LMFDB - Embedded newform 201.5.b.a.133.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,5,Mod(133,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("201.133");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	201.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$20.7773625799$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			133.6
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.38763i q^{2} -5.19615i q^{3} -24.8019 q^{4} -26.0927i q^{5} -33.1911 q^{6} -27.5510i q^{7} +56.2231i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-6.38763i q^{2} -5.19615i q^{3} -24.8019 q^{4} -26.0927i q^{5} -33.1911 q^{6} -27.5510i q^{7} +56.2231i q^{8} -27.0000 q^{9} -166.670 q^{10} -129.724i q^{11} +128.874i q^{12} -3.44094i q^{13} -175.986 q^{14} -135.581 q^{15} -37.6974 q^{16} -69.5786 q^{17} +172.466i q^{18} -102.676 q^{19} +647.147i q^{20} -143.159 q^{21} -828.628 q^{22} +618.229 q^{23} +292.144 q^{24} -55.8274 q^{25} -21.9795 q^{26} +140.296i q^{27} +683.317i q^{28} +836.808 q^{29} +866.045i q^{30} +348.993i q^{31} +1140.37i q^{32} -674.065 q^{33} +444.443i q^{34} -718.880 q^{35} +669.650 q^{36} -758.734 q^{37} +655.857i q^{38} -17.8797 q^{39} +1467.01 q^{40} +72.0464i q^{41} +914.450i q^{42} -2050.19i q^{43} +3217.39i q^{44} +704.502i q^{45} -3949.02i q^{46} +1503.63 q^{47} +195.881i q^{48} +1641.94 q^{49} +356.605i q^{50} +361.541i q^{51} +85.3418i q^{52} +1059.86i q^{53} +896.160 q^{54} -3384.84 q^{55} +1549.00 q^{56} +533.521i q^{57} -5345.22i q^{58} +2508.20 q^{59} +3362.67 q^{60} -964.680i q^{61} +2229.24 q^{62} +743.878i q^{63} +6681.08 q^{64} -89.7834 q^{65} +4305.68i q^{66} +(4292.75 + 1312.78i) q^{67} +1725.68 q^{68} -3212.41i q^{69} +4591.94i q^{70} +2055.04 q^{71} -1518.02i q^{72} -8215.98 q^{73} +4846.51i q^{74} +290.088i q^{75} +2546.56 q^{76} -3574.02 q^{77} +114.209i q^{78} -556.662i q^{79} +983.626i q^{80} +729.000 q^{81} +460.206 q^{82} -8228.85 q^{83} +3550.62 q^{84} +1815.49i q^{85} -13095.9 q^{86} -4348.18i q^{87} +7293.47 q^{88} -11111.0 q^{89} +4500.10 q^{90} -94.8015 q^{91} -15333.2 q^{92} +1813.42 q^{93} -9604.63i q^{94} +2679.09i q^{95} +5925.52 q^{96} -7099.63i q^{97} -10488.1i q^{98} +3502.54i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) $ 46 * q - 396 * q^4 - 1242 * q^9	$ 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) $ 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	6.38763i		−	1.59691i	−0.602056	−	0.798454i	$-0.705651\pi$
$2$		−	6.38763i		−	1.59691i	0.602056	−	0.798454i	$-0.294349\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−24.8019			−1.55012
$5$		−	26.0927i		−	1.04371i	−0.853035	−	0.521853i	$-0.825241\pi$
$5$		−	26.0927i		−	1.04371i	0.853035	−	0.521853i	$-0.174759\pi$
$6$	−33.1911			−0.921975
$7$		−	27.5510i		−	0.562266i	−0.959669	−	0.281133i	$-0.909290\pi$
$7$		−	27.5510i		−	0.562266i	0.959669	−	0.281133i	$-0.0907102\pi$
$8$			56.2231i			0.878486i
$9$	−27.0000			−0.333333
$10$	−166.670			−1.66670
$11$		−	129.724i		−	1.07210i	−0.844187	−	0.536049i	$-0.819916\pi$
$11$		−	129.724i		−	1.07210i	0.844187	−	0.536049i	$-0.180084\pi$
$12$			128.874i			0.894960i
$13$		−	3.44094i		−	0.0203606i	−0.999948	−	0.0101803i	$-0.996759\pi$
$13$		−	3.44094i		−	0.0203606i	0.999948	−	0.0101803i	$-0.00324055\pi$
$14$	−175.986			−0.897887
$15$	−135.581			−0.602584
$16$	−37.6974			−0.147255
$17$	−69.5786			−0.240756			−0.120378	−	0.992728i	$-0.538411\pi$
$17$	−69.5786			−0.240756			−0.120378	+	0.992728i	$0.538411\pi$
$18$			172.466i			0.532303i
$19$	−102.676			−0.284421			−0.142211	−	0.989836i	$-0.545421\pi$
$19$	−102.676			−0.284421			−0.142211	+	0.989836i	$0.545421\pi$
$20$			647.147i			1.61787i
$21$	−143.159			−0.324624
$22$	−828.628			−1.71204
$23$	618.229			1.16868			0.584338	−	0.811511i	$-0.301354\pi$
$23$	618.229			1.16868			0.584338	+	0.811511i	$0.301354\pi$
$24$	292.144			0.507194
$25$	−55.8274			−0.0893239
$26$	−21.9795			−0.0325140
$27$			140.296i			0.192450i
$28$			683.317i			0.871578i
$29$	836.808			0.995015			0.497508	−	0.867460i	$-0.334249\pi$
$29$	836.808			0.995015			0.497508	+	0.867460i	$0.334249\pi$
$30$			866.045i			0.962272i
$31$			348.993i			0.363156i	0.983377	+	0.181578i	$0.0581205\pi$
$31$			348.993i			0.363156i	−0.983377	+	0.181578i	$0.941880\pi$
$32$			1140.37i			1.11364i
$33$	−674.065			−0.618976
$34$			444.443i			0.384466i
$35$	−718.880			−0.586841
$36$	669.650			0.516705
$37$	−758.734			−0.554225			−0.277112	−	0.960838i	$-0.589377\pi$
$37$	−758.734			−0.554225			−0.277112	+	0.960838i	$0.589377\pi$
$38$			655.857i			0.454195i
$39$	−17.8797			−0.0117552
$40$	1467.01			0.916881
$41$			72.0464i			0.0428593i	0.999770	+	0.0214296i	$0.00682178\pi$
$41$			72.0464i			0.0428593i	−0.999770	+	0.0214296i	$0.993178\pi$
$42$			914.450i			0.518396i
$43$		−	2050.19i		−	1.10881i	−0.832247	−	0.554405i	$-0.812946\pi$
$43$		−	2050.19i		−	1.10881i	0.832247	−	0.554405i	$-0.187054\pi$
$44$			3217.39i			1.66188i
$45$			704.502i			0.347902i
$46$		−	3949.02i		−	1.86627i
$47$	1503.63			0.680683			0.340341	−	0.940302i	$-0.389457\pi$
$47$	1503.63			0.680683			0.340341	+	0.940302i	$0.389457\pi$
$48$			195.881i			0.0850180i
$49$	1641.94			0.683857
$50$			356.605i			0.142642i
$51$			361.541i			0.139001i
$52$			85.3418i			0.0315613i
$53$			1059.86i			0.377309i	0.982044	+	0.188654i	$0.0604126\pi$
$53$			1059.86i			0.377309i	−0.982044	+	0.188654i	$0.939587\pi$
$54$	896.160			0.307325
$55$	−3384.84			−1.11896
$56$	1549.00			0.493943
$57$			533.521i			0.164211i
$58$		−	5345.22i		−	1.58895i
$59$	2508.20			0.720540			0.360270	−	0.932848i	$-0.382685\pi$
$59$	2508.20			0.720540			0.360270	+	0.932848i	$0.382685\pi$
$60$	3362.67			0.934076
$61$		−	964.680i		−	0.259253i	−0.991563	−	0.129626i	$-0.958622\pi$
$61$		−	964.680i		−	0.259253i	0.991563	−	0.129626i	$-0.0413778\pi$
$62$	2229.24			0.579927
$63$			743.878i			0.187422i
$64$	6681.08			1.63112
$65$	−89.7834			−0.0212505
$66$			4305.68i			0.988448i
$67$	4292.75	+	1312.78i	0.956282	+	0.292445i
$67$	4292.75	+	1312.78i	0.956282	+	0.292445i
$68$	1725.68			0.373200
$69$		−	3212.41i		−	0.674735i
$70$			4591.94i			0.937131i
$71$	2055.04			0.407664			0.203832	−	0.979006i	$-0.434660\pi$
$71$	2055.04			0.407664			0.203832	+	0.979006i	$0.434660\pi$
$72$		−	1518.02i		−	0.292829i
$73$	−8215.98			−1.54175			−0.770875	−	0.636987i	$-0.780181\pi$
$73$	−8215.98			−1.54175			−0.770875	+	0.636987i	$0.780181\pi$
$74$			4846.51i			0.885046i
$75$			290.088i			0.0515712i
$76$	2546.56			0.440886
$77$	−3574.02			−0.602804
$78$			114.209i			0.0187720i
$79$		−	556.662i		−	0.0891944i	−0.999005	−	0.0445972i	$-0.985800\pi$
$79$		−	556.662i		−	0.0891944i	0.999005	−	0.0445972i	$-0.0142004\pi$
$80$			983.626i			0.153692i
$81$	729.000			0.111111
$82$	460.206			0.0684423
$83$	−8228.85			−1.19449			−0.597246	−	0.802058i	$-0.703738\pi$
$83$	−8228.85			−1.19449			−0.597246	+	0.802058i	$0.703738\pi$
$84$	3550.62			0.503206
$85$			1815.49i			0.251279i
$86$	−13095.9			−1.77067
$87$		−	4348.18i		−	0.574472i
$88$	7293.47			0.941822
$89$	−11111.0			−1.40273			−0.701363	−	0.712804i	$-0.747425\pi$
$89$	−11111.0			−1.40273			−0.701363	+	0.712804i	$0.747425\pi$
$90$	4500.10			0.555568
$91$	−94.8015			−0.0114481
$92$	−15333.2			−1.81158
$93$	1813.42			0.209668
$94$		−	9604.63i		−	1.08699i
$95$			2679.09i			0.296853i
$96$	5925.52			0.642960
$97$		−	7099.63i		−	0.754558i	−0.926100	−	0.377279i	$-0.876860\pi$
$97$		−	7099.63i		−	0.754558i	0.926100	−	0.377279i	$-0.123140\pi$
$98$		−	10488.1i		−	1.09206i
$99$			3502.54i			0.357366i
$100$	1384.62			0.138462
$101$			11905.6i			1.16711i	0.812075	+	0.583553i	$0.198338\pi$
$101$			11905.6i			1.16711i	−0.812075	+	0.583553i	$0.801662\pi$
$102$	2309.39			0.221972
$103$	−4723.37			−0.445223			−0.222611	−	0.974907i	$-0.571458\pi$
$103$	−4723.37			−0.445223			−0.222611	+	0.974907i	$0.571458\pi$
$104$	193.460			0.0178865
$105$			3735.41i			0.338813i
$106$	6770.00			0.602528
$107$	−13449.3			−1.17471			−0.587357	−	0.809328i	$-0.699832\pi$
$107$	−13449.3			−1.17471			−0.587357	+	0.809328i	$0.699832\pi$
$108$		−	3479.61i		−	0.298320i
$109$			2385.11i			0.200750i	0.994950	+	0.100375i	$0.0320043\pi$
$109$			2385.11i			0.200750i	−0.994950	+	0.100375i	$0.967996\pi$
$110$			21621.1i			1.78687i
$111$			3942.50i			0.319982i
$112$			1038.60i			0.0827967i
$113$		−	6859.57i		−	0.537205i	−0.963251	−	0.268602i	$-0.913438\pi$
$113$		−	6859.57i		−	0.537205i	0.963251	−	0.268602i	$-0.0865618\pi$
$114$	3407.94			0.262230
$115$		−	16131.3i		−	1.21975i
$116$	−20754.4			−1.54239
$117$			92.9054i			0.00678687i
$118$		−	16021.5i		−	1.15064i
$119$			1916.96i			0.135369i
$120$		−	7622.81i		−	0.529362i
$121$	−2187.26			−0.149393
$122$	−6162.02			−0.414003
$123$	374.364			0.0247448
$124$		−	8655.67i		−	0.562934i
$125$		−	14851.2i		−	0.950479i
$126$	4751.62			0.299296
$127$	−26625.3			−1.65077			−0.825386	−	0.564568i	$-0.809043\pi$
$127$	−26625.3			−1.65077			−0.825386	+	0.564568i	$0.809043\pi$
$128$		−	24430.5i		−	1.49112i
$129$	−10653.1			−0.640172
$130$			573.503i			0.0339351i
$131$	−9890.58			−0.576340			−0.288170	−	0.957579i	$-0.593047\pi$
$131$	−9890.58			−0.576340			−0.288170	+	0.957579i	$0.593047\pi$
$132$	16718.1			0.959484
$133$			2828.83i			0.159920i
$134$	8385.58	−	27420.5i	0.467007	−	1.52710i
$135$	3660.70			0.200861
$136$		−	3911.92i		−	0.211501i
$137$			2524.93i			0.134527i	0.997735	+	0.0672633i	$0.0214267\pi$
$137$			2524.93i			0.134527i	−0.997735	+	0.0672633i	$0.978573\pi$
$138$	−20519.7			−1.07749
$139$		−	5397.75i		−	0.279372i	−0.990196	−	0.139686i	$-0.955391\pi$
$139$		−	5397.75i		−	0.279372i	0.990196	−	0.139686i	$-0.0446093\pi$
$140$	17829.6			0.909672
$141$		−	7813.08i		−	0.392993i
$142$		−	13126.8i		−	0.651002i
$143$	−446.372			−0.0218285
$144$	1017.83			0.0490852
$145$		−	21834.5i		−	1.03850i
$146$			52480.7i			2.46203i
$147$		−	8531.77i		−	0.394825i
$148$	18818.0			0.859113
$149$	11173.9			0.503307			0.251653	−	0.967817i	$-0.419026\pi$
$149$	11173.9			0.503307			0.251653	+	0.967817i	$0.419026\pi$
$150$	1852.98			0.0823545
$151$	−731.872			−0.0320982			−0.0160491	−	0.999871i	$-0.505109\pi$
$151$	−731.872			−0.0320982			−0.0160491	+	0.999871i	$0.505109\pi$
$152$		−	5772.77i		−	0.249860i
$153$	1878.62			0.0802521
$154$			22829.6i			0.962623i
$155$	9106.16			0.379028
$156$	443.449			0.0182219
$157$	30.8220			0.00125044			0.000625218	−	1.00000i	$-0.499801\pi$
$157$	30.8220			0.00125044			0.000625218		1.00000i	$0.499801\pi$
$158$	−3555.75			−0.142435
$159$	5507.20			0.217839
$160$	29755.2			1.16231
$161$		−	17032.9i		−	0.657107i
$162$		−	4656.58i		−	0.177434i
$163$	−4184.50			−0.157496			−0.0787478	−	0.996895i	$-0.525092\pi$
$163$	−4184.50			−0.157496			−0.0787478	+	0.996895i	$0.525092\pi$
$164$		−	1786.89i		−	0.0664368i
$165$			17588.1i			0.646029i
$166$			52562.9i			1.90749i
$167$	29592.7			1.06109			0.530545	−	0.847657i	$-0.321987\pi$
$167$	29592.7			1.06109			0.530545	+	0.847657i	$0.321987\pi$
$168$		−	8048.86i		−	0.285178i
$169$	28549.2			0.999585
$170$	11596.7			0.401270
$171$	2772.26			0.0948071
$172$			50848.5i			1.71878i
$173$	−4482.30			−0.149765			−0.0748823	−	0.997192i	$-0.523858\pi$
$173$	−4482.30			−0.149765			−0.0748823	+	0.997192i	$0.523858\pi$
$174$	−27774.6			−0.917380
$175$			1538.10i			0.0502238i
$176$			4890.25i			0.157872i
$177$		−	13033.0i		−	0.416004i
$178$			70972.9i			2.24002i
$179$		−	34358.1i		−	1.07232i	−0.844118	−	0.536158i	$-0.819875\pi$
$179$		−	34358.1i		−	1.07232i	0.844118	−	0.536158i	$-0.180125\pi$
$180$		−	17473.0i		−	0.539289i
$181$	9231.90			0.281795			0.140898	−	0.990024i	$-0.455001\pi$
$181$	9231.90			0.281795			0.140898	+	0.990024i	$0.455001\pi$
$182$			605.557i			0.0182815i
$183$	−5012.62			−0.149680
$184$			34758.8i			1.02666i
$185$			19797.4i			0.578448i
$186$		−	11583.5i		−	0.334821i
$187$			9026.00i			0.258114i
$188$	−37292.8			−1.05514
$189$	3865.30			0.108208
$190$	17113.1			0.474046
$191$		−	10913.2i		−	0.299147i	−0.988751	−	0.149573i	$-0.952210\pi$
$191$		−	10913.2i		−	0.299147i	0.988751	−	0.149573i	$-0.0477901\pi$
$192$		−	34715.9i		−	0.941730i
$193$	12270.3			0.329413			0.164706	−	0.986343i	$-0.447332\pi$
$193$	12270.3			0.329413			0.164706	+	0.986343i	$0.447332\pi$
$194$	−45349.9			−1.20496
$195$			466.528i			0.0122690i
$196$	−40723.2			−1.06006
$197$		−	29831.7i		−	0.768679i	−0.923192	−	0.384339i	$-0.874429\pi$
$197$		−	29831.7i		−	0.768679i	0.923192	−	0.384339i	$-0.125571\pi$
$198$	22373.0			0.570680
$199$	27174.3			0.686203			0.343102	−	0.939298i	$-0.388522\pi$
$199$	27174.3			0.686203			0.343102	+	0.939298i	$0.388522\pi$
$200$		−	3138.79i		−	0.0784698i
$201$	6821.42	−	22305.8i	0.168843	−	0.552110i
$202$	76048.9			1.86376
$203$		−	23054.9i		−	0.559463i
$204$		−	8966.89i		−	0.215467i
$205$	1879.88			0.0447325
$206$			30171.1i			0.710980i
$207$	−16692.2			−0.389558
$208$			129.715i			0.00299821i
$209$			13319.5i			0.304927i
$210$	23860.4			0.541053
$211$	13281.1			0.298311			0.149155	−	0.988814i	$-0.452345\pi$
$211$	13281.1			0.298311			0.149155	+	0.988814i	$0.452345\pi$
$212$		−	26286.5i		−	0.584873i
$213$		−	10678.3i		−	0.235365i
$214$			85909.2i			1.87591i
$215$	−53494.9			−1.15727
$216$	−7887.88			−0.169065
$217$	9615.12			0.204190
$218$	15235.2			0.320580
$219$			42691.5i			0.890129i
$220$	83950.3			1.73451
$221$			239.416i			0.00490195i
$222$	25183.2			0.510982
$223$	−47015.0			−0.945425			−0.472712	−	0.881217i	$-0.656725\pi$
$223$	−47015.0			−0.945425			−0.472712	+	0.881217i	$0.656725\pi$
$224$	31418.3			0.626161
$225$	1507.34			0.0297746
$226$	−43816.4			−0.857867
$227$	77550.6			1.50499			0.752495	−	0.658598i	$-0.228850\pi$
$227$	77550.6			1.50499			0.752495	+	0.658598i	$0.228850\pi$
$228$		−	13232.3i		−	0.254546i
$229$		−	84493.0i		−	1.61120i	−0.592459	−	0.805600i	$-0.701843\pi$
$229$		−	84493.0i		−	1.61120i	0.592459	−	0.805600i	$-0.298157\pi$
$230$	−103041.			−1.94784
$231$			18571.2i			0.348029i
$232$			47047.9i			0.874106i
$233$			5749.04i			0.105897i	0.998597	+	0.0529485i	$0.0168619\pi$
$233$			5749.04i			0.105897i	−0.998597	+	0.0529485i	$0.983138\pi$
$234$	593.446			0.0108380
$235$		−	39233.7i		−	0.710433i
$236$	−62208.0			−1.11692
$237$	−2892.50			−0.0514964
$238$	12244.9			0.216172
$239$			26799.8i			0.469176i	0.972095	+	0.234588i	$0.0753741\pi$
$239$			26799.8i			0.469176i	−0.972095	+	0.234588i	$0.924626\pi$
$240$	5111.07			0.0887338
$241$	−50550.6			−0.870347			−0.435174	−	0.900347i	$-0.643313\pi$
$241$	−50550.6			−0.870347			−0.435174	+	0.900347i	$0.643313\pi$
$242$			13971.4i			0.238567i
$243$		−	3788.00i		−	0.0641500i
$244$			23925.9i			0.401872i
$245$		−	42842.6i		−	0.713746i
$246$		−	2391.30i		−	0.0395152i
$247$			353.303i			0.00579099i
$248$	−19621.5			−0.319027
$249$			42758.4i			0.689640i
$250$	−94864.2			−1.51783
$251$			66596.4i			1.05707i	0.848912	+	0.528535i	$0.177258\pi$
$251$			66596.4i			1.05707i	−0.848912	+	0.528535i	$0.822742\pi$
$252$		−	18449.6i		−	0.290526i
$253$		−	80199.0i		−	1.25293i
$254$			170073.i			2.63613i
$255$	9433.57			0.145076
$256$	−49155.5			−0.750053
$257$	−13575.0			−0.205529			−0.102764	−	0.994706i	$-0.532769\pi$
$257$	−13575.0			−0.205529			−0.102764	+	0.994706i	$0.532769\pi$
$258$			68048.1i			1.02230i
$259$			20903.9i			0.311622i
$260$	2226.79			0.0329407
$261$	−22593.8			−0.331672
$262$			63177.4i			0.920363i
$263$	70382.7			1.01755			0.508773	−	0.860901i	$-0.330099\pi$
$263$	70382.7			1.01755			0.508773	+	0.860901i	$0.330099\pi$
$264$		−	37898.0i		−	0.543761i
$265$	27654.6			0.393800
$266$	18069.6			0.255378
$267$			57734.4i			0.809864i
$268$	−106468.	−	32559.5i	−1.48235	−	0.453323i
$269$	65467.8			0.904739			0.452369	−	0.891831i	$-0.350579\pi$
$269$	65467.8			0.904739			0.452369	+	0.891831i	$0.350579\pi$
$270$		−	23383.2i		−	0.320757i
$271$			51284.7i			0.698311i	0.937065	+	0.349156i	$0.113532\pi$
$271$			51284.7i			0.698311i	−0.937065	+	0.349156i	$0.886468\pi$
$272$	2622.93			0.0354527
$273$			492.603i			0.00660955i
$274$	16128.3			0.214827
$275$			7242.15i			0.0957639i
$276$			79673.8i			1.04592i
$277$	−105350.			−1.37301			−0.686504	−	0.727126i	$-0.740856\pi$
$277$	−105350.			−1.37301			−0.686504	+	0.727126i	$0.740856\pi$
$278$	−34478.8			−0.446132
$279$		−	9422.81i		−	0.121052i
$280$		−	40417.7i		−	0.515531i
$281$			88008.8i			1.11459i	0.830316	+	0.557293i	$0.188160\pi$
$281$			88008.8i			1.11459i	−0.830316	+	0.557293i	$0.811840\pi$
$282$	−49907.1			−0.627573
$283$	68147.3			0.850895			0.425447	−	0.904983i	$-0.360117\pi$
$283$	68147.3			0.850895			0.425447	+	0.904983i	$0.360117\pi$
$284$	−50968.7			−0.631927
$285$	13921.0			0.171388
$286$			2851.26i			0.0348582i
$287$	1984.95			0.0240983
$288$		−	30789.9i		−	0.371213i
$289$	−78679.8			−0.942036
$290$	−139471.			−1.65840
$291$	−36890.8			−0.435644
$292$	203772.			2.38989
$293$	65026.9			0.757456			0.378728	−	0.925508i	$-0.376362\pi$
$293$	65026.9			0.757456			0.378728	+	0.925508i	$0.376362\pi$
$294$	−54497.8			−0.630499
$295$		−	65445.6i		−	0.752032i
$296$		−	42658.3i		−	0.486878i
$297$	18199.7			0.206325
$298$		−	71374.9i		−	0.803735i
$299$		−	2127.29i		−	0.0237949i
$300$		−	7194.72i		−	0.0799413i
$301$	−56484.9			−0.623446
$302$			4674.93i			0.0512579i
$303$	61863.5			0.673829
$304$	3870.62			0.0418826
$305$	−25171.1			−0.270584
$306$		−	12000.0i		−	0.128155i
$307$	124245.			1.31826			0.659129	−	0.752030i	$-0.270925\pi$
$307$	124245.			1.31826			0.659129	+	0.752030i	$0.270925\pi$
$308$	88642.5			0.934416
$309$			24543.3i			0.257049i
$310$		−	58166.8i		−	0.605274i
$311$			4438.27i			0.0458873i	0.999737	+	0.0229437i	$0.00730384\pi$
$311$			4438.27i			0.0458873i	−0.999737	+	0.0229437i	$0.992696\pi$
$312$		−	1005.25i		−	0.0103268i
$313$		−	153648.i		−	1.56834i	−0.620548	−	0.784169i	$-0.713090\pi$
$313$		−	153648.i		−	1.56834i	0.620548	−	0.784169i	$-0.286910\pi$
$314$		−	196.880i		−	0.00199683i
$315$	19409.8			0.195614
$316$			13806.3i			0.138262i
$317$	161062.			1.60278			0.801391	−	0.598141i	$-0.204094\pi$
$317$	161062.			1.60278			0.801391	+	0.598141i	$0.204094\pi$
$318$		−	35178.0i		−	0.347869i
$319$		−	108554.i		−	1.06675i
$320$		−	174327.i		−	1.70242i
$321$			69884.6i			0.678221i
$322$	−108800.			−1.04934
$323$	7144.06			0.0684763
$324$	−18080.6			−0.172235
$325$			192.099i			0.00181869i
$326$			26729.0i			0.251506i
$327$	12393.4			0.115903
$328$	−4050.67			−0.0376512
$329$		−	41426.5i		−	0.382725i
$330$	112347.			1.03165
$331$		−	101308.i		−	0.924676i	−0.886704	−	0.462338i	$-0.847011\pi$
$331$		−	101308.i		−	0.924676i	0.886704	−	0.462338i	$-0.152989\pi$
$332$	204091.			1.85160
$333$	20485.8			0.184742
$334$		−	189027.i		−	1.69446i
$335$	34254.0	−	112009.i	0.305226	−	0.998079i
$336$	5396.74			0.0478027
$337$		−	55025.1i		−	0.484508i	−0.970213	−	0.242254i	$-0.922113\pi$
$337$		−	55025.1i		−	0.484508i	0.970213	−	0.242254i	$-0.0778867\pi$
$338$		−	182362.i		−	1.59625i
$339$	−35643.4			−0.310155
$340$		−	45027.6i		−	0.389512i
$341$	45272.7			0.389339
$342$		−	17708.2i		−	0.151398i
$343$		−	111387.i		−	0.946776i
$344$	115268.			0.974074
$345$	−83820.5			−0.704226
$346$			28631.3i			0.239160i
$347$		−	89518.5i		−	0.743453i	−0.928342	−	0.371727i	$-0.878766\pi$
$347$		−	89518.5i		−	0.743453i	0.928342	−	0.371727i	$-0.121234\pi$
$348$			107843.i			0.890499i
$349$	−199541.			−1.63825			−0.819126	−	0.573614i	$-0.805541\pi$
$349$	−199541.			−1.63825			−0.819126	+	0.573614i	$0.805541\pi$
$350$	9824.85			0.0802028
$351$	482.751			0.00391840
$352$	147933.			1.19393
$353$		−	72319.2i		−	0.580369i	−0.956971	−	0.290185i	$-0.906283\pi$
$353$		−	72319.2i		−	0.580369i	0.956971	−	0.290185i	$-0.0937167\pi$
$354$	−83249.9			−0.664320
$355$		−	53621.4i		−	0.425482i
$356$	275573.			2.17439
$357$	9960.83			0.0781554
$358$	−219467.			−1.71239
$359$	121364.			0.941673			0.470837	−	0.882220i	$-0.343952\pi$
$359$	121364.			0.941673			0.470837	+	0.882220i	$0.343952\pi$
$360$	−39609.3			−0.305627
$361$	−119779.			−0.919104
$362$		−	58970.0i		−	0.450002i
$363$			11365.3i			0.0862520i
$364$	2351.25			0.0177459
$365$			214377.i			1.60913i
$366$			32018.8i			0.239025i
$367$			217044.i			1.61145i	0.592291	+	0.805724i	$0.298224\pi$
$367$			217044.i			1.61145i	−0.592291	+	0.805724i	$0.701776\pi$
$368$	−23305.6			−0.172094
$369$		−	1945.25i		−	0.0142864i
$370$	126458.			0.923729
$371$	29200.3			0.212148
$372$	−44976.2			−0.325010
$373$		−	208531.i		−	1.49883i	−0.662099	−	0.749417i	$-0.730334\pi$
$373$		−	208531.i		−	1.49883i	0.662099	−	0.749417i	$-0.269666\pi$
$374$	57654.8			0.412185
$375$	−77169.3			−0.548759
$376$			84538.6i			0.597970i
$377$		−	2879.41i		−	0.0202591i
$378$		−	24690.1i		−	0.172799i
$379$			73344.3i			0.510608i	0.966861	+	0.255304i	$0.0821756\pi$
$379$			73344.3i			0.510608i	−0.966861	+	0.255304i	$0.917824\pi$
$380$		−	66446.5i		−	0.460156i
$381$			138349.i			0.953074i
$382$	−69709.4			−0.477710
$383$			243035.i			1.65680i	0.560135	+	0.828401i	$0.310749\pi$
$383$			243035.i			1.65680i	−0.560135	+	0.828401i	$0.689251\pi$
$384$	−126944.			−0.860897
$385$			93255.8i			0.629151i
$386$		−	78378.1i		−	0.526042i
$387$			55355.1i			0.369603i
$388$			176084.i			1.16965i
$389$	−223731.			−1.47852			−0.739258	−	0.673422i	$-0.764824\pi$
$389$	−223731.			−1.47852			−0.739258	+	0.673422i	$0.764824\pi$
$390$	2980.01			0.0195924
$391$	−43015.5			−0.281366
$392$			92314.9i			0.600758i
$393$			51393.0i			0.332750i
$394$	−190554.			−1.22751
$395$	−14524.8			−0.0930928
$396$		−	86869.6i		−	0.553959i
$397$	−6676.35			−0.0423602			−0.0211801	−	0.999776i	$-0.506742\pi$
$397$	−6676.35			−0.0423602			−0.0211801	+	0.999776i	$0.506742\pi$
$398$		−	173580.i		−	1.09580i
$399$	14699.1			0.0923301
$400$	2104.55			0.0131534
$401$			226671.i			1.40964i	0.709387	+	0.704819i	$0.248972\pi$
$401$			226671.i			1.40964i	−0.709387	+	0.704819i	$0.751028\pi$
$402$	−142481.	−	43572.8i	−0.881669	−	0.269627i
$403$	1200.86			0.00739407
$404$		−	295282.i		−	1.80915i
$405$		−	19021.6i		−	0.115967i
$406$	−147266.			−0.893412
$407$			98425.8i			0.594183i
$408$	−20326.9			−0.122110
$409$			104656.i			0.625629i	0.949814	+	0.312814i	$0.101272\pi$
$409$			104656.i			0.625629i	−0.949814	+	0.312814i	$0.898728\pi$
$410$		−	12008.0i		−	0.0714337i
$411$	13119.9			0.0776689
$412$	117148.			0.690147
$413$		−	69103.5i		−	0.405135i
$414$			106624.i			0.622089i
$415$			214713.i			1.24670i
$416$	3923.93			0.0226744
$417$	−28047.5			−0.161296
$418$	85080.3			0.486941
$419$	349309.			1.98967			0.994837	−	0.101488i	$-0.0323604\pi$
$419$	349309.			1.98967			0.994837	+	0.101488i	$0.0323604\pi$
$420$		−	92645.1i		−	0.525199i
$421$	92126.8			0.519782			0.259891	−	0.965638i	$-0.416313\pi$
$421$	92126.8			0.519782			0.259891	+	0.965638i	$0.416313\pi$
$422$		−	84834.7i		−	0.476375i
$423$	−40598.0			−0.226894
$424$	−59588.6			−0.331460
$425$	3884.40			0.0215053
$426$	−68208.9			−0.375856
$427$	−26577.9			−0.145769
$428$	333568.			1.82094
$429$			2319.42i			0.0126027i
$430$			341706.i			1.84806i
$431$	−273034.			−1.46981			−0.734907	−	0.678168i	$-0.762774\pi$
$431$	−273034.			−1.46981			−0.734907	+	0.678168i	$0.762774\pi$
$432$		−	5288.80i		−	0.0283393i
$433$		−	309284.i		−	1.64961i	−0.565418	−	0.824805i	$-0.691285\pi$
$433$		−	309284.i		−	1.64961i	0.565418	−	0.824805i	$-0.308715\pi$
$434$		−	61417.8i		−	0.326073i
$435$	−113456.			−0.599581
$436$		−	59155.2i		−	0.311186i
$437$	−63477.4			−0.332396
$438$	272698.			1.42146
$439$	−215627.			−1.11886			−0.559429	−	0.828879i	$-0.688979\pi$
$439$	−215627.			−1.11886			−0.559429	+	0.828879i	$0.688979\pi$
$440$		−	190306.i		−	0.982986i
$441$	−44332.4			−0.227952
$442$	1529.30			0.00782796
$443$			100382.i			0.511501i	0.966743	+	0.255750i	$0.0823225\pi$
$443$			100382.i			0.511501i	−0.966743	+	0.255750i	$0.917677\pi$
$444$		−	97781.2i		−	0.496009i
$445$			289915.i			1.46403i
$446$			300315.i			1.50976i
$447$		−	58061.4i		−	0.290584i
$448$		−	184071.i		−	0.917126i
$449$	35831.1			0.177733			0.0888663	−	0.996044i	$-0.471676\pi$
$449$	35831.1			0.177733			0.0888663	+	0.996044i	$0.471676\pi$
$450$		−	9628.34i		−	0.0475474i
$451$	9346.13			0.0459493
$452$			170130.i			0.832730i
$453$			3802.92i			0.0185319i
$454$		−	495365.i		−	2.40333i
$455$			2473.62i			0.0119484i
$456$	−29996.2			−0.144257
$457$	−112395.			−0.538164			−0.269082	−	0.963117i	$-0.586720\pi$
$457$	−112395.			−0.538164			−0.269082	+	0.963117i	$0.586720\pi$
$458$	−539710.			−2.57294
$459$		−	9761.61i		−	0.0463336i
$460$			400085.i			1.89076i
$461$	−20086.9			−0.0945173			−0.0472586	−	0.998883i	$-0.515048\pi$
$461$	−20086.9			−0.0945173			−0.0472586	+	0.998883i	$0.515048\pi$
$462$	118626.			0.555770
$463$			385235.i			1.79707i	0.438906	+	0.898533i	$0.355366\pi$
$463$			385235.i			1.79707i	−0.438906	+	0.898533i	$0.644634\pi$
$464$	−31545.5			−0.146521
$465$		−	47317.0i		−	0.218832i
$466$	36722.8			0.169108
$467$	19665.7			0.0901726			0.0450863	−	0.998983i	$-0.485644\pi$
$467$	19665.7			0.0901726			0.0450863	+	0.998983i	$0.485644\pi$
$468$		−	2304.23i		−	0.0105204i
$469$	36168.6	−	118270.i	0.164432	−	0.537685i
$470$	−250610.			−1.13450
$471$		−	160.156i		−	0.000721940i
$472$			141019.i			0.632984i
$473$	−265958.			−1.18875
$474$			18476.2i			0.0822350i
$475$	5732.15			0.0254056
$476$		−	47544.2i		−	0.209838i
$477$		−	28616.2i		−	0.125770i
$478$	171187.			0.749231
$479$	21960.7			0.0957141			0.0478571	−	0.998854i	$-0.484761\pi$
$479$	21960.7			0.0957141			0.0478571	+	0.998854i	$0.484761\pi$
$480$		−	154613.i		−	0.671062i
$481$			2610.76i			0.0112843i
$482$			322899.i			1.38986i
$483$	−88505.3			−0.379381
$484$	54248.1			0.231576
$485$	−185248.			−0.787537
$486$	−24196.3			−0.102442
$487$			393762.i			1.66026i	0.557569	+	0.830131i	$0.311734\pi$
$487$			393762.i			1.66026i	−0.557569	+	0.830131i	$0.688266\pi$
$488$	54237.3			0.227750
$489$			21743.3i			0.0909301i
$490$	−273663.			−1.13979
$491$	225899.			0.937025			0.468513	−	0.883457i	$-0.344790\pi$
$491$	225899.			0.937025			0.468513	+	0.883457i	$0.344790\pi$
$492$	−9284.93			−0.0383573
$493$	−58223.9			−0.239556
$494$	2256.77			0.00924768
$495$	91390.7			0.372985
$496$		−	13156.1i		−	0.0534767i
$497$		−	56618.4i		−	0.229216i
$498$	273125.			1.10129
$499$			385550.i			1.54839i	0.632948	+	0.774194i	$0.281845\pi$
$499$			385550.i			1.54839i	−0.632948	+	0.774194i	$0.718155\pi$
$500$			368338.i			1.47335i
$501$		−	153768.i		−	0.612620i
$502$	425393.			1.68804
$503$		−	412160.i		−	1.62903i	−0.580140	−	0.814517i	$-0.697002\pi$
$503$		−	412160.i		−	1.62903i	0.580140	−	0.814517i	$-0.302998\pi$
$504$	−41823.1			−0.164648
$505$	310650.			1.21812
$506$	−512282.			−2.00082
$507$		−	148346.i		−	0.577111i
$508$	660357.			2.55889
$509$	−47323.5			−0.182659			−0.0913296	−	0.995821i	$-0.529112\pi$
$509$	−47323.5			−0.182659			−0.0913296	+	0.995821i	$0.529112\pi$
$510$		−	60258.2i		−	0.231673i
$511$			226359.i			0.866873i
$512$		−	76900.3i		−	0.293351i
$513$		−	14405.1i		−	0.0547369i
$514$			86711.9i			0.328211i
$515$			123245.i			0.464682i
$516$	264217.			0.992341
$517$		−	195056.i		−	0.729758i
$518$	133526.			0.497631
$519$			23290.7i			0.0864666i
$520$		−	5047.90i		−	0.0186683i
$521$		−	147361.i		−	0.542884i	−0.962455	−	0.271442i	$-0.912500\pi$
$521$		−	147361.i		−	0.542884i	0.962455	−	0.271442i	$-0.0875005\pi$
$522$			144321.i			0.529649i
$523$	179975.			0.657975			0.328988	−	0.944334i	$-0.393293\pi$
$523$	179975.			0.657975			0.328988	+	0.944334i	$0.393293\pi$
$524$	245305.			0.893395
$525$	7992.22			0.0289967
$526$		−	449579.i		−	1.62493i
$527$		−	24282.4i		−	0.0874321i
$528$	25410.5			0.0911476
$529$	102367.			0.365802
$530$		−	176647.i		−	0.628862i
$531$	−67721.3			−0.240180
$532$		−	70160.3i		−	0.247895i
$533$	247.908			0.000872640
$534$	368786.			1.29328
$535$			350928.i			1.22606i
$536$	−73808.7	+	241352.i	−0.256908	+	0.840080i
$537$	−178530.			−0.619102
$538$		−	418184.i		−	1.44479i
$539$		−	212999.i		−	0.733161i
$540$	−90792.2			−0.311359
$541$		−	161980.i		−	0.553436i	−0.960951	−	0.276718i	$-0.910753\pi$
$541$		−	161980.i		−	0.553436i	0.960951	−	0.276718i	$-0.0892467\pi$
$542$	327588.			1.11514
$543$		−	47970.4i		−	0.162695i
$544$		−	79345.1i		−	0.268116i
$545$	62234.0			0.209524
$546$	3146.57			0.0105548
$547$			317603.i			1.06148i	0.847536	+	0.530738i	$0.178085\pi$
$547$			317603.i			1.06148i	−0.847536	+	0.530738i	$0.821915\pi$
$548$		−	62622.9i		−	0.208532i
$549$			26046.4i			0.0864176i
$550$	46260.2			0.152926
$551$	−85920.2			−0.283004
$552$	180612.			0.592745
$553$	−15336.6			−0.0501510
$554$			672934.i			2.19257i
$555$	102870.			0.333967
$556$			133874.i			0.433059i
$557$	343417.			1.10691			0.553454	−	0.832880i	$-0.313309\pi$
$557$	343417.			1.10691			0.553454	+	0.832880i	$0.313309\pi$
$558$	−60189.4			−0.193309
$559$	−7054.58			−0.0225760
$560$	27099.9			0.0864155
$561$	46900.5			0.149022
$562$	562168.			1.77989
$563$			372962.i			1.17665i	0.808624	+	0.588326i	$0.200213\pi$
$563$			372962.i			1.17665i	−0.808624	+	0.588326i	$0.799787\pi$
$564$			193779.i			0.609184i
$565$	−178984.			−0.560684
$566$		−	435300.i		−	1.35880i
$567$		−	20084.7i		−	0.0624740i
$568$			115540.i			0.358127i
$569$	415702.			1.28398			0.641990	−	0.766713i	$-0.278109\pi$
$569$	415702.			1.28398			0.641990	+	0.766713i	$0.278109\pi$
$570$		−	88922.1i		−	0.273691i
$571$	−219226.			−0.672388			−0.336194	−	0.941793i	$-0.609140\pi$
$571$	−219226.			−0.672388			−0.336194	+	0.941793i	$0.609140\pi$
$572$	11070.9			0.0338368
$573$	−56706.5			−0.172713
$574$		−	12679.2i		−	0.0384828i
$575$	−34514.2			−0.104391
$576$	−180389.			−0.543708
$577$			215345.i			0.646819i	0.946259	+	0.323410i	$0.104829\pi$
$577$			215345.i			0.646819i	−0.946259	+	0.323410i	$0.895171\pi$
$578$			502578.i			1.50435i
$579$		−	63758.3i		−	0.190186i
$580$			541537.i			1.60980i
$581$			226713.i			0.671622i
$582$			235645.i			0.695684i
$583$	137489.			0.404512
$584$		−	461928.i		−	1.35440i
$585$	2424.15			0.00708350
$586$		−	415368.i		−	1.20959i
$587$		−	300574.i		−	0.872318i	−0.899870	−	0.436159i	$-0.856338\pi$
$587$		−	300574.i		−	0.872318i	0.899870	−	0.436159i	$-0.143662\pi$
$588$			211604.i			0.612025i
$589$		−	35833.2i		−	0.103289i
$590$	−418042.			−1.20093
$591$	−155010.			−0.443797
$592$	28602.3			0.0816126
$593$		−	622835.i		−	1.77118i	−0.464465	−	0.885591i	$-0.653753\pi$
$593$		−	622835.i		−	1.77118i	0.464465	−	0.885591i	$-0.346247\pi$
$594$		−	116253.i		−	0.329483i
$595$	50018.7			0.141286
$596$	−277134.			−0.780184
$597$		−	141202.i		−	0.396180i
$598$	−13588.4			−0.0379983
$599$		−	575044.i		−	1.60268i	−0.598208	−	0.801341i	$-0.704120\pi$
$599$		−	575044.i		−	1.60268i	0.598208	−	0.801341i	$-0.295880\pi$
$600$	−16309.6			−0.0453045
$601$	104592.			0.289566			0.144783	−	0.989463i	$-0.453752\pi$
$601$	104592.			0.289566			0.144783	+	0.989463i	$0.453752\pi$
$602$			360805.i			0.995587i
$603$	−115904.	−	35445.2i	−0.318761	−	0.0974815i
$604$	18151.8			0.0497560
$605$			57071.4i			0.155922i
$606$		−	395162.i		−	1.07604i
$607$	−93980.1			−0.255069			−0.127535	−	0.991834i	$-0.540706\pi$
$607$	−93980.1			−0.255069			−0.127535	+	0.991834i	$0.540706\pi$
$608$		−	117088.i		−	0.316743i
$609$	−119797.			−0.323006
$610$			160784.i			0.432098i
$611$		−	5173.90i		−	0.0138591i
$612$	−46593.3			−0.124400
$613$	109126.			0.290408			0.145204	−	0.989402i	$-0.453616\pi$
$613$	109126.			0.290408			0.145204	+	0.989402i	$0.453616\pi$
$614$		−	793629.i		−	2.10514i
$615$		−	9768.16i		−	0.0258263i
$616$		−	200943.i		−	0.529555i
$617$	607365.			1.59543			0.797717	−	0.603031i	$-0.206041\pi$
$617$	607365.			1.59543			0.797717	+	0.603031i	$0.206041\pi$
$618$	156774.			0.410484
$619$	−214533.			−0.559902			−0.279951	−	0.960014i	$-0.590318\pi$
$619$	−214533.			−0.559902			−0.279951	+	0.960014i	$0.590318\pi$
$620$	−225850.			−0.587538
$621$			86735.2i			0.224912i
$622$	28350.0			0.0732779
$623$			306119.i			0.788705i
$624$	674.017			0.00173102
$625$	−422400.			−1.08135
$626$	−981450.			−2.50449
$627$	69210.3			0.176050
$628$	−764.443			−0.00193832
$629$	52791.6			0.133433
$630$		−	123982.i		−	0.312377i
$631$			261016.i			0.655555i	0.944755	+	0.327778i	$0.106300\pi$
$631$			261016.i			0.655555i	−0.944755	+	0.327778i	$0.893700\pi$
$632$	31297.3			0.0783560
$633$		−	69010.5i		−	0.172230i
$634$		−	1.02880e6i		−	2.55950i
$635$			694725.i			1.72292i
$636$	−136589.			−0.337676
$637$		−	5649.82i		−	0.0139237i
$638$	−693402.			−1.70351
$639$	−55486.0			−0.135888
$640$	−637456.			−1.55629
$641$		−	294999.i		−	0.717966i	−0.933344	−	0.358983i	$-0.883124\pi$
$641$		−	294999.i		−	0.717966i	0.933344	−	0.358983i	$-0.116876\pi$
$642$	446397.			1.08306
$643$	121209.			0.293165			0.146582	−	0.989198i	$-0.453173\pi$
$643$	121209.			0.293165			0.146582	+	0.989198i	$0.453173\pi$
$644$			422447.i			1.01859i
$645$			277968.i			0.668152i
$646$		−	45633.6i		−	0.109350i
$647$		−	91605.5i		−	0.218833i	−0.993996	−	0.109417i	$-0.965102\pi$
$647$		−	91605.5i		−	0.218833i	0.993996	−	0.109417i	$-0.0348982\pi$
$648$			40986.6i			0.0976095i
$649$		−	325373.i		−	0.772489i
$650$	1227.06			0.00290428
$651$		−	49961.6i		−	0.117889i
$652$	103783.			0.244136
$653$		−	653749.i		−	1.53315i	−0.642155	−	0.766575i	$-0.721960\pi$
$653$		−	653749.i		−	1.53315i	0.642155	−	0.766575i	$-0.278040\pi$
$654$		−	79164.6i		−	0.185087i
$655$			258072.i			0.601530i
$656$		−	2715.96i		−	0.00631126i
$657$	221832.			0.513916
$658$	−264617.			−0.611177
$659$	664854.			1.53093			0.765465	−	0.643477i	$-0.222509\pi$
$659$	664854.			1.53093			0.765465	+	0.643477i	$0.222509\pi$
$660$		−	436219.i		−	1.00142i
$661$			407917.i			0.933618i	0.884358	+	0.466809i	$0.154596\pi$
$661$			407917.i			0.933618i	−0.884358	+	0.466809i	$0.845404\pi$
$662$	−647121.			−1.47662
$663$	1244.04			0.00283014
$664$		−	462651.i		−	1.04934i
$665$	73811.8			0.166910
$666$		−	130856.i		−	0.295015i
$667$	517339.			1.16285
$668$	−733955.			−1.64481
$669$			244297.i			0.545841i
$670$	−715475.	−	218802.i	−1.59384	−	0.487419i
$671$	−125142.			−0.277944
$672$		−	163254.i		−	0.361514i
$673$		−	189274.i		−	0.417889i	−0.977928	−	0.208944i	$-0.932997\pi$
$673$		−	189274.i		−	0.417889i	0.977928	−	0.208944i	$-0.0670027\pi$
$674$	−351480.			−0.773715
$675$		−	7832.37i		−	0.0171904i
$676$	−708072.			−1.54947
$677$			138223.i			0.301580i	0.988566	+	0.150790i	$0.0481817\pi$
$677$			138223.i			0.301580i	−0.988566	+	0.150790i	$0.951818\pi$
$678$			227677.i			0.495290i
$679$	−195602.			−0.424262
$680$	−102073.			−0.220745
$681$		−	402965.i		−	0.868906i
$682$		−	289185.i		−	0.621738i
$683$			209687.i			0.449500i	0.974416	+	0.224750i	$0.0721566\pi$
$683$			209687.i			0.449500i	−0.974416	+	0.224750i	$0.927843\pi$
$684$	−68757.1			−0.146962
$685$	65882.1			0.140406
$686$	−711501.			−1.51191
$687$	−439038.			−0.930227
$688$			77286.8i			0.163278i
$689$	3646.92			0.00768223
$690$			535414.i			1.12458i
$691$	−210505.			−0.440866			−0.220433	−	0.975402i	$-0.570747\pi$
$691$	−210505.			−0.440866			−0.220433	+	0.975402i	$0.570747\pi$
$692$	111169.			0.232152
$693$	96498.7			0.200935
$694$	−571811.			−1.18723
$695$	−140842.			−0.291583
$696$	244468.			0.504666
$697$		−	5012.89i		−	0.0103186i
$698$			1.27459e6i			2.61614i
$699$	29872.9			0.0611397
$700$		−	38147.8i		−	0.0778527i
$701$		−	591523.i		−	1.20375i	−0.798591	−	0.601874i	$-0.794421\pi$
$701$		−	591523.i		−	1.20375i	0.798591	−	0.601874i	$-0.205579\pi$
$702$		−	3083.63i		−	0.00625733i
$703$	77903.8			0.157633
$704$		−	866696.i		−	1.74872i
$705$	−203864.			−0.410169
$706$	−461949.			−0.926796
$707$	328013.			0.656224
$708$			323242.i			0.644854i
$709$	994854.			1.97910			0.989548	−	0.144206i	$-0.0460629\pi$
$709$	994854.			1.97910			0.989548	+	0.144206i	$0.0460629\pi$
$710$	−342514.			−0.679456
$711$			15029.9i			0.0297315i
$712$		−	624694.i		−	1.23227i
$713$			215758.i			0.424411i
$714$		−	63626.1i		−	0.124807i
$715$			11647.0i			0.0227826i
$716$			852144.i			1.66221i
$717$	139256.			0.270879
$718$		−	775227.i		−	1.50377i
$719$	479434.			0.927408			0.463704	−	0.885990i	$-0.346520\pi$
$719$	479434.			0.927408			0.463704	+	0.885990i	$0.346520\pi$
$720$		−	26557.9i		−	0.0512305i
$721$			130134.i			0.250334i
$722$			765102.i			1.46773i
$723$			262669.i			0.502495i
$724$	−228968.			−0.436816
$725$	−46716.8			−0.0888786
$726$	72597.6			0.137736
$727$		−	658414.i		−	1.24575i	−0.782322	−	0.622874i	$-0.785965\pi$
$727$		−	658414.i		−	1.24575i	0.782322	−	0.622874i	$-0.214035\pi$
$728$		−	5330.03i		−	0.0100570i
$729$	−19683.0			−0.0370370
$730$	1.36936e6			2.56964
$731$			142649.i			0.266953i
$732$	124322.			0.232021
$733$		−	382851.i		−	0.712561i	−0.934379	−	0.356281i	$-0.884045\pi$
$733$		−	382851.i		−	0.712561i	0.934379	−	0.356281i	$-0.115955\pi$
$734$	1.38640e6			2.57334
$735$	−222617.			−0.412081
$736$			705008.i			1.30148i
$737$	170299.	−	556872.i	0.313529	−	1.02523i
$738$	−12425.6			−0.0228141
$739$			58708.7i			0.107501i	0.998554	+	0.0537506i	$0.0171176\pi$
$739$			58708.7i			0.107501i	−0.998554	+	0.0537506i	$0.982882\pi$
$740$		−	491012.i		−	0.896662i
$741$	1835.81			0.00334343
$742$		−	186521.i		−	0.338781i
$743$	329126.			0.596189			0.298095	−	0.954536i	$-0.403649\pi$
$743$	329126.			0.596189			0.298095	+	0.954536i	$0.403649\pi$
$744$			101956.i			0.184190i
$745$		−	291557.i		−	0.525305i
$746$	−1.33202e6			−2.39350
$747$	222179.			0.398164
$748$		−	223862.i		−	0.400107i
$749$			370542.i			0.660502i
$750$			492929.i			0.876318i
$751$	401957.			0.712689			0.356344	−	0.934355i	$-0.384023\pi$
$751$	401957.			0.712689			0.356344	+	0.934355i	$0.384023\pi$
$752$	−56682.9			−0.100234
$753$	346045.			0.610299
$754$	−18392.6			−0.0323519
$755$			19096.5i			0.0335011i
$756$	−95866.7			−0.167735
$757$		−	760237.i		−	1.32665i	−0.748330	−	0.663326i	$-0.769144\pi$
$757$		−	760237.i		−	1.32665i	0.748330	−	0.663326i	$-0.230856\pi$
$758$	468496.			0.815395
$759$	−416726.			−0.723382
$760$	−150627.			−0.260781
$761$	−759423.			−1.31134			−0.655669	−	0.755049i	$-0.727613\pi$
$761$	−759423.			−1.31134			−0.655669	+	0.755049i	$0.727613\pi$
$762$	883724.			1.52197
$763$	65712.3			0.112875
$764$			270667.i			0.463713i
$765$		−	49018.3i		−	0.0837597i
$766$	1.55242e6			2.64576
$767$		−	8630.56i		−	0.0146706i
$768$			255419.i			0.433043i
$769$		−	367364.i		−	0.621218i	−0.950538	−	0.310609i	$-0.899467\pi$
$769$		−	367364.i		−	0.621218i	0.950538	−	0.310609i	$-0.100533\pi$
$770$	595684.			1.00470
$771$			70537.6i			0.118662i
$772$	−304326.			−0.510628
$773$	94085.3			0.157457			0.0787286	−	0.996896i	$-0.474914\pi$
$773$	94085.3			0.157457			0.0787286	+	0.996896i	$0.474914\pi$
$774$	353588.			0.590223
$775$		−	19483.4i		−	0.0324385i
$776$	399163.			0.662868
$777$	108620.			0.179915
$778$			1.42911e6i			2.36106i
$779$		−	7397.45i		−	0.0121901i
$780$		−	11570.8i		−	0.0190183i
$781$		−	266587.i		−	0.437056i
$782$			274767.i			0.449316i
$783$			117401.i			0.191491i
$784$	−61896.9			−0.100702
$785$		−	804.228i		−	0.00130509i
$786$	328279.			0.531372
$787$			478815.i			0.773069i	0.922275	+	0.386535i	$0.126328\pi$
$787$			478815.i			0.773069i	−0.922275	+	0.386535i	$0.873672\pi$
$788$			739881.i			1.19154i
$789$		−	365719.i		−	0.587481i
$790$			92779.1i			0.148661i
$791$	−188988.			−0.302052
$792$	−196924.			−0.313941
$793$	−3319.41			−0.00527855
$794$			42646.1i			0.0676453i
$795$		−	143697.i		−	0.227360i
$796$	−673974.			−1.06369
$797$	227172.			0.357633			0.178816	−	0.983882i	$-0.442773\pi$
$797$	227172.			0.357633			0.178816	+	0.983882i	$0.442773\pi$
$798$		−	93892.2i		−	0.147443i
$799$	−104620.			−0.163879
$800$		−	63663.7i		−	0.0994746i
$801$	299997.			0.467575
$802$	1.44789e6			2.25106
$803$			1.06581e6i			1.65291i
$804$	−169184.	+	553225.i	−0.261726	+	0.855835i
$805$	−444433.			−0.685827
$806$		−	7670.68i		−	0.0118077i
$807$		−	340181.i		−	0.522351i
$808$	−669372.			−1.02529
$809$		−	993312.i		−	1.51771i	−0.651260	−	0.758855i	$-0.725759\pi$
$809$		−	993312.i		−	1.51771i	0.651260	−	0.758855i	$-0.274241\pi$
$810$	−121503.			−0.185189
$811$			239593.i			0.364277i	0.983273	+	0.182138i	$0.0583019\pi$
$811$			239593.i			0.364277i	−0.983273	+	0.182138i	$0.941698\pi$
$812$			571805.i			0.867233i
$813$	266483.			0.403170
$814$	628708.			0.948856
$815$			109185.i			0.164379i
$816$		−	13629.2i		−	0.0204686i
$817$			210506.i			0.315369i
$818$	668503.			0.999071
$819$	2559.64			0.00381603
$820$	−46624.6			−0.0693406
$821$	−167716.			−0.248822			−0.124411	−	0.992231i	$-0.539704\pi$
$821$	−167716.			−0.248822			−0.124411	+	0.992231i	$0.539704\pi$
$822$		−	83805.2i		−	0.124030i
$823$	149009.			0.219995			0.109998	−	0.993932i	$-0.464916\pi$
$823$	149009.			0.219995			0.109998	+	0.993932i	$0.464916\pi$
$824$		−	265562.i		−	0.391122i
$825$	37631.3			0.0552893
$826$	−441408.			−0.646963
$827$	182988.			0.267554			0.133777	−	0.991011i	$-0.457289\pi$
$827$	182988.			0.267554			0.133777	+	0.991011i	$0.457289\pi$
$828$	413997.			0.603861
$829$	403950.			0.587785			0.293892	−	0.955839i	$-0.405049\pi$
$829$	403950.			0.587785			0.293892	+	0.955839i	$0.405049\pi$
$830$	1.37151e6			1.99086
$831$			547412.i			0.792707i
$832$		−	22989.2i		−	0.0332107i
$833$	−114244.			−0.164643
$834$			179157.i			0.257574i
$835$		−	772153.i		−	1.10747i
$836$		−	330349.i		−	0.472673i
$837$	−48962.3			−0.0698894
$838$		−	2.23126e6i		−	3.17733i
$839$	−659616.			−0.937060			−0.468530	−	0.883448i	$-0.655216\pi$
$839$	−659616.			−0.937060			−0.468530	+	0.883448i	$0.655216\pi$
$840$	−210016.			−0.297642
$841$	−7033.85			−0.00994492
$842$		−	588472.i		−	0.830045i
$843$	457307.			0.643506
$844$	−329396.			−0.462416
$845$		−	744924.i		−	1.04327i
$846$			259325.i			0.362329i
$847$			60261.3i			0.0839985i
$848$		−	39954.0i		−	0.0555608i
$849$		−	354104.i		−	0.491264i
$850$		−	24812.1i		−	0.0343420i
$851$	−469071.			−0.647709
$852$			264841.i			0.364843i
$853$	34170.9			0.0469633			0.0234817	−	0.999724i	$-0.492525\pi$
$853$	34170.9			0.0469633			0.0234817	+	0.999724i	$0.492525\pi$
$854$			169770.i			0.232780i
$855$		−	72335.5i		−	0.0989509i
$856$		−	756161.i		−	1.03197i
$857$			544691.i			0.741632i	0.928706	+	0.370816i	$0.120922\pi$
$857$			544691.i			0.741632i	−0.928706	+	0.370816i	$0.879078\pi$
$858$	14815.6			0.0201254
$859$	−642300.			−0.870466			−0.435233	−	0.900318i	$-0.643334\pi$
$859$	−642300.			−0.870466			−0.435233	+	0.900318i	$0.643334\pi$
$860$	1.32677e6			1.79391
$861$		−	10314.1i		−	0.0139132i
$862$			1.74404e6i			2.34716i
$863$	−1.42685e6			−1.91583			−0.957916	−	0.287047i	$-0.907326\pi$
$863$	−1.42685e6			−1.91583			−0.957916	+	0.287047i	$0.907326\pi$
$864$	−159989.			−0.214320
$865$			116955.i			0.156310i
$866$	−1.97559e6			−2.63427
$867$			408832.i			0.543885i
$868$	−238473.			−0.316519
$869$	−72212.3			−0.0956250
$870$			724713.i			0.957475i
$871$	4517.21	−	14771.1i	0.00595435	−	0.0194705i
$872$	−134098.			−0.176356
$873$			191690.i			0.251519i
$874$			405470.i			0.530806i
$875$	−409167.			−0.534422
$876$		−	1.05883e6i		−	1.37980i
$877$	−522810.			−0.679743			−0.339871	−	0.940472i	$-0.610384\pi$
$877$	−522810.			−0.679743			−0.339871	+	0.940472i	$0.610384\pi$
$878$			1.37735e6i			1.78671i
$879$		−	337890.i		−	0.437318i
$880$	127600.			0.164772
$881$	−1.44466e6			−1.86129			−0.930645	−	0.365924i	$-0.880753\pi$
$881$	−1.44466e6			−1.86129			−0.930645	+	0.365924i	$0.880753\pi$
$882$			283179.i			0.364019i
$883$		−	1.31234e6i		−	1.68315i	−0.540138	−	0.841576i	$-0.681628\pi$
$883$		−	1.31234e6i		−	1.68315i	0.540138	−	0.841576i	$-0.318372\pi$
$884$		−	5937.96i		−	0.00759859i
$885$	−340065.			−0.434186
$886$	641200.			0.816820
$887$	779499.			0.990759			0.495380	−	0.868677i	$-0.335029\pi$
$887$	779499.			0.990759			0.495380	+	0.868677i	$0.335029\pi$
$888$	−221659.			−0.281099
$889$			733555.i			0.928173i
$890$	1.85187e6			2.33793
$891$		−	94568.6i		−	0.119122i
$892$	1.16606e6			1.46552
$893$	−154387.			−0.193601
$894$	−370875.			−0.464037
$895$	−896494.			−1.11918
$896$	−673084.			−0.838404
$897$	−11053.7			−0.0137380
$898$		−	228876.i		−	0.283823i
$899$			292040.i			0.361346i
$900$	−37384.9			−0.0461542
$901$		−	73743.6i		−	0.0908395i
$902$		−	59699.7i		−	0.0733768i
$903$			293504.i			0.359947i
$904$	385666.			0.471927
$905$		−	240885.i		−	0.294112i
$906$	24291.6			0.0295938
$907$	−270030.			−0.328244			−0.164122	−	0.986440i	$-0.552479\pi$
$907$	−270030.			−0.328244			−0.164122	+	0.986440i	$0.552479\pi$
$908$	−1.92340e6			−2.33291
$909$		−	321452.i		−	0.389035i
$910$	15800.6			0.0190806
$911$	129234.			0.155718			0.0778591	−	0.996964i	$-0.475192\pi$
$911$	129234.			0.155718			0.0778591	+	0.996964i	$0.475192\pi$
$912$		−	20112.3i		−	0.0241809i
$913$			1.06748e6i			1.28061i
$914$			717939.i			0.859399i
$915$			130793.i			0.156222i
$916$			2.09558e6i			2.49755i
$917$			272496.i			0.324057i
$918$	−62353.6			−0.0739905
$919$			571698.i			0.676917i	0.940981	+	0.338458i	$0.109905\pi$
$919$			571698.i			0.676917i	−0.940981	+	0.338458i	$0.890095\pi$
$920$	906949.			1.07154
$921$		−	645594.i		−	0.761097i
$922$			128308.i			0.150935i
$923$		−	7071.26i		−	0.00830029i
$924$		−	460600.i		−	0.539486i
$925$	42358.2			0.0495055
$926$	2.46074e6			2.86975
$927$	127531.			0.148408
$928$			954267.i			1.10809i
$929$			982965.i			1.13896i	0.822007	+	0.569478i	$0.192854\pi$
$929$			982965.i			1.13896i	−0.822007	+	0.569478i	$0.807146\pi$
$930$	−302244.			−0.349455
$931$	−168588.			−0.194504
$932$		−	142587.i		−	0.164153i
$933$	23061.9			0.0264931
$934$		−	125617.i		−	0.143997i
$935$	235512.			0.269396
$936$	−5223.43			−0.00596217
$937$			1.04820e6i			1.19390i	0.802279	+	0.596949i	$0.203620\pi$
$937$			1.04820e6i			1.19390i	−0.802279	+	0.596949i	$0.796380\pi$
$938$	−755464.	−	231031.i	−0.858634	−	0.262582i
$939$	−798381.			−0.905480
$940$			973069.i			1.10125i
$941$		−	1.25324e6i		−	1.41532i	−0.706552	−	0.707661i	$-0.749751\pi$
$941$		−	1.25324e6i		−	1.41532i	0.706552	−	0.707661i	$-0.250249\pi$
$942$	−1023.02			−0.00115287
$943$			44541.2i			0.0500886i
$944$	−94552.5			−0.106103
$945$		−	100856.i		−	0.112938i
$946$			1.69884e6i			1.89833i
$947$	941646.			1.05000			0.524998	−	0.851104i	$-0.324066\pi$
$947$	941646.			1.05000			0.524998	+	0.851104i	$0.324066\pi$
$948$	71739.4			0.0798254
$949$			28270.7i			0.0313909i
$950$		−	36614.8i		−	0.0405705i
$951$		−	836903.i		−	0.925367i
$952$	−107778.			−0.118920
$953$	−10359.8			−0.0114069			−0.00570344	−	0.999984i	$-0.501815\pi$
$953$	−10359.8			−0.0114069			−0.00570344	+	0.999984i	$0.501815\pi$
$954$	−182790.			−0.200843
$955$	−284754.			−0.312222
$956$		−	664685.i		−	0.727277i
$957$	−564062.			−0.615890
$958$		−	140277.i		−	0.152847i
$959$	69564.4			0.0756397
$960$	−905831.			−0.982890
$961$	801725.			0.868118
$962$	16676.6			0.0180201
$963$	363131.			0.391571
$964$	1.25375e6			1.34914
$965$		−	320165.i		−	0.343810i
$966$			565340.i			0.605836i
$967$	−719864.			−0.769835			−0.384918	−	0.922951i	$-0.625770\pi$
$967$	−719864.			−0.769835			−0.384918	+	0.922951i	$0.625770\pi$
$968$		−	122974.i		−	0.131239i
$969$		−	37121.6i		−	0.0395348i
$970$			1.18330e6i			1.25762i
$971$	805931.			0.854790			0.427395	−	0.904065i	$-0.359431\pi$
$971$	805931.			0.854790			0.427395	+	0.904065i	$0.359431\pi$
$972$			93949.3i			0.0994400i
$973$	−148714.			−0.157081
$974$	2.51521e6			2.65129
$975$	998.176			0.00105002
$976$			36365.9i			0.0381764i
$977$	−984783.			−1.03169			−0.515847	−	0.856680i	$-0.672523\pi$
$977$	−984783.			−1.03169			−0.515847	+	0.856680i	$0.672523\pi$
$978$	138888.			0.145207
$979$			1.44136e6i			1.50386i
$980$			1.06258e6i			1.10639i
$981$		−	64398.0i		−	0.0669167i
$982$		−	1.44296e6i		−	1.49634i
$983$		−	119595.i		−	0.123767i	−0.998083	−	0.0618837i	$-0.980289\pi$
$983$		−	119595.i		−	0.123767i	0.998083	−	0.0618837i	$-0.0197108\pi$
$984$			21047.9i			0.0217380i
$985$	−778388.			−0.802275
$986$			371913.i			0.382549i
$987$	−215259.			−0.220966
$988$		−	8762.56i		−	0.00897671i
$989$		−	1.26749e6i		−	1.29584i
$990$		−	583770.i		−	0.595623i
$991$			1.00966e6i			1.02808i	0.857767	+	0.514039i	$0.171851\pi$
$991$			1.00966e6i			1.02808i	−0.857767	+	0.514039i	$0.828149\pi$
$992$	−397980.			−0.404425
$993$	−526414.			−0.533862
$994$	−361657.			−0.366037
$995$		−	709051.i		−	0.716195i
$996$		−	1.06049e6i		−	1.06902i
$997$	−1.12884e6			−1.13564			−0.567820	−	0.823153i	$-0.692213\pi$
$997$	−1.12884e6			−1.13564			−0.567820	+	0.823153i	$0.692213\pi$
$998$	2.46275e6			2.47263
$999$		−	106447.i		−	0.106661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.6	✓	46
67.66	odd	2	inner	201.5.b.a.133.41	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.6	✓	46	1.1	even	1	trivial
201.5.b.a.133.41	yes	46	67.66	odd	2	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.38763i q^{2} -5.19615i q^{3} -24.8019 q^{4} -26.0927i q^{5} -33.1911 q^{6} -27.5510i q^{7} +56.2231i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-6.38763i q^{2} -5.19615i q^{3} -24.8019 q^{4} -26.0927i q^{5} -33.1911 q^{6} -27.5510i q^{7} +56.2231i q^{8} -27.0000 q^{9} -166.670 q^{10} -129.724i q^{11} +128.874i q^{12} -3.44094i q^{13} -175.986 q^{14} -135.581 q^{15} -37.6974 q^{16} -69.5786 q^{17} +172.466i q^{18} -102.676 q^{19} +647.147i q^{20} -143.159 q^{21} -828.628 q^{22} +618.229 q^{23} +292.144 q^{24} -55.8274 q^{25} -21.9795 q^{26} +140.296i q^{27} +683.317i q^{28} +836.808 q^{29} +866.045i q^{30} +348.993i q^{31} +1140.37i q^{32} -674.065 q^{33} +444.443i q^{34} -718.880 q^{35} +669.650 q^{36} -758.734 q^{37} +655.857i q^{38} -17.8797 q^{39} +1467.01 q^{40} +72.0464i q^{41} +914.450i q^{42} -2050.19i q^{43} +3217.39i q^{44} +704.502i q^{45} -3949.02i q^{46} +1503.63 q^{47} +195.881i q^{48} +1641.94 q^{49} +356.605i q^{50} +361.541i q^{51} +85.3418i q^{52} +1059.86i q^{53} +896.160 q^{54} -3384.84 q^{55} +1549.00 q^{56} +533.521i q^{57} -5345.22i q^{58} +2508.20 q^{59} +3362.67 q^{60} -964.680i q^{61} +2229.24 q^{62} +743.878i q^{63} +6681.08 q^{64} -89.7834 q^{65} +4305.68i q^{66} +(4292.75 + 1312.78i) q^{67} +1725.68 q^{68} -3212.41i q^{69} +4591.94i q^{70} +2055.04 q^{71} -1518.02i q^{72} -8215.98 q^{73} +4846.51i q^{74} +290.088i q^{75} +2546.56 q^{76} -3574.02 q^{77} +114.209i q^{78} -556.662i q^{79} +983.626i q^{80} +729.000 q^{81} +460.206 q^{82} -8228.85 q^{83} +3550.62 q^{84} +1815.49i q^{85} -13095.9 q^{86} -4348.18i q^{87} +7293.47 q^{88} -11111.0 q^{89} +4500.10 q^{90} -94.8015 q^{91} -15333.2 q^{92} +1813.42 q^{93} -9604.63i q^{94} +2679.09i q^{95} +5925.52 q^{96} -7099.63i q^{97} -10488.1i q^{98} +3502.54i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 46 * q - 396 * q^4 - 1242 * q^9	\( 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) \) 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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