LMFDB - Embedded newform 201.5.b.a.133.3

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			133.3
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.56976i q^{2} -5.19615i q^{3} -41.3013 q^{4} +14.1982i q^{5} -39.3336 q^{6} -91.6507i q^{7} +191.525i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-7.56976i q^{2} -5.19615i q^{3} -41.3013 q^{4} +14.1982i q^{5} -39.3336 q^{6} -91.6507i q^{7} +191.525i q^{8} -27.0000 q^{9} +107.477 q^{10} +227.605i q^{11} +214.608i q^{12} +178.168i q^{13} -693.774 q^{14} +73.7758 q^{15} +788.977 q^{16} +138.475 q^{17} +204.384i q^{18} -511.998 q^{19} -586.402i q^{20} -476.231 q^{21} +1722.92 q^{22} -294.560 q^{23} +995.193 q^{24} +423.412 q^{25} +1348.69 q^{26} +140.296i q^{27} +3785.29i q^{28} -46.2171 q^{29} -558.465i q^{30} -900.725i q^{31} -2907.97i q^{32} +1182.67 q^{33} -1048.22i q^{34} +1301.27 q^{35} +1115.14 q^{36} -1234.35 q^{37} +3875.70i q^{38} +925.790 q^{39} -2719.30 q^{40} +183.333i q^{41} +3604.95i q^{42} +115.118i q^{43} -9400.39i q^{44} -383.350i q^{45} +2229.75i q^{46} +2104.26 q^{47} -4099.65i q^{48} -5998.84 q^{49} -3205.13i q^{50} -719.535i q^{51} -7358.59i q^{52} +2749.50i q^{53} +1062.01 q^{54} -3231.57 q^{55} +17553.4 q^{56} +2660.42i q^{57} +349.853i q^{58} -2279.42 q^{59} -3047.04 q^{60} +3178.54i q^{61} -6818.27 q^{62} +2474.57i q^{63} -9389.02 q^{64} -2529.66 q^{65} -8952.53i q^{66} +(-1745.45 + 4135.76i) q^{67} -5719.18 q^{68} +1530.58i q^{69} -9850.31i q^{70} -8200.28 q^{71} -5171.17i q^{72} +5721.56 q^{73} +9343.71i q^{74} -2200.12i q^{75} +21146.2 q^{76} +20860.2 q^{77} -7008.01i q^{78} +5896.73i q^{79} +11202.0i q^{80} +729.000 q^{81} +1387.79 q^{82} +1042.96 q^{83} +19669.0 q^{84} +1966.08i q^{85} +871.416 q^{86} +240.151i q^{87} -43592.0 q^{88} +9279.43 q^{89} -2901.87 q^{90} +16329.3 q^{91} +12165.7 q^{92} -4680.30 q^{93} -15928.7i q^{94} -7269.43i q^{95} -15110.3 q^{96} +7115.92i q^{97} +45409.8i q^{98} -6145.34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.56976i		−	1.89244i	−0.323523	−	0.946220i	$-0.604867\pi$
$2$		−	7.56976i		−	1.89244i	0.323523	−	0.946220i	$-0.395133\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−41.3013			−2.58133
$5$			14.1982i			0.567926i	0.958835	+	0.283963i	$0.0916493\pi$
$5$			14.1982i			0.567926i	−0.958835	+	0.283963i	$0.908351\pi$
$6$	−39.3336			−1.09260
$7$		−	91.6507i		−	1.87042i	−0.354091	−	0.935211i	$-0.615210\pi$
$7$		−	91.6507i		−	1.87042i	0.354091	−	0.935211i	$-0.384790\pi$
$8$			191.525i			2.99258i
$9$	−27.0000			−0.333333
$10$	107.477			1.07477
$11$			227.605i			1.88103i	0.339748	+	0.940517i	$0.389658\pi$
$11$			227.605i			1.88103i	−0.339748	+	0.940517i	$0.610342\pi$
$12$			214.608i			1.49033i
$13$			178.168i			1.05425i	0.849787	+	0.527125i	$0.176730\pi$
$13$			178.168i			1.05425i	−0.849787	+	0.527125i	$0.823270\pi$
$14$	−693.774			−3.53966
$15$	73.7758			0.327892
$16$	788.977			3.08194
$17$	138.475			0.479151			0.239575	−	0.970878i	$-0.422992\pi$
$17$	138.475			0.479151			0.239575	+	0.970878i	$0.422992\pi$
$18$			204.384i			0.630814i
$19$	−511.998			−1.41828			−0.709138	−	0.705069i	$-0.750916\pi$
$19$	−511.998			−1.41828			−0.709138	+	0.705069i	$0.750916\pi$
$20$		−	586.402i		−	1.46601i
$21$	−476.231			−1.07989
$22$	1722.92			3.55974
$23$	−294.560			−0.556824			−0.278412	−	0.960462i	$-0.589808\pi$
$23$	−294.560			−0.556824			−0.278412	+	0.960462i	$0.589808\pi$
$24$	995.193			1.72776
$25$	423.412			0.677460
$26$	1348.69			1.99511
$27$			140.296i			0.192450i
$28$			3785.29i			4.82818i
$29$	−46.2171			−0.0549550			−0.0274775	−	0.999622i	$-0.508747\pi$
$29$	−46.2171			−0.0549550			−0.0274775	+	0.999622i	$0.508747\pi$
$30$		−	558.465i		−	0.620517i
$31$		−	900.725i		−	0.937279i	−0.883390	−	0.468639i	$-0.844744\pi$
$31$		−	900.725i		−	0.937279i	0.883390	−	0.468639i	$-0.155256\pi$
$32$		−	2907.97i		−	2.83982i
$33$	1182.67			1.08602
$34$		−	1048.22i		−	0.906764i
$35$	1301.27			1.06226
$36$	1115.14			0.860444
$37$	−1234.35			−0.901641			−0.450821	−	0.892615i	$-0.648869\pi$
$37$	−1234.35			−0.901641			−0.450821	+	0.892615i	$0.648869\pi$
$38$			3875.70i			2.68401i
$39$	925.790			0.608672
$40$	−2719.30			−1.69956
$41$			183.333i			0.109062i	0.998512	+	0.0545309i	$0.0173663\pi$
$41$			183.333i			0.109062i	−0.998512	+	0.0545309i	$0.982634\pi$
$42$			3604.95i			2.04362i
$43$			115.118i			0.0622596i	0.999515	+	0.0311298i	$0.00991052\pi$
$43$			115.118i			0.0622596i	−0.999515	+	0.0311298i	$0.990089\pi$
$44$		−	9400.39i		−	4.85557i
$45$		−	383.350i		−	0.189309i
$46$			2229.75i			1.05376i
$47$	2104.26			0.952585			0.476292	−	0.879287i	$-0.341980\pi$
$47$	2104.26			0.952585			0.476292	+	0.879287i	$0.341980\pi$
$48$		−	4099.65i		−	1.77936i
$49$	−5998.84			−2.49848
$50$		−	3205.13i		−	1.28205i
$51$		−	719.535i		−	0.276638i
$52$		−	7358.59i		−	2.72137i
$53$			2749.50i			0.978819i	0.872054	+	0.489409i	$0.162788\pi$
$53$			2749.50i			0.978819i	−0.872054	+	0.489409i	$0.837212\pi$
$54$	1062.01			0.364200
$55$	−3231.57			−1.06829
$56$	17553.4			5.59738
$57$			2660.42i			0.818843i
$58$			349.853i			0.103999i
$59$	−2279.42			−0.654819			−0.327409	−	0.944883i	$-0.606176\pi$
$59$	−2279.42			−0.654819			−0.327409	+	0.944883i	$0.606176\pi$
$60$	−3047.04			−0.846399
$61$			3178.54i			0.854216i	0.904201	+	0.427108i	$0.140468\pi$
$61$			3178.54i			0.854216i	−0.904201	+	0.427108i	$0.859532\pi$
$62$	−6818.27			−1.77374
$63$			2474.57i			0.623474i
$64$	−9389.02			−2.29224
$65$	−2529.66			−0.598737
$66$		−	8952.53i		−	2.05522i
$67$	−1745.45	+	4135.76i	−0.388828	+	0.921310i
$67$	−1745.45	+	4135.76i	−0.388828	+	0.921310i
$68$	−5719.18			−1.23685
$69$			1530.58i			0.321483i
$70$		−	9850.31i		−	2.01027i
$71$	−8200.28			−1.62672			−0.813358	−	0.581764i	$-0.802363\pi$
$71$	−8200.28			−1.62672			−0.813358	+	0.581764i	$0.802363\pi$
$72$		−	5171.17i		−	0.997525i
$73$	5721.56			1.07367			0.536833	−	0.843689i	$-0.319621\pi$
$73$	5721.56			1.07367			0.536833	+	0.843689i	$0.319621\pi$
$74$			9343.71i			1.70630i
$75$		−	2200.12i		−	0.391132i
$76$	21146.2			3.66104
$77$	20860.2			3.51833
$78$		−	7008.01i		−	1.15188i
$79$			5896.73i			0.944837i	0.881374	+	0.472419i	$0.156619\pi$
$79$			5896.73i			0.944837i	−0.881374	+	0.472419i	$0.843381\pi$
$80$			11202.0i			1.75032i
$81$	729.000			0.111111
$82$	1387.79			0.206393
$83$	1042.96			0.151395			0.0756976	−	0.997131i	$-0.475882\pi$
$83$	1042.96			0.151395			0.0756976	+	0.997131i	$0.475882\pi$
$84$	19669.0			2.78755
$85$			1966.08i			0.272122i
$86$	871.416			0.117823
$87$			240.151i			0.0317283i
$88$	−43592.0			−5.62914
$89$	9279.43			1.17150			0.585749	−	0.810493i	$-0.300801\pi$
$89$	9279.43			1.17150			0.585749	+	0.810493i	$0.300801\pi$
$90$	−2901.87			−0.358256
$91$	16329.3			1.97189
$92$	12165.7			1.43735
$93$	−4680.30			−0.541138
$94$		−	15928.7i		−	1.80271i
$95$		−	7269.43i		−	0.805477i
$96$	−15110.3			−1.63957
$97$			7115.92i			0.756289i	0.925747	+	0.378144i	$0.123438\pi$
$97$			7115.92i			0.756289i	−0.925747	+	0.378144i	$0.876562\pi$
$98$			45409.8i			4.72822i
$99$		−	6145.34i		−	0.627011i
$100$	−17487.5			−1.74875
$101$			1076.94i			0.105572i	0.998606	+	0.0527860i	$0.0168101\pi$
$101$			1076.94i			0.105572i	−0.998606	+	0.0527860i	$0.983190\pi$
$102$	−5446.71			−0.523521
$103$	−4982.72			−0.469669			−0.234834	−	0.972035i	$-0.575455\pi$
$103$	−4982.72			−0.469669			−0.234834	+	0.972035i	$0.575455\pi$
$104$	−34123.7			−3.15493
$105$		−	6761.60i		−	0.613297i
$106$	20813.1			1.85236
$107$	441.259			0.0385413			0.0192706	−	0.999814i	$-0.493866\pi$
$107$	441.259			0.0385413			0.0192706	+	0.999814i	$0.493866\pi$
$108$		−	5794.41i		−	0.496778i
$109$			15711.0i			1.32236i	0.750226	+	0.661181i	$0.229945\pi$
$109$			15711.0i			1.32236i	−0.750226	+	0.661181i	$0.770055\pi$
$110$			24462.2i			2.02167i
$111$			6413.86i			0.520563i
$112$		−	72310.3i		−	5.76453i
$113$		−	3322.95i		−	0.260236i	−0.991499	−	0.130118i	$-0.958464\pi$
$113$		−	3322.95i		−	0.260236i	0.991499	−	0.130118i	$-0.0415356\pi$
$114$	20138.7			1.54961
$115$		−	4182.21i		−	0.316235i
$116$	1908.83			0.141857
$117$		−	4810.55i		−	0.351417i
$118$			17254.7i			1.23921i
$119$		−	12691.3i		−	0.896214i
$120$			14129.9i			0.981243i
$121$	−37163.1			−2.53829
$122$	24060.8			1.61655
$123$	952.626			0.0629669
$124$			37201.1i			2.41943i
$125$			14885.5i			0.952673i
$126$	18731.9			1.17989
$127$	−31675.4			−1.96388			−0.981938	−	0.189202i	$-0.939410\pi$
$127$	−31675.4			−1.96388			−0.981938	+	0.189202i	$0.939410\pi$
$128$			24545.1i			1.49811i
$129$	598.171			0.0359456
$130$			19148.9i			1.13307i
$131$	−3289.19			−0.191667			−0.0958333	−	0.995397i	$-0.530552\pi$
$131$	−3289.19			−0.191667			−0.0958333	+	0.995397i	$0.530552\pi$
$132$	−48845.8			−2.80337
$133$			46925.0i			2.65278i
$134$	31306.7	+	13212.6i	1.74353	+	0.735834i
$135$	−1991.95			−0.109297
$136$			26521.3i			1.43390i
$137$			7549.59i			0.402237i	0.979567	+	0.201119i	$0.0644577\pi$
$137$			7549.59i			0.402237i	−0.979567	+	0.201119i	$0.935542\pi$
$138$	11586.1			0.608387
$139$		−	31443.6i		−	1.62743i	−0.581262	−	0.813716i	$-0.697441\pi$
$139$		−	31443.6i		−	1.62743i	0.581262	−	0.813716i	$-0.302559\pi$
$140$	−53744.2			−2.74205
$141$		−	10934.1i		−	0.549975i
$142$			62074.1i			3.07846i
$143$	−40552.0			−1.98308
$144$	−21302.4			−1.02731
$145$		−	656.198i		−	0.0312104i
$146$		−	43310.9i		−	2.03185i
$147$			31170.9i			1.44250i
$148$	50980.1			2.32744
$149$	−4469.58			−0.201323			−0.100662	−	0.994921i	$-0.532096\pi$
$149$	−4469.58			−0.201323			−0.100662	+	0.994921i	$0.532096\pi$
$150$	−16654.4			−0.740193
$151$	17808.4			0.781034			0.390517	−	0.920596i	$-0.372296\pi$
$151$	17808.4			0.781034			0.390517	+	0.920596i	$0.372296\pi$
$152$		−	98060.4i		−	4.24430i
$153$	−3738.81			−0.159717
$154$		−	157906.i		−	6.65822i
$155$	12788.6			0.532305
$156$	−38236.3			−1.57118
$157$	29801.1			1.20902			0.604510	−	0.796598i	$-0.293369\pi$
$157$	29801.1			1.20902			0.604510	+	0.796598i	$0.293369\pi$
$158$	44636.8			1.78805
$159$	14286.8			0.565121
$160$	41287.8			1.61281
$161$			26996.6i			1.04150i
$162$		−	5518.36i		−	0.210271i
$163$	13505.9			0.508334			0.254167	−	0.967160i	$-0.418199\pi$
$163$	13505.9			0.508334			0.254167	+	0.967160i	$0.418199\pi$
$164$		−	7571.89i		−	0.281525i
$165$			16791.7i			0.616776i
$166$		−	7894.97i		−	0.286507i
$167$	−51003.8			−1.82882			−0.914408	−	0.404795i	$-0.867343\pi$
$167$	−51003.8			−1.82882			−0.914408	+	0.404795i	$0.867343\pi$
$168$		−	91210.1i		−	3.23165i
$169$	−3182.98			−0.111445
$170$	14882.8			0.514975
$171$	13823.9			0.472759
$172$		−	4754.52i		−	0.160713i
$173$	24595.5			0.821794			0.410897	−	0.911682i	$-0.365216\pi$
$173$	24595.5			0.821794			0.410897	+	0.911682i	$0.365216\pi$
$174$	1817.89			0.0600438
$175$		−	38806.0i		−	1.26714i
$176$			179575.i			5.79724i
$177$			11844.2i			0.378060i
$178$		−	70243.1i		−	2.21699i
$179$		−	51241.0i		−	1.59923i	−0.600512	−	0.799616i	$-0.705036\pi$
$179$		−	51241.0i		−	1.59923i	0.600512	−	0.799616i	$-0.294964\pi$
$180$			15832.9i			0.488669i
$181$	−51747.6			−1.57955			−0.789775	−	0.613397i	$-0.789803\pi$
$181$	−51747.6			−1.57955			−0.789775	+	0.613397i	$0.789803\pi$
$182$		−	123609.i		−	3.73169i
$183$	16516.2			0.493182
$184$		−	56415.6i		−	1.66634i
$185$		−	17525.5i		−	0.512066i
$186$			35428.8i			1.02407i
$187$			31517.5i			0.901299i
$188$	−86908.7			−2.45894
$189$	12858.2			0.359963
$190$	−55027.8			−1.52432
$191$			33376.3i			0.914895i	0.889237	+	0.457448i	$0.151236\pi$
$191$			33376.3i			0.914895i	−0.889237	+	0.457448i	$0.848764\pi$
$192$			48786.8i			1.32343i
$193$	−18561.9			−0.498320			−0.249160	−	0.968462i	$-0.580155\pi$
$193$	−18561.9			−0.498320			−0.249160	+	0.968462i	$0.580155\pi$
$194$	53865.8			1.43123
$195$			13144.5i			0.345681i
$196$	247760.			6.44940
$197$			27370.8i			0.705268i	0.935761	+	0.352634i	$0.114714\pi$
$197$			27370.8i			0.705268i	−0.935761	+	0.352634i	$0.885286\pi$
$198$	−46518.7			−1.18658
$199$	65260.4			1.64795			0.823974	−	0.566627i	$-0.191752\pi$
$199$	65260.4			1.64795			0.823974	+	0.566627i	$0.191752\pi$
$200$			81094.0i			2.02735i
$201$	21490.1	+	9069.62i	0.531919	+	0.224490i
$202$	8152.18			0.199789
$203$			4235.83i			0.102789i
$204$			29717.7i			0.714094i
$205$	−2602.99			−0.0619391
$206$			37718.0i			0.888820i
$207$	7953.12			0.185608
$208$			140571.i			3.24914i
$209$		−	116533.i		−	2.66783i
$210$	−51183.7			−1.16063
$211$	−46328.9			−1.04061			−0.520303	−	0.853981i	$-0.674181\pi$
$211$	−46328.9			−1.04061			−0.520303	+	0.853981i	$0.674181\pi$
$212$		−	113558.i		−	2.52666i
$213$			42609.9i			0.939185i
$214$		−	3340.23i		−	0.0729371i
$215$	−1634.46			−0.0353589
$216$	−26870.2			−0.575922
$217$	−82552.0			−1.75311
$218$	118928.			2.50249
$219$		−	29730.1i		−	0.619881i
$220$	133468.			2.75761
$221$			24671.8i			0.505145i
$222$	48551.4			0.985134
$223$	−53215.3			−1.07011			−0.535053	−	0.844819i	$-0.679708\pi$
$223$	−53215.3			−1.07011			−0.535053	+	0.844819i	$0.679708\pi$
$224$	−266517.			−5.31165
$225$	−11432.1			−0.225820
$226$	−25154.0			−0.492481
$227$	−84517.1			−1.64019			−0.820093	−	0.572231i	$-0.806078\pi$
$227$	−84517.1			−1.64019			−0.820093	+	0.572231i	$0.806078\pi$
$228$		−	109879.i		−	2.11370i
$229$			79395.6i			1.51400i	0.653416	+	0.756999i	$0.273335\pi$
$229$			79395.6i			1.51400i	−0.653416	+	0.756999i	$0.726665\pi$
$230$	−31658.3			−0.598456
$231$		−	108393.i		−	2.03131i
$232$		−	8851.73i		−	0.164457i
$233$			42417.7i			0.781332i	0.920533	+	0.390666i	$0.127755\pi$
$233$			42417.7i			0.781332i	−0.920533	+	0.390666i	$0.872245\pi$
$234$	−36414.7			−0.665036
$235$			29876.6i			0.540998i
$236$	94143.2			1.69030
$237$	30640.3			0.545502
$238$	−96070.0			−1.69603
$239$		−	20429.8i		−	0.357659i	−0.983880	−	0.178829i	$-0.942769\pi$
$239$		−	20429.8i		−	0.357659i	0.983880	−	0.178829i	$-0.0572310\pi$
$240$	58207.4			1.01055
$241$	−23429.4			−0.403392			−0.201696	−	0.979448i	$-0.564645\pi$
$241$	−23429.4			−0.403392			−0.201696	+	0.979448i	$0.564645\pi$
$242$			281315.i			4.80356i
$243$		−	3788.00i		−	0.0641500i
$244$		−	131278.i		−	2.20501i
$245$		−	85172.5i		−	1.41895i
$246$		−	7211.15i		−	0.119161i
$247$		−	91221.9i		−	1.49522i
$248$	172511.			2.80488
$249$		−	5419.39i		−	0.0874081i
$250$	112680.			1.80288
$251$			15370.4i			0.243970i	0.992532	+	0.121985i	$0.0389260\pi$
$251$			15370.4i			0.243970i	−0.992532	+	0.121985i	$0.961074\pi$
$252$		−	102203.i		−	1.60939i
$253$		−	67043.3i		−	1.04740i
$254$			239775.i			3.71652i
$255$	10216.1			0.157110
$256$	35576.3			0.542851
$257$	−69099.0			−1.04618			−0.523089	−	0.852278i	$-0.675221\pi$
$257$	−69099.0			−1.04618			−0.523089	+	0.852278i	$0.675221\pi$
$258$		−	4528.01i		−	0.0680249i
$259$			113129.i			1.68645i
$260$	104478.			1.54554
$261$	1247.86			0.0183183
$262$			24898.4i			0.362718i
$263$	57928.3			0.837489			0.418744	−	0.908104i	$-0.362470\pi$
$263$	57928.3			0.837489			0.418744	+	0.908104i	$0.362470\pi$
$264$			226511.i			3.24998i
$265$	−39037.9			−0.555897
$266$	355211.			5.02022
$267$		−	48217.3i		−	0.676364i
$268$	72089.3	−	170812.i	1.00369	−	2.37821i
$269$	104592.			1.44542			0.722711	−	0.691150i	$-0.242896\pi$
$269$	104592.			1.44542			0.722711	+	0.691150i	$0.242896\pi$
$270$			15078.6i			0.206839i
$271$		−	103204.i		−	1.40527i	−0.711550	−	0.702635i	$-0.752007\pi$
$271$		−	103204.i		−	1.40527i	0.711550	−	0.702635i	$-0.247993\pi$
$272$	109253.			1.47671
$273$		−	84849.3i		−	1.13847i
$274$	57148.6			0.761210
$275$			96370.8i			1.27432i
$276$		−	63214.9i		−	0.829853i
$277$	−90383.2			−1.17795			−0.588977	−	0.808150i	$-0.700469\pi$
$277$	−90383.2			−1.17795			−0.588977	+	0.808150i	$0.700469\pi$
$278$	−238021.			−3.07982
$279$			24319.6i			0.312426i
$280$			249226.i			3.17890i
$281$		−	110435.i		−	1.39860i	−0.714828	−	0.699300i	$-0.753495\pi$
$281$		−	110435.i		−	1.39860i	0.714828	−	0.699300i	$-0.246505\pi$
$282$	−82768.2			−1.04079
$283$	−12384.4			−0.154632			−0.0773162	−	0.997007i	$-0.524635\pi$
$283$	−12384.4			−0.154632			−0.0773162	+	0.997007i	$0.524635\pi$
$284$	338682.			4.19909
$285$	−37773.1			−0.465042
$286$			306969.i			3.75286i
$287$	16802.6			0.203992
$288$			78515.2i			0.946605i
$289$	−64345.8			−0.770415
$290$	−4967.26			−0.0590638
$291$	36975.4			0.436644
$292$	−236308.			−2.77149
$293$	−11335.7			−0.132042			−0.0660211	−	0.997818i	$-0.521030\pi$
$293$	−11335.7			−0.132042			−0.0660211	+	0.997818i	$0.521030\pi$
$294$	235956.			2.72984
$295$		−	32363.6i		−	0.371889i
$296$		−	236408.i		−	2.69823i
$297$	−31932.1			−0.362005
$298$			33833.6i			0.380992i
$299$		−	52481.3i		−	0.587032i
$300$			90867.6i			1.00964i
$301$	10550.6			0.116452
$302$		−	134805.i		−	1.47806i
$303$	5595.95			0.0609521
$304$	−403955.			−4.37105
$305$	−45129.4			−0.485132
$306$			28301.9i			0.302255i
$307$	62543.4			0.663598			0.331799	−	0.943350i	$-0.392344\pi$
$307$	62543.4			0.663598			0.331799	+	0.943350i	$0.392344\pi$
$308$	−861552.			−9.08197
$309$			25891.0i			0.271163i
$310$		−	96806.9i		−	1.00736i
$311$			113213.i			1.17051i	0.810850	+	0.585253i	$0.199005\pi$
$311$			113213.i			1.17051i	−0.810850	+	0.585253i	$0.800995\pi$
$312$			177312.i			1.82150i
$313$			15856.6i			0.161853i	0.996720	+	0.0809264i	$0.0257879\pi$
$313$			15856.6i			0.161853i	−0.996720	+	0.0809264i	$0.974212\pi$
$314$		−	225587.i		−	2.28800i
$315$	−35134.3			−0.354087
$316$		−	243543.i		−	2.43894i
$317$	27689.7			0.275550			0.137775	−	0.990464i	$-0.456005\pi$
$317$	27689.7			0.275550			0.137775	+	0.990464i	$0.456005\pi$
$318$		−	108148.i		−	1.06946i
$319$		−	10519.2i		−	0.103372i
$320$		−	133307.i		−	1.30182i
$321$		−	2292.85i		−	0.0222518i
$322$	204358.			1.97097
$323$	−70898.7			−0.679568
$324$	−30108.7			−0.286815
$325$			75438.7i			0.714213i
$326$		−	102237.i		−	0.961993i
$327$	81636.7			0.763466
$328$	−35112.8			−0.326376
$329$		−	192857.i		−	1.78173i
$330$	127109.			1.16721
$331$			69980.5i			0.638735i	0.947631	+	0.319368i	$0.103470\pi$
$331$			69980.5i			0.638735i	−0.947631	+	0.319368i	$0.896530\pi$
$332$	−43075.7			−0.390801
$333$	33327.4			0.300547
$334$			386087.i			3.46092i
$335$	−58720.2	−	24782.2i	−0.523236	−	0.220826i
$336$	−375735.			−3.32815
$337$		−	218116.i		−	1.92056i	−0.279040	−	0.960280i	$-0.590016\pi$
$337$		−	218116.i		−	1.92056i	0.279040	−	0.960280i	$-0.409984\pi$
$338$			24094.4i			0.210903i
$339$	−17266.6			−0.150247
$340$		−	81201.8i		−	0.702438i
$341$	205010.			1.76305
$342$		−	104644.i		−	0.894668i
$343$			329745.i			2.80278i
$344$	−22048.0			−0.186317
$345$	−21731.4			−0.182578
$346$		−	186182.i		−	1.55520i
$347$		−	111006.i		−	0.921911i	−0.887423	−	0.460955i	$-0.847507\pi$
$347$		−	111006.i		−	0.921911i	0.887423	−	0.460955i	$-0.152493\pi$
$348$		−	9918.56i		−	0.0819012i
$349$	−174738.			−1.43462			−0.717308	−	0.696756i	$-0.754626\pi$
$349$	−174738.			−1.43462			−0.717308	+	0.696756i	$0.754626\pi$
$350$	−293752.			−2.39798
$351$	−24996.3			−0.202891
$352$	661869.			5.34179
$353$		−	103672.i		−	0.831975i	−0.909370	−	0.415987i	$-0.863436\pi$
$353$		−	103672.i		−	0.831975i	0.909370	−	0.415987i	$-0.136564\pi$
$354$	89658.0			0.715455
$355$		−	116429.i		−	0.923855i
$356$	−383253.			−3.02402
$357$	−65945.9			−0.517429
$358$	−387882.			−3.02645
$359$	169246.			1.31319			0.656597	−	0.754241i	$-0.271995\pi$
$359$	169246.			1.31319			0.656597	+	0.754241i	$0.271995\pi$
$360$	73421.1			0.566521
$361$	131821.			1.01151
$362$			391717.i			2.98920i
$363$			193105.i			1.46548i
$364$	−674419.			−5.09011
$365$			81235.6i			0.609763i
$366$		−	125023.i		−	0.933317i
$367$		−	17695.9i		−	0.131383i	−0.997840	−	0.0656916i	$-0.979075\pi$
$367$		−	17695.9i		−	0.131383i	0.997840	−	0.0656916i	$-0.0209254\pi$
$368$	−232401.			−1.71610
$369$		−	4949.99i		−	0.0363539i
$370$	−132664.			−0.969054
$371$	251994.			1.83080
$372$	193303.			1.39686
$373$			70562.9i			0.507176i	0.967312	+	0.253588i	$0.0816108\pi$
$373$			70562.9i			0.507176i	−0.967312	+	0.253588i	$0.918389\pi$
$374$	238580.			1.70565
$375$	77347.4			0.550026
$376$			403018.i			2.85068i
$377$		−	8234.43i		−	0.0579363i
$378$		−	97333.8i		−	0.681208i
$379$			192070.i			1.33715i	0.743644	+	0.668576i	$0.233096\pi$
$379$			192070.i			1.33715i	−0.743644	+	0.668576i	$0.766904\pi$
$380$			300237.i			2.07920i
$381$			164590.i			1.13384i
$382$	252651.			1.73138
$383$		−	54024.8i		−	0.368295i	−0.982899	−	0.184147i	$-0.941048\pi$
$383$		−	54024.8i		−	0.368295i	0.982899	−	0.184147i	$-0.0589524\pi$
$384$	127540.			0.864936
$385$			296176.i			1.99815i
$386$			140509.i			0.943042i
$387$		−	3108.19i		−	0.0207532i
$388$		−	293897.i		−	1.95223i
$389$	−149579.			−0.988487			−0.494243	−	0.869324i	$-0.664555\pi$
$389$	−149579.			−0.988487			−0.494243	+	0.869324i	$0.664555\pi$
$390$	99500.8			0.654180
$391$	−40789.1			−0.266803
$392$		−	1.14893e6i		−	7.47688i
$393$			17091.1i			0.110659i
$394$	207190.			1.33468
$395$	−83722.7			−0.536598
$396$			253810.i			1.61852i
$397$	−10604.3			−0.0672822			−0.0336411	−	0.999434i	$-0.510710\pi$
$397$	−10604.3			−0.0672822			−0.0336411	+	0.999434i	$0.510710\pi$
$398$		−	494006.i		−	3.11864i
$399$	243829.			1.53158
$400$	334063.			2.08789
$401$			77808.4i			0.483880i	0.970291	+	0.241940i	$0.0777837\pi$
$401$			77808.4i			0.483880i	−0.970291	+	0.241940i	$0.922216\pi$
$402$	68654.9	−	162675.i	0.424834	−	1.00662i
$403$	160481.			0.988127
$404$		−	44479.1i		−	0.272517i
$405$			10350.5i			0.0631029i
$406$	32064.2			0.194522
$407$		−	280944.i		−	1.69602i
$408$	137809.			0.827860
$409$		−	147525.i		−	0.881898i	−0.897532	−	0.440949i	$-0.854642\pi$
$409$		−	147525.i		−	0.881898i	0.897532	−	0.440949i	$-0.145358\pi$
$410$			19704.0i			0.117216i
$411$	39228.8			0.232232
$412$	205793.			1.21237
$413$			208911.i			1.22479i
$414$		−	60203.2i		−	0.351252i
$415$			14808.1i			0.0859813i
$416$	518109.			2.99388
$417$	−163386.			−0.939599
$418$	−882130.			−5.04870
$419$	−104040.			−0.592617			−0.296309	−	0.955092i	$-0.595756\pi$
$419$	−104040.			−0.592617			−0.296309	+	0.955092i	$0.595756\pi$
$420$			279263.i			1.58312i
$421$	69042.5			0.389540			0.194770	−	0.980849i	$-0.437604\pi$
$421$	69042.5			0.389540			0.194770	+	0.980849i	$0.437604\pi$
$422$			350698.i			1.96929i
$423$	−56815.0			−0.317528
$424$	−526598.			−2.92919
$425$	58631.8			0.324605
$426$	322547.			1.77735
$427$	291315.			1.59774
$428$	−18224.6			−0.0994878
$429$			210715.i			1.14493i
$430$			12372.5i			0.0669145i
$431$	−3197.43			−0.0172126			−0.00860631	−	0.999963i	$-0.502740\pi$
$431$	−3197.43			−0.0172126			−0.00860631	+	0.999963i	$0.502740\pi$
$432$			110690.i			0.593120i
$433$		−	98513.5i		−	0.525436i	−0.964873	−	0.262718i	$-0.915381\pi$
$433$		−	98513.5i		−	0.525436i	0.964873	−	0.262718i	$-0.0846189\pi$
$434$			624899.i			3.31765i
$435$	−3409.70			−0.0180193
$436$		−	648884.i		−	3.41346i
$437$	150814.			0.789731
$438$	−225050.			−1.17309
$439$	−154103.			−0.799619			−0.399810	−	0.916598i	$-0.630924\pi$
$439$	−154103.			−0.799619			−0.399810	+	0.916598i	$0.630924\pi$
$440$		−	618926.i		−	3.19693i
$441$	161969.			0.832826
$442$	186760.			0.955957
$443$		−	26527.5i		−	0.135173i	−0.997713	−	0.0675864i	$-0.978470\pi$
$443$		−	26527.5i		−	0.135173i	0.997713	−	0.0675864i	$-0.0215298\pi$
$444$		−	264901.i		−	1.34375i
$445$			131751.i			0.665324i
$446$			402827.i			2.02511i
$447$			23224.6i			0.116234i
$448$			860510.i			4.28746i
$449$	154416.			0.765950			0.382975	−	0.923759i	$-0.374899\pi$
$449$	154416.			0.765950			0.382975	+	0.923759i	$0.374899\pi$
$450$			86538.5i			0.427351i
$451$	−41727.5			−0.205149
$452$			137242.i			0.671755i
$453$		−	92534.9i		−	0.450930i
$454$			639775.i			3.10395i
$455$			231845.i			1.11989i
$456$	−509537.			−2.45045
$457$	96586.4			0.462470			0.231235	−	0.972898i	$-0.425723\pi$
$457$	96586.4			0.462470			0.231235	+	0.972898i	$0.425723\pi$
$458$	601006.			2.86515
$459$			19427.4i			0.0922126i
$460$			172731.i			0.816308i
$461$	−208611.			−0.981604			−0.490802	−	0.871271i	$-0.663296\pi$
$461$	−208611.			−0.981604			−0.490802	+	0.871271i	$0.663296\pi$
$462$	−820506.			−3.84413
$463$		−	52010.0i		−	0.242619i	−0.992615	−	0.121309i	$-0.961291\pi$
$463$		−	52010.0i		−	0.242619i	0.992615	−	0.121309i	$-0.0387093\pi$
$464$	−36464.2			−0.169368
$465$		−	66451.7i		−	0.307327i
$466$	321092.			1.47862
$467$	93527.5			0.428850			0.214425	−	0.976740i	$-0.431212\pi$
$467$	93527.5			0.428850			0.214425	+	0.976740i	$0.431212\pi$
$468$			198682.i			0.907124i
$469$	379045.	+	159972.i	1.72324	+	0.727272i
$470$	226159.			1.02381
$471$		−	154851.i		−	0.698028i
$472$		−	436566.i		−	1.95959i
$473$	−26201.4			−0.117112
$474$		−	231940.i		−	1.03233i
$475$	−216786.			−0.960826
$476$			524167.i			2.31343i
$477$		−	74236.6i		−	0.326273i
$478$	−154649.			−0.676848
$479$	288962.			1.25942			0.629708	−	0.776832i	$-0.283175\pi$
$479$	288962.			1.25942			0.629708	+	0.776832i	$0.283175\pi$
$480$		−	214538.i		−	0.931154i
$481$		−	219922.i		−	0.950556i
$482$			177355.i			0.763395i
$483$	140279.			0.601308
$484$	1.53488e6			6.55216
$485$	−101033.			−0.429516
$486$	−28674.2			−0.121400
$487$		−	25080.2i		−	0.105748i	−0.998601	−	0.0528742i	$-0.983162\pi$
$487$		−	25080.2i		−	0.105748i	0.998601	−	0.0528742i	$-0.0168382\pi$
$488$	−608769.			−2.55631
$489$		−	70178.9i		−	0.293487i
$490$	−644736.			−2.68528
$491$	324072.			1.34425			0.672123	−	0.740439i	$-0.265383\pi$
$491$	324072.			1.34425			0.672123	+	0.740439i	$0.265383\pi$
$492$	−39344.7			−0.162538
$493$	−6399.90			−0.0263317
$494$	−690528.			−2.82961
$495$	87252.4			0.356096
$496$		−	710651.i		−	2.88864i
$497$			751561.i			3.04264i
$498$	−41023.5			−0.165415
$499$		−	103657.i		−	0.416290i	−0.978098	−	0.208145i	$-0.933257\pi$
$499$		−	103657.i		−	0.416290i	0.978098	−	0.208145i	$-0.0667426\pi$
$500$		−	614792.i		−	2.45917i
$501$			265024.i			1.05587i
$502$	116350.			0.461699
$503$			229644.i			0.907651i	0.891091	+	0.453825i	$0.149941\pi$
$503$			229644.i			0.907651i	−0.891091	+	0.453825i	$0.850059\pi$
$504$	−473941.			−1.86579
$505$	−15290.6			−0.0599571
$506$	−507502.			−1.98215
$507$			16539.3i			0.0643428i
$508$	1.30823e6			5.06942
$509$	−317405.			−1.22512			−0.612558	−	0.790425i	$-0.709860\pi$
$509$	−317405.			−1.22512			−0.612558	+	0.790425i	$0.709860\pi$
$510$		−	77333.2i		−	0.297321i
$511$		−	524385.i		−	2.00821i
$512$			123418.i			0.470801i
$513$		−	71831.3i		−	0.272948i
$514$			523063.i			1.97983i
$515$		−	70745.4i		−	0.266737i
$516$	−24705.2			−0.0927875
$517$			478940.i			1.79184i
$518$	856358.			3.19151
$519$		−	127802.i		−	0.474463i
$520$		−	484493.i		−	1.79177i
$521$		−	272318.i		−	1.00323i	−0.865091	−	0.501615i	$-0.832739\pi$
$521$		−	272318.i		−	1.00323i	0.865091	−	0.501615i	$-0.167261\pi$
$522$		−	9446.02i		−	0.0346663i
$523$	−111605.			−0.408018			−0.204009	−	0.978969i	$-0.565397\pi$
$523$	−111605.			−0.408018			−0.204009	+	0.978969i	$0.565397\pi$
$524$	135848.			0.494755
$525$	−201642.			−0.731581
$526$		−	438503.i		−	1.58490i
$527$		−	124728.i		−	0.449098i
$528$	933100.			3.34704
$529$	−193075.			−0.689947
$530$			295507.i			1.05200i
$531$	61544.4			0.218273
$532$		−	1.93806e6i		−	6.84769i
$533$	−32664.1			−0.114979
$534$	−364994.			−1.27998
$535$			6265.06i			0.0218886i
$536$	−792101.	−	334297.i	−2.75709	−	1.16360i
$537$	−266256.			−0.923317
$538$		−	791738.i		−	2.73538i
$539$		−	1.36537e6i		−	4.69972i
$540$	82270.0			0.282133
$541$		−	106205.i		−	0.362870i	−0.983403	−	0.181435i	$-0.941926\pi$
$541$		−	106205.i		−	0.362870i	0.983403	−	0.181435i	$-0.0580742\pi$
$542$	−781233.			−2.65939
$543$			268889.i			0.911953i
$544$		−	402680.i		−	1.36070i
$545$	−223067.			−0.751004
$546$	−642289.			−2.15449
$547$			369887.i			1.23621i	0.786094	+	0.618107i	$0.212100\pi$
$547$			369887.i			1.23621i	−0.786094	+	0.618107i	$0.787900\pi$
$548$		−	311808.i		−	1.03831i
$549$		−	85820.5i		−	0.284739i
$550$	729504.			2.41158
$551$	23663.1			0.0779414
$552$	−293144.			−0.962061
$553$	540439.			1.76724
$554$			684180.i			2.22921i
$555$	−91064.9			−0.295641
$556$			1.29866e6i			4.20094i
$557$	−104271.			−0.336089			−0.168045	−	0.985779i	$-0.553745\pi$
$557$	−104271.			−0.336089			−0.168045	+	0.985779i	$0.553745\pi$
$558$	184093.			0.591248
$559$	−20510.4			−0.0656372
$560$	1.02667e6			3.27383
$561$	163770.			0.520365
$562$	−835966.			−2.64677
$563$			232412.i			0.733233i	0.930372	+	0.366617i	$0.119484\pi$
$563$			232412.i			0.733233i	−0.930372	+	0.366617i	$0.880516\pi$
$564$			451591.i			1.41967i
$565$	47179.8			0.147795
$566$			93746.7i			0.292633i
$567$		−	66813.3i		−	0.207825i
$568$		−	1.57056e6i		−	4.86807i
$569$	−480059.			−1.48276			−0.741379	−	0.671086i	$-0.765828\pi$
$569$	−480059.			−1.48276			−0.741379	+	0.671086i	$0.765828\pi$
$570$			285933.i			0.880065i
$571$	380463.			1.16692			0.583459	−	0.812143i	$-0.301699\pi$
$571$	380463.			1.16692			0.583459	+	0.812143i	$0.301699\pi$
$572$	1.67485e6			5.11899
$573$	173428.			0.528215
$574$		−	127192.i		−	0.386042i
$575$	−124720.			−0.377226
$576$	253503.			0.764080
$577$			148307.i			0.445461i	0.974880	+	0.222730i	$0.0714969\pi$
$577$			148307.i			0.445461i	−0.974880	+	0.222730i	$0.928503\pi$
$578$			487082.i			1.45796i
$579$			96450.7i			0.287705i
$580$			27101.8i			0.0805643i
$581$		−	95588.2i		−	0.283173i
$582$		−	279895.i		−	0.826322i
$583$	−625801.			−1.84119
$584$			1.09582e6i			3.21303i
$585$	68300.9			0.199579
$586$			85808.5i			0.249882i
$587$		−	146036.i		−	0.423822i	−0.977289	−	0.211911i	$-0.932031\pi$
$587$		−	146036.i		−	0.423822i	0.977289	−	0.211911i	$-0.0679687\pi$
$588$		−	1.28740e6i		−	3.72356i
$589$			461169.i			1.32932i
$590$	−244985.			−0.703777
$591$	142223.			0.407187
$592$	−973871.			−2.77881
$593$			490331.i			1.39437i	0.716889	+	0.697187i	$0.245565\pi$
$593$			490331.i			1.39437i	−0.716889	+	0.697187i	$0.754435\pi$
$594$			241718.i			0.685073i
$595$	180193.			0.508983
$596$	184599.			0.519682
$597$		−	339103.i		−	0.951443i
$598$	−397271.			−1.11092
$599$		−	255873.i		−	0.713132i	−0.934270	−	0.356566i	$-0.883947\pi$
$599$		−	255873.i		−	0.713132i	0.934270	−	0.356566i	$-0.116053\pi$
$600$	421377.			1.17049
$601$	161719.			0.447725			0.223862	−	0.974621i	$-0.428133\pi$
$601$	161719.			0.447725			0.223862	+	0.974621i	$0.428133\pi$
$602$		−	79865.8i		−	0.220378i
$603$	47127.1	−	111666.i	0.129609	−	0.307103i
$604$	−735508.			−2.01611
$605$		−	527647.i		−	1.44156i
$606$		−	42360.0i		−	0.115348i
$607$	164078.			0.445320			0.222660	−	0.974896i	$-0.428526\pi$
$607$	164078.			0.445320			0.222660	+	0.974896i	$0.428526\pi$
$608$			1.48888e6i			4.02764i
$609$	22010.0			0.0593452
$610$			341619.i			0.918083i
$611$			374913.i			1.00426i
$612$	154418.			0.412282
$613$	110803.			0.294870			0.147435	−	0.989072i	$-0.452898\pi$
$613$	110803.			0.294870			0.147435	+	0.989072i	$0.452898\pi$
$614$		−	473439.i		−	1.25582i
$615$			13525.5i			0.0357605i
$616$			3.99524e6i			10.5289i
$617$	413315.			1.08570			0.542851	−	0.839829i	$-0.317345\pi$
$617$	413315.			1.08570			0.542851	+	0.839829i	$0.317345\pi$
$618$	195988.			0.513161
$619$	166830.			0.435405			0.217703	−	0.976015i	$-0.430144\pi$
$619$	166830.			0.435405			0.217703	+	0.976015i	$0.430144\pi$
$620$	−528187.			−1.37406
$621$		−	41325.6i		−	0.107161i
$622$	856992.			2.21511
$623$		−	850466.i		−	2.19119i
$624$	730427.			1.87589
$625$	53285.8			0.136412
$626$	120030.			0.306297
$627$	−605525.			−1.54027
$628$	−1.23082e6			−3.12088
$629$	−170926.			−0.432022
$630$			265958.i			0.670089i
$631$			587342.i			1.47514i	0.675272	+	0.737569i	$0.264026\pi$
$631$			587342.i			1.47514i	−0.675272	+	0.737569i	$0.735974\pi$
$632$	−1.12937e6			−2.82750
$633$			240732.i			0.600795i
$634$		−	209605.i		−	0.521461i
$635$		−	449732.i		−	1.11534i
$636$	−590065.			−1.45877
$637$		−	1.06880e6i		−	2.63402i
$638$	−79628.2			−0.195626
$639$	221407.			0.542239
$640$	−348495.			−0.850818
$641$			29452.9i			0.0716823i	0.999358	+	0.0358411i	$0.0114110\pi$
$641$			29452.9i			0.0716823i	−0.999358	+	0.0358411i	$0.988589\pi$
$642$	−17356.3			−0.0421102
$643$	461050.			1.11513			0.557566	−	0.830132i	$-0.311735\pi$
$643$	461050.			1.11513			0.557566	+	0.830132i	$0.311735\pi$
$644$		−	1.11500e6i		−	2.68845i
$645$			8492.92i			0.0204144i
$646$			536686.i			1.28604i
$647$			620014.i			1.48113i	0.671985	+	0.740565i	$0.265442\pi$
$647$			620014.i			1.48113i	−0.671985	+	0.740565i	$0.734558\pi$
$648$			139622.i			0.332508i
$649$		−	518808.i		−	1.23174i
$650$	571053.			1.35161
$651$			428953.i			1.01216i
$652$	−557813.			−1.31218
$653$			54562.6i			0.127958i	0.997951	+	0.0639792i	$0.0203791\pi$
$653$			54562.6i			0.127958i	−0.997951	+	0.0639792i	$0.979621\pi$
$654$		−	617970.i		−	1.44481i
$655$		−	46700.4i		−	0.108852i
$656$			144645.i			0.336122i
$657$	−154482.			−0.357889
$658$	−1.45988e6			−3.37183
$659$	−214022.			−0.492819			−0.246410	−	0.969166i	$-0.579251\pi$
$659$	−214022.			−0.492819			−0.246410	+	0.969166i	$0.579251\pi$
$660$		−	693521.i		−	1.59210i
$661$		−	73112.0i		−	0.167335i	−0.996494	−	0.0836673i	$-0.973337\pi$
$661$		−	73112.0i		−	0.167335i	0.996494	−	0.0836673i	$-0.0266633\pi$
$662$	529736.			1.20877
$663$	128198.			0.291646
$664$			199753.i			0.453062i
$665$	−666248.			−1.50658
$666$		−	252280.i		−	0.568768i
$667$	13613.7			0.0306002
$668$	2.10652e6			4.72078
$669$			276515.i			0.617826i
$670$	−187595.	+	444498.i	−0.417899	+	0.990194i
$671$	−723451.			−1.60681
$672$			1.38487e6i			3.06668i
$673$			126472.i			0.279231i	0.990206	+	0.139616i	$0.0445867\pi$
$673$			126472.i			0.279231i	−0.990206	+	0.139616i	$0.955413\pi$
$674$	−1.65109e6			−3.63454
$675$			59403.1i			0.130377i
$676$	131461.			0.287677
$677$		−	507521.i		−	1.10733i	−0.832740	−	0.553665i	$-0.813229\pi$
$677$		−	507521.i		−	1.10733i	0.832740	−	0.553665i	$-0.186771\pi$
$678$			130704.i			0.284334i
$679$	652179.			1.41458
$680$	−376554.			−0.814347
$681$			439164.i			0.946962i
$682$		−	1.55187e6i		−	3.33647i
$683$		−	119445.i		−	0.256052i	−0.991771	−	0.128026i	$-0.959136\pi$
$683$		−	119445.i		−	0.256052i	0.991771	−	0.128026i	$-0.0408640\pi$
$684$	−570947.			−1.22035
$685$	−107190.			−0.228441
$686$	2.49609e6			5.30410
$687$	412551.			0.874107
$688$			90825.5i			0.191880i
$689$	−489874.			−1.03192
$690$			164501.i			0.345519i
$691$	−172614.			−0.361510			−0.180755	−	0.983528i	$-0.557854\pi$
$691$	−172614.			−0.361510			−0.180755	+	0.983528i	$0.557854\pi$
$692$	−1.01583e6			−2.12132
$693$	−563224.			−1.17278
$694$	−840292.			−1.74466
$695$	446441.			0.924262
$696$	−45994.9			−0.0949492
$697$			25386.9i			0.0522571i
$698$			1.32272e6i			2.71492i
$699$	220409.			0.451102
$700$			1.60274e6i			3.27090i
$701$		−	48773.4i		−	0.0992538i	−0.998768	−	0.0496269i	$-0.984197\pi$
$701$		−	48773.4i		−	0.0992538i	0.998768	−	0.0496269i	$-0.0158032\pi$
$702$			189216.i			0.383959i
$703$	631983.			1.27878
$704$		−	2.13699e6i		−	4.31178i
$705$	155243.			0.312345
$706$	−784769.			−1.57446
$707$	98702.3			0.197464
$708$		−	489182.i		−	0.975897i
$709$	−642882.			−1.27891			−0.639453	−	0.768830i	$-0.720839\pi$
$709$	−642882.			−1.27891			−0.639453	+	0.768830i	$0.720839\pi$
$710$	−881338.			−1.74834
$711$		−	159212.i		−	0.314946i
$712$			1.77724e6i			3.50580i
$713$			265318.i			0.521900i
$714$			499194.i			0.979204i
$715$		−	575764.i		−	1.12624i
$716$			2.11632e6i			4.12815i
$717$	−106156.			−0.206494
$718$		−	1.28115e6i		−	2.48514i
$719$	404470.			0.782399			0.391200	−	0.920306i	$-0.372060\pi$
$719$	404470.			0.782399			0.391200	+	0.920306i	$0.372060\pi$
$720$		−	302455.i		−	0.583439i
$721$			456669.i			0.878479i
$722$		−	997853.i		−	1.91422i
$723$			121743.i			0.232898i
$724$	2.13724e6			4.07734
$725$	−19568.9			−0.0372298
$726$	1.46176e6			2.77333
$727$			36407.3i			0.0688842i	0.999407	+	0.0344421i	$0.0109654\pi$
$727$			36407.3i			0.0688842i	−0.999407	+	0.0344421i	$0.989035\pi$
$728$			3.12746e6i			5.90104i
$729$	−19683.0			−0.0370370
$730$	614935.			1.15394
$731$			15940.9i			0.0298317i
$732$	−682139.			−1.27307
$733$		−	499695.i		−	0.930030i	−0.885303	−	0.465015i	$-0.846049\pi$
$733$		−	499695.i		−	0.930030i	0.885303	−	0.465015i	$-0.153951\pi$
$734$	−133954.			−0.248635
$735$	−442569.			−0.819232
$736$			856572.i			1.58128i
$737$	−941320.	−	397273.i	−1.73302	−	0.731398i
$738$	−37470.2			−0.0687977
$739$		−	93823.6i		−	0.171800i	−0.996304	−	0.0859000i	$-0.972623\pi$
$739$		−	93823.6i		−	0.171800i	0.996304	−	0.0859000i	$-0.0273766\pi$
$740$			723824.i			1.32181i
$741$	−474003.			−0.863266
$742$		−	1.90753e6i		−	3.46469i
$743$	887458.			1.60757			0.803785	−	0.594919i	$-0.202816\pi$
$743$	887458.			1.60757			0.803785	+	0.594919i	$0.202816\pi$
$744$		−	896395.i		−	1.61940i
$745$		−	63459.7i		−	0.114337i
$746$	534144.			0.959801
$747$	−28160.0			−0.0504651
$748$		−	1.30171e6i		−	2.32655i
$749$		−	40441.7i		−	0.0720884i
$750$		−	585502.i		−	1.04089i
$751$	−620022.			−1.09933			−0.549664	−	0.835386i	$-0.685244\pi$
$751$	−620022.			−1.09933			−0.549664	+	0.835386i	$0.685244\pi$
$752$	1.66021e6			2.93581
$753$	79866.8			0.140856
$754$	−62332.7			−0.109641
$755$			252846.i			0.443570i
$756$	−531062.			−0.929183
$757$		−	885408.i		−	1.54508i	−0.634964	−	0.772542i	$-0.718985\pi$
$757$		−	885408.i		−	1.54508i	0.634964	−	0.772542i	$-0.281015\pi$
$758$	1.45392e6			2.53048
$759$	−348367.			−0.604719
$760$	1.39228e6			2.41045
$761$	−669478.			−1.15602			−0.578012	−	0.816028i	$-0.696171\pi$
$761$	−669478.			−1.15602			−0.578012	+	0.816028i	$0.696171\pi$
$762$	1.24591e6			2.14573
$763$	1.43992e6			2.47338
$764$		−	1.37848e6i		−	2.36165i
$765$		−	53084.3i		−	0.0907074i
$766$	−408955.			−0.696976
$767$		−	406121.i		−	0.690343i
$768$		−	184860.i		−	0.313415i
$769$			888577.i			1.50260i	0.659963	+	0.751298i	$0.270572\pi$
$769$			888577.i			1.50260i	−0.659963	+	0.751298i	$0.729428\pi$
$770$	2.24198e6			3.78138
$771$			359049.i			0.604011i
$772$	766632.			1.28633
$773$	−731622.			−1.22441			−0.612206	−	0.790698i	$-0.709718\pi$
$773$	−731622.			−1.22441			−0.612206	+	0.790698i	$0.709718\pi$
$774$	−23528.2			−0.0392742
$775$		−	381378.i		−	0.634969i
$776$	−1.36288e6			−2.26325
$777$	587834.			0.973672
$778$			1.13228e6i			1.87065i
$779$		−	93866.1i		−	0.154680i
$780$		−	542886.i		−	0.892317i
$781$		−	1.86642e6i		−	3.05991i
$782$			308764.i			0.504908i
$783$		−	6484.08i		−	0.0105761i
$784$	−4.73295e6			−7.70016
$785$			423121.i			0.686634i
$786$	129376.			0.209415
$787$			115955.i			0.187215i	0.995609	+	0.0936075i	$0.0298399\pi$
$787$			115955.i			0.187215i	−0.995609	+	0.0936075i	$0.970160\pi$
$788$		−	1.13045e6i		−	1.82053i
$789$		−	301004.i		−	0.483524i
$790$			633761.i			1.01548i
$791$	−304551.			−0.486751
$792$	1.17698e6			1.87638
$793$	−566315.			−0.900558
$794$			80271.9i			0.127328i
$795$			202847.i			0.320947i
$796$	−2.69534e6			−4.25390
$797$	956607.			1.50597			0.752986	−	0.658036i	$-0.228613\pi$
$797$	956607.			1.50597			0.752986	+	0.658036i	$0.228613\pi$
$798$		−	1.84573e6i		−	2.89843i
$799$	291386.			0.456432
$800$		−	1.23127e6i		−	1.92386i
$801$	−250545.			−0.390499
$802$	588991.			0.915714
$803$			1.30226e6i			2.01960i
$804$	−887567.	−	374587.i	−1.37306	−	0.579483i
$805$	−383302.			−0.591493
$806$		−	1.21480e6i		−	1.86997i
$807$		−	543477.i		−	0.834515i
$808$	−206261.			−0.315932
$809$		−	1.29201e6i		−	1.97410i	−0.160418	−	0.987049i	$-0.551284\pi$
$809$		−	1.29201e6i		−	1.97410i	0.160418	−	0.987049i	$-0.448716\pi$
$810$	78350.5			0.119419
$811$		−	653058.i		−	0.992910i	−0.868062	−	0.496455i	$-0.834635\pi$
$811$		−	653058.i		−	0.992910i	0.868062	−	0.496455i	$-0.165365\pi$
$812$		−	174945.i		−	0.265332i
$813$	−536266.			−0.811333
$814$	−2.12668e6			−3.20961
$815$			191759.i			0.288696i
$816$		−	567697.i		−	0.852582i
$817$		−	58940.2i		−	0.0883014i
$818$	−1.11673e6			−1.66894
$819$	−440890.			−0.657298
$820$	107507.			0.159885
$821$	804124.			1.19299			0.596495	−	0.802617i	$-0.296560\pi$
$821$	804124.			1.19299			0.596495	+	0.802617i	$0.296560\pi$
$822$		−	296953.i		−	0.439485i
$823$	−371192.			−0.548023			−0.274011	−	0.961726i	$-0.588351\pi$
$823$	−371192.			−0.548023			−0.274011	+	0.961726i	$0.588351\pi$
$824$		−	954314.i		−	1.40552i
$825$	500757.			0.735732
$826$	1.58140e6			2.31784
$827$	943220.			1.37912			0.689560	−	0.724229i	$-0.257804\pi$
$827$	943220.			1.37912			0.689560	+	0.724229i	$0.257804\pi$
$828$	−328474.			−0.479116
$829$	303769.			0.442012			0.221006	−	0.975272i	$-0.429066\pi$
$829$	303769.			0.442012			0.221006	+	0.975272i	$0.429066\pi$
$830$	112094.			0.162715
$831$			469645.i			0.680092i
$832$		−	1.67283e6i		−	2.41660i
$833$	−830687.			−1.19715
$834$			1.23679e6i			1.77813i
$835$		−	724160.i		−	1.03863i
$836$			4.81298e6i			6.88654i
$837$	126368.			0.180379
$838$			787562.i			1.12149i
$839$	−480491.			−0.682592			−0.341296	−	0.939956i	$-0.610866\pi$
$839$	−480491.			−0.682592			−0.341296	+	0.939956i	$0.610866\pi$
$840$	1.29501e6			1.83534
$841$	−705145.			−0.996980
$842$		−	522635.i		−	0.737182i
$843$	−573837.			−0.807483
$844$	1.91344e6			2.68615
$845$		−	45192.5i		−	0.0632926i
$846$			430076.i			0.600903i
$847$			3.40602e6i			4.74767i
$848$			2.16929e6i			3.01666i
$849$			64351.0i			0.0892771i
$850$		−	443829.i		−	0.614296i
$851$	363589.			0.502056
$852$		−	1.75984e6i		−	2.42435i
$853$	−183173.			−0.251746			−0.125873	−	0.992046i	$-0.540173\pi$
$853$	−183173.			−0.251746			−0.125873	+	0.992046i	$0.540173\pi$
$854$		−	2.20519e6i		−	3.02364i
$855$			196275.i			0.268492i
$856$			84512.1i			0.115338i
$857$			743073.i			1.01174i	0.862609	+	0.505871i	$0.168829\pi$
$857$			743073.i			1.01174i	−0.862609	+	0.505871i	$0.831171\pi$
$858$	1.59506e6			2.16672
$859$	−53213.5			−0.0721167			−0.0360583	−	0.999350i	$-0.511480\pi$
$859$	−53213.5			−0.0721167			−0.0360583	+	0.999350i	$0.511480\pi$
$860$	67505.5			0.0912729
$861$		−	87308.8i		−	0.117775i
$862$			24203.8i			0.0325739i
$863$	−1.27365e6			−1.71013			−0.855063	−	0.518525i	$-0.826481\pi$
$863$	−1.27365e6			−1.71013			−0.855063	+	0.518525i	$0.826481\pi$
$864$	407977.			0.546523
$865$			349210.i			0.466718i
$866$	−745724.			−0.994356
$867$			334351.i			0.444799i
$868$	3.40951e6			4.52535
$869$	−1.34213e6			−1.77727
$870$			25810.7i			0.0341005i
$871$	−736862.	−	310984.i	−0.971292	−	0.409922i
$872$	−3.00905e6			−3.95727
$873$		−	192130.i		−	0.252096i
$874$		−	1.14163e6i		−	1.49452i
$875$	1.36427e6			1.78190
$876$			1.22789e6i			1.60012i
$877$	515350.			0.670043			0.335022	−	0.942210i	$-0.391256\pi$
$877$	515350.			0.670043			0.335022	+	0.942210i	$0.391256\pi$
$878$			1.16653e6i			1.51323i
$879$			58902.0i			0.0762346i
$880$	−2.54964e6			−3.29240
$881$	1.19622e6			1.54121			0.770603	−	0.637315i	$-0.219955\pi$
$881$	1.19622e6			1.54121			0.770603	+	0.637315i	$0.219955\pi$
$882$		−	1.22607e6i		−	1.57607i
$883$		−	327688.i		−	0.420280i	−0.977671	−	0.210140i	$-0.932608\pi$
$883$		−	327688.i		−	0.420280i	0.977671	−	0.210140i	$-0.0673919\pi$
$884$		−	1.01898e6i		−	1.30395i
$885$	−168166.			−0.214710
$886$	−200807.			−0.255807
$887$	−943666.			−1.19942			−0.599710	−	0.800217i	$-0.704717\pi$
$887$	−943666.			−1.19942			−0.599710	+	0.800217i	$0.704717\pi$
$888$	−1.22841e6			−1.55782
$889$			2.90307e6i			3.67328i
$890$	997322.			1.25909
$891$			165924.i			0.209004i
$892$	2.19786e6			2.76230
$893$	−1.07738e6			−1.35103
$894$	175805.			0.219966
$895$	727528.			0.908246
$896$	2.24957e6			2.80210
$897$	−272701.			−0.338923
$898$		−	1.16890e6i		−	1.44952i
$899$			41628.9i			0.0515081i
$900$	472162.			0.582916
$901$			380736.i			0.469002i
$902$			315867.i			0.388232i
$903$		−	54822.7i		−	0.0672334i
$904$	636428.			0.778776
$905$		−	734721.i		−	0.897068i
$906$	−700468.			−0.853359
$907$	−635510.			−0.772517			−0.386259	−	0.922391i	$-0.626233\pi$
$907$	−635510.			−0.772517			−0.386259	+	0.922391i	$0.626233\pi$
$908$	3.49067e6			4.23386
$909$		−	29077.4i		−	0.0351907i
$910$	1.75501e6			2.11933
$911$	−954442.			−1.15004			−0.575020	−	0.818140i	$-0.695006\pi$
$911$	−954442.			−1.15004			−0.575020	+	0.818140i	$0.695006\pi$
$912$			2.09901e6i			2.52363i
$913$			237383.i			0.284780i
$914$		−	731136.i		−	0.875197i
$915$			234499.i			0.280091i
$916$		−	3.27914e6i		−	3.90813i
$917$			301456.i			0.358497i
$918$	147061.			0.174507
$919$		−	312119.i		−	0.369564i	−0.982780	−	0.184782i	$-0.940842\pi$
$919$		−	312119.i		−	0.369564i	0.982780	−	0.184782i	$-0.0591579\pi$
$920$	800997.			0.946358
$921$		−	324985.i		−	0.383128i
$922$			1.57914e6i			1.85763i
$923$		−	1.46103e6i		−	1.71497i
$924$			4.47675e6i			5.24348i
$925$	−522638.			−0.610826
$926$	−393703.			−0.459142
$927$	134533.			0.156556
$928$			134398.i			0.156062i
$929$			534195.i			0.618968i	0.950905	+	0.309484i	$0.100156\pi$
$929$			534195.i			0.618968i	−0.950905	+	0.309484i	$0.899844\pi$
$930$	−503024.			−0.581597
$931$	3.07140e6			3.54353
$932$		−	1.75191e6i		−	2.01688i
$933$	588270.			0.675792
$934$		−	707981.i		−	0.811573i
$935$	−447491.			−0.511871
$936$	921340.			1.05164
$937$			125629.i			0.143090i	0.997437	+	0.0715452i	$0.0227930\pi$
$937$			125629.i			0.143090i	−0.997437	+	0.0715452i	$0.977207\pi$
$938$	1.21095e6	−	2.86928e6i	1.37632	−	3.26113i
$939$	82393.1			0.0934457
$940$		−	1.23394e6i		−	1.39649i
$941$			1.56246e6i			1.76453i	0.470749	+	0.882267i	$0.343984\pi$
$941$			1.56246e6i			1.76453i	−0.470749	+	0.882267i	$0.656016\pi$
$942$	−1.17219e6			−1.32098
$943$		−	54002.5i		−	0.0607283i
$944$	−1.79841e6			−2.01811
$945$			182563.i			0.204432i
$946$			198339.i			0.221628i
$947$	1.35649e6			1.51257			0.756286	−	0.654242i	$-0.227012\pi$
$947$	1.35649e6			1.51257			0.756286	+	0.654242i	$0.227012\pi$
$948$	−1.26548e6			−1.40812
$949$			1.01940e6i			1.13191i
$950$			1.64102e6i			1.81831i
$951$		−	143880.i		−	0.159089i
$952$	2.43070e6			2.68199
$953$	1.58574e6			1.74601			0.873003	−	0.487715i	$-0.162170\pi$
$953$	1.58574e6			1.74601			0.873003	+	0.487715i	$0.162170\pi$
$954$	−561953.			−0.617452
$955$	−473882.			−0.519593
$956$			843778.i			0.923236i
$957$	−54659.6			−0.0596819
$958$		−	2.18737e6i		−	2.38337i
$959$	691925.			0.752353
$960$	−692682.			−0.751608
$961$	112215.			0.121508
$962$	−1.66475e6			−1.79887
$963$	−11914.0			−0.0128471
$964$	967665.			1.04129
$965$		−	263545.i		−	0.283009i
$966$		−	1.06188e6i		−	1.13794i
$967$	45149.3			0.0482834			0.0241417	−	0.999709i	$-0.492315\pi$
$967$	45149.3			0.0482834			0.0241417	+	0.999709i	$0.492315\pi$
$968$		−	7.11765e6i		−	7.59602i
$969$			368400.i			0.392349i
$970$			764796.i			0.812834i
$971$	−510387.			−0.541329			−0.270664	−	0.962674i	$-0.587243\pi$
$971$	−510387.			−0.541329			−0.270664	+	0.962674i	$0.587243\pi$
$972$			156449.i			0.165593i
$973$	−2.88183e6			−3.04399
$974$	−189852.			−0.200123
$975$	391991.			0.412351
$976$			2.50779e6i			2.63264i
$977$	−513720.			−0.538193			−0.269096	−	0.963113i	$-0.586725\pi$
$977$	−513720.			−0.538193			−0.269096	+	0.963113i	$0.586725\pi$
$978$	−531238.			−0.555407
$979$			2.11205e6i			2.20363i
$980$			3.51774e6i			3.66278i
$981$		−	424197.i		−	0.440787i
$982$		−	2.45315e6i		−	2.54391i
$983$			196304.i			0.203153i	0.994828	+	0.101576i	$0.0323886\pi$
$983$			196304.i			0.203153i	−0.994828	+	0.101576i	$0.967611\pi$
$984$			182452.i			0.188433i
$985$	−388614.			−0.400540
$986$			48445.7i			0.0498312i
$987$	−1.00211e6			−1.02869
$988$			3.76758e6i			3.85966i
$989$		−	33909.2i		−	0.0346676i
$990$		−	660480.i		−	0.673891i
$991$		−	1.24245e6i		−	1.26512i	−0.774513	−	0.632559i	$-0.782005\pi$
$991$		−	1.24245e6i		−	1.26512i	0.774513	−	0.632559i	$-0.217995\pi$
$992$	−2.61928e6			−2.66170
$993$	363629.			0.368774
$994$	5.68914e6			5.75802
$995$			926577.i			0.935913i
$996$			223828.i			0.225629i
$997$	702244.			0.706477			0.353238	−	0.935533i	$-0.385080\pi$
$997$	702244.			0.706477			0.353238	+	0.935533i	$0.385080\pi$
$998$	−784656.			−0.787804
$999$		−	173174.i		−	0.173521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.3	✓	46
67.66	odd	2	inner	201.5.b.a.133.44	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.3	✓	46	1.1	even	1	trivial
201.5.b.a.133.44	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)

\(f(q)\)	\(=\)	\(q-7.56976i q^{2} -5.19615i q^{3} -41.3013 q^{4} +14.1982i q^{5} -39.3336 q^{6} -91.6507i q^{7} +191.525i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-7.56976i q^{2} -5.19615i q^{3} -41.3013 q^{4} +14.1982i q^{5} -39.3336 q^{6} -91.6507i q^{7} +191.525i q^{8} -27.0000 q^{9} +107.477 q^{10} +227.605i q^{11} +214.608i q^{12} +178.168i q^{13} -693.774 q^{14} +73.7758 q^{15} +788.977 q^{16} +138.475 q^{17} +204.384i q^{18} -511.998 q^{19} -586.402i q^{20} -476.231 q^{21} +1722.92 q^{22} -294.560 q^{23} +995.193 q^{24} +423.412 q^{25} +1348.69 q^{26} +140.296i q^{27} +3785.29i q^{28} -46.2171 q^{29} -558.465i q^{30} -900.725i q^{31} -2907.97i q^{32} +1182.67 q^{33} -1048.22i q^{34} +1301.27 q^{35} +1115.14 q^{36} -1234.35 q^{37} +3875.70i q^{38} +925.790 q^{39} -2719.30 q^{40} +183.333i q^{41} +3604.95i q^{42} +115.118i q^{43} -9400.39i q^{44} -383.350i q^{45} +2229.75i q^{46} +2104.26 q^{47} -4099.65i q^{48} -5998.84 q^{49} -3205.13i q^{50} -719.535i q^{51} -7358.59i q^{52} +2749.50i q^{53} +1062.01 q^{54} -3231.57 q^{55} +17553.4 q^{56} +2660.42i q^{57} +349.853i q^{58} -2279.42 q^{59} -3047.04 q^{60} +3178.54i q^{61} -6818.27 q^{62} +2474.57i q^{63} -9389.02 q^{64} -2529.66 q^{65} -8952.53i q^{66} +(-1745.45 + 4135.76i) q^{67} -5719.18 q^{68} +1530.58i q^{69} -9850.31i q^{70} -8200.28 q^{71} -5171.17i q^{72} +5721.56 q^{73} +9343.71i q^{74} -2200.12i q^{75} +21146.2 q^{76} +20860.2 q^{77} -7008.01i q^{78} +5896.73i q^{79} +11202.0i q^{80} +729.000 q^{81} +1387.79 q^{82} +1042.96 q^{83} +19669.0 q^{84} +1966.08i q^{85} +871.416 q^{86} +240.151i q^{87} -43592.0 q^{88} +9279.43 q^{89} -2901.87 q^{90} +16329.3 q^{91} +12165.7 q^{92} -4680.30 q^{93} -15928.7i q^{94} -7269.43i q^{95} -15110.3 q^{96} +7115.92i q^{97} +45409.8i q^{98} -6145.34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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