LMFDB - Embedded newform 5070.2.a.bu.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.29590 q^{11} -1.00000 q^{12} -1.35690 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.04892 q^{17} +1.00000 q^{18} +3.24698 q^{19} +1.00000 q^{20} +1.35690 q^{21} -5.29590 q^{22} +1.33513 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} -1.35690 q^{28} -5.13706 q^{29} -1.00000 q^{30} +2.80194 q^{31} +1.00000 q^{32} +5.29590 q^{33} -2.04892 q^{34} -1.35690 q^{35} +1.00000 q^{36} -2.24698 q^{37} +3.24698 q^{38} +1.00000 q^{40} +10.6310 q^{41} +1.35690 q^{42} +4.41789 q^{43} -5.29590 q^{44} +1.00000 q^{45} +1.33513 q^{46} +4.82371 q^{47} -1.00000 q^{48} -5.15883 q^{49} +1.00000 q^{50} +2.04892 q^{51} +14.2349 q^{53} -1.00000 q^{54} -5.29590 q^{55} -1.35690 q^{56} -3.24698 q^{57} -5.13706 q^{58} +13.8998 q^{59} -1.00000 q^{60} -3.62565 q^{61} +2.80194 q^{62} -1.35690 q^{63} +1.00000 q^{64} +5.29590 q^{66} +9.03684 q^{67} -2.04892 q^{68} -1.33513 q^{69} -1.35690 q^{70} +11.7506 q^{71} +1.00000 q^{72} -12.1032 q^{73} -2.24698 q^{74} -1.00000 q^{75} +3.24698 q^{76} +7.18598 q^{77} +0.259061 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.6310 q^{82} +3.02177 q^{83} +1.35690 q^{84} -2.04892 q^{85} +4.41789 q^{86} +5.13706 q^{87} -5.29590 q^{88} -5.47650 q^{89} +1.00000 q^{90} +1.33513 q^{92} -2.80194 q^{93} +4.82371 q^{94} +3.24698 q^{95} -1.00000 q^{96} -5.85086 q^{97} -5.15883 q^{98} -5.29590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 2 q^{11} - 3 q^{12} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 5 q^{19} + 3 q^{20} - 2 q^{22} + 3 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{27} - 10 q^{29} - 3 q^{30} + 4 q^{31} + 3 q^{32} + 2 q^{33} + 3 q^{34} + 3 q^{36} - 2 q^{37} + 5 q^{38} + 3 q^{40} + 17 q^{41} + 19 q^{43} - 2 q^{44} + 3 q^{45} + 3 q^{46} + 7 q^{47} - 3 q^{48} - 7 q^{49} + 3 q^{50} - 3 q^{51} + 19 q^{53} - 3 q^{54} - 2 q^{55} - 5 q^{57} - 10 q^{58} + 19 q^{59} - 3 q^{60} + q^{61} + 4 q^{62} + 3 q^{64} + 2 q^{66} - q^{67} + 3 q^{68} - 3 q^{69} - q^{71} + 3 q^{72} - 15 q^{73} - 2 q^{74} - 3 q^{75} + 5 q^{76} + 7 q^{77} + 15 q^{79} + 3 q^{80} + 3 q^{81} + 17 q^{82} + 6 q^{83} + 3 q^{85} + 19 q^{86} + 10 q^{87} - 2 q^{88} + 9 q^{89} + 3 q^{90} + 3 q^{92} - 4 q^{93} + 7 q^{94} + 5 q^{95} - 3 q^{96} - 4 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 2 * q^11 - 3 * q^12 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^22 + 3 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^27 - 10 * q^29 - 3 * q^30 + 4 * q^31 + 3 * q^32 + 2 * q^33 + 3 * q^34 + 3 * q^36 - 2 * q^37 + 5 * q^38 + 3 * q^40 + 17 * q^41 + 19 * q^43 - 2 * q^44 + 3 * q^45 + 3 * q^46 + 7 * q^47 - 3 * q^48 - 7 * q^49 + 3 * q^50 - 3 * q^51 + 19 * q^53 - 3 * q^54 - 2 * q^55 - 5 * q^57 - 10 * q^58 + 19 * q^59 - 3 * q^60 + q^61 + 4 * q^62 + 3 * q^64 + 2 * q^66 - q^67 + 3 * q^68 - 3 * q^69 - q^71 + 3 * q^72 - 15 * q^73 - 2 * q^74 - 3 * q^75 + 5 * q^76 + 7 * q^77 + 15 * q^79 + 3 * q^80 + 3 * q^81 + 17 * q^82 + 6 * q^83 + 3 * q^85 + 19 * q^86 + 10 * q^87 - 2 * q^88 + 9 * q^89 + 3 * q^90 + 3 * q^92 - 4 * q^93 + 7 * q^94 + 5 * q^95 - 3 * q^96 - 4 * q^97 - 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−1.35690	−0.512858	−0.256429	−	0.966563i	$-0.582546\pi$
$7$	−1.35690	−0.512858	−0.256429	+	0.966563i	$0.582546\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−5.29590	−1.59677	−0.798387	−	0.602145i	$-0.794313\pi$
$11$	−5.29590	−1.59677	−0.798387	+	0.602145i	$0.794313\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.35690	−0.362646
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.04892	−0.496935	−0.248468	−	0.968640i	$-0.579927\pi$
$17$	−2.04892	−0.496935	−0.248468	+	0.968640i	$0.579927\pi$
$18$	1.00000	0.235702
$19$	3.24698	0.744908	0.372454	−	0.928051i	$-0.378516\pi$
$19$	3.24698	0.744908	0.372454	+	0.928051i	$0.378516\pi$
$20$	1.00000	0.223607
$21$	1.35690	0.296099
$22$	−5.29590	−1.12909
$23$	1.33513	0.278393	0.139196	−	0.990265i	$-0.455548\pi$
$23$	1.33513	0.278393	0.139196	+	0.990265i	$0.455548\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.35690	−0.256429
$29$	−5.13706	−0.953929	−0.476964	−	0.878923i	$-0.658263\pi$
$29$	−5.13706	−0.953929	−0.476964	+	0.878923i	$0.658263\pi$
$30$	−1.00000	−0.182574
$31$	2.80194	0.503243	0.251621	−	0.967826i	$-0.419036\pi$
$31$	2.80194	0.503243	0.251621	+	0.967826i	$0.419036\pi$
$32$	1.00000	0.176777
$33$	5.29590	0.921897
$34$	−2.04892	−0.351386
$35$	−1.35690	−0.229357
$36$	1.00000	0.166667
$37$	−2.24698	−0.369401	−0.184701	−	0.982795i	$-0.559132\pi$
$37$	−2.24698	−0.369401	−0.184701	+	0.982795i	$0.559132\pi$
$38$	3.24698	0.526730
$39$	0	0
$40$	1.00000	0.158114
$41$	10.6310	1.66029	0.830143	−	0.557550i	$-0.188258\pi$
$41$	10.6310	1.66029	0.830143	+	0.557550i	$0.188258\pi$
$42$	1.35690	0.209374
$43$	4.41789	0.673723	0.336861	−	0.941554i	$-0.390635\pi$
$43$	4.41789	0.673723	0.336861	+	0.941554i	$0.390635\pi$
$44$	−5.29590	−0.798387
$45$	1.00000	0.149071
$46$	1.33513	0.196854
$47$	4.82371	0.703610	0.351805	−	0.936073i	$-0.385568\pi$
$47$	4.82371	0.703610	0.351805	+	0.936073i	$0.385568\pi$
$48$	−1.00000	−0.144338
$49$	−5.15883	−0.736976
$50$	1.00000	0.141421
$51$	2.04892	0.286906
$52$	0	0
$53$	14.2349	1.95531	0.977657	−	0.210207i	$-0.0674139\pi$
$53$	14.2349	1.95531	0.977657	+	0.210207i	$0.0674139\pi$
$54$	−1.00000	−0.136083
$55$	−5.29590	−0.714099
$56$	−1.35690	−0.181323
$57$	−3.24698	−0.430073
$58$	−5.13706	−0.674529
$59$	13.8998	1.80960	0.904798	−	0.425841i	$-0.140022\pi$
$59$	13.8998	1.80960	0.904798	+	0.425841i	$0.140022\pi$
$60$	−1.00000	−0.129099
$61$	−3.62565	−0.464216	−0.232108	−	0.972690i	$-0.574562\pi$
$61$	−3.62565	−0.464216	−0.232108	+	0.972690i	$0.574562\pi$
$62$	2.80194	0.355846
$63$	−1.35690	−0.170953
$64$	1.00000	0.125000
$65$	0	0
$66$	5.29590	0.651880
$67$	9.03684	1.10403	0.552013	−	0.833836i	$-0.313860\pi$
$67$	9.03684	1.10403	0.552013	+	0.833836i	$0.313860\pi$
$68$	−2.04892	−0.248468
$69$	−1.33513	−0.160730
$70$	−1.35690	−0.162180
$71$	11.7506	1.39454	0.697271	−	0.716807i	$-0.254397\pi$
$71$	11.7506	1.39454	0.697271	+	0.716807i	$0.254397\pi$
$72$	1.00000	0.117851
$73$	−12.1032	−1.41657	−0.708287	−	0.705925i	$-0.750532\pi$
$73$	−12.1032	−1.41657	−0.708287	+	0.705925i	$0.750532\pi$
$74$	−2.24698	−0.261206
$75$	−1.00000	−0.115470
$76$	3.24698	0.372454
$77$	7.18598	0.818919
$78$	0	0
$79$	0.259061	0.0291467	0.0145733	−	0.999894i	$-0.495361\pi$
$79$	0.259061	0.0291467	0.0145733	+	0.999894i	$0.495361\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.6310	1.17400
$83$	3.02177	0.331682	0.165841	−	0.986152i	$-0.446966\pi$
$83$	3.02177	0.331682	0.165841	+	0.986152i	$0.446966\pi$
$84$	1.35690	0.148049
$85$	−2.04892	−0.222236
$86$	4.41789	0.476394
$87$	5.13706	0.550751
$88$	−5.29590	−0.564545
$89$	−5.47650	−0.580508	−0.290254	−	0.956950i	$-0.593740\pi$
$89$	−5.47650	−0.580508	−0.290254	+	0.956950i	$0.593740\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	1.33513	0.139196
$93$	−2.80194	−0.290547
$94$	4.82371	0.497527
$95$	3.24698	0.333133
$96$	−1.00000	−0.102062
$97$	−5.85086	−0.594064	−0.297032	−	0.954867i	$-0.595997\pi$
$97$	−5.85086	−0.594064	−0.297032	+	0.954867i	$0.595997\pi$
$98$	−5.15883	−0.521121
$99$	−5.29590	−0.532258
$100$	1.00000	0.100000
$101$	−8.39612	−0.835446	−0.417723	−	0.908575i	$-0.637172\pi$
$101$	−8.39612	−0.835446	−0.417723	+	0.908575i	$0.637172\pi$
$102$	2.04892	0.202873
$103$	13.6353	1.34353	0.671765	−	0.740765i	$-0.265537\pi$
$103$	13.6353	1.34353	0.671765	+	0.740765i	$0.265537\pi$
$104$	0	0
$105$	1.35690	0.132419
$106$	14.2349	1.38262
$107$	3.92394	0.379341	0.189671	−	0.981848i	$-0.439258\pi$
$107$	3.92394	0.379341	0.189671	+	0.981848i	$0.439258\pi$
$108$	−1.00000	−0.0962250
$109$	−0.554958	−0.0531553	−0.0265777	−	0.999647i	$-0.508461\pi$
$109$	−0.554958	−0.0531553	−0.0265777	+	0.999647i	$0.508461\pi$
$110$	−5.29590	−0.504944
$111$	2.24698	0.213274
$112$	−1.35690	−0.128215
$113$	4.39373	0.413328	0.206664	−	0.978412i	$-0.433739\pi$
$113$	4.39373	0.413328	0.206664	+	0.978412i	$0.433739\pi$
$114$	−3.24698	−0.304108
$115$	1.33513	0.124501
$116$	−5.13706	−0.476964
$117$	0	0
$118$	13.8998	1.27958
$119$	2.78017	0.254858
$120$	−1.00000	−0.0912871
$121$	17.0465	1.54968
$122$	−3.62565	−0.328251
$123$	−10.6310	−0.958567
$124$	2.80194	0.251621
$125$	1.00000	0.0894427
$126$	−1.35690	−0.120882
$127$	−2.23490	−0.198315	−0.0991576	−	0.995072i	$-0.531615\pi$
$127$	−2.23490	−0.198315	−0.0991576	+	0.995072i	$0.531615\pi$
$128$	1.00000	0.0883883
$129$	−4.41789	−0.388974
$130$	0	0
$131$	−8.51573	−0.744023	−0.372011	−	0.928228i	$-0.621332\pi$
$131$	−8.51573	−0.744023	−0.372011	+	0.928228i	$0.621332\pi$
$132$	5.29590	0.460949
$133$	−4.40581	−0.382032
$134$	9.03684	0.780664
$135$	−1.00000	−0.0860663
$136$	−2.04892	−0.175693
$137$	13.1685	1.12506	0.562531	−	0.826776i	$-0.309828\pi$
$137$	13.1685	1.12506	0.562531	+	0.826776i	$0.309828\pi$
$138$	−1.33513	−0.113653
$139$	7.17629	0.608685	0.304343	−	0.952563i	$-0.401563\pi$
$139$	7.17629	0.608685	0.304343	+	0.952563i	$0.401563\pi$
$140$	−1.35690	−0.114679
$141$	−4.82371	−0.406229
$142$	11.7506	0.986091
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.13706	−0.426610
$146$	−12.1032	−1.00167
$147$	5.15883	0.425493
$148$	−2.24698	−0.184701
$149$	−9.66248	−0.791581	−0.395791	−	0.918341i	$-0.629529\pi$
$149$	−9.66248	−0.791581	−0.395791	+	0.918341i	$0.629529\pi$
$150$	−1.00000	−0.0816497
$151$	7.35152	0.598258	0.299129	−	0.954213i	$-0.403304\pi$
$151$	7.35152	0.598258	0.299129	+	0.954213i	$0.403304\pi$
$152$	3.24698	0.263365
$153$	−2.04892	−0.165645
$154$	7.18598	0.579063
$155$	2.80194	0.225057
$156$	0	0
$157$	2.85325	0.227714	0.113857	−	0.993497i	$-0.463679\pi$
$157$	2.85325	0.227714	0.113857	+	0.993497i	$0.463679\pi$
$158$	0.259061	0.0206098
$159$	−14.2349	−1.12890
$160$	1.00000	0.0790569
$161$	−1.81163	−0.142776
$162$	1.00000	0.0785674
$163$	15.1075	1.18331	0.591656	−	0.806190i	$-0.298474\pi$
$163$	15.1075	1.18331	0.591656	+	0.806190i	$0.298474\pi$
$164$	10.6310	0.830143
$165$	5.29590	0.412285
$166$	3.02177	0.234535
$167$	16.0881	1.24494	0.622469	−	0.782644i	$-0.286130\pi$
$167$	16.0881	1.24494	0.622469	+	0.782644i	$0.286130\pi$
$168$	1.35690	0.104687
$169$	0	0
$170$	−2.04892	−0.157145
$171$	3.24698	0.248303
$172$	4.41789	0.336861
$173$	−15.4795	−1.17688	−0.588442	−	0.808540i	$-0.700258\pi$
$173$	−15.4795	−1.17688	−0.588442	+	0.808540i	$0.700258\pi$
$174$	5.13706	0.389440
$175$	−1.35690	−0.102572
$176$	−5.29590	−0.399193
$177$	−13.8998	−1.04477
$178$	−5.47650	−0.410481
$179$	19.0737	1.42563	0.712817	−	0.701351i	$-0.247419\pi$
$179$	19.0737	1.42563	0.712817	+	0.701351i	$0.247419\pi$
$180$	1.00000	0.0745356
$181$	2.16852	0.161185	0.0805925	−	0.996747i	$-0.474319\pi$
$181$	2.16852	0.161185	0.0805925	+	0.996747i	$0.474319\pi$
$182$	0	0
$183$	3.62565	0.268015
$184$	1.33513	0.0984268
$185$	−2.24698	−0.165201
$186$	−2.80194	−0.205448
$187$	10.8509	0.793493
$188$	4.82371	0.351805
$189$	1.35690	0.0986997
$190$	3.24698	0.235561
$191$	−11.7409	−0.849545	−0.424772	−	0.905300i	$-0.639646\pi$
$191$	−11.7409	−0.849545	−0.424772	+	0.905300i	$0.639646\pi$
$192$	−1.00000	−0.0721688
$193$	−24.6722	−1.77594	−0.887971	−	0.459900i	$-0.847885\pi$
$193$	−24.6722	−1.77594	−0.887971	+	0.459900i	$0.847885\pi$
$194$	−5.85086	−0.420067
$195$	0	0
$196$	−5.15883	−0.368488
$197$	26.2010	1.86675	0.933374	−	0.358906i	$-0.116850\pi$
$197$	26.2010	1.86675	0.933374	+	0.358906i	$0.116850\pi$
$198$	−5.29590	−0.376363
$199$	19.6722	1.39452	0.697262	−	0.716817i	$-0.254402\pi$
$199$	19.6722	1.39452	0.697262	+	0.716817i	$0.254402\pi$
$200$	1.00000	0.0707107
$201$	−9.03684	−0.637409
$202$	−8.39612	−0.590749
$203$	6.97046	0.489230
$204$	2.04892	0.143453
$205$	10.6310	0.742503
$206$	13.6353	0.950019
$207$	1.33513	0.0927976
$208$	0	0
$209$	−17.1957	−1.18945
$210$	1.35690	0.0936347
$211$	−16.2935	−1.12169	−0.560846	−	0.827920i	$-0.689524\pi$
$211$	−16.2935	−1.12169	−0.560846	+	0.827920i	$0.689524\pi$
$212$	14.2349	0.977657
$213$	−11.7506	−0.805140
$214$	3.92394	0.268235
$215$	4.41789	0.301298
$216$	−1.00000	−0.0680414
$217$	−3.80194	−0.258092
$218$	−0.554958	−0.0375865
$219$	12.1032	0.817859
$220$	−5.29590	−0.357049
$221$	0	0
$222$	2.24698	0.150807
$223$	−2.28083	−0.152736	−0.0763679	−	0.997080i	$-0.524332\pi$
$223$	−2.28083	−0.152736	−0.0763679	+	0.997080i	$0.524332\pi$
$224$	−1.35690	−0.0906614
$225$	1.00000	0.0666667
$226$	4.39373	0.292267
$227$	−3.37196	−0.223805	−0.111902	−	0.993719i	$-0.535694\pi$
$227$	−3.37196	−0.223805	−0.111902	+	0.993719i	$0.535694\pi$
$228$	−3.24698	−0.215036
$229$	18.3763	1.21434	0.607169	−	0.794573i	$-0.292305\pi$
$229$	18.3763	1.21434	0.607169	+	0.794573i	$0.292305\pi$
$230$	1.33513	0.0880356
$231$	−7.18598	−0.472803
$232$	−5.13706	−0.337265
$233$	10.0858	0.660740	0.330370	−	0.943852i	$-0.392827\pi$
$233$	10.0858	0.660740	0.330370	+	0.943852i	$0.392827\pi$
$234$	0	0
$235$	4.82371	0.314664
$236$	13.8998	0.904798
$237$	−0.259061	−0.0168278
$238$	2.78017	0.180211
$239$	−20.0834	−1.29908	−0.649542	−	0.760325i	$-0.725039\pi$
$239$	−20.0834	−1.29908	−0.649542	+	0.760325i	$0.725039\pi$
$240$	−1.00000	−0.0645497
$241$	2.99462	0.192901	0.0964503	−	0.995338i	$-0.469251\pi$
$241$	2.99462	0.192901	0.0964503	+	0.995338i	$0.469251\pi$
$242$	17.0465	1.09579
$243$	−1.00000	−0.0641500
$244$	−3.62565	−0.232108
$245$	−5.15883	−0.329586
$246$	−10.6310	−0.677809
$247$	0	0
$248$	2.80194	0.177923
$249$	−3.02177	−0.191497
$250$	1.00000	0.0632456
$251$	−7.20237	−0.454610	−0.227305	−	0.973824i	$-0.572991\pi$
$251$	−7.20237	−0.454610	−0.227305	+	0.973824i	$0.572991\pi$
$252$	−1.35690	−0.0854764
$253$	−7.07069	−0.444530
$254$	−2.23490	−0.140230
$255$	2.04892	0.128308
$256$	1.00000	0.0625000
$257$	−18.8291	−1.17453	−0.587263	−	0.809396i	$-0.699795\pi$
$257$	−18.8291	−1.17453	−0.587263	+	0.809396i	$0.699795\pi$
$258$	−4.41789	−0.275046
$259$	3.04892	0.189451
$260$	0	0
$261$	−5.13706	−0.317976
$262$	−8.51573	−0.526104
$263$	−17.9245	−1.10527	−0.552637	−	0.833422i	$-0.686378\pi$
$263$	−17.9245	−1.10527	−0.552637	+	0.833422i	$0.686378\pi$
$264$	5.29590	0.325940
$265$	14.2349	0.874443
$266$	−4.40581	−0.270138
$267$	5.47650	0.335156
$268$	9.03684	0.552013
$269$	−22.4045	−1.36603	−0.683013	−	0.730406i	$-0.739331\pi$
$269$	−22.4045	−1.36603	−0.683013	+	0.730406i	$0.739331\pi$
$270$	−1.00000	−0.0608581
$271$	−23.2325	−1.41127	−0.705637	−	0.708573i	$-0.749339\pi$
$271$	−23.2325	−1.41127	−0.705637	+	0.708573i	$0.749339\pi$
$272$	−2.04892	−0.124234
$273$	0	0
$274$	13.1685	0.795540
$275$	−5.29590	−0.319355
$276$	−1.33513	−0.0803651
$277$	−9.78448	−0.587892	−0.293946	−	0.955822i	$-0.594969\pi$
$277$	−9.78448	−0.587892	−0.293946	+	0.955822i	$0.594969\pi$
$278$	7.17629	0.430405
$279$	2.80194	0.167748
$280$	−1.35690	−0.0810900
$281$	21.6286	1.29026	0.645128	−	0.764075i	$-0.276804\pi$
$281$	21.6286	1.29026	0.645128	+	0.764075i	$0.276804\pi$
$282$	−4.82371	−0.287248
$283$	3.38942	0.201480	0.100740	−	0.994913i	$-0.467879\pi$
$283$	3.38942	0.201480	0.100740	+	0.994913i	$0.467879\pi$
$284$	11.7506	0.697271
$285$	−3.24698	−0.192334
$286$	0	0
$287$	−14.4252	−0.851492
$288$	1.00000	0.0589256
$289$	−12.8019	−0.753055
$290$	−5.13706	−0.301659
$291$	5.85086	0.342983
$292$	−12.1032	−0.708287
$293$	34.1280	1.99378	0.996889	−	0.0788243i	$-0.0251166\pi$
$293$	34.1280	1.99378	0.996889	+	0.0788243i	$0.0251166\pi$
$294$	5.15883	0.300869
$295$	13.8998	0.809276
$296$	−2.24698	−0.130603
$297$	5.29590	0.307299
$298$	−9.66248	−0.559733
$299$	0	0
$300$	−1.00000	−0.0577350
$301$	−5.99462	−0.345524
$302$	7.35152	0.423032
$303$	8.39612	0.482345
$304$	3.24698	0.186227
$305$	−3.62565	−0.207604
$306$	−2.04892	−0.117129
$307$	−15.6601	−0.893768	−0.446884	−	0.894592i	$-0.647466\pi$
$307$	−15.6601	−0.893768	−0.446884	+	0.894592i	$0.647466\pi$
$308$	7.18598	0.409459
$309$	−13.6353	−0.775687
$310$	2.80194	0.159139
$311$	25.7972	1.46282	0.731411	−	0.681937i	$-0.238862\pi$
$311$	25.7972	1.46282	0.731411	+	0.681937i	$0.238862\pi$
$312$	0	0
$313$	−15.6243	−0.883139	−0.441569	−	0.897227i	$-0.645578\pi$
$313$	−15.6243	−0.883139	−0.441569	+	0.897227i	$0.645578\pi$
$314$	2.85325	0.161018
$315$	−1.35690	−0.0764524
$316$	0.259061	0.0145733
$317$	−9.25965	−0.520074	−0.260037	−	0.965599i	$-0.583735\pi$
$317$	−9.25965	−0.520074	−0.260037	+	0.965599i	$0.583735\pi$
$318$	−14.2349	−0.798253
$319$	27.2054	1.52321
$320$	1.00000	0.0559017
$321$	−3.92394	−0.219013
$322$	−1.81163	−0.100958
$323$	−6.65279	−0.370171
$324$	1.00000	0.0555556
$325$	0	0
$326$	15.1075	0.836728
$327$	0.554958	0.0306893
$328$	10.6310	0.587000
$329$	−6.54527	−0.360852
$330$	5.29590	0.291530
$331$	21.8582	1.20143	0.600716	−	0.799462i	$-0.294882\pi$
$331$	21.8582	1.20143	0.600716	+	0.799462i	$0.294882\pi$
$332$	3.02177	0.165841
$333$	−2.24698	−0.123134
$334$	16.0881	0.880304
$335$	9.03684	0.493735
$336$	1.35690	0.0740247
$337$	14.5013	0.789934	0.394967	−	0.918695i	$-0.370756\pi$
$337$	14.5013	0.789934	0.394967	+	0.918695i	$0.370756\pi$
$338$	0	0
$339$	−4.39373	−0.238635
$340$	−2.04892	−0.111118
$341$	−14.8388	−0.803565
$342$	3.24698	0.175577
$343$	16.4983	0.890823
$344$	4.41789	0.238197
$345$	−1.33513	−0.0718807
$346$	−15.4795	−0.832182
$347$	7.84117	0.420936	0.210468	−	0.977601i	$-0.432501\pi$
$347$	7.84117	0.420936	0.210468	+	0.977601i	$0.432501\pi$
$348$	5.13706	0.275375
$349$	20.4252	1.09334	0.546668	−	0.837350i	$-0.315896\pi$
$349$	20.4252	1.09334	0.546668	+	0.837350i	$0.315896\pi$
$350$	−1.35690	−0.0725291
$351$	0	0
$352$	−5.29590	−0.282272
$353$	13.2905	0.707383	0.353692	−	0.935362i	$-0.384926\pi$
$353$	13.2905	0.707383	0.353692	+	0.935362i	$0.384926\pi$
$354$	−13.8998	−0.738765
$355$	11.7506	0.623659
$356$	−5.47650	−0.290254
$357$	−2.78017	−0.147142
$358$	19.0737	1.00807
$359$	−12.8267	−0.676967	−0.338483	−	0.940972i	$-0.609914\pi$
$359$	−12.8267	−0.676967	−0.338483	+	0.940972i	$0.609914\pi$
$360$	1.00000	0.0527046
$361$	−8.45712	−0.445112
$362$	2.16852	0.113975
$363$	−17.0465	−0.894710
$364$	0	0
$365$	−12.1032	−0.633511
$366$	3.62565	0.189516
$367$	−17.9554	−0.937264	−0.468632	−	0.883393i	$-0.655253\pi$
$367$	−17.9554	−0.937264	−0.468632	+	0.883393i	$0.655253\pi$
$368$	1.33513	0.0695982
$369$	10.6310	0.553429
$370$	−2.24698	−0.116815
$371$	−19.3153	−1.00280
$372$	−2.80194	−0.145274
$373$	27.8732	1.44322	0.721610	−	0.692300i	$-0.243402\pi$
$373$	27.8732	1.44322	0.721610	+	0.692300i	$0.243402\pi$
$374$	10.8509	0.561084
$375$	−1.00000	−0.0516398
$376$	4.82371	0.248764
$377$	0	0
$378$	1.35690	0.0697912
$379$	−13.8702	−0.712466	−0.356233	−	0.934397i	$-0.615939\pi$
$379$	−13.8702	−0.712466	−0.356233	+	0.934397i	$0.615939\pi$
$380$	3.24698	0.166567
$381$	2.23490	0.114497
$382$	−11.7409	−0.600719
$383$	26.8984	1.37445	0.687223	−	0.726446i	$-0.258829\pi$
$383$	26.8984	1.37445	0.687223	+	0.726446i	$0.258829\pi$
$384$	−1.00000	−0.0510310
$385$	7.18598	0.366231
$386$	−24.6722	−1.25578
$387$	4.41789	0.224574
$388$	−5.85086	−0.297032
$389$	−0.187309	−0.00949693	−0.00474846	−	0.999989i	$-0.501511\pi$
$389$	−0.187309	−0.00949693	−0.00474846	+	0.999989i	$0.501511\pi$
$390$	0	0
$391$	−2.73556	−0.138343
$392$	−5.15883	−0.260560
$393$	8.51573	0.429562
$394$	26.2010	1.31999
$395$	0.259061	0.0130348
$396$	−5.29590	−0.266129
$397$	8.58211	0.430724	0.215362	−	0.976534i	$-0.430907\pi$
$397$	8.58211	0.430724	0.215362	+	0.976534i	$0.430907\pi$
$398$	19.6722	0.986077
$399$	4.40581	0.220567
$400$	1.00000	0.0500000
$401$	23.9748	1.19724	0.598621	−	0.801032i	$-0.295715\pi$
$401$	23.9748	1.19724	0.598621	+	0.801032i	$0.295715\pi$
$402$	−9.03684	−0.450716
$403$	0	0
$404$	−8.39612	−0.417723
$405$	1.00000	0.0496904
$406$	6.97046	0.345938
$407$	11.8998	0.589850
$408$	2.04892	0.101437
$409$	−8.37926	−0.414328	−0.207164	−	0.978306i	$-0.566423\pi$
$409$	−8.37926	−0.414328	−0.207164	+	0.978306i	$0.566423\pi$
$410$	10.6310	0.525029
$411$	−13.1685	−0.649555
$412$	13.6353	0.671765
$413$	−18.8605	−0.928067
$414$	1.33513	0.0656178
$415$	3.02177	0.148333
$416$	0	0
$417$	−7.17629	−0.351425
$418$	−17.1957	−0.841068
$419$	37.0887	1.81190	0.905952	−	0.423381i	$-0.139157\pi$
$419$	37.0887	1.81190	0.905952	+	0.423381i	$0.139157\pi$
$420$	1.35690	0.0662097
$421$	4.90515	0.239062	0.119531	−	0.992830i	$-0.461861\pi$
$421$	4.90515	0.239062	0.119531	+	0.992830i	$0.461861\pi$
$422$	−16.2935	−0.793155
$423$	4.82371	0.234537
$424$	14.2349	0.691308
$425$	−2.04892	−0.0993871
$426$	−11.7506	−0.569320
$427$	4.91962	0.238077
$428$	3.92394	0.189671
$429$	0	0
$430$	4.41789	0.213050
$431$	−6.06531	−0.292156	−0.146078	−	0.989273i	$-0.546665\pi$
$431$	−6.06531	−0.292156	−0.146078	+	0.989273i	$0.546665\pi$
$432$	−1.00000	−0.0481125
$433$	−14.8877	−0.715457	−0.357728	−	0.933826i	$-0.616449\pi$
$433$	−14.8877	−0.715457	−0.357728	+	0.933826i	$0.616449\pi$
$434$	−3.80194	−0.182499
$435$	5.13706	0.246303
$436$	−0.554958	−0.0265777
$437$	4.33513	0.207377
$438$	12.1032	0.578314
$439$	−21.1336	−1.00865	−0.504326	−	0.863513i	$-0.668259\pi$
$439$	−21.1336	−1.00865	−0.504326	+	0.863513i	$0.668259\pi$
$440$	−5.29590	−0.252472
$441$	−5.15883	−0.245659
$442$	0	0
$443$	28.0683	1.33356	0.666782	−	0.745252i	$-0.267671\pi$
$443$	28.0683	1.33356	0.666782	+	0.745252i	$0.267671\pi$
$444$	2.24698	0.106637
$445$	−5.47650	−0.259611
$446$	−2.28083	−0.108000
$447$	9.66248	0.457020
$448$	−1.35690	−0.0641073
$449$	19.2446	0.908208	0.454104	−	0.890949i	$-0.349959\pi$
$449$	19.2446	0.908208	0.454104	+	0.890949i	$0.349959\pi$
$450$	1.00000	0.0471405
$451$	−56.3008	−2.65110
$452$	4.39373	0.206664
$453$	−7.35152	−0.345404
$454$	−3.37196	−0.158254
$455$	0	0
$456$	−3.24698	−0.152054
$457$	−37.8485	−1.77048	−0.885238	−	0.465138i	$-0.846005\pi$
$457$	−37.8485	−1.77048	−0.885238	+	0.465138i	$0.846005\pi$
$458$	18.3763	0.858667
$459$	2.04892	0.0956353
$460$	1.33513	0.0622506
$461$	−11.2228	−0.522699	−0.261349	−	0.965244i	$-0.584167\pi$
$461$	−11.2228	−0.522699	−0.261349	+	0.965244i	$0.584167\pi$
$462$	−7.18598	−0.334322
$463$	25.0726	1.16522	0.582611	−	0.812751i	$-0.302031\pi$
$463$	25.0726	1.16522	0.582611	+	0.812751i	$0.302031\pi$
$464$	−5.13706	−0.238482
$465$	−2.80194	−0.129937
$466$	10.0858	0.467213
$467$	36.9657	1.71057	0.855284	−	0.518160i	$-0.173383\pi$
$467$	36.9657	1.71057	0.855284	+	0.518160i	$0.173383\pi$
$468$	0	0
$469$	−12.2620	−0.566209
$470$	4.82371	0.222501
$471$	−2.85325	−0.131471
$472$	13.8998	0.639789
$473$	−23.3967	−1.07578
$474$	−0.259061	−0.0118991
$475$	3.24698	0.148982
$476$	2.78017	0.127429
$477$	14.2349	0.651771
$478$	−20.0834	−0.918592
$479$	31.4590	1.43740	0.718700	−	0.695320i	$-0.244737\pi$
$479$	31.4590	1.43740	0.718700	+	0.695320i	$0.244737\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	2.99462	0.136401
$483$	1.81163	0.0824319
$484$	17.0465	0.774842
$485$	−5.85086	−0.265674
$486$	−1.00000	−0.0453609
$487$	18.8713	0.855140	0.427570	−	0.903982i	$-0.359370\pi$
$487$	18.8713	0.855140	0.427570	+	0.903982i	$0.359370\pi$
$488$	−3.62565	−0.164125
$489$	−15.1075	−0.683186
$490$	−5.15883	−0.233052
$491$	−16.3961	−0.739947	−0.369973	−	0.929042i	$-0.620633\pi$
$491$	−16.3961	−0.739947	−0.369973	+	0.929042i	$0.620633\pi$
$492$	−10.6310	−0.479284
$493$	10.5254	0.474041
$494$	0	0
$495$	−5.29590	−0.238033
$496$	2.80194	0.125811
$497$	−15.9444	−0.715203
$498$	−3.02177	−0.135409
$499$	40.2452	1.80162	0.900811	−	0.434212i	$-0.142973\pi$
$499$	40.2452	1.80162	0.900811	+	0.434212i	$0.142973\pi$
$500$	1.00000	0.0447214
$501$	−16.0881	−0.718765
$502$	−7.20237	−0.321458
$503$	18.4004	0.820435	0.410217	−	0.911988i	$-0.365453\pi$
$503$	18.4004	0.820435	0.410217	+	0.911988i	$0.365453\pi$
$504$	−1.35690	−0.0604409
$505$	−8.39612	−0.373623
$506$	−7.07069	−0.314330
$507$	0	0
$508$	−2.23490	−0.0991576
$509$	−35.1377	−1.55745	−0.778725	−	0.627366i	$-0.784133\pi$
$509$	−35.1377	−1.55745	−0.778725	+	0.627366i	$0.784133\pi$
$510$	2.04892	0.0907276
$511$	16.4228	0.726502
$512$	1.00000	0.0441942
$513$	−3.24698	−0.143358
$514$	−18.8291	−0.830515
$515$	13.6353	0.600845
$516$	−4.41789	−0.194487
$517$	−25.5459	−1.12351
$518$	3.04892	0.133962
$519$	15.4795	0.679474
$520$	0	0
$521$	−35.2610	−1.54481	−0.772406	−	0.635129i	$-0.780947\pi$
$521$	−35.2610	−1.54481	−0.772406	+	0.635129i	$0.780947\pi$
$522$	−5.13706	−0.224843
$523$	14.3043	0.625482	0.312741	−	0.949839i	$-0.398753\pi$
$523$	14.3043	0.625482	0.312741	+	0.949839i	$0.398753\pi$
$524$	−8.51573	−0.372011
$525$	1.35690	0.0592198
$526$	−17.9245	−0.781546
$527$	−5.74094	−0.250079
$528$	5.29590	0.230474
$529$	−21.2174	−0.922497
$530$	14.2349	0.618324
$531$	13.8998	0.603199
$532$	−4.40581	−0.191016
$533$	0	0
$534$	5.47650	0.236991
$535$	3.92394	0.169647
$536$	9.03684	0.390332
$537$	−19.0737	−0.823090
$538$	−22.4045	−0.965926
$539$	27.3207	1.17678
$540$	−1.00000	−0.0430331
$541$	−44.2422	−1.90212	−0.951060	−	0.309006i	$-0.900004\pi$
$541$	−44.2422	−1.90212	−0.951060	+	0.309006i	$0.900004\pi$
$542$	−23.2325	−0.997922
$543$	−2.16852	−0.0930602
$544$	−2.04892	−0.0878466
$545$	−0.554958	−0.0237718
$546$	0	0
$547$	6.34481	0.271285	0.135642	−	0.990758i	$-0.456690\pi$
$547$	6.34481	0.271285	0.135642	+	0.990758i	$0.456690\pi$
$548$	13.1685	0.562531
$549$	−3.62565	−0.154739
$550$	−5.29590	−0.225818
$551$	−16.6799	−0.710589
$552$	−1.33513	−0.0568267
$553$	−0.351519	−0.0149481
$554$	−9.78448	−0.415703
$555$	2.24698	0.0953790
$556$	7.17629	0.304343
$557$	31.3884	1.32997	0.664984	−	0.746858i	$-0.268438\pi$
$557$	31.3884	1.32997	0.664984	+	0.746858i	$0.268438\pi$
$558$	2.80194	0.118615
$559$	0	0
$560$	−1.35690	−0.0573393
$561$	−10.8509	−0.458123
$562$	21.6286	0.912349
$563$	−44.4989	−1.87540	−0.937702	−	0.347441i	$-0.887051\pi$
$563$	−44.4989	−1.87540	−0.937702	+	0.347441i	$0.887051\pi$
$564$	−4.82371	−0.203115
$565$	4.39373	0.184846
$566$	3.38942	0.142468
$567$	−1.35690	−0.0569843
$568$	11.7506	0.493045
$569$	30.5394	1.28028	0.640140	−	0.768259i	$-0.278877\pi$
$569$	30.5394	1.28028	0.640140	+	0.768259i	$0.278877\pi$
$570$	−3.24698	−0.136001
$571$	−32.7614	−1.37102	−0.685511	−	0.728063i	$-0.740421\pi$
$571$	−32.7614	−1.37102	−0.685511	+	0.728063i	$0.740421\pi$
$572$	0	0
$573$	11.7409	0.490485
$574$	−14.4252	−0.602096
$575$	1.33513	0.0556786
$576$	1.00000	0.0416667
$577$	36.5870	1.52314	0.761569	−	0.648084i	$-0.224430\pi$
$577$	36.5870	1.52314	0.761569	+	0.648084i	$0.224430\pi$
$578$	−12.8019	−0.532490
$579$	24.6722	1.02534
$580$	−5.13706	−0.213305
$581$	−4.10023	−0.170106
$582$	5.85086	0.242526
$583$	−75.3866	−3.12219
$584$	−12.1032	−0.500834
$585$	0	0
$586$	34.1280	1.40981
$587$	22.4873	0.928148	0.464074	−	0.885796i	$-0.346387\pi$
$587$	22.4873	0.928148	0.464074	+	0.885796i	$0.346387\pi$
$588$	5.15883	0.212747
$589$	9.09783	0.374870
$590$	13.8998	0.572245
$591$	−26.2010	−1.07777
$592$	−2.24698	−0.0923503
$593$	39.5749	1.62515	0.812574	−	0.582858i	$-0.198066\pi$
$593$	39.5749	1.62515	0.812574	+	0.582858i	$0.198066\pi$
$594$	5.29590	0.217293
$595$	2.78017	0.113976
$596$	−9.66248	−0.395791
$597$	−19.6722	−0.805128
$598$	0	0
$599$	−31.3424	−1.28062	−0.640308	−	0.768118i	$-0.721193\pi$
$599$	−31.3424	−1.28062	−0.640308	+	0.768118i	$0.721193\pi$
$600$	−1.00000	−0.0408248
$601$	−32.9487	−1.34401	−0.672003	−	0.740549i	$-0.734566\pi$
$601$	−32.9487	−1.34401	−0.672003	+	0.740549i	$0.734566\pi$
$602$	−5.99462	−0.244323
$603$	9.03684	0.368008
$604$	7.35152	0.299129
$605$	17.0465	0.693040
$606$	8.39612	0.341069
$607$	−40.1739	−1.63061	−0.815304	−	0.579033i	$-0.803430\pi$
$607$	−40.1739	−1.63061	−0.815304	+	0.579033i	$0.803430\pi$
$608$	3.24698	0.131682
$609$	−6.97046	−0.282457
$610$	−3.62565	−0.146798
$611$	0	0
$612$	−2.04892	−0.0828226
$613$	11.3588	0.458778	0.229389	−	0.973335i	$-0.426327\pi$
$613$	11.3588	0.458778	0.229389	+	0.973335i	$0.426327\pi$
$614$	−15.6601	−0.631990
$615$	−10.6310	−0.428684
$616$	7.18598	0.289531
$617$	20.9172	0.842096	0.421048	−	0.907038i	$-0.361662\pi$
$617$	20.9172	0.842096	0.421048	+	0.907038i	$0.361662\pi$
$618$	−13.6353	−0.548494
$619$	−14.0562	−0.564967	−0.282483	−	0.959272i	$-0.591158\pi$
$619$	−14.0562	−0.564967	−0.282483	+	0.959272i	$0.591158\pi$
$620$	2.80194	0.112529
$621$	−1.33513	−0.0535767
$622$	25.7972	1.03437
$623$	7.43104	0.297718
$624$	0	0
$625$	1.00000	0.0400000
$626$	−15.6243	−0.624473
$627$	17.1957	0.686729
$628$	2.85325	0.113857
$629$	4.60388	0.183569
$630$	−1.35690	−0.0540600
$631$	−40.6601	−1.61865	−0.809326	−	0.587359i	$-0.800168\pi$
$631$	−40.6601	−1.61865	−0.809326	+	0.587359i	$0.800168\pi$
$632$	0.259061	0.0103049
$633$	16.2935	0.647609
$634$	−9.25965	−0.367748
$635$	−2.23490	−0.0886892
$636$	−14.2349	−0.564450
$637$	0	0
$638$	27.2054	1.07707
$639$	11.7506	0.464848
$640$	1.00000	0.0395285
$641$	−1.92633	−0.0760854	−0.0380427	−	0.999276i	$-0.512112\pi$
$641$	−1.92633	−0.0760854	−0.0380427	+	0.999276i	$0.512112\pi$
$642$	−3.92394	−0.154865
$643$	3.37973	0.133284	0.0666418	−	0.997777i	$-0.478772\pi$
$643$	3.37973	0.133284	0.0666418	+	0.997777i	$0.478772\pi$
$644$	−1.81163	−0.0713881
$645$	−4.41789	−0.173954
$646$	−6.65279	−0.261751
$647$	−10.8181	−0.425302	−0.212651	−	0.977128i	$-0.568210\pi$
$647$	−10.8181	−0.425302	−0.212651	+	0.977128i	$0.568210\pi$
$648$	1.00000	0.0392837
$649$	−73.6118	−2.88951
$650$	0	0
$651$	3.80194	0.149010
$652$	15.1075	0.591656
$653$	33.7646	1.32131	0.660656	−	0.750689i	$-0.270278\pi$
$653$	33.7646	1.32131	0.660656	+	0.750689i	$0.270278\pi$
$654$	0.554958	0.0217006
$655$	−8.51573	−0.332737
$656$	10.6310	0.415072
$657$	−12.1032	−0.472191
$658$	−6.54527	−0.255161
$659$	−16.8592	−0.656742	−0.328371	−	0.944549i	$-0.606500\pi$
$659$	−16.8592	−0.656742	−0.328371	+	0.944549i	$0.606500\pi$
$660$	5.29590	0.206143
$661$	−4.71140	−0.183252	−0.0916261	−	0.995793i	$-0.529206\pi$
$661$	−4.71140	−0.183252	−0.0916261	+	0.995793i	$0.529206\pi$
$662$	21.8582	0.849541
$663$	0	0
$664$	3.02177	0.117267
$665$	−4.40581	−0.170850
$666$	−2.24698	−0.0870687
$667$	−6.85862	−0.265567
$668$	16.0881	0.622469
$669$	2.28083	0.0881820
$670$	9.03684	0.349123
$671$	19.2010	0.741248
$672$	1.35690	0.0523434
$673$	3.12797	0.120574	0.0602871	−	0.998181i	$-0.480798\pi$
$673$	3.12797	0.120574	0.0602871	+	0.998181i	$0.480798\pi$
$674$	14.5013	0.558567
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−1.50737	−0.0579329	−0.0289664	−	0.999580i	$-0.509222\pi$
$677$	−1.50737	−0.0579329	−0.0289664	+	0.999580i	$0.509222\pi$
$678$	−4.39373	−0.168740
$679$	7.93900	0.304671
$680$	−2.04892	−0.0785724
$681$	3.37196	0.129214
$682$	−14.8388	−0.568206
$683$	−31.0726	−1.18896	−0.594480	−	0.804110i	$-0.702642\pi$
$683$	−31.0726	−1.18896	−0.594480	+	0.804110i	$0.702642\pi$
$684$	3.24698	0.124151
$685$	13.1685	0.503143
$686$	16.4983	0.629907
$687$	−18.3763	−0.701099
$688$	4.41789	0.168431
$689$	0	0
$690$	−1.33513	−0.0508274
$691$	26.7469	1.01750	0.508750	−	0.860914i	$-0.330108\pi$
$691$	26.7469	1.01750	0.508750	+	0.860914i	$0.330108\pi$
$692$	−15.4795	−0.588442
$693$	7.18598	0.272973
$694$	7.84117	0.297647
$695$	7.17629	0.272212
$696$	5.13706	0.194720
$697$	−21.7821	−0.825055
$698$	20.4252	0.773105
$699$	−10.0858	−0.381478
$700$	−1.35690	−0.0512858
$701$	11.2054	0.423221	0.211610	−	0.977354i	$-0.432129\pi$
$701$	11.2054	0.423221	0.211610	+	0.977354i	$0.432129\pi$
$702$	0	0
$703$	−7.29590	−0.275170
$704$	−5.29590	−0.199597
$705$	−4.82371	−0.181671
$706$	13.2905	0.500195
$707$	11.3927	0.428465
$708$	−13.8998	−0.522385
$709$	−26.9933	−1.01375	−0.506877	−	0.862018i	$-0.669200\pi$
$709$	−26.9933	−1.01375	−0.506877	+	0.862018i	$0.669200\pi$
$710$	11.7506	0.440993
$711$	0.259061	0.00971555
$712$	−5.47650	−0.205241
$713$	3.74094	0.140099
$714$	−2.78017	−0.104045
$715$	0	0
$716$	19.0737	0.712817
$717$	20.0834	0.750027
$718$	−12.8267	−0.478688
$719$	−15.4601	−0.576565	−0.288282	−	0.957545i	$-0.593084\pi$
$719$	−15.4601	−0.576565	−0.288282	+	0.957545i	$0.593084\pi$
$720$	1.00000	0.0372678
$721$	−18.5017	−0.689040
$722$	−8.45712	−0.314742
$723$	−2.99462	−0.111371
$724$	2.16852	0.0805925
$725$	−5.13706	−0.190786
$726$	−17.0465	−0.632656
$727$	−10.9148	−0.404809	−0.202404	−	0.979302i	$-0.564876\pi$
$727$	−10.9148	−0.404809	−0.202404	+	0.979302i	$0.564876\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−12.1032	−0.447960
$731$	−9.05190	−0.334797
$732$	3.62565	0.134008
$733$	13.5539	0.500624	0.250312	−	0.968165i	$-0.419467\pi$
$733$	13.5539	0.500624	0.250312	+	0.968165i	$0.419467\pi$
$734$	−17.9554	−0.662746
$735$	5.15883	0.190286
$736$	1.33513	0.0492134
$737$	−47.8582	−1.76288
$738$	10.6310	0.391333
$739$	−15.4679	−0.568995	−0.284498	−	0.958677i	$-0.591827\pi$
$739$	−15.4679	−0.568995	−0.284498	+	0.958677i	$0.591827\pi$
$740$	−2.24698	−0.0826006
$741$	0	0
$742$	−19.3153	−0.709086
$743$	−40.2040	−1.47494	−0.737471	−	0.675378i	$-0.763980\pi$
$743$	−40.2040	−1.47494	−0.737471	+	0.675378i	$0.763980\pi$
$744$	−2.80194	−0.102724
$745$	−9.66248	−0.354006
$746$	27.8732	1.02051
$747$	3.02177	0.110561
$748$	10.8509	0.396747
$749$	−5.32437	−0.194548
$750$	−1.00000	−0.0365148
$751$	−19.8465	−0.724211	−0.362105	−	0.932137i	$-0.617942\pi$
$751$	−19.8465	−0.724211	−0.362105	+	0.932137i	$0.617942\pi$
$752$	4.82371	0.175903
$753$	7.20237	0.262469
$754$	0	0
$755$	7.35152	0.267549
$756$	1.35690	0.0493498
$757$	39.8883	1.44976	0.724882	−	0.688873i	$-0.241894\pi$
$757$	39.8883	1.44976	0.724882	+	0.688873i	$0.241894\pi$
$758$	−13.8702	−0.503790
$759$	7.07069	0.256650
$760$	3.24698	0.117780
$761$	−31.8756	−1.15549	−0.577745	−	0.816217i	$-0.696067\pi$
$761$	−31.8756	−1.15549	−0.577745	+	0.816217i	$0.696067\pi$
$762$	2.23490	0.0809618
$763$	0.753020	0.0272612
$764$	−11.7409	−0.424772
$765$	−2.04892	−0.0740788
$766$	26.8984	0.971880
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	43.0672	1.55304	0.776522	−	0.630090i	$-0.216982\pi$
$769$	43.0672	1.55304	0.776522	+	0.630090i	$0.216982\pi$
$770$	7.18598	0.258965
$771$	18.8291	0.678113
$772$	−24.6722	−0.887971
$773$	−33.1282	−1.19154	−0.595770	−	0.803155i	$-0.703153\pi$
$773$	−33.1282	−1.19154	−0.595770	+	0.803155i	$0.703153\pi$
$774$	4.41789	0.158798
$775$	2.80194	0.100649
$776$	−5.85086	−0.210033
$777$	−3.04892	−0.109379
$778$	−0.187309	−0.00671534
$779$	34.5187	1.23676
$780$	0	0
$781$	−62.2301	−2.22677
$782$	−2.73556	−0.0978235
$783$	5.13706	0.183584
$784$	−5.15883	−0.184244
$785$	2.85325	0.101837
$786$	8.51573	0.303746
$787$	−35.9138	−1.28019	−0.640094	−	0.768297i	$-0.721105\pi$
$787$	−35.9138	−1.28019	−0.640094	+	0.768297i	$0.721105\pi$
$788$	26.2010	0.933374
$789$	17.9245	0.638130
$790$	0.259061	0.00921698
$791$	−5.96184	−0.211978
$792$	−5.29590	−0.188182
$793$	0	0
$794$	8.58211	0.304568
$795$	−14.2349	−0.504860
$796$	19.6722	0.697262
$797$	−29.7918	−1.05528	−0.527639	−	0.849468i	$-0.676923\pi$
$797$	−29.7918	−1.05528	−0.527639	+	0.849468i	$0.676923\pi$
$798$	4.40581	0.155964
$799$	−9.88338	−0.349649
$800$	1.00000	0.0353553
$801$	−5.47650	−0.193503
$802$	23.9748	0.846579
$803$	64.0974	2.26195
$804$	−9.03684	−0.318705
$805$	−1.81163	−0.0638514
$806$	0	0
$807$	22.4045	0.788675
$808$	−8.39612	−0.295375
$809$	1.52648	0.0536683	0.0268341	−	0.999640i	$-0.491457\pi$
$809$	1.52648	0.0536683	0.0268341	+	0.999640i	$0.491457\pi$
$810$	1.00000	0.0351364
$811$	−51.6039	−1.81206	−0.906029	−	0.423217i	$-0.860901\pi$
$811$	−51.6039	−1.81206	−0.906029	+	0.423217i	$0.860901\pi$
$812$	6.97046	0.244615
$813$	23.2325	0.814800
$814$	11.8998	0.417087
$815$	15.1075	0.529193
$816$	2.04892	0.0717265
$817$	14.3448	0.501862
$818$	−8.37926	−0.292974
$819$	0	0
$820$	10.6310	0.371251
$821$	17.4795	0.610038	0.305019	−	0.952346i	$-0.401337\pi$
$821$	17.4795	0.610038	0.305019	+	0.952346i	$0.401337\pi$
$822$	−13.1685	−0.459305
$823$	−25.5566	−0.890848	−0.445424	−	0.895320i	$-0.646947\pi$
$823$	−25.5566	−0.890848	−0.445424	+	0.895320i	$0.646947\pi$
$824$	13.6353	0.475009
$825$	5.29590	0.184379
$826$	−18.8605	−0.656242
$827$	−9.16182	−0.318588	−0.159294	−	0.987231i	$-0.550922\pi$
$827$	−9.16182	−0.318588	−0.159294	+	0.987231i	$0.550922\pi$
$828$	1.33513	0.0463988
$829$	48.6493	1.68966	0.844831	−	0.535034i	$-0.179701\pi$
$829$	48.6493	1.68966	0.844831	+	0.535034i	$0.179701\pi$
$830$	3.02177	0.104887
$831$	9.78448	0.339420
$832$	0	0
$833$	10.5700	0.366230
$834$	−7.17629	−0.248495
$835$	16.0881	0.556753
$836$	−17.1957	−0.594725
$837$	−2.80194	−0.0968491
$838$	37.0887	1.28121
$839$	−8.71246	−0.300788	−0.150394	−	0.988626i	$-0.548054\pi$
$839$	−8.71246	−0.300788	−0.150394	+	0.988626i	$0.548054\pi$
$840$	1.35690	0.0468174
$841$	−2.61058	−0.0900200
$842$	4.90515	0.169043
$843$	−21.6286	−0.744930
$844$	−16.2935	−0.560846
$845$	0	0
$846$	4.82371	0.165842
$847$	−23.1304	−0.794769
$848$	14.2349	0.488828
$849$	−3.38942	−0.116325
$850$	−2.04892	−0.0702773
$851$	−3.00000	−0.102839
$852$	−11.7506	−0.402570
$853$	−5.41060	−0.185255	−0.0926277	−	0.995701i	$-0.529527\pi$
$853$	−5.41060	−0.185255	−0.0926277	+	0.995701i	$0.529527\pi$
$854$	4.91962	0.168346
$855$	3.24698	0.111044
$856$	3.92394	0.134117
$857$	0.165275	0.00564570	0.00282285	−	0.999996i	$-0.499101\pi$
$857$	0.165275	0.00564570	0.00282285	+	0.999996i	$0.499101\pi$
$858$	0	0
$859$	47.0853	1.60653	0.803264	−	0.595622i	$-0.203095\pi$
$859$	47.0853	1.60653	0.803264	+	0.595622i	$0.203095\pi$
$860$	4.41789	0.150649
$861$	14.4252	0.491609
$862$	−6.06531	−0.206585
$863$	−31.2553	−1.06394	−0.531972	−	0.846762i	$-0.678549\pi$
$863$	−31.2553	−1.06394	−0.531972	+	0.846762i	$0.678549\pi$
$864$	−1.00000	−0.0340207
$865$	−15.4795	−0.526318
$866$	−14.8877	−0.505904
$867$	12.8019	0.434777
$868$	−3.80194	−0.129046
$869$	−1.37196	−0.0465406
$870$	5.13706	0.174163
$871$	0	0
$872$	−0.554958	−0.0187933
$873$	−5.85086	−0.198021
$874$	4.33513	0.146638
$875$	−1.35690	−0.0458715
$876$	12.1032	0.408930
$877$	16.9898	0.573706	0.286853	−	0.957975i	$-0.407391\pi$
$877$	16.9898	0.573706	0.286853	+	0.957975i	$0.407391\pi$
$878$	−21.1336	−0.713225
$879$	−34.1280	−1.15111
$880$	−5.29590	−0.178525
$881$	−3.29159	−0.110896	−0.0554482	−	0.998462i	$-0.517659\pi$
$881$	−3.29159	−0.110896	−0.0554482	+	0.998462i	$0.517659\pi$
$882$	−5.15883	−0.173707
$883$	17.3157	0.582721	0.291361	−	0.956613i	$-0.405892\pi$
$883$	17.3157	0.582721	0.291361	+	0.956613i	$0.405892\pi$
$884$	0	0
$885$	−13.8998	−0.467236
$886$	28.0683	0.942973
$887$	15.6775	0.526401	0.263200	−	0.964741i	$-0.415222\pi$
$887$	15.6775	0.526401	0.263200	+	0.964741i	$0.415222\pi$
$888$	2.24698	0.0754037
$889$	3.03252	0.101708
$890$	−5.47650	−0.183573
$891$	−5.29590	−0.177419
$892$	−2.28083	−0.0763679
$893$	15.6625	0.524125
$894$	9.66248	0.323162
$895$	19.0737	0.637563
$896$	−1.35690	−0.0453307
$897$	0	0
$898$	19.2446	0.642200
$899$	−14.3937	−0.480058
$900$	1.00000	0.0333333
$901$	−29.1661	−0.971665
$902$	−56.3008	−1.87461
$903$	5.99462	0.199489
$904$	4.39373	0.146133
$905$	2.16852	0.0720841
$906$	−7.35152	−0.244238
$907$	−25.8877	−0.859587	−0.429793	−	0.902927i	$-0.641414\pi$
$907$	−25.8877	−0.859587	−0.429793	+	0.902927i	$0.641414\pi$
$908$	−3.37196	−0.111902
$909$	−8.39612	−0.278482
$910$	0	0
$911$	−37.5220	−1.24316	−0.621579	−	0.783351i	$-0.713509\pi$
$911$	−37.5220	−1.24316	−0.621579	+	0.783351i	$0.713509\pi$
$912$	−3.24698	−0.107518
$913$	−16.0030	−0.529621
$914$	−37.8485	−1.25192
$915$	3.62565	0.119860
$916$	18.3763	0.607169
$917$	11.5550	0.381578
$918$	2.04892	0.0676243
$919$	−5.56358	−0.183526	−0.0917628	−	0.995781i	$-0.529250\pi$
$919$	−5.56358	−0.183526	−0.0917628	+	0.995781i	$0.529250\pi$
$920$	1.33513	0.0440178
$921$	15.6601	0.516017
$922$	−11.2228	−0.369604
$923$	0	0
$924$	−7.18598	−0.236401
$925$	−2.24698	−0.0738802
$926$	25.0726	0.823937
$927$	13.6353	0.447843
$928$	−5.13706	−0.168632
$929$	40.2602	1.32090	0.660448	−	0.750872i	$-0.270366\pi$
$929$	40.2602	1.32090	0.660448	+	0.750872i	$0.270366\pi$
$930$	−2.80194	−0.0918792
$931$	−16.7506	−0.548980
$932$	10.0858	0.330370
$933$	−25.7972	−0.844561
$934$	36.9657	1.20955
$935$	10.8509	0.354861
$936$	0	0
$937$	−30.5356	−0.997554	−0.498777	−	0.866730i	$-0.666217\pi$
$937$	−30.5356	−0.997554	−0.498777	+	0.866730i	$0.666217\pi$
$938$	−12.2620	−0.400370
$939$	15.6243	0.509880
$940$	4.82371	0.157332
$941$	−41.6461	−1.35762	−0.678812	−	0.734312i	$-0.737505\pi$
$941$	−41.6461	−1.35762	−0.678812	+	0.734312i	$0.737505\pi$
$942$	−2.85325	−0.0929638
$943$	14.1938	0.462212
$944$	13.8998	0.452399
$945$	1.35690	0.0441398
$946$	−23.3967	−0.760693
$947$	−21.7724	−0.707508	−0.353754	−	0.935339i	$-0.615095\pi$
$947$	−21.7724	−0.707508	−0.353754	+	0.935339i	$0.615095\pi$
$948$	−0.259061	−0.00841392
$949$	0	0
$950$	3.24698	0.105346
$951$	9.25965	0.300265
$952$	2.78017	0.0901057
$953$	−41.9560	−1.35909	−0.679544	−	0.733635i	$-0.737822\pi$
$953$	−41.9560	−1.35909	−0.679544	+	0.733635i	$0.737822\pi$
$954$	14.2349	0.460872
$955$	−11.7409	−0.379928
$956$	−20.0834	−0.649542
$957$	−27.2054	−0.879424
$958$	31.4590	1.01640
$959$	−17.8683	−0.576998
$960$	−1.00000	−0.0322749
$961$	−23.1491	−0.746747
$962$	0	0
$963$	3.92394	0.126447
$964$	2.99462	0.0964503
$965$	−24.6722	−0.794225
$966$	1.81163	0.0582881
$967$	−16.7041	−0.537168	−0.268584	−	0.963256i	$-0.586556\pi$
$967$	−16.7041	−0.537168	−0.268584	+	0.963256i	$0.586556\pi$
$968$	17.0465	0.547896
$969$	6.65279	0.213718
$970$	−5.85086	−0.187860
$971$	−20.7275	−0.665178	−0.332589	−	0.943072i	$-0.607922\pi$
$971$	−20.7275	−0.665178	−0.332589	+	0.943072i	$0.607922\pi$
$972$	−1.00000	−0.0320750
$973$	−9.73748	−0.312169
$974$	18.8713	0.604675
$975$	0	0
$976$	−3.62565	−0.116054
$977$	33.4547	1.07031	0.535156	−	0.844753i	$-0.320253\pi$
$977$	33.4547	1.07031	0.535156	+	0.844753i	$0.320253\pi$
$978$	−15.1075	−0.483085
$979$	29.0030	0.926939
$980$	−5.15883	−0.164793
$981$	−0.554958	−0.0177184
$982$	−16.3961	−0.523221
$983$	−31.8605	−1.01619	−0.508097	−	0.861300i	$-0.669651\pi$
$983$	−31.8605	−1.01619	−0.508097	+	0.861300i	$0.669651\pi$
$984$	−10.6310	−0.338905
$985$	26.2010	0.834835
$986$	10.5254	0.335198
$987$	6.54527	0.208338
$988$	0	0
$989$	5.89844	0.187560
$990$	−5.29590	−0.168315
$991$	−21.0925	−0.670024	−0.335012	−	0.942214i	$-0.608740\pi$
$991$	−21.0925	−0.670024	−0.335012	+	0.942214i	$0.608740\pi$
$992$	2.80194	0.0889616
$993$	−21.8582	−0.693647
$994$	−15.9444	−0.505725
$995$	19.6722	0.623650
$996$	−3.02177	−0.0957485
$997$	17.7832	0.563198	0.281599	−	0.959532i	$-0.409135\pi$
$997$	17.7832	0.563198	0.281599	+	0.959532i	$0.409135\pi$
$998$	40.2452	1.27394
$999$	2.24698	0.0710913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bu.1.2	yes	3
13.5	odd	4		5070.2.b.t.1351.2		6
13.8	odd	4		5070.2.b.t.1351.5		6
13.12	even	2		5070.2.a.bj.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5070.2.a.bj.1.2	✓	3	13.12	even	2
5070.2.a.bu.1.2	yes	3	1.1	even	1	trivial
5070.2.b.t.1351.2		6	13.5	odd	4
5070.2.b.t.1351.5		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.29590 q^{11} -1.00000 q^{12} -1.35690 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.04892 q^{17} +1.00000 q^{18} +3.24698 q^{19} +1.00000 q^{20} +1.35690 q^{21} -5.29590 q^{22} +1.33513 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} -1.35690 q^{28} -5.13706 q^{29} -1.00000 q^{30} +2.80194 q^{31} +1.00000 q^{32} +5.29590 q^{33} -2.04892 q^{34} -1.35690 q^{35} +1.00000 q^{36} -2.24698 q^{37} +3.24698 q^{38} +1.00000 q^{40} +10.6310 q^{41} +1.35690 q^{42} +4.41789 q^{43} -5.29590 q^{44} +1.00000 q^{45} +1.33513 q^{46} +4.82371 q^{47} -1.00000 q^{48} -5.15883 q^{49} +1.00000 q^{50} +2.04892 q^{51} +14.2349 q^{53} -1.00000 q^{54} -5.29590 q^{55} -1.35690 q^{56} -3.24698 q^{57} -5.13706 q^{58} +13.8998 q^{59} -1.00000 q^{60} -3.62565 q^{61} +2.80194 q^{62} -1.35690 q^{63} +1.00000 q^{64} +5.29590 q^{66} +9.03684 q^{67} -2.04892 q^{68} -1.33513 q^{69} -1.35690 q^{70} +11.7506 q^{71} +1.00000 q^{72} -12.1032 q^{73} -2.24698 q^{74} -1.00000 q^{75} +3.24698 q^{76} +7.18598 q^{77} +0.259061 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.6310 q^{82} +3.02177 q^{83} +1.35690 q^{84} -2.04892 q^{85} +4.41789 q^{86} +5.13706 q^{87} -5.29590 q^{88} -5.47650 q^{89} +1.00000 q^{90} +1.33513 q^{92} -2.80194 q^{93} +4.82371 q^{94} +3.24698 q^{95} -1.00000 q^{96} -5.85086 q^{97} -5.15883 q^{98} -5.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 2 q^{11} - 3 q^{12} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 5 q^{19} + 3 q^{20} - 2 q^{22} + 3 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{27} - 10 q^{29} - 3 q^{30} + 4 q^{31} + 3 q^{32} + 2 q^{33} + 3 q^{34} + 3 q^{36} - 2 q^{37} + 5 q^{38} + 3 q^{40} + 17 q^{41} + 19 q^{43} - 2 q^{44} + 3 q^{45} + 3 q^{46} + 7 q^{47} - 3 q^{48} - 7 q^{49} + 3 q^{50} - 3 q^{51} + 19 q^{53} - 3 q^{54} - 2 q^{55} - 5 q^{57} - 10 q^{58} + 19 q^{59} - 3 q^{60} + q^{61} + 4 q^{62} + 3 q^{64} + 2 q^{66} - q^{67} + 3 q^{68} - 3 q^{69} - q^{71} + 3 q^{72} - 15 q^{73} - 2 q^{74} - 3 q^{75} + 5 q^{76} + 7 q^{77} + 15 q^{79} + 3 q^{80} + 3 q^{81} + 17 q^{82} + 6 q^{83} + 3 q^{85} + 19 q^{86} + 10 q^{87} - 2 q^{88} + 9 q^{89} + 3 q^{90} + 3 q^{92} - 4 q^{93} + 7 q^{94} + 5 q^{95} - 3 q^{96} - 4 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 2 * q^11 - 3 * q^12 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^22 + 3 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^27 - 10 * q^29 - 3 * q^30 + 4 * q^31 + 3 * q^32 + 2 * q^33 + 3 * q^34 + 3 * q^36 - 2 * q^37 + 5 * q^38 + 3 * q^40 + 17 * q^41 + 19 * q^43 - 2 * q^44 + 3 * q^45 + 3 * q^46 + 7 * q^47 - 3 * q^48 - 7 * q^49 + 3 * q^50 - 3 * q^51 + 19 * q^53 - 3 * q^54 - 2 * q^55 - 5 * q^57 - 10 * q^58 + 19 * q^59 - 3 * q^60 + q^61 + 4 * q^62 + 3 * q^64 + 2 * q^66 - q^67 + 3 * q^68 - 3 * q^69 - q^71 + 3 * q^72 - 15 * q^73 - 2 * q^74 - 3 * q^75 + 5 * q^76 + 7 * q^77 + 15 * q^79 + 3 * q^80 + 3 * q^81 + 17 * q^82 + 6 * q^83 + 3 * q^85 + 19 * q^86 + 10 * q^87 - 2 * q^88 + 9 * q^89 + 3 * q^90 + 3 * q^92 - 4 * q^93 + 7 * q^94 + 5 * q^95 - 3 * q^96 - 4 * q^97 - 7 * q^98 - 2 * q^99

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