LMFDB - Embedded newform 726.4.a.z.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,4,Mod(1,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, 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("726.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	726.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:	$42.8353866642$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.12421225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 355x^{2} + 356x + 30964 $ x^4 - 2x^3 - 355x^2 + 356*x + 30964
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 11 $
Twist minimal:	no (minimal twist has level 66)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$12.8052$ of defining polynomial
Character	$\chi$	$=$	726.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.18714 q^{5} +6.00000 q^{6} +25.7192 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.18714 q^{5} +6.00000 q^{6} +25.7192 q^{7} +8.00000 q^{8} +9.00000 q^{9} -12.3743 q^{10} +12.0000 q^{12} +30.7630 q^{13} +51.4384 q^{14} -18.5614 q^{15} +16.0000 q^{16} +47.9850 q^{17} +18.0000 q^{18} -46.7480 q^{19} -24.7485 q^{20} +77.1576 q^{21} +2.04459 q^{23} +24.0000 q^{24} -86.7194 q^{25} +61.5261 q^{26} +27.0000 q^{27} +102.877 q^{28} +59.0080 q^{29} -37.1228 q^{30} +304.896 q^{31} +32.0000 q^{32} +95.9699 q^{34} -159.128 q^{35} +36.0000 q^{36} -303.823 q^{37} -93.4960 q^{38} +92.2891 q^{39} -49.4971 q^{40} +145.553 q^{41} +154.315 q^{42} -284.084 q^{43} -55.6842 q^{45} +4.08917 q^{46} +577.251 q^{47} +48.0000 q^{48} +318.477 q^{49} -173.439 q^{50} +143.955 q^{51} +123.052 q^{52} +655.216 q^{53} +54.0000 q^{54} +205.754 q^{56} -140.244 q^{57} +118.016 q^{58} -23.1802 q^{59} -74.2456 q^{60} -631.874 q^{61} +609.792 q^{62} +231.473 q^{63} +64.0000 q^{64} -190.335 q^{65} -655.918 q^{67} +191.940 q^{68} +6.13376 q^{69} -318.256 q^{70} +528.602 q^{71} +72.0000 q^{72} +447.652 q^{73} -607.646 q^{74} -260.158 q^{75} -186.992 q^{76} +184.578 q^{78} +985.464 q^{79} -98.9942 q^{80} +81.0000 q^{81} +291.106 q^{82} +128.459 q^{83} +308.630 q^{84} -296.889 q^{85} -568.167 q^{86} +177.024 q^{87} +1425.15 q^{89} -111.368 q^{90} +791.201 q^{91} +8.17835 q^{92} +914.688 q^{93} +1154.50 q^{94} +289.236 q^{95} +96.0000 q^{96} -142.553 q^{97} +636.954 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 21 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 21 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 21 q^{7} + 32 q^{8} + 36 q^{9} + 40 q^{10} + 48 q^{12} + 38 q^{13} + 42 q^{14} + 60 q^{15} + 64 q^{16} + 85 q^{17} + 72 q^{18} + 5 q^{19} + 80 q^{20} + 63 q^{21} + 316 q^{23} + 96 q^{24} + 318 q^{25} + 76 q^{26} + 108 q^{27} + 84 q^{28} + 123 q^{29} + 120 q^{30} + 436 q^{31} + 128 q^{32} + 170 q^{34} - 129 q^{35} + 144 q^{36} + 336 q^{37} + 10 q^{38} + 114 q^{39} + 160 q^{40} - 394 q^{41} + 126 q^{42} - 680 q^{43} + 180 q^{45} + 632 q^{46} + 1085 q^{47} + 192 q^{48} - 311 q^{49} + 636 q^{50} + 255 q^{51} + 152 q^{52} + 880 q^{53} + 216 q^{54} + 168 q^{56} + 15 q^{57} + 246 q^{58} + 724 q^{59} + 240 q^{60} + 355 q^{61} + 872 q^{62} + 189 q^{63} + 256 q^{64} - 2019 q^{65} - 869 q^{67} + 340 q^{68} + 948 q^{69} - 258 q^{70} - 331 q^{71} + 288 q^{72} + 1135 q^{73} + 672 q^{74} + 954 q^{75} + 20 q^{76} + 228 q^{78} + 1083 q^{79} + 320 q^{80} + 324 q^{81} - 788 q^{82} - 169 q^{83} + 252 q^{84} + 1104 q^{85} - 1360 q^{86} + 369 q^{87} - 258 q^{89} + 360 q^{90} + 874 q^{91} + 1264 q^{92} + 1308 q^{93} + 2170 q^{94} + 1555 q^{95} + 384 q^{96} - 248 q^{97} - 622 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 21 * q^7 + 32 * q^8 + 36 * q^9 + 40 * q^10 + 48 * q^12 + 38 * q^13 + 42 * q^14 + 60 * q^15 + 64 * q^16 + 85 * q^17 + 72 * q^18 + 5 * q^19 + 80 * q^20 + 63 * q^21 + 316 * q^23 + 96 * q^24 + 318 * q^25 + 76 * q^26 + 108 * q^27 + 84 * q^28 + 123 * q^29 + 120 * q^30 + 436 * q^31 + 128 * q^32 + 170 * q^34 - 129 * q^35 + 144 * q^36 + 336 * q^37 + 10 * q^38 + 114 * q^39 + 160 * q^40 - 394 * q^41 + 126 * q^42 - 680 * q^43 + 180 * q^45 + 632 * q^46 + 1085 * q^47 + 192 * q^48 - 311 * q^49 + 636 * q^50 + 255 * q^51 + 152 * q^52 + 880 * q^53 + 216 * q^54 + 168 * q^56 + 15 * q^57 + 246 * q^58 + 724 * q^59 + 240 * q^60 + 355 * q^61 + 872 * q^62 + 189 * q^63 + 256 * q^64 - 2019 * q^65 - 869 * q^67 + 340 * q^68 + 948 * q^69 - 258 * q^70 - 331 * q^71 + 288 * q^72 + 1135 * q^73 + 672 * q^74 + 954 * q^75 + 20 * q^76 + 228 * q^78 + 1083 * q^79 + 320 * q^80 + 324 * q^81 - 788 * q^82 - 169 * q^83 + 252 * q^84 + 1104 * q^85 - 1360 * q^86 + 369 * q^87 - 258 * q^89 + 360 * q^90 + 874 * q^91 + 1264 * q^92 + 1308 * q^93 + 2170 * q^94 + 1555 * q^95 + 384 * q^96 - 248 * q^97 - 622 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−6.18714	−0.553394	−0.276697	−	0.960957i	$-0.589240\pi$
$5$	−6.18714	−0.553394	−0.276697	+	0.960957i	$0.589240\pi$
$6$	6.00000	0.408248
$7$	25.7192	1.38871	0.694353	−	0.719634i	$-0.255691\pi$
$7$	25.7192	1.38871	0.694353	+	0.719634i	$0.255691\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−12.3743	−0.391309
$11$	0	0
$11$	0	0
$12$	12.0000	0.288675
$13$	30.7630	0.656318	0.328159	−	0.944623i	$-0.393572\pi$
$13$	30.7630	0.656318	0.328159	+	0.944623i	$0.393572\pi$
$14$	51.4384	0.981964
$15$	−18.5614	−0.319502
$16$	16.0000	0.250000
$17$	47.9850	0.684592	0.342296	−	0.939592i	$-0.388795\pi$
$17$	47.9850	0.684592	0.342296	+	0.939592i	$0.388795\pi$
$18$	18.0000	0.235702
$19$	−46.7480	−0.564459	−0.282230	−	0.959347i	$-0.591074\pi$
$19$	−46.7480	−0.564459	−0.282230	+	0.959347i	$0.591074\pi$
$20$	−24.7485	−0.276697
$21$	77.1576	0.801770
$22$	0	0
$23$	2.04459	0.0185359	0.00926795	−	0.999957i	$-0.497050\pi$
$23$	2.04459	0.0185359	0.00926795	+	0.999957i	$0.497050\pi$
$24$	24.0000	0.204124
$25$	−86.7194	−0.693755
$26$	61.5261	0.464087
$27$	27.0000	0.192450
$28$	102.877	0.694353
$29$	59.0080	0.377845	0.188923	−	0.981992i	$-0.439500\pi$
$29$	59.0080	0.377845	0.188923	+	0.981992i	$0.439500\pi$
$30$	−37.1228	−0.225922
$31$	304.896	1.76648	0.883241	−	0.468920i	$-0.155357\pi$
$31$	304.896	1.76648	0.883241	+	0.468920i	$0.155357\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	95.9699	0.484079
$35$	−159.128	−0.768502
$36$	36.0000	0.166667
$37$	−303.823	−1.34995	−0.674976	−	0.737840i	$-0.735846\pi$
$37$	−303.823	−1.34995	−0.674976	+	0.737840i	$0.735846\pi$
$38$	−93.4960	−0.399133
$39$	92.2891	0.378925
$40$	−49.4971	−0.195654
$41$	145.553	0.554428	0.277214	−	0.960808i	$-0.410589\pi$
$41$	145.553	0.554428	0.277214	+	0.960808i	$0.410589\pi$
$42$	154.315	0.566937
$43$	−284.084	−1.00750	−0.503748	−	0.863850i	$-0.668046\pi$
$43$	−284.084	−1.00750	−0.503748	+	0.863850i	$0.668046\pi$
$44$	0	0
$45$	−55.6842	−0.184465
$46$	4.08917	0.0131069
$47$	577.251	1.79151	0.895753	−	0.444552i	$-0.146637\pi$
$47$	577.251	1.79151	0.895753	+	0.444552i	$0.146637\pi$
$48$	48.0000	0.144338
$49$	318.477	0.928505
$50$	−173.439	−0.490559
$51$	143.955	0.395249
$52$	123.052	0.328159
$53$	655.216	1.69813	0.849065	−	0.528289i	$-0.177166\pi$
$53$	655.216	1.69813	0.849065	+	0.528289i	$0.177166\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	205.754	0.490982
$57$	−140.244	−0.325891
$58$	118.016	0.267177
$59$	−23.1802	−0.0511492	−0.0255746	−	0.999673i	$-0.508142\pi$
$59$	−23.1802	−0.0511492	−0.0255746	+	0.999673i	$0.508142\pi$
$60$	−74.2456	−0.159751
$61$	−631.874	−1.32628	−0.663140	−	0.748495i	$-0.730777\pi$
$61$	−631.874	−1.32628	−0.663140	+	0.748495i	$0.730777\pi$
$62$	609.792	1.24909
$63$	231.473	0.462902
$64$	64.0000	0.125000
$65$	−190.335	−0.363202
$66$	0	0
$67$	−655.918	−1.19602	−0.598009	−	0.801490i	$-0.704041\pi$
$67$	−655.918	−1.19602	−0.598009	+	0.801490i	$0.704041\pi$
$68$	191.940	0.342296
$69$	6.13376	0.0107017
$70$	−318.256	−0.543413
$71$	528.602	0.883571	0.441786	−	0.897121i	$-0.354345\pi$
$71$	528.602	0.883571	0.441786	+	0.897121i	$0.354345\pi$
$72$	72.0000	0.117851
$73$	447.652	0.717723	0.358861	−	0.933391i	$-0.383165\pi$
$73$	447.652	0.717723	0.358861	+	0.933391i	$0.383165\pi$
$74$	−607.646	−0.954560
$75$	−260.158	−0.400540
$76$	−186.992	−0.282230
$77$	0	0
$78$	184.578	0.267941
$79$	985.464	1.40346	0.701730	−	0.712443i	$-0.252411\pi$
$79$	985.464	1.40346	0.701730	+	0.712443i	$0.252411\pi$
$80$	−98.9942	−0.138349
$81$	81.0000	0.111111
$82$	291.106	0.392040
$83$	128.459	0.169882	0.0849411	−	0.996386i	$-0.472930\pi$
$83$	128.459	0.169882	0.0849411	+	0.996386i	$0.472930\pi$
$84$	308.630	0.400885
$85$	−296.889	−0.378849
$86$	−568.167	−0.712408
$87$	177.024	0.218149
$88$	0	0
$89$	1425.15	1.69736	0.848682	−	0.528904i	$-0.177397\pi$
$89$	1425.15	1.69736	0.848682	+	0.528904i	$0.177397\pi$
$90$	−111.368	−0.130436
$91$	791.201	0.911432
$92$	8.17835	0.00926795
$93$	914.688	1.01988
$94$	1154.50	1.26679
$95$	289.236	0.312368
$96$	96.0000	0.102062
$97$	−142.553	−0.149217	−0.0746084	−	0.997213i	$-0.523771\pi$
$97$	−142.553	−0.149217	−0.0746084	+	0.997213i	$0.523771\pi$
$98$	636.954	0.656552
$99$	0	0
$100$	−346.877	−0.346877
$101$	293.830	0.289477	0.144738	−	0.989470i	$-0.453766\pi$
$101$	293.830	0.289477	0.144738	+	0.989470i	$0.453766\pi$
$102$	287.910	0.279483
$103$	−1001.55	−0.958112	−0.479056	−	0.877784i	$-0.659021\pi$
$103$	−1001.55	−0.958112	−0.479056	+	0.877784i	$0.659021\pi$
$104$	246.104	0.232043
$105$	−477.384	−0.443695
$106$	1310.43	1.20076
$107$	−1604.00	−1.44920	−0.724602	−	0.689168i	$-0.757976\pi$
$107$	−1604.00	−1.44920	−0.724602	+	0.689168i	$0.757976\pi$
$108$	108.000	0.0962250
$109$	−323.134	−0.283951	−0.141975	−	0.989870i	$-0.545345\pi$
$109$	−323.134	−0.283951	−0.141975	+	0.989870i	$0.545345\pi$
$110$	0	0
$111$	−911.470	−0.779395
$112$	411.507	0.347177
$113$	−464.460	−0.386661	−0.193331	−	0.981134i	$-0.561929\pi$
$113$	−464.460	−0.386661	−0.193331	+	0.981134i	$0.561929\pi$
$114$	−280.488	−0.230439
$115$	−12.6501	−0.0102577
$116$	236.032	0.188923
$117$	276.867	0.218773
$118$	−46.3604	−0.0361680
$119$	1234.13	0.950697
$120$	−148.491	−0.112961
$121$	0	0
$122$	−1263.75	−0.937822
$123$	436.659	0.320099
$124$	1219.58	0.883241
$125$	1309.94	0.937314
$126$	462.946	0.327321
$127$	−327.549	−0.228861	−0.114430	−	0.993431i	$-0.536504\pi$
$127$	−327.549	−0.228861	−0.114430	+	0.993431i	$0.536504\pi$
$128$	128.000	0.0883883
$129$	−852.251	−0.581678
$130$	−380.670	−0.256823
$131$	−2871.12	−1.91489	−0.957447	−	0.288610i	$-0.906807\pi$
$131$	−2871.12	−1.91489	−0.957447	+	0.288610i	$0.906807\pi$
$132$	0	0
$133$	−1202.32	−0.783868
$134$	−1311.84	−0.845712
$135$	−167.053	−0.106501
$136$	383.880	0.242040
$137$	1143.36	0.713018	0.356509	−	0.934292i	$-0.383967\pi$
$137$	1143.36	0.713018	0.356509	+	0.934292i	$0.383967\pi$
$138$	12.2675	0.00756725
$139$	−336.573	−0.205379	−0.102690	−	0.994713i	$-0.532745\pi$
$139$	−336.573	−0.205379	−0.102690	+	0.994713i	$0.532745\pi$
$140$	−636.513	−0.384251
$141$	1731.75	1.03433
$142$	1057.20	0.624779
$143$	0	0
$144$	144.000	0.0833333
$145$	−365.091	−0.209097
$146$	895.305	0.507507
$147$	955.432	0.536073
$148$	−1215.29	−0.674976
$149$	−858.353	−0.471940	−0.235970	−	0.971760i	$-0.575827\pi$
$149$	−858.353	−0.471940	−0.235970	+	0.971760i	$0.575827\pi$
$150$	−520.316	−0.283224
$151$	−3086.90	−1.66363	−0.831814	−	0.555054i	$-0.812698\pi$
$151$	−3086.90	−1.66363	−0.831814	+	0.555054i	$0.812698\pi$
$152$	−373.984	−0.199566
$153$	431.865	0.228197
$154$	0	0
$155$	−1886.43	−0.977560
$156$	369.156	0.189463
$157$	1737.12	0.883039	0.441519	−	0.897252i	$-0.354440\pi$
$157$	1737.12	0.883039	0.441519	+	0.897252i	$0.354440\pi$
$158$	1970.93	0.992396
$159$	1965.65	0.980416
$160$	−197.988	−0.0978272
$161$	52.5851	0.0257409
$162$	162.000	0.0785674
$163$	−2382.91	−1.14506	−0.572528	−	0.819885i	$-0.694037\pi$
$163$	−2382.91	−1.14506	−0.572528	+	0.819885i	$0.694037\pi$
$164$	582.212	0.277214
$165$	0	0
$166$	256.918	0.120125
$167$	−2961.84	−1.37242	−0.686209	−	0.727404i	$-0.740726\pi$
$167$	−2961.84	−1.37242	−0.686209	+	0.727404i	$0.740726\pi$
$168$	617.261	0.283468
$169$	−1250.64	−0.569247
$170$	−593.779	−0.267887
$171$	−420.732	−0.188153
$172$	−1136.33	−0.503748
$173$	314.894	0.138387	0.0691936	−	0.997603i	$-0.477957\pi$
$173$	314.894	0.138387	0.0691936	+	0.997603i	$0.477957\pi$
$174$	354.048	0.154255
$175$	−2230.35	−0.963422
$176$	0	0
$177$	−69.5406	−0.0295310
$178$	2850.30	1.20022
$179$	−2412.21	−1.00725	−0.503624	−	0.863923i	$-0.668000\pi$
$179$	−2412.21	−1.00725	−0.503624	+	0.863923i	$0.668000\pi$
$180$	−222.737	−0.0922324
$181$	3908.18	1.60493	0.802466	−	0.596698i	$-0.203521\pi$
$181$	3908.18	1.60493	0.802466	+	0.596698i	$0.203521\pi$
$182$	1582.40	0.644480
$183$	−1895.62	−0.765729
$184$	16.3567	0.00655343
$185$	1879.80	0.747056
$186$	1829.38	0.721163
$187$	0	0
$188$	2309.01	0.895753
$189$	694.418	0.267257
$190$	578.472	0.220878
$191$	−912.609	−0.345728	−0.172864	−	0.984946i	$-0.555302\pi$
$191$	−912.609	−0.345728	−0.172864	+	0.984946i	$0.555302\pi$
$192$	192.000	0.0721688
$193$	533.160	0.198848	0.0994241	−	0.995045i	$-0.468300\pi$
$193$	533.160	0.198848	0.0994241	+	0.995045i	$0.468300\pi$
$194$	−285.105	−0.105512
$195$	−571.005	−0.209695
$196$	1273.91	0.464252
$197$	−2700.49	−0.976659	−0.488329	−	0.872659i	$-0.662394\pi$
$197$	−2700.49	−0.976659	−0.488329	+	0.872659i	$0.662394\pi$
$198$	0	0
$199$	4409.62	1.57080	0.785401	−	0.618987i	$-0.212457\pi$
$199$	4409.62	1.57080	0.785401	+	0.618987i	$0.212457\pi$
$200$	−693.755	−0.245279
$201$	−1967.76	−0.690521
$202$	587.659	0.204691
$203$	1517.64	0.524716
$204$	575.819	0.197625
$205$	−900.555	−0.306817
$206$	−2003.10	−0.677488
$207$	18.4013	0.00617864
$208$	492.208	0.164079
$209$	0	0
$210$	−954.769	−0.313740
$211$	5804.51	1.89383	0.946917	−	0.321479i	$-0.104180\pi$
$211$	5804.51	1.89383	0.946917	+	0.321479i	$0.104180\pi$
$212$	2620.86	0.849065
$213$	1585.81	0.510130
$214$	−3208.01	−1.02474
$215$	1757.66	0.557543
$216$	216.000	0.0680414
$217$	7841.68	2.45312
$218$	−646.268	−0.200784
$219$	1342.96	0.414377
$220$	0	0
$221$	1476.16	0.449310
$222$	−1822.94	−0.551116
$223$	−3466.84	−1.04106	−0.520530	−	0.853843i	$-0.674266\pi$
$223$	−3466.84	−1.04106	−0.520530	+	0.853843i	$0.674266\pi$
$224$	823.014	0.245491
$225$	−780.474	−0.231252
$226$	−928.920	−0.273411
$227$	4036.58	1.18025	0.590127	−	0.807311i	$-0.299078\pi$
$227$	4036.58	1.18025	0.590127	+	0.807311i	$0.299078\pi$
$228$	−560.976	−0.162945
$229$	−3078.22	−0.888272	−0.444136	−	0.895959i	$-0.646489\pi$
$229$	−3078.22	−0.888272	−0.444136	+	0.895959i	$0.646489\pi$
$230$	−25.3003	−0.00725326
$231$	0	0
$232$	472.064	0.133589
$233$	−1687.61	−0.474501	−0.237251	−	0.971449i	$-0.576246\pi$
$233$	−1687.61	−0.474501	−0.237251	+	0.971449i	$0.576246\pi$
$234$	553.735	0.154696
$235$	−3571.53	−0.991409
$236$	−92.7208	−0.0255746
$237$	2956.39	0.810288
$238$	2468.27	0.672244
$239$	−2421.76	−0.655442	−0.327721	−	0.944775i	$-0.606281\pi$
$239$	−2421.76	−0.655442	−0.327721	+	0.944775i	$0.606281\pi$
$240$	−296.982	−0.0798756
$241$	−6935.97	−1.85388	−0.926940	−	0.375209i	$-0.877571\pi$
$241$	−6935.97	−1.85388	−0.926940	+	0.375209i	$0.877571\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−2527.49	−0.663140
$245$	−1970.46	−0.513829
$246$	873.317	0.226344
$247$	−1438.11	−0.370464
$248$	2439.17	0.624545
$249$	385.378	0.0980816
$250$	2619.87	0.662781
$251$	−764.367	−0.192217	−0.0961085	−	0.995371i	$-0.530640\pi$
$251$	−764.367	−0.192217	−0.0961085	+	0.995371i	$0.530640\pi$
$252$	925.891	0.231451
$253$	0	0
$254$	−655.099	−0.161829
$255$	−890.668	−0.218729
$256$	256.000	0.0625000
$257$	1828.90	0.443906	0.221953	−	0.975057i	$-0.428757\pi$
$257$	1828.90	0.443906	0.221953	+	0.975057i	$0.428757\pi$
$258$	−1704.50	−0.411309
$259$	−7814.09	−1.87469
$260$	−761.340	−0.181601
$261$	531.072	0.125948
$262$	−5742.24	−1.35403
$263$	7853.83	1.84140	0.920700	−	0.390271i	$-0.127619\pi$
$263$	7853.83	1.84140	0.920700	+	0.390271i	$0.127619\pi$
$264$	0	0
$265$	−4053.91	−0.939735
$266$	−2404.64	−0.554278
$267$	4275.44	0.979973
$268$	−2623.67	−0.598009
$269$	−7656.82	−1.73548	−0.867741	−	0.497017i	$-0.834429\pi$
$269$	−7656.82	−1.73548	−0.867741	+	0.497017i	$0.834429\pi$
$270$	−334.105	−0.0753074
$271$	−7351.92	−1.64796	−0.823981	−	0.566618i	$-0.808251\pi$
$271$	−7351.92	−1.64796	−0.823981	+	0.566618i	$0.808251\pi$
$272$	767.759	0.171148
$273$	2373.60	0.526216
$274$	2286.71	0.504180
$275$	0	0
$276$	24.5350	0.00535085
$277$	4238.60	0.919396	0.459698	−	0.888075i	$-0.347958\pi$
$277$	4238.60	0.919396	0.459698	+	0.888075i	$0.347958\pi$
$278$	−673.146	−0.145225
$279$	2744.06	0.588827
$280$	−1273.03	−0.271706
$281$	−4243.25	−0.900822	−0.450411	−	0.892821i	$-0.648723\pi$
$281$	−4243.25	−0.900822	−0.450411	+	0.892821i	$0.648723\pi$
$282$	3463.51	0.731379
$283$	4069.93	0.854883	0.427442	−	0.904043i	$-0.359415\pi$
$283$	4069.93	0.854883	0.427442	+	0.904043i	$0.359415\pi$
$284$	2114.41	0.441786
$285$	867.708	0.180346
$286$	0	0
$287$	3743.50	0.769937
$288$	288.000	0.0589256
$289$	−2610.44	−0.531334
$290$	−730.181	−0.147854
$291$	−427.658	−0.0861504
$292$	1790.61	0.358861
$293$	−7903.75	−1.57591	−0.787955	−	0.615733i	$-0.788860\pi$
$293$	−7903.75	−1.57591	−0.787955	+	0.615733i	$0.788860\pi$
$294$	1910.86	0.379061
$295$	143.419	0.0283057
$296$	−2430.59	−0.477280
$297$	0	0
$298$	−1716.71	−0.333712
$299$	62.8977	0.0121654
$300$	−1040.63	−0.200270
$301$	−7306.40	−1.39912
$302$	−6173.79	−1.17636
$303$	881.489	0.167129
$304$	−747.968	−0.141115
$305$	3909.49	0.733956
$306$	863.729	0.161360
$307$	−4887.27	−0.908570	−0.454285	−	0.890856i	$-0.650105\pi$
$307$	−4887.27	−0.908570	−0.454285	+	0.890856i	$0.650105\pi$
$308$	0	0
$309$	−3004.65	−0.553166
$310$	−3772.86	−0.691240
$311$	−6555.16	−1.19521	−0.597603	−	0.801792i	$-0.703880\pi$
$311$	−6555.16	−1.19521	−0.597603	+	0.801792i	$0.703880\pi$
$312$	738.313	0.133970
$313$	−6473.07	−1.16894	−0.584472	−	0.811414i	$-0.698698\pi$
$313$	−6473.07	−1.16894	−0.584472	+	0.811414i	$0.698698\pi$
$314$	3474.23	0.624403
$315$	−1432.15	−0.256167
$316$	3941.86	0.701730
$317$	3732.52	0.661322	0.330661	−	0.943750i	$-0.392728\pi$
$317$	3732.52	0.661322	0.330661	+	0.943750i	$0.392728\pi$
$318$	3931.30	0.693259
$319$	0	0
$320$	−395.977	−0.0691743
$321$	−4812.01	−0.836698
$322$	105.170	0.0182016
$323$	−2243.20	−0.386424
$324$	324.000	0.0555556
$325$	−2667.75	−0.455324
$326$	−4765.82	−0.809676
$327$	−969.403	−0.163939
$328$	1164.42	0.196020
$329$	14846.4	2.48788
$330$	0	0
$331$	6093.87	1.01193	0.505966	−	0.862554i	$-0.331136\pi$
$331$	6093.87	1.01193	0.505966	+	0.862554i	$0.331136\pi$
$332$	513.837	0.0849411
$333$	−2734.41	−0.449984
$334$	−5923.67	−0.970446
$335$	4058.26	0.661869
$336$	1234.52	0.200442
$337$	−3220.27	−0.520531	−0.260266	−	0.965537i	$-0.583810\pi$
$337$	−3220.27	−0.520531	−0.260266	+	0.965537i	$0.583810\pi$
$338$	−2501.27	−0.402518
$339$	−1393.38	−0.223239
$340$	−1187.56	−0.189425
$341$	0	0
$342$	−841.464	−0.133044
$343$	−630.707	−0.0992857
$344$	−2272.67	−0.356204
$345$	−37.9504	−0.00592226
$346$	629.789	0.0978545
$347$	−2922.59	−0.452141	−0.226071	−	0.974111i	$-0.572588\pi$
$347$	−2922.59	−0.452141	−0.226071	+	0.974111i	$0.572588\pi$
$348$	708.096	0.109075
$349$	2398.61	0.367893	0.183946	−	0.982936i	$-0.441113\pi$
$349$	2398.61	0.367893	0.183946	+	0.982936i	$0.441113\pi$
$350$	−4460.70	−0.681242
$351$	830.602	0.126308
$352$	0	0
$353$	−8037.61	−1.21189	−0.605947	−	0.795505i	$-0.707206\pi$
$353$	−8037.61	−1.21189	−0.605947	+	0.795505i	$0.707206\pi$
$354$	−139.081	−0.0208816
$355$	−3270.53	−0.488963
$356$	5700.59	0.848682
$357$	3702.40	0.548885
$358$	−4824.43	−0.712231
$359$	6245.09	0.918115	0.459058	−	0.888406i	$-0.348187\pi$
$359$	6245.09	0.918115	0.459058	+	0.888406i	$0.348187\pi$
$360$	−445.474	−0.0652181
$361$	−4673.63	−0.681386
$362$	7816.36	1.13486
$363$	0	0
$364$	3164.80	0.455716
$365$	−2769.69	−0.397184
$366$	−3791.24	−0.541452
$367$	3605.89	0.512878	0.256439	−	0.966560i	$-0.417451\pi$
$367$	3605.89	0.512878	0.256439	+	0.966560i	$0.417451\pi$
$368$	32.7134	0.00463398
$369$	1309.98	0.184809
$370$	3759.59	0.528248
$371$	16851.6	2.35820
$372$	3658.75	0.509939
$373$	−1535.30	−0.213123	−0.106561	−	0.994306i	$-0.533984\pi$
$373$	−1535.30	−0.213123	−0.106561	+	0.994306i	$0.533984\pi$
$374$	0	0
$375$	3929.81	0.541159
$376$	4618.01	0.633393
$377$	1815.27	0.247987
$378$	1388.84	0.188979
$379$	−12947.9	−1.75485	−0.877426	−	0.479713i	$-0.840741\pi$
$379$	−12947.9	−1.75485	−0.877426	+	0.479713i	$0.840741\pi$
$380$	1156.94	0.156184
$381$	−982.648	−0.132133
$382$	−1825.22	−0.244467
$383$	−3063.26	−0.408683	−0.204341	−	0.978900i	$-0.565505\pi$
$383$	−3063.26	−0.408683	−0.204341	+	0.978900i	$0.565505\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	1066.32	0.140607
$387$	−2556.75	−0.335832
$388$	−570.211	−0.0746084
$389$	3662.10	0.477316	0.238658	−	0.971104i	$-0.423293\pi$
$389$	3662.10	0.477316	0.238658	+	0.971104i	$0.423293\pi$
$390$	−1142.01	−0.148277
$391$	98.1094	0.0126895
$392$	2547.82	0.328276
$393$	−8613.37	−1.10556
$394$	−5400.97	−0.690602
$395$	−6097.20	−0.776667
$396$	0	0
$397$	−5438.40	−0.687520	−0.343760	−	0.939057i	$-0.611701\pi$
$397$	−5438.40	−0.687520	−0.343760	+	0.939057i	$0.611701\pi$
$398$	8819.24	1.11072
$399$	−3606.96	−0.452566
$400$	−1387.51	−0.173439
$401$	3275.54	0.407912	0.203956	−	0.978980i	$-0.434620\pi$
$401$	3275.54	0.407912	0.203956	+	0.978980i	$0.434620\pi$
$402$	−3935.51	−0.488272
$403$	9379.52	1.15937
$404$	1175.32	0.144738
$405$	−501.158	−0.0614882
$406$	3035.28	0.371030
$407$	0	0
$408$	1151.64	0.139742
$409$	−28.2549	−0.00341593	−0.00170797	−	0.999999i	$-0.500544\pi$
$409$	−28.2549	−0.00341593	−0.00170797	+	0.999999i	$0.500544\pi$
$410$	−1801.11	−0.216952
$411$	3430.07	0.411661
$412$	−4006.20	−0.479056
$413$	−596.176	−0.0710312
$414$	36.8026	0.00436895
$415$	−794.795	−0.0940119
$416$	984.417	0.116022
$417$	−1009.72	−0.118576
$418$	0	0
$419$	2788.66	0.325143	0.162572	−	0.986697i	$-0.448021\pi$
$419$	2788.66	0.325143	0.162572	+	0.986697i	$0.448021\pi$
$420$	−1909.54	−0.221847
$421$	−8006.82	−0.926908	−0.463454	−	0.886121i	$-0.653390\pi$
$421$	−8006.82	−0.926908	−0.463454	+	0.886121i	$0.653390\pi$
$422$	11609.0	1.33914
$423$	5195.26	0.597169
$424$	5241.73	0.600380
$425$	−4161.22	−0.474939
$426$	3171.61	0.360717
$427$	−16251.3	−1.84181
$428$	−6416.01	−0.724602
$429$	0	0
$430$	3515.33	0.394242
$431$	−11372.5	−1.27099	−0.635495	−	0.772105i	$-0.719204\pi$
$431$	−11372.5	−1.27099	−0.635495	+	0.772105i	$0.719204\pi$
$432$	432.000	0.0481125
$433$	−2336.59	−0.259329	−0.129664	−	0.991558i	$-0.541390\pi$
$433$	−2336.59	−0.259329	−0.129664	+	0.991558i	$0.541390\pi$
$434$	15683.4	1.73462
$435$	−1095.27	−0.120722
$436$	−1292.54	−0.141975
$437$	−95.5803	−0.0104628
$438$	2685.91	0.293009
$439$	1689.97	0.183731	0.0918655	−	0.995771i	$-0.470717\pi$
$439$	1689.97	0.183731	0.0918655	+	0.995771i	$0.470717\pi$
$440$	0	0
$441$	2866.29	0.309502
$442$	2952.33	0.317710
$443$	6847.10	0.734347	0.367173	−	0.930153i	$-0.380326\pi$
$443$	6847.10	0.734347	0.367173	+	0.930153i	$0.380326\pi$
$444$	−3645.88	−0.389698
$445$	−8817.58	−0.939311
$446$	−6933.67	−0.736141
$447$	−2575.06	−0.272474
$448$	1646.03	0.173588
$449$	16416.6	1.72550	0.862749	−	0.505633i	$-0.168741\pi$
$449$	16416.6	1.72550	0.862749	+	0.505633i	$0.168741\pi$
$450$	−1560.95	−0.163520
$451$	0	0
$452$	−1857.84	−0.193331
$453$	−9260.69	−0.960497
$454$	8073.17	0.834565
$455$	−4895.26	−0.504381
$456$	−1121.95	−0.115220
$457$	14619.7	1.49646	0.748228	−	0.663442i	$-0.230905\pi$
$457$	14619.7	1.49646	0.748228	+	0.663442i	$0.230905\pi$
$458$	−6156.43	−0.628103
$459$	1295.59	0.131750
$460$	−50.6005	−0.00512883
$461$	−932.481	−0.0942082	−0.0471041	−	0.998890i	$-0.514999\pi$
$461$	−932.481	−0.0942082	−0.0471041	+	0.998890i	$0.514999\pi$
$462$	0	0
$463$	5806.81	0.582862	0.291431	−	0.956592i	$-0.405869\pi$
$463$	5806.81	0.582862	0.291431	+	0.956592i	$0.405869\pi$
$464$	944.128	0.0944613
$465$	−5659.30	−0.564395
$466$	−3375.21	−0.335523
$467$	−2143.97	−0.212444	−0.106222	−	0.994342i	$-0.533875\pi$
$467$	−2143.97	−0.212444	−0.106222	+	0.994342i	$0.533875\pi$
$468$	1107.47	0.109386
$469$	−16869.7	−1.66092
$470$	−7143.07	−0.701032
$471$	5211.35	0.509823
$472$	−185.442	−0.0180840
$473$	0	0
$474$	5912.78	0.572960
$475$	4053.96	0.391596
$476$	4936.54	0.475348
$477$	5896.95	0.566043
$478$	−4843.52	−0.463467
$479$	3401.22	0.324437	0.162219	−	0.986755i	$-0.448135\pi$
$479$	3401.22	0.324437	0.162219	+	0.986755i	$0.448135\pi$
$480$	−593.965	−0.0564806
$481$	−9346.52	−0.885997
$482$	−13871.9	−1.31089
$483$	157.755	0.0148615
$484$	0	0
$485$	881.993	0.0825758
$486$	486.000	0.0453609
$487$	9632.81	0.896313	0.448156	−	0.893955i	$-0.352081\pi$
$487$	9632.81	0.896313	0.448156	+	0.893955i	$0.352081\pi$
$488$	−5054.99	−0.468911
$489$	−7148.73	−0.661098
$490$	−3940.92	−0.363332
$491$	5594.16	0.514177	0.257088	−	0.966388i	$-0.417237\pi$
$491$	5594.16	0.514177	0.257088	+	0.966388i	$0.417237\pi$
$492$	1746.63	0.160050
$493$	2831.50	0.258670
$494$	−2876.22	−0.261958
$495$	0	0
$496$	4878.33	0.441620
$497$	13595.2	1.22702
$498$	770.755	0.0693542
$499$	−2295.31	−0.205917	−0.102958	−	0.994686i	$-0.532831\pi$
$499$	−2295.31	−0.205917	−0.102958	+	0.994686i	$0.532831\pi$
$500$	5239.75	0.468657
$501$	−8885.51	−0.792366
$502$	−1528.73	−0.135918
$503$	−6271.41	−0.555921	−0.277961	−	0.960592i	$-0.589658\pi$
$503$	−6271.41	−0.555921	−0.277961	+	0.960592i	$0.589658\pi$
$504$	1851.78	0.163661
$505$	−1817.96	−0.160195
$506$	0	0
$507$	−3751.91	−0.328655
$508$	−1310.20	−0.114430
$509$	8882.04	0.773457	0.386729	−	0.922194i	$-0.373605\pi$
$509$	8882.04	0.773457	0.386729	+	0.922194i	$0.373605\pi$
$510$	−1781.34	−0.154665
$511$	11513.3	0.996706
$512$	512.000	0.0441942
$513$	−1262.20	−0.108630
$514$	3657.81	0.313889
$515$	6196.72	0.530214
$516$	−3409.00	−0.290839
$517$	0	0
$518$	−15628.2	−1.32560
$519$	944.683	0.0798979
$520$	−1522.68	−0.128411
$521$	506.901	0.0426252	0.0213126	−	0.999773i	$-0.493215\pi$
$521$	506.901	0.0426252	0.0213126	+	0.999773i	$0.493215\pi$
$522$	1062.14	0.0890590
$523$	8415.97	0.703642	0.351821	−	0.936067i	$-0.385563\pi$
$523$	8415.97	0.703642	0.351821	+	0.936067i	$0.385563\pi$
$524$	−11484.5	−0.957447
$525$	−6691.06	−0.556232
$526$	15707.7	1.30207
$527$	14630.4	1.20932
$528$	0	0
$529$	−12162.8	−0.999656
$530$	−8107.82	−0.664493
$531$	−208.622	−0.0170497
$532$	−4809.28	−0.391934
$533$	4477.65	0.363881
$534$	8550.89	0.692946
$535$	9924.18	0.801981
$536$	−5247.35	−0.422856
$537$	−7236.64	−0.581534
$538$	−15313.6	−1.22717
$539$	0	0
$540$	−668.211	−0.0532504
$541$	−2292.00	−0.182145	−0.0910727	−	0.995844i	$-0.529030\pi$
$541$	−2292.00	−0.182145	−0.0910727	+	0.995844i	$0.529030\pi$
$542$	−14703.8	−1.16528
$543$	11724.5	0.926608
$544$	1535.52	0.121020
$545$	1999.28	0.157137
$546$	4747.20	0.372091
$547$	−9334.79	−0.729665	−0.364833	−	0.931073i	$-0.618874\pi$
$547$	−9334.79	−0.729665	−0.364833	+	0.931073i	$0.618874\pi$
$548$	4573.43	0.356509
$549$	−5686.86	−0.442094
$550$	0	0
$551$	−2758.51	−0.213278
$552$	49.0701	0.00378363
$553$	25345.3	1.94899
$554$	8477.20	0.650111
$555$	5639.39	0.431313
$556$	−1346.29	−0.102690
$557$	−3681.18	−0.280030	−0.140015	−	0.990149i	$-0.544715\pi$
$557$	−3681.18	−0.280030	−0.140015	+	0.990149i	$0.544715\pi$
$558$	5488.13	0.416364
$559$	−8739.27	−0.661238
$560$	−2546.05	−0.192125
$561$	0	0
$562$	−8486.50	−0.636978
$563$	23961.3	1.79369	0.896846	−	0.442342i	$-0.145852\pi$
$563$	23961.3	1.79369	0.896846	+	0.442342i	$0.145852\pi$
$564$	6927.02	0.517163
$565$	2873.68	0.213976
$566$	8139.85	0.604494
$567$	2083.26	0.154301
$568$	4228.82	0.312390
$569$	3727.10	0.274601	0.137301	−	0.990529i	$-0.456157\pi$
$569$	3727.10	0.274601	0.137301	+	0.990529i	$0.456157\pi$
$570$	1735.42	0.127524
$571$	−23463.5	−1.71965	−0.859823	−	0.510593i	$-0.829426\pi$
$571$	−23463.5	−1.71965	−0.859823	+	0.510593i	$0.829426\pi$
$572$	0	0
$573$	−2737.83	−0.199606
$574$	7487.01	0.544428
$575$	−177.305	−0.0128594
$576$	576.000	0.0416667
$577$	−1118.13	−0.0806729	−0.0403365	−	0.999186i	$-0.512843\pi$
$577$	−1118.13	−0.0806729	−0.0403365	+	0.999186i	$0.512843\pi$
$578$	−5220.89	−0.375710
$579$	1599.48	0.114805
$580$	−1460.36	−0.104549
$581$	3303.87	0.235917
$582$	−855.316	−0.0609175
$583$	0	0
$584$	3581.22	0.253753
$585$	−1713.02	−0.121067
$586$	−15807.5	−1.11434
$587$	−20399.2	−1.43436	−0.717178	−	0.696890i	$-0.754566\pi$
$587$	−20399.2	−1.43436	−0.717178	+	0.696890i	$0.754566\pi$
$588$	3821.73	0.268036
$589$	−14253.3	−0.997106
$590$	286.838	0.0200151
$591$	−8101.46	−0.563874
$592$	−4861.17	−0.337488
$593$	−2722.97	−0.188565	−0.0942826	−	0.995545i	$-0.530056\pi$
$593$	−2722.97	−0.188565	−0.0942826	+	0.995545i	$0.530056\pi$
$594$	0	0
$595$	−7635.76	−0.526110
$596$	−3433.41	−0.235970
$597$	13228.9	0.906903
$598$	125.795	0.00860227
$599$	−444.486	−0.0303192	−0.0151596	−	0.999885i	$-0.504826\pi$
$599$	−444.486	−0.0303192	−0.0151596	+	0.999885i	$0.504826\pi$
$600$	−2081.26	−0.141612
$601$	3564.00	0.241895	0.120947	−	0.992659i	$-0.461407\pi$
$601$	3564.00	0.241895	0.120947	+	0.992659i	$0.461407\pi$
$602$	−14612.8	−0.989325
$603$	−5903.27	−0.398673
$604$	−12347.6	−0.831814
$605$	0	0
$606$	1762.98	0.118178
$607$	9182.13	0.613989	0.306994	−	0.951711i	$-0.400677\pi$
$607$	9182.13	0.613989	0.306994	+	0.951711i	$0.400677\pi$
$608$	−1495.94	−0.0997832
$609$	4552.92	0.302945
$610$	7818.97	0.518985
$611$	17758.0	1.17580
$612$	1727.46	0.114099
$613$	−15822.6	−1.04253	−0.521263	−	0.853396i	$-0.674539\pi$
$613$	−15822.6	−1.04253	−0.521263	+	0.853396i	$0.674539\pi$
$614$	−9774.53	−0.642456
$615$	−2701.67	−0.177141
$616$	0	0
$617$	15442.0	1.00757	0.503784	−	0.863830i	$-0.331941\pi$
$617$	15442.0	1.00757	0.503784	+	0.863830i	$0.331941\pi$
$618$	−6009.30	−0.391148
$619$	4205.61	0.273082	0.136541	−	0.990634i	$-0.456401\pi$
$619$	4205.61	0.273082	0.136541	+	0.990634i	$0.456401\pi$
$620$	−7545.73	−0.488780
$621$	55.2038	0.00356724
$622$	−13110.3	−0.845138
$623$	36653.7	2.35714
$624$	1476.63	0.0947313
$625$	2735.17	0.175051
$626$	−12946.1	−0.826568
$627$	0	0
$628$	6948.47	0.441519
$629$	−14578.9	−0.924166
$630$	−2864.31	−0.181138
$631$	18506.4	1.16755	0.583777	−	0.811914i	$-0.301574\pi$
$631$	18506.4	1.16755	0.583777	+	0.811914i	$0.301574\pi$
$632$	7883.71	0.496198
$633$	17413.5	1.09341
$634$	7465.03	0.467625
$635$	2026.59	0.126650
$636$	7862.59	0.490208
$637$	9797.32	0.609394
$638$	0	0
$639$	4757.42	0.294524
$640$	−791.953	−0.0489136
$641$	20000.4	1.23240	0.616201	−	0.787589i	$-0.288671\pi$
$641$	20000.4	1.23240	0.616201	+	0.787589i	$0.288671\pi$
$642$	−9624.02	−0.591635
$643$	22453.5	1.37710	0.688552	−	0.725187i	$-0.258247\pi$
$643$	22453.5	1.37710	0.688552	+	0.725187i	$0.258247\pi$
$644$	210.341	0.0128705
$645$	5272.99	0.321897
$646$	−4486.40	−0.273243
$647$	12963.8	0.787727	0.393863	−	0.919169i	$-0.371138\pi$
$647$	12963.8	0.787727	0.393863	+	0.919169i	$0.371138\pi$
$648$	648.000	0.0392837
$649$	0	0
$650$	−5335.50	−0.321962
$651$	23525.0	1.41631
$652$	−9531.65	−0.572528
$653$	−5075.91	−0.304189	−0.152095	−	0.988366i	$-0.548602\pi$
$653$	−5075.91	−0.304189	−0.152095	+	0.988366i	$0.548602\pi$
$654$	−1938.81	−0.115922
$655$	17764.0	1.05969
$656$	2328.85	0.138607
$657$	4028.87	0.239241
$658$	29692.9	1.75919
$659$	29578.3	1.74842	0.874210	−	0.485548i	$-0.161380\pi$
$659$	29578.3	1.74842	0.874210	+	0.485548i	$0.161380\pi$
$660$	0	0
$661$	13835.2	0.814113	0.407056	−	0.913403i	$-0.366555\pi$
$661$	13835.2	0.814113	0.407056	+	0.913403i	$0.366555\pi$
$662$	12187.7	0.715543
$663$	4428.49	0.259409
$664$	1027.67	0.0600625
$665$	7438.92	0.433788
$666$	−5468.82	−0.318187
$667$	120.647	0.00700371
$668$	−11847.3	−0.686209
$669$	−10400.5	−0.601057
$670$	8116.51	0.468012
$671$	0	0
$672$	2469.04	0.141734
$673$	−14592.6	−0.835812	−0.417906	−	0.908490i	$-0.637236\pi$
$673$	−14592.6	−0.835812	−0.417906	+	0.908490i	$0.637236\pi$
$674$	−6440.53	−0.368071
$675$	−2341.42	−0.133513
$676$	−5002.54	−0.284624
$677$	−6957.20	−0.394959	−0.197479	−	0.980307i	$-0.563276\pi$
$677$	−6957.20	−0.394959	−0.197479	+	0.980307i	$0.563276\pi$
$678$	−2786.76	−0.157854
$679$	−3666.34	−0.207218
$680$	−2375.12	−0.133943
$681$	12109.8	0.681420
$682$	0	0
$683$	4828.48	0.270508	0.135254	−	0.990811i	$-0.456815\pi$
$683$	4828.48	0.270508	0.135254	+	0.990811i	$0.456815\pi$
$684$	−1682.93	−0.0940765
$685$	−7074.10	−0.394580
$686$	−1261.41	−0.0702056
$687$	−9234.65	−0.512844
$688$	−4545.34	−0.251874
$689$	20156.4	1.11451
$690$	−75.9008	−0.00418767
$691$	−13876.3	−0.763934	−0.381967	−	0.924176i	$-0.624753\pi$
$691$	−13876.3	−0.763934	−0.381967	+	0.924176i	$0.624753\pi$
$692$	1259.58	0.0691936
$693$	0	0
$694$	−5845.19	−0.319712
$695$	2082.42	0.113656
$696$	1416.19	0.0771274
$697$	6984.35	0.379557
$698$	4797.22	0.260140
$699$	−5062.82	−0.273953
$700$	−8921.41	−0.481711
$701$	10253.4	0.552445	0.276222	−	0.961094i	$-0.410917\pi$
$701$	10253.4	0.552445	0.276222	+	0.961094i	$0.410917\pi$
$702$	1661.20	0.0893135
$703$	14203.1	0.761993
$704$	0	0
$705$	−10714.6	−0.572390
$706$	−16075.2	−0.856939
$707$	7557.06	0.401998
$708$	−278.162	−0.0147655
$709$	28775.1	1.52422	0.762111	−	0.647447i	$-0.224163\pi$
$709$	28775.1	1.52422	0.762111	+	0.647447i	$0.224163\pi$
$710$	−6541.07	−0.345749
$711$	8869.18	0.467820
$712$	11401.2	0.600109
$713$	623.386	0.0327433
$714$	7404.81	0.388120
$715$	0	0
$716$	−9648.85	−0.503624
$717$	−7265.28	−0.378419
$718$	12490.2	0.649206
$719$	10314.7	0.535011	0.267506	−	0.963556i	$-0.413801\pi$
$719$	10314.7	0.535011	0.267506	+	0.963556i	$0.413801\pi$
$720$	−890.947	−0.0461162
$721$	−25759.0	−1.33054
$722$	−9347.25	−0.481813
$723$	−20807.9	−1.07034
$724$	15632.7	0.802466
$725$	−5117.14	−0.262132
$726$	0	0
$727$	16485.6	0.841013	0.420506	−	0.907290i	$-0.361852\pi$
$727$	16485.6	0.841013	0.420506	+	0.907290i	$0.361852\pi$
$728$	6329.60	0.322240
$729$	729.000	0.0370370
$730$	−5539.37	−0.280851
$731$	−13631.7	−0.689724
$732$	−7582.48	−0.382864
$733$	10119.9	0.509943	0.254971	−	0.966949i	$-0.417934\pi$
$733$	10119.9	0.509943	0.254971	+	0.966949i	$0.417934\pi$
$734$	7211.79	0.362659
$735$	−5911.38	−0.296659
$736$	65.4268	0.00327672
$737$	0	0
$738$	2619.95	0.130680
$739$	−2713.38	−0.135065	−0.0675326	−	0.997717i	$-0.521513\pi$
$739$	−2713.38	−0.135065	−0.0675326	+	0.997717i	$0.521513\pi$
$740$	7519.18	0.373528
$741$	−4314.33	−0.213888
$742$	33703.3	1.66750
$743$	13700.9	0.676497	0.338249	−	0.941057i	$-0.390166\pi$
$743$	13700.9	0.676497	0.338249	+	0.941057i	$0.390166\pi$
$744$	7317.50	0.360581
$745$	5310.75	0.261169
$746$	−3070.60	−0.150700
$747$	1156.13	0.0566274
$748$	0	0
$749$	−41253.7	−2.01252
$750$	7859.62	0.382657
$751$	−7831.68	−0.380535	−0.190268	−	0.981732i	$-0.560936\pi$
$751$	−7831.68	−0.380535	−0.190268	+	0.981732i	$0.560936\pi$
$752$	9236.02	0.447877
$753$	−2293.10	−0.110976
$754$	3630.53	0.175353
$755$	19099.0	0.920643
$756$	2777.67	0.133628
$757$	36879.2	1.77067	0.885335	−	0.464953i	$-0.153929\pi$
$757$	36879.2	1.77067	0.885335	+	0.464953i	$0.153929\pi$
$758$	−25895.8	−1.24087
$759$	0	0
$760$	2313.89	0.110439
$761$	−30071.5	−1.43245	−0.716224	−	0.697871i	$-0.754131\pi$
$761$	−30071.5	−1.43245	−0.716224	+	0.697871i	$0.754131\pi$
$762$	−1965.30	−0.0934320
$763$	−8310.75	−0.394324
$764$	−3650.44	−0.172864
$765$	−2672.00	−0.126283
$766$	−6126.53	−0.288982
$767$	−713.093	−0.0335701
$768$	768.000	0.0360844
$769$	23609.8	1.10714	0.553571	−	0.832802i	$-0.313265\pi$
$769$	23609.8	1.10714	0.553571	+	0.832802i	$0.313265\pi$
$770$	0	0
$771$	5486.71	0.256289
$772$	2132.64	0.0994241
$773$	16132.1	0.750622	0.375311	−	0.926899i	$-0.377536\pi$
$773$	16132.1	0.750622	0.375311	+	0.926899i	$0.377536\pi$
$774$	−5113.51	−0.237469
$775$	−26440.4	−1.22550
$776$	−1140.42	−0.0527561
$777$	−23442.3	−1.08235
$778$	7324.20	0.337513
$779$	−6804.30	−0.312952
$780$	−2284.02	−0.104847
$781$	0	0
$782$	196.219	0.00897285
$783$	1593.22	0.0727164
$784$	5095.63	0.232126
$785$	−10747.8	−0.488668
$786$	−17226.7	−0.781752
$787$	12473.2	0.564959	0.282480	−	0.959273i	$-0.408843\pi$
$787$	12473.2	0.564959	0.282480	+	0.959273i	$0.408843\pi$
$788$	−10801.9	−0.488329
$789$	23561.5	1.06313
$790$	−12194.4	−0.549186
$791$	−11945.5	−0.536959
$792$	0	0
$793$	−19438.3	−0.870461
$794$	−10876.8	−0.486150
$795$	−12161.7	−0.542556
$796$	17638.5	0.785401
$797$	−10468.1	−0.465246	−0.232623	−	0.972567i	$-0.574731\pi$
$797$	−10468.1	−0.465246	−0.232623	+	0.972567i	$0.574731\pi$
$798$	−7213.92	−0.320013
$799$	27699.4	1.22645
$800$	−2775.02	−0.122640
$801$	12826.3	0.565788
$802$	6551.08	0.288437
$803$	0	0
$804$	−7871.02	−0.345261
$805$	−325.351	−0.0142449
$806$	18759.0	0.819800
$807$	−22970.5	−1.00198
$808$	2350.64	0.102345
$809$	−17641.7	−0.766686	−0.383343	−	0.923606i	$-0.625227\pi$
$809$	−17641.7	−0.766686	−0.383343	+	0.923606i	$0.625227\pi$
$810$	−1002.32	−0.0434788
$811$	−17854.5	−0.773066	−0.386533	−	0.922276i	$-0.626328\pi$
$811$	−17854.5	−0.773066	−0.386533	+	0.922276i	$0.626328\pi$
$812$	6070.56	0.262358
$813$	−22055.8	−0.951451
$814$	0	0
$815$	14743.4	0.633667
$816$	2303.28	0.0988123
$817$	13280.3	0.568691
$818$	−56.5099	−0.00241543
$819$	7120.80	0.303811
$820$	−3602.22	−0.153409
$821$	14573.5	0.619511	0.309755	−	0.950816i	$-0.399753\pi$
$821$	14573.5	0.619511	0.309755	+	0.950816i	$0.399753\pi$
$822$	6860.14	0.291089
$823$	18565.3	0.786326	0.393163	−	0.919469i	$-0.371381\pi$
$823$	18565.3	0.786326	0.393163	+	0.919469i	$0.371381\pi$
$824$	−8012.39	−0.338744
$825$	0	0
$826$	−1192.35	−0.0502267
$827$	38779.4	1.63058	0.815291	−	0.579052i	$-0.196577\pi$
$827$	38779.4	1.63058	0.815291	+	0.579052i	$0.196577\pi$
$828$	73.6051	0.00308932
$829$	12060.0	0.505263	0.252631	−	0.967563i	$-0.418704\pi$
$829$	12060.0	0.505263	0.252631	+	0.967563i	$0.418704\pi$
$830$	−1589.59	−0.0664764
$831$	12715.8	0.530814
$832$	1968.83	0.0820397
$833$	15282.1	0.635647
$834$	−2019.44	−0.0838458
$835$	18325.3	0.759488
$836$	0	0
$837$	8232.19	0.339959
$838$	5577.32	0.229911
$839$	−28708.8	−1.18133	−0.590666	−	0.806916i	$-0.701135\pi$
$839$	−28708.8	−1.18133	−0.590666	+	0.806916i	$0.701135\pi$
$840$	−3819.08	−0.156870
$841$	−20907.1	−0.857233
$842$	−16013.6	−0.655423
$843$	−12729.8	−0.520090
$844$	23218.0	0.946917
$845$	7737.85	0.315018
$846$	10390.5	0.422262
$847$	0	0
$848$	10483.5	0.424532
$849$	12209.8	0.493567
$850$	−8322.45	−0.335833
$851$	−621.193	−0.0250226
$852$	6343.23	0.255065
$853$	8281.48	0.332418	0.166209	−	0.986091i	$-0.446847\pi$
$853$	8281.48	0.332418	0.166209	+	0.986091i	$0.446847\pi$
$854$	−32502.6	−1.30236
$855$	2603.12	0.104123
$856$	−12832.0	−0.512371
$857$	−21003.8	−0.837195	−0.418597	−	0.908172i	$-0.637478\pi$
$857$	−21003.8	−0.837195	−0.418597	+	0.908172i	$0.637478\pi$
$858$	0	0
$859$	120.604	0.00479040	0.00239520	−	0.999997i	$-0.499238\pi$
$859$	120.604	0.00479040	0.00239520	+	0.999997i	$0.499238\pi$
$860$	7030.66	0.278771
$861$	11230.5	0.444524
$862$	−22745.1	−0.898725
$863$	−24086.3	−0.950065	−0.475033	−	0.879968i	$-0.657564\pi$
$863$	−24086.3	−0.950065	−0.475033	+	0.879968i	$0.657564\pi$
$864$	864.000	0.0340207
$865$	−1948.29	−0.0765827
$866$	−4673.18	−0.183373
$867$	−7831.33	−0.306766
$868$	31366.7	1.22656
$869$	0	0
$870$	−2190.54	−0.0853637
$871$	−20178.0	−0.784967
$872$	−2585.07	−0.100392
$873$	−1282.97	−0.0497390
$874$	−191.161	−0.00739829
$875$	33690.5	1.30165
$876$	5371.83	0.207189
$877$	−3898.55	−0.150108	−0.0750539	−	0.997179i	$-0.523913\pi$
$877$	−3898.55	−0.150108	−0.0750539	+	0.997179i	$0.523913\pi$
$878$	3379.94	0.129918
$879$	−23711.2	−0.909852
$880$	0	0
$881$	27751.9	1.06128	0.530639	−	0.847598i	$-0.321952\pi$
$881$	27751.9	1.06128	0.530639	+	0.847598i	$0.321952\pi$
$882$	5732.59	0.218851
$883$	−9931.42	−0.378504	−0.189252	−	0.981929i	$-0.560606\pi$
$883$	−9931.42	−0.378504	−0.189252	+	0.981929i	$0.560606\pi$
$884$	5904.65	0.224655
$885$	430.257	0.0163423
$886$	13694.2	0.519261
$887$	−16262.0	−0.615586	−0.307793	−	0.951453i	$-0.599590\pi$
$887$	−16262.0	−0.615586	−0.307793	+	0.951453i	$0.599590\pi$
$888$	−7291.76	−0.275558
$889$	−8424.31	−0.317820
$890$	−17635.2	−0.664193
$891$	0	0
$892$	−13867.3	−0.520530
$893$	−26985.3	−1.01123
$894$	−5150.12	−0.192669
$895$	14924.7	0.557405
$896$	3292.06	0.122745
$897$	188.693	0.00702372
$898$	32833.2	1.22011
$899$	17991.3	0.667457
$900$	−3121.90	−0.115626
$901$	31440.5	1.16253
$902$	0	0
$903$	−21919.2	−0.807780
$904$	−3715.68	−0.136705
$905$	−24180.4	−0.888160
$906$	−18521.4	−0.679174
$907$	31520.9	1.15395	0.576976	−	0.816761i	$-0.304233\pi$
$907$	31520.9	1.15395	0.576976	+	0.816761i	$0.304233\pi$
$908$	16146.3	0.590127
$909$	2644.47	0.0964922
$910$	−9790.53	−0.356652
$911$	−48867.3	−1.77722	−0.888609	−	0.458665i	$-0.848328\pi$
$911$	−48867.3	−1.77722	−0.888609	+	0.458665i	$0.848328\pi$
$912$	−2243.90	−0.0814727
$913$	0	0
$914$	29239.4	1.05815
$915$	11728.5	0.423750
$916$	−12312.9	−0.444136
$917$	−73843.0	−2.65922
$918$	2591.19	0.0931611
$919$	18472.9	0.663073	0.331536	−	0.943442i	$-0.392433\pi$
$919$	18472.9	0.663073	0.331536	+	0.943442i	$0.392433\pi$
$920$	−101.201	−0.00362663
$921$	−14661.8	−0.524563
$922$	−1864.96	−0.0666153
$923$	16261.4	0.579904
$924$	0	0
$925$	26347.4	0.936536
$926$	11613.6	0.412146
$927$	−9013.94	−0.319371
$928$	1888.26	0.0667943
$929$	−40016.6	−1.41324	−0.706622	−	0.707591i	$-0.749782\pi$
$929$	−40016.6	−1.41324	−0.706622	+	0.707591i	$0.749782\pi$
$930$	−11318.6	−0.399087
$931$	−14888.2	−0.524103
$932$	−6750.42	−0.237251
$933$	−19665.5	−0.690052
$934$	−4287.95	−0.150220
$935$	0	0
$936$	2214.94	0.0773478
$937$	−20667.1	−0.720562	−0.360281	−	0.932844i	$-0.617319\pi$
$937$	−20667.1	−0.720562	−0.360281	+	0.932844i	$0.617319\pi$
$938$	−33739.4	−1.17445
$939$	−19419.2	−0.674890
$940$	−14286.1	−0.495705
$941$	−47773.6	−1.65502	−0.827510	−	0.561451i	$-0.810243\pi$
$941$	−47773.6	−1.65502	−0.827510	+	0.561451i	$0.810243\pi$
$942$	10422.7	0.360499
$943$	297.595	0.0102768
$944$	−370.883	−0.0127873
$945$	−4296.46	−0.147898
$946$	0	0
$947$	46098.8	1.58185	0.790924	−	0.611914i	$-0.209600\pi$
$947$	46098.8	1.58185	0.790924	+	0.611914i	$0.209600\pi$
$948$	11825.6	0.405144
$949$	13771.1	0.471054
$950$	8107.91	0.276900
$951$	11197.5	0.381814
$952$	9873.08	0.336122
$953$	−57230.1	−1.94529	−0.972646	−	0.232290i	$-0.925378\pi$
$953$	−57230.1	−1.94529	−0.972646	+	0.232290i	$0.925378\pi$
$954$	11793.9	0.400253
$955$	5646.44	0.191324
$956$	−9687.03	−0.327721
$957$	0	0
$958$	6802.43	0.229412
$959$	29406.2	0.990173
$960$	−1187.93	−0.0399378
$961$	63170.5	2.12046
$962$	−18693.0	−0.626495
$963$	−14436.0	−0.483068
$964$	−27743.9	−0.926940
$965$	−3298.73	−0.110041
$966$	315.511	0.0105087
$967$	−43977.3	−1.46247	−0.731237	−	0.682123i	$-0.761057\pi$
$967$	−43977.3	−1.46247	−0.731237	+	0.682123i	$0.761057\pi$
$968$	0	0
$969$	−6729.60	−0.223102
$970$	1763.99	0.0583899
$971$	3968.54	0.131160	0.0655800	−	0.997847i	$-0.479110\pi$
$971$	3968.54	0.131160	0.0655800	+	0.997847i	$0.479110\pi$
$972$	972.000	0.0320750
$973$	−8656.38	−0.285212
$974$	19265.6	0.633789
$975$	−8003.25	−0.262881
$976$	−10110.0	−0.331570
$977$	2691.26	0.0881278	0.0440639	−	0.999029i	$-0.485969\pi$
$977$	2691.26	0.0881278	0.0440639	+	0.999029i	$0.485969\pi$
$978$	−14297.5	−0.467467
$979$	0	0
$980$	−7881.85	−0.256915
$981$	−2908.21	−0.0946503
$982$	11188.3	0.363578
$983$	45874.5	1.48847	0.744237	−	0.667916i	$-0.232813\pi$
$983$	45874.5	1.48847	0.744237	+	0.667916i	$0.232813\pi$
$984$	3493.27	0.113172
$985$	16708.3	0.540477
$986$	5663.00	0.182907
$987$	44539.3	1.43638
$988$	−5752.44	−0.185232
$989$	−580.834	−0.0186749
$990$	0	0
$991$	−1102.69	−0.0353462	−0.0176731	−	0.999844i	$-0.505626\pi$
$991$	−1102.69	−0.0353462	−0.0176731	+	0.999844i	$0.505626\pi$
$992$	9756.67	0.312273
$993$	18281.6	0.584239
$994$	27190.5	0.867635
$995$	−27282.9	−0.869273
$996$	1541.51	0.0490408
$997$	−46230.7	−1.46855	−0.734274	−	0.678853i	$-0.762477\pi$
$997$	−46230.7	−1.46855	−0.734274	+	0.678853i	$0.762477\pi$
$998$	−4590.63	−0.145605
$999$	−8203.23	−0.259798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.4.a.z.1.2		4
3.2	odd	2		2178.4.a.bu.1.3		4
11.3	even	5		66.4.e.c.31.1	✓	8
11.4	even	5		66.4.e.c.49.1	yes	8
11.10	odd	2		726.4.a.w.1.2		4
33.14	odd	10		198.4.f.f.163.2		8
33.26	odd	10		198.4.f.f.181.2		8
33.32	even	2		2178.4.a.bz.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.4.e.c.31.1	✓	8	11.3	even	5
66.4.e.c.49.1	yes	8	11.4	even	5
198.4.f.f.163.2		8	33.14	odd	10
198.4.f.f.181.2		8	33.26	odd	10
726.4.a.w.1.2		4	11.10	odd	2
726.4.a.z.1.2		4	1.1	even	1	trivial
2178.4.a.bu.1.3		4	3.2	odd	2
2178.4.a.bz.1.3		4	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	726.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.18714 q^{5} +6.00000 q^{6} +25.7192 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.18714 q^{5} +6.00000 q^{6} +25.7192 q^{7} +8.00000 q^{8} +9.00000 q^{9} -12.3743 q^{10} +12.0000 q^{12} +30.7630 q^{13} +51.4384 q^{14} -18.5614 q^{15} +16.0000 q^{16} +47.9850 q^{17} +18.0000 q^{18} -46.7480 q^{19} -24.7485 q^{20} +77.1576 q^{21} +2.04459 q^{23} +24.0000 q^{24} -86.7194 q^{25} +61.5261 q^{26} +27.0000 q^{27} +102.877 q^{28} +59.0080 q^{29} -37.1228 q^{30} +304.896 q^{31} +32.0000 q^{32} +95.9699 q^{34} -159.128 q^{35} +36.0000 q^{36} -303.823 q^{37} -93.4960 q^{38} +92.2891 q^{39} -49.4971 q^{40} +145.553 q^{41} +154.315 q^{42} -284.084 q^{43} -55.6842 q^{45} +4.08917 q^{46} +577.251 q^{47} +48.0000 q^{48} +318.477 q^{49} -173.439 q^{50} +143.955 q^{51} +123.052 q^{52} +655.216 q^{53} +54.0000 q^{54} +205.754 q^{56} -140.244 q^{57} +118.016 q^{58} -23.1802 q^{59} -74.2456 q^{60} -631.874 q^{61} +609.792 q^{62} +231.473 q^{63} +64.0000 q^{64} -190.335 q^{65} -655.918 q^{67} +191.940 q^{68} +6.13376 q^{69} -318.256 q^{70} +528.602 q^{71} +72.0000 q^{72} +447.652 q^{73} -607.646 q^{74} -260.158 q^{75} -186.992 q^{76} +184.578 q^{78} +985.464 q^{79} -98.9942 q^{80} +81.0000 q^{81} +291.106 q^{82} +128.459 q^{83} +308.630 q^{84} -296.889 q^{85} -568.167 q^{86} +177.024 q^{87} +1425.15 q^{89} -111.368 q^{90} +791.201 q^{91} +8.17835 q^{92} +914.688 q^{93} +1154.50 q^{94} +289.236 q^{95} +96.0000 q^{96} -142.553 q^{97} +636.954 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 21 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 21 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 21 q^{7} + 32 q^{8} + 36 q^{9} + 40 q^{10} + 48 q^{12} + 38 q^{13} + 42 q^{14} + 60 q^{15} + 64 q^{16} + 85 q^{17} + 72 q^{18} + 5 q^{19} + 80 q^{20} + 63 q^{21} + 316 q^{23} + 96 q^{24} + 318 q^{25} + 76 q^{26} + 108 q^{27} + 84 q^{28} + 123 q^{29} + 120 q^{30} + 436 q^{31} + 128 q^{32} + 170 q^{34} - 129 q^{35} + 144 q^{36} + 336 q^{37} + 10 q^{38} + 114 q^{39} + 160 q^{40} - 394 q^{41} + 126 q^{42} - 680 q^{43} + 180 q^{45} + 632 q^{46} + 1085 q^{47} + 192 q^{48} - 311 q^{49} + 636 q^{50} + 255 q^{51} + 152 q^{52} + 880 q^{53} + 216 q^{54} + 168 q^{56} + 15 q^{57} + 246 q^{58} + 724 q^{59} + 240 q^{60} + 355 q^{61} + 872 q^{62} + 189 q^{63} + 256 q^{64} - 2019 q^{65} - 869 q^{67} + 340 q^{68} + 948 q^{69} - 258 q^{70} - 331 q^{71} + 288 q^{72} + 1135 q^{73} + 672 q^{74} + 954 q^{75} + 20 q^{76} + 228 q^{78} + 1083 q^{79} + 320 q^{80} + 324 q^{81} - 788 q^{82} - 169 q^{83} + 252 q^{84} + 1104 q^{85} - 1360 q^{86} + 369 q^{87} - 258 q^{89} + 360 q^{90} + 874 q^{91} + 1264 q^{92} + 1308 q^{93} + 2170 q^{94} + 1555 q^{95} + 384 q^{96} - 248 q^{97} - 622 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 21 * q^7 + 32 * q^8 + 36 * q^9 + 40 * q^10 + 48 * q^12 + 38 * q^13 + 42 * q^14 + 60 * q^15 + 64 * q^16 + 85 * q^17 + 72 * q^18 + 5 * q^19 + 80 * q^20 + 63 * q^21 + 316 * q^23 + 96 * q^24 + 318 * q^25 + 76 * q^26 + 108 * q^27 + 84 * q^28 + 123 * q^29 + 120 * q^30 + 436 * q^31 + 128 * q^32 + 170 * q^34 - 129 * q^35 + 144 * q^36 + 336 * q^37 + 10 * q^38 + 114 * q^39 + 160 * q^40 - 394 * q^41 + 126 * q^42 - 680 * q^43 + 180 * q^45 + 632 * q^46 + 1085 * q^47 + 192 * q^48 - 311 * q^49 + 636 * q^50 + 255 * q^51 + 152 * q^52 + 880 * q^53 + 216 * q^54 + 168 * q^56 + 15 * q^57 + 246 * q^58 + 724 * q^59 + 240 * q^60 + 355 * q^61 + 872 * q^62 + 189 * q^63 + 256 * q^64 - 2019 * q^65 - 869 * q^67 + 340 * q^68 + 948 * q^69 - 258 * q^70 - 331 * q^71 + 288 * q^72 + 1135 * q^73 + 672 * q^74 + 954 * q^75 + 20 * q^76 + 228 * q^78 + 1083 * q^79 + 320 * q^80 + 324 * q^81 - 788 * q^82 - 169 * q^83 + 252 * q^84 + 1104 * q^85 - 1360 * q^86 + 369 * q^87 - 258 * q^89 + 360 * q^90 + 874 * q^91 + 1264 * q^92 + 1308 * q^93 + 2170 * q^94 + 1555 * q^95 + 384 * q^96 - 248 * q^97 - 622 * q^98

Introduction

L-functions

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Database

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