LMFDB - Embedded newform 3549.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24698 q^{2} +1.00000 q^{3} +3.04892 q^{4} -1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +2.35690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.24698 q^{2} +1.00000 q^{3} +3.04892 q^{4} -1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +2.35690 q^{8} +1.00000 q^{9} -3.80194 q^{10} +5.29590 q^{11} +3.04892 q^{12} -2.24698 q^{14} -1.69202 q^{15} -0.801938 q^{16} -2.24698 q^{17} +2.24698 q^{18} +7.49396 q^{19} -5.15883 q^{20} -1.00000 q^{21} +11.8998 q^{22} +6.76271 q^{23} +2.35690 q^{24} -2.13706 q^{25} +1.00000 q^{27} -3.04892 q^{28} +7.56465 q^{29} -3.80194 q^{30} -3.89977 q^{31} -6.51573 q^{32} +5.29590 q^{33} -5.04892 q^{34} +1.69202 q^{35} +3.04892 q^{36} +9.57002 q^{37} +16.8388 q^{38} -3.98792 q^{40} -6.98792 q^{41} -2.24698 q^{42} -6.26875 q^{43} +16.1468 q^{44} -1.69202 q^{45} +15.1957 q^{46} +1.70410 q^{47} -0.801938 q^{48} +1.00000 q^{49} -4.80194 q^{50} -2.24698 q^{51} -4.20775 q^{53} +2.24698 q^{54} -8.96077 q^{55} -2.35690 q^{56} +7.49396 q^{57} +16.9976 q^{58} +6.26875 q^{59} -5.15883 q^{60} +6.16421 q^{61} -8.76271 q^{62} -1.00000 q^{63} -13.0368 q^{64} +11.8998 q^{66} +2.97285 q^{67} -6.85086 q^{68} +6.76271 q^{69} +3.80194 q^{70} +8.37867 q^{71} +2.35690 q^{72} +4.37867 q^{73} +21.5036 q^{74} -2.13706 q^{75} +22.8485 q^{76} -5.29590 q^{77} +5.40581 q^{79} +1.35690 q^{80} +1.00000 q^{81} -15.7017 q^{82} -0.131687 q^{83} -3.04892 q^{84} +3.80194 q^{85} -14.0858 q^{86} +7.56465 q^{87} +12.4819 q^{88} +5.89008 q^{89} -3.80194 q^{90} +20.6189 q^{92} -3.89977 q^{93} +3.82908 q^{94} -12.6799 q^{95} -6.51573 q^{96} +0.374354 q^{97} +2.24698 q^{98} +5.29590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * 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 $

$2$	2.24698	1.58885	0.794427	−	0.607359i	$-0.207771\pi$
$2$	2.24698	1.58885	0.794427	+	0.607359i	$0.207771\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.04892	1.52446
$5$	−1.69202	−0.756695	−0.378348	−	0.925664i	$-0.623508\pi$
$5$	−1.69202	−0.756695	−0.378348	+	0.925664i	$0.623508\pi$
$6$	2.24698	0.917326
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.35690	0.833289
$9$	1.00000	0.333333
$10$	−3.80194	−1.20228
$11$	5.29590	1.59677	0.798387	−	0.602145i	$-0.205687\pi$
$11$	5.29590	1.59677	0.798387	+	0.602145i	$0.205687\pi$
$12$	3.04892	0.880147
$13$	0	0
$13$	0	0
$14$	−2.24698	−0.600531
$15$	−1.69202	−0.436878
$16$	−0.801938	−0.200484
$17$	−2.24698	−0.544973	−0.272486	−	0.962160i	$-0.587846\pi$
$17$	−2.24698	−0.544973	−0.272486	+	0.962160i	$0.587846\pi$
$18$	2.24698	0.529618
$19$	7.49396	1.71923	0.859616	−	0.510941i	$-0.170703\pi$
$19$	7.49396	1.71923	0.859616	+	0.510941i	$0.170703\pi$
$20$	−5.15883	−1.15355
$21$	−1.00000	−0.218218
$22$	11.8998	2.53704
$23$	6.76271	1.41012	0.705061	−	0.709147i	$-0.250920\pi$
$23$	6.76271	1.41012	0.705061	+	0.709147i	$0.250920\pi$
$24$	2.35690	0.481099
$25$	−2.13706	−0.427413
$26$	0	0
$27$	1.00000	0.192450
$28$	−3.04892	−0.576191
$29$	7.56465	1.40472	0.702360	−	0.711822i	$-0.252130\pi$
$29$	7.56465	1.40472	0.702360	+	0.711822i	$0.252130\pi$
$30$	−3.80194	−0.694136
$31$	−3.89977	−0.700420	−0.350210	−	0.936671i	$-0.613890\pi$
$31$	−3.89977	−0.700420	−0.350210	+	0.936671i	$0.613890\pi$
$32$	−6.51573	−1.15183
$33$	5.29590	0.921897
$34$	−5.04892	−0.865882
$35$	1.69202	0.286004
$36$	3.04892	0.508153
$37$	9.57002	1.57330	0.786651	−	0.617398i	$-0.211813\pi$
$37$	9.57002	1.57330	0.786651	+	0.617398i	$0.211813\pi$
$38$	16.8388	2.73161
$39$	0	0
$40$	−3.98792	−0.630545
$41$	−6.98792	−1.09133	−0.545665	−	0.838004i	$-0.683723\pi$
$41$	−6.98792	−1.09133	−0.545665	+	0.838004i	$0.683723\pi$
$42$	−2.24698	−0.346716
$43$	−6.26875	−0.955975	−0.477988	−	0.878367i	$-0.658634\pi$
$43$	−6.26875	−0.955975	−0.477988	+	0.878367i	$0.658634\pi$
$44$	16.1468	2.43421
$45$	−1.69202	−0.252232
$46$	15.1957	2.24048
$47$	1.70410	0.248569	0.124284	−	0.992247i	$-0.460336\pi$
$47$	1.70410	0.248569	0.124284	+	0.992247i	$0.460336\pi$
$48$	−0.801938	−0.115750
$49$	1.00000	0.142857
$50$	−4.80194	−0.679097
$51$	−2.24698	−0.314640
$52$	0	0
$53$	−4.20775	−0.577979	−0.288990	−	0.957332i	$-0.593319\pi$
$53$	−4.20775	−0.577979	−0.288990	+	0.957332i	$0.593319\pi$
$54$	2.24698	0.305775
$55$	−8.96077	−1.20827
$56$	−2.35690	−0.314953
$57$	7.49396	0.992599
$58$	16.9976	2.23190
$59$	6.26875	0.816122	0.408061	−	0.912955i	$-0.366205\pi$
$59$	6.26875	0.816122	0.408061	+	0.912955i	$0.366205\pi$
$60$	−5.15883	−0.666003
$61$	6.16421	0.789246	0.394623	−	0.918843i	$-0.370875\pi$
$61$	6.16421	0.789246	0.394623	+	0.918843i	$0.370875\pi$
$62$	−8.76271	−1.11287
$63$	−1.00000	−0.125988
$64$	−13.0368	−1.62960
$65$	0	0
$66$	11.8998	1.46476
$67$	2.97285	0.363192	0.181596	−	0.983373i	$-0.441874\pi$
$67$	2.97285	0.363192	0.181596	+	0.983373i	$0.441874\pi$
$68$	−6.85086	−0.830788
$69$	6.76271	0.814135
$70$	3.80194	0.454418
$71$	8.37867	0.994365	0.497182	−	0.867646i	$-0.334368\pi$
$71$	8.37867	0.994365	0.497182	+	0.867646i	$0.334368\pi$
$72$	2.35690	0.277763
$73$	4.37867	0.512484	0.256242	−	0.966613i	$-0.417516\pi$
$73$	4.37867	0.512484	0.256242	+	0.966613i	$0.417516\pi$
$74$	21.5036	2.49975
$75$	−2.13706	−0.246767
$76$	22.8485	2.62090
$77$	−5.29590	−0.603523
$78$	0	0
$79$	5.40581	0.608202	0.304101	−	0.952640i	$-0.401644\pi$
$79$	5.40581	0.608202	0.304101	+	0.952640i	$0.401644\pi$
$80$	1.35690	0.151706
$81$	1.00000	0.111111
$82$	−15.7017	−1.73396
$83$	−0.131687	−0.0144545	−0.00722724	−	0.999974i	$-0.502301\pi$
$83$	−0.131687	−0.0144545	−0.00722724	+	0.999974i	$0.502301\pi$
$84$	−3.04892	−0.332664
$85$	3.80194	0.412378
$86$	−14.0858	−1.51891
$87$	7.56465	0.811015
$88$	12.4819	1.33057
$89$	5.89008	0.624348	0.312174	−	0.950025i	$-0.398943\pi$
$89$	5.89008	0.624348	0.312174	+	0.950025i	$0.398943\pi$
$90$	−3.80194	−0.400759
$91$	0	0
$92$	20.6189	2.14967
$93$	−3.89977	−0.404388
$94$	3.82908	0.394940
$95$	−12.6799	−1.30093
$96$	−6.51573	−0.665009
$97$	0.374354	0.0380099	0.0190050	−	0.999819i	$-0.493950\pi$
$97$	0.374354	0.0380099	0.0190050	+	0.999819i	$0.493950\pi$
$98$	2.24698	0.226979
$99$	5.29590	0.532258
$100$	−6.51573	−0.651573
$101$	−14.0248	−1.39552	−0.697758	−	0.716334i	$-0.745819\pi$
$101$	−14.0248	−1.39552	−0.697758	+	0.716334i	$0.745819\pi$
$102$	−5.04892	−0.499917
$103$	−14.9215	−1.47026	−0.735132	−	0.677924i	$-0.762880\pi$
$103$	−14.9215	−1.47026	−0.735132	+	0.677924i	$0.762880\pi$
$104$	0	0
$105$	1.69202	0.165124
$106$	−9.45473	−0.918325
$107$	8.13467	0.786408	0.393204	−	0.919451i	$-0.371367\pi$
$107$	8.13467	0.786408	0.393204	+	0.919451i	$0.371367\pi$
$108$	3.04892	0.293382
$109$	7.86294	0.753133	0.376566	−	0.926390i	$-0.377105\pi$
$109$	7.86294	0.753133	0.376566	+	0.926390i	$0.377105\pi$
$110$	−20.1347	−1.91977
$111$	9.57002	0.908346
$112$	0.801938	0.0757760
$113$	6.10023	0.573861	0.286931	−	0.957951i	$-0.407365\pi$
$113$	6.10023	0.573861	0.286931	+	0.957951i	$0.407365\pi$
$114$	16.8388	1.57710
$115$	−11.4426	−1.06703
$116$	23.0640	2.14144
$117$	0	0
$118$	14.0858	1.29670
$119$	2.24698	0.205980
$120$	−3.98792	−0.364045
$121$	17.0465	1.54968
$122$	13.8509	1.25400
$123$	−6.98792	−0.630079
$124$	−11.8901	−1.06776
$125$	12.0761	1.08012
$126$	−2.24698	−0.200177
$127$	−20.1075	−1.78425	−0.892127	−	0.451785i	$-0.850788\pi$
$127$	−20.1075	−1.78425	−0.892127	+	0.451785i	$0.850788\pi$
$128$	−16.2620	−1.43738
$129$	−6.26875	−0.551933
$130$	0	0
$131$	−3.69202	−0.322573	−0.161287	−	0.986908i	$-0.551564\pi$
$131$	−3.69202	−0.322573	−0.161287	+	0.986908i	$0.551564\pi$
$132$	16.1468	1.40539
$133$	−7.49396	−0.649809
$134$	6.67994	0.577059
$135$	−1.69202	−0.145626
$136$	−5.29590	−0.454119
$137$	1.84654	0.157761	0.0788804	−	0.996884i	$-0.474865\pi$
$137$	1.84654	0.157761	0.0788804	+	0.996884i	$0.474865\pi$
$138$	15.1957	1.29354
$139$	−14.5090	−1.23064	−0.615320	−	0.788278i	$-0.710973\pi$
$139$	−14.5090	−1.23064	−0.615320	+	0.788278i	$0.710973\pi$
$140$	5.15883	0.436001
$141$	1.70410	0.143511
$142$	18.8267	1.57990
$143$	0	0
$144$	−0.801938	−0.0668281
$145$	−12.7995	−1.06294
$146$	9.83877	0.814263
$147$	1.00000	0.0824786
$148$	29.1782	2.39843
$149$	−12.4058	−1.01632	−0.508162	−	0.861262i	$-0.669675\pi$
$149$	−12.4058	−1.01632	−0.508162	+	0.861262i	$0.669675\pi$
$150$	−4.80194	−0.392077
$151$	−1.32975	−0.108213	−0.0541067	−	0.998535i	$-0.517231\pi$
$151$	−1.32975	−0.108213	−0.0541067	+	0.998535i	$0.517231\pi$
$152$	17.6625	1.43262
$153$	−2.24698	−0.181658
$154$	−11.8998	−0.958911
$155$	6.59850	0.530004
$156$	0	0
$157$	−8.43727	−0.673368	−0.336684	−	0.941618i	$-0.609305\pi$
$157$	−8.43727	−0.673368	−0.336684	+	0.941618i	$0.609305\pi$
$158$	12.1468	0.966344
$159$	−4.20775	−0.333696
$160$	11.0248	0.871583
$161$	−6.76271	−0.532976
$162$	2.24698	0.176539
$163$	−14.1836	−1.11094	−0.555472	−	0.831535i	$-0.687462\pi$
$163$	−14.1836	−1.11094	−0.555472	+	0.831535i	$0.687462\pi$
$164$	−21.3056	−1.66369
$165$	−8.96077	−0.697595
$166$	−0.295897	−0.0229661
$167$	−8.87800	−0.687000	−0.343500	−	0.939153i	$-0.611613\pi$
$167$	−8.87800	−0.687000	−0.343500	+	0.939153i	$0.611613\pi$
$168$	−2.35690	−0.181838
$169$	0	0
$170$	8.54288	0.655209
$171$	7.49396	0.573077
$172$	−19.1129	−1.45734
$173$	−24.3230	−1.84925	−0.924623	−	0.380883i	$-0.875620\pi$
$173$	−24.3230	−1.84925	−0.924623	+	0.380883i	$0.875620\pi$
$174$	16.9976	1.28859
$175$	2.13706	0.161547
$176$	−4.24698	−0.320128
$177$	6.26875	0.471188
$178$	13.2349	0.991998
$179$	−12.8702	−0.961966	−0.480983	−	0.876730i	$-0.659720\pi$
$179$	−12.8702	−0.961966	−0.480983	+	0.876730i	$0.659720\pi$
$180$	−5.15883	−0.384517
$181$	9.25667	0.688043	0.344021	−	0.938962i	$-0.388211\pi$
$181$	9.25667	0.688043	0.344021	+	0.938962i	$0.388211\pi$
$182$	0	0
$183$	6.16421	0.455672
$184$	15.9390	1.17504
$185$	−16.1927	−1.19051
$186$	−8.76271	−0.642513
$187$	−11.8998	−0.870198
$188$	5.19567	0.378933
$189$	−1.00000	−0.0727393
$190$	−28.4916	−2.06700
$191$	−3.37867	−0.244472	−0.122236	−	0.992501i	$-0.539006\pi$
$191$	−3.37867	−0.244472	−0.122236	+	0.992501i	$0.539006\pi$
$192$	−13.0368	−0.940853
$193$	24.9148	1.79341	0.896705	−	0.442629i	$-0.145954\pi$
$193$	24.9148	1.79341	0.896705	+	0.442629i	$0.145954\pi$
$194$	0.841166	0.0603922
$195$	0	0
$196$	3.04892	0.217780
$197$	−16.8291	−1.19902	−0.599511	−	0.800366i	$-0.704638\pi$
$197$	−16.8291	−1.19902	−0.599511	+	0.800366i	$0.704638\pi$
$198$	11.8998	0.845680
$199$	16.3002	1.15549	0.577746	−	0.816217i	$-0.303933\pi$
$199$	16.3002	1.15549	0.577746	+	0.816217i	$0.303933\pi$
$200$	−5.03684	−0.356158
$201$	2.97285	0.209689
$202$	−31.5133	−2.21727
$203$	−7.56465	−0.530934
$204$	−6.85086	−0.479656
$205$	11.8237	0.825804
$206$	−33.5284	−2.33603
$207$	6.76271	0.470041
$208$	0	0
$209$	39.6872	2.74522
$210$	3.80194	0.262359
$211$	−13.5308	−0.931498	−0.465749	−	0.884917i	$-0.654215\pi$
$211$	−13.5308	−0.931498	−0.465749	+	0.884917i	$0.654215\pi$
$212$	−12.8291	−0.881105
$213$	8.37867	0.574097
$214$	18.2784	1.24949
$215$	10.6069	0.723382
$216$	2.35690	0.160366
$217$	3.89977	0.264734
$218$	17.6679	1.19662
$219$	4.37867	0.295883
$220$	−27.3207	−1.84196
$221$	0	0
$222$	21.5036	1.44323
$223$	9.61596	0.643932	0.321966	−	0.946751i	$-0.395656\pi$
$223$	9.61596	0.643932	0.321966	+	0.946751i	$0.395656\pi$
$224$	6.51573	0.435350
$225$	−2.13706	−0.142471
$226$	13.7071	0.911782
$227$	−11.3381	−0.752537	−0.376268	−	0.926511i	$-0.622793\pi$
$227$	−11.3381	−0.752537	−0.376268	+	0.926511i	$0.622793\pi$
$228$	22.8485	1.51318
$229$	5.28083	0.348967	0.174484	−	0.984660i	$-0.444174\pi$
$229$	5.28083	0.348967	0.174484	+	0.984660i	$0.444174\pi$
$230$	−25.7114	−1.69536
$231$	−5.29590	−0.348444
$232$	17.8291	1.17054
$233$	3.09783	0.202946	0.101473	−	0.994838i	$-0.467644\pi$
$233$	3.09783	0.202946	0.101473	+	0.994838i	$0.467644\pi$
$234$	0	0
$235$	−2.88338	−0.188091
$236$	19.1129	1.24414
$237$	5.40581	0.351145
$238$	5.04892	0.327273
$239$	−10.7138	−0.693018	−0.346509	−	0.938047i	$-0.612633\pi$
$239$	−10.7138	−0.693018	−0.346509	+	0.938047i	$0.612633\pi$
$240$	1.35690	0.0875873
$241$	−16.2282	−1.04535	−0.522675	−	0.852532i	$-0.675066\pi$
$241$	−16.2282	−1.04535	−0.522675	+	0.852532i	$0.675066\pi$
$242$	38.3032	2.46222
$243$	1.00000	0.0641500
$244$	18.7942	1.20317
$245$	−1.69202	−0.108099
$246$	−15.7017	−1.00110
$247$	0	0
$248$	−9.19136	−0.583652
$249$	−0.131687	−0.00834529
$250$	27.1347	1.71615
$251$	−21.9433	−1.38505	−0.692525	−	0.721394i	$-0.743502\pi$
$251$	−21.9433	−1.38505	−0.692525	+	0.721394i	$0.743502\pi$
$252$	−3.04892	−0.192064
$253$	35.8146	2.25165
$254$	−45.1812	−2.83492
$255$	3.80194	0.238087
$256$	−10.4668	−0.654176
$257$	21.5429	1.34381	0.671904	−	0.740638i	$-0.265477\pi$
$257$	21.5429	1.34381	0.671904	+	0.740638i	$0.265477\pi$
$258$	−14.0858	−0.876941
$259$	−9.57002	−0.594652
$260$	0	0
$261$	7.56465	0.468240
$262$	−8.29590	−0.512522
$263$	−12.5550	−0.774172	−0.387086	−	0.922044i	$-0.626518\pi$
$263$	−12.5550	−0.774172	−0.387086	+	0.922044i	$0.626518\pi$
$264$	12.4819	0.768206
$265$	7.11960	0.437354
$266$	−16.8388	−1.03245
$267$	5.89008	0.360467
$268$	9.06398	0.553671
$269$	0.716185	0.0436665	0.0218333	−	0.999762i	$-0.493050\pi$
$269$	0.716185	0.0436665	0.0218333	+	0.999762i	$0.493050\pi$
$270$	−3.80194	−0.231379
$271$	−5.01507	−0.304644	−0.152322	−	0.988331i	$-0.548675\pi$
$271$	−5.01507	−0.304644	−0.152322	+	0.988331i	$0.548675\pi$
$272$	1.80194	0.109259
$273$	0	0
$274$	4.14914	0.250659
$275$	−11.3177	−0.682481
$276$	20.6189	1.24111
$277$	−10.5375	−0.633137	−0.316568	−	0.948570i	$-0.602531\pi$
$277$	−10.5375	−0.633137	−0.316568	+	0.948570i	$0.602531\pi$
$278$	−32.6015	−1.95531
$279$	−3.89977	−0.233473
$280$	3.98792	0.238324
$281$	3.04461	0.181626	0.0908130	−	0.995868i	$-0.471053\pi$
$281$	3.04461	0.181626	0.0908130	+	0.995868i	$0.471053\pi$
$282$	3.82908	0.228019
$283$	4.35690	0.258991	0.129495	−	0.991580i	$-0.458664\pi$
$283$	4.35690	0.258991	0.129495	+	0.991580i	$0.458664\pi$
$284$	25.5459	1.51587
$285$	−12.6799	−0.751095
$286$	0	0
$287$	6.98792	0.412484
$288$	−6.51573	−0.383943
$289$	−11.9511	−0.703005
$290$	−28.7603	−1.68886
$291$	0.374354	0.0219450
$292$	13.3502	0.781261
$293$	−27.7222	−1.61955	−0.809773	−	0.586744i	$-0.800410\pi$
$293$	−27.7222	−1.61955	−0.809773	+	0.586744i	$0.800410\pi$
$294$	2.24698	0.131047
$295$	−10.6069	−0.617555
$296$	22.5555	1.31101
$297$	5.29590	0.307299
$298$	−27.8756	−1.61479
$299$	0	0
$300$	−6.51573	−0.376186
$301$	6.26875	0.361325
$302$	−2.98792	−0.171935
$303$	−14.0248	−0.805701
$304$	−6.00969	−0.344679
$305$	−10.4300	−0.597219
$306$	−5.04892	−0.288627
$307$	16.5332	0.943599	0.471799	−	0.881706i	$-0.343605\pi$
$307$	16.5332	0.943599	0.471799	+	0.881706i	$0.343605\pi$
$308$	−16.1468	−0.920047
$309$	−14.9215	−0.848857
$310$	14.8267	0.842100
$311$	−25.7482	−1.46005	−0.730024	−	0.683421i	$-0.760491\pi$
$311$	−25.7482	−1.46005	−0.730024	+	0.683421i	$0.760491\pi$
$312$	0	0
$313$	−24.1618	−1.36571	−0.682853	−	0.730555i	$-0.739261\pi$
$313$	−24.1618	−1.36571	−0.682853	+	0.730555i	$0.739261\pi$
$314$	−18.9584	−1.06988
$315$	1.69202	0.0953346
$316$	16.4819	0.927178
$317$	4.11423	0.231078	0.115539	−	0.993303i	$-0.463140\pi$
$317$	4.11423	0.231078	0.115539	+	0.993303i	$0.463140\pi$
$318$	−9.45473	−0.530195
$319$	40.0616	2.24302
$320$	22.0586	1.23311
$321$	8.13467	0.454033
$322$	−15.1957	−0.846822
$323$	−16.8388	−0.936934
$324$	3.04892	0.169384
$325$	0	0
$326$	−31.8702	−1.76513
$327$	7.86294	0.434821
$328$	−16.4698	−0.909392
$329$	−1.70410	−0.0939502
$330$	−20.1347	−1.10838
$331$	24.8267	1.36460	0.682299	−	0.731073i	$-0.260980\pi$
$331$	24.8267	1.36460	0.682299	+	0.731073i	$0.260980\pi$
$332$	−0.401501	−0.0220352
$333$	9.57002	0.524434
$334$	−19.9487	−1.09154
$335$	−5.03013	−0.274825
$336$	0.801938	0.0437493
$337$	32.7415	1.78354	0.891772	−	0.452484i	$-0.149462\pi$
$337$	32.7415	1.78354	0.891772	+	0.452484i	$0.149462\pi$
$338$	0	0
$339$	6.10023	0.331319
$340$	11.5918	0.628653
$341$	−20.6528	−1.11841
$342$	16.8388	0.910537
$343$	−1.00000	−0.0539949
$344$	−14.7748	−0.796603
$345$	−11.4426	−0.616052
$346$	−54.6534	−2.93818
$347$	0.302602	0.0162445	0.00812226	−	0.999967i	$-0.497415\pi$
$347$	0.302602	0.0162445	0.00812226	+	0.999967i	$0.497415\pi$
$348$	23.0640	1.23636
$349$	−27.9801	−1.49774	−0.748872	−	0.662715i	$-0.769404\pi$
$349$	−27.9801	−1.49774	−0.748872	+	0.662715i	$0.769404\pi$
$350$	4.80194	0.256674
$351$	0	0
$352$	−34.5066	−1.83921
$353$	−0.124391	−0.00662065	−0.00331033	−	0.999995i	$-0.501054\pi$
$353$	−0.124391	−0.00662065	−0.00331033	+	0.999995i	$0.501054\pi$
$354$	14.0858	0.748649
$355$	−14.1769	−0.752431
$356$	17.9584	0.951792
$357$	2.24698	0.118923
$358$	−28.9191	−1.52842
$359$	−20.5241	−1.08322	−0.541610	−	0.840630i	$-0.682185\pi$
$359$	−20.5241	−1.08322	−0.541610	+	0.840630i	$0.682185\pi$
$360$	−3.98792	−0.210182
$361$	37.1594	1.95576
$362$	20.7995	1.09320
$363$	17.0465	0.894710
$364$	0	0
$365$	−7.40880	−0.387794
$366$	13.8509	0.723996
$367$	−15.3653	−0.802060	−0.401030	−	0.916065i	$-0.631348\pi$
$367$	−15.3653	−0.802060	−0.401030	+	0.916065i	$0.631348\pi$
$368$	−5.42327	−0.282708
$369$	−6.98792	−0.363777
$370$	−36.3846	−1.89155
$371$	4.20775	0.218456
$372$	−11.8901	−0.616472
$373$	−4.85192	−0.251223	−0.125611	−	0.992080i	$-0.540089\pi$
$373$	−4.85192	−0.251223	−0.125611	+	0.992080i	$0.540089\pi$
$374$	−26.7385	−1.38262
$375$	12.0761	0.623605
$376$	4.01639	0.207130
$377$	0	0
$378$	−2.24698	−0.115572
$379$	5.34913	0.274766	0.137383	−	0.990518i	$-0.456131\pi$
$379$	5.34913	0.274766	0.137383	+	0.990518i	$0.456131\pi$
$380$	−38.6601	−1.98322
$381$	−20.1075	−1.03014
$382$	−7.59179	−0.388430
$383$	1.34050	0.0684965	0.0342482	−	0.999413i	$-0.489096\pi$
$383$	1.34050	0.0684965	0.0342482	+	0.999413i	$0.489096\pi$
$384$	−16.2620	−0.829869
$385$	8.96077	0.456683
$386$	55.9831	2.84947
$387$	−6.26875	−0.318658
$388$	1.14138	0.0579445
$389$	−17.1051	−0.867265	−0.433632	−	0.901090i	$-0.642768\pi$
$389$	−17.1051	−0.867265	−0.433632	+	0.901090i	$0.642768\pi$
$390$	0	0
$391$	−15.1957	−0.768478
$392$	2.35690	0.119041
$393$	−3.69202	−0.186238
$394$	−37.8146	−1.90507
$395$	−9.14675	−0.460223
$396$	16.1468	0.811405
$397$	−10.0204	−0.502912	−0.251456	−	0.967869i	$-0.580909\pi$
$397$	−10.0204	−0.502912	−0.251456	+	0.967869i	$0.580909\pi$
$398$	36.6262	1.83591
$399$	−7.49396	−0.375167
$400$	1.71379	0.0856896
$401$	8.82669	0.440784	0.220392	−	0.975411i	$-0.429266\pi$
$401$	8.82669	0.440784	0.220392	+	0.975411i	$0.429266\pi$
$402$	6.67994	0.333165
$403$	0	0
$404$	−42.7603	−2.12741
$405$	−1.69202	−0.0840772
$406$	−16.9976	−0.843577
$407$	50.6819	2.51221
$408$	−5.29590	−0.262186
$409$	−0.522434	−0.0258327	−0.0129164	−	0.999917i	$-0.504112\pi$
$409$	−0.522434	−0.0258327	−0.0129164	+	0.999917i	$0.504112\pi$
$410$	26.5676	1.31208
$411$	1.84654	0.0910833
$412$	−45.4946	−2.24136
$413$	−6.26875	−0.308465
$414$	15.1957	0.746826
$415$	0.222816	0.0109376
$416$	0	0
$417$	−14.5090	−0.710510
$418$	89.1764	4.36176
$419$	11.0653	0.540576	0.270288	−	0.962780i	$-0.412881\pi$
$419$	11.0653	0.540576	0.270288	+	0.962780i	$0.412881\pi$
$420$	5.15883	0.251725
$421$	5.26444	0.256573	0.128287	−	0.991737i	$-0.459052\pi$
$421$	5.26444	0.256573	0.128287	+	0.991737i	$0.459052\pi$
$422$	−30.4034	−1.48002
$423$	1.70410	0.0828563
$424$	−9.91723	−0.481623
$425$	4.80194	0.232928
$426$	18.8267	0.912156
$427$	−6.16421	−0.298307
$428$	24.8019	1.19885
$429$	0	0
$430$	23.8334	1.14935
$431$	10.0519	0.484183	0.242092	−	0.970253i	$-0.422167\pi$
$431$	10.0519	0.484183	0.242092	+	0.970253i	$0.422167\pi$
$432$	−0.801938	−0.0385832
$433$	28.1400	1.35232	0.676162	−	0.736753i	$-0.263642\pi$
$433$	28.1400	1.35232	0.676162	+	0.736753i	$0.263642\pi$
$434$	8.76271	0.420623
$435$	−12.7995	−0.613691
$436$	23.9734	1.14812
$437$	50.6795	2.42433
$438$	9.83877	0.470115
$439$	−26.5719	−1.26821	−0.634105	−	0.773247i	$-0.718631\pi$
$439$	−26.5719	−1.26821	−0.634105	+	0.773247i	$0.718631\pi$
$440$	−21.1196	−1.00684
$441$	1.00000	0.0476190
$442$	0	0
$443$	−35.1957	−1.67220	−0.836098	−	0.548580i	$-0.815169\pi$
$443$	−35.1957	−1.67220	−0.836098	+	0.548580i	$0.815169\pi$
$444$	29.1782	1.38474
$445$	−9.96615	−0.472441
$446$	21.6069	1.02311
$447$	−12.4058	−0.586775
$448$	13.0368	0.615933
$449$	21.1981	1.00040	0.500199	−	0.865910i	$-0.333260\pi$
$449$	21.1981	1.00040	0.500199	+	0.865910i	$0.333260\pi$
$450$	−4.80194	−0.226366
$451$	−37.0073	−1.74261
$452$	18.5991	0.874828
$453$	−1.32975	−0.0624770
$454$	−25.4765	−1.19567
$455$	0	0
$456$	17.6625	0.827121
$457$	−36.2398	−1.69523	−0.847613	−	0.530615i	$-0.821961\pi$
$457$	−36.2398	−1.69523	−0.847613	+	0.530615i	$0.821961\pi$
$458$	11.8659	0.554458
$459$	−2.24698	−0.104880
$460$	−34.8877	−1.62665
$461$	33.3226	1.55199	0.775993	−	0.630741i	$-0.217249\pi$
$461$	33.3226	1.55199	0.775993	+	0.630741i	$0.217249\pi$
$462$	−11.8998	−0.553628
$463$	31.3497	1.45694	0.728472	−	0.685075i	$-0.240231\pi$
$463$	31.3497	1.45694	0.728472	+	0.685075i	$0.240231\pi$
$464$	−6.06638	−0.281624
$465$	6.59850	0.305998
$466$	6.96077	0.322452
$467$	1.57540	0.0729008	0.0364504	−	0.999335i	$-0.488395\pi$
$467$	1.57540	0.0729008	0.0364504	+	0.999335i	$0.488395\pi$
$468$	0	0
$469$	−2.97285	−0.137274
$470$	−6.47889	−0.298849
$471$	−8.43727	−0.388769
$472$	14.7748	0.680065
$473$	−33.1987	−1.52648
$474$	12.1468	0.557919
$475$	−16.0151	−0.734822
$476$	6.85086	0.314008
$477$	−4.20775	−0.192660
$478$	−24.0737	−1.10110
$479$	19.6407	0.897407	0.448704	−	0.893681i	$-0.351886\pi$
$479$	19.6407	0.897407	0.448704	+	0.893681i	$0.351886\pi$
$480$	11.0248	0.503209
$481$	0	0
$482$	−36.4644	−1.66091
$483$	−6.76271	−0.307714
$484$	51.9734	2.36243
$485$	−0.633415	−0.0287619
$486$	2.24698	0.101925
$487$	19.0814	0.864663	0.432331	−	0.901715i	$-0.357691\pi$
$487$	19.0814	0.864663	0.432331	+	0.901715i	$0.357691\pi$
$488$	14.5284	0.657670
$489$	−14.1836	−0.641404
$490$	−3.80194	−0.171754
$491$	15.8582	0.715668	0.357834	−	0.933785i	$-0.383515\pi$
$491$	15.8582	0.715668	0.357834	+	0.933785i	$0.383515\pi$
$492$	−21.3056	−0.960530
$493$	−16.9976	−0.765534
$494$	0	0
$495$	−8.96077	−0.402757
$496$	3.12737	0.140423
$497$	−8.37867	−0.375835
$498$	−0.295897	−0.0132595
$499$	−17.1806	−0.769109	−0.384555	−	0.923102i	$-0.625645\pi$
$499$	−17.1806	−0.769109	−0.384555	+	0.923102i	$0.625645\pi$
$500$	36.8189	1.64659
$501$	−8.87800	−0.396640
$502$	−49.3062	−2.20064
$503$	7.45042	0.332198	0.166099	−	0.986109i	$-0.446883\pi$
$503$	7.45042	0.332198	0.166099	+	0.986109i	$0.446883\pi$
$504$	−2.35690	−0.104984
$505$	23.7302	1.05598
$506$	80.4747	3.57754
$507$	0	0
$508$	−61.3062	−2.72002
$509$	12.2392	0.542493	0.271247	−	0.962510i	$-0.412564\pi$
$509$	12.2392	0.542493	0.271247	+	0.962510i	$0.412564\pi$
$510$	8.54288	0.378285
$511$	−4.37867	−0.193701
$512$	9.00538	0.397985
$513$	7.49396	0.330866
$514$	48.4064	2.13511
$515$	25.2476	1.11254
$516$	−19.1129	−0.841399
$517$	9.02475	0.396908
$518$	−21.5036	−0.944816
$519$	−24.3230	−1.06766
$520$	0	0
$521$	42.0646	1.84288	0.921441	−	0.388518i	$-0.127013\pi$
$521$	42.0646	1.84288	0.921441	+	0.388518i	$0.127013\pi$
$522$	16.9976	0.743965
$523$	2.04593	0.0894624	0.0447312	−	0.998999i	$-0.485757\pi$
$523$	2.04593	0.0894624	0.0447312	+	0.998999i	$0.485757\pi$
$524$	−11.2567	−0.491750
$525$	2.13706	0.0932691
$526$	−28.2107	−1.23005
$527$	8.76271	0.381710
$528$	−4.24698	−0.184826
$529$	22.7342	0.988445
$530$	15.9976	0.694892
$531$	6.26875	0.272041
$532$	−22.8485	−0.990606
$533$	0	0
$534$	13.2349	0.572730
$535$	−13.7640	−0.595071
$536$	7.00670	0.302644
$537$	−12.8702	−0.555392
$538$	1.60925	0.0693798
$539$	5.29590	0.228110
$540$	−5.15883	−0.222001
$541$	25.8495	1.11136	0.555679	−	0.831397i	$-0.312458\pi$
$541$	25.8495	1.11136	0.555679	+	0.831397i	$0.312458\pi$
$542$	−11.2687	−0.484034
$543$	9.25667	0.397242
$544$	14.6407	0.627715
$545$	−13.3043	−0.569892
$546$	0	0
$547$	22.6866	0.970011	0.485005	−	0.874511i	$-0.338818\pi$
$547$	22.6866	0.970011	0.485005	+	0.874511i	$0.338818\pi$
$548$	5.62996	0.240500
$549$	6.16421	0.263082
$550$	−25.4306	−1.08436
$551$	56.6892	2.41504
$552$	15.9390	0.678409
$553$	−5.40581	−0.229879
$554$	−23.6775	−1.00596
$555$	−16.1927	−0.687341
$556$	−44.2368	−1.87606
$557$	−10.0828	−0.427221	−0.213610	−	0.976919i	$-0.568522\pi$
$557$	−10.0828	−0.427221	−0.213610	+	0.976919i	$0.568522\pi$
$558$	−8.76271	−0.370955
$559$	0	0
$560$	−1.35690	−0.0573393
$561$	−11.8998	−0.502409
$562$	6.84117	0.288577
$563$	2.89785	0.122130	0.0610650	−	0.998134i	$-0.480550\pi$
$563$	2.89785	0.122130	0.0610650	+	0.998134i	$0.480550\pi$
$564$	5.19567	0.218777
$565$	−10.3217	−0.434238
$566$	9.78986	0.411498
$567$	−1.00000	−0.0419961
$568$	19.7476	0.828593
$569$	28.3967	1.19045	0.595226	−	0.803558i	$-0.297062\pi$
$569$	28.3967	1.19045	0.595226	+	0.803558i	$0.297062\pi$
$570$	−28.4916	−1.19338
$571$	39.6262	1.65831	0.829153	−	0.559021i	$-0.188823\pi$
$571$	39.6262	1.65831	0.829153	+	0.559021i	$0.188823\pi$
$572$	0	0
$573$	−3.37867	−0.141146
$574$	15.7017	0.655377
$575$	−14.4523	−0.602704
$576$	−13.0368	−0.543201
$577$	12.8170	0.533579	0.266789	−	0.963755i	$-0.414037\pi$
$577$	12.8170	0.533579	0.266789	+	0.963755i	$0.414037\pi$
$578$	−26.8538	−1.11697
$579$	24.9148	1.03543
$580$	−39.0248	−1.62041
$581$	0.131687	0.00546328
$582$	0.841166	0.0348675
$583$	−22.2838	−0.922901
$584$	10.3201	0.427047
$585$	0	0
$586$	−62.2911	−2.57322
$587$	−48.2127	−1.98995	−0.994975	−	0.100128i	$-0.968075\pi$
$587$	−48.2127	−1.98995	−0.994975	+	0.100128i	$0.968075\pi$
$588$	3.04892	0.125735
$589$	−29.2247	−1.20418
$590$	−23.8334	−0.981205
$591$	−16.8291	−0.692256
$592$	−7.67456	−0.315423
$593$	−15.5539	−0.638722	−0.319361	−	0.947633i	$-0.603468\pi$
$593$	−15.5539	−0.638722	−0.319361	+	0.947633i	$0.603468\pi$
$594$	11.8998	0.488254
$595$	−3.80194	−0.155864
$596$	−37.8243	−1.54934
$597$	16.3002	0.667123
$598$	0	0
$599$	−16.0422	−0.655467	−0.327734	−	0.944770i	$-0.606285\pi$
$599$	−16.0422	−0.655467	−0.327734	+	0.944770i	$0.606285\pi$
$600$	−5.03684	−0.205628
$601$	23.7657	0.969423	0.484711	−	0.874674i	$-0.338925\pi$
$601$	23.7657	0.969423	0.484711	+	0.874674i	$0.338925\pi$
$602$	14.0858	0.574092
$603$	2.97285	0.121064
$604$	−4.05429	−0.164967
$605$	−28.8431	−1.17264
$606$	−31.5133	−1.28014
$607$	42.6335	1.73044	0.865221	−	0.501391i	$-0.167178\pi$
$607$	42.6335	1.73044	0.865221	+	0.501391i	$0.167178\pi$
$608$	−48.8286	−1.98026
$609$	−7.56465	−0.306535
$610$	−23.4359	−0.948894
$611$	0	0
$612$	−6.85086	−0.276929
$613$	19.5652	0.790233	0.395116	−	0.918631i	$-0.370704\pi$
$613$	19.5652	0.790233	0.395116	+	0.918631i	$0.370704\pi$
$614$	37.1497	1.49924
$615$	11.8237	0.476778
$616$	−12.4819	−0.502909
$617$	−45.1390	−1.81723	−0.908614	−	0.417638i	$-0.862858\pi$
$617$	−45.1390	−1.81723	−0.908614	+	0.417638i	$0.862858\pi$
$618$	−33.5284	−1.34871
$619$	2.87071	0.115383	0.0576917	−	0.998334i	$-0.481626\pi$
$619$	2.87071	0.115383	0.0576917	+	0.998334i	$0.481626\pi$
$620$	20.1183	0.807969
$621$	6.76271	0.271378
$622$	−57.8558	−2.31980
$623$	−5.89008	−0.235981
$624$	0	0
$625$	−9.74764	−0.389906
$626$	−54.2911	−2.16991
$627$	39.6872	1.58496
$628$	−25.7245	−1.02652
$629$	−21.5036	−0.857407
$630$	3.80194	0.151473
$631$	−19.4499	−0.774290	−0.387145	−	0.922019i	$-0.626539\pi$
$631$	−19.4499	−0.774290	−0.387145	+	0.922019i	$0.626539\pi$
$632$	12.7409	0.506807
$633$	−13.5308	−0.537801
$634$	9.24459	0.367149
$635$	34.0224	1.35014
$636$	−12.8291	−0.508706
$637$	0	0
$638$	90.0176	3.56383
$639$	8.37867	0.331455
$640$	27.5157	1.08765
$641$	−2.87130	−0.113409	−0.0567047	−	0.998391i	$-0.518059\pi$
$641$	−2.87130	−0.113409	−0.0567047	+	0.998391i	$0.518059\pi$
$642$	18.2784	0.721392
$643$	26.6474	1.05087	0.525436	−	0.850833i	$-0.323902\pi$
$643$	26.6474	1.05087	0.525436	+	0.850833i	$0.323902\pi$
$644$	−20.6189	−0.812500
$645$	10.6069	0.417645
$646$	−37.8364	−1.48865
$647$	7.80386	0.306801	0.153401	−	0.988164i	$-0.450978\pi$
$647$	7.80386	0.306801	0.153401	+	0.988164i	$0.450978\pi$
$648$	2.35690	0.0925876
$649$	33.1987	1.30316
$650$	0	0
$651$	3.89977	0.152844
$652$	−43.2446	−1.69359
$653$	−15.5724	−0.609396	−0.304698	−	0.952449i	$-0.598555\pi$
$653$	−15.5724	−0.609396	−0.304698	+	0.952449i	$0.598555\pi$
$654$	17.6679	0.690868
$655$	6.24698	0.244090
$656$	5.60388	0.218795
$657$	4.37867	0.170828
$658$	−3.82908	−0.149273
$659$	−29.8165	−1.16149	−0.580744	−	0.814087i	$-0.697238\pi$
$659$	−29.8165	−1.16149	−0.580744	+	0.814087i	$0.697238\pi$
$660$	−27.3207	−1.06345
$661$	−15.0640	−0.585921	−0.292961	−	0.956125i	$-0.594640\pi$
$661$	−15.0640	−0.585921	−0.292961	+	0.956125i	$0.594640\pi$
$662$	55.7851	2.16815
$663$	0	0
$664$	−0.310371	−0.0120447
$665$	12.6799	0.491707
$666$	21.5036	0.833249
$667$	51.1575	1.98083
$668$	−27.0683	−1.04730
$669$	9.61596	0.371774
$670$	−11.3026	−0.436658
$671$	32.6450	1.26025
$672$	6.51573	0.251350
$673$	−16.2118	−0.624919	−0.312459	−	0.949931i	$-0.601153\pi$
$673$	−16.2118	−0.624919	−0.312459	+	0.949931i	$0.601153\pi$
$674$	73.5695	2.83379
$675$	−2.13706	−0.0822556
$676$	0	0
$677$	5.36419	0.206163	0.103081	−	0.994673i	$-0.467130\pi$
$677$	5.36419	0.206163	0.103081	+	0.994673i	$0.467130\pi$
$678$	13.7071	0.526418
$679$	−0.374354	−0.0143664
$680$	8.96077	0.343630
$681$	−11.3381	−0.434477
$682$	−46.4064	−1.77699
$683$	47.8920	1.83254	0.916268	−	0.400565i	$-0.131186\pi$
$683$	47.8920	1.83254	0.916268	+	0.400565i	$0.131186\pi$
$684$	22.8485	0.873633
$685$	−3.12439	−0.119377
$686$	−2.24698	−0.0857901
$687$	5.28083	0.201476
$688$	5.02715	0.191658
$689$	0	0
$690$	−25.7114	−0.978816
$691$	11.7554	0.447197	0.223598	−	0.974681i	$-0.428220\pi$
$691$	11.7554	0.447197	0.223598	+	0.974681i	$0.428220\pi$
$692$	−74.1590	−2.81910
$693$	−5.29590	−0.201174
$694$	0.679940	0.0258102
$695$	24.5496	0.931219
$696$	17.8291	0.675810
$697$	15.7017	0.594745
$698$	−62.8708	−2.37970
$699$	3.09783	0.117171
$700$	6.51573	0.246271
$701$	−8.59611	−0.324670	−0.162335	−	0.986736i	$-0.551903\pi$
$701$	−8.59611	−0.324670	−0.162335	+	0.986736i	$0.551903\pi$
$702$	0	0
$703$	71.7174	2.70487
$704$	−69.0417	−2.60211
$705$	−2.88338	−0.108594
$706$	−0.279503	−0.0105193
$707$	14.0248	0.527455
$708$	19.1129	0.718307
$709$	29.0355	1.09045	0.545226	−	0.838289i	$-0.316444\pi$
$709$	29.0355	1.09045	0.545226	+	0.838289i	$0.316444\pi$
$710$	−31.8552	−1.19550
$711$	5.40581	0.202734
$712$	13.8823	0.520262
$713$	−26.3730	−0.987678
$714$	5.04892	0.188951
$715$	0	0
$716$	−39.2403	−1.46648
$717$	−10.7138	−0.400114
$718$	−46.1172	−1.72108
$719$	40.0562	1.49384	0.746922	−	0.664911i	$-0.231531\pi$
$719$	40.0562	1.49384	0.746922	+	0.664911i	$0.231531\pi$
$720$	1.35690	0.0505685
$721$	14.9215	0.555707
$722$	83.4965	3.10742
$723$	−16.2282	−0.603533
$724$	28.2228	1.04889
$725$	−16.1661	−0.600395
$726$	38.3032	1.42156
$727$	−12.4004	−0.459907	−0.229953	−	0.973202i	$-0.573857\pi$
$727$	−12.4004	−0.459907	−0.229953	+	0.973202i	$0.573857\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.6474	−0.616149
$731$	14.0858	0.520980
$732$	18.7942	0.694652
$733$	−39.9245	−1.47465	−0.737323	−	0.675540i	$-0.763910\pi$
$733$	−39.9245	−1.47465	−0.737323	+	0.675540i	$0.763910\pi$
$734$	−34.5254	−1.27436
$735$	−1.69202	−0.0624112
$736$	−44.0640	−1.62422
$737$	15.7439	0.579935
$738$	−15.7017	−0.577988
$739$	26.1032	0.960222	0.480111	−	0.877208i	$-0.340596\pi$
$739$	26.1032	0.960222	0.480111	+	0.877208i	$0.340596\pi$
$740$	−49.3702	−1.81488
$741$	0	0
$742$	9.45473	0.347094
$743$	−17.3496	−0.636495	−0.318248	−	0.948008i	$-0.603094\pi$
$743$	−17.3496	−0.636495	−0.318248	+	0.948008i	$0.603094\pi$
$744$	−9.19136	−0.336972
$745$	20.9909	0.769047
$746$	−10.9022	−0.399157
$747$	−0.131687	−0.00481816
$748$	−36.2814	−1.32658
$749$	−8.13467	−0.297234
$750$	27.1347	0.990818
$751$	−17.1927	−0.627370	−0.313685	−	0.949527i	$-0.601564\pi$
$751$	−17.1927	−0.627370	−0.313685	+	0.949527i	$0.601564\pi$
$752$	−1.36658	−0.0498342
$753$	−21.9433	−0.799659
$754$	0	0
$755$	2.24996	0.0818846
$756$	−3.04892	−0.110888
$757$	1.30234	0.0473343	0.0236672	−	0.999720i	$-0.492466\pi$
$757$	1.30234	0.0473343	0.0236672	+	0.999720i	$0.492466\pi$
$758$	12.0194	0.436563
$759$	35.8146	1.29999
$760$	−29.8853	−1.08405
$761$	4.17390	0.151304	0.0756519	−	0.997134i	$-0.475896\pi$
$761$	4.17390	0.151304	0.0756519	+	0.997134i	$0.475896\pi$
$762$	−45.1812	−1.63674
$763$	−7.86294	−0.284657
$764$	−10.3013	−0.372687
$765$	3.80194	0.137459
$766$	3.01208	0.108831
$767$	0	0
$768$	−10.4668	−0.377689
$769$	11.6668	0.420715	0.210358	−	0.977624i	$-0.432537\pi$
$769$	11.6668	0.420715	0.210358	+	0.977624i	$0.432537\pi$
$770$	20.1347	0.725603
$771$	21.5429	0.775848
$772$	75.9633	2.73398
$773$	3.66594	0.131855	0.0659273	−	0.997824i	$-0.478999\pi$
$773$	3.66594	0.131855	0.0659273	+	0.997824i	$0.478999\pi$
$774$	−14.0858	−0.506302
$775$	8.33406	0.299368
$776$	0.882314	0.0316732
$777$	−9.57002	−0.343323
$778$	−38.4349	−1.37796
$779$	−52.3672	−1.87625
$780$	0	0
$781$	44.3726	1.58777
$782$	−34.1444	−1.22100
$783$	7.56465	0.270338
$784$	−0.801938	−0.0286406
$785$	14.2760	0.509534
$786$	−8.29590	−0.295905
$787$	20.7772	0.740627	0.370313	−	0.928907i	$-0.379250\pi$
$787$	20.7772	0.740627	0.370313	+	0.928907i	$0.379250\pi$
$788$	−51.3105	−1.82786
$789$	−12.5550	−0.446968
$790$	−20.5526	−0.731227
$791$	−6.10023	−0.216899
$792$	12.4819	0.443524
$793$	0	0
$794$	−22.5157	−0.799053
$795$	7.11960	0.252506
$796$	49.6980	1.76150
$797$	−13.3773	−0.473850	−0.236925	−	0.971528i	$-0.576140\pi$
$797$	−13.3773	−0.473850	−0.236925	+	0.971528i	$0.576140\pi$
$798$	−16.8388	−0.596086
$799$	−3.82908	−0.135463
$800$	13.9245	0.492306
$801$	5.89008	0.208116
$802$	19.8334	0.700342
$803$	23.1890	0.818321
$804$	9.06398	0.319662
$805$	11.4426	0.403300
$806$	0	0
$807$	0.716185	0.0252109
$808$	−33.0549	−1.16287
$809$	−11.8836	−0.417807	−0.208903	−	0.977936i	$-0.566989\pi$
$809$	−11.8836	−0.417807	−0.208903	+	0.977936i	$0.566989\pi$
$810$	−3.80194	−0.133586
$811$	0.178211	0.00625783	0.00312892	−	0.999995i	$-0.499004\pi$
$811$	0.178211	0.00625783	0.00312892	+	0.999995i	$0.499004\pi$
$812$	−23.0640	−0.809387
$813$	−5.01507	−0.175886
$814$	113.881	3.99153
$815$	23.9989	0.840646
$816$	1.80194	0.0630804
$817$	−46.9778	−1.64354
$818$	−1.17390	−0.0410444
$819$	0	0
$820$	36.0495	1.25890
$821$	31.5555	1.10130	0.550648	−	0.834737i	$-0.314381\pi$
$821$	31.5555	1.10130	0.550648	+	0.834737i	$0.314381\pi$
$822$	4.14914	0.144718
$823$	37.4940	1.30696	0.653479	−	0.756945i	$-0.273309\pi$
$823$	37.4940	1.30696	0.653479	+	0.756945i	$0.273309\pi$
$824$	−35.1685	−1.22515
$825$	−11.3177	−0.394031
$826$	−14.0858	−0.490106
$827$	−40.3749	−1.40397	−0.701987	−	0.712190i	$-0.747704\pi$
$827$	−40.3749	−1.40397	−0.701987	+	0.712190i	$0.747704\pi$
$828$	20.6189	0.716558
$829$	−34.8552	−1.21057	−0.605285	−	0.796009i	$-0.706941\pi$
$829$	−34.8552	−1.21057	−0.605285	+	0.796009i	$0.706941\pi$
$830$	0.500664	0.0173783
$831$	−10.5375	−0.365542
$832$	0	0
$833$	−2.24698	−0.0778532
$834$	−32.6015	−1.12890
$835$	15.0218	0.519850
$836$	121.003	4.18498
$837$	−3.89977	−0.134796
$838$	24.8635	0.858896
$839$	−23.9259	−0.826012	−0.413006	−	0.910728i	$-0.635521\pi$
$839$	−23.9259	−0.826012	−0.413006	+	0.910728i	$0.635521\pi$
$840$	3.98792	0.137596
$841$	28.2239	0.973237
$842$	11.8291	0.407657
$843$	3.04461	0.104862
$844$	−41.2543	−1.42003
$845$	0	0
$846$	3.82908	0.131647
$847$	−17.0465	−0.585726
$848$	3.37435	0.115876
$849$	4.35690	0.149528
$850$	10.7899	0.370089
$851$	64.7193	2.21855
$852$	25.5459	0.875187
$853$	−39.9101	−1.36649	−0.683247	−	0.730187i	$-0.739433\pi$
$853$	−39.9101	−1.36649	−0.683247	+	0.730187i	$0.739433\pi$
$854$	−13.8509	−0.473967
$855$	−12.6799	−0.433645
$856$	19.1726	0.655305
$857$	−12.0392	−0.411252	−0.205626	−	0.978631i	$-0.565923\pi$
$857$	−12.0392	−0.411252	−0.205626	+	0.978631i	$0.565923\pi$
$858$	0	0
$859$	13.6993	0.467415	0.233707	−	0.972307i	$-0.424914\pi$
$859$	13.6993	0.467415	0.233707	+	0.972307i	$0.424914\pi$
$860$	32.3394	1.10277
$861$	6.98792	0.238148
$862$	22.5864	0.769296
$863$	−7.45712	−0.253843	−0.126922	−	0.991913i	$-0.540510\pi$
$863$	−7.45712	−0.253843	−0.126922	+	0.991913i	$0.540510\pi$
$864$	−6.51573	−0.221670
$865$	41.1551	1.39932
$866$	63.2301	2.14865
$867$	−11.9511	−0.405880
$868$	11.8901	0.403576
$869$	28.6286	0.971160
$870$	−28.7603	−0.975066
$871$	0	0
$872$	18.5321	0.627577
$873$	0.374354	0.0126700
$874$	113.876	3.85190
$875$	−12.0761	−0.408245
$876$	13.3502	0.451061
$877$	−34.9487	−1.18013	−0.590067	−	0.807355i	$-0.700899\pi$
$877$	−34.9487	−1.18013	−0.590067	+	0.807355i	$0.700899\pi$
$878$	−59.7066	−2.01500
$879$	−27.7222	−0.935045
$880$	7.18598	0.242239
$881$	−45.5792	−1.53560	−0.767802	−	0.640687i	$-0.778649\pi$
$881$	−45.5792	−1.53560	−0.767802	+	0.640687i	$0.778649\pi$
$882$	2.24698	0.0756597
$883$	5.39240	0.181469	0.0907344	−	0.995875i	$-0.471079\pi$
$883$	5.39240	0.181469	0.0907344	+	0.995875i	$0.471079\pi$
$884$	0	0
$885$	−10.6069	−0.356546
$886$	−79.0840	−2.65688
$887$	−42.8525	−1.43885	−0.719423	−	0.694572i	$-0.755594\pi$
$887$	−42.8525	−1.43885	−0.719423	+	0.694572i	$0.755594\pi$
$888$	22.5555	0.756915
$889$	20.1075	0.674385
$890$	−22.3937	−0.750640
$891$	5.29590	0.177419
$892$	29.3183	0.981648
$893$	12.7705	0.427348
$894$	−27.8756	−0.932300
$895$	21.7767	0.727915
$896$	16.2620	0.543277
$897$	0	0
$898$	47.6316	1.58949
$899$	−29.5004	−0.983893
$900$	−6.51573	−0.217191
$901$	9.45473	0.314983
$902$	−83.1546	−2.76875
$903$	6.26875	0.208611
$904$	14.3776	0.478192
$905$	−15.6625	−0.520639
$906$	−2.98792	−0.0992669
$907$	38.6122	1.28210	0.641049	−	0.767500i	$-0.278499\pi$
$907$	38.6122	1.28210	0.641049	+	0.767500i	$0.278499\pi$
$908$	−34.5690	−1.14721
$909$	−14.0248	−0.465172
$910$	0	0
$911$	−2.88663	−0.0956382	−0.0478191	−	0.998856i	$-0.515227\pi$
$911$	−2.88663	−0.0956382	−0.0478191	+	0.998856i	$0.515227\pi$
$912$	−6.00969	−0.199001
$913$	−0.697398	−0.0230805
$914$	−81.4301	−2.69347
$915$	−10.4300	−0.344804
$916$	16.1008	0.531986
$917$	3.69202	0.121921
$918$	−5.04892	−0.166639
$919$	−37.3381	−1.23167	−0.615835	−	0.787875i	$-0.711181\pi$
$919$	−37.3381	−1.23167	−0.615835	+	0.787875i	$0.711181\pi$
$920$	−26.9691	−0.889146
$921$	16.5332	0.544787
$922$	74.8751	2.46588
$923$	0	0
$924$	−16.1468	−0.531189
$925$	−20.4517	−0.672449
$926$	70.4422	2.31487
$927$	−14.9215	−0.490088
$928$	−49.2892	−1.61800
$929$	1.92825	0.0632637	0.0316319	−	0.999500i	$-0.489930\pi$
$929$	1.92825	0.0632637	0.0316319	+	0.999500i	$0.489930\pi$
$930$	14.8267	0.486186
$931$	7.49396	0.245605
$932$	9.44504	0.309383
$933$	−25.7482	−0.842959
$934$	3.53989	0.115829
$935$	20.1347	0.658474
$936$	0	0
$937$	49.0810	1.60341	0.801703	−	0.597723i	$-0.203928\pi$
$937$	49.0810	1.60341	0.801703	+	0.597723i	$0.203928\pi$
$938$	−6.67994	−0.218108
$939$	−24.1618	−0.788491
$940$	−8.79118	−0.286737
$941$	−8.92394	−0.290912	−0.145456	−	0.989365i	$-0.546465\pi$
$941$	−8.92394	−0.290912	−0.145456	+	0.989365i	$0.546465\pi$
$942$	−18.9584	−0.617697
$943$	−47.2573	−1.53891
$944$	−5.02715	−0.163620
$945$	1.69202	0.0550415
$946$	−74.5967	−2.42535
$947$	−52.9700	−1.72129	−0.860647	−	0.509203i	$-0.829940\pi$
$947$	−52.9700	−1.72129	−0.860647	+	0.509203i	$0.829940\pi$
$948$	16.4819	0.535306
$949$	0	0
$950$	−35.9855	−1.16752
$951$	4.11423	0.133413
$952$	5.29590	0.171641
$953$	10.4099	0.337209	0.168604	−	0.985684i	$-0.446074\pi$
$953$	10.4099	0.337209	0.168604	+	0.985684i	$0.446074\pi$
$954$	−9.45473	−0.306108
$955$	5.71678	0.184991
$956$	−32.6655	−1.05648
$957$	40.0616	1.29501
$958$	44.1323	1.42585
$959$	−1.84654	−0.0596280
$960$	22.0586	0.711938
$961$	−15.7918	−0.509412
$962$	0	0
$963$	8.13467	0.262136
$964$	−49.4784	−1.59359
$965$	−42.1564	−1.35706
$966$	−15.1957	−0.488913
$967$	−51.0689	−1.64226	−0.821132	−	0.570738i	$-0.806657\pi$
$967$	−51.0689	−1.64226	−0.821132	+	0.570738i	$0.806657\pi$
$968$	40.1769	1.29133
$969$	−16.8388	−0.540939
$970$	−1.42327	−0.0456985
$971$	44.7706	1.43676	0.718378	−	0.695653i	$-0.244885\pi$
$971$	44.7706	1.43676	0.718378	+	0.695653i	$0.244885\pi$
$972$	3.04892	0.0977941
$973$	14.5090	0.465138
$974$	42.8756	1.37382
$975$	0	0
$976$	−4.94331	−0.158232
$977$	16.1468	0.516580	0.258290	−	0.966067i	$-0.416841\pi$
$977$	16.1468	0.516580	0.258290	+	0.966067i	$0.416841\pi$
$978$	−31.8702	−1.01910
$979$	31.1933	0.996941
$980$	−5.15883	−0.164793
$981$	7.86294	0.251044
$982$	35.6329	1.13709
$983$	−53.2198	−1.69745	−0.848725	−	0.528835i	$-0.822629\pi$
$983$	−53.2198	−1.69745	−0.848725	+	0.528835i	$0.822629\pi$
$984$	−16.4698	−0.525038
$985$	28.4752	0.907294
$986$	−38.1933	−1.21632
$987$	−1.70410	−0.0542422
$988$	0	0
$989$	−42.3937	−1.34804
$990$	−20.1347	−0.639922
$991$	26.0935	0.828888	0.414444	−	0.910075i	$-0.363976\pi$
$991$	26.0935	0.828888	0.414444	+	0.910075i	$0.363976\pi$
$992$	25.4099	0.806764
$993$	24.8267	0.787851
$994$	−18.8267	−0.597146
$995$	−27.5803	−0.874354
$996$	−0.401501	−0.0127221
$997$	3.47325	0.109999	0.0549995	−	0.998486i	$-0.482484\pi$
$997$	3.47325	0.109999	0.0549995	+	0.998486i	$0.482484\pi$
$998$	−38.6045	−1.22200
$999$	9.57002	0.302782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.u.1.3		3
13.4	even	6		273.2.k.c.211.3	yes	6
13.10	even	6		273.2.k.c.22.3	✓	6
13.12	even	2		3549.2.a.i.1.1		3
39.17	odd	6		819.2.o.e.757.1		6
39.23	odd	6		819.2.o.e.568.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.3	✓	6	13.10	even	6
273.2.k.c.211.3	yes	6	13.4	even	6
819.2.o.e.568.1		6	39.23	odd	6
819.2.o.e.757.1		6	39.17	odd	6
3549.2.a.i.1.1		3	13.12	even	2
3549.2.a.u.1.3		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24698 q^{2} +1.00000 q^{3} +3.04892 q^{4} -1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +2.35690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.24698 q^{2} +1.00000 q^{3} +3.04892 q^{4} -1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +2.35690 q^{8} +1.00000 q^{9} -3.80194 q^{10} +5.29590 q^{11} +3.04892 q^{12} -2.24698 q^{14} -1.69202 q^{15} -0.801938 q^{16} -2.24698 q^{17} +2.24698 q^{18} +7.49396 q^{19} -5.15883 q^{20} -1.00000 q^{21} +11.8998 q^{22} +6.76271 q^{23} +2.35690 q^{24} -2.13706 q^{25} +1.00000 q^{27} -3.04892 q^{28} +7.56465 q^{29} -3.80194 q^{30} -3.89977 q^{31} -6.51573 q^{32} +5.29590 q^{33} -5.04892 q^{34} +1.69202 q^{35} +3.04892 q^{36} +9.57002 q^{37} +16.8388 q^{38} -3.98792 q^{40} -6.98792 q^{41} -2.24698 q^{42} -6.26875 q^{43} +16.1468 q^{44} -1.69202 q^{45} +15.1957 q^{46} +1.70410 q^{47} -0.801938 q^{48} +1.00000 q^{49} -4.80194 q^{50} -2.24698 q^{51} -4.20775 q^{53} +2.24698 q^{54} -8.96077 q^{55} -2.35690 q^{56} +7.49396 q^{57} +16.9976 q^{58} +6.26875 q^{59} -5.15883 q^{60} +6.16421 q^{61} -8.76271 q^{62} -1.00000 q^{63} -13.0368 q^{64} +11.8998 q^{66} +2.97285 q^{67} -6.85086 q^{68} +6.76271 q^{69} +3.80194 q^{70} +8.37867 q^{71} +2.35690 q^{72} +4.37867 q^{73} +21.5036 q^{74} -2.13706 q^{75} +22.8485 q^{76} -5.29590 q^{77} +5.40581 q^{79} +1.35690 q^{80} +1.00000 q^{81} -15.7017 q^{82} -0.131687 q^{83} -3.04892 q^{84} +3.80194 q^{85} -14.0858 q^{86} +7.56465 q^{87} +12.4819 q^{88} +5.89008 q^{89} -3.80194 q^{90} +20.6189 q^{92} -3.89977 q^{93} +3.82908 q^{94} -12.6799 q^{95} -6.51573 q^{96} +0.374354 q^{97} +2.24698 q^{98} +5.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * q^98 + 2 * q^99

Introduction

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Modular forms

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Database

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