0.0484890
$178$	−9.51396	−0.00400619
$179$	1001.23	0.418076	0.209038	−	0.977908i	$-0.432967\pi$
$179$	1001.23	0.418076	0.209038	+	0.977908i	$0.432967\pi$
$180$	−2071.09	−0.857611
$181$	75.9214	0.0311779	0.0155889	−	0.999878i	$-0.495038\pi$
$181$	75.9214	0.0311779	0.0155889	+	0.999878i	$0.495038\pi$
$182$	0	0
$183$	−1728.17	−0.698089
$184$	−421.985	−0.169071
$185$	513.853	0.204212
$186$	1681.94	0.663043
$187$	195.661	0.0765140
$188$	1240.80	0.481353
$189$	1186.84	0.456772
$190$	−519.641	−0.198414
$191$	−3203.58	−1.21363	−0.606814	−	0.794844i	$-0.707553\pi$
$191$	−3203.58	−1.21363	−0.606814	+	0.794844i	$0.707553\pi$
$192$	2585.53	0.971845
$193$	−683.922	−0.255076	−0.127538	−	0.991834i	$-0.540708\pi$
$193$	−683.922	−0.255076	−0.127538	+	0.991834i	$0.540708\pi$
$194$	−845.383	−0.312861
$195$	0	0
$196$	−3257.50	−1.18714
$197$	−3474.48	−1.25658	−0.628290	−	0.777979i	$-0.716245\pi$
$197$	−3474.48	−1.25658	−0.628290	+	0.777979i	$0.716245\pi$
$198$	857.756	0.307869
$199$	2622.61	0.934230	0.467115	−	0.884197i	$-0.345293\pi$
$199$	2622.61	0.934230	0.467115	+	0.884197i	$0.345293\pi$
$200$	−526.321	−0.186083
$201$	−1006.94	−0.353353
$202$	2431.18	0.846819
$203$	−2067.32	−0.714766
$204$	668.888	0.229566
$205$	−1442.08	−0.491313
$206$	−1418.17	−0.479653
$207$	396.323	0.133074
$208$	0	0
$209$	129.664	0.0429142
$210$	−1178.86	−0.387376
$211$	−1972.59	−0.643597	−0.321798	−	0.946808i	$-0.604287\pi$
$211$	−1972.59	−0.643597	−0.321798	+	0.946808i	$0.604287\pi$
$212$	3239.12	1.04936
$213$	3227.60	1.03827
$214$	−7138.32	−2.28021
$215$	−828.602	−0.262838
$216$	2547.39	0.802445
$217$	−1042.40	−0.326097
$218$	−3079.88	−0.956862
$219$	755.734	0.233186
$220$	−1310.67	−0.401661
$221$	0	0
$222$	−727.534	−0.219950
$223$	−4873.07	−1.46334	−0.731670	−	0.681659i	$-0.761259\pi$
$223$	−4873.07	−1.46334	−0.731670	+	0.681659i	$0.761259\pi$
$224$	−1817.33	−0.542077
$225$	494.314	0.146463
$226$	8127.14	2.39208
$227$	4120.63	1.20483	0.602413	−	0.798184i	$-0.294206\pi$
$227$	4120.63	1.20483	0.602413	+	0.798184i	$0.294206\pi$
$228$	443.272	0.128756
$229$	3453.40	0.996538	0.498269	−	0.867022i	$-0.333969\pi$
$229$	3453.40	0.996538	0.498269	+	0.867022i	$0.333969\pi$
$230$	−1005.14	−0.288160
$231$	294.157	0.0837839
$232$	−4437.23	−1.25568
$233$	2922.61	0.821745	0.410873	−	0.911693i	$-0.365224\pi$
$233$	2922.61	0.821745	0.410873	+	0.911693i	$0.365224\pi$
$234$	0	0
$235$	1005.55	0.279127
$236$	446.435	0.123137
$237$	2071.54	0.567768
$238$	−688.060	−0.187396
$239$	706.036	0.191086	0.0955432	−	0.995425i	$-0.469541\pi$
$239$	706.036	0.191086	0.0955432	+	0.995425i	$0.469541\pi$
$240$	425.945	0.114561
$241$	−2933.05	−0.783959	−0.391980	−	0.919974i	$-0.628210\pi$
$241$	−2933.05	−0.783959	−0.391980	+	0.919974i	$0.628210\pi$
$242$	542.823	0.144190
$243$	−3847.96	−1.01583
$244$	6756.82	1.77279
$245$	−2639.90	−0.688397
$246$	2041.76	0.529177
$247$	0	0
$248$	−2237.38	−0.572879
$249$	−128.461	−0.0326944
$250$	−6764.09	−1.71119
$251$	5942.05	1.49426	0.747129	−	0.664679i	$-0.231432\pi$
$251$	5942.05	1.49426	0.747129	+	0.664679i	$0.231432\pi$
$252$	−1817.35	−0.454295
$253$	250.809	0.0623251
$254$	−6233.46	−1.53985
$255$	542.072	0.133121
$256$	−2544.85	−0.621301
$257$	−2798.50	−0.679244	−0.339622	−	0.940562i	$-0.610299\pi$
$257$	−2798.50	−0.679244	−0.339622	+	0.940562i	$0.610299\pi$
$258$	1173.17	0.283094
$259$	450.898	0.108176
$260$	0	0
$261$	4167.39	0.988333
$262$	8526.76	2.01063
$263$	−4124.16	−0.966945	−0.483473	−	0.875359i	$-0.660625\pi$
$263$	−4124.16	−0.966945	−0.483473	+	0.875359i	$0.660625\pi$
$264$	631.368	0.147189
$265$	2625.01	0.608502
$266$	−455.977	−0.105104
$267$	6.57706	0.00150753
$268$	3936.93	0.897337
$269$	−3331.24	−0.755053	−0.377527	−	0.925999i	$-0.623225\pi$
$269$	−3331.24	−0.755053	−0.377527	+	0.925999i	$0.623225\pi$
$270$	6067.72	1.36766
$271$	3643.13	0.816621	0.408310	−	0.912843i	$-0.366118\pi$
$271$	3643.13	0.816621	0.408310	+	0.912843i	$0.366118\pi$
$272$	248.610	0.0554199
$273$	0	0
$274$	−4833.08	−1.06561
$275$	312.822	0.0685959
$276$	857.419	0.186995
$277$	−2351.56	−0.510077	−0.255039	−	0.966931i	$-0.582088\pi$
$277$	−2351.56	−0.510077	−0.255039	+	0.966931i	$0.582088\pi$
$278$	3792.94	0.818294
$279$	2101.32	0.450906
$280$	1568.16	0.334698
$281$	1829.32	0.388356	0.194178	−	0.980966i	$-0.437796\pi$
$281$	1829.32	0.388356	0.194178	+	0.980966i	$0.437796\pi$
$282$	−1423.70	−0.300639
$283$	−6251.02	−1.31302	−0.656510	−	0.754317i	$-0.727968\pi$
$283$	−6251.02	−1.31302	−0.656510	+	0.754317i	$0.727968\pi$
$284$	−12619.3	−2.63668
$285$	359.231	0.0746633
$286$	0	0
$287$	−1265.40	−0.260259
$288$	3663.44	0.749549
$289$	−4596.61	−0.935602
$290$	−10569.2	−2.14015
$291$	584.419	0.117729
$292$	−2954.77	−0.592174
$293$	−7472.16	−1.48986	−0.744929	−	0.667144i	$-0.767517\pi$
$293$	−7472.16	−1.48986	−0.744929	+	0.667144i	$0.767517\pi$
$294$	3737.69	0.741450
$295$	361.795	0.0714051
$296$	967.793	0.190040
$297$	−1514.06	−0.295807
$298$	5194.23	1.00971
$299$	0	0
$300$	1069.42	0.205809
$301$	−727.086	−0.139231
$302$	−4558.49	−0.868581
$303$	−1680.69	−0.318658
$304$	164.754	0.0310832
$305$	5475.78	1.02801
$306$	1387.02	0.259119
$307$	3289.40	0.611518	0.305759	−	0.952109i	$-0.401090\pi$
$307$	3289.40	0.611518	0.305759	+	0.952109i	$0.401090\pi$
$308$	−1150.09	−0.212768
$309$	980.389	0.180493
$310$	−5329.29	−0.976398
$311$	2232.80	0.407108	0.203554	−	0.979064i	$-0.434751\pi$
$311$	2232.80	0.407108	0.203554	+	0.979064i	$0.434751\pi$
$312$	0	0
$313$	−764.799	−0.138112	−0.0690559	−	0.997613i	$-0.521999\pi$
$313$	−764.799	−0.138112	−0.0690559	+	0.997613i	$0.521999\pi$
$314$	16559.9	2.97621
$315$	−1472.80	−0.263437
$316$	−8099.32	−1.44184
$317$	−8583.96	−1.52089	−0.760447	−	0.649400i	$-0.775020\pi$
$317$	−8583.96	−1.52089	−0.760447	+	0.649400i	$0.775020\pi$
$318$	−3716.59	−0.655397
$319$	2637.29	0.462884
$320$	−8192.33	−1.43114
$321$	4934.77	0.858043
$322$	−881.995	−0.152645
$323$	209.671	0.0361190
$324$	514.653	0.0882464
$325$	0	0
$326$	−2762.81	−0.469380
$327$	2129.14	0.360067
$328$	−2716.02	−0.457217
$329$	882.356	0.147860
$330$	1503.88	0.250865
$331$	5204.60	0.864262	0.432131	−	0.901811i	$-0.357762\pi$
$331$	5204.60	0.864262	0.432131	+	0.901811i	$0.357762\pi$
$332$	502.258	0.0830270
$333$	−908.939	−0.149578
$334$	−16283.6	−2.66767
$335$	3190.52	0.520349
$336$	373.761	0.0606855
$337$	−2679.22	−0.433076	−0.216538	−	0.976274i	$-0.569477\pi$
$337$	−2679.22	−0.433076	−0.216538	+	0.976274i	$0.569477\pi$
$338$	0	0
$339$	−5618.35	−0.900138
$340$	−2119.39	−0.338060
$341$	1329.80	0.211181
$342$	919.177	0.145332
$343$	−5274.06	−0.830240
$344$	−1560.59	−0.244597
$345$	694.860	0.108435
$346$	4893.19	0.760288
$347$	10469.4	1.61967	0.809837	−	0.586655i	$-0.199556\pi$
$347$	10469.4	1.61967	0.809837	+	0.586655i	$0.199556\pi$
$348$	9015.88	1.38880
$349$	5313.07	0.814906	0.407453	−	0.913226i	$-0.366417\pi$
$349$	5313.07	0.814906	0.407453	+	0.913226i	$0.366417\pi$
$350$	−1100.07	−0.168003
$351$	0	0
$352$	2318.37	0.351050
$353$	8028.68	1.21055	0.605274	−	0.796017i	$-0.293064\pi$
$353$	8028.68	1.21055	0.605274	+	0.796017i	$0.293064\pi$
$354$	−512.244	−0.0769080
$355$	−10226.8	−1.52896
$356$	−25.7150	−0.00382835
$357$	475.660	0.0705171
$358$	4491.67	0.663106
$359$	12253.3	1.80140	0.900699	−	0.434444i	$-0.143055\pi$
$359$	12253.3	1.80140	0.900699	+	0.434444i	$0.143055\pi$
$360$	−3161.16	−0.462799
$361$	−6720.05	−0.979742
$362$	340.594	0.0494509
$363$	−375.257	−0.0542587
$364$	0	0
$365$	−2394.57	−0.343390
$366$	−7752.84	−1.10723
$367$	4681.85	0.665915	0.332957	−	0.942942i	$-0.391953\pi$
$367$	4681.85	0.665915	0.332957	+	0.942942i	$0.391953\pi$
$368$	318.683	0.0451426
$369$	2550.85	0.359870
$370$	2305.22	0.323899
$371$	2303.41	0.322337
$372$	4546.07	0.633610
$373$	−5297.92	−0.735431	−0.367715	−	0.929938i	$-0.619860\pi$
$373$	−5297.92	−0.735431	−0.367715	+	0.929938i	$0.619860\pi$
$374$	877.761	0.121358
$375$	4676.06	0.643922
$376$	1893.86	0.259756
$377$	0	0
$378$	5324.33	0.724482
$379$	4991.94	0.676567	0.338283	−	0.941044i	$-0.390154\pi$
$379$	4991.94	0.676567	0.338283	+	0.941044i	$0.390154\pi$
$380$	−1404.52	−0.189607
$381$	4309.24	0.579446
$382$	−14371.7	−1.92493
$383$	5751.49	0.767330	0.383665	−	0.923472i	$-0.374662\pi$
$383$	5751.49	0.767330	0.383665	+	0.923472i	$0.374662\pi$
$384$	6369.96	0.846525
$385$	−932.046	−0.123380
$386$	−3068.17	−0.404574
$387$	1465.69	0.192520
$388$	−2284.96	−0.298972
$389$	−11224.6	−1.46300	−0.731501	−	0.681840i	$-0.761180\pi$
$389$	−11224.6	−1.46300	−0.731501	+	0.681840i	$0.761180\pi$
$390$	0	0
$391$	405.566	0.0524562
$392$	−4972.01	−0.640623
$393$	−5894.61	−0.756599
$394$	−15587.0	−1.99305
$395$	−6563.75	−0.836097
$396$	2318.40	0.294203
$397$	−3598.94	−0.454976	−0.227488	−	0.973781i	$-0.573051\pi$
$397$	−3598.94	−0.454976	−0.227488	+	0.973781i	$0.573051\pi$
$398$	11765.4	1.48177
$399$	315.220	0.0395508
$400$	397.477	0.0496847
$401$	8619.82	1.07345	0.536725	−	0.843757i	$-0.319661\pi$
$401$	8619.82	1.07345	0.536725	+	0.843757i	$0.319661\pi$
$402$	−4517.27	−0.560451
$403$	0	0
$404$	6571.17	0.809228
$405$	417.079	0.0511724
$406$	−9274.30	−1.13368
$407$	−575.214	−0.0700548
$408$	1020.94	0.123883
$409$	−2659.63	−0.321541	−0.160771	−	0.986992i	$-0.551398\pi$
$409$	−2659.63	−0.321541	−0.160771	+	0.986992i	$0.551398\pi$
$410$	−6469.38	−0.779268
$411$	3341.14	0.400988
$412$	−3833.13	−0.458361
$413$	317.469	0.0378248
$414$	1777.96	0.211068
$415$	407.034	0.0481458
$416$	0	0
$417$	−2622.09	−0.307924
$418$	581.693	0.0680659
$419$	−1164.77	−0.135807	−0.0679033	−	0.997692i	$-0.521631\pi$
$419$	−1164.77	−0.135807	−0.0679033	+	0.997692i	$0.521631\pi$
$420$	−3186.30	−0.370180
$421$	9472.19	1.09655	0.548273	−	0.836299i	$-0.315285\pi$
$421$	9472.19	1.09655	0.548273	+	0.836299i	$0.315285\pi$
$422$	−8849.33	−1.02080
$423$	−1778.69	−0.204451
$424$	4943.95	0.566273
$425$	505.843	0.0577341
$426$	14479.5	1.64679
$427$	4804.92	0.544558
$428$	−19294.0	−2.17899
$429$	0	0
$430$	−3717.23	−0.416885
$431$	−8400.35	−0.938818	−0.469409	−	0.882981i	$-0.655533\pi$
$431$	−8400.35	−0.938818	−0.469409	+	0.882981i	$0.655533\pi$
$432$	−1923.79	−0.214256
$433$	−17038.0	−1.89098	−0.945490	−	0.325650i	$-0.894417\pi$
$433$	−17038.0	−1.89098	−0.945490	+	0.325650i	$0.894417\pi$
$434$	−4676.38	−0.517219
$435$	7306.54	0.805338
$436$	−8324.52	−0.914386
$437$	268.769	0.0294210
$438$	3390.33	0.369854
$439$	−12507.8	−1.35983	−0.679915	−	0.733291i	$-0.737983\pi$
$439$	−12507.8	−1.35983	−0.679915	+	0.733291i	$0.737983\pi$
$440$	−2000.51	−0.216751
$441$	4669.65	0.504227
$442$	0	0
$443$	642.746	0.0689341	0.0344670	−	0.999406i	$-0.489027\pi$
$443$	642.746	0.0689341	0.0344670	+	0.999406i	$0.489027\pi$
$444$	−1966.43	−0.210186
$445$	−20.8397	−0.00221999
$446$	−21861.3	−2.32099
$447$	−3590.81	−0.379954
$448$	−7188.65	−0.758106
$449$	−14640.3	−1.53879	−0.769397	−	0.638770i	$-0.779443\pi$
$449$	−14640.3	−1.53879	−0.769397	+	0.638770i	$0.779443\pi$
$450$	2217.56	0.232304
$451$	1614.28	0.168545
$452$	21966.6	2.28589
$453$	3151.31	0.326847
$454$	18485.7	1.91096
$455$	0	0
$456$	676.578	0.0694817
$457$	3422.08	0.350280	0.175140	−	0.984544i	$-0.443962\pi$
$457$	3422.08	0.350280	0.175140	+	0.984544i	$0.443962\pi$
$458$	15492.4	1.58060
$459$	−2448.28	−0.248967
$460$	−2716.76	−0.275369
$461$	17658.7	1.78405	0.892024	−	0.451987i	$-0.149285\pi$
$461$	17658.7	1.78405	0.892024	+	0.451987i	$0.149285\pi$
$462$	1319.63	0.132889
$463$	−649.912	−0.0652353	−0.0326177	−	0.999468i	$-0.510384\pi$
$463$	−649.912	−0.0652353	−0.0326177	+	0.999468i	$0.510384\pi$
$464$	3350.99	0.335272
$465$	3684.18	0.367418
$466$	13111.3	1.30336
$467$	9249.66	0.916538	0.458269	−	0.888813i	$-0.348470\pi$
$467$	9249.66	0.916538	0.458269	+	0.888813i	$0.348470\pi$
$468$	0	0
$469$	2799.64	0.275640
$470$	4511.04	0.442721
$471$	−11448.0	−1.11995
$472$	681.406	0.0664496
$473$	927.548	0.0901664
$474$	9293.23	0.900532
$475$	335.222	0.0323812
$476$	−1859.74	−0.179078
$477$	−4643.30	−0.445707
$478$	3167.38	0.303080
$479$	8463.05	0.807279	0.403640	−	0.914918i	$-0.367745\pi$
$479$	8463.05	0.807279	0.403640	+	0.914918i	$0.367745\pi$
$480$	6422.99	0.610766
$481$	0	0
$482$	−13158.1	−1.24343
$483$	609.729	0.0574402
$484$	1467.18	0.137789
$485$	−1851.75	−0.173368
$486$	−17262.5	−1.61120
$487$	−3015.91	−0.280624	−0.140312	−	0.990107i	$-0.544811\pi$
$487$	−3015.91	−0.280624	−0.140312	+	0.990107i	$0.544811\pi$
$488$	10313.1	0.956665
$489$	1909.95	0.176628
$490$	−11843.0	−1.09186
$491$	−1977.40	−0.181749	−0.0908744	−	0.995862i	$-0.528966\pi$
$491$	−1977.40	−0.181749	−0.0908744	+	0.995862i	$0.528966\pi$
$492$	5518.61	0.505687
$493$	4264.58	0.389589
$494$	0	0
$495$	1878.85	0.170602
$496$	1689.67	0.152961
$497$	−8973.83	−0.809922
$498$	−576.295	−0.0518562
$499$	16408.3	1.47201	0.736006	−	0.676975i	$-0.236709\pi$
$499$	16408.3	1.47201	0.736006	+	0.676975i	$0.236709\pi$
$500$	−18282.5	−1.63523
$501$	11257.0	1.00384
$502$	26656.9	2.37003
$503$	2556.42	0.226611	0.113305	−	0.993560i	$-0.463856\pi$
$503$	2556.42	0.226611	0.113305	+	0.993560i	$0.463856\pi$
$504$	−2773.87	−0.245155
$505$	5325.33	0.469256
$506$	1125.17	0.0988532
$507$	0	0
$508$	−16848.3	−1.47150
$509$	−5486.98	−0.477812	−0.238906	−	0.971043i	$-0.576789\pi$
$509$	−5486.98	−0.477812	−0.238906	+	0.971043i	$0.576789\pi$
$510$	2431.81	0.211142
$511$	−2101.20	−0.181901
$512$	5015.17	0.432893
$513$	−1622.48	−0.139638
$514$	−12554.5	−1.07734
$515$	−3106.40	−0.265795
$516$	3170.92	0.270527
$517$	−1125.63	−0.0957544
$518$	2022.79	0.171576
$519$	−3382.70	−0.286096
$520$	0	0
$521$	15234.6	1.28107	0.640535	−	0.767929i	$-0.278712\pi$
$521$	15234.6	1.28107	0.640535	+	0.767929i	$0.278712\pi$
$522$	18695.5	1.56759
$523$	16173.0	1.35219	0.676096	−	0.736814i	$-0.263670\pi$
$523$	16173.0	1.35219	0.676096	+	0.736814i	$0.263670\pi$
$524$	23046.7	1.92138
$525$	760.485	0.0632196
$526$	−18501.6	−1.53366
$527$	2150.33	0.177742
$528$	−476.809	−0.0393001
$529$	−11647.1	−0.957271
$530$	11776.2	0.965139
$531$	−639.967	−0.0523017
$532$	−1232.45	−0.100439
$533$	0	0
$534$	29.5056	0.00239107
$535$	−15636.0	−1.26356
$536$	6009.05	0.484237
$537$	−3105.12	−0.249527
$538$	−14944.4	−1.19758
$539$	2955.14	0.236154
$540$	16400.3	1.30695
$541$	19107.0	1.51844	0.759218	−	0.650836i	$-0.225582\pi$
$541$	19107.0	1.51844	0.759218	+	0.650836i	$0.225582\pi$
$542$	16343.6	1.29523
$543$	−235.455	−0.0186084
$544$	3748.88	0.295463
$545$	−6746.26	−0.530235
$546$	0	0
$547$	14133.7	1.10478	0.552389	−	0.833587i	$-0.313716\pi$
$547$	14133.7	1.10478	0.552389	+	0.833587i	$0.313716\pi$
$548$	−13063.2	−1.01831
$549$	−9685.94	−0.752980
$550$	1403.36	0.108799
$551$	2826.14	0.218508
$552$	1308.70	0.100910
$553$	−5759.60	−0.442899
$554$	−10549.4	−0.809028
$555$	−1593.61	−0.121883
$556$	10251.8	0.781969
$557$	−17938.4	−1.36458	−0.682291	−	0.731080i	$-0.739016\pi$
$557$	−17938.4	−1.36458	−0.682291	+	0.731080i	$0.739016\pi$
$558$	9426.82	0.715178
$559$	0	0
$560$	−1184.27	−0.0893656
$561$	−606.803	−0.0456671
$562$	8206.59	0.615968
$563$	23055.3	1.72587	0.862935	−	0.505316i	$-0.168624\pi$
$563$	23055.3	1.72587	0.862935	+	0.505316i	$0.168624\pi$
$564$	−3848.08	−0.287293
$565$	17801.9	1.32554
$566$	−28043.0	−2.08257
$567$	365.981	0.0271071
$568$	−19261.1	−1.42285
$569$	21468.3	1.58172	0.790858	−	0.611999i	$-0.209634\pi$
$569$	21468.3	1.58172	0.790858	+	0.611999i	$0.209634\pi$
$570$	1611.56	0.118423
$571$	−449.105	−0.0329150	−0.0164575	−	0.999865i	$-0.505239\pi$
$571$	−449.105	−0.0329150	−0.0164575	+	0.999865i	$0.505239\pi$
$572$	0	0
$573$	9935.27	0.724349
$574$	−5676.78	−0.412795
$575$	648.419	0.0470277
$576$	14491.2	1.04826
$577$	15957.3	1.15132	0.575660	−	0.817689i	$-0.304745\pi$
$577$	15957.3	1.15132	0.575660	+	0.817689i	$0.304745\pi$
$578$	−20621.0	−1.48395
$579$	2121.05	0.152241
$580$	−28567.1	−2.04515
$581$	357.166	0.0255039
$582$	2621.79	0.186729
$583$	−2938.47	−0.208746
$584$	−4509.94	−0.319560
$585$	0	0
$586$	−33521.2	−2.36305
$587$	12714.1	0.893983	0.446991	−	0.894538i	$-0.352495\pi$
$587$	12714.1	0.893983	0.446991	+	0.894538i	$0.352495\pi$
$588$	10102.5	0.708536
$589$	1425.02	0.0996895
$590$	1623.06	0.113255
$591$	10775.4	0.749984
$592$	−730.877	−0.0507413
$593$	−3431.40	−0.237624	−0.118812	−	0.992917i	$-0.537909\pi$
$593$	−3431.40	−0.237624	−0.118812	+	0.992917i	$0.537909\pi$
$594$	−6792.28	−0.469176
$595$	−1507.15	−0.103844
$596$	14039.3	0.964889
$597$	−8133.50	−0.557591
$598$	0	0
$599$	6955.11	0.474421	0.237210	−	0.971458i	$-0.423767\pi$
$599$	6955.11	0.474421	0.237210	+	0.971458i	$0.423767\pi$
$600$	1632.28	0.111063
$601$	10610.9	0.720176	0.360088	−	0.932918i	$-0.382747\pi$
$601$	10610.9	0.720176	0.360088	+	0.932918i	$0.382747\pi$
$602$	−3261.81	−0.220833
$603$	−5643.62	−0.381138
$604$	−12321.0	−0.830024
$605$	1189.02	0.0799014
$606$	−7539.82	−0.505420
$607$	28180.1	1.88434	0.942172	−	0.335130i	$-0.108780\pi$
$607$	28180.1	1.88434	0.942172	+	0.335130i	$0.108780\pi$
$608$	2484.39	0.165716
$609$	6411.38	0.426605
$610$	24565.1	1.63051
$611$	0	0
$612$	3748.93	0.247617
$613$	11607.7	0.764816	0.382408	−	0.923994i	$-0.375095\pi$
$613$	11607.7	0.764816	0.382408	+	0.923994i	$0.375095\pi$
$614$	14756.7	0.969923
$615$	4472.32	0.293238
$616$	−1755.42	−0.114818
$617$	13429.2	0.876239	0.438120	−	0.898917i	$-0.355645\pi$
$617$	13429.2	0.876239	0.438120	+	0.898917i	$0.355645\pi$
$618$	4398.16	0.286278
$619$	6624.75	0.430164	0.215082	−	0.976596i	$-0.430998\pi$
$619$	6624.75	0.430164	0.215082	+	0.976596i	$0.430998\pi$
$620$	−14404.4	−0.933055
$621$	−3138.35	−0.202798
$622$	10016.7	0.645710
$623$	−18.2865	−0.00117598
$624$	0	0
$625$	−11261.5	−0.720734
$626$	−3431.00	−0.219058
$627$	−402.128	−0.0256132
$628$	44759.3	2.84409
$629$	−930.138	−0.0589619
$630$	−6607.17	−0.417835
$631$	30815.6	1.94414	0.972068	−	0.234699i	$-0.0754106\pi$
$631$	30815.6	1.94414	0.972068	+	0.234699i	$0.0754106\pi$
$632$	−12362.2	−0.778073
$633$	6117.60	0.384128
$634$	−38508.9	−2.41228
$635$	−13654.0	−0.853293
$636$	−10045.5	−0.626304
$637$	0	0
$638$	11831.3	0.734176
$639$	18089.8	1.11991
$640$	−20183.4	−1.24659
$641$	10263.0	0.632396	0.316198	−	0.948693i	$-0.397594\pi$
$641$	10263.0	0.632396	0.316198	+	0.948693i	$0.397594\pi$
$642$	22138.1	1.36093
$643$	17400.4	1.06719	0.533597	−	0.845739i	$-0.320840\pi$
$643$	17400.4	1.06719	0.533597	+	0.845739i	$0.320840\pi$
$644$	−2383.92	−0.145869
$645$	2569.74	0.156874
$646$	940.615	0.0572879
$647$	−21073.7	−1.28052	−0.640258	−	0.768160i	$-0.721172\pi$
$647$	−21073.7	−1.28052	−0.640258	+	0.768160i	$0.721172\pi$
$648$	785.529	0.0476211
$649$	−404.998	−0.0244954
$650$	0	0
$651$	3232.81	0.194630
$652$	−7467.52	−0.448544
$653$	21122.3	1.26582	0.632909	−	0.774226i	$-0.281861\pi$
$653$	21122.3	1.26582	0.632909	+	0.774226i	$0.281861\pi$
$654$	9551.64	0.571099
$655$	18677.3	1.11417
$656$	2051.14	0.122079
$657$	4235.68	0.251522
$658$	3958.38	0.234519
$659$	−2294.48	−0.135630	−0.0678150	−	0.997698i	$-0.521603\pi$
$659$	−2294.48	−0.135630	−0.0678150	+	0.997698i	$0.521603\pi$
$660$	4064.78	0.239729
$661$	5326.29	0.313417	0.156709	−	0.987645i	$-0.449912\pi$
$661$	5326.29	0.313417	0.156709	+	0.987645i	$0.449912\pi$
$662$	23348.6	1.37080
$663$	0	0
$664$	766.610	0.0448046
$665$	−998.787	−0.0582425
$666$	−4077.63	−0.237245
$667$	5466.59	0.317342
$668$	−44012.6	−2.54925
$669$	15112.9	0.873388
$670$	14313.1	0.825320
$671$	−6129.66	−0.352657
$672$	5636.08	0.323536
$673$	−21320.5	−1.22116	−0.610582	−	0.791953i	$-0.709064\pi$
$673$	−21320.5	−1.22116	−0.610582	+	0.791953i	$0.709064\pi$
$674$	−12019.4	−0.686898
$675$	−3914.31	−0.223203
$676$	0	0
$677$	28198.9	1.60085	0.800423	−	0.599435i	$-0.204608\pi$
$677$	28198.9	1.60085	0.800423	+	0.599435i	$0.204608\pi$
$678$	−25204.7	−1.42770
$679$	−1624.88	−0.0918370
$680$	−3234.89	−0.182430
$681$	−12779.3	−0.719096
$682$	5965.68	0.334953
$683$	16100.4	0.901999	0.450999	−	0.892524i	$-0.351068\pi$
$683$	16100.4	0.901999	0.450999	+	0.892524i	$0.351068\pi$
$684$	2484.42	0.138880
$685$	−10586.5	−0.590496
$686$	−23660.2	−1.31684
$687$	−10710.0	−0.594779
$688$	1178.56	0.0653084
$689$	0	0
$690$	3117.24	0.171987
$691$	−21688.9	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$691$	−21688.9	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$692$	13225.7	0.726538
$693$	1648.67	0.0903718
$694$	46967.2	2.56895
$695$	8308.18	0.453449
$696$	13761.2	0.749448
$697$	2610.35	0.141856
$698$	23835.2	1.29252
$699$	−9063.90	−0.490455
$700$	−2973.34	−0.160546
$701$	−29827.3	−1.60708	−0.803538	−	0.595254i	$-0.797051\pi$
$701$	−29827.3	−1.60708	−0.803538	+	0.595254i	$0.797051\pi$
$702$	0	0
$703$	−616.403	−0.0330698
$704$	9170.60	0.490952
$705$	−3118.52	−0.166596
$706$	36017.8	1.92004
$707$	4672.90	0.248575
$708$	−1384.53	−0.0734940
$709$	3920.43	0.207666	0.103833	−	0.994595i	$-0.466889\pi$
$709$	3920.43	0.207666	0.103833	+	0.994595i	$0.466889\pi$
$710$	−45878.7	−2.42507
$711$	11610.4	0.612412
$712$	−39.2495	−0.00206592
$713$	2756.42	0.144781
$714$	2133.88	0.111847
$715$	0	0
$716$	12140.4	0.633671
$717$	−2189.63	−0.114049
$718$	54969.8	2.85718
$719$	−23010.7	−1.19354	−0.596770	−	0.802413i	$-0.703549\pi$
$719$	−23010.7	−1.19354	−0.596770	+	0.802413i	$0.703549\pi$
$720$	2387.31	0.123569
$721$	−2725.82	−0.140797
$722$	−30147.1	−1.55396
$723$	9096.26	0.467903
$724$	920.583	0.0472558
$725$	6818.21	0.349272
$726$	−1683.46	−0.0860592
$727$	14629.1	0.746303	0.373151	−	0.927770i	$-0.378277\pi$
$727$	14629.1	0.746303	0.373151	+	0.927770i	$0.378277\pi$
$728$	0	0
$729$	10787.7	0.548071
$730$	−10742.4	−0.544648
$731$	1499.87	0.0758889
$732$	−20954.9	−1.05808
$733$	−15935.7	−0.802998	−0.401499	−	0.915859i	$-0.631511\pi$
$733$	−15935.7	−0.802998	−0.401499	+	0.915859i	$0.631511\pi$
$734$	21003.5	1.05620
$735$	8187.14	0.410867
$736$	4805.54	0.240672
$737$	−3571.51	−0.178505
$738$	11443.5	0.570786
$739$	−19010.5	−0.946295	−0.473147	−	0.880983i	$-0.656882\pi$
$739$	−19010.5	−0.946295	−0.473147	+	0.880983i	$0.656882\pi$
$740$	6230.71	0.309521
$741$	0	0
$742$	10333.4	0.511255
$743$	−4385.47	−0.216537	−0.108269	−	0.994122i	$-0.534531\pi$
$743$	−4385.47	−0.216537	−0.108269	+	0.994122i	$0.534531\pi$
$744$	6938.79	0.341920
$745$	11377.6	0.559521
$746$	−23767.2	−1.16646
$747$	−719.990	−0.0352651
$748$	2372.48	0.115971
$749$	−13720.3	−0.669333
$750$	20977.5	1.02132
$751$	−33553.9	−1.63036	−0.815180	−	0.579208i	$-0.803362\pi$
$751$	−33553.9	−1.63036	−0.815180	+	0.579208i	$0.803362\pi$
$752$	−1430.24	−0.0693558
$753$	−18428.1	−0.891842
$754$	0	0
$755$	−9985.05	−0.481315
$756$	14391.0	0.692322
$757$	−574.864	−0.0276008	−0.0138004	−	0.999905i	$-0.504393\pi$
$757$	−574.864	−0.0276008	−0.0138004	+	0.999905i	$0.504393\pi$
$758$	22394.6	1.07310
$759$	−777.835	−0.0371984
$760$	−2143.76	−0.102319
$761$	−19680.5	−0.937472	−0.468736	−	0.883338i	$-0.655290\pi$
$761$	−19680.5	−0.937472	−0.468736	+	0.883338i	$0.655290\pi$
$762$	19331.8	0.919053
$763$	−5919.75	−0.280877
$764$	−38844.9	−1.83948
$765$	3038.16	0.143588
$766$	25802.0	1.21705
$767$	0	0
$768$	7892.33	0.370820
$769$	−17330.8	−0.812700	−0.406350	−	0.913718i	$-0.633199\pi$
$769$	−17330.8	−0.812700	−0.406350	+	0.913718i	$0.633199\pi$
$770$	−4181.29	−0.195692
$771$	8679.00	0.405404
$772$	−8292.87	−0.386615
$773$	−17236.1	−0.801992	−0.400996	−	0.916080i	$-0.631336\pi$
$773$	−17236.1	−0.801992	−0.400996	+	0.916080i	$0.631336\pi$
$774$	6575.29	0.305354
$775$	3437.94	0.159348
$776$	−3487.60	−0.161337
$777$	−1398.37	−0.0645641
$778$	−50355.0	−2.32045
$779$	1729.88	0.0795626
$780$	0	0
$781$	11448.0	0.524508
$782$	1819.43	0.0832002
$783$	−33000.1	−1.50617
$784$	3754.86	0.171049
$785$	36273.3	1.64923
$786$	−26444.0	−1.20004
$787$	7728.14	0.350036	0.175018	−	0.984565i	$-0.444002\pi$
$787$	7728.14	0.350036	0.175018	+	0.984565i	$0.444002\pi$
$788$	−42129.6	−1.90458
$789$	12790.3	0.577117
$790$	−29445.9	−1.32613
$791$	15620.9	0.702170
$792$	3538.64	0.158763
$793$	0	0
$794$	−16145.3	−0.721633
$795$	−8140.94	−0.363182
$796$	31800.4	1.41600
$797$	−38193.7	−1.69748	−0.848739	−	0.528813i	$-0.822637\pi$
$797$	−38193.7	−1.69748	−0.848739	+	0.528813i	$0.822637\pi$
$798$	1414.12	0.0627311
$799$	−1820.17	−0.0805921
$800$	5993.71	0.264887
$801$	36.8626	0.00162606
$802$	38669.8	1.70259
$803$	2680.51	0.117800
$804$	−12209.6	−0.535572
$805$	−1931.95	−0.0845866
$806$	0	0
$807$	10331.2	0.450650
$808$	10029.8	0.436690
$809$	12499.6	0.543217	0.271609	−	0.962408i	$-0.412444\pi$
$809$	12499.6	0.543217	0.271609	+	0.962408i	$0.412444\pi$
$810$	1871.08	0.0811641
$811$	−13978.2	−0.605229	−0.302614	−	0.953113i	$-0.597859\pi$
$811$	−13978.2	−0.605229	−0.302614	+	0.953113i	$0.597859\pi$
$812$	−25067.2	−1.08336
$813$	−11298.4	−0.487396
$814$	−2580.49	−0.111113
$815$	−6051.74	−0.260102
$816$	−771.014	−0.0330771
$817$	993.967	0.0425636
$818$	−11931.5	−0.509994
$819$	0	0
$820$	−17485.9	−0.744676
$821$	−27403.2	−1.16489	−0.582447	−	0.812869i	$-0.697904\pi$
$821$	−27403.2	−1.16489	−0.582447	+	0.812869i	$0.697904\pi$
$822$	14988.8	0.636004
$823$	7846.05	0.332316	0.166158	−	0.986099i	$-0.446864\pi$
$823$	7846.05	0.332316	0.166158	+	0.986099i	$0.446864\pi$
$824$	−5850.60	−0.247349
$825$	−970.155	−0.0409412
$826$	1424.21	0.0599936
$827$	−42267.1	−1.77723	−0.888616	−	0.458652i	$-0.848332\pi$
$827$	−42267.1	−1.77723	−0.888616	+	0.458652i	$0.848332\pi$
$828$	4805.60	0.201698
$829$	−40746.4	−1.70710	−0.853548	−	0.521014i	$-0.825554\pi$
$829$	−40746.4	−1.70710	−0.853548	+	0.521014i	$0.825554\pi$
$830$	1826.01	0.0763636
$831$	7292.88	0.304437
$832$	0	0
$833$	4778.56	0.198760
$834$	−11763.1	−0.488395
$835$	−35668.2	−1.47826
$836$	1572.24	0.0650444
$837$	−16639.7	−0.687157
$838$	−5225.35	−0.215402
$839$	−31840.9	−1.31022	−0.655108	−	0.755536i	$-0.727377\pi$
$839$	−31840.9	−1.31022	−0.655108	+	0.755536i	$0.727377\pi$
$840$	−4863.34	−0.199763
$841$	33093.0	1.35688
$842$	42493.6	1.73922
$843$	−5673.27	−0.231789
$844$	−23918.6	−0.975488
$845$	0	0
$846$	−7979.45	−0.324278
$847$	1043.34	0.0423255
$848$	−3733.67	−0.151197
$849$	19386.3	0.783670
$850$	2269.28	0.0915715
$851$	−1192.31	−0.0480278
$852$	39136.1	1.57369
$853$	−45295.8	−1.81817	−0.909084	−	0.416612i	$-0.863217\pi$
$853$	−45295.8	−1.81817	−0.909084	+	0.416612i	$0.863217\pi$
$854$	21555.5	0.863718
$855$	2013.39	0.0805340
$856$	−29448.9	−1.17587
$857$	−14773.3	−0.588852	−0.294426	−	0.955674i	$-0.595128\pi$
$857$	−14773.3	−0.588852	−0.294426	+	0.955674i	$0.595128\pi$
$858$	0	0
$859$	14882.1	0.591117	0.295559	−	0.955325i	$-0.404494\pi$
$859$	14882.1	0.591117	0.295559	+	0.955325i	$0.404494\pi$
$860$	−10047.2	−0.398379
$861$	3924.40	0.155335
$862$	−37685.1	−1.48905
$863$	−9186.08	−0.362338	−0.181169	−	0.983452i	$-0.557988\pi$
$863$	−9186.08	−0.362338	−0.181169	+	0.983452i	$0.557988\pi$
$864$	−29009.5	−1.14227
$865$	10718.2	0.421306
$866$	−76434.9	−2.99927
$867$	14255.5	0.558410
$868$	−12639.6	−0.494260
$869$	7347.55	0.286822
$870$	32778.2	1.27734
$871$	0	0
$872$	−12705.9	−0.493438
$873$	3275.51	0.126986
$874$	1205.74	0.0466643
$875$	−13001.1	−0.502304
$876$	9163.63	0.353436
$877$	2904.88	0.111848	0.0559241	−	0.998435i	$-0.482190\pi$
$877$	2904.88	0.111848	0.0559241	+	0.998435i	$0.482190\pi$
$878$	−56111.8	−2.15681
$879$	23173.4	0.889215
$880$	1510.79	0.0578734
$881$	47716.5	1.82475	0.912377	−	0.409351i	$-0.134245\pi$
$881$	47716.5	1.82475	0.912377	+	0.409351i	$0.134245\pi$
$882$	20948.7	0.799750
$883$	−27433.8	−1.04555	−0.522774	−	0.852471i	$-0.675103\pi$
$883$	−27433.8	−1.04555	−0.522774	+	0.852471i	$0.675103\pi$
$884$	0	0
$885$	−1122.03	−0.0426178
$886$	2883.45	0.109336
$887$	−6749.32	−0.255490	−0.127745	−	0.991807i	$-0.540774\pi$
$887$	−6749.32	−0.255490	−0.127745	+	0.991807i	$0.540774\pi$
$888$	−3001.42	−0.113425
$889$	−11981.2	−0.452008
$890$	−93.4897	−0.00352110
$891$	−466.884	−0.0175546
$892$	−59088.3	−2.21796
$893$	−1206.23	−0.0452015
$894$	−16108.9	−0.602641
$895$	9838.68	0.367453
$896$	−17710.7	−0.660348
$897$	0	0
$898$	−65678.5	−2.44067
$899$	28984.1	1.07528
$900$	5993.79	0.221992
$901$	−4751.59	−0.175692
$902$	7241.90	0.267327
$903$	2254.91	0.0830994
$904$	33528.2	1.23355
$905$	746.048	0.0274027
$906$	14137.2	0.518409
$907$	−5906.83	−0.216244	−0.108122	−	0.994138i	$-0.534484\pi$
$907$	−5906.83	−0.216244	−0.108122	+	0.994138i	$0.534484\pi$
$908$	49964.5	1.82614
$909$	−9419.82	−0.343714
$910$	0	0
$911$	10019.7	0.364397	0.182199	−	0.983262i	$-0.441679\pi$
$911$	10019.7	0.364397	0.182199	+	0.983262i	$0.441679\pi$
$912$	−510.952	−0.0185519
$913$	−455.639	−0.0165164
$914$	15351.9	0.555576
$915$	−16982.0	−0.613562
$916$	41874.1	1.51044
$917$	16389.0	0.590200
$918$	−10983.3	−0.394884
$919$	−40764.6	−1.46322	−0.731611	−	0.681722i	$-0.761231\pi$
$919$	−40764.6	−1.46322	−0.731611	+	0.681722i	$0.761231\pi$
$920$	−4146.67	−0.148600
$921$	−10201.4	−0.364982
$922$	79219.3	2.82966
$923$	0	0
$924$	3566.79	0.126990
$925$	−1487.10	−0.0528602
$926$	−2915.60	−0.103469
$927$	5494.81	0.194685
$928$	50530.9	1.78745
$929$	27217.3	0.961215	0.480608	−	0.876936i	$-0.340416\pi$
$929$	27217.3	0.961215	0.480608	+	0.876936i	$0.340416\pi$
$930$	16527.7	0.582759
$931$	3166.75	0.111478
$932$	35438.0	1.24551
$933$	−6924.59	−0.242980
$934$	41495.3	1.45371
$935$	1922.67	0.0672494
$936$	0	0
$937$	−3801.36	−0.132535	−0.0662673	−	0.997802i	$-0.521109\pi$
$937$	−3801.36	−0.132535	−0.0662673	+	0.997802i	$0.521109\pi$
$938$	12559.6	0.437190
$939$	2371.87	0.0824314
$940$	12192.8	0.423069
$941$	15737.2	0.545183	0.272592	−	0.962130i	$-0.412119\pi$
$941$	15737.2	0.545183	0.272592	+	0.962130i	$0.412119\pi$
$942$	−51357.2	−1.77634
$943$	3346.09	0.115550
$944$	−514.597	−0.0177423
$945$	11662.6	0.401464
$946$	4161.11	0.143012
$947$	1384.15	0.0474962	0.0237481	−	0.999718i	$-0.492440\pi$
$947$	1384.15	0.0474962	0.0237481	+	0.999718i	$0.492440\pi$
$948$	25118.4	0.860557
$949$	0	0
$950$	1503.85	0.0513595
$951$	26621.4	0.907739
$952$	−2838.57	−0.0966370
$953$	−30604.1	−1.04026	−0.520128	−	0.854088i	$-0.674116\pi$
$953$	−30604.1	−1.04026	−0.520128	+	0.854088i	$0.674116\pi$
$954$	−20830.5	−0.706931
$955$	−31480.3	−1.06668
$956$	8561.01	0.289626
$957$	−8179.04	−0.276270
$958$	37966.5	1.28042
$959$	−9289.51	−0.312799
$960$	25406.9	0.854170
$961$	−15176.4	−0.509427
$962$	0	0
$963$	27658.0	0.925511
$964$	−35564.6	−1.18823
$965$	−6720.61	−0.224191
$966$	2735.33	0.0911054
$967$	−29081.3	−0.967107	−0.483553	−	0.875315i	$-0.660654\pi$
$967$	−29081.3	−0.967107	−0.483553	+	0.875315i	$0.660654\pi$
$968$	2239.40	0.0743564
$969$	−650.254	−0.0215574
$970$	−8307.22	−0.274978
$971$	16464.6	0.544155	0.272078	−	0.962275i	$-0.412289\pi$
$971$	16464.6	0.544155	0.272078	+	0.962275i	$0.412289\pi$
$972$	−46658.3	−1.53968
$973$	7290.30	0.240202
$974$	−13529.8	−0.445095
$975$	0	0
$976$	−7788.46	−0.255433
$977$	−28050.2	−0.918531	−0.459265	−	0.888299i	$-0.651887\pi$
$977$	−28050.2	−0.918531	−0.459265	+	0.888299i	$0.651887\pi$
$978$	8568.30	0.280147
$979$	23.3282	0.000761565 0
$980$	−32010.1	−1.04339
$981$	11933.3	0.388379
$982$	−8870.88	−0.288270
$983$	−33731.0	−1.09446	−0.547228	−	0.836983i	$-0.684317\pi$
$983$	−33731.0	−1.09446	−0.547228	+	0.836983i	$0.684317\pi$
$984$	8423.20	0.272888
$985$	−34142.2	−1.10443
$986$	19131.5	0.617923
$987$	−2736.45	−0.0882495
$988$	0	0
$989$	1922.63	0.0618159
$990$	8428.81	0.270591
$991$	6682.85	0.214216	0.107108	−	0.994247i	$-0.465841\pi$
$991$	6682.85	0.214216	0.107108	+	0.994247i	$0.465841\pi$
$992$	25479.2	0.815488
$993$	−16141.0	−0.515831
$994$	−40257.9	−1.28461
$995$	25771.3	0.821110
$996$	−1557.65	−0.0495543
$997$	21045.0	0.668506	0.334253	−	0.942483i	$-0.391516\pi$
$997$	21045.0	0.668506	0.334253	+	0.942483i	$0.391516\pi$
$998$	73609.7	2.33475
$999$	7197.58	0.227949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.35	yes	39
13.12	even	2		1859.4.a.n.1.5	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.5	✓	39	13.12	even	2
1859.4.a.o.1.35	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)

\(f(q)\)	\(=\)	\(q+4.48614 q^{2} -3.10130 q^{3} +12.1255 q^{4} +9.82658 q^{5} -13.9129 q^{6} +8.62268 q^{7} +18.5074 q^{8} -17.3819 q^{9} +O(q^{10})\)	\(q+4.48614 q^{2} -3.10130 q^{3} +12.1255 q^{4} +9.82658 q^{5} -13.9129 q^{6} +8.62268 q^{7} +18.5074 q^{8} -17.3819 q^{9} +44.0834 q^{10} -11.0000 q^{11} -37.6047 q^{12} +38.6826 q^{14} -30.4752 q^{15} -13.9768 q^{16} -17.7873 q^{17} -77.9778 q^{18} -11.7877 q^{19} +119.152 q^{20} -26.7415 q^{21} -49.3476 q^{22} -22.8008 q^{23} -57.3971 q^{24} -28.4384 q^{25} +137.642 q^{27} +104.554 q^{28} -239.754 q^{29} -136.716 q^{30} -120.891 q^{31} -210.761 q^{32} +34.1143 q^{33} -79.7965 q^{34} +84.7314 q^{35} -210.764 q^{36} +52.2922 q^{37} -52.8812 q^{38} +181.865 q^{40} -146.753 q^{41} -119.966 q^{42} -84.3225 q^{43} -133.380 q^{44} -170.805 q^{45} -102.288 q^{46} +102.330 q^{47} +43.3463 q^{48} -268.649 q^{49} -127.579 q^{50} +55.1639 q^{51} +267.134 q^{53} +617.480 q^{54} -108.092 q^{55} +159.584 q^{56} +36.5571 q^{57} -1075.57 q^{58} +36.8180 q^{59} -369.526 q^{60} +557.242 q^{61} -542.334 q^{62} -149.879 q^{63} -833.691 q^{64} +153.042 q^{66} +324.683 q^{67} -215.680 q^{68} +70.7123 q^{69} +380.117 q^{70} -1040.72 q^{71} -321.695 q^{72} -243.683 q^{73} +234.590 q^{74} +88.1959 q^{75} -142.931 q^{76} -94.8495 q^{77} -667.959 q^{79} -137.344 q^{80} +42.4440 q^{81} -658.355 q^{82} +41.4217 q^{83} -324.253 q^{84} -174.789 q^{85} -378.283 q^{86} +743.549 q^{87} -203.582 q^{88} -2.12074 q^{89} -766.255 q^{90} -276.471 q^{92} +374.919 q^{93} +459.066 q^{94} -115.833 q^{95} +653.634 q^{96} -188.443 q^{97} -1205.20 q^{98} +191.201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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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