LMFDB - Embedded newform 7381.2.a.i.1.19

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			1.19
Root			$-2.80778$ 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)

$f(q)$	$=$	$q+2.80778 q^{2} -0.314338 q^{3} +5.88364 q^{4} -0.925514 q^{5} -0.882592 q^{6} -2.15050 q^{7} +10.9044 q^{8} -2.90119 q^{9} +O(q^{10})$	\(q+2.80778 q^{2} -0.314338 q^{3} +5.88364 q^{4} -0.925514 q^{5} -0.882592 q^{6} -2.15050 q^{7} +10.9044 q^{8} -2.90119 q^{9} -2.59864 q^{10} -1.84945 q^{12} -1.28180 q^{13} -6.03813 q^{14} +0.290924 q^{15} +18.8499 q^{16} -3.37980 q^{17} -8.14591 q^{18} -2.49477 q^{19} -5.44539 q^{20} +0.675983 q^{21} -4.09102 q^{23} -3.42767 q^{24} -4.14342 q^{25} -3.59902 q^{26} +1.85497 q^{27} -12.6528 q^{28} -3.04284 q^{29} +0.816851 q^{30} +4.27147 q^{31} +31.1176 q^{32} -9.48975 q^{34} +1.99032 q^{35} -17.0696 q^{36} -10.1339 q^{37} -7.00478 q^{38} +0.402918 q^{39} -10.0922 q^{40} -8.77104 q^{41} +1.89801 q^{42} -6.55254 q^{43} +2.68509 q^{45} -11.4867 q^{46} -1.94970 q^{47} -5.92524 q^{48} -2.37535 q^{49} -11.6338 q^{50} +1.06240 q^{51} -7.54165 q^{52} +3.62325 q^{53} +5.20834 q^{54} -23.4499 q^{56} +0.784201 q^{57} -8.54363 q^{58} +14.7925 q^{59} +1.71169 q^{60} +1.00000 q^{61} +11.9934 q^{62} +6.23901 q^{63} +49.6717 q^{64} +1.18632 q^{65} +7.30698 q^{67} -19.8855 q^{68} +1.28596 q^{69} +5.58838 q^{70} -1.70617 q^{71} -31.6358 q^{72} -9.85356 q^{73} -28.4537 q^{74} +1.30243 q^{75} -14.6783 q^{76} +1.13131 q^{78} -0.979456 q^{79} -17.4459 q^{80} +8.12049 q^{81} -24.6272 q^{82} +1.70128 q^{83} +3.97724 q^{84} +3.12806 q^{85} -18.3981 q^{86} +0.956480 q^{87} +17.1623 q^{89} +7.53916 q^{90} +2.75651 q^{91} -24.0701 q^{92} -1.34268 q^{93} -5.47433 q^{94} +2.30895 q^{95} -9.78145 q^{96} -7.48635 q^{97} -6.66947 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.80778	1.98540	0.992701	−	0.120604i	$-0.0384831\pi$
$2$	2.80778	1.98540	0.992701	+	0.120604i	$0.0384831\pi$
$3$	−0.314338	−0.181483	−0.0907415	−	0.995874i	$-0.528924\pi$
$3$	−0.314338	−0.181483	−0.0907415	+	0.995874i	$0.528924\pi$
$4$	5.88364	2.94182
$5$	−0.925514	−0.413902	−0.206951	−	0.978351i	$-0.566354\pi$
$5$	−0.925514	−0.413902	−0.206951	+	0.978351i	$0.566354\pi$
$6$	−0.882592	−0.360317
$7$	−2.15050	−0.812812	−0.406406	−	0.913692i	$-0.633218\pi$
$7$	−2.15050	−0.812812	−0.406406	+	0.913692i	$0.633218\pi$
$8$	10.9044	3.85529
$9$	−2.90119	−0.967064
$10$	−2.59864	−0.821762
$11$	0	0
$11$	0	0
$12$	−1.84945	−0.533890
$13$	−1.28180	−0.355508	−0.177754	−	0.984075i	$-0.556883\pi$
$13$	−1.28180	−0.355508	−0.177754	+	0.984075i	$0.556883\pi$
$14$	−6.03813	−1.61376
$15$	0.290924	0.0751162
$16$	18.8499	4.71248
$17$	−3.37980	−0.819723	−0.409861	−	0.912148i	$-0.634423\pi$
$17$	−3.37980	−0.819723	−0.409861	+	0.912148i	$0.634423\pi$
$18$	−8.14591	−1.92001
$19$	−2.49477	−0.572340	−0.286170	−	0.958179i	$-0.592382\pi$
$19$	−2.49477	−0.572340	−0.286170	+	0.958179i	$0.592382\pi$
$20$	−5.44539	−1.21763
$21$	0.675983	0.147512
$22$	0	0
$23$	−4.09102	−0.853036	−0.426518	−	0.904479i	$-0.640260\pi$
$23$	−4.09102	−0.853036	−0.426518	+	0.904479i	$0.640260\pi$
$24$	−3.42767	−0.699669
$25$	−4.14342	−0.828685
$26$	−3.59902	−0.705825
$27$	1.85497	0.356989
$28$	−12.6528	−2.39115
$29$	−3.04284	−0.565041	−0.282521	−	0.959261i	$-0.591171\pi$
$29$	−3.04284	−0.565041	−0.282521	+	0.959261i	$0.591171\pi$
$30$	0.816851	0.149136
$31$	4.27147	0.767178	0.383589	−	0.923504i	$-0.374688\pi$
$31$	4.27147	0.767178	0.383589	+	0.923504i	$0.374688\pi$
$32$	31.1176	5.50087
$33$	0	0
$34$	−9.48975	−1.62748
$35$	1.99032	0.336425
$36$	−17.0696	−2.84493
$37$	−10.1339	−1.66600	−0.832999	−	0.553275i	$-0.813378\pi$
$37$	−10.1339	−1.66600	−0.832999	+	0.553275i	$0.813378\pi$
$38$	−7.00478	−1.13632
$39$	0.402918	0.0645186
$40$	−10.0922	−1.59571
$41$	−8.77104	−1.36981	−0.684903	−	0.728634i	$-0.740156\pi$
$41$	−8.77104	−1.36981	−0.684903	+	0.728634i	$0.740156\pi$
$42$	1.89801	0.292870
$43$	−6.55254	−0.999253	−0.499626	−	0.866241i	$-0.666529\pi$
$43$	−6.55254	−0.999253	−0.499626	+	0.866241i	$0.666529\pi$
$44$	0	0
$45$	2.68509	0.400270
$46$	−11.4867	−1.69362
$47$	−1.94970	−0.284393	−0.142197	−	0.989838i	$-0.545417\pi$
$47$	−1.94970	−0.284393	−0.142197	+	0.989838i	$0.545417\pi$
$48$	−5.92524	−0.855235
$49$	−2.37535	−0.339336
$50$	−11.6338	−1.64527
$51$	1.06240	0.148766
$52$	−7.54165	−1.04584
$53$	3.62325	0.497691	0.248846	−	0.968543i	$-0.419949\pi$
$53$	3.62325	0.497691	0.248846	+	0.968543i	$0.419949\pi$
$54$	5.20834	0.708766
$55$	0	0
$56$	−23.4499	−3.13363
$57$	0.784201	0.103870
$58$	−8.54363	−1.12183
$59$	14.7925	1.92582	0.962911	−	0.269819i	$-0.0869639\pi$
$59$	14.7925	1.92582	0.962911	+	0.269819i	$0.0869639\pi$
$60$	1.71169	0.220978
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	11.9934	1.52316
$63$	6.23901	0.786042
$64$	49.6717	6.20896
$65$	1.18632	0.147145
$66$	0	0
$67$	7.30698	0.892690	0.446345	−	0.894861i	$-0.352725\pi$
$67$	7.30698	0.892690	0.446345	+	0.894861i	$0.352725\pi$
$68$	−19.8855	−2.41148
$69$	1.28596	0.154812
$70$	5.58838	0.667939
$71$	−1.70617	−0.202486	−0.101243	−	0.994862i	$-0.532282\pi$
$71$	−1.70617	−0.202486	−0.101243	+	0.994862i	$0.532282\pi$
$72$	−31.6358	−3.72831
$73$	−9.85356	−1.15327	−0.576636	−	0.817001i	$-0.695635\pi$
$73$	−9.85356	−1.15327	−0.576636	+	0.817001i	$0.695635\pi$
$74$	−28.4537	−3.30767
$75$	1.30243	0.150392
$76$	−14.6783	−1.68372
$77$	0	0
$78$	1.13131	0.128095
$79$	−0.979456	−0.110197	−0.0550987	−	0.998481i	$-0.517547\pi$
$79$	−0.979456	−0.110197	−0.0550987	+	0.998481i	$0.517547\pi$
$80$	−17.4459	−1.95051
$81$	8.12049	0.902277
$82$	−24.6272	−2.71962
$83$	1.70128	0.186740	0.0933700	−	0.995631i	$-0.470236\pi$
$83$	1.70128	0.186740	0.0933700	+	0.995631i	$0.470236\pi$
$84$	3.97724	0.433952
$85$	3.12806	0.339285
$86$	−18.3981	−1.98392
$87$	0.956480	0.102545
$88$	0	0
$89$	17.1623	1.81920	0.909602	−	0.415481i	$-0.136387\pi$
$89$	17.1623	1.81920	0.909602	+	0.415481i	$0.136387\pi$
$90$	7.53916	0.794697
$91$	2.75651	0.288961
$92$	−24.0701	−2.50948
$93$	−1.34268	−0.139230
$94$	−5.47433	−0.564634
$95$	2.30895	0.236893
$96$	−9.78145	−0.998315
$97$	−7.48635	−0.760123	−0.380062	−	0.924961i	$-0.624097\pi$
$97$	−7.48635	−0.760123	−0.380062	+	0.924961i	$0.624097\pi$
$98$	−6.66947	−0.673718
$99$	0	0
$100$	−24.3784	−2.43784
$101$	−13.8305	−1.37619	−0.688093	−	0.725623i	$-0.741552\pi$
$101$	−13.8305	−1.37619	−0.688093	+	0.725623i	$0.741552\pi$
$102$	2.98299	0.295360
$103$	18.9824	1.87039	0.935197	−	0.354127i	$-0.115222\pi$
$103$	18.9824	1.87039	0.935197	+	0.354127i	$0.115222\pi$
$104$	−13.9773	−1.37058
$105$	−0.625632	−0.0610554
$106$	10.1733	0.988116
$107$	4.24599	0.410475	0.205237	−	0.978712i	$-0.434203\pi$
$107$	4.24599	0.410475	0.205237	+	0.978712i	$0.434203\pi$
$108$	10.9140	1.05020
$109$	3.61620	0.346369	0.173185	−	0.984889i	$-0.444594\pi$
$109$	3.61620	0.346369	0.173185	+	0.984889i	$0.444594\pi$
$110$	0	0
$111$	3.18546	0.302350
$112$	−40.5367	−3.83036
$113$	−9.77038	−0.919120	−0.459560	−	0.888147i	$-0.651993\pi$
$113$	−9.77038	−0.919120	−0.459560	+	0.888147i	$0.651993\pi$
$114$	2.20187	0.206224
$115$	3.78629	0.353074
$116$	−17.9030	−1.66225
$117$	3.71875	0.343799
$118$	41.5342	3.82353
$119$	7.26827	0.666281
$120$	3.17235	0.289595
$121$	0	0
$122$	2.80778	0.254205
$123$	2.75707	0.248597
$124$	25.1318	2.25690
$125$	8.46237	0.756897
$126$	17.5178	1.56061
$127$	−14.8970	−1.32189	−0.660947	−	0.750432i	$-0.729845\pi$
$127$	−14.8970	−1.32189	−0.660947	+	0.750432i	$0.729845\pi$
$128$	77.2320	6.82641
$129$	2.05971	0.181347
$130$	3.33094	0.292143
$131$	−5.18238	−0.452787	−0.226393	−	0.974036i	$-0.572693\pi$
$131$	−5.18238	−0.452787	−0.226393	+	0.974036i	$0.572693\pi$
$132$	0	0
$133$	5.36501	0.465205
$134$	20.5164	1.77235
$135$	−1.71680	−0.147758
$136$	−36.8548	−3.16027
$137$	0.507156	0.0433292	0.0216646	−	0.999765i	$-0.493103\pi$
$137$	0.507156	0.0433292	0.0216646	+	0.999765i	$0.493103\pi$
$138$	3.61070	0.307363
$139$	11.6343	0.986809	0.493405	−	0.869800i	$-0.335752\pi$
$139$	11.6343	0.986809	0.493405	+	0.869800i	$0.335752\pi$
$140$	11.7103	0.989701
$141$	0.612865	0.0516125
$142$	−4.79056	−0.402015
$143$	0	0
$144$	−54.6872	−4.55727
$145$	2.81619	0.233872
$146$	−27.6666	−2.28971
$147$	0.746663	0.0615837
$148$	−59.6240	−4.90106
$149$	−6.22561	−0.510022	−0.255011	−	0.966938i	$-0.582079\pi$
$149$	−6.22561	−0.510022	−0.255011	+	0.966938i	$0.582079\pi$
$150$	3.65695	0.298589
$151$	−15.4941	−1.26089	−0.630447	−	0.776232i	$-0.717128\pi$
$151$	−15.4941	−1.26089	−0.630447	+	0.776232i	$0.717128\pi$
$152$	−27.2040	−2.20654
$153$	9.80546	0.792724
$154$	0	0
$155$	−3.95330	−0.317537
$156$	2.37063	0.189802
$157$	5.74821	0.458757	0.229379	−	0.973337i	$-0.426331\pi$
$157$	5.74821	0.458757	0.229379	+	0.973337i	$0.426331\pi$
$158$	−2.75010	−0.218786
$159$	−1.13892	−0.0903225
$160$	−28.7998	−2.27682
$161$	8.79773	0.693358
$162$	22.8006	1.79138
$163$	−20.2692	−1.58761	−0.793805	−	0.608173i	$-0.791903\pi$
$163$	−20.2692	−1.58761	−0.793805	+	0.608173i	$0.791903\pi$
$164$	−51.6056	−4.02972
$165$	0	0
$166$	4.77683	0.370754
$167$	16.4779	1.27510	0.637548	−	0.770411i	$-0.279949\pi$
$167$	16.4779	1.27510	0.637548	+	0.770411i	$0.279949\pi$
$168$	7.37120	0.568700
$169$	−11.3570	−0.873614
$170$	8.78290	0.673617
$171$	7.23781	0.553489
$172$	−38.5528	−2.93962
$173$	−9.01499	−0.685397	−0.342698	−	0.939445i	$-0.611341\pi$
$173$	−9.01499	−0.685397	−0.342698	+	0.939445i	$0.611341\pi$
$174$	2.68559	0.203594
$175$	8.91043	0.673565
$176$	0	0
$177$	−4.64985	−0.349504
$178$	48.1881	3.61185
$179$	−6.57826	−0.491683	−0.245841	−	0.969310i	$-0.579064\pi$
$179$	−6.57826	−0.491683	−0.245841	+	0.969310i	$0.579064\pi$
$180$	15.7981	1.17752
$181$	6.52787	0.485213	0.242606	−	0.970125i	$-0.421998\pi$
$181$	6.52787	0.485213	0.242606	+	0.970125i	$0.421998\pi$
$182$	7.73968	0.573704
$183$	−0.314338	−0.0232365
$184$	−44.6101	−3.28870
$185$	9.37903	0.689560
$186$	−3.76996	−0.276427
$187$	0	0
$188$	−11.4713	−0.836633
$189$	−3.98911	−0.290165
$190$	6.48302	0.470328
$191$	0.270665	0.0195847	0.00979233	−	0.999952i	$-0.496883\pi$
$191$	0.270665	0.0195847	0.00979233	+	0.999952i	$0.496883\pi$
$192$	−15.6137	−1.12682
$193$	−14.1506	−1.01858	−0.509290	−	0.860595i	$-0.670092\pi$
$193$	−14.1506	−1.01858	−0.509290	+	0.860595i	$0.670092\pi$
$194$	−21.0200	−1.50915
$195$	−0.372907	−0.0267044
$196$	−13.9757	−0.998265
$197$	−4.32566	−0.308190	−0.154095	−	0.988056i	$-0.549246\pi$
$197$	−4.32566	−0.308190	−0.154095	+	0.988056i	$0.549246\pi$
$198$	0	0
$199$	−15.7244	−1.11467	−0.557336	−	0.830287i	$-0.688176\pi$
$199$	−15.7244	−1.11467	−0.557336	+	0.830287i	$0.688176\pi$
$200$	−45.1816	−3.19482
$201$	−2.29686	−0.162008
$202$	−38.8330	−2.73228
$203$	6.54363	0.459273
$204$	6.25078	0.437642
$205$	8.11772	0.566966
$206$	53.2985	3.71348
$207$	11.8688	0.824940
$208$	−24.1618	−1.67532
$209$	0	0
$210$	−1.75664	−0.121220
$211$	16.5499	1.13934	0.569672	−	0.821872i	$-0.307070\pi$
$211$	16.5499	1.13934	0.569672	+	0.821872i	$0.307070\pi$
$212$	21.3179	1.46412
$213$	0.536315	0.0367477
$214$	11.9218	0.814957
$215$	6.06447	0.413593
$216$	20.2273	1.37629
$217$	−9.18579	−0.623572
$218$	10.1535	0.687682
$219$	3.09735	0.209299
$220$	0	0
$221$	4.33224	0.291418
$222$	8.94407	0.600286
$223$	7.41270	0.496391	0.248196	−	0.968710i	$-0.420162\pi$
$223$	7.41270	0.496391	0.248196	+	0.968710i	$0.420162\pi$
$224$	−66.9185	−4.47118
$225$	12.0209	0.801391
$226$	−27.4331	−1.82482
$227$	7.12725	0.473052	0.236526	−	0.971625i	$-0.423991\pi$
$227$	7.12725	0.473052	0.236526	+	0.971625i	$0.423991\pi$
$228$	4.61396	0.305567
$229$	−7.06659	−0.466973	−0.233487	−	0.972360i	$-0.575014\pi$
$229$	−7.06659	−0.466973	−0.233487	+	0.972360i	$0.575014\pi$
$230$	10.6311	0.700993
$231$	0	0
$232$	−33.1804	−2.17840
$233$	8.29637	0.543514	0.271757	−	0.962366i	$-0.412395\pi$
$233$	8.29637	0.543514	0.271757	+	0.962366i	$0.412395\pi$
$234$	10.4414	0.682578
$235$	1.80447	0.117711
$236$	87.0338	5.66542
$237$	0.307880	0.0199990
$238$	20.4077	1.32284
$239$	−22.5856	−1.46094	−0.730470	−	0.682945i	$-0.760699\pi$
$239$	−22.5856	−1.46094	−0.730470	+	0.682945i	$0.760699\pi$
$240$	5.48389	0.353984
$241$	−25.6415	−1.65171	−0.825857	−	0.563880i	$-0.809308\pi$
$241$	−25.6415	−1.65171	−0.825857	+	0.563880i	$0.809308\pi$
$242$	0	0
$243$	−8.11748	−0.520736
$244$	5.88364	0.376661
$245$	2.19842	0.140452
$246$	7.74125	0.493564
$247$	3.19780	0.203471
$248$	46.5778	2.95770
$249$	−0.534778	−0.0338901
$250$	23.7605	1.50274
$251$	8.82926	0.557298	0.278649	−	0.960393i	$-0.410113\pi$
$251$	8.82926	0.557298	0.278649	+	0.960393i	$0.410113\pi$
$252$	36.7081	2.31239
$253$	0	0
$254$	−41.8275	−2.62449
$255$	−0.983266	−0.0615745
$256$	117.507	7.34420
$257$	−0.859825	−0.0536344	−0.0268172	−	0.999640i	$-0.508537\pi$
$257$	−0.859825	−0.0536344	−0.0268172	+	0.999640i	$0.508537\pi$
$258$	5.78322	0.360047
$259$	21.7929	1.35414
$260$	6.97990	0.432875
$261$	8.82787	0.546431
$262$	−14.5510	−0.898963
$263$	25.3778	1.56486	0.782430	−	0.622739i	$-0.213980\pi$
$263$	25.3778	1.56486	0.782430	+	0.622739i	$0.213980\pi$
$264$	0	0
$265$	−3.35336	−0.205996
$266$	15.0638	0.923619
$267$	−5.39477	−0.330155
$268$	42.9916	2.62613
$269$	−20.8909	−1.27374	−0.636869	−	0.770972i	$-0.719771\pi$
$269$	−20.8909	−1.27374	−0.636869	+	0.770972i	$0.719771\pi$
$270$	−4.82039	−0.293360
$271$	9.70675	0.589643	0.294821	−	0.955552i	$-0.404740\pi$
$271$	9.70675	0.589643	0.294821	+	0.955552i	$0.404740\pi$
$272$	−63.7090	−3.86293
$273$	−0.866476	−0.0524415
$274$	1.42398	0.0860259
$275$	0	0
$276$	7.56613	0.455428
$277$	13.9726	0.839533	0.419767	−	0.907632i	$-0.362112\pi$
$277$	13.9726	0.839533	0.419767	+	0.907632i	$0.362112\pi$
$278$	32.6666	1.95921
$279$	−12.3924	−0.741911
$280$	21.7032	1.29702
$281$	−24.9986	−1.49129	−0.745646	−	0.666343i	$-0.767859\pi$
$281$	−24.9986	−1.49129	−0.745646	+	0.666343i	$0.767859\pi$
$282$	1.72079	0.102472
$283$	11.3548	0.674971	0.337486	−	0.941331i	$-0.390424\pi$
$283$	11.3548	0.674971	0.337486	+	0.941331i	$0.390424\pi$
$284$	−10.0385	−0.595676
$285$	−0.725789	−0.0429920
$286$	0	0
$287$	18.8621	1.11340
$288$	−90.2782	−5.31969
$289$	−5.57692	−0.328054
$290$	7.90725	0.464330
$291$	2.35324	0.137949
$292$	−57.9748	−3.39272
$293$	2.47923	0.144838	0.0724190	−	0.997374i	$-0.476928\pi$
$293$	2.47923	0.144838	0.0724190	+	0.997374i	$0.476928\pi$
$294$	2.09647	0.122268
$295$	−13.6907	−0.797102
$296$	−110.504	−6.42290
$297$	0	0
$298$	−17.4802	−1.01260
$299$	5.24387	0.303261
$300$	7.66305	0.442427
$301$	14.0912	0.812205
$302$	−43.5041	−2.50338
$303$	4.34745	0.249754
$304$	−47.0263	−2.69714
$305$	−0.925514	−0.0529948
$306$	27.5316	1.57388
$307$	−9.35056	−0.533665	−0.266832	−	0.963743i	$-0.585977\pi$
$307$	−9.35056	−0.533665	−0.266832	+	0.963743i	$0.585977\pi$
$308$	0	0
$309$	−5.96690	−0.339445
$310$	−11.1000	−0.630438
$311$	−25.7183	−1.45835	−0.729175	−	0.684327i	$-0.760096\pi$
$311$	−25.7183	−1.45835	−0.729175	+	0.684327i	$0.760096\pi$
$312$	4.39359	0.248738
$313$	21.0513	1.18989	0.594944	−	0.803767i	$-0.297174\pi$
$313$	21.0513	1.18989	0.594944	+	0.803767i	$0.297174\pi$
$314$	16.1397	0.910818
$315$	−5.77429	−0.325345
$316$	−5.76276	−0.324181
$317$	11.2767	0.633362	0.316681	−	0.948532i	$-0.397432\pi$
$317$	11.2767	0.633362	0.316681	+	0.948532i	$0.397432\pi$
$318$	−3.19785	−0.179326
$319$	0	0
$320$	−45.9718	−2.56990
$321$	−1.33467	−0.0744942
$322$	24.7021	1.37659
$323$	8.43184	0.469160
$324$	47.7780	2.65433
$325$	5.31104	0.294604
$326$	−56.9116	−3.15204
$327$	−1.13671	−0.0628601
$328$	−95.6430	−5.28100
$329$	4.19283	0.231158
$330$	0	0
$331$	8.75133	0.481016	0.240508	−	0.970647i	$-0.422686\pi$
$331$	8.75133	0.481016	0.240508	+	0.970647i	$0.422686\pi$
$332$	10.0097	0.549355
$333$	29.4003	1.61113
$334$	46.2662	2.53158
$335$	−6.76272	−0.369487
$336$	12.7422	0.695145
$337$	9.44596	0.514554	0.257277	−	0.966338i	$-0.417175\pi$
$337$	9.44596	0.514554	0.257277	+	0.966338i	$0.417175\pi$
$338$	−31.8879	−1.73448
$339$	3.07120	0.166805
$340$	18.4043	0.998116
$341$	0	0
$342$	20.3222	1.09890
$343$	20.1617	1.08863
$344$	−71.4515	−3.85241
$345$	−1.19018	−0.0640769
$346$	−25.3121	−1.36079
$347$	33.9545	1.82277	0.911385	−	0.411554i	$-0.135014\pi$
$347$	33.9545	1.82277	0.911385	+	0.411554i	$0.135014\pi$
$348$	5.62758	0.301670
$349$	−14.7560	−0.789869	−0.394935	−	0.918709i	$-0.629233\pi$
$349$	−14.7560	−0.789869	−0.394935	+	0.918709i	$0.629233\pi$
$350$	25.0185	1.33730
$351$	−2.37770	−0.126912
$352$	0	0
$353$	34.1765	1.81903	0.909516	−	0.415668i	$-0.136452\pi$
$353$	34.1765	1.81903	0.909516	+	0.415668i	$0.136452\pi$
$354$	−13.0558	−0.693906
$355$	1.57909	0.0838093
$356$	100.977	5.35177
$357$	−2.28469	−0.120919
$358$	−18.4703	−0.976187
$359$	21.4057	1.12975	0.564874	−	0.825177i	$-0.308925\pi$
$359$	21.4057	1.12975	0.564874	+	0.825177i	$0.308925\pi$
$360$	29.2793	1.54316
$361$	−12.7761	−0.672427
$362$	18.3288	0.963342
$363$	0	0
$364$	16.2183	0.850071
$365$	9.11961	0.477342
$366$	−0.882592	−0.0461338
$367$	−17.5398	−0.915569	−0.457785	−	0.889063i	$-0.651357\pi$
$367$	−17.5398	−0.915569	−0.457785	+	0.889063i	$0.651357\pi$
$368$	−77.1153	−4.01991
$369$	25.4465	1.32469
$370$	26.3343	1.36905
$371$	−7.79179	−0.404529
$372$	−7.89987	−0.409589
$373$	25.2457	1.30717	0.653586	−	0.756852i	$-0.273264\pi$
$373$	25.2457	1.30717	0.653586	+	0.756852i	$0.273264\pi$
$374$	0	0
$375$	−2.66004	−0.137364
$376$	−21.2603	−1.09642
$377$	3.90032	0.200876
$378$	−11.2005	−0.576094
$379$	−37.0350	−1.90236	−0.951180	−	0.308636i	$-0.900127\pi$
$379$	−37.0350	−1.90236	−0.951180	+	0.308636i	$0.900127\pi$
$380$	13.5850	0.696896
$381$	4.68269	0.239901
$382$	0.759969	0.0388834
$383$	−23.3312	−1.19217	−0.596085	−	0.802922i	$-0.703278\pi$
$383$	−23.3312	−1.19217	−0.596085	+	0.802922i	$0.703278\pi$
$384$	−24.2769	−1.23888
$385$	0	0
$386$	−39.7317	−2.02229
$387$	19.0102	0.966341
$388$	−44.0469	−2.23614
$389$	−20.1435	−1.02132	−0.510658	−	0.859784i	$-0.670598\pi$
$389$	−20.1435	−1.02132	−0.510658	+	0.859784i	$0.670598\pi$
$390$	−1.04704	−0.0530189
$391$	13.8268	0.699253
$392$	−25.9018	−1.30824
$393$	1.62902	0.0821731
$394$	−12.1455	−0.611881
$395$	0.906500	0.0456110
$396$	0	0
$397$	31.2800	1.56990	0.784949	−	0.619561i	$-0.212689\pi$
$397$	31.2800	1.56990	0.784949	+	0.619561i	$0.212689\pi$
$398$	−44.1506	−2.21307
$399$	−1.68642	−0.0844268
$400$	−78.1032	−3.90516
$401$	7.49218	0.374142	0.187071	−	0.982346i	$-0.440101\pi$
$401$	7.49218	0.374142	0.187071	+	0.982346i	$0.440101\pi$
$402$	−6.44908	−0.321651
$403$	−5.47517	−0.272738
$404$	−81.3736	−4.04849
$405$	−7.51563	−0.373454
$406$	18.3731	0.911841
$407$	0	0
$408$	11.5848	0.573535
$409$	27.4150	1.35558	0.677792	−	0.735253i	$-0.262937\pi$
$409$	27.4150	1.35558	0.677792	+	0.735253i	$0.262937\pi$
$410$	22.7928	1.12566
$411$	−0.159418	−0.00786352
$412$	111.686	5.50236
$413$	−31.8113	−1.56533
$414$	33.3251	1.63784
$415$	−1.57456	−0.0772922
$416$	−39.8866	−1.95560
$417$	−3.65710	−0.179089
$418$	0	0
$419$	−7.28945	−0.356113	−0.178057	−	0.984020i	$-0.556981\pi$
$419$	−7.28945	−0.356113	−0.178057	+	0.984020i	$0.556981\pi$
$420$	−3.68099	−0.179614
$421$	11.5102	0.560972	0.280486	−	0.959858i	$-0.409504\pi$
$421$	11.5102	0.560972	0.280486	+	0.959858i	$0.409504\pi$
$422$	46.4686	2.26206
$423$	5.65646	0.275026
$424$	39.5093	1.91874
$425$	14.0040	0.679292
$426$	1.50586	0.0729589
$427$	−2.15050	−0.104070
$428$	24.9818	1.20754
$429$	0	0
$430$	17.0277	0.821148
$431$	−32.4200	−1.56161	−0.780807	−	0.624772i	$-0.785192\pi$
$431$	−32.4200	−1.56161	−0.780807	+	0.624772i	$0.785192\pi$
$432$	34.9660	1.68230
$433$	7.53054	0.361894	0.180947	−	0.983493i	$-0.442084\pi$
$433$	7.53054	0.361894	0.180947	+	0.983493i	$0.442084\pi$
$434$	−25.7917	−1.23804
$435$	−0.885235	−0.0424438
$436$	21.2764	1.01896
$437$	10.2062	0.488227
$438$	8.69667	0.415543
$439$	38.7914	1.85141	0.925705	−	0.378246i	$-0.123473\pi$
$439$	38.7914	1.85141	0.925705	+	0.378246i	$0.123473\pi$
$440$	0	0
$441$	6.89135	0.328159
$442$	12.1640	0.578581
$443$	−33.6344	−1.59802	−0.799008	−	0.601320i	$-0.794642\pi$
$443$	−33.6344	−1.59802	−0.799008	+	0.601320i	$0.794642\pi$
$444$	18.7421	0.889459
$445$	−15.8840	−0.752973
$446$	20.8132	0.985535
$447$	1.95695	0.0925604
$448$	−106.819	−5.04672
$449$	0.126699	0.00597931	0.00298966	−	0.999996i	$-0.499048\pi$
$449$	0.126699	0.00597931	0.00298966	+	0.999996i	$0.499048\pi$
$450$	33.7520	1.59108
$451$	0	0
$452$	−57.4854	−2.70389
$453$	4.87039	0.228831
$454$	20.0118	0.939198
$455$	−2.55119	−0.119602
$456$	8.55125	0.400449
$457$	−32.4488	−1.51789	−0.758947	−	0.651153i	$-0.774286\pi$
$457$	−32.4488	−1.51789	−0.758947	+	0.651153i	$0.774286\pi$
$458$	−19.8414	−0.927129
$459$	−6.26943	−0.292632
$460$	22.2772	1.03868
$461$	32.4994	1.51365	0.756825	−	0.653618i	$-0.226750\pi$
$461$	32.4994	1.51365	0.756825	+	0.653618i	$0.226750\pi$
$462$	0	0
$463$	14.2867	0.663958	0.331979	−	0.943287i	$-0.392284\pi$
$463$	14.2867	0.663958	0.331979	+	0.943287i	$0.392284\pi$
$464$	−57.3573	−2.66275
$465$	1.24267	0.0576276
$466$	23.2944	1.07909
$467$	35.9475	1.66345	0.831726	−	0.555187i	$-0.187353\pi$
$467$	35.9475	1.66345	0.831726	+	0.555187i	$0.187353\pi$
$468$	21.8798	1.01139
$469$	−15.7137	−0.725590
$470$	5.06657	0.233704
$471$	−1.80688	−0.0832567
$472$	161.304	7.42460
$473$	0	0
$474$	0.864460	0.0397059
$475$	10.3369	0.474290
$476$	42.7639	1.96008
$477$	−10.5117	−0.481299
$478$	−63.4154	−2.90055
$479$	−17.5255	−0.800762	−0.400381	−	0.916349i	$-0.631122\pi$
$479$	−17.5255	−0.800762	−0.400381	+	0.916349i	$0.631122\pi$
$480$	9.05286	0.413205
$481$	12.9896	0.592275
$482$	−71.9957	−3.27932
$483$	−2.76546	−0.125833
$484$	0	0
$485$	6.92872	0.314617
$486$	−22.7921	−1.03387
$487$	17.3183	0.784769	0.392384	−	0.919801i	$-0.371650\pi$
$487$	17.3183	0.784769	0.392384	+	0.919801i	$0.371650\pi$
$488$	10.9044	0.493619
$489$	6.37139	0.288124
$490$	6.17268	0.278853
$491$	18.0984	0.816768	0.408384	−	0.912810i	$-0.366092\pi$
$491$	18.0984	0.816768	0.408384	+	0.912810i	$0.366092\pi$
$492$	16.2216	0.731326
$493$	10.2842	0.463177
$494$	8.97873	0.403972
$495$	0	0
$496$	80.5168	3.61531
$497$	3.66913	0.164583
$498$	−1.50154	−0.0672855
$499$	7.27284	0.325577	0.162788	−	0.986661i	$-0.447951\pi$
$499$	7.27284	0.325577	0.162788	+	0.986661i	$0.447951\pi$
$500$	49.7895	2.22665
$501$	−5.17961	−0.231408
$502$	24.7906	1.10646
$503$	−21.3581	−0.952312	−0.476156	−	0.879361i	$-0.657970\pi$
$503$	−21.3581	−0.952312	−0.476156	+	0.879361i	$0.657970\pi$
$504$	68.0327	3.03042
$505$	12.8003	0.569606
$506$	0	0
$507$	3.56993	0.158546
$508$	−87.6485	−3.88877
$509$	−34.8721	−1.54568	−0.772840	−	0.634601i	$-0.781165\pi$
$509$	−34.8721	−1.54568	−0.772840	+	0.634601i	$0.781165\pi$
$510$	−2.76080	−0.122250
$511$	21.1901	0.937394
$512$	175.470	7.75477
$513$	−4.62772	−0.204319
$514$	−2.41420	−0.106486
$515$	−17.5685	−0.774161
$516$	12.1186	0.533491
$517$	0	0
$518$	61.1896	2.68852
$519$	2.83375	0.124388
$520$	12.9362	0.567288
$521$	19.0611	0.835083	0.417541	−	0.908658i	$-0.362892\pi$
$521$	19.0611	0.835083	0.417541	+	0.908658i	$0.362892\pi$
$522$	24.7867	1.08489
$523$	3.89662	0.170387	0.0851936	−	0.996364i	$-0.472849\pi$
$523$	3.89662	0.170387	0.0851936	+	0.996364i	$0.472849\pi$
$524$	−30.4912	−1.33202
$525$	−2.80089	−0.122241
$526$	71.2552	3.10687
$527$	−14.4367	−0.628874
$528$	0	0
$529$	−6.26357	−0.272329
$530$	−9.41551	−0.408984
$531$	−42.9159	−1.86239
$532$	31.5658	1.36855
$533$	11.2427	0.486977
$534$	−15.1473	−0.655489
$535$	−3.92972	−0.169897
$536$	79.6783	3.44158
$537$	2.06780	0.0892320
$538$	−58.6570	−2.52888
$539$	0	0
$540$	−10.1010	−0.434679
$541$	12.8680	0.553240	0.276620	−	0.960979i	$-0.410786\pi$
$541$	12.8680	0.553240	0.276620	+	0.960979i	$0.410786\pi$
$542$	27.2544	1.17068
$543$	−2.05196	−0.0880579
$544$	−105.171	−4.50919
$545$	−3.34684	−0.143363
$546$	−2.43288	−0.104117
$547$	−34.3657	−1.46937	−0.734685	−	0.678408i	$-0.762670\pi$
$547$	−34.3657	−1.46937	−0.734685	+	0.678408i	$0.762670\pi$
$548$	2.98392	0.127467
$549$	−2.90119	−0.123820
$550$	0	0
$551$	7.59120	0.323396
$552$	14.0226	0.596843
$553$	2.10632	0.0895698
$554$	39.2321	1.66681
$555$	−2.94818	−0.125143
$556$	68.4520	2.90301
$557$	12.3790	0.524514	0.262257	−	0.964998i	$-0.415533\pi$
$557$	12.3790	0.524514	0.262257	+	0.964998i	$0.415533\pi$
$558$	−34.7950	−1.47299
$559$	8.39905	0.355242
$560$	37.5173	1.58540
$561$	0	0
$562$	−70.1906	−2.96081
$563$	−9.49421	−0.400133	−0.200067	−	0.979782i	$-0.564116\pi$
$563$	−9.49421	−0.400133	−0.200067	+	0.979782i	$0.564116\pi$
$564$	3.60587	0.151835
$565$	9.04263	0.380426
$566$	31.8817	1.34009
$567$	−17.4631	−0.733382
$568$	−18.6048	−0.780641
$569$	−6.04259	−0.253318	−0.126659	−	0.991946i	$-0.540425\pi$
$569$	−6.04259	−0.253318	−0.126659	+	0.991946i	$0.540425\pi$
$570$	−2.03786	−0.0853565
$571$	1.82447	0.0763518	0.0381759	−	0.999271i	$-0.487845\pi$
$571$	1.82447	0.0763518	0.0381759	+	0.999271i	$0.487845\pi$
$572$	0	0
$573$	−0.0850803	−0.00355428
$574$	52.9607	2.21054
$575$	16.9508	0.706898
$576$	−144.107	−6.00446
$577$	23.1142	0.962257	0.481128	−	0.876650i	$-0.340227\pi$
$577$	23.1142	0.962257	0.481128	+	0.876650i	$0.340227\pi$
$578$	−15.6588	−0.651320
$579$	4.44805	0.184855
$580$	16.5694	0.688009
$581$	−3.65861	−0.151785
$582$	6.60739	0.273885
$583$	0	0
$584$	−107.447	−4.44620
$585$	−3.44175	−0.142299
$586$	6.96113	0.287562
$587$	7.48479	0.308930	0.154465	−	0.987998i	$-0.450635\pi$
$587$	7.48479	0.308930	0.154465	+	0.987998i	$0.450635\pi$
$588$	4.39309	0.181168
$589$	−10.6563	−0.439087
$590$	−38.4404	−1.58257
$591$	1.35972	0.0559313
$592$	−191.022	−7.85098
$593$	−32.3650	−1.32907	−0.664535	−	0.747257i	$-0.731370\pi$
$593$	−32.3650	−1.32907	−0.664535	+	0.747257i	$0.731370\pi$
$594$	0	0
$595$	−6.72688	−0.275775
$596$	−36.6293	−1.50039
$597$	4.94276	0.202294
$598$	14.7236	0.602094
$599$	−4.41532	−0.180405	−0.0902025	−	0.995923i	$-0.528751\pi$
$599$	−4.41532	−0.180405	−0.0902025	+	0.995923i	$0.528751\pi$
$600$	14.2023	0.579805
$601$	−6.09179	−0.248489	−0.124245	−	0.992252i	$-0.539651\pi$
$601$	−6.09179	−0.248489	−0.124245	+	0.992252i	$0.539651\pi$
$602$	39.5651	1.61255
$603$	−21.1990	−0.863288
$604$	−91.1618	−3.70932
$605$	0	0
$606$	12.2067	0.495862
$607$	5.02420	0.203926	0.101963	−	0.994788i	$-0.467488\pi$
$607$	5.02420	0.203926	0.101963	+	0.994788i	$0.467488\pi$
$608$	−77.6314	−3.14837
$609$	−2.05691	−0.0833502
$610$	−2.59864	−0.105216
$611$	2.49913	0.101104
$612$	57.6918	2.33205
$613$	−24.6618	−0.996081	−0.498041	−	0.867154i	$-0.665947\pi$
$613$	−24.6618	−0.996081	−0.498041	+	0.867154i	$0.665947\pi$
$614$	−26.2543	−1.05954
$615$	−2.55171	−0.102895
$616$	0	0
$617$	−20.6110	−0.829769	−0.414884	−	0.909874i	$-0.636178\pi$
$617$	−20.6110	−0.829769	−0.414884	+	0.909874i	$0.636178\pi$
$618$	−16.7537	−0.673934
$619$	−9.61501	−0.386460	−0.193230	−	0.981153i	$-0.561896\pi$
$619$	−9.61501	−0.386460	−0.193230	+	0.981153i	$0.561896\pi$
$620$	−23.2598	−0.934136
$621$	−7.58870	−0.304524
$622$	−72.2113	−2.89541
$623$	−36.9076	−1.47867
$624$	7.59498	0.304042
$625$	12.8851	0.515403
$626$	59.1073	2.36240
$627$	0	0
$628$	33.8204	1.34958
$629$	34.2505	1.36566
$630$	−16.2130	−0.645939
$631$	−5.13378	−0.204372	−0.102186	−	0.994765i	$-0.532584\pi$
$631$	−5.13378	−0.204372	−0.102186	+	0.994765i	$0.532584\pi$
$632$	−10.6804	−0.424843
$633$	−5.20227	−0.206772
$634$	31.6625	1.25748
$635$	13.7874	0.547135
$636$	−6.70101	−0.265712
$637$	3.04473	0.120636
$638$	0	0
$639$	4.94994	0.195817
$640$	−71.4793	−2.82547
$641$	29.1002	1.14939	0.574694	−	0.818368i	$-0.305121\pi$
$641$	29.1002	1.14939	0.574694	+	0.818368i	$0.305121\pi$
$642$	−3.74747	−0.147901
$643$	16.4391	0.648295	0.324148	−	0.946007i	$-0.394923\pi$
$643$	16.4391	0.648295	0.324148	+	0.946007i	$0.394923\pi$
$644$	51.7627	2.03973
$645$	−1.90629	−0.0750601
$646$	23.6748	0.931472
$647$	−4.33767	−0.170531	−0.0852657	−	0.996358i	$-0.527174\pi$
$647$	−4.33767	−0.170531	−0.0852657	+	0.996358i	$0.527174\pi$
$648$	88.5491	3.47854
$649$	0	0
$650$	14.9123	0.584907
$651$	2.88744	0.113168
$652$	−119.257	−4.67046
$653$	−10.1254	−0.396237	−0.198118	−	0.980178i	$-0.563483\pi$
$653$	−10.1254	−0.396237	−0.198118	+	0.980178i	$0.563483\pi$
$654$	−3.19163	−0.124803
$655$	4.79636	0.187409
$656$	−165.333	−6.45519
$657$	28.5871	1.11529
$658$	11.7726	0.458942
$659$	−39.5009	−1.53873	−0.769367	−	0.638807i	$-0.779428\pi$
$659$	−39.5009	−1.53873	−0.769367	+	0.638807i	$0.779428\pi$
$660$	0	0
$661$	−9.22386	−0.358767	−0.179383	−	0.983779i	$-0.557410\pi$
$661$	−9.22386	−0.358767	−0.179383	+	0.983779i	$0.557410\pi$
$662$	24.5718	0.955011
$663$	−1.36179	−0.0528874
$664$	18.5515	0.719937
$665$	−4.96539	−0.192550
$666$	82.5496	3.19873
$667$	12.4483	0.482001
$668$	96.9497	3.75110
$669$	−2.33009	−0.0900865
$670$	−18.9882	−0.733579
$671$	0	0
$672$	21.0350	0.811443
$673$	−38.6270	−1.48896	−0.744481	−	0.667644i	$-0.767303\pi$
$673$	−38.6270	−1.48896	−0.744481	+	0.667644i	$0.767303\pi$
$674$	26.5222	1.02160
$675$	−7.68592	−0.295831
$676$	−66.8204	−2.57002
$677$	−40.8075	−1.56836	−0.784180	−	0.620534i	$-0.786916\pi$
$677$	−40.8075	−1.56836	−0.784180	+	0.620534i	$0.786916\pi$
$678$	8.62326	0.331174
$679$	16.0994	0.617838
$680$	34.1096	1.30804
$681$	−2.24036	−0.0858509
$682$	0	0
$683$	35.7397	1.36754	0.683770	−	0.729698i	$-0.260339\pi$
$683$	35.7397	1.36754	0.683770	+	0.729698i	$0.260339\pi$
$684$	42.5847	1.62827
$685$	−0.469380	−0.0179341
$686$	56.6096	2.16137
$687$	2.22130	0.0847477
$688$	−123.515	−4.70896
$689$	−4.64428	−0.176933
$690$	−3.34175	−0.127218
$691$	−45.6560	−1.73684	−0.868418	−	0.495833i	$-0.834863\pi$
$691$	−45.6560	−1.73684	−0.868418	+	0.495833i	$0.834863\pi$
$692$	−53.0409	−2.01631
$693$	0	0
$694$	95.3367	3.61893
$695$	−10.7677	−0.408443
$696$	10.4298	0.395342
$697$	29.6444	1.12286
$698$	−41.4316	−1.56821
$699$	−2.60786	−0.0986385
$700$	52.4258	1.98151
$701$	44.8562	1.69419	0.847097	−	0.531438i	$-0.178348\pi$
$701$	44.8562	1.69419	0.847097	+	0.531438i	$0.178348\pi$
$702$	−6.67606	−0.251972
$703$	25.2817	0.953517
$704$	0	0
$705$	−0.567215	−0.0213625
$706$	95.9602	3.61151
$707$	29.7425	1.11858
$708$	−27.3580	−1.02818
$709$	36.1315	1.35695	0.678473	−	0.734626i	$-0.262642\pi$
$709$	36.1315	1.35695	0.678473	+	0.734626i	$0.262642\pi$
$710$	4.43373	0.166395
$711$	2.84159	0.106568
$712$	187.145	7.01356
$713$	−17.4747	−0.654431
$714$	−6.41491	−0.240072
$715$	0	0
$716$	−38.7041	−1.44644
$717$	7.09950	0.265136
$718$	60.1024	2.24300
$719$	13.3034	0.496134	0.248067	−	0.968743i	$-0.420205\pi$
$719$	13.3034	0.496134	0.248067	+	0.968743i	$0.420205\pi$
$720$	50.6138	1.88626
$721$	−40.8217	−1.52028
$722$	−35.8725	−1.33504
$723$	8.06009	0.299758
$724$	38.4076	1.42741
$725$	12.6078	0.468241
$726$	0	0
$727$	2.51921	0.0934324	0.0467162	−	0.998908i	$-0.485124\pi$
$727$	2.51921	0.0934324	0.0467162	+	0.998908i	$0.485124\pi$
$728$	30.0581	1.11403
$729$	−21.8098	−0.807772
$730$	25.6059	0.947715
$731$	22.1463	0.819110
$732$	−1.84945	−0.0683576
$733$	43.4999	1.60671	0.803353	−	0.595503i	$-0.203047\pi$
$733$	43.4999	1.60671	0.803353	+	0.595503i	$0.203047\pi$
$734$	−49.2479	−1.81777
$735$	−0.691047	−0.0254896
$736$	−127.303	−4.69244
$737$	0	0
$738$	71.4482	2.63004
$739$	3.09184	0.113735	0.0568675	−	0.998382i	$-0.481889\pi$
$739$	3.09184	0.113735	0.0568675	+	0.998382i	$0.481889\pi$
$740$	55.1828	2.02856
$741$	−1.00519	−0.0369266
$742$	−21.8776	−0.803153
$743$	15.2046	0.557802	0.278901	−	0.960320i	$-0.410030\pi$
$743$	15.2046	0.557802	0.278901	+	0.960320i	$0.410030\pi$
$744$	−14.6412	−0.536771
$745$	5.76189	0.211099
$746$	70.8844	2.59526
$747$	−4.93575	−0.180590
$748$	0	0
$749$	−9.13099	−0.333639
$750$	−7.46881	−0.272723
$751$	36.4173	1.32889	0.664443	−	0.747339i	$-0.268669\pi$
$751$	36.4173	1.32889	0.664443	+	0.747339i	$0.268669\pi$
$752$	−36.7517	−1.34020
$753$	−2.77537	−0.101140
$754$	10.9512	0.398820
$755$	14.3400	0.521887
$756$	−23.4705	−0.853612
$757$	−31.5613	−1.14712	−0.573558	−	0.819165i	$-0.694437\pi$
$757$	−31.5613	−1.14712	−0.573558	+	0.819165i	$0.694437\pi$
$758$	−103.986	−3.77695
$759$	0	0
$760$	25.1777	0.913291
$761$	0.550823	0.0199673	0.00998365	−	0.999950i	$-0.496822\pi$
$761$	0.550823	0.0199673	0.00998365	+	0.999950i	$0.496822\pi$
$762$	13.1480	0.476301
$763$	−7.77664	−0.281533
$764$	1.59250	0.0576145
$765$	−9.07509	−0.328111
$766$	−65.5089	−2.36693
$767$	−18.9611	−0.684644
$768$	−36.9369	−1.33285
$769$	11.4441	0.412684	0.206342	−	0.978480i	$-0.433844\pi$
$769$	11.4441	0.412684	0.206342	+	0.978480i	$0.433844\pi$
$770$	0	0
$771$	0.270276	0.00973374
$772$	−83.2567	−2.99648
$773$	14.4160	0.518507	0.259254	−	0.965809i	$-0.416523\pi$
$773$	14.4160	0.518507	0.259254	+	0.965809i	$0.416523\pi$
$774$	53.3764	1.91858
$775$	−17.6985	−0.635749
$776$	−81.6342	−2.93050
$777$	−6.85032	−0.245754
$778$	−56.5585	−2.02772
$779$	21.8818	0.783995
$780$	−2.19405	−0.0785595
$781$	0	0
$782$	38.8227	1.38830
$783$	−5.64437	−0.201713
$784$	−44.7752	−1.59911
$785$	−5.32005	−0.189881
$786$	4.57393	0.163147
$787$	41.1337	1.46626	0.733128	−	0.680090i	$-0.238059\pi$
$787$	41.1337	1.46626	0.733128	+	0.680090i	$0.238059\pi$
$788$	−25.4506	−0.906640
$789$	−7.97719	−0.283995
$790$	2.54525	0.0905561
$791$	21.0112	0.747072
$792$	0	0
$793$	−1.28180	−0.0455181
$794$	87.8274	3.11688
$795$	1.05409	0.0373847
$796$	−92.5165	−3.27916
$797$	−9.03032	−0.319870	−0.159935	−	0.987128i	$-0.551129\pi$
$797$	−9.03032	−0.319870	−0.159935	+	0.987128i	$0.551129\pi$
$798$	−4.73511	−0.167621
$799$	6.58961	0.233124
$800$	−128.934	−4.55849
$801$	−49.7912	−1.75929
$802$	21.0364	0.742822
$803$	0	0
$804$	−13.5139	−0.476598
$805$	−8.14242	−0.286983
$806$	−15.3731	−0.541494
$807$	6.56679	0.231162
$808$	−150.813	−5.30559
$809$	−31.6245	−1.11186	−0.555928	−	0.831230i	$-0.687637\pi$
$809$	−31.6245	−1.11186	−0.555928	+	0.831230i	$0.687637\pi$
$810$	−21.1022	−0.741457
$811$	−1.29817	−0.0455850	−0.0227925	−	0.999740i	$-0.507256\pi$
$811$	−1.29817	−0.0455850	−0.0227925	+	0.999740i	$0.507256\pi$
$812$	38.5003	1.35110
$813$	−3.05120	−0.107010
$814$	0	0
$815$	18.7595	0.657115
$816$	20.0261	0.701055
$817$	16.3471	0.571912
$818$	76.9754	2.69138
$819$	−7.99717	−0.279444
$820$	47.7617	1.66791
$821$	−3.13968	−0.109575	−0.0547877	−	0.998498i	$-0.517448\pi$
$821$	−3.13968	−0.109575	−0.0547877	+	0.998498i	$0.517448\pi$
$822$	−0.447611	−0.0156122
$823$	−26.7530	−0.932551	−0.466276	−	0.884639i	$-0.654404\pi$
$823$	−26.7530	−0.932551	−0.466276	+	0.884639i	$0.654404\pi$
$824$	206.992	7.21091
$825$	0	0
$826$	−89.3192	−3.10781
$827$	45.5079	1.58246	0.791232	−	0.611517i	$-0.209440\pi$
$827$	45.5079	1.58246	0.791232	+	0.611517i	$0.209440\pi$
$828$	69.8319	2.42683
$829$	−35.0823	−1.21846	−0.609230	−	0.792994i	$-0.708521\pi$
$829$	−35.0823	−1.21846	−0.609230	+	0.792994i	$0.708521\pi$
$830$	−4.42102	−0.153456
$831$	−4.39212	−0.152361
$832$	−63.6692	−2.20733
$833$	8.02822	0.278161
$834$	−10.2683	−0.355564
$835$	−15.2505	−0.527765
$836$	0	0
$837$	7.92344	0.273874
$838$	−20.4672	−0.707028
$839$	−25.6791	−0.886540	−0.443270	−	0.896388i	$-0.646182\pi$
$839$	−25.6791	−0.886540	−0.443270	+	0.896388i	$0.646182\pi$
$840$	−6.82214	−0.235386
$841$	−19.7411	−0.680728
$842$	32.3181	1.11375
$843$	7.85800	0.270644
$844$	97.3738	3.35174
$845$	10.5110	0.361591
$846$	15.8821	0.546038
$847$	0	0
$848$	68.2979	2.34536
$849$	−3.56923	−0.122496
$850$	39.3201	1.34867
$851$	41.4578	1.42116
$852$	3.15548	0.108105
$853$	46.7559	1.60089	0.800446	−	0.599405i	$-0.204596\pi$
$853$	46.7559	1.60089	0.800446	+	0.599405i	$0.204596\pi$
$854$	−6.03813	−0.206621
$855$	−6.69870	−0.229091
$856$	46.2999	1.58250
$857$	−34.3556	−1.17357	−0.586783	−	0.809744i	$-0.699606\pi$
$857$	−34.3556	−1.17357	−0.586783	+	0.809744i	$0.699606\pi$
$858$	0	0
$859$	−10.8578	−0.370463	−0.185231	−	0.982695i	$-0.559303\pi$
$859$	−10.8578	−0.370463	−0.185231	+	0.982695i	$0.559303\pi$
$860$	35.6811	1.21672
$861$	−5.92908	−0.202062
$862$	−91.0282	−3.10043
$863$	−15.5913	−0.530733	−0.265366	−	0.964148i	$-0.585493\pi$
$863$	−15.5913	−0.530733	−0.265366	+	0.964148i	$0.585493\pi$
$864$	57.7222	1.96375
$865$	8.34350	0.283687
$866$	21.1441	0.718506
$867$	1.75304	0.0595363
$868$	−54.0459	−1.83444
$869$	0	0
$870$	−2.48555	−0.0842680
$871$	−9.36610	−0.317358
$872$	39.4325	1.33535
$873$	21.7193	0.735088
$874$	28.6567	0.969326
$875$	−18.1983	−0.615215
$876$	18.2237	0.615720
$877$	4.18657	0.141370	0.0706852	−	0.997499i	$-0.477481\pi$
$877$	4.18657	0.141370	0.0706852	+	0.997499i	$0.477481\pi$
$878$	108.918	3.67579
$879$	−0.779315	−0.0262856
$880$	0	0
$881$	30.4025	1.02428	0.512142	−	0.858901i	$-0.328852\pi$
$881$	30.4025	1.02428	0.512142	+	0.858901i	$0.328852\pi$
$882$	19.3494	0.651528
$883$	19.6875	0.662538	0.331269	−	0.943536i	$-0.392523\pi$
$883$	19.6875	0.662538	0.331269	+	0.943536i	$0.392523\pi$
$884$	25.4893	0.857298
$885$	4.30350	0.144661
$886$	−94.4379	−3.17270
$887$	−50.0134	−1.67929	−0.839643	−	0.543138i	$-0.817236\pi$
$887$	−50.0134	−1.67929	−0.839643	+	0.543138i	$0.817236\pi$
$888$	34.7355	1.16565
$889$	32.0360	1.07445
$890$	−44.5987	−1.49495
$891$	0	0
$892$	43.6136	1.46029
$893$	4.86406	0.162770
$894$	5.49468	0.183769
$895$	6.08827	0.203509
$896$	−166.087	−5.54859
$897$	−1.64835	−0.0550367
$898$	0.355744	0.0118713
$899$	−12.9974	−0.433488
$900$	70.7264	2.35755
$901$	−12.2459	−0.407969
$902$	0	0
$903$	−4.42941	−0.147401
$904$	−106.540	−3.54348
$905$	−6.04164	−0.200831
$906$	13.6750	0.454321
$907$	−31.0590	−1.03130	−0.515648	−	0.856801i	$-0.672449\pi$
$907$	−31.0590	−1.03130	−0.515648	+	0.856801i	$0.672449\pi$
$908$	41.9341	1.39163
$909$	40.1249	1.33086
$910$	−7.16319	−0.237457
$911$	−30.0086	−0.994231	−0.497115	−	0.867684i	$-0.665607\pi$
$911$	−30.0086	−0.994231	−0.497115	+	0.867684i	$0.665607\pi$
$912$	14.7821	0.489485
$913$	0	0
$914$	−91.1093	−3.01363
$915$	0.290924	0.00961765
$916$	−41.5772	−1.37375
$917$	11.1447	0.368031
$918$	−17.6032	−0.580992
$919$	−50.0513	−1.65104	−0.825520	−	0.564373i	$-0.809118\pi$
$919$	−50.0513	−1.65104	−0.825520	+	0.564373i	$0.809118\pi$
$920$	41.2873	1.36120
$921$	2.93924	0.0968511
$922$	91.2513	3.00520
$923$	2.18698	0.0719852
$924$	0	0
$925$	41.9889	1.38059
$926$	40.1139	1.31822
$927$	−55.0717	−1.80879
$928$	−94.6860	−3.10822
$929$	−22.9587	−0.753250	−0.376625	−	0.926366i	$-0.622915\pi$
$929$	−22.9587	−0.753250	−0.376625	+	0.926366i	$0.622915\pi$
$930$	3.48915	0.114414
$931$	5.92596	0.194216
$932$	48.8129	1.59892
$933$	8.08423	0.264666
$934$	100.933	3.30262
$935$	0	0
$936$	40.5508	1.32544
$937$	−11.9593	−0.390693	−0.195347	−	0.980734i	$-0.562583\pi$
$937$	−11.9593	−0.390693	−0.195347	+	0.980734i	$0.562583\pi$
$938$	−44.1205	−1.44059
$939$	−6.61721	−0.215944
$940$	10.6169	0.346284
$941$	37.0349	1.20730	0.603651	−	0.797249i	$-0.293712\pi$
$941$	37.0349	1.20730	0.603651	+	0.797249i	$0.293712\pi$
$942$	−5.07333	−0.165298
$943$	35.8825	1.16849
$944$	278.838	9.07540
$945$	3.69197	0.120100
$946$	0	0
$947$	19.8675	0.645607	0.322804	−	0.946466i	$-0.395375\pi$
$947$	19.8675	0.645607	0.322804	+	0.946466i	$0.395375\pi$
$948$	1.81145	0.0588333
$949$	12.6303	0.409997
$950$	29.0238	0.941655
$951$	−3.54469	−0.114944
$952$	79.2561	2.56871
$953$	53.6192	1.73690	0.868449	−	0.495779i	$-0.165117\pi$
$953$	53.6192	1.73690	0.868449	+	0.495779i	$0.165117\pi$
$954$	−29.5146	−0.955572
$955$	−0.250504	−0.00810614
$956$	−132.885	−4.29782
$957$	0	0
$958$	−49.2079	−1.58983
$959$	−1.09064	−0.0352185
$960$	14.4507	0.466394
$961$	−12.7546	−0.411437
$962$	36.4719	1.17590
$963$	−12.3184	−0.396955
$964$	−150.865	−4.85904
$965$	13.0965	0.421592
$966$	−7.76481	−0.249829
$967$	−26.4148	−0.849444	−0.424722	−	0.905324i	$-0.639628\pi$
$967$	−26.4148	−0.849444	−0.424722	+	0.905324i	$0.639628\pi$
$968$	0	0
$969$	−2.65045	−0.0851446
$970$	19.4543	0.624641
$971$	−13.0181	−0.417771	−0.208886	−	0.977940i	$-0.566984\pi$
$971$	−13.0181	−0.417771	−0.208886	+	0.977940i	$0.566984\pi$
$972$	−47.7603	−1.53191
$973$	−25.0196	−0.802091
$974$	48.6261	1.55808
$975$	−1.66946	−0.0534656
$976$	18.8499	0.603371
$977$	31.6372	1.01216	0.506081	−	0.862486i	$-0.331094\pi$
$977$	31.6372	1.01216	0.506081	+	0.862486i	$0.331094\pi$
$978$	17.8895	0.572042
$979$	0	0
$980$	12.9347	0.413184
$981$	−10.4913	−0.334961
$982$	50.8163	1.62161
$983$	9.72173	0.310075	0.155037	−	0.987909i	$-0.450450\pi$
$983$	9.72173	0.310075	0.155037	+	0.987909i	$0.450450\pi$
$984$	30.0642	0.958412
$985$	4.00345	0.127561
$986$	28.8758	0.919593
$987$	−1.31796	−0.0419513
$988$	18.8147	0.598576
$989$	26.8065	0.852399
$990$	0	0
$991$	−14.9500	−0.474902	−0.237451	−	0.971399i	$-0.576312\pi$
$991$	−14.9500	−0.474902	−0.237451	+	0.971399i	$0.576312\pi$
$992$	132.918	4.22015
$993$	−2.75087	−0.0872963
$994$	10.3021	0.326763
$995$	14.5531	0.461365
$996$	−3.14644	−0.0996987
$997$	−24.9411	−0.789893	−0.394946	−	0.918704i	$-0.629237\pi$
$997$	−24.9411	−0.789893	−0.394946	+	0.918704i	$0.629237\pi$
$998$	20.4205	0.646401
$999$	−18.7980	−0.594742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.i.1.19		19
11.10	odd	2		671.2.a.c.1.1	✓	19
33.32	even	2		6039.2.a.k.1.19		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.1	✓	19	11.10	odd	2
6039.2.a.k.1.19		19	33.32	even	2
7381.2.a.i.1.19		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)

\(f(q)\)	\(=\)	\(q+2.80778 q^{2} -0.314338 q^{3} +5.88364 q^{4} -0.925514 q^{5} -0.882592 q^{6} -2.15050 q^{7} +10.9044 q^{8} -2.90119 q^{9} +O(q^{10})\)	\(q+2.80778 q^{2} -0.314338 q^{3} +5.88364 q^{4} -0.925514 q^{5} -0.882592 q^{6} -2.15050 q^{7} +10.9044 q^{8} -2.90119 q^{9} -2.59864 q^{10} -1.84945 q^{12} -1.28180 q^{13} -6.03813 q^{14} +0.290924 q^{15} +18.8499 q^{16} -3.37980 q^{17} -8.14591 q^{18} -2.49477 q^{19} -5.44539 q^{20} +0.675983 q^{21} -4.09102 q^{23} -3.42767 q^{24} -4.14342 q^{25} -3.59902 q^{26} +1.85497 q^{27} -12.6528 q^{28} -3.04284 q^{29} +0.816851 q^{30} +4.27147 q^{31} +31.1176 q^{32} -9.48975 q^{34} +1.99032 q^{35} -17.0696 q^{36} -10.1339 q^{37} -7.00478 q^{38} +0.402918 q^{39} -10.0922 q^{40} -8.77104 q^{41} +1.89801 q^{42} -6.55254 q^{43} +2.68509 q^{45} -11.4867 q^{46} -1.94970 q^{47} -5.92524 q^{48} -2.37535 q^{49} -11.6338 q^{50} +1.06240 q^{51} -7.54165 q^{52} +3.62325 q^{53} +5.20834 q^{54} -23.4499 q^{56} +0.784201 q^{57} -8.54363 q^{58} +14.7925 q^{59} +1.71169 q^{60} +1.00000 q^{61} +11.9934 q^{62} +6.23901 q^{63} +49.6717 q^{64} +1.18632 q^{65} +7.30698 q^{67} -19.8855 q^{68} +1.28596 q^{69} +5.58838 q^{70} -1.70617 q^{71} -31.6358 q^{72} -9.85356 q^{73} -28.4537 q^{74} +1.30243 q^{75} -14.6783 q^{76} +1.13131 q^{78} -0.979456 q^{79} -17.4459 q^{80} +8.12049 q^{81} -24.6272 q^{82} +1.70128 q^{83} +3.97724 q^{84} +3.12806 q^{85} -18.3981 q^{86} +0.956480 q^{87} +17.1623 q^{89} +7.53916 q^{90} +2.75651 q^{91} -24.0701 q^{92} -1.34268 q^{93} -5.47433 q^{94} +2.30895 q^{95} -9.78145 q^{96} -7.48635 q^{97} -6.66947 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 5 q^{2} + 23 q^{4} - q^{6} - 9 q^{7} - 9 q^{8} + 29 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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