LMFDB - Embedded newform 578.2.a.h.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(1,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3,3,3,6,3,3,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	578.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.87939 q^{3} +1.00000 q^{4} +1.65270 q^{5} +2.87939 q^{6} -2.41147 q^{7} +1.00000 q^{8} +5.29086 q^{9} +1.65270 q^{10} +0.467911 q^{11} +2.87939 q^{12} -6.22668 q^{13} -2.41147 q^{14} +4.75877 q^{15} +1.00000 q^{16} +5.29086 q^{18} -5.90167 q^{19} +1.65270 q^{20} -6.94356 q^{21} +0.467911 q^{22} +1.92127 q^{23} +2.87939 q^{24} -2.26857 q^{25} -6.22668 q^{26} +6.59627 q^{27} -2.41147 q^{28} +4.90167 q^{29} +4.75877 q^{30} +0.837496 q^{31} +1.00000 q^{32} +1.34730 q^{33} -3.98545 q^{35} +5.29086 q^{36} +1.16250 q^{37} -5.90167 q^{38} -17.9290 q^{39} +1.65270 q^{40} +4.04189 q^{41} -6.94356 q^{42} -2.65270 q^{43} +0.467911 q^{44} +8.74422 q^{45} +1.92127 q^{46} -3.98545 q^{47} +2.87939 q^{48} -1.18479 q^{49} -2.26857 q^{50} -6.22668 q^{52} +1.49020 q^{53} +6.59627 q^{54} +0.773318 q^{55} -2.41147 q^{56} -16.9932 q^{57} +4.90167 q^{58} +13.8084 q^{59} +4.75877 q^{60} +4.41147 q^{61} +0.837496 q^{62} -12.7588 q^{63} +1.00000 q^{64} -10.2909 q^{65} +1.34730 q^{66} +2.10607 q^{67} +5.53209 q^{69} -3.98545 q^{70} -12.2686 q^{71} +5.29086 q^{72} +13.0496 q^{73} +1.16250 q^{74} -6.53209 q^{75} -5.90167 q^{76} -1.12836 q^{77} -17.9290 q^{78} -8.82295 q^{79} +1.65270 q^{80} +3.12061 q^{81} +4.04189 q^{82} +8.88713 q^{83} -6.94356 q^{84} -2.65270 q^{86} +14.1138 q^{87} +0.467911 q^{88} +14.3628 q^{89} +8.74422 q^{90} +15.0155 q^{91} +1.92127 q^{92} +2.41147 q^{93} -3.98545 q^{94} -9.75372 q^{95} +2.87939 q^{96} +13.0000 q^{97} -1.18479 q^{98} +2.47565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 6 q^{19} + 6 q^{20} - 6 q^{21} + 6 q^{22} - 3 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 6 * q^19 + 6 * q^20 - 6 * q^21 + 6 * q^22 - 3 * q^23 + 3 * q^24 + 3 * q^25 - 12 * q^26 + 6 * q^27 + 3 * q^28 + 3 * q^29 + 3 * q^30 + 3 * q^32 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 6 * q^38 - 21 * q^39 + 6 * q^40 + 9 * q^41 - 6 * q^42 - 9 * q^43 + 6 * q^44 - 3 * q^45 - 3 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^50 - 12 * q^52 + 3 * q^53 + 6 * q^54 + 9 * q^55 + 3 * q^56 - 9 * q^57 + 3 * q^58 + 3 * q^59 + 3 * q^60 + 3 * q^61 - 27 * q^63 + 3 * q^64 - 15 * q^65 + 3 * q^66 - 6 * q^67 + 12 * q^69 + 6 * q^70 - 27 * q^71 + 12 * q^73 + 6 * q^74 - 15 * q^75 - 6 * q^76 + 15 * q^77 - 21 * q^78 - 6 * q^79 + 6 * q^80 + 15 * q^81 + 9 * q^82 - 3 * q^83 - 6 * q^84 - 9 * q^86 + 6 * q^87 + 6 * q^88 - 6 * q^89 - 3 * q^90 - 3 * q^91 - 3 * q^92 - 3 * q^93 + 6 * q^94 - 33 * q^95 + 3 * q^96 + 39 * q^97 - 12 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.87939	1.66241	0.831207	−	0.555963i	$-0.187650\pi$
$3$	2.87939	1.66241	0.831207	+	0.555963i	$0.187650\pi$
$4$	1.00000	0.500000
$5$	1.65270	0.739112	0.369556	−	0.929209i	$-0.379510\pi$
$5$	1.65270	0.739112	0.369556	+	0.929209i	$0.379510\pi$
$6$	2.87939	1.17550
$7$	−2.41147	−0.911452	−0.455726	−	0.890120i	$-0.650620\pi$
$7$	−2.41147	−0.911452	−0.455726	+	0.890120i	$0.650620\pi$
$8$	1.00000	0.353553
$9$	5.29086	1.76362
$10$	1.65270	0.522631
$11$	0.467911	0.141081	0.0705403	−	0.997509i	$-0.477528\pi$
$11$	0.467911	0.141081	0.0705403	+	0.997509i	$0.477528\pi$
$12$	2.87939	0.831207
$13$	−6.22668	−1.72697	−0.863485	−	0.504374i	$-0.831723\pi$
$13$	−6.22668	−1.72697	−0.863485	+	0.504374i	$0.831723\pi$
$14$	−2.41147	−0.644494
$15$	4.75877	1.22871
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	5.29086	1.24707
$19$	−5.90167	−1.35394	−0.676968	−	0.736012i	$-0.736707\pi$
$19$	−5.90167	−1.35394	−0.676968	+	0.736012i	$0.736707\pi$
$20$	1.65270	0.369556
$21$	−6.94356	−1.51521
$22$	0.467911	0.0997590
$23$	1.92127	0.400613	0.200307	−	0.979733i	$-0.435806\pi$
$23$	1.92127	0.400613	0.200307	+	0.979733i	$0.435806\pi$
$24$	2.87939	0.587752
$25$	−2.26857	−0.453714
$26$	−6.22668	−1.22115
$27$	6.59627	1.26945
$28$	−2.41147	−0.455726
$29$	4.90167	0.910218	0.455109	−	0.890436i	$-0.349600\pi$
$29$	4.90167	0.910218	0.455109	+	0.890436i	$0.349600\pi$
$30$	4.75877	0.868829
$31$	0.837496	0.150419	0.0752094	−	0.997168i	$-0.476037\pi$
$31$	0.837496	0.150419	0.0752094	+	0.997168i	$0.476037\pi$
$32$	1.00000	0.176777
$33$	1.34730	0.234534
$34$	0	0
$35$	−3.98545	−0.673664
$36$	5.29086	0.881810
$37$	1.16250	0.191114	0.0955572	−	0.995424i	$-0.469537\pi$
$37$	1.16250	0.191114	0.0955572	+	0.995424i	$0.469537\pi$
$38$	−5.90167	−0.957378
$39$	−17.9290	−2.87094
$40$	1.65270	0.261315
$41$	4.04189	0.631237	0.315619	−	0.948886i	$-0.397788\pi$
$41$	4.04189	0.631237	0.315619	+	0.948886i	$0.397788\pi$
$42$	−6.94356	−1.07142
$43$	−2.65270	−0.404534	−0.202267	−	0.979330i	$-0.564831\pi$
$43$	−2.65270	−0.404534	−0.202267	+	0.979330i	$0.564831\pi$
$44$	0.467911	0.0705403
$45$	8.74422	1.30351
$46$	1.92127	0.283276
$47$	−3.98545	−0.581338	−0.290669	−	0.956824i	$-0.593878\pi$
$47$	−3.98545	−0.581338	−0.290669	+	0.956824i	$0.593878\pi$
$48$	2.87939	0.415603
$49$	−1.18479	−0.169256
$50$	−2.26857	−0.320824
$51$	0	0
$52$	−6.22668	−0.863485
$53$	1.49020	0.204695	0.102347	−	0.994749i	$-0.467365\pi$
$53$	1.49020	0.204695	0.102347	+	0.994749i	$0.467365\pi$
$54$	6.59627	0.897638
$55$	0.773318	0.104274
$56$	−2.41147	−0.322247
$57$	−16.9932	−2.25080
$58$	4.90167	0.643621
$59$	13.8084	1.79770	0.898850	−	0.438256i	$-0.144404\pi$
$59$	13.8084	1.79770	0.898850	+	0.438256i	$0.144404\pi$
$60$	4.75877	0.614355
$61$	4.41147	0.564831	0.282416	−	0.959292i	$-0.408864\pi$
$61$	4.41147	0.564831	0.282416	+	0.959292i	$0.408864\pi$
$62$	0.837496	0.106362
$63$	−12.7588	−1.60745
$64$	1.00000	0.125000
$65$	−10.2909	−1.27642
$66$	1.34730	0.165841
$67$	2.10607	0.257297	0.128649	−	0.991690i	$-0.458936\pi$
$67$	2.10607	0.257297	0.128649	+	0.991690i	$0.458936\pi$
$68$	0	0
$69$	5.53209	0.665985
$70$	−3.98545	−0.476353
$71$	−12.2686	−1.45601	−0.728006	−	0.685571i	$-0.759553\pi$
$71$	−12.2686	−1.45601	−0.728006	+	0.685571i	$0.759553\pi$
$72$	5.29086	0.623534
$73$	13.0496	1.52734	0.763672	−	0.645605i	$-0.223395\pi$
$73$	13.0496	1.52734	0.763672	+	0.645605i	$0.223395\pi$
$74$	1.16250	0.135138
$75$	−6.53209	−0.754261
$76$	−5.90167	−0.676968
$77$	−1.12836	−0.128588
$78$	−17.9290	−2.03006
$79$	−8.82295	−0.992659	−0.496330	−	0.868134i	$-0.665319\pi$
$79$	−8.82295	−0.992659	−0.496330	+	0.868134i	$0.665319\pi$
$80$	1.65270	0.184778
$81$	3.12061	0.346735
$82$	4.04189	0.446352
$83$	8.88713	0.975489	0.487744	−	0.872986i	$-0.337820\pi$
$83$	8.88713	0.975489	0.487744	+	0.872986i	$0.337820\pi$
$84$	−6.94356	−0.757605
$85$	0	0
$86$	−2.65270	−0.286048
$87$	14.1138	1.51316
$88$	0.467911	0.0498795
$89$	14.3628	1.52245	0.761226	−	0.648487i	$-0.224598\pi$
$89$	14.3628	1.52245	0.761226	+	0.648487i	$0.224598\pi$
$90$	8.74422	0.921722
$91$	15.0155	1.57405
$92$	1.92127	0.200307
$93$	2.41147	0.250058
$94$	−3.98545	−0.411068
$95$	−9.75372	−1.00071
$96$	2.87939	0.293876
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	−1.18479	−0.119682
$99$	2.47565	0.248812
$100$	−2.26857	−0.226857
$101$	−15.3550	−1.52788	−0.763942	−	0.645285i	$-0.776738\pi$
$101$	−15.3550	−1.52788	−0.763942	+	0.645285i	$0.776738\pi$
$102$	0	0
$103$	4.49525	0.442930	0.221465	−	0.975168i	$-0.428916\pi$
$103$	4.49525	0.442930	0.221465	+	0.975168i	$0.428916\pi$
$104$	−6.22668	−0.610576
$105$	−11.4757	−1.11991
$106$	1.49020	0.144741
$107$	18.9786	1.83473	0.917367	−	0.398041i	$-0.130310\pi$
$107$	18.9786	1.83473	0.917367	+	0.398041i	$0.130310\pi$
$108$	6.59627	0.634726
$109$	−12.0915	−1.15816	−0.579079	−	0.815272i	$-0.696588\pi$
$109$	−12.0915	−1.15816	−0.579079	+	0.815272i	$0.696588\pi$
$110$	0.773318	0.0737330
$111$	3.34730	0.317711
$112$	−2.41147	−0.227863
$113$	1.27126	0.119590	0.0597950	−	0.998211i	$-0.480955\pi$
$113$	1.27126	0.119590	0.0597950	+	0.998211i	$0.480955\pi$
$114$	−16.9932	−1.59156
$115$	3.17530	0.296098
$116$	4.90167	0.455109
$117$	−32.9445	−3.04572
$118$	13.8084	1.27117
$119$	0	0
$120$	4.75877	0.434414
$121$	−10.7811	−0.980096
$122$	4.41147	0.399396
$123$	11.6382	1.04938
$124$	0.837496	0.0752094
$125$	−12.0128	−1.07446
$126$	−12.7588	−1.13664
$127$	−4.24897	−0.377035	−0.188518	−	0.982070i	$-0.560368\pi$
$127$	−4.24897	−0.377035	−0.188518	+	0.982070i	$0.560368\pi$
$128$	1.00000	0.0883883
$129$	−7.63816	−0.672502
$130$	−10.2909	−0.902568
$131$	−18.4415	−1.61124	−0.805621	−	0.592432i	$-0.798168\pi$
$131$	−18.4415	−1.61124	−0.805621	+	0.592432i	$0.798168\pi$
$132$	1.34730	0.117267
$133$	14.2317	1.23405
$134$	2.10607	0.181936
$135$	10.9017	0.938267
$136$	0	0
$137$	−4.79561	−0.409716	−0.204858	−	0.978792i	$-0.565673\pi$
$137$	−4.79561	−0.409716	−0.204858	+	0.978792i	$0.565673\pi$
$138$	5.53209	0.470923
$139$	−4.51249	−0.382744	−0.191372	−	0.981518i	$-0.561294\pi$
$139$	−4.51249	−0.382744	−0.191372	+	0.981518i	$0.561294\pi$
$140$	−3.98545	−0.336832
$141$	−11.4757	−0.966424
$142$	−12.2686	−1.02956
$143$	−2.91353	−0.243642
$144$	5.29086	0.440905
$145$	8.10101	0.672753
$146$	13.0496	1.08000
$147$	−3.41147	−0.281374
$148$	1.16250	0.0955572
$149$	11.3696	0.931433	0.465716	−	0.884934i	$-0.345797\pi$
$149$	11.3696	0.931433	0.465716	+	0.884934i	$0.345797\pi$
$150$	−6.53209	−0.533343
$151$	−6.51485	−0.530171	−0.265086	−	0.964225i	$-0.585400\pi$
$151$	−6.51485	−0.530171	−0.265086	+	0.964225i	$0.585400\pi$
$152$	−5.90167	−0.478689
$153$	0	0
$154$	−1.12836	−0.0909255
$155$	1.38413	0.111176
$156$	−17.9290	−1.43547
$157$	−9.55169	−0.762308	−0.381154	−	0.924512i	$-0.624473\pi$
$157$	−9.55169	−0.762308	−0.381154	+	0.924512i	$0.624473\pi$
$158$	−8.82295	−0.701916
$159$	4.29086	0.340287
$160$	1.65270	0.130658
$161$	−4.63310	−0.365140
$162$	3.12061	0.245179
$163$	11.5963	0.908290	0.454145	−	0.890928i	$-0.349945\pi$
$163$	11.5963	0.908290	0.454145	+	0.890928i	$0.349945\pi$
$164$	4.04189	0.315619
$165$	2.22668	0.173347
$166$	8.88713	0.689775
$167$	−0.879385	−0.0680489	−0.0340244	−	0.999421i	$-0.510832\pi$
$167$	−0.879385	−0.0680489	−0.0340244	+	0.999421i	$0.510832\pi$
$168$	−6.94356	−0.535708
$169$	25.7716	1.98243
$170$	0	0
$171$	−31.2249	−2.38783
$172$	−2.65270	−0.202267
$173$	17.1138	1.30114	0.650569	−	0.759447i	$-0.274530\pi$
$173$	17.1138	1.30114	0.650569	+	0.759447i	$0.274530\pi$
$174$	14.1138	1.06996
$175$	5.47060	0.413538
$176$	0.467911	0.0352701
$177$	39.7597	2.98852
$178$	14.3628	1.07654
$179$	−14.2567	−1.06560	−0.532798	−	0.846242i	$-0.678860\pi$
$179$	−14.2567	−1.06560	−0.532798	+	0.846242i	$0.678860\pi$
$180$	8.74422	0.651756
$181$	−10.7939	−0.802301	−0.401150	−	0.916012i	$-0.631390\pi$
$181$	−10.7939	−0.802301	−0.401150	+	0.916012i	$0.631390\pi$
$182$	15.0155	1.11302
$183$	12.7023	0.938984
$184$	1.92127	0.141638
$185$	1.92127	0.141255
$186$	2.41147	0.176818
$187$	0	0
$188$	−3.98545	−0.290669
$189$	−15.9067	−1.15704
$190$	−9.75372	−0.707609
$191$	−9.09926	−0.658399	−0.329200	−	0.944260i	$-0.606779\pi$
$191$	−9.09926	−0.658399	−0.329200	+	0.944260i	$0.606779\pi$
$192$	2.87939	0.207802
$193$	7.98545	0.574805	0.287403	−	0.957810i	$-0.407208\pi$
$193$	7.98545	0.574805	0.287403	+	0.957810i	$0.407208\pi$
$194$	13.0000	0.933346
$195$	−29.6313	−2.12194
$196$	−1.18479	−0.0846280
$197$	−18.9786	−1.35217	−0.676086	−	0.736823i	$-0.736325\pi$
$197$	−18.9786	−1.35217	−0.676086	+	0.736823i	$0.736325\pi$
$198$	2.47565	0.175937
$199$	−1.36959	−0.0970873	−0.0485437	−	0.998821i	$-0.515458\pi$
$199$	−1.36959	−0.0970873	−0.0485437	+	0.998821i	$0.515458\pi$
$200$	−2.26857	−0.160412
$201$	6.06418	0.427734
$202$	−15.3550	−1.08038
$203$	−11.8203	−0.829620
$204$	0	0
$205$	6.68004	0.466555
$206$	4.49525	0.313199
$207$	10.1652	0.706530
$208$	−6.22668	−0.431743
$209$	−2.76146	−0.191014
$210$	−11.4757	−0.791895
$211$	−12.4338	−0.855976	−0.427988	−	0.903785i	$-0.640777\pi$
$211$	−12.4338	−0.855976	−0.427988	+	0.903785i	$0.640777\pi$
$212$	1.49020	0.102347
$213$	−35.3259	−2.42049
$214$	18.9786	1.29735
$215$	−4.38413	−0.298995
$216$	6.59627	0.448819
$217$	−2.01960	−0.137099
$218$	−12.0915	−0.818941
$219$	37.5749	2.53908
$220$	0.773318	0.0521371
$221$	0	0
$222$	3.34730	0.224656
$223$	−5.37733	−0.360092	−0.180046	−	0.983658i	$-0.557625\pi$
$223$	−5.37733	−0.360092	−0.180046	+	0.983658i	$0.557625\pi$
$224$	−2.41147	−0.161123
$225$	−12.0027	−0.800179
$226$	1.27126	0.0845629
$227$	−11.0574	−0.733903	−0.366952	−	0.930240i	$-0.619599\pi$
$227$	−11.0574	−0.733903	−0.366952	+	0.930240i	$0.619599\pi$
$228$	−16.9932	−1.12540
$229$	23.9659	1.58371	0.791854	−	0.610710i	$-0.209116\pi$
$229$	23.9659	1.58371	0.791854	+	0.610710i	$0.209116\pi$
$230$	3.17530	0.209373
$231$	−3.24897	−0.213767
$232$	4.90167	0.321811
$233$	−10.4534	−0.684823	−0.342411	−	0.939550i	$-0.611244\pi$
$233$	−10.4534	−0.684823	−0.342411	+	0.939550i	$0.611244\pi$
$234$	−32.9445	−2.15365
$235$	−6.58677	−0.429674
$236$	13.8084	0.898850
$237$	−25.4047	−1.65021
$238$	0	0
$239$	1.86484	0.120626	0.0603131	−	0.998180i	$-0.480790\pi$
$239$	1.86484	0.120626	0.0603131	+	0.998180i	$0.480790\pi$
$240$	4.75877	0.307177
$241$	18.3696	1.18329	0.591644	−	0.806199i	$-0.298479\pi$
$241$	18.3696	1.18329	0.591644	+	0.806199i	$0.298479\pi$
$242$	−10.7811	−0.693033
$243$	−10.8033	−0.693035
$244$	4.41147	0.282416
$245$	−1.95811	−0.125099
$246$	11.6382	0.742022
$247$	36.7478	2.33821
$248$	0.837496	0.0531811
$249$	25.5895	1.62167
$250$	−12.0128	−0.759756
$251$	−1.30810	−0.0825663	−0.0412831	−	0.999147i	$-0.513145\pi$
$251$	−1.30810	−0.0825663	−0.0412831	+	0.999147i	$0.513145\pi$
$252$	−12.7588	−0.803727
$253$	0.898986	0.0565187
$254$	−4.24897	−0.266604
$255$	0	0
$256$	1.00000	0.0625000
$257$	11.9736	0.746892	0.373446	−	0.927652i	$-0.378176\pi$
$257$	11.9736	0.746892	0.373446	+	0.927652i	$0.378176\pi$
$258$	−7.63816	−0.475531
$259$	−2.80335	−0.174192
$260$	−10.2909	−0.638212
$261$	25.9341	1.60528
$262$	−18.4415	−1.13932
$263$	−14.5253	−0.895667	−0.447834	−	0.894117i	$-0.647804\pi$
$263$	−14.5253	−0.895667	−0.447834	+	0.894117i	$0.647804\pi$
$264$	1.34730	0.0829204
$265$	2.46286	0.151292
$266$	14.2317	0.872604
$267$	41.3560	2.53094
$268$	2.10607	0.128649
$269$	27.9786	1.70589	0.852944	−	0.522002i	$-0.174815\pi$
$269$	27.9786	1.70589	0.852944	+	0.522002i	$0.174815\pi$
$270$	10.9017	0.663455
$271$	−13.3678	−0.812038	−0.406019	−	0.913865i	$-0.633083\pi$
$271$	−13.3678	−0.812038	−0.406019	+	0.913865i	$0.633083\pi$
$272$	0	0
$273$	43.2354	2.61672
$274$	−4.79561	−0.289713
$275$	−1.06149	−0.0640102
$276$	5.53209	0.332993
$277$	0.595333	0.0357701	0.0178850	−	0.999840i	$-0.494307\pi$
$277$	0.595333	0.0357701	0.0178850	+	0.999840i	$0.494307\pi$
$278$	−4.51249	−0.270641
$279$	4.43107	0.265281
$280$	−3.98545	−0.238176
$281$	17.8999	1.06782	0.533910	−	0.845541i	$-0.320722\pi$
$281$	17.8999	1.06782	0.533910	+	0.845541i	$0.320722\pi$
$282$	−11.4757	−0.683365
$283$	−3.95130	−0.234881	−0.117440	−	0.993080i	$-0.537469\pi$
$283$	−3.95130	−0.234881	−0.117440	+	0.993080i	$0.537469\pi$
$284$	−12.2686	−0.728006
$285$	−28.0847	−1.66359
$286$	−2.91353	−0.172281
$287$	−9.74691	−0.575342
$288$	5.29086	0.311767
$289$	0	0
$290$	8.10101	0.475708
$291$	37.4320	2.19430
$292$	13.0496	0.763672
$293$	28.0479	1.63857	0.819287	−	0.573383i	$-0.194369\pi$
$293$	28.0479	1.63857	0.819287	+	0.573383i	$0.194369\pi$
$294$	−3.41147	−0.198961
$295$	22.8212	1.32870
$296$	1.16250	0.0675692
$297$	3.08647	0.179095
$298$	11.3696	0.658622
$299$	−11.9632	−0.691848
$300$	−6.53209	−0.377130
$301$	6.39693	0.368713
$302$	−6.51485	−0.374888
$303$	−44.2131	−2.53997
$304$	−5.90167	−0.338484
$305$	7.29086	0.417473
$306$	0	0
$307$	21.5202	1.22822	0.614112	−	0.789219i	$-0.289514\pi$
$307$	21.5202	1.22822	0.614112	+	0.789219i	$0.289514\pi$
$308$	−1.12836	−0.0642940
$309$	12.9436	0.736334
$310$	1.38413	0.0786135
$311$	−4.72874	−0.268142	−0.134071	−	0.990972i	$-0.542805\pi$
$311$	−4.72874	−0.268142	−0.134071	+	0.990972i	$0.542805\pi$
$312$	−17.9290	−1.01503
$313$	17.6331	0.996682	0.498341	−	0.866981i	$-0.333943\pi$
$313$	17.6331	0.996682	0.498341	+	0.866981i	$0.333943\pi$
$314$	−9.55169	−0.539033
$315$	−21.0865	−1.18809
$316$	−8.82295	−0.496330
$317$	17.7939	0.999402	0.499701	−	0.866198i	$-0.333443\pi$
$317$	17.7939	0.999402	0.499701	+	0.866198i	$0.333443\pi$
$318$	4.29086	0.240619
$319$	2.29355	0.128414
$320$	1.65270	0.0923889
$321$	54.6468	3.05009
$322$	−4.63310	−0.258193
$323$	0	0
$324$	3.12061	0.173367
$325$	14.1257	0.783551
$326$	11.5963	0.642258
$327$	−34.8161	−1.92534
$328$	4.04189	0.223176
$329$	9.61081	0.529861
$330$	2.22668	0.122575
$331$	−34.9590	−1.92152	−0.960761	−	0.277376i	$-0.910535\pi$
$331$	−34.9590	−1.92152	−0.960761	+	0.277376i	$0.910535\pi$
$332$	8.88713	0.487744
$333$	6.15064	0.337053
$334$	−0.879385	−0.0481178
$335$	3.48070	0.190171
$336$	−6.94356	−0.378802
$337$	−15.6631	−0.853225	−0.426613	−	0.904434i	$-0.640293\pi$
$337$	−15.6631	−0.853225	−0.426613	+	0.904434i	$0.640293\pi$
$338$	25.7716	1.40179
$339$	3.66044	0.198808
$340$	0	0
$341$	0.391874	0.0212212
$342$	−31.2249	−1.68845
$343$	19.7374	1.06572
$344$	−2.65270	−0.143024
$345$	9.14290	0.492237
$346$	17.1138	0.920044
$347$	−10.4466	−0.560801	−0.280400	−	0.959883i	$-0.590467\pi$
$347$	−10.4466	−0.560801	−0.280400	+	0.959883i	$0.590467\pi$
$348$	14.1138	0.756580
$349$	−8.32770	−0.445771	−0.222886	−	0.974845i	$-0.571548\pi$
$349$	−8.32770	−0.445771	−0.222886	+	0.974845i	$0.571548\pi$
$350$	5.47060	0.292416
$351$	−41.0729	−2.19231
$352$	0.467911	0.0249397
$353$	7.20439	0.383451	0.191726	−	0.981449i	$-0.438592\pi$
$353$	7.20439	0.383451	0.191726	+	0.981449i	$0.438592\pi$
$354$	39.7597	2.11320
$355$	−20.2763	−1.07615
$356$	14.3628	0.761226
$357$	0	0
$358$	−14.2567	−0.753491
$359$	12.1557	0.641553	0.320777	−	0.947155i	$-0.396056\pi$
$359$	12.1557	0.641553	0.320777	+	0.947155i	$0.396056\pi$
$360$	8.74422	0.460861
$361$	15.8298	0.833145
$362$	−10.7939	−0.567312
$363$	−31.0428	−1.62933
$364$	15.0155	0.787025
$365$	21.5672	1.12888
$366$	12.7023	0.663962
$367$	36.1702	1.88807	0.944036	−	0.329843i	$-0.106996\pi$
$367$	36.1702	1.88807	0.944036	+	0.329843i	$0.106996\pi$
$368$	1.92127	0.100153
$369$	21.3851	1.11326
$370$	1.92127	0.0998823
$371$	−3.59358	−0.186569
$372$	2.41147	0.125029
$373$	28.0077	1.45019	0.725093	−	0.688651i	$-0.241797\pi$
$373$	28.0077	1.45019	0.725093	+	0.688651i	$0.241797\pi$
$374$	0	0
$375$	−34.5895	−1.78619
$376$	−3.98545	−0.205534
$377$	−30.5212	−1.57192
$378$	−15.9067	−0.818154
$379$	0.0709849	0.00364625	0.00182312	−	0.999998i	$-0.499420\pi$
$379$	0.0709849	0.00364625	0.00182312	+	0.999998i	$0.499420\pi$
$380$	−9.75372	−0.500355
$381$	−12.2344	−0.626788
$382$	−9.09926	−0.465559
$383$	−16.9341	−0.865290	−0.432645	−	0.901564i	$-0.642420\pi$
$383$	−16.9341	−0.865290	−0.432645	+	0.901564i	$0.642420\pi$
$384$	2.87939	0.146938
$385$	−1.86484	−0.0950409
$386$	7.98545	0.406449
$387$	−14.0351	−0.713443
$388$	13.0000	0.659975
$389$	−30.6364	−1.55333	−0.776664	−	0.629916i	$-0.783089\pi$
$389$	−30.6364	−1.55333	−0.776664	+	0.629916i	$0.783089\pi$
$390$	−29.6313	−1.50044
$391$	0	0
$392$	−1.18479	−0.0598411
$393$	−53.1002	−2.67855
$394$	−18.9786	−0.956130
$395$	−14.5817	−0.733686
$396$	2.47565	0.124406
$397$	0.681799	0.0342185	0.0171093	−	0.999854i	$-0.494554\pi$
$397$	0.681799	0.0342185	0.0171093	+	0.999854i	$0.494554\pi$
$398$	−1.36959	−0.0686511
$399$	40.9786	2.05150
$400$	−2.26857	−0.113429
$401$	16.3797	0.817963	0.408981	−	0.912543i	$-0.365884\pi$
$401$	16.3797	0.817963	0.408981	+	0.912543i	$0.365884\pi$
$402$	6.06418	0.302454
$403$	−5.21482	−0.259769
$404$	−15.3550	−0.763942
$405$	5.15745	0.256276
$406$	−11.8203	−0.586630
$407$	0.543948	0.0269625
$408$	0	0
$409$	−1.64084	−0.0811345	−0.0405673	−	0.999177i	$-0.512917\pi$
$409$	−1.64084	−0.0811345	−0.0405673	+	0.999177i	$0.512917\pi$
$410$	6.68004	0.329904
$411$	−13.8084	−0.681118
$412$	4.49525	0.221465
$413$	−33.2986	−1.63852
$414$	10.1652	0.499592
$415$	14.6878	0.720995
$416$	−6.22668	−0.305288
$417$	−12.9932	−0.636279
$418$	−2.76146	−0.135067
$419$	29.4861	1.44049	0.720245	−	0.693720i	$-0.244030\pi$
$419$	29.4861	1.44049	0.720245	+	0.693720i	$0.244030\pi$
$420$	−11.4757	−0.559954
$421$	20.2550	0.987166	0.493583	−	0.869699i	$-0.335687\pi$
$421$	20.2550	0.987166	0.493583	+	0.869699i	$0.335687\pi$
$422$	−12.4338	−0.605266
$423$	−21.0865	−1.02526
$424$	1.49020	0.0723705
$425$	0	0
$426$	−35.3259	−1.71155
$427$	−10.6382	−0.514816
$428$	18.9786	0.917367
$429$	−8.38919	−0.405034
$430$	−4.38413	−0.211422
$431$	3.18573	0.153451	0.0767255	−	0.997052i	$-0.475553\pi$
$431$	3.18573	0.153451	0.0767255	+	0.997052i	$0.475553\pi$
$432$	6.59627	0.317363
$433$	−5.41653	−0.260302	−0.130151	−	0.991494i	$-0.541546\pi$
$433$	−5.41653	−0.260302	−0.130151	+	0.991494i	$0.541546\pi$
$434$	−2.01960	−0.0969439
$435$	23.3259	1.11839
$436$	−12.0915	−0.579079
$437$	−11.3387	−0.542405
$438$	37.5749	1.79540
$439$	2.00505	0.0956959	0.0478480	−	0.998855i	$-0.484764\pi$
$439$	2.00505	0.0956959	0.0478480	+	0.998855i	$0.484764\pi$
$440$	0.773318	0.0368665
$441$	−6.26857	−0.298503
$442$	0	0
$443$	0.0760373	0.00361264	0.00180632	−	0.999998i	$-0.499425\pi$
$443$	0.0760373	0.00361264	0.00180632	+	0.999998i	$0.499425\pi$
$444$	3.34730	0.158856
$445$	23.7374	1.12526
$446$	−5.37733	−0.254624
$447$	32.7374	1.54843
$448$	−2.41147	−0.113931
$449$	12.1489	0.573342	0.286671	−	0.958029i	$-0.407451\pi$
$449$	12.1489	0.573342	0.286671	+	0.958029i	$0.407451\pi$
$450$	−12.0027	−0.565812
$451$	1.89124	0.0890552
$452$	1.27126	0.0597950
$453$	−18.7588	−0.881364
$454$	−11.0574	−0.518948
$455$	24.8161	1.16340
$456$	−16.9932	−0.795779
$457$	−9.51249	−0.444975	−0.222488	−	0.974935i	$-0.571418\pi$
$457$	−9.51249	−0.444975	−0.222488	+	0.974935i	$0.571418\pi$
$458$	23.9659	1.11985
$459$	0	0
$460$	3.17530	0.148049
$461$	10.6459	0.495829	0.247914	−	0.968782i	$-0.420255\pi$
$461$	10.6459	0.495829	0.247914	+	0.968782i	$0.420255\pi$
$462$	−3.24897	−0.151156
$463$	−20.2172	−0.939572	−0.469786	−	0.882780i	$-0.655669\pi$
$463$	−20.2172	−0.939572	−0.469786	+	0.882780i	$0.655669\pi$
$464$	4.90167	0.227555
$465$	3.98545	0.184821
$466$	−10.4534	−0.484243
$467$	−18.5936	−0.860408	−0.430204	−	0.902732i	$-0.641558\pi$
$467$	−18.5936	−0.860408	−0.430204	+	0.902732i	$0.641558\pi$
$468$	−32.9445	−1.52286
$469$	−5.07873	−0.234514
$470$	−6.58677	−0.303825
$471$	−27.5030	−1.26727
$472$	13.8084	0.635583
$473$	−1.24123	−0.0570718
$474$	−25.4047	−1.16688
$475$	13.3884	0.614300
$476$	0	0
$477$	7.88444	0.361004
$478$	1.86484	0.0852957
$479$	−25.1284	−1.14814	−0.574072	−	0.818805i	$-0.694637\pi$
$479$	−25.1284	−1.14814	−0.574072	+	0.818805i	$0.694637\pi$
$480$	4.75877	0.217207
$481$	−7.23854	−0.330049
$482$	18.3696	0.836712
$483$	−13.3405	−0.607013
$484$	−10.7811	−0.490048
$485$	21.4851	0.975590
$486$	−10.8033	−0.490050
$487$	26.6955	1.20969	0.604845	−	0.796343i	$-0.293235\pi$
$487$	26.6955	1.20969	0.604845	+	0.796343i	$0.293235\pi$
$488$	4.41147	0.199698
$489$	33.3901	1.50995
$490$	−1.95811	−0.0884584
$491$	−4.79797	−0.216529	−0.108265	−	0.994122i	$-0.534529\pi$
$491$	−4.79797	−0.216529	−0.108265	+	0.994122i	$0.534529\pi$
$492$	11.6382	0.524689
$493$	0	0
$494$	36.7478	1.65336
$495$	4.09152	0.183900
$496$	0.837496	0.0376047
$497$	29.5853	1.32708
$498$	25.5895	1.14669
$499$	−7.02734	−0.314587	−0.157293	−	0.987552i	$-0.550277\pi$
$499$	−7.02734	−0.314587	−0.157293	+	0.987552i	$0.550277\pi$
$500$	−12.0128	−0.537228
$501$	−2.53209	−0.113125
$502$	−1.30810	−0.0583832
$503$	−33.0692	−1.47448	−0.737242	−	0.675629i	$-0.763872\pi$
$503$	−33.0692	−1.47448	−0.737242	+	0.675629i	$0.763872\pi$
$504$	−12.7588	−0.568321
$505$	−25.3773	−1.12928
$506$	0.898986	0.0399648
$507$	74.2063	3.29562
$508$	−4.24897	−0.188518
$509$	0.182104	0.00807163	0.00403581	−	0.999992i	$-0.498715\pi$
$509$	0.182104	0.00807163	0.00403581	+	0.999992i	$0.498715\pi$
$510$	0	0
$511$	−31.4688	−1.39210
$512$	1.00000	0.0441942
$513$	−38.9290	−1.71876
$514$	11.9736	0.528133
$515$	7.42932	0.327375
$516$	−7.63816	−0.336251
$517$	−1.86484	−0.0820155
$518$	−2.80335	−0.123172
$519$	49.2772	2.16303
$520$	−10.2909	−0.451284
$521$	−32.8976	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$521$	−32.8976	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$522$	25.9341	1.13510
$523$	−27.3756	−1.19705	−0.598525	−	0.801104i	$-0.704246\pi$
$523$	−27.3756	−1.19705	−0.598525	+	0.801104i	$0.704246\pi$
$524$	−18.4415	−0.805621
$525$	15.7520	0.687472
$526$	−14.5253	−0.633332
$527$	0	0
$528$	1.34730	0.0586335
$529$	−19.3087	−0.839509
$530$	2.46286	0.106980
$531$	73.0583	3.17046
$532$	14.2317	0.617024
$533$	−25.1676	−1.09013
$534$	41.3560	1.78965
$535$	31.3661	1.35607
$536$	2.10607	0.0909682
$537$	−41.0506	−1.77146
$538$	27.9786	1.20625
$539$	−0.554378	−0.0238787
$540$	10.9017	0.469133
$541$	−12.3865	−0.532537	−0.266269	−	0.963899i	$-0.585791\pi$
$541$	−12.3865	−0.532537	−0.266269	+	0.963899i	$0.585791\pi$
$542$	−13.3678	−0.574197
$543$	−31.0797	−1.33376
$544$	0	0
$545$	−19.9837	−0.856008
$546$	43.2354	1.85030
$547$	−0.626296	−0.0267785	−0.0133892	−	0.999910i	$-0.504262\pi$
$547$	−0.626296	−0.0267785	−0.0133892	+	0.999910i	$0.504262\pi$
$548$	−4.79561	−0.204858
$549$	23.3405	0.996148
$550$	−1.06149	−0.0452621
$551$	−28.9281	−1.23238
$552$	5.53209	0.235461
$553$	21.2763	0.904761
$554$	0.595333	0.0252933
$555$	5.53209	0.234824
$556$	−4.51249	−0.191372
$557$	−31.1516	−1.31993	−0.659967	−	0.751294i	$-0.729430\pi$
$557$	−31.1516	−1.31993	−0.659967	+	0.751294i	$0.729430\pi$
$558$	4.43107	0.187582
$559$	16.5175	0.698618
$560$	−3.98545	−0.168416
$561$	0	0
$562$	17.8999	0.755063
$563$	−10.1607	−0.428225	−0.214112	−	0.976809i	$-0.568686\pi$
$563$	−10.1607	−0.428225	−0.214112	+	0.976809i	$0.568686\pi$
$564$	−11.4757	−0.483212
$565$	2.10101	0.0883903
$566$	−3.95130	−0.166086
$567$	−7.52528	−0.316032
$568$	−12.2686	−0.514778
$569$	−13.3577	−0.559985	−0.279992	−	0.960002i	$-0.590332\pi$
$569$	−13.3577	−0.559985	−0.279992	+	0.960002i	$0.590332\pi$
$570$	−28.0847	−1.17634
$571$	−5.14971	−0.215509	−0.107754	−	0.994178i	$-0.534366\pi$
$571$	−5.14971	−0.215509	−0.107754	+	0.994178i	$0.534366\pi$
$572$	−2.91353	−0.121821
$573$	−26.2003	−1.09453
$574$	−9.74691	−0.406828
$575$	−4.35855	−0.181764
$576$	5.29086	0.220452
$577$	−6.24628	−0.260036	−0.130018	−	0.991512i	$-0.541504\pi$
$577$	−6.24628	−0.260036	−0.130018	+	0.991512i	$0.541504\pi$
$578$	0	0
$579$	22.9932	0.955564
$580$	8.10101	0.336376
$581$	−21.4311	−0.889111
$582$	37.4320	1.55161
$583$	0.697281	0.0288784
$584$	13.0496	0.539998
$585$	−54.4475	−2.25113
$586$	28.0479	1.15865
$587$	−30.5340	−1.26027	−0.630136	−	0.776485i	$-0.717001\pi$
$587$	−30.5340	−1.26027	−0.630136	+	0.776485i	$0.717001\pi$
$588$	−3.41147	−0.140687
$589$	−4.94263	−0.203657
$590$	22.8212	0.939534
$591$	−54.6468	−2.24787
$592$	1.16250	0.0477786
$593$	−23.7306	−0.974499	−0.487250	−	0.873263i	$-0.662000\pi$
$593$	−23.7306	−0.974499	−0.487250	+	0.873263i	$0.662000\pi$
$594$	3.08647	0.126639
$595$	0	0
$596$	11.3696	0.465716
$597$	−3.94356	−0.161399
$598$	−11.9632	−0.489210
$599$	8.16344	0.333549	0.166775	−	0.985995i	$-0.446665\pi$
$599$	8.16344	0.333549	0.166775	+	0.985995i	$0.446665\pi$
$600$	−6.53209	−0.266671
$601$	−31.0770	−1.26766	−0.633828	−	0.773474i	$-0.718517\pi$
$601$	−31.0770	−1.26766	−0.633828	+	0.773474i	$0.718517\pi$
$602$	6.39693	0.260719
$603$	11.1429	0.453774
$604$	−6.51485	−0.265086
$605$	−17.8179	−0.724400
$606$	−44.2131	−1.79603
$607$	−5.73885	−0.232933	−0.116466	−	0.993195i	$-0.537157\pi$
$607$	−5.73885	−0.232933	−0.116466	+	0.993195i	$0.537157\pi$
$608$	−5.90167	−0.239344
$609$	−34.0351	−1.37917
$610$	7.29086	0.295198
$611$	24.8161	1.00395
$612$	0	0
$613$	−33.1762	−1.33998	−0.669988	−	0.742372i	$-0.733701\pi$
$613$	−33.1762	−1.33998	−0.669988	+	0.742372i	$0.733701\pi$
$614$	21.5202	0.868486
$615$	19.2344	0.775607
$616$	−1.12836	−0.0454627
$617$	14.9736	0.602814	0.301407	−	0.953496i	$-0.402544\pi$
$617$	14.9736	0.602814	0.301407	+	0.953496i	$0.402544\pi$
$618$	12.9436	0.520666
$619$	−20.1985	−0.811847	−0.405924	−	0.913907i	$-0.633050\pi$
$619$	−20.1985	−0.811847	−0.405924	+	0.913907i	$0.633050\pi$
$620$	1.38413	0.0555881
$621$	12.6732	0.508560
$622$	−4.72874	−0.189605
$623$	−34.6355	−1.38764
$624$	−17.9290	−0.717735
$625$	−8.51073	−0.340429
$626$	17.6331	0.704761
$627$	−7.95130	−0.317544
$628$	−9.55169	−0.381154
$629$	0	0
$630$	−21.0865	−0.840105
$631$	4.05737	0.161521	0.0807607	−	0.996734i	$-0.474265\pi$
$631$	4.05737	0.161521	0.0807607	+	0.996734i	$0.474265\pi$
$632$	−8.82295	−0.350958
$633$	−35.8016	−1.42299
$634$	17.7939	0.706684
$635$	−7.02229	−0.278671
$636$	4.29086	0.170144
$637$	7.37733	0.292300
$638$	2.29355	0.0908024
$639$	−64.9113	−2.56785
$640$	1.65270	0.0653288
$641$	−10.7956	−0.426401	−0.213200	−	0.977008i	$-0.568389\pi$
$641$	−10.7956	−0.426401	−0.213200	+	0.977008i	$0.568389\pi$
$642$	54.6468	2.15674
$643$	16.5348	0.652068	0.326034	−	0.945358i	$-0.394288\pi$
$643$	16.5348	0.652068	0.326034	+	0.945358i	$0.394288\pi$
$644$	−4.63310	−0.182570
$645$	−12.6236	−0.497054
$646$	0	0
$647$	49.4397	1.94368	0.971839	−	0.235648i	$-0.0757211\pi$
$647$	49.4397	1.94368	0.971839	+	0.235648i	$0.0757211\pi$
$648$	3.12061	0.122589
$649$	6.46110	0.253621
$650$	14.1257	0.554054
$651$	−5.81521	−0.227916
$652$	11.5963	0.454145
$653$	31.0479	1.21500	0.607499	−	0.794321i	$-0.292173\pi$
$653$	31.0479	1.21500	0.607499	+	0.794321i	$0.292173\pi$
$654$	−34.8161	−1.36142
$655$	−30.4783	−1.19089
$656$	4.04189	0.157809
$657$	69.0438	2.69365
$658$	9.61081	0.374669
$659$	45.3783	1.76769	0.883843	−	0.467784i	$-0.154947\pi$
$659$	45.3783	1.76769	0.883843	+	0.467784i	$0.154947\pi$
$660$	2.22668	0.0866735
$661$	24.3141	0.945708	0.472854	−	0.881141i	$-0.343224\pi$
$661$	24.3141	0.945708	0.472854	+	0.881141i	$0.343224\pi$
$662$	−34.9590	−1.35872
$663$	0	0
$664$	8.88713	0.344887
$665$	23.5208	0.912099
$666$	6.15064	0.238333
$667$	9.41746	0.364646
$668$	−0.879385	−0.0340244
$669$	−15.4834	−0.598623
$670$	3.48070	0.134471
$671$	2.06418	0.0796867
$672$	−6.94356	−0.267854
$673$	16.8658	0.650128	0.325064	−	0.945692i	$-0.394614\pi$
$673$	16.8658	0.650128	0.325064	+	0.945692i	$0.394614\pi$
$674$	−15.6631	−0.603321
$675$	−14.9641	−0.575968
$676$	25.7716	0.991214
$677$	20.7939	0.799173	0.399586	−	0.916696i	$-0.369154\pi$
$677$	20.7939	0.799173	0.399586	+	0.916696i	$0.369154\pi$
$678$	3.66044	0.140579
$679$	−31.3492	−1.20307
$680$	0	0
$681$	−31.8384	−1.22005
$682$	0.391874	0.0150056
$683$	−4.19522	−0.160526	−0.0802628	−	0.996774i	$-0.525576\pi$
$683$	−4.19522	−0.160526	−0.0802628	+	0.996774i	$0.525576\pi$
$684$	−31.2249	−1.19391
$685$	−7.92572	−0.302826
$686$	19.7374	0.753578
$687$	69.0069	2.63278
$688$	−2.65270	−0.101133
$689$	−9.27900	−0.353502
$690$	9.14290	0.348064
$691$	39.9195	1.51861	0.759305	−	0.650735i	$-0.225539\pi$
$691$	39.9195	1.51861	0.759305	+	0.650735i	$0.225539\pi$
$692$	17.1138	0.650569
$693$	−5.96997	−0.226780
$694$	−10.4466	−0.396546
$695$	−7.45781	−0.282891
$696$	14.1138	0.534982
$697$	0	0
$698$	−8.32770	−0.315208
$699$	−30.0993	−1.13846
$700$	5.47060	0.206769
$701$	−33.6100	−1.26943	−0.634716	−	0.772746i	$-0.718883\pi$
$701$	−33.6100	−1.26943	−0.634716	+	0.772746i	$0.718883\pi$
$702$	−41.0729	−1.55019
$703$	−6.86072	−0.258757
$704$	0.467911	0.0176351
$705$	−18.9659	−0.714295
$706$	7.20439	0.271141
$707$	37.0283	1.39259
$708$	39.7597	1.49426
$709$	43.6468	1.63919	0.819596	−	0.572943i	$-0.194198\pi$
$709$	43.6468	1.63919	0.819596	+	0.572943i	$0.194198\pi$
$710$	−20.2763	−0.760956
$711$	−46.6810	−1.75067
$712$	14.3628	0.538268
$713$	1.60906	0.0602598
$714$	0	0
$715$	−4.81521	−0.180079
$716$	−14.2567	−0.532798
$717$	5.36959	0.200531
$718$	12.1557	0.453647
$719$	−43.5458	−1.62398	−0.811992	−	0.583668i	$-0.801617\pi$
$719$	−43.5458	−1.62398	−0.811992	+	0.583668i	$0.801617\pi$
$720$	8.74422	0.325878
$721$	−10.8402	−0.403710
$722$	15.8298	0.589122
$723$	52.8931	1.96712
$724$	−10.7939	−0.401150
$725$	−11.1198	−0.412979
$726$	−31.0428	−1.15211
$727$	18.3473	0.680464	0.340232	−	0.940342i	$-0.389494\pi$
$727$	18.3473	0.680464	0.340232	+	0.940342i	$0.389494\pi$
$728$	15.0155	0.556511
$729$	−40.4688	−1.49885
$730$	21.5672	0.798237
$731$	0	0
$732$	12.7023	0.469492
$733$	34.9495	1.29089	0.645446	−	0.763806i	$-0.276672\pi$
$733$	34.9495	1.29089	0.645446	+	0.763806i	$0.276672\pi$
$734$	36.1702	1.33507
$735$	−5.63816	−0.207967
$736$	1.92127	0.0708191
$737$	0.985452	0.0362996
$738$	21.3851	0.787195
$739$	−6.58408	−0.242199	−0.121100	−	0.992640i	$-0.538642\pi$
$739$	−6.58408	−0.242199	−0.121100	+	0.992640i	$0.538642\pi$
$740$	1.92127	0.0706274
$741$	105.811	3.88707
$742$	−3.59358	−0.131924
$743$	−8.32232	−0.305316	−0.152658	−	0.988279i	$-0.548783\pi$
$743$	−8.32232	−0.305316	−0.152658	+	0.988279i	$0.548783\pi$
$744$	2.41147	0.0884089
$745$	18.7906	0.688433
$746$	28.0077	1.02544
$747$	47.0205	1.72039
$748$	0	0
$749$	−45.7665	−1.67227
$750$	−34.5895	−1.26303
$751$	−51.4662	−1.87803	−0.939013	−	0.343881i	$-0.888258\pi$
$751$	−51.4662	−1.87803	−0.939013	+	0.343881i	$0.888258\pi$
$752$	−3.98545	−0.145334
$753$	−3.76651	−0.137259
$754$	−30.5212	−1.11152
$755$	−10.7671	−0.391856
$756$	−15.9067	−0.578522
$757$	−22.5371	−0.819126	−0.409563	−	0.912282i	$-0.634319\pi$
$757$	−22.5371	−0.819126	−0.409563	+	0.912282i	$0.634319\pi$
$758$	0.0709849	0.00257829
$759$	2.58853	0.0939575
$760$	−9.75372	−0.353805
$761$	−8.39599	−0.304354	−0.152177	−	0.988353i	$-0.548628\pi$
$761$	−8.39599	−0.304354	−0.152177	+	0.988353i	$0.548628\pi$
$762$	−12.2344	−0.443206
$763$	29.1584	1.05560
$764$	−9.09926	−0.329200
$765$	0	0
$766$	−16.9341	−0.611853
$767$	−85.9805	−3.10458
$768$	2.87939	0.103901
$769$	−32.0063	−1.15418	−0.577089	−	0.816682i	$-0.695811\pi$
$769$	−32.0063	−1.15418	−0.577089	+	0.816682i	$0.695811\pi$
$770$	−1.86484	−0.0672041
$771$	34.4766	1.24164
$772$	7.98545	0.287403
$773$	−22.4165	−0.806266	−0.403133	−	0.915141i	$-0.632079\pi$
$773$	−22.4165	−0.806266	−0.403133	+	0.915141i	$0.632079\pi$
$774$	−14.0351	−0.504481
$775$	−1.89992	−0.0682471
$776$	13.0000	0.466673
$777$	−8.07192	−0.289578
$778$	−30.6364	−1.09837
$779$	−23.8539	−0.854655
$780$	−29.6313	−1.06097
$781$	−5.74060	−0.205415
$782$	0	0
$783$	32.3327	1.15548
$784$	−1.18479	−0.0423140
$785$	−15.7861	−0.563430
$786$	−53.1002	−1.89402
$787$	−33.4133	−1.19106	−0.595528	−	0.803334i	$-0.703057\pi$
$787$	−33.4133	−1.19106	−0.595528	+	0.803334i	$0.703057\pi$
$788$	−18.9786	−0.676086
$789$	−41.8239	−1.48897
$790$	−14.5817	−0.518794
$791$	−3.06561	−0.109000
$792$	2.47565	0.0879685
$793$	−27.4688	−0.975447
$794$	0.681799	0.0241962
$795$	7.09152	0.251510
$796$	−1.36959	−0.0485437
$797$	24.2422	0.858701	0.429351	−	0.903138i	$-0.358742\pi$
$797$	24.2422	0.858701	0.429351	+	0.903138i	$0.358742\pi$
$798$	40.9786	1.45063
$799$	0	0
$800$	−2.26857	−0.0802061
$801$	75.9914	2.68503
$802$	16.3797	0.578387
$803$	6.10607	0.215478
$804$	6.06418	0.213867
$805$	−7.65715	−0.269879
$806$	−5.21482	−0.183684
$807$	80.5613	2.83589
$808$	−15.3550	−0.540188
$809$	45.0969	1.58552	0.792761	−	0.609532i	$-0.208643\pi$
$809$	45.0969	1.58552	0.792761	+	0.609532i	$0.208643\pi$
$810$	5.15745	0.181214
$811$	38.1539	1.33977	0.669883	−	0.742467i	$-0.266344\pi$
$811$	38.1539	1.33977	0.669883	+	0.742467i	$0.266344\pi$
$812$	−11.8203	−0.414810
$813$	−38.4911	−1.34994
$814$	0.543948	0.0190654
$815$	19.1652	0.671327
$816$	0	0
$817$	15.6554	0.547713
$818$	−1.64084	−0.0573708
$819$	79.4448	2.77603
$820$	6.68004	0.233277
$821$	30.4888	1.06407	0.532033	−	0.846724i	$-0.321428\pi$
$821$	30.4888	1.06407	0.532033	+	0.846724i	$0.321428\pi$
$822$	−13.8084	−0.481623
$823$	42.6269	1.48588	0.742940	−	0.669358i	$-0.233431\pi$
$823$	42.6269	1.48588	0.742940	+	0.669358i	$0.233431\pi$
$824$	4.49525	0.156600
$825$	−3.05644	−0.106411
$826$	−33.2986	−1.15861
$827$	−13.2585	−0.461042	−0.230521	−	0.973067i	$-0.574043\pi$
$827$	−13.2585	−0.461042	−0.230521	+	0.973067i	$0.574043\pi$
$828$	10.1652	0.353265
$829$	−6.68779	−0.232276	−0.116138	−	0.993233i	$-0.537052\pi$
$829$	−6.68779	−0.232276	−0.116138	+	0.993233i	$0.537052\pi$
$830$	14.6878	0.509820
$831$	1.71419	0.0594647
$832$	−6.22668	−0.215871
$833$	0	0
$834$	−12.9932	−0.449917
$835$	−1.45336	−0.0502957
$836$	−2.76146	−0.0955071
$837$	5.52435	0.190949
$838$	29.4861	1.01858
$839$	−9.91178	−0.342193	−0.171096	−	0.985254i	$-0.554731\pi$
$839$	−9.91178	−0.342193	−0.171096	+	0.985254i	$0.554731\pi$
$840$	−11.4757	−0.395948
$841$	−4.97359	−0.171503
$842$	20.2550	0.698032
$843$	51.5408	1.77516
$844$	−12.4338	−0.427988
$845$	42.5928	1.46524
$846$	−21.0865	−0.724968
$847$	25.9982	0.893310
$848$	1.49020	0.0511737
$849$	−11.3773	−0.390469
$850$	0	0
$851$	2.23349	0.0765630
$852$	−35.3259	−1.21025
$853$	5.57304	0.190817	0.0954087	−	0.995438i	$-0.469584\pi$
$853$	5.57304	0.190817	0.0954087	+	0.995438i	$0.469584\pi$
$854$	−10.6382	−0.364030
$855$	−51.6056	−1.76487
$856$	18.9786	0.648677
$857$	13.9453	0.476363	0.238181	−	0.971221i	$-0.423449\pi$
$857$	13.9453	0.476363	0.238181	+	0.971221i	$0.423449\pi$
$858$	−8.38919	−0.286402
$859$	−36.0401	−1.22967	−0.614837	−	0.788654i	$-0.710778\pi$
$859$	−36.0401	−1.22967	−0.614837	+	0.788654i	$0.710778\pi$
$860$	−4.38413	−0.149498
$861$	−28.0651	−0.956456
$862$	3.18573	0.108506
$863$	−23.4088	−0.796844	−0.398422	−	0.917202i	$-0.630442\pi$
$863$	−23.4088	−0.796844	−0.398422	+	0.917202i	$0.630442\pi$
$864$	6.59627	0.224410
$865$	28.2841	0.961687
$866$	−5.41653	−0.184061
$867$	0	0
$868$	−2.01960	−0.0685497
$869$	−4.12836	−0.140045
$870$	23.3259	0.790823
$871$	−13.1138	−0.444344
$872$	−12.0915	−0.409470
$873$	68.7812	2.32789
$874$	−11.3387	−0.383538
$875$	28.9685	0.979315
$876$	37.5749	1.26954
$877$	−46.3988	−1.56678	−0.783388	−	0.621533i	$-0.786510\pi$
$877$	−46.3988	−1.56678	−0.783388	+	0.621533i	$0.786510\pi$
$878$	2.00505	0.0676672
$879$	80.7606	2.72399
$880$	0.773318	0.0260686
$881$	33.8138	1.13922	0.569608	−	0.821917i	$-0.307095\pi$
$881$	33.8138	1.13922	0.569608	+	0.821917i	$0.307095\pi$
$882$	−6.26857	−0.211074
$883$	−37.5776	−1.26459	−0.632293	−	0.774729i	$-0.717886\pi$
$883$	−37.5776	−1.26459	−0.632293	+	0.774729i	$0.717886\pi$
$884$	0	0
$885$	65.7110	2.20885
$886$	0.0760373	0.00255452
$887$	13.4097	0.450254	0.225127	−	0.974329i	$-0.427720\pi$
$887$	13.4097	0.450254	0.225127	+	0.974329i	$0.427720\pi$
$888$	3.34730	0.112328
$889$	10.2463	0.343649
$890$	23.7374	0.795680
$891$	1.46017	0.0489175
$892$	−5.37733	−0.180046
$893$	23.5208	0.787095
$894$	32.7374	1.09490
$895$	−23.5621	−0.787595
$896$	−2.41147	−0.0805617
$897$	−34.4466	−1.15014
$898$	12.1489	0.405414
$899$	4.10513	0.136914
$900$	−12.0027	−0.400090
$901$	0	0
$902$	1.89124	0.0629716
$903$	18.4192	0.612953
$904$	1.27126	0.0422814
$905$	−17.8390	−0.592990
$906$	−18.7588	−0.623218
$907$	28.0933	0.932822	0.466411	−	0.884568i	$-0.345547\pi$
$907$	28.0933	0.932822	0.466411	+	0.884568i	$0.345547\pi$
$908$	−11.0574	−0.366952
$909$	−81.2413	−2.69461
$910$	24.8161	0.822647
$911$	−22.4593	−0.744111	−0.372056	−	0.928210i	$-0.621347\pi$
$911$	−22.4593	−0.744111	−0.372056	+	0.928210i	$0.621347\pi$
$912$	−16.9932	−0.562701
$913$	4.15839	0.137622
$914$	−9.51249	−0.314645
$915$	20.9932	0.694014
$916$	23.9659	0.791854
$917$	44.4712	1.46857
$918$	0	0
$919$	51.0215	1.68304	0.841521	−	0.540224i	$-0.181660\pi$
$919$	51.0215	1.68304	0.841521	+	0.540224i	$0.181660\pi$
$920$	3.17530	0.104686
$921$	61.9650	2.04182
$922$	10.6459	0.350604
$923$	76.3925	2.51449
$924$	−3.24897	−0.106883
$925$	−2.63722	−0.0867113
$926$	−20.2172	−0.664378
$927$	23.7837	0.781161
$928$	4.90167	0.160905
$929$	−37.3637	−1.22586	−0.612932	−	0.790136i	$-0.710010\pi$
$929$	−37.3637	−1.22586	−0.612932	+	0.790136i	$0.710010\pi$
$930$	3.98545	0.130688
$931$	6.99226	0.229162
$932$	−10.4534	−0.342411
$933$	−13.6159	−0.445763
$934$	−18.5936	−0.608400
$935$	0	0
$936$	−32.9445	−1.07682
$937$	18.1480	0.592868	0.296434	−	0.955053i	$-0.404203\pi$
$937$	18.1480	0.592868	0.296434	+	0.955053i	$0.404203\pi$
$938$	−5.07873	−0.165826
$939$	50.7725	1.65690
$940$	−6.58677	−0.214837
$941$	27.1385	0.884689	0.442344	−	0.896845i	$-0.354147\pi$
$941$	27.1385	0.884689	0.442344	+	0.896845i	$0.354147\pi$
$942$	−27.5030	−0.896096
$943$	7.76558	0.252882
$944$	13.8084	0.449425
$945$	−26.2891	−0.855185
$946$	−1.24123	−0.0403559
$947$	−53.0934	−1.72530	−0.862652	−	0.505799i	$-0.831198\pi$
$947$	−53.0934	−1.72530	−0.862652	+	0.505799i	$0.831198\pi$
$948$	−25.4047	−0.825105
$949$	−81.2559	−2.63768
$950$	13.3884	0.434376
$951$	51.2354	1.66142
$952$	0	0
$953$	5.62454	0.182197	0.0910984	−	0.995842i	$-0.470962\pi$
$953$	5.62454	0.182197	0.0910984	+	0.995842i	$0.470962\pi$
$954$	7.88444	0.255268
$955$	−15.0384	−0.486631
$956$	1.86484	0.0603131
$957$	6.60401	0.213477
$958$	−25.1284	−0.811860
$959$	11.5645	0.373437
$960$	4.75877	0.153589
$961$	−30.2986	−0.977374
$962$	−7.23854	−0.233380
$963$	100.413	3.23577
$964$	18.3696	0.591644
$965$	13.1976	0.424845
$966$	−13.3405	−0.429223
$967$	6.73111	0.216458	0.108229	−	0.994126i	$-0.465482\pi$
$967$	6.73111	0.216458	0.108229	+	0.994126i	$0.465482\pi$
$968$	−10.7811	−0.346516
$969$	0	0
$970$	21.4851	0.689847
$971$	−21.1465	−0.678624	−0.339312	−	0.940674i	$-0.610194\pi$
$971$	−21.1465	−0.678624	−0.339312	+	0.940674i	$0.610194\pi$
$972$	−10.8033	−0.346518
$973$	10.8817	0.348853
$974$	26.6955	0.855380
$975$	40.6732	1.30259
$976$	4.41147	0.141208
$977$	42.3242	1.35407	0.677035	−	0.735951i	$-0.263264\pi$
$977$	42.3242	1.35407	0.677035	+	0.735951i	$0.263264\pi$
$978$	33.3901	1.06770
$979$	6.72050	0.214788
$980$	−1.95811	−0.0625496
$981$	−63.9745	−2.04255
$982$	−4.79797	−0.153109
$983$	−7.81883	−0.249382	−0.124691	−	0.992196i	$-0.539794\pi$
$983$	−7.81883	−0.249382	−0.124691	+	0.992196i	$0.539794\pi$
$984$	11.6382	0.371011
$985$	−31.3661	−0.999406
$986$	0	0
$987$	27.6732	0.880849
$988$	36.7478	1.16910
$989$	−5.09657	−0.162062
$990$	4.09152	0.130037
$991$	−5.30304	−0.168457	−0.0842284	−	0.996446i	$-0.526843\pi$
$991$	−5.30304	−0.168457	−0.0842284	+	0.996446i	$0.526843\pi$
$992$	0.837496	0.0265905
$993$	−100.661	−3.19437
$994$	29.5853	0.938390
$995$	−2.26352	−0.0717584
$996$	25.5895	0.810833
$997$	32.8949	1.04179	0.520895	−	0.853620i	$-0.325598\pi$
$997$	32.8949	1.04179	0.520895	+	0.853620i	$0.325598\pi$
$998$	−7.02734	−0.222447
$999$	7.66819	0.242611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.a.h.1.3	yes	3
3.2	odd	2		5202.2.a.bg.1.2		3
4.3	odd	2		4624.2.a.bc.1.1		3
17.2	even	8		578.2.c.h.327.6		12
17.3	odd	16		578.2.d.i.179.6		24
17.4	even	4		578.2.b.e.577.1		6
17.5	odd	16		578.2.d.i.399.1		24
17.6	odd	16		578.2.d.i.155.6		24
17.7	odd	16		578.2.d.i.423.1		24
17.8	even	8		578.2.c.h.251.1		12
17.9	even	8		578.2.c.h.251.6		12
17.10	odd	16		578.2.d.i.423.6		24
17.11	odd	16		578.2.d.i.155.1		24
17.12	odd	16		578.2.d.i.399.6		24
17.13	even	4		578.2.b.e.577.6		6
17.14	odd	16		578.2.d.i.179.1		24
17.15	even	8		578.2.c.h.327.1		12
17.16	even	2		578.2.a.g.1.1	✓	3
51.50	odd	2		5202.2.a.bi.1.2		3
68.67	odd	2		4624.2.a.bh.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.2.a.g.1.1	✓	3	17.16	even	2
578.2.a.h.1.3	yes	3	1.1	even	1	trivial
578.2.b.e.577.1		6	17.4	even	4
578.2.b.e.577.6		6	17.13	even	4
578.2.c.h.251.1		12	17.8	even	8
578.2.c.h.251.6		12	17.9	even	8
578.2.c.h.327.1		12	17.15	even	8
578.2.c.h.327.6		12	17.2	even	8
578.2.d.i.155.1		24	17.11	odd	16
578.2.d.i.155.6		24	17.6	odd	16
578.2.d.i.179.1		24	17.14	odd	16
578.2.d.i.179.6		24	17.3	odd	16
578.2.d.i.399.1		24	17.5	odd	16
578.2.d.i.399.6		24	17.12	odd	16
578.2.d.i.423.1		24	17.7	odd	16
578.2.d.i.423.6		24	17.10	odd	16
4624.2.a.bc.1.1		3	4.3	odd	2
4624.2.a.bh.1.3		3	68.67	odd	2
5202.2.a.bg.1.2		3	3.2	odd	2
5202.2.a.bi.1.2		3	51.50	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.87939 q^{3} +1.00000 q^{4} +1.65270 q^{5} +2.87939 q^{6} -2.41147 q^{7} +1.00000 q^{8} +5.29086 q^{9} +1.65270 q^{10} +0.467911 q^{11} +2.87939 q^{12} -6.22668 q^{13} -2.41147 q^{14} +4.75877 q^{15} +1.00000 q^{16} +5.29086 q^{18} -5.90167 q^{19} +1.65270 q^{20} -6.94356 q^{21} +0.467911 q^{22} +1.92127 q^{23} +2.87939 q^{24} -2.26857 q^{25} -6.22668 q^{26} +6.59627 q^{27} -2.41147 q^{28} +4.90167 q^{29} +4.75877 q^{30} +0.837496 q^{31} +1.00000 q^{32} +1.34730 q^{33} -3.98545 q^{35} +5.29086 q^{36} +1.16250 q^{37} -5.90167 q^{38} -17.9290 q^{39} +1.65270 q^{40} +4.04189 q^{41} -6.94356 q^{42} -2.65270 q^{43} +0.467911 q^{44} +8.74422 q^{45} +1.92127 q^{46} -3.98545 q^{47} +2.87939 q^{48} -1.18479 q^{49} -2.26857 q^{50} -6.22668 q^{52} +1.49020 q^{53} +6.59627 q^{54} +0.773318 q^{55} -2.41147 q^{56} -16.9932 q^{57} +4.90167 q^{58} +13.8084 q^{59} +4.75877 q^{60} +4.41147 q^{61} +0.837496 q^{62} -12.7588 q^{63} +1.00000 q^{64} -10.2909 q^{65} +1.34730 q^{66} +2.10607 q^{67} +5.53209 q^{69} -3.98545 q^{70} -12.2686 q^{71} +5.29086 q^{72} +13.0496 q^{73} +1.16250 q^{74} -6.53209 q^{75} -5.90167 q^{76} -1.12836 q^{77} -17.9290 q^{78} -8.82295 q^{79} +1.65270 q^{80} +3.12061 q^{81} +4.04189 q^{82} +8.88713 q^{83} -6.94356 q^{84} -2.65270 q^{86} +14.1138 q^{87} +0.467911 q^{88} +14.3628 q^{89} +8.74422 q^{90} +15.0155 q^{91} +1.92127 q^{92} +2.41147 q^{93} -3.98545 q^{94} -9.75372 q^{95} +2.87939 q^{96} +13.0000 q^{97} -1.18479 q^{98} +2.47565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 6 q^{19} + 6 q^{20} - 6 q^{21} + 6 q^{22} - 3 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 6 * q^19 + 6 * q^20 - 6 * q^21 + 6 * q^22 - 3 * q^23 + 3 * q^24 + 3 * q^25 - 12 * q^26 + 6 * q^27 + 3 * q^28 + 3 * q^29 + 3 * q^30 + 3 * q^32 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 6 * q^38 - 21 * q^39 + 6 * q^40 + 9 * q^41 - 6 * q^42 - 9 * q^43 + 6 * q^44 - 3 * q^45 - 3 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^50 - 12 * q^52 + 3 * q^53 + 6 * q^54 + 9 * q^55 + 3 * q^56 - 9 * q^57 + 3 * q^58 + 3 * q^59 + 3 * q^60 + 3 * q^61 - 27 * q^63 + 3 * q^64 - 15 * q^65 + 3 * q^66 - 6 * q^67 + 12 * q^69 + 6 * q^70 - 27 * q^71 + 12 * q^73 + 6 * q^74 - 15 * q^75 - 6 * q^76 + 15 * q^77 - 21 * q^78 - 6 * q^79 + 6 * q^80 + 15 * q^81 + 9 * q^82 - 3 * q^83 - 6 * q^84 - 9 * q^86 + 6 * q^87 + 6 * q^88 - 6 * q^89 - 3 * q^90 - 3 * q^91 - 3 * q^92 - 3 * q^93 + 6 * q^94 - 33 * q^95 + 3 * q^96 + 39 * q^97 - 12 * q^99

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