LMFDB - Embedded newform 1859.4.a.o.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.40771 q^{2} -4.57703 q^{3} -2.20293 q^{4} +18.4699 q^{5} +11.0201 q^{6} +11.7306 q^{7} +24.5657 q^{8} -6.05084 q^{9} +O(q^{10})$	\(q-2.40771 q^{2} -4.57703 q^{3} -2.20293 q^{4} +18.4699 q^{5} +11.0201 q^{6} +11.7306 q^{7} +24.5657 q^{8} -6.05084 q^{9} -44.4701 q^{10} -11.0000 q^{11} +10.0829 q^{12} -28.2440 q^{14} -84.5371 q^{15} -41.5236 q^{16} +129.585 q^{17} +14.5687 q^{18} +45.1493 q^{19} -40.6879 q^{20} -53.6915 q^{21} +26.4848 q^{22} -95.0462 q^{23} -112.438 q^{24} +216.137 q^{25} +151.275 q^{27} -25.8418 q^{28} -10.2976 q^{29} +203.541 q^{30} -317.352 q^{31} -96.5488 q^{32} +50.3473 q^{33} -312.004 q^{34} +216.664 q^{35} +13.3296 q^{36} -71.2002 q^{37} -108.706 q^{38} +453.726 q^{40} -144.226 q^{41} +129.273 q^{42} -252.934 q^{43} +24.2323 q^{44} -111.758 q^{45} +228.844 q^{46} -44.9183 q^{47} +190.055 q^{48} -205.392 q^{49} -520.394 q^{50} -593.115 q^{51} -552.962 q^{53} -364.225 q^{54} -203.169 q^{55} +288.172 q^{56} -206.649 q^{57} +24.7937 q^{58} +432.410 q^{59} +186.230 q^{60} -432.414 q^{61} +764.093 q^{62} -70.9803 q^{63} +564.650 q^{64} -121.222 q^{66} +433.750 q^{67} -285.467 q^{68} +435.029 q^{69} -521.663 q^{70} -522.342 q^{71} -148.643 q^{72} -752.378 q^{73} +171.429 q^{74} -989.263 q^{75} -99.4609 q^{76} -129.037 q^{77} +707.418 q^{79} -766.937 q^{80} -529.015 q^{81} +347.255 q^{82} +253.746 q^{83} +118.279 q^{84} +2393.42 q^{85} +608.992 q^{86} +47.1326 q^{87} -270.223 q^{88} -1620.57 q^{89} +269.082 q^{90} +209.380 q^{92} +1452.53 q^{93} +108.150 q^{94} +833.902 q^{95} +441.906 q^{96} -1543.85 q^{97} +494.524 q^{98} +66.5593 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40771	−0.851254	−0.425627	−	0.904899i	$-0.639946\pi$
$2$	−2.40771	−0.851254	−0.425627	+	0.904899i	$0.639946\pi$
$3$	−4.57703	−0.880849	−0.440424	−	0.897790i	$-0.645172\pi$
$3$	−4.57703	−0.880849	−0.440424	+	0.897790i	$0.645172\pi$
$4$	−2.20293	−0.275367
$5$	18.4699	1.65200	0.825998	−	0.563673i	$-0.190612\pi$
$5$	18.4699	1.65200	0.825998	+	0.563673i	$0.190612\pi$
$6$	11.0201	0.749826
$7$	11.7306	0.633395	0.316698	−	0.948527i	$-0.397426\pi$
$7$	11.7306	0.633395	0.316698	+	0.948527i	$0.397426\pi$
$8$	24.5657	1.08566
$9$	−6.05084	−0.224105
$10$	−44.4701	−1.40627
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	10.0829	0.242556
$13$	0	0
$13$	0	0
$14$	−28.2440	−0.539180
$15$	−84.5371	−1.45516
$16$	−41.5236	−0.648807
$17$	129.585	1.84877	0.924383	−	0.381465i	$-0.124580\pi$
$17$	129.585	1.84877	0.924383	+	0.381465i	$0.124580\pi$
$18$	14.5687	0.190771
$19$	45.1493	0.545156	0.272578	−	0.962134i	$-0.412124\pi$
$19$	45.1493	0.545156	0.272578	+	0.962134i	$0.412124\pi$
$20$	−40.6879	−0.454905
$21$	−53.6915	−0.557926
$22$	26.4848	0.256663
$23$	−95.0462	−0.861674	−0.430837	−	0.902430i	$-0.641782\pi$
$23$	−95.0462	−0.861674	−0.430837	+	0.902430i	$0.641782\pi$
$24$	−112.438	−0.956303
$25$	216.137	1.72909
$26$	0	0
$27$	151.275	1.07825
$28$	−25.8418	−0.174416
$29$	−10.2976	−0.0659387	−0.0329694	−	0.999456i	$-0.510496\pi$
$29$	−10.2976	−0.0659387	−0.0329694	+	0.999456i	$0.510496\pi$
$30$	203.541	1.23871
$31$	−317.352	−1.83865	−0.919326	−	0.393498i	$-0.871265\pi$
$31$	−317.352	−1.83865	−0.919326	+	0.393498i	$0.871265\pi$
$32$	−96.5488	−0.533362
$33$	50.3473	0.265586
$34$	−312.004	−1.57377
$35$	216.664	1.04637
$36$	13.3296	0.0617111
$37$	−71.2002	−0.316358	−0.158179	−	0.987410i	$-0.550562\pi$
$37$	−71.2002	−0.316358	−0.158179	+	0.987410i	$0.550562\pi$
$38$	−108.706	−0.464066
$39$	0	0
$40$	453.726	1.79351
$41$	−144.226	−0.549374	−0.274687	−	0.961534i	$-0.588574\pi$
$41$	−144.226	−0.549374	−0.274687	+	0.961534i	$0.588574\pi$
$42$	129.273	0.474936
$43$	−252.934	−0.897025	−0.448512	−	0.893777i	$-0.648046\pi$
$43$	−252.934	−0.897025	−0.448512	+	0.893777i	$0.648046\pi$
$44$	24.2323	0.0830261
$45$	−111.758	−0.370221
$46$	228.844	0.733504
$47$	−44.9183	−0.139404	−0.0697022	−	0.997568i	$-0.522205\pi$
$47$	−44.9183	−0.139404	−0.0697022	+	0.997568i	$0.522205\pi$
$48$	190.055	0.571501
$49$	−205.392	−0.598810
$50$	−520.394	−1.47190
$51$	−593.115	−1.62848
$52$	0	0
$53$	−552.962	−1.43312	−0.716558	−	0.697527i	$-0.754284\pi$
$53$	−552.962	−1.43312	−0.716558	+	0.697527i	$0.754284\pi$
$54$	−364.225	−0.917866
$55$	−203.169	−0.498096
$56$	288.172	0.687653
$57$	−206.649	−0.480200
$58$	24.7937	0.0561306
$59$	432.410	0.954151	0.477076	−	0.878862i	$-0.341697\pi$
$59$	432.410	0.954151	0.477076	+	0.878862i	$0.341697\pi$
$60$	186.230	0.400702
$61$	−432.414	−0.907622	−0.453811	−	0.891098i	$-0.649936\pi$
$61$	−432.414	−0.907622	−0.453811	+	0.891098i	$0.649936\pi$
$62$	764.093	1.56516
$63$	−70.9803	−0.141947
$64$	564.650	1.10283
$65$	0	0
$66$	−121.222	−0.226081
$67$	433.750	0.790910	0.395455	−	0.918485i	$-0.370587\pi$
$67$	433.750	0.790910	0.395455	+	0.918485i	$0.370587\pi$
$68$	−285.467	−0.509088
$69$	435.029	0.759005
$70$	−521.663	−0.890724
$71$	−522.342	−0.873107	−0.436554	−	0.899678i	$-0.643801\pi$
$71$	−522.342	−0.873107	−0.436554	+	0.899678i	$0.643801\pi$
$72$	−148.643	−0.243302
$73$	−752.378	−1.20629	−0.603145	−	0.797631i	$-0.706086\pi$
$73$	−752.378	−1.20629	−0.603145	+	0.797631i	$0.706086\pi$
$74$	171.429	0.269301
$75$	−989.263	−1.52307
$76$	−99.4609	−0.150118
$77$	−129.037	−0.190976
$78$	0	0
$79$	707.418	1.00748	0.503739	−	0.863856i	$-0.331957\pi$
$79$	707.418	1.00748	0.503739	+	0.863856i	$0.331957\pi$
$80$	−766.937	−1.07183
$81$	−529.015	−0.725672
$82$	347.255	0.467657
$83$	253.746	0.335569	0.167785	−	0.985824i	$-0.446339\pi$
$83$	253.746	0.335569	0.167785	+	0.985824i	$0.446339\pi$
$84$	118.279	0.153634
$85$	2393.42	3.05416
$86$	608.992	0.763596
$87$	47.1326	0.0580821
$88$	−270.223	−0.327339
$89$	−1620.57	−1.93011	−0.965056	−	0.262045i	$-0.915603\pi$
$89$	−1620.57	−1.93011	−0.965056	+	0.262045i	$0.915603\pi$
$90$	269.082	0.315152
$91$	0	0
$92$	209.380	0.237276
$93$	1452.53	1.61957
$94$	108.150	0.118669
$95$	833.902	0.900596
$96$	441.906	0.469811
$97$	−1543.85	−1.61603	−0.808014	−	0.589164i	$-0.799457\pi$
$97$	−1543.85	−1.61603	−0.808014	+	0.589164i	$0.799457\pi$
$98$	494.524	0.509740
$99$	66.5593	0.0675703
$100$	−476.134	−0.476134
$101$	−553.809	−0.545605	−0.272802	−	0.962070i	$-0.587950\pi$
$101$	−553.809	−0.545605	−0.272802	+	0.962070i	$0.587950\pi$
$102$	1428.05	1.38625
$103$	−396.119	−0.378939	−0.189470	−	0.981887i	$-0.560677\pi$
$103$	−396.119	−0.378939	−0.189470	+	0.981887i	$0.560677\pi$
$104$	0	0
$105$	−991.675	−0.921691
$106$	1331.37	1.21995
$107$	1303.18	1.17742	0.588708	−	0.808346i	$-0.299637\pi$
$107$	1303.18	1.17742	0.588708	+	0.808346i	$0.299637\pi$
$108$	−333.248	−0.296914
$109$	2170.38	1.90720	0.953599	−	0.301079i	$-0.0973469\pi$
$109$	2170.38	1.90720	0.953599	+	0.301079i	$0.0973469\pi$
$110$	489.171	0.424006
$111$	325.885	0.278663
$112$	−487.099	−0.410951
$113$	−1081.79	−0.900585	−0.450292	−	0.892881i	$-0.648680\pi$
$113$	−1081.79	−0.900585	−0.450292	+	0.892881i	$0.648680\pi$
$114$	497.552	0.408772
$115$	−1755.49	−1.42348
$116$	22.6850	0.0181573
$117$	0	0
$118$	−1041.12	−0.812225
$119$	1520.12	1.17100
$120$	−2076.71	−1.57981
$121$	121.000	0.0909091
$122$	1041.13	0.772617
$123$	660.127	0.483916
$124$	699.106	0.506303
$125$	1683.28	1.20446
$126$	170.900	0.120833
$127$	−245.465	−0.171508	−0.0857539	−	0.996316i	$-0.527330\pi$
$127$	−245.465	−0.171508	−0.0857539	+	0.996316i	$0.527330\pi$
$128$	−587.125	−0.405429
$129$	1157.68	0.790143
$130$	0	0
$131$	1235.48	0.824006	0.412003	−	0.911182i	$-0.364829\pi$
$131$	1235.48	0.824006	0.412003	+	0.911182i	$0.364829\pi$
$132$	−110.912	−0.0731335
$133$	529.630	0.345299
$134$	−1044.34	−0.673266
$135$	2794.02	1.78127
$136$	3183.35	2.00713
$137$	−506.523	−0.315877	−0.157939	−	0.987449i	$-0.550485\pi$
$137$	−506.523	−0.315877	−0.157939	+	0.987449i	$0.550485\pi$
$138$	−1047.42	−0.646106
$139$	3053.63	1.86335	0.931675	−	0.363294i	$-0.118348\pi$
$139$	3053.63	1.86335	0.931675	+	0.363294i	$0.118348\pi$
$140$	−477.295	−0.288134
$141$	205.592	0.122794
$142$	1257.65	0.743236
$143$	0	0
$144$	251.253	0.145401
$145$	−190.196	−0.108931
$146$	1811.51	1.02686
$147$	940.084	0.527461
$148$	156.849	0.0871143
$149$	1644.34	0.904094	0.452047	−	0.891994i	$-0.350694\pi$
$149$	1644.34	0.904094	0.452047	+	0.891994i	$0.350694\pi$
$150$	2381.86	1.29652
$151$	2132.00	1.14900	0.574501	−	0.818504i	$-0.305196\pi$
$151$	2132.00	1.14900	0.574501	+	0.818504i	$0.305196\pi$
$152$	1109.12	0.591854
$153$	−784.100	−0.414318
$154$	310.684	0.162569
$155$	−5861.46	−3.03745
$156$	0	0
$157$	−107.526	−0.0546592	−0.0273296	−	0.999626i	$-0.508700\pi$
$157$	−107.526	−0.0546592	−0.0273296	+	0.999626i	$0.508700\pi$
$158$	−1703.26	−0.857620
$159$	2530.92	1.26236
$160$	−1783.24	−0.881111
$161$	−1114.95	−0.545780
$162$	1273.71	0.617731
$163$	−414.833	−0.199339	−0.0996694	−	0.995021i	$-0.531779\pi$
$163$	−414.833	−0.199339	−0.0996694	+	0.995021i	$0.531779\pi$
$164$	317.720	0.151279
$165$	929.908	0.438747
$166$	−610.947	−0.285655
$167$	−740.392	−0.343073	−0.171537	−	0.985178i	$-0.554873\pi$
$167$	−740.392	−0.343073	−0.171537	+	0.985178i	$0.554873\pi$
$168$	−1318.97	−0.605718
$169$	0	0
$170$	−5762.67	−2.59986
$171$	−273.191	−0.122172
$172$	557.196	0.247011
$173$	−901.910	−0.396364	−0.198182	−	0.980165i	$-0.563504\pi$
$173$	−901.910	−0.396364	−0.198182	+	0.980165i	$0.563504\pi$
$174$	−113.482	−0.0494426
$175$	2535.42	1.09520
$176$	456.760	0.195623
$177$	−1979.15	−0.840463
$178$	3901.86	1.64302
$179$	1984.25	0.828545	0.414273	−	0.910153i	$-0.364036\pi$
$179$	1984.25	0.828545	0.414273	+	0.910153i	$0.364036\pi$
$180$	246.196	0.101946
$181$	−1110.92	−0.456208	−0.228104	−	0.973637i	$-0.573253\pi$
$181$	−1110.92	−0.456208	−0.228104	+	0.973637i	$0.573253\pi$
$182$	0	0
$183$	1979.17	0.799478
$184$	−2334.88	−0.935486
$185$	−1315.06	−0.522622
$186$	−3497.27	−1.37867
$187$	−1425.44	−0.557424
$188$	98.9520	0.0383873
$189$	1774.55	0.682960
$190$	−2007.80	−0.766636
$191$	−2480.33	−0.939635	−0.469818	−	0.882764i	$-0.655680\pi$
$191$	−2480.33	−0.939635	−0.469818	+	0.882764i	$0.655680\pi$
$192$	−2584.42	−0.971429
$193$	−3963.14	−1.47810	−0.739048	−	0.673652i	$-0.764725\pi$
$193$	−3963.14	−1.47810	−0.739048	+	0.673652i	$0.764725\pi$
$194$	3717.15	1.37565
$195$	0	0
$196$	452.465	0.164892
$197$	−867.537	−0.313753	−0.156877	−	0.987618i	$-0.550143\pi$
$197$	−867.537	−0.313753	−0.156877	+	0.987618i	$0.550143\pi$
$198$	−160.255	−0.0575195
$199$	−3098.89	−1.10389	−0.551946	−	0.833880i	$-0.686114\pi$
$199$	−3098.89	−1.10389	−0.551946	+	0.833880i	$0.686114\pi$
$200$	5309.55	1.87721
$201$	−1985.28	−0.696672
$202$	1333.41	0.464448
$203$	−120.798	−0.0417653
$204$	1306.59	0.448430
$205$	−2663.84	−0.907564
$206$	953.739	0.322573
$207$	575.110	0.193106
$208$	0	0
$209$	−496.642	−0.164371
$210$	2387.67	0.784593
$211$	4711.87	1.53734	0.768669	−	0.639647i	$-0.220919\pi$
$211$	4711.87	1.53734	0.768669	+	0.639647i	$0.220919\pi$
$212$	1218.14	0.394632
$213$	2390.77	0.769075
$214$	−3137.69	−1.00228
$215$	−4671.66	−1.48188
$216$	3716.17	1.17062
$217$	−3722.75	−1.16459
$218$	−5225.64	−1.62351
$219$	3443.65	1.06256
$220$	447.567	0.137159
$221$	0	0
$222$	−784.637	−0.237213
$223$	1727.40	0.518722	0.259361	−	0.965780i	$-0.416488\pi$
$223$	1727.40	0.518722	0.259361	+	0.965780i	$0.416488\pi$
$224$	−1132.58	−0.337829
$225$	−1307.81	−0.387499
$226$	2604.63	0.766626
$227$	−2606.51	−0.762115	−0.381057	−	0.924551i	$-0.624440\pi$
$227$	−2606.51	−0.762115	−0.381057	+	0.924551i	$0.624440\pi$
$228$	455.235	0.132231
$229$	−4753.60	−1.37173	−0.685867	−	0.727727i	$-0.740577\pi$
$229$	−4753.60	−1.37173	−0.685867	+	0.727727i	$0.740577\pi$
$230$	4226.72	1.21175
$231$	590.606	0.168221
$232$	−252.969	−0.0715871
$233$	1950.66	0.548464	0.274232	−	0.961664i	$-0.411576\pi$
$233$	1950.66	0.548464	0.274232	+	0.961664i	$0.411576\pi$
$234$	0	0
$235$	−829.636	−0.230296
$236$	−952.569	−0.262741
$237$	−3237.87	−0.887436
$238$	−3660.00	−0.996819
$239$	3406.13	0.921859	0.460929	−	0.887437i	$-0.347516\pi$
$239$	3406.13	0.921859	0.460929	+	0.887437i	$0.347516\pi$
$240$	3510.29	0.944117
$241$	1378.77	0.368526	0.184263	−	0.982877i	$-0.441010\pi$
$241$	1378.77	0.368526	0.184263	+	0.982877i	$0.441010\pi$
$242$	−291.333	−0.0773867
$243$	−1663.10	−0.439045
$244$	952.579	0.249929
$245$	−3793.57	−0.989233
$246$	−1589.39	−0.411935
$247$	0	0
$248$	−7795.99	−1.99615
$249$	−1161.40	−0.295586
$250$	−4052.86	−1.02530
$251$	−6296.69	−1.58344	−0.791720	−	0.610884i	$-0.790814\pi$
$251$	−6296.69	−1.58344	−0.791720	+	0.610884i	$0.790814\pi$
$252$	156.365	0.0390875
$253$	1045.51	0.259805
$254$	591.008	0.145997
$255$	−10954.8	−2.69025
$256$	−3103.58	−0.757709
$257$	−1016.40	−0.246697	−0.123348	−	0.992363i	$-0.539363\pi$
$257$	−1016.40	−0.246697	−0.123348	+	0.992363i	$0.539363\pi$
$258$	−2787.37	−0.672613
$259$	−835.224	−0.200380
$260$	0	0
$261$	62.3094	0.0147772
$262$	−2974.69	−0.701438
$263$	−610.303	−0.143091	−0.0715455	−	0.997437i	$-0.522793\pi$
$263$	−610.303	−0.143091	−0.0715455	+	0.997437i	$0.522793\pi$
$264$	1236.82	0.288336
$265$	−10213.1	−2.36750
$266$	−1275.20	−0.293937
$267$	7417.38	1.70014
$268$	−955.522	−0.217790
$269$	−8213.36	−1.86163	−0.930813	−	0.365496i	$-0.880899\pi$
$269$	−8213.36	−1.86163	−0.930813	+	0.365496i	$0.880899\pi$
$270$	−6727.20	−1.51631
$271$	−6686.95	−1.49891	−0.749453	−	0.662058i	$-0.769683\pi$
$271$	−6686.95	−1.49891	−0.749453	+	0.662058i	$0.769683\pi$
$272$	−5380.85	−1.19949
$273$	0	0
$274$	1219.56	0.268892
$275$	−2377.50	−0.521341
$276$	−958.339	−0.209005
$277$	−196.206	−0.0425590	−0.0212795	−	0.999774i	$-0.506774\pi$
$277$	−196.206	−0.0425590	−0.0212795	+	0.999774i	$0.506774\pi$
$278$	−7352.26	−1.58618
$279$	1920.25	0.412051
$280$	5322.49	1.13600
$281$	−5088.36	−1.08023	−0.540117	−	0.841590i	$-0.681620\pi$
$281$	−5088.36	−1.08023	−0.540117	+	0.841590i	$0.681620\pi$
$282$	−495.006	−0.104529
$283$	−2292.59	−0.481556	−0.240778	−	0.970580i	$-0.577403\pi$
$283$	−2292.59	−0.481556	−0.240778	+	0.970580i	$0.577403\pi$
$284$	1150.68	0.240424
$285$	−3816.79	−0.793289
$286$	0	0
$287$	−1691.87	−0.347971
$288$	584.201	0.119529
$289$	11879.3	2.41794
$290$	457.937	0.0927276
$291$	7066.26	1.42348
$292$	1657.44	0.332172
$293$	4571.70	0.911541	0.455771	−	0.890097i	$-0.349364\pi$
$293$	4571.70	0.911541	0.455771	+	0.890097i	$0.349364\pi$
$294$	−2263.45	−0.449004
$295$	7986.55	1.57625
$296$	−1749.08	−0.343457
$297$	−1664.02	−0.325105
$298$	−3959.11	−0.769613
$299$	0	0
$300$	2179.28	0.419402
$301$	−2967.08	−0.568171
$302$	−5133.23	−0.978093
$303$	2534.80	0.480595
$304$	−1874.76	−0.353701
$305$	−7986.64	−1.49939
$306$	1887.88	0.352690
$307$	9348.91	1.73802	0.869008	−	0.494799i	$-0.164758\pi$
$307$	9348.91	1.73802	0.869008	+	0.494799i	$0.164758\pi$
$308$	284.260	0.0525884
$309$	1813.04	0.333788
$310$	14112.7	2.58564
$311$	−4755.07	−0.866994	−0.433497	−	0.901155i	$-0.642721\pi$
$311$	−4755.07	−0.866994	−0.433497	+	0.901155i	$0.642721\pi$
$312$	0	0
$313$	5817.68	1.05059	0.525295	−	0.850920i	$-0.323955\pi$
$313$	5817.68	1.05059	0.525295	+	0.850920i	$0.323955\pi$
$314$	258.891	0.0465289
$315$	−1311.00	−0.234496
$316$	−1558.39	−0.277426
$317$	−9078.94	−1.60859	−0.804297	−	0.594228i	$-0.797458\pi$
$317$	−9078.94	−1.60859	−0.804297	+	0.594228i	$0.797458\pi$
$318$	−6093.72	−1.07459
$319$	113.274	0.0198813
$320$	10429.0	1.82188
$321$	−5964.70	−1.03713
$322$	2684.49	0.464598
$323$	5850.68	1.00787
$324$	1165.38	0.199826
$325$	0	0
$326$	998.797	0.169688
$327$	−9933.88	−1.67995
$328$	−3543.02	−0.596434
$329$	−526.921	−0.0882981
$330$	−2238.95	−0.373485
$331$	2127.19	0.353235	0.176617	−	0.984280i	$-0.443484\pi$
$331$	2127.19	0.353235	0.176617	+	0.984280i	$0.443484\pi$
$332$	−558.985	−0.0924046
$333$	430.821	0.0708974
$334$	1782.65	0.292042
$335$	8011.31	1.30658
$336$	2229.46	0.361986
$337$	−8413.45	−1.35997	−0.679985	−	0.733226i	$-0.738014\pi$
$337$	−8413.45	−1.35997	−0.679985	+	0.733226i	$0.738014\pi$
$338$	0	0
$339$	4951.37	0.793279
$340$	−5272.55	−0.841012
$341$	3490.88	0.554374
$342$	657.765	0.104000
$343$	−6432.99	−1.01268
$344$	−6213.50	−0.973865
$345$	8034.93	1.25387
$346$	2171.54	0.337406
$347$	355.308	0.0549681	0.0274840	−	0.999622i	$-0.491250\pi$
$347$	355.308	0.0549681	0.0274840	+	0.999622i	$0.491250\pi$
$348$	−103.830	−0.0159939
$349$	175.952	0.0269871	0.0134935	−	0.999909i	$-0.495705\pi$
$349$	175.952	0.0269871	0.0134935	+	0.999909i	$0.495705\pi$
$350$	−6104.56	−0.932293
$351$	0	0
$352$	1062.04	0.160815
$353$	1427.83	0.215285	0.107643	−	0.994190i	$-0.465670\pi$
$353$	1427.83	0.215285	0.107643	+	0.994190i	$0.465670\pi$
$354$	4765.22	0.715448
$355$	−9647.60	−1.44237
$356$	3570.00	0.531488
$357$	−6957.62	−1.03147
$358$	−4777.49	−0.705302
$359$	−13456.4	−1.97828	−0.989142	−	0.146961i	$-0.953051\pi$
$359$	−13456.4	−1.97828	−0.989142	+	0.146961i	$0.953051\pi$
$360$	−2745.42	−0.401935
$361$	−4820.54	−0.702805
$362$	2674.76	0.388349
$363$	−553.820	−0.0800772
$364$	0	0
$365$	−13896.3	−1.99279
$366$	−4765.27	−0.680559
$367$	10278.6	1.46196	0.730980	−	0.682398i	$-0.239063\pi$
$367$	10278.6	1.46196	0.730980	+	0.682398i	$0.239063\pi$
$368$	3946.66	0.559060
$369$	872.690	0.123118
$370$	3166.28	0.444884
$371$	−6486.60	−0.907729
$372$	−3199.83	−0.445976
$373$	7793.81	1.08190	0.540949	−	0.841055i	$-0.318065\pi$
$373$	7793.81	1.08190	0.540949	+	0.841055i	$0.318065\pi$
$374$	3432.04	0.474510
$375$	−7704.42	−1.06095
$376$	−1103.45	−0.151346
$377$	0	0
$378$	−4272.60	−0.581372
$379$	2298.84	0.311566	0.155783	−	0.987791i	$-0.450210\pi$
$379$	2298.84	0.311566	0.155783	+	0.987791i	$0.450210\pi$
$380$	−1837.03	−0.247994
$381$	1123.50	0.151072
$382$	5971.91	0.799868
$383$	−10802.4	−1.44119	−0.720597	−	0.693354i	$-0.756132\pi$
$383$	−10802.4	−1.44119	−0.720597	+	0.693354i	$0.756132\pi$
$384$	2687.28	0.357122
$385$	−2383.30	−0.315491
$386$	9542.08	1.25824
$387$	1530.46	0.201028
$388$	3401.01	0.445000
$389$	−11240.4	−1.46507	−0.732535	−	0.680730i	$-0.761663\pi$
$389$	−11240.4	−1.46507	−0.732535	+	0.680730i	$0.761663\pi$
$390$	0	0
$391$	−12316.6	−1.59303
$392$	−5045.60	−0.650105
$393$	−5654.84	−0.725825
$394$	2088.78	0.267084
$395$	13065.9	1.66435
$396$	−146.626	−0.0186066
$397$	5693.07	0.719716	0.359858	−	0.933007i	$-0.382825\pi$
$397$	5693.07	0.719716	0.359858	+	0.933007i	$0.382825\pi$
$398$	7461.23	0.939692
$399$	−2424.13	−0.304156
$400$	−8974.78	−1.12185
$401$	13689.4	1.70478	0.852389	−	0.522909i	$-0.175153\pi$
$401$	13689.4	1.70478	0.852389	+	0.522909i	$0.175153\pi$
$402$	4779.99	0.593045
$403$	0	0
$404$	1220.00	0.150241
$405$	−9770.84	−1.19881
$406$	290.846	0.0355529
$407$	783.202	0.0953855
$408$	−14570.3	−1.76798
$409$	9361.64	1.13179	0.565896	−	0.824476i	$-0.308530\pi$
$409$	9361.64	1.13179	0.565896	+	0.824476i	$0.308530\pi$
$410$	6413.76	0.772568
$411$	2318.37	0.278240
$412$	872.622	0.104347
$413$	5072.44	0.604355
$414$	−1384.70	−0.164382
$415$	4686.66	0.554359
$416$	0	0
$417$	−13976.5	−1.64133
$418$	1195.77	0.139921
$419$	8906.98	1.03851	0.519254	−	0.854620i	$-0.326210\pi$
$419$	8906.98	1.03851	0.519254	+	0.854620i	$0.326210\pi$
$420$	2184.59	0.253803
$421$	2730.40	0.316085	0.158043	−	0.987432i	$-0.449482\pi$
$421$	2730.40	0.316085	0.158043	+	0.987432i	$0.449482\pi$
$422$	−11344.8	−1.30866
$423$	271.794	0.0312413
$424$	−13583.9	−1.55588
$425$	28008.1	3.19669
$426$	−5756.29	−0.654679
$427$	−5072.50	−0.574884
$428$	−2870.82	−0.324221
$429$	0	0
$430$	11248.0	1.26146
$431$	−2063.89	−0.230659	−0.115329	−	0.993327i	$-0.536792\pi$
$431$	−2063.89	−0.230659	−0.115329	+	0.993327i	$0.536792\pi$
$432$	−6281.47	−0.699577
$433$	−7508.42	−0.833329	−0.416665	−	0.909060i	$-0.636801\pi$
$433$	−7508.42	−0.833329	−0.416665	+	0.909060i	$0.636801\pi$
$434$	8963.30	0.991364
$435$	870.533	0.0959514
$436$	−4781.20	−0.525179
$437$	−4291.27	−0.469747
$438$	−8291.32	−0.904508
$439$	−3687.61	−0.400912	−0.200456	−	0.979703i	$-0.564242\pi$
$439$	−3687.61	−0.400912	−0.200456	+	0.979703i	$0.564242\pi$
$440$	−4990.98	−0.540763
$441$	1242.79	0.134197
$442$	0	0
$443$	853.321	0.0915180	0.0457590	−	0.998953i	$-0.485429\pi$
$443$	853.321	0.0915180	0.0457590	+	0.998953i	$0.485429\pi$
$444$	−717.903	−0.0767346
$445$	−29931.7	−3.18854
$446$	−4159.07	−0.441565
$447$	−7526.21	−0.796370
$448$	6623.71	0.698529
$449$	−9450.02	−0.993261	−0.496630	−	0.867962i	$-0.665430\pi$
$449$	−9450.02	−0.993261	−0.496630	+	0.867962i	$0.665430\pi$
$450$	3148.82	0.329860
$451$	1586.49	0.165643
$452$	2383.11	0.247991
$453$	−9758.20	−1.01210
$454$	6275.72	0.648753
$455$	0	0
$456$	−5076.49	−0.521334
$457$	5500.78	0.563054	0.281527	−	0.959553i	$-0.409159\pi$
$457$	5500.78	0.563054	0.281527	+	0.959553i	$0.409159\pi$
$458$	11445.3	1.16769
$459$	19602.9	1.99344
$460$	3867.23	0.391980
$461$	1548.74	0.156468	0.0782341	−	0.996935i	$-0.475072\pi$
$461$	1548.74	0.156468	0.0782341	+	0.996935i	$0.475072\pi$
$462$	−1422.01	−0.143199
$463$	13236.3	1.32860	0.664300	−	0.747466i	$-0.268730\pi$
$463$	13236.3	1.32860	0.664300	+	0.747466i	$0.268730\pi$
$464$	427.595	0.0427815
$465$	26828.1	2.67553
$466$	−4696.63	−0.466882
$467$	−17547.1	−1.73873	−0.869363	−	0.494174i	$-0.835471\pi$
$467$	−17547.1	−1.73873	−0.869363	+	0.494174i	$0.835471\pi$
$468$	0	0
$469$	5088.17	0.500959
$470$	1997.52	0.196040
$471$	492.149	0.0481465
$472$	10622.4	1.03588
$473$	2782.27	0.270463
$474$	7795.86	0.755434
$475$	9758.42	0.942625
$476$	−3348.72	−0.322454
$477$	3345.89	0.321169
$478$	−8200.97	−0.784736
$479$	8047.11	0.767603	0.383801	−	0.923416i	$-0.374615\pi$
$479$	8047.11	0.767603	0.383801	+	0.923416i	$0.374615\pi$
$480$	8161.95	0.776126
$481$	0	0
$482$	−3319.69	−0.313709
$483$	5103.17	0.480750
$484$	−266.555	−0.0250333
$485$	−28514.8	−2.66967
$486$	4004.26	0.373739
$487$	9021.11	0.839396	0.419698	−	0.907664i	$-0.362136\pi$
$487$	9021.11	0.839396	0.419698	+	0.907664i	$0.362136\pi$
$488$	−10622.6	−0.985370
$489$	1898.70	0.175587
$490$	9133.81	0.842088
$491$	17987.8	1.65332	0.826659	−	0.562703i	$-0.190238\pi$
$491$	17987.8	1.65332	0.826659	+	0.562703i	$0.190238\pi$
$492$	−1454.21	−0.133254
$493$	−1334.42	−0.121905
$494$	0	0
$495$	1229.34	0.111626
$496$	13177.6	1.19293
$497$	−6127.41	−0.553022
$498$	2796.32	0.251619
$499$	−2981.75	−0.267498	−0.133749	−	0.991015i	$-0.542702\pi$
$499$	−2981.75	−0.267498	−0.133749	+	0.991015i	$0.542702\pi$
$500$	−3708.16	−0.331668
$501$	3388.79	0.302196
$502$	15160.6	1.34791
$503$	−7991.88	−0.708430	−0.354215	−	0.935164i	$-0.615252\pi$
$503$	−7991.88	−0.708430	−0.354215	+	0.935164i	$0.615252\pi$
$504$	−1743.68	−0.154107
$505$	−10228.8	−0.901337
$506$	−2517.28	−0.221160
$507$	0	0
$508$	540.743	0.0472275
$509$	−256.100	−0.0223015	−0.0111507	−	0.999938i	$-0.503549\pi$
$509$	−256.100	−0.0223015	−0.0111507	+	0.999938i	$0.503549\pi$
$510$	26375.9	2.29009
$511$	−8825.88	−0.764059
$512$	12169.5	1.05043
$513$	6829.94	0.587815
$514$	2447.19	0.210002
$515$	−7316.27	−0.626006
$516$	−2550.30	−0.217579
$517$	494.101	0.0420320
$518$	2010.98	0.170574
$519$	4128.06	0.349137
$520$	0	0
$521$	22619.4	1.90206	0.951032	−	0.309092i	$-0.100025\pi$
$521$	22619.4	1.90206	0.951032	+	0.309092i	$0.100025\pi$
$522$	−150.023	−0.0125792
$523$	−18131.8	−1.51596	−0.757979	−	0.652279i	$-0.773813\pi$
$523$	−18131.8	−1.51596	−0.757979	+	0.652279i	$0.773813\pi$
$524$	−2721.69	−0.226904
$525$	−11604.7	−0.964705
$526$	1469.43	0.121807
$527$	−41124.2	−3.39924
$528$	−2090.60	−0.172314
$529$	−3133.21	−0.257517
$530$	24590.3	2.01535
$531$	−2616.44	−0.213830
$532$	−1166.74	−0.0950838
$533$	0	0
$534$	−17858.9	−1.44725
$535$	24069.6	1.94509
$536$	10655.4	0.858660
$537$	−9081.95	−0.729823
$538$	19775.4	1.58472
$539$	2259.31	0.180548
$540$	−6155.04	−0.490502
$541$	4602.24	0.365741	0.182870	−	0.983137i	$-0.441461\pi$
$541$	4602.24	0.365741	0.182870	+	0.983137i	$0.441461\pi$
$542$	16100.2	1.27595
$543$	5084.69	0.401851
$544$	−12511.3	−0.986061
$545$	40086.6	3.15068
$546$	0	0
$547$	−8403.02	−0.656832	−0.328416	−	0.944533i	$-0.606515\pi$
$547$	−8403.02	−0.656832	−0.328416	+	0.944533i	$0.606515\pi$
$548$	1115.84	0.0869820
$549$	2616.47	0.203403
$550$	5724.34	0.443794
$551$	−464.931	−0.0359469
$552$	10686.8	0.824022
$553$	8298.47	0.638132
$554$	472.406	0.0362285
$555$	6019.06	0.460351
$556$	−6726.94	−0.513104
$557$	−15390.7	−1.17078	−0.585392	−	0.810750i	$-0.699059\pi$
$557$	−15390.7	−1.17078	−0.585392	+	0.810750i	$0.699059\pi$
$558$	−4623.40	−0.350760
$559$	0	0
$560$	−8996.66	−0.678890
$561$	6524.26	0.491006
$562$	12251.3	0.919554
$563$	−15387.6	−1.15188	−0.575940	−	0.817492i	$-0.695364\pi$
$563$	−15387.6	−1.15188	−0.575940	+	0.817492i	$0.695364\pi$
$564$	−452.906	−0.0338134
$565$	−19980.5	−1.48776
$566$	5519.89	0.409927
$567$	−6205.68	−0.459637
$568$	−12831.7	−0.947898
$569$	3646.84	0.268688	0.134344	−	0.990935i	$-0.457107\pi$
$569$	3646.84	0.268688	0.134344	+	0.990935i	$0.457107\pi$
$570$	9189.73	0.675290
$571$	7405.73	0.542767	0.271384	−	0.962471i	$-0.412519\pi$
$571$	7405.73	0.542767	0.271384	+	0.962471i	$0.412519\pi$
$572$	0	0
$573$	11352.5	0.827677
$574$	4073.52	0.296212
$575$	−20543.0	−1.48991
$576$	−3416.61	−0.247151
$577$	−1173.52	−0.0846695	−0.0423348	−	0.999103i	$-0.513480\pi$
$577$	−1173.52	−0.0846695	−0.0423348	+	0.999103i	$0.513480\pi$
$578$	−28602.0	−2.05828
$579$	18139.4	1.30198
$580$	418.989	0.0299958
$581$	2976.61	0.212548
$582$	−17013.5	−1.21174
$583$	6082.58	0.432101
$584$	−18482.7	−1.30962
$585$	0	0
$586$	−11007.3	−0.775953
$587$	5215.57	0.366728	0.183364	−	0.983045i	$-0.441301\pi$
$587$	5215.57	0.366728	0.183364	+	0.983045i	$0.441301\pi$
$588$	−2070.94	−0.145245
$589$	−14328.2	−1.00235
$590$	−19229.3	−1.34179
$591$	3970.74	0.276369
$592$	2956.49	0.205255
$593$	10652.9	0.737713	0.368856	−	0.929486i	$-0.379749\pi$
$593$	10652.9	0.737713	0.368856	+	0.929486i	$0.379749\pi$
$594$	4006.48	0.276747
$595$	28076.4	1.93449
$596$	−3622.38	−0.248957
$597$	14183.7	0.972362
$598$	0	0
$599$	−6884.06	−0.469574	−0.234787	−	0.972047i	$-0.575439\pi$
$599$	−6884.06	−0.469574	−0.234787	+	0.972047i	$0.575439\pi$
$600$	−24301.9	−1.65354
$601$	6245.02	0.423860	0.211930	−	0.977285i	$-0.432025\pi$
$601$	6245.02	0.423860	0.211930	+	0.977285i	$0.432025\pi$
$602$	7143.86	0.483658
$603$	−2624.55	−0.177247
$604$	−4696.64	−0.316397
$605$	2234.86	0.150182
$606$	−6103.06	−0.409109
$607$	−19146.6	−1.28029	−0.640144	−	0.768255i	$-0.721125\pi$
$607$	−19146.6	−1.28029	−0.640144	+	0.768255i	$0.721125\pi$
$608$	−4359.11	−0.290765
$609$	552.895	0.0367889
$610$	19229.5	1.27636
$611$	0	0
$612$	1727.32	0.114089
$613$	−20712.3	−1.36470	−0.682351	−	0.731025i	$-0.739042\pi$
$613$	−20712.3	−1.36470	−0.682351	+	0.731025i	$0.739042\pi$
$614$	−22509.5	−1.47949
$615$	12192.5	0.799427
$616$	−3169.89	−0.207335
$617$	17596.3	1.14814	0.574069	−	0.818807i	$-0.305364\pi$
$617$	17596.3	1.14814	0.574069	+	0.818807i	$0.305364\pi$
$618$	−4365.29	−0.284138
$619$	2010.45	0.130544	0.0652720	−	0.997868i	$-0.479208\pi$
$619$	2010.45	0.130544	0.0652720	+	0.997868i	$0.479208\pi$
$620$	12912.4	0.836411
$621$	−14378.1	−0.929102
$622$	11448.8	0.738032
$623$	−19010.3	−1.22252
$624$	0	0
$625$	4072.95	0.260669
$626$	−14007.3	−0.894320
$627$	2273.14	0.144786
$628$	236.872	0.0150513
$629$	−9226.49	−0.584872
$630$	3156.50	0.199616
$631$	−28855.7	−1.82049	−0.910243	−	0.414075i	$-0.864105\pi$
$631$	−28855.7	−1.82049	−0.910243	+	0.414075i	$0.864105\pi$
$632$	17378.2	1.09378
$633$	−21566.3	−1.35416
$634$	21859.5	1.36932
$635$	−4533.71	−0.283330
$636$	−5575.45	−0.347611
$637$	0	0
$638$	−272.731	−0.0169240
$639$	3160.61	0.195668
$640$	−10844.1	−0.669768
$641$	−4050.17	−0.249567	−0.124783	−	0.992184i	$-0.539824\pi$
$641$	−4050.17	−0.249567	−0.124783	+	0.992184i	$0.539824\pi$
$642$	14361.3	0.882857
$643$	−19015.9	−1.16627	−0.583135	−	0.812375i	$-0.698174\pi$
$643$	−19015.9	−1.16627	−0.583135	+	0.812375i	$0.698174\pi$
$644$	2456.17	0.150290
$645$	21382.3	1.30531
$646$	−14086.7	−0.857950
$647$	−416.405	−0.0253022	−0.0126511	−	0.999920i	$-0.504027\pi$
$647$	−416.405	−0.0253022	−0.0126511	+	0.999920i	$0.504027\pi$
$648$	−12995.6	−0.787833
$649$	−4756.50	−0.287687
$650$	0	0
$651$	17039.1	1.02583
$652$	913.849	0.0548912
$653$	9132.39	0.547287	0.273643	−	0.961831i	$-0.411771\pi$
$653$	9132.39	0.547287	0.273643	+	0.961831i	$0.411771\pi$
$654$	23917.9	1.43007
$655$	22819.3	1.36126
$656$	5988.79	0.356438
$657$	4552.52	0.270336
$658$	1268.67	0.0751641
$659$	−15473.9	−0.914685	−0.457342	−	0.889291i	$-0.651199\pi$
$659$	−15473.9	−0.914685	−0.457342	+	0.889291i	$0.651199\pi$
$660$	−2048.52	−0.120816
$661$	−31347.3	−1.84458	−0.922291	−	0.386497i	$-0.873685\pi$
$661$	−31347.3	−1.84458	−0.922291	+	0.386497i	$0.873685\pi$
$662$	−5121.65	−0.300692
$663$	0	0
$664$	6233.45	0.364315
$665$	9782.21	0.570433
$666$	−1037.29	−0.0603517
$667$	978.752	0.0568177
$668$	1631.03	0.0944709
$669$	−7906.34	−0.456916
$670$	−19288.9	−1.11223
$671$	4756.56	0.273658
$672$	5183.84	0.297576
$673$	−20295.5	−1.16246	−0.581229	−	0.813740i	$-0.697428\pi$
$673$	−20295.5	−1.16246	−0.581229	+	0.813740i	$0.697428\pi$
$674$	20257.2	1.15768
$675$	32696.0	1.86440
$676$	0	0
$677$	26929.7	1.52880	0.764398	−	0.644745i	$-0.223037\pi$
$677$	26929.7	1.52880	0.764398	+	0.644745i	$0.223037\pi$
$678$	−11921.5	−0.675282
$679$	−18110.4	−1.02358
$680$	58796.1	3.31578
$681$	11930.1	0.671308
$682$	−8405.02	−0.471913
$683$	17010.5	0.952985	0.476493	−	0.879178i	$-0.341908\pi$
$683$	17010.5	0.952985	0.476493	+	0.879178i	$0.341908\pi$
$684$	601.822	0.0336422
$685$	−9355.42	−0.521828
$686$	15488.8	0.862047
$687$	21757.4	1.20829
$688$	10502.7	0.581996
$689$	0	0
$690$	−19345.8	−1.06736
$691$	7228.11	0.397931	0.198965	−	0.980007i	$-0.436242\pi$
$691$	7228.11	0.397931	0.198965	+	0.980007i	$0.436242\pi$
$692$	1986.85	0.109145
$693$	780.783	0.0427987
$694$	−855.478	−0.0467918
$695$	56400.2	3.07825
$696$	1157.84	0.0630574
$697$	−18689.6	−1.01566
$698$	−423.641	−0.0229728
$699$	−8928.22	−0.483114
$700$	−5585.36	−0.301581
$701$	1302.50	0.0701778	0.0350889	−	0.999384i	$-0.488829\pi$
$701$	1302.50	0.0701778	0.0350889	+	0.999384i	$0.488829\pi$
$702$	0	0
$703$	−3214.64	−0.172464
$704$	−6211.16	−0.332517
$705$	3797.26	0.202856
$706$	−3437.80	−0.183262
$707$	−6496.54	−0.345583
$708$	4359.93	0.231435
$709$	−11053.1	−0.585484	−0.292742	−	0.956191i	$-0.594568\pi$
$709$	−11053.1	−0.585484	−0.292742	+	0.956191i	$0.594568\pi$
$710$	23228.6	1.22782
$711$	−4280.48	−0.225781
$712$	−39810.4	−2.09545
$713$	30163.2	1.58432
$714$	16751.9	0.878047
$715$	0	0
$716$	−4371.16	−0.228154
$717$	−15589.9	−0.812018
$718$	32399.2	1.68402
$719$	18492.6	0.959192	0.479596	−	0.877489i	$-0.340783\pi$
$719$	18492.6	0.959192	0.479596	+	0.877489i	$0.340783\pi$
$720$	4640.61	0.240202
$721$	−4646.73	−0.240018
$722$	11606.5	0.598266
$723$	−6310.69	−0.324615
$724$	2447.27	0.125625
$725$	−2225.70	−0.114014
$726$	1333.44	0.0681660
$727$	−8002.72	−0.408259	−0.204130	−	0.978944i	$-0.565436\pi$
$727$	−8002.72	−0.408259	−0.204130	+	0.978944i	$0.565436\pi$
$728$	0	0
$729$	21895.4	1.11240
$730$	33458.4	1.69637
$731$	−32776.5	−1.65839
$732$	−4359.98	−0.220150
$733$	−3707.20	−0.186806	−0.0934029	−	0.995628i	$-0.529774\pi$
$733$	−3707.20	−0.186806	−0.0934029	+	0.995628i	$0.529774\pi$
$734$	−24747.9	−1.24450
$735$	17363.2	0.871365
$736$	9176.60	0.459584
$737$	−4771.25	−0.238468
$738$	−2101.18	−0.104804
$739$	14333.7	0.713497	0.356748	−	0.934201i	$-0.383885\pi$
$739$	14333.7	0.713497	0.356748	+	0.934201i	$0.383885\pi$
$740$	2896.99	0.143913
$741$	0	0
$742$	15617.9	0.772708
$743$	16436.6	0.811576	0.405788	−	0.913967i	$-0.366997\pi$
$743$	16436.6	0.811576	0.405788	+	0.913967i	$0.366997\pi$
$744$	35682.4	1.75831
$745$	30370.9	1.49356
$746$	−18765.2	−0.920970
$747$	−1535.38	−0.0752028
$748$	3140.14	0.153496
$749$	15287.2	0.745770
$750$	18550.0	0.903135
$751$	−28724.7	−1.39571	−0.697855	−	0.716239i	$-0.745862\pi$
$751$	−28724.7	−1.39571	−0.697855	+	0.716239i	$0.745862\pi$
$752$	1865.17	0.0904465
$753$	28820.1	1.39477
$754$	0	0
$755$	39377.7	1.89815
$756$	−3909.21	−0.188064
$757$	1997.12	0.0958874	0.0479437	−	0.998850i	$-0.484733\pi$
$757$	1997.12	0.0958874	0.0479437	+	0.998850i	$0.484733\pi$
$758$	−5534.94	−0.265222
$759$	−4785.32	−0.228849
$760$	20485.4	0.977741
$761$	−14732.9	−0.701796	−0.350898	−	0.936414i	$-0.614124\pi$
$761$	−14732.9	−0.701796	−0.350898	+	0.936414i	$0.614124\pi$
$762$	−2705.06	−0.128601
$763$	25459.9	1.20801
$764$	5464.00	0.258744
$765$	−14482.2	−0.684453
$766$	26009.1	1.22682
$767$	0	0
$768$	14205.2	0.667428
$769$	−34088.2	−1.59850	−0.799252	−	0.600995i	$-0.794771\pi$
$769$	−34088.2	−1.59850	−0.799252	+	0.600995i	$0.794771\pi$
$770$	5738.30	0.268563
$771$	4652.07	0.217303
$772$	8730.52	0.407018
$773$	−16039.0	−0.746290	−0.373145	−	0.927773i	$-0.621721\pi$
$773$	−16039.0	−0.746290	−0.373145	+	0.927773i	$0.621721\pi$
$774$	−3684.91	−0.171126
$775$	−68591.5	−3.17920
$776$	−37925.9	−1.75446
$777$	3822.84	0.176504
$778$	27063.7	1.24715
$779$	−6511.71	−0.299495
$780$	0	0
$781$	5745.76	0.263252
$782$	29654.8	1.35608
$783$	−1557.77	−0.0710986
$784$	8528.62	0.388512
$785$	−1985.99	−0.0902969
$786$	13615.2	0.617861
$787$	−838.861	−0.0379951	−0.0189976	−	0.999820i	$-0.506047\pi$
$787$	−838.861	−0.0379951	−0.0189976	+	0.999820i	$0.506047\pi$
$788$	1911.12	0.0863972
$789$	2793.37	0.126042
$790$	−31459.0	−1.41679
$791$	−12690.1	−0.570426
$792$	1635.07	0.0733584
$793$	0	0
$794$	−13707.3	−0.612661
$795$	46745.8	2.08541
$796$	6826.64	0.303975
$797$	13620.5	0.605350	0.302675	−	0.953094i	$-0.402120\pi$
$797$	13620.5	0.605350	0.302675	+	0.953094i	$0.402120\pi$
$798$	5836.61	0.258914
$799$	−5820.75	−0.257726
$800$	−20867.7	−0.922232
$801$	9805.80	0.432548
$802$	−32960.1	−1.45120
$803$	8276.16	0.363710
$804$	4373.45	0.191840
$805$	−20593.1	−0.901627
$806$	0	0
$807$	37592.8	1.63981
$808$	−13604.7	−0.592342
$809$	−7262.77	−0.315631	−0.157816	−	0.987469i	$-0.550445\pi$
$809$	−7262.77	−0.315631	−0.157816	+	0.987469i	$0.550445\pi$
$810$	23525.3	1.02049
$811$	−28239.3	−1.22271	−0.611354	−	0.791358i	$-0.709375\pi$
$811$	−28239.3	−1.22271	−0.611354	+	0.791358i	$0.709375\pi$
$812$	266.110	0.0115008
$813$	30606.3	1.32031
$814$	−1885.72	−0.0811973
$815$	−7661.91	−0.329307
$816$	24628.3	1.05657
$817$	−11419.8	−0.489018
$818$	−22540.1	−0.963443
$819$	0	0
$820$	5868.26	0.249913
$821$	16336.3	0.694448	0.347224	−	0.937782i	$-0.387124\pi$
$821$	16336.3	0.694448	0.347224	+	0.937782i	$0.387124\pi$
$822$	−5581.96	−0.236853
$823$	11880.0	0.503171	0.251585	−	0.967835i	$-0.419048\pi$
$823$	11880.0	0.503171	0.251585	+	0.967835i	$0.419048\pi$
$824$	−9730.93	−0.411399
$825$	10881.9	0.459223
$826$	−12213.0	−0.514460
$827$	−20324.5	−0.854598	−0.427299	−	0.904110i	$-0.640535\pi$
$827$	−20324.5	−0.854598	−0.427299	+	0.904110i	$0.640535\pi$
$828$	−1266.93	−0.0531749
$829$	−37819.8	−1.58448	−0.792241	−	0.610208i	$-0.791086\pi$
$829$	−37819.8	−1.58448	−0.792241	+	0.610208i	$0.791086\pi$
$830$	−11284.1	−0.471901
$831$	898.038	0.0374881
$832$	0	0
$833$	−26615.8	−1.10706
$834$	33651.5	1.39719
$835$	−13674.9	−0.566756
$836$	1094.07	0.0452622
$837$	−48007.3	−1.98253
$838$	−21445.4	−0.884034
$839$	−6680.46	−0.274893	−0.137446	−	0.990509i	$-0.543889\pi$
$839$	−6680.46	−0.274893	−0.137446	+	0.990509i	$0.543889\pi$
$840$	−24361.2	−1.00064
$841$	−24283.0	−0.995652
$842$	−6574.02	−0.269069
$843$	23289.5	0.951523
$844$	−10379.9	−0.423331
$845$	0	0
$846$	−654.400	−0.0265943
$847$	1419.41	0.0575814
$848$	22961.0	0.929816
$849$	10493.2	0.424178
$850$	−67435.4	−2.72119
$851$	6767.31	0.272597
$852$	−5266.71	−0.211778
$853$	41446.2	1.66365	0.831824	−	0.555039i	$-0.187297\pi$
$853$	41446.2	1.66365	0.831824	+	0.555039i	$0.187297\pi$
$854$	12213.1	0.489372
$855$	−5045.81	−0.201828
$856$	32013.6	1.27827
$857$	7849.20	0.312863	0.156432	−	0.987689i	$-0.450001\pi$
$857$	7849.20	0.312863	0.156432	+	0.987689i	$0.450001\pi$
$858$	0	0
$859$	5721.60	0.227263	0.113631	−	0.993523i	$-0.463752\pi$
$859$	5721.60	0.227263	0.113631	+	0.993523i	$0.463752\pi$
$860$	10291.3	0.408061
$861$	7743.71	0.306510
$862$	4969.25	0.196349
$863$	−21276.0	−0.839215	−0.419607	−	0.907706i	$-0.637832\pi$
$863$	−21276.0	−0.839215	−0.419607	+	0.907706i	$0.637832\pi$
$864$	−14605.4	−0.575098
$865$	−16658.2	−0.654792
$866$	18078.1	0.709375
$867$	−54372.0	−2.12984
$868$	8200.96	0.320690
$869$	−7781.60	−0.303766
$870$	−2095.99	−0.0816790
$871$	0	0
$872$	53316.9	2.07057
$873$	9341.62	0.362160
$874$	10332.1	0.399874
$875$	19746.0	0.762898
$876$	−7586.14	−0.292593
$877$	5613.91	0.216156	0.108078	−	0.994142i	$-0.465530\pi$
$877$	5613.91	0.216156	0.108078	+	0.994142i	$0.465530\pi$
$878$	8878.71	0.341278
$879$	−20924.8	−0.802930
$880$	8436.30	0.323168
$881$	41056.7	1.57007	0.785037	−	0.619449i	$-0.212644\pi$
$881$	41056.7	1.57007	0.785037	+	0.619449i	$0.212644\pi$
$882$	−2992.29	−0.114235
$883$	26195.9	0.998371	0.499185	−	0.866495i	$-0.333633\pi$
$883$	26195.9	0.998371	0.499185	+	0.866495i	$0.333633\pi$
$884$	0	0
$885$	−36554.7	−1.38844
$886$	−2054.55	−0.0779051
$887$	−39654.8	−1.50110	−0.750551	−	0.660813i	$-0.770212\pi$
$887$	−39654.8	−1.50110	−0.750551	+	0.660813i	$0.770212\pi$
$888$	8005.59	0.302534
$889$	−2879.46	−0.108632
$890$	72066.9	2.71426
$891$	5819.16	0.218798
$892$	−3805.34	−0.142839
$893$	−2028.03	−0.0759971
$894$	18120.9	0.677913
$895$	36648.8	1.36875
$896$	−6887.35	−0.256797
$897$	0	0
$898$	22752.9	0.845517
$899$	3267.98	0.121238
$900$	2881.01	0.106704
$901$	−71655.7	−2.64950
$902$	−3819.80	−0.141004
$903$	13580.4	0.500473
$904$	−26574.9	−0.977730
$905$	−20518.5	−0.753655
$906$	23494.9	0.861552
$907$	−1095.45	−0.0401036	−0.0200518	−	0.999799i	$-0.506383\pi$
$907$	−1095.45	−0.0401036	−0.0200518	+	0.999799i	$0.506383\pi$
$908$	5741.96	0.209861
$909$	3351.01	0.122273
$910$	0	0
$911$	3036.59	0.110436	0.0552178	−	0.998474i	$-0.482415\pi$
$911$	3036.59	0.110436	0.0552178	+	0.998474i	$0.482415\pi$
$912$	8580.84	0.311557
$913$	−2791.21	−0.101178
$914$	−13244.3	−0.479302
$915$	36555.0	1.32074
$916$	10471.9	0.377730
$917$	14493.0	0.521922
$918$	−47198.2	−1.69692
$919$	−37684.4	−1.35266	−0.676329	−	0.736600i	$-0.736430\pi$
$919$	−37684.4	−1.35266	−0.676329	+	0.736600i	$0.736430\pi$
$920$	−43124.9	−1.54542
$921$	−42790.2	−1.53093
$922$	−3728.91	−0.133194
$923$	0	0
$924$	−1301.06	−0.0463224
$925$	−15389.0	−0.547012
$926$	−31869.1	−1.13098
$927$	2396.85	0.0849222
$928$	994.224	0.0351692
$929$	45013.6	1.58972	0.794859	−	0.606794i	$-0.207545\pi$
$929$	45013.6	1.58972	0.794859	+	0.606794i	$0.207545\pi$
$930$	−64594.2	−2.27756
$931$	−9273.30	−0.326445
$932$	−4297.17	−0.151029
$933$	21764.1	0.763691
$934$	42248.4	1.48010
$935$	−26327.7	−0.920863
$936$	0	0
$937$	−36777.5	−1.28225	−0.641125	−	0.767437i	$-0.721532\pi$
$937$	−36777.5	−1.28225	−0.641125	+	0.767437i	$0.721532\pi$
$938$	−12250.8	−0.426443
$939$	−26627.7	−0.925412
$940$	1827.63	0.0634157
$941$	51102.8	1.77035	0.885176	−	0.465255i	$-0.154038\pi$
$941$	51102.8	1.77035	0.885176	+	0.465255i	$0.154038\pi$
$942$	−1184.95	−0.0409849
$943$	13708.2	0.473382
$944$	−17955.2	−0.619060
$945$	32775.7	1.12825
$946$	−6698.91	−0.230233
$947$	23954.4	0.821979	0.410989	−	0.911640i	$-0.365183\pi$
$947$	23954.4	0.821979	0.410989	+	0.911640i	$0.365183\pi$
$948$	7132.81	0.244370
$949$	0	0
$950$	−23495.4	−0.802413
$951$	41554.5	1.41693
$952$	37342.8	1.27131
$953$	−39285.1	−1.33533	−0.667665	−	0.744462i	$-0.732706\pi$
$953$	−39285.1	−1.33533	−0.667665	+	0.744462i	$0.732706\pi$
$954$	−8055.92	−0.273396
$955$	−45811.4	−1.55227
$956$	−7503.47	−0.253849
$957$	−518.458	−0.0175124
$958$	−19375.1	−0.653425
$959$	−5941.84	−0.200075
$960$	−47733.9	−1.60480
$961$	70921.6	2.38064
$962$	0	0
$963$	−7885.36	−0.263865
$964$	−3037.35	−0.101480
$965$	−73198.6	−2.44181
$966$	−12287.0	−0.409240
$967$	35410.9	1.17760	0.588799	−	0.808280i	$-0.299601\pi$
$967$	35410.9	1.17760	0.588799	+	0.808280i	$0.299601\pi$
$968$	2972.45	0.0986964
$969$	−26778.7	−0.887778
$970$	68655.4	2.27257
$971$	32519.4	1.07476	0.537382	−	0.843339i	$-0.319413\pi$
$971$	32519.4	1.07476	0.537382	+	0.843339i	$0.319413\pi$
$972$	3663.69	0.120898
$973$	35821.1	1.18024
$974$	−21720.2	−0.714539
$975$	0	0
$976$	17955.4	0.588871
$977$	−52184.7	−1.70884	−0.854420	−	0.519583i	$-0.826087\pi$
$977$	−52184.7	−1.70884	−0.854420	+	0.519583i	$0.826087\pi$
$978$	−4571.52	−0.149469
$979$	17826.3	0.581950
$980$	8356.97	0.272402
$981$	−13132.6	−0.427413
$982$	−43309.5	−1.40739
$983$	−2540.86	−0.0824425	−0.0412212	−	0.999150i	$-0.513125\pi$
$983$	−2540.86	−0.0824425	−0.0412212	+	0.999150i	$0.513125\pi$
$984$	16216.5	0.525368
$985$	−16023.3	−0.518320
$986$	3212.90	0.103772
$987$	2411.73	0.0777773
$988$	0	0
$989$	24040.4	0.772943
$990$	−2959.90	−0.0950220
$991$	15748.2	0.504802	0.252401	−	0.967623i	$-0.418780\pi$
$991$	15748.2	0.504802	0.252401	+	0.967623i	$0.418780\pi$
$992$	30640.0	0.980666
$993$	−9736.18	−0.311146
$994$	14753.0	0.470762
$995$	−57236.1	−1.82362
$996$	2558.49	0.0813944
$997$	−20786.2	−0.660285	−0.330142	−	0.943931i	$-0.607097\pi$
$997$	−20786.2	−0.660285	−0.330142	+	0.943931i	$0.607097\pi$
$998$	7179.20	0.227709
$999$	−10770.8	−0.341113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.12	yes	39
13.12	even	2		1859.4.a.n.1.28	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.28	✓	39	13.12	even	2
1859.4.a.o.1.12	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)

\(f(q)\)	\(=\)	\(q-2.40771 q^{2} -4.57703 q^{3} -2.20293 q^{4} +18.4699 q^{5} +11.0201 q^{6} +11.7306 q^{7} +24.5657 q^{8} -6.05084 q^{9} +O(q^{10})\)	\(q-2.40771 q^{2} -4.57703 q^{3} -2.20293 q^{4} +18.4699 q^{5} +11.0201 q^{6} +11.7306 q^{7} +24.5657 q^{8} -6.05084 q^{9} -44.4701 q^{10} -11.0000 q^{11} +10.0829 q^{12} -28.2440 q^{14} -84.5371 q^{15} -41.5236 q^{16} +129.585 q^{17} +14.5687 q^{18} +45.1493 q^{19} -40.6879 q^{20} -53.6915 q^{21} +26.4848 q^{22} -95.0462 q^{23} -112.438 q^{24} +216.137 q^{25} +151.275 q^{27} -25.8418 q^{28} -10.2976 q^{29} +203.541 q^{30} -317.352 q^{31} -96.5488 q^{32} +50.3473 q^{33} -312.004 q^{34} +216.664 q^{35} +13.3296 q^{36} -71.2002 q^{37} -108.706 q^{38} +453.726 q^{40} -144.226 q^{41} +129.273 q^{42} -252.934 q^{43} +24.2323 q^{44} -111.758 q^{45} +228.844 q^{46} -44.9183 q^{47} +190.055 q^{48} -205.392 q^{49} -520.394 q^{50} -593.115 q^{51} -552.962 q^{53} -364.225 q^{54} -203.169 q^{55} +288.172 q^{56} -206.649 q^{57} +24.7937 q^{58} +432.410 q^{59} +186.230 q^{60} -432.414 q^{61} +764.093 q^{62} -70.9803 q^{63} +564.650 q^{64} -121.222 q^{66} +433.750 q^{67} -285.467 q^{68} +435.029 q^{69} -521.663 q^{70} -522.342 q^{71} -148.643 q^{72} -752.378 q^{73} +171.429 q^{74} -989.263 q^{75} -99.4609 q^{76} -129.037 q^{77} +707.418 q^{79} -766.937 q^{80} -529.015 q^{81} +347.255 q^{82} +253.746 q^{83} +118.279 q^{84} +2393.42 q^{85} +608.992 q^{86} +47.1326 q^{87} -270.223 q^{88} -1620.57 q^{89} +269.082 q^{90} +209.380 q^{92} +1452.53 q^{93} +108.150 q^{94} +833.902 q^{95} +441.906 q^{96} -1543.85 q^{97} +494.524 q^{98} +66.5593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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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