LMFDB - Embedded newform 1617.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.814115$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.185885 q^{2} +1.00000 q^{3} -1.96545 q^{4} -0.737118 q^{5} +0.185885 q^{6} -0.737118 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.185885 q^{2} +1.00000 q^{3} -1.96545 q^{4} -0.737118 q^{5} +0.185885 q^{6} -0.737118 q^{8} +1.00000 q^{9} -0.137020 q^{10} -1.00000 q^{11} -1.96545 q^{12} -1.45666 q^{13} -0.737118 q^{15} +3.79387 q^{16} +0.694676 q^{17} +0.185885 q^{18} +2.62823 q^{19} +1.44877 q^{20} -0.185885 q^{22} +4.77956 q^{23} -0.737118 q^{24} -4.45666 q^{25} -0.270771 q^{26} +1.00000 q^{27} +0.434454 q^{29} -0.137020 q^{30} +2.04887 q^{31} +2.17946 q^{32} -1.00000 q^{33} +0.129130 q^{34} -1.96545 q^{36} +7.38755 q^{37} +0.488549 q^{38} -1.45666 q^{39} +0.543344 q^{40} +9.34511 q^{41} -0.108889 q^{43} +1.96545 q^{44} -0.737118 q^{45} +0.888450 q^{46} +2.28046 q^{47} +3.79387 q^{48} -0.828427 q^{50} +0.694676 q^{51} +2.86298 q^{52} -0.877293 q^{53} +0.185885 q^{54} +0.737118 q^{55} +2.62823 q^{57} +0.0807587 q^{58} +4.21136 q^{59} +1.44877 q^{60} +13.6035 q^{61} +0.380854 q^{62} -7.18262 q^{64} +1.07373 q^{65} -0.185885 q^{66} -4.05153 q^{67} -1.36535 q^{68} +4.77956 q^{69} -7.42999 q^{71} -0.737118 q^{72} +3.52576 q^{73} +1.37324 q^{74} -4.45666 q^{75} -5.16564 q^{76} -0.270771 q^{78} +0.0977317 q^{79} -2.79653 q^{80} +1.00000 q^{81} +1.73712 q^{82} +16.3387 q^{83} -0.512058 q^{85} -0.0202409 q^{86} +0.434454 q^{87} +0.737118 q^{88} +5.71312 q^{89} -0.137020 q^{90} -9.39397 q^{92} +2.04887 q^{93} +0.423904 q^{94} -1.93732 q^{95} +2.17946 q^{96} -5.14225 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * q^97 - 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 $

$2$	0.185885	0.131441	0.0657204	−	0.997838i	$-0.479065\pi$
$2$	0.185885	0.131441	0.0657204	+	0.997838i	$0.479065\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96545	−0.982723
$5$	−0.737118	−0.329649	−0.164825	−	0.986323i	$-0.552706\pi$
$5$	−0.737118	−0.329649	−0.164825	+	0.986323i	$0.552706\pi$
$6$	0.185885	0.0758874
$7$	0	0
$7$	0	0
$8$	−0.737118	−0.260611
$9$	1.00000	0.333333
$10$	−0.137020	−0.0433294
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.96545	−0.567376
$13$	−1.45666	−0.404004	−0.202002	−	0.979385i	$-0.564745\pi$
$13$	−1.45666	−0.404004	−0.202002	+	0.979385i	$0.564745\pi$
$14$	0	0
$15$	−0.737118	−0.190323
$16$	3.79387	0.948468
$17$	0.694676	0.168484	0.0842418	−	0.996445i	$-0.473153\pi$
$17$	0.694676	0.168484	0.0842418	+	0.996445i	$0.473153\pi$
$18$	0.185885	0.0438136
$19$	2.62823	0.602957	0.301479	−	0.953473i	$-0.402520\pi$
$19$	2.62823	0.602957	0.301479	+	0.953473i	$0.402520\pi$
$20$	1.44877	0.323954
$21$	0	0
$22$	−0.185885	−0.0396309
$23$	4.77956	0.996607	0.498304	−	0.867003i	$-0.333956\pi$
$23$	4.77956	0.996607	0.498304	+	0.867003i	$0.333956\pi$
$24$	−0.737118	−0.150464
$25$	−4.45666	−0.891331
$26$	−0.270771	−0.0531026
$27$	1.00000	0.192450
$28$	0	0
$29$	0.434454	0.0806762	0.0403381	−	0.999186i	$-0.487157\pi$
$29$	0.434454	0.0806762	0.0403381	+	0.999186i	$0.487157\pi$
$30$	−0.137020	−0.0250162
$31$	2.04887	0.367987	0.183994	−	0.982927i	$-0.441097\pi$
$31$	2.04887	0.367987	0.183994	+	0.982927i	$0.441097\pi$
$32$	2.17946	0.385278
$33$	−1.00000	−0.174078
$34$	0.129130	0.0221456
$35$	0	0
$36$	−1.96545	−0.327574
$37$	7.38755	1.21451	0.607253	−	0.794509i	$-0.292272\pi$
$37$	7.38755	1.21451	0.607253	+	0.794509i	$0.292272\pi$
$38$	0.488549	0.0792532
$39$	−1.45666	−0.233252
$40$	0.543344	0.0859102
$41$	9.34511	1.45946	0.729730	−	0.683735i	$-0.239646\pi$
$41$	9.34511	1.45946	0.729730	+	0.683735i	$0.239646\pi$
$42$	0	0
$43$	−0.108889	−0.0166054	−0.00830272	−	0.999966i	$-0.502643\pi$
$43$	−0.108889	−0.0166054	−0.00830272	+	0.999966i	$0.502643\pi$
$44$	1.96545	0.296302
$45$	−0.737118	−0.109883
$46$	0.888450	0.130995
$47$	2.28046	0.332640	0.166320	−	0.986072i	$-0.446812\pi$
$47$	2.28046	0.332640	0.166320	+	0.986072i	$0.446812\pi$
$48$	3.79387	0.547599
$49$	0	0
$50$	−0.828427	−0.117157
$51$	0.694676	0.0972740
$52$	2.86298	0.397024
$53$	−0.877293	−0.120505	−0.0602527	−	0.998183i	$-0.519191\pi$
$53$	−0.877293	−0.120505	−0.0602527	+	0.998183i	$0.519191\pi$
$54$	0.185885	0.0252958
$55$	0.737118	0.0993930
$56$	0	0
$57$	2.62823	0.348117
$58$	0.0807587	0.0106041
$59$	4.21136	0.548272	0.274136	−	0.961691i	$-0.411608\pi$
$59$	4.21136	0.548272	0.274136	+	0.961691i	$0.411608\pi$
$60$	1.44877	0.187035
$61$	13.6035	1.74175	0.870877	−	0.491502i	$-0.163552\pi$
$61$	13.6035	1.74175	0.870877	+	0.491502i	$0.163552\pi$
$62$	0.380854	0.0483685
$63$	0	0
$64$	−7.18262	−0.897827
$65$	1.07373	0.133180
$66$	−0.185885	−0.0228809
$67$	−4.05153	−0.494973	−0.247486	−	0.968891i	$-0.579605\pi$
$67$	−4.05153	−0.494973	−0.247486	+	0.968891i	$0.579605\pi$
$68$	−1.36535	−0.165573
$69$	4.77956	0.575392
$70$	0	0
$71$	−7.42999	−0.881778	−0.440889	−	0.897562i	$-0.645337\pi$
$71$	−7.42999	−0.881778	−0.440889	+	0.897562i	$0.645337\pi$
$72$	−0.737118	−0.0868702
$73$	3.52576	0.412659	0.206330	−	0.978483i	$-0.433848\pi$
$73$	3.52576	0.412659	0.206330	+	0.978483i	$0.433848\pi$
$74$	1.37324	0.159636
$75$	−4.45666	−0.514610
$76$	−5.16564	−0.592540
$77$	0	0
$78$	−0.270771	−0.0306588
$79$	0.0977317	0.0109957	0.00549784	−	0.999985i	$-0.498250\pi$
$79$	0.0977317	0.0109957	0.00549784	+	0.999985i	$0.498250\pi$
$80$	−2.79653	−0.312662
$81$	1.00000	0.111111
$82$	1.73712	0.191833
$83$	16.3387	1.79340	0.896702	−	0.442635i	$-0.145956\pi$
$83$	16.3387	1.79340	0.896702	+	0.442635i	$0.145956\pi$
$84$	0	0
$85$	−0.512058	−0.0555405
$86$	−0.0202409	−0.00218263
$87$	0.434454	0.0465784
$88$	0.737118	0.0785771
$89$	5.71312	0.605589	0.302794	−	0.953056i	$-0.402080\pi$
$89$	5.71312	0.605589	0.302794	+	0.953056i	$0.402080\pi$
$90$	−0.137020	−0.0144431
$91$	0	0
$92$	−9.39397	−0.979389
$93$	2.04887	0.212457
$94$	0.423904	0.0437224
$95$	−1.93732	−0.198764
$96$	2.17946	0.222440
$97$	−5.14225	−0.522116	−0.261058	−	0.965323i	$-0.584071\pi$
$97$	−5.14225	−0.522116	−0.261058	+	0.965323i	$0.584071\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	8.75932	0.875932
$101$	−6.23148	−0.620056	−0.310028	−	0.950727i	$-0.600338\pi$
$101$	−6.23148	−0.620056	−0.310028	+	0.950727i	$0.600338\pi$
$102$	0.129130	0.0127858
$103$	14.0195	1.38139	0.690693	−	0.723148i	$-0.257306\pi$
$103$	14.0195	1.38139	0.690693	+	0.723148i	$0.257306\pi$
$104$	1.07373	0.105288
$105$	0	0
$106$	−0.163076	−0.0158393
$107$	−7.98826	−0.772254	−0.386127	−	0.922446i	$-0.626187\pi$
$107$	−7.98826	−0.772254	−0.386127	+	0.922446i	$0.626187\pi$
$108$	−1.96545	−0.189125
$109$	−6.26664	−0.600236	−0.300118	−	0.953902i	$-0.597026\pi$
$109$	−6.26664	−0.600236	−0.300118	+	0.953902i	$0.597026\pi$
$110$	0.137020	0.0130643
$111$	7.38755	0.701195
$112$	0	0
$113$	11.8304	1.11291	0.556455	−	0.830878i	$-0.312161\pi$
$113$	11.8304	1.11291	0.556455	+	0.830878i	$0.312161\pi$
$114$	0.488549	0.0457568
$115$	−3.52310	−0.328531
$116$	−0.853897	−0.0792824
$117$	−1.45666	−0.134668
$118$	0.782829	0.0720653
$119$	0	0
$120$	0.543344	0.0496003
$121$	1.00000	0.0909091
$122$	2.52870	0.228937
$123$	9.34511	0.842620
$124$	−4.02694	−0.361630
$125$	6.97068	0.623476
$126$	0	0
$127$	1.46308	0.129827	0.0649137	−	0.997891i	$-0.479323\pi$
$127$	1.46308	0.129827	0.0649137	+	0.997891i	$0.479323\pi$
$128$	−5.69407	−0.503289
$129$	−0.108889	−0.00958715
$130$	0.199590	0.0175052
$131$	9.75082	0.851933	0.425967	−	0.904739i	$-0.359934\pi$
$131$	9.75082	0.851933	0.425967	+	0.904739i	$0.359934\pi$
$132$	1.96545	0.171070
$133$	0	0
$134$	−0.753119	−0.0650596
$135$	−0.737118	−0.0634411
$136$	−0.512058	−0.0439086
$137$	7.91065	0.675853	0.337926	−	0.941173i	$-0.390275\pi$
$137$	7.91065	0.675853	0.337926	+	0.941173i	$0.390275\pi$
$138$	0.888450	0.0756299
$139$	−2.63927	−0.223860	−0.111930	−	0.993716i	$-0.535703\pi$
$139$	−2.63927	−0.223860	−0.111930	+	0.993716i	$0.535703\pi$
$140$	0	0
$141$	2.28046	0.192050
$142$	−1.38113	−0.115902
$143$	1.45666	0.121812
$144$	3.79387	0.316156
$145$	−0.320244	−0.0265948
$146$	0.655388	0.0542403
$147$	0	0
$148$	−14.5198	−1.19352
$149$	15.8554	1.29892	0.649461	−	0.760395i	$-0.274995\pi$
$149$	15.8554	1.29892	0.649461	+	0.760395i	$0.274995\pi$
$150$	−0.828427	−0.0676408
$151$	−17.5728	−1.43006	−0.715028	−	0.699096i	$-0.753586\pi$
$151$	−17.5728	−1.43006	−0.715028	+	0.699096i	$0.753586\pi$
$152$	−1.93732	−0.157137
$153$	0.694676	0.0561612
$154$	0	0
$155$	−1.51026	−0.121307
$156$	2.86298	0.229222
$157$	13.3009	1.06152	0.530762	−	0.847521i	$-0.321906\pi$
$157$	13.3009	1.06152	0.530762	+	0.847521i	$0.321906\pi$
$158$	0.0181669	0.00144528
$159$	−0.877293	−0.0695739
$160$	−1.60652	−0.127007
$161$	0	0
$162$	0.185885	0.0146045
$163$	−16.8618	−1.32072	−0.660359	−	0.750950i	$-0.729596\pi$
$163$	−16.8618	−1.32072	−0.660359	+	0.750950i	$0.729596\pi$
$164$	−18.3673	−1.43425
$165$	0.737118	0.0573846
$166$	3.03712	0.235726
$167$	−11.6876	−0.904410	−0.452205	−	0.891914i	$-0.649362\pi$
$167$	−11.6876	−0.904410	−0.452205	+	0.891914i	$0.649362\pi$
$168$	0	0
$169$	−10.8782	−0.836781
$170$	−0.0951841	−0.00730029
$171$	2.62823	0.200986
$172$	0.214016	0.0163185
$173$	−18.4800	−1.40501	−0.702503	−	0.711681i	$-0.747934\pi$
$173$	−18.4800	−1.40501	−0.702503	+	0.711681i	$0.747934\pi$
$174$	0.0807587	0.00612230
$175$	0	0
$176$	−3.79387	−0.285974
$177$	4.21136	0.316545
$178$	1.06198	0.0795991
$179$	−6.81026	−0.509023	−0.254511	−	0.967070i	$-0.581915\pi$
$179$	−6.81026	−0.509023	−0.254511	+	0.967070i	$0.581915\pi$
$180$	1.44877	0.107985
$181$	−6.93732	−0.515647	−0.257823	−	0.966192i	$-0.583005\pi$
$181$	−6.93732	−0.515647	−0.257823	+	0.966192i	$0.583005\pi$
$182$	0	0
$183$	13.6035	1.00560
$184$	−3.52310	−0.259727
$185$	−5.44550	−0.400361
$186$	0.380854	0.0279256
$187$	−0.694676	−0.0507997
$188$	−4.48213	−0.326893
$189$	0	0
$190$	−0.360119	−0.0261258
$191$	16.6727	1.20640	0.603199	−	0.797591i	$-0.293893\pi$
$191$	16.6727	1.20640	0.603199	+	0.797591i	$0.293893\pi$
$192$	−7.18262	−0.518361
$193$	−26.5031	−1.90774	−0.953869	−	0.300224i	$-0.902939\pi$
$193$	−26.5031	−1.90774	−0.953869	+	0.300224i	$0.902939\pi$
$194$	−0.955869	−0.0686274
$195$	1.07373	0.0768913
$196$	0	0
$197$	16.2336	1.15659	0.578297	−	0.815827i	$-0.303718\pi$
$197$	16.2336	1.15659	0.578297	+	0.815827i	$0.303718\pi$
$198$	−0.185885	−0.0132103
$199$	0.199096	0.0141135	0.00705676	−	0.999975i	$-0.497754\pi$
$199$	0.199096	0.0141135	0.00705676	+	0.999975i	$0.497754\pi$
$200$	3.28508	0.232290
$201$	−4.05153	−0.285773
$202$	−1.15834	−0.0815006
$203$	0	0
$204$	−1.36535	−0.0955935
$205$	−6.88845	−0.481110
$206$	2.60603	0.181571
$207$	4.77956	0.332202
$208$	−5.52637	−0.383185
$209$	−2.62823	−0.181798
$210$	0	0
$211$	−5.86179	−0.403542	−0.201771	−	0.979433i	$-0.564670\pi$
$211$	−5.86179	−0.403542	−0.201771	+	0.979433i	$0.564670\pi$
$212$	1.72427	0.118424
$213$	−7.42999	−0.509095
$214$	−1.48490	−0.101506
$215$	0.0802642	0.00547397
$216$	−0.737118	−0.0501546
$217$	0	0
$218$	−1.16488	−0.0788954
$219$	3.52576	0.238249
$220$	−1.44877	−0.0976758
$221$	−1.01190	−0.0680680
$222$	1.37324	0.0921656
$223$	−4.26218	−0.285417	−0.142708	−	0.989765i	$-0.545581\pi$
$223$	−4.26218	−0.285417	−0.142708	+	0.989765i	$0.545581\pi$
$224$	0	0
$225$	−4.45666	−0.297110
$226$	2.19910	0.146282
$227$	13.9558	0.926276	0.463138	−	0.886286i	$-0.346723\pi$
$227$	13.9558	0.926276	0.463138	+	0.886286i	$0.346723\pi$
$228$	−5.16564	−0.342103
$229$	−20.0804	−1.32695	−0.663476	−	0.748198i	$-0.730919\pi$
$229$	−20.0804	−1.32695	−0.663476	+	0.748198i	$0.730919\pi$
$230$	−0.654893	−0.0431824
$231$	0	0
$232$	−0.320244	−0.0210251
$233$	−12.6211	−0.826836	−0.413418	−	0.910541i	$-0.635665\pi$
$233$	−12.6211	−0.826836	−0.413418	+	0.910541i	$0.635665\pi$
$234$	−0.270771	−0.0177009
$235$	−1.68097	−0.109654
$236$	−8.27719	−0.538799
$237$	0.0977317	0.00634835
$238$	0	0
$239$	20.4384	1.32205	0.661024	−	0.750364i	$-0.270122\pi$
$239$	20.4384	1.32205	0.661024	+	0.750364i	$0.270122\pi$
$240$	−2.79653	−0.180516
$241$	4.97138	0.320234	0.160117	−	0.987098i	$-0.448813\pi$
$241$	4.97138	0.320234	0.160117	+	0.987098i	$0.448813\pi$
$242$	0.185885	0.0119492
$243$	1.00000	0.0641500
$244$	−26.7370	−1.71166
$245$	0	0
$246$	1.73712	0.110755
$247$	−3.82843	−0.243597
$248$	−1.51026	−0.0959014
$249$	16.3387	1.03542
$250$	1.29575	0.0819502
$251$	5.12467	0.323466	0.161733	−	0.986835i	$-0.448292\pi$
$251$	5.12467	0.323466	0.161733	+	0.986835i	$0.448292\pi$
$252$	0	0
$253$	−4.77956	−0.300488
$254$	0.271965	0.0170646
$255$	−0.512058	−0.0320663
$256$	13.3068	0.831674
$257$	−2.25184	−0.140466	−0.0702329	−	0.997531i	$-0.522374\pi$
$257$	−2.25184	−0.140466	−0.0702329	+	0.997531i	$0.522374\pi$
$258$	−0.0202409	−0.00126014
$259$	0	0
$260$	−2.11036	−0.130879
$261$	0.434454	0.0268921
$262$	1.81254	0.111979
$263$	12.1018	0.746227	0.373113	−	0.927786i	$-0.378290\pi$
$263$	12.1018	0.746227	0.373113	+	0.927786i	$0.378290\pi$
$264$	0.737118	0.0453665
$265$	0.646669	0.0397245
$266$	0	0
$267$	5.71312	0.349637
$268$	7.96306	0.486421
$269$	−30.7974	−1.87775	−0.938876	−	0.344256i	$-0.888131\pi$
$269$	−30.7974	−1.87775	−0.938876	+	0.344256i	$0.888131\pi$
$270$	−0.137020	−0.00833874
$271$	−1.29514	−0.0786741	−0.0393370	−	0.999226i	$-0.512525\pi$
$271$	−1.29514	−0.0786741	−0.0393370	+	0.999226i	$0.512525\pi$
$272$	2.63551	0.159801
$273$	0	0
$274$	1.47047	0.0888346
$275$	4.45666	0.268746
$276$	−9.39397	−0.565451
$277$	10.9680	0.659004	0.329502	−	0.944155i	$-0.393119\pi$
$277$	10.9680	0.659004	0.329502	+	0.944155i	$0.393119\pi$
$278$	−0.490602	−0.0294244
$279$	2.04887	0.122662
$280$	0	0
$281$	27.6386	1.64878	0.824390	−	0.566023i	$-0.191519\pi$
$281$	27.6386	1.64878	0.824390	+	0.566023i	$0.191519\pi$
$282$	0.423904	0.0252431
$283$	31.1516	1.85177	0.925885	−	0.377805i	$-0.123321\pi$
$283$	31.1516	1.85177	0.925885	+	0.377805i	$0.123321\pi$
$284$	14.6033	0.866544
$285$	−1.93732	−0.114757
$286$	0.270771	0.0160110
$287$	0	0
$288$	2.17946	0.128426
$289$	−16.5174	−0.971613
$290$	−0.0595287	−0.00349565
$291$	−5.14225	−0.301444
$292$	−6.92970	−0.405530
$293$	−5.88942	−0.344064	−0.172032	−	0.985091i	$-0.555033\pi$
$293$	−5.88942	−0.344064	−0.172032	+	0.985091i	$0.555033\pi$
$294$	0	0
$295$	−3.10427	−0.180737
$296$	−5.44550	−0.316513
$297$	−1.00000	−0.0580259
$298$	2.94728	0.170731
$299$	−6.96218	−0.402633
$300$	8.75932	0.505720
$301$	0	0
$302$	−3.26653	−0.187968
$303$	−6.23148	−0.357989
$304$	9.97117	0.571886
$305$	−10.0274	−0.574168
$306$	0.129130	0.00738187
$307$	−26.2089	−1.49582	−0.747909	−	0.663801i	$-0.768942\pi$
$307$	−26.2089	−1.49582	−0.747909	+	0.663801i	$0.768942\pi$
$308$	0	0
$309$	14.0195	0.797544
$310$	−0.280735	−0.0159447
$311$	17.2002	0.975334	0.487667	−	0.873030i	$-0.337848\pi$
$311$	17.2002	0.975334	0.487667	+	0.873030i	$0.337848\pi$
$312$	1.07373	0.0607879
$313$	−7.62616	−0.431056	−0.215528	−	0.976498i	$-0.569147\pi$
$313$	−7.62616	−0.431056	−0.215528	+	0.976498i	$0.569147\pi$
$314$	2.47244	0.139528
$315$	0	0
$316$	−0.192086	−0.0108057
$317$	−16.7353	−0.939949	−0.469975	−	0.882680i	$-0.655737\pi$
$317$	−16.7353	−0.939949	−0.469975	+	0.882680i	$0.655737\pi$
$318$	−0.163076	−0.00914484
$319$	−0.434454	−0.0243248
$320$	5.29444	0.295968
$321$	−7.98826	−0.445861
$322$	0	0
$323$	1.82577	0.101588
$324$	−1.96545	−0.109191
$325$	6.49182	0.360101
$326$	−3.13436	−0.173596
$327$	−6.26664	−0.346546
$328$	−6.88845	−0.380351
$329$	0	0
$330$	0.137020	0.00754268
$331$	−12.1550	−0.668098	−0.334049	−	0.942556i	$-0.608415\pi$
$331$	−12.1550	−0.668098	−0.334049	+	0.942556i	$0.608415\pi$
$332$	−32.1128	−1.76242
$333$	7.38755	0.404835
$334$	−2.17254	−0.118876
$335$	2.98645	0.163167
$336$	0	0
$337$	20.6634	1.12561	0.562805	−	0.826590i	$-0.309722\pi$
$337$	20.6634	1.12561	0.562805	+	0.826590i	$0.309722\pi$
$338$	−2.02209	−0.109987
$339$	11.8304	0.642538
$340$	1.00642	0.0545809
$341$	−2.04887	−0.110952
$342$	0.488549	0.0264177
$343$	0	0
$344$	0.0802642	0.00432755
$345$	−3.52310	−0.189677
$346$	−3.43515	−0.184675
$347$	24.4829	1.31431	0.657155	−	0.753755i	$-0.271760\pi$
$347$	24.4829	1.31431	0.657155	+	0.753755i	$0.271760\pi$
$348$	−0.853897	−0.0457737
$349$	4.48708	0.240188	0.120094	−	0.992763i	$-0.461680\pi$
$349$	4.48708	0.240188	0.120094	+	0.992763i	$0.461680\pi$
$350$	0	0
$351$	−1.45666	−0.0777506
$352$	−2.17946	−0.116166
$353$	27.5632	1.46704	0.733519	−	0.679668i	$-0.237876\pi$
$353$	27.5632	1.46704	0.733519	+	0.679668i	$0.237876\pi$
$354$	0.782829	0.0416069
$355$	5.47678	0.290678
$356$	−11.2288	−0.595126
$357$	0	0
$358$	−1.26593	−0.0669064
$359$	−29.9273	−1.57950	−0.789751	−	0.613428i	$-0.789790\pi$
$359$	−29.9273	−1.57950	−0.789751	+	0.613428i	$0.789790\pi$
$360$	0.543344	0.0286367
$361$	−12.0924	−0.636443
$362$	−1.28955	−0.0677770
$363$	1.00000	0.0524864
$364$	0	0
$365$	−2.59890	−0.136033
$366$	2.52870	0.132177
$367$	−12.8782	−0.672234	−0.336117	−	0.941820i	$-0.609114\pi$
$367$	−12.8782	−0.672234	−0.336117	+	0.941820i	$0.609114\pi$
$368$	18.1331	0.945251
$369$	9.34511	0.486487
$370$	−1.01224	−0.0526238
$371$	0	0
$372$	−4.02694	−0.208787
$373$	−20.5408	−1.06356	−0.531782	−	0.846881i	$-0.678478\pi$
$373$	−20.5408	−1.06356	−0.531782	+	0.846881i	$0.678478\pi$
$374$	−0.129130	−0.00667715
$375$	6.97068	0.359964
$376$	−1.68097	−0.0866894
$377$	−0.632851	−0.0325935
$378$	0	0
$379$	−31.8961	−1.63839	−0.819197	−	0.573512i	$-0.805581\pi$
$379$	−31.8961	−1.63839	−0.819197	+	0.573512i	$0.805581\pi$
$380$	3.80769	0.195330
$381$	1.46308	0.0749558
$382$	3.09922	0.158570
$383$	−4.18555	−0.213872	−0.106936	−	0.994266i	$-0.534104\pi$
$383$	−4.18555	−0.213872	−0.106936	+	0.994266i	$0.534104\pi$
$384$	−5.69407	−0.290574
$385$	0	0
$386$	−4.92654	−0.250755
$387$	−0.108889	−0.00553514
$388$	10.1068	0.513096
$389$	22.1789	1.12451	0.562256	−	0.826963i	$-0.309933\pi$
$389$	22.1789	1.12451	0.562256	+	0.826963i	$0.309933\pi$
$390$	0.199590	0.0101067
$391$	3.32024	0.167912
$392$	0	0
$393$	9.75082	0.491864
$394$	3.01758	0.152024
$395$	−0.0720398	−0.00362472
$396$	1.96545	0.0987674
$397$	1.37736	0.0691279	0.0345640	−	0.999402i	$-0.488996\pi$
$397$	1.37736	0.0691279	0.0345640	+	0.999402i	$0.488996\pi$
$398$	0.0370090	0.00185509
$399$	0	0
$400$	−16.9080	−0.845400
$401$	19.1656	0.957082	0.478541	−	0.878065i	$-0.341166\pi$
$401$	19.1656	0.957082	0.478541	+	0.878065i	$0.341166\pi$
$402$	−0.753119	−0.0375622
$403$	−2.98449	−0.148668
$404$	12.2476	0.609343
$405$	−0.737118	−0.0366277
$406$	0	0
$407$	−7.38755	−0.366187
$408$	−0.512058	−0.0253507
$409$	−29.4900	−1.45819	−0.729094	−	0.684414i	$-0.760058\pi$
$409$	−29.4900	−1.45819	−0.729094	+	0.684414i	$0.760058\pi$
$410$	−1.28046	−0.0632375
$411$	7.91065	0.390204
$412$	−27.5547	−1.35752
$413$	0	0
$414$	0.888450	0.0436650
$415$	−12.0435	−0.591194
$416$	−3.17473	−0.155654
$417$	−2.63927	−0.129246
$418$	−0.488549	−0.0238957
$419$	−28.8026	−1.40710	−0.703550	−	0.710646i	$-0.748403\pi$
$419$	−28.8026	−1.40710	−0.703550	+	0.710646i	$0.748403\pi$
$420$	0	0
$421$	21.8452	1.06467	0.532335	−	0.846534i	$-0.321315\pi$
$421$	21.8452	1.06467	0.532335	+	0.846534i	$0.321315\pi$
$422$	−1.08962	−0.0530419
$423$	2.28046	0.110880
$424$	0.646669	0.0314050
$425$	−3.09593	−0.150175
$426$	−1.38113	−0.0669158
$427$	0	0
$428$	15.7005	0.758912
$429$	1.45666	0.0703280
$430$	0.0149199	0.000719503 0
$431$	5.93078	0.285676	0.142838	−	0.989746i	$-0.454377\pi$
$431$	5.93078	0.285676	0.142838	+	0.989746i	$0.454377\pi$
$432$	3.79387	0.182533
$433$	12.3728	0.594597	0.297298	−	0.954785i	$-0.403914\pi$
$433$	12.3728	0.594597	0.297298	+	0.954785i	$0.403914\pi$
$434$	0	0
$435$	−0.320244	−0.0153545
$436$	12.3168	0.589866
$437$	12.5618	0.600912
$438$	0.655388	0.0313156
$439$	15.3102	0.730715	0.365358	−	0.930867i	$-0.380947\pi$
$439$	15.3102	0.730715	0.365358	+	0.930867i	$0.380947\pi$
$440$	−0.543344	−0.0259029
$441$	0	0
$442$	−0.188098	−0.00894691
$443$	−24.0535	−1.14282	−0.571408	−	0.820666i	$-0.693603\pi$
$443$	−24.0535	−1.14282	−0.571408	+	0.820666i	$0.693603\pi$
$444$	−14.5198	−0.689081
$445$	−4.21124	−0.199632
$446$	−0.792277	−0.0375154
$447$	15.8554	0.749933
$448$	0	0
$449$	−10.9447	−0.516513	−0.258256	−	0.966076i	$-0.583148\pi$
$449$	−10.9447	−0.516513	−0.258256	+	0.966076i	$0.583148\pi$
$450$	−0.828427	−0.0390524
$451$	−9.34511	−0.440044
$452$	−23.2520	−1.09368
$453$	−17.5728	−0.825643
$454$	2.59417	0.121750
$455$	0	0
$456$	−1.93732	−0.0907231
$457$	−29.2520	−1.36835	−0.684175	−	0.729318i	$-0.739838\pi$
$457$	−29.2520	−1.36835	−0.684175	+	0.729318i	$0.739838\pi$
$458$	−3.73266	−0.174416
$459$	0.694676	0.0324247
$460$	6.92447	0.322855
$461$	13.8527	0.645185	0.322592	−	0.946538i	$-0.395446\pi$
$461$	13.8527	0.645185	0.322592	+	0.946538i	$0.395446\pi$
$462$	0	0
$463$	17.3553	0.806570	0.403285	−	0.915074i	$-0.367868\pi$
$463$	17.3553	0.806570	0.403285	+	0.915074i	$0.367868\pi$
$464$	1.64827	0.0765188
$465$	−1.51026	−0.0700365
$466$	−2.34608	−0.108680
$467$	−11.0749	−0.512487	−0.256244	−	0.966612i	$-0.582485\pi$
$467$	−11.0749	−0.512487	−0.256244	+	0.966612i	$0.582485\pi$
$468$	2.86298	0.132341
$469$	0	0
$470$	−0.312468	−0.0144131
$471$	13.3009	0.612871
$472$	−3.10427	−0.142885
$473$	0.108889	0.00500673
$474$	0.0181669	0.000834433 0
$475$	−11.7131	−0.537435
$476$	0	0
$477$	−0.877293	−0.0401685
$478$	3.79919	0.173771
$479$	35.1983	1.60825	0.804125	−	0.594460i	$-0.202634\pi$
$479$	35.1983	1.60825	0.804125	+	0.594460i	$0.202634\pi$
$480$	−1.60652	−0.0733274
$481$	−10.7611	−0.490665
$482$	0.924106	0.0420919
$483$	0	0
$484$	−1.96545	−0.0893385
$485$	3.79045	0.172115
$486$	0.185885	0.00843193
$487$	−7.00180	−0.317282	−0.158641	−	0.987336i	$-0.550711\pi$
$487$	−7.00180	−0.317282	−0.158641	+	0.987336i	$0.550711\pi$
$488$	−10.0274	−0.453920
$489$	−16.8618	−0.762516
$490$	0	0
$491$	14.5894	0.658412	0.329206	−	0.944258i	$-0.393219\pi$
$491$	14.5894	0.658412	0.329206	+	0.944258i	$0.393219\pi$
$492$	−18.3673	−0.828062
$493$	0.301805	0.0135926
$494$	−0.711649	−0.0320186
$495$	0.737118	0.0331310
$496$	7.77314	0.349024
$497$	0	0
$498$	3.03712	0.136097
$499$	−20.5720	−0.920928	−0.460464	−	0.887678i	$-0.652317\pi$
$499$	−20.5720	−0.920928	−0.460464	+	0.887678i	$0.652317\pi$
$500$	−13.7005	−0.612705
$501$	−11.6876	−0.522161
$502$	0.952601	0.0425167
$503$	29.3811	1.31004	0.655020	−	0.755612i	$-0.272660\pi$
$503$	29.3811	1.31004	0.655020	+	0.755612i	$0.272660\pi$
$504$	0	0
$505$	4.59334	0.204401
$506$	−0.888450	−0.0394964
$507$	−10.8782	−0.483116
$508$	−2.87560	−0.127584
$509$	10.2908	0.456132	0.228066	−	0.973646i	$-0.426760\pi$
$509$	10.2908	0.456132	0.228066	+	0.973646i	$0.426760\pi$
$510$	−0.0951841	−0.00421482
$511$	0	0
$512$	13.8617	0.612605
$513$	2.62823	0.116039
$514$	−0.418584	−0.0184629
$515$	−10.3341	−0.455373
$516$	0.214016	0.00942152
$517$	−2.28046	−0.100295
$518$	0	0
$519$	−18.4800	−0.811180
$520$	−0.791465	−0.0347080
$521$	6.89210	0.301948	0.150974	−	0.988538i	$-0.451759\pi$
$521$	6.89210	0.301948	0.150974	+	0.988538i	$0.451759\pi$
$522$	0.0807587	0.00353471
$523$	30.8606	1.34944	0.674719	−	0.738074i	$-0.264265\pi$
$523$	30.8606	1.34944	0.674719	+	0.738074i	$0.264265\pi$
$524$	−19.1647	−0.837215
$525$	0	0
$526$	2.24954	0.0980847
$527$	1.42330	0.0619998
$528$	−3.79387	−0.165107
$529$	−0.155794	−0.00677365
$530$	0.120206	0.00522143
$531$	4.21136	0.182757
$532$	0	0
$533$	−13.6126	−0.589628
$534$	1.06198	0.0459566
$535$	5.88829	0.254573
$536$	2.98645	0.128995
$537$	−6.81026	−0.293884
$538$	−5.72479	−0.246813
$539$	0	0
$540$	1.44877	0.0623450
$541$	31.0493	1.33491	0.667457	−	0.744649i	$-0.267383\pi$
$541$	31.0493	1.33491	0.667457	+	0.744649i	$0.267383\pi$
$542$	−0.240747	−0.0103410
$543$	−6.93732	−0.297709
$544$	1.51402	0.0649130
$545$	4.61926	0.197867
$546$	0	0
$547$	35.7208	1.52731	0.763656	−	0.645624i	$-0.223403\pi$
$547$	35.7208	1.52731	0.763656	+	0.645624i	$0.223403\pi$
$548$	−15.5480	−0.664176
$549$	13.6035	0.580584
$550$	0.828427	0.0353243
$551$	1.14185	0.0486443
$552$	−3.52310	−0.149953
$553$	0	0
$554$	2.03879	0.0866200
$555$	−5.44550	−0.231149
$556$	5.18735	0.219993
$557$	−38.9278	−1.64942	−0.824712	−	0.565553i	$-0.808663\pi$
$557$	−38.9278	−1.64942	−0.824712	+	0.565553i	$0.808663\pi$
$558$	0.380854	0.0161228
$559$	0.158614	0.00670866
$560$	0	0
$561$	−0.694676	−0.0293292
$562$	5.13761	0.216717
$563$	−30.6398	−1.29131	−0.645657	−	0.763628i	$-0.723416\pi$
$563$	−30.6398	−1.29131	−0.645657	+	0.763628i	$0.723416\pi$
$564$	−4.48213	−0.188732
$565$	−8.72040	−0.366870
$566$	5.79063	0.243398
$567$	0	0
$568$	5.47678	0.229801
$569$	−3.34788	−0.140350	−0.0701752	−	0.997535i	$-0.522356\pi$
$569$	−3.34788	−0.140350	−0.0701752	+	0.997535i	$0.522356\pi$
$570$	−0.360119	−0.0150837
$571$	13.7741	0.576429	0.288215	−	0.957566i	$-0.406938\pi$
$571$	13.7741	0.576429	0.288215	+	0.957566i	$0.406938\pi$
$572$	−2.86298	−0.119707
$573$	16.6727	0.696514
$574$	0	0
$575$	−21.3009	−0.888307
$576$	−7.18262	−0.299276
$577$	−25.1746	−1.04803	−0.524017	−	0.851708i	$-0.675567\pi$
$577$	−25.1746	−1.04803	−0.524017	+	0.851708i	$0.675567\pi$
$578$	−3.07035	−0.127710
$579$	−26.5031	−1.10143
$580$	0.629423	0.0261354
$581$	0	0
$582$	−0.955869	−0.0396220
$583$	0.877293	0.0363338
$584$	−2.59890	−0.107543
$585$	1.07373	0.0443932
$586$	−1.09476	−0.0452240
$587$	−31.2072	−1.28806	−0.644029	−	0.765001i	$-0.722738\pi$
$587$	−31.2072	−1.28806	−0.644029	+	0.765001i	$0.722738\pi$
$588$	0	0
$589$	5.38489	0.221880
$590$	−0.577038	−0.0237563
$591$	16.2336	0.667759
$592$	28.0274	1.15192
$593$	−5.19937	−0.213512	−0.106756	−	0.994285i	$-0.534046\pi$
$593$	−5.19937	−0.213512	−0.106756	+	0.994285i	$0.534046\pi$
$594$	−0.185885	−0.00762697
$595$	0	0
$596$	−31.1629	−1.27648
$597$	0.199096	0.00814845
$598$	−1.29417	−0.0529224
$599$	39.2252	1.60270	0.801350	−	0.598196i	$-0.204116\pi$
$599$	39.2252	1.60270	0.801350	+	0.598196i	$0.204116\pi$
$600$	3.28508	0.134113
$601$	43.0250	1.75503	0.877514	−	0.479552i	$-0.159201\pi$
$601$	43.0250	1.75503	0.877514	+	0.479552i	$0.159201\pi$
$602$	0	0
$603$	−4.05153	−0.164991
$604$	34.5385	1.40535
$605$	−0.737118	−0.0299681
$606$	−1.15834	−0.0470544
$607$	14.3595	0.582835	0.291417	−	0.956596i	$-0.405873\pi$
$607$	14.3595	0.582835	0.291417	+	0.956596i	$0.405873\pi$
$608$	5.72813	0.232306
$609$	0	0
$610$	−1.86395	−0.0754691
$611$	−3.32185	−0.134388
$612$	−1.36535	−0.0551909
$613$	−38.9985	−1.57513	−0.787567	−	0.616229i	$-0.788660\pi$
$613$	−38.9985	−1.57513	−0.787567	+	0.616229i	$0.788660\pi$
$614$	−4.87184	−0.196612
$615$	−6.88845	−0.277769
$616$	0	0
$617$	12.6511	0.509315	0.254658	−	0.967031i	$-0.418037\pi$
$617$	12.6511	0.509315	0.254658	+	0.967031i	$0.418037\pi$
$618$	2.60603	0.104830
$619$	−11.3799	−0.457397	−0.228699	−	0.973497i	$-0.573447\pi$
$619$	−11.3799	−0.457397	−0.228699	+	0.973497i	$0.573447\pi$
$620$	2.96833	0.119211
$621$	4.77956	0.191797
$622$	3.19726	0.128199
$623$	0	0
$624$	−5.52637	−0.221232
$625$	17.1451	0.685803
$626$	−1.41759	−0.0566583
$627$	−2.62823	−0.104961
$628$	−26.1421	−1.04318
$629$	5.13195	0.204624
$630$	0	0
$631$	−2.50877	−0.0998725	−0.0499363	−	0.998752i	$-0.515902\pi$
$631$	−2.50877	−0.0998725	−0.0499363	+	0.998752i	$0.515902\pi$
$632$	−0.0720398	−0.00286559
$633$	−5.86179	−0.232985
$634$	−3.11085	−0.123548
$635$	−1.07846	−0.0427975
$636$	1.72427	0.0683719
$637$	0	0
$638$	−0.0807587	−0.00319727
$639$	−7.42999	−0.293926
$640$	4.19720	0.165909
$641$	−41.1124	−1.62384	−0.811921	−	0.583768i	$-0.801578\pi$
$641$	−41.1124	−1.62384	−0.811921	+	0.583768i	$0.801578\pi$
$642$	−1.48490	−0.0586043
$643$	−7.14757	−0.281873	−0.140936	−	0.990019i	$-0.545011\pi$
$643$	−7.14757	−0.281873	−0.140936	+	0.990019i	$0.545011\pi$
$644$	0	0
$645$	0.0802642	0.00316040
$646$	0.339383	0.0133529
$647$	−14.6680	−0.576659	−0.288330	−	0.957531i	$-0.593100\pi$
$647$	−14.6680	−0.576659	−0.288330	+	0.957531i	$0.593100\pi$
$648$	−0.737118	−0.0289567
$649$	−4.21136	−0.165310
$650$	1.20673	0.0473320
$651$	0	0
$652$	33.1409	1.29790
$653$	42.7955	1.67472	0.837358	−	0.546655i	$-0.184099\pi$
$653$	42.7955	1.67472	0.837358	+	0.546655i	$0.184099\pi$
$654$	−1.16488	−0.0455503
$655$	−7.18751	−0.280839
$656$	35.4542	1.38425
$657$	3.52576	0.137553
$658$	0	0
$659$	−48.3904	−1.88502	−0.942511	−	0.334176i	$-0.891542\pi$
$659$	−48.3904	−1.88502	−0.942511	+	0.334176i	$0.891542\pi$
$660$	−1.44877	−0.0563932
$661$	−27.9721	−1.08799	−0.543993	−	0.839090i	$-0.683088\pi$
$661$	−27.9721	−1.08799	−0.543993	+	0.839090i	$0.683088\pi$
$662$	−2.25943	−0.0878154
$663$	−1.01190	−0.0392991
$664$	−12.0435	−0.467380
$665$	0	0
$666$	1.37324	0.0532119
$667$	2.07650	0.0804025
$668$	22.9713	0.888785
$669$	−4.26218	−0.164785
$670$	0.555138	0.0214469
$671$	−13.6035	−0.525158
$672$	0	0
$673$	−36.9653	−1.42491	−0.712453	−	0.701720i	$-0.752416\pi$
$673$	−36.9653	−1.42491	−0.712453	+	0.701720i	$0.752416\pi$
$674$	3.84103	0.147951
$675$	−4.45666	−0.171537
$676$	21.3804	0.822324
$677$	−36.1775	−1.39041	−0.695206	−	0.718810i	$-0.744687\pi$
$677$	−36.1775	−1.39041	−0.695206	+	0.718810i	$0.744687\pi$
$678$	2.19910	0.0844558
$679$	0	0
$680$	0.377447	0.0144745
$681$	13.9558	0.534786
$682$	−0.380854	−0.0145837
$683$	−18.1417	−0.694171	−0.347086	−	0.937833i	$-0.612829\pi$
$683$	−18.1417	−0.694171	−0.347086	+	0.937833i	$0.612829\pi$
$684$	−5.16564	−0.197513
$685$	−5.83109	−0.222794
$686$	0	0
$687$	−20.0804	−0.766116
$688$	−0.413112	−0.0157497
$689$	1.27791	0.0486847
$690$	−0.654893	−0.0249314
$691$	19.3125	0.734683	0.367342	−	0.930086i	$-0.380268\pi$
$691$	19.3125	0.734683	0.367342	+	0.930086i	$0.380268\pi$
$692$	36.3214	1.38073
$693$	0	0
$694$	4.55101	0.172754
$695$	1.94546	0.0737954
$696$	−0.320244	−0.0121388
$697$	6.49182	0.245895
$698$	0.834083	0.0315705
$699$	−12.6211	−0.477374
$700$	0	0
$701$	40.8768	1.54389	0.771947	−	0.635687i	$-0.219283\pi$
$701$	40.8768	1.54389	0.771947	+	0.635687i	$0.219283\pi$
$702$	−0.270771	−0.0102196
$703$	19.4162	0.732295
$704$	7.18262	0.270705
$705$	−1.68097	−0.0633090
$706$	5.12359	0.192829
$707$	0	0
$708$	−8.27719	−0.311076
$709$	29.7385	1.11685	0.558427	−	0.829554i	$-0.311405\pi$
$709$	29.7385	1.11685	0.558427	+	0.829554i	$0.311405\pi$
$710$	1.01805	0.0382069
$711$	0.0977317	0.00366522
$712$	−4.21124	−0.157823
$713$	9.79268	0.366739
$714$	0	0
$715$	−1.07373	−0.0401552
$716$	13.3852	0.500229
$717$	20.4384	0.763285
$718$	−5.56304	−0.207611
$719$	−1.47174	−0.0548865	−0.0274432	−	0.999623i	$-0.508737\pi$
$719$	−1.47174	−0.0548865	−0.0274432	+	0.999623i	$0.508737\pi$
$720$	−2.79653	−0.104221
$721$	0	0
$722$	−2.24780	−0.0836545
$723$	4.97138	0.184887
$724$	13.6349	0.506738
$725$	−1.93621	−0.0719092
$726$	0.185885	0.00689885
$727$	35.9124	1.33192	0.665958	−	0.745989i	$-0.268023\pi$
$727$	35.9124	1.33192	0.665958	+	0.745989i	$0.268023\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.483098	−0.0178803
$731$	−0.0756426	−0.00279774
$732$	−26.7370	−0.988228
$733$	6.64049	0.245272	0.122636	−	0.992452i	$-0.460865\pi$
$733$	6.64049	0.245272	0.122636	+	0.992452i	$0.460865\pi$
$734$	−2.39386	−0.0883590
$735$	0	0
$736$	10.4169	0.383971
$737$	4.05153	0.149240
$738$	1.73712	0.0639442
$739$	37.9825	1.39721	0.698604	−	0.715509i	$-0.253805\pi$
$739$	37.9825	1.39721	0.698604	+	0.715509i	$0.253805\pi$
$740$	10.7028	0.393444
$741$	−3.82843	−0.140641
$742$	0	0
$743$	27.4601	1.00741	0.503707	−	0.863875i	$-0.331969\pi$
$743$	27.4601	1.00741	0.503707	+	0.863875i	$0.331969\pi$
$744$	−1.51026	−0.0553687
$745$	−11.6873	−0.428189
$746$	−3.81824	−0.139796
$747$	16.3387	0.597801
$748$	1.36535	0.0499221
$749$	0	0
$750$	1.29575	0.0473140
$751$	11.3194	0.413052	0.206526	−	0.978441i	$-0.433784\pi$
$751$	11.3194	0.413052	0.206526	+	0.978441i	$0.433784\pi$
$752$	8.65178	0.315498
$753$	5.12467	0.186753
$754$	−0.117638	−0.00428411
$755$	12.9533	0.471417
$756$	0	0
$757$	−5.58955	−0.203156	−0.101578	−	0.994828i	$-0.532389\pi$
$757$	−5.58955	−0.203156	−0.101578	+	0.994828i	$0.532389\pi$
$758$	−5.92902	−0.215352
$759$	−4.77956	−0.173487
$760$	1.42803	0.0518001
$761$	34.8768	1.26428	0.632141	−	0.774854i	$-0.282176\pi$
$761$	34.8768	1.26428	0.632141	+	0.774854i	$0.282176\pi$
$762$	0.271965	0.00985225
$763$	0	0
$764$	−32.7694	−1.18556
$765$	−0.512058	−0.0185135
$766$	−0.778033	−0.0281115
$767$	−6.13450	−0.221504
$768$	13.3068	0.480167
$769$	25.1994	0.908713	0.454357	−	0.890820i	$-0.349869\pi$
$769$	25.1994	0.908713	0.454357	+	0.890820i	$0.349869\pi$
$770$	0	0
$771$	−2.25184	−0.0810979
$772$	52.0905	1.87478
$773$	44.1959	1.58962	0.794808	−	0.606861i	$-0.207572\pi$
$773$	44.1959	1.58962	0.794808	+	0.606861i	$0.207572\pi$
$774$	−0.0202409	−0.000727544 0
$775$	−9.13109	−0.327998
$776$	3.79045	0.136069
$777$	0	0
$778$	4.12272	0.147807
$779$	24.5611	0.879992
$780$	−2.11036	−0.0755629
$781$	7.42999	0.265866
$782$	0.617185	0.0220705
$783$	0.434454	0.0155261
$784$	0	0
$785$	−9.80431	−0.349931
$786$	1.81254	0.0646510
$787$	13.0628	0.465638	0.232819	−	0.972520i	$-0.425205\pi$
$787$	13.0628	0.465638	0.232819	+	0.972520i	$0.425205\pi$
$788$	−31.9062	−1.13661
$789$	12.1018	0.430834
$790$	−0.0133911	−0.000476436 0
$791$	0	0
$792$	0.737118	0.0261924
$793$	−19.8157	−0.703675
$794$	0.256032	0.00908623
$795$	0.646669	0.0229350
$796$	−0.391312	−0.0138697
$797$	−32.9154	−1.16592	−0.582962	−	0.812500i	$-0.698106\pi$
$797$	−32.9154	−1.16592	−0.582962	+	0.812500i	$0.698106\pi$
$798$	0	0
$799$	1.58418	0.0560443
$800$	−9.71312	−0.343410
$801$	5.71312	0.201863
$802$	3.56260	0.125800
$803$	−3.52576	−0.124421
$804$	7.96306	0.280835
$805$	0	0
$806$	−0.554774	−0.0195411
$807$	−30.7974	−1.08412
$808$	4.59334	0.161593
$809$	28.1035	0.988066	0.494033	−	0.869443i	$-0.335522\pi$
$809$	28.1035	0.988066	0.494033	+	0.869443i	$0.335522\pi$
$810$	−0.137020	−0.00481437
$811$	37.4361	1.31456	0.657280	−	0.753647i	$-0.271707\pi$
$811$	37.4361	1.31456	0.657280	+	0.753647i	$0.271707\pi$
$812$	0	0
$813$	−1.29514	−0.0454225
$814$	−1.37324	−0.0481319
$815$	12.4291	0.435374
$816$	2.63551	0.0922614
$817$	−0.286186	−0.0100124
$818$	−5.48176	−0.191665
$819$	0	0
$820$	13.5389	0.472798
$821$	10.1890	0.355600	0.177800	−	0.984067i	$-0.443102\pi$
$821$	10.1890	0.355600	0.177800	+	0.984067i	$0.443102\pi$
$822$	1.47047	0.0512887
$823$	−3.80372	−0.132589	−0.0662947	−	0.997800i	$-0.521118\pi$
$823$	−3.80372	−0.132589	−0.0662947	+	0.997800i	$0.521118\pi$
$824$	−10.3341	−0.360004
$825$	4.45666	0.155161
$826$	0	0
$827$	−42.3768	−1.47359	−0.736793	−	0.676119i	$-0.763661\pi$
$827$	−42.3768	−1.47359	−0.736793	+	0.676119i	$0.763661\pi$
$828$	−9.39397	−0.326463
$829$	−44.6643	−1.55126	−0.775628	−	0.631191i	$-0.782566\pi$
$829$	−44.6643	−1.55126	−0.775628	+	0.631191i	$0.782566\pi$
$830$	−2.23872	−0.0777071
$831$	10.9680	0.380476
$832$	10.4626	0.362726
$833$	0	0
$834$	−0.490602	−0.0169882
$835$	8.61511	0.298138
$836$	5.16564	0.178658
$837$	2.04887	0.0708192
$838$	−5.35399	−0.184950
$839$	35.5777	1.22828	0.614140	−	0.789197i	$-0.289503\pi$
$839$	35.5777	1.22828	0.614140	+	0.789197i	$0.289503\pi$
$840$	0	0
$841$	−28.8112	−0.993491
$842$	4.06070	0.139941
$843$	27.6386	0.951923
$844$	11.5210	0.396570
$845$	8.01849	0.275844
$846$	0.423904	0.0145741
$847$	0	0
$848$	−3.32834	−0.114296
$849$	31.1516	1.06912
$850$	−0.575488	−0.0197391
$851$	35.3092	1.21039
$852$	14.6033	0.500299
$853$	8.32083	0.284900	0.142450	−	0.989802i	$-0.454502\pi$
$853$	8.32083	0.284900	0.142450	+	0.989802i	$0.454502\pi$
$854$	0	0
$855$	−1.93732	−0.0662548
$856$	5.88829	0.201258
$857$	−26.5648	−0.907438	−0.453719	−	0.891145i	$-0.649903\pi$
$857$	−26.5648	−0.907438	−0.453719	+	0.891145i	$0.649903\pi$
$858$	0.270771	0.00924397
$859$	21.0501	0.718221	0.359111	−	0.933295i	$-0.383080\pi$
$859$	21.0501	0.718221	0.359111	+	0.933295i	$0.383080\pi$
$860$	−0.157755	−0.00537940
$861$	0	0
$862$	1.10245	0.0375494
$863$	41.7854	1.42239	0.711197	−	0.702993i	$-0.248154\pi$
$863$	41.7854	1.42239	0.711197	+	0.702993i	$0.248154\pi$
$864$	2.17946	0.0741468
$865$	13.6219	0.463159
$866$	2.29991	0.0781543
$867$	−16.5174	−0.560961
$868$	0	0
$869$	−0.0977317	−0.00331532
$870$	−0.0595287	−0.00201821
$871$	5.90168	0.199971
$872$	4.61926	0.156428
$873$	−5.14225	−0.174039
$874$	2.33505	0.0789843
$875$	0	0
$876$	−6.92970	−0.234133
$877$	18.5386	0.626004	0.313002	−	0.949752i	$-0.398665\pi$
$877$	18.5386	0.626004	0.313002	+	0.949752i	$0.398665\pi$
$878$	2.84594	0.0960458
$879$	−5.88942	−0.198645
$880$	2.79653	0.0942712
$881$	−41.9600	−1.41367	−0.706833	−	0.707380i	$-0.749877\pi$
$881$	−41.9600	−1.41367	−0.706833	+	0.707380i	$0.749877\pi$
$882$	0	0
$883$	14.7832	0.497495	0.248747	−	0.968568i	$-0.419981\pi$
$883$	14.7832	0.497495	0.248747	+	0.968568i	$0.419981\pi$
$884$	1.98884	0.0668920
$885$	−3.10427	−0.104349
$886$	−4.47119	−0.150213
$887$	55.1139	1.85055	0.925273	−	0.379303i	$-0.123836\pi$
$887$	55.1139	1.85055	0.925273	+	0.379303i	$0.123836\pi$
$888$	−5.44550	−0.182739
$889$	0	0
$890$	−0.782808	−0.0262398
$891$	−1.00000	−0.0335013
$892$	8.37709	0.280486
$893$	5.99358	0.200567
$894$	2.94728	0.0985718
$895$	5.01997	0.167799
$896$	0	0
$897$	−6.96218	−0.232460
$898$	−2.03446	−0.0678909
$899$	0.890139	0.0296878
$900$	8.75932	0.291977
$901$	−0.609434	−0.0203032
$902$	−1.73712	−0.0578397
$903$	0	0
$904$	−8.72040	−0.290036
$905$	5.11362	0.169983
$906$	−3.26653	−0.108523
$907$	27.0841	0.899312	0.449656	−	0.893202i	$-0.351547\pi$
$907$	27.0841	0.899312	0.449656	+	0.893202i	$0.351547\pi$
$908$	−27.4293	−0.910273
$909$	−6.23148	−0.206685
$910$	0	0
$911$	−19.2161	−0.636659	−0.318330	−	0.947980i	$-0.603122\pi$
$911$	−19.2161	−0.636659	−0.318330	+	0.947980i	$0.603122\pi$
$912$	9.97117	0.330178
$913$	−16.3387	−0.540732
$914$	−5.43752	−0.179857
$915$	−10.0274	−0.331496
$916$	39.4670	1.30403
$917$	0	0
$918$	0.129130	0.00426193
$919$	−18.5892	−0.613201	−0.306600	−	0.951838i	$-0.599192\pi$
$919$	−18.5892	−0.613201	−0.306600	+	0.951838i	$0.599192\pi$
$920$	2.59694	0.0856187
$921$	−26.2089	−0.863611
$922$	2.57501	0.0848036
$923$	10.8229	0.356242
$924$	0	0
$925$	−32.9238	−1.08253
$926$	3.22610	0.106016
$927$	14.0195	0.460462
$928$	0.946877	0.0310828
$929$	−12.5848	−0.412895	−0.206448	−	0.978458i	$-0.566190\pi$
$929$	−12.5848	−0.412895	−0.206448	+	0.978458i	$0.566190\pi$
$930$	−0.280735	−0.00920565
$931$	0	0
$932$	24.8061	0.812551
$933$	17.2002	0.563109
$934$	−2.05867	−0.0673617
$935$	0.512058	0.0167461
$936$	1.07373	0.0350959
$937$	22.7111	0.741940	0.370970	−	0.928645i	$-0.379025\pi$
$937$	22.7111	0.741940	0.370970	+	0.928645i	$0.379025\pi$
$938$	0	0
$939$	−7.62616	−0.248870
$940$	3.30386	0.107760
$941$	37.8880	1.23511	0.617557	−	0.786526i	$-0.288122\pi$
$941$	37.8880	1.23511	0.617557	+	0.786526i	$0.288122\pi$
$942$	2.47244	0.0805563
$943$	44.6655	1.45451
$944$	15.9774	0.520018
$945$	0	0
$946$	0.0202409	0.000658088 0
$947$	−25.1364	−0.816824	−0.408412	−	0.912798i	$-0.633917\pi$
$947$	−25.1364	−0.816824	−0.408412	+	0.912798i	$0.633917\pi$
$948$	−0.192086	−0.00623868
$949$	−5.13583	−0.166716
$950$	−2.17730	−0.0706408
$951$	−16.7353	−0.542680
$952$	0	0
$953$	−6.35610	−0.205894	−0.102947	−	0.994687i	$-0.532827\pi$
$953$	−6.35610	−0.205894	−0.102947	+	0.994687i	$0.532827\pi$
$954$	−0.163076	−0.00527978
$955$	−12.2898	−0.397688
$956$	−40.1705	−1.29921
$957$	−0.434454	−0.0140439
$958$	6.54285	0.211390
$959$	0	0
$960$	5.29444	0.170877
$961$	−26.8021	−0.864585
$962$	−2.00033	−0.0644934
$963$	−7.98826	−0.257418
$964$	−9.77097	−0.314702
$965$	19.5359	0.628884
$966$	0	0
$967$	−27.9034	−0.897313	−0.448657	−	0.893704i	$-0.648097\pi$
$967$	−27.9034	−0.897313	−0.448657	+	0.893704i	$0.648097\pi$
$968$	−0.737118	−0.0236919
$969$	1.82577	0.0586521
$970$	0.704588	0.0226230
$971$	1.69091	0.0542640	0.0271320	−	0.999632i	$-0.491363\pi$
$971$	1.69091	0.0542640	0.0271320	+	0.999632i	$0.491363\pi$
$972$	−1.96545	−0.0630417
$973$	0	0
$974$	−1.30153	−0.0417038
$975$	6.49182	0.207905
$976$	51.6101	1.65200
$977$	−41.7981	−1.33724	−0.668620	−	0.743604i	$-0.733115\pi$
$977$	−41.7981	−1.33724	−0.668620	+	0.743604i	$0.733115\pi$
$978$	−3.13436	−0.100226
$979$	−5.71312	−0.182592
$980$	0	0
$981$	−6.26664	−0.200079
$982$	2.71196	0.0865422
$983$	44.7004	1.42572	0.712861	−	0.701305i	$-0.247399\pi$
$983$	44.7004	1.42572	0.712861	+	0.701305i	$0.247399\pi$
$984$	−6.88845	−0.219596
$985$	−11.9661	−0.381270
$986$	0.0561011	0.00178662
$987$	0	0
$988$	7.52457	0.239388
$989$	−0.520442	−0.0165491
$990$	0.137020	0.00435477
$991$	26.0860	0.828650	0.414325	−	0.910129i	$-0.364018\pi$
$991$	26.0860	0.828650	0.414325	+	0.910129i	$0.364018\pi$
$992$	4.46543	0.141777
$993$	−12.1550	−0.385727
$994$	0	0
$995$	−0.146757	−0.00465252
$996$	−32.1128	−1.01753
$997$	17.2538	0.546435	0.273217	−	0.961952i	$-0.411912\pi$
$997$	17.2538	0.546435	0.273217	+	0.961952i	$0.411912\pi$
$998$	−3.82403	−0.121047
$999$	7.38755	0.233732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.y.1.2	yes	4
3.2	odd	2		4851.2.a.br.1.3		4
7.6	odd	2		1617.2.a.w.1.2	✓	4
21.20	even	2		4851.2.a.bs.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.w.1.2	✓	4	7.6	odd	2
1617.2.a.y.1.2	yes	4	1.1	even	1	trivial
4851.2.a.br.1.3		4	3.2	odd	2
4851.2.a.bs.1.3		4	21.20	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+0.185885 q^{2} +1.00000 q^{3} -1.96545 q^{4} -0.737118 q^{5} +0.185885 q^{6} -0.737118 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.185885 q^{2} +1.00000 q^{3} -1.96545 q^{4} -0.737118 q^{5} +0.185885 q^{6} -0.737118 q^{8} +1.00000 q^{9} -0.137020 q^{10} -1.00000 q^{11} -1.96545 q^{12} -1.45666 q^{13} -0.737118 q^{15} +3.79387 q^{16} +0.694676 q^{17} +0.185885 q^{18} +2.62823 q^{19} +1.44877 q^{20} -0.185885 q^{22} +4.77956 q^{23} -0.737118 q^{24} -4.45666 q^{25} -0.270771 q^{26} +1.00000 q^{27} +0.434454 q^{29} -0.137020 q^{30} +2.04887 q^{31} +2.17946 q^{32} -1.00000 q^{33} +0.129130 q^{34} -1.96545 q^{36} +7.38755 q^{37} +0.488549 q^{38} -1.45666 q^{39} +0.543344 q^{40} +9.34511 q^{41} -0.108889 q^{43} +1.96545 q^{44} -0.737118 q^{45} +0.888450 q^{46} +2.28046 q^{47} +3.79387 q^{48} -0.828427 q^{50} +0.694676 q^{51} +2.86298 q^{52} -0.877293 q^{53} +0.185885 q^{54} +0.737118 q^{55} +2.62823 q^{57} +0.0807587 q^{58} +4.21136 q^{59} +1.44877 q^{60} +13.6035 q^{61} +0.380854 q^{62} -7.18262 q^{64} +1.07373 q^{65} -0.185885 q^{66} -4.05153 q^{67} -1.36535 q^{68} +4.77956 q^{69} -7.42999 q^{71} -0.737118 q^{72} +3.52576 q^{73} +1.37324 q^{74} -4.45666 q^{75} -5.16564 q^{76} -0.270771 q^{78} +0.0977317 q^{79} -2.79653 q^{80} +1.00000 q^{81} +1.73712 q^{82} +16.3387 q^{83} -0.512058 q^{85} -0.0202409 q^{86} +0.434454 q^{87} +0.737118 q^{88} +5.71312 q^{89} -0.137020 q^{90} -9.39397 q^{92} +2.04887 q^{93} +0.423904 q^{94} -1.93732 q^{95} +2.17946 q^{96} -5.14225 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more