LMFDB - Embedded newform 8470.2.a.cj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 8 $ x^3 - x^2 - 7*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.51820$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} -1.00000 q^{10} -2.85952 q^{12} +2.17687 q^{13} -1.00000 q^{14} -2.85952 q^{15} +1.00000 q^{16} +3.85952 q^{17} -5.17687 q^{18} +1.68265 q^{19} +1.00000 q^{20} -2.85952 q^{21} +6.85952 q^{23} +2.85952 q^{24} +1.00000 q^{25} -2.17687 q^{26} -6.22482 q^{27} +1.00000 q^{28} -2.00000 q^{29} +2.85952 q^{30} +0.682649 q^{31} -1.00000 q^{32} -3.85952 q^{34} +1.00000 q^{35} +5.17687 q^{36} -3.71905 q^{37} -1.68265 q^{38} -6.22482 q^{39} -1.00000 q^{40} +9.03640 q^{41} +2.85952 q^{42} +5.85952 q^{43} +5.17687 q^{45} -6.85952 q^{46} +4.68265 q^{47} -2.85952 q^{48} +1.00000 q^{49} -1.00000 q^{50} -11.0364 q^{51} +2.17687 q^{52} +13.5786 q^{53} +6.22482 q^{54} -1.00000 q^{56} -4.81158 q^{57} +2.00000 q^{58} -7.75544 q^{59} -2.85952 q^{60} +8.89592 q^{61} -0.682649 q^{62} +5.17687 q^{63} +1.00000 q^{64} +2.17687 q^{65} +9.85952 q^{67} +3.85952 q^{68} -19.6150 q^{69} -1.00000 q^{70} -0.542173 q^{71} -5.17687 q^{72} -5.85952 q^{73} +3.71905 q^{74} -2.85952 q^{75} +1.68265 q^{76} +6.22482 q^{78} +0.317351 q^{79} +1.00000 q^{80} +2.26940 q^{81} -9.03640 q^{82} -4.85952 q^{83} -2.85952 q^{84} +3.85952 q^{85} -5.85952 q^{86} +5.71905 q^{87} -0.682649 q^{89} -5.17687 q^{90} +2.17687 q^{91} +6.85952 q^{92} -1.95205 q^{93} -4.68265 q^{94} +1.68265 q^{95} +2.85952 q^{96} +16.6150 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 13 * q^9	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9} - 3 q^{10} + 2 q^{12} + 4 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + q^{17} - 13 q^{18} - 3 q^{19} + 3 q^{20} + 2 q^{21} + 10 q^{23} - 2 q^{24} + 3 q^{25} - 4 q^{26} + 8 q^{27} + 3 q^{28} - 6 q^{29} - 2 q^{30} - 6 q^{31} - 3 q^{32} - q^{34} + 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 8 q^{39} - 3 q^{40} + 14 q^{41} - 2 q^{42} + 7 q^{43} + 13 q^{45} - 10 q^{46} + 6 q^{47} + 2 q^{48} + 3 q^{49} - 3 q^{50} - 20 q^{51} + 4 q^{52} + 9 q^{53} - 8 q^{54} - 3 q^{56} - 28 q^{57} + 6 q^{58} + 11 q^{59} + 2 q^{60} + 3 q^{61} + 6 q^{62} + 13 q^{63} + 3 q^{64} + 4 q^{65} + 19 q^{67} + q^{68} - 14 q^{69} - 3 q^{70} + 17 q^{71} - 13 q^{72} - 7 q^{73} - 10 q^{74} + 2 q^{75} - 3 q^{76} - 8 q^{78} + 9 q^{79} + 3 q^{80} + 39 q^{81} - 14 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 7 q^{86} - 4 q^{87} + 6 q^{89} - 13 q^{90} + 4 q^{91} + 10 q^{92} - 30 q^{93} - 6 q^{94} - 3 q^{95} - 2 q^{96} + 5 q^{97} - 3 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 13 * q^9 - 3 * q^10 + 2 * q^12 + 4 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + q^17 - 13 * q^18 - 3 * q^19 + 3 * q^20 + 2 * q^21 + 10 * q^23 - 2 * q^24 + 3 * q^25 - 4 * q^26 + 8 * q^27 + 3 * q^28 - 6 * q^29 - 2 * q^30 - 6 * q^31 - 3 * q^32 - q^34 + 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 8 * q^39 - 3 * q^40 + 14 * q^41 - 2 * q^42 + 7 * q^43 + 13 * q^45 - 10 * q^46 + 6 * q^47 + 2 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 4 * q^52 + 9 * q^53 - 8 * q^54 - 3 * q^56 - 28 * q^57 + 6 * q^58 + 11 * q^59 + 2 * q^60 + 3 * q^61 + 6 * q^62 + 13 * q^63 + 3 * q^64 + 4 * q^65 + 19 * q^67 + q^68 - 14 * q^69 - 3 * q^70 + 17 * q^71 - 13 * q^72 - 7 * q^73 - 10 * q^74 + 2 * q^75 - 3 * q^76 - 8 * q^78 + 9 * q^79 + 3 * q^80 + 39 * q^81 - 14 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 7 * q^86 - 4 * q^87 + 6 * q^89 - 13 * q^90 + 4 * q^91 + 10 * q^92 - 30 * q^93 - 6 * q^94 - 3 * q^95 - 2 * q^96 + 5 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.85952	−1.65095	−0.825473	−	0.564441i	$-0.809092\pi$
$3$	−2.85952	−1.65095	−0.825473	+	0.564441i	$0.809092\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.85952	1.16740
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	5.17687	1.72562
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−2.85952	−0.825473
$13$	2.17687	0.603756	0.301878	−	0.953347i	$-0.402386\pi$
$13$	2.17687	0.603756	0.301878	+	0.953347i	$0.402386\pi$
$14$	−1.00000	−0.267261
$15$	−2.85952	−0.738326
$16$	1.00000	0.250000
$17$	3.85952	0.936072	0.468036	−	0.883709i	$-0.344962\pi$
$17$	3.85952	0.936072	0.468036	+	0.883709i	$0.344962\pi$
$18$	−5.17687	−1.22020
$19$	1.68265	0.386026	0.193013	−	0.981196i	$-0.438174\pi$
$19$	1.68265	0.386026	0.193013	+	0.981196i	$0.438174\pi$
$20$	1.00000	0.223607
$21$	−2.85952	−0.623999
$22$	0	0
$23$	6.85952	1.43031	0.715155	−	0.698966i	$-0.246356\pi$
$23$	6.85952	1.43031	0.715155	+	0.698966i	$0.246356\pi$
$24$	2.85952	0.583698
$25$	1.00000	0.200000
$26$	−2.17687	−0.426920
$27$	−6.22482	−1.19797
$28$	1.00000	0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	2.85952	0.522075
$31$	0.682649	0.122607	0.0613037	−	0.998119i	$-0.480474\pi$
$31$	0.682649	0.122607	0.0613037	+	0.998119i	$0.480474\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.85952	−0.661903
$35$	1.00000	0.169031
$36$	5.17687	0.862812
$37$	−3.71905	−0.611408	−0.305704	−	0.952127i	$-0.598892\pi$
$37$	−3.71905	−0.611408	−0.305704	+	0.952127i	$0.598892\pi$
$38$	−1.68265	−0.272962
$39$	−6.22482	−0.996769
$40$	−1.00000	−0.158114
$41$	9.03640	1.41125	0.705624	−	0.708586i	$-0.250667\pi$
$41$	9.03640	1.41125	0.705624	+	0.708586i	$0.250667\pi$
$42$	2.85952	0.441234
$43$	5.85952	0.893569	0.446784	−	0.894642i	$-0.352569\pi$
$43$	5.85952	0.893569	0.446784	+	0.894642i	$0.352569\pi$
$44$	0	0
$45$	5.17687	0.771723
$46$	−6.85952	−1.01138
$47$	4.68265	0.683035	0.341517	−	0.939875i	$-0.389059\pi$
$47$	4.68265	0.683035	0.341517	+	0.939875i	$0.389059\pi$
$48$	−2.85952	−0.412737
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−11.0364	−1.54540
$52$	2.17687	0.301878
$53$	13.5786	1.86516	0.932580	−	0.360963i	$-0.117552\pi$
$53$	13.5786	1.86516	0.932580	+	0.360963i	$0.117552\pi$
$54$	6.22482	0.847091
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−4.81158	−0.637309
$58$	2.00000	0.262613
$59$	−7.75544	−1.00967	−0.504836	−	0.863215i	$-0.668447\pi$
$59$	−7.75544	−1.00967	−0.504836	+	0.863215i	$0.668447\pi$
$60$	−2.85952	−0.369163
$61$	8.89592	1.13901	0.569503	−	0.821989i	$-0.307136\pi$
$61$	8.89592	1.13901	0.569503	+	0.821989i	$0.307136\pi$
$62$	−0.682649	−0.0866966
$63$	5.17687	0.652225
$64$	1.00000	0.125000
$65$	2.17687	0.270008
$66$	0	0
$67$	9.85952	1.20453	0.602266	−	0.798295i	$-0.294265\pi$
$67$	9.85952	1.20453	0.602266	+	0.798295i	$0.294265\pi$
$68$	3.85952	0.468036
$69$	−19.6150	−2.36136
$70$	−1.00000	−0.119523
$71$	−0.542173	−0.0643441	−0.0321720	−	0.999482i	$-0.510242\pi$
$71$	−0.542173	−0.0643441	−0.0321720	+	0.999482i	$0.510242\pi$
$72$	−5.17687	−0.610100
$73$	−5.85952	−0.685805	−0.342903	−	0.939371i	$-0.611410\pi$
$73$	−5.85952	−0.685805	−0.342903	+	0.939371i	$0.611410\pi$
$74$	3.71905	0.432330
$75$	−2.85952	−0.330189
$76$	1.68265	0.193013
$77$	0	0
$78$	6.22482	0.704822
$79$	0.317351	0.0357047	0.0178524	−	0.999841i	$-0.494317\pi$
$79$	0.317351	0.0357047	0.0178524	+	0.999841i	$0.494317\pi$
$80$	1.00000	0.111803
$81$	2.26940	0.252156
$82$	−9.03640	−0.997903
$83$	−4.85952	−0.533402	−0.266701	−	0.963779i	$-0.585934\pi$
$83$	−4.85952	−0.533402	−0.266701	+	0.963779i	$0.585934\pi$
$84$	−2.85952	−0.312000
$85$	3.85952	0.418624
$86$	−5.85952	−0.631849
$87$	5.71905	0.613146
$88$	0	0
$89$	−0.682649	−0.0723607	−0.0361803	−	0.999345i	$-0.511519\pi$
$89$	−0.682649	−0.0723607	−0.0361803	+	0.999345i	$0.511519\pi$
$90$	−5.17687	−0.545690
$91$	2.17687	0.228198
$92$	6.85952	0.715155
$93$	−1.95205	−0.202418
$94$	−4.68265	−0.482978
$95$	1.68265	0.172636
$96$	2.85952	0.291849
$97$	16.6150	1.68699	0.843497	−	0.537134i	$-0.180493\pi$
$97$	16.6150	1.68699	0.843497	+	0.537134i	$0.180493\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−3.54217	−0.352459	−0.176230	−	0.984349i	$-0.556390\pi$
$101$	−3.54217	−0.352459	−0.176230	+	0.984349i	$0.556390\pi$
$102$	11.0364	1.09277
$103$	9.50578	0.936632	0.468316	−	0.883561i	$-0.344861\pi$
$103$	9.50578	0.936632	0.468316	+	0.883561i	$0.344861\pi$
$104$	−2.17687	−0.213460
$105$	−2.85952	−0.279061
$106$	−13.5786	−1.31887
$107$	7.17687	0.693815	0.346907	−	0.937899i	$-0.387232\pi$
$107$	7.17687	0.693815	0.346907	+	0.937899i	$0.387232\pi$
$108$	−6.22482	−0.598984
$109$	13.3901	1.28254	0.641272	−	0.767314i	$-0.278407\pi$
$109$	13.3901	1.28254	0.641272	+	0.767314i	$0.278407\pi$
$110$	0	0
$111$	10.6347	1.00940
$112$	1.00000	0.0944911
$113$	−10.2497	−0.964208	−0.482104	−	0.876114i	$-0.660127\pi$
$113$	−10.2497	−0.964208	−0.482104	+	0.876114i	$0.660127\pi$
$114$	4.81158	0.450645
$115$	6.85952	0.639654
$116$	−2.00000	−0.185695
$117$	11.2694	1.04186
$118$	7.75544	0.713947
$119$	3.85952	0.353802
$120$	2.85952	0.261038
$121$	0	0
$122$	−8.89592	−0.805399
$123$	−25.8398	−2.32990
$124$	0.682649	0.0613037
$125$	1.00000	0.0894427
$126$	−5.17687	−0.461193
$127$	−20.9323	−1.85744	−0.928721	−	0.370778i	$-0.879091\pi$
$127$	−20.9323	−1.85744	−0.928721	+	0.370778i	$0.879091\pi$
$128$	−1.00000	−0.0883883
$129$	−16.7554	−1.47523
$130$	−2.17687	−0.190924
$131$	−6.57857	−0.574772	−0.287386	−	0.957815i	$-0.592786\pi$
$131$	−6.57857	−0.574772	−0.287386	+	0.957815i	$0.592786\pi$
$132$	0	0
$133$	1.68265	0.145904
$134$	−9.85952	−0.851733
$135$	−6.22482	−0.535747
$136$	−3.85952	−0.330951
$137$	4.53062	0.387077	0.193539	−	0.981093i	$-0.438004\pi$
$137$	4.53062	0.387077	0.193539	+	0.981093i	$0.438004\pi$
$138$	19.6150	1.66974
$139$	13.4017	1.13672	0.568359	−	0.822781i	$-0.307579\pi$
$139$	13.4017	1.13672	0.568359	+	0.822781i	$0.307579\pi$
$140$	1.00000	0.0845154
$141$	−13.3901	−1.12765
$142$	0.542173	0.0454981
$143$	0	0
$144$	5.17687	0.431406
$145$	−2.00000	−0.166091
$146$	5.85952	0.484938
$147$	−2.85952	−0.235850
$148$	−3.71905	−0.305704
$149$	13.3653	1.09493	0.547464	−	0.836829i	$-0.315593\pi$
$149$	13.3653	1.09493	0.547464	+	0.836829i	$0.315593\pi$
$150$	2.85952	0.233479
$151$	−16.8595	−1.37201	−0.686004	−	0.727598i	$-0.740637\pi$
$151$	−16.8595	−1.37201	−0.686004	+	0.727598i	$0.740637\pi$
$152$	−1.68265	−0.136481
$153$	19.9803	1.61531
$154$	0	0
$155$	0.682649	0.0548317
$156$	−6.22482	−0.498385
$157$	14.2497	1.13725	0.568624	−	0.822598i	$-0.307476\pi$
$157$	14.2497	1.13725	0.568624	+	0.822598i	$0.307476\pi$
$158$	−0.317351	−0.0252471
$159$	−38.8282	−3.07928
$160$	−1.00000	−0.0790569
$161$	6.85952	0.540606
$162$	−2.26940	−0.178301
$163$	14.2612	1.11702	0.558512	−	0.829496i	$-0.311372\pi$
$163$	14.2612	1.11702	0.558512	+	0.829496i	$0.311372\pi$
$164$	9.03640	0.705624
$165$	0	0
$166$	4.85952	0.377172
$167$	−9.57857	−0.741212	−0.370606	−	0.928790i	$-0.620850\pi$
$167$	−9.57857	−0.741212	−0.370606	+	0.928790i	$0.620850\pi$
$168$	2.85952	0.220617
$169$	−8.26122	−0.635478
$170$	−3.85952	−0.296012
$171$	8.71086	0.666136
$172$	5.85952	0.446784
$173$	−0.353748	−0.0268950	−0.0134475	−	0.999910i	$-0.504281\pi$
$173$	−0.353748	−0.0268950	−0.0134475	+	0.999910i	$0.504281\pi$
$174$	−5.71905	−0.433560
$175$	1.00000	0.0755929
$176$	0	0
$177$	22.1769	1.66692
$178$	0.682649	0.0511667
$179$	2.40170	0.179511	0.0897556	−	0.995964i	$-0.471391\pi$
$179$	2.40170	0.179511	0.0897556	+	0.995964i	$0.471391\pi$
$180$	5.17687	0.385861
$181$	−21.0728	−1.56633	−0.783164	−	0.621815i	$-0.786396\pi$
$181$	−21.0728	−1.56633	−0.783164	+	0.621815i	$0.786396\pi$
$182$	−2.17687	−0.161361
$183$	−25.4381	−1.88044
$184$	−6.85952	−0.505691
$185$	−3.71905	−0.273430
$186$	1.95205	0.143131
$187$	0	0
$188$	4.68265	0.341517
$189$	−6.22482	−0.452789
$190$	−1.68265	−0.122072
$191$	−21.0051	−1.51988	−0.759938	−	0.649995i	$-0.774771\pi$
$191$	−21.0051	−1.51988	−0.759938	+	0.649995i	$0.774771\pi$
$192$	−2.85952	−0.206368
$193$	−6.24967	−0.449861	−0.224931	−	0.974375i	$-0.572216\pi$
$193$	−6.24967	−0.449861	−0.224931	+	0.974375i	$0.572216\pi$
$194$	−16.6150	−1.19289
$195$	−6.22482	−0.445769
$196$	1.00000	0.0714286
$197$	18.2612	1.30106	0.650529	−	0.759481i	$-0.274547\pi$
$197$	18.2612	1.30106	0.650529	+	0.759481i	$0.274547\pi$
$198$	0	0
$199$	−22.1456	−1.56986	−0.784930	−	0.619585i	$-0.787301\pi$
$199$	−22.1456	−1.56986	−0.784930	+	0.619585i	$0.787301\pi$
$200$	−1.00000	−0.0707107
$201$	−28.1935	−1.98862
$202$	3.54217	0.249226
$203$	−2.00000	−0.140372
$204$	−11.0364	−0.772702
$205$	9.03640	0.631129
$206$	−9.50578	−0.662299
$207$	35.5109	2.46818
$208$	2.17687	0.150939
$209$	0	0
$210$	2.85952	0.197326
$211$	−19.7918	−1.36253	−0.681263	−	0.732038i	$-0.738569\pi$
$211$	−19.7918	−1.36253	−0.681263	+	0.732038i	$0.738569\pi$
$212$	13.5786	0.932580
$213$	1.55036	0.106229
$214$	−7.17687	−0.490601
$215$	5.85952	0.399616
$216$	6.22482	0.423545
$217$	0.682649	0.0463413
$218$	−13.3901	−0.906895
$219$	16.7554	1.13223
$220$	0	0
$221$	8.40170	0.565159
$222$	−10.6347	−0.713754
$223$	−12.2133	−0.817861	−0.408931	−	0.912565i	$-0.634098\pi$
$223$	−12.2133	−0.817861	−0.408931	+	0.912565i	$0.634098\pi$
$224$	−1.00000	−0.0668153
$225$	5.17687	0.345125
$226$	10.2497	0.681798
$227$	1.92721	0.127913	0.0639566	−	0.997953i	$-0.479628\pi$
$227$	1.92721	0.127913	0.0639566	+	0.997953i	$0.479628\pi$
$228$	−4.81158	−0.318654
$229$	26.2612	1.73539	0.867695	−	0.497097i	$-0.165601\pi$
$229$	26.2612	1.73539	0.867695	+	0.497097i	$0.165601\pi$
$230$	−6.85952	−0.452304
$231$	0	0
$232$	2.00000	0.131306
$233$	7.26122	0.475698	0.237849	−	0.971302i	$-0.423558\pi$
$233$	7.26122	0.475698	0.237849	+	0.971302i	$0.423558\pi$
$234$	−11.2694	−0.736704
$235$	4.68265	0.305462
$236$	−7.75544	−0.504836
$237$	−0.907472	−0.0589466
$238$	−3.85952	−0.250176
$239$	−26.9323	−1.74211	−0.871053	−	0.491188i	$-0.836563\pi$
$239$	−26.9323	−1.74211	−0.871053	+	0.491188i	$0.836563\pi$
$240$	−2.85952	−0.184581
$241$	−11.7918	−0.759579	−0.379790	−	0.925073i	$-0.624004\pi$
$241$	−11.7918	−0.759579	−0.379790	+	0.925073i	$0.624004\pi$
$242$	0	0
$243$	12.1851	0.781672
$244$	8.89592	0.569503
$245$	1.00000	0.0638877
$246$	25.8398	1.64748
$247$	3.66292	0.233066
$248$	−0.682649	−0.0433483
$249$	13.8959	0.880618
$250$	−1.00000	−0.0632456
$251$	0.823126	0.0519553	0.0259776	−	0.999663i	$-0.491730\pi$
$251$	0.823126	0.0519553	0.0259776	+	0.999663i	$0.491730\pi$
$252$	5.17687	0.326112
$253$	0	0
$254$	20.9323	1.31341
$255$	−11.0364	−0.691126
$256$	1.00000	0.0625000
$257$	−7.93232	−0.494804	−0.247402	−	0.968913i	$-0.579577\pi$
$257$	−7.93232	−0.494804	−0.247402	+	0.968913i	$0.579577\pi$
$258$	16.7554	1.04315
$259$	−3.71905	−0.231090
$260$	2.17687	0.135004
$261$	−10.3537	−0.640881
$262$	6.57857	0.406425
$263$	4.22482	0.260514	0.130257	−	0.991480i	$-0.458420\pi$
$263$	4.22482	0.260514	0.130257	+	0.991480i	$0.458420\pi$
$264$	0	0
$265$	13.5786	0.834125
$266$	−1.68265	−0.103170
$267$	1.95205	0.119464
$268$	9.85952	0.602266
$269$	26.5109	1.61640	0.808199	−	0.588910i	$-0.200443\pi$
$269$	26.5109	1.61640	0.808199	+	0.588910i	$0.200443\pi$
$270$	6.22482	0.378831
$271$	−19.1571	−1.16371	−0.581857	−	0.813291i	$-0.697674\pi$
$271$	−19.1571	−1.16371	−0.581857	+	0.813291i	$0.697674\pi$
$272$	3.85952	0.234018
$273$	−6.22482	−0.376743
$274$	−4.53062	−0.273705
$275$	0	0
$276$	−19.6150	−1.18068
$277$	0.0479481	0.00288092	0.00144046	−	0.999999i	$-0.499541\pi$
$277$	0.0479481	0.00288092	0.00144046	+	0.999999i	$0.499541\pi$
$278$	−13.4017	−0.803780
$279$	3.53399	0.211574
$280$	−1.00000	−0.0597614
$281$	−14.0843	−0.840202	−0.420101	−	0.907477i	$-0.638005\pi$
$281$	−14.0843	−0.840202	−0.420101	+	0.907477i	$0.638005\pi$
$282$	13.3901	0.797372
$283$	−3.49422	−0.207710	−0.103855	−	0.994592i	$-0.533118\pi$
$283$	−3.49422	−0.207710	−0.103855	+	0.994592i	$0.533118\pi$
$284$	−0.542173	−0.0321720
$285$	−4.81158	−0.285013
$286$	0	0
$287$	9.03640	0.533402
$288$	−5.17687	−0.305050
$289$	−2.10408	−0.123769
$290$	2.00000	0.117444
$291$	−47.5109	−2.78514
$292$	−5.85952	−0.342903
$293$	4.88437	0.285348	0.142674	−	0.989770i	$-0.454430\pi$
$293$	4.88437	0.285348	0.142674	+	0.989770i	$0.454430\pi$
$294$	2.85952	0.166771
$295$	−7.75544	−0.451539
$296$	3.71905	0.216165
$297$	0	0
$298$	−13.3653	−0.774231
$299$	14.9323	0.863558
$300$	−2.85952	−0.165095
$301$	5.85952	0.337737
$302$	16.8595	0.970157
$303$	10.1289	0.581892
$304$	1.68265	0.0965066
$305$	8.89592	0.509379
$306$	−19.9803	−1.14220
$307$	−19.7190	−1.12543	−0.562713	−	0.826653i	$-0.690242\pi$
$307$	−19.7190	−1.12543	−0.562713	+	0.826653i	$0.690242\pi$
$308$	0	0
$309$	−27.1820	−1.54633
$310$	−0.682649	−0.0387719
$311$	22.1935	1.25848	0.629240	−	0.777211i	$-0.283366\pi$
$311$	22.1935	1.25848	0.629240	+	0.777211i	$0.283366\pi$
$312$	6.22482	0.352411
$313$	3.51089	0.198447	0.0992236	−	0.995065i	$-0.468364\pi$
$313$	3.51089	0.198447	0.0992236	+	0.995065i	$0.468364\pi$
$314$	−14.2497	−0.804155
$315$	5.17687	0.291684
$316$	0.317351	0.0178524
$317$	−5.50578	−0.309235	−0.154618	−	0.987974i	$-0.549415\pi$
$317$	−5.50578	−0.309235	−0.154618	+	0.987974i	$0.549415\pi$
$318$	38.8282	2.17738
$319$	0	0
$320$	1.00000	0.0559017
$321$	−20.5224	−1.14545
$322$	−6.85952	−0.382266
$323$	6.49422	0.361348
$324$	2.26940	0.126078
$325$	2.17687	0.120751
$326$	−14.2612	−0.789856
$327$	−38.2894	−2.11741
$328$	−9.03640	−0.498952
$329$	4.68265	0.258163
$330$	0	0
$331$	−13.4629	−0.739990	−0.369995	−	0.929034i	$-0.620641\pi$
$331$	−13.4629	−0.739990	−0.369995	+	0.929034i	$0.620641\pi$
$332$	−4.85952	−0.266701
$333$	−19.2530	−1.05506
$334$	9.57857	0.524116
$335$	9.85952	0.538683
$336$	−2.85952	−0.156000
$337$	−19.3340	−1.05319	−0.526595	−	0.850116i	$-0.676532\pi$
$337$	−19.3340	−1.05319	−0.526595	+	0.850116i	$0.676532\pi$
$338$	8.26122	0.449351
$339$	29.3092	1.59186
$340$	3.85952	0.209312
$341$	0	0
$342$	−8.71086	−0.471030
$343$	1.00000	0.0539949
$344$	−5.85952	−0.315924
$345$	−19.6150	−1.05603
$346$	0.353748	0.0190176
$347$	−20.0531	−1.07650	−0.538252	−	0.842784i	$-0.680915\pi$
$347$	−20.0531	−1.07650	−0.538252	+	0.842784i	$0.680915\pi$
$348$	5.71905	0.306573
$349$	−29.2612	−1.56632	−0.783159	−	0.621822i	$-0.786393\pi$
$349$	−29.2612	−1.56632	−0.783159	+	0.621822i	$0.786393\pi$
$350$	−1.00000	−0.0534522
$351$	−13.5507	−0.723280
$352$	0	0
$353$	3.50578	0.186594	0.0932968	−	0.995638i	$-0.470259\pi$
$353$	3.50578	0.186594	0.0932968	+	0.995638i	$0.470259\pi$
$354$	−22.1769	−1.17869
$355$	−0.542173	−0.0287755
$356$	−0.682649	−0.0361803
$357$	−11.0364	−0.584108
$358$	−2.40170	−0.126934
$359$	−36.2612	−1.91379	−0.956897	−	0.290428i	$-0.906202\pi$
$359$	−36.2612	−1.91379	−0.956897	+	0.290428i	$0.906202\pi$
$360$	−5.17687	−0.272845
$361$	−16.1687	−0.850984
$362$	21.0728	1.10756
$363$	0	0
$364$	2.17687	0.114099
$365$	−5.85952	−0.306701
$366$	25.4381	1.32967
$367$	−1.29762	−0.0677351	−0.0338675	−	0.999426i	$-0.510782\pi$
$367$	−1.29762	−0.0677351	−0.0338675	+	0.999426i	$0.510782\pi$
$368$	6.85952	0.357577
$369$	46.7803	2.43528
$370$	3.71905	0.193344
$371$	13.5786	0.704964
$372$	−1.95205	−0.101209
$373$	−16.8231	−0.871068	−0.435534	−	0.900172i	$-0.643441\pi$
$373$	−16.8231	−0.871068	−0.435534	+	0.900172i	$0.643441\pi$
$374$	0	0
$375$	−2.85952	−0.147665
$376$	−4.68265	−0.241489
$377$	−4.35375	−0.224229
$378$	6.22482	0.320170
$379$	4.70750	0.241808	0.120904	−	0.992664i	$-0.461421\pi$
$379$	4.70750	0.241808	0.120904	+	0.992664i	$0.461421\pi$
$380$	1.68265	0.0863181
$381$	59.8565	3.06654
$382$	21.0051	1.07472
$383$	−17.6514	−0.901943	−0.450971	−	0.892538i	$-0.648922\pi$
$383$	−17.6514	−0.901943	−0.450971	+	0.892538i	$0.648922\pi$
$384$	2.85952	0.145924
$385$	0	0
$386$	6.24967	0.318100
$387$	30.3340	1.54196
$388$	16.6150	0.843497
$389$	27.9126	1.41522	0.707612	−	0.706601i	$-0.249772\pi$
$389$	27.9126	1.41522	0.707612	+	0.706601i	$0.249772\pi$
$390$	6.22482	0.315206
$391$	26.4745	1.33887
$392$	−1.00000	−0.0505076
$393$	18.8116	0.948918
$394$	−18.2612	−0.919987
$395$	0.317351	0.0159676
$396$	0	0
$397$	−4.35375	−0.218508	−0.109254	−	0.994014i	$-0.534846\pi$
$397$	−4.35375	−0.218508	−0.109254	+	0.994014i	$0.534846\pi$
$398$	22.1456	1.11006
$399$	−4.81158	−0.240880
$400$	1.00000	0.0500000
$401$	−6.56191	−0.327686	−0.163843	−	0.986486i	$-0.552389\pi$
$401$	−6.56191	−0.327686	−0.163843	+	0.986486i	$0.552389\pi$
$402$	28.1935	1.40617
$403$	1.48604	0.0740250
$404$	−3.54217	−0.176230
$405$	2.26940	0.112768
$406$	2.00000	0.0992583
$407$	0	0
$408$	11.0364	0.546383
$409$	15.7918	0.780856	0.390428	−	0.920633i	$-0.372327\pi$
$409$	15.7918	0.780856	0.390428	+	0.920633i	$0.372327\pi$
$410$	−9.03640	−0.446276
$411$	−12.9554	−0.639044
$412$	9.50578	0.468316
$413$	−7.75544	−0.381620
$414$	−35.5109	−1.74526
$415$	−4.85952	−0.238545
$416$	−2.17687	−0.106730
$417$	−38.3225	−1.87666
$418$	0	0
$419$	28.7670	1.40536	0.702680	−	0.711506i	$-0.251987\pi$
$419$	28.7670	1.40536	0.702680	+	0.711506i	$0.251987\pi$
$420$	−2.85952	−0.139530
$421$	−12.1456	−0.591940	−0.295970	−	0.955197i	$-0.595643\pi$
$421$	−12.1456	−0.591940	−0.295970	+	0.955197i	$0.595643\pi$
$422$	19.7918	0.963452
$423$	24.2415	1.17866
$424$	−13.5786	−0.659434
$425$	3.85952	0.187214
$426$	−1.55036	−0.0751150
$427$	8.89592	0.430504
$428$	7.17687	0.346907
$429$	0	0
$430$	−5.85952	−0.282571
$431$	−22.9126	−1.10366	−0.551830	−	0.833957i	$-0.686070\pi$
$431$	−22.9126	−1.10366	−0.551830	+	0.833957i	$0.686070\pi$
$432$	−6.22482	−0.299492
$433$	−7.69420	−0.369760	−0.184880	−	0.982761i	$-0.559190\pi$
$433$	−7.69420	−0.369760	−0.184880	+	0.982761i	$0.559190\pi$
$434$	−0.682649	−0.0327682
$435$	5.71905	0.274207
$436$	13.3901	0.641272
$437$	11.5422	0.552137
$438$	−16.7554	−0.800606
$439$	−41.1092	−1.96203	−0.981017	−	0.193920i	$-0.937880\pi$
$439$	−41.1092	−1.96203	−0.981017	+	0.193920i	$0.937880\pi$
$440$	0	0
$441$	5.17687	0.246518
$442$	−8.40170	−0.399628
$443$	16.8034	0.798353	0.399177	−	0.916874i	$-0.369296\pi$
$443$	16.8034	0.798353	0.399177	+	0.916874i	$0.369296\pi$
$444$	10.6347	0.504701
$445$	−0.682649	−0.0323607
$446$	12.2133	0.578315
$447$	−38.2184	−1.80767
$448$	1.00000	0.0472456
$449$	24.4381	1.15330	0.576652	−	0.816990i	$-0.304359\pi$
$449$	24.4381	1.15330	0.576652	+	0.816990i	$0.304359\pi$
$450$	−5.17687	−0.244040
$451$	0	0
$452$	−10.2497	−0.482104
$453$	48.2102	2.26511
$454$	−1.92721	−0.0904482
$455$	2.17687	0.102053
$456$	4.81158	0.225323
$457$	−12.3225	−0.576421	−0.288210	−	0.957567i	$-0.593060\pi$
$457$	−12.3225	−0.576421	−0.288210	+	0.957567i	$0.593060\pi$
$458$	−26.2612	−1.22711
$459$	−24.0248	−1.12138
$460$	6.85952	0.319827
$461$	3.38503	0.157657	0.0788283	−	0.996888i	$-0.474882\pi$
$461$	3.38503	0.157657	0.0788283	+	0.996888i	$0.474882\pi$
$462$	0	0
$463$	35.6629	1.65740	0.828698	−	0.559696i	$-0.189082\pi$
$463$	35.6629	1.65740	0.828698	+	0.559696i	$0.189082\pi$
$464$	−2.00000	−0.0928477
$465$	−1.95205	−0.0905242
$466$	−7.26122	−0.336369
$467$	19.7357	0.913260	0.456630	−	0.889657i	$-0.349056\pi$
$467$	19.7357	0.913260	0.456630	+	0.889657i	$0.349056\pi$
$468$	11.2694	0.520928
$469$	9.85952	0.455270
$470$	−4.68265	−0.215995
$471$	−40.7473	−1.87753
$472$	7.75544	0.356973
$473$	0	0
$474$	0.907472	0.0416815
$475$	1.68265	0.0772052
$476$	3.85952	0.176901
$477$	70.2945	3.21857
$478$	26.9323	1.23186
$479$	6.40170	0.292501	0.146250	−	0.989248i	$-0.453279\pi$
$479$	6.40170	0.292501	0.146250	+	0.989248i	$0.453279\pi$
$480$	2.85952	0.130519
$481$	−8.09590	−0.369141
$482$	11.7918	0.537104
$483$	−19.6150	−0.892512
$484$	0	0
$485$	16.6150	0.754447
$486$	−12.1851	−0.552725
$487$	43.1738	1.95639	0.978196	−	0.207684i	$-0.0665927\pi$
$487$	43.1738	1.95639	0.978196	+	0.207684i	$0.0665927\pi$
$488$	−8.89592	−0.402699
$489$	−40.7803	−1.84415
$490$	−1.00000	−0.0451754
$491$	33.2779	1.50181	0.750905	−	0.660410i	$-0.229618\pi$
$491$	33.2779	1.50181	0.750905	+	0.660410i	$0.229618\pi$
$492$	−25.8398	−1.16495
$493$	−7.71905	−0.347648
$494$	−3.66292	−0.164802
$495$	0	0
$496$	0.682649	0.0306519
$497$	−0.542173	−0.0243198
$498$	−13.8959	−0.622691
$499$	−22.6347	−1.01327	−0.506634	−	0.862161i	$-0.669111\pi$
$499$	−22.6347	−1.01327	−0.506634	+	0.862161i	$0.669111\pi$
$500$	1.00000	0.0447214
$501$	27.3901	1.22370
$502$	−0.823126	−0.0367379
$503$	12.1405	0.541317	0.270659	−	0.962675i	$-0.412759\pi$
$503$	12.1405	0.541317	0.270659	+	0.962675i	$0.412759\pi$
$504$	−5.17687	−0.230596
$505$	−3.54217	−0.157625
$506$	0	0
$507$	23.6232	1.04914
$508$	−20.9323	−0.928721
$509$	25.4265	1.12701	0.563506	−	0.826112i	$-0.309452\pi$
$509$	25.4265	1.12701	0.563506	+	0.826112i	$0.309452\pi$
$510$	11.0364	0.488700
$511$	−5.85952	−0.259210
$512$	−1.00000	−0.0441942
$513$	−10.4742	−0.462447
$514$	7.93232	0.349880
$515$	9.50578	0.418875
$516$	−16.7554	−0.737617
$517$	0	0
$518$	3.71905	0.163406
$519$	1.01155	0.0444021
$520$	−2.17687	−0.0954622
$521$	27.3653	1.19890	0.599448	−	0.800414i	$-0.295387\pi$
$521$	27.3653	1.19890	0.599448	+	0.800414i	$0.295387\pi$
$522$	10.3537	0.453171
$523$	19.2364	0.841148	0.420574	−	0.907258i	$-0.361829\pi$
$523$	19.2364	0.841148	0.420574	+	0.907258i	$0.361829\pi$
$524$	−6.57857	−0.287386
$525$	−2.85952	−0.124800
$526$	−4.22482	−0.184211
$527$	2.63470	0.114769
$528$	0	0
$529$	24.0531	1.04579
$530$	−13.5786	−0.589815
$531$	−40.1490	−1.74232
$532$	1.68265	0.0729521
$533$	19.6711	0.852050
$534$	−1.95205	−0.0844735
$535$	7.17687	0.310283
$536$	−9.85952	−0.425867
$537$	−6.86771	−0.296363
$538$	−26.5109	−1.14297
$539$	0	0
$540$	−6.22482	−0.267874
$541$	−19.5109	−0.838839	−0.419419	−	0.907793i	$-0.637766\pi$
$541$	−19.5109	−0.838839	−0.419419	+	0.907793i	$0.637766\pi$
$542$	19.1571	0.822870
$543$	60.2581	2.58592
$544$	−3.85952	−0.165476
$545$	13.3901	0.573571
$546$	6.22482	0.266398
$547$	−33.8595	−1.44773	−0.723864	−	0.689942i	$-0.757636\pi$
$547$	−33.8595	−1.44773	−0.723864	+	0.689942i	$0.757636\pi$
$548$	4.53062	0.193539
$549$	46.0531	1.96550
$550$	0	0
$551$	−3.36530	−0.143367
$552$	19.6150	0.834868
$553$	0.317351	0.0134951
$554$	−0.0479481	−0.00203712
$555$	10.6347	0.451418
$556$	13.4017	0.568359
$557$	−25.7670	−1.09178	−0.545891	−	0.837856i	$-0.683809\pi$
$557$	−25.7670	−1.09178	−0.545891	+	0.837856i	$0.683809\pi$
$558$	−3.53399	−0.149606
$559$	12.7554	0.539498
$560$	1.00000	0.0422577
$561$	0	0
$562$	14.0843	0.594112
$563$	−1.84797	−0.0778828	−0.0389414	−	0.999241i	$-0.512399\pi$
$563$	−1.84797	−0.0778828	−0.0389414	+	0.999241i	$0.512399\pi$
$564$	−13.3901	−0.563827
$565$	−10.2497	−0.431207
$566$	3.49422	0.146873
$567$	2.26940	0.0953059
$568$	0.542173	0.0227491
$569$	31.2184	1.30874	0.654371	−	0.756173i	$-0.272933\pi$
$569$	31.2184	1.30874	0.654371	+	0.756173i	$0.272933\pi$
$570$	4.81158	0.201535
$571$	−8.42654	−0.352640	−0.176320	−	0.984333i	$-0.556419\pi$
$571$	−8.42654	−0.352640	−0.176320	+	0.984333i	$0.556419\pi$
$572$	0	0
$573$	60.0646	2.50924
$574$	−9.03640	−0.377172
$575$	6.85952	0.286062
$576$	5.17687	0.215703
$577$	10.0051	0.416518	0.208259	−	0.978074i	$-0.433220\pi$
$577$	10.0051	0.416518	0.208259	+	0.978074i	$0.433220\pi$
$578$	2.10408	0.0875182
$579$	17.8711	0.742696
$580$	−2.00000	−0.0830455
$581$	−4.85952	−0.201607
$582$	47.5109	1.96939
$583$	0	0
$584$	5.85952	0.242469
$585$	11.2694	0.465932
$586$	−4.88437	−0.201771
$587$	−1.79828	−0.0742229	−0.0371115	−	0.999311i	$-0.511816\pi$
$587$	−1.79828	−0.0742229	−0.0371115	+	0.999311i	$0.511816\pi$
$588$	−2.85952	−0.117925
$589$	1.14866	0.0473297
$590$	7.75544	0.319287
$591$	−52.2184	−2.14798
$592$	−3.71905	−0.152852
$593$	39.3225	1.61478	0.807390	−	0.590018i	$-0.200879\pi$
$593$	39.3225	1.61478	0.807390	+	0.590018i	$0.200879\pi$
$594$	0	0
$595$	3.85952	0.158225
$596$	13.3653	0.547464
$597$	63.3258	2.59175
$598$	−14.9323	−0.610628
$599$	25.7554	1.05234	0.526169	−	0.850380i	$-0.323628\pi$
$599$	25.7554	1.05234	0.526169	+	0.850380i	$0.323628\pi$
$600$	2.85952	0.116740
$601$	27.1092	1.10581	0.552904	−	0.833245i	$-0.313520\pi$
$601$	27.1092	1.10581	0.552904	+	0.833245i	$0.313520\pi$
$602$	−5.85952	−0.238816
$603$	51.0415	2.07857
$604$	−16.8595	−0.686004
$605$	0	0
$606$	−10.1289	−0.411459
$607$	30.0300	1.21888	0.609439	−	0.792833i	$-0.291395\pi$
$607$	30.0300	1.21888	0.609439	+	0.792833i	$0.291395\pi$
$608$	−1.68265	−0.0682404
$609$	5.71905	0.231747
$610$	−8.89592	−0.360185
$611$	10.1935	0.412386
$612$	19.9803	0.807654
$613$	22.5901	0.912406	0.456203	−	0.889876i	$-0.349209\pi$
$613$	22.5901	0.912406	0.456203	+	0.889876i	$0.349209\pi$
$614$	19.7190	0.795796
$615$	−25.8398	−1.04196
$616$	0	0
$617$	−20.7306	−0.834582	−0.417291	−	0.908773i	$-0.637020\pi$
$617$	−20.7306	−0.834582	−0.417291	+	0.908773i	$0.637020\pi$
$618$	27.1820	1.09342
$619$	29.8085	1.19810	0.599052	−	0.800710i	$-0.295544\pi$
$619$	29.8085	1.19810	0.599052	+	0.800710i	$0.295544\pi$
$620$	0.682649	0.0274159
$621$	−42.6993	−1.71346
$622$	−22.1935	−0.889880
$623$	−0.682649	−0.0273498
$624$	−6.22482	−0.249192
$625$	1.00000	0.0400000
$626$	−3.51089	−0.140323
$627$	0	0
$628$	14.2497	0.568624
$629$	−14.3537	−0.572321
$630$	−5.17687	−0.206252
$631$	22.3340	0.889103	0.444552	−	0.895753i	$-0.353363\pi$
$631$	22.3340	0.889103	0.444552	+	0.895753i	$0.353363\pi$
$632$	−0.317351	−0.0126235
$633$	56.5952	2.24946
$634$	5.50578	0.218662
$635$	−20.9323	−0.830674
$636$	−38.8282	−1.53964
$637$	2.17687	0.0862509
$638$	0	0
$639$	−2.80676	−0.111034
$640$	−1.00000	−0.0395285
$641$	−4.06124	−0.160409	−0.0802047	−	0.996778i	$-0.525557\pi$
$641$	−4.06124	−0.160409	−0.0802047	+	0.996778i	$0.525557\pi$
$642$	20.5224	0.809956
$643$	−35.0218	−1.38112	−0.690562	−	0.723273i	$-0.742637\pi$
$643$	−35.0218	−1.38112	−0.690562	+	0.723273i	$0.742637\pi$
$644$	6.85952	0.270303
$645$	−16.7554	−0.659745
$646$	−6.49422	−0.255512
$647$	29.2248	1.14895	0.574473	−	0.818523i	$-0.305207\pi$
$647$	29.2248	1.14895	0.574473	+	0.818523i	$0.305207\pi$
$648$	−2.26940	−0.0891505
$649$	0	0
$650$	−2.17687	−0.0853840
$651$	−1.95205	−0.0765069
$652$	14.2612	0.558512
$653$	−19.9323	−0.780012	−0.390006	−	0.920812i	$-0.627527\pi$
$653$	−19.9323	−0.780012	−0.390006	+	0.920812i	$0.627527\pi$
$654$	38.2894	1.49724
$655$	−6.57857	−0.257046
$656$	9.03640	0.352812
$657$	−30.3340	−1.18344
$658$	−4.68265	−0.182549
$659$	−24.6201	−0.959062	−0.479531	−	0.877525i	$-0.659193\pi$
$659$	−24.6201	−0.959062	−0.479531	+	0.877525i	$0.659193\pi$
$660$	0	0
$661$	25.7606	1.00197	0.500985	−	0.865456i	$-0.332971\pi$
$661$	25.7606	1.00197	0.500985	+	0.865456i	$0.332971\pi$
$662$	13.4629	0.523252
$663$	−24.0248	−0.933048
$664$	4.85952	0.188586
$665$	1.68265	0.0652503
$666$	19.2530	0.746040
$667$	−13.7190	−0.531204
$668$	−9.57857	−0.370606
$669$	34.9241	1.35025
$670$	−9.85952	−0.380907
$671$	0	0
$672$	2.85952	0.110309
$673$	5.54217	0.213635	0.106818	−	0.994279i	$-0.465934\pi$
$673$	5.54217	0.213635	0.106818	+	0.994279i	$0.465934\pi$
$674$	19.3340	0.744718
$675$	−6.22482	−0.239594
$676$	−8.26122	−0.317739
$677$	−34.4912	−1.32560	−0.662801	−	0.748795i	$-0.730633\pi$
$677$	−34.4912	−1.32560	−0.662801	+	0.748795i	$0.730633\pi$
$678$	−29.3092	−1.12561
$679$	16.6150	0.637624
$680$	−3.85952	−0.148006
$681$	−5.51089	−0.211178
$682$	0	0
$683$	−22.8231	−0.873303	−0.436651	−	0.899631i	$-0.643836\pi$
$683$	−22.8231	−0.873303	−0.436651	+	0.899631i	$0.643836\pi$
$684$	8.71086	0.333068
$685$	4.53062	0.173106
$686$	−1.00000	−0.0381802
$687$	−75.0946	−2.86504
$688$	5.85952	0.223392
$689$	29.5588	1.12610
$690$	19.6150	0.746729
$691$	−21.9075	−0.833399	−0.416700	−	0.909044i	$-0.636813\pi$
$691$	−21.9075	−0.833399	−0.416700	+	0.909044i	$0.636813\pi$
$692$	−0.353748	−0.0134475
$693$	0	0
$694$	20.0531	0.761204
$695$	13.4017	0.508355
$696$	−5.71905	−0.216780
$697$	34.8762	1.32103
$698$	29.2612	1.10755
$699$	−20.7636	−0.785353
$700$	1.00000	0.0377964
$701$	12.6826	0.479017	0.239509	−	0.970894i	$-0.423014\pi$
$701$	12.6826	0.479017	0.239509	+	0.970894i	$0.423014\pi$
$702$	13.5507	0.511436
$703$	−6.25785	−0.236019
$704$	0	0
$705$	−13.3901	−0.504302
$706$	−3.50578	−0.131942
$707$	−3.54217	−0.133217
$708$	22.1769	0.833458
$709$	47.3027	1.77649	0.888246	−	0.459369i	$-0.151924\pi$
$709$	47.3027	1.77649	0.888246	+	0.459369i	$0.151924\pi$
$710$	0.542173	0.0203474
$711$	1.64288	0.0616130
$712$	0.682649	0.0255834
$713$	4.68265	0.175367
$714$	11.0364	0.413027
$715$	0	0
$716$	2.40170	0.0897556
$717$	77.0136	2.87613
$718$	36.2612	1.35326
$719$	−12.9388	−0.482534	−0.241267	−	0.970459i	$-0.577563\pi$
$719$	−12.9388	−0.482534	−0.241267	+	0.970459i	$0.577563\pi$
$720$	5.17687	0.192931
$721$	9.50578	0.354014
$722$	16.1687	0.601736
$723$	33.7190	1.25402
$724$	−21.0728	−0.783164
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	32.4993	1.20533	0.602667	−	0.797993i	$-0.294105\pi$
$727$	32.4993	1.20533	0.602667	+	0.797993i	$0.294105\pi$
$728$	−2.17687	−0.0806803
$729$	−41.6517	−1.54265
$730$	5.85952	0.216871
$731$	22.6150	0.836445
$732$	−25.4381	−0.940219
$733$	41.6878	1.53977	0.769886	−	0.638181i	$-0.220313\pi$
$733$	41.6878	1.53977	0.769886	+	0.638181i	$0.220313\pi$
$734$	1.29762	0.0478959
$735$	−2.85952	−0.105475
$736$	−6.85952	−0.252845
$737$	0	0
$738$	−46.7803	−1.72201
$739$	6.40170	0.235490	0.117745	−	0.993044i	$-0.462433\pi$
$739$	6.40170	0.235490	0.117745	+	0.993044i	$0.462433\pi$
$740$	−3.71905	−0.136715
$741$	−10.4742	−0.384779
$742$	−13.5786	−0.498485
$743$	−33.2299	−1.21909	−0.609544	−	0.792752i	$-0.708647\pi$
$743$	−33.2299	−1.21909	−0.609544	+	0.792752i	$0.708647\pi$
$744$	1.95205	0.0715657
$745$	13.3653	0.489667
$746$	16.8231	0.615938
$747$	−25.1571	−0.920452
$748$	0	0
$749$	7.17687	0.262237
$750$	2.85952	0.104415
$751$	31.3820	1.14514	0.572572	−	0.819854i	$-0.305946\pi$
$751$	31.3820	1.14514	0.572572	+	0.819854i	$0.305946\pi$
$752$	4.68265	0.170759
$753$	−2.35375	−0.0857753
$754$	4.35375	0.158554
$755$	−16.8595	−0.613581
$756$	−6.22482	−0.226395
$757$	−36.4548	−1.32497	−0.662485	−	0.749075i	$-0.730498\pi$
$757$	−36.4548	−1.32497	−0.662485	+	0.749075i	$0.730498\pi$
$758$	−4.70750	−0.170984
$759$	0	0
$760$	−1.68265	−0.0610361
$761$	45.4860	1.64887	0.824434	−	0.565958i	$-0.191494\pi$
$761$	45.4860	1.64887	0.824434	+	0.565958i	$0.191494\pi$
$762$	−59.8565	−2.16837
$763$	13.3901	0.484756
$764$	−21.0051	−0.759938
$765$	19.9803	0.722388
$766$	17.6514	0.637770
$767$	−16.8826	−0.609596
$768$	−2.85952	−0.103184
$769$	−3.57346	−0.128862	−0.0644311	−	0.997922i	$-0.520523\pi$
$769$	−3.57346	−0.128862	−0.0644311	+	0.997922i	$0.520523\pi$
$770$	0	0
$771$	22.6826	0.816896
$772$	−6.24967	−0.224931
$773$	39.4068	1.41736	0.708682	−	0.705528i	$-0.249290\pi$
$773$	39.4068	1.41736	0.708682	+	0.705528i	$0.249290\pi$
$774$	−30.3340	−1.09033
$775$	0.682649	0.0245215
$776$	−16.6150	−0.596443
$777$	10.6347	0.381518
$778$	−27.9126	−1.00071
$779$	15.2051	0.544779
$780$	−6.22482	−0.222884
$781$	0	0
$782$	−26.4745	−0.946726
$783$	12.4496	0.444914
$784$	1.00000	0.0357143
$785$	14.2497	0.508592
$786$	−18.8116	−0.670987
$787$	22.4993	0.802015	0.401007	−	0.916075i	$-0.368660\pi$
$787$	22.4993	0.802015	0.401007	+	0.916075i	$0.368660\pi$
$788$	18.2612	0.650529
$789$	−12.0810	−0.430094
$790$	−0.317351	−0.0112908
$791$	−10.2497	−0.364436
$792$	0	0
$793$	19.3653	0.687682
$794$	4.35375	0.154509
$795$	−38.8282	−1.37710
$796$	−22.1456	−0.784930
$797$	25.2612	0.894798	0.447399	−	0.894334i	$-0.352350\pi$
$797$	25.2612	0.894798	0.447399	+	0.894334i	$0.352350\pi$
$798$	4.81158	0.170328
$799$	18.0728	0.639370
$800$	−1.00000	−0.0353553
$801$	−3.53399	−0.124867
$802$	6.56191	0.231709
$803$	0	0
$804$	−28.1935	−0.994309
$805$	6.85952	0.241766
$806$	−1.48604	−0.0523436
$807$	−75.8085	−2.66859
$808$	3.54217	0.124613
$809$	−45.0415	−1.58358	−0.791788	−	0.610797i	$-0.790849\pi$
$809$	−45.0415	−1.58358	−0.791788	+	0.610797i	$0.790849\pi$
$810$	−2.26940	−0.0797387
$811$	−44.9490	−1.57837	−0.789186	−	0.614154i	$-0.789497\pi$
$811$	−44.9490	−1.57837	−0.789186	+	0.614154i	$0.789497\pi$
$812$	−2.00000	−0.0701862
$813$	54.7803	1.92123
$814$	0	0
$815$	14.2612	0.499549
$816$	−11.0364	−0.386351
$817$	9.85952	0.344941
$818$	−15.7918	−0.552149
$819$	11.2694	0.393785
$820$	9.03640	0.315565
$821$	6.52244	0.227635	0.113817	−	0.993502i	$-0.463692\pi$
$821$	6.52244	0.227635	0.113817	+	0.993502i	$0.463692\pi$
$822$	12.9554	0.451872
$823$	38.4496	1.34027	0.670135	−	0.742239i	$-0.266236\pi$
$823$	38.4496	1.34027	0.670135	+	0.742239i	$0.266236\pi$
$824$	−9.50578	−0.331149
$825$	0	0
$826$	7.75544	0.269846
$827$	55.3704	1.92542	0.962709	−	0.270539i	$-0.0872020\pi$
$827$	55.3704	1.92542	0.962709	+	0.270539i	$0.0872020\pi$
$828$	35.5109	1.23409
$829$	−50.7721	−1.76339	−0.881694	−	0.471821i	$-0.843597\pi$
$829$	−50.7721	−1.76339	−0.881694	+	0.471821i	$0.843597\pi$
$830$	4.85952	0.168677
$831$	−0.137109	−0.00475625
$832$	2.17687	0.0754695
$833$	3.85952	0.133725
$834$	38.3225	1.32700
$835$	−9.57857	−0.331480
$836$	0	0
$837$	−4.24937	−0.146880
$838$	−28.7670	−0.993739
$839$	42.6201	1.47141	0.735704	−	0.677303i	$-0.236851\pi$
$839$	42.6201	1.47141	0.735704	+	0.677303i	$0.236851\pi$
$840$	2.85952	0.0986629
$841$	−25.0000	−0.862069
$842$	12.1456	0.418565
$843$	40.2745	1.38713
$844$	−19.7918	−0.681263
$845$	−8.26122	−0.284195
$846$	−24.2415	−0.833439
$847$	0	0
$848$	13.5786	0.466290
$849$	9.99182	0.342918
$850$	−3.85952	−0.132381
$851$	−25.5109	−0.874502
$852$	1.55036	0.0531143
$853$	2.12718	0.0728333	0.0364166	−	0.999337i	$-0.488406\pi$
$853$	2.12718	0.0728333	0.0364166	+	0.999337i	$0.488406\pi$
$854$	−8.89592	−0.304412
$855$	8.71086	0.297905
$856$	−7.17687	−0.245301
$857$	52.6680	1.79911	0.899553	−	0.436812i	$-0.143893\pi$
$857$	52.6680	1.79911	0.899553	+	0.436812i	$0.143893\pi$
$858$	0	0
$859$	−36.9687	−1.26136	−0.630678	−	0.776045i	$-0.717223\pi$
$859$	−36.9687	−1.26136	−0.630678	+	0.776045i	$0.717223\pi$
$860$	5.85952	0.199808
$861$	−25.8398	−0.880618
$862$	22.9126	0.780406
$863$	−36.6680	−1.24819	−0.624097	−	0.781347i	$-0.714533\pi$
$863$	−36.6680	−1.24819	−0.624097	+	0.781347i	$0.714533\pi$
$864$	6.22482	0.211773
$865$	−0.353748	−0.0120278
$866$	7.69420	0.261460
$867$	6.01666	0.204337
$868$	0.682649	0.0231706
$869$	0	0
$870$	−5.71905	−0.193894
$871$	21.4629	0.727244
$872$	−13.3901	−0.453448
$873$	86.0136	2.91112
$874$	−11.5422	−0.390420
$875$	1.00000	0.0338062
$876$	16.7554	0.566114
$877$	−16.7752	−0.566458	−0.283229	−	0.959052i	$-0.591406\pi$
$877$	−16.7752	−0.566458	−0.283229	+	0.959052i	$0.591406\pi$
$878$	41.1092	1.38737
$879$	−13.9670	−0.471094
$880$	0	0
$881$	40.2415	1.35577	0.677885	−	0.735168i	$-0.262897\pi$
$881$	40.2415	1.35577	0.677885	+	0.735168i	$0.262897\pi$
$882$	−5.17687	−0.174314
$883$	−20.4068	−0.686744	−0.343372	−	0.939200i	$-0.611569\pi$
$883$	−20.4068	−0.686744	−0.343372	+	0.939200i	$0.611569\pi$
$884$	8.40170	0.282580
$885$	22.1769	0.745467
$886$	−16.8034	−0.564521
$887$	11.9752	0.402086	0.201043	−	0.979582i	$-0.435567\pi$
$887$	11.9752	0.402086	0.201043	+	0.979582i	$0.435567\pi$
$888$	−10.6347	−0.356877
$889$	−20.9323	−0.702047
$890$	0.682649	0.0228825
$891$	0	0
$892$	−12.2133	−0.408931
$893$	7.87926	0.263669
$894$	38.2184	1.27821
$895$	2.40170	0.0802798
$896$	−1.00000	−0.0334077
$897$	−42.6993	−1.42569
$898$	−24.4381	−0.815510
$899$	−1.36530	−0.0455353
$900$	5.17687	0.172562
$901$	52.4068	1.74592
$902$	0	0
$903$	−16.7554	−0.557586
$904$	10.2497	0.340899
$905$	−21.0728	−0.700483
$906$	−48.2102	−1.60168
$907$	−21.8116	−0.724241	−0.362121	−	0.932131i	$-0.617947\pi$
$907$	−21.8116	−0.724241	−0.362121	+	0.932131i	$0.617947\pi$
$908$	1.92721	0.0639566
$909$	−18.3374	−0.608213
$910$	−2.17687	−0.0721627
$911$	−22.1820	−0.734922	−0.367461	−	0.930039i	$-0.619773\pi$
$911$	−22.1820	−0.734922	−0.367461	+	0.930039i	$0.619773\pi$
$912$	−4.81158	−0.159327
$913$	0	0
$914$	12.3225	0.407591
$915$	−25.4381	−0.840957
$916$	26.2612	0.867695
$917$	−6.57857	−0.217244
$918$	24.0248	0.792938
$919$	16.8531	0.555932	0.277966	−	0.960591i	$-0.410340\pi$
$919$	16.8531	0.555932	0.277966	+	0.960591i	$0.410340\pi$
$920$	−6.85952	−0.226152
$921$	56.3871	1.85802
$922$	−3.38503	−0.111480
$923$	−1.18024	−0.0388481
$924$	0	0
$925$	−3.71905	−0.122282
$926$	−35.6629	−1.17196
$927$	49.2102	1.61628
$928$	2.00000	0.0656532
$929$	−17.2694	−0.566591	−0.283295	−	0.959033i	$-0.591428\pi$
$929$	−17.2694	−0.566591	−0.283295	+	0.959033i	$0.591428\pi$
$930$	1.95205	0.0640103
$931$	1.68265	0.0551466
$932$	7.26122	0.237849
$933$	−63.4629	−2.07768
$934$	−19.7357	−0.645772
$935$	0	0
$936$	−11.2694	−0.368352
$937$	−45.5837	−1.48915	−0.744577	−	0.667537i	$-0.767349\pi$
$937$	−45.5837	−1.48915	−0.744577	+	0.667537i	$0.767349\pi$
$938$	−9.85952	−0.321925
$939$	−10.0395	−0.327626
$940$	4.68265	0.152731
$941$	36.1987	1.18004	0.590021	−	0.807388i	$-0.299119\pi$
$941$	36.1987	1.18004	0.590021	+	0.807388i	$0.299119\pi$
$942$	40.7473	1.32762
$943$	61.9854	2.01852
$944$	−7.75544	−0.252418
$945$	−6.22482	−0.202493
$946$	0	0
$947$	−33.3276	−1.08300	−0.541500	−	0.840701i	$-0.682144\pi$
$947$	−33.3276	−1.08300	−0.541500	+	0.840701i	$0.682144\pi$
$948$	−0.907472	−0.0294733
$949$	−12.7554	−0.414059
$950$	−1.68265	−0.0545924
$951$	15.7439	0.510531
$952$	−3.85952	−0.125088
$953$	−39.1884	−1.26944	−0.634719	−	0.772743i	$-0.718884\pi$
$953$	−39.1884	−1.26944	−0.634719	+	0.772743i	$0.718884\pi$
$954$	−70.2945	−2.27587
$955$	−21.0051	−0.679709
$956$	−26.9323	−0.871053
$957$	0	0
$958$	−6.40170	−0.206829
$959$	4.53062	0.146301
$960$	−2.85952	−0.0922907
$961$	−30.5340	−0.984967
$962$	8.09590	0.261022
$963$	37.1538	1.19726
$964$	−11.7918	−0.379790
$965$	−6.24967	−0.201184
$966$	19.6150	0.631101
$967$	23.8646	0.767435	0.383717	−	0.923451i	$-0.374644\pi$
$967$	23.8646	0.767435	0.383717	+	0.923451i	$0.374644\pi$
$968$	0	0
$969$	−18.5704	−0.596567
$970$	−16.6150	−0.533474
$971$	−21.0479	−0.675461	−0.337730	−	0.941243i	$-0.609659\pi$
$971$	−21.0479	−0.675461	−0.337730	+	0.941243i	$0.609659\pi$
$972$	12.1851	0.390836
$973$	13.4017	0.429639
$974$	−43.1738	−1.38338
$975$	−6.22482	−0.199354
$976$	8.89592	0.284751
$977$	−54.9177	−1.75697	−0.878486	−	0.477767i	$-0.841446\pi$
$977$	−54.9177	−1.75697	−0.878486	+	0.477767i	$0.841446\pi$
$978$	40.7803	1.30401
$979$	0	0
$980$	1.00000	0.0319438
$981$	69.3191	2.21319
$982$	−33.2779	−1.06194
$983$	−36.2912	−1.15751	−0.578754	−	0.815502i	$-0.696461\pi$
$983$	−36.2912	−1.15751	−0.578754	+	0.815502i	$0.696461\pi$
$984$	25.8398	0.823742
$985$	18.2612	0.581851
$986$	7.71905	0.245825
$987$	−13.3901	−0.426213
$988$	3.66292	0.116533
$989$	40.1935	1.27808
$990$	0	0
$991$	6.83979	0.217273	0.108637	−	0.994082i	$-0.465352\pi$
$991$	6.83979	0.217273	0.108637	+	0.994082i	$0.465352\pi$
$992$	−0.682649	−0.0216741
$993$	38.4976	1.22168
$994$	0.542173	0.0171967
$995$	−22.1456	−0.702062
$996$	13.8959	0.440309
$997$	11.4694	0.363239	0.181619	−	0.983369i	$-0.441866\pi$
$997$	11.4694	0.363239	0.181619	+	0.983369i	$0.441866\pi$
$998$	22.6347	0.716489
$999$	23.1504	0.732446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cj.1.1	✓	3
11.10	odd	2		8470.2.a.cm.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cj.1.1	✓	3	1.1	even	1	trivial
8470.2.a.cm.1.1	yes	3	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} -1.00000 q^{10} -2.85952 q^{12} +2.17687 q^{13} -1.00000 q^{14} -2.85952 q^{15} +1.00000 q^{16} +3.85952 q^{17} -5.17687 q^{18} +1.68265 q^{19} +1.00000 q^{20} -2.85952 q^{21} +6.85952 q^{23} +2.85952 q^{24} +1.00000 q^{25} -2.17687 q^{26} -6.22482 q^{27} +1.00000 q^{28} -2.00000 q^{29} +2.85952 q^{30} +0.682649 q^{31} -1.00000 q^{32} -3.85952 q^{34} +1.00000 q^{35} +5.17687 q^{36} -3.71905 q^{37} -1.68265 q^{38} -6.22482 q^{39} -1.00000 q^{40} +9.03640 q^{41} +2.85952 q^{42} +5.85952 q^{43} +5.17687 q^{45} -6.85952 q^{46} +4.68265 q^{47} -2.85952 q^{48} +1.00000 q^{49} -1.00000 q^{50} -11.0364 q^{51} +2.17687 q^{52} +13.5786 q^{53} +6.22482 q^{54} -1.00000 q^{56} -4.81158 q^{57} +2.00000 q^{58} -7.75544 q^{59} -2.85952 q^{60} +8.89592 q^{61} -0.682649 q^{62} +5.17687 q^{63} +1.00000 q^{64} +2.17687 q^{65} +9.85952 q^{67} +3.85952 q^{68} -19.6150 q^{69} -1.00000 q^{70} -0.542173 q^{71} -5.17687 q^{72} -5.85952 q^{73} +3.71905 q^{74} -2.85952 q^{75} +1.68265 q^{76} +6.22482 q^{78} +0.317351 q^{79} +1.00000 q^{80} +2.26940 q^{81} -9.03640 q^{82} -4.85952 q^{83} -2.85952 q^{84} +3.85952 q^{85} -5.85952 q^{86} +5.71905 q^{87} -0.682649 q^{89} -5.17687 q^{90} +2.17687 q^{91} +6.85952 q^{92} -1.95205 q^{93} -4.68265 q^{94} +1.68265 q^{95} +2.85952 q^{96} +16.6150 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 13 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9} - 3 q^{10} + 2 q^{12} + 4 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + q^{17} - 13 q^{18} - 3 q^{19} + 3 q^{20} + 2 q^{21} + 10 q^{23} - 2 q^{24} + 3 q^{25} - 4 q^{26} + 8 q^{27} + 3 q^{28} - 6 q^{29} - 2 q^{30} - 6 q^{31} - 3 q^{32} - q^{34} + 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 8 q^{39} - 3 q^{40} + 14 q^{41} - 2 q^{42} + 7 q^{43} + 13 q^{45} - 10 q^{46} + 6 q^{47} + 2 q^{48} + 3 q^{49} - 3 q^{50} - 20 q^{51} + 4 q^{52} + 9 q^{53} - 8 q^{54} - 3 q^{56} - 28 q^{57} + 6 q^{58} + 11 q^{59} + 2 q^{60} + 3 q^{61} + 6 q^{62} + 13 q^{63} + 3 q^{64} + 4 q^{65} + 19 q^{67} + q^{68} - 14 q^{69} - 3 q^{70} + 17 q^{71} - 13 q^{72} - 7 q^{73} - 10 q^{74} + 2 q^{75} - 3 q^{76} - 8 q^{78} + 9 q^{79} + 3 q^{80} + 39 q^{81} - 14 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 7 q^{86} - 4 q^{87} + 6 q^{89} - 13 q^{90} + 4 q^{91} + 10 q^{92} - 30 q^{93} - 6 q^{94} - 3 q^{95} - 2 q^{96} + 5 q^{97} - 3 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 13 * q^9 - 3 * q^10 + 2 * q^12 + 4 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + q^17 - 13 * q^18 - 3 * q^19 + 3 * q^20 + 2 * q^21 + 10 * q^23 - 2 * q^24 + 3 * q^25 - 4 * q^26 + 8 * q^27 + 3 * q^28 - 6 * q^29 - 2 * q^30 - 6 * q^31 - 3 * q^32 - q^34 + 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 8 * q^39 - 3 * q^40 + 14 * q^41 - 2 * q^42 + 7 * q^43 + 13 * q^45 - 10 * q^46 + 6 * q^47 + 2 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 4 * q^52 + 9 * q^53 - 8 * q^54 - 3 * q^56 - 28 * q^57 + 6 * q^58 + 11 * q^59 + 2 * q^60 + 3 * q^61 + 6 * q^62 + 13 * q^63 + 3 * q^64 + 4 * q^65 + 19 * q^67 + q^68 - 14 * q^69 - 3 * q^70 + 17 * q^71 - 13 * q^72 - 7 * q^73 - 10 * q^74 + 2 * q^75 - 3 * q^76 - 8 * q^78 + 9 * q^79 + 3 * q^80 + 39 * q^81 - 14 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 7 * q^86 - 4 * q^87 + 6 * q^89 - 13 * q^90 + 4 * q^91 + 10 * q^92 - 30 * q^93 - 6 * q^94 - 3 * q^95 - 2 * q^96 + 5 * q^97 - 3 * q^98

Introduction

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