LMFDB - Embedded newform 1859.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 34x^{4} - 26x^{3} + 249x^{2} + 274x - 200 $ x^6 - 34x^4 - 26x^3 + 249x^2 + 274x - 200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.30499$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.30499 q^{2} +0.708355 q^{3} +2.92295 q^{4} +6.96953 q^{5} +2.34111 q^{6} -22.1312 q^{7} -16.7796 q^{8} -26.4982 q^{9} +O(q^{10})$	\(q+3.30499 q^{2} +0.708355 q^{3} +2.92295 q^{4} +6.96953 q^{5} +2.34111 q^{6} -22.1312 q^{7} -16.7796 q^{8} -26.4982 q^{9} +23.0342 q^{10} -11.0000 q^{11} +2.07049 q^{12} -73.1432 q^{14} +4.93690 q^{15} -78.8400 q^{16} +86.4814 q^{17} -87.5764 q^{18} +151.481 q^{19} +20.3716 q^{20} -15.6767 q^{21} -36.3549 q^{22} +3.92554 q^{23} -11.8859 q^{24} -76.4256 q^{25} -37.8958 q^{27} -64.6882 q^{28} -216.373 q^{29} +16.3164 q^{30} +236.187 q^{31} -126.328 q^{32} -7.79191 q^{33} +285.820 q^{34} -154.244 q^{35} -77.4530 q^{36} +21.1940 q^{37} +500.644 q^{38} -116.946 q^{40} +23.9019 q^{41} -51.8114 q^{42} -276.726 q^{43} -32.1524 q^{44} -184.680 q^{45} +12.9739 q^{46} +336.941 q^{47} -55.8467 q^{48} +146.788 q^{49} -252.586 q^{50} +61.2595 q^{51} +473.478 q^{53} -125.245 q^{54} -76.6648 q^{55} +371.352 q^{56} +107.303 q^{57} -715.112 q^{58} -442.262 q^{59} +14.4303 q^{60} +839.880 q^{61} +780.597 q^{62} +586.436 q^{63} +213.206 q^{64} -25.7522 q^{66} -807.435 q^{67} +252.781 q^{68} +2.78068 q^{69} -509.774 q^{70} +962.098 q^{71} +444.630 q^{72} +1078.51 q^{73} +70.0461 q^{74} -54.1365 q^{75} +442.772 q^{76} +243.443 q^{77} -919.108 q^{79} -549.478 q^{80} +688.609 q^{81} +78.9954 q^{82} +257.516 q^{83} -45.8222 q^{84} +602.735 q^{85} -914.576 q^{86} -153.269 q^{87} +184.576 q^{88} -14.5883 q^{89} -610.366 q^{90} +11.4741 q^{92} +167.305 q^{93} +1113.59 q^{94} +1055.75 q^{95} -89.4854 q^{96} +1534.67 q^{97} +485.132 q^{98} +291.481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} - 52 q^{10} - 66 q^{11} - 19 q^{12} - 120 q^{14} + 23 q^{15} + 26 q^{16} - 117 q^{17} + 27 q^{18} + 67 q^{19} - 10 q^{20} - 19 q^{21} - 66 q^{22} - 158 q^{23} + 609 q^{24} - 234 q^{25} - 531 q^{27} + 670 q^{28} - 145 q^{29} - 211 q^{30} + 58 q^{31} + 364 q^{32} + 66 q^{33} - 43 q^{34} - 210 q^{35} + 383 q^{36} + 753 q^{37} + 738 q^{38} + 4 q^{40} + 232 q^{41} + 1593 q^{42} - 390 q^{43} - 286 q^{44} + 107 q^{45} - 5 q^{46} + 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} + 363 q^{51} - 65 q^{53} - 1917 q^{54} - 88 q^{55} + 1816 q^{56} + 1657 q^{57} + 1685 q^{58} - 1735 q^{59} - 871 q^{60} + 421 q^{61} + 3394 q^{62} + 125 q^{63} + 570 q^{64} - 165 q^{66} + 703 q^{67} + 209 q^{68} - 272 q^{69} - 1968 q^{70} - 445 q^{71} - 1035 q^{72} + 2340 q^{73} + 1135 q^{74} + 1941 q^{75} + 1208 q^{76} - 583 q^{77} - 1234 q^{79} - 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} + 1146 q^{86} + 2462 q^{87} - 396 q^{88} + 442 q^{89} + 113 q^{90} + 2737 q^{92} + 982 q^{93} + 2733 q^{94} - 504 q^{95} + 1153 q^{96} + 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 - 52 * q^10 - 66 * q^11 - 19 * q^12 - 120 * q^14 + 23 * q^15 + 26 * q^16 - 117 * q^17 + 27 * q^18 + 67 * q^19 - 10 * q^20 - 19 * q^21 - 66 * q^22 - 158 * q^23 + 609 * q^24 - 234 * q^25 - 531 * q^27 + 670 * q^28 - 145 * q^29 - 211 * q^30 + 58 * q^31 + 364 * q^32 + 66 * q^33 - 43 * q^34 - 210 * q^35 + 383 * q^36 + 753 * q^37 + 738 * q^38 + 4 * q^40 + 232 * q^41 + 1593 * q^42 - 390 * q^43 - 286 * q^44 + 107 * q^45 - 5 * q^46 + 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 + 363 * q^51 - 65 * q^53 - 1917 * q^54 - 88 * q^55 + 1816 * q^56 + 1657 * q^57 + 1685 * q^58 - 1735 * q^59 - 871 * q^60 + 421 * q^61 + 3394 * q^62 + 125 * q^63 + 570 * q^64 - 165 * q^66 + 703 * q^67 + 209 * q^68 - 272 * q^69 - 1968 * q^70 - 445 * q^71 - 1035 * q^72 + 2340 * q^73 + 1135 * q^74 + 1941 * q^75 + 1208 * q^76 - 583 * q^77 - 1234 * q^79 - 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 + 1146 * q^86 + 2462 * q^87 - 396 * q^88 + 442 * q^89 + 113 * q^90 + 2737 * q^92 + 982 * q^93 + 2733 * q^94 - 504 * q^95 + 1153 * q^96 + 2682 * q^97 - 2036 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.30499	1.16849	0.584245	−	0.811577i	$-0.301391\pi$
$2$	3.30499	1.16849	0.584245	+	0.811577i	$0.301391\pi$
$3$	0.708355	0.136323	0.0681615	−	0.997674i	$-0.478287\pi$
$3$	0.708355	0.136323	0.0681615	+	0.997674i	$0.478287\pi$
$4$	2.92295	0.365369
$5$	6.96953	0.623374	0.311687	−	0.950185i	$-0.399106\pi$
$5$	6.96953	0.623374	0.311687	+	0.950185i	$0.399106\pi$
$6$	2.34111	0.159292
$7$	−22.1312	−1.19497	−0.597485	−	0.801880i	$-0.703833\pi$
$7$	−22.1312	−1.19497	−0.597485	+	0.801880i	$0.703833\pi$
$8$	−16.7796	−0.741560
$9$	−26.4982	−0.981416
$10$	23.0342	0.728406
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	2.07049	0.0498082
$13$	0	0
$13$	0	0
$14$	−73.1432	−1.39631
$15$	4.93690	0.0849802
$16$	−78.8400	−1.23187
$17$	86.4814	1.23381	0.616906	−	0.787037i	$-0.288386\pi$
$17$	86.4814	1.23381	0.616906	+	0.787037i	$0.288386\pi$
$18$	−87.5764	−1.14677
$19$	151.481	1.82906	0.914532	−	0.404513i	$-0.132559\pi$
$19$	151.481	1.82906	0.914532	+	0.404513i	$0.132559\pi$
$20$	20.3716	0.227761
$21$	−15.6767	−0.162902
$22$	−36.3549	−0.352313
$23$	3.92554	0.0355883	0.0177942	−	0.999842i	$-0.494336\pi$
$23$	3.92554	0.0355883	0.0177942	+	0.999842i	$0.494336\pi$
$24$	−11.8859	−0.101092
$25$	−76.4256	−0.611405
$26$	0	0
$27$	−37.8958	−0.270113
$28$	−64.6882	−0.436605
$29$	−216.373	−1.38550	−0.692751	−	0.721177i	$-0.743601\pi$
$29$	−216.373	−1.38550	−0.692751	+	0.721177i	$0.743601\pi$
$30$	16.3164	0.0992985
$31$	236.187	1.36840	0.684202	−	0.729293i	$-0.260151\pi$
$31$	236.187	1.36840	0.684202	+	0.729293i	$0.260151\pi$
$32$	−126.328	−0.697872
$33$	−7.79191	−0.0411029
$34$	285.820	1.44170
$35$	−154.244	−0.744913
$36$	−77.4530	−0.358579
$37$	21.1940	0.0941697	0.0470848	−	0.998891i	$-0.485007\pi$
$37$	21.1940	0.0941697	0.0470848	+	0.998891i	$0.485007\pi$
$38$	500.644	2.13724
$39$	0	0
$40$	−116.946	−0.462269
$41$	23.9019	0.0910450	0.0455225	−	0.998963i	$-0.485505\pi$
$41$	23.9019	0.0910450	0.0455225	+	0.998963i	$0.485505\pi$
$42$	−51.8114	−0.190349
$43$	−276.726	−0.981403	−0.490701	−	0.871328i	$-0.663259\pi$
$43$	−276.726	−0.981403	−0.490701	+	0.871328i	$0.663259\pi$
$44$	−32.1524	−0.110163
$45$	−184.680	−0.611789
$46$	12.9739	0.0415846
$47$	336.941	1.04570	0.522851	−	0.852424i	$-0.324869\pi$
$47$	336.941	1.04570	0.522851	+	0.852424i	$0.324869\pi$
$48$	−55.8467	−0.167933
$49$	146.788	0.427953
$50$	−252.586	−0.714421
$51$	61.2595	0.168197
$52$	0	0
$53$	473.478	1.22712	0.613558	−	0.789650i	$-0.289738\pi$
$53$	473.478	1.22712	0.613558	+	0.789650i	$0.289738\pi$
$54$	−125.245	−0.315624
$55$	−76.6648	−0.187954
$56$	371.352	0.886142
$57$	107.303	0.249344
$58$	−715.112	−1.61894
$59$	−442.262	−0.975891	−0.487945	−	0.872874i	$-0.662253\pi$
$59$	−442.262	−0.975891	−0.487945	+	0.872874i	$0.662253\pi$
$60$	14.4303	0.0310491
$61$	839.880	1.76288	0.881440	−	0.472296i	$-0.156575\pi$
$61$	839.880	1.76288	0.881440	+	0.472296i	$0.156575\pi$
$62$	780.597	1.59897
$63$	586.436	1.17276
$64$	213.206	0.416418
$65$	0	0
$66$	−25.7522	−0.0480284
$67$	−807.435	−1.47230	−0.736148	−	0.676820i	$-0.763357\pi$
$67$	−807.435	−1.47230	−0.736148	+	0.676820i	$0.763357\pi$
$68$	252.781	0.450796
$69$	2.78068	0.00485151
$70$	−509.774	−0.870423
$71$	962.098	1.60817	0.804085	−	0.594515i	$-0.202656\pi$
$71$	962.098	1.60817	0.804085	+	0.594515i	$0.202656\pi$
$72$	444.630	0.727779
$73$	1078.51	1.72918	0.864590	−	0.502478i	$-0.167578\pi$
$73$	1078.51	1.72918	0.864590	+	0.502478i	$0.167578\pi$
$74$	70.0461	0.110036
$75$	−54.1365	−0.0833486
$76$	442.772	0.668283
$77$	243.443	0.360297
$78$	0	0
$79$	−919.108	−1.30896	−0.654479	−	0.756080i	$-0.727112\pi$
$79$	−919.108	−1.30896	−0.654479	+	0.756080i	$0.727112\pi$
$80$	−549.478	−0.767918
$81$	688.609	0.944593
$82$	78.9954	0.106385
$83$	257.516	0.340555	0.170278	−	0.985396i	$-0.445534\pi$
$83$	257.516	0.340555	0.170278	+	0.985396i	$0.445534\pi$
$84$	−45.8222	−0.0595192
$85$	602.735	0.769126
$86$	−914.576	−1.14676
$87$	−153.269	−0.188876
$88$	184.576	0.223589
$89$	−14.5883	−0.0173748	−0.00868738	−	0.999962i	$-0.502765\pi$
$89$	−14.5883	−0.0173748	−0.00868738	+	0.999962i	$0.502765\pi$
$90$	−610.366	−0.714869
$91$	0	0
$92$	11.4741	0.0130029
$93$	167.305	0.186545
$94$	1113.59	1.22189
$95$	1055.75	1.14019
$96$	−89.4854	−0.0951361
$97$	1534.67	1.60641	0.803206	−	0.595702i	$-0.203126\pi$
$97$	1534.67	1.60641	0.803206	+	0.595702i	$0.203126\pi$
$98$	485.132	0.500059
$99$	291.481	0.295908
$100$	−223.388	−0.223388
$101$	−684.444	−0.674304	−0.337152	−	0.941450i	$-0.609464\pi$
$101$	−684.444	−0.674304	−0.337152	+	0.941450i	$0.609464\pi$
$102$	202.462	0.196537
$103$	1201.92	1.14979	0.574896	−	0.818227i	$-0.305043\pi$
$103$	1201.92	1.14979	0.574896	+	0.818227i	$0.305043\pi$
$104$	0	0
$105$	−109.259	−0.101549
$106$	1564.84	1.43387
$107$	1833.16	1.65624	0.828122	−	0.560548i	$-0.189410\pi$
$107$	1833.16	1.65624	0.828122	+	0.560548i	$0.189410\pi$
$108$	−110.767	−0.0986907
$109$	1835.74	1.61314	0.806568	−	0.591142i	$-0.201323\pi$
$109$	1835.74	1.61314	0.806568	+	0.591142i	$0.201323\pi$
$110$	−253.376	−0.219623
$111$	15.0129	0.0128375
$112$	1744.82	1.47205
$113$	−281.017	−0.233946	−0.116973	−	0.993135i	$-0.537319\pi$
$113$	−281.017	−0.233946	−0.116973	+	0.993135i	$0.537319\pi$
$114$	354.634	0.291355
$115$	27.3592	0.0221848
$116$	−632.449	−0.506219
$117$	0	0
$118$	−1461.67	−1.14032
$119$	−1913.93	−1.47437
$120$	−82.8392	−0.0630179
$121$	121.000	0.0909091
$122$	2775.80	2.05991
$123$	16.9310	0.0124115
$124$	690.364	0.499972
$125$	−1403.84	−1.00451
$126$	1938.17	1.37036
$127$	484.188	0.338305	0.169152	−	0.985590i	$-0.445897\pi$
$127$	484.188	0.338305	0.169152	+	0.985590i	$0.445897\pi$
$128$	1715.27	1.18445
$129$	−196.020	−0.133788
$130$	0	0
$131$	−1636.65	−1.09156	−0.545781	−	0.837928i	$-0.683767\pi$
$131$	−1636.65	−1.09156	−0.545781	+	0.837928i	$0.683767\pi$
$132$	−22.7753	−0.0150177
$133$	−3352.46	−2.18568
$134$	−2668.56	−1.72036
$135$	−264.116	−0.168381
$136$	−1451.12	−0.914946
$137$	−977.197	−0.609398	−0.304699	−	0.952449i	$-0.598556\pi$
$137$	−977.197	−0.609398	−0.304699	+	0.952449i	$0.598556\pi$
$138$	9.19010	0.00566894
$139$	2014.13	1.22904	0.614519	−	0.788902i	$-0.289350\pi$
$139$	2014.13	1.22904	0.614519	+	0.788902i	$0.289350\pi$
$140$	−450.847	−0.272168
$141$	238.674	0.142553
$142$	3179.72	1.87913
$143$	0	0
$144$	2089.12	1.20898
$145$	−1508.02	−0.863685
$146$	3564.47	2.02053
$147$	103.978	0.0583398
$148$	61.9491	0.0344067
$149$	43.6199	0.0239831	0.0119915	−	0.999928i	$-0.496183\pi$
$149$	43.6199	0.0239831	0.0119915	+	0.999928i	$0.496183\pi$
$150$	−178.921	−0.0973920
$151$	684.254	0.368767	0.184383	−	0.982854i	$-0.440971\pi$
$151$	684.254	0.368767	0.184383	+	0.982854i	$0.440971\pi$
$152$	−2541.80	−1.35636
$153$	−2291.60	−1.21088
$154$	804.575	0.421003
$155$	1646.12	0.853027
$156$	0	0
$157$	580.088	0.294879	0.147440	−	0.989071i	$-0.452897\pi$
$157$	580.088	0.294879	0.147440	+	0.989071i	$0.452897\pi$
$158$	−3037.64	−1.52951
$159$	335.390	0.167284
$160$	−880.450	−0.435035
$161$	−86.8767	−0.0425270
$162$	2275.84	1.10375
$163$	3767.67	1.81047	0.905234	−	0.424913i	$-0.139695\pi$
$163$	3767.67	1.81047	0.905234	+	0.424913i	$0.139695\pi$
$164$	69.8639	0.0332650
$165$	−54.3059	−0.0256225
$166$	851.088	0.397935
$167$	−487.617	−0.225946	−0.112973	−	0.993598i	$-0.536037\pi$
$167$	−487.617	−0.225946	−0.112973	+	0.993598i	$0.536037\pi$
$168$	263.049	0.120802
$169$	0	0
$170$	1992.03	0.898716
$171$	−4013.99	−1.79507
$172$	−808.856	−0.358574
$173$	−489.162	−0.214973	−0.107486	−	0.994207i	$-0.534280\pi$
$173$	−489.162	−0.214973	−0.107486	+	0.994207i	$0.534280\pi$
$174$	−506.553	−0.220699
$175$	1691.39	0.730611
$176$	867.240	0.371424
$177$	−313.278	−0.133036
$178$	−48.2141	−0.0203022
$179$	2505.10	1.04603	0.523017	−	0.852322i	$-0.324806\pi$
$179$	2505.10	1.04603	0.523017	+	0.852322i	$0.324806\pi$
$180$	−539.811	−0.223529
$181$	−439.967	−0.180677	−0.0903383	−	0.995911i	$-0.528795\pi$
$181$	−439.967	−0.180677	−0.0903383	+	0.995911i	$0.528795\pi$
$182$	0	0
$183$	594.934	0.240321
$184$	−65.8689	−0.0263909
$185$	147.713	0.0587029
$186$	552.940	0.217976
$187$	−951.295	−0.372008
$188$	984.863	0.382066
$189$	838.677	0.322776
$190$	3489.26	1.33230
$191$	−1251.19	−0.473996	−0.236998	−	0.971510i	$-0.576163\pi$
$191$	−1251.19	−0.473996	−0.236998	+	0.971510i	$0.576163\pi$
$192$	151.025	0.0567673
$193$	−2070.87	−0.772355	−0.386178	−	0.922424i	$-0.626205\pi$
$193$	−2070.87	−0.772355	−0.386178	+	0.922424i	$0.626205\pi$
$194$	5072.06	1.87708
$195$	0	0
$196$	429.053	0.156361
$197$	−4079.42	−1.47536	−0.737682	−	0.675148i	$-0.764080\pi$
$197$	−4079.42	−1.47536	−0.737682	+	0.675148i	$0.764080\pi$
$198$	963.340	0.345766
$199$	−4268.20	−1.52043	−0.760213	−	0.649674i	$-0.774905\pi$
$199$	−4268.20	−1.52043	−0.760213	+	0.649674i	$0.774905\pi$
$200$	1282.39	0.453394
$201$	−571.951	−0.200708
$202$	−2262.08	−0.787918
$203$	4788.59	1.65563
$204$	179.058	0.0614539
$205$	166.585	0.0567551
$206$	3972.33	1.34352
$207$	−104.020	−0.0349269
$208$	0	0
$209$	−1666.30	−0.551484
$210$	−361.101	−0.118659
$211$	2592.23	0.845765	0.422882	−	0.906185i	$-0.361018\pi$
$211$	2592.23	0.845765	0.422882	+	0.906185i	$0.361018\pi$
$212$	1383.95	0.448350
$213$	681.507	0.219231
$214$	6058.57	1.93530
$215$	−1928.65	−0.611781
$216$	635.875	0.200305
$217$	−5227.10	−1.63520
$218$	6067.09	1.88493
$219$	763.969	0.235727
$220$	−224.087	−0.0686726
$221$	0	0
$222$	49.6175	0.0150005
$223$	−2961.82	−0.889409	−0.444704	−	0.895677i	$-0.646691\pi$
$223$	−2961.82	−0.889409	−0.444704	+	0.895677i	$0.646691\pi$
$224$	2795.79	0.833937
$225$	2025.14	0.600043
$226$	−928.758	−0.273363
$227$	−1015.73	−0.296989	−0.148494	−	0.988913i	$-0.547443\pi$
$227$	−1015.73	−0.296989	−0.148494	+	0.988913i	$0.547443\pi$
$228$	313.640	0.0911023
$229$	−1098.76	−0.317067	−0.158533	−	0.987354i	$-0.550677\pi$
$229$	−1098.76	−0.317067	−0.158533	+	0.987354i	$0.550677\pi$
$230$	90.4217	0.0259227
$231$	172.444	0.0491168
$232$	3630.66	1.02743
$233$	−6467.39	−1.81842	−0.909212	−	0.416334i	$-0.863315\pi$
$233$	−6467.39	−1.81842	−0.909212	+	0.416334i	$0.863315\pi$
$234$	0	0
$235$	2348.32	0.651863
$236$	−1292.71	−0.356560
$237$	−651.055	−0.178441
$238$	−6325.52	−1.72278
$239$	−3106.94	−0.840884	−0.420442	−	0.907320i	$-0.638125\pi$
$239$	−3106.94	−0.840884	−0.420442	+	0.907320i	$0.638125\pi$
$240$	−389.225	−0.104685
$241$	−5115.98	−1.36742	−0.683712	−	0.729752i	$-0.739635\pi$
$241$	−5115.98	−1.36742	−0.683712	+	0.729752i	$0.739635\pi$
$242$	399.904	0.106226
$243$	1510.96	0.398882
$244$	2454.93	0.644101
$245$	1023.04	0.266775
$246$	55.9568	0.0145027
$247$	0	0
$248$	−3963.13	−1.01475
$249$	182.413	0.0464255
$250$	−4639.68	−1.17376
$251$	4701.10	1.18219	0.591097	−	0.806600i	$-0.298695\pi$
$251$	4701.10	1.18219	0.591097	+	0.806600i	$0.298695\pi$
$252$	1714.12	0.428491
$253$	−43.1809	−0.0107303
$254$	1600.24	0.395306
$255$	426.950	0.104850
$256$	3963.30	0.967603
$257$	2559.43	0.621217	0.310608	−	0.950538i	$-0.399467\pi$
$257$	2559.43	0.621217	0.310608	+	0.950538i	$0.399467\pi$
$258$	−647.845	−0.156330
$259$	−469.049	−0.112530
$260$	0	0
$261$	5733.52	1.35975
$262$	−5409.10	−1.27548
$263$	−497.687	−0.116687	−0.0583435	−	0.998297i	$-0.518582\pi$
$263$	−497.687	−0.116687	−0.0583435	+	0.998297i	$0.518582\pi$
$264$	130.745	0.0304803
$265$	3299.92	0.764952
$266$	−11079.8	−2.55394
$267$	−10.3337	−0.00236858
$268$	−2360.09	−0.537931
$269$	−1973.66	−0.447347	−0.223673	−	0.974664i	$-0.571805\pi$
$269$	−1973.66	−0.447347	−0.223673	+	0.974664i	$0.571805\pi$
$270$	−872.899	−0.196752
$271$	−5490.35	−1.23068	−0.615341	−	0.788261i	$-0.710982\pi$
$271$	−5490.35	−1.23068	−0.615341	+	0.788261i	$0.710982\pi$
$272$	−6818.19	−1.51990
$273$	0	0
$274$	−3229.63	−0.712076
$275$	840.682	0.184346
$276$	8.12777	0.00177259
$277$	−1346.91	−0.292160	−0.146080	−	0.989273i	$-0.546666\pi$
$277$	−1346.91	−0.292160	−0.146080	+	0.989273i	$0.546666\pi$
$278$	6656.68	1.43612
$279$	−6258.55	−1.34297
$280$	2588.15	0.552398
$281$	5762.37	1.22333	0.611663	−	0.791119i	$-0.290501\pi$
$281$	5762.37	1.22333	0.611663	+	0.791119i	$0.290501\pi$
$282$	788.816	0.166572
$283$	266.842	0.0560498	0.0280249	−	0.999607i	$-0.491078\pi$
$283$	266.842	0.0560498	0.0280249	+	0.999607i	$0.491078\pi$
$284$	2812.16	0.587575
$285$	747.849	0.155434
$286$	0	0
$287$	−528.976	−0.108796
$288$	3347.48	0.684903
$289$	2566.03	0.522293
$290$	−4983.99	−1.00921
$291$	1087.09	0.218991
$292$	3152.43	0.631788
$293$	3929.28	0.783451	0.391726	−	0.920082i	$-0.371878\pi$
$293$	3929.28	0.783451	0.391726	+	0.920082i	$0.371878\pi$
$294$	343.646	0.0681695
$295$	−3082.36	−0.608345
$296$	−355.627	−0.0698325
$297$	416.853	0.0814420
$298$	144.163	0.0280240
$299$	0	0
$300$	−158.238	−0.0304530
$301$	6124.26	1.17275
$302$	2261.45	0.430901
$303$	−484.830	−0.0919232
$304$	−11942.8	−2.25318
$305$	5853.57	1.09893
$306$	−7573.72	−1.41490
$307$	5187.96	0.964471	0.482236	−	0.876042i	$-0.339825\pi$
$307$	5187.96	0.964471	0.482236	+	0.876042i	$0.339825\pi$
$308$	711.571	0.131641
$309$	851.385	0.156743
$310$	5440.39	0.996754
$311$	6258.26	1.14107	0.570536	−	0.821272i	$-0.306735\pi$
$311$	6258.26	1.14107	0.570536	+	0.821272i	$0.306735\pi$
$312$	0	0
$313$	3614.08	0.652652	0.326326	−	0.945257i	$-0.394189\pi$
$313$	3614.08	0.652652	0.326326	+	0.945257i	$0.394189\pi$
$314$	1917.18	0.344564
$315$	4087.19	0.731069
$316$	−2686.51	−0.478253
$317$	−6.54772	−0.00116012	−0.000580058	−	1.00000i	$-0.500185\pi$
$317$	−6.54772	−0.00116012	−0.000580058		1.00000i	$0.500185\pi$
$318$	1108.46	0.195470
$319$	2380.11	0.417744
$320$	1485.94	0.259584
$321$	1298.53	0.225784
$322$	−287.126	−0.0496923
$323$	13100.3	2.25672
$324$	2012.77	0.345125
$325$	0	0
$326$	12452.1	2.11551
$327$	1300.35	0.219908
$328$	−401.064	−0.0675154
$329$	−7456.90	−1.24958
$330$	−179.481	−0.0299396
$331$	−3601.54	−0.598063	−0.299031	−	0.954243i	$-0.596664\pi$
$331$	−3601.54	−0.598063	−0.299031	+	0.954243i	$0.596664\pi$
$332$	752.707	0.124428
$333$	−561.605	−0.0924197
$334$	−1611.57	−0.264015
$335$	−5627.44	−0.917791
$336$	1235.95	0.200675
$337$	−4452.51	−0.719714	−0.359857	−	0.933008i	$-0.617174\pi$
$337$	−4452.51	−0.719714	−0.359857	+	0.933008i	$0.617174\pi$
$338$	0	0
$339$	−199.060	−0.0318922
$340$	1761.76	0.281015
$341$	−2598.06	−0.412589
$342$	−13266.2	−2.09752
$343$	4342.40	0.683579
$344$	4643.35	0.727769
$345$	19.3800	0.00302430
$346$	−1616.67	−0.251193
$347$	1275.09	0.197263	0.0986316	−	0.995124i	$-0.468553\pi$
$347$	1275.09	0.197263	0.0986316	+	0.995124i	$0.468553\pi$
$348$	−447.998	−0.0690093
$349$	6336.14	0.971822	0.485911	−	0.874008i	$-0.338488\pi$
$349$	6336.14	0.971822	0.485911	+	0.874008i	$0.338488\pi$
$350$	5590.02	0.853711
$351$	0	0
$352$	1389.61	0.210416
$353$	1652.39	0.249144	0.124572	−	0.992211i	$-0.460244\pi$
$353$	1652.39	0.249144	0.124572	+	0.992211i	$0.460244\pi$
$354$	−1035.38	−0.155452
$355$	6705.37	1.00249
$356$	−42.6408	−0.00634819
$357$	−1355.74	−0.200990
$358$	8279.33	1.22228
$359$	−1793.71	−0.263701	−0.131850	−	0.991270i	$-0.542092\pi$
$359$	−1793.71	−0.263701	−0.131850	+	0.991270i	$0.542092\pi$
$360$	3098.86	0.453679
$361$	16087.6	2.34548
$362$	−1454.09	−0.211119
$363$	85.7110	0.0123930
$364$	0	0
$365$	7516.72	1.07793
$366$	1966.25	0.280813
$367$	−1708.10	−0.242949	−0.121475	−	0.992595i	$-0.538762\pi$
$367$	−1708.10	−0.242949	−0.121475	+	0.992595i	$0.538762\pi$
$368$	−309.489	−0.0438403
$369$	−633.357	−0.0893530
$370$	488.188	0.0685938
$371$	−10478.6	−1.46637
$372$	489.023	0.0681577
$373$	12673.3	1.75925	0.879626	−	0.475667i	$-0.157793\pi$
$373$	12673.3	1.75925	0.879626	+	0.475667i	$0.157793\pi$
$374$	−3144.02	−0.434688
$375$	−994.419	−0.136938
$376$	−5653.74	−0.775451
$377$	0	0
$378$	2771.82	0.377161
$379$	2473.75	0.335271	0.167636	−	0.985849i	$-0.446387\pi$
$379$	2473.75	0.335271	0.167636	+	0.985849i	$0.446387\pi$
$380$	3085.92	0.416590
$381$	342.977	0.0461187
$382$	−4135.18	−0.553859
$383$	4312.68	0.575373	0.287686	−	0.957725i	$-0.407114\pi$
$383$	4312.68	0.575373	0.287686	+	0.957725i	$0.407114\pi$
$384$	1215.02	0.161468
$385$	1696.68	0.224600
$386$	−6844.21	−0.902489
$387$	7332.75	0.963164
$388$	4485.76	0.586932
$389$	−4833.51	−0.629996	−0.314998	−	0.949092i	$-0.602004\pi$
$389$	−4833.51	−0.629996	−0.314998	+	0.949092i	$0.602004\pi$
$390$	0	0
$391$	339.486	0.0439093
$392$	−2463.04	−0.317353
$393$	−1159.33	−0.148805
$394$	−13482.4	−1.72395
$395$	−6405.75	−0.815971
$396$	851.983	0.108116
$397$	−8906.01	−1.12589	−0.562947	−	0.826493i	$-0.690332\pi$
$397$	−8906.01	−1.12589	−0.562947	+	0.826493i	$0.690332\pi$
$398$	−14106.4	−1.77660
$399$	−2374.73	−0.297958
$400$	6025.39	0.753174
$401$	8362.36	1.04139	0.520694	−	0.853744i	$-0.325673\pi$
$401$	8362.36	1.04139	0.520694	+	0.853744i	$0.325673\pi$
$402$	−1890.29	−0.234525
$403$	0	0
$404$	−2000.60	−0.246370
$405$	4799.28	0.588835
$406$	15826.2	1.93459
$407$	−233.134	−0.0283932
$408$	−1027.91	−0.124728
$409$	13906.3	1.68122	0.840611	−	0.541639i	$-0.182196\pi$
$409$	13906.3	1.68122	0.840611	+	0.541639i	$0.182196\pi$
$410$	550.561	0.0663177
$411$	−692.203	−0.0830750
$412$	3513.15	0.420098
$413$	9787.76	1.16616
$414$	−343.784	−0.0408118
$415$	1794.77	0.212293
$416$	0	0
$417$	1426.72	0.167546
$418$	−5507.09	−0.644403
$419$	−9290.27	−1.08320	−0.541599	−	0.840637i	$-0.682181\pi$
$419$	−9290.27	−1.08320	−0.541599	+	0.840637i	$0.682181\pi$
$420$	−319.360	−0.0371027
$421$	2856.55	0.330688	0.165344	−	0.986236i	$-0.447127\pi$
$421$	2856.55	0.330688	0.165344	+	0.986236i	$0.447127\pi$
$422$	8567.28	0.988267
$423$	−8928.35	−1.02627
$424$	−7944.76	−0.909981
$425$	−6609.39	−0.754359
$426$	2252.37	0.256169
$427$	−18587.5	−2.10659
$428$	5358.23	0.605139
$429$	0	0
$430$	−6374.17	−0.714860
$431$	−3667.97	−0.409931	−0.204965	−	0.978769i	$-0.565708\pi$
$431$	−3667.97	−0.409931	−0.204965	+	0.978769i	$0.565708\pi$
$432$	2987.70	0.332745
$433$	−3725.43	−0.413470	−0.206735	−	0.978397i	$-0.566284\pi$
$433$	−3725.43	−0.413470	−0.206735	+	0.978397i	$0.566284\pi$
$434$	−17275.5	−1.91072
$435$	−1068.22	−0.117740
$436$	5365.77	0.589389
$437$	594.646	0.0650933
$438$	2524.91	0.275445
$439$	1217.51	0.132365	0.0661827	−	0.997808i	$-0.478918\pi$
$439$	1217.51	0.132365	0.0661827	+	0.997808i	$0.478918\pi$
$440$	1286.41	0.139379
$441$	−3889.62	−0.420000
$442$	0	0
$443$	7517.95	0.806295	0.403148	−	0.915135i	$-0.367916\pi$
$443$	7517.95	0.806295	0.403148	+	0.915135i	$0.367916\pi$
$444$	43.8820	0.00469042
$445$	−101.673	−0.0108310
$446$	−9788.78	−1.03927
$447$	30.8984	0.00326945
$448$	−4718.49	−0.497606
$449$	−7005.79	−0.736356	−0.368178	−	0.929755i	$-0.620018\pi$
$449$	−7005.79	−0.736356	−0.368178	+	0.929755i	$0.620018\pi$
$450$	6693.08	0.701144
$451$	−262.921	−0.0274511
$452$	−821.398	−0.0854764
$453$	484.695	0.0502714
$454$	−3356.98	−0.347029
$455$	0	0
$456$	−1800.50	−0.184903
$457$	13686.0	1.40089	0.700443	−	0.713709i	$-0.252986\pi$
$457$	13686.0	1.40089	0.700443	+	0.713709i	$0.252986\pi$
$458$	−3631.40	−0.370490
$459$	−3277.28	−0.333268
$460$	79.9694	0.00810564
$461$	2910.52	0.294048	0.147024	−	0.989133i	$-0.453030\pi$
$461$	2910.52	0.294048	0.147024	+	0.989133i	$0.453030\pi$
$462$	569.925	0.0573925
$463$	−7087.70	−0.711433	−0.355716	−	0.934594i	$-0.615763\pi$
$463$	−7087.70	−0.711433	−0.355716	+	0.934594i	$0.615763\pi$
$464$	17058.9	1.70676
$465$	1166.03	0.116287
$466$	−21374.6	−2.12481
$467$	8875.33	0.879446	0.439723	−	0.898133i	$-0.355077\pi$
$467$	8875.33	0.879446	0.439723	+	0.898133i	$0.355077\pi$
$468$	0	0
$469$	17869.5	1.75935
$470$	7761.18	0.761695
$471$	410.908	0.0401989
$472$	7420.97	0.723682
$473$	3043.99	0.295904
$474$	−2151.73	−0.208507
$475$	−11577.1	−1.11830
$476$	−5594.33	−0.538688
$477$	−12546.3	−1.20431
$478$	−10268.4	−0.982564
$479$	11753.2	1.12113	0.560563	−	0.828112i	$-0.310585\pi$
$479$	11753.2	1.12113	0.560563	+	0.828112i	$0.310585\pi$
$480$	−623.671	−0.0593053
$481$	0	0
$482$	−16908.2	−1.59782
$483$	−61.5396	−0.00579741
$484$	353.677	0.0332153
$485$	10695.9	1.00139
$486$	4993.72	0.466090
$487$	−14715.3	−1.36923	−0.684613	−	0.728907i	$-0.740029\pi$
$487$	−14715.3	−1.36923	−0.684613	+	0.728907i	$0.740029\pi$
$488$	−14092.9	−1.30728
$489$	2668.85	0.246809
$490$	3381.14	0.311724
$491$	−20102.7	−1.84771	−0.923853	−	0.382748i	$-0.874978\pi$
$491$	−20102.7	−1.84771	−0.923853	+	0.382748i	$0.874978\pi$
$492$	49.4885	0.00453478
$493$	−18712.3	−1.70945
$494$	0	0
$495$	2031.48	0.184461
$496$	−18621.0	−1.68570
$497$	−21292.3	−1.92171
$498$	602.873	0.0542477
$499$	9589.90	0.860326	0.430163	−	0.902751i	$-0.358456\pi$
$499$	9589.90	0.860326	0.430163	+	0.902751i	$0.358456\pi$
$500$	−4103.36	−0.367016
$501$	−345.406	−0.0308016
$502$	15537.1	1.38138
$503$	10324.5	0.915201	0.457601	−	0.889158i	$-0.348709\pi$
$503$	10324.5	0.915201	0.457601	+	0.889158i	$0.348709\pi$
$504$	−9840.17	−0.869674
$505$	−4770.25	−0.420344
$506$	−142.712	−0.0125382
$507$	0	0
$508$	1415.26	0.123606
$509$	−8817.95	−0.767876	−0.383938	−	0.923359i	$-0.625432\pi$
$509$	−8817.95	−0.767876	−0.383938	+	0.923359i	$0.625432\pi$
$510$	1411.07	0.122516
$511$	−23868.7	−2.06632
$512$	−623.495	−0.0538180
$513$	−5740.50	−0.494053
$514$	8458.88	0.725886
$515$	8376.81	0.716750
$516$	−572.957	−0.0488819
$517$	−3706.36	−0.315291
$518$	−1550.20	−0.131490
$519$	−346.500	−0.0293057
$520$	0	0
$521$	−11158.2	−0.938289	−0.469145	−	0.883121i	$-0.655438\pi$
$521$	−11158.2	−0.938289	−0.469145	+	0.883121i	$0.655438\pi$
$522$	18949.2	1.58886
$523$	−16128.8	−1.34849	−0.674247	−	0.738506i	$-0.735532\pi$
$523$	−16128.8	−1.34849	−0.674247	+	0.738506i	$0.735532\pi$
$524$	−4783.84	−0.398822
$525$	1198.10	0.0995991
$526$	−1644.85	−0.136348
$527$	20425.8	1.68835
$528$	614.314	0.0506337
$529$	−12151.6	−0.998733
$530$	10906.2	0.893839
$531$	11719.1	0.957755
$532$	−9799.07	−0.798578
$533$	0	0
$534$	−34.1527	−0.00276766
$535$	12776.3	1.03246
$536$	13548.4	1.09180
$537$	1774.50	0.142599
$538$	−6522.93	−0.522720
$539$	−1614.67	−0.129033
$540$	−771.996	−0.0615212
$541$	4965.84	0.394636	0.197318	−	0.980340i	$-0.436777\pi$
$541$	4965.84	0.394636	0.197318	+	0.980340i	$0.436777\pi$
$542$	−18145.5	−1.43804
$543$	−311.653	−0.0246304
$544$	−10925.1	−0.861044
$545$	12794.2	1.00559
$546$	0	0
$547$	−8798.04	−0.687710	−0.343855	−	0.939023i	$-0.611733\pi$
$547$	−8798.04	−0.687710	−0.343855	+	0.939023i	$0.611733\pi$
$548$	−2856.30	−0.222655
$549$	−22255.3	−1.73012
$550$	2778.44	0.215406
$551$	−32776.6	−2.53417
$552$	−46.6586	−0.00359769
$553$	20340.9	1.56417
$554$	−4451.53	−0.341386
$555$	104.633	0.00800256
$556$	5887.20	0.449052
$557$	−12283.9	−0.934443	−0.467222	−	0.884140i	$-0.654745\pi$
$557$	−12283.9	−0.934443	−0.467222	+	0.884140i	$0.654745\pi$
$558$	−20684.4	−1.56925
$559$	0	0
$560$	12160.6	0.917639
$561$	−673.855	−0.0507133
$562$	19044.6	1.42944
$563$	12074.8	0.903895	0.451948	−	0.892045i	$-0.350729\pi$
$563$	12074.8	0.903895	0.451948	+	0.892045i	$0.350729\pi$
$564$	697.633	0.0520845
$565$	−1958.56	−0.145836
$566$	881.909	0.0654936
$567$	−15239.7	−1.12876
$568$	−16143.6	−1.19255
$569$	2576.41	0.189822	0.0949111	−	0.995486i	$-0.469743\pi$
$569$	2576.41	0.189822	0.0949111	+	0.995486i	$0.469743\pi$
$570$	2471.63	0.181623
$571$	−860.552	−0.0630701	−0.0315350	−	0.999503i	$-0.510040\pi$
$571$	−860.552	−0.0630701	−0.0315350	+	0.999503i	$0.510040\pi$
$572$	0	0
$573$	−886.290	−0.0646166
$574$	−1748.26	−0.127127
$575$	−300.012	−0.0217589
$576$	−5649.58	−0.408679
$577$	6026.03	0.434778	0.217389	−	0.976085i	$-0.430246\pi$
$577$	6026.03	0.434778	0.217389	+	0.976085i	$0.430246\pi$
$578$	8480.68	0.610294
$579$	−1466.91	−0.105290
$580$	−4407.87	−0.315564
$581$	−5699.13	−0.406953
$582$	3592.82	0.255889
$583$	−5208.25	−0.369989
$584$	−18097.0	−1.28229
$585$	0	0
$586$	12986.2	0.915455
$587$	13465.6	0.946820	0.473410	−	0.880842i	$-0.343023\pi$
$587$	13465.6	0.946820	0.473410	+	0.880842i	$0.343023\pi$
$588$	303.922	0.0213156
$589$	35778.0	2.50290
$590$	−10187.1	−0.710845
$591$	−2889.68	−0.201126
$592$	−1670.94	−0.116005
$593$	20586.9	1.42564	0.712819	−	0.701348i	$-0.247418\pi$
$593$	20586.9	1.42564	0.712819	+	0.701348i	$0.247418\pi$
$594$	1377.70	0.0951642
$595$	−13339.2	−0.919083
$596$	127.499	0.00876267
$597$	−3023.40	−0.207269
$598$	0	0
$599$	58.8586	0.00401485	0.00200743	−	0.999998i	$-0.499361\pi$
$599$	58.8586	0.00401485	0.00200743	+	0.999998i	$0.499361\pi$
$600$	908.389	0.0618080
$601$	3496.22	0.237294	0.118647	−	0.992936i	$-0.462144\pi$
$601$	3496.22	0.237294	0.118647	+	0.992936i	$0.462144\pi$
$602$	20240.6	1.37034
$603$	21395.6	1.44494
$604$	2000.04	0.134736
$605$	843.313	0.0566703
$606$	−1602.36	−0.107411
$607$	−11976.1	−0.800814	−0.400407	−	0.916337i	$-0.631131\pi$
$607$	−11976.1	−0.800814	−0.400407	+	0.916337i	$0.631131\pi$
$608$	−19136.4	−1.27645
$609$	3392.03	0.225701
$610$	19346.0	1.28409
$611$	0	0
$612$	−6698.24	−0.442419
$613$	−23201.1	−1.52868	−0.764341	−	0.644812i	$-0.776935\pi$
$613$	−23201.1	−1.52868	−0.764341	+	0.644812i	$0.776935\pi$
$614$	17146.2	1.12697
$615$	118.001	0.00773702
$616$	−4084.87	−0.267182
$617$	13115.6	0.855774	0.427887	−	0.903832i	$-0.359258\pi$
$617$	13115.6	0.855774	0.427887	+	0.903832i	$0.359258\pi$
$618$	2813.82	0.183153
$619$	−4224.60	−0.274315	−0.137157	−	0.990549i	$-0.543797\pi$
$619$	−4224.60	−0.274315	−0.137157	+	0.990549i	$0.543797\pi$
$620$	4811.51	0.311669
$621$	−148.761	−0.00961285
$622$	20683.5	1.33333
$623$	322.855	0.0207623
$624$	0	0
$625$	−230.918	−0.0147787
$626$	11944.5	0.762617
$627$	−1180.33	−0.0751799
$628$	1695.57	0.107740
$629$	1832.89	0.116188
$630$	13508.1	0.854247
$631$	5178.19	0.326689	0.163344	−	0.986569i	$-0.447772\pi$
$631$	5178.19	0.326689	0.163344	+	0.986569i	$0.447772\pi$
$632$	15422.3	0.970672
$633$	1836.22	0.115297
$634$	−21.6401	−0.00135558
$635$	3374.56	0.210890
$636$	980.329	0.0611204
$637$	0	0
$638$	7866.23	0.488130
$639$	−25493.9	−1.57828
$640$	11954.6	0.738356
$641$	8465.61	0.521640	0.260820	−	0.965387i	$-0.416007\pi$
$641$	8465.61	0.521640	0.260820	+	0.965387i	$0.416007\pi$
$642$	4291.62	0.263826
$643$	−22470.5	−1.37815	−0.689076	−	0.724689i	$-0.741983\pi$
$643$	−22470.5	−1.37815	−0.689076	+	0.724689i	$0.741983\pi$
$644$	−253.936	−0.0155380
$645$	−1366.17	−0.0833998
$646$	43296.4	2.63696
$647$	−3001.22	−0.182365	−0.0911824	−	0.995834i	$-0.529065\pi$
$647$	−3001.22	−0.182365	−0.0911824	+	0.995834i	$0.529065\pi$
$648$	−11554.6	−0.700473
$649$	4864.88	0.294242
$650$	0	0
$651$	−3702.64	−0.222916
$652$	11012.7	0.661488
$653$	26421.7	1.58340	0.791701	−	0.610908i	$-0.209196\pi$
$653$	26421.7	1.58340	0.791701	+	0.610908i	$0.209196\pi$
$654$	4297.66	0.256960
$655$	−11406.7	−0.680451
$656$	−1884.42	−0.112156
$657$	−28578.6	−1.69705
$658$	−24645.0	−1.46012
$659$	−20426.0	−1.20741	−0.603704	−	0.797208i	$-0.706309\pi$
$659$	−20426.0	−1.20741	−0.603704	+	0.797208i	$0.706309\pi$
$660$	−158.733	−0.00936166
$661$	13679.3	0.804939	0.402469	−	0.915433i	$-0.368152\pi$
$661$	13679.3	0.804939	0.402469	+	0.915433i	$0.368152\pi$
$662$	−11903.1	−0.698830
$663$	0	0
$664$	−4321.02	−0.252542
$665$	−23365.1	−1.36249
$666$	−1856.10	−0.107991
$667$	−849.382	−0.0493077
$668$	−1425.28	−0.0825534
$669$	−2098.02	−0.121247
$670$	−18598.6	−1.07243
$671$	−9238.69	−0.531528
$672$	1980.41	0.113685
$673$	−23205.5	−1.32913	−0.664566	−	0.747230i	$-0.731384\pi$
$673$	−23205.5	−1.32913	−0.664566	+	0.747230i	$0.731384\pi$
$674$	−14715.5	−0.840978
$675$	2896.21	0.165148
$676$	0	0
$677$	−10625.8	−0.603223	−0.301612	−	0.953431i	$-0.597525\pi$
$677$	−10625.8	−0.603223	−0.301612	+	0.953431i	$0.597525\pi$
$678$	−657.891	−0.0372657
$679$	−33964.0	−1.91961
$680$	−10113.6	−0.570354
$681$	−719.499	−0.0404864
$682$	−8586.56	−0.482106
$683$	−11611.8	−0.650532	−0.325266	−	0.945623i	$-0.605454\pi$
$683$	−11611.8	−0.650532	−0.325266	+	0.945623i	$0.605454\pi$
$684$	−11732.7	−0.655863
$685$	−6810.61	−0.379883
$686$	14351.6	0.798755
$687$	−778.315	−0.0432235
$688$	21817.1	1.20896
$689$	0	0
$690$	64.0507	0.00353387
$691$	12857.9	0.707869	0.353935	−	0.935270i	$-0.384844\pi$
$691$	12857.9	0.707869	0.353935	+	0.935270i	$0.384844\pi$
$692$	−1429.79	−0.0785443
$693$	−6450.80	−0.353601
$694$	4214.15	0.230500
$695$	14037.5	0.766150
$696$	2571.80	0.140063
$697$	2067.07	0.112332
$698$	20940.9	1.13556
$699$	−4581.21	−0.247893
$700$	4943.84	0.266942
$701$	15880.3	0.855620	0.427810	−	0.903869i	$-0.359285\pi$
$701$	15880.3	0.855620	0.427810	+	0.903869i	$0.359285\pi$
$702$	0	0
$703$	3210.50	0.172242
$704$	−2345.26	−0.125555
$705$	1663.45	0.0888639
$706$	5461.13	0.291122
$707$	15147.5	0.805773
$708$	−915.696	−0.0486073
$709$	6122.44	0.324306	0.162153	−	0.986766i	$-0.448156\pi$
$709$	6122.44	0.324306	0.162153	+	0.986766i	$0.448156\pi$
$710$	22161.2	1.17140
$711$	24354.7	1.28463
$712$	244.785	0.0128844
$713$	927.163	0.0486992
$714$	−4480.72	−0.234855
$715$	0	0
$716$	7322.29	0.382188
$717$	−2200.82	−0.114632
$718$	−5928.20	−0.308132
$719$	26351.3	1.36681	0.683406	−	0.730039i	$-0.260498\pi$
$719$	26351.3	1.36681	0.683406	+	0.730039i	$0.260498\pi$
$720$	14560.2	0.753647
$721$	−26599.8	−1.37397
$722$	53169.4	2.74067
$723$	−3623.93	−0.186411
$724$	−1286.00	−0.0660136
$725$	16536.5	0.847103
$726$	283.274	0.0144811
$727$	28765.8	1.46749	0.733743	−	0.679427i	$-0.237772\pi$
$727$	28765.8	1.46749	0.733743	+	0.679427i	$0.237772\pi$
$728$	0	0
$729$	−17522.1	−0.890217
$730$	24842.7	1.25955
$731$	−23931.6	−1.21087
$732$	1738.96	0.0878058
$733$	34549.2	1.74093	0.870467	−	0.492226i	$-0.163817\pi$
$733$	34549.2	1.74093	0.870467	+	0.492226i	$0.163817\pi$
$734$	−5645.27	−0.283884
$735$	724.678	0.0363675
$736$	−495.907	−0.0248361
$737$	8881.78	0.443914
$738$	−2093.24	−0.104408
$739$	−1676.06	−0.0834302	−0.0417151	−	0.999130i	$-0.513282\pi$
$739$	−1676.06	−0.0834302	−0.0417151	+	0.999130i	$0.513282\pi$
$740$	431.756	0.0214482
$741$	0	0
$742$	−34631.7	−1.71343
$743$	−266.516	−0.0131595	−0.00657977	−	0.999978i	$-0.502094\pi$
$743$	−266.516	−0.0131595	−0.00657977	+	0.999978i	$0.502094\pi$
$744$	−2807.30	−0.138334
$745$	304.010	0.0149504
$746$	41885.2	2.05567
$747$	−6823.72	−0.334226
$748$	−2780.59	−0.135920
$749$	−40569.9	−1.97916
$750$	−3286.54	−0.160010
$751$	13501.0	0.656002	0.328001	−	0.944677i	$-0.393625\pi$
$751$	13501.0	0.656002	0.328001	+	0.944677i	$0.393625\pi$
$752$	−26564.5	−1.28817
$753$	3330.05	0.161160
$754$	0	0
$755$	4768.93	0.229880
$756$	2451.41	0.117932
$757$	−13216.2	−0.634545	−0.317273	−	0.948334i	$-0.602767\pi$
$757$	−13216.2	−0.634545	−0.317273	+	0.948334i	$0.602767\pi$
$758$	8175.70	0.391761
$759$	−30.5874	−0.00146278
$760$	−17715.1	−0.845520
$761$	−195.675	−0.00932089	−0.00466044	−	0.999989i	$-0.501483\pi$
$761$	−195.675	−0.00932089	−0.00466044	+	0.999989i	$0.501483\pi$
$762$	1133.53	0.0538893
$763$	−40627.0	−1.92765
$764$	−3657.18	−0.173183
$765$	−15971.4	−0.754833
$766$	14253.4	0.672317
$767$	0	0
$768$	2807.42	0.131907
$769$	9702.13	0.454964	0.227482	−	0.973782i	$-0.426951\pi$
$769$	9702.13	0.454964	0.227482	+	0.973782i	$0.426951\pi$
$770$	5607.51	0.262442
$771$	1812.98	0.0846862
$772$	−6053.05	−0.282194
$773$	5696.94	0.265077	0.132539	−	0.991178i	$-0.457687\pi$
$773$	5696.94	0.265077	0.132539	+	0.991178i	$0.457687\pi$
$774$	24234.7	1.12545
$775$	−18050.8	−0.836649
$776$	−25751.1	−1.19125
$777$	−332.253	−0.0153404
$778$	−15974.7	−0.736144
$779$	3620.69	0.166527
$780$	0	0
$781$	−10583.1	−0.484881
$782$	1122.00	0.0513076
$783$	8199.64	0.374241
$784$	−11572.8	−0.527184
$785$	4042.94	0.183820
$786$	−3831.57	−0.173877
$787$	−30160.4	−1.36608	−0.683039	−	0.730382i	$-0.739342\pi$
$787$	−30160.4	−1.36608	−0.683039	+	0.730382i	$0.739342\pi$
$788$	−11923.9	−0.539052
$789$	−352.539	−0.0159071
$790$	−21170.9	−0.953453
$791$	6219.23	0.279558
$792$	−4890.93	−0.219434
$793$	0	0
$794$	−29434.3	−1.31560
$795$	2337.51	0.104281
$796$	−12475.7	−0.555516
$797$	28309.7	1.25819	0.629096	−	0.777327i	$-0.283425\pi$
$797$	28309.7	1.25819	0.629096	+	0.777327i	$0.283425\pi$
$798$	−7848.46	−0.348161
$799$	29139.2	1.29020
$800$	9654.73	0.426683
$801$	386.563	0.0170519
$802$	27637.5	1.21685
$803$	−11863.6	−0.521367
$804$	−1671.78	−0.0733324
$805$	−605.490	−0.0265102
$806$	0	0
$807$	−1398.05	−0.0609837
$808$	11484.7	0.500037
$809$	20947.9	0.910370	0.455185	−	0.890397i	$-0.349573\pi$
$809$	20947.9	0.910370	0.455185	+	0.890397i	$0.349573\pi$
$810$	15861.6	0.688048
$811$	−24223.1	−1.04882	−0.524408	−	0.851467i	$-0.675713\pi$
$811$	−24223.1	−1.04882	−0.524408	+	0.851467i	$0.675713\pi$
$812$	13996.8	0.604916
$813$	−3889.12	−0.167770
$814$	−770.507	−0.0331772
$815$	26258.9	1.12860
$816$	−4829.70	−0.207198
$817$	−41918.8	−1.79505
$818$	45960.0	1.96449
$819$	0	0
$820$	486.919	0.0207365
$821$	15956.3	0.678293	0.339146	−	0.940734i	$-0.389862\pi$
$821$	15956.3	0.678293	0.339146	+	0.940734i	$0.389862\pi$
$822$	−2287.72	−0.0970723
$823$	10379.9	0.439634	0.219817	−	0.975541i	$-0.429454\pi$
$823$	10379.9	0.439634	0.219817	+	0.975541i	$0.429454\pi$
$824$	−20167.7	−0.852640
$825$	595.501	0.0251305
$826$	32348.4	1.36265
$827$	22085.8	0.928658	0.464329	−	0.885663i	$-0.346296\pi$
$827$	22085.8	0.928658	0.464329	+	0.885663i	$0.346296\pi$
$828$	−304.045	−0.0127612
$829$	−26716.1	−1.11929	−0.559643	−	0.828734i	$-0.689062\pi$
$829$	−26716.1	−1.11929	−0.559643	+	0.828734i	$0.689062\pi$
$830$	5931.68	0.248062
$831$	−954.093	−0.0398281
$832$	0	0
$833$	12694.4	0.528014
$834$	4715.29	0.195776
$835$	−3398.46	−0.140849
$836$	−4870.50	−0.201495
$837$	−8950.50	−0.369623
$838$	−30704.2	−1.26570
$839$	27121.6	1.11602	0.558010	−	0.829835i	$-0.311565\pi$
$839$	27121.6	1.11602	0.558010	+	0.829835i	$0.311565\pi$
$840$	1833.33	0.0753045
$841$	22428.5	0.919615
$842$	9440.86	0.386405
$843$	4081.81	0.166767
$844$	7576.95	0.309016
$845$	0	0
$846$	−29508.1	−1.19918
$847$	−2677.87	−0.108634
$848$	−37329.0	−1.51165
$849$	189.019	0.00764088
$850$	−21844.0	−0.881461
$851$	83.1980	0.00335134
$852$	1992.01	0.0801000
$853$	18890.1	0.758249	0.379124	−	0.925346i	$-0.376225\pi$
$853$	18890.1	0.758249	0.379124	+	0.925346i	$0.376225\pi$
$854$	−61431.5	−2.46153
$855$	−27975.6	−1.11900
$856$	−30759.6	−1.22820
$857$	−25142.5	−1.00216	−0.501080	−	0.865401i	$-0.667064\pi$
$857$	−25142.5	−1.00216	−0.501080	+	0.865401i	$0.667064\pi$
$858$	0	0
$859$	32680.5	1.29807	0.649037	−	0.760757i	$-0.275172\pi$
$859$	32680.5	1.29807	0.649037	+	0.760757i	$0.275172\pi$
$860$	−5637.35	−0.223525
$861$	−374.703	−0.0148314
$862$	−12122.6	−0.479000
$863$	22222.2	0.876537	0.438268	−	0.898844i	$-0.355592\pi$
$863$	22222.2	0.876537	0.438268	+	0.898844i	$0.355592\pi$
$864$	4787.31	0.188504
$865$	−3409.23	−0.134008
$866$	−12312.5	−0.483136
$867$	1817.66	0.0712006
$868$	−15278.5	−0.597451
$869$	10110.2	0.394666
$870$	−3530.44	−0.137578
$871$	0	0
$872$	−30802.9	−1.19624
$873$	−40666.0	−1.57656
$874$	1965.30	0.0760609
$875$	31068.6	1.20036
$876$	2233.04	0.0861273
$877$	24195.3	0.931603	0.465802	−	0.884889i	$-0.345766\pi$
$877$	24195.3	0.931603	0.465802	+	0.884889i	$0.345766\pi$
$878$	4023.84	0.154668
$879$	2783.33	0.106802
$880$	6044.25	0.231536
$881$	10252.3	0.392063	0.196032	−	0.980598i	$-0.437194\pi$
$881$	10252.3	0.392063	0.196032	+	0.980598i	$0.437194\pi$
$882$	−12855.1	−0.490766
$883$	11708.4	0.446229	0.223115	−	0.974792i	$-0.428378\pi$
$883$	11708.4	0.446229	0.223115	+	0.974792i	$0.428378\pi$
$884$	0	0
$885$	−2183.40	−0.0829314
$886$	24846.8	0.942148
$887$	24248.5	0.917907	0.458953	−	0.888460i	$-0.348224\pi$
$887$	24248.5	0.917907	0.458953	+	0.888460i	$0.348224\pi$
$888$	−251.911	−0.00951978
$889$	−10715.6	−0.404264
$890$	−336.029	−0.0126559
$891$	−7574.69	−0.284806
$892$	−8657.25	−0.324962
$893$	51040.4	1.91265
$894$	102.119	0.00382032
$895$	17459.4	0.652070
$896$	−37960.9	−1.41538
$897$	0	0
$898$	−23154.1	−0.860424
$899$	−51104.7	−1.89593
$900$	5919.39	0.219237
$901$	40947.0	1.51403
$902$	−868.949	−0.0320763
$903$	4338.15	0.159872
$904$	4715.35	0.173485
$905$	−3066.36	−0.112629
$906$	1601.91	0.0587417
$907$	−15266.4	−0.558888	−0.279444	−	0.960162i	$-0.590150\pi$
$907$	−15266.4	−0.558888	−0.279444	+	0.960162i	$0.590150\pi$
$908$	−2968.93	−0.108510
$909$	18136.6	0.661773
$910$	0	0
$911$	−17741.5	−0.645228	−0.322614	−	0.946531i	$-0.604562\pi$
$911$	−17741.5	−0.645228	−0.322614	+	0.946531i	$0.604562\pi$
$912$	−8459.74	−0.307160
$913$	−2832.68	−0.102681
$914$	45232.1	1.63692
$915$	4146.41	0.149810
$916$	−3211.63	−0.115846
$917$	36220.9	1.30438
$918$	−10831.4	−0.389421
$919$	−19860.4	−0.712876	−0.356438	−	0.934319i	$-0.616009\pi$
$919$	−19860.4	−0.712876	−0.356438	+	0.934319i	$0.616009\pi$
$920$	−459.076	−0.0164514
$921$	3674.92	0.131480
$922$	9619.22	0.343593
$923$	0	0
$924$	504.045	0.0179457
$925$	−1619.77	−0.0575758
$926$	−23424.8	−0.831302
$927$	−31848.7	−1.12842
$928$	27334.1	0.966903
$929$	8436.00	0.297929	0.148964	−	0.988843i	$-0.452406\pi$
$929$	8436.00	0.297929	0.148964	+	0.988843i	$0.452406\pi$
$930$	3853.73	0.135880
$931$	22235.6	0.782754
$932$	−18903.8	−0.664395
$933$	4433.07	0.155554
$934$	29332.9	1.02762
$935$	−6630.08	−0.231900
$936$	0	0
$937$	22075.1	0.769650	0.384825	−	0.922990i	$-0.374262\pi$
$937$	22075.1	0.769650	0.384825	+	0.922990i	$0.374262\pi$
$938$	59058.4	2.05578
$939$	2560.06	0.0889715
$940$	6864.03	0.238170
$941$	14090.7	0.488143	0.244072	−	0.969757i	$-0.421517\pi$
$941$	14090.7	0.488143	0.244072	+	0.969757i	$0.421517\pi$
$942$	1358.05	0.0469720
$943$	93.8277	0.00324014
$944$	34867.9	1.20217
$945$	5845.18	0.201210
$946$	10060.3	0.345761
$947$	17211.7	0.590608	0.295304	−	0.955403i	$-0.404579\pi$
$947$	17211.7	0.590608	0.295304	+	0.955403i	$0.404579\pi$
$948$	−1903.00	−0.0651968
$949$	0	0
$950$	−38262.1	−1.30672
$951$	−4.63811	−0.000158150 0
$952$	32115.0	1.09333
$953$	34999.9	1.18967	0.594837	−	0.803846i	$-0.297217\pi$
$953$	34999.9	1.18967	0.594837	+	0.803846i	$0.297217\pi$
$954$	−41465.4	−1.40723
$955$	−8720.24	−0.295477
$956$	−9081.42	−0.307232
$957$	1685.96	0.0569482
$958$	38844.3	1.31002
$959$	21626.5	0.728213
$960$	1052.58	0.0353872
$961$	25993.5	0.872529
$962$	0	0
$963$	−48575.4	−1.62546
$964$	−14953.7	−0.499614
$965$	−14433.0	−0.481466
$966$	−203.388	−0.00677421
$967$	37334.0	1.24155	0.620777	−	0.783988i	$-0.286817\pi$
$967$	37334.0	1.24155	0.620777	+	0.783988i	$0.286817\pi$
$968$	−2030.33	−0.0674146
$969$	9279.68	0.307643
$970$	35349.9	1.17012
$971$	−33613.0	−1.11091	−0.555455	−	0.831547i	$-0.687456\pi$
$971$	−33613.0	−1.11091	−0.555455	+	0.831547i	$0.687456\pi$
$972$	4416.47	0.145739
$973$	−44575.0	−1.46866
$974$	−48633.9	−1.59993
$975$	0	0
$976$	−66216.1	−2.17165
$977$	34516.4	1.13027	0.565137	−	0.824997i	$-0.308823\pi$
$977$	34516.4	1.13027	0.565137	+	0.824997i	$0.308823\pi$
$978$	8820.50	0.288393
$979$	160.471	0.00523869
$980$	2990.30	0.0974711
$981$	−48643.8	−1.58316
$982$	−66439.3	−2.15902
$983$	−27499.6	−0.892269	−0.446134	−	0.894966i	$-0.647200\pi$
$983$	−27499.6	−0.892269	−0.446134	+	0.894966i	$0.647200\pi$
$984$	−284.096	−0.00920390
$985$	−28431.7	−0.919703
$986$	−61843.8	−1.99747
$987$	−5282.14	−0.170347
$988$	0	0
$989$	−1086.30	−0.0349265
$990$	6714.03	0.215541
$991$	−51415.9	−1.64811	−0.824056	−	0.566508i	$-0.808294\pi$
$991$	−51415.9	−1.64811	−0.824056	+	0.566508i	$0.808294\pi$
$992$	−29837.2	−0.954971
$993$	−2551.17	−0.0815297
$994$	−70370.9	−2.24550
$995$	−29747.4	−0.947794
$996$	533.184	0.0169624
$997$	−369.727	−0.0117446	−0.00587230	−	0.999983i	$-0.501869\pi$
$997$	−369.727	−0.0117446	−0.00587230	+	0.999983i	$0.501869\pi$
$998$	31694.5	1.00528
$999$	−803.164	−0.0254364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.c.1.4		6
13.12	even	2		143.4.a.b.1.3	✓	6
39.38	odd	2		1287.4.a.f.1.4		6
52.51	odd	2		2288.4.a.m.1.3		6
143.142	odd	2		1573.4.a.d.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.b.1.3	✓	6	13.12	even	2
1287.4.a.f.1.4		6	39.38	odd	2
1573.4.a.d.1.4		6	143.142	odd	2
1859.4.a.c.1.4		6	1.1	even	1	trivial
2288.4.a.m.1.3		6	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.30499 q^{2} +0.708355 q^{3} +2.92295 q^{4} +6.96953 q^{5} +2.34111 q^{6} -22.1312 q^{7} -16.7796 q^{8} -26.4982 q^{9} +O(q^{10})\)	\(q+3.30499 q^{2} +0.708355 q^{3} +2.92295 q^{4} +6.96953 q^{5} +2.34111 q^{6} -22.1312 q^{7} -16.7796 q^{8} -26.4982 q^{9} +23.0342 q^{10} -11.0000 q^{11} +2.07049 q^{12} -73.1432 q^{14} +4.93690 q^{15} -78.8400 q^{16} +86.4814 q^{17} -87.5764 q^{18} +151.481 q^{19} +20.3716 q^{20} -15.6767 q^{21} -36.3549 q^{22} +3.92554 q^{23} -11.8859 q^{24} -76.4256 q^{25} -37.8958 q^{27} -64.6882 q^{28} -216.373 q^{29} +16.3164 q^{30} +236.187 q^{31} -126.328 q^{32} -7.79191 q^{33} +285.820 q^{34} -154.244 q^{35} -77.4530 q^{36} +21.1940 q^{37} +500.644 q^{38} -116.946 q^{40} +23.9019 q^{41} -51.8114 q^{42} -276.726 q^{43} -32.1524 q^{44} -184.680 q^{45} +12.9739 q^{46} +336.941 q^{47} -55.8467 q^{48} +146.788 q^{49} -252.586 q^{50} +61.2595 q^{51} +473.478 q^{53} -125.245 q^{54} -76.6648 q^{55} +371.352 q^{56} +107.303 q^{57} -715.112 q^{58} -442.262 q^{59} +14.4303 q^{60} +839.880 q^{61} +780.597 q^{62} +586.436 q^{63} +213.206 q^{64} -25.7522 q^{66} -807.435 q^{67} +252.781 q^{68} +2.78068 q^{69} -509.774 q^{70} +962.098 q^{71} +444.630 q^{72} +1078.51 q^{73} +70.0461 q^{74} -54.1365 q^{75} +442.772 q^{76} +243.443 q^{77} -919.108 q^{79} -549.478 q^{80} +688.609 q^{81} +78.9954 q^{82} +257.516 q^{83} -45.8222 q^{84} +602.735 q^{85} -914.576 q^{86} -153.269 q^{87} +184.576 q^{88} -14.5883 q^{89} -610.366 q^{90} +11.4741 q^{92} +167.305 q^{93} +1113.59 q^{94} +1055.75 q^{95} -89.4854 q^{96} +1534.67 q^{97} +485.132 q^{98} +291.481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} - 52 q^{10} - 66 q^{11} - 19 q^{12} - 120 q^{14} + 23 q^{15} + 26 q^{16} - 117 q^{17} + 27 q^{18} + 67 q^{19} - 10 q^{20} - 19 q^{21} - 66 q^{22} - 158 q^{23} + 609 q^{24} - 234 q^{25} - 531 q^{27} + 670 q^{28} - 145 q^{29} - 211 q^{30} + 58 q^{31} + 364 q^{32} + 66 q^{33} - 43 q^{34} - 210 q^{35} + 383 q^{36} + 753 q^{37} + 738 q^{38} + 4 q^{40} + 232 q^{41} + 1593 q^{42} - 390 q^{43} - 286 q^{44} + 107 q^{45} - 5 q^{46} + 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} + 363 q^{51} - 65 q^{53} - 1917 q^{54} - 88 q^{55} + 1816 q^{56} + 1657 q^{57} + 1685 q^{58} - 1735 q^{59} - 871 q^{60} + 421 q^{61} + 3394 q^{62} + 125 q^{63} + 570 q^{64} - 165 q^{66} + 703 q^{67} + 209 q^{68} - 272 q^{69} - 1968 q^{70} - 445 q^{71} - 1035 q^{72} + 2340 q^{73} + 1135 q^{74} + 1941 q^{75} + 1208 q^{76} - 583 q^{77} - 1234 q^{79} - 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} + 1146 q^{86} + 2462 q^{87} - 396 q^{88} + 442 q^{89} + 113 q^{90} + 2737 q^{92} + 982 q^{93} + 2733 q^{94} - 504 q^{95} + 1153 q^{96} + 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 - 52 * q^10 - 66 * q^11 - 19 * q^12 - 120 * q^14 + 23 * q^15 + 26 * q^16 - 117 * q^17 + 27 * q^18 + 67 * q^19 - 10 * q^20 - 19 * q^21 - 66 * q^22 - 158 * q^23 + 609 * q^24 - 234 * q^25 - 531 * q^27 + 670 * q^28 - 145 * q^29 - 211 * q^30 + 58 * q^31 + 364 * q^32 + 66 * q^33 - 43 * q^34 - 210 * q^35 + 383 * q^36 + 753 * q^37 + 738 * q^38 + 4 * q^40 + 232 * q^41 + 1593 * q^42 - 390 * q^43 - 286 * q^44 + 107 * q^45 - 5 * q^46 + 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 + 363 * q^51 - 65 * q^53 - 1917 * q^54 - 88 * q^55 + 1816 * q^56 + 1657 * q^57 + 1685 * q^58 - 1735 * q^59 - 871 * q^60 + 421 * q^61 + 3394 * q^62 + 125 * q^63 + 570 * q^64 - 165 * q^66 + 703 * q^67 + 209 * q^68 - 272 * q^69 - 1968 * q^70 - 445 * q^71 - 1035 * q^72 + 2340 * q^73 + 1135 * q^74 + 1941 * q^75 + 1208 * q^76 - 583 * q^77 - 1234 * q^79 - 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 + 1146 * q^86 + 2462 * q^87 - 396 * q^88 + 442 * q^89 + 113 * q^90 + 2737 * q^92 + 982 * q^93 + 2733 * q^94 - 504 * q^95 + 1153 * q^96 + 2682 * q^97 - 2036 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more