LMFDB - Embedded newform 7098.2.a.ct.1.6

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:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 281
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			1.6
Root			$3.41496$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.41496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} +3.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} +1.00000 q^{18} +1.93665 q^{19} +3.41496 q^{20} +1.00000 q^{21} +3.24698 q^{22} +3.28422 q^{23} +1.00000 q^{24} +6.66194 q^{25} +1.00000 q^{27} +1.00000 q^{28} -3.64112 q^{29} +3.41496 q^{30} -3.10698 q^{31} +1.00000 q^{32} +3.24698 q^{33} +1.80194 q^{34} +3.41496 q^{35} +1.00000 q^{36} -4.80172 q^{37} +1.93665 q^{38} +3.41496 q^{40} -4.58189 q^{41} +1.00000 q^{42} +5.11205 q^{43} +3.24698 q^{44} +3.41496 q^{45} +3.28422 q^{46} -10.5966 q^{47} +1.00000 q^{48} +1.00000 q^{49} +6.66194 q^{50} +1.80194 q^{51} -2.46409 q^{53} +1.00000 q^{54} +11.0883 q^{55} +1.00000 q^{56} +1.93665 q^{57} -3.64112 q^{58} +13.2749 q^{59} +3.41496 q^{60} -1.76668 q^{61} -3.10698 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} -12.4092 q^{67} +1.80194 q^{68} +3.28422 q^{69} +3.41496 q^{70} -2.66429 q^{71} +1.00000 q^{72} +0.368396 q^{73} -4.80172 q^{74} +6.66194 q^{75} +1.93665 q^{76} +3.24698 q^{77} -15.0033 q^{79} +3.41496 q^{80} +1.00000 q^{81} -4.58189 q^{82} -1.43401 q^{83} +1.00000 q^{84} +6.15354 q^{85} +5.11205 q^{86} -3.64112 q^{87} +3.24698 q^{88} +5.10615 q^{89} +3.41496 q^{90} +3.28422 q^{92} -3.10698 q^{93} -10.5966 q^{94} +6.61356 q^{95} +1.00000 q^{96} -11.9553 q^{97} +1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * 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
$5$	3.41496	1.52722	0.763608	−	0.645680i	$-0.223426\pi$
$5$	3.41496	1.52722	0.763608	+	0.645680i	$0.223426\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.41496	1.07990
$11$	3.24698	0.979001	0.489501	−	0.872003i	$-0.337179\pi$
$11$	3.24698	0.979001	0.489501	+	0.872003i	$0.337179\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	3.41496	0.881738
$16$	1.00000	0.250000
$17$	1.80194	0.437034	0.218517	−	0.975833i	$-0.429878\pi$
$17$	1.80194	0.437034	0.218517	+	0.975833i	$0.429878\pi$
$18$	1.00000	0.235702
$19$	1.93665	0.444297	0.222149	−	0.975013i	$-0.428693\pi$
$19$	1.93665	0.444297	0.222149	+	0.975013i	$0.428693\pi$
$20$	3.41496	0.763608
$21$	1.00000	0.218218
$22$	3.24698	0.692258
$23$	3.28422	0.684808	0.342404	−	0.939553i	$-0.388759\pi$
$23$	3.28422	0.684808	0.342404	+	0.939553i	$0.388759\pi$
$24$	1.00000	0.204124
$25$	6.66194	1.33239
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−3.64112	−0.676139	−0.338069	−	0.941121i	$-0.609774\pi$
$29$	−3.64112	−0.676139	−0.338069	+	0.941121i	$0.609774\pi$
$30$	3.41496	0.623483
$31$	−3.10698	−0.558030	−0.279015	−	0.960287i	$-0.590008\pi$
$31$	−3.10698	−0.558030	−0.279015	+	0.960287i	$0.590008\pi$
$32$	1.00000	0.176777
$33$	3.24698	0.565227
$34$	1.80194	0.309030
$35$	3.41496	0.577233
$36$	1.00000	0.166667
$37$	−4.80172	−0.789398	−0.394699	−	0.918810i	$-0.629151\pi$
$37$	−4.80172	−0.789398	−0.394699	+	0.918810i	$0.629151\pi$
$38$	1.93665	0.314165
$39$	0	0
$40$	3.41496	0.539952
$41$	−4.58189	−0.715571	−0.357785	−	0.933804i	$-0.616468\pi$
$41$	−4.58189	−0.715571	−0.357785	+	0.933804i	$0.616468\pi$
$42$	1.00000	0.154303
$43$	5.11205	0.779581	0.389790	−	0.920904i	$-0.372547\pi$
$43$	5.11205	0.779581	0.389790	+	0.920904i	$0.372547\pi$
$44$	3.24698	0.489501
$45$	3.41496	0.509072
$46$	3.28422	0.484232
$47$	−10.5966	−1.54567	−0.772836	−	0.634605i	$-0.781163\pi$
$47$	−10.5966	−1.54567	−0.772836	+	0.634605i	$0.781163\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	6.66194	0.942140
$51$	1.80194	0.252322
$52$	0	0
$53$	−2.46409	−0.338469	−0.169235	−	0.985576i	$-0.554130\pi$
$53$	−2.46409	−0.338469	−0.169235	+	0.985576i	$0.554130\pi$
$54$	1.00000	0.136083
$55$	11.0883	1.49515
$56$	1.00000	0.133631
$57$	1.93665	0.256515
$58$	−3.64112	−0.478102
$59$	13.2749	1.72824	0.864120	−	0.503286i	$-0.167876\pi$
$59$	13.2749	1.72824	0.864120	+	0.503286i	$0.167876\pi$
$60$	3.41496	0.440869
$61$	−1.76668	−0.226200	−0.113100	−	0.993584i	$-0.536078\pi$
$61$	−1.76668	−0.226200	−0.113100	+	0.993584i	$0.536078\pi$
$62$	−3.10698	−0.394587
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	3.24698	0.399676
$67$	−12.4092	−1.51603	−0.758013	−	0.652240i	$-0.773830\pi$
$67$	−12.4092	−1.51603	−0.758013	+	0.652240i	$0.773830\pi$
$68$	1.80194	0.218517
$69$	3.28422	0.395374
$70$	3.41496	0.408166
$71$	−2.66429	−0.316193	−0.158097	−	0.987424i	$-0.550536\pi$
$71$	−2.66429	−0.316193	−0.158097	+	0.987424i	$0.550536\pi$
$72$	1.00000	0.117851
$73$	0.368396	0.0431175	0.0215587	−	0.999768i	$-0.493137\pi$
$73$	0.368396	0.0431175	0.0215587	+	0.999768i	$0.493137\pi$
$74$	−4.80172	−0.558189
$75$	6.66194	0.769254
$76$	1.93665	0.222149
$77$	3.24698	0.370028
$78$	0	0
$79$	−15.0033	−1.68801	−0.844004	−	0.536336i	$-0.819808\pi$
$79$	−15.0033	−1.68801	−0.844004	+	0.536336i	$0.819808\pi$
$80$	3.41496	0.381804
$81$	1.00000	0.111111
$82$	−4.58189	−0.505985
$83$	−1.43401	−0.157403	−0.0787014	−	0.996898i	$-0.525077\pi$
$83$	−1.43401	−0.157403	−0.0787014	+	0.996898i	$0.525077\pi$
$84$	1.00000	0.109109
$85$	6.15354	0.667445
$86$	5.11205	0.551247
$87$	−3.64112	−0.390369
$88$	3.24698	0.346129
$89$	5.10615	0.541251	0.270625	−	0.962685i	$-0.412770\pi$
$89$	5.10615	0.541251	0.270625	+	0.962685i	$0.412770\pi$
$90$	3.41496	0.359968
$91$	0	0
$92$	3.28422	0.342404
$93$	−3.10698	−0.322179
$94$	−10.5966	−1.09296
$95$	6.61356	0.678537
$96$	1.00000	0.102062
$97$	−11.9553	−1.21387	−0.606936	−	0.794750i	$-0.707602\pi$
$97$	−11.9553	−1.21387	−0.606936	+	0.794750i	$0.707602\pi$
$98$	1.00000	0.101015
$99$	3.24698	0.326334
$100$	6.66194	0.666194
$101$	−18.5354	−1.84434	−0.922170	−	0.386785i	$-0.873585\pi$
$101$	−18.5354	−1.84434	−0.922170	+	0.386785i	$0.873585\pi$
$102$	1.80194	0.178418
$103$	18.2577	1.79899	0.899493	−	0.436936i	$-0.143936\pi$
$103$	18.2577	1.79899	0.899493	+	0.436936i	$0.143936\pi$
$104$	0	0
$105$	3.41496	0.333266
$106$	−2.46409	−0.239334
$107$	−15.0210	−1.45213	−0.726066	−	0.687625i	$-0.758653\pi$
$107$	−15.0210	−1.45213	−0.726066	+	0.687625i	$0.758653\pi$
$108$	1.00000	0.0962250
$109$	11.7533	1.12577	0.562883	−	0.826536i	$-0.309692\pi$
$109$	11.7533	1.12577	0.562883	+	0.826536i	$0.309692\pi$
$110$	11.0883	1.05723
$111$	−4.80172	−0.455759
$112$	1.00000	0.0944911
$113$	3.69957	0.348026	0.174013	−	0.984743i	$-0.444326\pi$
$113$	3.69957	0.348026	0.174013	+	0.984743i	$0.444326\pi$
$114$	1.93665	0.181384
$115$	11.2155	1.04585
$116$	−3.64112	−0.338069
$117$	0	0
$118$	13.2749	1.22205
$119$	1.80194	0.165183
$120$	3.41496	0.311742
$121$	−0.457123	−0.0415567
$122$	−1.76668	−0.159948
$123$	−4.58189	−0.413135
$124$	−3.10698	−0.279015
$125$	5.67545	0.507627
$126$	1.00000	0.0890871
$127$	3.89724	0.345824	0.172912	−	0.984937i	$-0.444682\pi$
$127$	3.89724	0.345824	0.172912	+	0.984937i	$0.444682\pi$
$128$	1.00000	0.0883883
$129$	5.11205	0.450091
$130$	0	0
$131$	−17.6740	−1.54418	−0.772091	−	0.635511i	$-0.780789\pi$
$131$	−17.6740	−1.54418	−0.772091	+	0.635511i	$0.780789\pi$
$132$	3.24698	0.282613
$133$	1.93665	0.167928
$134$	−12.4092	−1.07199
$135$	3.41496	0.293913
$136$	1.80194	0.154515
$137$	−14.9195	−1.27466	−0.637331	−	0.770590i	$-0.719962\pi$
$137$	−14.9195	−1.27466	−0.637331	+	0.770590i	$0.719962\pi$
$138$	3.28422	0.279572
$139$	−3.27513	−0.277793	−0.138897	−	0.990307i	$-0.544356\pi$
$139$	−3.27513	−0.277793	−0.138897	+	0.990307i	$0.544356\pi$
$140$	3.41496	0.288617
$141$	−10.5966	−0.892395
$142$	−2.66429	−0.223582
$143$	0	0
$144$	1.00000	0.0833333
$145$	−12.4343	−1.03261
$146$	0.368396	0.0304887
$147$	1.00000	0.0824786
$148$	−4.80172	−0.394699
$149$	8.92475	0.731144	0.365572	−	0.930783i	$-0.380873\pi$
$149$	8.92475	0.731144	0.365572	+	0.930783i	$0.380873\pi$
$150$	6.66194	0.543945
$151$	−0.712364	−0.0579714	−0.0289857	−	0.999580i	$-0.509228\pi$
$151$	−0.712364	−0.0579714	−0.0289857	+	0.999580i	$0.509228\pi$
$152$	1.93665	0.157083
$153$	1.80194	0.145678
$154$	3.24698	0.261649
$155$	−10.6102	−0.852232
$156$	0	0
$157$	−14.1436	−1.12879	−0.564393	−	0.825506i	$-0.690890\pi$
$157$	−14.1436	−1.12879	−0.564393	+	0.825506i	$0.690890\pi$
$158$	−15.0033	−1.19360
$159$	−2.46409	−0.195415
$160$	3.41496	0.269976
$161$	3.28422	0.258833
$162$	1.00000	0.0785674
$163$	15.6565	1.22632	0.613158	−	0.789960i	$-0.289899\pi$
$163$	15.6565	1.22632	0.613158	+	0.789960i	$0.289899\pi$
$164$	−4.58189	−0.357785
$165$	11.0883	0.863223
$166$	−1.43401	−0.111301
$167$	19.6904	1.52369	0.761845	−	0.647759i	$-0.224294\pi$
$167$	19.6904	1.52369	0.761845	+	0.647759i	$0.224294\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	6.15354	0.471955
$171$	1.93665	0.148099
$172$	5.11205	0.389790
$173$	16.3915	1.24622	0.623112	−	0.782132i	$-0.285868\pi$
$173$	16.3915	1.24622	0.623112	+	0.782132i	$0.285868\pi$
$174$	−3.64112	−0.276033
$175$	6.66194	0.503595
$176$	3.24698	0.244750
$177$	13.2749	0.997800
$178$	5.10615	0.382722
$179$	−17.0906	−1.27741	−0.638704	−	0.769452i	$-0.720529\pi$
$179$	−17.0906	−1.27741	−0.638704	+	0.769452i	$0.720529\pi$
$180$	3.41496	0.254536
$181$	21.3647	1.58803	0.794015	−	0.607899i	$-0.207987\pi$
$181$	21.3647	1.58803	0.794015	+	0.607899i	$0.207987\pi$
$182$	0	0
$183$	−1.76668	−0.130597
$184$	3.28422	0.242116
$185$	−16.3977	−1.20558
$186$	−3.10698	−0.227815
$187$	5.85086	0.427857
$188$	−10.5966	−0.772836
$189$	1.00000	0.0727393
$190$	6.61356	0.479798
$191$	16.2973	1.17923	0.589614	−	0.807685i	$-0.299280\pi$
$191$	16.2973	1.17923	0.589614	+	0.807685i	$0.299280\pi$
$192$	1.00000	0.0721688
$193$	18.7221	1.34765	0.673824	−	0.738892i	$-0.264651\pi$
$193$	18.7221	1.34765	0.673824	+	0.738892i	$0.264651\pi$
$194$	−11.9553	−0.858338
$195$	0	0
$196$	1.00000	0.0714286
$197$	6.35011	0.452426	0.226213	−	0.974078i	$-0.427365\pi$
$197$	6.35011	0.452426	0.226213	+	0.974078i	$0.427365\pi$
$198$	3.24698	0.230753
$199$	11.9820	0.849380	0.424690	−	0.905339i	$-0.360383\pi$
$199$	11.9820	0.849380	0.424690	+	0.905339i	$0.360383\pi$
$200$	6.66194	0.471070
$201$	−12.4092	−0.875278
$202$	−18.5354	−1.30414
$203$	−3.64112	−0.255556
$204$	1.80194	0.126161
$205$	−15.6470	−1.09283
$206$	18.2577	1.27207
$207$	3.28422	0.228269
$208$	0	0
$209$	6.28825	0.434967
$210$	3.41496	0.235654
$211$	9.42870	0.649099	0.324549	−	0.945869i	$-0.394787\pi$
$211$	9.42870	0.649099	0.324549	+	0.945869i	$0.394787\pi$
$212$	−2.46409	−0.169235
$213$	−2.66429	−0.182554
$214$	−15.0210	−1.02681
$215$	17.4575	1.19059
$216$	1.00000	0.0680414
$217$	−3.10698	−0.210916
$218$	11.7533	0.796037
$219$	0.368396	0.0248939
$220$	11.0883	0.747573
$221$	0	0
$222$	−4.80172	−0.322270
$223$	−15.9921	−1.07091	−0.535456	−	0.844563i	$-0.679860\pi$
$223$	−15.9921	−1.07091	−0.535456	+	0.844563i	$0.679860\pi$
$224$	1.00000	0.0668153
$225$	6.66194	0.444129
$226$	3.69957	0.246092
$227$	4.11815	0.273331	0.136665	−	0.990617i	$-0.456361\pi$
$227$	4.11815	0.273331	0.136665	+	0.990617i	$0.456361\pi$
$228$	1.93665	0.128258
$229$	0.403067	0.0266354	0.0133177	−	0.999911i	$-0.495761\pi$
$229$	0.403067	0.0266354	0.0133177	+	0.999911i	$0.495761\pi$
$230$	11.2155	0.739527
$231$	3.24698	0.213636
$232$	−3.64112	−0.239051
$233$	−18.7561	−1.22875	−0.614376	−	0.789014i	$-0.710592\pi$
$233$	−18.7561	−1.22875	−0.614376	+	0.789014i	$0.710592\pi$
$234$	0	0
$235$	−36.1869	−2.36058
$236$	13.2749	0.864120
$237$	−15.0033	−0.974572
$238$	1.80194	0.116802
$239$	−10.3497	−0.669466	−0.334733	−	0.942313i	$-0.608646\pi$
$239$	−10.3497	−0.669466	−0.334733	+	0.942313i	$0.608646\pi$
$240$	3.41496	0.220435
$241$	−9.33396	−0.601253	−0.300627	−	0.953742i	$-0.597196\pi$
$241$	−9.33396	−0.601253	−0.300627	+	0.953742i	$0.597196\pi$
$242$	−0.457123	−0.0293850
$243$	1.00000	0.0641500
$244$	−1.76668	−0.113100
$245$	3.41496	0.218174
$246$	−4.58189	−0.292131
$247$	0	0
$248$	−3.10698	−0.197293
$249$	−1.43401	−0.0908766
$250$	5.67545	0.358947
$251$	−30.9745	−1.95509	−0.977547	−	0.210718i	$-0.932420\pi$
$251$	−30.9745	−1.95509	−0.977547	+	0.210718i	$0.932420\pi$
$252$	1.00000	0.0629941
$253$	10.6638	0.670428
$254$	3.89724	0.244535
$255$	6.15354	0.385350
$256$	1.00000	0.0625000
$257$	−2.27305	−0.141789	−0.0708944	−	0.997484i	$-0.522585\pi$
$257$	−2.27305	−0.141789	−0.0708944	+	0.997484i	$0.522585\pi$
$258$	5.11205	0.318263
$259$	−4.80172	−0.298364
$260$	0	0
$261$	−3.64112	−0.225380
$262$	−17.6740	−1.09190
$263$	−18.5834	−1.14590	−0.572950	−	0.819590i	$-0.694201\pi$
$263$	−18.5834	−1.14590	−0.572950	+	0.819590i	$0.694201\pi$
$264$	3.24698	0.199838
$265$	−8.41477	−0.516915
$266$	1.93665	0.118743
$267$	5.10615	0.312491
$268$	−12.4092	−0.758013
$269$	26.7522	1.63111	0.815555	−	0.578679i	$-0.196432\pi$
$269$	26.7522	1.63111	0.815555	+	0.578679i	$0.196432\pi$
$270$	3.41496	0.207828
$271$	5.33182	0.323885	0.161943	−	0.986800i	$-0.448224\pi$
$271$	5.33182	0.323885	0.161943	+	0.986800i	$0.448224\pi$
$272$	1.80194	0.109259
$273$	0	0
$274$	−14.9195	−0.901323
$275$	21.6312	1.30441
$276$	3.28422	0.197687
$277$	25.0045	1.50238	0.751188	−	0.660088i	$-0.229481\pi$
$277$	25.0045	1.50238	0.751188	+	0.660088i	$0.229481\pi$
$278$	−3.27513	−0.196429
$279$	−3.10698	−0.186010
$280$	3.41496	0.204083
$281$	13.8066	0.823633	0.411817	−	0.911267i	$-0.364894\pi$
$281$	13.8066	0.823633	0.411817	+	0.911267i	$0.364894\pi$
$282$	−10.5966	−0.631018
$283$	−22.0224	−1.30910	−0.654548	−	0.756021i	$-0.727141\pi$
$283$	−22.0224	−1.30910	−0.654548	+	0.756021i	$0.727141\pi$
$284$	−2.66429	−0.158097
$285$	6.61356	0.391754
$286$	0	0
$287$	−4.58189	−0.270460
$288$	1.00000	0.0589256
$289$	−13.7530	−0.809001
$290$	−12.4343	−0.730165
$291$	−11.9553	−0.700830
$292$	0.368396	0.0215587
$293$	−2.17514	−0.127073	−0.0635364	−	0.997980i	$-0.520238\pi$
$293$	−2.17514	−0.127073	−0.0635364	+	0.997980i	$0.520238\pi$
$294$	1.00000	0.0583212
$295$	45.3331	2.63939
$296$	−4.80172	−0.279094
$297$	3.24698	0.188409
$298$	8.92475	0.516997
$299$	0	0
$300$	6.66194	0.384627
$301$	5.11205	0.294654
$302$	−0.712364	−0.0409920
$303$	−18.5354	−1.06483
$304$	1.93665	0.111074
$305$	−6.03315	−0.345457
$306$	1.80194	0.103010
$307$	21.5338	1.22900	0.614500	−	0.788917i	$-0.289358\pi$
$307$	21.5338	1.22900	0.614500	+	0.788917i	$0.289358\pi$
$308$	3.24698	0.185014
$309$	18.2577	1.03864
$310$	−10.6102	−0.602619
$311$	−10.5043	−0.595644	−0.297822	−	0.954621i	$-0.596260\pi$
$311$	−10.5043	−0.595644	−0.297822	+	0.954621i	$0.596260\pi$
$312$	0	0
$313$	−16.0754	−0.908635	−0.454317	−	0.890840i	$-0.650117\pi$
$313$	−16.0754	−0.908635	−0.454317	+	0.890840i	$0.650117\pi$
$314$	−14.1436	−0.798172
$315$	3.41496	0.192411
$316$	−15.0033	−0.844004
$317$	15.3743	0.863508	0.431754	−	0.901991i	$-0.357895\pi$
$317$	15.3743	0.863508	0.431754	+	0.901991i	$0.357895\pi$
$318$	−2.46409	−0.138179
$319$	−11.8226	−0.661941
$320$	3.41496	0.190902
$321$	−15.0210	−0.838389
$322$	3.28422	0.183023
$323$	3.48972	0.194173
$324$	1.00000	0.0555556
$325$	0	0
$326$	15.6565	0.867136
$327$	11.7533	0.649962
$328$	−4.58189	−0.252992
$329$	−10.5966	−0.584209
$330$	11.0883	0.610391
$331$	−8.21249	−0.451399	−0.225700	−	0.974197i	$-0.572467\pi$
$331$	−8.21249	−0.451399	−0.225700	+	0.974197i	$0.572467\pi$
$332$	−1.43401	−0.0787014
$333$	−4.80172	−0.263133
$334$	19.6904	1.07741
$335$	−42.3769	−2.31530
$336$	1.00000	0.0545545
$337$	−18.4567	−1.00540	−0.502701	−	0.864460i	$-0.667660\pi$
$337$	−18.4567	−1.00540	−0.502701	+	0.864460i	$0.667660\pi$
$338$	0	0
$339$	3.69957	0.200933
$340$	6.15354	0.333723
$341$	−10.0883	−0.546312
$342$	1.93665	0.104722
$343$	1.00000	0.0539949
$344$	5.11205	0.275623
$345$	11.2155	0.603821
$346$	16.3915	0.881214
$347$	31.3648	1.68375	0.841876	−	0.539671i	$-0.181451\pi$
$347$	31.3648	1.68375	0.841876	+	0.539671i	$0.181451\pi$
$348$	−3.64112	−0.195184
$349$	−6.96959	−0.373073	−0.186537	−	0.982448i	$-0.559726\pi$
$349$	−6.96959	−0.373073	−0.186537	+	0.982448i	$0.559726\pi$
$350$	6.66194	0.356096
$351$	0	0
$352$	3.24698	0.173065
$353$	13.0978	0.697127	0.348563	−	0.937285i	$-0.386670\pi$
$353$	13.0978	0.697127	0.348563	+	0.937285i	$0.386670\pi$
$354$	13.2749	0.705551
$355$	−9.09845	−0.482895
$356$	5.10615	0.270625
$357$	1.80194	0.0953687
$358$	−17.0906	−0.903264
$359$	−8.01400	−0.422963	−0.211481	−	0.977382i	$-0.567829\pi$
$359$	−8.01400	−0.422963	−0.211481	+	0.977382i	$0.567829\pi$
$360$	3.41496	0.179984
$361$	−15.2494	−0.802600
$362$	21.3647	1.12291
$363$	−0.457123	−0.0239928
$364$	0	0
$365$	1.25806	0.0658497
$366$	−1.76668	−0.0923460
$367$	−25.7361	−1.34342	−0.671708	−	0.740816i	$-0.734439\pi$
$367$	−25.7361	−1.34342	−0.671708	+	0.740816i	$0.734439\pi$
$368$	3.28422	0.171202
$369$	−4.58189	−0.238524
$370$	−16.3977	−0.852474
$371$	−2.46409	−0.127929
$372$	−3.10698	−0.161089
$373$	−0.973483	−0.0504050	−0.0252025	−	0.999682i	$-0.508023\pi$
$373$	−0.973483	−0.0504050	−0.0252025	+	0.999682i	$0.508023\pi$
$374$	5.85086	0.302541
$375$	5.67545	0.293079
$376$	−10.5966	−0.546478
$377$	0	0
$378$	1.00000	0.0514344
$379$	−5.27383	−0.270899	−0.135449	−	0.990784i	$-0.543248\pi$
$379$	−5.27383	−0.270899	−0.135449	+	0.990784i	$0.543248\pi$
$380$	6.61356	0.339269
$381$	3.89724	0.199662
$382$	16.2973	0.833840
$383$	11.1179	0.568100	0.284050	−	0.958810i	$-0.408322\pi$
$383$	11.1179	0.568100	0.284050	+	0.958810i	$0.408322\pi$
$384$	1.00000	0.0510310
$385$	11.0883	0.565112
$386$	18.7221	0.952931
$387$	5.11205	0.259860
$388$	−11.9553	−0.606936
$389$	−13.6798	−0.693595	−0.346797	−	0.937940i	$-0.612731\pi$
$389$	−13.6798	−0.693595	−0.346797	+	0.937940i	$0.612731\pi$
$390$	0	0
$391$	5.91797	0.299284
$392$	1.00000	0.0505076
$393$	−17.6740	−0.891534
$394$	6.35011	0.319914
$395$	−51.2358	−2.57795
$396$	3.24698	0.163167
$397$	16.3683	0.821500	0.410750	−	0.911748i	$-0.365267\pi$
$397$	16.3683	0.821500	0.410750	+	0.911748i	$0.365267\pi$
$398$	11.9820	0.600603
$399$	1.93665	0.0969536
$400$	6.66194	0.333097
$401$	−35.9089	−1.79320	−0.896602	−	0.442837i	$-0.853972\pi$
$401$	−35.9089	−1.79320	−0.896602	+	0.442837i	$0.853972\pi$
$402$	−12.4092	−0.618915
$403$	0	0
$404$	−18.5354	−0.922170
$405$	3.41496	0.169691
$406$	−3.64112	−0.180706
$407$	−15.5911	−0.772822
$408$	1.80194	0.0892092
$409$	12.4416	0.615197	0.307599	−	0.951516i	$-0.400475\pi$
$409$	12.4416	0.615197	0.307599	+	0.951516i	$0.400475\pi$
$410$	−15.6470	−0.772748
$411$	−14.9195	−0.735927
$412$	18.2577	0.899493
$413$	13.2749	0.653213
$414$	3.28422	0.161411
$415$	−4.89708	−0.240388
$416$	0	0
$417$	−3.27513	−0.160384
$418$	6.28825	0.307568
$419$	9.73591	0.475630	0.237815	−	0.971310i	$-0.423569\pi$
$419$	9.73591	0.475630	0.237815	+	0.971310i	$0.423569\pi$
$420$	3.41496	0.166633
$421$	24.4352	1.19090	0.595449	−	0.803393i	$-0.296974\pi$
$421$	24.4352	1.19090	0.595449	+	0.803393i	$0.296974\pi$
$422$	9.42870	0.458982
$423$	−10.5966	−0.515224
$424$	−2.46409	−0.119667
$425$	12.0044	0.582299
$426$	−2.66429	−0.129085
$427$	−1.76668	−0.0854957
$428$	−15.0210	−0.726066
$429$	0	0
$430$	17.4575	0.841873
$431$	38.2356	1.84174	0.920872	−	0.389864i	$-0.127478\pi$
$431$	38.2356	1.84174	0.920872	+	0.389864i	$0.127478\pi$
$432$	1.00000	0.0481125
$433$	31.9423	1.53505	0.767524	−	0.641021i	$-0.221489\pi$
$433$	31.9423	1.53505	0.767524	+	0.641021i	$0.221489\pi$
$434$	−3.10698	−0.149140
$435$	−12.4343	−0.596177
$436$	11.7533	0.562883
$437$	6.36038	0.304258
$438$	0.368396	0.0176026
$439$	20.6203	0.984152	0.492076	−	0.870552i	$-0.336238\pi$
$439$	20.6203	0.984152	0.492076	+	0.870552i	$0.336238\pi$
$440$	11.0883	0.528614
$441$	1.00000	0.0476190
$442$	0	0
$443$	−0.760370	−0.0361263	−0.0180631	−	0.999837i	$-0.505750\pi$
$443$	−0.760370	−0.0361263	−0.0180631	+	0.999837i	$0.505750\pi$
$444$	−4.80172	−0.227880
$445$	17.4373	0.826606
$446$	−15.9921	−0.757250
$447$	8.92475	0.422126
$448$	1.00000	0.0472456
$449$	19.8729	0.937859	0.468929	−	0.883236i	$-0.344640\pi$
$449$	19.8729	0.937859	0.468929	+	0.883236i	$0.344640\pi$
$450$	6.66194	0.314047
$451$	−14.8773	−0.700545
$452$	3.69957	0.174013
$453$	−0.712364	−0.0334698
$454$	4.11815	0.193274
$455$	0	0
$456$	1.93665	0.0906918
$457$	39.0448	1.82644	0.913220	−	0.407466i	$-0.133587\pi$
$457$	39.0448	1.82644	0.913220	+	0.407466i	$0.133587\pi$
$458$	0.403067	0.0188341
$459$	1.80194	0.0841073
$460$	11.2155	0.522925
$461$	−25.0785	−1.16802	−0.584011	−	0.811746i	$-0.698517\pi$
$461$	−25.0785	−1.16802	−0.584011	+	0.811746i	$0.698517\pi$
$462$	3.24698	0.151063
$463$	11.3140	0.525807	0.262904	−	0.964822i	$-0.415320\pi$
$463$	11.3140	0.525807	0.262904	+	0.964822i	$0.415320\pi$
$464$	−3.64112	−0.169035
$465$	−10.6102	−0.492036
$466$	−18.7561	−0.868858
$467$	12.6861	0.587043	0.293521	−	0.955952i	$-0.405173\pi$
$467$	12.6861	0.587043	0.293521	+	0.955952i	$0.405173\pi$
$468$	0	0
$469$	−12.4092	−0.573004
$470$	−36.1869	−1.66918
$471$	−14.1436	−0.651705
$472$	13.2749	0.611025
$473$	16.5987	0.763211
$474$	−15.0033	−0.689127
$475$	12.9018	0.591976
$476$	1.80194	0.0825917
$477$	−2.46409	−0.112823
$478$	−10.3497	−0.473384
$479$	5.31845	0.243006	0.121503	−	0.992591i	$-0.461229\pi$
$479$	5.31845	0.243006	0.121503	+	0.992591i	$0.461229\pi$
$480$	3.41496	0.155871
$481$	0	0
$482$	−9.33396	−0.425150
$483$	3.28422	0.149437
$484$	−0.457123	−0.0207783
$485$	−40.8267	−1.85385
$486$	1.00000	0.0453609
$487$	−31.2192	−1.41468	−0.707338	−	0.706875i	$-0.750104\pi$
$487$	−31.2192	−1.41468	−0.707338	+	0.706875i	$0.750104\pi$
$488$	−1.76668	−0.0799739
$489$	15.6565	0.708014
$490$	3.41496	0.154272
$491$	24.9801	1.12734	0.563668	−	0.826001i	$-0.309390\pi$
$491$	24.9801	1.12734	0.563668	+	0.826001i	$0.309390\pi$
$492$	−4.58189	−0.206567
$493$	−6.56107	−0.295496
$494$	0	0
$495$	11.0883	0.498382
$496$	−3.10698	−0.139507
$497$	−2.66429	−0.119510
$498$	−1.43401	−0.0642595
$499$	8.22457	0.368182	0.184091	−	0.982909i	$-0.441066\pi$
$499$	8.22457	0.368182	0.184091	+	0.982909i	$0.441066\pi$
$500$	5.67545	0.253814
$501$	19.6904	0.879703
$502$	−30.9745	−1.38246
$503$	−28.4248	−1.26740	−0.633700	−	0.773579i	$-0.718465\pi$
$503$	−28.4248	−1.26740	−0.633700	+	0.773579i	$0.718465\pi$
$504$	1.00000	0.0445435
$505$	−63.2975	−2.81670
$506$	10.6638	0.474064
$507$	0	0
$508$	3.89724	0.172912
$509$	8.58953	0.380724	0.190362	−	0.981714i	$-0.439034\pi$
$509$	8.58953	0.380724	0.190362	+	0.981714i	$0.439034\pi$
$510$	6.15354	0.272483
$511$	0.368396	0.0162969
$512$	1.00000	0.0441942
$513$	1.93665	0.0855050
$514$	−2.27305	−0.100260
$515$	62.3493	2.74744
$516$	5.11205	0.225046
$517$	−34.4069	−1.51322
$518$	−4.80172	−0.210975
$519$	16.3915	0.719508
$520$	0	0
$521$	24.0161	1.05216	0.526082	−	0.850434i	$-0.323660\pi$
$521$	24.0161	1.05216	0.526082	+	0.850434i	$0.323660\pi$
$522$	−3.64112	−0.159367
$523$	−28.7110	−1.25544	−0.627721	−	0.778438i	$-0.716012\pi$
$523$	−28.7110	−1.25544	−0.627721	+	0.778438i	$0.716012\pi$
$524$	−17.6740	−0.772091
$525$	6.66194	0.290751
$526$	−18.5834	−0.810274
$527$	−5.59858	−0.243878
$528$	3.24698	0.141307
$529$	−12.2139	−0.531038
$530$	−8.41477	−0.365514
$531$	13.2749	0.576080
$532$	1.93665	0.0839642
$533$	0	0
$534$	5.10615	0.220965
$535$	−51.2960	−2.21772
$536$	−12.4092	−0.535996
$537$	−17.0906	−0.737512
$538$	26.7522	1.15337
$539$	3.24698	0.139857
$540$	3.41496	0.146956
$541$	−13.3317	−0.573173	−0.286587	−	0.958054i	$-0.592521\pi$
$541$	−13.3317	−0.573173	−0.286587	+	0.958054i	$0.592521\pi$
$542$	5.33182	0.229021
$543$	21.3647	0.916849
$544$	1.80194	0.0772574
$545$	40.1372	1.71929
$546$	0	0
$547$	9.82136	0.419931	0.209965	−	0.977709i	$-0.432665\pi$
$547$	9.82136	0.419931	0.209965	+	0.977709i	$0.432665\pi$
$548$	−14.9195	−0.637331
$549$	−1.76668	−0.0754002
$550$	21.6312	0.922356
$551$	−7.05156	−0.300406
$552$	3.28422	0.139786
$553$	−15.0033	−0.638007
$554$	25.0045	1.06234
$555$	−16.3977	−0.696042
$556$	−3.27513	−0.138897
$557$	25.6623	1.08735	0.543674	−	0.839297i	$-0.317033\pi$
$557$	25.6623	1.08735	0.543674	+	0.839297i	$0.317033\pi$
$558$	−3.10698	−0.131529
$559$	0	0
$560$	3.41496	0.144308
$561$	5.85086	0.247023
$562$	13.8066	0.582396
$563$	−39.5263	−1.66584	−0.832918	−	0.553396i	$-0.813331\pi$
$563$	−39.5263	−1.66584	−0.832918	+	0.553396i	$0.813331\pi$
$564$	−10.5966	−0.446197
$565$	12.6339	0.531511
$566$	−22.0224	−0.925670
$567$	1.00000	0.0419961
$568$	−2.66429	−0.111791
$569$	4.74188	0.198790	0.0993949	−	0.995048i	$-0.468309\pi$
$569$	4.74188	0.198790	0.0993949	+	0.995048i	$0.468309\pi$
$570$	6.61356	0.277012
$571$	−7.02759	−0.294095	−0.147048	−	0.989129i	$-0.546977\pi$
$571$	−7.02759	−0.294095	−0.147048	+	0.989129i	$0.546977\pi$
$572$	0	0
$573$	16.2973	0.680828
$574$	−4.58189	−0.191244
$575$	21.8793	0.912429
$576$	1.00000	0.0416667
$577$	10.9656	0.456503	0.228251	−	0.973602i	$-0.426699\pi$
$577$	10.9656	0.456503	0.228251	+	0.973602i	$0.426699\pi$
$578$	−13.7530	−0.572050
$579$	18.7221	0.778065
$580$	−12.4343	−0.516305
$581$	−1.43401	−0.0594927
$582$	−11.9553	−0.495562
$583$	−8.00086	−0.331362
$584$	0.368396	0.0152443
$585$	0	0
$586$	−2.17514	−0.0898541
$587$	−28.8685	−1.19153	−0.595766	−	0.803158i	$-0.703151\pi$
$587$	−28.8685	−1.19153	−0.595766	+	0.803158i	$0.703151\pi$
$588$	1.00000	0.0412393
$589$	−6.01712	−0.247931
$590$	45.3331	1.86633
$591$	6.35011	0.261208
$592$	−4.80172	−0.197350
$593$	17.5637	0.721255	0.360628	−	0.932710i	$-0.382563\pi$
$593$	17.5637	0.721255	0.360628	+	0.932710i	$0.382563\pi$
$594$	3.24698	0.133225
$595$	6.15354	0.252271
$596$	8.92475	0.365572
$597$	11.9820	0.490390
$598$	0	0
$599$	9.82575	0.401469	0.200735	−	0.979646i	$-0.435667\pi$
$599$	9.82575	0.401469	0.200735	+	0.979646i	$0.435667\pi$
$600$	6.66194	0.271972
$601$	22.3197	0.910438	0.455219	−	0.890380i	$-0.349561\pi$
$601$	22.3197	0.910438	0.455219	+	0.890380i	$0.349561\pi$
$602$	5.11205	0.208352
$603$	−12.4092	−0.505342
$604$	−0.712364	−0.0289857
$605$	−1.56106	−0.0634660
$606$	−18.5354	−0.752948
$607$	29.0228	1.17800	0.588999	−	0.808134i	$-0.299522\pi$
$607$	29.0228	1.17800	0.588999	+	0.808134i	$0.299522\pi$
$608$	1.93665	0.0785414
$609$	−3.64112	−0.147546
$610$	−6.03315	−0.244275
$611$	0	0
$612$	1.80194	0.0728390
$613$	−36.4576	−1.47251	−0.736255	−	0.676704i	$-0.763408\pi$
$613$	−36.4576	−1.47251	−0.736255	+	0.676704i	$0.763408\pi$
$614$	21.5338	0.869035
$615$	−15.6470	−0.630946
$616$	3.24698	0.130825
$617$	−33.4147	−1.34522	−0.672612	−	0.739995i	$-0.734828\pi$
$617$	−33.4147	−1.34522	−0.672612	+	0.739995i	$0.734828\pi$
$618$	18.2577	0.734433
$619$	−12.8283	−0.515614	−0.257807	−	0.966196i	$-0.583000\pi$
$619$	−12.8283	−0.515614	−0.257807	+	0.966196i	$0.583000\pi$
$620$	−10.6102	−0.426116
$621$	3.28422	0.131791
$622$	−10.5043	−0.421184
$623$	5.10615	0.204574
$624$	0	0
$625$	−13.9283	−0.557131
$626$	−16.0754	−0.642502
$627$	6.28825	0.251129
$628$	−14.1436	−0.564393
$629$	−8.65240	−0.344994
$630$	3.41496	0.136055
$631$	28.1757	1.12166	0.560828	−	0.827933i	$-0.310483\pi$
$631$	28.1757	1.12166	0.560828	+	0.827933i	$0.310483\pi$
$632$	−15.0033	−0.596801
$633$	9.42870	0.374757
$634$	15.3743	0.610592
$635$	13.3089	0.528148
$636$	−2.46409	−0.0977076
$637$	0	0
$638$	−11.8226	−0.468063
$639$	−2.66429	−0.105398
$640$	3.41496	0.134988
$641$	48.0176	1.89658	0.948291	−	0.317404i	$-0.102811\pi$
$641$	48.0176	1.89658	0.948291	+	0.317404i	$0.102811\pi$
$642$	−15.0210	−0.592830
$643$	8.71604	0.343727	0.171864	−	0.985121i	$-0.445021\pi$
$643$	8.71604	0.343727	0.171864	+	0.985121i	$0.445021\pi$
$644$	3.28422	0.129417
$645$	17.4575	0.687386
$646$	3.48972	0.137301
$647$	27.8665	1.09555	0.547773	−	0.836627i	$-0.315476\pi$
$647$	27.8665	1.09555	0.547773	+	0.836627i	$0.315476\pi$
$648$	1.00000	0.0392837
$649$	43.1032	1.69195
$650$	0	0
$651$	−3.10698	−0.121772
$652$	15.6565	0.613158
$653$	−12.1077	−0.473810	−0.236905	−	0.971533i	$-0.576133\pi$
$653$	−12.1077	−0.473810	−0.236905	+	0.971533i	$0.576133\pi$
$654$	11.7533	0.459592
$655$	−60.3559	−2.35830
$656$	−4.58189	−0.178893
$657$	0.368396	0.0143725
$658$	−10.5966	−0.413098
$659$	−23.4234	−0.912448	−0.456224	−	0.889865i	$-0.650798\pi$
$659$	−23.4234	−0.912448	−0.456224	+	0.889865i	$0.650798\pi$
$660$	11.0883	0.431611
$661$	5.85897	0.227888	0.113944	−	0.993487i	$-0.463652\pi$
$661$	5.85897	0.227888	0.113944	+	0.993487i	$0.463652\pi$
$662$	−8.21249	−0.319187
$663$	0	0
$664$	−1.43401	−0.0556503
$665$	6.61356	0.256463
$666$	−4.80172	−0.186063
$667$	−11.9582	−0.463025
$668$	19.6904	0.761845
$669$	−15.9921	−0.618292
$670$	−42.3769	−1.63716
$671$	−5.73638	−0.221451
$672$	1.00000	0.0385758
$673$	−12.6299	−0.486845	−0.243423	−	0.969920i	$-0.578270\pi$
$673$	−12.6299	−0.486845	−0.243423	+	0.969920i	$0.578270\pi$
$674$	−18.4567	−0.710927
$675$	6.66194	0.256418
$676$	0	0
$677$	14.8183	0.569515	0.284757	−	0.958600i	$-0.408087\pi$
$677$	14.8183	0.569515	0.284757	+	0.958600i	$0.408087\pi$
$678$	3.69957	0.142081
$679$	−11.9553	−0.458801
$680$	6.15354	0.235978
$681$	4.11815	0.157808
$682$	−10.0883	−0.386301
$683$	−26.9967	−1.03300	−0.516499	−	0.856288i	$-0.672765\pi$
$683$	−26.9967	−1.03300	−0.516499	+	0.856288i	$0.672765\pi$
$684$	1.93665	0.0740495
$685$	−50.9496	−1.94668
$686$	1.00000	0.0381802
$687$	0.403067	0.0153780
$688$	5.11205	0.194895
$689$	0	0
$690$	11.2155	0.426966
$691$	−14.4624	−0.550174	−0.275087	−	0.961419i	$-0.588707\pi$
$691$	−14.4624	−0.550174	−0.275087	+	0.961419i	$0.588707\pi$
$692$	16.3915	0.623112
$693$	3.24698	0.123343
$694$	31.3648	1.19059
$695$	−11.1844	−0.424250
$696$	−3.64112	−0.138016
$697$	−8.25628	−0.312729
$698$	−6.96959	−0.263803
$699$	−18.7561	−0.709420
$700$	6.66194	0.251798
$701$	31.2297	1.17953	0.589764	−	0.807575i	$-0.299221\pi$
$701$	31.2297	1.17953	0.589764	+	0.807575i	$0.299221\pi$
$702$	0	0
$703$	−9.29923	−0.350727
$704$	3.24698	0.122375
$705$	−36.1869	−1.36288
$706$	13.0978	0.492943
$707$	−18.5354	−0.697095
$708$	13.2749	0.498900
$709$	23.8268	0.894834	0.447417	−	0.894325i	$-0.352344\pi$
$709$	23.8268	0.894834	0.447417	+	0.894325i	$0.352344\pi$
$710$	−9.09845	−0.341459
$711$	−15.0033	−0.562670
$712$	5.10615	0.191361
$713$	−10.2040	−0.382143
$714$	1.80194	0.0674358
$715$	0	0
$716$	−17.0906	−0.638704
$717$	−10.3497	−0.386516
$718$	−8.01400	−0.299080
$719$	37.7147	1.40652	0.703261	−	0.710931i	$-0.251726\pi$
$719$	37.7147	1.40652	0.703261	+	0.710931i	$0.251726\pi$
$720$	3.41496	0.127268
$721$	18.2577	0.679952
$722$	−15.2494	−0.567524
$723$	−9.33396	−0.347134
$724$	21.3647	0.794015
$725$	−24.2569	−0.900879
$726$	−0.457123	−0.0169654
$727$	40.5041	1.50222	0.751108	−	0.660180i	$-0.229520\pi$
$727$	40.5041	1.50222	0.751108	+	0.660180i	$0.229520\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.25806	0.0465627
$731$	9.21160	0.340703
$732$	−1.76668	−0.0652985
$733$	46.1126	1.70321	0.851604	−	0.524185i	$-0.175630\pi$
$733$	46.1126	1.70321	0.851604	+	0.524185i	$0.175630\pi$
$734$	−25.7361	−0.949938
$735$	3.41496	0.125963
$736$	3.28422	0.121058
$737$	−40.2924	−1.48419
$738$	−4.58189	−0.168662
$739$	−12.9995	−0.478195	−0.239097	−	0.970996i	$-0.576852\pi$
$739$	−12.9995	−0.478195	−0.239097	+	0.970996i	$0.576852\pi$
$740$	−16.3977	−0.602790
$741$	0	0
$742$	−2.46409	−0.0904597
$743$	31.1171	1.14158	0.570788	−	0.821098i	$-0.306638\pi$
$743$	31.1171	1.14158	0.570788	+	0.821098i	$0.306638\pi$
$744$	−3.10698	−0.113907
$745$	30.4777	1.11662
$746$	−0.973483	−0.0356417
$747$	−1.43401	−0.0524676
$748$	5.85086	0.213928
$749$	−15.0210	−0.548854
$750$	5.67545	0.207238
$751$	−49.5868	−1.80945	−0.904725	−	0.425997i	$-0.859924\pi$
$751$	−49.5868	−1.80945	−0.904725	+	0.425997i	$0.859924\pi$
$752$	−10.5966	−0.386418
$753$	−30.9745	−1.12877
$754$	0	0
$755$	−2.43269	−0.0885348
$756$	1.00000	0.0363696
$757$	−24.1697	−0.878462	−0.439231	−	0.898374i	$-0.644749\pi$
$757$	−24.1697	−0.878462	−0.439231	+	0.898374i	$0.644749\pi$
$758$	−5.27383	−0.191554
$759$	10.6638	0.387072
$760$	6.61356	0.239899
$761$	52.4508	1.90134	0.950670	−	0.310204i	$-0.100397\pi$
$761$	52.4508	1.90134	0.950670	+	0.310204i	$0.100397\pi$
$762$	3.89724	0.141182
$763$	11.7533	0.425500
$764$	16.2973	0.589614
$765$	6.15354	0.222482
$766$	11.1179	0.401707
$767$	0	0
$768$	1.00000	0.0360844
$769$	21.4549	0.773685	0.386842	−	0.922146i	$-0.373566\pi$
$769$	21.4549	0.773685	0.386842	+	0.922146i	$0.373566\pi$
$770$	11.0883	0.399595
$771$	−2.27305	−0.0818618
$772$	18.7221	0.673824
$773$	−19.1744	−0.689654	−0.344827	−	0.938666i	$-0.612062\pi$
$773$	−19.1744	−0.689654	−0.344827	+	0.938666i	$0.612062\pi$
$774$	5.11205	0.183749
$775$	−20.6985	−0.743512
$776$	−11.9553	−0.429169
$777$	−4.80172	−0.172261
$778$	−13.6798	−0.490446
$779$	−8.87349	−0.317926
$780$	0	0
$781$	−8.65090	−0.309554
$782$	5.91797	0.211626
$783$	−3.64112	−0.130123
$784$	1.00000	0.0357143
$785$	−48.2999	−1.72390
$786$	−17.6740	−0.630410
$787$	0.0274054	0.000976897 0	0.000488449	−	1.00000i	$-0.499845\pi$
$787$	0.0274054	0.000976897 0	0.000488449		1.00000i	$0.499845\pi$
$788$	6.35011	0.226213
$789$	−18.5834	−0.661586
$790$	−51.2358	−1.82289
$791$	3.69957	0.131542
$792$	3.24698	0.115376
$793$	0	0
$794$	16.3683	0.580888
$795$	−8.41477	−0.298441
$796$	11.9820	0.424690
$797$	6.95916	0.246506	0.123253	−	0.992375i	$-0.460667\pi$
$797$	6.95916	0.246506	0.123253	+	0.992375i	$0.460667\pi$
$798$	1.93665	0.0685565
$799$	−19.0944	−0.675512
$800$	6.66194	0.235535
$801$	5.10615	0.180417
$802$	−35.9089	−1.26799
$803$	1.19617	0.0422120
$804$	−12.4092	−0.437639
$805$	11.2155	0.395294
$806$	0	0
$807$	26.7522	0.941722
$808$	−18.5354	−0.652072
$809$	−35.2083	−1.23786	−0.618930	−	0.785446i	$-0.712433\pi$
$809$	−35.2083	−1.23786	−0.618930	+	0.785446i	$0.712433\pi$
$810$	3.41496	0.119989
$811$	25.6464	0.900567	0.450284	−	0.892886i	$-0.351323\pi$
$811$	25.6464	0.900567	0.450284	+	0.892886i	$0.351323\pi$
$812$	−3.64112	−0.127778
$813$	5.33182	0.186995
$814$	−15.5911	−0.546467
$815$	53.4665	1.87285
$816$	1.80194	0.0630804
$817$	9.90024	0.346366
$818$	12.4416	0.435010
$819$	0	0
$820$	−15.6470	−0.546415
$821$	31.8661	1.11214	0.556068	−	0.831137i	$-0.312309\pi$
$821$	31.8661	1.11214	0.556068	+	0.831137i	$0.312309\pi$
$822$	−14.9195	−0.520379
$823$	−48.6456	−1.69568	−0.847839	−	0.530254i	$-0.822097\pi$
$823$	−48.6456	−1.69568	−0.847839	+	0.530254i	$0.822097\pi$
$824$	18.2577	0.636037
$825$	21.6312	0.753101
$826$	13.2749	0.461891
$827$	−3.18286	−0.110679	−0.0553394	−	0.998468i	$-0.517624\pi$
$827$	−3.18286	−0.110679	−0.0553394	+	0.998468i	$0.517624\pi$
$828$	3.28422	0.114135
$829$	−0.573876	−0.0199315	−0.00996576	−	0.999950i	$-0.503172\pi$
$829$	−0.573876	−0.0199315	−0.00996576	+	0.999950i	$0.503172\pi$
$830$	−4.89708	−0.169980
$831$	25.0045	0.867398
$832$	0	0
$833$	1.80194	0.0624334
$834$	−3.27513	−0.113409
$835$	67.2419	2.32700
$836$	6.28825	0.217484
$837$	−3.10698	−0.107393
$838$	9.73591	0.336321
$839$	−30.7253	−1.06076	−0.530378	−	0.847762i	$-0.677950\pi$
$839$	−30.7253	−1.06076	−0.530378	+	0.847762i	$0.677950\pi$
$840$	3.41496	0.117827
$841$	−15.7423	−0.542836
$842$	24.4352	0.842092
$843$	13.8066	0.475525
$844$	9.42870	0.324549
$845$	0	0
$846$	−10.5966	−0.364319
$847$	−0.457123	−0.0157069
$848$	−2.46409	−0.0846173
$849$	−22.0224	−0.755806
$850$	12.0044	0.411747
$851$	−15.7699	−0.540586
$852$	−2.66429	−0.0912772
$853$	−23.5695	−0.807005	−0.403502	−	0.914979i	$-0.632207\pi$
$853$	−23.5695	−0.807005	−0.403502	+	0.914979i	$0.632207\pi$
$854$	−1.76668	−0.0604546
$855$	6.61356	0.226179
$856$	−15.0210	−0.513406
$857$	−18.7309	−0.639834	−0.319917	−	0.947446i	$-0.603655\pi$
$857$	−18.7309	−0.639834	−0.319917	+	0.947446i	$0.603655\pi$
$858$	0	0
$859$	−35.0464	−1.19577	−0.597884	−	0.801582i	$-0.703992\pi$
$859$	−35.0464	−1.19577	−0.597884	+	0.801582i	$0.703992\pi$
$860$	17.4575	0.595294
$861$	−4.58189	−0.156150
$862$	38.2356	1.30231
$863$	35.2615	1.20032	0.600158	−	0.799881i	$-0.295104\pi$
$863$	35.2615	1.20032	0.600158	+	0.799881i	$0.295104\pi$
$864$	1.00000	0.0340207
$865$	55.9764	1.90325
$866$	31.9423	1.08544
$867$	−13.7530	−0.467077
$868$	−3.10698	−0.105458
$869$	−48.7156	−1.65256
$870$	−12.4343	−0.421561
$871$	0	0
$872$	11.7533	0.398019
$873$	−11.9553	−0.404624
$874$	6.36038	0.215143
$875$	5.67545	0.191865
$876$	0.368396	0.0124469
$877$	31.7171	1.07101	0.535506	−	0.844532i	$-0.320121\pi$
$877$	31.7171	1.07101	0.535506	+	0.844532i	$0.320121\pi$
$878$	20.6203	0.695900
$879$	−2.17514	−0.0733656
$880$	11.0883	0.373786
$881$	−16.3131	−0.549602	−0.274801	−	0.961501i	$-0.588612\pi$
$881$	−16.3131	−0.549602	−0.274801	+	0.961501i	$0.588612\pi$
$882$	1.00000	0.0336718
$883$	−20.4148	−0.687014	−0.343507	−	0.939150i	$-0.611615\pi$
$883$	−20.4148	−0.687014	−0.343507	+	0.939150i	$0.611615\pi$
$884$	0	0
$885$	45.3331	1.52386
$886$	−0.760370	−0.0255451
$887$	−8.78093	−0.294835	−0.147417	−	0.989074i	$-0.547096\pi$
$887$	−8.78093	−0.294835	−0.147417	+	0.989074i	$0.547096\pi$
$888$	−4.80172	−0.161135
$889$	3.89724	0.130709
$890$	17.4373	0.584499
$891$	3.24698	0.108778
$892$	−15.9921	−0.535456
$893$	−20.5219	−0.686738
$894$	8.92475	0.298488
$895$	−58.3635	−1.95088
$896$	1.00000	0.0334077
$897$	0	0
$898$	19.8729	0.663166
$899$	11.3129	0.377306
$900$	6.66194	0.222065
$901$	−4.44014	−0.147923
$902$	−14.8773	−0.495360
$903$	5.11205	0.170119
$904$	3.69957	0.123046
$905$	72.9597	2.42526
$906$	−0.712364	−0.0236667
$907$	12.4859	0.414588	0.207294	−	0.978279i	$-0.433534\pi$
$907$	12.4859	0.414588	0.207294	+	0.978279i	$0.433534\pi$
$908$	4.11815	0.136665
$909$	−18.5354	−0.614780
$910$	0	0
$911$	−15.1753	−0.502780	−0.251390	−	0.967886i	$-0.580888\pi$
$911$	−15.1753	−0.502780	−0.251390	+	0.967886i	$0.580888\pi$
$912$	1.93665	0.0641288
$913$	−4.65620	−0.154098
$914$	39.0448	1.29149
$915$	−6.03315	−0.199450
$916$	0.403067	0.0133177
$917$	−17.6740	−0.583646
$918$	1.80194	0.0594728
$919$	−0.144447	−0.00476487	−0.00238243	−	0.999997i	$-0.500758\pi$
$919$	−0.144447	−0.00476487	−0.00238243	+	0.999997i	$0.500758\pi$
$920$	11.2155	0.369764
$921$	21.5338	0.709564
$922$	−25.0785	−0.825916
$923$	0	0
$924$	3.24698	0.106818
$925$	−31.9888	−1.05178
$926$	11.3140	0.371802
$927$	18.2577	0.599662
$928$	−3.64112	−0.119526
$929$	40.2284	1.31985	0.659926	−	0.751331i	$-0.270588\pi$
$929$	40.2284	1.31985	0.659926	+	0.751331i	$0.270588\pi$
$930$	−10.6102	−0.347922
$931$	1.93665	0.0634710
$932$	−18.7561	−0.614376
$933$	−10.5043	−0.343895
$934$	12.6861	0.415102
$935$	19.9804	0.653430
$936$	0	0
$937$	29.4246	0.961261	0.480630	−	0.876923i	$-0.340408\pi$
$937$	29.4246	0.961261	0.480630	+	0.876923i	$0.340408\pi$
$938$	−12.4092	−0.405175
$939$	−16.0754	−0.524600
$940$	−36.1869	−1.18029
$941$	−23.6938	−0.772395	−0.386197	−	0.922416i	$-0.626212\pi$
$941$	−23.6938	−0.772395	−0.386197	+	0.922416i	$0.626212\pi$
$942$	−14.1436	−0.460825
$943$	−15.0479	−0.490028
$944$	13.2749	0.432060
$945$	3.41496	0.111089
$946$	16.5987	0.539671
$947$	16.5847	0.538932	0.269466	−	0.963010i	$-0.413153\pi$
$947$	16.5847	0.538932	0.269466	+	0.963010i	$0.413153\pi$
$948$	−15.0033	−0.487286
$949$	0	0
$950$	12.9018	0.418590
$951$	15.3743	0.498546
$952$	1.80194	0.0584011
$953$	17.5290	0.567820	0.283910	−	0.958851i	$-0.408368\pi$
$953$	17.5290	0.567820	0.283910	+	0.958851i	$0.408368\pi$
$954$	−2.46409	−0.0797779
$955$	55.6545	1.80094
$956$	−10.3497	−0.334733
$957$	−11.8226	−0.382172
$958$	5.31845	0.171831
$959$	−14.9195	−0.481777
$960$	3.41496	0.110217
$961$	−21.3467	−0.688603
$962$	0	0
$963$	−15.0210	−0.484044
$964$	−9.33396	−0.300627
$965$	63.9353	2.05815
$966$	3.28422	0.105668
$967$	−44.7198	−1.43809	−0.719045	−	0.694963i	$-0.755421\pi$
$967$	−44.7198	−1.43809	−0.719045	+	0.694963i	$0.755421\pi$
$968$	−0.457123	−0.0146925
$969$	3.48972	0.112106
$970$	−40.8267	−1.31087
$971$	−31.6941	−1.01711	−0.508555	−	0.861029i	$-0.669820\pi$
$971$	−31.6941	−1.01711	−0.508555	+	0.861029i	$0.669820\pi$
$972$	1.00000	0.0320750
$973$	−3.27513	−0.104996
$974$	−31.2192	−1.00033
$975$	0	0
$976$	−1.76668	−0.0565501
$977$	43.1638	1.38093	0.690467	−	0.723364i	$-0.257405\pi$
$977$	43.1638	1.38093	0.690467	+	0.723364i	$0.257405\pi$
$978$	15.6565	0.500641
$979$	16.5796	0.529885
$980$	3.41496	0.109087
$981$	11.7533	0.375255
$982$	24.9801	0.797147
$983$	−58.3576	−1.86132	−0.930659	−	0.365887i	$-0.880766\pi$
$983$	−58.3576	−1.86132	−0.930659	+	0.365887i	$0.880766\pi$
$984$	−4.58189	−0.146065
$985$	21.6853	0.690953
$986$	−6.56107	−0.208947
$987$	−10.5966	−0.337293
$988$	0	0
$989$	16.7891	0.533863
$990$	11.0883	0.352409
$991$	−38.6339	−1.22725	−0.613623	−	0.789599i	$-0.710288\pi$
$991$	−38.6339	−1.22725	−0.613623	+	0.789599i	$0.710288\pi$
$992$	−3.10698	−0.0986467
$993$	−8.21249	−0.260615
$994$	−2.66429	−0.0845062
$995$	40.9180	1.29719
$996$	−1.43401	−0.0454383
$997$	13.4648	0.426433	0.213217	−	0.977005i	$-0.431606\pi$
$997$	13.4648	0.426433	0.213217	+	0.977005i	$0.431606\pi$
$998$	8.22457	0.260344
$999$	−4.80172	−0.151920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.ct.1.6	yes	6
13.12	even	2		7098.2.a.cr.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.1	✓	6	13.12	even	2
7098.2.a.ct.1.6	yes	6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.41496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} +3.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} +1.00000 q^{18} +1.93665 q^{19} +3.41496 q^{20} +1.00000 q^{21} +3.24698 q^{22} +3.28422 q^{23} +1.00000 q^{24} +6.66194 q^{25} +1.00000 q^{27} +1.00000 q^{28} -3.64112 q^{29} +3.41496 q^{30} -3.10698 q^{31} +1.00000 q^{32} +3.24698 q^{33} +1.80194 q^{34} +3.41496 q^{35} +1.00000 q^{36} -4.80172 q^{37} +1.93665 q^{38} +3.41496 q^{40} -4.58189 q^{41} +1.00000 q^{42} +5.11205 q^{43} +3.24698 q^{44} +3.41496 q^{45} +3.28422 q^{46} -10.5966 q^{47} +1.00000 q^{48} +1.00000 q^{49} +6.66194 q^{50} +1.80194 q^{51} -2.46409 q^{53} +1.00000 q^{54} +11.0883 q^{55} +1.00000 q^{56} +1.93665 q^{57} -3.64112 q^{58} +13.2749 q^{59} +3.41496 q^{60} -1.76668 q^{61} -3.10698 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} -12.4092 q^{67} +1.80194 q^{68} +3.28422 q^{69} +3.41496 q^{70} -2.66429 q^{71} +1.00000 q^{72} +0.368396 q^{73} -4.80172 q^{74} +6.66194 q^{75} +1.93665 q^{76} +3.24698 q^{77} -15.0033 q^{79} +3.41496 q^{80} +1.00000 q^{81} -4.58189 q^{82} -1.43401 q^{83} +1.00000 q^{84} +6.15354 q^{85} +5.11205 q^{86} -3.64112 q^{87} +3.24698 q^{88} +5.10615 q^{89} +3.41496 q^{90} +3.28422 q^{92} -3.10698 q^{93} -10.5966 q^{94} +6.61356 q^{95} +1.00000 q^{96} -11.9553 q^{97} +1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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