LMFDB - Embedded newform 2075.4.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2075,4,Mod(1,2075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2075, 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("2075.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2075 = 5^{2} \cdot 83 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2075.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:	$122.428963262$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 101 x^{18} + 508 x^{17} + 4106 x^{16} - 21051 x^{15} - 85533 x^{14} + 459851 x^{13} + \cdots + 7355648 $ x^20 - 5x^19 - 101x^18 + 508x^17 + 4106x^16 - 21051x^15 - 85533x^14 + 459851x^13 + 950035x^12 - 5717403x^11 - 5024847x^10 + 40747858x^9 + 3953468x^8 - 158522845x^7 + 73661713x^6 + 287557807x^5 - 265600882x^4 - 123949792x^3 + 215898584x^2 - 72947120*x + 7355648
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 415)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.89887$ of defining polynomial
Character	$\chi$	$=$	2075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.89887 q^{2} -8.46043 q^{3} +0.403470 q^{4} +24.5257 q^{6} -30.5247 q^{7} +22.0214 q^{8} +44.5789 q^{9} +O(q^{10})$	\(q-2.89887 q^{2} -8.46043 q^{3} +0.403470 q^{4} +24.5257 q^{6} -30.5247 q^{7} +22.0214 q^{8} +44.5789 q^{9} +42.6205 q^{11} -3.41353 q^{12} +35.8865 q^{13} +88.4872 q^{14} -67.0650 q^{16} -83.2325 q^{17} -129.228 q^{18} +7.77726 q^{19} +258.252 q^{21} -123.551 q^{22} +7.94479 q^{23} -186.310 q^{24} -104.030 q^{26} -148.725 q^{27} -12.3158 q^{28} -214.108 q^{29} -154.845 q^{31} +18.2418 q^{32} -360.588 q^{33} +241.280 q^{34} +17.9862 q^{36} -270.488 q^{37} -22.5453 q^{38} -303.615 q^{39} +393.148 q^{41} -748.639 q^{42} -342.041 q^{43} +17.1961 q^{44} -23.0310 q^{46} +94.5356 q^{47} +567.398 q^{48} +588.756 q^{49} +704.183 q^{51} +14.4791 q^{52} +434.824 q^{53} +431.134 q^{54} -672.195 q^{56} -65.7989 q^{57} +620.673 q^{58} +49.9421 q^{59} -759.968 q^{61} +448.878 q^{62} -1360.75 q^{63} +483.639 q^{64} +1045.30 q^{66} +801.852 q^{67} -33.5818 q^{68} -67.2164 q^{69} -1003.73 q^{71} +981.688 q^{72} +535.773 q^{73} +784.111 q^{74} +3.13789 q^{76} -1300.98 q^{77} +880.141 q^{78} +1239.93 q^{79} +54.6451 q^{81} -1139.69 q^{82} +83.0000 q^{83} +104.197 q^{84} +991.534 q^{86} +1811.45 q^{87} +938.562 q^{88} -635.511 q^{89} -1095.42 q^{91} +3.20549 q^{92} +1310.06 q^{93} -274.047 q^{94} -154.334 q^{96} +650.708 q^{97} -1706.73 q^{98} +1899.97 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 12 q^{3} + 67 q^{4} + 17 q^{6} - 31 q^{7} - 36 q^{8} + 216 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 12 * q^3 + 67 * q^4 + 17 * q^6 - 31 * q^7 - 36 * q^8 + 216 * q^9	\( 20 q - 5 q^{2} - 12 q^{3} + 67 q^{4} + 17 q^{6} - 31 q^{7} - 36 q^{8} + 216 q^{9} + 36 q^{11} - 44 q^{12} - 67 q^{13} + 89 q^{14} + 375 q^{16} - 425 q^{17} + 11 q^{18} - 251 q^{19} - 23 q^{21} - 447 q^{22} - 584 q^{23} + 152 q^{24} + 799 q^{26} - 477 q^{27} - 831 q^{28} + 252 q^{29} + 329 q^{31} - 1088 q^{32} - 1405 q^{33} + 189 q^{34} + 1126 q^{36} - 260 q^{37} - 2204 q^{38} + 40 q^{39} + 1830 q^{41} - 1782 q^{42} + 87 q^{43} + 86 q^{44} - 549 q^{46} - 1028 q^{47} - 2931 q^{48} + 1531 q^{49} + 981 q^{51} - 623 q^{52} - 1491 q^{53} + 595 q^{54} + 1930 q^{56} - 1184 q^{57} - 1075 q^{58} + 782 q^{59} - 686 q^{61} - 797 q^{62} - 1554 q^{63} + 714 q^{64} + 1688 q^{66} - 661 q^{67} - 3632 q^{68} + 1326 q^{69} + 298 q^{71} - 1378 q^{72} - 656 q^{73} + 348 q^{74} - 3262 q^{76} - 1231 q^{77} - 587 q^{78} - 748 q^{79} + 2356 q^{81} - 526 q^{82} + 1660 q^{83} + 1927 q^{84} + 2632 q^{86} - 4001 q^{87} - 2200 q^{88} + 3702 q^{89} + 112 q^{91} - 7797 q^{92} - 1542 q^{93} - 1773 q^{94} + 18 q^{96} - 4506 q^{97} - 1942 q^{98} + 10603 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 12 * q^3 + 67 * q^4 + 17 * q^6 - 31 * q^7 - 36 * q^8 + 216 * q^9 + 36 * q^11 - 44 * q^12 - 67 * q^13 + 89 * q^14 + 375 * q^16 - 425 * q^17 + 11 * q^18 - 251 * q^19 - 23 * q^21 - 447 * q^22 - 584 * q^23 + 152 * q^24 + 799 * q^26 - 477 * q^27 - 831 * q^28 + 252 * q^29 + 329 * q^31 - 1088 * q^32 - 1405 * q^33 + 189 * q^34 + 1126 * q^36 - 260 * q^37 - 2204 * q^38 + 40 * q^39 + 1830 * q^41 - 1782 * q^42 + 87 * q^43 + 86 * q^44 - 549 * q^46 - 1028 * q^47 - 2931 * q^48 + 1531 * q^49 + 981 * q^51 - 623 * q^52 - 1491 * q^53 + 595 * q^54 + 1930 * q^56 - 1184 * q^57 - 1075 * q^58 + 782 * q^59 - 686 * q^61 - 797 * q^62 - 1554 * q^63 + 714 * q^64 + 1688 * q^66 - 661 * q^67 - 3632 * q^68 + 1326 * q^69 + 298 * q^71 - 1378 * q^72 - 656 * q^73 + 348 * q^74 - 3262 * q^76 - 1231 * q^77 - 587 * q^78 - 748 * q^79 + 2356 * q^81 - 526 * q^82 + 1660 * q^83 + 1927 * q^84 + 2632 * q^86 - 4001 * q^87 - 2200 * q^88 + 3702 * q^89 + 112 * q^91 - 7797 * q^92 - 1542 * q^93 - 1773 * q^94 + 18 * q^96 - 4506 * q^97 - 1942 * q^98 + 10603 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.89887	−1.02491	−0.512453	−	0.858715i	$-0.671263\pi$
$2$	−2.89887	−1.02491	−0.512453	+	0.858715i	$0.671263\pi$
$3$	−8.46043	−1.62821	−0.814105	−	0.580718i	$-0.802772\pi$
$3$	−8.46043	−1.62821	−0.814105	+	0.580718i	$0.802772\pi$
$4$	0.403470	0.0504338
$5$	0	0
$5$	0	0
$6$	24.5257	1.66876
$7$	−30.5247	−1.64818	−0.824089	−	0.566461i	$-0.808312\pi$
$7$	−30.5247	−1.64818	−0.824089	+	0.566461i	$0.808312\pi$
$8$	22.0214	0.973217
$9$	44.5789	1.65107
$10$	0	0
$11$	42.6205	1.16823	0.584116	−	0.811670i	$-0.301441\pi$
$11$	42.6205	1.16823	0.584116	+	0.811670i	$0.301441\pi$
$12$	−3.41353	−0.0821168
$13$	35.8865	0.765624	0.382812	−	0.923826i	$-0.374956\pi$
$13$	35.8865	0.765624	0.382812	+	0.923826i	$0.374956\pi$
$14$	88.4872	1.68923
$15$	0	0
$16$	−67.0650	−1.04789
$17$	−83.2325	−1.18746	−0.593731	−	0.804664i	$-0.702346\pi$
$17$	−83.2325	−1.18746	−0.593731	+	0.804664i	$0.702346\pi$
$18$	−129.228	−1.69219
$19$	7.77726	0.0939066	0.0469533	−	0.998897i	$-0.485049\pi$
$19$	7.77726	0.0939066	0.0469533	+	0.998897i	$0.485049\pi$
$20$	0	0
$21$	258.252	2.68358
$22$	−123.551	−1.19733
$23$	7.94479	0.0720263	0.0360131	−	0.999351i	$-0.488534\pi$
$23$	7.94479	0.0720263	0.0360131	+	0.999351i	$0.488534\pi$
$24$	−186.310	−1.58460
$25$	0	0
$26$	−104.030	−0.784693
$27$	−148.725	−1.06008
$28$	−12.3158	−0.0831238
$29$	−214.108	−1.37100	−0.685498	−	0.728074i	$-0.740415\pi$
$29$	−214.108	−1.37100	−0.685498	+	0.728074i	$0.740415\pi$
$30$	0	0
$31$	−154.845	−0.897131	−0.448566	−	0.893750i	$-0.648065\pi$
$31$	−154.845	−0.897131	−0.448566	+	0.893750i	$0.648065\pi$
$32$	18.2418	0.100773
$33$	−360.588	−1.90213
$34$	241.280	1.21704
$35$	0	0
$36$	17.9862	0.0832696
$37$	−270.488	−1.20184	−0.600919	−	0.799310i	$-0.705199\pi$
$37$	−270.488	−1.20184	−0.600919	+	0.799310i	$0.705199\pi$
$38$	−22.5453	−0.0962455
$39$	−303.615	−1.24660
$40$	0	0
$41$	393.148	1.49755	0.748774	−	0.662826i	$-0.230643\pi$
$41$	393.148	1.49755	0.748774	+	0.662826i	$0.230643\pi$
$42$	−748.639	−2.75042
$43$	−342.041	−1.21304	−0.606521	−	0.795068i	$-0.707435\pi$
$43$	−342.041	−1.21304	−0.606521	+	0.795068i	$0.707435\pi$
$44$	17.1961	0.0589184
$45$	0	0
$46$	−23.0310	−0.0738202
$47$	94.5356	0.293392	0.146696	−	0.989182i	$-0.453136\pi$
$47$	94.5356	0.293392	0.146696	+	0.989182i	$0.453136\pi$
$48$	567.398	1.70619
$49$	588.756	1.71649
$50$	0	0
$51$	704.183	1.93344
$52$	14.4791	0.0386133
$53$	434.824	1.12694	0.563468	−	0.826138i	$-0.309467\pi$
$53$	434.824	1.12694	0.563468	+	0.826138i	$0.309467\pi$
$54$	431.134	1.08648
$55$	0	0
$56$	−672.195	−1.60403
$57$	−65.7989	−0.152900
$58$	620.673	1.40514
$59$	49.9421	0.110202	0.0551010	−	0.998481i	$-0.482452\pi$
$59$	49.9421	0.110202	0.0551010	+	0.998481i	$0.482452\pi$
$60$	0	0
$61$	−759.968	−1.59515	−0.797573	−	0.603222i	$-0.793883\pi$
$61$	−759.968	−1.59515	−0.797573	+	0.603222i	$0.793883\pi$
$62$	448.878	0.919476
$63$	−1360.75	−2.72125
$64$	483.639	0.944607
$65$	0	0
$66$	1045.30	1.94950
$67$	801.852	1.46212	0.731058	−	0.682315i	$-0.239027\pi$
$67$	801.852	1.46212	0.731058	+	0.682315i	$0.239027\pi$
$68$	−33.5818	−0.0598881
$69$	−67.2164	−0.117274
$70$	0	0
$71$	−1003.73	−1.67776	−0.838878	−	0.544319i	$-0.816788\pi$
$71$	−1003.73	−1.67776	−0.838878	+	0.544319i	$0.816788\pi$
$72$	981.688	1.60685
$73$	535.773	0.859006	0.429503	−	0.903065i	$-0.358689\pi$
$73$	535.773	0.859006	0.429503	+	0.903065i	$0.358689\pi$
$74$	784.111	1.23177
$75$	0	0
$76$	3.13789	0.00473606
$77$	−1300.98	−1.92545
$78$	880.141	1.27765
$79$	1239.93	1.76587	0.882934	−	0.469498i	$-0.155565\pi$
$79$	1239.93	1.76587	0.882934	+	0.469498i	$0.155565\pi$
$80$	0	0
$81$	54.6451	0.0749589
$82$	−1139.69	−1.53485
$83$	83.0000	0.109764
$83$	83.0000	0.109764
$84$	104.197	0.135343
$85$	0	0
$86$	991.534	1.24325
$87$	1811.45	2.23227
$88$	938.562	1.13694
$89$	−635.511	−0.756900	−0.378450	−	0.925622i	$-0.623543\pi$
$89$	−635.511	−0.756900	−0.378450	+	0.925622i	$0.623543\pi$
$90$	0	0
$91$	−1095.42	−1.26188
$92$	3.20549	0.00363255
$93$	1310.06	1.46072
$94$	−274.047	−0.300700
$95$	0	0
$96$	−154.334	−0.164079
$97$	650.708	0.681128	0.340564	−	0.940221i	$-0.389382\pi$
$97$	650.708	0.681128	0.340564	+	0.940221i	$0.389382\pi$
$98$	−1706.73	−1.75924
$99$	1899.97	1.92883
$100$	0	0
$101$	−674.390	−0.664400	−0.332200	−	0.943209i	$-0.607791\pi$
$101$	−674.390	−0.664400	−0.332200	+	0.943209i	$0.607791\pi$
$102$	−2041.34	−1.98159
$103$	402.978	0.385501	0.192751	−	0.981248i	$-0.438259\pi$
$103$	402.978	0.385501	0.192751	+	0.981248i	$0.438259\pi$
$104$	790.270	0.745118
$105$	0	0
$106$	−1260.50	−1.15500
$107$	232.253	0.209839	0.104920	−	0.994481i	$-0.466542\pi$
$107$	232.253	0.209839	0.104920	+	0.994481i	$0.466542\pi$
$108$	−60.0059	−0.0534636
$109$	−727.229	−0.639045	−0.319523	−	0.947579i	$-0.603523\pi$
$109$	−727.229	−0.639045	−0.319523	+	0.947579i	$0.603523\pi$
$110$	0	0
$111$	2288.45	1.95684
$112$	2047.14	1.72711
$113$	284.991	0.237254	0.118627	−	0.992939i	$-0.462151\pi$
$113$	284.991	0.237254	0.118627	+	0.992939i	$0.462151\pi$
$114$	190.743	0.156708
$115$	0	0
$116$	−86.3862	−0.0691445
$117$	1599.78	1.26410
$118$	−144.776	−0.112947
$119$	2540.64	1.95715
$120$	0	0
$121$	485.505	0.364767
$122$	2203.05	1.63488
$123$	−3326.20	−2.43832
$124$	−62.4755	−0.0452457
$125$	0	0
$126$	3944.66	2.78903
$127$	2196.67	1.53482	0.767412	−	0.641155i	$-0.221544\pi$
$127$	2196.67	1.53482	0.767412	+	0.641155i	$0.221544\pi$
$128$	−1547.94	−1.06891
$129$	2893.81	1.97509
$130$	0	0
$131$	2662.75	1.77592	0.887959	−	0.459923i	$-0.152123\pi$
$131$	2662.75	1.77592	0.887959	+	0.459923i	$0.152123\pi$
$132$	−145.486	−0.0959315
$133$	−237.398	−0.154775
$134$	−2324.47	−1.49853
$135$	0	0
$136$	−1832.89	−1.15566
$137$	−1439.75	−0.897856	−0.448928	−	0.893568i	$-0.648194\pi$
$137$	−1439.75	−0.897856	−0.448928	+	0.893568i	$0.648194\pi$
$138$	194.852	0.120195
$139$	33.7244	0.0205789	0.0102895	−	0.999947i	$-0.496725\pi$
$139$	33.7244	0.0205789	0.0102895	+	0.999947i	$0.496725\pi$
$140$	0	0
$141$	−799.812	−0.477704
$142$	2909.68	1.71954
$143$	1529.50	0.894427
$144$	−2989.68	−1.73014
$145$	0	0
$146$	−1553.14	−0.880401
$147$	−4981.12	−2.79480
$148$	−109.134	−0.0606132
$149$	−1660.18	−0.912800	−0.456400	−	0.889775i	$-0.650861\pi$
$149$	−1660.18	−0.912800	−0.456400	+	0.889775i	$0.650861\pi$
$150$	0	0
$151$	1170.21	0.630662	0.315331	−	0.948982i	$-0.397884\pi$
$151$	1170.21	0.630662	0.315331	+	0.948982i	$0.397884\pi$
$152$	171.266	0.0913915
$153$	−3710.41	−1.96058
$154$	3771.37	1.97341
$155$	0	0
$156$	−122.500	−0.0628706
$157$	913.549	0.464389	0.232195	−	0.972669i	$-0.425409\pi$
$157$	913.549	0.464389	0.232195	+	0.972669i	$0.425409\pi$
$158$	−3594.41	−1.80985
$159$	−3678.80	−1.83489
$160$	0	0
$161$	−242.512	−0.118712
$162$	−158.409	−0.0768259
$163$	3500.06	1.68188	0.840938	−	0.541132i	$-0.182004\pi$
$163$	3500.06	1.68188	0.840938	+	0.541132i	$0.182004\pi$
$164$	158.624	0.0755270
$165$	0	0
$166$	−240.607	−0.112498
$167$	−3095.26	−1.43424	−0.717121	−	0.696948i	$-0.754541\pi$
$167$	−3095.26	−1.43424	−0.717121	+	0.696948i	$0.754541\pi$
$168$	5687.06	2.61170
$169$	−909.161	−0.413819
$170$	0	0
$171$	346.701	0.155046
$172$	−138.003	−0.0611782
$173$	37.9338	0.0166708	0.00833541	−	0.999965i	$-0.497347\pi$
$173$	37.9338	0.0166708	0.00833541	+	0.999965i	$0.497347\pi$
$174$	−5251.16	−2.28787
$175$	0	0
$176$	−2858.34	−1.22418
$177$	−422.532	−0.179432
$178$	1842.27	0.775752
$179$	3662.91	1.52949	0.764745	−	0.644334i	$-0.222865\pi$
$179$	3662.91	1.52949	0.764745	+	0.644334i	$0.222865\pi$
$180$	0	0
$181$	2349.31	0.964768	0.482384	−	0.875960i	$-0.339771\pi$
$181$	2349.31	0.964768	0.482384	+	0.875960i	$0.339771\pi$
$182$	3175.49	1.29331
$183$	6429.66	2.59723
$184$	174.955	0.0700972
$185$	0	0
$186$	−3797.70	−1.49710
$187$	−3547.41	−1.38723
$188$	38.1423	0.0147969
$189$	4539.77	1.74719
$190$	0	0
$191$	−3529.88	−1.33724	−0.668620	−	0.743604i	$-0.733115\pi$
$191$	−3529.88	−1.33724	−0.668620	+	0.743604i	$0.733115\pi$
$192$	−4091.79	−1.53802
$193$	−3129.07	−1.16702	−0.583511	−	0.812105i	$-0.698322\pi$
$193$	−3129.07	−1.16702	−0.583511	+	0.812105i	$0.698322\pi$
$194$	−1886.32	−0.698093
$195$	0	0
$196$	237.545	0.0865690
$197$	1131.10	0.409072	0.204536	−	0.978859i	$-0.434431\pi$
$197$	1131.10	0.409072	0.204536	+	0.978859i	$0.434431\pi$
$198$	−5507.78	−1.97687
$199$	3811.27	1.35766	0.678829	−	0.734296i	$-0.262488\pi$
$199$	3811.27	1.35766	0.678829	+	0.734296i	$0.262488\pi$
$200$	0	0
$201$	−6784.01	−2.38063
$202$	1954.97	0.680948
$203$	6535.58	2.25964
$204$	284.117	0.0975105
$205$	0	0
$206$	−1168.18	−0.395103
$207$	354.170	0.118920
$208$	−2406.73	−0.802290
$209$	331.470	0.109705
$210$	0	0
$211$	3376.94	1.10179	0.550895	−	0.834574i	$-0.314286\pi$
$211$	3376.94	1.10179	0.550895	+	0.834574i	$0.314286\pi$
$212$	175.438	0.0568356
$213$	8491.98	2.73174
$214$	−673.273	−0.215065
$215$	0	0
$216$	−3275.12	−1.03168
$217$	4726.61	1.47863
$218$	2108.15	0.654962
$219$	−4532.87	−1.39864
$220$	0	0
$221$	−2986.92	−0.909149
$222$	−6633.92	−2.00558
$223$	−1880.17	−0.564599	−0.282300	−	0.959326i	$-0.591097\pi$
$223$	−1880.17	−0.564599	−0.282300	+	0.959326i	$0.591097\pi$
$224$	−556.826	−0.166092
$225$	0	0
$226$	−826.153	−0.243163
$227$	−622.664	−0.182060	−0.0910301	−	0.995848i	$-0.529016\pi$
$227$	−622.664	−0.182060	−0.0910301	+	0.995848i	$0.529016\pi$
$228$	−26.5479	−0.00771131
$229$	−1580.94	−0.456207	−0.228104	−	0.973637i	$-0.573252\pi$
$229$	−1580.94	−0.456207	−0.228104	+	0.973637i	$0.573252\pi$
$230$	0	0
$231$	11006.8	3.13504
$232$	−4714.96	−1.33428
$233$	6637.34	1.86621	0.933104	−	0.359606i	$-0.117089\pi$
$233$	6637.34	1.86621	0.933104	+	0.359606i	$0.117089\pi$
$234$	−4637.55	−1.29558
$235$	0	0
$236$	20.1502	0.00555790
$237$	−10490.4	−2.87520
$238$	−7365.01	−2.00589
$239$	4420.69	1.19645	0.598223	−	0.801330i	$-0.295874\pi$
$239$	4420.69	1.19645	0.598223	+	0.801330i	$0.295874\pi$
$240$	0	0
$241$	−813.002	−0.217303	−0.108652	−	0.994080i	$-0.534653\pi$
$241$	−813.002	−0.217303	−0.108652	+	0.994080i	$0.534653\pi$
$242$	−1407.42	−0.373852
$243$	3553.24	0.938028
$244$	−306.624	−0.0804493
$245$	0	0
$246$	9642.24	2.49905
$247$	279.098	0.0718972
$248$	−3409.91	−0.873103
$249$	−702.216	−0.178719
$250$	0	0
$251$	−717.181	−0.180351	−0.0901754	−	0.995926i	$-0.528743\pi$
$251$	−717.181	−0.180351	−0.0901754	+	0.995926i	$0.528743\pi$
$252$	−549.024	−0.137243
$253$	338.611	0.0841434
$254$	−6367.86	−1.57305
$255$	0	0
$256$	618.180	0.150923
$257$	5061.39	1.22849	0.614243	−	0.789117i	$-0.289462\pi$
$257$	5061.39	1.22849	0.614243	+	0.789117i	$0.289462\pi$
$258$	−8388.80	−2.02428
$259$	8256.57	1.98084
$260$	0	0
$261$	−9544.70	−2.26361
$262$	−7718.96	−1.82015
$263$	−6350.81	−1.48900	−0.744501	−	0.667621i	$-0.767313\pi$
$263$	−6350.81	−1.48900	−0.744501	+	0.667621i	$0.767313\pi$
$264$	−7940.64	−1.85118
$265$	0	0
$266$	688.188	0.158630
$267$	5376.70	1.23239
$268$	323.523	0.0737401
$269$	5374.78	1.21824	0.609119	−	0.793078i	$-0.291523\pi$
$269$	5374.78	1.21824	0.609119	+	0.793078i	$0.291523\pi$
$270$	0	0
$271$	−707.446	−0.158577	−0.0792884	−	0.996852i	$-0.525265\pi$
$271$	−707.446	−0.158577	−0.0792884	+	0.996852i	$0.525265\pi$
$272$	5581.98	1.24433
$273$	9267.75	2.05461
$274$	4173.66	0.920219
$275$	0	0
$276$	−27.1198	−0.00591456
$277$	−1380.79	−0.299509	−0.149754	−	0.988723i	$-0.547848\pi$
$277$	−1380.79	−0.299509	−0.149754	+	0.988723i	$0.547848\pi$
$278$	−97.7628	−0.0210915
$279$	−6902.83	−1.48123
$280$	0	0
$281$	4801.41	1.01932	0.509659	−	0.860377i	$-0.329772\pi$
$281$	4801.41	1.01932	0.509659	+	0.860377i	$0.329772\pi$
$282$	2318.55	0.489602
$283$	2863.43	0.601459	0.300730	−	0.953709i	$-0.402770\pi$
$283$	2863.43	0.601459	0.300730	+	0.953709i	$0.402770\pi$
$284$	−404.975	−0.0846156
$285$	0	0
$286$	−4433.82	−0.916704
$287$	−12000.7	−2.46822
$288$	813.200	0.166383
$289$	2014.65	0.410065
$290$	0	0
$291$	−5505.27	−1.10902
$292$	216.168	0.0433229
$293$	266.808	0.0531983	0.0265992	−	0.999646i	$-0.491532\pi$
$293$	266.808	0.0531983	0.0265992	+	0.999646i	$0.491532\pi$
$294$	14439.7	2.86441
$295$	0	0
$296$	−5956.53	−1.16965
$297$	−6338.71	−1.23842
$298$	4812.65	0.935535
$299$	285.111	0.0551450
$300$	0	0
$301$	10440.7	1.99931
$302$	−3392.28	−0.646370
$303$	5705.63	1.08178
$304$	−521.582	−0.0984038
$305$	0	0
$306$	10756.0	2.00941
$307$	−1846.22	−0.343223	−0.171611	−	0.985165i	$-0.554897\pi$
$307$	−1846.22	−0.343223	−0.171611	+	0.985165i	$0.554897\pi$
$308$	−524.905	−0.0971079
$309$	−3409.37	−0.627677
$310$	0	0
$311$	−2178.16	−0.397145	−0.198572	−	0.980086i	$-0.563631\pi$
$311$	−2178.16	−0.397145	−0.198572	+	0.980086i	$0.563631\pi$
$312$	−6686.02	−1.21321
$313$	9233.74	1.66748	0.833741	−	0.552155i	$-0.186194\pi$
$313$	9233.74	1.66748	0.833741	+	0.552155i	$0.186194\pi$
$314$	−2648.26	−0.475956
$315$	0	0
$316$	500.276	0.0890593
$317$	−8020.30	−1.42103	−0.710513	−	0.703685i	$-0.751537\pi$
$317$	−8020.30	−1.42103	−0.710513	+	0.703685i	$0.751537\pi$
$318$	10664.4	1.88059
$319$	−9125.39	−1.60164
$320$	0	0
$321$	−1964.96	−0.341662
$322$	703.012	0.121669
$323$	−647.321	−0.111510
$324$	22.0476	0.00378046
$325$	0	0
$326$	−10146.2	−1.72377
$327$	6152.67	1.04050
$328$	8657.67	1.45744
$329$	−2885.67	−0.483563
$330$	0	0
$331$	2369.61	0.393491	0.196745	−	0.980455i	$-0.436963\pi$
$331$	2369.61	0.393491	0.196745	+	0.980455i	$0.436963\pi$
$332$	33.4880	0.00553582
$333$	−12058.1	−1.98432
$334$	8972.77	1.46996
$335$	0	0
$336$	−17319.7	−2.81210
$337$	−5010.47	−0.809903	−0.404952	−	0.914338i	$-0.632712\pi$
$337$	−5010.47	−0.809903	−0.404952	+	0.914338i	$0.632712\pi$
$338$	2635.54	0.424126
$339$	−2411.15	−0.386299
$340$	0	0
$341$	−6599.59	−1.04806
$342$	−1005.04	−0.158908
$343$	−7501.61	−1.18090
$344$	−7532.22	−1.18055
$345$	0	0
$346$	−109.965	−0.0170860
$347$	−5957.54	−0.921665	−0.460832	−	0.887487i	$-0.652449\pi$
$347$	−5957.54	−0.921665	−0.460832	+	0.887487i	$0.652449\pi$
$348$	730.865	0.112582
$349$	−9553.43	−1.46528	−0.732641	−	0.680615i	$-0.761713\pi$
$349$	−9553.43	−1.46528	−0.732641	+	0.680615i	$0.761713\pi$
$350$	0	0
$351$	−5337.20	−0.811620
$352$	777.476	0.117726
$353$	−11313.8	−1.70587	−0.852937	−	0.522014i	$-0.825181\pi$
$353$	−11313.8	−1.70587	−0.852937	+	0.522014i	$0.825181\pi$
$354$	1224.87	0.183901
$355$	0	0
$356$	−256.410	−0.0381733
$357$	−21494.9	−3.18665
$358$	−10618.3	−1.56758
$359$	108.796	0.0159945	0.00799725	−	0.999968i	$-0.497454\pi$
$359$	108.796	0.0159945	0.00799725	+	0.999968i	$0.497454\pi$
$360$	0	0
$361$	−6798.51	−0.991182
$362$	−6810.36	−0.988797
$363$	−4107.58	−0.593918
$364$	−441.970	−0.0636416
$365$	0	0
$366$	−18638.8	−2.66192
$367$	−6747.48	−0.959716	−0.479858	−	0.877346i	$-0.659312\pi$
$367$	−6747.48	−0.959716	−0.479858	+	0.877346i	$0.659312\pi$
$368$	−532.817	−0.0754756
$369$	17526.1	2.47255
$370$	0	0
$371$	−13272.9	−1.85739
$372$	528.570	0.0736695
$373$	8591.08	1.19257	0.596286	−	0.802772i	$-0.296642\pi$
$373$	8591.08	1.19257	0.596286	+	0.802772i	$0.296642\pi$
$374$	10283.5	1.42178
$375$	0	0
$376$	2081.81	0.285534
$377$	−7683.59	−1.04967
$378$	−13160.2	−1.79071
$379$	1118.18	0.151549	0.0757746	−	0.997125i	$-0.475857\pi$
$379$	1118.18	0.151549	0.0757746	+	0.997125i	$0.475857\pi$
$380$	0	0
$381$	−18584.7	−2.49901
$382$	10232.7	1.37055
$383$	−12136.6	−1.61919	−0.809597	−	0.586987i	$-0.800314\pi$
$383$	−12136.6	−1.61919	−0.809597	+	0.586987i	$0.800314\pi$
$384$	13096.3	1.74041
$385$	0	0
$386$	9070.78	1.19609
$387$	−15247.8	−2.00281
$388$	262.541	0.0343519
$389$	−2514.21	−0.327700	−0.163850	−	0.986485i	$-0.552391\pi$
$389$	−2514.21	−0.327700	−0.163850	+	0.986485i	$0.552391\pi$
$390$	0	0
$391$	−661.265	−0.0855284
$392$	12965.2	1.67052
$393$	−22528.0	−2.89157
$394$	−3278.90	−0.419261
$395$	0	0
$396$	766.582	0.0972782
$397$	1771.83	0.223994	0.111997	−	0.993709i	$-0.464275\pi$
$397$	1771.83	0.223994	0.111997	+	0.993709i	$0.464275\pi$
$398$	−11048.4	−1.39147
$399$	2008.49	0.252006
$400$	0	0
$401$	16028.7	1.99610	0.998049	−	0.0624279i	$-0.0198843\pi$
$401$	16028.7	1.99610	0.998049	+	0.0624279i	$0.0198843\pi$
$402$	19666.0	2.43993
$403$	−5556.86	−0.686866
$404$	−272.096	−0.0335082
$405$	0	0
$406$	−18945.8	−2.31593
$407$	−11528.3	−1.40403
$408$	15507.1	1.88165
$409$	7453.54	0.901110	0.450555	−	0.892749i	$-0.351226\pi$
$409$	7453.54	0.901110	0.450555	+	0.892749i	$0.351226\pi$
$410$	0	0
$411$	12180.9	1.46190
$412$	162.590	0.0194423
$413$	−1524.47	−0.181632
$414$	−1026.69	−0.121882
$415$	0	0
$416$	654.635	0.0771542
$417$	−285.323	−0.0335068
$418$	−960.891	−0.112437
$419$	510.467	0.0595177	0.0297589	−	0.999557i	$-0.490526\pi$
$419$	510.467	0.0595177	0.0297589	+	0.999557i	$0.490526\pi$
$420$	0	0
$421$	−4196.48	−0.485805	−0.242902	−	0.970051i	$-0.578099\pi$
$421$	−4196.48	−0.485805	−0.242902	+	0.970051i	$0.578099\pi$
$422$	−9789.31	−1.12923
$423$	4214.29	0.484411
$424$	9575.42	1.09675
$425$	0	0
$426$	−24617.2	−2.79978
$427$	23197.8	2.62909
$428$	93.7073	0.0105830
$429$	−12940.2	−1.45632
$430$	0	0
$431$	7708.60	0.861508	0.430754	−	0.902469i	$-0.358248\pi$
$431$	7708.60	0.861508	0.430754	+	0.902469i	$0.358248\pi$
$432$	9974.21	1.11084
$433$	991.950	0.110093	0.0550463	−	0.998484i	$-0.482469\pi$
$433$	991.950	0.110093	0.0550463	+	0.998484i	$0.482469\pi$
$434$	−13701.8	−1.51546
$435$	0	0
$436$	−293.415	−0.0322294
$437$	61.7887	0.00676374
$438$	13140.2	1.43348
$439$	10603.8	1.15283	0.576415	−	0.817157i	$-0.304451\pi$
$439$	10603.8	1.15283	0.576415	+	0.817157i	$0.304451\pi$
$440$	0	0
$441$	26246.0	2.83404
$442$	8658.71	0.931793
$443$	11044.4	1.18450	0.592251	−	0.805753i	$-0.298239\pi$
$443$	11044.4	1.18450	0.592251	+	0.805753i	$0.298239\pi$
$444$	923.320	0.0986910
$445$	0	0
$446$	5450.38	0.578662
$447$	14045.8	1.48623
$448$	−14762.9	−1.55688
$449$	−6089.74	−0.640073	−0.320036	−	0.947405i	$-0.603695\pi$
$449$	−6089.74	−0.640073	−0.320036	+	0.947405i	$0.603695\pi$
$450$	0	0
$451$	16756.2	1.74948
$452$	114.985	0.0119656
$453$	−9900.44	−1.02685
$454$	1805.03	0.186595
$455$	0	0
$456$	−1448.98	−0.148805
$457$	−4673.62	−0.478386	−0.239193	−	0.970972i	$-0.576883\pi$
$457$	−4673.62	−0.478386	−0.239193	+	0.970972i	$0.576883\pi$
$458$	4582.94	0.467570
$459$	12378.7	1.25880
$460$	0	0
$461$	1936.74	0.195668	0.0978340	−	0.995203i	$-0.468809\pi$
$461$	1936.74	0.195668	0.0978340	+	0.995203i	$0.468809\pi$
$462$	−31907.4	−3.21313
$463$	−1854.47	−0.186144	−0.0930720	−	0.995659i	$-0.529669\pi$
$463$	−1854.47	−0.186144	−0.0930720	+	0.995659i	$0.529669\pi$
$464$	14359.2	1.43665
$465$	0	0
$466$	−19240.8	−1.91269
$467$	2905.78	0.287930	0.143965	−	0.989583i	$-0.454015\pi$
$467$	2905.78	0.287930	0.143965	+	0.989583i	$0.454015\pi$
$468$	645.462	0.0637532
$469$	−24476.3	−2.40983
$470$	0	0
$471$	−7729.02	−0.756124
$472$	1099.80	0.107250
$473$	−14578.0	−1.41711
$474$	30410.3	2.94682
$475$	0	0
$476$	1025.07	0.0987063
$477$	19383.9	1.86065
$478$	−12815.0	−1.22625
$479$	−2005.49	−0.191301	−0.0956504	−	0.995415i	$-0.530493\pi$
$479$	−2005.49	−0.191301	−0.0956504	+	0.995415i	$0.530493\pi$
$480$	0	0
$481$	−9706.87	−0.920156
$482$	2356.79	0.222715
$483$	2051.76	0.193288
$484$	195.887	0.0183966
$485$	0	0
$486$	−10300.4	−0.961391
$487$	−14998.8	−1.39561	−0.697803	−	0.716290i	$-0.745839\pi$
$487$	−14998.8	−1.39561	−0.697803	+	0.716290i	$0.745839\pi$
$488$	−16735.6	−1.55242
$489$	−29612.0	−2.73845
$490$	0	0
$491$	6689.71	0.614872	0.307436	−	0.951569i	$-0.400529\pi$
$491$	6689.71	0.614872	0.307436	+	0.951569i	$0.400529\pi$
$492$	−1342.02	−0.122974
$493$	17820.8	1.62801
$494$	−809.071	−0.0736879
$495$	0	0
$496$	10384.7	0.940095
$497$	30638.5	2.76524
$498$	2035.63	0.183171
$499$	21514.1	1.93007	0.965035	−	0.262120i	$-0.0844216\pi$
$499$	21514.1	1.93007	0.965035	+	0.262120i	$0.0844216\pi$
$500$	0	0
$501$	26187.2	2.33525
$502$	2079.02	0.184843
$503$	−10403.0	−0.922159	−0.461080	−	0.887359i	$-0.652538\pi$
$503$	−10403.0	−0.922159	−0.461080	+	0.887359i	$0.652538\pi$
$504$	−29965.7	−2.64837
$505$	0	0
$506$	−981.590	−0.0862391
$507$	7691.89	0.673785
$508$	886.289	0.0774069
$509$	−9085.21	−0.791149	−0.395574	−	0.918434i	$-0.629454\pi$
$509$	−9085.21	−0.791149	−0.395574	+	0.918434i	$0.629454\pi$
$510$	0	0
$511$	−16354.3	−1.41579
$512$	10591.5	0.914225
$513$	−1156.67	−0.0995482
$514$	−14672.3	−1.25908
$515$	0	0
$516$	1167.57	0.0996110
$517$	4029.15	0.342750
$518$	−23934.7	−2.03018
$519$	−320.936	−0.0271436
$520$	0	0
$521$	3136.99	0.263789	0.131894	−	0.991264i	$-0.457894\pi$
$521$	3136.99	0.263789	0.131894	+	0.991264i	$0.457894\pi$
$522$	27668.9	2.31999
$523$	13655.4	1.14170	0.570850	−	0.821054i	$-0.306614\pi$
$523$	13655.4	1.14170	0.570850	+	0.821054i	$0.306614\pi$
$524$	1074.34	0.0895662
$525$	0	0
$526$	18410.2	1.52609
$527$	12888.2	1.06531
$528$	24182.8	1.99322
$529$	−12103.9	−0.994812
$530$	0	0
$531$	2226.36	0.181951
$532$	−95.7831	−0.00780587
$533$	14108.7	1.14656
$534$	−15586.4	−1.26309
$535$	0	0
$536$	17657.9	1.42296
$537$	−30989.8	−2.49033
$538$	−15580.8	−1.24858
$539$	25093.0	2.00526
$540$	0	0
$541$	24561.6	1.95192	0.975958	−	0.217960i	$-0.0699402\pi$
$541$	24561.6	1.95192	0.975958	+	0.217960i	$0.0699402\pi$
$542$	2050.80	0.162526
$543$	−19876.2	−1.57084
$544$	−1518.31	−0.119664
$545$	0	0
$546$	−26866.0	−2.10579
$547$	1400.50	0.109472	0.0547358	−	0.998501i	$-0.482568\pi$
$547$	1400.50	0.109472	0.0547358	+	0.998501i	$0.482568\pi$
$548$	−580.897	−0.0452823
$549$	−33878.5	−2.63370
$550$	0	0
$551$	−1665.17	−0.128746
$552$	−1480.20	−0.114133
$553$	−37848.6	−2.91046
$554$	4002.75	0.306968
$555$	0	0
$556$	13.6068	0.00103787
$557$	4415.56	0.335894	0.167947	−	0.985796i	$-0.446286\pi$
$557$	4415.56	0.335894	0.167947	+	0.985796i	$0.446286\pi$
$558$	20010.4	1.51812
$559$	−12274.7	−0.928734
$560$	0	0
$561$	30012.6	2.25870
$562$	−13918.7	−1.04471
$563$	−11060.2	−0.827941	−0.413971	−	0.910290i	$-0.635858\pi$
$563$	−11060.2	−0.827941	−0.413971	+	0.910290i	$0.635858\pi$
$564$	−322.700	−0.0240924
$565$	0	0
$566$	−8300.71	−0.616440
$567$	−1668.02	−0.123546
$568$	−22103.5	−1.63282
$569$	−15709.4	−1.15742	−0.578709	−	0.815534i	$-0.696443\pi$
$569$	−15709.4	−1.15742	−0.578709	+	0.815534i	$0.696443\pi$
$570$	0	0
$571$	−20679.1	−1.51558	−0.757788	−	0.652501i	$-0.773720\pi$
$571$	−20679.1	−1.51558	−0.757788	+	0.652501i	$0.773720\pi$
$572$	617.107	0.0451093
$573$	29864.3	2.17731
$574$	34788.6	2.52970
$575$	0	0
$576$	21560.1	1.55961
$577$	13087.1	0.944233	0.472117	−	0.881536i	$-0.343490\pi$
$577$	13087.1	0.944233	0.472117	+	0.881536i	$0.343490\pi$
$578$	−5840.21	−0.420278
$579$	26473.3	1.90016
$580$	0	0
$581$	−2533.55	−0.180911
$582$	15959.1	1.13664
$583$	18532.4	1.31652
$584$	11798.5	0.835999
$585$	0	0
$586$	−773.444	−0.0545233
$587$	−2951.64	−0.207542	−0.103771	−	0.994601i	$-0.533091\pi$
$587$	−2951.64	−0.207542	−0.103771	+	0.994601i	$0.533091\pi$
$588$	−2009.73	−0.140952
$589$	−1204.27	−0.0842465
$590$	0	0
$591$	−9569.56	−0.666056
$592$	18140.3	1.25939
$593$	−7400.19	−0.512461	−0.256230	−	0.966616i	$-0.582481\pi$
$593$	−7400.19	−0.512461	−0.256230	+	0.966616i	$0.582481\pi$
$594$	18375.1	1.26926
$595$	0	0
$596$	−669.833	−0.0460359
$597$	−32245.0	−2.21055
$598$	−826.500	−0.0565185
$599$	21370.8	1.45774	0.728871	−	0.684651i	$-0.240045\pi$
$599$	21370.8	1.45774	0.728871	+	0.684651i	$0.240045\pi$
$600$	0	0
$601$	−3044.93	−0.206664	−0.103332	−	0.994647i	$-0.532950\pi$
$601$	−3044.93	−0.206664	−0.103332	+	0.994647i	$0.532950\pi$
$602$	−30266.3	−2.04910
$603$	35745.6	2.41406
$604$	472.143	0.0318067
$605$	0	0
$606$	−16539.9	−1.10873
$607$	3541.29	0.236798	0.118399	−	0.992966i	$-0.462224\pi$
$607$	3541.29	0.236798	0.118399	+	0.992966i	$0.462224\pi$
$608$	141.871	0.00946324
$609$	−55293.8	−3.67918
$610$	0	0
$611$	3392.55	0.224628
$612$	−1497.04	−0.0988794
$613$	−7749.20	−0.510583	−0.255291	−	0.966864i	$-0.582171\pi$
$613$	−7749.20	−0.510583	−0.255291	+	0.966864i	$0.582171\pi$
$614$	5351.96	0.351771
$615$	0	0
$616$	−28649.3	−1.87388
$617$	−5825.27	−0.380092	−0.190046	−	0.981775i	$-0.560864\pi$
$617$	−5825.27	−0.380092	−0.190046	+	0.981775i	$0.560864\pi$
$618$	9883.33	0.643310
$619$	−24823.3	−1.61185	−0.805923	−	0.592020i	$-0.798331\pi$
$619$	−24823.3	−1.61185	−0.805923	+	0.592020i	$0.798331\pi$
$620$	0	0
$621$	−1181.59	−0.0763533
$622$	6314.21	0.407036
$623$	19398.8	1.24750
$624$	20361.9	1.30630
$625$	0	0
$626$	−26767.5	−1.70901
$627$	−2804.38	−0.178622
$628$	368.590	0.0234209
$629$	22513.4	1.42714
$630$	0	0
$631$	6113.64	0.385705	0.192853	−	0.981228i	$-0.438226\pi$
$631$	6113.64	0.385705	0.192853	+	0.981228i	$0.438226\pi$
$632$	27305.1	1.71857
$633$	−28570.3	−1.79395
$634$	23249.8	1.45642
$635$	0	0
$636$	−1484.28	−0.0925404
$637$	21128.4	1.31419
$638$	26453.4	1.64153
$639$	−44745.1	−2.77009
$640$	0	0
$641$	2528.95	0.155831	0.0779155	−	0.996960i	$-0.475174\pi$
$641$	2528.95	0.155831	0.0779155	+	0.996960i	$0.475174\pi$
$642$	5696.18	0.350172
$643$	19714.9	1.20914	0.604571	−	0.796552i	$-0.293345\pi$
$643$	19714.9	1.20914	0.604571	+	0.796552i	$0.293345\pi$
$644$	−97.8464	−0.00598709
$645$	0	0
$646$	1876.50	0.114288
$647$	−11660.1	−0.708508	−0.354254	−	0.935149i	$-0.615265\pi$
$647$	−11660.1	−0.708508	−0.354254	+	0.935149i	$0.615265\pi$
$648$	1203.36	0.0729513
$649$	2128.56	0.128741
$650$	0	0
$651$	−39989.1	−2.40752
$652$	1412.17	0.0848233
$653$	28938.2	1.73421	0.867106	−	0.498123i	$-0.165977\pi$
$653$	28938.2	1.73421	0.867106	+	0.498123i	$0.165977\pi$
$654$	−17835.8	−1.06642
$655$	0	0
$656$	−26366.5	−1.56927
$657$	23884.1	1.41828
$658$	8365.19	0.495607
$659$	29254.1	1.72925	0.864626	−	0.502416i	$-0.167556\pi$
$659$	29254.1	1.72925	0.864626	+	0.502416i	$0.167556\pi$
$660$	0	0
$661$	−29291.5	−1.72361	−0.861806	−	0.507238i	$-0.830666\pi$
$661$	−29291.5	−1.72361	−0.861806	+	0.507238i	$0.830666\pi$
$662$	−6869.19	−0.403291
$663$	25270.6	1.48029
$664$	1827.77	0.106824
$665$	0	0
$666$	34954.8	2.03374
$667$	−1701.04	−0.0987477
$668$	−1248.85	−0.0723342
$669$	15907.1	0.919286
$670$	0	0
$671$	−32390.2	−1.86350
$672$	4710.99	0.270432
$673$	−8943.03	−0.512226	−0.256113	−	0.966647i	$-0.582442\pi$
$673$	−8943.03	−0.512226	−0.256113	+	0.966647i	$0.582442\pi$
$674$	14524.7	0.830075
$675$	0	0
$676$	−366.819	−0.0208705
$677$	7183.11	0.407784	0.203892	−	0.978993i	$-0.434641\pi$
$677$	7183.11	0.407784	0.203892	+	0.978993i	$0.434641\pi$
$678$	6989.61	0.395921
$679$	−19862.7	−1.12262
$680$	0	0
$681$	5268.01	0.296432
$682$	19131.4	1.07416
$683$	5862.29	0.328425	0.164213	−	0.986425i	$-0.447492\pi$
$683$	5862.29	0.328425	0.164213	+	0.986425i	$0.447492\pi$
$684$	139.884	0.00781956
$685$	0	0
$686$	21746.2	1.21031
$687$	13375.4	0.742801
$688$	22939.0	1.27113
$689$	15604.3	0.862810
$690$	0	0
$691$	−23664.2	−1.30279	−0.651397	−	0.758737i	$-0.725817\pi$
$691$	−23664.2	−1.30279	−0.651397	+	0.758737i	$0.725817\pi$
$692$	15.3051	0.000840772 0
$693$	−57996.0	−3.17906
$694$	17270.2	0.944620
$695$	0	0
$696$	39890.6	2.17248
$697$	−32722.7	−1.77828
$698$	27694.2	1.50178
$699$	−56154.7	−3.03858
$700$	0	0
$701$	4362.78	0.235064	0.117532	−	0.993069i	$-0.462502\pi$
$701$	4362.78	0.235064	0.117532	+	0.993069i	$0.462502\pi$
$702$	15471.9	0.831835
$703$	−2103.66	−0.112860
$704$	20612.9	1.10352
$705$	0	0
$706$	32797.3	1.74836
$707$	20585.5	1.09505
$708$	−170.479	−0.00904942
$709$	4110.95	0.217757	0.108879	−	0.994055i	$-0.465274\pi$
$709$	4110.95	0.217757	0.108879	+	0.994055i	$0.465274\pi$
$710$	0	0
$711$	55274.9	2.91557
$712$	−13994.8	−0.736628
$713$	−1230.22	−0.0646170
$714$	62311.1	3.26602
$715$	0	0
$716$	1477.87	0.0771379
$717$	−37400.9	−1.94807
$718$	−315.385	−0.0163929
$719$	27498.0	1.42629	0.713145	−	0.701016i	$-0.247270\pi$
$719$	27498.0	1.42629	0.713145	+	0.701016i	$0.247270\pi$
$720$	0	0
$721$	−12300.8	−0.635374
$722$	19708.0	1.01587
$723$	6878.34	0.353815
$724$	947.877	0.0486569
$725$	0	0
$726$	11907.4	0.608710
$727$	16435.0	0.838434	0.419217	−	0.907886i	$-0.362305\pi$
$727$	16435.0	0.838434	0.419217	+	0.907886i	$0.362305\pi$
$728$	−24122.7	−1.22809
$729$	−31537.4	−1.60227
$730$	0	0
$731$	28468.9	1.44044
$732$	2594.17	0.130988
$733$	−8396.30	−0.423089	−0.211545	−	0.977368i	$-0.567849\pi$
$733$	−8396.30	−0.423089	−0.211545	+	0.977368i	$0.567849\pi$
$734$	19560.1	0.983619
$735$	0	0
$736$	144.928	0.00725829
$737$	34175.3	1.70809
$738$	−50806.0	−2.53414
$739$	−13109.2	−0.652545	−0.326272	−	0.945276i	$-0.605793\pi$
$739$	−13109.2	−0.652545	−0.326272	+	0.945276i	$0.605793\pi$
$740$	0	0
$741$	−2361.29	−0.117064
$742$	38476.3	1.90365
$743$	21436.0	1.05843	0.529213	−	0.848489i	$-0.322487\pi$
$743$	21436.0	1.05843	0.529213	+	0.848489i	$0.322487\pi$
$744$	28849.3	1.42160
$745$	0	0
$746$	−24904.5	−1.22228
$747$	3700.04	0.181228
$748$	−1431.27	−0.0699633
$749$	−7089.46	−0.345852
$750$	0	0
$751$	−11865.5	−0.576537	−0.288268	−	0.957550i	$-0.593080\pi$
$751$	−11865.5	−0.576537	−0.288268	+	0.957550i	$0.593080\pi$
$752$	−6340.03	−0.307443
$753$	6067.66	0.293649
$754$	22273.7	1.07581
$755$	0	0
$756$	1831.66	0.0881176
$757$	−12747.5	−0.612041	−0.306020	−	0.952025i	$-0.598998\pi$
$757$	−12747.5	−0.612041	−0.306020	+	0.952025i	$0.598998\pi$
$758$	−3241.47	−0.155324
$759$	−2864.79	−0.137003
$760$	0	0
$761$	27815.8	1.32500	0.662499	−	0.749063i	$-0.269496\pi$
$761$	27815.8	1.32500	0.662499	+	0.749063i	$0.269496\pi$
$762$	53874.8	2.56126
$763$	22198.4	1.05326
$764$	−1424.20	−0.0674421
$765$	0	0
$766$	35182.5	1.65952
$767$	1792.25	0.0843733
$768$	−5230.07	−0.245734
$769$	10034.1	0.470533	0.235267	−	0.971931i	$-0.424404\pi$
$769$	10034.1	0.470533	0.235267	+	0.971931i	$0.424404\pi$
$770$	0	0
$771$	−42821.5	−2.00023
$772$	−1262.49	−0.0588573
$773$	4602.78	0.214166	0.107083	−	0.994250i	$-0.465849\pi$
$773$	4602.78	0.214166	0.107083	+	0.994250i	$0.465849\pi$
$774$	44201.5	2.05270
$775$	0	0
$776$	14329.5	0.662885
$777$	−69854.1	−3.22523
$778$	7288.36	0.335862
$779$	3057.62	0.140630
$780$	0	0
$781$	−42779.4	−1.96001
$782$	1916.92	0.0876586
$783$	31843.2	1.45336
$784$	−39484.9	−1.79869
$785$	0	0
$786$	65305.7	2.96359
$787$	−24131.7	−1.09301	−0.546507	−	0.837454i	$-0.684043\pi$
$787$	−24131.7	−1.09301	−0.546507	+	0.837454i	$0.684043\pi$
$788$	456.363	0.0206311
$789$	53730.6	2.42441
$790$	0	0
$791$	−8699.26	−0.391037
$792$	41840.0	1.87717
$793$	−27272.6	−1.22128
$794$	−5136.31	−0.229573
$795$	0	0
$796$	1537.73	0.0684718
$797$	−895.812	−0.0398134	−0.0199067	−	0.999802i	$-0.506337\pi$
$797$	−895.812	−0.0398134	−0.0199067	+	0.999802i	$0.506337\pi$
$798$	−5822.36	−0.258282
$799$	−7868.44	−0.348392
$800$	0	0
$801$	−28330.4	−1.24969
$802$	−46465.2	−2.04582
$803$	22834.9	1.00352
$804$	−2737.15	−0.120064
$805$	0	0
$806$	16108.6	0.703973
$807$	−45473.0	−1.98355
$808$	−14851.0	−0.646605
$809$	−15363.7	−0.667688	−0.333844	−	0.942628i	$-0.608346\pi$
$809$	−15363.7	−0.667688	−0.333844	+	0.942628i	$0.608346\pi$
$810$	0	0
$811$	28990.9	1.25525	0.627625	−	0.778516i	$-0.284027\pi$
$811$	28990.9	1.25525	0.627625	+	0.778516i	$0.284027\pi$
$812$	2636.91	0.113962
$813$	5985.30	0.258196
$814$	33419.2	1.43900
$815$	0	0
$816$	−47226.0	−2.02603
$817$	−2660.14	−0.113913
$818$	−21606.9	−0.923553
$819$	−48832.7	−2.08346
$820$	0	0
$821$	−12746.8	−0.541860	−0.270930	−	0.962599i	$-0.587331\pi$
$821$	−12746.8	−0.541860	−0.270930	+	0.962599i	$0.587331\pi$
$822$	−35311.0	−1.49831
$823$	29882.9	1.26568	0.632838	−	0.774284i	$-0.281890\pi$
$823$	29882.9	1.26568	0.632838	+	0.774284i	$0.281890\pi$
$824$	8874.13	0.375176
$825$	0	0
$826$	4419.24	0.186156
$827$	10928.1	0.459501	0.229751	−	0.973250i	$-0.426209\pi$
$827$	10928.1	0.459501	0.229751	+	0.973250i	$0.426209\pi$
$828$	142.897	0.00599760
$829$	5117.67	0.214408	0.107204	−	0.994237i	$-0.465810\pi$
$829$	5117.67	0.214408	0.107204	+	0.994237i	$0.465810\pi$
$830$	0	0
$831$	11682.1	0.487663
$832$	17356.1	0.723214
$833$	−49003.6	−2.03826
$834$	827.115	0.0343413
$835$	0	0
$836$	133.738	0.00553282
$837$	23029.3	0.951028
$838$	−1479.78	−0.0610001
$839$	−9585.09	−0.394415	−0.197207	−	0.980362i	$-0.563187\pi$
$839$	−9585.09	−0.394415	−0.197207	+	0.980362i	$0.563187\pi$
$840$	0	0
$841$	21453.3	0.879630
$842$	12165.1	0.497904
$843$	−40622.0	−1.65966
$844$	1362.49	0.0555675
$845$	0	0
$846$	−12216.7	−0.496476
$847$	−14819.9	−0.601201
$848$	−29161.4	−1.18091
$849$	−24225.8	−0.979302
$850$	0	0
$851$	−2148.97	−0.0865639
$852$	3426.26	0.137772
$853$	−1838.35	−0.0737913	−0.0368956	−	0.999319i	$-0.511747\pi$
$853$	−1838.35	−0.0737913	−0.0368956	+	0.999319i	$0.511747\pi$
$854$	−67247.4	−2.69457
$855$	0	0
$856$	5114.54	0.204219
$857$	17958.3	0.715803	0.357902	−	0.933759i	$-0.383492\pi$
$857$	17958.3	0.715803	0.357902	+	0.933759i	$0.383492\pi$
$858$	37512.0	1.49259
$859$	−30181.3	−1.19881	−0.599403	−	0.800448i	$-0.704595\pi$
$859$	−30181.3	−1.19881	−0.599403	+	0.800448i	$0.704595\pi$
$860$	0	0
$861$	101531.	4.01879
$862$	−22346.2	−0.882965
$863$	−11558.5	−0.455918	−0.227959	−	0.973671i	$-0.573205\pi$
$863$	−11558.5	−0.455918	−0.227959	+	0.973671i	$0.573205\pi$
$864$	−2713.01	−0.106827
$865$	0	0
$866$	−2875.54	−0.112835
$867$	−17044.8	−0.667671
$868$	1907.04	0.0745729
$869$	52846.6	2.06294
$870$	0	0
$871$	28775.6	1.11943
$872$	−16014.6	−0.621930
$873$	29007.8	1.12459
$874$	−179.118	−0.00693220
$875$	0	0
$876$	−1828.88	−0.0705388
$877$	−10092.1	−0.388580	−0.194290	−	0.980944i	$-0.562240\pi$
$877$	−10092.1	−0.388580	−0.194290	+	0.980944i	$0.562240\pi$
$878$	−30739.1	−1.18154
$879$	−2257.31	−0.0866181
$880$	0	0
$881$	25516.7	0.975800	0.487900	−	0.872900i	$-0.337763\pi$
$881$	25516.7	0.975800	0.487900	+	0.872900i	$0.337763\pi$
$882$	−76084.0	−2.90463
$883$	−45428.3	−1.73135	−0.865677	−	0.500603i	$-0.833112\pi$
$883$	−45428.3	−1.73135	−0.865677	+	0.500603i	$0.833112\pi$
$884$	−1205.13	−0.0458518
$885$	0	0
$886$	−32016.3	−1.21400
$887$	−17167.2	−0.649850	−0.324925	−	0.945740i	$-0.605339\pi$
$887$	−17167.2	−0.649850	−0.324925	+	0.945740i	$0.605339\pi$
$888$	50394.8	1.90443
$889$	−67052.5	−2.52966
$890$	0	0
$891$	2329.00	0.0875695
$892$	−758.593	−0.0284749
$893$	735.228	0.0275515
$894$	−40717.1	−1.52325
$895$	0	0
$896$	47250.5	1.76175
$897$	−2412.16	−0.0897877
$898$	17653.4	0.656015
$899$	33153.7	1.22996
$900$	0	0
$901$	−36191.5	−1.33819
$902$	−48574.0	−1.79306
$903$	−88332.7	−3.25529
$904$	6275.90	0.230900
$905$	0	0
$906$	28700.1	1.05243
$907$	21054.9	0.770801	0.385401	−	0.922749i	$-0.374063\pi$
$907$	21054.9	0.770801	0.385401	+	0.922749i	$0.374063\pi$
$908$	−251.226	−0.00918198
$909$	−30063.6	−1.09697
$910$	0	0
$911$	−4530.45	−0.164764	−0.0823822	−	0.996601i	$-0.526253\pi$
$911$	−4530.45	−0.164764	−0.0823822	+	0.996601i	$0.526253\pi$
$912$	4412.80	0.160222
$913$	3537.50	0.128230
$914$	13548.2	0.490301
$915$	0	0
$916$	−637.862	−0.0230082
$917$	−81279.4	−2.92703
$918$	−35884.4	−1.29015
$919$	−19342.3	−0.694280	−0.347140	−	0.937813i	$-0.612847\pi$
$919$	−19342.3	−0.694280	−0.347140	+	0.937813i	$0.612847\pi$
$920$	0	0
$921$	15619.8	0.558838
$922$	−5614.36	−0.200541
$923$	−36020.3	−1.28453
$924$	4440.92	0.158112
$925$	0	0
$926$	5375.88	0.190780
$927$	17964.3	0.636489
$928$	−3905.73	−0.138159
$929$	−31748.7	−1.12125	−0.560625	−	0.828070i	$-0.689439\pi$
$929$	−31748.7	−1.12125	−0.560625	+	0.828070i	$0.689439\pi$
$930$	0	0
$931$	4578.90	0.161190
$932$	2677.97	0.0941199
$933$	18428.2	0.646635
$934$	−8423.49	−0.295102
$935$	0	0
$936$	35229.3	1.23024
$937$	183.834	0.00640940	0.00320470	−	0.999995i	$-0.498980\pi$
$937$	183.834	0.00640940	0.00320470	+	0.999995i	$0.498980\pi$
$938$	70953.6	2.46985
$939$	−78121.4	−2.71501
$940$	0	0
$941$	−26805.6	−0.928627	−0.464313	−	0.885671i	$-0.653699\pi$
$941$	−26805.6	−0.928627	−0.464313	+	0.885671i	$0.653699\pi$
$942$	22405.4	0.774956
$943$	3123.48	0.107863
$944$	−3349.37	−0.115480
$945$	0	0
$946$	42259.7	1.45241
$947$	41938.0	1.43907	0.719536	−	0.694455i	$-0.244355\pi$
$947$	41938.0	1.43907	0.719536	+	0.694455i	$0.244355\pi$
$948$	−4232.55	−0.145007
$949$	19227.0	0.657676
$950$	0	0
$951$	67855.2	2.31373
$952$	55948.5	1.90473
$953$	−39460.9	−1.34130	−0.670652	−	0.741772i	$-0.733986\pi$
$953$	−39460.9	−1.34130	−0.670652	+	0.741772i	$0.733986\pi$
$954$	−56191.6	−1.90699
$955$	0	0
$956$	1783.62	0.0603413
$957$	77204.7	2.60781
$958$	5813.65	0.196065
$959$	43948.0	1.47983
$960$	0	0
$961$	−5813.88	−0.195156
$962$	28139.0	0.943074
$963$	10353.6	0.346459
$964$	−328.022	−0.0109594
$965$	0	0
$966$	−5947.79	−0.198102
$967$	−5635.86	−0.187422	−0.0937109	−	0.995599i	$-0.529873\pi$
$967$	−5635.86	−0.187422	−0.0937109	+	0.995599i	$0.529873\pi$
$968$	10691.5	0.354998
$969$	5476.61	0.181562
$970$	0	0
$971$	47662.7	1.57525	0.787626	−	0.616154i	$-0.211310\pi$
$971$	47662.7	1.57525	0.787626	+	0.616154i	$0.211310\pi$
$972$	1433.63	0.0473083
$973$	−1029.43	−0.0339177
$974$	43479.6	1.43037
$975$	0	0
$976$	50967.3	1.67154
$977$	−6095.63	−0.199607	−0.0998037	−	0.995007i	$-0.531821\pi$
$977$	−6095.63	−0.199607	−0.0998037	+	0.995007i	$0.531821\pi$
$978$	85841.5	2.80665
$979$	−27085.8	−0.884235
$980$	0	0
$981$	−32419.0	−1.05511
$982$	−19392.6	−0.630187
$983$	54910.1	1.78165	0.890824	−	0.454349i	$-0.150128\pi$
$983$	54910.1	1.78165	0.890824	+	0.454349i	$0.150128\pi$
$984$	−73247.6	−2.37302
$985$	0	0
$986$	−51660.1	−1.66855
$987$	24414.0	0.787342
$988$	112.608	0.00362604
$989$	−2717.45	−0.0873708
$990$	0	0
$991$	−2704.17	−0.0866808	−0.0433404	−	0.999060i	$-0.513800\pi$
$991$	−2704.17	−0.0866808	−0.0433404	+	0.999060i	$0.513800\pi$
$992$	−2824.67	−0.0904065
$993$	−20047.9	−0.640686
$994$	−88817.1	−2.83411
$995$	0	0
$996$	−283.323	−0.00901349
$997$	−838.643	−0.0266400	−0.0133200	−	0.999911i	$-0.504240\pi$
$997$	−838.643	−0.0266400	−0.0133200	+	0.999911i	$0.504240\pi$
$998$	−62366.8	−1.97814
$999$	40228.3	1.27404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2075.4.a.f.1.6		20
5.4	even	2		415.4.a.b.1.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.4.a.b.1.15	✓	20	5.4	even	2
2075.4.a.f.1.6		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2075 = 5^{2} \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.89887 q^{2} -8.46043 q^{3} +0.403470 q^{4} +24.5257 q^{6} -30.5247 q^{7} +22.0214 q^{8} +44.5789 q^{9} +O(q^{10})\)	\(q-2.89887 q^{2} -8.46043 q^{3} +0.403470 q^{4} +24.5257 q^{6} -30.5247 q^{7} +22.0214 q^{8} +44.5789 q^{9} +42.6205 q^{11} -3.41353 q^{12} +35.8865 q^{13} +88.4872 q^{14} -67.0650 q^{16} -83.2325 q^{17} -129.228 q^{18} +7.77726 q^{19} +258.252 q^{21} -123.551 q^{22} +7.94479 q^{23} -186.310 q^{24} -104.030 q^{26} -148.725 q^{27} -12.3158 q^{28} -214.108 q^{29} -154.845 q^{31} +18.2418 q^{32} -360.588 q^{33} +241.280 q^{34} +17.9862 q^{36} -270.488 q^{37} -22.5453 q^{38} -303.615 q^{39} +393.148 q^{41} -748.639 q^{42} -342.041 q^{43} +17.1961 q^{44} -23.0310 q^{46} +94.5356 q^{47} +567.398 q^{48} +588.756 q^{49} +704.183 q^{51} +14.4791 q^{52} +434.824 q^{53} +431.134 q^{54} -672.195 q^{56} -65.7989 q^{57} +620.673 q^{58} +49.9421 q^{59} -759.968 q^{61} +448.878 q^{62} -1360.75 q^{63} +483.639 q^{64} +1045.30 q^{66} +801.852 q^{67} -33.5818 q^{68} -67.2164 q^{69} -1003.73 q^{71} +981.688 q^{72} +535.773 q^{73} +784.111 q^{74} +3.13789 q^{76} -1300.98 q^{77} +880.141 q^{78} +1239.93 q^{79} +54.6451 q^{81} -1139.69 q^{82} +83.0000 q^{83} +104.197 q^{84} +991.534 q^{86} +1811.45 q^{87} +938.562 q^{88} -635.511 q^{89} -1095.42 q^{91} +3.20549 q^{92} +1310.06 q^{93} -274.047 q^{94} -154.334 q^{96} +650.708 q^{97} -1706.73 q^{98} +1899.97 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 12 q^{3} + 67 q^{4} + 17 q^{6} - 31 q^{7} - 36 q^{8} + 216 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 12 * q^3 + 67 * q^4 + 17 * q^6 - 31 * q^7 - 36 * q^8 + 216 * q^9	\( 20 q - 5 q^{2} - 12 q^{3} + 67 q^{4} + 17 q^{6} - 31 q^{7} - 36 q^{8} + 216 q^{9} + 36 q^{11} - 44 q^{12} - 67 q^{13} + 89 q^{14} + 375 q^{16} - 425 q^{17} + 11 q^{18} - 251 q^{19} - 23 q^{21} - 447 q^{22} - 584 q^{23} + 152 q^{24} + 799 q^{26} - 477 q^{27} - 831 q^{28} + 252 q^{29} + 329 q^{31} - 1088 q^{32} - 1405 q^{33} + 189 q^{34} + 1126 q^{36} - 260 q^{37} - 2204 q^{38} + 40 q^{39} + 1830 q^{41} - 1782 q^{42} + 87 q^{43} + 86 q^{44} - 549 q^{46} - 1028 q^{47} - 2931 q^{48} + 1531 q^{49} + 981 q^{51} - 623 q^{52} - 1491 q^{53} + 595 q^{54} + 1930 q^{56} - 1184 q^{57} - 1075 q^{58} + 782 q^{59} - 686 q^{61} - 797 q^{62} - 1554 q^{63} + 714 q^{64} + 1688 q^{66} - 661 q^{67} - 3632 q^{68} + 1326 q^{69} + 298 q^{71} - 1378 q^{72} - 656 q^{73} + 348 q^{74} - 3262 q^{76} - 1231 q^{77} - 587 q^{78} - 748 q^{79} + 2356 q^{81} - 526 q^{82} + 1660 q^{83} + 1927 q^{84} + 2632 q^{86} - 4001 q^{87} - 2200 q^{88} + 3702 q^{89} + 112 q^{91} - 7797 q^{92} - 1542 q^{93} - 1773 q^{94} + 18 q^{96} - 4506 q^{97} - 1942 q^{98} + 10603 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 12 * q^3 + 67 * q^4 + 17 * q^6 - 31 * q^7 - 36 * q^8 + 216 * q^9 + 36 * q^11 - 44 * q^12 - 67 * q^13 + 89 * q^14 + 375 * q^16 - 425 * q^17 + 11 * q^18 - 251 * q^19 - 23 * q^21 - 447 * q^22 - 584 * q^23 + 152 * q^24 + 799 * q^26 - 477 * q^27 - 831 * q^28 + 252 * q^29 + 329 * q^31 - 1088 * q^32 - 1405 * q^33 + 189 * q^34 + 1126 * q^36 - 260 * q^37 - 2204 * q^38 + 40 * q^39 + 1830 * q^41 - 1782 * q^42 + 87 * q^43 + 86 * q^44 - 549 * q^46 - 1028 * q^47 - 2931 * q^48 + 1531 * q^49 + 981 * q^51 - 623 * q^52 - 1491 * q^53 + 595 * q^54 + 1930 * q^56 - 1184 * q^57 - 1075 * q^58 + 782 * q^59 - 686 * q^61 - 797 * q^62 - 1554 * q^63 + 714 * q^64 + 1688 * q^66 - 661 * q^67 - 3632 * q^68 + 1326 * q^69 + 298 * q^71 - 1378 * q^72 - 656 * q^73 + 348 * q^74 - 3262 * q^76 - 1231 * q^77 - 587 * q^78 - 748 * q^79 + 2356 * q^81 - 526 * q^82 + 1660 * q^83 + 1927 * q^84 + 2632 * q^86 - 4001 * q^87 - 2200 * q^88 + 3702 * q^89 + 112 * q^91 - 7797 * q^92 - 1542 * q^93 - 1773 * q^94 + 18 * q^96 - 4506 * q^97 - 1942 * q^98 + 10603 * q^99

Introduction

L-functions

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