LMFDB - Embedded newform 7098.2.a.ci.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.04892 q^{10} +2.13706 q^{11} -1.00000 q^{12} -1.00000 q^{14} +3.04892 q^{15} +1.00000 q^{16} -1.40581 q^{17} +1.00000 q^{18} +2.13706 q^{19} -3.04892 q^{20} +1.00000 q^{21} +2.13706 q^{22} -2.26875 q^{23} -1.00000 q^{24} +4.29590 q^{25} -1.00000 q^{27} -1.00000 q^{28} -2.58211 q^{29} +3.04892 q^{30} -6.34481 q^{31} +1.00000 q^{32} -2.13706 q^{33} -1.40581 q^{34} +3.04892 q^{35} +1.00000 q^{36} +10.6528 q^{37} +2.13706 q^{38} -3.04892 q^{40} -4.43296 q^{41} +1.00000 q^{42} -9.55496 q^{43} +2.13706 q^{44} -3.04892 q^{45} -2.26875 q^{46} -3.98792 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.29590 q^{50} +1.40581 q^{51} +6.46681 q^{53} -1.00000 q^{54} -6.51573 q^{55} -1.00000 q^{56} -2.13706 q^{57} -2.58211 q^{58} -3.44504 q^{59} +3.04892 q^{60} +9.98792 q^{61} -6.34481 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.13706 q^{66} +11.3937 q^{67} -1.40581 q^{68} +2.26875 q^{69} +3.04892 q^{70} +4.21983 q^{71} +1.00000 q^{72} +5.84548 q^{73} +10.6528 q^{74} -4.29590 q^{75} +2.13706 q^{76} -2.13706 q^{77} -10.7071 q^{79} -3.04892 q^{80} +1.00000 q^{81} -4.43296 q^{82} +8.94869 q^{83} +1.00000 q^{84} +4.28621 q^{85} -9.55496 q^{86} +2.58211 q^{87} +2.13706 q^{88} -3.73556 q^{89} -3.04892 q^{90} -2.26875 q^{92} +6.34481 q^{93} -3.98792 q^{94} -6.51573 q^{95} -1.00000 q^{96} -5.10321 q^{97} +1.00000 q^{98} +2.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{16} + 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{21} + q^{22} + q^{23} - 3 q^{24} - q^{25} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 4 q^{31} + 3 q^{32} - q^{33} + 9 q^{34} + 3 q^{36} + 14 q^{37} + q^{38} + 6 q^{41} + 3 q^{42} - 29 q^{43} + q^{44} + q^{46} + 7 q^{47} - 3 q^{48} + 3 q^{49} - q^{50} - 9 q^{51} + 16 q^{53} - 3 q^{54} - 7 q^{55} - 3 q^{56} - q^{57} - 2 q^{58} - 10 q^{59} + 11 q^{61} + 4 q^{62} - 3 q^{63} + 3 q^{64} - q^{66} + 2 q^{67} + 9 q^{68} - q^{69} + 14 q^{71} + 3 q^{72} + 7 q^{73} + 14 q^{74} + q^{75} + q^{76} - q^{77} - 2 q^{79} + 3 q^{81} + 6 q^{82} - 5 q^{83} + 3 q^{84} + 21 q^{85} - 29 q^{86} + 2 q^{87} + q^{88} + q^{92} - 4 q^{93} + 7 q^{94} - 7 q^{95} - 3 q^{96} + 6 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^11 - 3 * q^12 - 3 * q^14 + 3 * q^16 + 9 * q^17 + 3 * q^18 + q^19 + 3 * q^21 + q^22 + q^23 - 3 * q^24 - q^25 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 4 * q^31 + 3 * q^32 - q^33 + 9 * q^34 + 3 * q^36 + 14 * q^37 + q^38 + 6 * q^41 + 3 * q^42 - 29 * q^43 + q^44 + q^46 + 7 * q^47 - 3 * q^48 + 3 * q^49 - q^50 - 9 * q^51 + 16 * q^53 - 3 * q^54 - 7 * q^55 - 3 * q^56 - q^57 - 2 * q^58 - 10 * q^59 + 11 * q^61 + 4 * q^62 - 3 * q^63 + 3 * q^64 - q^66 + 2 * q^67 + 9 * q^68 - q^69 + 14 * q^71 + 3 * q^72 + 7 * q^73 + 14 * q^74 + q^75 + q^76 - q^77 - 2 * q^79 + 3 * q^81 + 6 * q^82 - 5 * q^83 + 3 * q^84 + 21 * q^85 - 29 * q^86 + 2 * q^87 + q^88 + q^92 - 4 * q^93 + 7 * q^94 - 7 * q^95 - 3 * q^96 + 6 * q^97 + 3 * q^98 + 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
$5$	−3.04892	−1.36352	−0.681759	−	0.731577i	$-0.738785\pi$
$5$	−3.04892	−1.36352	−0.681759	+	0.731577i	$0.738785\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.04892	−0.964152
$11$	2.13706	0.644349	0.322174	−	0.946680i	$-0.395586\pi$
$11$	2.13706	0.644349	0.322174	+	0.946680i	$0.395586\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	3.04892	0.787227
$16$	1.00000	0.250000
$17$	−1.40581	−0.340960	−0.170480	−	0.985361i	$-0.554532\pi$
$17$	−1.40581	−0.340960	−0.170480	+	0.985361i	$0.554532\pi$
$18$	1.00000	0.235702
$19$	2.13706	0.490276	0.245138	−	0.969488i	$-0.421167\pi$
$19$	2.13706	0.490276	0.245138	+	0.969488i	$0.421167\pi$
$20$	−3.04892	−0.681759
$21$	1.00000	0.218218
$22$	2.13706	0.455623
$23$	−2.26875	−0.473067	−0.236534	−	0.971623i	$-0.576011\pi$
$23$	−2.26875	−0.473067	−0.236534	+	0.971623i	$0.576011\pi$
$24$	−1.00000	−0.204124
$25$	4.29590	0.859179
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−2.58211	−0.479485	−0.239742	−	0.970837i	$-0.577063\pi$
$29$	−2.58211	−0.479485	−0.239742	+	0.970837i	$0.577063\pi$
$30$	3.04892	0.556654
$31$	−6.34481	−1.13956	−0.569781	−	0.821796i	$-0.692972\pi$
$31$	−6.34481	−1.13956	−0.569781	+	0.821796i	$0.692972\pi$
$32$	1.00000	0.176777
$33$	−2.13706	−0.372015
$34$	−1.40581	−0.241095
$35$	3.04892	0.515361
$36$	1.00000	0.166667
$37$	10.6528	1.75131	0.875654	−	0.482939i	$-0.160431\pi$
$37$	10.6528	1.75131	0.875654	+	0.482939i	$0.160431\pi$
$38$	2.13706	0.346677
$39$	0	0
$40$	−3.04892	−0.482076
$41$	−4.43296	−0.692312	−0.346156	−	0.938177i	$-0.612513\pi$
$41$	−4.43296	−0.692312	−0.346156	+	0.938177i	$0.612513\pi$
$42$	1.00000	0.154303
$43$	−9.55496	−1.45712	−0.728559	−	0.684983i	$-0.759809\pi$
$43$	−9.55496	−1.45712	−0.728559	+	0.684983i	$0.759809\pi$
$44$	2.13706	0.322174
$45$	−3.04892	−0.454506
$46$	−2.26875	−0.334509
$47$	−3.98792	−0.581698	−0.290849	−	0.956769i	$-0.593938\pi$
$47$	−3.98792	−0.581698	−0.290849	+	0.956769i	$0.593938\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.29590	0.607532
$51$	1.40581	0.196853
$52$	0	0
$53$	6.46681	0.888285	0.444142	−	0.895956i	$-0.353508\pi$
$53$	6.46681	0.888285	0.444142	+	0.895956i	$0.353508\pi$
$54$	−1.00000	−0.136083
$55$	−6.51573	−0.878581
$56$	−1.00000	−0.133631
$57$	−2.13706	−0.283061
$58$	−2.58211	−0.339047
$59$	−3.44504	−0.448506	−0.224253	−	0.974531i	$-0.571994\pi$
$59$	−3.44504	−0.448506	−0.224253	+	0.974531i	$0.571994\pi$
$60$	3.04892	0.393614
$61$	9.98792	1.27882	0.639411	−	0.768865i	$-0.279178\pi$
$61$	9.98792	1.27882	0.639411	+	0.768865i	$0.279178\pi$
$62$	−6.34481	−0.805792
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.13706	−0.263054
$67$	11.3937	1.39197	0.695983	−	0.718058i	$-0.254969\pi$
$67$	11.3937	1.39197	0.695983	+	0.718058i	$0.254969\pi$
$68$	−1.40581	−0.170480
$69$	2.26875	0.273125
$70$	3.04892	0.364415
$71$	4.21983	0.500802	0.250401	−	0.968142i	$-0.419438\pi$
$71$	4.21983	0.500802	0.250401	+	0.968142i	$0.419438\pi$
$72$	1.00000	0.117851
$73$	5.84548	0.684161	0.342081	−	0.939671i	$-0.388868\pi$
$73$	5.84548	0.684161	0.342081	+	0.939671i	$0.388868\pi$
$74$	10.6528	1.23836
$75$	−4.29590	−0.496047
$76$	2.13706	0.245138
$77$	−2.13706	−0.243541
$78$	0	0
$79$	−10.7071	−1.20464	−0.602321	−	0.798254i	$-0.705757\pi$
$79$	−10.7071	−1.20464	−0.602321	+	0.798254i	$0.705757\pi$
$80$	−3.04892	−0.340879
$81$	1.00000	0.111111
$82$	−4.43296	−0.489539
$83$	8.94869	0.982246	0.491123	−	0.871090i	$-0.336586\pi$
$83$	8.94869	0.982246	0.491123	+	0.871090i	$0.336586\pi$
$84$	1.00000	0.109109
$85$	4.28621	0.464905
$86$	−9.55496	−1.03034
$87$	2.58211	0.276831
$88$	2.13706	0.227812
$89$	−3.73556	−0.395969	−0.197984	−	0.980205i	$-0.563440\pi$
$89$	−3.73556	−0.395969	−0.197984	+	0.980205i	$0.563440\pi$
$90$	−3.04892	−0.321384
$91$	0	0
$92$	−2.26875	−0.236534
$93$	6.34481	0.657927
$94$	−3.98792	−0.411322
$95$	−6.51573	−0.668500
$96$	−1.00000	−0.102062
$97$	−5.10321	−0.518153	−0.259076	−	0.965857i	$-0.583418\pi$
$97$	−5.10321	−0.518153	−0.259076	+	0.965857i	$0.583418\pi$
$98$	1.00000	0.101015
$99$	2.13706	0.214783
$100$	4.29590	0.429590
$101$	−12.2174	−1.21568	−0.607840	−	0.794059i	$-0.707964\pi$
$101$	−12.2174	−1.21568	−0.607840	+	0.794059i	$0.707964\pi$
$102$	1.40581	0.139196
$103$	−4.53319	−0.446668	−0.223334	−	0.974742i	$-0.571694\pi$
$103$	−4.53319	−0.446668	−0.223334	+	0.974742i	$0.571694\pi$
$104$	0	0
$105$	−3.04892	−0.297544
$106$	6.46681	0.628112
$107$	−12.5254	−1.21088	−0.605439	−	0.795892i	$-0.707002\pi$
$107$	−12.5254	−1.21088	−0.605439	+	0.795892i	$0.707002\pi$
$108$	−1.00000	−0.0962250
$109$	−1.15883	−0.110996	−0.0554981	−	0.998459i	$-0.517675\pi$
$109$	−1.15883	−0.110996	−0.0554981	+	0.998459i	$0.517675\pi$
$110$	−6.51573	−0.621250
$111$	−10.6528	−1.01112
$112$	−1.00000	−0.0944911
$113$	4.34721	0.408951	0.204475	−	0.978872i	$-0.434451\pi$
$113$	4.34721	0.408951	0.204475	+	0.978872i	$0.434451\pi$
$114$	−2.13706	−0.200154
$115$	6.91723	0.645035
$116$	−2.58211	−0.239742
$117$	0	0
$118$	−3.44504	−0.317142
$119$	1.40581	0.128871
$120$	3.04892	0.278327
$121$	−6.43296	−0.584815
$122$	9.98792	0.904264
$123$	4.43296	0.399707
$124$	−6.34481	−0.569781
$125$	2.14675	0.192011
$126$	−1.00000	−0.0890871
$127$	18.2959	1.62350	0.811749	−	0.584006i	$-0.198516\pi$
$127$	18.2959	1.62350	0.811749	+	0.584006i	$0.198516\pi$
$128$	1.00000	0.0883883
$129$	9.55496	0.841267
$130$	0	0
$131$	3.52781	0.308226	0.154113	−	0.988053i	$-0.450748\pi$
$131$	3.52781	0.308226	0.154113	+	0.988053i	$0.450748\pi$
$132$	−2.13706	−0.186007
$133$	−2.13706	−0.185307
$134$	11.3937	0.984268
$135$	3.04892	0.262409
$136$	−1.40581	−0.120547
$137$	0.249373	0.0213053	0.0106527	−	0.999943i	$-0.496609\pi$
$137$	0.249373	0.0213053	0.0106527	+	0.999943i	$0.496609\pi$
$138$	2.26875	0.193129
$139$	0.168522	0.0142939	0.00714694	−	0.999974i	$-0.497725\pi$
$139$	0.168522	0.0142939	0.00714694	+	0.999974i	$0.497725\pi$
$140$	3.04892	0.257681
$141$	3.98792	0.335843
$142$	4.21983	0.354120
$143$	0	0
$144$	1.00000	0.0833333
$145$	7.87263	0.653786
$146$	5.84548	0.483775
$147$	−1.00000	−0.0824786
$148$	10.6528	0.875654
$149$	16.3327	1.33803	0.669015	−	0.743249i	$-0.266716\pi$
$149$	16.3327	1.33803	0.669015	+	0.743249i	$0.266716\pi$
$150$	−4.29590	−0.350759
$151$	24.3448	1.98115	0.990576	−	0.136961i	$-0.0437335\pi$
$151$	24.3448	1.98115	0.990576	+	0.136961i	$0.0437335\pi$
$152$	2.13706	0.173339
$153$	−1.40581	−0.113653
$154$	−2.13706	−0.172209
$155$	19.3448	1.55381
$156$	0	0
$157$	−12.0978	−0.965512	−0.482756	−	0.875755i	$-0.660364\pi$
$157$	−12.0978	−0.965512	−0.482756	+	0.875755i	$0.660364\pi$
$158$	−10.7071	−0.851810
$159$	−6.46681	−0.512852
$160$	−3.04892	−0.241038
$161$	2.26875	0.178803
$162$	1.00000	0.0785674
$163$	14.0707	1.10210	0.551051	−	0.834472i	$-0.314227\pi$
$163$	14.0707	1.10210	0.551051	+	0.834472i	$0.314227\pi$
$164$	−4.43296	−0.346156
$165$	6.51573	0.507249
$166$	8.94869	0.694553
$167$	19.9541	1.54409	0.772046	−	0.635567i	$-0.219233\pi$
$167$	19.9541	1.54409	0.772046	+	0.635567i	$0.219233\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	4.28621	0.328737
$171$	2.13706	0.163425
$172$	−9.55496	−0.728559
$173$	−6.61596	−0.503002	−0.251501	−	0.967857i	$-0.580924\pi$
$173$	−6.61596	−0.503002	−0.251501	+	0.967857i	$0.580924\pi$
$174$	2.58211	0.195749
$175$	−4.29590	−0.324739
$176$	2.13706	0.161087
$177$	3.44504	0.258945
$178$	−3.73556	−0.279992
$179$	−7.49396	−0.560125	−0.280062	−	0.959982i	$-0.590355\pi$
$179$	−7.49396	−0.560125	−0.280062	+	0.959982i	$0.590355\pi$
$180$	−3.04892	−0.227253
$181$	19.1226	1.42137	0.710685	−	0.703510i	$-0.248385\pi$
$181$	19.1226	1.42137	0.710685	+	0.703510i	$0.248385\pi$
$182$	0	0
$183$	−9.98792	−0.738328
$184$	−2.26875	−0.167254
$185$	−32.4795	−2.38794
$186$	6.34481	0.465224
$187$	−3.00431	−0.219697
$188$	−3.98792	−0.290849
$189$	1.00000	0.0727393
$190$	−6.51573	−0.472701
$191$	23.2403	1.68161	0.840804	−	0.541340i	$-0.182083\pi$
$191$	23.2403	1.68161	0.840804	+	0.541340i	$0.182083\pi$
$192$	−1.00000	−0.0721688
$193$	4.00538	0.288313	0.144157	−	0.989555i	$-0.453953\pi$
$193$	4.00538	0.288313	0.144157	+	0.989555i	$0.453953\pi$
$194$	−5.10321	−0.366389
$195$	0	0
$196$	1.00000	0.0714286
$197$	−7.75840	−0.552763	−0.276381	−	0.961048i	$-0.589135\pi$
$197$	−7.75840	−0.552763	−0.276381	+	0.961048i	$0.589135\pi$
$198$	2.13706	0.151874
$199$	14.5526	1.03160	0.515802	−	0.856708i	$-0.327494\pi$
$199$	14.5526	1.03160	0.515802	+	0.856708i	$0.327494\pi$
$200$	4.29590	0.303766
$201$	−11.3937	−0.803652
$202$	−12.2174	−0.859616
$203$	2.58211	0.181228
$204$	1.40581	0.0984266
$205$	13.5157	0.943979
$206$	−4.53319	−0.315842
$207$	−2.26875	−0.157689
$208$	0	0
$209$	4.56704	0.315909
$210$	−3.04892	−0.210395
$211$	3.80194	0.261736	0.130868	−	0.991400i	$-0.458224\pi$
$211$	3.80194	0.261736	0.130868	+	0.991400i	$0.458224\pi$
$212$	6.46681	0.444142
$213$	−4.21983	−0.289138
$214$	−12.5254	−0.856220
$215$	29.1323	1.98680
$216$	−1.00000	−0.0680414
$217$	6.34481	0.430714
$218$	−1.15883	−0.0784861
$219$	−5.84548	−0.395001
$220$	−6.51573	−0.439290
$221$	0	0
$222$	−10.6528	−0.714969
$223$	−23.1347	−1.54921	−0.774606	−	0.632444i	$-0.782052\pi$
$223$	−23.1347	−1.54921	−0.774606	+	0.632444i	$0.782052\pi$
$224$	−1.00000	−0.0668153
$225$	4.29590	0.286393
$226$	4.34721	0.289172
$227$	−2.72348	−0.180764	−0.0903819	−	0.995907i	$-0.528809\pi$
$227$	−2.72348	−0.180764	−0.0903819	+	0.995907i	$0.528809\pi$
$228$	−2.13706	−0.141530
$229$	11.7385	0.775705	0.387852	−	0.921721i	$-0.373217\pi$
$229$	11.7385	0.775705	0.387852	+	0.921721i	$0.373217\pi$
$230$	6.91723	0.456109
$231$	2.13706	0.140608
$232$	−2.58211	−0.169524
$233$	9.92931	0.650491	0.325245	−	0.945630i	$-0.394553\pi$
$233$	9.92931	0.650491	0.325245	+	0.945630i	$0.394553\pi$
$234$	0	0
$235$	12.1588	0.793155
$236$	−3.44504	−0.224253
$237$	10.7071	0.695500
$238$	1.40581	0.0911253
$239$	22.1172	1.43064	0.715322	−	0.698795i	$-0.246280\pi$
$239$	22.1172	1.43064	0.715322	+	0.698795i	$0.246280\pi$
$240$	3.04892	0.196807
$241$	24.5429	1.58095	0.790473	−	0.612497i	$-0.209835\pi$
$241$	24.5429	1.58095	0.790473	+	0.612497i	$0.209835\pi$
$242$	−6.43296	−0.413526
$243$	−1.00000	−0.0641500
$244$	9.98792	0.639411
$245$	−3.04892	−0.194788
$246$	4.43296	0.282635
$247$	0	0
$248$	−6.34481	−0.402896
$249$	−8.94869	−0.567100
$250$	2.14675	0.135773
$251$	27.2489	1.71994	0.859968	−	0.510349i	$-0.170484\pi$
$251$	27.2489	1.71994	0.859968	+	0.510349i	$0.170484\pi$
$252$	−1.00000	−0.0629941
$253$	−4.84846	−0.304820
$254$	18.2959	1.14799
$255$	−4.28621	−0.268413
$256$	1.00000	0.0625000
$257$	17.2349	1.07508	0.537542	−	0.843237i	$-0.319353\pi$
$257$	17.2349	1.07508	0.537542	+	0.843237i	$0.319353\pi$
$258$	9.55496	0.594866
$259$	−10.6528	−0.661932
$260$	0	0
$261$	−2.58211	−0.159828
$262$	3.52781	0.217949
$263$	8.46011	0.521673	0.260836	−	0.965383i	$-0.416002\pi$
$263$	8.46011	0.521673	0.260836	+	0.965383i	$0.416002\pi$
$264$	−2.13706	−0.131527
$265$	−19.7168	−1.21119
$266$	−2.13706	−0.131032
$267$	3.73556	0.228613
$268$	11.3937	0.695983
$269$	1.29590	0.0790122	0.0395061	−	0.999219i	$-0.487422\pi$
$269$	1.29590	0.0790122	0.0395061	+	0.999219i	$0.487422\pi$
$270$	3.04892	0.185551
$271$	−5.46250	−0.331823	−0.165912	−	0.986141i	$-0.553057\pi$
$271$	−5.46250	−0.331823	−0.165912	+	0.986141i	$0.553057\pi$
$272$	−1.40581	−0.0852399
$273$	0	0
$274$	0.249373	0.0150651
$275$	9.18060	0.553611
$276$	2.26875	0.136563
$277$	1.01746	0.0611332	0.0305666	−	0.999533i	$-0.490269\pi$
$277$	1.01746	0.0611332	0.0305666	+	0.999533i	$0.490269\pi$
$278$	0.168522	0.0101073
$279$	−6.34481	−0.379854
$280$	3.04892	0.182208
$281$	−23.7482	−1.41670	−0.708350	−	0.705861i	$-0.750560\pi$
$281$	−23.7482	−1.41670	−0.708350	+	0.705861i	$0.750560\pi$
$282$	3.98792	0.237477
$283$	−19.9148	−1.18381	−0.591907	−	0.806006i	$-0.701625\pi$
$283$	−19.9148	−1.18381	−0.591907	+	0.806006i	$0.701625\pi$
$284$	4.21983	0.250401
$285$	6.51573	0.385959
$286$	0	0
$287$	4.43296	0.261669
$288$	1.00000	0.0589256
$289$	−15.0237	−0.883746
$290$	7.87263	0.462296
$291$	5.10321	0.299156
$292$	5.84548	0.342081
$293$	9.15213	0.534673	0.267337	−	0.963603i	$-0.413856\pi$
$293$	9.15213	0.534673	0.267337	+	0.963603i	$0.413856\pi$
$294$	−1.00000	−0.0583212
$295$	10.5036	0.611546
$296$	10.6528	0.619181
$297$	−2.13706	−0.124005
$298$	16.3327	0.946130
$299$	0	0
$300$	−4.29590	−0.248024
$301$	9.55496	0.550739
$302$	24.3448	1.40089
$303$	12.2174	0.701874
$304$	2.13706	0.122569
$305$	−30.4523	−1.74370
$306$	−1.40581	−0.0803650
$307$	22.2784	1.27150	0.635749	−	0.771896i	$-0.280691\pi$
$307$	22.2784	1.27150	0.635749	+	0.771896i	$0.280691\pi$
$308$	−2.13706	−0.121770
$309$	4.53319	0.257884
$310$	19.3448	1.09871
$311$	−0.254749	−0.0144455	−0.00722275	−	0.999974i	$-0.502299\pi$
$311$	−0.254749	−0.0144455	−0.00722275	+	0.999974i	$0.502299\pi$
$312$	0	0
$313$	24.1129	1.36294	0.681471	−	0.731845i	$-0.261341\pi$
$313$	24.1129	1.36294	0.681471	+	0.731845i	$0.261341\pi$
$314$	−12.0978	−0.682720
$315$	3.04892	0.171787
$316$	−10.7071	−0.602321
$317$	−12.8321	−0.720721	−0.360360	−	0.932813i	$-0.617346\pi$
$317$	−12.8321	−0.720721	−0.360360	+	0.932813i	$0.617346\pi$
$318$	−6.46681	−0.362641
$319$	−5.51812	−0.308956
$320$	−3.04892	−0.170440
$321$	12.5254	0.699101
$322$	2.26875	0.126432
$323$	−3.00431	−0.167164
$324$	1.00000	0.0555556
$325$	0	0
$326$	14.0707	0.779303
$327$	1.15883	0.0640836
$328$	−4.43296	−0.244769
$329$	3.98792	0.219861
$330$	6.51573	0.358679
$331$	29.0707	1.59787	0.798935	−	0.601418i	$-0.205397\pi$
$331$	29.0707	1.59787	0.798935	+	0.601418i	$0.205397\pi$
$332$	8.94869	0.491123
$333$	10.6528	0.583769
$334$	19.9541	1.09184
$335$	−34.7385	−1.89797
$336$	1.00000	0.0545545
$337$	17.7821	0.968652	0.484326	−	0.874888i	$-0.339065\pi$
$337$	17.7821	0.968652	0.484326	+	0.874888i	$0.339065\pi$
$338$	0	0
$339$	−4.34721	−0.236108
$340$	4.28621	0.232452
$341$	−13.5593	−0.734276
$342$	2.13706	0.115559
$343$	−1.00000	−0.0539949
$344$	−9.55496	−0.515169
$345$	−6.91723	−0.372411
$346$	−6.61596	−0.355676
$347$	−10.5144	−0.564443	−0.282221	−	0.959349i	$-0.591071\pi$
$347$	−10.5144	−0.564443	−0.282221	+	0.959349i	$0.591071\pi$
$348$	2.58211	0.138415
$349$	18.1274	0.970336	0.485168	−	0.874421i	$-0.338758\pi$
$349$	18.1274	0.970336	0.485168	+	0.874421i	$0.338758\pi$
$350$	−4.29590	−0.229625
$351$	0	0
$352$	2.13706	0.113906
$353$	−16.1715	−0.860722	−0.430361	−	0.902657i	$-0.641614\pi$
$353$	−16.1715	−0.860722	−0.430361	+	0.902657i	$0.641614\pi$
$354$	3.44504	0.183102
$355$	−12.8659	−0.682852
$356$	−3.73556	−0.197984
$357$	−1.40581	−0.0744035
$358$	−7.49396	−0.396068
$359$	7.77240	0.410211	0.205106	−	0.978740i	$-0.434246\pi$
$359$	7.77240	0.410211	0.205106	+	0.978740i	$0.434246\pi$
$360$	−3.04892	−0.160692
$361$	−14.4330	−0.759629
$362$	19.1226	1.00506
$363$	6.43296	0.337643
$364$	0	0
$365$	−17.8224	−0.932866
$366$	−9.98792	−0.522077
$367$	−2.07846	−0.108495	−0.0542473	−	0.998528i	$-0.517276\pi$
$367$	−2.07846	−0.108495	−0.0542473	+	0.998528i	$0.517276\pi$
$368$	−2.26875	−0.118267
$369$	−4.43296	−0.230771
$370$	−32.4795	−1.68853
$371$	−6.46681	−0.335740
$372$	6.34481	0.328963
$373$	8.10752	0.419792	0.209896	−	0.977724i	$-0.432688\pi$
$373$	8.10752	0.419792	0.209896	+	0.977724i	$0.432688\pi$
$374$	−3.00431	−0.155349
$375$	−2.14675	−0.110858
$376$	−3.98792	−0.205661
$377$	0	0
$378$	1.00000	0.0514344
$379$	13.4222	0.689452	0.344726	−	0.938703i	$-0.387972\pi$
$379$	13.4222	0.689452	0.344726	+	0.938703i	$0.387972\pi$
$380$	−6.51573	−0.334250
$381$	−18.2959	−0.937327
$382$	23.2403	1.18908
$383$	12.4209	0.634677	0.317339	−	0.948312i	$-0.397211\pi$
$383$	12.4209	0.634677	0.317339	+	0.948312i	$0.397211\pi$
$384$	−1.00000	−0.0510310
$385$	6.51573	0.332072
$386$	4.00538	0.203868
$387$	−9.55496	−0.485706
$388$	−5.10321	−0.259076
$389$	37.5666	1.90470	0.952350	−	0.305007i	$-0.0986587\pi$
$389$	37.5666	1.90470	0.952350	+	0.305007i	$0.0986587\pi$
$390$	0	0
$391$	3.18944	0.161297
$392$	1.00000	0.0505076
$393$	−3.52781	−0.177955
$394$	−7.75840	−0.390862
$395$	32.6450	1.64255
$396$	2.13706	0.107391
$397$	36.1159	1.81260	0.906302	−	0.422630i	$-0.138893\pi$
$397$	36.1159	1.81260	0.906302	+	0.422630i	$0.138893\pi$
$398$	14.5526	0.729454
$399$	2.13706	0.106987
$400$	4.29590	0.214795
$401$	−9.82610	−0.490692	−0.245346	−	0.969436i	$-0.578902\pi$
$401$	−9.82610	−0.490692	−0.245346	+	0.969436i	$0.578902\pi$
$402$	−11.3937	−0.568268
$403$	0	0
$404$	−12.2174	−0.607840
$405$	−3.04892	−0.151502
$406$	2.58211	0.128148
$407$	22.7657	1.12845
$408$	1.40581	0.0695981
$409$	−3.09352	−0.152965	−0.0764824	−	0.997071i	$-0.524369\pi$
$409$	−3.09352	−0.152965	−0.0764824	+	0.997071i	$0.524369\pi$
$410$	13.5157	0.667494
$411$	−0.249373	−0.0123006
$412$	−4.53319	−0.223334
$413$	3.44504	0.169519
$414$	−2.26875	−0.111503
$415$	−27.2838	−1.33931
$416$	0	0
$417$	−0.168522	−0.00825257
$418$	4.56704	0.223381
$419$	−20.1535	−0.984561	−0.492280	−	0.870437i	$-0.663837\pi$
$419$	−20.1535	−0.984561	−0.492280	+	0.870437i	$0.663837\pi$
$420$	−3.04892	−0.148772
$421$	11.2034	0.546022	0.273011	−	0.962011i	$-0.411980\pi$
$421$	11.2034	0.546022	0.273011	+	0.962011i	$0.411980\pi$
$422$	3.80194	0.185075
$423$	−3.98792	−0.193899
$424$	6.46681	0.314056
$425$	−6.03923	−0.292946
$426$	−4.21983	−0.204452
$427$	−9.98792	−0.483349
$428$	−12.5254	−0.605439
$429$	0	0
$430$	29.1323	1.40488
$431$	−38.9898	−1.87807	−0.939037	−	0.343816i	$-0.888280\pi$
$431$	−38.9898	−1.87807	−0.939037	+	0.343816i	$0.888280\pi$
$432$	−1.00000	−0.0481125
$433$	23.4426	1.12658	0.563291	−	0.826259i	$-0.309535\pi$
$433$	23.4426	1.12658	0.563291	+	0.826259i	$0.309535\pi$
$434$	6.34481	0.304561
$435$	−7.87263	−0.377463
$436$	−1.15883	−0.0554981
$437$	−4.84846	−0.231933
$438$	−5.84548	−0.279308
$439$	−26.8592	−1.28192	−0.640960	−	0.767574i	$-0.721464\pi$
$439$	−26.8592	−1.28192	−0.640960	+	0.767574i	$0.721464\pi$
$440$	−6.51573	−0.310625
$441$	1.00000	0.0476190
$442$	0	0
$443$	−11.1347	−0.529024	−0.264512	−	0.964382i	$-0.585211\pi$
$443$	−11.1347	−0.529024	−0.264512	+	0.964382i	$0.585211\pi$
$444$	−10.6528	−0.505559
$445$	11.3894	0.539910
$446$	−23.1347	−1.09546
$447$	−16.3327	−0.772512
$448$	−1.00000	−0.0472456
$449$	27.0858	1.27826	0.639128	−	0.769100i	$-0.279295\pi$
$449$	27.0858	1.27826	0.639128	+	0.769100i	$0.279295\pi$
$450$	4.29590	0.202511
$451$	−9.47352	−0.446090
$452$	4.34721	0.204475
$453$	−24.3448	−1.14382
$454$	−2.72348	−0.127819
$455$	0	0
$456$	−2.13706	−0.100077
$457$	3.40880	0.159457	0.0797284	−	0.996817i	$-0.474595\pi$
$457$	3.40880	0.159457	0.0797284	+	0.996817i	$0.474595\pi$
$458$	11.7385	0.548506
$459$	1.40581	0.0656177
$460$	6.91723	0.322518
$461$	−30.9178	−1.43999	−0.719993	−	0.693981i	$-0.755855\pi$
$461$	−30.9178	−1.43999	−0.719993	+	0.693981i	$0.755855\pi$
$462$	2.13706	0.0994252
$463$	35.0465	1.62875	0.814375	−	0.580339i	$-0.197080\pi$
$463$	35.0465	1.62875	0.814375	+	0.580339i	$0.197080\pi$
$464$	−2.58211	−0.119871
$465$	−19.3448	−0.897094
$466$	9.92931	0.459967
$467$	4.04652	0.187251	0.0936254	−	0.995607i	$-0.470154\pi$
$467$	4.04652	0.187251	0.0936254	+	0.995607i	$0.470154\pi$
$468$	0	0
$469$	−11.3937	−0.526114
$470$	12.1588	0.560845
$471$	12.0978	0.557439
$472$	−3.44504	−0.158571
$473$	−20.4196	−0.938892
$474$	10.7071	0.491793
$475$	9.18060	0.421235
$476$	1.40581	0.0644353
$477$	6.46681	0.296095
$478$	22.1172	1.01162
$479$	−16.0411	−0.732939	−0.366469	−	0.930430i	$-0.619434\pi$
$479$	−16.0411	−0.732939	−0.366469	+	0.930430i	$0.619434\pi$
$480$	3.04892	0.139163
$481$	0	0
$482$	24.5429	1.11790
$483$	−2.26875	−0.103232
$484$	−6.43296	−0.292407
$485$	15.5593	0.706510
$486$	−1.00000	−0.0453609
$487$	36.7724	1.66632	0.833158	−	0.553035i	$-0.186530\pi$
$487$	36.7724	1.66632	0.833158	+	0.553035i	$0.186530\pi$
$488$	9.98792	0.452132
$489$	−14.0707	−0.636298
$490$	−3.04892	−0.137736
$491$	−7.69069	−0.347076	−0.173538	−	0.984827i	$-0.555520\pi$
$491$	−7.69069	−0.347076	−0.173538	+	0.984827i	$0.555520\pi$
$492$	4.43296	0.199853
$493$	3.62996	0.163485
$494$	0	0
$495$	−6.51573	−0.292860
$496$	−6.34481	−0.284891
$497$	−4.21983	−0.189285
$498$	−8.94869	−0.401000
$499$	−21.8213	−0.976856	−0.488428	−	0.872604i	$-0.662430\pi$
$499$	−21.8213	−0.976856	−0.488428	+	0.872604i	$0.662430\pi$
$500$	2.14675	0.0960057
$501$	−19.9541	−0.891482
$502$	27.2489	1.21618
$503$	0.875018	0.0390151	0.0195076	−	0.999810i	$-0.493790\pi$
$503$	0.875018	0.0390151	0.0195076	+	0.999810i	$0.493790\pi$
$504$	−1.00000	−0.0445435
$505$	37.2500	1.65760
$506$	−4.84846	−0.215540
$507$	0	0
$508$	18.2959	0.811749
$509$	−40.2043	−1.78202	−0.891012	−	0.453980i	$-0.850004\pi$
$509$	−40.2043	−1.78202	−0.891012	+	0.453980i	$0.850004\pi$
$510$	−4.28621	−0.189796
$511$	−5.84548	−0.258589
$512$	1.00000	0.0441942
$513$	−2.13706	−0.0943537
$514$	17.2349	0.760199
$515$	13.8213	0.609040
$516$	9.55496	0.420634
$517$	−8.52243	−0.374816
$518$	−10.6528	−0.468057
$519$	6.61596	0.290408
$520$	0	0
$521$	−4.36898	−0.191408	−0.0957042	−	0.995410i	$-0.530510\pi$
$521$	−4.36898	−0.191408	−0.0957042	+	0.995410i	$0.530510\pi$
$522$	−2.58211	−0.113016
$523$	−9.54958	−0.417574	−0.208787	−	0.977961i	$-0.566952\pi$
$523$	−9.54958	−0.417574	−0.208787	+	0.977961i	$0.566952\pi$
$524$	3.52781	0.154113
$525$	4.29590	0.187488
$526$	8.46011	0.368878
$527$	8.91962	0.388545
$528$	−2.13706	−0.0930037
$529$	−17.8528	−0.776208
$530$	−19.7168	−0.856442
$531$	−3.44504	−0.149502
$532$	−2.13706	−0.0926534
$533$	0	0
$534$	3.73556	0.161654
$535$	38.1890	1.65105
$536$	11.3937	0.492134
$537$	7.49396	0.323388
$538$	1.29590	0.0558701
$539$	2.13706	0.0920498
$540$	3.04892	0.131205
$541$	4.13813	0.177912	0.0889560	−	0.996036i	$-0.471647\pi$
$541$	4.13813	0.177912	0.0889560	+	0.996036i	$0.471647\pi$
$542$	−5.46250	−0.234634
$543$	−19.1226	−0.820629
$544$	−1.40581	−0.0602737
$545$	3.53319	0.151345
$546$	0	0
$547$	−17.0242	−0.727901	−0.363950	−	0.931418i	$-0.618572\pi$
$547$	−17.0242	−0.727901	−0.363950	+	0.931418i	$0.618572\pi$
$548$	0.249373	0.0106527
$549$	9.98792	0.426274
$550$	9.18060	0.391462
$551$	−5.51812	−0.235080
$552$	2.26875	0.0965644
$553$	10.7071	0.455312
$554$	1.01746	0.0432277
$555$	32.4795	1.37868
$556$	0.168522	0.00714694
$557$	−18.9778	−0.804113	−0.402057	−	0.915615i	$-0.631705\pi$
$557$	−18.9778	−0.804113	−0.402057	+	0.915615i	$0.631705\pi$
$558$	−6.34481	−0.268597
$559$	0	0
$560$	3.04892	0.128840
$561$	3.00431	0.126842
$562$	−23.7482	−1.00176
$563$	−31.3840	−1.32268	−0.661340	−	0.750086i	$-0.730012\pi$
$563$	−31.3840	−1.32268	−0.661340	+	0.750086i	$0.730012\pi$
$564$	3.98792	0.167922
$565$	−13.2543	−0.557612
$566$	−19.9148	−0.837083
$567$	−1.00000	−0.0419961
$568$	4.21983	0.177060
$569$	30.4196	1.27525	0.637627	−	0.770345i	$-0.279916\pi$
$569$	30.4196	1.27525	0.637627	+	0.770345i	$0.279916\pi$
$570$	6.51573	0.272914
$571$	−26.4534	−1.10704	−0.553520	−	0.832836i	$-0.686716\pi$
$571$	−26.4534	−1.10704	−0.553520	+	0.832836i	$0.686716\pi$
$572$	0	0
$573$	−23.2403	−0.970876
$574$	4.43296	0.185028
$575$	−9.74632	−0.406449
$576$	1.00000	0.0416667
$577$	−6.25667	−0.260469	−0.130234	−	0.991483i	$-0.541573\pi$
$577$	−6.25667	−0.260469	−0.130234	+	0.991483i	$0.541573\pi$
$578$	−15.0237	−0.624903
$579$	−4.00538	−0.166458
$580$	7.87263	0.326893
$581$	−8.94869	−0.371254
$582$	5.10321	0.211535
$583$	13.8200	0.572365
$584$	5.84548	0.241888
$585$	0	0
$586$	9.15213	0.378071
$587$	−16.9028	−0.697651	−0.348826	−	0.937188i	$-0.613419\pi$
$587$	−16.9028	−0.697651	−0.348826	+	0.937188i	$0.613419\pi$
$588$	−1.00000	−0.0412393
$589$	−13.5593	−0.558700
$590$	10.5036	0.432428
$591$	7.75840	0.319138
$592$	10.6528	0.437827
$593$	8.60089	0.353196	0.176598	−	0.984283i	$-0.443491\pi$
$593$	8.60089	0.353196	0.176598	+	0.984283i	$0.443491\pi$
$594$	−2.13706	−0.0876848
$595$	−4.28621	−0.175717
$596$	16.3327	0.669015
$597$	−14.5526	−0.595597
$598$	0	0
$599$	−28.3744	−1.15934	−0.579672	−	0.814850i	$-0.696819\pi$
$599$	−28.3744	−1.15934	−0.579672	+	0.814850i	$0.696819\pi$
$600$	−4.29590	−0.175379
$601$	30.3394	1.23757	0.618786	−	0.785560i	$-0.287625\pi$
$601$	30.3394	1.23757	0.618786	+	0.785560i	$0.287625\pi$
$602$	9.55496	0.389431
$603$	11.3937	0.463989
$604$	24.3448	0.990576
$605$	19.6136	0.797405
$606$	12.2174	0.496300
$607$	9.64609	0.391523	0.195761	−	0.980652i	$-0.437282\pi$
$607$	9.64609	0.391523	0.195761	+	0.980652i	$0.437282\pi$
$608$	2.13706	0.0866694
$609$	−2.58211	−0.104632
$610$	−30.4523	−1.23298
$611$	0	0
$612$	−1.40581	−0.0568266
$613$	27.1444	1.09635	0.548175	−	0.836364i	$-0.315323\pi$
$613$	27.1444	1.09635	0.548175	+	0.836364i	$0.315323\pi$
$614$	22.2784	0.899085
$615$	−13.5157	−0.545007
$616$	−2.13706	−0.0861047
$617$	30.4510	1.22591	0.612956	−	0.790117i	$-0.289980\pi$
$617$	30.4510	1.22591	0.612956	+	0.790117i	$0.289980\pi$
$618$	4.53319	0.182352
$619$	3.06578	0.123224	0.0616121	−	0.998100i	$-0.480376\pi$
$619$	3.06578	0.123224	0.0616121	+	0.998100i	$0.480376\pi$
$620$	19.3448	0.776906
$621$	2.26875	0.0910418
$622$	−0.254749	−0.0102145
$623$	3.73556	0.149662
$624$	0	0
$625$	−28.0248	−1.12099
$626$	24.1129	0.963745
$627$	−4.56704	−0.182390
$628$	−12.0978	−0.482756
$629$	−14.9758	−0.597126
$630$	3.04892	0.121472
$631$	17.7791	0.707775	0.353887	−	0.935288i	$-0.384860\pi$
$631$	17.7791	0.707775	0.353887	+	0.935288i	$0.384860\pi$
$632$	−10.7071	−0.425905
$633$	−3.80194	−0.151113
$634$	−12.8321	−0.509627
$635$	−55.7827	−2.21367
$636$	−6.46681	−0.256426
$637$	0	0
$638$	−5.51812	−0.218465
$639$	4.21983	0.166934
$640$	−3.04892	−0.120519
$641$	−41.9754	−1.65793	−0.828964	−	0.559303i	$-0.811069\pi$
$641$	−41.9754	−1.65793	−0.828964	+	0.559303i	$0.811069\pi$
$642$	12.5254	0.494339
$643$	−26.7222	−1.05382	−0.526909	−	0.849921i	$-0.676649\pi$
$643$	−26.7222	−1.05382	−0.526909	+	0.849921i	$0.676649\pi$
$644$	2.26875	0.0894013
$645$	−29.1323	−1.14708
$646$	−3.00431	−0.118203
$647$	−33.7399	−1.32645	−0.663226	−	0.748419i	$-0.730813\pi$
$647$	−33.7399	−1.32645	−0.663226	+	0.748419i	$0.730813\pi$
$648$	1.00000	0.0392837
$649$	−7.36227	−0.288994
$650$	0	0
$651$	−6.34481	−0.248673
$652$	14.0707	0.551051
$653$	−14.8374	−0.580634	−0.290317	−	0.956931i	$-0.593761\pi$
$653$	−14.8374	−0.580634	−0.290317	+	0.956931i	$0.593761\pi$
$654$	1.15883	0.0453140
$655$	−10.7560	−0.420272
$656$	−4.43296	−0.173078
$657$	5.84548	0.228054
$658$	3.98792	0.155465
$659$	−25.0508	−0.975842	−0.487921	−	0.872888i	$-0.662245\pi$
$659$	−25.0508	−0.975842	−0.487921	+	0.872888i	$0.662245\pi$
$660$	6.51573	0.253624
$661$	34.5816	1.34507	0.672535	−	0.740066i	$-0.265206\pi$
$661$	34.5816	1.34507	0.672535	+	0.740066i	$0.265206\pi$
$662$	29.0707	1.12986
$663$	0	0
$664$	8.94869	0.347277
$665$	6.51573	0.252669
$666$	10.6528	0.412787
$667$	5.85815	0.226829
$668$	19.9541	0.772046
$669$	23.1347	0.894438
$670$	−34.7385	−1.34207
$671$	21.3448	0.824007
$672$	1.00000	0.0385758
$673$	24.7791	0.955164	0.477582	−	0.878587i	$-0.341513\pi$
$673$	24.7791	0.955164	0.477582	+	0.878587i	$0.341513\pi$
$674$	17.7821	0.684940
$675$	−4.29590	−0.165349
$676$	0	0
$677$	−38.1347	−1.46563	−0.732817	−	0.680426i	$-0.761795\pi$
$677$	−38.1347	−1.46563	−0.732817	+	0.680426i	$0.761795\pi$
$678$	−4.34721	−0.166953
$679$	5.10321	0.195843
$680$	4.28621	0.164369
$681$	2.72348	0.104364
$682$	−13.5593	−0.519211
$683$	−38.6407	−1.47855	−0.739273	−	0.673406i	$-0.764831\pi$
$683$	−38.6407	−1.47855	−0.739273	+	0.673406i	$0.764831\pi$
$684$	2.13706	0.0817127
$685$	−0.760316	−0.0290502
$686$	−1.00000	−0.0381802
$687$	−11.7385	−0.447853
$688$	−9.55496	−0.364279
$689$	0	0
$690$	−6.91723	−0.263334
$691$	6.00969	0.228619	0.114310	−	0.993445i	$-0.463534\pi$
$691$	6.00969	0.228619	0.114310	+	0.993445i	$0.463534\pi$
$692$	−6.61596	−0.251501
$693$	−2.13706	−0.0811803
$694$	−10.5144	−0.399121
$695$	−0.513811	−0.0194899
$696$	2.58211	0.0978744
$697$	6.23191	0.236051
$698$	18.1274	0.686131
$699$	−9.92931	−0.375561
$700$	−4.29590	−0.162370
$701$	24.3642	0.920223	0.460111	−	0.887861i	$-0.347809\pi$
$701$	24.3642	0.920223	0.460111	+	0.887861i	$0.347809\pi$
$702$	0	0
$703$	22.7657	0.858624
$704$	2.13706	0.0805436
$705$	−12.1588	−0.457928
$706$	−16.1715	−0.608623
$707$	12.2174	0.459484
$708$	3.44504	0.129473
$709$	−26.1239	−0.981104	−0.490552	−	0.871412i	$-0.663205\pi$
$709$	−26.1239	−0.981104	−0.490552	+	0.871412i	$0.663205\pi$
$710$	−12.8659	−0.482849
$711$	−10.7071	−0.401547
$712$	−3.73556	−0.139996
$713$	14.3948	0.539089
$714$	−1.40581	−0.0526112
$715$	0	0
$716$	−7.49396	−0.280062
$717$	−22.1172	−0.825982
$718$	7.77240	0.290063
$719$	−4.64981	−0.173409	−0.0867043	−	0.996234i	$-0.527634\pi$
$719$	−4.64981	−0.173409	−0.0867043	+	0.996234i	$0.527634\pi$
$720$	−3.04892	−0.113626
$721$	4.53319	0.168825
$722$	−14.4330	−0.537139
$723$	−24.5429	−0.912759
$724$	19.1226	0.710685
$725$	−11.0925	−0.411964
$726$	6.43296	0.238750
$727$	−28.4292	−1.05438	−0.527191	−	0.849747i	$-0.676755\pi$
$727$	−28.4292	−1.05438	−0.527191	+	0.849747i	$0.676755\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.8224	−0.659636
$731$	13.4325	0.496818
$732$	−9.98792	−0.369164
$733$	9.99356	0.369120	0.184560	−	0.982821i	$-0.440914\pi$
$733$	9.99356	0.369120	0.184560	+	0.982821i	$0.440914\pi$
$734$	−2.07846	−0.0767173
$735$	3.04892	0.112461
$736$	−2.26875	−0.0836272
$737$	24.3491	0.896912
$738$	−4.43296	−0.163180
$739$	−13.5101	−0.496977	−0.248488	−	0.968635i	$-0.579934\pi$
$739$	−13.5101	−0.496977	−0.248488	+	0.968635i	$0.579934\pi$
$740$	−32.4795	−1.19397
$741$	0	0
$742$	−6.46681	−0.237404
$743$	38.1540	1.39974	0.699868	−	0.714272i	$-0.253242\pi$
$743$	38.1540	1.39974	0.699868	+	0.714272i	$0.253242\pi$
$744$	6.34481	0.232612
$745$	−49.7972	−1.82443
$746$	8.10752	0.296838
$747$	8.94869	0.327415
$748$	−3.00431	−0.109849
$749$	12.5254	0.457669
$750$	−2.14675	−0.0783883
$751$	−24.1473	−0.881149	−0.440575	−	0.897716i	$-0.645225\pi$
$751$	−24.1473	−0.881149	−0.440575	+	0.897716i	$0.645225\pi$
$752$	−3.98792	−0.145424
$753$	−27.2489	−0.993005
$754$	0	0
$755$	−74.2253	−2.70134
$756$	1.00000	0.0363696
$757$	−7.27173	−0.264296	−0.132148	−	0.991230i	$-0.542187\pi$
$757$	−7.27173	−0.264296	−0.132148	+	0.991230i	$0.542187\pi$
$758$	13.4222	0.487516
$759$	4.84846	0.175988
$760$	−6.51573	−0.236350
$761$	27.7894	1.00736	0.503682	−	0.863889i	$-0.331978\pi$
$761$	27.7894	1.00736	0.503682	+	0.863889i	$0.331978\pi$
$762$	−18.2959	−0.662790
$763$	1.15883	0.0419526
$764$	23.2403	0.840804
$765$	4.28621	0.154968
$766$	12.4209	0.448785
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−12.5894	−0.453985	−0.226993	−	0.973896i	$-0.572889\pi$
$769$	−12.5894	−0.453985	−0.226993	+	0.973896i	$0.572889\pi$
$770$	6.51573	0.234811
$771$	−17.2349	−0.620700
$772$	4.00538	0.144157
$773$	42.4935	1.52838	0.764192	−	0.644989i	$-0.223138\pi$
$773$	42.4935	1.52838	0.764192	+	0.644989i	$0.223138\pi$
$774$	−9.55496	−0.343446
$775$	−27.2567	−0.979088
$776$	−5.10321	−0.183195
$777$	10.6528	0.382167
$778$	37.5666	1.34683
$779$	−9.47352	−0.339424
$780$	0	0
$781$	9.01805	0.322691
$782$	3.18944	0.114054
$783$	2.58211	0.0922769
$784$	1.00000	0.0357143
$785$	36.8853	1.31649
$786$	−3.52781	−0.125833
$787$	−30.9017	−1.10153	−0.550763	−	0.834662i	$-0.685663\pi$
$787$	−30.9017	−1.10153	−0.550763	+	0.834662i	$0.685663\pi$
$788$	−7.75840	−0.276381
$789$	−8.46011	−0.301188
$790$	32.6450	1.16146
$791$	−4.34721	−0.154569
$792$	2.13706	0.0759372
$793$	0	0
$794$	36.1159	1.28170
$795$	19.7168	0.699282
$796$	14.5526	0.515802
$797$	52.3038	1.85270	0.926348	−	0.376670i	$-0.122931\pi$
$797$	52.3038	1.85270	0.926348	+	0.376670i	$0.122931\pi$
$798$	2.13706	0.0756512
$799$	5.60627	0.198336
$800$	4.29590	0.151883
$801$	−3.73556	−0.131990
$802$	−9.82610	−0.346972
$803$	12.4922	0.440839
$804$	−11.3937	−0.401826
$805$	−6.91723	−0.243800
$806$	0	0
$807$	−1.29590	−0.0456177
$808$	−12.2174	−0.429808
$809$	31.7942	1.11782	0.558912	−	0.829227i	$-0.311219\pi$
$809$	31.7942	1.11782	0.558912	+	0.829227i	$0.311219\pi$
$810$	−3.04892	−0.107128
$811$	−12.3196	−0.432599	−0.216300	−	0.976327i	$-0.569399\pi$
$811$	−12.3196	−0.432599	−0.216300	+	0.976327i	$0.569399\pi$
$812$	2.58211	0.0906141
$813$	5.46250	0.191578
$814$	22.7657	0.797937
$815$	−42.9004	−1.50273
$816$	1.40581	0.0492133
$817$	−20.4196	−0.714390
$818$	−3.09352	−0.108162
$819$	0	0
$820$	13.5157	0.471990
$821$	−41.0901	−1.43405	−0.717027	−	0.697046i	$-0.754497\pi$
$821$	−41.0901	−1.43405	−0.717027	+	0.697046i	$0.754497\pi$
$822$	−0.249373	−0.00869787
$823$	−2.76164	−0.0962649	−0.0481324	−	0.998841i	$-0.515327\pi$
$823$	−2.76164	−0.0962649	−0.0481324	+	0.998841i	$0.515327\pi$
$824$	−4.53319	−0.157921
$825$	−9.18060	−0.319628
$826$	3.44504	0.119868
$827$	28.6098	0.994862	0.497431	−	0.867504i	$-0.334277\pi$
$827$	28.6098	0.994862	0.497431	+	0.867504i	$0.334277\pi$
$828$	−2.26875	−0.0788445
$829$	−50.4741	−1.75304	−0.876519	−	0.481367i	$-0.840140\pi$
$829$	−50.4741	−1.75304	−0.876519	+	0.481367i	$0.840140\pi$
$830$	−27.2838	−0.947035
$831$	−1.01746	−0.0352952
$832$	0	0
$833$	−1.40581	−0.0487085
$834$	−0.168522	−0.00583545
$835$	−60.8383	−2.10540
$836$	4.56704	0.157954
$837$	6.34481	0.219309
$838$	−20.1535	−0.696190
$839$	−38.4185	−1.32635	−0.663177	−	0.748463i	$-0.730792\pi$
$839$	−38.4185	−1.32635	−0.663177	+	0.748463i	$0.730792\pi$
$840$	−3.04892	−0.105198
$841$	−22.3327	−0.770094
$842$	11.2034	0.386096
$843$	23.7482	0.817933
$844$	3.80194	0.130868
$845$	0	0
$846$	−3.98792	−0.137107
$847$	6.43296	0.221039
$848$	6.46681	0.222071
$849$	19.9148	0.683475
$850$	−6.03923	−0.207144
$851$	−24.1685	−0.828486
$852$	−4.21983	−0.144569
$853$	−7.09677	−0.242989	−0.121494	−	0.992592i	$-0.538769\pi$
$853$	−7.09677	−0.242989	−0.121494	+	0.992592i	$0.538769\pi$
$854$	−9.98792	−0.341780
$855$	−6.51573	−0.222833
$856$	−12.5254	−0.428110
$857$	−37.8901	−1.29430	−0.647150	−	0.762362i	$-0.724039\pi$
$857$	−37.8901	−1.29430	−0.647150	+	0.762362i	$0.724039\pi$
$858$	0	0
$859$	32.9329	1.12366	0.561828	−	0.827254i	$-0.310098\pi$
$859$	32.9329	1.12366	0.561828	+	0.827254i	$0.310098\pi$
$860$	29.1323	0.993402
$861$	−4.43296	−0.151075
$862$	−38.9898	−1.32800
$863$	−27.3400	−0.930665	−0.465333	−	0.885136i	$-0.654065\pi$
$863$	−27.3400	−0.930665	−0.465333	+	0.885136i	$0.654065\pi$
$864$	−1.00000	−0.0340207
$865$	20.1715	0.685852
$866$	23.4426	0.796614
$867$	15.0237	0.510231
$868$	6.34481	0.215357
$869$	−22.8817	−0.776209
$870$	−7.87263	−0.266907
$871$	0	0
$872$	−1.15883	−0.0392431
$873$	−5.10321	−0.172718
$874$	−4.84846	−0.164002
$875$	−2.14675	−0.0725735
$876$	−5.84548	−0.197500
$877$	7.54852	0.254895	0.127448	−	0.991845i	$-0.459322\pi$
$877$	7.54852	0.254895	0.127448	+	0.991845i	$0.459322\pi$
$878$	−26.8592	−0.906455
$879$	−9.15213	−0.308694
$880$	−6.51573	−0.219645
$881$	−9.14138	−0.307981	−0.153990	−	0.988072i	$-0.549212\pi$
$881$	−9.14138	−0.307981	−0.153990	+	0.988072i	$0.549212\pi$
$882$	1.00000	0.0336718
$883$	31.5838	1.06288	0.531439	−	0.847097i	$-0.321651\pi$
$883$	31.5838	1.06288	0.531439	+	0.847097i	$0.321651\pi$
$884$	0	0
$885$	−10.5036	−0.353076
$886$	−11.1347	−0.374077
$887$	57.3159	1.92448	0.962239	−	0.272205i	$-0.0877530\pi$
$887$	57.3159	1.92448	0.962239	+	0.272205i	$0.0877530\pi$
$888$	−10.6528	−0.357484
$889$	−18.2959	−0.613625
$890$	11.3894	0.381774
$891$	2.13706	0.0715943
$892$	−23.1347	−0.774606
$893$	−8.52243	−0.285192
$894$	−16.3327	−0.546248
$895$	22.8485	0.763740
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	27.0858	0.903863
$899$	16.3830	0.546403
$900$	4.29590	0.143197
$901$	−9.09113	−0.302869
$902$	−9.47352	−0.315434
$903$	−9.55496	−0.317969
$904$	4.34721	0.144586
$905$	−58.3032	−1.93806
$906$	−24.3448	−0.808802
$907$	−35.9963	−1.19524	−0.597618	−	0.801781i	$-0.703886\pi$
$907$	−35.9963	−1.19524	−0.597618	+	0.801781i	$0.703886\pi$
$908$	−2.72348	−0.0903819
$909$	−12.2174	−0.405227
$910$	0	0
$911$	−8.76569	−0.290420	−0.145210	−	0.989401i	$-0.546386\pi$
$911$	−8.76569	−0.290420	−0.145210	+	0.989401i	$0.546386\pi$
$912$	−2.13706	−0.0707652
$913$	19.1239	0.632909
$914$	3.40880	0.112753
$915$	30.4523	1.00672
$916$	11.7385	0.387852
$917$	−3.52781	−0.116499
$918$	1.40581	0.0463987
$919$	28.5695	0.942422	0.471211	−	0.882020i	$-0.343817\pi$
$919$	28.5695	0.942422	0.471211	+	0.882020i	$0.343817\pi$
$920$	6.91723	0.228054
$921$	−22.2784	−0.734100
$922$	−30.9178	−1.01822
$923$	0	0
$924$	2.13706	0.0703042
$925$	45.7633	1.50469
$926$	35.0465	1.15170
$927$	−4.53319	−0.148889
$928$	−2.58211	−0.0847618
$929$	−23.2644	−0.763281	−0.381641	−	0.924311i	$-0.624641\pi$
$929$	−23.2644	−0.763281	−0.381641	+	0.924311i	$0.624641\pi$
$930$	−19.3448	−0.634341
$931$	2.13706	0.0700394
$932$	9.92931	0.325245
$933$	0.254749	0.00834012
$934$	4.04652	0.132406
$935$	9.15990	0.299561
$936$	0	0
$937$	57.3491	1.87351	0.936757	−	0.349980i	$-0.113812\pi$
$937$	57.3491	1.87351	0.936757	+	0.349980i	$0.113812\pi$
$938$	−11.3937	−0.372019
$939$	−24.1129	−0.786895
$940$	12.1588	0.396577
$941$	50.8840	1.65877	0.829385	−	0.558677i	$-0.188691\pi$
$941$	50.8840	1.65877	0.829385	+	0.558677i	$0.188691\pi$
$942$	12.0978	0.394169
$943$	10.0573	0.327510
$944$	−3.44504	−0.112127
$945$	−3.04892	−0.0991813
$946$	−20.4196	−0.663897
$947$	−9.63593	−0.313126	−0.156563	−	0.987668i	$-0.550041\pi$
$947$	−9.63593	−0.313126	−0.156563	+	0.987668i	$0.550041\pi$
$948$	10.7071	0.347750
$949$	0	0
$950$	9.18060	0.297858
$951$	12.8321	0.416108
$952$	1.40581	0.0455627
$953$	−6.38345	−0.206780	−0.103390	−	0.994641i	$-0.532969\pi$
$953$	−6.38345	−0.206780	−0.103390	+	0.994641i	$0.532969\pi$
$954$	6.46681	0.209371
$955$	−70.8577	−2.29290
$956$	22.1172	0.715322
$957$	5.51812	0.178376
$958$	−16.0411	−0.518266
$959$	−0.249373	−0.00805266
$960$	3.04892	0.0984034
$961$	9.25667	0.298602
$962$	0	0
$963$	−12.5254	−0.403626
$964$	24.5429	0.790473
$965$	−12.2121	−0.393120
$966$	−2.26875	−0.0729958
$967$	−28.8692	−0.928370	−0.464185	−	0.885738i	$-0.653653\pi$
$967$	−28.8692	−0.928370	−0.464185	+	0.885738i	$0.653653\pi$
$968$	−6.43296	−0.206763
$969$	3.00431	0.0965124
$970$	15.5593	0.499578
$971$	−35.9661	−1.15421	−0.577104	−	0.816670i	$-0.695817\pi$
$971$	−35.9661	−1.15421	−0.577104	+	0.816670i	$0.695817\pi$
$972$	−1.00000	−0.0320750
$973$	−0.168522	−0.00540258
$974$	36.7724	1.17826
$975$	0	0
$976$	9.98792	0.319705
$977$	42.2664	1.35222	0.676110	−	0.736800i	$-0.263664\pi$
$977$	42.2664	1.35222	0.676110	+	0.736800i	$0.263664\pi$
$978$	−14.0707	−0.449931
$979$	−7.98313	−0.255142
$980$	−3.04892	−0.0973941
$981$	−1.15883	−0.0369987
$982$	−7.69069	−0.245420
$983$	39.2435	1.25167	0.625837	−	0.779954i	$-0.284758\pi$
$983$	39.2435	1.25167	0.625837	+	0.779954i	$0.284758\pi$
$984$	4.43296	0.141318
$985$	23.6547	0.753702
$986$	3.62996	0.115601
$987$	−3.98792	−0.126937
$988$	0	0
$989$	21.6778	0.689314
$990$	−6.51573	−0.207083
$991$	31.1892	0.990758	0.495379	−	0.868677i	$-0.335029\pi$
$991$	31.1892	0.990758	0.495379	+	0.868677i	$0.335029\pi$
$992$	−6.34481	−0.201448
$993$	−29.0707	−0.922530
$994$	−4.21983	−0.133845
$995$	−44.3696	−1.40661
$996$	−8.94869	−0.283550
$997$	−23.7275	−0.751458	−0.375729	−	0.926730i	$-0.622608\pi$
$997$	−23.7275	−0.751458	−0.375729	+	0.926730i	$0.622608\pi$
$998$	−21.8213	−0.690742
$999$	−10.6528	−0.337039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.ci.1.1	yes	3
13.12	even	2		7098.2.a.cd.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cd.1.3	✓	3	13.12	even	2
7098.2.a.ci.1.1	yes	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.04892 q^{10} +2.13706 q^{11} -1.00000 q^{12} -1.00000 q^{14} +3.04892 q^{15} +1.00000 q^{16} -1.40581 q^{17} +1.00000 q^{18} +2.13706 q^{19} -3.04892 q^{20} +1.00000 q^{21} +2.13706 q^{22} -2.26875 q^{23} -1.00000 q^{24} +4.29590 q^{25} -1.00000 q^{27} -1.00000 q^{28} -2.58211 q^{29} +3.04892 q^{30} -6.34481 q^{31} +1.00000 q^{32} -2.13706 q^{33} -1.40581 q^{34} +3.04892 q^{35} +1.00000 q^{36} +10.6528 q^{37} +2.13706 q^{38} -3.04892 q^{40} -4.43296 q^{41} +1.00000 q^{42} -9.55496 q^{43} +2.13706 q^{44} -3.04892 q^{45} -2.26875 q^{46} -3.98792 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.29590 q^{50} +1.40581 q^{51} +6.46681 q^{53} -1.00000 q^{54} -6.51573 q^{55} -1.00000 q^{56} -2.13706 q^{57} -2.58211 q^{58} -3.44504 q^{59} +3.04892 q^{60} +9.98792 q^{61} -6.34481 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.13706 q^{66} +11.3937 q^{67} -1.40581 q^{68} +2.26875 q^{69} +3.04892 q^{70} +4.21983 q^{71} +1.00000 q^{72} +5.84548 q^{73} +10.6528 q^{74} -4.29590 q^{75} +2.13706 q^{76} -2.13706 q^{77} -10.7071 q^{79} -3.04892 q^{80} +1.00000 q^{81} -4.43296 q^{82} +8.94869 q^{83} +1.00000 q^{84} +4.28621 q^{85} -9.55496 q^{86} +2.58211 q^{87} +2.13706 q^{88} -3.73556 q^{89} -3.04892 q^{90} -2.26875 q^{92} +6.34481 q^{93} -3.98792 q^{94} -6.51573 q^{95} -1.00000 q^{96} -5.10321 q^{97} +1.00000 q^{98} +2.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{16} + 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{21} + q^{22} + q^{23} - 3 q^{24} - q^{25} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 4 q^{31} + 3 q^{32} - q^{33} + 9 q^{34} + 3 q^{36} + 14 q^{37} + q^{38} + 6 q^{41} + 3 q^{42} - 29 q^{43} + q^{44} + q^{46} + 7 q^{47} - 3 q^{48} + 3 q^{49} - q^{50} - 9 q^{51} + 16 q^{53} - 3 q^{54} - 7 q^{55} - 3 q^{56} - q^{57} - 2 q^{58} - 10 q^{59} + 11 q^{61} + 4 q^{62} - 3 q^{63} + 3 q^{64} - q^{66} + 2 q^{67} + 9 q^{68} - q^{69} + 14 q^{71} + 3 q^{72} + 7 q^{73} + 14 q^{74} + q^{75} + q^{76} - q^{77} - 2 q^{79} + 3 q^{81} + 6 q^{82} - 5 q^{83} + 3 q^{84} + 21 q^{85} - 29 q^{86} + 2 q^{87} + q^{88} + q^{92} - 4 q^{93} + 7 q^{94} - 7 q^{95} - 3 q^{96} + 6 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^11 - 3 * q^12 - 3 * q^14 + 3 * q^16 + 9 * q^17 + 3 * q^18 + q^19 + 3 * q^21 + q^22 + q^23 - 3 * q^24 - q^25 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 4 * q^31 + 3 * q^32 - q^33 + 9 * q^34 + 3 * q^36 + 14 * q^37 + q^38 + 6 * q^41 + 3 * q^42 - 29 * q^43 + q^44 + q^46 + 7 * q^47 - 3 * q^48 + 3 * q^49 - q^50 - 9 * q^51 + 16 * q^53 - 3 * q^54 - 7 * q^55 - 3 * q^56 - q^57 - 2 * q^58 - 10 * q^59 + 11 * q^61 + 4 * q^62 - 3 * q^63 + 3 * q^64 - q^66 + 2 * q^67 + 9 * q^68 - q^69 + 14 * q^71 + 3 * q^72 + 7 * q^73 + 14 * q^74 + q^75 + q^76 - q^77 - 2 * q^79 + 3 * q^81 + 6 * q^82 - 5 * q^83 + 3 * q^84 + 21 * q^85 - 29 * q^86 + 2 * q^87 + q^88 + q^92 - 4 * q^93 + 7 * q^94 - 7 * q^95 - 3 * q^96 + 6 * q^97 + 3 * q^98 + q^99

Introduction

L-functions

Modular forms

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Database

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