LMFDB - Embedded newform 1050.3.f.a.601.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(601,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.601");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.f (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.4
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.a.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -1.75736 q^{11} +3.46410i q^{12} -18.7554i q^{13} +(-8.82843 + 4.47871i) q^{14} +4.00000 q^{16} -23.4803i q^{17} -4.24264 q^{18} -23.0600i q^{19} +(-5.48528 - 10.8126i) q^{21} -2.48528 q^{22} -18.7279 q^{23} +4.89898i q^{24} -26.5241i q^{26} -5.19615i q^{27} +(-12.4853 + 6.33386i) q^{28} +30.0000 q^{29} +8.60927i q^{31} +5.65685 q^{32} -3.04384i q^{33} -33.2061i q^{34} -6.00000 q^{36} +70.9117 q^{37} -32.6118i q^{38} +32.4853 q^{39} +41.3951i q^{41} +(-7.75736 - 15.2913i) q^{42} -10.4264 q^{43} -3.51472 q^{44} -26.4853 q^{46} -38.6995i q^{47} +6.92820i q^{48} +(28.9411 - 39.5400i) q^{49} +40.6690 q^{51} -37.5108i q^{52} +37.0294 q^{53} -7.34847i q^{54} +(-17.6569 + 8.95743i) q^{56} +39.9411 q^{57} +42.4264 q^{58} -97.4872i q^{59} +16.7262i q^{61} +12.1753i q^{62} +(18.7279 - 9.50079i) q^{63} +8.00000 q^{64} -4.30463i q^{66} -60.9706 q^{67} -46.9606i q^{68} -32.4377i q^{69} -110.610 q^{71} -8.48528 q^{72} +56.7585i q^{73} +100.284 q^{74} -46.1200i q^{76} +(10.9706 - 5.56543i) q^{77} +45.9411 q^{78} -69.8234 q^{79} +9.00000 q^{81} +58.5416i q^{82} -6.43583i q^{83} +(-10.9706 - 21.6251i) q^{84} -14.7452 q^{86} +51.9615i q^{87} -4.97056 q^{88} -42.0915i q^{89} +(59.3970 + 117.083i) q^{91} -37.4558 q^{92} -14.9117 q^{93} -54.7293i q^{94} +9.79796i q^{96} -51.7153i q^{97} +(40.9289 - 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 8 q^{7} - 12 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 8 * q^7 - 12 * q^9	$ 4 q + 8 q^{4} - 8 q^{7} - 12 q^{9} - 24 q^{11} - 24 q^{14} + 16 q^{16} + 12 q^{21} + 24 q^{22} - 24 q^{23} - 16 q^{28} + 120 q^{29} - 24 q^{36} + 80 q^{37} + 96 q^{39} - 48 q^{42} + 128 q^{43} - 48 q^{44} - 72 q^{46} - 20 q^{49} - 24 q^{51} + 216 q^{53} - 48 q^{56} + 24 q^{57} + 24 q^{63} + 32 q^{64} - 176 q^{67} - 120 q^{71} + 288 q^{74} - 24 q^{77} + 48 q^{78} + 128 q^{79} + 36 q^{81} + 24 q^{84} - 240 q^{86} + 48 q^{88} - 48 q^{92} + 144 q^{93} + 192 q^{98} + 72 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 + 16 * q^16 + 12 * q^21 + 24 * q^22 - 24 * q^23 - 16 * q^28 + 120 * q^29 - 24 * q^36 + 80 * q^37 + 96 * q^39 - 48 * q^42 + 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 - 24 * q^51 + 216 * q^53 - 48 * q^56 + 24 * q^57 + 24 * q^63 + 32 * q^64 - 176 * q^67 - 120 * q^71 + 288 * q^74 - 24 * q^77 + 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 - 240 * q^86 + 48 * q^88 - 48 * q^92 + 144 * q^93 + 192 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.24264	+	3.16693i	−0.891806	+	0.452418i
$7$	−6.24264	+	3.16693i	−0.891806	+	0.452418i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−1.75736			−0.159760			−0.0798800	−	0.996804i	$-0.525454\pi$
$11$	−1.75736			−0.159760			−0.0798800	+	0.996804i	$0.525454\pi$
$12$			3.46410i			0.288675i
$13$		−	18.7554i		−	1.44272i	−0.692559	−	0.721361i	$-0.743517\pi$
$13$		−	18.7554i		−	1.44272i	0.692559	−	0.721361i	$-0.256483\pi$
$14$	−8.82843	+	4.47871i	−0.630602	+	0.319908i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	23.4803i		−	1.38119i	−0.723240	−	0.690597i	$-0.757348\pi$
$17$		−	23.4803i		−	1.38119i	0.723240	−	0.690597i	$-0.242652\pi$
$18$	−4.24264			−0.235702
$19$		−	23.0600i		−	1.21369i	−0.794822	−	0.606843i	$-0.792436\pi$
$19$		−	23.0600i		−	1.21369i	0.794822	−	0.606843i	$-0.207564\pi$
$20$		0			0
$21$	−5.48528	−	10.8126i	−0.261204	−	0.514884i
$22$	−2.48528			−0.112967
$23$	−18.7279			−0.814257			−0.407129	−	0.913371i	$-0.633470\pi$
$23$	−18.7279			−0.814257			−0.407129	+	0.913371i	$0.633470\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$		−	26.5241i		−	1.02016i
$27$		−	5.19615i		−	0.192450i
$28$	−12.4853	+	6.33386i	−0.445903	+	0.226209i
$29$	30.0000			1.03448			0.517241	−	0.855840i	$-0.326959\pi$
$29$	30.0000			1.03448			0.517241	+	0.855840i	$0.326959\pi$
$30$		0			0
$31$			8.60927i			0.277718i	0.990312	+	0.138859i	$0.0443435\pi$
$31$			8.60927i			0.277718i	−0.990312	+	0.138859i	$0.955656\pi$
$32$	5.65685			0.176777
$33$		−	3.04384i		−	0.0922374i
$34$		−	33.2061i		−	0.976651i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	70.9117			1.91653			0.958266	−	0.285878i	$-0.0922852\pi$
$37$	70.9117			1.91653			0.958266	+	0.285878i	$0.0922852\pi$
$38$		−	32.6118i		−	0.858205i
$39$	32.4853			0.832956
$40$		0			0
$41$			41.3951i			1.00964i	0.863225	+	0.504819i	$0.168441\pi$
$41$			41.3951i			1.00964i	−0.863225	+	0.504819i	$0.831559\pi$
$42$	−7.75736	−	15.2913i	−0.184699	−	0.364078i
$43$	−10.4264			−0.242475			−0.121237	−	0.992624i	$-0.538686\pi$
$43$	−10.4264			−0.242475			−0.121237	+	0.992624i	$0.538686\pi$
$44$	−3.51472			−0.0798800
$45$		0			0
$46$	−26.4853			−0.575767
$47$		−	38.6995i		−	0.823393i	−0.911321	−	0.411696i	$-0.864936\pi$
$47$		−	38.6995i		−	0.823393i	0.911321	−	0.411696i	$-0.135064\pi$
$48$			6.92820i			0.144338i
$49$	28.9411	−	39.5400i	0.590635	−	0.806939i
$50$		0			0
$51$	40.6690			0.797432
$52$		−	37.5108i		−	0.721361i
$53$	37.0294			0.698669			0.349334	−	0.936998i	$-0.386408\pi$
$53$	37.0294			0.698669			0.349334	+	0.936998i	$0.386408\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−17.6569	+	8.95743i	−0.315301	+	0.159954i
$57$	39.9411			0.700721
$58$	42.4264			0.731490
$59$		−	97.4872i		−	1.65233i	−0.563431	−	0.826163i	$-0.690519\pi$
$59$		−	97.4872i		−	1.65233i	0.563431	−	0.826163i	$-0.309481\pi$
$60$		0			0
$61$			16.7262i			0.274199i	0.990557	+	0.137100i	$0.0437781\pi$
$61$			16.7262i			0.274199i	−0.990557	+	0.137100i	$0.956222\pi$
$62$			12.1753i			0.196376i
$63$	18.7279	−	9.50079i	0.297269	−	0.150806i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	4.30463i		−	0.0652217i
$67$	−60.9706			−0.910008			−0.455004	−	0.890489i	$-0.650362\pi$
$67$	−60.9706			−0.910008			−0.455004	+	0.890489i	$0.650362\pi$
$68$		−	46.9606i		−	0.690597i
$69$		−	32.4377i		−	0.470112i
$70$		0			0
$71$	−110.610			−1.55789			−0.778945	−	0.627092i	$-0.784245\pi$
$71$	−110.610			−1.55789			−0.778945	+	0.627092i	$0.784245\pi$
$72$	−8.48528			−0.117851
$73$			56.7585i			0.777514i	0.921340	+	0.388757i	$0.127095\pi$
$73$			56.7585i			0.777514i	−0.921340	+	0.388757i	$0.872905\pi$
$74$	100.284			1.35519
$75$		0			0
$76$		−	46.1200i		−	0.606843i
$77$	10.9706	−	5.56543i	0.142475	−	0.0722783i
$78$	45.9411			0.588989
$79$	−69.8234			−0.883840			−0.441920	−	0.897054i	$-0.645703\pi$
$79$	−69.8234			−0.883840			−0.441920	+	0.897054i	$0.645703\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			58.5416i			0.713922i
$83$		−	6.43583i		−	0.0775401i	−0.999248	−	0.0387701i	$-0.987656\pi$
$83$		−	6.43583i		−	0.0775401i	0.999248	−	0.0387701i	$-0.0123440\pi$
$84$	−10.9706	−	21.6251i	−0.130602	−	0.257442i
$85$		0			0
$86$	−14.7452			−0.171455
$87$			51.9615i			0.597259i
$88$	−4.97056			−0.0564837
$89$		−	42.0915i		−	0.472938i	−0.971639	−	0.236469i	$-0.924010\pi$
$89$		−	42.0915i		−	0.472938i	0.971639	−	0.236469i	$-0.0759901\pi$
$90$		0			0
$91$	59.3970	+	117.083i	0.652714	+	1.28663i
$92$	−37.4558			−0.407129
$93$	−14.9117			−0.160341
$94$		−	54.7293i		−	0.582227i
$95$		0			0
$96$			9.79796i			0.102062i
$97$		−	51.7153i		−	0.533148i	−0.963814	−	0.266574i	$-0.914108\pi$
$97$		−	51.7153i		−	0.533148i	0.963814	−	0.266574i	$-0.0858916\pi$
$98$	40.9289	−	55.9180i	0.417642	−	0.570592i
$99$	5.27208			0.0532533
$100$		0			0
$101$			6.60991i			0.0654447i	0.999464	+	0.0327223i	$0.0104177\pi$
$101$			6.60991i			0.0654447i	−0.999464	+	0.0327223i	$0.989582\pi$
$102$	57.5147			0.563870
$103$		−	175.871i		−	1.70748i	−0.520696	−	0.853742i	$-0.674327\pi$
$103$		−	175.871i		−	1.70748i	0.520696	−	0.853742i	$-0.325673\pi$
$104$		−	53.0482i		−	0.510079i
$105$		0			0
$106$	52.3675			0.494033
$107$	46.2426			0.432174			0.216087	−	0.976374i	$-0.430670\pi$
$107$	46.2426			0.432174			0.216087	+	0.976374i	$0.430670\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−35.9411			−0.329735			−0.164868	−	0.986316i	$-0.552720\pi$
$109$	−35.9411			−0.329735			−0.164868	+	0.986316i	$0.552720\pi$
$110$		0			0
$111$			122.823i			1.10651i
$112$	−24.9706	+	12.6677i	−0.222951	+	0.113105i
$113$	73.0294			0.646278			0.323139	−	0.946351i	$-0.395262\pi$
$113$	73.0294			0.646278			0.323139	+	0.946351i	$0.395262\pi$
$114$	56.4853			0.495485
$115$		0			0
$116$	60.0000			0.517241
$117$			56.2662i			0.480907i
$118$		−	137.868i		−	1.16837i
$119$	74.3604	+	146.579i	0.624877	+	1.23176i
$120$		0			0
$121$	−117.912			−0.974477
$122$			23.6544i			0.193888i
$123$	−71.6985			−0.582915
$124$			17.2185i			0.138859i
$125$		0			0
$126$	26.4853	−	13.4361i	0.210201	−	0.106636i
$127$	−89.9411			−0.708198			−0.354099	−	0.935208i	$-0.615212\pi$
$127$	−89.9411			−0.708198			−0.354099	+	0.935208i	$0.615212\pi$
$128$	11.3137			0.0883883
$129$		−	18.0591i		−	0.139993i
$130$		0			0
$131$			12.1753i			0.0929415i	0.998920	+	0.0464708i	$0.0147974\pi$
$131$			12.1753i			0.0929415i	−0.998920	+	0.0464708i	$0.985203\pi$
$132$		−	6.08767i		−	0.0461187i
$133$	73.0294	+	143.955i	0.549094	+	1.08237i
$134$	−86.2254			−0.643473
$135$		0			0
$136$		−	66.4123i		−	0.488326i
$137$	−165.765			−1.20996			−0.604980	−	0.796241i	$-0.706819\pi$
$137$	−165.765			−1.20996			−0.604980	+	0.796241i	$0.706819\pi$
$138$		−	45.8739i		−	0.332419i
$139$		−	220.514i		−	1.58643i	−0.608941	−	0.793215i	$-0.708406\pi$
$139$		−	220.514i		−	1.58643i	0.608941	−	0.793215i	$-0.291594\pi$
$140$		0			0
$141$	67.0294			0.475386
$142$	−156.426			−1.10159
$143$			32.9600i			0.230489i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$			80.2687i			0.549786i
$147$	68.4853	+	50.1275i	0.465886	+	0.341003i
$148$	141.823			0.958266
$149$	210.853			1.41512			0.707560	−	0.706653i	$-0.249796\pi$
$149$	210.853			1.41512			0.707560	+	0.706653i	$0.249796\pi$
$150$		0			0
$151$	−72.3675			−0.479255			−0.239628	−	0.970865i	$-0.577025\pi$
$151$	−72.3675			−0.479255			−0.239628	+	0.970865i	$0.577025\pi$
$152$		−	65.2236i		−	0.429103i
$153$			70.4409i			0.460398i
$154$	15.5147	−	7.87071i	0.100745	−	0.0511085i
$155$		0			0
$156$	64.9706			0.416478
$157$		−	233.674i		−	1.48837i	−0.667974	−	0.744184i	$-0.732838\pi$
$157$		−	233.674i		−	1.48837i	0.667974	−	0.744184i	$-0.267162\pi$
$158$	−98.7452			−0.624969
$159$			64.1369i			0.403377i
$160$		0			0
$161$	116.912	−	59.3100i	0.726160	−	0.368385i
$162$	12.7279			0.0785674
$163$	73.0883			0.448395			0.224197	−	0.974544i	$-0.428024\pi$
$163$	73.0883			0.448395			0.224197	+	0.974544i	$0.428024\pi$
$164$			82.7903i			0.504819i
$165$		0			0
$166$		−	9.10164i		−	0.0548292i
$167$			39.3958i			0.235903i	0.993019	+	0.117951i	$0.0376327\pi$
$167$			39.3958i			0.235903i	−0.993019	+	0.117951i	$0.962367\pi$
$168$	−15.5147	−	30.5826i	−0.0923495	−	0.182039i
$169$	−182.765			−1.08145
$170$		0			0
$171$			69.1801i			0.404562i
$172$	−20.8528			−0.121237
$173$		−	23.8284i		−	0.137737i	−0.997626	−	0.0688683i	$-0.978061\pi$
$173$		−	23.8284i		−	0.137737i	0.997626	−	0.0688683i	$-0.0219388\pi$
$174$			73.4847i			0.422326i
$175$		0			0
$176$	−7.02944			−0.0399400
$177$	168.853			0.953971
$178$		−	59.5263i		−	0.334417i
$179$	−12.9045			−0.0720924			−0.0360462	−	0.999350i	$-0.511476\pi$
$179$	−12.9045			−0.0720924			−0.0360462	+	0.999350i	$0.511476\pi$
$180$		0			0
$181$			65.3678i			0.361148i	0.983561	+	0.180574i	$0.0577955\pi$
$181$			65.3678i			0.361148i	−0.983561	+	0.180574i	$0.942204\pi$
$182$	84.0000	+	165.581i	0.461538	+	0.909783i
$183$	−28.9706			−0.158309
$184$	−52.9706			−0.287883
$185$		0			0
$186$	−21.0883			−0.113378
$187$			41.2633i			0.220659i
$188$		−	77.3989i		−	0.411696i
$189$	16.4558	+	32.4377i	0.0870680	+	0.171628i
$190$		0			0
$191$	−100.066			−0.523906			−0.261953	−	0.965081i	$-0.584367\pi$
$191$	−100.066			−0.523906			−0.261953	+	0.965081i	$0.584367\pi$
$192$			13.8564i			0.0721688i
$193$	−78.9117			−0.408869			−0.204434	−	0.978880i	$-0.565536\pi$
$193$	−78.9117			−0.408869			−0.204434	+	0.978880i	$0.565536\pi$
$194$		−	73.1365i		−	0.376992i
$195$		0			0
$196$	57.8823	−	79.0800i	0.295318	−	0.403469i
$197$	183.941			0.933711			0.466856	−	0.884334i	$-0.345387\pi$
$197$	183.941			0.933711			0.466856	+	0.884334i	$0.345387\pi$
$198$	7.45584			0.0376558
$199$			170.029i			0.854419i	0.904153	+	0.427210i	$0.140503\pi$
$199$			170.029i			0.854419i	−0.904153	+	0.427210i	$0.859497\pi$
$200$		0			0
$201$		−	105.604i		−	0.525394i
$202$			9.34783i			0.0462764i
$203$	−187.279	+	95.0079i	−0.922558	+	0.468019i
$204$	81.3381			0.398716
$205$		0			0
$206$		−	248.719i		−	1.20737i
$207$	56.1838			0.271419
$208$		−	75.0215i		−	0.360680i
$209$			40.5247i			0.193898i
$210$		0			0
$211$	21.5736			0.102245			0.0511223	−	0.998692i	$-0.483720\pi$
$211$	21.5736			0.102245			0.0511223	+	0.998692i	$0.483720\pi$
$212$	74.0589			0.349334
$213$		−	191.582i		−	0.899448i
$214$	65.3970			0.305593
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−27.2649	−	53.7446i	−0.125645	−	0.247671i
$218$	−50.8284			−0.233158
$219$	−98.3087			−0.448898
$220$		0			0
$221$	−440.382			−1.99268
$222$			173.697i			0.782421i
$223$			119.359i			0.535240i	0.963525	+	0.267620i	$0.0862372\pi$
$223$			119.359i			0.535240i	−0.963525	+	0.267620i	$0.913763\pi$
$224$	−35.3137	+	17.9149i	−0.157650	+	0.0799770i
$225$		0			0
$226$	103.279			0.456988
$227$			169.843i			0.748207i	0.927387	+	0.374103i	$0.122049\pi$
$227$			169.843i			0.748207i	−0.927387	+	0.374103i	$0.877951\pi$
$228$	79.8823			0.350361
$229$		−	110.011i		−	0.480396i	−0.970724	−	0.240198i	$-0.922788\pi$
$229$		−	110.011i		−	0.480396i	0.970724	−	0.240198i	$-0.0772124\pi$
$230$		0			0
$231$	9.63961	+	19.0016i	0.0417299	+	0.0822579i
$232$	84.8528			0.365745
$233$	−57.2649			−0.245772			−0.122886	−	0.992421i	$-0.539215\pi$
$233$	−57.2649			−0.245772			−0.122886	+	0.992421i	$0.539215\pi$
$234$			79.5724i			0.340053i
$235$		0			0
$236$		−	194.974i		−	0.826163i
$237$		−	120.938i		−	0.510285i
$238$	105.161	+	207.294i	0.441855	+	0.870983i
$239$	281.522			1.17792			0.588958	−	0.808164i	$-0.299538\pi$
$239$	281.522			1.17792			0.588958	+	0.808164i	$0.299538\pi$
$240$		0			0
$241$			168.306i			0.698366i	0.937055	+	0.349183i	$0.113541\pi$
$241$			168.306i			0.698366i	−0.937055	+	0.349183i	$0.886459\pi$
$242$	−166.752			−0.689059
$243$			15.5885i			0.0641500i
$244$			33.4523i			0.137100i
$245$		0			0
$246$	−101.397			−0.412183
$247$	−432.500			−1.75101
$248$			24.3507i			0.0981882i
$249$	11.1472			0.0447678
$250$		0			0
$251$			106.096i			0.422695i	0.977411	+	0.211348i	$0.0677852\pi$
$251$			106.096i			0.422695i	−0.977411	+	0.211348i	$0.932215\pi$
$252$	37.4558	−	19.0016i	0.148634	−	0.0754031i
$253$	32.9117			0.130086
$254$	−127.196			−0.500771
$255$		0			0
$256$	16.0000			0.0625000
$257$			290.462i			1.13020i	0.825021	+	0.565102i	$0.191163\pi$
$257$			290.462i			1.13020i	−0.825021	+	0.565102i	$0.808837\pi$
$258$		−	25.5394i		−	0.0989898i
$259$	−442.676	+	224.572i	−1.70917	+	0.867074i
$260$		0			0
$261$	−90.0000			−0.344828
$262$			17.2185i			0.0657196i
$263$	89.0223			0.338488			0.169244	−	0.985574i	$-0.445867\pi$
$263$	89.0223			0.338488			0.169244	+	0.985574i	$0.445867\pi$
$264$		−	8.60927i		−	0.0326109i
$265$		0			0
$266$	103.279	+	203.584i	0.388268	+	0.765352i
$267$	72.9045			0.273051
$268$	−121.941			−0.455004
$269$			191.498i			0.711888i	0.934507	+	0.355944i	$0.115841\pi$
$269$			191.498i			0.711888i	−0.934507	+	0.355944i	$0.884159\pi$
$270$		0			0
$271$		−	217.440i		−	0.802362i	−0.915999	−	0.401181i	$-0.868600\pi$
$271$		−	217.440i		−	0.802362i	0.915999	−	0.401181i	$-0.131400\pi$
$272$		−	93.9211i		−	0.345298i
$273$	−202.794	+	102.879i	−0.742835	+	0.376845i
$274$	−234.426			−0.855571
$275$		0			0
$276$		−	64.8754i		−	0.235056i
$277$	−290.676			−1.04937			−0.524686	−	0.851296i	$-0.675817\pi$
$277$	−290.676			−1.04937			−0.524686	+	0.851296i	$0.675817\pi$
$278$		−	311.854i		−	1.12178i
$279$		−	25.8278i		−	0.0925728i
$280$		0			0
$281$	18.8528			0.0670919			0.0335459	−	0.999437i	$-0.489320\pi$
$281$	18.8528			0.0670919			0.0335459	+	0.999437i	$0.489320\pi$
$282$	94.7939			0.336149
$283$			401.734i			1.41955i	0.704426	+	0.709777i	$0.251204\pi$
$283$			401.734i			1.41955i	−0.704426	+	0.709777i	$0.748796\pi$
$284$	−221.220			−0.778945
$285$		0			0
$286$			46.6124i			0.162980i
$287$	−131.095	−	258.415i	−0.456779	−	0.900401i
$288$	−16.9706			−0.0589256
$289$	−262.324			−0.907695
$290$		0			0
$291$	89.5736			0.307813
$292$			113.517i			0.388757i
$293$			280.893i			0.958679i	0.877629	+	0.479340i	$0.159124\pi$
$293$			280.893i			0.958679i	−0.877629	+	0.479340i	$0.840876\pi$
$294$	96.8528	+	70.8910i	0.329431	+	0.241126i
$295$		0			0
$296$	200.569			0.677596
$297$			9.13151i			0.0307458i
$298$	298.191			1.00064
$299$			351.249i			1.17475i
$300$		0			0
$301$	65.0883	−	33.0197i	0.216240	−	0.109700i
$302$	−102.343			−0.338885
$303$	−11.4487			−0.0377845
$304$		−	92.2401i		−	0.303421i
$305$		0			0
$306$			99.6184i			0.325550i
$307$		−	152.318i		−	0.496151i	−0.968741	−	0.248076i	$-0.920202\pi$
$307$		−	152.318i		−	0.496151i	0.968741	−	0.248076i	$-0.0797982\pi$
$308$	21.9411	−	11.1309i	0.0712374	−	0.0361392i
$309$	304.617			0.985817
$310$		0			0
$311$		−	283.156i		−	0.910470i	−0.890371	−	0.455235i	$-0.849555\pi$
$311$		−	283.156i		−	0.910470i	0.890371	−	0.455235i	$-0.150445\pi$
$312$	91.8823			0.294494
$313$		−	48.5819i		−	0.155214i	−0.996984	−	0.0776069i	$-0.975272\pi$
$313$		−	48.5819i		−	0.155214i	0.996984	−	0.0776069i	$-0.0247279\pi$
$314$		−	330.465i		−	1.05244i
$315$		0			0
$316$	−139.647			−0.441920
$317$	578.029			1.82343			0.911717	−	0.410819i	$-0.134757\pi$
$317$	578.029			1.82343			0.911717	+	0.410819i	$0.134757\pi$
$318$			90.7032i			0.285230i
$319$	−52.7208			−0.165269
$320$		0			0
$321$			80.0946i			0.249516i
$322$	165.338	−	83.8770i	0.513472	−	0.260488i
$323$	−541.456			−1.67633
$324$	18.0000			0.0555556
$325$		0			0
$326$	103.362			0.317063
$327$		−	62.2519i		−	0.190373i
$328$			117.083i			0.356961i
$329$	122.558	+	241.587i	0.372518	+	0.734307i
$330$		0			0
$331$	332.368			1.00413			0.502066	−	0.864829i	$-0.332574\pi$
$331$	332.368			1.00413			0.502066	+	0.864829i	$0.332574\pi$
$332$		−	12.8717i		−	0.0387701i
$333$	−212.735			−0.638844
$334$			55.7141i			0.166809i
$335$		0			0
$336$	−21.9411	−	43.2503i	−0.0653010	−	0.128721i
$337$	−88.1766			−0.261652			−0.130826	−	0.991405i	$-0.541763\pi$
$337$	−88.1766			−0.261652			−0.130826	+	0.991405i	$0.541763\pi$
$338$	−258.468			−0.764698
$339$			126.491i			0.373129i
$340$		0			0
$341$		−	15.1296i		−	0.0443683i
$342$			97.8354i			0.286068i
$343$	−55.4487	+	338.488i	−0.161658	+	0.986847i
$344$	−29.4903			−0.0857277
$345$		0			0
$346$		−	33.6985i		−	0.0973945i
$347$	320.080			0.922422			0.461211	−	0.887291i	$-0.347415\pi$
$347$	320.080			0.922422			0.461211	+	0.887291i	$0.347415\pi$
$348$			103.923i			0.298629i
$349$		−	333.046i		−	0.954287i	−0.878825	−	0.477143i	$-0.841672\pi$
$349$		−	333.046i		−	0.954287i	0.878825	−	0.477143i	$-0.158328\pi$
$350$		0			0
$351$	−97.4558			−0.277652
$352$	−9.94113			−0.0282418
$353$			655.712i			1.85754i	0.370654	+	0.928771i	$0.379134\pi$
$353$			655.712i			1.85754i	−0.370654	+	0.928771i	$0.620866\pi$
$354$	238.794			0.674559
$355$		0			0
$356$		−	84.1829i		−	0.236469i
$357$	−253.882	+	128.796i	−0.711155	+	0.360773i
$358$	−18.2498			−0.0509770
$359$	−97.7574			−0.272305			−0.136152	−	0.990688i	$-0.543474\pi$
$359$	−97.7574			−0.272305			−0.136152	+	0.990688i	$0.543474\pi$
$360$		0			0
$361$	−170.765			−0.473032
$362$			92.4440i			0.255370i
$363$		−	204.229i		−	0.562614i
$364$	118.794	+	234.166i	0.326357	+	0.643314i
$365$		0			0
$366$	−40.9706			−0.111941
$367$			321.057i			0.874815i	0.899263	+	0.437408i	$0.144103\pi$
$367$			321.057i			0.874815i	−0.899263	+	0.437408i	$0.855897\pi$
$368$	−74.9117			−0.203564
$369$		−	124.185i		−	0.336546i
$370$		0			0
$371$	−231.161	+	117.270i	−0.623077	+	0.316091i
$372$	−29.8234			−0.0801704
$373$	−187.470			−0.502601			−0.251300	−	0.967909i	$-0.580858\pi$
$373$	−187.470			−0.502601			−0.251300	+	0.967909i	$0.580858\pi$
$374$			58.3551i			0.156030i
$375$		0			0
$376$		−	109.459i		−	0.291113i
$377$		−	562.662i		−	1.49247i
$378$	23.2721	+	45.8739i	0.0615663	+	0.121359i
$379$	−357.103			−0.942223			−0.471112	−	0.882074i	$-0.656147\pi$
$379$	−357.103			−0.942223			−0.471112	+	0.882074i	$0.656147\pi$
$380$		0			0
$381$		−	155.783i		−	0.408878i
$382$	−141.515			−0.370457
$383$		−	622.230i		−	1.62462i	−0.583225	−	0.812311i	$-0.698209\pi$
$383$		−	622.230i		−	1.62462i	0.583225	−	0.812311i	$-0.301791\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−111.598			−0.289114
$387$	31.2792			0.0808249
$388$		−	103.431i		−	0.266574i
$389$	227.470			0.584756			0.292378	−	0.956303i	$-0.405553\pi$
$389$	227.470			0.584756			0.292378	+	0.956303i	$0.405553\pi$
$390$		0			0
$391$			439.737i			1.12465i
$392$	81.8579	−	111.836i	0.208821	−	0.285296i
$393$	−21.0883			−0.0536598
$394$	260.132			0.660234
$395$		0			0
$396$	10.5442			0.0266267
$397$		−	720.329i		−	1.81443i	−0.420666	−	0.907216i	$-0.638204\pi$
$397$		−	720.329i		−	1.81443i	0.420666	−	0.907216i	$-0.361796\pi$
$398$			240.458i			0.604166i
$399$	−249.338	+	126.491i	−0.624908	+	0.317019i
$400$		0			0
$401$	697.176			1.73859			0.869296	−	0.494291i	$-0.164572\pi$
$401$	697.176			1.73859			0.869296	+	0.494291i	$0.164572\pi$
$402$		−	149.347i		−	0.371509i
$403$	161.470			0.400670
$404$			13.2198i			0.0327223i
$405$		0			0
$406$	−264.853	+	134.361i	−0.652347	+	0.330939i
$407$	−124.617			−0.306185
$408$	115.029			0.281935
$409$			102.386i			0.250333i	0.992136	+	0.125166i	$0.0399465\pi$
$409$			102.386i			0.250333i	−0.992136	+	0.125166i	$0.960053\pi$
$410$		0			0
$411$		−	287.113i		−	0.698571i
$412$		−	351.742i		−	0.853742i
$413$	308.735	+	608.578i	0.747543	+	1.47355i
$414$	79.4558			0.191922
$415$		0			0
$416$		−	106.096i		−	0.255040i
$417$	381.941			0.915926
$418$			57.3106i			0.137107i
$419$			391.426i			0.934191i	0.884207	+	0.467095i	$0.154700\pi$
$419$			391.426i			0.934191i	−0.884207	+	0.467095i	$0.845300\pi$
$420$		0			0
$421$	354.441			0.841902			0.420951	−	0.907083i	$-0.361696\pi$
$421$	354.441			0.841902			0.420951	+	0.907083i	$0.361696\pi$
$422$	30.5097			0.0722978
$423$			116.098i			0.274464i
$424$	104.735			0.247017
$425$		0			0
$426$		−	270.938i		−	0.636006i
$427$	−52.9706	−	104.415i	−0.124053	−	0.244533i
$428$	92.4853			0.216087
$429$	−57.0883			−0.133073
$430$		0			0
$431$	585.286			1.35797			0.678987	−	0.734151i	$-0.262419\pi$
$431$	585.286			1.35797			0.678987	+	0.734151i	$0.262419\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			392.207i			0.905789i	0.891564	+	0.452895i	$0.149609\pi$
$433$			392.207i			0.905789i	−0.891564	+	0.452895i	$0.850391\pi$
$434$	−38.5584	−	76.0063i	−0.0888443	−	0.175130i
$435$		0			0
$436$	−71.8823			−0.164868
$437$			431.866i			0.988252i
$438$	−139.029			−0.317419
$439$		−	392.513i		−	0.894106i	−0.894507	−	0.447053i	$-0.852473\pi$
$439$		−	392.513i		−	0.894106i	0.894507	−	0.447053i	$-0.147527\pi$
$440$		0			0
$441$	−86.8234	+	118.620i	−0.196878	+	0.268980i
$442$	−622.794			−1.40904
$443$	814.742			1.83915			0.919574	−	0.392918i	$-0.128534\pi$
$443$	814.742			1.83915			0.919574	+	0.392918i	$0.128534\pi$
$444$			245.645i			0.553255i
$445$		0			0
$446$			168.798i			0.378472i
$447$			365.208i			0.817020i
$448$	−49.9411	+	25.3354i	−0.111476	+	0.0565523i
$449$	180.323			0.401610			0.200805	−	0.979631i	$-0.435644\pi$
$449$	180.323			0.401610			0.200805	+	0.979631i	$0.435644\pi$
$450$		0			0
$451$		−	72.7461i		−	0.161300i
$452$	146.059			0.323139
$453$		−	125.344i		−	0.276698i
$454$			240.194i			0.529062i
$455$		0			0
$456$	112.971			0.247742
$457$	−280.177			−0.613078			−0.306539	−	0.951858i	$-0.599171\pi$
$457$	−280.177			−0.613078			−0.306539	+	0.951858i	$0.599171\pi$
$458$		−	155.579i		−	0.339691i
$459$	−122.007			−0.265811
$460$		0			0
$461$			406.297i			0.881338i	0.897670	+	0.440669i	$0.145259\pi$
$461$			406.297i			0.881338i	−0.897670	+	0.440669i	$0.854741\pi$
$462$	13.6325	+	26.8723i	0.0295075	+	0.0581651i
$463$	−457.470			−0.988056			−0.494028	−	0.869446i	$-0.664476\pi$
$463$	−457.470			−0.988056			−0.494028	+	0.869446i	$0.664476\pi$
$464$	120.000			0.258621
$465$		0			0
$466$	−80.9848			−0.173787
$467$			643.711i			1.37840i	0.724573	+	0.689198i	$0.242037\pi$
$467$			643.711i			1.37840i	−0.724573	+	0.689198i	$0.757963\pi$
$468$			112.532i			0.240454i
$469$	380.617	−	193.089i	0.811551	−	0.411705i
$470$		0			0
$471$	404.735			0.859310
$472$		−	275.735i		−	0.584185i
$473$	18.3229			0.0387377
$474$		−	171.032i		−	0.360826i
$475$		0			0
$476$	148.721	+	293.158i	0.312439	+	0.615878i
$477$	−111.088			−0.232890
$478$	398.132			0.832912
$479$			168.535i			0.351847i	0.984404	+	0.175924i	$0.0562912\pi$
$479$			168.535i			0.351847i	−0.984404	+	0.175924i	$0.943709\pi$
$480$		0			0
$481$		−	1329.98i		−	2.76502i
$482$			238.021i			0.493819i
$483$	102.728	+	202.497i	0.212687	+	0.419248i
$484$	−235.823			−0.487238
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	2.77965			0.00570771			0.00285385	−	0.999996i	$-0.499092\pi$
$487$	2.77965			0.00570771			0.00285385	+	0.999996i	$0.499092\pi$
$488$			47.3087i			0.0969441i
$489$			126.593i			0.258881i
$490$		0			0
$491$	−247.477			−0.504027			−0.252014	−	0.967724i	$-0.581093\pi$
$491$	−247.477			−0.504027			−0.252014	+	0.967724i	$0.581093\pi$
$492$	−143.397			−0.291457
$493$		−	704.409i		−	1.42882i
$494$	−611.647			−1.23815
$495$		0			0
$496$			34.4371i			0.0694296i
$497$	690.500	−	350.295i	1.38934	−	0.704818i
$498$	15.7645			0.0316556
$499$	−483.426			−0.968789			−0.484394	−	0.874850i	$-0.660960\pi$
$499$	−483.426			−0.968789			−0.484394	+	0.874850i	$0.660960\pi$
$500$		0			0
$501$	−68.2355			−0.136199
$502$			150.043i			0.298891i
$503$		−	58.7033i		−	0.116706i	−0.998296	−	0.0583532i	$-0.981415\pi$
$503$		−	58.7033i		−	0.116706i	0.998296	−	0.0583532i	$-0.0185849\pi$
$504$	52.9706	−	26.8723i	0.105100	−	0.0533180i
$505$		0			0
$506$	46.5442			0.0919845
$507$		−	316.557i		−	0.624374i
$508$	−179.882			−0.354099
$509$			68.8793i			0.135323i	0.997708	+	0.0676614i	$0.0215537\pi$
$509$			68.8793i			0.135323i	−0.997708	+	0.0676614i	$0.978446\pi$
$510$		0			0
$511$	−179.750	−	354.323i	−0.351762	−	0.693392i
$512$	22.6274			0.0441942
$513$	−119.823			−0.233574
$514$			410.776i			0.799175i
$515$		0			0
$516$		−	36.1181i		−	0.0699964i
$517$			68.0089i			0.131545i
$518$	−626.039	+	317.593i	−1.20857	+	0.613114i
$519$	41.2721			0.0795223
$520$		0			0
$521$			292.720i			0.561843i	0.959731	+	0.280922i	$0.0906401\pi$
$521$			292.720i			0.561843i	−0.959731	+	0.280922i	$0.909360\pi$
$522$	−127.279			−0.243830
$523$		−	493.056i		−	0.942746i	−0.881934	−	0.471373i	$-0.843759\pi$
$523$		−	493.056i		−	0.942746i	0.881934	−	0.471373i	$-0.156241\pi$
$524$			24.3507i			0.0464708i
$525$		0			0
$526$	125.897			0.239347
$527$	202.148			0.383583
$528$		−	12.1753i		−	0.0230594i
$529$	−178.265			−0.336985
$530$		0			0
$531$			292.462i			0.550775i
$532$	146.059	+	287.911i	0.274547	+	0.541186i
$533$	776.382			1.45663
$534$	103.103			0.193076
$535$		0			0
$536$	−172.451			−0.321737
$537$		−	22.3513i		−	0.0416226i
$538$			270.819i			0.503381i
$539$	−50.8600	+	69.4860i	−0.0943598	+	0.128916i
$540$		0			0
$541$	−1037.85			−1.91840			−0.959198	−	0.282736i	$-0.908758\pi$
$541$	−1037.85			−1.91840			−0.959198	+	0.282736i	$0.908758\pi$
$542$		−	307.507i		−	0.567356i
$543$	−113.220			−0.208509
$544$		−	132.825i		−	0.244163i
$545$		0			0
$546$	−286.794	+	145.492i	−0.525264	+	0.266469i
$547$	130.530			0.238629			0.119314	−	0.992857i	$-0.461930\pi$
$547$	130.530			0.238629			0.119314	+	0.992857i	$0.461930\pi$
$548$	−331.529			−0.604980
$549$		−	50.1785i		−	0.0913998i
$550$		0			0
$551$		−	691.801i		−	1.25554i
$552$		−	91.7477i		−	0.166210i
$553$	435.882	−	221.126i	0.788214	−	0.399866i
$554$	−411.078			−0.742018
$555$		0			0
$556$		−	441.028i		−	0.793215i
$557$	−665.147			−1.19416			−0.597080	−	0.802182i	$-0.703673\pi$
$557$	−665.147			−1.19416			−0.597080	+	0.802182i	$0.703673\pi$
$558$		−	36.5260i		−	0.0654588i
$559$			195.551i			0.349823i
$560$		0			0
$561$	−71.4701			−0.127398
$562$	26.6619			0.0474411
$563$		−	829.295i		−	1.47299i	−0.676441	−	0.736497i	$-0.736479\pi$
$563$		−	829.295i		−	1.47299i	0.676441	−	0.736497i	$-0.263521\pi$
$564$	134.059			0.237693
$565$		0			0
$566$			568.137i			1.00378i
$567$	−56.1838	+	28.5024i	−0.0990895	+	0.0502687i
$568$	−312.853			−0.550797
$569$	706.971			1.24248			0.621240	−	0.783621i	$-0.286629\pi$
$569$	706.971			1.24248			0.621240	+	0.783621i	$0.286629\pi$
$570$		0			0
$571$	−366.912			−0.642577			−0.321289	−	0.946981i	$-0.604116\pi$
$571$	−366.912			−0.642577			−0.321289	+	0.946981i	$0.604116\pi$
$572$			65.9199i			0.115245i
$573$		−	173.319i		−	0.302477i
$574$	−185.397	−	365.454i	−0.322991	−	0.636679i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$			390.357i			0.676528i	0.941051	+	0.338264i	$0.109840\pi$
$577$			390.357i			0.676528i	−0.941051	+	0.338264i	$0.890160\pi$
$578$	−370.982			−0.641837
$579$		−	136.679i		−	0.236061i
$580$		0			0
$581$	20.3818	+	40.1766i	0.0350806	+	0.0691507i
$582$	126.676			0.217657
$583$	−65.0740			−0.111619
$584$			160.537i			0.274893i
$585$		0			0
$586$			397.243i			0.677889i
$587$			702.499i			1.19676i	0.801212	+	0.598381i	$0.204189\pi$
$587$			702.499i			1.19676i	−0.801212	+	0.598381i	$0.795811\pi$
$588$	136.971	+	100.255i	0.232943	+	0.170502i
$589$	198.530			0.337063
$590$		0			0
$591$			318.595i			0.539078i
$592$	283.647			0.479133
$593$		−	942.519i		−	1.58941i	−0.606997	−	0.794704i	$-0.707626\pi$
$593$		−	942.519i		−	1.58941i	0.606997	−	0.794704i	$-0.292374\pi$
$594$			12.9139i			0.0217406i
$595$		0			0
$596$	421.706			0.707560
$597$	−294.500			−0.493299
$598$			496.742i			0.830672i
$599$	−952.109			−1.58950			−0.794749	−	0.606939i	$-0.792397\pi$
$599$	−952.109			−1.58950			−0.794749	+	0.606939i	$0.792397\pi$
$600$		0			0
$601$			729.804i			1.21432i	0.794581	+	0.607158i	$0.207690\pi$
$601$			729.804i			1.21432i	−0.794581	+	0.607158i	$0.792310\pi$
$602$	92.0488	−	46.6969i	0.152905	−	0.0775696i
$603$	182.912			0.303336
$604$	−144.735			−0.239628
$605$		0			0
$606$	−16.1909			−0.0267177
$607$			1006.34i			1.65789i	0.559332	+	0.828944i	$0.311058\pi$
$607$			1006.34i			1.65789i	−0.559332	+	0.828944i	$0.688942\pi$
$608$		−	130.447i		−	0.214551i
$609$	−164.558	−	324.377i	−0.270211	−	0.532639i
$610$		0			0
$611$	−725.823			−1.18793
$612$			140.882i			0.230199i
$613$	199.588			0.325592			0.162796	−	0.986660i	$-0.447949\pi$
$613$	199.588			0.325592			0.162796	+	0.986660i	$0.447949\pi$
$614$		−	215.411i		−	0.350832i
$615$		0			0
$616$	31.0294	−	15.7414i	0.0503725	−	0.0255542i
$617$	353.294			0.572599			0.286299	−	0.958140i	$-0.407575\pi$
$617$	353.294			0.572599			0.286299	+	0.958140i	$0.407575\pi$
$618$	430.794			0.697078
$619$		−	56.2064i		−	0.0908020i	−0.998969	−	0.0454010i	$-0.985543\pi$
$619$		−	56.2064i		−	0.0908020i	0.998969	−	0.0454010i	$-0.0144566\pi$
$620$		0			0
$621$			97.3131i			0.156704i
$622$		−	400.443i		−	0.643799i
$623$	133.301	+	262.762i	0.213966	+	0.421769i
$624$	129.941			0.208239
$625$		0			0
$626$		−	68.7052i		−	0.109753i
$627$	−70.1909			−0.111947
$628$		−	467.348i		−	0.744184i
$629$		−	1665.03i		−	2.64710i
$630$		0			0
$631$	807.322			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$631$	807.322			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$632$	−197.490			−0.312485
$633$			37.3666i			0.0590309i
$634$	817.456			1.28936
$635$		0			0
$636$			128.274i			0.201688i
$637$	−741.588	−	542.802i	−1.16419	−	0.852122i
$638$	−74.5584			−0.116863
$639$	331.831			0.519297
$640$		0			0
$641$	1016.35			1.58557			0.792786	−	0.609500i	$-0.208630\pi$
$641$	1016.35			1.58557			0.792786	+	0.609500i	$0.208630\pi$
$642$			113.271i			0.176434i
$643$			404.688i			0.629375i	0.949195	+	0.314687i	$0.101900\pi$
$643$			404.688i			0.629375i	−0.949195	+	0.314687i	$0.898100\pi$
$644$	233.823	−	118.620i	0.363080	−	0.184193i
$645$		0			0
$646$	−765.734			−1.18535
$647$			940.604i			1.45379i	0.686747	+	0.726896i	$0.259038\pi$
$647$			940.604i			1.45379i	−0.686747	+	0.726896i	$0.740962\pi$
$648$	25.4558			0.0392837
$649$			171.320i			0.263975i
$650$		0			0
$651$	93.0883	−	47.2243i	0.142993	−	0.0725411i
$652$	146.177			0.224197
$653$	−731.970			−1.12093			−0.560467	−	0.828177i	$-0.689378\pi$
$653$	−731.970			−1.12093			−0.560467	+	0.828177i	$0.689378\pi$
$654$		−	88.0374i		−	0.134614i
$655$		0			0
$656$			165.581i			0.252409i
$657$		−	170.276i		−	0.259171i
$658$	173.324	+	341.655i	0.263410	+	0.519233i
$659$	904.316			1.37225			0.686127	−	0.727481i	$-0.259309\pi$
$659$	904.316			1.37225			0.686127	+	0.727481i	$0.259309\pi$
$660$		0			0
$661$		−	335.881i		−	0.508141i	−0.967186	−	0.254070i	$-0.918231\pi$
$661$		−	335.881i		−	0.508141i	0.967186	−	0.254070i	$-0.0817695\pi$
$662$	470.039			0.710028
$663$		−	762.764i		−	1.15047i
$664$		−	18.2033i		−	0.0274146i
$665$		0			0
$666$	−300.853			−0.451731
$667$	−561.838			−0.842335
$668$			78.7916i			0.117951i
$669$	−206.735			−0.309021
$670$		0			0
$671$		−	29.3939i		−	0.0438061i
$672$	−31.0294	−	61.1651i	−0.0461748	−	0.0910195i
$673$	−1191.44			−1.77034			−0.885171	−	0.465266i	$-0.845959\pi$
$673$	−1191.44			−1.77034			−0.885171	+	0.465266i	$0.845959\pi$
$674$	−124.701			−0.185016
$675$		0			0
$676$	−365.529			−0.540723
$677$		−	1211.07i		−	1.78888i	−0.447186	−	0.894441i	$-0.647574\pi$
$677$		−	1211.07i		−	1.78888i	0.447186	−	0.894441i	$-0.352426\pi$
$678$			178.885i			0.263842i
$679$	163.779	+	322.840i	0.241206	+	0.475464i
$680$		0			0
$681$	−294.177			−0.431977
$682$		−	21.3965i		−	0.0313731i
$683$	1233.89			1.80657			0.903287	−	0.429038i	$-0.141147\pi$
$683$	1233.89			1.80657			0.903287	+	0.429038i	$0.141147\pi$
$684$			138.360i			0.202281i
$685$		0			0
$686$	−78.4163	+	478.695i	−0.114309	+	0.697806i
$687$	190.544			0.277357
$688$	−41.7056			−0.0606186
$689$		−	694.501i		−	1.00798i
$690$		0			0
$691$		−	86.7045i		−	0.125477i	−0.998030	−	0.0627384i	$-0.980017\pi$
$691$		−	86.7045i		−	0.125477i	0.998030	−	0.0627384i	$-0.0199834\pi$
$692$		−	47.6569i		−	0.0688683i
$693$	−32.9117	+	16.6963i	−0.0474916	+	0.0240928i
$694$	452.662			0.652251
$695$		0			0
$696$			146.969i			0.211163i
$697$	971.970			1.39450
$698$		−	470.998i		−	0.674783i
$699$		−	99.1858i		−	0.141897i
$700$		0			0
$701$	−149.147			−0.212763			−0.106382	−	0.994325i	$-0.533927\pi$
$701$	−149.147			−0.212763			−0.106382	+	0.994325i	$0.533927\pi$
$702$	−137.823			−0.196330
$703$		−	1635.22i		−	2.32607i
$704$	−14.0589			−0.0199700
$705$		0			0
$706$			927.317i			1.31348i
$707$	−20.9331	−	41.2633i	−0.0296084	−	0.0583639i
$708$	337.706			0.476985
$709$	189.647			0.267485			0.133742	−	0.991016i	$-0.457301\pi$
$709$	189.647			0.267485			0.133742	+	0.991016i	$0.457301\pi$
$710$		0			0
$711$	209.470			0.294613
$712$		−	119.053i		−	0.167209i
$713$		−	161.234i		−	0.226134i
$714$	−359.044	+	182.145i	−0.502862	+	0.255105i
$715$		0			0
$716$	−25.8091			−0.0360462
$717$			487.610i			0.680070i
$718$	−138.250			−0.192548
$719$		−	12.0064i		−	0.0166987i	−0.999965	−	0.00834937i	$-0.997342\pi$
$719$		−	12.0064i		−	0.0166987i	0.999965	−	0.00834937i	$-0.00265772\pi$
$720$		0			0
$721$	556.971	+	1097.90i	0.772497	+	1.52274i
$722$	−241.497			−0.334484
$723$	−291.515			−0.403202
$724$			130.736i			0.180574i
$725$		0			0
$726$		−	288.823i		−	0.397828i
$727$			417.169i			0.573823i	0.957957	+	0.286911i	$0.0926286\pi$
$727$			417.169i			0.573823i	−0.957957	+	0.286911i	$0.907371\pi$
$728$	168.000	+	331.161i	0.230769	+	0.454892i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			244.815i			0.334904i
$732$	−57.9411			−0.0791545
$733$		−	1286.99i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$733$		−	1286.99i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$734$			454.043i			0.618588i
$735$		0			0
$736$	−105.941			−0.143942
$737$	107.147			0.145383
$738$		−	175.625i		−	0.237974i
$739$	1333.47			1.80443			0.902213	−	0.431292i	$-0.141942\pi$
$739$	1333.47			1.80443			0.902213	+	0.431292i	$0.141942\pi$
$740$		0			0
$741$		−	749.111i		−	1.01095i
$742$	−326.912	+	165.844i	−0.440582	+	0.223510i
$743$	776.476			1.04506			0.522528	−	0.852622i	$-0.324989\pi$
$743$	776.476			1.04506			0.522528	+	0.852622i	$0.324989\pi$
$744$	−42.1766			−0.0566890
$745$		0			0
$746$	−265.123			−0.355392
$747$			19.3075i			0.0258467i
$748$			82.5266i			0.110330i
$749$	−288.676	+	146.447i	−0.385415	+	0.195524i
$750$		0			0
$751$	48.8385			0.0650313			0.0325157	−	0.999471i	$-0.489648\pi$
$751$	48.8385			0.0650313			0.0325157	+	0.999471i	$0.489648\pi$
$752$		−	154.798i		−	0.205848i
$753$	−183.765			−0.244043
$754$		−	795.724i		−	1.05534i
$755$		0			0
$756$	32.9117	+	64.8754i	0.0435340	+	0.0858141i
$757$	1279.47			1.69019			0.845093	−	0.534620i	$-0.179545\pi$
$757$	1279.47			1.69019			0.845093	+	0.534620i	$0.179545\pi$
$758$	−505.019			−0.666252
$759$			57.0047i			0.0751050i
$760$		0			0
$761$		−	1316.12i		−	1.72947i	−0.502231	−	0.864734i	$-0.667487\pi$
$761$		−	1316.12i		−	1.72947i	0.502231	−	0.864734i	$-0.332513\pi$
$762$		−	220.310i		−	0.289121i
$763$	224.368	−	113.823i	0.294060	−	0.149178i
$764$	−200.132			−0.261953
$765$		0			0
$766$		−	879.966i		−	1.14878i
$767$	−1828.41			−2.38385
$768$			27.7128i			0.0360844i
$769$		−	110.324i		−	0.143464i	−0.997424	−	0.0717320i	$-0.977147\pi$
$769$		−	110.324i		−	0.143464i	0.997424	−	0.0717320i	$-0.0228526\pi$
$770$		0			0
$771$	−503.095			−0.652523
$772$	−157.823			−0.204434
$773$			717.634i			0.928375i	0.885737	+	0.464187i	$0.153654\pi$
$773$			717.634i			0.928375i	−0.885737	+	0.464187i	$0.846346\pi$
$774$	44.2355			0.0571518
$775$		0			0
$776$		−	146.273i		−	0.188496i
$777$	−388.971	−	766.738i	−0.500606	−	0.986792i
$778$	321.691			0.413485
$779$	954.573			1.22538
$780$		0			0
$781$	194.382			0.248888
$782$			621.882i			0.795245i
$783$		−	155.885i		−	0.199086i
$784$	115.765	−	158.160i	0.147659	−	0.201735i
$785$		0			0
$786$	−29.8234			−0.0379432
$787$			347.191i			0.441158i	0.975369	+	0.220579i	$0.0707946\pi$
$787$			347.191i			0.441158i	−0.975369	+	0.220579i	$0.929205\pi$
$788$	367.882			0.466856
$789$			154.191i			0.195426i
$790$		0			0
$791$	−455.897	+	231.279i	−0.576355	+	0.292388i
$792$	14.9117			0.0188279
$793$	313.706			0.395593
$794$		−	1018.70i		−	1.28300i
$795$		0			0
$796$			340.059i			0.427210i
$797$		−	361.246i		−	0.453257i	−0.973981	−	0.226629i	$-0.927230\pi$
$797$		−	361.246i		−	0.453257i	0.973981	−	0.226629i	$-0.0727704\pi$
$798$	−352.617	+	178.885i	−0.441876	+	0.224166i
$799$	−908.674			−1.13726
$800$		0			0
$801$			126.274i			0.157646i
$802$	985.955			1.22937
$803$		−	99.7451i		−	0.124216i
$804$		−	211.208i		−	0.262697i
$805$		0			0
$806$	228.353			0.283317
$807$	−331.684			−0.411009
$808$			18.6957i			0.0231382i
$809$	−113.147			−0.139861			−0.0699303	−	0.997552i	$-0.522278\pi$
$809$	−113.147			−0.139861			−0.0699303	+	0.997552i	$0.522278\pi$
$810$		0			0
$811$			134.182i			0.165453i	0.996572	+	0.0827264i	$0.0263628\pi$
$811$			134.182i			0.165453i	−0.996572	+	0.0827264i	$0.973637\pi$
$812$	−374.558	+	190.016i	−0.461279	+	0.234010i
$813$	376.617			0.463244
$814$	−176.235			−0.216506
$815$		0			0
$816$	162.676			0.199358
$817$			240.433i			0.294288i
$818$			144.796i			0.177012i
$819$	−178.191	−	351.249i	−0.217571	−	0.428876i
$820$		0			0
$821$	491.677			0.598876			0.299438	−	0.954116i	$-0.403201\pi$
$821$	491.677			0.598876			0.299438	+	0.954116i	$0.403201\pi$
$822$		−	406.038i		−	0.493964i
$823$	941.852			1.14441			0.572207	−	0.820110i	$-0.306088\pi$
$823$	941.852			1.14441			0.572207	+	0.820110i	$0.306088\pi$
$824$		−	497.438i		−	0.603687i
$825$		0			0
$826$	436.617	+	860.659i	0.528592	+	1.04196i
$827$	−966.978			−1.16926			−0.584630	−	0.811300i	$-0.698760\pi$
$827$	−966.978			−1.16926			−0.584630	+	0.811300i	$0.698760\pi$
$828$	112.368			0.135710
$829$		−	1185.53i		−	1.43007i	−0.699088	−	0.715035i	$-0.746411\pi$
$829$		−	1185.53i		−	1.43007i	0.699088	−	0.715035i	$-0.253589\pi$
$830$		0			0
$831$		−	503.466i		−	0.605856i
$832$		−	150.043i		−	0.180340i
$833$	−928.410	−	679.546i	−1.11454	−	0.815781i
$834$	540.146			0.647657
$835$		0			0
$836$			81.0495i			0.0969491i
$837$	44.7351			0.0534469
$838$			553.560i			0.660573i
$839$			1376.91i			1.64113i	0.571550	+	0.820567i	$0.306342\pi$
$839$			1376.91i			1.64113i	−0.571550	+	0.820567i	$0.693658\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	501.255			0.595315
$843$			32.6540i			0.0387355i
$844$	43.1472			0.0511223
$845$		0			0
$846$			164.188i			0.194076i
$847$	736.080	−	373.418i	0.869044	−	0.440871i
$848$	148.118			0.174667
$849$	−695.823			−0.819580
$850$		0			0
$851$	−1328.03			−1.56055
$852$		−	383.165i		−	0.449724i
$853$			175.006i			0.205165i	0.994725	+	0.102582i	$0.0327105\pi$
$853$			175.006i			0.205165i	−0.994725	+	0.102582i	$0.967289\pi$
$854$	−74.9117	−	147.666i	−0.0877186	−	0.172911i
$855$		0			0
$856$	130.794			0.152797
$857$			61.7471i			0.0720503i	0.999351	+	0.0360252i	$0.0114696\pi$
$857$			61.7471i			0.0720503i	−0.999351	+	0.0360252i	$0.988530\pi$
$858$	−80.7351			−0.0940968
$859$		−	191.306i		−	0.222708i	−0.993781	−	0.111354i	$-0.964481\pi$
$859$		−	191.306i		−	0.222708i	0.993781	−	0.111354i	$-0.0355188\pi$
$860$		0			0
$861$	447.588	−	227.064i	0.519847	−	0.263721i
$862$	827.720			0.960232
$863$	494.507			0.573009			0.286504	−	0.958079i	$-0.407507\pi$
$863$	494.507			0.573009			0.286504	+	0.958079i	$0.407507\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			554.664i			0.640490i
$867$		−	454.358i		−	0.524058i
$868$	−54.5299	−	107.489i	−0.0628224	−	0.123835i
$869$	122.705			0.141202
$870$		0			0
$871$			1143.53i			1.31289i
$872$	−101.657			−0.116579
$873$			155.146i			0.177716i
$874$			610.751i			0.698800i
$875$		0			0
$876$	−196.617			−0.224449
$877$	454.353			0.518077			0.259038	−	0.965867i	$-0.416594\pi$
$877$	454.353			0.518077			0.259038	+	0.965867i	$0.416594\pi$
$878$		−	555.097i		−	0.632229i
$879$	−486.521			−0.553494
$880$		0			0
$881$			143.493i			0.162875i	0.996678	+	0.0814375i	$0.0259511\pi$
$881$			143.493i			0.162875i	−0.996678	+	0.0814375i	$0.974049\pi$
$882$	−122.787	+	167.754i	−0.139214	+	0.190197i
$883$	927.986			1.05095			0.525473	−	0.850810i	$-0.323888\pi$
$883$	927.986			1.05095			0.525473	+	0.850810i	$0.323888\pi$
$884$	−880.764			−0.996339
$885$		0			0
$886$	1152.22			1.30047
$887$		−	958.265i		−	1.08034i	−0.841555	−	0.540172i	$-0.818359\pi$
$887$		−	958.265i		−	1.08034i	0.841555	−	0.540172i	$-0.181641\pi$
$888$			347.395i			0.391210i
$889$	561.470	−	284.837i	0.631575	−	0.320402i
$890$		0			0
$891$	−15.8162			−0.0177511
$892$			238.717i			0.267620i
$893$	−892.410			−0.999340
$894$			516.482i			0.577720i
$895$		0			0
$896$	−70.6274	+	35.8297i	−0.0788252	+	0.0399885i
$897$	−608.382			−0.678241
$898$	255.015			0.283981
$899$			258.278i			0.287295i
$900$		0			0
$901$		−	869.462i		−	0.964996i
$902$		−	102.879i		−	0.114056i
$903$	57.1918	+	112.736i	0.0633353	+	0.124846i
$904$	206.558			0.228494
$905$		0			0
$906$		−	177.264i		−	0.195655i
$907$	552.721			0.609394			0.304697	−	0.952449i	$-0.401445\pi$
$907$	552.721			0.609394			0.304697	+	0.952449i	$0.401445\pi$
$908$			339.686i			0.374103i
$909$		−	19.8297i		−	0.0218149i
$910$		0			0
$911$	142.742			0.156687			0.0783437	−	0.996926i	$-0.475037\pi$
$911$	142.742			0.156687			0.0783437	+	0.996926i	$0.475037\pi$
$912$	159.765			0.175180
$913$			11.3101i			0.0123878i
$914$	−396.230			−0.433512
$915$		0			0
$916$		−	220.021i		−	0.240198i
$917$	−38.5584	−	76.0063i	−0.0420485	−	0.0828858i
$918$	−172.544			−0.187957
$919$	1086.45			1.18221			0.591107	−	0.806593i	$-0.298691\pi$
$919$	1086.45			1.18221			0.591107	+	0.806593i	$0.298691\pi$
$920$		0			0
$921$	263.823			0.286453
$922$			574.591i			0.623200i
$923$			2074.54i			2.24760i
$924$	19.2792	+	38.0031i	0.0208650	+	0.0411289i
$925$		0			0
$926$	−646.960			−0.698661
$927$			527.613i			0.569161i
$928$	169.706			0.182872
$929$		−	1550.75i		−	1.66927i	−0.550806	−	0.834633i	$-0.685680\pi$
$929$		−	1550.75i		−	1.66927i	0.550806	−	0.834633i	$-0.314320\pi$
$930$		0			0
$931$	−911.793	−	667.383i	−0.979370	−	0.716845i
$932$	−114.530			−0.122886
$933$	490.441			0.525660
$934$			910.345i			0.974673i
$935$		0			0
$936$			159.145i			0.170026i
$937$		−	759.317i		−	0.810370i	−0.914235	−	0.405185i	$-0.867207\pi$
$937$		−	759.317i		−	0.810370i	0.914235	−	0.405185i	$-0.132793\pi$
$938$	538.274	−	273.070i	0.573853	−	0.291119i
$939$	84.1463			0.0896127
$940$		0			0
$941$			36.3519i			0.0386312i	0.999813	+	0.0193156i	$0.00614873\pi$
$941$			36.3519i			0.0386312i	−0.999813	+	0.0193156i	$0.993851\pi$
$942$	572.382			0.607624
$943$		−	775.245i		−	0.822105i
$944$		−	389.949i		−	0.413081i
$945$		0			0
$946$	25.9126			0.0273917
$947$	−92.5370			−0.0977160			−0.0488580	−	0.998806i	$-0.515558\pi$
$947$	−92.5370			−0.0977160			−0.0488580	+	0.998806i	$0.515558\pi$
$948$		−	241.875i		−	0.255143i
$949$	1064.53			1.12174
$950$		0			0
$951$			1001.17i			1.05276i
$952$	210.323	+	414.588i	0.220927	+	0.435492i
$953$	1361.29			1.42843			0.714215	−	0.699927i	$-0.246784\pi$
$953$	1361.29			1.42843			0.714215	+	0.699927i	$0.246784\pi$
$954$	−157.103			−0.164678
$955$		0			0
$956$	563.044			0.588958
$957$		−	91.3151i		−	0.0954180i
$958$			238.344i			0.248794i
$959$	1034.81	−	524.964i	1.07905	−	0.547408i
$960$		0			0
$961$	886.881			0.922873
$962$		−	1880.87i		−	1.95517i
$963$	−138.728			−0.144058
$964$			336.612i			0.349183i
$965$		0			0
$966$	145.279	+	286.374i	0.150393	+	0.296453i
$967$	−481.677			−0.498115			−0.249057	−	0.968489i	$-0.580121\pi$
$967$	−481.677			−0.498115			−0.249057	+	0.968489i	$0.580121\pi$
$968$	−333.505			−0.344530
$969$		−	937.829i		−	0.967832i
$970$		0			0
$971$		−	1427.34i		−	1.46997i	−0.678082	−	0.734987i	$-0.737188\pi$
$971$		−	1427.34i		−	1.46997i	0.678082	−	0.734987i	$-0.262812\pi$
$972$			31.1769i			0.0320750i
$973$	698.352	+	1376.59i	0.717730	+	1.41479i
$974$	3.93102			0.00403596
$975$		0			0
$976$			66.9046i			0.0685498i
$977$	1356.26			1.38819			0.694095	−	0.719883i	$-0.255805\pi$
$977$	1356.26			1.38819			0.694095	+	0.719883i	$0.255805\pi$
$978$			179.029i			0.183056i
$979$			73.9698i			0.0755565i
$980$		0			0
$981$	107.823			0.109912
$982$	−349.986			−0.356401
$983$		−	1315.51i		−	1.33826i	−0.743146	−	0.669129i	$-0.766667\pi$
$983$		−	1315.51i		−	1.33826i	0.743146	−	0.669129i	$-0.233333\pi$
$984$	−202.794			−0.206091
$985$		0			0
$986$		−	996.184i		−	1.01033i
$987$	−418.441	+	212.277i	−0.423952	+	0.215073i
$988$	−864.999			−0.875505
$989$	195.265			0.197437
$990$		0			0
$991$	1043.28			1.05275			0.526377	−	0.850251i	$-0.323550\pi$
$991$	1043.28			1.05275			0.526377	+	0.850251i	$0.323550\pi$
$992$			48.7014i			0.0490941i
$993$			575.677i			0.579736i
$994$	976.514	−	495.391i	0.982408	−	0.498382i
$995$		0			0
$996$	22.2944			0.0223839
$997$		−	820.328i		−	0.822796i	−0.911456	−	0.411398i	$-0.865041\pi$
$997$		−	820.328i		−	0.822796i	0.911456	−	0.411398i	$-0.134959\pi$
$998$	−683.667			−0.685037
$999$		−	368.468i		−	0.368837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.a.601.4		4
5.2	odd	4		1050.3.h.a.349.7		8
5.3	odd	4		1050.3.h.a.349.2		8
5.4	even	2		42.3.c.a.13.1	✓	4
7.6	odd	2	inner	1050.3.f.a.601.3		4
15.14	odd	2		126.3.c.b.55.4		4
20.19	odd	2		336.3.f.c.97.3		4
35.4	even	6		294.3.g.b.19.2		4
35.9	even	6		294.3.g.c.31.2		4
35.13	even	4		1050.3.h.a.349.3		8
35.19	odd	6		294.3.g.b.31.2		4
35.24	odd	6		294.3.g.c.19.2		4
35.27	even	4		1050.3.h.a.349.6		8
35.34	odd	2		42.3.c.a.13.2	yes	4
40.19	odd	2		1344.3.f.e.769.2		4
40.29	even	2		1344.3.f.f.769.4		4
60.59	even	2		1008.3.f.g.433.4		4
105.44	odd	6		882.3.n.d.325.1		4
105.59	even	6		882.3.n.d.19.1		4
105.74	odd	6		882.3.n.a.19.1		4
105.89	even	6		882.3.n.a.325.1		4
105.104	even	2		126.3.c.b.55.3		4
140.139	even	2		336.3.f.c.97.2		4
280.69	odd	2		1344.3.f.f.769.1		4
280.139	even	2		1344.3.f.e.769.3		4
420.419	odd	2		1008.3.f.g.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.1	✓	4	5.4	even	2
42.3.c.a.13.2	yes	4	35.34	odd	2
126.3.c.b.55.3		4	105.104	even	2
126.3.c.b.55.4		4	15.14	odd	2
294.3.g.b.19.2		4	35.4	even	6
294.3.g.b.31.2		4	35.19	odd	6
294.3.g.c.19.2		4	35.24	odd	6
294.3.g.c.31.2		4	35.9	even	6
336.3.f.c.97.2		4	140.139	even	2
336.3.f.c.97.3		4	20.19	odd	2
882.3.n.a.19.1		4	105.74	odd	6
882.3.n.a.325.1		4	105.89	even	6
882.3.n.d.19.1		4	105.59	even	6
882.3.n.d.325.1		4	105.44	odd	6
1008.3.f.g.433.1		4	420.419	odd	2
1008.3.f.g.433.4		4	60.59	even	2
1050.3.f.a.601.3		4	7.6	odd	2	inner
1050.3.f.a.601.4		4	1.1	even	1	trivial
1050.3.h.a.349.2		8	5.3	odd	4
1050.3.h.a.349.3		8	35.13	even	4
1050.3.h.a.349.6		8	35.27	even	4
1050.3.h.a.349.7		8	5.2	odd	4
1344.3.f.e.769.2		4	40.19	odd	2
1344.3.f.e.769.3		4	280.139	even	2
1344.3.f.f.769.1		4	280.69	odd	2
1344.3.f.f.769.4		4	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -1.75736 q^{11} +3.46410i q^{12} -18.7554i q^{13} +(-8.82843 + 4.47871i) q^{14} +4.00000 q^{16} -23.4803i q^{17} -4.24264 q^{18} -23.0600i q^{19} +(-5.48528 - 10.8126i) q^{21} -2.48528 q^{22} -18.7279 q^{23} +4.89898i q^{24} -26.5241i q^{26} -5.19615i q^{27} +(-12.4853 + 6.33386i) q^{28} +30.0000 q^{29} +8.60927i q^{31} +5.65685 q^{32} -3.04384i q^{33} -33.2061i q^{34} -6.00000 q^{36} +70.9117 q^{37} -32.6118i q^{38} +32.4853 q^{39} +41.3951i q^{41} +(-7.75736 - 15.2913i) q^{42} -10.4264 q^{43} -3.51472 q^{44} -26.4853 q^{46} -38.6995i q^{47} +6.92820i q^{48} +(28.9411 - 39.5400i) q^{49} +40.6690 q^{51} -37.5108i q^{52} +37.0294 q^{53} -7.34847i q^{54} +(-17.6569 + 8.95743i) q^{56} +39.9411 q^{57} +42.4264 q^{58} -97.4872i q^{59} +16.7262i q^{61} +12.1753i q^{62} +(18.7279 - 9.50079i) q^{63} +8.00000 q^{64} -4.30463i q^{66} -60.9706 q^{67} -46.9606i q^{68} -32.4377i q^{69} -110.610 q^{71} -8.48528 q^{72} +56.7585i q^{73} +100.284 q^{74} -46.1200i q^{76} +(10.9706 - 5.56543i) q^{77} +45.9411 q^{78} -69.8234 q^{79} +9.00000 q^{81} +58.5416i q^{82} -6.43583i q^{83} +(-10.9706 - 21.6251i) q^{84} -14.7452 q^{86} +51.9615i q^{87} -4.97056 q^{88} -42.0915i q^{89} +(59.3970 + 117.083i) q^{91} -37.4558 q^{92} -14.9117 q^{93} -54.7293i q^{94} +9.79796i q^{96} -51.7153i q^{97} +(40.9289 - 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 8 q^{7} - 12 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 8 * q^7 - 12 * q^9	\( 4 q + 8 q^{4} - 8 q^{7} - 12 q^{9} - 24 q^{11} - 24 q^{14} + 16 q^{16} + 12 q^{21} + 24 q^{22} - 24 q^{23} - 16 q^{28} + 120 q^{29} - 24 q^{36} + 80 q^{37} + 96 q^{39} - 48 q^{42} + 128 q^{43} - 48 q^{44} - 72 q^{46} - 20 q^{49} - 24 q^{51} + 216 q^{53} - 48 q^{56} + 24 q^{57} + 24 q^{63} + 32 q^{64} - 176 q^{67} - 120 q^{71} + 288 q^{74} - 24 q^{77} + 48 q^{78} + 128 q^{79} + 36 q^{81} + 24 q^{84} - 240 q^{86} + 48 q^{88} - 48 q^{92} + 144 q^{93} + 192 q^{98} + 72 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 + 16 * q^16 + 12 * q^21 + 24 * q^22 - 24 * q^23 - 16 * q^28 + 120 * q^29 - 24 * q^36 + 80 * q^37 + 96 * q^39 - 48 * q^42 + 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 - 24 * q^51 + 216 * q^53 - 48 * q^56 + 24 * q^57 + 24 * q^63 + 32 * q^64 - 176 * q^67 - 120 * q^71 + 288 * q^74 - 24 * q^77 + 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 - 240 * q^86 + 48 * q^88 - 48 * q^92 + 144 * q^93 + 192 * q^98 + 72 * q^99

Introduction

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