LMFDB - Embedded newform 7381.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.31423$ of defining polynomial
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31423 q^{2} -1.97692 q^{3} -0.272811 q^{4} -1.38757 q^{5} +2.59812 q^{6} -2.03012 q^{7} +2.98699 q^{8} +0.908205 q^{9} +O(q^{10})$	\(q-1.31423 q^{2} -1.97692 q^{3} -0.272811 q^{4} -1.38757 q^{5} +2.59812 q^{6} -2.03012 q^{7} +2.98699 q^{8} +0.908205 q^{9} +1.82358 q^{10} +0.539326 q^{12} -5.73746 q^{13} +2.66804 q^{14} +2.74312 q^{15} -3.37995 q^{16} -6.94204 q^{17} -1.19359 q^{18} +3.55211 q^{19} +0.378545 q^{20} +4.01339 q^{21} +0.806289 q^{23} -5.90503 q^{24} -3.07464 q^{25} +7.54032 q^{26} +4.13531 q^{27} +0.553841 q^{28} -8.32766 q^{29} -3.60507 q^{30} +4.54221 q^{31} -1.53195 q^{32} +9.12341 q^{34} +2.81694 q^{35} -0.247769 q^{36} +8.85665 q^{37} -4.66828 q^{38} +11.3425 q^{39} -4.14466 q^{40} +4.04638 q^{41} -5.27450 q^{42} -0.832544 q^{43} -1.26020 q^{45} -1.05965 q^{46} +4.66753 q^{47} +6.68189 q^{48} -2.87860 q^{49} +4.04077 q^{50} +13.7238 q^{51} +1.56524 q^{52} -9.49286 q^{53} -5.43473 q^{54} -6.06395 q^{56} -7.02224 q^{57} +10.9444 q^{58} -12.6362 q^{59} -0.748353 q^{60} +1.00000 q^{61} -5.96948 q^{62} -1.84377 q^{63} +8.77324 q^{64} +7.96114 q^{65} +6.13660 q^{67} +1.89387 q^{68} -1.59397 q^{69} -3.70210 q^{70} +12.3352 q^{71} +2.71280 q^{72} -8.32305 q^{73} -11.6396 q^{74} +6.07832 q^{75} -0.969057 q^{76} -14.9066 q^{78} -3.78450 q^{79} +4.68993 q^{80} -10.8998 q^{81} -5.31786 q^{82} +12.6260 q^{83} -1.09490 q^{84} +9.63258 q^{85} +1.09415 q^{86} +16.4631 q^{87} -14.8592 q^{89} +1.65619 q^{90} +11.6478 q^{91} -0.219965 q^{92} -8.97957 q^{93} -6.13418 q^{94} -4.92881 q^{95} +3.02855 q^{96} +7.09938 q^{97} +3.78312 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 5 q^{2} + 23 q^{4} - q^{6} - 9 q^{7} - 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q - 5 * q^2 + 23 * q^4 - q^6 - 9 * q^7 - 9 * q^8 + 29 * q^9	$ 19 q - 5 q^{2} + 23 q^{4} - q^{6} - 9 q^{7} - 9 q^{8} + 29 q^{9} - 7 q^{10} - 4 q^{12} - 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} - 9 q^{17} - 10 q^{18} - 17 q^{19} - 6 q^{20} - 18 q^{21} - 10 q^{23} - 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} - 36 q^{28} - 27 q^{29} + 30 q^{30} + 7 q^{31} - 8 q^{32} - 5 q^{34} - 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} - 24 q^{39} - 10 q^{40} - 19 q^{41} + 21 q^{42} - 20 q^{43} - 32 q^{45} - 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} - 36 q^{50} - 47 q^{51} + 28 q^{52} + 3 q^{53} + 33 q^{54} - 44 q^{56} - 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} + 19 q^{61} + 11 q^{62} + 32 q^{63} + 47 q^{64} - 25 q^{65} + 3 q^{67} - 38 q^{68} + 3 q^{70} - 19 q^{71} - 34 q^{72} - 20 q^{73} + 22 q^{74} - 50 q^{75} + 25 q^{76} - 94 q^{78} - 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} - q^{83} + 28 q^{84} - 24 q^{85} - 27 q^{86} + 58 q^{87} - 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} - 64 q^{94} + 3 q^{95} + 26 q^{96} + 21 q^{97} + 87 q^{98}+O(q^{100}) $ 19 * q - 5 * q^2 + 23 * q^4 - q^6 - 9 * q^7 - 9 * q^8 + 29 * q^9 - 7 * q^10 - 4 * q^12 - 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 - 9 * q^17 - 10 * q^18 - 17 * q^19 - 6 * q^20 - 18 * q^21 - 10 * q^23 - 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 - 36 * q^28 - 27 * q^29 + 30 * q^30 + 7 * q^31 - 8 * q^32 - 5 * q^34 - 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 - 24 * q^39 - 10 * q^40 - 19 * q^41 + 21 * q^42 - 20 * q^43 - 32 * q^45 - 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 - 36 * q^50 - 47 * q^51 + 28 * q^52 + 3 * q^53 + 33 * q^54 - 44 * q^56 - 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 + 19 * q^61 + 11 * q^62 + 32 * q^63 + 47 * q^64 - 25 * q^65 + 3 * q^67 - 38 * q^68 + 3 * q^70 - 19 * q^71 - 34 * q^72 - 20 * q^73 + 22 * q^74 - 50 * q^75 + 25 * q^76 - 94 * q^78 - 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 - q^83 + 28 * q^84 - 24 * q^85 - 27 * q^86 + 58 * q^87 - 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 - 64 * q^94 + 3 * q^95 + 26 * q^96 + 21 * q^97 + 87 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.31423	−0.929298	−0.464649	−	0.885495i	$-0.653819\pi$
$2$	−1.31423	−0.929298	−0.464649	+	0.885495i	$0.653819\pi$
$3$	−1.97692	−1.14137	−0.570687	−	0.821168i	$-0.693323\pi$
$3$	−1.97692	−1.14137	−0.570687	+	0.821168i	$0.693323\pi$
$4$	−0.272811	−0.136406
$5$	−1.38757	−0.620541	−0.310271	−	0.950648i	$-0.600420\pi$
$5$	−1.38757	−0.620541	−0.310271	+	0.950648i	$0.600420\pi$
$6$	2.59812	1.06068
$7$	−2.03012	−0.767315	−0.383657	−	0.923476i	$-0.625336\pi$
$7$	−2.03012	−0.767315	−0.383657	+	0.923476i	$0.625336\pi$
$8$	2.98699	1.05606
$9$	0.908205	0.302735
$10$	1.82358	0.576668
$11$	0	0
$11$	0	0
$12$	0.539326	0.155690
$13$	−5.73746	−1.59129	−0.795643	−	0.605766i	$-0.792867\pi$
$13$	−5.73746	−1.59129	−0.795643	+	0.605766i	$0.792867\pi$
$14$	2.66804	0.713064
$15$	2.74312	0.708270
$16$	−3.37995	−0.844988
$17$	−6.94204	−1.68369	−0.841846	−	0.539718i	$-0.818531\pi$
$17$	−6.94204	−1.68369	−0.841846	+	0.539718i	$0.818531\pi$
$18$	−1.19359	−0.281331
$19$	3.55211	0.814911	0.407455	−	0.913225i	$-0.366416\pi$
$19$	3.55211	0.814911	0.407455	+	0.913225i	$0.366416\pi$
$20$	0.378545	0.0846453
$21$	4.01339	0.875793
$22$	0	0
$23$	0.806289	0.168123	0.0840615	−	0.996461i	$-0.473211\pi$
$23$	0.806289	0.168123	0.0840615	+	0.996461i	$0.473211\pi$
$24$	−5.90503	−1.20536
$25$	−3.07464	−0.614929
$26$	7.54032	1.47878
$27$	4.13531	0.795840
$28$	0.553841	0.104666
$29$	−8.32766	−1.54641	−0.773204	−	0.634158i	$-0.781347\pi$
$29$	−8.32766	−1.54641	−0.773204	+	0.634158i	$0.781347\pi$
$30$	−3.60507	−0.658193
$31$	4.54221	0.815804	0.407902	−	0.913026i	$-0.366260\pi$
$31$	4.54221	0.815804	0.407902	+	0.913026i	$0.366260\pi$
$32$	−1.53195	−0.270814
$33$	0	0
$34$	9.12341	1.56465
$35$	2.81694	0.476150
$36$	−0.247769	−0.0412948
$37$	8.85665	1.45602	0.728012	−	0.685565i	$-0.240445\pi$
$37$	8.85665	1.45602	0.728012	+	0.685565i	$0.240445\pi$
$38$	−4.66828	−0.757295
$39$	11.3425	1.81625
$40$	−4.14466	−0.655328
$41$	4.04638	0.631939	0.315969	−	0.948769i	$-0.397670\pi$
$41$	4.04638	0.631939	0.315969	+	0.948769i	$0.397670\pi$
$42$	−5.27450	−0.813873
$43$	−0.832544	−0.126962	−0.0634809	−	0.997983i	$-0.520220\pi$
$43$	−0.832544	−0.126962	−0.0634809	+	0.997983i	$0.520220\pi$
$44$	0	0
$45$	−1.26020	−0.187860
$46$	−1.05965	−0.156236
$47$	4.66753	0.680829	0.340414	−	0.940276i	$-0.389433\pi$
$47$	4.66753	0.680829	0.340414	+	0.940276i	$0.389433\pi$
$48$	6.68189	0.964447
$49$	−2.87860	−0.411228
$50$	4.04077	0.571452
$51$	13.7238	1.92172
$52$	1.56524	0.217060
$53$	−9.49286	−1.30394	−0.651972	−	0.758243i	$-0.726058\pi$
$53$	−9.49286	−1.30394	−0.651972	+	0.758243i	$0.726058\pi$
$54$	−5.43473	−0.739573
$55$	0	0
$56$	−6.06395	−0.810330
$57$	−7.02224	−0.930118
$58$	10.9444	1.43707
$59$	−12.6362	−1.64510	−0.822549	−	0.568694i	$-0.807449\pi$
$59$	−12.6362	−1.64510	−0.822549	+	0.568694i	$0.807449\pi$
$60$	−0.748353	−0.0966120
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−5.96948	−0.758125
$63$	−1.84377	−0.232293
$64$	8.77324	1.09665
$65$	7.96114	0.987458
$66$	0	0
$67$	6.13660	0.749705	0.374852	−	0.927085i	$-0.377693\pi$
$67$	6.13660	0.749705	0.374852	+	0.927085i	$0.377693\pi$
$68$	1.89387	0.229665
$69$	−1.59397	−0.191891
$70$	−3.70210	−0.442486
$71$	12.3352	1.46392	0.731958	−	0.681350i	$-0.238607\pi$
$71$	12.3352	1.46392	0.731958	+	0.681350i	$0.238607\pi$
$72$	2.71280	0.319706
$73$	−8.32305	−0.974139	−0.487070	−	0.873363i	$-0.661934\pi$
$73$	−8.32305	−0.974139	−0.487070	+	0.873363i	$0.661934\pi$
$74$	−11.6396	−1.35308
$75$	6.07832	0.701864
$76$	−0.969057	−0.111158
$77$	0	0
$78$	−14.9066	−1.68784
$79$	−3.78450	−0.425789	−0.212895	−	0.977075i	$-0.568289\pi$
$79$	−3.78450	−0.425789	−0.212895	+	0.977075i	$0.568289\pi$
$80$	4.68993	0.524350
$81$	−10.8998	−1.21109
$82$	−5.31786	−0.587259
$83$	12.6260	1.38588	0.692939	−	0.720996i	$-0.256315\pi$
$83$	12.6260	1.38588	0.692939	+	0.720996i	$0.256315\pi$
$84$	−1.09490	−0.119463
$85$	9.63258	1.04480
$86$	1.09415	0.117985
$87$	16.4631	1.76503
$88$	0	0
$89$	−14.8592	−1.57507	−0.787534	−	0.616271i	$-0.788643\pi$
$89$	−14.8592	−1.57507	−0.787534	+	0.616271i	$0.788643\pi$
$90$	1.65619	0.174577
$91$	11.6478	1.22102
$92$	−0.219965	−0.0229329
$93$	−8.97957	−0.931138
$94$	−6.13418	−0.632693
$95$	−4.92881	−0.505686
$96$	3.02855	0.309100
$97$	7.09938	0.720833	0.360417	−	0.932791i	$-0.382635\pi$
$97$	7.09938	0.720833	0.360417	+	0.932791i	$0.382635\pi$
$98$	3.78312	0.382153
$99$	0	0
$100$	0.838797	0.0838797
$101$	−14.2585	−1.41877	−0.709387	−	0.704819i	$-0.751028\pi$
$101$	−14.2585	−1.41877	−0.709387	+	0.704819i	$0.751028\pi$
$102$	−18.0362	−1.78585
$103$	1.69876	0.167384	0.0836920	−	0.996492i	$-0.473329\pi$
$103$	1.69876	0.167384	0.0836920	+	0.996492i	$0.473329\pi$
$104$	−17.1377	−1.68049
$105$	−5.56887	−0.543466
$106$	12.4758	1.21175
$107$	14.6034	1.41176	0.705881	−	0.708331i	$-0.250551\pi$
$107$	14.6034	1.41176	0.705881	+	0.708331i	$0.250551\pi$
$108$	−1.12816	−0.108557
$109$	−7.22627	−0.692151	−0.346076	−	0.938207i	$-0.612486\pi$
$109$	−7.22627	−0.692151	−0.346076	+	0.938207i	$0.612486\pi$
$110$	0	0
$111$	−17.5089	−1.66187
$112$	6.86172	0.648372
$113$	17.4970	1.64598	0.822990	−	0.568056i	$-0.192304\pi$
$113$	17.4970	1.64598	0.822990	+	0.568056i	$0.192304\pi$
$114$	9.22880	0.864357
$115$	−1.11878	−0.104327
$116$	2.27188	0.210939
$117$	−5.21079	−0.481738
$118$	16.6069	1.52879
$119$	14.0932	1.29192
$120$	8.19365	0.747975
$121$	0	0
$122$	−1.31423	−0.118984
$123$	−7.99936	−0.721278
$124$	−1.23917	−0.111280
$125$	11.2042	1.00213
$126$	2.42313	0.215869
$127$	−2.20928	−0.196042	−0.0980209	−	0.995184i	$-0.531251\pi$
$127$	−2.20928	−0.196042	−0.0980209	+	0.995184i	$0.531251\pi$
$128$	−8.46610	−0.748305
$129$	1.64587	0.144911
$130$	−10.4627	−0.917643
$131$	2.07784	0.181541	0.0907707	−	0.995872i	$-0.471067\pi$
$131$	2.07784	0.181541	0.0907707	+	0.995872i	$0.471067\pi$
$132$	0	0
$133$	−7.21123	−0.625293
$134$	−8.06487	−0.696699
$135$	−5.73804	−0.493852
$136$	−20.7358	−1.77808
$137$	10.7795	0.920951	0.460476	−	0.887672i	$-0.347679\pi$
$137$	10.7795	0.920951	0.460476	+	0.887672i	$0.347679\pi$
$138$	2.09483	0.178324
$139$	11.4790	0.973636	0.486818	−	0.873504i	$-0.338158\pi$
$139$	11.4790	0.973636	0.486818	+	0.873504i	$0.338158\pi$
$140$	−0.768494	−0.0649496
$141$	−9.22732	−0.777080
$142$	−16.2112	−1.36041
$143$	0	0
$144$	−3.06969	−0.255807
$145$	11.5552	0.959609
$146$	10.9384	0.905266
$147$	5.69075	0.469365
$148$	−2.41619	−0.198610
$149$	11.4894	0.941246	0.470623	−	0.882334i	$-0.344029\pi$
$149$	11.4894	0.941246	0.470623	+	0.882334i	$0.344029\pi$
$150$	−7.98828	−0.652240
$151$	2.05463	0.167204	0.0836018	−	0.996499i	$-0.473358\pi$
$151$	2.05463	0.167204	0.0836018	+	0.996499i	$0.473358\pi$
$152$	10.6101	0.860594
$153$	−6.30479	−0.509712
$154$	0	0
$155$	−6.30264	−0.506240
$156$	−3.09436	−0.247747
$157$	24.4022	1.94751	0.973755	−	0.227600i	$-0.0730879\pi$
$157$	24.4022	1.94751	0.973755	+	0.227600i	$0.0730879\pi$
$158$	4.97368	0.395685
$159$	18.7666	1.48829
$160$	2.12570	0.168051
$161$	−1.63687	−0.129003
$162$	14.3248	1.12546
$163$	−9.62670	−0.754021	−0.377011	−	0.926209i	$-0.623048\pi$
$163$	−9.62670	−0.754021	−0.377011	+	0.926209i	$0.623048\pi$
$164$	−1.10390	−0.0862000
$165$	0	0
$166$	−16.5933	−1.28789
$167$	16.8772	1.30600	0.652999	−	0.757359i	$-0.273511\pi$
$167$	16.8772	1.30600	0.652999	+	0.757359i	$0.273511\pi$
$168$	11.9879	0.924890
$169$	19.9185	1.53219
$170$	−12.6594	−0.970930
$171$	3.22605	0.246702
$172$	0.227127	0.0173183
$173$	5.79912	0.440899	0.220450	−	0.975398i	$-0.429248\pi$
$173$	5.79912	0.440899	0.220450	+	0.975398i	$0.429248\pi$
$174$	−21.6362	−1.64024
$175$	6.24191	0.471844
$176$	0	0
$177$	24.9808	1.87767
$178$	19.5283	1.46371
$179$	4.27998	0.319900	0.159950	−	0.987125i	$-0.448867\pi$
$179$	4.27998	0.319900	0.159950	+	0.987125i	$0.448867\pi$
$180$	0.343797	0.0256251
$181$	−20.1052	−1.49441	−0.747205	−	0.664594i	$-0.768605\pi$
$181$	−20.1052	−1.49441	−0.747205	+	0.664594i	$0.768605\pi$
$182$	−15.3078	−1.13469
$183$	−1.97692	−0.146138
$184$	2.40837	0.177548
$185$	−12.2892	−0.903523
$186$	11.8012	0.865304
$187$	0	0
$188$	−1.27335	−0.0928689
$189$	−8.39519	−0.610660
$190$	6.47757	0.469933
$191$	9.14553	0.661748	0.330874	−	0.943675i	$-0.392657\pi$
$191$	9.14553	0.661748	0.330874	+	0.943675i	$0.392657\pi$
$192$	−17.3440	−1.25169
$193$	−19.5388	−1.40644	−0.703218	−	0.710974i	$-0.748254\pi$
$193$	−19.5388	−1.40644	−0.703218	+	0.710974i	$0.748254\pi$
$194$	−9.33019	−0.669869
$195$	−15.7385	−1.12706
$196$	0.785314	0.0560938
$197$	21.7664	1.55079	0.775395	−	0.631476i	$-0.217551\pi$
$197$	21.7664	1.55079	0.775395	+	0.631476i	$0.217551\pi$
$198$	0	0
$199$	21.7232	1.53992	0.769958	−	0.638094i	$-0.220277\pi$
$199$	21.7232	1.53992	0.769958	+	0.638094i	$0.220277\pi$
$200$	−9.18392	−0.649401
$201$	−12.1316	−0.855694
$202$	18.7389	1.31846
$203$	16.9062	1.18658
$204$	−3.74402	−0.262134
$205$	−5.61465	−0.392144
$206$	−2.23256	−0.155550
$207$	0.732276	0.0508967
$208$	19.3923	1.34462
$209$	0	0
$210$	7.31875	0.505042
$211$	−3.03388	−0.208861	−0.104430	−	0.994532i	$-0.533302\pi$
$211$	−3.03388	−0.208861	−0.104430	+	0.994532i	$0.533302\pi$
$212$	2.58976	0.177865
$213$	−24.3856	−1.67087
$214$	−19.1921	−1.31195
$215$	1.15522	0.0787850
$216$	12.3521	0.840454
$217$	−9.22124	−0.625979
$218$	9.49695	0.643215
$219$	16.4540	1.11186
$220$	0	0
$221$	39.8297	2.67924
$222$	23.0106	1.54437
$223$	4.76902	0.319357	0.159678	−	0.987169i	$-0.448954\pi$
$223$	4.76902	0.319357	0.159678	+	0.987169i	$0.448954\pi$
$224$	3.11006	0.207800
$225$	−2.79241	−0.186160
$226$	−22.9950	−1.52961
$227$	26.6405	1.76819	0.884095	−	0.467307i	$-0.154776\pi$
$227$	26.6405	1.76819	0.884095	+	0.467307i	$0.154776\pi$
$228$	1.91575	0.126873
$229$	11.6882	0.772377	0.386188	−	0.922420i	$-0.373792\pi$
$229$	11.6882	0.772377	0.386188	+	0.922420i	$0.373792\pi$
$230$	1.47034	0.0969510
$231$	0	0
$232$	−24.8746	−1.63310
$233$	3.48827	0.228524	0.114262	−	0.993451i	$-0.463550\pi$
$233$	3.48827	0.228524	0.114262	+	0.993451i	$0.463550\pi$
$234$	6.84816	0.447678
$235$	−6.47653	−0.422482
$236$	3.44731	0.224401
$237$	7.48164	0.485985
$238$	−18.5216	−1.20058
$239$	−18.1468	−1.17382	−0.586911	−	0.809652i	$-0.699656\pi$
$239$	−18.1468	−1.17382	−0.586911	+	0.809652i	$0.699656\pi$
$240$	−9.27160	−0.598479
$241$	4.01737	0.258782	0.129391	−	0.991594i	$-0.458698\pi$
$241$	4.01737	0.258782	0.129391	+	0.991594i	$0.458698\pi$
$242$	0	0
$243$	9.14205	0.586463
$244$	−0.272811	−0.0174650
$245$	3.99426	0.255184
$246$	10.5130	0.670282
$247$	−20.3801	−1.29676
$248$	13.5675	0.861538
$249$	−24.9605	−1.58181
$250$	−14.7248	−0.931277
$251$	−7.05879	−0.445547	−0.222774	−	0.974870i	$-0.571511\pi$
$251$	−7.05879	−0.445547	−0.222774	+	0.974870i	$0.571511\pi$
$252$	0.503001	0.0316861
$253$	0	0
$254$	2.90349	0.182181
$255$	−19.0428	−1.19251
$256$	−6.42011	−0.401257
$257$	−6.03995	−0.376762	−0.188381	−	0.982096i	$-0.560324\pi$
$257$	−6.03995	−0.376762	−0.188381	+	0.982096i	$0.560324\pi$
$258$	−2.16305	−0.134665
$259$	−17.9801	−1.11723
$260$	−2.17189	−0.134695
$261$	−7.56322	−0.468152
$262$	−2.73075	−0.168706
$263$	−11.0908	−0.683890	−0.341945	−	0.939720i	$-0.611086\pi$
$263$	−11.0908	−0.683890	−0.341945	+	0.939720i	$0.611086\pi$
$264$	0	0
$265$	13.1720	0.809151
$266$	9.47718	0.581083
$267$	29.3754	1.79774
$268$	−1.67413	−0.102264
$269$	5.22740	0.318720	0.159360	−	0.987221i	$-0.449057\pi$
$269$	5.22740	0.318720	0.159360	+	0.987221i	$0.449057\pi$
$270$	7.54108	0.458935
$271$	13.4323	0.815956	0.407978	−	0.912992i	$-0.366234\pi$
$271$	13.4323	0.815956	0.407978	+	0.912992i	$0.366234\pi$
$272$	23.4638	1.42270
$273$	−23.0267	−1.39364
$274$	−14.1666	−0.855838
$275$	0	0
$276$	0.434852	0.0261750
$277$	−31.7919	−1.91019	−0.955096	−	0.296297i	$-0.904248\pi$
$277$	−31.7919	−1.91019	−0.955096	+	0.296297i	$0.904248\pi$
$278$	−15.0860	−0.904797
$279$	4.12525	0.246972
$280$	8.41417	0.502843
$281$	−22.8024	−1.36028	−0.680140	−	0.733083i	$-0.738081\pi$
$281$	−22.8024	−1.36028	−0.680140	+	0.733083i	$0.738081\pi$
$282$	12.1268	0.722139
$283$	19.0479	1.13228	0.566140	−	0.824309i	$-0.308436\pi$
$283$	19.0479	1.13228	0.566140	+	0.824309i	$0.308436\pi$
$284$	−3.36517	−0.199686
$285$	9.74386	0.577177
$286$	0	0
$287$	−8.21466	−0.484896
$288$	−1.39133	−0.0819848
$289$	31.1919	1.83482
$290$	−15.1862	−0.891763
$291$	−14.0349	−0.822740
$292$	2.27062	0.132878
$293$	4.36266	0.254869	0.127435	−	0.991847i	$-0.459326\pi$
$293$	4.36266	0.254869	0.127435	+	0.991847i	$0.459326\pi$
$294$	−7.47893	−0.436180
$295$	17.5337	1.02085
$296$	26.4547	1.53765
$297$	0	0
$298$	−15.0996	−0.874698
$299$	−4.62605	−0.267532
$300$	−1.65823	−0.0957382
$301$	1.69017	0.0974197
$302$	−2.70025	−0.155382
$303$	28.1879	1.61935
$304$	−12.0060	−0.688590
$305$	−1.38757	−0.0794522
$306$	8.28592	0.473675
$307$	11.4166	0.651580	0.325790	−	0.945442i	$-0.394370\pi$
$307$	11.4166	0.651580	0.325790	+	0.945442i	$0.394370\pi$
$308$	0	0
$309$	−3.35831	−0.191048
$310$	8.28309	0.470448
$311$	−30.5731	−1.73364	−0.866820	−	0.498621i	$-0.833840\pi$
$311$	−30.5731	−1.73364	−0.866820	+	0.498621i	$0.833840\pi$
$312$	33.8799	1.91807
$313$	9.04130	0.511044	0.255522	−	0.966803i	$-0.417753\pi$
$313$	9.04130	0.511044	0.255522	+	0.966803i	$0.417753\pi$
$314$	−32.0700	−1.80982
$315$	2.55836	0.144147
$316$	1.03245	0.0580801
$317$	−21.5081	−1.20802	−0.604009	−	0.796978i	$-0.706431\pi$
$317$	−21.5081	−1.20802	−0.604009	+	0.796978i	$0.706431\pi$
$318$	−24.6636	−1.38306
$319$	0	0
$320$	−12.1735	−0.680519
$321$	−28.8697	−1.61135
$322$	2.15121	0.119882
$323$	−24.6589	−1.37206
$324$	2.97358	0.165199
$325$	17.6406	0.978527
$326$	12.6517	0.700710
$327$	14.2858	0.790004
$328$	12.0865	0.667365
$329$	−9.47566	−0.522410
$330$	0	0
$331$	−23.2813	−1.27966	−0.639829	−	0.768518i	$-0.720995\pi$
$331$	−23.2813	−1.27966	−0.639829	+	0.768518i	$0.720995\pi$
$332$	−3.44450	−0.189042
$333$	8.04365	0.440789
$334$	−22.1804	−1.21366
$335$	−8.51497	−0.465223
$336$	−13.5651	−0.740035
$337$	13.9809	0.761586	0.380793	−	0.924660i	$-0.375651\pi$
$337$	13.9809	0.761586	0.380793	+	0.924660i	$0.375651\pi$
$338$	−26.1774	−1.42386
$339$	−34.5902	−1.87868
$340$	−2.62788	−0.142517
$341$	0	0
$342$	−4.23975	−0.229260
$343$	20.0548	1.08286
$344$	−2.48680	−0.134079
$345$	2.21175	0.119076
$346$	−7.62135	−0.409726
$347$	21.9732	1.17959	0.589793	−	0.807555i	$-0.299209\pi$
$347$	21.9732	1.17959	0.589793	+	0.807555i	$0.299209\pi$
$348$	−4.49132	−0.240760
$349$	−12.0629	−0.645710	−0.322855	−	0.946448i	$-0.604643\pi$
$349$	−12.0629	−0.645710	−0.322855	+	0.946448i	$0.604643\pi$
$350$	−8.20327	−0.438483
$351$	−23.7262	−1.26641
$352$	0	0
$353$	−1.86971	−0.0995146	−0.0497573	−	0.998761i	$-0.515845\pi$
$353$	−1.86971	−0.0995146	−0.0497573	+	0.998761i	$0.515845\pi$
$354$	−32.8304	−1.74492
$355$	−17.1159	−0.908420
$356$	4.05375	0.214848
$357$	−27.8611	−1.47457
$358$	−5.62485	−0.297283
$359$	−32.2819	−1.70377	−0.851886	−	0.523727i	$-0.824541\pi$
$359$	−32.2819	−1.70377	−0.851886	+	0.523727i	$0.824541\pi$
$360$	−3.76420	−0.198391
$361$	−6.38249	−0.335921
$362$	26.4228	1.38875
$363$	0	0
$364$	−3.17764	−0.166554
$365$	11.5488	0.604494
$366$	2.59812	0.135806
$367$	15.1555	0.791112	0.395556	−	0.918442i	$-0.370552\pi$
$367$	15.1555	0.791112	0.395556	+	0.918442i	$0.370552\pi$
$368$	−2.72522	−0.142062
$369$	3.67494	0.191310
$370$	16.1508	0.839642
$371$	19.2717	1.00054
$372$	2.44973	0.127012
$373$	4.47779	0.231851	0.115926	−	0.993258i	$-0.463017\pi$
$373$	4.47779	0.231851	0.115926	+	0.993258i	$0.463017\pi$
$374$	0	0
$375$	−22.1497	−1.14380
$376$	13.9418	0.718996
$377$	47.7796	2.46078
$378$	11.0332	0.567485
$379$	12.5805	0.646215	0.323107	−	0.946362i	$-0.395273\pi$
$379$	12.5805	0.646215	0.323107	+	0.946362i	$0.395273\pi$
$380$	1.34464	0.0689784
$381$	4.36756	0.223757
$382$	−12.0193	−0.614961
$383$	−4.18886	−0.214041	−0.107020	−	0.994257i	$-0.534131\pi$
$383$	−4.18886	−0.214041	−0.107020	+	0.994257i	$0.534131\pi$
$384$	16.7368	0.854096
$385$	0	0
$386$	25.6784	1.30700
$387$	−0.756121	−0.0384358
$388$	−1.93679	−0.0983257
$389$	−21.2015	−1.07496	−0.537480	−	0.843277i	$-0.680623\pi$
$389$	−21.2015	−1.07496	−0.537480	+	0.843277i	$0.680623\pi$
$390$	20.6840	1.04737
$391$	−5.59729	−0.283067
$392$	−8.59833	−0.434281
$393$	−4.10771	−0.207207
$394$	−28.6059	−1.44115
$395$	5.25127	0.264220
$396$	0	0
$397$	6.72041	0.337288	0.168644	−	0.985677i	$-0.446061\pi$
$397$	6.72041	0.337288	0.168644	+	0.985677i	$0.446061\pi$
$398$	−28.5492	−1.43104
$399$	14.2560	0.713693
$400$	10.3921	0.519607
$401$	2.60439	0.130057	0.0650286	−	0.997883i	$-0.479286\pi$
$401$	2.60439	0.130057	0.0650286	+	0.997883i	$0.479286\pi$
$402$	15.9436	0.795194
$403$	−26.0607	−1.29818
$404$	3.88988	0.193529
$405$	15.1242	0.751529
$406$	−22.2185	−1.10269
$407$	0	0
$408$	40.9929	2.02945
$409$	−2.08400	−0.103047	−0.0515237	−	0.998672i	$-0.516408\pi$
$409$	−2.08400	−0.103047	−0.0515237	+	0.998672i	$0.516408\pi$
$410$	7.37891	0.364418
$411$	−21.3101	−1.05115
$412$	−0.463441	−0.0228321
$413$	25.6531	1.26231
$414$	−0.962375	−0.0472982
$415$	−17.5194	−0.859995
$416$	8.78953	0.430942
$417$	−22.6930	−1.11128
$418$	0	0
$419$	−24.0304	−1.17396	−0.586982	−	0.809600i	$-0.699684\pi$
$419$	−24.0304	−1.17396	−0.586982	+	0.809600i	$0.699684\pi$
$420$	1.51925	0.0741318
$421$	1.01272	0.0493568	0.0246784	−	0.999695i	$-0.492144\pi$
$421$	1.01272	0.0493568	0.0246784	+	0.999695i	$0.492144\pi$
$422$	3.98720	0.194094
$423$	4.23907	0.206111
$424$	−28.3550	−1.37704
$425$	21.3443	1.03535
$426$	32.0482	1.55274
$427$	−2.03012	−0.0982446
$428$	−3.98397	−0.192572
$429$	0	0
$430$	−1.51821	−0.0732147
$431$	16.4442	0.792088	0.396044	−	0.918232i	$-0.370383\pi$
$431$	16.4442	0.792088	0.396044	+	0.918232i	$0.370383\pi$
$432$	−13.9771	−0.672475
$433$	−22.5857	−1.08540	−0.542700	−	0.839926i	$-0.682598\pi$
$433$	−22.5857	−1.08540	−0.542700	+	0.839926i	$0.682598\pi$
$434$	12.1188	0.581721
$435$	−22.8437	−1.09527
$436$	1.97141	0.0944134
$437$	2.86403	0.137005
$438$	−21.6243	−1.03325
$439$	34.8689	1.66420	0.832101	−	0.554625i	$-0.187138\pi$
$439$	34.8689	1.66420	0.832101	+	0.554625i	$0.187138\pi$
$440$	0	0
$441$	−2.61436	−0.124493
$442$	−52.3452	−2.48981
$443$	−31.1718	−1.48102	−0.740508	−	0.672048i	$-0.765415\pi$
$443$	−31.1718	−1.48102	−0.740508	+	0.672048i	$0.765415\pi$
$444$	4.77662	0.226688
$445$	20.6182	0.977395
$446$	−6.26756	−0.296778
$447$	−22.7135	−1.07431
$448$	−17.8108	−0.841479
$449$	25.8963	1.22212	0.611060	−	0.791584i	$-0.290743\pi$
$449$	25.8963	1.22212	0.611060	+	0.791584i	$0.290743\pi$
$450$	3.66985	0.172998
$451$	0	0
$452$	−4.77338	−0.224521
$453$	−4.06184	−0.190842
$454$	−35.0116	−1.64317
$455$	−16.1621	−0.757691
$456$	−20.9753	−0.982260
$457$	−6.73065	−0.314847	−0.157423	−	0.987531i	$-0.550319\pi$
$457$	−6.73065	−0.314847	−0.157423	+	0.987531i	$0.550319\pi$
$458$	−15.3609	−0.717768
$459$	−28.7075	−1.33995
$460$	0.305217	0.0142308
$461$	−38.5957	−1.79758	−0.898791	−	0.438378i	$-0.855553\pi$
$461$	−38.5957	−1.79758	−0.898791	+	0.438378i	$0.855553\pi$
$462$	0	0
$463$	28.2081	1.31094	0.655472	−	0.755220i	$-0.272470\pi$
$463$	28.2081	1.31094	0.655472	+	0.755220i	$0.272470\pi$
$464$	28.1471	1.30670
$465$	12.4598	0.577809
$466$	−4.58437	−0.212367
$467$	−16.3664	−0.757346	−0.378673	−	0.925531i	$-0.623619\pi$
$467$	−16.3664	−0.757346	−0.378673	+	0.925531i	$0.623619\pi$
$468$	1.42156	0.0657118
$469$	−12.4581	−0.575260
$470$	8.51162	0.392612
$471$	−48.2412	−2.22284
$472$	−37.7443	−1.73732
$473$	0	0
$474$	−9.83257	−0.451625
$475$	−10.9215	−0.501112
$476$	−3.84478	−0.176225
$477$	−8.62146	−0.394750
$478$	23.8490	1.09083
$479$	16.7773	0.766572	0.383286	−	0.923630i	$-0.374792\pi$
$479$	16.7773	0.766572	0.383286	+	0.923630i	$0.374792\pi$
$480$	−4.20233	−0.191809
$481$	−50.8147	−2.31695
$482$	−5.27974	−0.240485
$483$	3.23595	0.147241
$484$	0	0
$485$	−9.85091	−0.447307
$486$	−12.0147	−0.544998
$487$	−28.7178	−1.30133	−0.650665	−	0.759365i	$-0.725510\pi$
$487$	−28.7178	−1.30133	−0.650665	+	0.759365i	$0.725510\pi$
$488$	2.98699	0.135215
$489$	19.0312	0.860621
$490$	−5.24936	−0.237142
$491$	−32.6549	−1.47369	−0.736847	−	0.676060i	$-0.763686\pi$
$491$	−32.6549	−1.47369	−0.736847	+	0.676060i	$0.763686\pi$
$492$	2.18232	0.0983864
$493$	57.8109	2.60367
$494$	26.7841	1.20507
$495$	0	0
$496$	−15.3524	−0.689345
$497$	−25.0419	−1.12328
$498$	32.8037	1.46997
$499$	−7.11998	−0.318734	−0.159367	−	0.987219i	$-0.550945\pi$
$499$	−7.11998	−0.318734	−0.159367	+	0.987219i	$0.550945\pi$
$500$	−3.05662	−0.136696
$501$	−33.3648	−1.49063
$502$	9.27685	0.414046
$503$	12.3496	0.550641	0.275321	−	0.961352i	$-0.411216\pi$
$503$	12.3496	0.550641	0.275321	+	0.961352i	$0.411216\pi$
$504$	−5.50731	−0.245315
$505$	19.7847	0.880408
$506$	0	0
$507$	−39.3772	−1.74880
$508$	0.602716	0.0267412
$509$	−11.4262	−0.506459	−0.253229	−	0.967406i	$-0.581493\pi$
$509$	−11.4262	−0.506459	−0.253229	+	0.967406i	$0.581493\pi$
$510$	25.0266	1.10819
$511$	16.8968	0.747472
$512$	25.3697	1.12119
$513$	14.6891	0.648539
$514$	7.93786	0.350124
$515$	−2.35715	−0.103869
$516$	−0.449012	−0.0197667
$517$	0	0
$518$	23.6299	1.03824
$519$	−11.4644	−0.503231
$520$	23.7798	1.04281
$521$	−30.2067	−1.32338	−0.661690	−	0.749777i	$-0.730161\pi$
$521$	−30.2067	−1.32338	−0.661690	+	0.749777i	$0.730161\pi$
$522$	9.93978	0.435052
$523$	2.64676	0.115735	0.0578674	−	0.998324i	$-0.481570\pi$
$523$	2.64676	0.115735	0.0578674	+	0.998324i	$0.481570\pi$
$524$	−0.566857	−0.0247633
$525$	−12.3397	−0.538550
$526$	14.5758	0.635537
$527$	−31.5322	−1.37356
$528$	0	0
$529$	−22.3499	−0.971735
$530$	−17.3110	−0.751943
$531$	−11.4763	−0.498029
$532$	1.96731	0.0852935
$533$	−23.2160	−1.00559
$534$	−38.6058	−1.67064
$535$	−20.2632	−0.876056
$536$	18.3299	0.791733
$537$	−8.46116	−0.365126
$538$	−6.86998	−0.296186
$539$	0	0
$540$	1.56540	0.0673642
$541$	−16.9705	−0.729617	−0.364809	−	0.931082i	$-0.618866\pi$
$541$	−16.9705	−0.729617	−0.364809	+	0.931082i	$0.618866\pi$
$542$	−17.6531	−0.758266
$543$	39.7464	1.70568
$544$	10.6349	0.455967
$545$	10.0270	0.429509
$546$	30.2622	1.29510
$547$	12.3888	0.529707	0.264853	−	0.964289i	$-0.414676\pi$
$547$	12.3888	0.529707	0.264853	+	0.964289i	$0.414676\pi$
$548$	−2.94076	−0.125623
$549$	0.908205	0.0387612
$550$	0	0
$551$	−29.5808	−1.26018
$552$	−4.76116	−0.202648
$553$	7.68300	0.326714
$554$	41.7818	1.77514
$555$	24.2948	1.03126
$556$	−3.13160	−0.132809
$557$	28.0597	1.18893	0.594463	−	0.804123i	$-0.297365\pi$
$557$	28.0597	1.18893	0.594463	+	0.804123i	$0.297365\pi$
$558$	−5.42151	−0.229511
$559$	4.77669	0.202033
$560$	−9.52113	−0.402341
$561$	0	0
$562$	29.9675	1.26410
$563$	−34.0521	−1.43513	−0.717563	−	0.696493i	$-0.754743\pi$
$563$	−34.0521	−1.43513	−0.717563	+	0.696493i	$0.754743\pi$
$564$	2.51732	0.105998
$565$	−24.2784	−1.02140
$566$	−25.0332	−1.05223
$567$	22.1279	0.929285
$568$	36.8450	1.54598
$569$	4.18354	0.175383	0.0876916	−	0.996148i	$-0.472051\pi$
$569$	4.18354	0.175383	0.0876916	+	0.996148i	$0.472051\pi$
$570$	−12.8056	−0.536369
$571$	19.9054	0.833013	0.416507	−	0.909133i	$-0.363254\pi$
$571$	19.9054	0.833013	0.416507	+	0.909133i	$0.363254\pi$
$572$	0	0
$573$	−18.0800	−0.755302
$574$	10.7959	0.450613
$575$	−2.47905	−0.103384
$576$	7.96790	0.331996
$577$	−26.0834	−1.08587	−0.542933	−	0.839776i	$-0.682686\pi$
$577$	−26.0834	−1.08587	−0.542933	+	0.839776i	$0.682686\pi$
$578$	−40.9932	−1.70509
$579$	38.6267	1.60527
$580$	−3.15240	−0.130896
$581$	−25.6322	−1.06340
$582$	18.4450	0.764571
$583$	0	0
$584$	−24.8608	−1.02875
$585$	7.23035	0.298938
$586$	−5.73352	−0.236849
$587$	−16.9706	−0.700451	−0.350225	−	0.936665i	$-0.613895\pi$
$587$	−16.9706	−0.700451	−0.350225	+	0.936665i	$0.613895\pi$
$588$	−1.55250	−0.0640240
$589$	16.1344	0.664808
$590$	−23.0432	−0.948675
$591$	−43.0304	−1.77003
$592$	−29.9350	−1.23032
$593$	28.1953	1.15784	0.578921	−	0.815383i	$-0.303474\pi$
$593$	28.1953	1.15784	0.578921	+	0.815383i	$0.303474\pi$
$594$	0	0
$595$	−19.5553	−0.801691
$596$	−3.13443	−0.128391
$597$	−42.9450	−1.75762
$598$	6.07968	0.248617
$599$	16.6875	0.681834	0.340917	−	0.940093i	$-0.389263\pi$
$599$	16.6875	0.681834	0.340917	+	0.940093i	$0.389263\pi$
$600$	18.1559	0.741210
$601$	34.9576	1.42595	0.712975	−	0.701189i	$-0.247347\pi$
$601$	34.9576	1.42595	0.712975	+	0.701189i	$0.247347\pi$
$602$	−2.22126	−0.0905319
$603$	5.57329	0.226962
$604$	−0.560527	−0.0228075
$605$	0	0
$606$	−37.0452	−1.50486
$607$	−16.5940	−0.673528	−0.336764	−	0.941589i	$-0.609332\pi$
$607$	−16.5940	−0.673528	−0.336764	+	0.941589i	$0.609332\pi$
$608$	−5.44168	−0.220689
$609$	−33.4221	−1.35433
$610$	1.82358	0.0738347
$611$	−26.7798	−1.08339
$612$	1.72002	0.0695277
$613$	−8.29426	−0.335002	−0.167501	−	0.985872i	$-0.553570\pi$
$613$	−8.29426	−0.335002	−0.167501	+	0.985872i	$0.553570\pi$
$614$	−15.0040	−0.605512
$615$	11.0997	0.447583
$616$	0	0
$617$	39.9235	1.60726	0.803630	−	0.595129i	$-0.202899\pi$
$617$	39.9235	1.60726	0.803630	+	0.595129i	$0.202899\pi$
$618$	4.41358	0.177540
$619$	6.86944	0.276106	0.138053	−	0.990425i	$-0.455916\pi$
$619$	6.86944	0.276106	0.138053	+	0.990425i	$0.455916\pi$
$620$	1.71943	0.0690540
$621$	3.33425	0.133799
$622$	40.1799	1.61107
$623$	30.1660	1.20857
$624$	−38.3371	−1.53471
$625$	−0.173355	−0.00693420
$626$	−11.8823	−0.474912
$627$	0	0
$628$	−6.65720	−0.265651
$629$	−61.4832	−2.45150
$630$	−3.36226	−0.133956
$631$	−37.2753	−1.48390	−0.741952	−	0.670453i	$-0.766100\pi$
$631$	−37.2753	−1.48390	−0.741952	+	0.670453i	$0.766100\pi$
$632$	−11.3042	−0.449659
$633$	5.99772	0.238388
$634$	28.2666	1.12261
$635$	3.06553	0.121652
$636$	−5.11974	−0.203011
$637$	16.5158	0.654381
$638$	0	0
$639$	11.2029	0.443178
$640$	11.7473	0.464354
$641$	−28.5638	−1.12820	−0.564101	−	0.825706i	$-0.690777\pi$
$641$	−28.5638	−1.12820	−0.564101	+	0.825706i	$0.690777\pi$
$642$	37.9413	1.49742
$643$	13.8862	0.547618	0.273809	−	0.961784i	$-0.411716\pi$
$643$	13.8862	0.547618	0.273809	+	0.961784i	$0.411716\pi$
$644$	0.446556	0.0175968
$645$	−2.28377	−0.0899232
$646$	32.4074	1.27505
$647$	−2.36581	−0.0930097	−0.0465048	−	0.998918i	$-0.514808\pi$
$647$	−2.36581	−0.0930097	−0.0465048	+	0.998918i	$0.514808\pi$
$648$	−32.5575	−1.27898
$649$	0	0
$650$	−23.1838	−0.909343
$651$	18.2296	0.714476
$652$	2.62627	0.102853
$653$	−44.6721	−1.74815	−0.874077	−	0.485788i	$-0.838533\pi$
$653$	−44.6721	−1.74815	−0.874077	+	0.485788i	$0.838533\pi$
$654$	−18.7747	−0.734149
$655$	−2.88315	−0.112654
$656$	−13.6766	−0.533980
$657$	−7.55904	−0.294906
$658$	12.4532	0.485474
$659$	3.04987	0.118806	0.0594031	−	0.998234i	$-0.481080\pi$
$659$	3.04987	0.118806	0.0594031	+	0.998234i	$0.481080\pi$
$660$	0	0
$661$	15.0839	0.586694	0.293347	−	0.956006i	$-0.405231\pi$
$661$	15.0839	0.586694	0.293347	+	0.956006i	$0.405231\pi$
$662$	30.5969	1.18918
$663$	−78.7400	−3.05801
$664$	37.7135	1.46357
$665$	10.0061	0.388020
$666$	−10.5712	−0.409625
$667$	−6.71450	−0.259986
$668$	−4.60429	−0.178145
$669$	−9.42795	−0.364506
$670$	11.1906	0.432330
$671$	0	0
$672$	−6.14833	−0.237177
$673$	−0.744519	−0.0286991	−0.0143495	−	0.999897i	$-0.504568\pi$
$673$	−0.744519	−0.0286991	−0.0143495	+	0.999897i	$0.504568\pi$
$674$	−18.3740	−0.707740
$675$	−12.7146	−0.489385
$676$	−5.43399	−0.208999
$677$	21.5042	0.826475	0.413237	−	0.910623i	$-0.364398\pi$
$677$	21.5042	0.826475	0.413237	+	0.910623i	$0.364398\pi$
$678$	45.4593	1.74585
$679$	−14.4126	−0.553106
$680$	28.7724	1.10337
$681$	−52.6660	−2.01817
$682$	0	0
$683$	32.8678	1.25765	0.628825	−	0.777547i	$-0.283536\pi$
$683$	32.8678	1.25765	0.628825	+	0.777547i	$0.283536\pi$
$684$	−0.880102	−0.0336515
$685$	−14.9573	−0.571488
$686$	−26.3565	−1.00630
$687$	−23.1066	−0.881571
$688$	2.81396	0.107281
$689$	54.4649	2.07495
$690$	−2.90673	−0.110657
$691$	40.7898	1.55172	0.775859	−	0.630906i	$-0.217317\pi$
$691$	40.7898	1.55172	0.775859	+	0.630906i	$0.217317\pi$
$692$	−1.58207	−0.0601411
$693$	0	0
$694$	−28.8778	−1.09619
$695$	−15.9279	−0.604181
$696$	49.1750	1.86398
$697$	−28.0901	−1.06399
$698$	15.8533	0.600057
$699$	−6.89602	−0.260831
$700$	−1.70286	−0.0643622
$701$	−16.5302	−0.624339	−0.312169	−	0.950026i	$-0.601056\pi$
$701$	−16.5302	−0.624339	−0.312169	+	0.950026i	$0.601056\pi$
$702$	31.1815	1.17687
$703$	31.4598	1.18653
$704$	0	0
$705$	12.8036	0.482210
$706$	2.45722	0.0924787
$707$	28.9465	1.08865
$708$	−6.81505	−0.256125
$709$	9.67562	0.363375	0.181688	−	0.983356i	$-0.441844\pi$
$709$	9.67562	0.363375	0.181688	+	0.983356i	$0.441844\pi$
$710$	22.4942	0.844192
$711$	−3.43710	−0.128901
$712$	−44.3841	−1.66337
$713$	3.66233	0.137155
$714$	36.6158	1.37031
$715$	0	0
$716$	−1.16763	−0.0436362
$717$	35.8748	1.33977
$718$	42.4257	1.58331
$719$	0.412582	0.0153867	0.00769336	−	0.999970i	$-0.497551\pi$
$719$	0.412582	0.0153867	0.00769336	+	0.999970i	$0.497551\pi$
$720$	4.25941	0.158739
$721$	−3.44870	−0.128436
$722$	8.38803	0.312170
$723$	−7.94202	−0.295367
$724$	5.48493	0.203846
$725$	25.6046	0.950930
$726$	0	0
$727$	−3.71500	−0.137782	−0.0688908	−	0.997624i	$-0.521946\pi$
$727$	−3.71500	−0.137782	−0.0688908	+	0.997624i	$0.521946\pi$
$728$	34.7917	1.28947
$729$	14.6263	0.541713
$730$	−15.1778	−0.561755
$731$	5.77955	0.213765
$732$	0.539326	0.0199340
$733$	20.3180	0.750464	0.375232	−	0.926931i	$-0.377563\pi$
$733$	20.3180	0.750464	0.375232	+	0.926931i	$0.377563\pi$
$734$	−19.9178	−0.735179
$735$	−7.89633	−0.291260
$736$	−1.23520	−0.0455300
$737$	0	0
$738$	−4.82970	−0.177784
$739$	13.1912	0.485248	0.242624	−	0.970120i	$-0.421992\pi$
$739$	13.1912	0.485248	0.242624	+	0.970120i	$0.421992\pi$
$740$	3.35264	0.123246
$741$	40.2898	1.48008
$742$	−25.3273	−0.929796
$743$	−36.2465	−1.32975	−0.664877	−	0.746953i	$-0.731516\pi$
$743$	−36.2465	−1.32975	−0.664877	+	0.746953i	$0.731516\pi$
$744$	−26.8219	−0.983337
$745$	−15.9423	−0.584082
$746$	−5.88483	−0.215459
$747$	11.4670	0.419554
$748$	0	0
$749$	−29.6467	−1.08327
$750$	29.1097	1.06294
$751$	25.4285	0.927901	0.463950	−	0.885861i	$-0.346432\pi$
$751$	25.4285	0.927901	0.463950	+	0.885861i	$0.346432\pi$
$752$	−15.7760	−0.575292
$753$	13.9547	0.508536
$754$	−62.7932	−2.28679
$755$	−2.85095	−0.103757
$756$	2.29030	0.0832975
$757$	−1.51402	−0.0550280	−0.0275140	−	0.999621i	$-0.508759\pi$
$757$	−1.51402	−0.0550280	−0.0275140	+	0.999621i	$0.508759\pi$
$758$	−16.5336	−0.600526
$759$	0	0
$760$	−14.7223	−0.534034
$761$	22.5979	0.819172	0.409586	−	0.912272i	$-0.365673\pi$
$761$	22.5979	0.819172	0.409586	+	0.912272i	$0.365673\pi$
$762$	−5.73996	−0.207937
$763$	14.6702	0.531098
$764$	−2.49501	−0.0902661
$765$	8.74836	0.316298
$766$	5.50510	0.198907
$767$	72.4999	2.61782
$768$	12.6920	0.457984
$769$	11.8829	0.428509	0.214254	−	0.976778i	$-0.431268\pi$
$769$	11.8829	0.428509	0.214254	+	0.976778i	$0.431268\pi$
$770$	0	0
$771$	11.9405	0.430026
$772$	5.33042	0.191846
$773$	−14.3931	−0.517683	−0.258841	−	0.965920i	$-0.583341\pi$
$773$	−14.3931	−0.517683	−0.258841	+	0.965920i	$0.583341\pi$
$774$	0.993713	0.0357183
$775$	−13.9657	−0.501661
$776$	21.2058	0.761243
$777$	35.5452	1.27518
$778$	27.8636	0.998957
$779$	14.3732	0.514973
$780$	4.29365	0.153737
$781$	0	0
$782$	7.35610	0.263054
$783$	−34.4374	−1.23069
$784$	9.72952	0.347483
$785$	−33.8598	−1.20851
$786$	5.39846	0.192557
$787$	4.50354	0.160534	0.0802668	−	0.996773i	$-0.474423\pi$
$787$	4.50354	0.160534	0.0802668	+	0.996773i	$0.474423\pi$
$788$	−5.93812	−0.211537
$789$	21.9257	0.780574
$790$	−6.90135	−0.245539
$791$	−35.5211	−1.26298
$792$	0	0
$793$	−5.73746	−0.203743
$794$	−8.83213	−0.313441
$795$	−26.0400	−0.923544
$796$	−5.92633	−0.210053
$797$	0.483472	0.0171255	0.00856273	−	0.999963i	$-0.497274\pi$
$797$	0.483472	0.0171255	0.00856273	+	0.999963i	$0.497274\pi$
$798$	−18.7356	−0.663234
$799$	−32.4022	−1.14631
$800$	4.71021	0.166531
$801$	−13.4952	−0.476828
$802$	−3.42276	−0.120862
$803$	0	0
$804$	3.30962	0.116721
$805$	2.27127	0.0800518
$806$	34.2497	1.20639
$807$	−10.3341	−0.363779
$808$	−42.5899	−1.49831
$809$	13.2547	0.466010	0.233005	−	0.972476i	$-0.425144\pi$
$809$	13.2547	0.466010	0.233005	+	0.972476i	$0.425144\pi$
$810$	−19.8767	−0.698394
$811$	25.8912	0.909162	0.454581	−	0.890705i	$-0.349789\pi$
$811$	25.8912	0.909162	0.454581	+	0.890705i	$0.349789\pi$
$812$	−4.61220	−0.161856
$813$	−26.5546	−0.931311
$814$	0	0
$815$	13.3577	0.467901
$816$	−46.3859	−1.62383
$817$	−2.95729	−0.103463
$818$	2.73885	0.0957617
$819$	10.5786	0.369645
$820$	1.53174	0.0534906
$821$	29.0101	1.01246	0.506230	−	0.862399i	$-0.331039\pi$
$821$	29.0101	1.01246	0.506230	+	0.862399i	$0.331039\pi$
$822$	28.0063	0.976831
$823$	51.9525	1.81095	0.905476	−	0.424398i	$-0.139514\pi$
$823$	51.9525	1.81095	0.905476	+	0.424398i	$0.139514\pi$
$824$	5.07418	0.176767
$825$	0	0
$826$	−33.7140	−1.17306
$827$	7.79500	0.271059	0.135529	−	0.990773i	$-0.456727\pi$
$827$	7.79500	0.271059	0.135529	+	0.990773i	$0.456727\pi$
$828$	−0.199773	−0.00694260
$829$	21.1894	0.735940	0.367970	−	0.929838i	$-0.380053\pi$
$829$	21.1894	0.735940	0.367970	+	0.929838i	$0.380053\pi$
$830$	23.0245	0.799191
$831$	62.8500	2.18024
$832$	−50.3361	−1.74509
$833$	19.9833	0.692381
$834$	29.8238	1.03271
$835$	−23.4183	−0.810425
$836$	0	0
$837$	18.7834	0.649250
$838$	31.5814	1.09096
$839$	−16.8696	−0.582402	−0.291201	−	0.956662i	$-0.594055\pi$
$839$	−16.8696	−0.582402	−0.291201	+	0.956662i	$0.594055\pi$
$840$	−16.6341	−0.573932
$841$	40.3499	1.39138
$842$	−1.33094	−0.0458672
$843$	45.0785	1.55259
$844$	0.827675	0.0284898
$845$	−27.6383	−0.950787
$846$	−5.57110	−0.191538
$847$	0	0
$848$	32.0854	1.10182
$849$	−37.6561	−1.29236
$850$	−28.0512	−0.962149
$851$	7.14102	0.244791
$852$	6.65267	0.227917
$853$	−40.2710	−1.37885	−0.689426	−	0.724356i	$-0.742137\pi$
$853$	−40.2710	−1.37885	−0.689426	+	0.724356i	$0.742137\pi$
$854$	2.66804	0.0912985
$855$	−4.47637	−0.153089
$856$	43.6201	1.49090
$857$	−54.7718	−1.87097	−0.935485	−	0.353366i	$-0.885037\pi$
$857$	−54.7718	−1.87097	−0.935485	+	0.353366i	$0.885037\pi$
$858$	0	0
$859$	25.8871	0.883257	0.441629	−	0.897198i	$-0.354401\pi$
$859$	25.8871	0.883257	0.441629	+	0.897198i	$0.354401\pi$
$860$	−0.315156	−0.0107467
$861$	16.2397	0.553447
$862$	−21.6114	−0.736086
$863$	−13.5251	−0.460399	−0.230199	−	0.973143i	$-0.573938\pi$
$863$	−13.5251	−0.460399	−0.230199	+	0.973143i	$0.573938\pi$
$864$	−6.33510	−0.215525
$865$	−8.04670	−0.273596
$866$	29.6827	1.00866
$867$	−61.6639	−2.09421
$868$	2.51566	0.0853870
$869$	0	0
$870$	30.0218	1.01784
$871$	−35.2085	−1.19299
$872$	−21.5848	−0.730953
$873$	6.44769	0.218221
$874$	−3.76398	−0.127319
$875$	−22.7458	−0.768949
$876$	−4.48883	−0.151664
$877$	−50.5645	−1.70744	−0.853721	−	0.520730i	$-0.825660\pi$
$877$	−50.5645	−1.70744	−0.853721	+	0.520730i	$0.825660\pi$
$878$	−45.8256	−1.54654
$879$	−8.62462	−0.290901
$880$	0	0
$881$	24.1533	0.813744	0.406872	−	0.913485i	$-0.366619\pi$
$881$	24.1533	0.813744	0.406872	+	0.913485i	$0.366619\pi$
$882$	3.43585	0.115691
$883$	−52.5172	−1.76735	−0.883673	−	0.468105i	$-0.844937\pi$
$883$	−52.5172	−1.76735	−0.883673	+	0.468105i	$0.844937\pi$
$884$	−10.8660	−0.365463
$885$	−34.6627	−1.16517
$886$	40.9667	1.37630
$887$	−24.0349	−0.807013	−0.403507	−	0.914977i	$-0.632209\pi$
$887$	−24.0349	−0.807013	−0.403507	+	0.914977i	$0.632209\pi$
$888$	−52.2987	−1.75503
$889$	4.48511	0.150426
$890$	−27.0969	−0.908291
$891$	0	0
$892$	−1.30104	−0.0435621
$893$	16.5796	0.554815
$894$	29.8507	0.998358
$895$	−5.93878	−0.198511
$896$	17.1872	0.574185
$897$	9.14533	0.305354
$898$	−34.0335	−1.13571
$899$	−37.8259	−1.26157
$900$	0.761800	0.0253933
$901$	65.8998	2.19544
$902$	0	0
$903$	−3.34132	−0.111192
$904$	52.2633	1.73825
$905$	27.8975	0.927343
$906$	5.33817	0.177349
$907$	−27.3556	−0.908328	−0.454164	−	0.890918i	$-0.650062\pi$
$907$	−27.3556	−0.908328	−0.454164	+	0.890918i	$0.650062\pi$
$908$	−7.26782	−0.241191
$909$	−12.9496	−0.429512
$910$	21.2407	0.704121
$911$	3.27520	0.108512	0.0542562	−	0.998527i	$-0.482721\pi$
$911$	3.27520	0.108512	0.0542562	+	0.998527i	$0.482721\pi$
$912$	23.7348	0.785938
$913$	0	0
$914$	8.84559	0.292586
$915$	2.74312	0.0906846
$916$	−3.18867	−0.105357
$917$	−4.21827	−0.139299
$918$	37.7281	1.24521
$919$	9.33515	0.307938	0.153969	−	0.988076i	$-0.450794\pi$
$919$	9.33515	0.307938	0.153969	+	0.988076i	$0.450794\pi$
$920$	−3.34179	−0.110176
$921$	−22.5697	−0.743696
$922$	50.7235	1.67049
$923$	−70.7726	−2.32951
$924$	0	0
$925$	−27.2310	−0.895351
$926$	−37.0718	−1.21826
$927$	1.54282	0.0506730
$928$	12.7576	0.418789
$929$	−41.7443	−1.36958	−0.684792	−	0.728738i	$-0.740107\pi$
$929$	−41.7443	−1.36958	−0.684792	+	0.728738i	$0.740107\pi$
$930$	−16.3750	−0.536957
$931$	−10.2251	−0.335114
$932$	−0.951639	−0.0311720
$933$	60.4405	1.97873
$934$	21.5091	0.703800
$935$	0	0
$936$	−15.5646	−0.508744
$937$	−17.4250	−0.569250	−0.284625	−	0.958639i	$-0.591869\pi$
$937$	−17.4250	−0.569250	−0.284625	+	0.958639i	$0.591869\pi$
$938$	16.3727	0.534587
$939$	−17.8739	−0.583293
$940$	1.76687	0.0576290
$941$	−29.2922	−0.954899	−0.477450	−	0.878659i	$-0.658439\pi$
$941$	−29.2922	−0.954899	−0.477450	+	0.878659i	$0.658439\pi$
$942$	63.3998	2.06568
$943$	3.26255	0.106243
$944$	42.7099	1.39009
$945$	11.6489	0.378940
$946$	0	0
$947$	8.76532	0.284835	0.142417	−	0.989807i	$-0.454513\pi$
$947$	8.76532	0.284835	0.142417	+	0.989807i	$0.454513\pi$
$948$	−2.04108	−0.0662911
$949$	47.7532	1.55013
$950$	14.3533	0.465682
$951$	42.5198	1.37880
$952$	42.0962	1.36435
$953$	32.0962	1.03970	0.519849	−	0.854258i	$-0.325988\pi$
$953$	32.0962	1.03970	0.519849	+	0.854258i	$0.325988\pi$
$954$	11.3305	0.366840
$955$	−12.6901	−0.410642
$956$	4.95066	0.160116
$957$	0	0
$958$	−22.0491	−0.712374
$959$	−21.8836	−0.706659
$960$	24.0660	0.776727
$961$	−10.3684	−0.334463
$962$	66.7819	2.15314
$963$	13.2629	0.427390
$964$	−1.09599	−0.0352993
$965$	27.1116	0.872752
$966$	−4.25277	−0.136831
$967$	−6.77178	−0.217766	−0.108883	−	0.994055i	$-0.534727\pi$
$967$	−6.77178	−0.217766	−0.108883	+	0.994055i	$0.534727\pi$
$968$	0	0
$969$	48.7486	1.56603
$970$	12.9463	0.415681
$971$	24.4938	0.786045	0.393022	−	0.919529i	$-0.371429\pi$
$971$	24.4938	0.786045	0.393022	+	0.919529i	$0.371429\pi$
$972$	−2.49405	−0.0799968
$973$	−23.3038	−0.747085
$974$	37.7417	1.20932
$975$	−34.8741	−1.11687
$976$	−3.37995	−0.108190
$977$	−34.4114	−1.10092	−0.550459	−	0.834862i	$-0.685547\pi$
$977$	−34.4114	−1.10092	−0.550459	+	0.834862i	$0.685547\pi$
$978$	−25.0113	−0.799773
$979$	0	0
$980$	−1.08968	−0.0348085
$981$	−6.56294	−0.209538
$982$	42.9158	1.36950
$983$	−24.8714	−0.793275	−0.396638	−	0.917975i	$-0.629823\pi$
$983$	−24.8714	−0.793275	−0.396638	+	0.917975i	$0.629823\pi$
$984$	−23.8940	−0.761713
$985$	−30.2024	−0.962329
$986$	−75.9766	−2.41959
$987$	18.7326	0.596265
$988$	5.55993	0.176885
$989$	−0.671271	−0.0213452
$990$	0	0
$991$	30.8026	0.978475	0.489238	−	0.872151i	$-0.337275\pi$
$991$	30.8026	0.978475	0.489238	+	0.872151i	$0.337275\pi$
$992$	−6.95845	−0.220931
$993$	46.0253	1.46057
$994$	32.9107	1.04387
$995$	−30.1425	−0.955582
$996$	6.80950	0.215767
$997$	−23.9102	−0.757244	−0.378622	−	0.925551i	$-0.623602\pi$
$997$	−23.9102	−0.757244	−0.378622	+	0.925551i	$0.623602\pi$
$998$	9.35726	0.296199
$999$	36.6250	1.15876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.i.1.7		19
11.10	odd	2		671.2.a.c.1.13	✓	19
33.32	even	2		6039.2.a.k.1.7		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.13	✓	19	11.10	odd	2
6039.2.a.k.1.7		19	33.32	even	2
7381.2.a.i.1.7		19	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31423 q^{2} -1.97692 q^{3} -0.272811 q^{4} -1.38757 q^{5} +2.59812 q^{6} -2.03012 q^{7} +2.98699 q^{8} +0.908205 q^{9} +O(q^{10})\)	\(q-1.31423 q^{2} -1.97692 q^{3} -0.272811 q^{4} -1.38757 q^{5} +2.59812 q^{6} -2.03012 q^{7} +2.98699 q^{8} +0.908205 q^{9} +1.82358 q^{10} +0.539326 q^{12} -5.73746 q^{13} +2.66804 q^{14} +2.74312 q^{15} -3.37995 q^{16} -6.94204 q^{17} -1.19359 q^{18} +3.55211 q^{19} +0.378545 q^{20} +4.01339 q^{21} +0.806289 q^{23} -5.90503 q^{24} -3.07464 q^{25} +7.54032 q^{26} +4.13531 q^{27} +0.553841 q^{28} -8.32766 q^{29} -3.60507 q^{30} +4.54221 q^{31} -1.53195 q^{32} +9.12341 q^{34} +2.81694 q^{35} -0.247769 q^{36} +8.85665 q^{37} -4.66828 q^{38} +11.3425 q^{39} -4.14466 q^{40} +4.04638 q^{41} -5.27450 q^{42} -0.832544 q^{43} -1.26020 q^{45} -1.05965 q^{46} +4.66753 q^{47} +6.68189 q^{48} -2.87860 q^{49} +4.04077 q^{50} +13.7238 q^{51} +1.56524 q^{52} -9.49286 q^{53} -5.43473 q^{54} -6.06395 q^{56} -7.02224 q^{57} +10.9444 q^{58} -12.6362 q^{59} -0.748353 q^{60} +1.00000 q^{61} -5.96948 q^{62} -1.84377 q^{63} +8.77324 q^{64} +7.96114 q^{65} +6.13660 q^{67} +1.89387 q^{68} -1.59397 q^{69} -3.70210 q^{70} +12.3352 q^{71} +2.71280 q^{72} -8.32305 q^{73} -11.6396 q^{74} +6.07832 q^{75} -0.969057 q^{76} -14.9066 q^{78} -3.78450 q^{79} +4.68993 q^{80} -10.8998 q^{81} -5.31786 q^{82} +12.6260 q^{83} -1.09490 q^{84} +9.63258 q^{85} +1.09415 q^{86} +16.4631 q^{87} -14.8592 q^{89} +1.65619 q^{90} +11.6478 q^{91} -0.219965 q^{92} -8.97957 q^{93} -6.13418 q^{94} -4.92881 q^{95} +3.02855 q^{96} +7.09938 q^{97} +3.78312 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 5 q^{2} + 23 q^{4} - q^{6} - 9 q^{7} - 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q - 5 * q^2 + 23 * q^4 - q^6 - 9 * q^7 - 9 * q^8 + 29 * q^9	\( 19 q - 5 q^{2} + 23 q^{4} - q^{6} - 9 q^{7} - 9 q^{8} + 29 q^{9} - 7 q^{10} - 4 q^{12} - 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} - 9 q^{17} - 10 q^{18} - 17 q^{19} - 6 q^{20} - 18 q^{21} - 10 q^{23} - 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} - 36 q^{28} - 27 q^{29} + 30 q^{30} + 7 q^{31} - 8 q^{32} - 5 q^{34} - 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} - 24 q^{39} - 10 q^{40} - 19 q^{41} + 21 q^{42} - 20 q^{43} - 32 q^{45} - 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} - 36 q^{50} - 47 q^{51} + 28 q^{52} + 3 q^{53} + 33 q^{54} - 44 q^{56} - 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} + 19 q^{61} + 11 q^{62} + 32 q^{63} + 47 q^{64} - 25 q^{65} + 3 q^{67} - 38 q^{68} + 3 q^{70} - 19 q^{71} - 34 q^{72} - 20 q^{73} + 22 q^{74} - 50 q^{75} + 25 q^{76} - 94 q^{78} - 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} - q^{83} + 28 q^{84} - 24 q^{85} - 27 q^{86} + 58 q^{87} - 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} - 64 q^{94} + 3 q^{95} + 26 q^{96} + 21 q^{97} + 87 q^{98}+O(q^{100}) \) 19 * q - 5 * q^2 + 23 * q^4 - q^6 - 9 * q^7 - 9 * q^8 + 29 * q^9 - 7 * q^10 - 4 * q^12 - 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 - 9 * q^17 - 10 * q^18 - 17 * q^19 - 6 * q^20 - 18 * q^21 - 10 * q^23 - 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 - 36 * q^28 - 27 * q^29 + 30 * q^30 + 7 * q^31 - 8 * q^32 - 5 * q^34 - 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 - 24 * q^39 - 10 * q^40 - 19 * q^41 + 21 * q^42 - 20 * q^43 - 32 * q^45 - 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 - 36 * q^50 - 47 * q^51 + 28 * q^52 + 3 * q^53 + 33 * q^54 - 44 * q^56 - 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 + 19 * q^61 + 11 * q^62 + 32 * q^63 + 47 * q^64 - 25 * q^65 + 3 * q^67 - 38 * q^68 + 3 * q^70 - 19 * q^71 - 34 * q^72 - 20 * q^73 + 22 * q^74 - 50 * q^75 + 25 * q^76 - 94 * q^78 - 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 - q^83 + 28 * q^84 - 24 * q^85 - 27 * q^86 + 58 * q^87 - 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 - 64 * q^94 + 3 * q^95 + 26 * q^96 + 21 * q^97 + 87 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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