LMFDB - Embedded newform 8673.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 17 x^{10} + 52 x^{9} + 101 x^{8} - 316 x^{7} - 260 x^{6} + 830 x^{5} + 287 x^{4} + \cdots - 61 $ x^12 - 3x^11 - 17x^10 + 52x^9 + 101x^8 - 316x^7 - 260x^6 + 830x^5 + 287x^4 - 941x^3 - 77x^2 + 360*x - 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1239)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.74074$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74074 q^{2} +1.00000 q^{3} +5.51163 q^{4} +1.27795 q^{5} -2.74074 q^{6} -9.62444 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.74074 q^{2} +1.00000 q^{3} +5.51163 q^{4} +1.27795 q^{5} -2.74074 q^{6} -9.62444 q^{8} +1.00000 q^{9} -3.50251 q^{10} +1.77747 q^{11} +5.51163 q^{12} +0.760974 q^{13} +1.27795 q^{15} +15.3548 q^{16} +2.62625 q^{17} -2.74074 q^{18} -1.44882 q^{19} +7.04356 q^{20} -4.87157 q^{22} +4.56717 q^{23} -9.62444 q^{24} -3.36686 q^{25} -2.08563 q^{26} +1.00000 q^{27} +1.01649 q^{29} -3.50251 q^{30} -5.38120 q^{31} -22.8345 q^{32} +1.77747 q^{33} -7.19786 q^{34} +5.51163 q^{36} +6.63407 q^{37} +3.97082 q^{38} +0.760974 q^{39} -12.2995 q^{40} +6.05166 q^{41} -5.77591 q^{43} +9.79674 q^{44} +1.27795 q^{45} -12.5174 q^{46} -0.264292 q^{47} +15.3548 q^{48} +9.22766 q^{50} +2.62625 q^{51} +4.19420 q^{52} +0.888762 q^{53} -2.74074 q^{54} +2.27151 q^{55} -1.44882 q^{57} -2.78594 q^{58} +1.00000 q^{59} +7.04356 q^{60} +4.47713 q^{61} +14.7484 q^{62} +31.8738 q^{64} +0.972483 q^{65} -4.87157 q^{66} -9.54490 q^{67} +14.4749 q^{68} +4.56717 q^{69} +8.50827 q^{71} -9.62444 q^{72} +9.99846 q^{73} -18.1822 q^{74} -3.36686 q^{75} -7.98534 q^{76} -2.08563 q^{78} +10.5343 q^{79} +19.6226 q^{80} +1.00000 q^{81} -16.5860 q^{82} +11.8387 q^{83} +3.35621 q^{85} +15.8302 q^{86} +1.01649 q^{87} -17.1071 q^{88} -10.2082 q^{89} -3.50251 q^{90} +25.1725 q^{92} -5.38120 q^{93} +0.724353 q^{94} -1.85151 q^{95} -22.8345 q^{96} -2.08174 q^{97} +1.77747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * 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 $

$2$	−2.74074	−1.93799	−0.968996	−	0.247076i	$-0.920530\pi$
$2$	−2.74074	−1.93799	−0.968996	+	0.247076i	$0.920530\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.51163	2.75581
$5$	1.27795	0.571515	0.285757	−	0.958302i	$-0.407755\pi$
$5$	1.27795	0.571515	0.285757	+	0.958302i	$0.407755\pi$
$6$	−2.74074	−1.11890
$7$	0	0
$7$	0	0
$8$	−9.62444	−3.40275
$9$	1.00000	0.333333
$10$	−3.50251	−1.10759
$11$	1.77747	0.535926	0.267963	−	0.963429i	$-0.413649\pi$
$11$	1.77747	0.535926	0.267963	+	0.963429i	$0.413649\pi$
$12$	5.51163	1.59107
$13$	0.760974	0.211056	0.105528	−	0.994416i	$-0.466347\pi$
$13$	0.760974	0.211056	0.105528	+	0.994416i	$0.466347\pi$
$14$	0	0
$15$	1.27795	0.329964
$16$	15.3548	3.83870
$17$	2.62625	0.636960	0.318480	−	0.947930i	$-0.396828\pi$
$17$	2.62625	0.636960	0.318480	+	0.947930i	$0.396828\pi$
$18$	−2.74074	−0.645997
$19$	−1.44882	−0.332381	−0.166191	−	0.986094i	$-0.553147\pi$
$19$	−1.44882	−0.332381	−0.166191	+	0.986094i	$0.553147\pi$
$20$	7.04356	1.57499
$21$	0	0
$22$	−4.87157	−1.03862
$23$	4.56717	0.952321	0.476160	−	0.879359i	$-0.342028\pi$
$23$	4.56717	0.952321	0.476160	+	0.879359i	$0.342028\pi$
$24$	−9.62444	−1.96458
$25$	−3.36686	−0.673371
$26$	−2.08563	−0.409025
$27$	1.00000	0.192450
$28$	0	0
$29$	1.01649	0.188758	0.0943790	−	0.995536i	$-0.469913\pi$
$29$	1.01649	0.188758	0.0943790	+	0.995536i	$0.469913\pi$
$30$	−3.50251	−0.639468
$31$	−5.38120	−0.966492	−0.483246	−	0.875485i	$-0.660542\pi$
$31$	−5.38120	−0.966492	−0.483246	+	0.875485i	$0.660542\pi$
$32$	−22.8345	−4.03661
$33$	1.77747	0.309417
$34$	−7.19786	−1.23442
$35$	0	0
$36$	5.51163	0.918605
$37$	6.63407	1.09063	0.545317	−	0.838230i	$-0.316409\pi$
$37$	6.63407	1.09063	0.545317	+	0.838230i	$0.316409\pi$
$38$	3.97082	0.644153
$39$	0.760974	0.121853
$40$	−12.2995	−1.94472
$41$	6.05166	0.945110	0.472555	−	0.881301i	$-0.343332\pi$
$41$	6.05166	0.945110	0.472555	+	0.881301i	$0.343332\pi$
$42$	0	0
$43$	−5.77591	−0.880818	−0.440409	−	0.897797i	$-0.645167\pi$
$43$	−5.77591	−0.880818	−0.440409	+	0.897797i	$0.645167\pi$
$44$	9.79674	1.47691
$45$	1.27795	0.190505
$46$	−12.5174	−1.84559
$47$	−0.264292	−0.0385509	−0.0192754	−	0.999814i	$-0.506136\pi$
$47$	−0.264292	−0.0385509	−0.0192754	+	0.999814i	$0.506136\pi$
$48$	15.3548	2.21627
$49$	0	0
$50$	9.22766	1.30499
$51$	2.62625	0.367749
$52$	4.19420	0.581632
$53$	0.888762	0.122081	0.0610404	−	0.998135i	$-0.480558\pi$
$53$	0.888762	0.122081	0.0610404	+	0.998135i	$0.480558\pi$
$54$	−2.74074	−0.372967
$55$	2.27151	0.306290
$56$	0	0
$57$	−1.44882	−0.191901
$58$	−2.78594	−0.365812
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	7.04356	0.909320
$61$	4.47713	0.573238	0.286619	−	0.958045i	$-0.407469\pi$
$61$	4.47713	0.573238	0.286619	+	0.958045i	$0.407469\pi$
$62$	14.7484	1.87305
$63$	0	0
$64$	31.8738	3.98423
$65$	0.972483	0.120622
$66$	−4.87157	−0.599648
$67$	−9.54490	−1.16610	−0.583048	−	0.812438i	$-0.698140\pi$
$67$	−9.54490	−1.16610	−0.583048	+	0.812438i	$0.698140\pi$
$68$	14.4749	1.75534
$69$	4.56717	0.549823
$70$	0	0
$71$	8.50827	1.00975	0.504873	−	0.863194i	$-0.331539\pi$
$71$	8.50827	1.00975	0.504873	+	0.863194i	$0.331539\pi$
$72$	−9.62444	−1.13425
$73$	9.99846	1.17023	0.585116	−	0.810950i	$-0.301049\pi$
$73$	9.99846	1.17023	0.585116	+	0.810950i	$0.301049\pi$
$74$	−18.1822	−2.11364
$75$	−3.36686	−0.388771
$76$	−7.98534	−0.915982
$77$	0	0
$78$	−2.08563	−0.236151
$79$	10.5343	1.18520	0.592599	−	0.805498i	$-0.298102\pi$
$79$	10.5343	1.18520	0.592599	+	0.805498i	$0.298102\pi$
$80$	19.6226	2.19387
$81$	1.00000	0.111111
$82$	−16.5860	−1.83162
$83$	11.8387	1.29947	0.649735	−	0.760161i	$-0.274880\pi$
$83$	11.8387	1.29947	0.649735	+	0.760161i	$0.274880\pi$
$84$	0	0
$85$	3.35621	0.364032
$86$	15.8302	1.70702
$87$	1.01649	0.108979
$88$	−17.1071	−1.82363
$89$	−10.2082	−1.08207	−0.541035	−	0.841000i	$-0.681967\pi$
$89$	−10.2082	−1.08207	−0.541035	+	0.841000i	$0.681967\pi$
$90$	−3.50251	−0.369197
$91$	0	0
$92$	25.1725	2.62442
$93$	−5.38120	−0.558004
$94$	0.724353	0.0747113
$95$	−1.85151	−0.189961
$96$	−22.8345	−2.33054
$97$	−2.08174	−0.211368	−0.105684	−	0.994400i	$-0.533703\pi$
$97$	−2.08174	−0.211368	−0.105684	+	0.994400i	$0.533703\pi$
$98$	0	0
$99$	1.77747	0.178642
$100$	−18.5569	−1.85569
$101$	−11.8276	−1.17689	−0.588443	−	0.808538i	$-0.700259\pi$
$101$	−11.8276	−1.17689	−0.588443	+	0.808538i	$0.700259\pi$
$102$	−7.19786	−0.712695
$103$	−11.6328	−1.14621	−0.573106	−	0.819482i	$-0.694261\pi$
$103$	−11.6328	−1.14621	−0.573106	+	0.819482i	$0.694261\pi$
$104$	−7.32395	−0.718172
$105$	0	0
$106$	−2.43586	−0.236592
$107$	11.6234	1.12367	0.561836	−	0.827249i	$-0.310095\pi$
$107$	11.6234	1.12367	0.561836	+	0.827249i	$0.310095\pi$
$108$	5.51163	0.530357
$109$	−7.16344	−0.686133	−0.343067	−	0.939311i	$-0.611466\pi$
$109$	−7.16344	−0.686133	−0.343067	+	0.939311i	$0.611466\pi$
$110$	−6.22559	−0.593587
$111$	6.63407	0.629678
$112$	0	0
$113$	17.7663	1.67131	0.835656	−	0.549253i	$-0.185088\pi$
$113$	17.7663	1.67131	0.835656	+	0.549253i	$0.185088\pi$
$114$	3.97082	0.371902
$115$	5.83659	0.544265
$116$	5.60253	0.520182
$117$	0.760974	0.0703520
$118$	−2.74074	−0.252305
$119$	0	0
$120$	−12.2995	−1.12279
$121$	−7.84061	−0.712783
$122$	−12.2706	−1.11093
$123$	6.05166	0.545660
$124$	−29.6592	−2.66347
$125$	−10.6924	−0.956356
$126$	0	0
$127$	7.03718	0.624449	0.312224	−	0.950008i	$-0.398926\pi$
$127$	7.03718	0.624449	0.312224	+	0.950008i	$0.398926\pi$
$128$	−41.6886	−3.68479
$129$	−5.77591	−0.508540
$130$	−2.66532	−0.233764
$131$	0.135477	0.0118366	0.00591832	−	0.999982i	$-0.498116\pi$
$131$	0.135477	0.0118366	0.00591832	+	0.999982i	$0.498116\pi$
$132$	9.79674	0.852696
$133$	0	0
$134$	26.1601	2.25988
$135$	1.27795	0.109988
$136$	−25.2762	−2.16742
$137$	9.19494	0.785577	0.392788	−	0.919629i	$-0.371510\pi$
$137$	9.19494	0.785577	0.392788	+	0.919629i	$0.371510\pi$
$138$	−12.5174	−1.06555
$139$	−16.4278	−1.39339	−0.696695	−	0.717367i	$-0.745347\pi$
$139$	−16.4278	−1.39339	−0.696695	+	0.717367i	$0.745347\pi$
$140$	0	0
$141$	−0.264292	−0.0222574
$142$	−23.3189	−1.95688
$143$	1.35261	0.113111
$144$	15.3548	1.27957
$145$	1.29902	0.107878
$146$	−27.4031	−2.26790
$147$	0	0
$148$	36.5645	3.00559
$149$	14.4209	1.18141	0.590704	−	0.806889i	$-0.298850\pi$
$149$	14.4209	1.18141	0.590704	+	0.806889i	$0.298850\pi$
$150$	9.22766	0.753435
$151$	22.0789	1.79676	0.898379	−	0.439222i	$-0.144746\pi$
$151$	22.0789	1.79676	0.898379	+	0.439222i	$0.144746\pi$
$152$	13.9441	1.13101
$153$	2.62625	0.212320
$154$	0	0
$155$	−6.87688	−0.552364
$156$	4.19420	0.335805
$157$	−22.0650	−1.76098	−0.880491	−	0.474063i	$-0.842787\pi$
$157$	−22.0650	−1.76098	−0.880491	+	0.474063i	$0.842787\pi$
$158$	−28.8716	−2.29690
$159$	0.888762	0.0704834
$160$	−29.1813	−2.30698
$161$	0	0
$162$	−2.74074	−0.215332
$163$	1.81546	0.142198	0.0710990	−	0.997469i	$-0.477349\pi$
$163$	1.81546	0.142198	0.0710990	+	0.997469i	$0.477349\pi$
$164$	33.3545	2.60455
$165$	2.27151	0.176836
$166$	−32.4468	−2.51836
$167$	7.91611	0.612567	0.306283	−	0.951940i	$-0.400914\pi$
$167$	7.91611	0.612567	0.306283	+	0.951940i	$0.400914\pi$
$168$	0	0
$169$	−12.4209	−0.955455
$170$	−9.19848	−0.705491
$171$	−1.44882	−0.110794
$172$	−31.8347	−2.42737
$173$	−3.97713	−0.302376	−0.151188	−	0.988505i	$-0.548310\pi$
$173$	−3.97713	−0.302376	−0.151188	+	0.988505i	$0.548310\pi$
$174$	−2.78594	−0.211201
$175$	0	0
$176$	27.2926	2.05726
$177$	1.00000	0.0751646
$178$	27.9781	2.09704
$179$	−6.70995	−0.501525	−0.250763	−	0.968049i	$-0.580681\pi$
$179$	−6.70995	−0.501525	−0.250763	+	0.968049i	$0.580681\pi$
$180$	7.04356	0.524996
$181$	−5.43426	−0.403925	−0.201963	−	0.979393i	$-0.564732\pi$
$181$	−5.43426	−0.403925	−0.201963	+	0.979393i	$0.564732\pi$
$182$	0	0
$183$	4.47713	0.330959
$184$	−43.9565	−3.24051
$185$	8.47798	0.623314
$186$	14.7484	1.08141
$187$	4.66808	0.341364
$188$	−1.45668	−0.106239
$189$	0	0
$190$	5.07450	0.368143
$191$	6.84792	0.495498	0.247749	−	0.968824i	$-0.420309\pi$
$191$	6.84792	0.495498	0.247749	+	0.968824i	$0.420309\pi$
$192$	31.8738	2.30029
$193$	23.0598	1.65988	0.829941	−	0.557851i	$-0.188374\pi$
$193$	23.0598	1.65988	0.829941	+	0.557851i	$0.188374\pi$
$194$	5.70549	0.409630
$195$	0.972483	0.0696409
$196$	0	0
$197$	−11.1880	−0.797116	−0.398558	−	0.917143i	$-0.630489\pi$
$197$	−11.1880	−0.797116	−0.398558	+	0.917143i	$0.630489\pi$
$198$	−4.87157	−0.346207
$199$	22.2279	1.57569	0.787846	−	0.615872i	$-0.211196\pi$
$199$	22.2279	1.57569	0.787846	+	0.615872i	$0.211196\pi$
$200$	32.4041	2.29132
$201$	−9.54490	−0.673246
$202$	32.4162	2.28080
$203$	0	0
$204$	14.4749	1.01345
$205$	7.73369	0.540144
$206$	31.8823	2.22135
$207$	4.56717	0.317440
$208$	11.6846	0.810181
$209$	−2.57522	−0.178132
$210$	0	0
$211$	1.63839	0.112791	0.0563957	−	0.998408i	$-0.482039\pi$
$211$	1.63839	0.112791	0.0563957	+	0.998408i	$0.482039\pi$
$212$	4.89852	0.336432
$213$	8.50827	0.582977
$214$	−31.8565	−2.17767
$215$	−7.38130	−0.503400
$216$	−9.62444	−0.654860
$217$	0	0
$218$	19.6331	1.32972
$219$	9.99846	0.675634
$220$	12.5197	0.844078
$221$	1.99851	0.134434
$222$	−18.1822	−1.22031
$223$	23.8153	1.59479	0.797394	−	0.603459i	$-0.206211\pi$
$223$	23.8153	1.59479	0.797394	+	0.603459i	$0.206211\pi$
$224$	0	0
$225$	−3.36686	−0.224457
$226$	−48.6927	−3.23899
$227$	−10.4857	−0.695962	−0.347981	−	0.937502i	$-0.613133\pi$
$227$	−10.4857	−0.695962	−0.347981	+	0.937502i	$0.613133\pi$
$228$	−7.98534	−0.528842
$229$	−24.6975	−1.63205	−0.816027	−	0.578014i	$-0.803828\pi$
$229$	−24.6975	−1.63205	−0.816027	+	0.578014i	$0.803828\pi$
$230$	−15.9966	−1.05478
$231$	0	0
$232$	−9.78318	−0.642297
$233$	27.9894	1.83365	0.916824	−	0.399292i	$-0.130744\pi$
$233$	27.9894	1.83365	0.916824	+	0.399292i	$0.130744\pi$
$234$	−2.08563	−0.136342
$235$	−0.337750	−0.0220324
$236$	5.51163	0.358776
$237$	10.5343	0.684274
$238$	0	0
$239$	20.6290	1.33438	0.667191	−	0.744887i	$-0.267496\pi$
$239$	20.6290	1.33438	0.667191	+	0.744887i	$0.267496\pi$
$240$	19.6226	1.26663
$241$	−5.58416	−0.359707	−0.179854	−	0.983693i	$-0.557562\pi$
$241$	−5.58416	−0.359707	−0.179854	+	0.983693i	$0.557562\pi$
$242$	21.4890	1.38137
$243$	1.00000	0.0641500
$244$	24.6763	1.57974
$245$	0	0
$246$	−16.5860	−1.05748
$247$	−1.10251	−0.0701512
$248$	51.7910	3.28873
$249$	11.8387	0.750249
$250$	29.3050	1.85341
$251$	1.36456	0.0861300	0.0430650	−	0.999072i	$-0.486288\pi$
$251$	1.36456	0.0861300	0.0430650	+	0.999072i	$0.486288\pi$
$252$	0	0
$253$	8.11799	0.510374
$254$	−19.2870	−1.21018
$255$	3.35621	0.210174
$256$	50.5098	3.15686
$257$	26.0891	1.62739	0.813697	−	0.581289i	$-0.197451\pi$
$257$	26.0891	1.62739	0.813697	+	0.581289i	$0.197451\pi$
$258$	15.8302	0.985548
$259$	0	0
$260$	5.35996	0.332411
$261$	1.01649	0.0629193
$262$	−0.371306	−0.0229393
$263$	−6.21570	−0.383277	−0.191638	−	0.981466i	$-0.561380\pi$
$263$	−6.21570	−0.383277	−0.191638	+	0.981466i	$0.561380\pi$
$264$	−17.1071	−1.05287
$265$	1.13579	0.0697710
$266$	0	0
$267$	−10.2082	−0.624734
$268$	−52.6080	−3.21354
$269$	−7.71529	−0.470410	−0.235205	−	0.971946i	$-0.575576\pi$
$269$	−7.71529	−0.470410	−0.235205	+	0.971946i	$0.575576\pi$
$270$	−3.50251	−0.213156
$271$	24.2205	1.47129	0.735645	−	0.677367i	$-0.236879\pi$
$271$	24.2205	1.47129	0.735645	+	0.677367i	$0.236879\pi$
$272$	40.3256	2.44510
$273$	0	0
$274$	−25.2009	−1.52244
$275$	−5.98447	−0.360877
$276$	25.1725	1.51521
$277$	−0.0949038	−0.00570222	−0.00285111	−	0.999996i	$-0.500908\pi$
$277$	−0.0949038	−0.00570222	−0.00285111	+	0.999996i	$0.500908\pi$
$278$	45.0243	2.70038
$279$	−5.38120	−0.322164
$280$	0	0
$281$	8.81635	0.525939	0.262970	−	0.964804i	$-0.415298\pi$
$281$	8.81635	0.525939	0.262970	+	0.964804i	$0.415298\pi$
$282$	0.724353	0.0431346
$283$	16.9106	1.00523	0.502617	−	0.864509i	$-0.332371\pi$
$283$	16.9106	1.00523	0.502617	+	0.864509i	$0.332371\pi$
$284$	46.8944	2.78267
$285$	−1.85151	−0.109674
$286$	−3.70713	−0.219207
$287$	0	0
$288$	−22.8345	−1.34554
$289$	−10.1028	−0.594282
$290$	−3.56028	−0.209067
$291$	−2.08174	−0.122034
$292$	55.1078	3.22494
$293$	−3.12553	−0.182596	−0.0912978	−	0.995824i	$-0.529102\pi$
$293$	−3.12553	−0.182596	−0.0912978	+	0.995824i	$0.529102\pi$
$294$	0	0
$295$	1.27795	0.0744049
$296$	−63.8493	−3.71116
$297$	1.77747	0.103139
$298$	−39.5239	−2.28956
$299$	3.47550	0.200993
$300$	−18.5569	−1.07138
$301$	0	0
$302$	−60.5125	−3.48210
$303$	−11.8276	−0.679476
$304$	−22.2463	−1.27591
$305$	5.72153	0.327614
$306$	−7.19786	−0.411475
$307$	10.5592	0.602648	0.301324	−	0.953522i	$-0.402571\pi$
$307$	10.5592	0.602648	0.301324	+	0.953522i	$0.402571\pi$
$308$	0	0
$309$	−11.6328	−0.661765
$310$	18.8477	1.07048
$311$	5.78202	0.327869	0.163934	−	0.986471i	$-0.447582\pi$
$311$	5.78202	0.327869	0.163934	+	0.986471i	$0.447582\pi$
$312$	−7.32395	−0.414637
$313$	−25.0791	−1.41755	−0.708777	−	0.705433i	$-0.750753\pi$
$313$	−25.0791	−1.41755	−0.708777	+	0.705433i	$0.750753\pi$
$314$	60.4744	3.41277
$315$	0	0
$316$	58.0609	3.26618
$317$	−12.7544	−0.716360	−0.358180	−	0.933652i	$-0.616603\pi$
$317$	−12.7544	−0.716360	−0.358180	+	0.933652i	$0.616603\pi$
$318$	−2.43586	−0.136596
$319$	1.80678	0.101160
$320$	40.7330	2.27704
$321$	11.6234	0.648752
$322$	0	0
$323$	−3.80496	−0.211714
$324$	5.51163	0.306202
$325$	−2.56209	−0.142119
$326$	−4.97571	−0.275579
$327$	−7.16344	−0.396139
$328$	−58.2438	−3.21598
$329$	0	0
$330$	−6.22559	−0.342708
$331$	22.9945	1.26389	0.631947	−	0.775012i	$-0.282256\pi$
$331$	22.9945	1.26389	0.631947	+	0.775012i	$0.282256\pi$
$332$	65.2507	3.58110
$333$	6.63407	0.363545
$334$	−21.6960	−1.18715
$335$	−12.1979	−0.666441
$336$	0	0
$337$	25.7404	1.40217	0.701084	−	0.713078i	$-0.252700\pi$
$337$	25.7404	1.40217	0.701084	+	0.713078i	$0.252700\pi$
$338$	34.0424	1.85167
$339$	17.7663	0.964932
$340$	18.4982	1.00320
$341$	−9.56490	−0.517968
$342$	3.97082	0.214718
$343$	0	0
$344$	55.5899	2.99721
$345$	5.83659	0.314232
$346$	10.9003	0.586002
$347$	17.5806	0.943773	0.471887	−	0.881659i	$-0.343573\pi$
$347$	17.5806	0.943773	0.471887	+	0.881659i	$0.343573\pi$
$348$	5.60253	0.300327
$349$	−1.04515	−0.0559454	−0.0279727	−	0.999609i	$-0.508905\pi$
$349$	−1.04515	−0.0559454	−0.0279727	+	0.999609i	$0.508905\pi$
$350$	0	0
$351$	0.760974	0.0406178
$352$	−40.5876	−2.16333
$353$	−29.8126	−1.58676	−0.793382	−	0.608724i	$-0.791682\pi$
$353$	−29.8126	−1.58676	−0.793382	+	0.608724i	$0.791682\pi$
$354$	−2.74074	−0.145668
$355$	10.8731	0.577085
$356$	−56.2640	−2.98199
$357$	0	0
$358$	18.3902	0.971952
$359$	−22.8721	−1.20715	−0.603573	−	0.797308i	$-0.706257\pi$
$359$	−22.8721	−1.20715	−0.603573	+	0.797308i	$0.706257\pi$
$360$	−12.2995	−0.648241
$361$	−16.9009	−0.889523
$362$	14.8939	0.782804
$363$	−7.84061	−0.411525
$364$	0	0
$365$	12.7775	0.668804
$366$	−12.2706	−0.641396
$367$	−18.6848	−0.975341	−0.487670	−	0.873028i	$-0.662153\pi$
$367$	−18.6848	−0.975341	−0.487670	+	0.873028i	$0.662153\pi$
$368$	70.1279	3.65567
$369$	6.05166	0.315037
$370$	−23.2359	−1.20798
$371$	0	0
$372$	−29.6592	−1.53776
$373$	−6.83922	−0.354122	−0.177061	−	0.984200i	$-0.556659\pi$
$373$	−6.83922	−0.354122	−0.177061	+	0.984200i	$0.556659\pi$
$374$	−12.7940	−0.661560
$375$	−10.6924	−0.552152
$376$	2.54366	0.131179
$377$	0.773524	0.0398385
$378$	0	0
$379$	19.1152	0.981881	0.490940	−	0.871193i	$-0.336653\pi$
$379$	19.1152	0.981881	0.490940	+	0.871193i	$0.336653\pi$
$380$	−10.2048	−0.523497
$381$	7.03718	0.360526
$382$	−18.7683	−0.960271
$383$	−9.47663	−0.484233	−0.242116	−	0.970247i	$-0.577842\pi$
$383$	−9.47663	−0.484233	−0.242116	+	0.970247i	$0.577842\pi$
$384$	−41.6886	−2.12741
$385$	0	0
$386$	−63.2008	−3.21684
$387$	−5.77591	−0.293606
$388$	−11.4738	−0.582492
$389$	−7.08023	−0.358982	−0.179491	−	0.983760i	$-0.557445\pi$
$389$	−7.08023	−0.358982	−0.179491	+	0.983760i	$0.557445\pi$
$390$	−2.66532	−0.134964
$391$	11.9945	0.606590
$392$	0	0
$393$	0.135477	0.00683389
$394$	30.6635	1.54480
$395$	13.4622	0.677357
$396$	9.79674	0.492305
$397$	33.1501	1.66376	0.831879	−	0.554957i	$-0.187265\pi$
$397$	33.1501	1.66376	0.831879	+	0.554957i	$0.187265\pi$
$398$	−60.9207	−3.05368
$399$	0	0
$400$	−51.6974	−2.58487
$401$	28.6647	1.43145	0.715723	−	0.698385i	$-0.246097\pi$
$401$	28.6647	1.43145	0.715723	+	0.698385i	$0.246097\pi$
$402$	26.1601	1.30474
$403$	−4.09495	−0.203984
$404$	−65.1892	−3.24328
$405$	1.27795	0.0635016
$406$	0	0
$407$	11.7918	0.584500
$408$	−25.2762	−1.25136
$409$	19.5377	0.966078	0.483039	−	0.875599i	$-0.339533\pi$
$409$	19.5377	0.966078	0.483039	+	0.875599i	$0.339533\pi$
$410$	−21.1960	−1.04680
$411$	9.19494	0.453553
$412$	−64.1155	−3.15874
$413$	0	0
$414$	−12.5174	−0.615197
$415$	15.1293	0.742666
$416$	−17.3765	−0.851952
$417$	−16.4278	−0.804475
$418$	7.05801	0.345218
$419$	−1.87278	−0.0914913	−0.0457457	−	0.998953i	$-0.514566\pi$
$419$	−1.87278	−0.0914913	−0.0457457	+	0.998953i	$0.514566\pi$
$420$	0	0
$421$	−16.7291	−0.815327	−0.407664	−	0.913132i	$-0.633656\pi$
$421$	−16.7291	−0.815327	−0.407664	+	0.913132i	$0.633656\pi$
$422$	−4.49039	−0.218589
$423$	−0.264292	−0.0128503
$424$	−8.55384	−0.415411
$425$	−8.84222	−0.428910
$426$	−23.3189	−1.12981
$427$	0	0
$428$	64.0636	3.09663
$429$	1.35261	0.0653044
$430$	20.2302	0.975586
$431$	−28.9646	−1.39517	−0.697587	−	0.716500i	$-0.745743\pi$
$431$	−28.9646	−1.39517	−0.697587	+	0.716500i	$0.745743\pi$
$432$	15.3548	0.738758
$433$	−23.9506	−1.15099	−0.575497	−	0.817804i	$-0.695192\pi$
$433$	−23.9506	−1.15099	−0.575497	+	0.817804i	$0.695192\pi$
$434$	0	0
$435$	1.29902	0.0622834
$436$	−39.4822	−1.89086
$437$	−6.61699	−0.316534
$438$	−27.4031	−1.30937
$439$	−19.8383	−0.946831	−0.473415	−	0.880839i	$-0.656979\pi$
$439$	−19.8383	−0.946831	−0.473415	+	0.880839i	$0.656979\pi$
$440$	−21.8620	−1.04223
$441$	0	0
$442$	−5.47739	−0.260533
$443$	−10.8313	−0.514611	−0.257305	−	0.966330i	$-0.582835\pi$
$443$	−10.8313	−0.514611	−0.257305	+	0.966330i	$0.582835\pi$
$444$	36.5645	1.73528
$445$	−13.0456	−0.618419
$446$	−65.2713	−3.09069
$447$	14.4209	0.682086
$448$	0	0
$449$	−15.3292	−0.723432	−0.361716	−	0.932288i	$-0.617809\pi$
$449$	−15.3292	−0.723432	−0.361716	+	0.932288i	$0.617809\pi$
$450$	9.22766	0.434996
$451$	10.7566	0.506510
$452$	97.9212	4.60582
$453$	22.0789	1.03736
$454$	28.7386	1.34877
$455$	0	0
$456$	13.9441	0.652990
$457$	39.0231	1.82542	0.912712	−	0.408603i	$-0.133984\pi$
$457$	39.0231	1.82542	0.912712	+	0.408603i	$0.133984\pi$
$458$	67.6892	3.16291
$459$	2.62625	0.122583
$460$	32.1691	1.49989
$461$	31.4509	1.46481	0.732406	−	0.680868i	$-0.238397\pi$
$461$	31.4509	1.46481	0.732406	+	0.680868i	$0.238397\pi$
$462$	0	0
$463$	2.69973	0.125467	0.0627336	−	0.998030i	$-0.480018\pi$
$463$	2.69973	0.125467	0.0627336	+	0.998030i	$0.480018\pi$
$464$	15.6080	0.724585
$465$	−6.87688	−0.318908
$466$	−76.7116	−3.55359
$467$	−10.3165	−0.477391	−0.238696	−	0.971094i	$-0.576720\pi$
$467$	−10.3165	−0.477391	−0.238696	+	0.971094i	$0.576720\pi$
$468$	4.19420	0.193877
$469$	0	0
$470$	0.925684	0.0426986
$471$	−22.0650	−1.01670
$472$	−9.62444	−0.443001
$473$	−10.2665	−0.472054
$474$	−28.8716	−1.32612
$475$	4.87796	0.223816
$476$	0	0
$477$	0.888762	0.0406936
$478$	−56.5387	−2.58602
$479$	−11.6906	−0.534156	−0.267078	−	0.963675i	$-0.586058\pi$
$479$	−11.6906	−0.534156	−0.267078	+	0.963675i	$0.586058\pi$
$480$	−29.1813	−1.33194
$481$	5.04835	0.230185
$482$	15.3047	0.697110
$483$	0	0
$484$	−43.2145	−1.96430
$485$	−2.66035	−0.120800
$486$	−2.74074	−0.124322
$487$	−1.46266	−0.0662796	−0.0331398	−	0.999451i	$-0.510551\pi$
$487$	−1.46266	−0.0662796	−0.0331398	+	0.999451i	$0.510551\pi$
$488$	−43.0899	−1.95059
$489$	1.81546	0.0820981
$490$	0	0
$491$	−30.9405	−1.39632	−0.698162	−	0.715940i	$-0.745998\pi$
$491$	−30.9405	−1.39632	−0.698162	+	0.715940i	$0.745998\pi$
$492$	33.3545	1.50374
$493$	2.66957	0.120231
$494$	3.02169	0.135952
$495$	2.27151	0.102097
$496$	−82.6272	−3.71007
$497$	0	0
$498$	−32.4468	−1.45398
$499$	22.2659	0.996757	0.498379	−	0.866960i	$-0.333929\pi$
$499$	22.2659	0.996757	0.498379	+	0.866960i	$0.333929\pi$
$500$	−58.9325	−2.63554
$501$	7.91611	0.353666
$502$	−3.73988	−0.166919
$503$	6.00562	0.267777	0.133889	−	0.990996i	$-0.457254\pi$
$503$	6.00562	0.267777	0.133889	+	0.990996i	$0.457254\pi$
$504$	0	0
$505$	−15.1150	−0.672608
$506$	−22.2493	−0.989100
$507$	−12.4209	−0.551632
$508$	38.7863	1.72086
$509$	−10.6362	−0.471442	−0.235721	−	0.971821i	$-0.575745\pi$
$509$	−10.6362	−0.471442	−0.235721	+	0.971821i	$0.575745\pi$
$510$	−9.19848	−0.407315
$511$	0	0
$512$	−55.0568	−2.43319
$513$	−1.44882	−0.0639668
$514$	−71.5034	−3.15388
$515$	−14.8660	−0.655076
$516$	−31.8347	−1.40144
$517$	−0.469770	−0.0206604
$518$	0	0
$519$	−3.97713	−0.174577
$520$	−9.35961	−0.410446
$521$	−14.3038	−0.626662	−0.313331	−	0.949644i	$-0.601445\pi$
$521$	−14.3038	−0.626662	−0.313331	+	0.949644i	$0.601445\pi$
$522$	−2.78594	−0.121937
$523$	−22.1436	−0.968273	−0.484136	−	0.874993i	$-0.660866\pi$
$523$	−22.1436	−0.968273	−0.484136	+	0.874993i	$0.660866\pi$
$524$	0.746697	0.0326196
$525$	0	0
$526$	17.0356	0.742787
$527$	−14.1324	−0.615617
$528$	27.2926	1.18776
$529$	−2.14097	−0.0930856
$530$	−3.11290	−0.135216
$531$	1.00000	0.0433963
$532$	0	0
$533$	4.60515	0.199471
$534$	27.9781	1.21073
$535$	14.8540	0.642195
$536$	91.8644	3.96794
$537$	−6.70995	−0.289556
$538$	21.1456	0.911650
$539$	0	0
$540$	7.04356	0.303107
$541$	−19.8893	−0.855107	−0.427554	−	0.903990i	$-0.640624\pi$
$541$	−19.8893	−0.855107	−0.427554	+	0.903990i	$0.640624\pi$
$542$	−66.3820	−2.85135
$543$	−5.43426	−0.233206
$544$	−59.9693	−2.57116
$545$	−9.15449	−0.392135
$546$	0	0
$547$	12.4566	0.532605	0.266303	−	0.963889i	$-0.414198\pi$
$547$	12.4566	0.532605	0.266303	+	0.963889i	$0.414198\pi$
$548$	50.6791	2.16490
$549$	4.47713	0.191079
$550$	16.4019	0.699378
$551$	−1.47271	−0.0627397
$552$	−43.9565	−1.87091
$553$	0	0
$554$	0.260106	0.0110509
$555$	8.47798	0.359870
$556$	−90.5441	−3.83993
$557$	−19.3122	−0.818285	−0.409143	−	0.912470i	$-0.634172\pi$
$557$	−19.3122	−0.818285	−0.409143	+	0.912470i	$0.634172\pi$
$558$	14.7484	0.624351
$559$	−4.39532	−0.185902
$560$	0	0
$561$	4.66808	0.197086
$562$	−24.1633	−1.01927
$563$	−2.78155	−0.117228	−0.0586142	−	0.998281i	$-0.518668\pi$
$563$	−2.78155	−0.117228	−0.0586142	+	0.998281i	$0.518668\pi$
$564$	−1.45668	−0.0613372
$565$	22.7043	0.955179
$566$	−46.3476	−1.94813
$567$	0	0
$568$	−81.8874	−3.43592
$569$	18.5022	0.775654	0.387827	−	0.921732i	$-0.373226\pi$
$569$	18.5022	0.775654	0.387827	+	0.921732i	$0.373226\pi$
$570$	5.07450	0.212547
$571$	−43.3857	−1.81563	−0.907817	−	0.419366i	$-0.862252\pi$
$571$	−43.3857	−1.81563	−0.907817	+	0.419366i	$0.862252\pi$
$572$	7.45506	0.311712
$573$	6.84792	0.286076
$574$	0	0
$575$	−15.3770	−0.641265
$576$	31.8738	1.32808
$577$	−25.7884	−1.07359	−0.536793	−	0.843714i	$-0.680364\pi$
$577$	−25.7884	−1.07359	−0.536793	+	0.843714i	$0.680364\pi$
$578$	27.6891	1.15171
$579$	23.0598	0.958333
$580$	7.15973	0.297292
$581$	0	0
$582$	5.70549	0.236500
$583$	1.57974	0.0654263
$584$	−96.2297	−3.98201
$585$	0.972483	0.0402072
$586$	8.56626	0.353869
$587$	39.9208	1.64771	0.823853	−	0.566803i	$-0.191820\pi$
$587$	39.9208	1.64771	0.823853	+	0.566803i	$0.191820\pi$
$588$	0	0
$589$	7.79637	0.321244
$590$	−3.50251	−0.144196
$591$	−11.1880	−0.460215
$592$	101.865	4.18662
$593$	47.0018	1.93013	0.965067	−	0.262005i	$-0.0843837\pi$
$593$	47.0018	1.93013	0.965067	+	0.262005i	$0.0843837\pi$
$594$	−4.87157	−0.199883
$595$	0	0
$596$	79.4827	3.25574
$597$	22.2279	0.909727
$598$	−9.52541	−0.389523
$599$	12.1484	0.496372	0.248186	−	0.968712i	$-0.420166\pi$
$599$	12.1484	0.496372	0.248186	+	0.968712i	$0.420166\pi$
$600$	32.4041	1.32289
$601$	−26.8032	−1.09333	−0.546663	−	0.837353i	$-0.684102\pi$
$601$	−26.8032	−1.09333	−0.546663	+	0.837353i	$0.684102\pi$
$602$	0	0
$603$	−9.54490	−0.388699
$604$	121.691	4.95153
$605$	−10.0199	−0.407366
$606$	32.4162	1.31682
$607$	−8.36024	−0.339332	−0.169666	−	0.985502i	$-0.554269\pi$
$607$	−8.36024	−0.339332	−0.169666	+	0.985502i	$0.554269\pi$
$608$	33.0831	1.34170
$609$	0	0
$610$	−15.6812	−0.634913
$611$	−0.201119	−0.00813640
$612$	14.4749	0.585114
$613$	−20.1487	−0.813798	−0.406899	−	0.913473i	$-0.633390\pi$
$613$	−20.1487	−0.813798	−0.406899	+	0.913473i	$0.633390\pi$
$614$	−28.9401	−1.16793
$615$	7.73369	0.311852
$616$	0	0
$617$	27.9019	1.12329	0.561644	−	0.827379i	$-0.310169\pi$
$617$	27.9019	1.12329	0.561644	+	0.827379i	$0.310169\pi$
$618$	31.8823	1.28250
$619$	14.5057	0.583032	0.291516	−	0.956566i	$-0.405840\pi$
$619$	14.5057	0.583032	0.291516	+	0.956566i	$0.405840\pi$
$620$	−37.9028	−1.52221
$621$	4.56717	0.183274
$622$	−15.8470	−0.635407
$623$	0	0
$624$	11.6846	0.467758
$625$	3.17000	0.126800
$626$	68.7351	2.74721
$627$	−2.57522	−0.102845
$628$	−121.614	−4.85294
$629$	17.4228	0.694691
$630$	0	0
$631$	−31.0381	−1.23561	−0.617803	−	0.786333i	$-0.711977\pi$
$631$	−31.0381	−1.23561	−0.617803	+	0.786333i	$0.711977\pi$
$632$	−101.386	−4.03293
$633$	1.63839	0.0651201
$634$	34.9565	1.38830
$635$	8.99313	0.356882
$636$	4.89852	0.194239
$637$	0	0
$638$	−4.95191	−0.196048
$639$	8.50827	0.336582
$640$	−53.2758	−2.10591
$641$	19.8122	0.782536	0.391268	−	0.920277i	$-0.372037\pi$
$641$	19.8122	0.782536	0.391268	+	0.920277i	$0.372037\pi$
$642$	−31.8565	−1.25728
$643$	40.2683	1.58803	0.794014	−	0.607899i	$-0.207987\pi$
$643$	40.2683	1.58803	0.794014	+	0.607899i	$0.207987\pi$
$644$	0	0
$645$	−7.38130	−0.290638
$646$	10.4284	0.410300
$647$	−24.2984	−0.955267	−0.477634	−	0.878559i	$-0.658505\pi$
$647$	−24.2984	−0.955267	−0.477634	+	0.878559i	$0.658505\pi$
$648$	−9.62444	−0.378084
$649$	1.77747	0.0697717
$650$	7.02201	0.275426
$651$	0	0
$652$	10.0062	0.391872
$653$	41.9795	1.64279	0.821393	−	0.570363i	$-0.193197\pi$
$653$	41.9795	1.64279	0.821393	+	0.570363i	$0.193197\pi$
$654$	19.6331	0.767715
$655$	0.173132	0.00676482
$656$	92.9220	3.62799
$657$	9.99846	0.390077
$658$	0	0
$659$	34.9922	1.36310	0.681551	−	0.731771i	$-0.261306\pi$
$659$	34.9922	1.36310	0.681551	+	0.731771i	$0.261306\pi$
$660$	12.5197	0.487328
$661$	23.7388	0.923331	0.461666	−	0.887054i	$-0.347252\pi$
$661$	23.7388	0.923331	0.461666	+	0.887054i	$0.347252\pi$
$662$	−63.0219	−2.44942
$663$	1.99851	0.0776157
$664$	−113.941	−4.42178
$665$	0	0
$666$	−18.1822	−0.704547
$667$	4.64250	0.179758
$668$	43.6307	1.68812
$669$	23.8153	0.920751
$670$	33.4311	1.29156
$671$	7.95795	0.307213
$672$	0	0
$673$	−20.1924	−0.778360	−0.389180	−	0.921162i	$-0.627242\pi$
$673$	−20.1924	−0.778360	−0.389180	+	0.921162i	$0.627242\pi$
$674$	−70.5476	−2.71739
$675$	−3.36686	−0.129590
$676$	−68.4595	−2.63306
$677$	5.89999	0.226755	0.113377	−	0.993552i	$-0.463833\pi$
$677$	5.89999	0.226755	0.113377	+	0.993552i	$0.463833\pi$
$678$	−48.6927	−1.87003
$679$	0	0
$680$	−32.3016	−1.23871
$681$	−10.4857	−0.401814
$682$	26.2149	1.00382
$683$	−30.5984	−1.17082	−0.585408	−	0.810739i	$-0.699066\pi$
$683$	−30.5984	−1.17082	−0.585408	+	0.810739i	$0.699066\pi$
$684$	−7.98534	−0.305327
$685$	11.7506	0.448969
$686$	0	0
$687$	−24.6975	−0.942267
$688$	−88.6879	−3.38119
$689$	0.676324	0.0257659
$690$	−15.9966	−0.608978
$691$	−33.5176	−1.27507	−0.637534	−	0.770422i	$-0.720046\pi$
$691$	−33.5176	−1.27507	−0.637534	+	0.770422i	$0.720046\pi$
$692$	−21.9205	−0.833292
$693$	0	0
$694$	−48.1836	−1.82903
$695$	−20.9939	−0.796343
$696$	−9.78318	−0.370830
$697$	15.8932	0.601997
$698$	2.86447	0.108422
$699$	27.9894	1.05866
$700$	0	0
$701$	8.49541	0.320867	0.160434	−	0.987047i	$-0.448711\pi$
$701$	8.49541	0.320867	0.160434	+	0.987047i	$0.448711\pi$
$702$	−2.08563	−0.0787169
$703$	−9.61156	−0.362507
$704$	56.6546	2.13525
$705$	−0.337750	−0.0127204
$706$	81.7084	3.07514
$707$	0	0
$708$	5.51163	0.207140
$709$	2.21847	0.0833164	0.0416582	−	0.999132i	$-0.486736\pi$
$709$	2.21847	0.0833164	0.0416582	+	0.999132i	$0.486736\pi$
$710$	−29.8003	−1.11839
$711$	10.5343	0.395066
$712$	98.2486	3.68202
$713$	−24.5768	−0.920410
$714$	0	0
$715$	1.72856	0.0646443
$716$	−36.9828	−1.38211
$717$	20.6290	0.770406
$718$	62.6865	2.33944
$719$	31.5401	1.17625	0.588124	−	0.808771i	$-0.299867\pi$
$719$	31.5401	1.17625	0.588124	+	0.808771i	$0.299867\pi$
$720$	19.6226	0.731291
$721$	0	0
$722$	46.3210	1.72389
$723$	−5.58416	−0.207677
$724$	−29.9516	−1.11314
$725$	−3.42239	−0.127104
$726$	21.4890	0.797533
$727$	27.3493	1.01433	0.507165	−	0.861849i	$-0.330693\pi$
$727$	27.3493	1.01433	0.507165	+	0.861849i	$0.330693\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−35.0197	−1.29614
$731$	−15.1690	−0.561046
$732$	24.6763	0.912062
$733$	28.4495	1.05081	0.525403	−	0.850854i	$-0.323915\pi$
$733$	28.4495	1.05081	0.525403	+	0.850854i	$0.323915\pi$
$734$	51.2102	1.89020
$735$	0	0
$736$	−104.289	−3.84415
$737$	−16.9657	−0.624941
$738$	−16.5860	−0.610539
$739$	−29.4346	−1.08277	−0.541384	−	0.840776i	$-0.682099\pi$
$739$	−29.4346	−1.08277	−0.541384	+	0.840776i	$0.682099\pi$
$740$	46.7275	1.71774
$741$	−1.10251	−0.0405018
$742$	0	0
$743$	−18.8812	−0.692683	−0.346341	−	0.938109i	$-0.612576\pi$
$743$	−18.8812	−0.692683	−0.346341	+	0.938109i	$0.612576\pi$
$744$	51.7910	1.89875
$745$	18.4291	0.675191
$746$	18.7445	0.686285
$747$	11.8387	0.433157
$748$	25.7287	0.940735
$749$	0	0
$750$	29.3050	1.07007
$751$	34.5423	1.26046	0.630232	−	0.776407i	$-0.282960\pi$
$751$	34.5423	1.26046	0.630232	+	0.776407i	$0.282960\pi$
$752$	−4.05814	−0.147985
$753$	1.36456	0.0497272
$754$	−2.12003	−0.0772068
$755$	28.2157	1.02687
$756$	0	0
$757$	30.4195	1.10561	0.552807	−	0.833309i	$-0.313557\pi$
$757$	30.4195	1.10561	0.552807	+	0.833309i	$0.313557\pi$
$758$	−52.3896	−1.90288
$759$	8.11799	0.294664
$760$	17.8197	0.646390
$761$	5.84550	0.211899	0.105950	−	0.994371i	$-0.466212\pi$
$761$	5.84550	0.211899	0.105950	+	0.994371i	$0.466212\pi$
$762$	−19.2870	−0.698696
$763$	0	0
$764$	37.7432	1.36550
$765$	3.35621	0.121344
$766$	25.9729	0.938440
$767$	0.760974	0.0274772
$768$	50.5098	1.82262
$769$	−5.53636	−0.199646	−0.0998232	−	0.995005i	$-0.531828\pi$
$769$	−5.53636	−0.199646	−0.0998232	+	0.995005i	$0.531828\pi$
$770$	0	0
$771$	26.0891	0.939577
$772$	127.097	4.57433
$773$	−38.2785	−1.37678	−0.688391	−	0.725340i	$-0.741682\pi$
$773$	−38.2785	−1.37678	−0.688391	+	0.725340i	$0.741682\pi$
$774$	15.8302	0.569006
$775$	18.1177	0.650808
$776$	20.0356	0.719235
$777$	0	0
$778$	19.4050	0.695704
$779$	−8.76775	−0.314137
$780$	5.35996	0.191918
$781$	15.1232	0.541150
$782$	−32.8739	−1.17557
$783$	1.01649	0.0363265
$784$	0	0
$785$	−28.1979	−1.00643
$786$	−0.371306	−0.0132440
$787$	−9.55900	−0.340742	−0.170371	−	0.985380i	$-0.554497\pi$
$787$	−9.55900	−0.340742	−0.170371	+	0.985380i	$0.554497\pi$
$788$	−61.6644	−2.19670
$789$	−6.21570	−0.221285
$790$	−36.8964	−1.31271
$791$	0	0
$792$	−17.1071	−0.607875
$793$	3.40698	0.120985
$794$	−90.8558	−3.22435
$795$	1.13579	0.0402823
$796$	122.512	4.34232
$797$	52.2182	1.84966	0.924832	−	0.380376i	$-0.124206\pi$
$797$	52.2182	1.84966	0.924832	+	0.380376i	$0.124206\pi$
$798$	0	0
$799$	−0.694097	−0.0245554
$800$	76.8806	2.71814
$801$	−10.2082	−0.360690
$802$	−78.5623	−2.77413
$803$	17.7719	0.627158
$804$	−52.6080	−1.85534
$805$	0	0
$806$	11.2232	0.395319
$807$	−7.71529	−0.271591
$808$	113.834	4.00466
$809$	6.36849	0.223904	0.111952	−	0.993714i	$-0.464290\pi$
$809$	6.36849	0.223904	0.111952	+	0.993714i	$0.464290\pi$
$810$	−3.50251	−0.123066
$811$	17.6790	0.620794	0.310397	−	0.950607i	$-0.399538\pi$
$811$	17.6790	0.620794	0.310397	+	0.950607i	$0.399538\pi$
$812$	0	0
$813$	24.2205	0.849450
$814$	−32.3183	−1.13276
$815$	2.32006	0.0812683
$816$	40.3256	1.41168
$817$	8.36824	0.292768
$818$	−53.5477	−1.87225
$819$	0	0
$820$	42.6252	1.48854
$821$	−49.9778	−1.74424	−0.872119	−	0.489295i	$-0.837254\pi$
$821$	−49.9778	−1.74424	−0.872119	+	0.489295i	$0.837254\pi$
$822$	−25.2009	−0.878982
$823$	40.7009	1.41874	0.709372	−	0.704835i	$-0.248979\pi$
$823$	40.7009	1.41874	0.709372	+	0.704835i	$0.248979\pi$
$824$	111.959	3.90028
$825$	−5.98447	−0.208353
$826$	0	0
$827$	−41.5556	−1.44503	−0.722515	−	0.691355i	$-0.757014\pi$
$827$	−41.5556	−1.44503	−0.722515	+	0.691355i	$0.757014\pi$
$828$	25.1725	0.874806
$829$	−37.1610	−1.29066	−0.645328	−	0.763906i	$-0.723279\pi$
$829$	−37.1610	−1.29066	−0.645328	+	0.763906i	$0.723279\pi$
$830$	−41.4653	−1.43928
$831$	−0.0949038	−0.00329218
$832$	24.2551	0.840895
$833$	0	0
$834$	45.0243	1.55907
$835$	10.1164	0.350091
$836$	−14.1937	−0.490899
$837$	−5.38120	−0.186001
$838$	5.13280	0.177309
$839$	27.1077	0.935860	0.467930	−	0.883766i	$-0.345000\pi$
$839$	27.1077	0.935860	0.467930	+	0.883766i	$0.345000\pi$
$840$	0	0
$841$	−27.9667	−0.964370
$842$	45.8501	1.58010
$843$	8.81635	0.303651
$844$	9.03019	0.310832
$845$	−15.8733	−0.546057
$846$	0.724353	0.0249038
$847$	0	0
$848$	13.6468	0.468631
$849$	16.9106	0.580372
$850$	24.2342	0.831225
$851$	30.2989	1.03863
$852$	46.8944	1.60658
$853$	46.7386	1.60030	0.800149	−	0.599801i	$-0.204754\pi$
$853$	46.7386	1.60030	0.800149	+	0.599801i	$0.204754\pi$
$854$	0	0
$855$	−1.85151	−0.0633203
$856$	−111.868	−3.82358
$857$	−7.93087	−0.270914	−0.135457	−	0.990783i	$-0.543250\pi$
$857$	−7.93087	−0.270914	−0.135457	+	0.990783i	$0.543250\pi$
$858$	−3.70713	−0.126559
$859$	−49.7233	−1.69654	−0.848268	−	0.529567i	$-0.822354\pi$
$859$	−49.7233	−1.69654	−0.848268	+	0.529567i	$0.822354\pi$
$860$	−40.6830	−1.38728
$861$	0	0
$862$	79.3842	2.70384
$863$	−24.4906	−0.833669	−0.416835	−	0.908982i	$-0.636861\pi$
$863$	−24.4906	−0.833669	−0.416835	+	0.908982i	$0.636861\pi$
$864$	−22.8345	−0.776846
$865$	−5.08256	−0.172812
$866$	65.6424	2.23062
$867$	−10.1028	−0.343109
$868$	0	0
$869$	18.7243	0.635178
$870$	−3.56028	−0.120705
$871$	−7.26342	−0.246112
$872$	68.9441	2.33474
$873$	−2.08174	−0.0704561
$874$	18.1354	0.613440
$875$	0	0
$876$	55.1078	1.86192
$877$	43.6009	1.47230	0.736149	−	0.676820i	$-0.236642\pi$
$877$	43.6009	1.47230	0.736149	+	0.676820i	$0.236642\pi$
$878$	54.3715	1.83495
$879$	−3.12553	−0.105422
$880$	34.8785	1.17575
$881$	−32.5222	−1.09570	−0.547850	−	0.836577i	$-0.684553\pi$
$881$	−32.5222	−1.09570	−0.547850	+	0.836577i	$0.684553\pi$
$882$	0	0
$883$	−57.7708	−1.94414	−0.972071	−	0.234688i	$-0.924593\pi$
$883$	−57.7708	−1.94414	−0.972071	+	0.234688i	$0.924593\pi$
$884$	11.0150	0.370476
$885$	1.27795	0.0429577
$886$	29.6857	0.997311
$887$	−1.40970	−0.0473330	−0.0236665	−	0.999720i	$-0.507534\pi$
$887$	−1.40970	−0.0473330	−0.0236665	+	0.999720i	$0.507534\pi$
$888$	−63.8493	−2.14264
$889$	0	0
$890$	35.7544	1.19849
$891$	1.77747	0.0595474
$892$	131.261	4.39494
$893$	0.382910	0.0128136
$894$	−39.5239	−1.32188
$895$	−8.57495	−0.286629
$896$	0	0
$897$	3.47550	0.116043
$898$	42.0134	1.40200
$899$	−5.46995	−0.182433
$900$	−18.5569	−0.618562
$901$	2.33411	0.0777606
$902$	−29.4811	−0.981612
$903$	0	0
$904$	−170.991	−5.68706
$905$	−6.94468	−0.230849
$906$	−60.5125	−2.01039
$907$	41.2103	1.36837	0.684183	−	0.729310i	$-0.260159\pi$
$907$	41.2103	1.36837	0.684183	+	0.729310i	$0.260159\pi$
$908$	−57.7934	−1.91794
$909$	−11.8276	−0.392296
$910$	0	0
$911$	−15.8301	−0.524475	−0.262237	−	0.965003i	$-0.584460\pi$
$911$	−15.8301	−0.524475	−0.262237	+	0.965003i	$0.584460\pi$
$912$	−22.2463	−0.736648
$913$	21.0430	0.696420
$914$	−106.952	−3.53766
$915$	5.72153	0.189148
$916$	−136.123	−4.49764
$917$	0	0
$918$	−7.19786	−0.237565
$919$	−1.74267	−0.0574855	−0.0287428	−	0.999587i	$-0.509150\pi$
$919$	−1.74267	−0.0574855	−0.0287428	+	0.999587i	$0.509150\pi$
$920$	−56.1740	−1.85200
$921$	10.5592	0.347939
$922$	−86.1985	−2.83880
$923$	6.47457	0.213113
$924$	0	0
$925$	−22.3360	−0.734402
$926$	−7.39925	−0.243155
$927$	−11.6328	−0.382070
$928$	−23.2111	−0.761943
$929$	−24.4805	−0.803178	−0.401589	−	0.915820i	$-0.631542\pi$
$929$	−24.4805	−0.803178	−0.401589	+	0.915820i	$0.631542\pi$
$930$	18.8477	0.618040
$931$	0	0
$932$	154.267	5.05319
$933$	5.78202	0.189295
$934$	28.2748	0.925180
$935$	5.96555	0.195094
$936$	−7.32395	−0.239391
$937$	22.3246	0.729312	0.364656	−	0.931142i	$-0.381187\pi$
$937$	22.3246	0.729312	0.364656	+	0.931142i	$0.381187\pi$
$938$	0	0
$939$	−25.0791	−0.818425
$940$	−1.86155	−0.0607172
$941$	22.5915	0.736461	0.368231	−	0.929734i	$-0.379964\pi$
$941$	22.5915	0.736461	0.368231	+	0.929734i	$0.379964\pi$
$942$	60.4744	1.97036
$943$	27.6389	0.900048
$944$	15.3548	0.499756
$945$	0	0
$946$	28.1377	0.914836
$947$	23.0082	0.747665	0.373832	−	0.927496i	$-0.378044\pi$
$947$	23.0082	0.747665	0.373832	+	0.927496i	$0.378044\pi$
$948$	58.0609	1.88573
$949$	7.60857	0.246985
$950$	−13.3692	−0.433754
$951$	−12.7544	−0.413591
$952$	0	0
$953$	40.7505	1.32004	0.660020	−	0.751248i	$-0.270548\pi$
$953$	40.7505	1.32004	0.660020	+	0.751248i	$0.270548\pi$
$954$	−2.43586	−0.0788639
$955$	8.75126	0.283184
$956$	113.700	3.67731
$957$	1.80678	0.0584050
$958$	32.0408	1.03519
$959$	0	0
$960$	40.7330	1.31465
$961$	−2.04270	−0.0658936
$962$	−13.8362	−0.446097
$963$	11.6234	0.374557
$964$	−30.7778	−0.991286
$965$	29.4692	0.948647
$966$	0	0
$967$	0.585190	0.0188185	0.00940923	−	0.999956i	$-0.497005\pi$
$967$	0.585190	0.0188185	0.00940923	+	0.999956i	$0.497005\pi$
$968$	75.4615	2.42543
$969$	−3.80496	−0.122233
$970$	7.29130	0.234110
$971$	53.4562	1.71549	0.857745	−	0.514075i	$-0.171865\pi$
$971$	53.4562	1.71549	0.857745	+	0.514075i	$0.171865\pi$
$972$	5.51163	0.176786
$973$	0	0
$974$	4.00877	0.128449
$975$	−2.56209	−0.0820525
$976$	68.7454	2.20049
$977$	27.9917	0.895535	0.447768	−	0.894150i	$-0.352219\pi$
$977$	27.9917	0.895535	0.447768	+	0.894150i	$0.352219\pi$
$978$	−4.97571	−0.159106
$979$	−18.1448	−0.579910
$980$	0	0
$981$	−7.16344	−0.228711
$982$	84.7996	2.70606
$983$	0.249108	0.00794530	0.00397265	−	0.999992i	$-0.498735\pi$
$983$	0.249108	0.00794530	0.00397265	+	0.999992i	$0.498735\pi$
$984$	−58.2438	−1.85675
$985$	−14.2977	−0.455563
$986$	−7.31658	−0.233007
$987$	0	0
$988$	−6.07664	−0.193324
$989$	−26.3796	−0.838821
$990$	−6.22559	−0.197862
$991$	−9.85564	−0.313075	−0.156537	−	0.987672i	$-0.550033\pi$
$991$	−9.85564	−0.313075	−0.156537	+	0.987672i	$0.550033\pi$
$992$	122.877	3.90135
$993$	22.9945	0.729709
$994$	0	0
$995$	28.4060	0.900531
$996$	65.2507	2.06755
$997$	−23.0643	−0.730455	−0.365227	−	0.930918i	$-0.619009\pi$
$997$	−23.0643	−0.730455	−0.365227	+	0.930918i	$0.619009\pi$
$998$	−61.0248	−1.93171
$999$	6.63407	0.209893

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.ba.1.1		12
7.6	odd	2		1239.2.a.i.1.1	✓	12
21.20	even	2		3717.2.a.q.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1239.2.a.i.1.1	✓	12	7.6	odd	2
3717.2.a.q.1.12		12	21.20	even	2
8673.2.a.ba.1.1		12	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:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74074 q^{2} +1.00000 q^{3} +5.51163 q^{4} +1.27795 q^{5} -2.74074 q^{6} -9.62444 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.74074 q^{2} +1.00000 q^{3} +5.51163 q^{4} +1.27795 q^{5} -2.74074 q^{6} -9.62444 q^{8} +1.00000 q^{9} -3.50251 q^{10} +1.77747 q^{11} +5.51163 q^{12} +0.760974 q^{13} +1.27795 q^{15} +15.3548 q^{16} +2.62625 q^{17} -2.74074 q^{18} -1.44882 q^{19} +7.04356 q^{20} -4.87157 q^{22} +4.56717 q^{23} -9.62444 q^{24} -3.36686 q^{25} -2.08563 q^{26} +1.00000 q^{27} +1.01649 q^{29} -3.50251 q^{30} -5.38120 q^{31} -22.8345 q^{32} +1.77747 q^{33} -7.19786 q^{34} +5.51163 q^{36} +6.63407 q^{37} +3.97082 q^{38} +0.760974 q^{39} -12.2995 q^{40} +6.05166 q^{41} -5.77591 q^{43} +9.79674 q^{44} +1.27795 q^{45} -12.5174 q^{46} -0.264292 q^{47} +15.3548 q^{48} +9.22766 q^{50} +2.62625 q^{51} +4.19420 q^{52} +0.888762 q^{53} -2.74074 q^{54} +2.27151 q^{55} -1.44882 q^{57} -2.78594 q^{58} +1.00000 q^{59} +7.04356 q^{60} +4.47713 q^{61} +14.7484 q^{62} +31.8738 q^{64} +0.972483 q^{65} -4.87157 q^{66} -9.54490 q^{67} +14.4749 q^{68} +4.56717 q^{69} +8.50827 q^{71} -9.62444 q^{72} +9.99846 q^{73} -18.1822 q^{74} -3.36686 q^{75} -7.98534 q^{76} -2.08563 q^{78} +10.5343 q^{79} +19.6226 q^{80} +1.00000 q^{81} -16.5860 q^{82} +11.8387 q^{83} +3.35621 q^{85} +15.8302 q^{86} +1.01649 q^{87} -17.1071 q^{88} -10.2082 q^{89} -3.50251 q^{90} +25.1725 q^{92} -5.38120 q^{93} +0.724353 q^{94} -1.85151 q^{95} -22.8345 q^{96} -2.08174 q^{97} +1.77747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * q^99

Introduction

L-functions

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