LMFDB - Embedded newform 5577.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.89122$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46793 q^{2} -1.00000 q^{3} +4.09069 q^{4} +0.776183 q^{5} +2.46793 q^{6} -2.69175 q^{7} -5.15968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46793 q^{2} -1.00000 q^{3} +4.09069 q^{4} +0.776183 q^{5} +2.46793 q^{6} -2.69175 q^{7} -5.15968 q^{8} +1.00000 q^{9} -1.91557 q^{10} +1.00000 q^{11} -4.09069 q^{12} +6.64306 q^{14} -0.776183 q^{15} +4.55237 q^{16} +2.62136 q^{17} -2.46793 q^{18} -6.69175 q^{19} +3.17512 q^{20} +2.69175 q^{21} -2.46793 q^{22} -8.02655 q^{23} +5.15968 q^{24} -4.39754 q^{25} -1.00000 q^{27} -11.0111 q^{28} -8.09695 q^{29} +1.91557 q^{30} +6.34106 q^{31} -0.915567 q^{32} -1.00000 q^{33} -6.46933 q^{34} -2.08929 q^{35} +4.09069 q^{36} +0.398941 q^{37} +16.5148 q^{38} -4.00486 q^{40} -6.87313 q^{41} -6.64306 q^{42} +7.23786 q^{43} +4.09069 q^{44} +0.776183 q^{45} +19.8090 q^{46} +4.53692 q^{47} -4.55237 q^{48} +0.245516 q^{49} +10.8528 q^{50} -2.62136 q^{51} -2.75448 q^{53} +2.46793 q^{54} +0.776183 q^{55} +13.8886 q^{56} +6.69175 q^{57} +19.9827 q^{58} -10.8104 q^{59} -3.17512 q^{60} -5.02796 q^{61} -15.6493 q^{62} -2.69175 q^{63} -6.84517 q^{64} +2.46793 q^{66} +4.95756 q^{67} +10.7232 q^{68} +8.02655 q^{69} +5.15623 q^{70} +5.96382 q^{71} -5.15968 q^{72} -3.79648 q^{73} -0.984558 q^{74} +4.39754 q^{75} -27.3739 q^{76} -2.69175 q^{77} +2.14564 q^{79} +3.53347 q^{80} +1.00000 q^{81} +16.9624 q^{82} -3.73375 q^{83} +11.0111 q^{84} +2.03465 q^{85} -17.8625 q^{86} +8.09695 q^{87} -5.15968 q^{88} -2.37724 q^{89} -1.91557 q^{90} -32.8341 q^{92} -6.34106 q^{93} -11.1968 q^{94} -5.19402 q^{95} +0.915567 q^{96} +17.8355 q^{97} -0.605916 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^9	$ 4 q + 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 2 q^{18} - 18 q^{19} + 10 q^{20} + 2 q^{21} + 2 q^{22} + 4 q^{25} - 4 q^{27} + 6 q^{28} - 10 q^{29} + 2 q^{30} - 12 q^{31} + 2 q^{32} - 4 q^{33} - 36 q^{34} + 22 q^{35} + 8 q^{36} + 2 q^{37} + 4 q^{38} + 20 q^{40} - 2 q^{41} - 12 q^{42} + 28 q^{43} + 8 q^{44} + 30 q^{46} - 6 q^{47} - 12 q^{48} + 8 q^{49} + 36 q^{50} + 8 q^{51} - 4 q^{53} - 2 q^{54} + 48 q^{56} + 18 q^{57} + 6 q^{58} - 16 q^{59} - 10 q^{60} - 10 q^{61} - 34 q^{62} - 2 q^{63} - 12 q^{64} - 2 q^{66} - 34 q^{68} + 58 q^{70} - 10 q^{71} + 6 q^{73} + 14 q^{74} - 4 q^{75} - 26 q^{76} - 2 q^{77} - 8 q^{79} + 48 q^{80} + 4 q^{81} + 12 q^{82} + 8 q^{83} - 6 q^{84} + 18 q^{85} + 8 q^{86} + 10 q^{87} - 6 q^{89} - 2 q^{90} - 28 q^{92} + 12 q^{93} - 46 q^{94} + 22 q^{95} - 2 q^{96} - 10 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 2 * q^18 - 18 * q^19 + 10 * q^20 + 2 * q^21 + 2 * q^22 + 4 * q^25 - 4 * q^27 + 6 * q^28 - 10 * q^29 + 2 * q^30 - 12 * q^31 + 2 * q^32 - 4 * q^33 - 36 * q^34 + 22 * q^35 + 8 * q^36 + 2 * q^37 + 4 * q^38 + 20 * q^40 - 2 * q^41 - 12 * q^42 + 28 * q^43 + 8 * q^44 + 30 * q^46 - 6 * q^47 - 12 * q^48 + 8 * q^49 + 36 * q^50 + 8 * q^51 - 4 * q^53 - 2 * q^54 + 48 * q^56 + 18 * q^57 + 6 * q^58 - 16 * q^59 - 10 * q^60 - 10 * q^61 - 34 * q^62 - 2 * q^63 - 12 * q^64 - 2 * q^66 - 34 * q^68 + 58 * q^70 - 10 * q^71 + 6 * q^73 + 14 * q^74 - 4 * q^75 - 26 * q^76 - 2 * q^77 - 8 * q^79 + 48 * q^80 + 4 * q^81 + 12 * q^82 + 8 * q^83 - 6 * q^84 + 18 * q^85 + 8 * q^86 + 10 * q^87 - 6 * q^89 - 2 * q^90 - 28 * q^92 + 12 * q^93 - 46 * q^94 + 22 * q^95 - 2 * q^96 - 10 * q^97 + 34 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46793	−1.74509	−0.872546	−	0.488532i	$-0.837532\pi$
$2$	−2.46793	−1.74509	−0.872546	+	0.488532i	$0.837532\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.09069	2.04535
$5$	0.776183	0.347120	0.173560	−	0.984823i	$-0.444473\pi$
$5$	0.776183	0.347120	0.173560	+	0.984823i	$0.444473\pi$
$6$	2.46793	1.00753
$7$	−2.69175	−1.01739	−0.508693	−	0.860948i	$-0.669871\pi$
$7$	−2.69175	−1.01739	−0.508693	+	0.860948i	$0.669871\pi$
$8$	−5.15968	−1.82422
$9$	1.00000	0.333333
$10$	−1.91557	−0.605755
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.09069	−1.18088
$13$	0	0
$13$	0	0
$14$	6.64306	1.77543
$15$	−0.776183	−0.200410
$16$	4.55237	1.13809
$17$	2.62136	0.635773	0.317886	−	0.948129i	$-0.397027\pi$
$17$	2.62136	0.635773	0.317886	+	0.948129i	$0.397027\pi$
$18$	−2.46793	−0.581697
$19$	−6.69175	−1.53519	−0.767596	−	0.640934i	$-0.778547\pi$
$19$	−6.69175	−1.53519	−0.767596	+	0.640934i	$0.778547\pi$
$20$	3.17512	0.709979
$21$	2.69175	0.587388
$22$	−2.46793	−0.526165
$23$	−8.02655	−1.67365	−0.836826	−	0.547469i	$-0.815592\pi$
$23$	−8.02655	−1.67365	−0.836826	+	0.547469i	$0.815592\pi$
$24$	5.15968	1.05322
$25$	−4.39754	−0.879508
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−11.0111	−2.08090
$29$	−8.09695	−1.50357	−0.751783	−	0.659411i	$-0.770806\pi$
$29$	−8.09695	−1.50357	−0.751783	+	0.659411i	$0.770806\pi$
$30$	1.91557	0.349733
$31$	6.34106	1.13889	0.569444	−	0.822030i	$-0.307158\pi$
$31$	6.34106	1.13889	0.569444	+	0.822030i	$0.307158\pi$
$32$	−0.915567	−0.161851
$33$	−1.00000	−0.174078
$34$	−6.46933	−1.10948
$35$	−2.08929	−0.353154
$36$	4.09069	0.681782
$37$	0.398941	0.0655854	0.0327927	−	0.999462i	$-0.489560\pi$
$37$	0.398941	0.0655854	0.0327927	+	0.999462i	$0.489560\pi$
$38$	16.5148	2.67905
$39$	0	0
$40$	−4.00486	−0.633223
$41$	−6.87313	−1.07340	−0.536701	−	0.843772i	$-0.680330\pi$
$41$	−6.87313	−1.07340	−0.536701	+	0.843772i	$0.680330\pi$
$42$	−6.64306	−1.02505
$43$	7.23786	1.10376	0.551882	−	0.833923i	$-0.313910\pi$
$43$	7.23786	1.10376	0.551882	+	0.833923i	$0.313910\pi$
$44$	4.09069	0.616695
$45$	0.776183	0.115707
$46$	19.8090	2.92068
$47$	4.53692	0.661778	0.330889	−	0.943670i	$-0.392651\pi$
$47$	4.53692	0.661778	0.330889	+	0.943670i	$0.392651\pi$
$48$	−4.55237	−0.657077
$49$	0.245516	0.0350737
$50$	10.8528	1.53482
$51$	−2.62136	−0.367063
$52$	0	0
$53$	−2.75448	−0.378358	−0.189179	−	0.981943i	$-0.560583\pi$
$53$	−2.75448	−0.378358	−0.189179	+	0.981943i	$0.560583\pi$
$54$	2.46793	0.335843
$55$	0.776183	0.104660
$56$	13.8886	1.85594
$57$	6.69175	0.886344
$58$	19.9827	2.62386
$59$	−10.8104	−1.40739	−0.703697	−	0.710500i	$-0.748469\pi$
$59$	−10.8104	−1.40739	−0.703697	+	0.710500i	$0.748469\pi$
$60$	−3.17512	−0.409907
$61$	−5.02796	−0.643764	−0.321882	−	0.946780i	$-0.604315\pi$
$61$	−5.02796	−0.643764	−0.321882	+	0.946780i	$0.604315\pi$
$62$	−15.6493	−1.98746
$63$	−2.69175	−0.339129
$64$	−6.84517	−0.855647
$65$	0	0
$66$	2.46793	0.303781
$67$	4.95756	0.605663	0.302831	−	0.953044i	$-0.402068\pi$
$67$	4.95756	0.605663	0.302831	+	0.953044i	$0.402068\pi$
$68$	10.7232	1.30037
$69$	8.02655	0.966284
$70$	5.15623	0.616287
$71$	5.96382	0.707775	0.353888	−	0.935288i	$-0.384860\pi$
$71$	5.96382	0.707775	0.353888	+	0.935288i	$0.384860\pi$
$72$	−5.15968	−0.608074
$73$	−3.79648	−0.444344	−0.222172	−	0.975007i	$-0.571315\pi$
$73$	−3.79648	−0.444344	−0.222172	+	0.975007i	$0.571315\pi$
$74$	−0.984558	−0.114453
$75$	4.39754	0.507784
$76$	−27.3739	−3.14000
$77$	−2.69175	−0.306753
$78$	0	0
$79$	2.14564	0.241403	0.120702	−	0.992689i	$-0.461486\pi$
$79$	2.14564	0.241403	0.120702	+	0.992689i	$0.461486\pi$
$80$	3.53347	0.395054
$81$	1.00000	0.111111
$82$	16.9624	1.87319
$83$	−3.73375	−0.409832	−0.204916	−	0.978780i	$-0.565692\pi$
$83$	−3.73375	−0.409832	−0.204916	+	0.978780i	$0.565692\pi$
$84$	11.0111	1.20141
$85$	2.03465	0.220689
$86$	−17.8625	−1.92617
$87$	8.09695	0.868084
$88$	−5.15968	−0.550024
$89$	−2.37724	−0.251987	−0.125994	−	0.992031i	$-0.540212\pi$
$89$	−2.37724	−0.251987	−0.125994	+	0.992031i	$0.540212\pi$
$90$	−1.91557	−0.201918
$91$	0	0
$92$	−32.8341	−3.42320
$93$	−6.34106	−0.657538
$94$	−11.1968	−1.15486
$95$	−5.19402	−0.532895
$96$	0.915567	0.0934446
$97$	17.8355	1.81093	0.905463	−	0.424426i	$-0.139524\pi$
$97$	17.8355	1.81093	0.905463	+	0.424426i	$0.139524\pi$
$98$	−0.605916	−0.0612067
$99$	1.00000	0.100504
$100$	−17.9890	−1.79890
$101$	−11.1096	−1.10545	−0.552723	−	0.833365i	$-0.686411\pi$
$101$	−11.1096	−1.10545	−0.552723	+	0.833365i	$0.686411\pi$
$102$	6.46933	0.640559
$103$	10.1814	1.00320	0.501601	−	0.865099i	$-0.332745\pi$
$103$	10.1814	1.00320	0.501601	+	0.865099i	$0.332745\pi$
$104$	0	0
$105$	2.08929	0.203894
$106$	6.79788	0.660269
$107$	3.06133	0.295950	0.147975	−	0.988991i	$-0.452724\pi$
$107$	3.06133	0.295950	0.147975	+	0.988991i	$0.452724\pi$
$108$	−4.09069	−0.393627
$109$	−13.1800	−1.26241	−0.631207	−	0.775615i	$-0.717440\pi$
$109$	−13.1800	−1.26241	−0.631207	+	0.775615i	$0.717440\pi$
$110$	−1.91557	−0.182642
$111$	−0.398941	−0.0378658
$112$	−12.2538	−1.15788
$113$	4.50074	0.423394	0.211697	−	0.977335i	$-0.432101\pi$
$113$	4.50074	0.423394	0.211697	+	0.977335i	$0.432101\pi$
$114$	−16.5148	−1.54675
$115$	−6.23007	−0.580957
$116$	−33.1221	−3.07531
$117$	0	0
$118$	26.6793	2.45603
$119$	−7.05604	−0.646826
$120$	4.00486	0.365592
$121$	1.00000	0.0909091
$122$	12.4087	1.12343
$123$	6.87313	0.619729
$124$	25.9393	2.32942
$125$	−7.29421	−0.652414
$126$	6.64306	0.591810
$127$	19.9687	1.77193	0.885967	−	0.463749i	$-0.153496\pi$
$127$	19.9687	1.77193	0.885967	+	0.463749i	$0.153496\pi$
$128$	18.7246	1.65503
$129$	−7.23786	−0.637258
$130$	0	0
$131$	4.92335	0.430155	0.215078	−	0.976597i	$-0.431000\pi$
$131$	4.92335	0.430155	0.215078	+	0.976597i	$0.431000\pi$
$132$	−4.09069	−0.356049
$133$	18.0125	1.56188
$134$	−12.2349	−1.05694
$135$	−0.776183	−0.0668032
$136$	−13.5254	−1.15979
$137$	13.1876	1.12670	0.563348	−	0.826220i	$-0.309513\pi$
$137$	13.1876	1.12670	0.563348	+	0.826220i	$0.309513\pi$
$138$	−19.8090	−1.68625
$139$	11.0203	0.934729	0.467365	−	0.884065i	$-0.345203\pi$
$139$	11.0203	0.934729	0.467365	+	0.884065i	$0.345203\pi$
$140$	−8.54664	−0.722323
$141$	−4.53692	−0.382078
$142$	−14.7183	−1.23513
$143$	0	0
$144$	4.55237	0.379364
$145$	−6.28471	−0.521917
$146$	9.36946	0.775422
$147$	−0.245516	−0.0202498
$148$	1.63194	0.134145
$149$	−8.25663	−0.676409	−0.338205	−	0.941073i	$-0.609820\pi$
$149$	−8.25663	−0.676409	−0.338205	+	0.941073i	$0.609820\pi$
$150$	−10.8528	−0.886130
$151$	3.61510	0.294193	0.147096	−	0.989122i	$-0.453007\pi$
$151$	3.61510	0.294193	0.147096	+	0.989122i	$0.453007\pi$
$152$	34.5273	2.80053
$153$	2.62136	0.211924
$154$	6.64306	0.535313
$155$	4.92182	0.395330
$156$	0	0
$157$	20.0672	1.60153	0.800766	−	0.598977i	$-0.204426\pi$
$157$	20.0672	1.60153	0.800766	+	0.598977i	$0.204426\pi$
$158$	−5.29530	−0.421271
$159$	2.75448	0.218445
$160$	−0.710647	−0.0561816
$161$	21.6055	1.70275
$162$	−2.46793	−0.193899
$163$	−17.9827	−1.40852	−0.704258	−	0.709945i	$-0.748720\pi$
$163$	−17.9827	−1.40852	−0.704258	+	0.709945i	$0.748720\pi$
$164$	−28.1158	−2.19548
$165$	−0.776183	−0.0604258
$166$	9.21463	0.715194
$167$	−9.74626	−0.754188	−0.377094	−	0.926175i	$-0.623077\pi$
$167$	−9.74626	−0.754188	−0.377094	+	0.926175i	$0.623077\pi$
$168$	−13.8886	−1.07153
$169$	0	0
$170$	−5.02138	−0.385123
$171$	−6.69175	−0.511731
$172$	29.6078	2.25758
$173$	−14.9841	−1.13922	−0.569611	−	0.821915i	$-0.692906\pi$
$173$	−14.9841	−1.13922	−0.569611	+	0.821915i	$0.692906\pi$
$174$	−19.9827	−1.51489
$175$	11.8371	0.894799
$176$	4.55237	0.343147
$177$	10.8104	0.812559
$178$	5.86687	0.439741
$179$	−14.5273	−1.08582	−0.542911	−	0.839790i	$-0.682678\pi$
$179$	−14.5273	−1.08582	−0.542911	+	0.839790i	$0.682678\pi$
$180$	3.17512	0.236660
$181$	0.909310	0.0675885	0.0337942	−	0.999429i	$-0.489241\pi$
$181$	0.909310	0.0675885	0.0337942	+	0.999429i	$0.489241\pi$
$182$	0	0
$183$	5.02796	0.371677
$184$	41.4145	3.05312
$185$	0.309651	0.0227660
$186$	15.6493	1.14746
$187$	2.62136	0.191693
$188$	18.5592	1.35357
$189$	2.69175	0.195796
$190$	12.8185	0.929951
$191$	12.4448	0.900477	0.450238	−	0.892908i	$-0.351339\pi$
$191$	12.4448	0.900477	0.450238	+	0.892908i	$0.351339\pi$
$192$	6.84517	0.494008
$193$	−18.3406	−1.32019	−0.660093	−	0.751184i	$-0.729483\pi$
$193$	−18.3406	−1.32019	−0.660093	+	0.751184i	$0.729483\pi$
$194$	−44.0169	−3.16023
$195$	0	0
$196$	1.00433	0.0717377
$197$	7.96535	0.567508	0.283754	−	0.958897i	$-0.408420\pi$
$197$	7.96535	0.567508	0.283754	+	0.958897i	$0.408420\pi$
$198$	−2.46793	−0.175388
$199$	−14.6415	−1.03791	−0.518955	−	0.854801i	$-0.673679\pi$
$199$	−14.6415	−1.03791	−0.518955	+	0.854801i	$0.673679\pi$
$200$	22.6899	1.60442
$201$	−4.95756	−0.349680
$202$	27.4177	1.92910
$203$	21.7950	1.52971
$204$	−10.7232	−0.750771
$205$	−5.33481	−0.372599
$206$	−25.1270	−1.75068
$207$	−8.02655	−0.557884
$208$	0	0
$209$	−6.69175	−0.462878
$210$	−5.15623	−0.355813
$211$	14.9716	1.03069	0.515344	−	0.856983i	$-0.327664\pi$
$211$	14.9716	1.03069	0.515344	+	0.856983i	$0.327664\pi$
$212$	−11.2677	−0.773872
$213$	−5.96382	−0.408634
$214$	−7.55517	−0.516461
$215$	5.61790	0.383138
$216$	5.15968	0.351072
$217$	−17.0686	−1.15869
$218$	32.5273	2.20303
$219$	3.79648	0.256542
$220$	3.17512	0.214067
$221$	0	0
$222$	0.984558	0.0660792
$223$	26.2003	1.75450	0.877250	−	0.480033i	$-0.159375\pi$
$223$	26.2003	1.75450	0.877250	+	0.480033i	$0.159375\pi$
$224$	2.46448	0.164665
$225$	−4.39754	−0.293169
$226$	−11.1075	−0.738862
$227$	−24.2441	−1.60914	−0.804569	−	0.593859i	$-0.797604\pi$
$227$	−24.2441	−1.60914	−0.804569	+	0.593859i	$0.797604\pi$
$228$	27.3739	1.81288
$229$	6.43954	0.425537	0.212768	−	0.977103i	$-0.431752\pi$
$229$	6.43954	0.425537	0.212768	+	0.977103i	$0.431752\pi$
$230$	15.3754	1.01382
$231$	2.69175	0.177104
$232$	41.7777	2.74284
$233$	−24.0536	−1.57580	−0.787900	−	0.615803i	$-0.788832\pi$
$233$	−24.0536	−1.57580	−0.787900	+	0.615803i	$0.788832\pi$
$234$	0	0
$235$	3.52148	0.229716
$236$	−44.2220	−2.87861
$237$	−2.14564	−0.139374
$238$	17.4138	1.12877
$239$	−5.01391	−0.324323	−0.162162	−	0.986764i	$-0.551847\pi$
$239$	−5.01391	−0.324323	−0.162162	+	0.986764i	$0.551847\pi$
$240$	−3.53347	−0.228084
$241$	24.9890	1.60968	0.804841	−	0.593491i	$-0.202251\pi$
$241$	24.9890	1.60968	0.804841	+	0.593491i	$0.202251\pi$
$242$	−2.46793	−0.158645
$243$	−1.00000	−0.0641500
$244$	−20.5678	−1.31672
$245$	0.190565	0.0121748
$246$	−16.9624	−1.08148
$247$	0	0
$248$	−32.7179	−2.07759
$249$	3.73375	0.236617
$250$	18.0016	1.13852
$251$	18.0406	1.13871	0.569356	−	0.822091i	$-0.307193\pi$
$251$	18.0406	1.13871	0.569356	+	0.822091i	$0.307193\pi$
$252$	−11.0111	−0.693635
$253$	−8.02655	−0.504625
$254$	−49.2813	−3.09219
$255$	−2.03465	−0.127415
$256$	−32.5206	−2.03254
$257$	−21.1298	−1.31804	−0.659019	−	0.752126i	$-0.729028\pi$
$257$	−21.1298	−1.31804	−0.659019	+	0.752126i	$0.729028\pi$
$258$	17.8625	1.11207
$259$	−1.07385	−0.0667257
$260$	0	0
$261$	−8.09695	−0.501188
$262$	−12.1505	−0.750660
$263$	11.8592	0.731271	0.365635	−	0.930758i	$-0.380852\pi$
$263$	11.8592	0.731271	0.365635	+	0.930758i	$0.380852\pi$
$264$	5.15968	0.317556
$265$	−2.13798	−0.131335
$266$	−44.4537	−2.72563
$267$	2.37724	0.145485
$268$	20.2799	1.23879
$269$	−0.322165	−0.0196427	−0.00982136	−	0.999952i	$-0.503126\pi$
$269$	−0.322165	−0.0196427	−0.00982136	+	0.999952i	$0.503126\pi$
$270$	1.91557	0.116578
$271$	−26.2944	−1.59727	−0.798636	−	0.601814i	$-0.794445\pi$
$271$	−26.2944	−1.59727	−0.798636	+	0.601814i	$0.794445\pi$
$272$	11.9334	0.723567
$273$	0	0
$274$	−32.5462	−1.96619
$275$	−4.39754	−0.265182
$276$	32.8341	1.97638
$277$	−8.89247	−0.534297	−0.267148	−	0.963655i	$-0.586081\pi$
$277$	−8.89247	−0.534297	−0.267148	+	0.963655i	$0.586081\pi$
$278$	−27.1974	−1.63119
$279$	6.34106	0.379629
$280$	10.7801	0.644232
$281$	−23.5833	−1.40686	−0.703432	−	0.710763i	$-0.748350\pi$
$281$	−23.5833	−1.40686	−0.703432	+	0.710763i	$0.748350\pi$
$282$	11.1968	0.666761
$283$	8.13754	0.483727	0.241863	−	0.970310i	$-0.422241\pi$
$283$	8.13754	0.483727	0.241863	+	0.970310i	$0.422241\pi$
$284$	24.3961	1.44764
$285$	5.19402	0.307667
$286$	0	0
$287$	18.5007	1.09206
$288$	−0.915567	−0.0539503
$289$	−10.1285	−0.595793
$290$	15.5102	0.910793
$291$	−17.8355	−1.04554
$292$	−15.5302	−0.908838
$293$	−19.8649	−1.16052	−0.580260	−	0.814431i	$-0.697049\pi$
$293$	−19.8649	−1.16052	−0.580260	+	0.814431i	$0.697049\pi$
$294$	0.605916	0.0353377
$295$	−8.39084	−0.488534
$296$	−2.05841	−0.119642
$297$	−1.00000	−0.0580259
$298$	20.3768	1.18040
$299$	0	0
$300$	17.9890	1.03859
$301$	−19.4825	−1.12295
$302$	−8.92182	−0.513393
$303$	11.1096	0.638229
$304$	−30.4633	−1.74719
$305$	−3.90261	−0.223463
$306$	−6.46933	−0.369827
$307$	23.3305	1.33154	0.665770	−	0.746157i	$-0.268103\pi$
$307$	23.3305	1.33154	0.665770	+	0.746157i	$0.268103\pi$
$308$	−11.0111	−0.627416
$309$	−10.1814	−0.579198
$310$	−12.1467	−0.689888
$311$	−4.43359	−0.251406	−0.125703	−	0.992068i	$-0.540119\pi$
$311$	−4.43359	−0.251406	−0.125703	+	0.992068i	$0.540119\pi$
$312$	0	0
$313$	−17.4129	−0.984233	−0.492116	−	0.870529i	$-0.663777\pi$
$313$	−17.4129	−0.984233	−0.492116	+	0.870529i	$0.663777\pi$
$314$	−49.5244	−2.79482
$315$	−2.08929	−0.117718
$316$	8.77715	0.493753
$317$	30.8752	1.73412	0.867062	−	0.498201i	$-0.166006\pi$
$317$	30.8752	1.73412	0.867062	+	0.498201i	$0.166006\pi$
$318$	−6.79788	−0.381206
$319$	−8.09695	−0.453342
$320$	−5.31311	−0.297012
$321$	−3.06133	−0.170867
$322$	−53.3209	−2.97145
$323$	−17.5415	−0.976033
$324$	4.09069	0.227261
$325$	0	0
$326$	44.3801	2.45799
$327$	13.1800	0.728855
$328$	35.4632	1.95813
$329$	−12.2123	−0.673284
$330$	1.91557	0.105448
$331$	−6.72749	−0.369776	−0.184888	−	0.982760i	$-0.559192\pi$
$331$	−6.72749	−0.369776	−0.184888	+	0.982760i	$0.559192\pi$
$332$	−15.2736	−0.838248
$333$	0.398941	0.0218618
$334$	24.0531	1.31613
$335$	3.84798	0.210237
$336$	12.2538	0.668501
$337$	−5.06133	−0.275708	−0.137854	−	0.990453i	$-0.544021\pi$
$337$	−5.06133	−0.275708	−0.137854	+	0.990453i	$0.544021\pi$
$338$	0	0
$339$	−4.50074	−0.244447
$340$	8.32313	0.451385
$341$	6.34106	0.343388
$342$	16.5148	0.893017
$343$	18.1814	0.981702
$344$	−37.3450	−2.01351
$345$	6.23007	0.335416
$346$	36.9798	1.98805
$347$	−4.34303	−0.233146	−0.116573	−	0.993182i	$-0.537191\pi$
$347$	−4.34303	−0.233146	−0.116573	+	0.993182i	$0.537191\pi$
$348$	33.1221	1.77553
$349$	−20.2779	−1.08545	−0.542725	−	0.839910i	$-0.682607\pi$
$349$	−20.2779	−1.08545	−0.542725	+	0.839910i	$0.682607\pi$
$350$	−29.2131	−1.56151
$351$	0	0
$352$	−0.915567	−0.0487999
$353$	36.5630	1.94605	0.973027	−	0.230691i	$-0.0740986\pi$
$353$	36.5630	1.94605	0.973027	+	0.230691i	$0.0740986\pi$
$354$	−26.6793	−1.41799
$355$	4.62901	0.245683
$356$	−9.72456	−0.515401
$357$	7.05604	0.373445
$358$	35.8524	1.89486
$359$	27.8621	1.47051	0.735253	−	0.677793i	$-0.237063\pi$
$359$	27.8621	1.47051	0.735253	+	0.677793i	$0.237063\pi$
$360$	−4.00486	−0.211074
$361$	25.7795	1.35682
$362$	−2.24412	−0.117948
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−2.94676	−0.154241
$366$	−12.4087	−0.648611
$367$	10.4476	0.545362	0.272681	−	0.962104i	$-0.412090\pi$
$367$	10.4476	0.545362	0.272681	+	0.962104i	$0.412090\pi$
$368$	−36.5398	−1.90477
$369$	−6.87313	−0.357801
$370$	−0.764197	−0.0397287
$371$	7.41438	0.384936
$372$	−25.9393	−1.34489
$373$	−17.8842	−0.926011	−0.463006	−	0.886355i	$-0.653229\pi$
$373$	−17.8842	−0.926011	−0.463006	+	0.886355i	$0.653229\pi$
$374$	−6.46933	−0.334521
$375$	7.29421	0.376671
$376$	−23.4091	−1.20723
$377$	0	0
$378$	−6.64306	−0.341682
$379$	13.6200	0.699610	0.349805	−	0.936822i	$-0.386248\pi$
$379$	13.6200	0.699610	0.349805	+	0.936822i	$0.386248\pi$
$380$	−21.2471	−1.08995
$381$	−19.9687	−1.02303
$382$	−30.7130	−1.57141
$383$	−4.62901	−0.236532	−0.118266	−	0.992982i	$-0.537733\pi$
$383$	−4.62901	−0.236532	−0.118266	+	0.992982i	$0.537733\pi$
$384$	−18.7246	−0.955534
$385$	−2.08929	−0.106480
$386$	45.2634	2.30385
$387$	7.23786	0.367921
$388$	72.9597	3.70397
$389$	5.34290	0.270896	0.135448	−	0.990784i	$-0.456753\pi$
$389$	5.34290	0.270896	0.135448	+	0.990784i	$0.456753\pi$
$390$	0	0
$391$	−21.0405	−1.06406
$392$	−1.26678	−0.0639822
$393$	−4.92335	−0.248350
$394$	−19.6579	−0.990353
$395$	1.66541	0.0837958
$396$	4.09069	0.205565
$397$	−28.0700	−1.40879	−0.704397	−	0.709806i	$-0.748783\pi$
$397$	−28.0700	−1.40879	−0.704397	+	0.709806i	$0.748783\pi$
$398$	36.1343	1.81125
$399$	−18.0125	−0.901754
$400$	−20.0192	−1.00096
$401$	−32.3942	−1.61769	−0.808844	−	0.588023i	$-0.799906\pi$
$401$	−32.3942	−1.61769	−0.808844	+	0.588023i	$0.799906\pi$
$402$	12.2349	0.610223
$403$	0	0
$404$	−45.4459	−2.26102
$405$	0.776183	0.0385688
$406$	−53.7885	−2.66948
$407$	0.398941	0.0197748
$408$	13.5254	0.669606
$409$	22.4380	1.10949	0.554744	−	0.832021i	$-0.312816\pi$
$409$	22.4380	1.10949	0.554744	+	0.832021i	$0.312816\pi$
$410$	13.1659	0.650219
$411$	−13.1876	−0.650498
$412$	41.6489	2.05189
$413$	29.0989	1.43186
$414$	19.8090	0.973559
$415$	−2.89807	−0.142261
$416$	0	0
$417$	−11.0203	−0.539666
$418$	16.5148	0.807765
$419$	40.6113	1.98399	0.991996	−	0.126272i	$-0.0403011\pi$
$419$	40.6113	1.98399	0.991996	+	0.126272i	$0.0403011\pi$
$420$	8.54664	0.417033
$421$	2.67241	0.130245	0.0651227	−	0.997877i	$-0.479256\pi$
$421$	2.67241	0.130245	0.0651227	+	0.997877i	$0.479256\pi$
$422$	−36.9489	−1.79864
$423$	4.53692	0.220593
$424$	14.2123	0.690209
$425$	−11.5275	−0.559167
$426$	14.7183	0.713104
$427$	13.5340	0.654956
$428$	12.5230	0.605321
$429$	0	0
$430$	−13.8646	−0.668610
$431$	25.9972	1.25224	0.626121	−	0.779726i	$-0.284642\pi$
$431$	25.9972	1.25224	0.626121	+	0.779726i	$0.284642\pi$
$432$	−4.55237	−0.219026
$433$	18.9765	0.911951	0.455975	−	0.889992i	$-0.349291\pi$
$433$	18.9765	0.911951	0.455975	+	0.889992i	$0.349291\pi$
$434$	42.1240	2.02202
$435$	6.28471	0.301329
$436$	−53.9152	−2.58207
$437$	53.7117	2.56938
$438$	−9.36946	−0.447690
$439$	16.8586	0.804619	0.402310	−	0.915504i	$-0.368208\pi$
$439$	16.8586	0.804619	0.402310	+	0.915504i	$0.368208\pi$
$440$	−4.00486	−0.190924
$441$	0.245516	0.0116912
$442$	0	0
$443$	34.5105	1.63964	0.819821	−	0.572620i	$-0.194073\pi$
$443$	34.5105	1.63964	0.819821	+	0.572620i	$0.194073\pi$
$444$	−1.63194	−0.0774486
$445$	−1.84517	−0.0874697
$446$	−64.6605	−3.06176
$447$	8.25663	0.390525
$448$	18.4255	0.870523
$449$	−5.12363	−0.241799	−0.120899	−	0.992665i	$-0.538578\pi$
$449$	−5.12363	−0.241799	−0.120899	+	0.992665i	$0.538578\pi$
$450$	10.8528	0.511607
$451$	−6.87313	−0.323643
$452$	18.4111	0.865988
$453$	−3.61510	−0.169852
$454$	59.8328	2.80809
$455$	0	0
$456$	−34.5273	−1.61689
$457$	19.9248	0.932045	0.466022	−	0.884773i	$-0.345687\pi$
$457$	19.9248	0.932045	0.466022	+	0.884773i	$0.345687\pi$
$458$	−15.8923	−0.742600
$459$	−2.62136	−0.122354
$460$	−25.4853	−1.18826
$461$	10.4661	0.487454	0.243727	−	0.969844i	$-0.421630\pi$
$461$	10.4661	0.487454	0.243727	+	0.969844i	$0.421630\pi$
$462$	−6.64306	−0.309063
$463$	36.5558	1.69889	0.849447	−	0.527675i	$-0.176936\pi$
$463$	36.5558	1.69889	0.849447	+	0.527675i	$0.176936\pi$
$464$	−36.8603	−1.71119
$465$	−4.92182	−0.228244
$466$	59.3625	2.74992
$467$	−2.43079	−0.112484	−0.0562418	−	0.998417i	$-0.517912\pi$
$467$	−2.43079	−0.112484	−0.0562418	+	0.998417i	$0.517912\pi$
$468$	0	0
$469$	−13.3445	−0.616193
$470$	−8.69078	−0.400876
$471$	−20.0672	−0.924646
$472$	55.7782	2.56740
$473$	7.23786	0.332797
$474$	5.29530	0.243221
$475$	29.4272	1.35021
$476$	−28.8641	−1.32298
$477$	−2.75448	−0.126119
$478$	12.3740	0.565974
$479$	1.96535	0.0897990	0.0448995	−	0.998992i	$-0.485703\pi$
$479$	1.96535	0.0897990	0.0448995	+	0.998992i	$0.485703\pi$
$480$	0.710647	0.0324365
$481$	0	0
$482$	−61.6711	−2.80904
$483$	−21.6055	−0.983083
$484$	4.09069	0.185940
$485$	13.8436	0.628608
$486$	2.46793	0.111948
$487$	−22.4863	−1.01895	−0.509475	−	0.860486i	$-0.670160\pi$
$487$	−22.4863	−1.01895	−0.509475	+	0.860486i	$0.670160\pi$
$488$	25.9426	1.17437
$489$	17.9827	0.813207
$490$	−0.470301	−0.0212461
$491$	17.2914	0.780350	0.390175	−	0.920741i	$-0.372414\pi$
$491$	17.2914	0.780350	0.390175	+	0.920741i	$0.372414\pi$
$492$	28.1158	1.26756
$493$	−21.2250	−0.955926
$494$	0	0
$495$	0.776183	0.0348868
$496$	28.8668	1.29616
$497$	−16.0531	−0.720080
$498$	−9.21463	−0.412918
$499$	−3.71485	−0.166299	−0.0831497	−	0.996537i	$-0.526498\pi$
$499$	−3.71485	−0.166299	−0.0831497	+	0.996537i	$0.526498\pi$
$500$	−29.8384	−1.33441
$501$	9.74626	0.435431
$502$	−44.5230	−1.98716
$503$	−7.68064	−0.342463	−0.171231	−	0.985231i	$-0.554775\pi$
$503$	−7.68064	−0.342463	−0.171231	+	0.985231i	$0.554775\pi$
$504$	13.8886	0.618646
$505$	−8.62307	−0.383722
$506$	19.8090	0.880617
$507$	0	0
$508$	81.6857	3.62422
$509$	−29.0035	−1.28556	−0.642778	−	0.766053i	$-0.722218\pi$
$509$	−29.0035	−1.28556	−0.642778	+	0.766053i	$0.722218\pi$
$510$	5.02138	0.222351
$511$	10.2192	0.452070
$512$	42.8095	1.89193
$513$	6.69175	0.295448
$514$	52.1468	2.30010
$515$	7.90261	0.348231
$516$	−29.6078	−1.30341
$517$	4.53692	0.199534
$518$	2.65018	0.116442
$519$	14.9841	0.657730
$520$	0	0
$521$	32.5973	1.42811	0.714056	−	0.700089i	$-0.246856\pi$
$521$	32.5973	1.42811	0.714056	+	0.700089i	$0.246856\pi$
$522$	19.9827	0.874620
$523$	−10.7304	−0.469207	−0.234603	−	0.972091i	$-0.575379\pi$
$523$	−10.7304	−0.469207	−0.234603	+	0.972091i	$0.575379\pi$
$524$	20.1399	0.879816
$525$	−11.8371	−0.516612
$526$	−29.2677	−1.27613
$527$	16.6222	0.724074
$528$	−4.55237	−0.198116
$529$	41.4256	1.80111
$530$	5.27640	0.229192
$531$	−10.8104	−0.469131
$532$	73.6836	3.19459
$533$	0	0
$534$	−5.86687	−0.253884
$535$	2.37616	0.102730
$536$	−25.5794	−1.10486
$537$	14.5273	0.626899
$538$	0.795080	0.0342784
$539$	0.245516	0.0105751
$540$	−3.17512	−0.136636
$541$	−12.4910	−0.537031	−0.268516	−	0.963275i	$-0.586533\pi$
$541$	−12.4910	−0.537031	−0.268516	+	0.963275i	$0.586533\pi$
$542$	64.8929	2.78739
$543$	−0.909310	−0.0390222
$544$	−2.40003	−0.102900
$545$	−10.2301	−0.438208
$546$	0	0
$547$	14.2377	0.608761	0.304381	−	0.952550i	$-0.401550\pi$
$547$	14.2377	0.608761	0.304381	+	0.952550i	$0.401550\pi$
$548$	53.9465	2.30448
$549$	−5.02796	−0.214588
$550$	10.8528	0.462766
$551$	54.1827	2.30826
$552$	−41.4145	−1.76272
$553$	−5.77553	−0.245600
$554$	21.9460	0.932397
$555$	−0.309651	−0.0131439
$556$	45.0806	1.91184
$557$	28.4633	1.20603	0.603014	−	0.797730i	$-0.293966\pi$
$557$	28.4633	1.20603	0.603014	+	0.797730i	$0.293966\pi$
$558$	−15.6493	−0.662488
$559$	0	0
$560$	−9.51121	−0.401922
$561$	−2.62136	−0.110674
$562$	58.2021	2.45511
$563$	−29.8998	−1.26013	−0.630063	−	0.776544i	$-0.716971\pi$
$563$	−29.8998	−1.26013	−0.630063	+	0.776544i	$0.716971\pi$
$564$	−18.5592	−0.781481
$565$	3.49340	0.146968
$566$	−20.0829	−0.844147
$567$	−2.69175	−0.113043
$568$	−30.7714	−1.29114
$569$	21.5572	0.903726	0.451863	−	0.892087i	$-0.350760\pi$
$569$	21.5572	0.903726	0.451863	+	0.892087i	$0.350760\pi$
$570$	−12.8185	−0.536908
$571$	−38.0830	−1.59372	−0.796862	−	0.604162i	$-0.793508\pi$
$571$	−38.0830	−1.59372	−0.796862	+	0.604162i	$0.793508\pi$
$572$	0	0
$573$	−12.4448	−0.519890
$574$	−45.6586	−1.90575
$575$	35.2971	1.47199
$576$	−6.84517	−0.285216
$577$	−19.7463	−0.822048	−0.411024	−	0.911625i	$-0.634829\pi$
$577$	−19.7463	−0.822048	−0.411024	+	0.911625i	$0.634829\pi$
$578$	24.9964	1.03971
$579$	18.3406	0.762210
$580$	−25.7088	−1.06750
$581$	10.0503	0.416957
$582$	44.0169	1.82456
$583$	−2.75448	−0.114079
$584$	19.5886	0.810583
$585$	0	0
$586$	49.0252	2.02521
$587$	5.48001	0.226184	0.113092	−	0.993585i	$-0.463925\pi$
$587$	5.48001	0.226184	0.113092	+	0.993585i	$0.463925\pi$
$588$	−1.00433	−0.0414178
$589$	−42.4328	−1.74841
$590$	20.7080	0.852536
$591$	−7.96535	−0.327651
$592$	1.81612	0.0746422
$593$	−35.0670	−1.44003	−0.720015	−	0.693958i	$-0.755865\pi$
$593$	−35.0670	−1.44003	−0.720015	+	0.693958i	$0.755865\pi$
$594$	2.46793	0.101260
$595$	−5.47678	−0.224526
$596$	−33.7753	−1.38349
$597$	14.6415	0.599238
$598$	0	0
$599$	17.3401	0.708497	0.354249	−	0.935151i	$-0.384737\pi$
$599$	17.3401	0.708497	0.354249	+	0.935151i	$0.384737\pi$
$600$	−22.6899	−0.926312
$601$	16.0253	0.653685	0.326842	−	0.945079i	$-0.394015\pi$
$601$	16.0253	0.653685	0.326842	+	0.945079i	$0.394015\pi$
$602$	48.0815	1.95966
$603$	4.95756	0.201888
$604$	14.7883	0.601726
$605$	0.776183	0.0315563
$606$	−27.4177	−1.11377
$607$	−27.2673	−1.10675	−0.553373	−	0.832934i	$-0.686660\pi$
$607$	−27.2673	−1.10675	−0.553373	+	0.832934i	$0.686660\pi$
$608$	6.12674	0.248472
$609$	−21.7950	−0.883176
$610$	9.63138	0.389963
$611$	0	0
$612$	10.7232	0.433458
$613$	7.92195	0.319965	0.159982	−	0.987120i	$-0.448856\pi$
$613$	7.92195	0.319965	0.159982	+	0.987120i	$0.448856\pi$
$614$	−57.5780	−2.32366
$615$	5.33481	0.215120
$616$	13.8886	0.559586
$617$	28.8293	1.16062	0.580312	−	0.814394i	$-0.302931\pi$
$617$	28.8293	1.16062	0.580312	+	0.814394i	$0.302931\pi$
$618$	25.1270	1.01075
$619$	−3.75794	−0.151044	−0.0755222	−	0.997144i	$-0.524062\pi$
$619$	−3.75794	−0.151044	−0.0755222	+	0.997144i	$0.524062\pi$
$620$	20.1337	0.808587
$621$	8.02655	0.322095
$622$	10.9418	0.438727
$623$	6.39894	0.256368
$624$	0	0
$625$	16.3261	0.653042
$626$	42.9737	1.71758
$627$	6.69175	0.267243
$628$	82.0885	3.27569
$629$	1.04577	0.0416974
$630$	5.15623	0.205429
$631$	−14.7525	−0.587288	−0.293644	−	0.955915i	$-0.594868\pi$
$631$	−14.7525	−0.587288	−0.293644	+	0.955915i	$0.594868\pi$
$632$	−11.0708	−0.440374
$633$	−14.9716	−0.595068
$634$	−76.1979	−3.02620
$635$	15.4993	0.615073
$636$	11.2677	0.446795
$637$	0	0
$638$	19.9827	0.791123
$639$	5.96382	0.235925
$640$	14.5337	0.574494
$641$	−26.5133	−1.04721	−0.523605	−	0.851961i	$-0.675413\pi$
$641$	−26.5133	−1.04721	−0.523605	+	0.851961i	$0.675413\pi$
$642$	7.55517	0.298179
$643$	17.7371	0.699482	0.349741	−	0.936846i	$-0.386270\pi$
$643$	17.7371	0.699482	0.349741	+	0.936846i	$0.386270\pi$
$644$	88.3813	3.48271
$645$	−5.61790	−0.221205
$646$	43.2912	1.70327
$647$	−32.2751	−1.26886	−0.634432	−	0.772978i	$-0.718766\pi$
$647$	−32.2751	−1.26886	−0.634432	+	0.772978i	$0.718766\pi$
$648$	−5.15968	−0.202691
$649$	−10.8104	−0.424345
$650$	0	0
$651$	17.0686	0.668969
$652$	−73.5617	−2.88090
$653$	−3.25803	−0.127497	−0.0637483	−	0.997966i	$-0.520305\pi$
$653$	−3.25803	−0.127497	−0.0637483	+	0.997966i	$0.520305\pi$
$654$	−32.5273	−1.27192
$655$	3.82142	0.149315
$656$	−31.2890	−1.22163
$657$	−3.79648	−0.148115
$658$	30.1390	1.17494
$659$	39.0368	1.52066	0.760329	−	0.649539i	$-0.225038\pi$
$659$	39.0368	1.52066	0.760329	+	0.649539i	$0.225038\pi$
$660$	−3.17512	−0.123592
$661$	38.9194	1.51379	0.756895	−	0.653537i	$-0.226715\pi$
$661$	38.9194	1.51379	0.756895	+	0.653537i	$0.226715\pi$
$662$	16.6030	0.645293
$663$	0	0
$664$	19.2649	0.747625
$665$	13.9810	0.542160
$666$	−0.984558	−0.0381509
$667$	64.9906	2.51645
$668$	−39.8689	−1.54258
$669$	−26.2003	−1.01296
$670$	−9.49654	−0.366883
$671$	−5.02796	−0.194102
$672$	−2.46448	−0.0950692
$673$	34.5466	1.33167	0.665837	−	0.746097i	$-0.268074\pi$
$673$	34.5466	1.33167	0.665837	+	0.746097i	$0.268074\pi$
$674$	12.4910	0.481137
$675$	4.39754	0.169261
$676$	0	0
$677$	25.4362	0.977591	0.488796	−	0.872398i	$-0.337436\pi$
$677$	25.4362	0.977591	0.488796	+	0.872398i	$0.337436\pi$
$678$	11.1075	0.426582
$679$	−48.0088	−1.84241
$680$	−10.4982	−0.402586
$681$	24.2441	0.929037
$682$	−15.6493	−0.599243
$683$	−9.81027	−0.375379	−0.187690	−	0.982228i	$-0.560100\pi$
$683$	−9.81027	−0.375379	−0.187690	+	0.982228i	$0.560100\pi$
$684$	−27.3739	−1.04667
$685$	10.2360	0.391098
$686$	−44.8704	−1.71316
$687$	−6.43954	−0.245684
$688$	32.9494	1.25618
$689$	0	0
$690$	−15.3754	−0.585332
$691$	6.32133	0.240475	0.120237	−	0.992745i	$-0.461634\pi$
$691$	6.32133	0.240475	0.120237	+	0.992745i	$0.461634\pi$
$692$	−61.2954	−2.33010
$693$	−2.69175	−0.102251
$694$	10.7183	0.406861
$695$	8.55377	0.324463
$696$	−41.7777	−1.58358
$697$	−18.0169	−0.682440
$698$	50.0445	1.89421
$699$	24.0536	0.909789
$700$	48.4218	1.83017
$701$	30.4082	1.14850	0.574251	−	0.818679i	$-0.305293\pi$
$701$	30.4082	1.14850	0.574251	+	0.818679i	$0.305293\pi$
$702$	0	0
$703$	−2.66961	−0.100686
$704$	−6.84517	−0.257987
$705$	−3.52148	−0.132627
$706$	−90.2351	−3.39604
$707$	29.9042	1.12466
$708$	44.2220	1.66196
$709$	38.0014	1.42717	0.713586	−	0.700568i	$-0.247070\pi$
$709$	38.0014	1.42717	0.713586	+	0.700568i	$0.247070\pi$
$710$	−11.4241	−0.428739
$711$	2.14564	0.0804678
$712$	12.2658	0.459681
$713$	−50.8969	−1.90610
$714$	−17.4138	−0.651696
$715$	0	0
$716$	−59.4267	−2.22088
$717$	5.01391	0.187248
$718$	−68.7618	−2.56617
$719$	34.7670	1.29659	0.648295	−	0.761389i	$-0.275482\pi$
$719$	34.7670	1.29659	0.648295	+	0.761389i	$0.275482\pi$
$720$	3.53347	0.131685
$721$	−27.4057	−1.02064
$722$	−63.6221	−2.36777
$723$	−24.9890	−0.929350
$724$	3.71970	0.138242
$725$	35.6067	1.32240
$726$	2.46793	0.0915936
$727$	27.5746	1.02269	0.511343	−	0.859377i	$-0.329148\pi$
$727$	27.5746	1.02269	0.511343	+	0.859377i	$0.329148\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	7.27241	0.269164
$731$	18.9730	0.701742
$732$	20.5678	0.760208
$733$	−20.5076	−0.757464	−0.378732	−	0.925506i	$-0.623640\pi$
$733$	−20.5076	−0.757464	−0.378732	+	0.925506i	$0.623640\pi$
$734$	−25.7841	−0.951707
$735$	−0.190565	−0.00702910
$736$	7.34885	0.270882
$737$	4.95756	0.182614
$738$	16.9624	0.624395
$739$	29.7241	1.09342	0.546710	−	0.837322i	$-0.315880\pi$
$739$	29.7241	1.09342	0.546710	+	0.837322i	$0.315880\pi$
$740$	1.26669	0.0465643
$741$	0	0
$742$	−18.2982	−0.671748
$743$	−5.01986	−0.184161	−0.0920804	−	0.995752i	$-0.529352\pi$
$743$	−5.01986	−0.184161	−0.0920804	+	0.995752i	$0.529352\pi$
$744$	32.7179	1.19950
$745$	−6.40865	−0.234795
$746$	44.1371	1.61597
$747$	−3.73375	−0.136611
$748$	10.7232	0.392078
$749$	−8.24035	−0.301096
$750$	−18.0016	−0.657326
$751$	−17.7309	−0.647011	−0.323506	−	0.946226i	$-0.604861\pi$
$751$	−17.7309	−0.647011	−0.323506	+	0.946226i	$0.604861\pi$
$752$	20.6537	0.753164
$753$	−18.0406	−0.657436
$754$	0	0
$755$	2.80598	0.102120
$756$	11.0111	0.400470
$757$	−32.8369	−1.19348	−0.596740	−	0.802435i	$-0.703537\pi$
$757$	−32.8369	−1.19348	−0.596740	+	0.802435i	$0.703537\pi$
$758$	−33.6131	−1.22088
$759$	8.02655	0.291345
$760$	26.7995	0.972120
$761$	−40.7015	−1.47543	−0.737713	−	0.675114i	$-0.764094\pi$
$761$	−40.7015	−1.47543	−0.737713	+	0.675114i	$0.764094\pi$
$762$	49.2813	1.78527
$763$	35.4772	1.28436
$764$	50.9080	1.84179
$765$	2.03465	0.0735630
$766$	11.4241	0.412769
$767$	0	0
$768$	32.5206	1.17349
$769$	31.1712	1.12406	0.562032	−	0.827116i	$-0.310020\pi$
$769$	31.1712	1.12406	0.562032	+	0.827116i	$0.310020\pi$
$770$	5.15623	0.185817
$771$	21.1298	0.760970
$772$	−75.0258	−2.70024
$773$	−9.63553	−0.346566	−0.173283	−	0.984872i	$-0.555437\pi$
$773$	−9.63553	−0.346566	−0.173283	+	0.984872i	$0.555437\pi$
$774$	−17.8625	−0.642056
$775$	−27.8851	−1.00166
$776$	−92.0258	−3.30353
$777$	1.07385	0.0385241
$778$	−13.1859	−0.472738
$779$	45.9933	1.64788
$780$	0	0
$781$	5.96382	0.213402
$782$	51.9265	1.85689
$783$	8.09695	0.289361
$784$	1.11768	0.0399170
$785$	15.5758	0.555923
$786$	12.1505	0.433394
$787$	29.7241	1.05955	0.529775	−	0.848138i	$-0.322276\pi$
$787$	29.7241	1.05955	0.529775	+	0.848138i	$0.322276\pi$
$788$	32.5838	1.16075
$789$	−11.8592	−0.422199
$790$	−4.11012	−0.146231
$791$	−12.1149	−0.430755
$792$	−5.15968	−0.183341
$793$	0	0
$794$	69.2750	2.45848
$795$	2.13798	0.0758265
$796$	−59.8940	−2.12288
$797$	4.82571	0.170935	0.0854677	−	0.996341i	$-0.472762\pi$
$797$	4.82571	0.170935	0.0854677	+	0.996341i	$0.472762\pi$
$798$	44.4537	1.57364
$799$	11.8929	0.420741
$800$	4.02624	0.142349
$801$	−2.37724	−0.0839957
$802$	79.9466	2.82301
$803$	−3.79648	−0.133975
$804$	−20.2799	−0.715215
$805$	16.7698	0.591058
$806$	0	0
$807$	0.322165	0.0113407
$808$	57.3219	2.01658
$809$	−31.6284	−1.11200	−0.555998	−	0.831183i	$-0.687664\pi$
$809$	−31.6284	−1.11200	−0.555998	+	0.831183i	$0.687664\pi$
$810$	−1.91557	−0.0673062
$811$	30.2655	1.06276	0.531382	−	0.847132i	$-0.321673\pi$
$811$	30.2655	1.06276	0.531382	+	0.847132i	$0.321673\pi$
$812$	89.1564	3.12878
$813$	26.2944	0.922186
$814$	−0.984558	−0.0345088
$815$	−13.9579	−0.488923
$816$	−11.9334	−0.417752
$817$	−48.4339	−1.69449
$818$	−55.3755	−1.93616
$819$	0	0
$820$	−21.8230	−0.762093
$821$	18.9833	0.662521	0.331261	−	0.943539i	$-0.392526\pi$
$821$	18.9833	0.662521	0.331261	+	0.943539i	$0.392526\pi$
$822$	32.5462	1.13518
$823$	−24.6234	−0.858318	−0.429159	−	0.903229i	$-0.641190\pi$
$823$	−24.6234	−0.858318	−0.429159	+	0.903229i	$0.641190\pi$
$824$	−52.5327	−1.83006
$825$	4.39754	0.153103
$826$	−71.8141	−2.49873
$827$	−23.7784	−0.826855	−0.413427	−	0.910537i	$-0.635668\pi$
$827$	−23.7784	−0.826855	−0.413427	+	0.910537i	$0.635668\pi$
$828$	−32.8341	−1.14107
$829$	44.5973	1.54893	0.774463	−	0.632619i	$-0.218020\pi$
$829$	44.5973	1.54893	0.774463	+	0.632619i	$0.218020\pi$
$830$	7.15224	0.248258
$831$	8.89247	0.308476
$832$	0	0
$833$	0.643584	0.0222989
$834$	27.1974	0.941767
$835$	−7.56488	−0.261793
$836$	−27.3739	−0.946745
$837$	−6.34106	−0.219179
$838$	−100.226	−3.46225
$839$	22.1090	0.763288	0.381644	−	0.924309i	$-0.375358\pi$
$839$	22.1090	0.763288	0.381644	+	0.924309i	$0.375358\pi$
$840$	−10.7801	−0.371948
$841$	36.5606	1.26071
$842$	−6.59533	−0.227290
$843$	23.5833	0.812253
$844$	61.2442	2.10811
$845$	0	0
$846$	−11.1968	−0.384955
$847$	−2.69175	−0.0924896
$848$	−12.5394	−0.430605
$849$	−8.13754	−0.279280
$850$	28.4492	0.975798
$851$	−3.20212	−0.109767
$852$	−24.3961	−0.835798
$853$	17.8689	0.611820	0.305910	−	0.952060i	$-0.401039\pi$
$853$	17.8689	0.611820	0.305910	+	0.952060i	$0.401039\pi$
$854$	−33.4010	−1.14296
$855$	−5.19402	−0.177632
$856$	−15.7955	−0.539879
$857$	11.6521	0.398029	0.199014	−	0.979997i	$-0.436226\pi$
$857$	11.6521	0.398029	0.199014	+	0.979997i	$0.436226\pi$
$858$	0	0
$859$	52.8576	1.80348	0.901740	−	0.432279i	$-0.142290\pi$
$859$	52.8576	1.80348	0.901740	+	0.432279i	$0.142290\pi$
$860$	22.9811	0.783649
$861$	−18.5007	−0.630504
$862$	−64.1593	−2.18528
$863$	−51.1483	−1.74111	−0.870554	−	0.492072i	$-0.836240\pi$
$863$	−51.1483	−1.74111	−0.870554	+	0.492072i	$0.836240\pi$
$864$	0.915567	0.0311482
$865$	−11.6304	−0.395446
$866$	−46.8326	−1.59144
$867$	10.1285	0.343981
$868$	−69.8222	−2.36992
$869$	2.14564	0.0727859
$870$	−15.5102	−0.525846
$871$	0	0
$872$	68.0045	2.30292
$873$	17.8355	0.603642
$874$	−132.557	−4.48380
$875$	19.6342	0.663757
$876$	15.5302	0.524718
$877$	28.0125	0.945915	0.472958	−	0.881085i	$-0.343186\pi$
$877$	28.0125	0.945915	0.472958	+	0.881085i	$0.343186\pi$
$878$	−41.6060	−1.40413
$879$	19.8649	0.670027
$880$	3.53347	0.119113
$881$	16.2095	0.546111	0.273055	−	0.961998i	$-0.411966\pi$
$881$	16.2095	0.546111	0.273055	+	0.961998i	$0.411966\pi$
$882$	−0.605916	−0.0204022
$883$	−50.4100	−1.69643	−0.848216	−	0.529650i	$-0.822323\pi$
$883$	−50.4100	−1.69643	−0.848216	+	0.529650i	$0.822323\pi$
$884$	0	0
$885$	8.39084	0.282055
$886$	−85.1695	−2.86132
$887$	49.4717	1.66110	0.830548	−	0.556947i	$-0.188027\pi$
$887$	49.4717	1.66110	0.830548	+	0.556947i	$0.188027\pi$
$888$	2.05841	0.0690756
$889$	−53.7507	−1.80274
$890$	4.55377	0.152643
$891$	1.00000	0.0335013
$892$	107.177	3.58856
$893$	−30.3600	−1.01596
$894$	−20.3768	−0.681502
$895$	−11.2758	−0.376910
$896$	−50.4018	−1.68381
$897$	0	0
$898$	12.6448	0.421961
$899$	−51.3432	−1.71239
$900$	−17.9890	−0.599632
$901$	−7.22049	−0.240549
$902$	16.9624	0.564787
$903$	19.4825	0.648337
$904$	−23.2224	−0.772366
$905$	0.705791	0.0234613
$906$	8.92182	0.296408
$907$	−59.3623	−1.97109	−0.985547	−	0.169403i	$-0.945816\pi$
$907$	−59.3623	−1.97109	−0.985547	+	0.169403i	$0.945816\pi$
$908$	−99.1752	−3.29124
$909$	−11.1096	−0.368482
$910$	0	0
$911$	−23.7337	−0.786334	−0.393167	−	0.919467i	$-0.628621\pi$
$911$	−23.7337	−0.786334	−0.393167	+	0.919467i	$0.628621\pi$
$912$	30.4633	1.00874
$913$	−3.73375	−0.123569
$914$	−49.1732	−1.62650
$915$	3.90261	0.129016
$916$	26.3421	0.870369
$917$	−13.2524	−0.437634
$918$	6.46933	0.213520
$919$	37.1293	1.22478	0.612392	−	0.790555i	$-0.290208\pi$
$919$	37.1293	1.22478	0.612392	+	0.790555i	$0.290208\pi$
$920$	32.1452	1.05980
$921$	−23.3305	−0.768765
$922$	−25.8296	−0.850653
$923$	0	0
$924$	11.0111	0.362239
$925$	−1.75436	−0.0576829
$926$	−90.2173	−2.96472
$927$	10.1814	0.334400
$928$	7.41330	0.243353
$929$	3.10364	0.101827	0.0509136	−	0.998703i	$-0.483787\pi$
$929$	3.10364	0.101827	0.0509136	+	0.998703i	$0.483787\pi$
$930$	12.1467	0.398307
$931$	−1.64293	−0.0538448
$932$	−98.3956	−3.22306
$933$	4.43359	0.145149
$934$	5.99903	0.196294
$935$	2.03465	0.0665403
$936$	0	0
$937$	23.1072	0.754880	0.377440	−	0.926034i	$-0.376804\pi$
$937$	23.1072	0.754880	0.377440	+	0.926034i	$0.376804\pi$
$938$	32.9334	1.07531
$939$	17.4129	0.568247
$940$	14.4053	0.469849
$941$	−1.36416	−0.0444704	−0.0222352	−	0.999753i	$-0.507078\pi$
$941$	−1.36416	−0.0444704	−0.0222352	+	0.999753i	$0.507078\pi$
$942$	49.5244	1.61359
$943$	55.1676	1.79650
$944$	−49.2129	−1.60174
$945$	2.08929	0.0679646
$946$	−17.8625	−0.580761
$947$	18.6209	0.605098	0.302549	−	0.953134i	$-0.402162\pi$
$947$	18.6209	0.605098	0.302549	+	0.953134i	$0.402162\pi$
$948$	−8.77715	−0.285069
$949$	0	0
$950$	−72.6244	−2.35625
$951$	−30.8752	−1.00120
$952$	36.4069	1.17995
$953$	19.4237	0.629194	0.314597	−	0.949225i	$-0.398131\pi$
$953$	19.4237	0.629194	0.314597	+	0.949225i	$0.398131\pi$
$954$	6.79788	0.220090
$955$	9.65947	0.312573
$956$	−20.5104	−0.663353
$957$	8.09695	0.261737
$958$	−4.85034	−0.156708
$959$	−35.4978	−1.14628
$960$	5.31311	0.171480
$961$	9.20907	0.297067
$962$	0	0
$963$	3.06133	0.0986501
$964$	102.222	3.29235
$965$	−14.2357	−0.458263
$966$	53.3209	1.71557
$967$	10.2413	0.329338	0.164669	−	0.986349i	$-0.447344\pi$
$967$	10.2413	0.329338	0.164669	+	0.986349i	$0.447344\pi$
$968$	−5.15968	−0.165838
$969$	17.5415	0.563513
$970$	−34.1652	−1.09698
$971$	8.71822	0.279781	0.139890	−	0.990167i	$-0.455325\pi$
$971$	8.71822	0.279781	0.139890	+	0.990167i	$0.455325\pi$
$972$	−4.09069	−0.131209
$973$	−29.6639	−0.950980
$974$	55.4946	1.77816
$975$	0	0
$976$	−22.8891	−0.732662
$977$	56.9127	1.82080	0.910400	−	0.413730i	$-0.135774\pi$
$977$	56.9127	1.82080	0.910400	+	0.413730i	$0.135774\pi$
$978$	−44.3801	−1.41912
$979$	−2.37724	−0.0759770
$980$	0.779542	0.0249016
$981$	−13.1800	−0.420804
$982$	−42.6740	−1.36178
$983$	−25.1270	−0.801425	−0.400713	−	0.916204i	$-0.631237\pi$
$983$	−25.1270	−0.801425	−0.400713	+	0.916204i	$0.631237\pi$
$984$	−35.4632	−1.13052
$985$	6.18257	0.196993
$986$	52.3818	1.66818
$987$	12.2123	0.388721
$988$	0	0
$989$	−58.0951	−1.84732
$990$	−1.91557	−0.0608807
$991$	−12.8268	−0.407458	−0.203729	−	0.979027i	$-0.565306\pi$
$991$	−12.8268	−0.407458	−0.203729	+	0.979027i	$0.565306\pi$
$992$	−5.80567	−0.184330
$993$	6.72749	0.213490
$994$	39.6180	1.25661
$995$	−11.3645	−0.360279
$996$	15.2736	0.483962
$997$	2.62596	0.0831650	0.0415825	−	0.999135i	$-0.486760\pi$
$997$	2.62596	0.0831650	0.0415825	+	0.999135i	$0.486760\pi$
$998$	9.16799	0.290208
$999$	−0.398941	−0.0126219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.m.1.1		4
13.12	even	2		429.2.a.h.1.4	✓	4
39.38	odd	2		1287.2.a.m.1.1		4
52.51	odd	2		6864.2.a.bz.1.2		4
143.142	odd	2		4719.2.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.h.1.4	✓	4	13.12	even	2
1287.2.a.m.1.1		4	39.38	odd	2
4719.2.a.z.1.1		4	143.142	odd	2
5577.2.a.m.1.1		4	1.1	even	1	trivial
6864.2.a.bz.1.2		4	52.51	odd	2

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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46793 q^{2} -1.00000 q^{3} +4.09069 q^{4} +0.776183 q^{5} +2.46793 q^{6} -2.69175 q^{7} -5.15968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46793 q^{2} -1.00000 q^{3} +4.09069 q^{4} +0.776183 q^{5} +2.46793 q^{6} -2.69175 q^{7} -5.15968 q^{8} +1.00000 q^{9} -1.91557 q^{10} +1.00000 q^{11} -4.09069 q^{12} +6.64306 q^{14} -0.776183 q^{15} +4.55237 q^{16} +2.62136 q^{17} -2.46793 q^{18} -6.69175 q^{19} +3.17512 q^{20} +2.69175 q^{21} -2.46793 q^{22} -8.02655 q^{23} +5.15968 q^{24} -4.39754 q^{25} -1.00000 q^{27} -11.0111 q^{28} -8.09695 q^{29} +1.91557 q^{30} +6.34106 q^{31} -0.915567 q^{32} -1.00000 q^{33} -6.46933 q^{34} -2.08929 q^{35} +4.09069 q^{36} +0.398941 q^{37} +16.5148 q^{38} -4.00486 q^{40} -6.87313 q^{41} -6.64306 q^{42} +7.23786 q^{43} +4.09069 q^{44} +0.776183 q^{45} +19.8090 q^{46} +4.53692 q^{47} -4.55237 q^{48} +0.245516 q^{49} +10.8528 q^{50} -2.62136 q^{51} -2.75448 q^{53} +2.46793 q^{54} +0.776183 q^{55} +13.8886 q^{56} +6.69175 q^{57} +19.9827 q^{58} -10.8104 q^{59} -3.17512 q^{60} -5.02796 q^{61} -15.6493 q^{62} -2.69175 q^{63} -6.84517 q^{64} +2.46793 q^{66} +4.95756 q^{67} +10.7232 q^{68} +8.02655 q^{69} +5.15623 q^{70} +5.96382 q^{71} -5.15968 q^{72} -3.79648 q^{73} -0.984558 q^{74} +4.39754 q^{75} -27.3739 q^{76} -2.69175 q^{77} +2.14564 q^{79} +3.53347 q^{80} +1.00000 q^{81} +16.9624 q^{82} -3.73375 q^{83} +11.0111 q^{84} +2.03465 q^{85} -17.8625 q^{86} +8.09695 q^{87} -5.15968 q^{88} -2.37724 q^{89} -1.91557 q^{90} -32.8341 q^{92} -6.34106 q^{93} -11.1968 q^{94} -5.19402 q^{95} +0.915567 q^{96} +17.8355 q^{97} -0.605916 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 2 q^{18} - 18 q^{19} + 10 q^{20} + 2 q^{21} + 2 q^{22} + 4 q^{25} - 4 q^{27} + 6 q^{28} - 10 q^{29} + 2 q^{30} - 12 q^{31} + 2 q^{32} - 4 q^{33} - 36 q^{34} + 22 q^{35} + 8 q^{36} + 2 q^{37} + 4 q^{38} + 20 q^{40} - 2 q^{41} - 12 q^{42} + 28 q^{43} + 8 q^{44} + 30 q^{46} - 6 q^{47} - 12 q^{48} + 8 q^{49} + 36 q^{50} + 8 q^{51} - 4 q^{53} - 2 q^{54} + 48 q^{56} + 18 q^{57} + 6 q^{58} - 16 q^{59} - 10 q^{60} - 10 q^{61} - 34 q^{62} - 2 q^{63} - 12 q^{64} - 2 q^{66} - 34 q^{68} + 58 q^{70} - 10 q^{71} + 6 q^{73} + 14 q^{74} - 4 q^{75} - 26 q^{76} - 2 q^{77} - 8 q^{79} + 48 q^{80} + 4 q^{81} + 12 q^{82} + 8 q^{83} - 6 q^{84} + 18 q^{85} + 8 q^{86} + 10 q^{87} - 6 q^{89} - 2 q^{90} - 28 q^{92} + 12 q^{93} - 46 q^{94} + 22 q^{95} - 2 q^{96} - 10 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 2 * q^18 - 18 * q^19 + 10 * q^20 + 2 * q^21 + 2 * q^22 + 4 * q^25 - 4 * q^27 + 6 * q^28 - 10 * q^29 + 2 * q^30 - 12 * q^31 + 2 * q^32 - 4 * q^33 - 36 * q^34 + 22 * q^35 + 8 * q^36 + 2 * q^37 + 4 * q^38 + 20 * q^40 - 2 * q^41 - 12 * q^42 + 28 * q^43 + 8 * q^44 + 30 * q^46 - 6 * q^47 - 12 * q^48 + 8 * q^49 + 36 * q^50 + 8 * q^51 - 4 * q^53 - 2 * q^54 + 48 * q^56 + 18 * q^57 + 6 * q^58 - 16 * q^59 - 10 * q^60 - 10 * q^61 - 34 * q^62 - 2 * q^63 - 12 * q^64 - 2 * q^66 - 34 * q^68 + 58 * q^70 - 10 * q^71 + 6 * q^73 + 14 * q^74 - 4 * q^75 - 26 * q^76 - 2 * q^77 - 8 * q^79 + 48 * q^80 + 4 * q^81 + 12 * q^82 + 8 * q^83 - 6 * q^84 + 18 * q^85 + 8 * q^86 + 10 * q^87 - 6 * q^89 - 2 * q^90 - 28 * q^92 + 12 * q^93 - 46 * q^94 + 22 * q^95 - 2 * q^96 - 10 * q^97 + 34 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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