LMFDB - Embedded newform 3549.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.10710$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43986 q^{2} +1.00000 q^{3} +0.0731828 q^{4} -0.926817 q^{5} -1.43986 q^{6} -1.00000 q^{7} +2.77434 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.43986 q^{2} +1.00000 q^{3} +0.0731828 q^{4} -0.926817 q^{5} -1.43986 q^{6} -1.00000 q^{7} +2.77434 q^{8} +1.00000 q^{9} +1.33448 q^{10} -4.21419 q^{11} +0.0731828 q^{12} +1.43986 q^{14} -0.926817 q^{15} -4.14101 q^{16} -2.87971 q^{17} -1.43986 q^{18} +1.28738 q^{19} -0.0678271 q^{20} -1.00000 q^{21} +6.06783 q^{22} -8.02072 q^{23} +2.77434 q^{24} -4.14101 q^{25} +1.00000 q^{27} -0.0731828 q^{28} +3.28738 q^{29} +1.33448 q^{30} +7.04680 q^{31} +0.413779 q^{32} -4.21419 q^{33} +4.14637 q^{34} +0.926817 q^{35} +0.0731828 q^{36} -8.57475 q^{37} -1.85363 q^{38} -2.57130 q^{40} +12.0678 q^{41} +1.43986 q^{42} +7.14101 q^{43} -0.308407 q^{44} -0.926817 q^{45} +11.5487 q^{46} -1.95289 q^{47} -4.14101 q^{48} +1.00000 q^{49} +5.96245 q^{50} -2.87971 q^{51} -5.14101 q^{53} -1.43986 q^{54} +3.90579 q^{55} -2.77434 q^{56} +1.28738 q^{57} -4.73334 q^{58} +7.33448 q^{59} -0.0678271 q^{60} +7.75942 q^{61} -10.1464 q^{62} -1.00000 q^{63} +7.68624 q^{64} +6.06783 q^{66} -12.0414 q^{67} -0.210745 q^{68} -8.02072 q^{69} -1.33448 q^{70} -10.7889 q^{71} +2.77434 q^{72} +8.32568 q^{73} +12.3464 q^{74} -4.14101 q^{75} +0.0942138 q^{76} +4.21419 q^{77} +4.47204 q^{79} +3.83796 q^{80} +1.00000 q^{81} -17.3759 q^{82} +3.80653 q^{83} -0.0731828 q^{84} +2.66896 q^{85} -10.2820 q^{86} +3.28738 q^{87} -11.6916 q^{88} +5.64793 q^{89} +1.33448 q^{90} -0.586979 q^{92} +7.04680 q^{93} +2.81188 q^{94} -1.19316 q^{95} +0.413779 q^{96} -6.90043 q^{97} -1.43986 q^{98} -4.21419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 4 q^{10} + 2 q^{11} + 7 q^{12} + q^{14} + 3 q^{15} + 9 q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + 32 q^{20} - 4 q^{21} - 8 q^{22} + 3 q^{23} - 3 q^{24} + 9 q^{25} + 4 q^{27} - 7 q^{28} + q^{29} - 4 q^{30} - 3 q^{31} - 7 q^{32} + 2 q^{33} + 30 q^{34} - 3 q^{35} + 7 q^{36} - 10 q^{37} + 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 3 q^{43} + 12 q^{44} + 3 q^{45} + 18 q^{46} - 5 q^{47} + 9 q^{48} + 4 q^{49} - 13 q^{50} - 2 q^{51} + 5 q^{53} - q^{54} + 10 q^{55} + 3 q^{56} - 7 q^{57} + 4 q^{58} + 20 q^{59} + 32 q^{60} + 12 q^{61} - 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} - 10 q^{68} + 3 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 6 q^{74} + 9 q^{75} + 6 q^{76} - 2 q^{77} + 11 q^{79} + 42 q^{80} + 4 q^{81} + 10 q^{82} - q^{83} - 7 q^{84} - 8 q^{85} + 10 q^{86} + q^{87} - 60 q^{88} + 5 q^{89} - 4 q^{90} + 34 q^{92} - 3 q^{93} + 34 q^{94} + 13 q^{95} - 7 q^{96} + 17 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 4 * q^10 + 2 * q^11 + 7 * q^12 + q^14 + 3 * q^15 + 9 * q^16 - 2 * q^17 - q^18 - 7 * q^19 + 32 * q^20 - 4 * q^21 - 8 * q^22 + 3 * q^23 - 3 * q^24 + 9 * q^25 + 4 * q^27 - 7 * q^28 + q^29 - 4 * q^30 - 3 * q^31 - 7 * q^32 + 2 * q^33 + 30 * q^34 - 3 * q^35 + 7 * q^36 - 10 * q^37 + 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 3 * q^43 + 12 * q^44 + 3 * q^45 + 18 * q^46 - 5 * q^47 + 9 * q^48 + 4 * q^49 - 13 * q^50 - 2 * q^51 + 5 * q^53 - q^54 + 10 * q^55 + 3 * q^56 - 7 * q^57 + 4 * q^58 + 20 * q^59 + 32 * q^60 + 12 * q^61 - 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 - 10 * q^68 + 3 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 6 * q^74 + 9 * q^75 + 6 * q^76 - 2 * q^77 + 11 * q^79 + 42 * q^80 + 4 * q^81 + 10 * q^82 - q^83 - 7 * q^84 - 8 * q^85 + 10 * q^86 + q^87 - 60 * q^88 + 5 * q^89 - 4 * q^90 + 34 * q^92 - 3 * q^93 + 34 * q^94 + 13 * q^95 - 7 * q^96 + 17 * q^97 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.43986	−1.01813	−0.509066	−	0.860728i	$-0.670009\pi$
$2$	−1.43986	−1.01813	−0.509066	+	0.860728i	$0.670009\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0731828	0.0365914
$5$	−0.926817	−0.414485	−0.207243	−	0.978290i	$-0.566449\pi$
$5$	−0.926817	−0.414485	−0.207243	+	0.978290i	$0.566449\pi$
$6$	−1.43986	−0.587818
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.77434	0.980876
$9$	1.00000	0.333333
$10$	1.33448	0.422000
$11$	−4.21419	−1.27063	−0.635313	−	0.772254i	$-0.719129\pi$
$11$	−4.21419	−1.27063	−0.635313	+	0.772254i	$0.719129\pi$
$12$	0.0731828	0.0211261
$13$	0	0
$13$	0	0
$14$	1.43986	0.384817
$15$	−0.926817	−0.239303
$16$	−4.14101	−1.03525
$17$	−2.87971	−0.698432	−0.349216	−	0.937042i	$-0.613552\pi$
$17$	−2.87971	−0.698432	−0.349216	+	0.937042i	$0.613552\pi$
$18$	−1.43986	−0.339377
$19$	1.28738	0.295344	0.147672	−	0.989036i	$-0.452822\pi$
$19$	1.28738	0.295344	0.147672	+	0.989036i	$0.452822\pi$
$20$	−0.0678271	−0.0151666
$21$	−1.00000	−0.218218
$22$	6.06783	1.29367
$23$	−8.02072	−1.67244	−0.836218	−	0.548397i	$-0.815238\pi$
$23$	−8.02072	−1.67244	−0.836218	+	0.548397i	$0.815238\pi$
$24$	2.77434	0.566309
$25$	−4.14101	−0.828202
$26$	0	0
$27$	1.00000	0.192450
$28$	−0.0731828	−0.0138303
$29$	3.28738	0.610450	0.305225	−	0.952280i	$-0.401268\pi$
$29$	3.28738	0.610450	0.305225	+	0.952280i	$0.401268\pi$
$30$	1.33448	0.243642
$31$	7.04680	1.26564	0.632821	−	0.774298i	$-0.281897\pi$
$31$	7.04680	1.26564	0.632821	+	0.774298i	$0.281897\pi$
$32$	0.413779	0.0731465
$33$	−4.21419	−0.733597
$34$	4.14637	0.711096
$35$	0.926817	0.156661
$36$	0.0731828	0.0121971
$37$	−8.57475	−1.40968	−0.704840	−	0.709366i	$-0.748981\pi$
$37$	−8.57475	−1.40968	−0.704840	+	0.709366i	$0.748981\pi$
$38$	−1.85363	−0.300699
$39$	0	0
$40$	−2.57130	−0.406559
$41$	12.0678	1.88468	0.942339	−	0.334660i	$-0.108621\pi$
$41$	12.0678	1.88468	0.942339	+	0.334660i	$0.108621\pi$
$42$	1.43986	0.222174
$43$	7.14101	1.08899	0.544497	−	0.838763i	$-0.316721\pi$
$43$	7.14101	1.08899	0.544497	+	0.838763i	$0.316721\pi$
$44$	−0.308407	−0.0464940
$45$	−0.926817	−0.138162
$46$	11.5487	1.70276
$47$	−1.95289	−0.284859	−0.142429	−	0.989805i	$-0.545491\pi$
$47$	−1.95289	−0.284859	−0.142429	+	0.989805i	$0.545491\pi$
$48$	−4.14101	−0.597703
$49$	1.00000	0.142857
$50$	5.96245	0.843218
$51$	−2.87971	−0.403240
$52$	0	0
$53$	−5.14101	−0.706172	−0.353086	−	0.935591i	$-0.614868\pi$
$53$	−5.14101	−0.706172	−0.353086	+	0.935591i	$0.614868\pi$
$54$	−1.43986	−0.195939
$55$	3.90579	0.526656
$56$	−2.77434	−0.370736
$57$	1.28738	0.170517
$58$	−4.73334	−0.621519
$59$	7.33448	0.954868	0.477434	−	0.878668i	$-0.341567\pi$
$59$	7.33448	0.954868	0.477434	+	0.878668i	$0.341567\pi$
$60$	−0.0678271	−0.00875644
$61$	7.75942	0.993492	0.496746	−	0.867896i	$-0.334528\pi$
$61$	7.75942	0.993492	0.496746	+	0.867896i	$0.334528\pi$
$62$	−10.1464	−1.28859
$63$	−1.00000	−0.125988
$64$	7.68624	0.960780
$65$	0	0
$66$	6.06783	0.746898
$67$	−12.0414	−1.47110	−0.735548	−	0.677473i	$-0.763075\pi$
$67$	−12.0414	−1.47110	−0.735548	+	0.677473i	$0.763075\pi$
$68$	−0.210745	−0.0255566
$69$	−8.02072	−0.965581
$70$	−1.33448	−0.159501
$71$	−10.7889	−1.28041	−0.640206	−	0.768203i	$-0.721151\pi$
$71$	−10.7889	−1.28041	−0.640206	+	0.768203i	$0.721151\pi$
$72$	2.77434	0.326959
$73$	8.32568	0.974447	0.487224	−	0.873277i	$-0.338010\pi$
$73$	8.32568	0.974447	0.487224	+	0.873277i	$0.338010\pi$
$74$	12.3464	1.43524
$75$	−4.14101	−0.478163
$76$	0.0942138	0.0108071
$77$	4.21419	0.480252
$78$	0	0
$79$	4.47204	0.503144	0.251572	−	0.967839i	$-0.419052\pi$
$79$	4.47204	0.503144	0.251572	+	0.967839i	$0.419052\pi$
$80$	3.83796	0.429097
$81$	1.00000	0.111111
$82$	−17.3759	−1.91885
$83$	3.80653	0.417821	0.208910	−	0.977935i	$-0.433008\pi$
$83$	3.80653	0.417821	0.208910	+	0.977935i	$0.433008\pi$
$84$	−0.0731828	−0.00798490
$85$	2.66896	0.289490
$86$	−10.2820	−1.10874
$87$	3.28738	0.352444
$88$	−11.6916	−1.24633
$89$	5.64793	0.598680	0.299340	−	0.954147i	$-0.403234\pi$
$89$	5.64793	0.598680	0.299340	+	0.954147i	$0.403234\pi$
$90$	1.33448	0.140667
$91$	0	0
$92$	−0.586979	−0.0611968
$93$	7.04680	0.730719
$94$	2.81188	0.290024
$95$	−1.19316	−0.122416
$96$	0.413779	0.0422312
$97$	−6.90043	−0.700633	−0.350316	−	0.936631i	$-0.613926\pi$
$97$	−6.90043	−0.700633	−0.350316	+	0.936631i	$0.613926\pi$
$98$	−1.43986	−0.145447
$99$	−4.21419	−0.423542
$100$	−0.303051	−0.0303051
$101$	−10.9739	−1.09195	−0.545973	−	0.837803i	$-0.683840\pi$
$101$	−10.9739	−1.09195	−0.545973	+	0.837803i	$0.683840\pi$
$102$	4.14637	0.410551
$103$	16.4284	1.61874	0.809368	−	0.587301i	$-0.199810\pi$
$103$	16.4284	1.61874	0.809368	+	0.587301i	$0.199810\pi$
$104$	0	0
$105$	0.926817	0.0904481
$106$	7.40231	0.718976
$107$	−3.45446	−0.333955	−0.166978	−	0.985961i	$-0.553401\pi$
$107$	−3.45446	−0.333955	−0.166978	+	0.985961i	$0.553401\pi$
$108$	0.0731828	0.00704202
$109$	−4.66896	−0.447206	−0.223603	−	0.974680i	$-0.571782\pi$
$109$	−4.66896	−0.447206	−0.223603	+	0.974680i	$0.571782\pi$
$110$	−5.62377	−0.536205
$111$	−8.57475	−0.813879
$112$	4.14101	0.391289
$113$	−3.28738	−0.309250	−0.154625	−	0.987973i	$-0.549417\pi$
$113$	−3.28738	−0.309250	−0.154625	+	0.987973i	$0.549417\pi$
$114$	−1.85363	−0.173609
$115$	7.43374	0.693200
$116$	0.240579	0.0223372
$117$	0	0
$118$	−10.5606	−0.972181
$119$	2.87971	0.263983
$120$	−2.57130	−0.234727
$121$	6.75942	0.614493
$122$	−11.1724	−1.01151
$123$	12.0678	1.08812
$124$	0.515704	0.0463116
$125$	8.47204	0.757763
$126$	1.43986	0.128272
$127$	−0.428386	−0.0380131	−0.0190065	−	0.999819i	$-0.506050\pi$
$127$	−0.428386	−0.0380131	−0.0190065	+	0.999819i	$0.506050\pi$
$128$	−11.8946	−1.05135
$129$	7.14101	0.628731
$130$	0	0
$131$	14.1878	1.23959	0.619797	−	0.784762i	$-0.287215\pi$
$131$	14.1878	1.23959	0.619797	+	0.784762i	$0.287215\pi$
$132$	−0.308407	−0.0268433
$133$	−1.28738	−0.111630
$134$	17.3379	1.49777
$135$	−0.926817	−0.0797677
$136$	−7.98929	−0.685076
$137$	−14.7070	−1.25650	−0.628250	−	0.778011i	$-0.716229\pi$
$137$	−14.7070	−1.25650	−0.628250	+	0.778011i	$0.716229\pi$
$138$	11.5487	0.983089
$139$	9.85363	0.835774	0.417887	−	0.908499i	$-0.362771\pi$
$139$	9.85363	0.835774	0.417887	+	0.908499i	$0.362771\pi$
$140$	0.0678271	0.00573244
$141$	−1.95289	−0.164463
$142$	15.5345	1.30363
$143$	0	0
$144$	−4.14101	−0.345084
$145$	−3.04680	−0.253023
$146$	−11.9878	−0.992115
$147$	1.00000	0.0824786
$148$	−0.627525	−0.0515822
$149$	3.38663	0.277444	0.138722	−	0.990331i	$-0.455701\pi$
$149$	3.38663	0.277444	0.138722	+	0.990331i	$0.455701\pi$
$150$	5.96245	0.486832
$151$	21.8951	1.78180	0.890898	−	0.454204i	$-0.150076\pi$
$151$	21.8951	1.78180	0.890898	+	0.454204i	$0.150076\pi$
$152$	3.57161	0.289696
$153$	−2.87971	−0.232811
$154$	−6.06783	−0.488959
$155$	−6.53109	−0.524590
$156$	0	0
$157$	−0.867482	−0.0692326	−0.0346163	−	0.999401i	$-0.511021\pi$
$157$	−0.867482	−0.0692326	−0.0346163	+	0.999401i	$0.511021\pi$
$158$	−6.43910	−0.512267
$159$	−5.14101	−0.407709
$160$	−0.383498	−0.0303182
$161$	8.02072	0.632121
$162$	−1.43986	−0.113126
$163$	−4.42839	−0.346858	−0.173429	−	0.984846i	$-0.555485\pi$
$163$	−4.42839	−0.346858	−0.173429	+	0.984846i	$0.555485\pi$
$164$	0.883158	0.0689630
$165$	3.90579	0.304065
$166$	−5.48085	−0.425396
$167$	−20.5276	−1.58848	−0.794238	−	0.607606i	$-0.792130\pi$
$167$	−20.5276	−1.58848	−0.794238	+	0.607606i	$0.792130\pi$
$168$	−2.77434	−0.214045
$169$	0	0
$170$	−3.84292	−0.294739
$171$	1.28738	0.0984481
$172$	0.522599	0.0398478
$173$	15.0154	1.14160	0.570799	−	0.821090i	$-0.306634\pi$
$173$	15.0154	1.14160	0.570799	+	0.821090i	$0.306634\pi$
$174$	−4.73334	−0.358834
$175$	4.14101	0.313031
$176$	17.4510	1.31542
$177$	7.33448	0.551293
$178$	−8.13221	−0.609535
$179$	−5.35176	−0.400009	−0.200004	−	0.979795i	$-0.564096\pi$
$179$	−5.35176	−0.400009	−0.200004	+	0.979795i	$0.564096\pi$
$180$	−0.0678271	−0.00505553
$181$	11.4667	0.852312	0.426156	−	0.904650i	$-0.359867\pi$
$181$	11.4667	0.852312	0.426156	+	0.904650i	$0.359867\pi$
$182$	0	0
$183$	7.75942	0.573593
$184$	−22.2522	−1.64045
$185$	7.94723	0.584292
$186$	−10.1464	−0.743968
$187$	12.1357	0.887447
$188$	−0.142918	−0.0104234
$189$	−1.00000	−0.0727393
$190$	1.71798	0.124635
$191$	20.1756	1.45985	0.729927	−	0.683525i	$-0.239554\pi$
$191$	20.1756	1.45985	0.729927	+	0.683525i	$0.239554\pi$
$192$	7.68624	0.554706
$193$	26.3756	1.89856	0.949279	−	0.314435i	$-0.101815\pi$
$193$	26.3756	1.89856	0.949279	+	0.314435i	$0.101815\pi$
$194$	9.93562	0.713336
$195$	0	0
$196$	0.0731828	0.00522734
$197$	20.1322	1.43436	0.717180	−	0.696888i	$-0.245432\pi$
$197$	20.1322	1.43436	0.717180	+	0.696888i	$0.245432\pi$
$198$	6.06783	0.431222
$199$	1.75942	0.124722	0.0623610	−	0.998054i	$-0.480137\pi$
$199$	1.75942	0.124722	0.0623610	+	0.998054i	$0.480137\pi$
$200$	−11.4886	−0.812364
$201$	−12.0414	−0.849338
$202$	15.8009	1.11174
$203$	−3.28738	−0.230729
$204$	−0.210745	−0.0147551
$205$	−11.1847	−0.781171
$206$	−23.6545	−1.64809
$207$	−8.02072	−0.557479
$208$	0	0
$209$	−5.42525	−0.375272
$210$	−1.33448	−0.0920880
$211$	15.5694	1.07184	0.535921	−	0.844268i	$-0.319965\pi$
$211$	15.5694	1.07184	0.535921	+	0.844268i	$0.319965\pi$
$212$	−0.376234	−0.0258398
$213$	−10.7889	−0.739246
$214$	4.97392	0.340010
$215$	−6.61841	−0.451372
$216$	2.77434	0.188770
$217$	−7.04680	−0.478368
$218$	6.72263	0.455314
$219$	8.32568	0.562597
$220$	0.285836	0.0192711
$221$	0	0
$222$	12.3464	0.828636
$223$	11.5694	0.774744	0.387372	−	0.921923i	$-0.373383\pi$
$223$	11.5694	0.774744	0.387372	+	0.921923i	$0.373383\pi$
$224$	−0.413779	−0.0276468
$225$	−4.14101	−0.276067
$226$	4.73334	0.314857
$227$	11.0418	0.732867	0.366433	−	0.930444i	$-0.380579\pi$
$227$	11.0418	0.732867	0.366433	+	0.930444i	$0.380579\pi$
$228$	0.0942138	0.00623946
$229$	13.7073	0.905802	0.452901	−	0.891561i	$-0.350389\pi$
$229$	13.7073	0.905802	0.452901	+	0.891561i	$0.350389\pi$
$230$	−10.7035	−0.705769
$231$	4.21419	0.277274
$232$	9.12029	0.598776
$233$	1.23522	0.0809222	0.0404611	−	0.999181i	$-0.487117\pi$
$233$	1.23522	0.0809222	0.0404611	+	0.999181i	$0.487117\pi$
$234$	0	0
$235$	1.80997	0.118070
$236$	0.536758	0.0349400
$237$	4.47204	0.290491
$238$	−4.14637	−0.268769
$239$	−19.1061	−1.23587	−0.617936	−	0.786228i	$-0.712031\pi$
$239$	−19.1061	−1.23587	−0.617936	+	0.786228i	$0.712031\pi$
$240$	3.83796	0.247739
$241$	12.0329	0.775110	0.387555	−	0.921847i	$-0.373320\pi$
$241$	12.0329	0.775110	0.387555	+	0.921847i	$0.373320\pi$
$242$	−9.73259	−0.625634
$243$	1.00000	0.0641500
$244$	0.567856	0.0363533
$245$	−0.926817	−0.0592122
$246$	−17.3759	−1.10785
$247$	0	0
$248$	19.5502	1.24144
$249$	3.80653	0.241229
$250$	−12.1985	−0.771502
$251$	−15.0031	−0.946990	−0.473495	−	0.880797i	$-0.657008\pi$
$251$	−15.0031	−0.946990	−0.473495	+	0.880797i	$0.657008\pi$
$252$	−0.0731828	−0.00461008
$253$	33.8009	2.12504
$254$	0.616813	0.0387023
$255$	2.66896	0.167137
$256$	1.75406	0.109629
$257$	−13.0261	−0.812544	−0.406272	−	0.913752i	$-0.633172\pi$
$257$	−13.0261	−0.812544	−0.406272	+	0.913752i	$0.633172\pi$
$258$	−10.2820	−0.640131
$259$	8.57475	0.532809
$260$	0	0
$261$	3.28738	0.203483
$262$	−20.4284	−1.26207
$263$	−2.59547	−0.160044	−0.0800218	−	0.996793i	$-0.525499\pi$
$263$	−2.59547	−0.160044	−0.0800218	+	0.996793i	$0.525499\pi$
$264$	−11.6916	−0.719568
$265$	4.76478	0.292698
$266$	1.85363	0.113654
$267$	5.64793	0.345648
$268$	−0.881227	−0.0538295
$269$	−23.3081	−1.42112	−0.710560	−	0.703637i	$-0.751558\pi$
$269$	−23.3081	−1.42112	−0.710560	+	0.703637i	$0.751558\pi$
$270$	1.33448	0.0812140
$271$	6.05215	0.367642	0.183821	−	0.982960i	$-0.441153\pi$
$271$	6.05215	0.367642	0.183821	+	0.982960i	$0.441153\pi$
$272$	11.9249	0.723054
$273$	0	0
$274$	21.1759	1.27928
$275$	17.4510	1.05234
$276$	−0.586979	−0.0353320
$277$	15.1932	0.912869	0.456434	−	0.889757i	$-0.349126\pi$
$277$	15.1932	0.912869	0.456434	+	0.889757i	$0.349126\pi$
$278$	−14.1878	−0.850928
$279$	7.04680	0.421881
$280$	2.57130	0.153665
$281$	7.57506	0.451890	0.225945	−	0.974140i	$-0.427453\pi$
$281$	7.57506	0.451890	0.225945	+	0.974140i	$0.427453\pi$
$282$	2.81188	0.167445
$283$	19.0974	1.13522	0.567610	−	0.823298i	$-0.307868\pi$
$283$	19.0974	1.13522	0.567610	+	0.823298i	$0.307868\pi$
$284$	−0.789565	−0.0468521
$285$	−1.19316	−0.0706768
$286$	0	0
$287$	−12.0678	−0.712341
$288$	0.413779	0.0243822
$289$	−8.70727	−0.512192
$290$	4.38695	0.257610
$291$	−6.90043	−0.404510
$292$	0.609297	0.0356564
$293$	3.79430	0.221665	0.110833	−	0.993839i	$-0.464648\pi$
$293$	3.79430	0.221665	0.110833	+	0.993839i	$0.464648\pi$
$294$	−1.43986	−0.0839741
$295$	−6.79772	−0.395779
$296$	−23.7893	−1.38272
$297$	−4.21419	−0.244532
$298$	−4.87626	−0.282474
$299$	0	0
$300$	−0.303051	−0.0174966
$301$	−7.14101	−0.411601
$302$	−31.5257	−1.81410
$303$	−10.9739	−0.630435
$304$	−5.33104	−0.305756
$305$	−7.19156	−0.411788
$306$	4.14637	0.237032
$307$	5.19316	0.296389	0.148195	−	0.988958i	$-0.452654\pi$
$307$	5.19316	0.296389	0.148195	+	0.988958i	$0.452654\pi$
$308$	0.308407	0.0175731
$309$	16.4284	0.934578
$310$	9.40383	0.534101
$311$	−13.8536	−0.785568	−0.392784	−	0.919631i	$-0.628488\pi$
$311$	−13.8536	−0.785568	−0.392784	+	0.919631i	$0.628488\pi$
$312$	0	0
$313$	−32.6162	−1.84358	−0.921788	−	0.387694i	$-0.873272\pi$
$313$	−32.6162	−1.84358	−0.921788	+	0.387694i	$0.873272\pi$
$314$	1.24905	0.0704879
$315$	0.926817	0.0522202
$316$	0.327277	0.0184108
$317$	−12.0380	−0.676121	−0.338061	−	0.941124i	$-0.609771\pi$
$317$	−12.0380	−0.676121	−0.338061	+	0.941124i	$0.609771\pi$
$318$	7.40231	0.415101
$319$	−13.8536	−0.775655
$320$	−7.12374	−0.398229
$321$	−3.45446	−0.192809
$322$	−11.5487	−0.643583
$323$	−3.70727	−0.206278
$324$	0.0731828	0.00406571
$325$	0	0
$326$	6.37623	0.353147
$327$	−4.66896	−0.258194
$328$	33.4802	1.84864
$329$	1.95289	0.107666
$330$	−5.62377	−0.309578
$331$	26.2820	1.44459	0.722295	−	0.691585i	$-0.243087\pi$
$331$	26.2820	1.44459	0.722295	+	0.691585i	$0.243087\pi$
$332$	0.278572	0.0152886
$333$	−8.57475	−0.469893
$334$	29.5568	1.61728
$335$	11.1602	0.609748
$336$	4.14101	0.225911
$337$	26.2905	1.43214	0.716068	−	0.698031i	$-0.245940\pi$
$337$	26.2905	1.43214	0.716068	+	0.698031i	$0.245940\pi$
$338$	0	0
$339$	−3.28738	−0.178546
$340$	0.195322	0.0105928
$341$	−29.6966	−1.60816
$342$	−1.85363	−0.100233
$343$	−1.00000	−0.0539949
$344$	19.8116	1.06817
$345$	7.43374	0.400219
$346$	−21.6199	−1.16230
$347$	16.4928	0.885378	0.442689	−	0.896675i	$-0.354025\pi$
$347$	16.4928	0.885378	0.442689	+	0.896675i	$0.354025\pi$
$348$	0.240579	0.0128964
$349$	−14.1793	−0.759001	−0.379501	−	0.925191i	$-0.623904\pi$
$349$	−14.1793	−0.759001	−0.379501	+	0.925191i	$0.623904\pi$
$350$	−5.96245	−0.318707
$351$	0	0
$352$	−1.74375	−0.0929419
$353$	29.8272	1.58754	0.793772	−	0.608215i	$-0.208114\pi$
$353$	29.8272	1.58754	0.793772	+	0.608215i	$0.208114\pi$
$354$	−10.5606	−0.561289
$355$	9.99938	0.530712
$356$	0.413332	0.0219065
$357$	2.87971	0.152410
$358$	7.70575	0.407262
$359$	−1.34671	−0.0710767	−0.0355383	−	0.999368i	$-0.511315\pi$
$359$	−1.34671	−0.0710767	−0.0355383	+	0.999368i	$0.511315\pi$
$360$	−2.57130	−0.135520
$361$	−17.3427	−0.912772
$362$	−16.5104	−0.867766
$363$	6.75942	0.354778
$364$	0	0
$365$	−7.71638	−0.403894
$366$	−11.1724	−0.583993
$367$	36.1771	1.88843	0.944214	−	0.329331i	$-0.106823\pi$
$367$	36.1771	1.88843	0.944214	+	0.329331i	$0.106823\pi$
$368$	33.2139	1.73139
$369$	12.0678	0.628226
$370$	−11.4429	−0.594886
$371$	5.14101	0.266908
$372$	0.515704	0.0267380
$373$	−16.9089	−0.875511	−0.437755	−	0.899094i	$-0.644226\pi$
$373$	−16.9089	−0.875511	−0.437755	+	0.899094i	$0.644226\pi$
$374$	−17.4736	−0.903538
$375$	8.47204	0.437495
$376$	−5.41798	−0.279411
$377$	0	0
$378$	1.43986	0.0740582
$379$	11.6131	0.596523	0.298261	−	0.954484i	$-0.403593\pi$
$379$	11.6131	0.596523	0.298261	+	0.954484i	$0.403593\pi$
$380$	−0.0873190	−0.00447937
$381$	−0.428386	−0.0219469
$382$	−29.0499	−1.48632
$383$	−14.6134	−0.746708	−0.373354	−	0.927689i	$-0.621792\pi$
$383$	−14.6134	−0.746708	−0.373354	+	0.927689i	$0.621792\pi$
$384$	−11.8946	−0.606995
$385$	−3.90579	−0.199057
$386$	−37.9771	−1.93298
$387$	7.14101	0.362998
$388$	−0.504993	−0.0256371
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	23.0974	1.16808
$392$	2.77434	0.140125
$393$	14.1878	0.715680
$394$	−28.9875	−1.46037
$395$	−4.14477	−0.208546
$396$	−0.308407	−0.0154980
$397$	−25.6982	−1.28975	−0.644877	−	0.764287i	$-0.723091\pi$
$397$	−25.6982	−1.28975	−0.644877	+	0.764287i	$0.723091\pi$
$398$	−2.53331	−0.126983
$399$	−1.28738	−0.0644494
$400$	17.1480	0.857398
$401$	19.5637	0.976966	0.488483	−	0.872573i	$-0.337550\pi$
$401$	19.5637	0.976966	0.488483	+	0.872573i	$0.337550\pi$
$402$	17.3379	0.864737
$403$	0	0
$404$	−0.803103	−0.0399559
$405$	−0.926817	−0.0460539
$406$	4.73334	0.234912
$407$	36.1357	1.79118
$408$	−7.98929	−0.395529
$409$	−3.19316	−0.157892	−0.0789458	−	0.996879i	$-0.525155\pi$
$409$	−3.19316	−0.157892	−0.0789458	+	0.996879i	$0.525155\pi$
$410$	16.1043	0.795335
$411$	−14.7070	−0.725441
$412$	1.20228	0.0592319
$413$	−7.33448	−0.360906
$414$	11.5487	0.567586
$415$	−3.52796	−0.173181
$416$	0	0
$417$	9.85363	0.482535
$418$	7.81157	0.382076
$419$	30.2292	1.47680	0.738398	−	0.674366i	$-0.235583\pi$
$419$	30.2292	1.47680	0.738398	+	0.674366i	$0.235583\pi$
$420$	0.0678271	0.00330962
$421$	−26.9510	−1.31351	−0.656755	−	0.754104i	$-0.728072\pi$
$421$	−26.9510	−1.31351	−0.656755	+	0.754104i	$0.728072\pi$
$422$	−22.4177	−1.09128
$423$	−1.95289	−0.0949529
$424$	−14.2629	−0.692668
$425$	11.9249	0.578443
$426$	15.5345	0.752650
$427$	−7.75942	−0.375505
$428$	−0.252807	−0.0122199
$429$	0	0
$430$	9.52955	0.459556
$431$	−16.7713	−0.807847	−0.403923	−	0.914793i	$-0.632354\pi$
$431$	−16.7713	−0.807847	−0.403923	+	0.914793i	$0.632354\pi$
$432$	−4.14101	−0.199234
$433$	25.8530	1.24242	0.621208	−	0.783646i	$-0.286642\pi$
$433$	25.8530	1.24242	0.621208	+	0.783646i	$0.286642\pi$
$434$	10.1464	0.487041
$435$	−3.04680	−0.146083
$436$	−0.341688	−0.0163639
$437$	−10.3257	−0.493944
$438$	−11.9878	−0.572798
$439$	25.0553	1.19582	0.597912	−	0.801562i	$-0.295997\pi$
$439$	25.0553	1.19582	0.597912	+	0.801562i	$0.295997\pi$
$440$	10.8360	0.516585
$441$	1.00000	0.0476190
$442$	0	0
$443$	4.64762	0.220815	0.110408	−	0.993886i	$-0.464784\pi$
$443$	4.64762	0.220815	0.110408	+	0.993886i	$0.464784\pi$
$444$	−0.627525	−0.0297810
$445$	−5.23460	−0.248144
$446$	−16.6583	−0.788791
$447$	3.38663	0.160182
$448$	−7.68624	−0.363141
$449$	−0.494696	−0.0233462	−0.0116731	−	0.999932i	$-0.503716\pi$
$449$	−0.494696	−0.0233462	−0.0116731	+	0.999932i	$0.503716\pi$
$450$	5.96245	0.281073
$451$	−50.8561	−2.39472
$452$	−0.240579	−0.0113159
$453$	21.8951	1.02872
$454$	−15.8985	−0.746155
$455$	0	0
$456$	3.57161	0.167256
$457$	−26.4698	−1.23821	−0.619103	−	0.785310i	$-0.712504\pi$
$457$	−26.4698	−1.23821	−0.619103	+	0.785310i	$0.712504\pi$
$458$	−19.7365	−0.922225
$459$	−2.87971	−0.134413
$460$	0.544022	0.0253652
$461$	1.08168	0.0503786	0.0251893	−	0.999683i	$-0.491981\pi$
$461$	1.08168	0.0503786	0.0251893	+	0.999683i	$0.491981\pi$
$462$	−6.06783	−0.282301
$463$	32.7098	1.52015	0.760076	−	0.649834i	$-0.225162\pi$
$463$	32.7098	1.52015	0.760076	+	0.649834i	$0.225162\pi$
$464$	−13.6131	−0.631970
$465$	−6.53109	−0.302872
$466$	−1.77854	−0.0823894
$467$	−17.0797	−0.790356	−0.395178	−	0.918605i	$-0.629317\pi$
$467$	−17.0797	−0.790356	−0.395178	+	0.918605i	$0.629317\pi$
$468$	0	0
$469$	12.0414	0.556022
$470$	−2.60610	−0.120211
$471$	−0.867482	−0.0399715
$472$	20.3483	0.936608
$473$	−30.0936	−1.38370
$474$	−6.43910	−0.295758
$475$	−5.33104	−0.244605
$476$	0.210745	0.00965950
$477$	−5.14101	−0.235391
$478$	27.5101	1.25828
$479$	17.1790	0.784929	0.392464	−	0.919767i	$-0.371623\pi$
$479$	17.1790	0.784929	0.392464	+	0.919767i	$0.371623\pi$
$480$	−0.383498	−0.0175042
$481$	0	0
$482$	−17.3257	−0.789164
$483$	8.02072	0.364955
$484$	0.494674	0.0224852
$485$	6.39544	0.290402
$486$	−1.43986	−0.0653132
$487$	4.28264	0.194065	0.0970325	−	0.995281i	$-0.469065\pi$
$487$	4.28264	0.194065	0.0970325	+	0.995281i	$0.469065\pi$
$488$	21.5273	0.974493
$489$	−4.42839	−0.200259
$490$	1.33448	0.0602858
$491$	27.4545	1.23900	0.619501	−	0.784996i	$-0.287335\pi$
$491$	27.4545	1.23900	0.619501	+	0.784996i	$0.287335\pi$
$492$	0.883158	0.0398158
$493$	−9.46669	−0.426358
$494$	0	0
$495$	3.90579	0.175552
$496$	−29.1809	−1.31026
$497$	10.7889	0.483950
$498$	−5.48085	−0.245603
$499$	37.0452	1.65837	0.829185	−	0.558974i	$-0.188805\pi$
$499$	37.0452	1.65837	0.829185	+	0.558974i	$0.188805\pi$
$500$	0.620008	0.0277276
$501$	−20.5276	−0.917108
$502$	21.6023	0.964160
$503$	3.23744	0.144350	0.0721752	−	0.997392i	$-0.477006\pi$
$503$	3.23744	0.144350	0.0721752	+	0.997392i	$0.477006\pi$
$504$	−2.77434	−0.123579
$505$	10.1708	0.452596
$506$	−48.6683	−2.16357
$507$	0	0
$508$	−0.0313505	−0.00139095
$509$	30.4877	1.35134	0.675672	−	0.737202i	$-0.263853\pi$
$509$	30.4877	1.35134	0.675672	+	0.737202i	$0.263853\pi$
$510$	−3.84292	−0.170167
$511$	−8.32568	−0.368306
$512$	21.2637	0.939730
$513$	1.28738	0.0568390
$514$	18.7557	0.827277
$515$	−15.2261	−0.670943
$516$	0.522599	0.0230062
$517$	8.22987	0.361949
$518$	−12.3464	−0.542470
$519$	15.0154	0.659101
$520$	0	0
$521$	−25.3602	−1.11105	−0.555526	−	0.831499i	$-0.687483\pi$
$521$	−25.3602	−1.11105	−0.555526	+	0.831499i	$0.687483\pi$
$522$	−4.73334	−0.207173
$523$	−7.00314	−0.306226	−0.153113	−	0.988209i	$-0.548930\pi$
$523$	−7.00314	−0.306226	−0.153113	+	0.988209i	$0.548930\pi$
$524$	1.03830	0.0453585
$525$	4.14101	0.180728
$526$	3.73710	0.162945
$527$	−20.2927	−0.883965
$528$	17.4510	0.759458
$529$	41.3320	1.79704
$530$	−6.86059	−0.298005
$531$	7.33448	0.318289
$532$	−0.0942138	−0.00408469
$533$	0	0
$534$	−8.13221	−0.351915
$535$	3.20165	0.138420
$536$	−33.4070	−1.44296
$537$	−5.35176	−0.230945
$538$	33.5603	1.44689
$539$	−4.21419	−0.181518
$540$	−0.0678271	−0.00291881
$541$	1.42463	0.0612495	0.0306248	−	0.999531i	$-0.490250\pi$
$541$	1.42463	0.0612495	0.0306248	+	0.999531i	$0.490250\pi$
$542$	−8.71422	−0.374308
$543$	11.4667	0.492083
$544$	−1.19156	−0.0510879
$545$	4.32728	0.185360
$546$	0	0
$547$	−22.0499	−0.942787	−0.471394	−	0.881923i	$-0.656249\pi$
$547$	−22.0499	−0.942787	−0.471394	+	0.881923i	$0.656249\pi$
$548$	−1.07630	−0.0459771
$549$	7.75942	0.331164
$550$	−25.1269	−1.07142
$551$	4.23209	0.180293
$552$	−22.2522	−0.947116
$553$	−4.47204	−0.190171
$554$	−21.8760	−0.929420
$555$	7.94723	0.337341
$556$	0.721117	0.0305822
$557$	9.08319	0.384867	0.192434	−	0.981310i	$-0.438362\pi$
$557$	9.08319	0.384867	0.192434	+	0.981310i	$0.438362\pi$
$558$	−10.1464	−0.429530
$559$	0	0
$560$	−3.83796	−0.162183
$561$	12.1357	0.512368
$562$	−10.9070	−0.460084
$563$	34.1350	1.43862	0.719310	−	0.694689i	$-0.244458\pi$
$563$	34.1350	1.43862	0.719310	+	0.694689i	$0.244458\pi$
$564$	−0.142918	−0.00601794
$565$	3.04680	0.128180
$566$	−27.4974	−1.15580
$567$	−1.00000	−0.0419961
$568$	−29.9322	−1.25593
$569$	1.23522	0.0517833	0.0258916	−	0.999665i	$-0.491758\pi$
$569$	1.23522	0.0517833	0.0258916	+	0.999665i	$0.491758\pi$
$570$	1.71798	0.0719583
$571$	−26.4613	−1.10737	−0.553686	−	0.832725i	$-0.686779\pi$
$571$	−26.4613	−1.10737	−0.553686	+	0.832725i	$0.686779\pi$
$572$	0	0
$573$	20.1756	0.842847
$574$	17.3759	0.725257
$575$	33.2139	1.38511
$576$	7.68624	0.320260
$577$	23.2852	0.969374	0.484687	−	0.874688i	$-0.338934\pi$
$577$	23.2852	0.969374	0.484687	+	0.874688i	$0.338934\pi$
$578$	12.5372	0.521479
$579$	26.3756	1.09613
$580$	−0.222973	−0.00925846
$581$	−3.80653	−0.157921
$582$	9.93562	0.411845
$583$	21.6652	0.897281
$584$	23.0982	0.955812
$585$	0	0
$586$	−5.46324	−0.225684
$587$	10.7155	0.442274	0.221137	−	0.975243i	$-0.429023\pi$
$587$	10.7155	0.442274	0.221137	+	0.975243i	$0.429023\pi$
$588$	0.0731828	0.00301801
$589$	9.07187	0.373800
$590$	9.78774	0.402955
$591$	20.1322	0.828128
$592$	35.5081	1.45938
$593$	−14.1008	−0.579049	−0.289525	−	0.957171i	$-0.593497\pi$
$593$	−14.1008	−0.579049	−0.289525	+	0.957171i	$0.593497\pi$
$594$	6.06783	0.248966
$595$	−2.66896	−0.109417
$596$	0.247843	0.0101521
$597$	1.75942	0.0720083
$598$	0	0
$599$	−38.9296	−1.59062	−0.795311	−	0.606202i	$-0.792692\pi$
$599$	−38.9296	−1.59062	−0.795311	+	0.606202i	$0.792692\pi$
$600$	−11.4886	−0.469018
$601$	−32.6162	−1.33044	−0.665221	−	0.746646i	$-0.731663\pi$
$601$	−32.6162	−1.33044	−0.665221	+	0.746646i	$0.731663\pi$
$602$	10.2820	0.419064
$603$	−12.0414	−0.490365
$604$	1.60234	0.0651984
$605$	−6.26475	−0.254698
$606$	15.8009	0.641866
$607$	19.3203	0.784188	0.392094	−	0.919925i	$-0.371751\pi$
$607$	19.3203	0.784188	0.392094	+	0.919925i	$0.371751\pi$
$608$	0.532689	0.0216034
$609$	−3.28738	−0.133211
$610$	10.3548	0.419254
$611$	0	0
$612$	−0.210745	−0.00851888
$613$	−35.3197	−1.42655	−0.713275	−	0.700885i	$-0.752789\pi$
$613$	−35.3197	−1.42655	−0.713275	+	0.700885i	$0.752789\pi$
$614$	−7.47740	−0.301763
$615$	−11.1847	−0.451009
$616$	11.6916	0.471068
$617$	24.4318	0.983589	0.491794	−	0.870711i	$-0.336341\pi$
$617$	24.4318	0.983589	0.491794	+	0.870711i	$0.336341\pi$
$618$	−23.6545	−0.951523
$619$	−2.90892	−0.116919	−0.0584597	−	0.998290i	$-0.518619\pi$
$619$	−2.90892	−0.116919	−0.0584597	+	0.998290i	$0.518619\pi$
$620$	−0.477964	−0.0191955
$621$	−8.02072	−0.321860
$622$	19.9472	0.799811
$623$	−5.64793	−0.226280
$624$	0	0
$625$	12.8530	0.514121
$626$	46.9626	1.87700
$627$	−5.42525	−0.216664
$628$	−0.0634848	−0.00253332
$629$	24.6928	0.984566
$630$	−1.33448	−0.0531671
$631$	−5.66521	−0.225528	−0.112764	−	0.993622i	$-0.535970\pi$
$631$	−5.66521	−0.225528	−0.112764	+	0.993622i	$0.535970\pi$
$632$	12.4070	0.493522
$633$	15.5694	0.618828
$634$	17.3330	0.688380
$635$	0.397035	0.0157559
$636$	−0.376234	−0.0149186
$637$	0	0
$638$	19.9472	0.789718
$639$	−10.7889	−0.426804
$640$	11.0241	0.435768
$641$	12.2842	0.485198	0.242599	−	0.970127i	$-0.422000\pi$
$641$	12.2842	0.485198	0.242599	+	0.970127i	$0.422000\pi$
$642$	4.97392	0.196305
$643$	−9.14950	−0.360821	−0.180411	−	0.983591i	$-0.557743\pi$
$643$	−9.14950	−0.360821	−0.180411	+	0.983591i	$0.557743\pi$
$644$	0.586979	0.0231302
$645$	−6.61841	−0.260600
$646$	5.33793	0.210018
$647$	38.4108	1.51008	0.755042	−	0.655677i	$-0.227617\pi$
$647$	38.4108	1.51008	0.755042	+	0.655677i	$0.227617\pi$
$648$	2.77434	0.108986
$649$	−30.9089	−1.21328
$650$	0	0
$651$	−7.04680	−0.276186
$652$	−0.324082	−0.0126920
$653$	28.4805	1.11453	0.557265	−	0.830335i	$-0.311851\pi$
$653$	28.4805	1.11453	0.557265	+	0.830335i	$0.311851\pi$
$654$	6.72263	0.262876
$655$	−13.1495	−0.513794
$656$	−49.9730	−1.95112
$657$	8.32568	0.324816
$658$	−2.81188	−0.109619
$659$	−30.4384	−1.18571	−0.592856	−	0.805309i	$-0.702000\pi$
$659$	−30.4384	−1.18571	−0.592856	+	0.805309i	$0.702000\pi$
$660$	0.285836	0.0111262
$661$	−36.7710	−1.43023	−0.715114	−	0.699008i	$-0.753625\pi$
$661$	−36.7710	−1.43023	−0.715114	+	0.699008i	$0.753625\pi$
$662$	−37.8423	−1.47078
$663$	0	0
$664$	10.5606	0.409830
$665$	1.19316	0.0462688
$666$	12.3464	0.478413
$667$	−26.3671	−1.02094
$668$	−1.50227	−0.0581246
$669$	11.5694	0.447299
$670$	−16.0691	−0.620803
$671$	−32.6997	−1.26236
$672$	−0.413779	−0.0159619
$673$	26.7961	1.03291	0.516457	−	0.856313i	$-0.327250\pi$
$673$	26.7961	1.03291	0.516457	+	0.856313i	$0.327250\pi$
$674$	−37.8545	−1.45810
$675$	−4.14101	−0.159388
$676$	0	0
$677$	−20.3050	−0.780383	−0.390191	−	0.920734i	$-0.627591\pi$
$677$	−20.3050	−0.780383	−0.390191	+	0.920734i	$0.627591\pi$
$678$	4.73334	0.181783
$679$	6.90043	0.264814
$680$	7.40461	0.283954
$681$	11.0418	0.423121
$682$	42.7587	1.63732
$683$	−44.9240	−1.71897	−0.859484	−	0.511162i	$-0.829215\pi$
$683$	−44.9240	−1.71897	−0.859484	+	0.511162i	$0.829215\pi$
$684$	0.0942138	0.00360235
$685$	13.6307	0.520801
$686$	1.43986	0.0549739
$687$	13.7073	0.522965
$688$	−29.5710	−1.12738
$689$	0	0
$690$	−10.7035	−0.407476
$691$	−22.0085	−0.837243	−0.418621	−	0.908161i	$-0.637487\pi$
$691$	−22.0085	−0.837243	−0.418621	+	0.908161i	$0.637487\pi$
$692$	1.09887	0.0417726
$693$	4.21419	0.160084
$694$	−23.7472	−0.901431
$695$	−9.13252	−0.346416
$696$	9.12029	0.345704
$697$	−34.7518	−1.31632
$698$	20.4162	0.772763
$699$	1.23522	0.0467205
$700$	0.303051	0.0114542
$701$	31.4645	1.18840	0.594198	−	0.804319i	$-0.297469\pi$
$701$	31.4645	1.18840	0.594198	+	0.804319i	$0.297469\pi$
$702$	0	0
$703$	−11.0389	−0.416341
$704$	−32.3913	−1.22079
$705$	1.80997	0.0681676
$706$	−42.9469	−1.61633
$707$	10.9739	0.412717
$708$	0.536758	0.0201726
$709$	25.3373	0.951563	0.475781	−	0.879564i	$-0.342165\pi$
$709$	25.3373	0.951563	0.475781	+	0.879564i	$0.342165\pi$
$710$	−14.3977	−0.540334
$711$	4.47204	0.167715
$712$	15.6693	0.587231
$713$	−56.5204	−2.11670
$714$	−4.14637	−0.155174
$715$	0	0
$716$	−0.391657	−0.0146369
$717$	−19.1061	−0.713532
$718$	1.93907	0.0723654
$719$	−43.8002	−1.63347	−0.816737	−	0.577011i	$-0.804219\pi$
$719$	−43.8002	−1.63347	−0.816737	+	0.577011i	$0.804219\pi$
$720$	3.83796	0.143032
$721$	−16.4284	−0.611825
$722$	24.9709	0.929322
$723$	12.0329	0.447510
$724$	0.839165	0.0311873
$725$	−13.6131	−0.505576
$726$	−9.73259	−0.361210
$727$	0.944090	0.0350144	0.0175072	−	0.999847i	$-0.494427\pi$
$727$	0.944090	0.0350144	0.0175072	+	0.999847i	$0.494427\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.1105	0.411217
$731$	−20.5640	−0.760588
$732$	0.567856	0.0209886
$733$	5.09957	0.188357	0.0941784	−	0.995555i	$-0.469978\pi$
$733$	5.09957	0.188357	0.0941784	+	0.995555i	$0.469978\pi$
$734$	−52.0898	−1.92267
$735$	−0.926817	−0.0341862
$736$	−3.31881	−0.122333
$737$	50.7450	1.86921
$738$	−17.3759	−0.639617
$739$	8.25129	0.303529	0.151764	−	0.988417i	$-0.451505\pi$
$739$	8.25129	0.303529	0.151764	+	0.988417i	$0.451505\pi$
$740$	0.581601	0.0213801
$741$	0	0
$742$	−7.40231	−0.271747
$743$	−38.4962	−1.41229	−0.706145	−	0.708068i	$-0.749567\pi$
$743$	−38.4962	−1.41229	−0.706145	+	0.708068i	$0.749567\pi$
$744$	19.5502	0.716745
$745$	−3.13879	−0.114996
$746$	24.3464	0.891385
$747$	3.80653	0.139274
$748$	0.888121	0.0324729
$749$	3.45446	0.126223
$750$	−12.1985	−0.445427
$751$	−41.3175	−1.50770	−0.753848	−	0.657049i	$-0.771805\pi$
$751$	−41.3175	−1.50770	−0.753848	+	0.657049i	$0.771805\pi$
$752$	8.08695	0.294901
$753$	−15.0031	−0.546745
$754$	0	0
$755$	−20.2927	−0.738528
$756$	−0.0731828	−0.00266163
$757$	−39.7158	−1.44349	−0.721747	−	0.692157i	$-0.756661\pi$
$757$	−39.7158	−1.44349	−0.721747	+	0.692157i	$0.756661\pi$
$758$	−16.7211	−0.607338
$759$	33.8009	1.22689
$760$	−3.31023	−0.120075
$761$	−10.7390	−0.389289	−0.194644	−	0.980874i	$-0.562355\pi$
$761$	−10.7390	−0.389289	−0.194644	+	0.980874i	$0.562355\pi$
$762$	0.616813	0.0223448
$763$	4.66896	0.169028
$764$	1.47651	0.0534181
$765$	2.66896	0.0964966
$766$	21.0411	0.760247
$767$	0	0
$768$	1.75406	0.0632944
$769$	50.5549	1.82306	0.911529	−	0.411237i	$-0.134903\pi$
$769$	50.5549	1.82306	0.911529	+	0.411237i	$0.134903\pi$
$770$	5.62377	0.202666
$771$	−13.0261	−0.469123
$772$	1.93024	0.0694709
$773$	−8.91770	−0.320747	−0.160374	−	0.987056i	$-0.551270\pi$
$773$	−8.91770	−0.320747	−0.160374	+	0.987056i	$0.551270\pi$
$774$	−10.2820	−0.369580
$775$	−29.1809	−1.04821
$776$	−19.1441	−0.687234
$777$	8.57475	0.307617
$778$	−8.63913	−0.309728
$779$	15.5358	0.556629
$780$	0	0
$781$	45.4667	1.62693
$782$	−33.2568	−1.18926
$783$	3.28738	0.117481
$784$	−4.14101	−0.147893
$785$	0.803998	0.0286959
$786$	−20.4284	−0.728656
$787$	−22.3671	−0.797302	−0.398651	−	0.917103i	$-0.630521\pi$
$787$	−22.3671	−0.797302	−0.398651	+	0.917103i	$0.630521\pi$
$788$	1.47333	0.0524853
$789$	−2.59547	−0.0924012
$790$	5.96787	0.212327
$791$	3.28738	0.116886
$792$	−11.6916	−0.415443
$793$	0	0
$794$	37.0016	1.31314
$795$	4.76478	0.168989
$796$	0.128759	0.00456375
$797$	20.5518	0.727983	0.363991	−	0.931402i	$-0.381414\pi$
$797$	20.5518	0.727983	0.363991	+	0.931402i	$0.381414\pi$
$798$	1.85363	0.0656179
$799$	5.62377	0.198955
$800$	−1.71346	−0.0605801
$801$	5.64793	0.199560
$802$	−28.1689	−0.994680
$803$	−35.0860	−1.23816
$804$	−0.881227	−0.0310785
$805$	−7.43374	−0.262005
$806$	0	0
$807$	−23.3081	−0.820484
$808$	−30.4454	−1.07106
$809$	7.83443	0.275444	0.137722	−	0.990471i	$-0.456022\pi$
$809$	7.83443	0.275444	0.137722	+	0.990471i	$0.456022\pi$
$810$	1.33448	0.0468889
$811$	47.5502	1.66971	0.834857	−	0.550468i	$-0.185551\pi$
$811$	47.5502	1.66971	0.834857	+	0.550468i	$0.185551\pi$
$812$	−0.240579	−0.00844268
$813$	6.05215	0.212258
$814$	−52.0301	−1.82365
$815$	4.10430	0.143767
$816$	11.9249	0.417455
$817$	9.19316	0.321628
$818$	4.59769	0.160754
$819$	0	0
$820$	−0.818526	−0.0285842
$821$	−4.42494	−0.154431	−0.0772157	−	0.997014i	$-0.524603\pi$
$821$	−4.42494	−0.154431	−0.0772157	+	0.997014i	$0.524603\pi$
$822$	21.1759	0.738594
$823$	−28.7525	−1.00225	−0.501124	−	0.865375i	$-0.667080\pi$
$823$	−28.7525	−1.00225	−0.501124	+	0.865375i	$0.667080\pi$
$824$	45.5779	1.58778
$825$	17.4510	0.607566
$826$	10.5606	0.367450
$827$	5.58667	0.194267	0.0971337	−	0.995271i	$-0.469033\pi$
$827$	5.58667	0.194267	0.0971337	+	0.995271i	$0.469033\pi$
$828$	−0.586979	−0.0203989
$829$	53.4974	1.85804	0.929021	−	0.370027i	$-0.120652\pi$
$829$	53.4974	1.85804	0.929021	+	0.370027i	$0.120652\pi$
$830$	5.07974	0.176320
$831$	15.1932	0.527045
$832$	0	0
$833$	−2.87971	−0.0997760
$834$	−14.1878	−0.491284
$835$	19.0254	0.658400
$836$	−0.397035	−0.0137317
$837$	7.04680	0.243573
$838$	−43.5257	−1.50357
$839$	43.0405	1.48592	0.742962	−	0.669334i	$-0.233420\pi$
$839$	43.0405	1.48592	0.742962	+	0.669334i	$0.233420\pi$
$840$	2.57130	0.0887184
$841$	−18.1932	−0.627350
$842$	38.8055	1.33733
$843$	7.57506	0.260899
$844$	1.13941	0.0392202
$845$	0	0
$846$	2.81188	0.0966745
$847$	−6.75942	−0.232256
$848$	21.2890	0.731066
$849$	19.0974	0.655419
$850$	−17.1701	−0.588931
$851$	68.7757	2.35760
$852$	−0.789565	−0.0270501
$853$	30.7434	1.05263	0.526316	−	0.850289i	$-0.323573\pi$
$853$	30.7434	1.05263	0.526316	+	0.850289i	$0.323573\pi$
$854$	11.1724	0.382313
$855$	−1.19316	−0.0408053
$856$	−9.58384	−0.327569
$857$	−24.5449	−0.838438	−0.419219	−	0.907885i	$-0.637696\pi$
$857$	−24.5449	−0.838438	−0.419219	+	0.907885i	$0.637696\pi$
$858$	0	0
$859$	−52.1243	−1.77846	−0.889229	−	0.457461i	$-0.848759\pi$
$859$	−52.1243	−1.77846	−0.889229	+	0.457461i	$0.848759\pi$
$860$	−0.484354	−0.0165163
$861$	−12.0678	−0.411270
$862$	24.1483	0.822494
$863$	−22.2563	−0.757612	−0.378806	−	0.925476i	$-0.623665\pi$
$863$	−22.2563	−0.757612	−0.378806	+	0.925476i	$0.623665\pi$
$864$	0.413779	0.0140771
$865$	−13.9165	−0.473175
$866$	−37.2246	−1.26494
$867$	−8.70727	−0.295714
$868$	−0.515704	−0.0175041
$869$	−18.8461	−0.639309
$870$	4.38695	0.148731
$871$	0	0
$872$	−12.9533	−0.438654
$873$	−6.90043	−0.233544
$874$	14.8675	0.502900
$875$	−8.47204	−0.286407
$876$	0.609297	0.0205862
$877$	−41.0547	−1.38632	−0.693159	−	0.720785i	$-0.743782\pi$
$877$	−41.0547	−1.38632	−0.693159	+	0.720785i	$0.743782\pi$
$878$	−36.0760	−1.21751
$879$	3.79430	0.127979
$880$	−16.1739	−0.545222
$881$	−31.0568	−1.04633	−0.523165	−	0.852231i	$-0.675249\pi$
$881$	−31.0568	−1.04633	−0.523165	+	0.852231i	$0.675249\pi$
$882$	−1.43986	−0.0484824
$883$	−56.5357	−1.90258	−0.951289	−	0.308300i	$-0.900240\pi$
$883$	−56.5357	−1.90258	−0.951289	+	0.308300i	$0.900240\pi$
$884$	0	0
$885$	−6.79772	−0.228503
$886$	−6.69190	−0.224819
$887$	9.94785	0.334016	0.167008	−	0.985956i	$-0.446589\pi$
$887$	9.94785	0.334016	0.167008	+	0.985956i	$0.446589\pi$
$888$	−23.7893	−0.798315
$889$	0.428386	0.0143676
$890$	7.53707	0.252643
$891$	−4.21419	−0.141181
$892$	0.846681	0.0283490
$893$	−2.51411	−0.0841314
$894$	−4.87626	−0.163087
$895$	4.96010	0.165798
$896$	11.8946	0.397372
$897$	0	0
$898$	0.712291	0.0237695
$899$	23.1655	0.772612
$900$	−0.303051	−0.0101017
$901$	14.8046	0.493213
$902$	73.2255	2.43814
$903$	−7.14101	−0.237638
$904$	−9.12029	−0.303336
$905$	−10.6275	−0.353271
$906$	−31.5257	−1.04737
$907$	−31.2936	−1.03909	−0.519544	−	0.854444i	$-0.673898\pi$
$907$	−31.2936	−1.03909	−0.519544	+	0.854444i	$0.673898\pi$
$908$	0.808067	0.0268166
$909$	−10.9739	−0.363982
$910$	0	0
$911$	−9.39320	−0.311210	−0.155605	−	0.987819i	$-0.549733\pi$
$911$	−9.39320	−0.311210	−0.155605	+	0.987819i	$0.549733\pi$
$912$	−5.33104	−0.176528
$913$	−16.0414	−0.530894
$914$	38.1127	1.26066
$915$	−7.19156	−0.237746
$916$	1.00314	0.0331446
$917$	−14.1878	−0.468523
$918$	4.14637	0.136850
$919$	21.7066	0.716036	0.358018	−	0.933715i	$-0.383453\pi$
$919$	21.7066	0.716036	0.358018	+	0.933715i	$0.383453\pi$
$920$	20.6237	0.679944
$921$	5.19316	0.171120
$922$	−1.55746	−0.0512921
$923$	0	0
$924$	0.308407	0.0101458
$925$	35.5081	1.16750
$926$	−47.0974	−1.54771
$927$	16.4284	0.539579
$928$	1.36025	0.0446523
$929$	−35.6787	−1.17058	−0.585289	−	0.810824i	$-0.699019\pi$
$929$	−35.6787	−1.17058	−0.585289	+	0.810824i	$0.699019\pi$
$930$	9.40383	0.308364
$931$	1.28738	0.0421920
$932$	0.0903972	0.00296106
$933$	−13.8536	−0.453548
$934$	24.5924	0.804687
$935$	−11.2475	−0.367834
$936$	0	0
$937$	−47.0866	−1.53825	−0.769127	−	0.639096i	$-0.779309\pi$
$937$	−47.0866	−1.53825	−0.769127	+	0.639096i	$0.779309\pi$
$938$	−17.3379	−0.566103
$939$	−32.6162	−1.06439
$940$	0.132459	0.00432034
$941$	−45.2923	−1.47649	−0.738244	−	0.674534i	$-0.764345\pi$
$941$	−45.2923	−1.47649	−0.738244	+	0.674534i	$0.764345\pi$
$942$	1.24905	0.0406962
$943$	−96.7927	−3.15200
$944$	−30.3722	−0.988530
$945$	0.926817	0.0301494
$946$	43.3304	1.40879
$947$	−4.77134	−0.155048	−0.0775238	−	0.996991i	$-0.524701\pi$
$947$	−4.77134	−0.155048	−0.0775238	+	0.996991i	$0.524701\pi$
$948$	0.327277	0.0106295
$949$	0	0
$950$	7.67592	0.249040
$951$	−12.0380	−0.390359
$952$	7.98929	0.258934
$953$	−3.95572	−0.128138	−0.0640692	−	0.997945i	$-0.520408\pi$
$953$	−3.95572	−0.128138	−0.0640692	+	0.997945i	$0.520408\pi$
$954$	7.40231	0.239659
$955$	−18.6991	−0.605088
$956$	−1.39824	−0.0452223
$957$	−13.8536	−0.447824
$958$	−24.7353	−0.799160
$959$	14.7070	0.474912
$960$	−7.12374	−0.229918
$961$	18.6573	0.601850
$962$	0	0
$963$	−3.45446	−0.111318
$964$	0.880605	0.0283624
$965$	−24.4454	−0.786924
$966$	−11.5487	−0.371573
$967$	−50.2292	−1.61526	−0.807632	−	0.589687i	$-0.799251\pi$
$967$	−50.2292	−1.61526	−0.807632	+	0.589687i	$0.799251\pi$
$968$	18.7529	0.602742
$969$	−3.70727	−0.119095
$970$	−9.20850	−0.295667
$971$	38.6576	1.24058	0.620291	−	0.784372i	$-0.287014\pi$
$971$	38.6576	1.24058	0.620291	+	0.784372i	$0.287014\pi$
$972$	0.0731828	0.00234734
$973$	−9.85363	−0.315893
$974$	−6.16638	−0.197584
$975$	0	0
$976$	−32.1318	−1.02852
$977$	20.6134	0.659480	0.329740	−	0.944072i	$-0.393039\pi$
$977$	20.6134	0.659480	0.329740	+	0.944072i	$0.393039\pi$
$978$	6.37623	0.203889
$979$	−23.8015	−0.760699
$980$	−0.0678271	−0.00216666
$981$	−4.66896	−0.149069
$982$	−39.5304	−1.26147
$983$	4.48620	0.143088	0.0715438	−	0.997437i	$-0.477207\pi$
$983$	4.48620	0.143088	0.0715438	+	0.997437i	$0.477207\pi$
$984$	33.4802	1.06731
$985$	−18.6589	−0.594521
$986$	13.6307	0.434089
$987$	1.95289	0.0621613
$988$	0	0
$989$	−57.2760	−1.82127
$990$	−5.62377	−0.178735
$991$	−32.7971	−1.04183	−0.520917	−	0.853607i	$-0.674410\pi$
$991$	−32.7971	−1.04183	−0.520917	+	0.853607i	$0.674410\pi$
$992$	2.91582	0.0925773
$993$	26.2820	0.834035
$994$	−15.5345	−0.492725
$995$	−1.63066	−0.0516954
$996$	0.278572	0.00882691
$997$	0.491870	0.0155777	0.00778884	−	0.999970i	$-0.497521\pi$
$997$	0.491870	0.0155777	0.00778884	+	0.999970i	$0.497521\pi$
$998$	−53.3397	−1.68844
$999$	−8.57475	−0.271293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.w.1.2		4
13.12	even	2		273.2.a.e.1.3	✓	4
39.38	odd	2		819.2.a.k.1.2		4
52.51	odd	2		4368.2.a.br.1.3		4
65.64	even	2		6825.2.a.bg.1.2		4
91.90	odd	2		1911.2.a.s.1.3		4
273.272	even	2		5733.2.a.bf.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.3	✓	4	13.12	even	2
819.2.a.k.1.2		4	39.38	odd	2
1911.2.a.s.1.3		4	91.90	odd	2
3549.2.a.w.1.2		4	1.1	even	1	trivial
4368.2.a.br.1.3		4	52.51	odd	2
5733.2.a.bf.1.2		4	273.272	even	2
6825.2.a.bg.1.2		4	65.64	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43986 q^{2} +1.00000 q^{3} +0.0731828 q^{4} -0.926817 q^{5} -1.43986 q^{6} -1.00000 q^{7} +2.77434 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.43986 q^{2} +1.00000 q^{3} +0.0731828 q^{4} -0.926817 q^{5} -1.43986 q^{6} -1.00000 q^{7} +2.77434 q^{8} +1.00000 q^{9} +1.33448 q^{10} -4.21419 q^{11} +0.0731828 q^{12} +1.43986 q^{14} -0.926817 q^{15} -4.14101 q^{16} -2.87971 q^{17} -1.43986 q^{18} +1.28738 q^{19} -0.0678271 q^{20} -1.00000 q^{21} +6.06783 q^{22} -8.02072 q^{23} +2.77434 q^{24} -4.14101 q^{25} +1.00000 q^{27} -0.0731828 q^{28} +3.28738 q^{29} +1.33448 q^{30} +7.04680 q^{31} +0.413779 q^{32} -4.21419 q^{33} +4.14637 q^{34} +0.926817 q^{35} +0.0731828 q^{36} -8.57475 q^{37} -1.85363 q^{38} -2.57130 q^{40} +12.0678 q^{41} +1.43986 q^{42} +7.14101 q^{43} -0.308407 q^{44} -0.926817 q^{45} +11.5487 q^{46} -1.95289 q^{47} -4.14101 q^{48} +1.00000 q^{49} +5.96245 q^{50} -2.87971 q^{51} -5.14101 q^{53} -1.43986 q^{54} +3.90579 q^{55} -2.77434 q^{56} +1.28738 q^{57} -4.73334 q^{58} +7.33448 q^{59} -0.0678271 q^{60} +7.75942 q^{61} -10.1464 q^{62} -1.00000 q^{63} +7.68624 q^{64} +6.06783 q^{66} -12.0414 q^{67} -0.210745 q^{68} -8.02072 q^{69} -1.33448 q^{70} -10.7889 q^{71} +2.77434 q^{72} +8.32568 q^{73} +12.3464 q^{74} -4.14101 q^{75} +0.0942138 q^{76} +4.21419 q^{77} +4.47204 q^{79} +3.83796 q^{80} +1.00000 q^{81} -17.3759 q^{82} +3.80653 q^{83} -0.0731828 q^{84} +2.66896 q^{85} -10.2820 q^{86} +3.28738 q^{87} -11.6916 q^{88} +5.64793 q^{89} +1.33448 q^{90} -0.586979 q^{92} +7.04680 q^{93} +2.81188 q^{94} -1.19316 q^{95} +0.413779 q^{96} -6.90043 q^{97} -1.43986 q^{98} -4.21419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 4 q^{10} + 2 q^{11} + 7 q^{12} + q^{14} + 3 q^{15} + 9 q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + 32 q^{20} - 4 q^{21} - 8 q^{22} + 3 q^{23} - 3 q^{24} + 9 q^{25} + 4 q^{27} - 7 q^{28} + q^{29} - 4 q^{30} - 3 q^{31} - 7 q^{32} + 2 q^{33} + 30 q^{34} - 3 q^{35} + 7 q^{36} - 10 q^{37} + 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 3 q^{43} + 12 q^{44} + 3 q^{45} + 18 q^{46} - 5 q^{47} + 9 q^{48} + 4 q^{49} - 13 q^{50} - 2 q^{51} + 5 q^{53} - q^{54} + 10 q^{55} + 3 q^{56} - 7 q^{57} + 4 q^{58} + 20 q^{59} + 32 q^{60} + 12 q^{61} - 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} - 10 q^{68} + 3 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 6 q^{74} + 9 q^{75} + 6 q^{76} - 2 q^{77} + 11 q^{79} + 42 q^{80} + 4 q^{81} + 10 q^{82} - q^{83} - 7 q^{84} - 8 q^{85} + 10 q^{86} + q^{87} - 60 q^{88} + 5 q^{89} - 4 q^{90} + 34 q^{92} - 3 q^{93} + 34 q^{94} + 13 q^{95} - 7 q^{96} + 17 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 4 * q^10 + 2 * q^11 + 7 * q^12 + q^14 + 3 * q^15 + 9 * q^16 - 2 * q^17 - q^18 - 7 * q^19 + 32 * q^20 - 4 * q^21 - 8 * q^22 + 3 * q^23 - 3 * q^24 + 9 * q^25 + 4 * q^27 - 7 * q^28 + q^29 - 4 * q^30 - 3 * q^31 - 7 * q^32 + 2 * q^33 + 30 * q^34 - 3 * q^35 + 7 * q^36 - 10 * q^37 + 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 3 * q^43 + 12 * q^44 + 3 * q^45 + 18 * q^46 - 5 * q^47 + 9 * q^48 + 4 * q^49 - 13 * q^50 - 2 * q^51 + 5 * q^53 - q^54 + 10 * q^55 + 3 * q^56 - 7 * q^57 + 4 * q^58 + 20 * q^59 + 32 * q^60 + 12 * q^61 - 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 - 10 * q^68 + 3 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 6 * q^74 + 9 * q^75 + 6 * q^76 - 2 * q^77 + 11 * q^79 + 42 * q^80 + 4 * q^81 + 10 * q^82 - q^83 - 7 * q^84 - 8 * q^85 + 10 * q^86 + q^87 - 60 * q^88 + 5 * q^89 - 4 * q^90 + 34 * q^92 - 3 * q^93 + 34 * q^94 + 13 * q^95 - 7 * q^96 + 17 * q^97 - q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more