LMFDB - Embedded newform 1050.3.f.b.601.7

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:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.7
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.b.601.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -15.9625 q^{11} +3.46410i q^{12} +6.19954i q^{13} +(-1.47723 - 9.78866i) q^{14} +4.00000 q^{16} -19.7410i q^{17} -4.24264 q^{18} +29.3912i q^{19} +(11.9886 - 1.80922i) q^{21} -22.5744 q^{22} -18.3412 q^{23} +4.89898i q^{24} +8.76747i q^{26} -5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} -53.2909 q^{29} +37.4949i q^{31} +5.65685 q^{32} -27.6479i q^{33} -27.9179i q^{34} -6.00000 q^{36} -61.0349 q^{37} +41.5654i q^{38} -10.7379 q^{39} +21.3433i q^{41} +(16.9545 - 2.55863i) q^{42} -25.9827 q^{43} -31.9250 q^{44} -25.9383 q^{46} -10.3419i q^{47} +6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} +34.1924 q^{51} +12.3991i q^{52} +64.7326 q^{53} -7.34847i q^{54} +(-2.95445 - 19.5773i) q^{56} -50.9070 q^{57} -75.3647 q^{58} -18.0219i q^{59} -91.8436i q^{61} +53.0258i q^{62} +(3.13367 + 20.7649i) q^{63} +8.00000 q^{64} -39.1000i q^{66} +18.2351 q^{67} -39.4819i q^{68} -31.7678i q^{69} +108.465 q^{71} -8.48528 q^{72} +73.5614i q^{73} -86.3164 q^{74} +58.7823i q^{76} +(16.6737 + 110.486i) q^{77} -15.1857 q^{78} -57.1904 q^{79} +9.00000 q^{81} +30.1840i q^{82} -36.1402i q^{83} +(23.9772 - 3.61845i) q^{84} -36.7451 q^{86} -92.3026i q^{87} -45.1488 q^{88} -133.352i q^{89} +(42.9109 - 6.47576i) q^{91} -36.6823 q^{92} -64.9431 q^{93} -14.6257i q^{94} +9.79796i q^{96} -29.2749i q^{97} +(-66.2104 + 20.4496i) q^{98} +47.8875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 24 * q^9	$ 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * 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
$7$	−1.04456	−	6.92163i	−0.149222	−	0.988804i
$7$	−1.04456	−	6.92163i	−0.149222	−	0.988804i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−15.9625			−1.45114			−0.725568	−	0.688150i	$-0.758423\pi$
$11$	−15.9625			−1.45114			−0.725568	+	0.688150i	$0.758423\pi$
$12$			3.46410i			0.288675i
$13$			6.19954i			0.476887i	0.971156	+	0.238444i	$0.0766372\pi$
$13$			6.19954i			0.476887i	−0.971156	+	0.238444i	$0.923363\pi$
$14$	−1.47723	−	9.78866i	−0.105516	−	0.699190i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	19.7410i		−	1.16123i	−0.814177	−	0.580617i	$-0.802812\pi$
$17$		−	19.7410i		−	1.16123i	0.814177	−	0.580617i	$-0.197188\pi$
$18$	−4.24264			−0.235702
$19$			29.3912i			1.54690i	0.633856	+	0.773451i	$0.281471\pi$
$19$			29.3912i			1.54690i	−0.633856	+	0.773451i	$0.718529\pi$
$20$		0			0
$21$	11.9886	−	1.80922i	0.570886	−	0.0861535i
$22$	−22.5744			−1.02611
$23$	−18.3412			−0.797442			−0.398721	−	0.917072i	$-0.630546\pi$
$23$	−18.3412			−0.797442			−0.398721	+	0.917072i	$0.630546\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$			8.76747i			0.337210i
$27$		−	5.19615i		−	0.192450i
$28$	−2.08911	−	13.8433i	−0.0746112	−	0.494402i
$29$	−53.2909			−1.83762			−0.918809	−	0.394702i	$-0.870848\pi$
$29$	−53.2909			−1.83762			−0.918809	+	0.394702i	$0.870848\pi$
$30$		0			0
$31$			37.4949i			1.20951i	0.796411	+	0.604756i	$0.206729\pi$
$31$			37.4949i			1.20951i	−0.796411	+	0.604756i	$0.793271\pi$
$32$	5.65685			0.176777
$33$		−	27.6479i		−	0.837814i
$34$		−	27.9179i		−	0.821116i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−61.0349			−1.64959			−0.824796	−	0.565430i	$-0.808710\pi$
$37$	−61.0349			−1.64959			−0.824796	+	0.565430i	$0.808710\pi$
$38$			41.5654i			1.09383i
$39$	−10.7379			−0.275331
$40$		0			0
$41$			21.3433i			0.520569i	0.965532	+	0.260285i	$0.0838164\pi$
$41$			21.3433i			0.520569i	−0.965532	+	0.260285i	$0.916184\pi$
$42$	16.9545	−	2.55863i	0.403677	−	0.0609198i
$43$	−25.9827			−0.604249			−0.302125	−	0.953268i	$-0.597696\pi$
$43$	−25.9827			−0.604249			−0.302125	+	0.953268i	$0.597696\pi$
$44$	−31.9250			−0.725568
$45$		0			0
$46$	−25.9383			−0.563876
$47$		−	10.3419i		−	0.220041i	−0.993929	−	0.110021i	$-0.964908\pi$
$47$		−	10.3419i		−	0.220041i	0.993929	−	0.110021i	$-0.0350917\pi$
$48$			6.92820i			0.144338i
$49$	−46.8178	+	14.4601i	−0.955465	+	0.295103i
$50$		0			0
$51$	34.1924			0.670438
$52$			12.3991i			0.238444i
$53$	64.7326			1.22137			0.610685	−	0.791874i	$-0.290894\pi$
$53$	64.7326			1.22137			0.610685	+	0.791874i	$0.290894\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−2.95445	−	19.5773i	−0.0527581	−	0.349595i
$57$	−50.9070			−0.893105
$58$	−75.3647			−1.29939
$59$		−	18.0219i		−	0.305455i	−0.988268	−	0.152728i	$-0.951194\pi$
$59$		−	18.0219i		−	0.305455i	0.988268	−	0.152728i	$-0.0488057\pi$
$60$		0			0
$61$		−	91.8436i		−	1.50563i	−0.658231	−	0.752816i	$-0.728695\pi$
$61$		−	91.8436i		−	1.50563i	0.658231	−	0.752816i	$-0.271305\pi$
$62$			53.0258i			0.855255i
$63$	3.13367	+	20.7649i	0.0497408	+	0.329601i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	39.1000i		−	0.592424i
$67$	18.2351			0.272166			0.136083	−	0.990697i	$-0.456549\pi$
$67$	18.2351			0.272166			0.136083	+	0.990697i	$0.456549\pi$
$68$		−	39.4819i		−	0.580617i
$69$		−	31.7678i		−	0.460403i
$70$		0			0
$71$	108.465			1.52768			0.763841	−	0.645404i	$-0.223311\pi$
$71$	108.465			1.52768			0.763841	+	0.645404i	$0.223311\pi$
$72$	−8.48528			−0.117851
$73$			73.5614i			1.00769i	0.863794	+	0.503845i	$0.168082\pi$
$73$			73.5614i			1.00769i	−0.863794	+	0.503845i	$0.831918\pi$
$74$	−86.3164			−1.16644
$75$		0			0
$76$			58.7823i			0.773451i
$77$	16.6737	+	110.486i	0.216542	+	1.43489i
$78$	−15.1857			−0.194688
$79$	−57.1904			−0.723929			−0.361964	−	0.932192i	$-0.617894\pi$
$79$	−57.1904			−0.723929			−0.361964	+	0.932192i	$0.617894\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			30.1840i			0.368098i
$83$		−	36.1402i		−	0.435425i	−0.976013	−	0.217712i	$-0.930141\pi$
$83$		−	36.1402i		−	0.435425i	0.976013	−	0.217712i	$-0.0698594\pi$
$84$	23.9772	−	3.61845i	0.285443	−	0.0430768i
$85$		0			0
$86$	−36.7451			−0.427269
$87$		−	92.3026i		−	1.06095i
$88$	−45.1488			−0.513054
$89$		−	133.352i		−	1.49833i	−0.662382	−	0.749166i	$-0.730455\pi$
$89$		−	133.352i		−	1.49833i	0.662382	−	0.749166i	$-0.269545\pi$
$90$		0			0
$91$	42.9109	−	6.47576i	0.471548	−	0.0711622i
$92$	−36.6823			−0.398721
$93$	−64.9431			−0.698312
$94$		−	14.6257i		−	0.155593i
$95$		0			0
$96$			9.79796i			0.102062i
$97$		−	29.2749i		−	0.301803i	−0.988549	−	0.150902i	$-0.951782\pi$
$97$		−	29.2749i		−	0.301803i	0.988549	−	0.150902i	$-0.0482176\pi$
$98$	−66.2104	+	20.4496i	−0.675616	+	0.208669i
$99$	47.8875			0.483712
$100$		0			0
$101$			58.3844i			0.578063i	0.957320	+	0.289032i	$0.0933332\pi$
$101$			58.3844i			0.578063i	−0.957320	+	0.289032i	$0.906667\pi$
$102$	48.3553			0.474071
$103$		−	102.996i		−	0.999957i	−0.866038	−	0.499978i	$-0.833341\pi$
$103$		−	102.996i		−	0.999957i	0.866038	−	0.499978i	$-0.166659\pi$
$104$			17.5349i			0.168605i
$105$		0			0
$106$	91.5457			0.863638
$107$	58.8093			0.549619			0.274810	−	0.961499i	$-0.411385\pi$
$107$	58.8093			0.549619			0.274810	+	0.961499i	$0.411385\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−202.689			−1.85954			−0.929768	−	0.368147i	$-0.879992\pi$
$109$	−202.689			−1.85954			−0.929768	+	0.368147i	$0.879992\pi$
$110$		0			0
$111$		−	105.716i		−	0.952392i
$112$	−4.17822	−	27.6865i	−0.0373056	−	0.247201i
$113$	−169.018			−1.49574			−0.747869	−	0.663846i	$-0.768923\pi$
$113$	−169.018			−1.49574			−0.747869	+	0.663846i	$0.768923\pi$
$114$	−71.9933			−0.631520
$115$		0			0
$116$	−106.582			−0.918809
$117$		−	18.5986i		−	0.158962i
$118$		−	25.4868i		−	0.215989i
$119$	−136.640	+	20.6205i	−1.14823	+	0.173282i
$120$		0			0
$121$	133.802			1.10580
$122$		−	129.886i		−	1.06464i
$123$	−36.9678			−0.300551
$124$			74.9898i			0.604756i
$125$		0			0
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	47.5171			0.374150			0.187075	−	0.982346i	$-0.440099\pi$
$127$	47.5171			0.374150			0.187075	+	0.982346i	$0.440099\pi$
$128$	11.3137			0.0883883
$129$		−	45.0034i		−	0.348864i
$130$		0			0
$131$		−	13.8166i		−	0.105470i	−0.998609	−	0.0527351i	$-0.983206\pi$
$131$		−	13.8166i		−	0.105470i	0.998609	−	0.0527351i	$-0.0167939\pi$
$132$		−	55.2957i		−	0.418907i
$133$	203.435	−	30.7007i	1.52958	−	0.230832i
$134$	25.7883			0.192450
$135$		0			0
$136$		−	55.8359i		−	0.410558i
$137$	−113.381			−0.827600			−0.413800	−	0.910368i	$-0.635799\pi$
$137$	−113.381			−0.827600			−0.413800	+	0.910368i	$0.635799\pi$
$138$		−	44.9265i		−	0.325554i
$139$			127.380i			0.916400i	0.888849	+	0.458200i	$0.151506\pi$
$139$			127.380i			0.916400i	−0.888849	+	0.458200i	$0.848494\pi$
$140$		0			0
$141$	17.9128			0.127041
$142$	153.393			1.08023
$143$		−	98.9601i		−	0.692029i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$			104.031i			0.712544i
$147$	−25.0455	−	81.0908i	−0.170378	−	0.551638i
$148$	−122.070			−0.824796
$149$	232.201			1.55839			0.779197	−	0.626779i	$-0.215627\pi$
$149$	232.201			1.55839			0.779197	+	0.626779i	$0.215627\pi$
$150$		0			0
$151$	−111.750			−0.740067			−0.370033	−	0.929018i	$-0.620654\pi$
$151$	−111.750			−0.740067			−0.370033	+	0.929018i	$0.620654\pi$
$152$			83.1307i			0.546913i
$153$			59.2229i			0.387078i
$154$	23.5802	+	156.252i	0.153118	+	1.01462i
$155$		0			0
$156$	−21.4758			−0.137666
$157$			264.635i			1.68557i	0.538247	+	0.842787i	$0.319087\pi$
$157$			264.635i			1.68557i	−0.538247	+	0.842787i	$0.680913\pi$
$158$	−80.8794			−0.511895
$159$			112.120i			0.705158i
$160$		0			0
$161$	19.1584	+	126.951i	0.118996	+	0.788513i
$162$	12.7279			0.0785674
$163$	−53.4448			−0.327882			−0.163941	−	0.986470i	$-0.552421\pi$
$163$	−53.4448			−0.327882			−0.163941	+	0.986470i	$0.552421\pi$
$164$			42.6867i			0.260285i
$165$		0			0
$166$		−	51.1100i		−	0.307892i
$167$		−	149.019i		−	0.892330i	−0.894951	−	0.446165i	$-0.852789\pi$
$167$		−	149.019i		−	0.892330i	0.894951	−	0.446165i	$-0.147211\pi$
$168$	33.9089	−	5.11726i	0.201839	−	0.0304599i
$169$	130.566			0.772578
$170$		0			0
$171$		−	88.1735i		−	0.515634i
$172$	−51.9655			−0.302125
$173$		−	36.9558i		−	0.213617i	−0.994280	−	0.106809i	$-0.965937\pi$
$173$		−	36.9558i		−	0.213617i	0.994280	−	0.106809i	$-0.0340633\pi$
$174$		−	130.536i		−	0.750204i
$175$		0			0
$176$	−63.8500			−0.362784
$177$	31.2148			0.176355
$178$		−	188.588i		−	1.05948i
$179$	118.481			0.661905			0.330952	−	0.943647i	$-0.392630\pi$
$179$	118.481			0.661905			0.330952	+	0.943647i	$0.392630\pi$
$180$		0			0
$181$			206.745i			1.14224i	0.820868	+	0.571118i	$0.193490\pi$
$181$			206.745i			1.14224i	−0.820868	+	0.571118i	$0.806510\pi$
$182$	60.6851	−	9.15811i	0.333435	−	0.0503193i
$183$	159.078			0.869277
$184$	−51.8766			−0.281938
$185$		0			0
$186$	−91.8434			−0.493781
$187$			315.115i			1.68511i
$188$		−	20.6839i		−	0.110021i
$189$	−35.9658	+	5.42767i	−0.190295	+	0.0287178i
$190$		0			0
$191$	188.143			0.985041			0.492520	−	0.870301i	$-0.336076\pi$
$191$	188.143			0.985041			0.492520	+	0.870301i	$0.336076\pi$
$192$			13.8564i			0.0721688i
$193$	−10.2372			−0.0530425			−0.0265213	−	0.999648i	$-0.508443\pi$
$193$	−10.2372			−0.0530425			−0.0265213	+	0.999648i	$0.508443\pi$
$194$		−	41.4009i		−	0.213407i
$195$		0			0
$196$	−93.6356	+	28.9201i	−0.477733	+	0.147552i
$197$	−218.831			−1.11082			−0.555408	−	0.831578i	$-0.687438\pi$
$197$	−218.831			−1.11082			−0.555408	+	0.831578i	$0.687438\pi$
$198$	67.7232			0.342036
$199$			110.865i			0.557111i	0.960420	+	0.278556i	$0.0898556\pi$
$199$			110.865i			0.557111i	−0.960420	+	0.278556i	$0.910144\pi$
$200$		0			0
$201$			31.5841i			0.157135i
$202$			82.5680i			0.408752i
$203$	55.6654	+	368.860i	0.274214	+	1.81704i
$204$	68.3847			0.335219
$205$		0			0
$206$		−	145.658i		−	0.707076i
$207$	55.0235			0.265814
$208$			24.7981i			0.119222i
$209$		−	469.156i		−	2.24477i
$210$		0			0
$211$	116.823			0.553665			0.276833	−	0.960918i	$-0.410715\pi$
$211$	116.823			0.553665			0.276833	+	0.960918i	$0.410715\pi$
$212$	129.465			0.610685
$213$			187.868i			0.882008i
$214$	83.1689			0.388640
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	259.526	−	39.1655i	1.19597	−	0.180486i
$218$	−286.646			−1.31489
$219$	−127.412			−0.581790
$220$		0			0
$221$	122.385			0.553777
$222$		−	149.504i		−	0.673443i
$223$		−	85.7012i		−	0.384310i	−0.981365	−	0.192155i	$-0.938452\pi$
$223$		−	85.7012i		−	0.384310i	0.981365	−	0.192155i	$-0.0615477\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$		0			0
$226$	−239.028			−1.05765
$227$		−	113.389i		−	0.499513i	−0.968309	−	0.249757i	$-0.919649\pi$
$227$		−	113.389i		−	0.499513i	0.968309	−	0.249757i	$-0.0803506\pi$
$228$	−101.814			−0.446552
$229$			49.2031i			0.214861i	0.994213	+	0.107430i	$0.0342623\pi$
$229$			49.2031i			0.214861i	−0.994213	+	0.107430i	$0.965738\pi$
$230$		0			0
$231$	−191.368	+	28.8798i	−0.828434	+	0.125021i
$232$	−150.729			−0.649696
$233$	115.412			0.495329			0.247665	−	0.968846i	$-0.420337\pi$
$233$	115.412			0.495329			0.247665	+	0.968846i	$0.420337\pi$
$234$		−	26.3024i		−	0.112403i
$235$		0			0
$236$		−	36.0437i		−	0.152728i
$237$		−	99.0567i		−	0.417961i
$238$	−193.238	+	29.1619i	−0.811922	+	0.122529i
$239$	152.491			0.638039			0.319020	−	0.947748i	$-0.396646\pi$
$239$	152.491			0.638039			0.319020	+	0.947748i	$0.396646\pi$
$240$		0			0
$241$		−	415.112i		−	1.72245i	−0.508220	−	0.861227i	$-0.669696\pi$
$241$		−	415.112i		−	1.72245i	0.508220	−	0.861227i	$-0.330304\pi$
$242$	189.224			0.781918
$243$			15.5885i			0.0641500i
$244$		−	183.687i		−	0.752816i
$245$		0			0
$246$	−52.2803			−0.212522
$247$	−182.211			−0.737698
$248$			106.052i			0.427627i
$249$	62.5967			0.251393
$250$		0			0
$251$			274.805i			1.09484i	0.836858	+	0.547421i	$0.184390\pi$
$251$			274.805i			1.09484i	−0.836858	+	0.547421i	$0.815610\pi$
$252$	6.26734	+	41.5298i	0.0248704	+	0.164801i
$253$	292.771			1.15720
$254$	67.1993			0.264564
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	65.7720i		−	0.255922i	−0.991779	−	0.127961i	$-0.959157\pi$
$257$		−	65.7720i		−	0.255922i	0.991779	−	0.127961i	$-0.0408433\pi$
$258$		−	63.6444i		−	0.246684i
$259$	63.7544	+	422.461i	0.246156	+	1.63112i
$260$		0			0
$261$	159.873			0.612539
$262$		−	19.5396i		−	0.0745787i
$263$	154.046			0.585728			0.292864	−	0.956154i	$-0.405392\pi$
$263$	154.046			0.585728			0.292864	+	0.956154i	$0.405392\pi$
$264$		−	78.2000i		−	0.296212i
$265$		0			0
$266$	287.700	−	43.4174i	1.08158	−	0.163223i
$267$	230.972			0.865062
$268$	36.4702			0.136083
$269$			103.741i			0.385653i	0.981233	+	0.192827i	$0.0617655\pi$
$269$			103.741i			0.385653i	−0.981233	+	0.192827i	$0.938235\pi$
$270$		0			0
$271$			53.1971i			0.196299i	0.995172	+	0.0981496i	$0.0312924\pi$
$271$			53.1971i			0.196299i	−0.995172	+	0.0981496i	$0.968708\pi$
$272$		−	78.9639i		−	0.290308i
$273$	11.2164	+	74.3238i	0.0410855	+	0.272248i
$274$	−160.345			−0.585202
$275$		0			0
$276$		−	63.5356i		−	0.230202i
$277$	−226.731			−0.818523			−0.409261	−	0.912417i	$-0.634214\pi$
$277$	−226.731			−0.818523			−0.409261	+	0.912417i	$0.634214\pi$
$278$			180.142i			0.647993i
$279$		−	112.485i		−	0.403171i
$280$		0			0
$281$	−343.766			−1.22337			−0.611683	−	0.791103i	$-0.709507\pi$
$281$	−343.766			−1.22337			−0.611683	+	0.791103i	$0.709507\pi$
$282$	25.3325			0.0898315
$283$			130.649i			0.461659i	0.972994	+	0.230829i	$0.0741439\pi$
$283$			130.649i			0.461659i	−0.972994	+	0.230829i	$0.925856\pi$
$284$	216.931			0.763841
$285$		0			0
$286$		−	139.951i		−	0.489338i
$287$	147.731	−	22.2943i	0.514741	−	0.0776806i
$288$	−16.9706			−0.0589256
$289$	−100.706			−0.348462
$290$		0			0
$291$	50.7056			0.174246
$292$			147.123i			0.503845i
$293$			137.051i			0.467750i	0.972267	+	0.233875i	$0.0751406\pi$
$293$			137.051i			0.467750i	−0.972267	+	0.233875i	$0.924859\pi$
$294$	−35.4198	−	114.680i	−0.120475	−	0.390067i
$295$		0			0
$296$	−172.633			−0.583219
$297$			82.9436i			0.279271i
$298$	328.382			1.10195
$299$		−	113.707i		−	0.380290i
$300$		0			0
$301$	27.1404	+	179.843i	0.0901675	+	0.597484i
$302$	−158.038			−0.523306
$303$	−101.125			−0.333745
$304$			117.565i			0.386726i
$305$		0			0
$306$			83.7538i			0.273705i
$307$			137.544i			0.448026i	0.974586	+	0.224013i	$0.0719158\pi$
$307$			137.544i			0.448026i	−0.974586	+	0.224013i	$0.928084\pi$
$308$	33.3475	+	220.973i	0.108271	+	0.717445i
$309$	178.394			0.577325
$310$		0			0
$311$			564.525i			1.81519i	0.419845	+	0.907596i	$0.362084\pi$
$311$			564.525i			1.81519i	−0.419845	+	0.907596i	$0.637916\pi$
$312$	−30.3714			−0.0973442
$313$		−	573.653i		−	1.83276i	−0.400312	−	0.916379i	$-0.631098\pi$
$313$		−	573.653i		−	1.83276i	0.400312	−	0.916379i	$-0.368902\pi$
$314$			374.251i			1.19188i
$315$		0			0
$316$	−114.381			−0.361964
$317$	64.7265			0.204185			0.102092	−	0.994775i	$-0.467446\pi$
$317$	64.7265			0.204185			0.102092	+	0.994775i	$0.467446\pi$
$318$			158.562i			0.498622i
$319$	850.657			2.66664
$320$		0			0
$321$			101.861i			0.317323i
$322$	27.0940	+	179.535i	0.0841430	+	0.557563i
$323$	580.210			1.79631
$324$	18.0000			0.0555556
$325$		0			0
$326$	−75.5823			−0.231848
$327$		−	351.068i		−	1.07360i
$328$			60.3681i			0.184049i
$329$	−71.5830	+	10.8027i	−0.217578	+	0.0328351i
$330$		0			0
$331$	126.403			0.381883			0.190941	−	0.981601i	$-0.438846\pi$
$331$	126.403			0.381883			0.190941	+	0.981601i	$0.438846\pi$
$332$		−	72.2805i		−	0.217712i
$333$	183.105			0.549864
$334$		−	210.745i		−	0.630973i
$335$		0			0
$336$	47.9544	−	7.23690i	0.142722	−	0.0215384i
$337$	−73.6716			−0.218610			−0.109305	−	0.994008i	$-0.534863\pi$
$337$	−73.6716			−0.218610			−0.109305	+	0.994008i	$0.534863\pi$
$338$	184.648			0.546295
$339$		−	292.748i		−	0.863565i
$340$		0			0
$341$		−	598.512i		−	1.75517i
$342$		−	124.696i		−	0.364608i
$343$	148.991	+	308.951i	0.434376	+	0.900732i
$344$	−73.4902			−0.213634
$345$		0			0
$346$		−	52.2634i		−	0.151050i
$347$	−553.102			−1.59395			−0.796977	−	0.604010i	$-0.793569\pi$
$347$	−553.102			−1.59395			−0.796977	+	0.604010i	$0.793569\pi$
$348$		−	184.605i		−	0.530475i
$349$			372.885i			1.06844i	0.845346	+	0.534219i	$0.179394\pi$
$349$			372.885i			1.06844i	−0.845346	+	0.534219i	$0.820606\pi$
$350$		0			0
$351$	32.2137			0.0917770
$352$	−90.2976			−0.256527
$353$		−	486.089i		−	1.37702i	−0.725226	−	0.688511i	$-0.758265\pi$
$353$		−	486.089i		−	1.37702i	0.725226	−	0.688511i	$-0.241735\pi$
$354$	44.1444			0.124702
$355$		0			0
$356$		−	266.703i		−	0.749166i
$357$	−35.7158	−	236.667i	−0.100044	−	0.662932i
$358$	167.557			0.468037
$359$	309.378			0.861776			0.430888	−	0.902405i	$-0.358200\pi$
$359$	309.378			0.861776			0.430888	+	0.902405i	$0.358200\pi$
$360$		0			0
$361$	−502.840			−1.39291
$362$			292.381i			0.807683i
$363$			231.751i			0.638433i
$364$	85.8217	−	12.9515i	0.235774	−	0.0355811i
$365$		0			0
$366$	224.970			0.614672
$367$			440.140i			1.19929i	0.800266	+	0.599645i	$0.204692\pi$
$367$			440.140i			1.19929i	−0.800266	+	0.599645i	$0.795308\pi$
$368$	−73.3646			−0.199360
$369$		−	64.0300i		−	0.173523i
$370$		0			0
$371$	−67.6168	−	448.055i	−0.182256	−	1.20769i
$372$	−129.886			−0.349156
$373$	443.742			1.18966			0.594829	−	0.803852i	$-0.297220\pi$
$373$	443.742			1.18966			0.594829	+	0.803852i	$0.297220\pi$
$374$			445.640i			1.19155i
$375$		0			0
$376$		−	29.2514i		−	0.0777964i
$377$		−	330.379i		−	0.876337i
$378$	−50.8634	+	7.67589i	−0.134559	+	0.0203066i
$379$	−443.999			−1.17150			−0.585750	−	0.810492i	$-0.699200\pi$
$379$	−443.999			−1.17150			−0.585750	+	0.810492i	$0.699200\pi$
$380$		0			0
$381$			82.3020i			0.216016i
$382$	266.074			0.696529
$383$		−	580.969i		−	1.51689i	−0.651736	−	0.758446i	$-0.725959\pi$
$383$		−	580.969i		−	1.51689i	0.651736	−	0.758446i	$-0.274041\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−14.4776			−0.0375067
$387$	77.9482			0.201416
$388$		−	58.5498i		−	0.150902i
$389$	−552.150			−1.41941			−0.709704	−	0.704500i	$-0.751171\pi$
$389$	−552.150			−1.41941			−0.709704	+	0.704500i	$0.751171\pi$
$390$		0			0
$391$			362.072i			0.926016i
$392$	−132.421	+	40.8992i	−0.337808	+	0.104335i
$393$	23.9310			0.0608933
$394$	−309.473			−0.785466
$395$		0			0
$396$	95.7750			0.241856
$397$			169.026i			0.425757i	0.977079	+	0.212879i	$0.0682839\pi$
$397$			169.026i			0.425757i	−0.977079	+	0.212879i	$0.931716\pi$
$398$			156.787i			0.393937i
$399$	53.1752	+	352.359i	0.133271	+	0.883105i
$400$		0			0
$401$	57.9535			0.144522			0.0722612	−	0.997386i	$-0.476978\pi$
$401$	57.9535			0.144522			0.0722612	+	0.997386i	$0.476978\pi$
$402$			44.6667i			0.111111i
$403$	−232.451			−0.576801
$404$			116.769i			0.289032i
$405$		0			0
$406$	78.7227	+	521.647i	0.193898	+	1.28484i
$407$	974.270			2.39378
$408$	96.7106			0.237036
$409$			436.098i			1.06625i	0.846035	+	0.533127i	$0.178983\pi$
$409$			436.098i			1.06625i	−0.846035	+	0.533127i	$0.821017\pi$
$410$		0			0
$411$		−	196.382i		−	0.477815i
$412$		−	205.991i		−	0.499978i
$413$	−124.741	+	18.8248i	−0.302035	+	0.0455807i
$414$	77.8150			0.187959
$415$		0			0
$416$			35.0699i			0.0843026i
$417$	−220.628			−0.529084
$418$		−	663.487i		−	1.58729i
$419$		−	831.867i		−	1.98536i	−0.120767	−	0.992681i	$-0.538536\pi$
$419$		−	831.867i		−	1.98536i	0.120767	−	0.992681i	$-0.461464\pi$
$420$		0			0
$421$	38.1367			0.0905861			0.0452930	−	0.998974i	$-0.485578\pi$
$421$	38.1367			0.0905861			0.0452930	+	0.998974i	$0.485578\pi$
$422$	165.213			0.391501
$423$			31.0258i			0.0733471i
$424$	183.091			0.431819
$425$		0			0
$426$			265.685i			0.623674i
$427$	−635.707	+	95.9358i	−1.48877	+	0.224674i
$428$	117.619			0.274810
$429$	171.404			0.399543
$430$		0			0
$431$	−135.897			−0.315305			−0.157653	−	0.987495i	$-0.550393\pi$
$431$	−135.897			−0.315305			−0.157653	+	0.987495i	$0.550393\pi$
$432$		−	20.7846i		−	0.0481125i
$433$		−	133.395i		−	0.308072i	−0.988065	−	0.154036i	$-0.950773\pi$
$433$		−	133.395i		−	0.308072i	0.988065	−	0.154036i	$-0.0492271\pi$
$434$	367.025	−	55.3884i	0.845679	−	0.127623i
$435$		0			0
$436$	−405.379			−0.929768
$437$		−	539.068i		−	1.23356i
$438$	−180.188			−0.411388
$439$			377.550i			0.860022i	0.902824	+	0.430011i	$0.141490\pi$
$439$			377.550i			0.860022i	−0.902824	+	0.430011i	$0.858510\pi$
$440$		0			0
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	173.078			0.391580
$443$	219.563			0.495628			0.247814	−	0.968808i	$-0.420288\pi$
$443$	219.563			0.495628			0.247814	+	0.968808i	$0.420288\pi$
$444$		−	211.431i		−	0.476196i
$445$		0			0
$446$		−	121.200i		−	0.271748i
$447$			402.184i			0.899740i
$448$	−8.35645	−	55.3730i	−0.0186528	−	0.123600i
$449$	110.769			0.246701			0.123350	−	0.992363i	$-0.460636\pi$
$449$	110.769			0.246701			0.123350	+	0.992363i	$0.460636\pi$
$450$		0			0
$451$		−	340.693i		−	0.755417i
$452$	−338.037			−0.747869
$453$		−	193.557i		−	0.427278i
$454$		−	160.357i		−	0.353209i
$455$		0			0
$456$	−143.987			−0.315760
$457$	−570.254			−1.24782			−0.623911	−	0.781496i	$-0.714457\pi$
$457$	−570.254			−1.24782			−0.623911	+	0.781496i	$0.714457\pi$
$458$			69.5837i			0.151929i
$459$	−102.577			−0.223479
$460$		0			0
$461$			293.487i			0.636631i	0.947985	+	0.318315i	$0.103117\pi$
$461$			293.487i			0.636631i	−0.947985	+	0.318315i	$0.896883\pi$
$462$	−270.636	+	40.8421i	−0.585791	+	0.0884029i
$463$	−633.258			−1.36773			−0.683864	−	0.729609i	$-0.739702\pi$
$463$	−633.258			−1.36773			−0.683864	+	0.729609i	$0.739702\pi$
$464$	−213.164			−0.459405
$465$		0			0
$466$	163.217			0.350251
$467$			459.735i			0.984444i	0.870470	+	0.492222i	$0.163815\pi$
$467$			459.735i			0.984444i	−0.870470	+	0.492222i	$0.836185\pi$
$468$		−	37.1972i		−	0.0794812i
$469$	−19.0476	−	126.217i	−0.0406132	−	0.269119i
$470$		0			0
$471$	−458.362			−0.973167
$472$		−	50.9735i		−	0.107995i
$473$	414.749			0.876849
$474$		−	140.087i		−	0.295543i
$475$		0			0
$476$	−273.279	+	41.2411i	−0.574116	+	0.0866409i
$477$	−194.198			−0.407123
$478$	215.655			0.451162
$479$			232.289i			0.484945i	0.970158	+	0.242473i	$0.0779585\pi$
$479$			232.289i			0.484945i	−0.970158	+	0.242473i	$0.922042\pi$
$480$		0			0
$481$		−	378.388i		−	0.786670i
$482$		−	587.056i		−	1.21796i
$483$	−219.885	+	33.1833i	−0.455248	+	0.0687024i
$484$	267.603			0.552899
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	304.948			0.626176			0.313088	−	0.949724i	$-0.398637\pi$
$487$	304.948			0.626176			0.313088	+	0.949724i	$0.398637\pi$
$488$		−	259.773i		−	0.532321i
$489$		−	92.5690i		−	0.189303i
$490$		0			0
$491$	−666.975			−1.35840			−0.679201	−	0.733953i	$-0.737673\pi$
$491$	−666.975			−1.35840			−0.679201	+	0.733953i	$0.737673\pi$
$492$	−73.9355			−0.150275
$493$			1052.01i			2.13390i
$494$	−257.686			−0.521632
$495$		0			0
$496$			149.980i			0.302378i
$497$	−113.298	−	750.757i	−0.227964	−	1.51058i
$498$	88.5252			0.177761
$499$	963.488			1.93084			0.965419	−	0.260705i	$-0.0839549\pi$
$499$	963.488			1.93084			0.965419	+	0.260705i	$0.0839549\pi$
$500$		0			0
$501$	258.109			0.515187
$502$			388.633i			0.774170i
$503$			335.211i			0.666424i	0.942852	+	0.333212i	$0.108133\pi$
$503$			335.211i			0.666424i	−0.942852	+	0.333212i	$0.891867\pi$
$504$	8.86335	+	58.7319i	0.0175860	+	0.116532i
$505$		0			0
$506$	414.041			0.818262
$507$			226.147i			0.446048i
$508$	95.0342			0.187075
$509$		−	906.823i		−	1.78158i	−0.454417	−	0.890789i	$-0.650152\pi$
$509$		−	906.823i		−	1.78158i	0.454417	−	0.890789i	$-0.349848\pi$
$510$		0			0
$511$	509.164	−	76.8390i	0.996407	−	0.150370i
$512$	22.6274			0.0441942
$513$	152.721			0.297702
$514$		−	93.0157i		−	0.180964i
$515$		0			0
$516$		−	90.0068i		−	0.174432i
$517$			165.083i			0.319310i
$518$	90.1623	+	597.450i	0.174059	+	1.15338i
$519$	64.0094			0.123332
$520$		0			0
$521$		−	218.031i		−	0.418486i	−0.977864	−	0.209243i	$-0.932900\pi$
$521$		−	218.031i		−	0.418486i	0.977864	−	0.209243i	$-0.0670999\pi$
$522$	226.094			0.433131
$523$		−	239.568i		−	0.458066i	−0.973419	−	0.229033i	$-0.926444\pi$
$523$		−	239.568i		−	0.458066i	0.973419	−	0.229033i	$-0.0735563\pi$
$524$		−	27.6332i		−	0.0527351i
$525$		0			0
$526$	217.855			0.414172
$527$	740.185			1.40453
$528$		−	110.591i		−	0.209454i
$529$	−192.602			−0.364087
$530$		0			0
$531$			54.0656i			0.101818i
$532$	406.869	−	61.4014i	0.764792	−	0.115416i
$533$	−132.319			−0.248253
$534$	326.643			0.611691
$535$		0			0
$536$	51.5767			0.0962252
$537$			205.215i			0.382151i
$538$			146.711i			0.272698i
$539$	747.330	−	230.819i	1.38651	−	0.428235i
$540$		0			0
$541$	−228.274			−0.421949			−0.210974	−	0.977492i	$-0.567664\pi$
$541$	−228.274			−0.421949			−0.210974	+	0.977492i	$0.567664\pi$
$542$			75.2320i			0.138804i
$543$	−358.092			−0.659470
$544$		−	111.672i		−	0.205279i
$545$		0			0
$546$	15.8623	+	105.110i	0.0290519	+	0.192509i
$547$	898.348			1.64232			0.821159	−	0.570699i	$-0.193328\pi$
$547$	898.348			1.64232			0.821159	+	0.570699i	$0.193328\pi$
$548$	−226.762			−0.413800
$549$			275.531i			0.501877i
$550$		0			0
$551$		−	1566.28i		−	2.84262i
$552$		−	89.8530i		−	0.162777i
$553$	59.7386	+	395.850i	0.108026	+	0.715824i
$554$	−320.646			−0.578783
$555$		0			0
$556$			254.759i			0.458200i
$557$	−185.202			−0.332500			−0.166250	−	0.986084i	$-0.553166\pi$
$557$	−185.202			−0.332500			−0.166250	+	0.986084i	$0.553166\pi$
$558$		−	159.077i		−	0.285085i
$559$		−	161.081i		−	0.288159i
$560$		0			0
$561$	−545.796			−0.972898
$562$	−486.159			−0.865051
$563$		−	42.3604i		−	0.0752405i	−0.999292	−	0.0376203i	$-0.988022\pi$
$563$		−	42.3604i		−	0.0752405i	0.999292	−	0.0376203i	$-0.0119777\pi$
$564$	35.8255			0.0635205
$565$		0			0
$566$			184.766i			0.326442i
$567$	−9.40101	−	62.2946i	−0.0165803	−	0.109867i
$568$	306.787			0.540117
$569$	−339.139			−0.596027			−0.298013	−	0.954562i	$-0.596324\pi$
$569$	−339.139			−0.596027			−0.298013	+	0.954562i	$0.596324\pi$
$570$		0			0
$571$	922.951			1.61638			0.808188	−	0.588924i	$-0.200448\pi$
$571$	922.951			1.61638			0.808188	+	0.588924i	$0.200448\pi$
$572$		−	197.920i		−	0.346014i
$573$			325.873i			0.568714i
$574$	208.923	−	31.5289i	0.363977	−	0.0549285i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$			606.088i			1.05041i	0.850975	+	0.525206i	$0.176012\pi$
$577$			606.088i			1.05041i	−0.850975	+	0.525206i	$0.823988\pi$
$578$	−142.419			−0.246400
$579$		−	17.7314i		−	0.0306241i
$580$		0			0
$581$	−250.149	+	37.7505i	−0.430549	+	0.0649751i
$582$	71.7085			0.123211
$583$	−1033.29			−1.77237
$584$			208.063i			0.356272i
$585$		0			0
$586$			193.819i			0.330749i
$587$			210.428i			0.358481i	0.983805	+	0.179240i	$0.0573640\pi$
$587$			210.428i			0.358481i	−0.983805	+	0.179240i	$0.942636\pi$
$588$	−50.0911	−	162.182i	−0.0851889	−	0.275819i
$589$	−1102.02			−1.87100
$590$		0			0
$591$		−	379.026i		−	0.641330i
$592$	−244.140			−0.412398
$593$		−	520.732i		−	0.878132i	−0.898455	−	0.439066i	$-0.855309\pi$
$593$		−	520.732i		−	0.878132i	0.898455	−	0.439066i	$-0.144691\pi$
$594$			117.300i			0.197475i
$595$		0			0
$596$	464.402			0.779197
$597$	−192.024			−0.321648
$598$		−	160.806i		−	0.268906i
$599$	−336.725			−0.562145			−0.281073	−	0.959686i	$-0.590690\pi$
$599$	−336.725			−0.562145			−0.281073	+	0.959686i	$0.590690\pi$
$600$		0			0
$601$			992.938i			1.65214i	0.563566	+	0.826071i	$0.309429\pi$
$601$			992.938i			1.65214i	−0.563566	+	0.826071i	$0.690571\pi$
$602$	38.3823	+	254.336i	0.0637581	+	0.422485i
$603$	−54.7053			−0.0907220
$604$	−223.500			−0.370033
$605$		0			0
$606$	−143.012			−0.235993
$607$		−	678.834i		−	1.11834i	−0.829052	−	0.559171i	$-0.811119\pi$
$607$		−	678.834i		−	1.11834i	0.829052	−	0.559171i	$-0.188881\pi$
$608$			166.261i			0.273456i
$609$	−638.884	+	96.4152i	−1.04907	+	0.158317i
$610$		0			0
$611$	64.1152			0.104935
$612$			118.446i			0.193539i
$613$	−212.334			−0.346385			−0.173193	−	0.984888i	$-0.555408\pi$
$613$	−212.334			−0.346385			−0.173193	+	0.984888i	$0.555408\pi$
$614$			194.517i			0.316802i
$615$		0			0
$616$	47.1604	+	312.503i	0.0765592	+	0.507310i
$617$	−283.176			−0.458957			−0.229478	−	0.973314i	$-0.573702\pi$
$617$	−283.176			−0.458957			−0.229478	+	0.973314i	$0.573702\pi$
$618$	252.287			0.408231
$619$		−	502.207i		−	0.811320i	−0.914024	−	0.405660i	$-0.867042\pi$
$619$		−	502.207i		−	0.811320i	0.914024	−	0.405660i	$-0.132958\pi$
$620$		0			0
$621$			95.3035i			0.153468i
$622$			798.358i			1.28353i
$623$	−923.009	+	139.293i	−1.48156	+	0.223585i
$624$	−42.9516			−0.0688328
$625$		0			0
$626$		−	811.268i		−	1.29596i
$627$	812.603			1.29602
$628$			529.270i			0.842787i
$629$			1204.89i			1.91556i
$630$		0			0
$631$	−246.851			−0.391206			−0.195603	−	0.980683i	$-0.562666\pi$
$631$	−246.851			−0.391206			−0.195603	+	0.980683i	$0.562666\pi$
$632$	−161.759			−0.255948
$633$			202.344i			0.319659i
$634$	91.5371			0.144380
$635$		0			0
$636$			224.240i			0.352579i
$637$	−89.6456	−	290.249i	−0.140731	−	0.455649i
$638$	1203.01			1.88560
$639$	−325.396			−0.509227
$640$		0			0
$641$	366.399			0.571606			0.285803	−	0.958288i	$-0.407740\pi$
$641$	366.399			0.571606			0.285803	+	0.958288i	$0.407740\pi$
$642$			144.053i			0.224381i
$643$			529.036i			0.822763i	0.911463	+	0.411381i	$0.134954\pi$
$643$			529.036i			0.822763i	−0.911463	+	0.411381i	$0.865046\pi$
$644$	38.3167	+	253.901i	0.0594981	+	0.394257i
$645$		0			0
$646$	820.540			1.27019
$647$			361.039i			0.558020i	0.960288	+	0.279010i	$0.0900062\pi$
$647$			361.039i			0.558020i	−0.960288	+	0.279010i	$0.909994\pi$
$648$	25.4558			0.0392837
$649$			287.674i			0.443257i
$650$		0			0
$651$	67.8367	+	449.512i	0.104204	+	0.690494i
$652$	−106.890			−0.163941
$653$	−1216.58			−1.86306			−0.931532	−	0.363658i	$-0.881528\pi$
$653$	−1216.58			−1.86306			−0.931532	+	0.363658i	$0.881528\pi$
$654$		−	496.485i		−	0.759152i
$655$		0			0
$656$			85.3734i			0.130142i
$657$		−	220.684i		−	0.335897i
$658$	−101.234	+	15.2774i	−0.153851	+	0.0232179i
$659$	331.022			0.502310			0.251155	−	0.967947i	$-0.419190\pi$
$659$	331.022			0.502310			0.251155	+	0.967947i	$0.419190\pi$
$660$		0			0
$661$			970.308i			1.46794i	0.679182	+	0.733970i	$0.262335\pi$
$661$			970.308i			1.46794i	−0.679182	+	0.733970i	$0.737665\pi$
$662$	178.761			0.270032
$663$			211.977i			0.319724i
$664$		−	102.220i		−	0.153946i
$665$		0			0
$666$	258.949			0.388813
$667$	977.417			1.46539
$668$		−	298.038i		−	0.446165i
$669$	148.439			0.221882
$670$		0			0
$671$			1466.05i			2.18488i
$672$	67.8178	−	10.2345i	0.100919	−	0.0152299i
$673$	−886.937			−1.31789			−0.658943	−	0.752193i	$-0.728996\pi$
$673$	−886.937			−1.31789			−0.658943	+	0.752193i	$0.728996\pi$
$674$	−104.187			−0.154581
$675$		0			0
$676$	261.132			0.386289
$677$			13.9949i			0.0206720i	0.999947	+	0.0103360i	$0.00329010\pi$
$677$			13.9949i			0.0206720i	−0.999947	+	0.0103360i	$0.996710\pi$
$678$		−	414.009i		−	0.610633i
$679$	−202.630	+	30.5793i	−0.298424	+	0.0450357i
$680$		0			0
$681$	196.396			0.288394
$682$		−	846.424i		−	1.24109i
$683$	−1080.03			−1.58130			−0.790651	−	0.612267i	$-0.790258\pi$
$683$	−1080.03			−1.58130			−0.790651	+	0.612267i	$0.790258\pi$
$684$		−	176.347i		−	0.257817i
$685$		0			0
$686$	210.705	+	436.923i	0.307150	+	0.636914i
$687$	−85.2223			−0.124050
$688$	−103.931			−0.151062
$689$			401.312i			0.582456i
$690$		0			0
$691$		−	810.183i		−	1.17248i	−0.810138	−	0.586240i	$-0.800608\pi$
$691$		−	810.183i		−	1.17248i	0.810138	−	0.586240i	$-0.199392\pi$
$692$		−	73.9117i		−	0.106809i
$693$	−50.0212	−	331.459i	−0.0721807	−	0.478297i
$694$	−782.204			−1.12710
$695$		0			0
$696$		−	261.071i		−	0.375102i
$697$	421.338			0.604502
$698$			527.339i			0.755500i
$699$			199.899i			0.285978i
$700$		0			0
$701$	588.867			0.840039			0.420019	−	0.907515i	$-0.362023\pi$
$701$	588.867			0.840039			0.420019	+	0.907515i	$0.362023\pi$
$702$	45.5571			0.0648962
$703$		−	1793.89i		−	2.55176i
$704$	−127.700			−0.181392
$705$		0			0
$706$		−	687.433i		−	0.973701i
$707$	404.115	−	60.9858i	0.571591	−	0.0862599i
$708$	62.4295			0.0881773
$709$	−1141.19			−1.60958			−0.804789	−	0.593561i	$-0.797722\pi$
$709$	−1141.19			−1.60958			−0.804789	+	0.593561i	$0.797722\pi$
$710$		0			0
$711$	171.571			0.241310
$712$		−	377.175i		−	0.529740i
$713$		−	687.700i		−	0.964516i
$714$	−50.5098	−	334.697i	−0.0707420	−	0.468764i
$715$		0			0
$716$	236.962			0.330952
$717$			264.123i			0.368372i
$718$	437.526			0.609368
$719$			28.4620i			0.0395856i	0.999804	+	0.0197928i	$0.00630065\pi$
$719$			28.4620i			0.0395856i	−0.999804	+	0.0197928i	$0.993699\pi$
$720$		0			0
$721$	−712.897	+	107.585i	−0.988761	+	0.149216i
$722$	−711.123			−0.984935
$723$	718.994			0.994460
$724$			413.489i			0.571118i
$725$		0			0
$726$			327.746i			0.451440i
$727$		−	821.139i		−	1.12949i	−0.825266	−	0.564745i	$-0.808975\pi$
$727$		−	821.139i		−	1.12949i	0.825266	−	0.564745i	$-0.191025\pi$
$728$	121.370	−	18.3162i	0.166717	−	0.0251597i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			512.924i			0.701674i
$732$	318.155			0.434639
$733$		−	1135.68i		−	1.54936i	−0.632353	−	0.774680i	$-0.717911\pi$
$733$		−	1135.68i		−	1.54936i	0.632353	−	0.774680i	$-0.282089\pi$
$734$			622.451i			0.848026i
$735$		0			0
$736$	−103.753			−0.140969
$737$	−291.078			−0.394950
$738$		−	90.5521i		−	0.122699i
$739$	449.526			0.608289			0.304145	−	0.952626i	$-0.401629\pi$
$739$	449.526			0.608289			0.304145	+	0.952626i	$0.401629\pi$
$740$		0			0
$741$		−	315.600i		−	0.425910i
$742$	−95.6246	−	633.645i	−0.128874	−	0.853969i
$743$	−27.5435			−0.0370707			−0.0185353	−	0.999828i	$-0.505900\pi$
$743$	−27.5435			−0.0370707			−0.0185353	+	0.999828i	$0.505900\pi$
$744$	−183.687			−0.246891
$745$		0			0
$746$	627.547			0.841215
$747$			108.421i			0.145142i
$748$			630.231i			0.842554i
$749$	−61.4296	−	407.056i	−0.0820155	−	0.543466i
$750$		0			0
$751$	−1424.00			−1.89614			−0.948070	−	0.318062i	$-0.896968\pi$
$751$	−1424.00			−1.89614			−0.948070	+	0.318062i	$0.896968\pi$
$752$		−	41.3678i		−	0.0550103i
$753$	−475.976			−0.632107
$754$		−	467.226i		−	0.619664i
$755$		0			0
$756$	−71.9316	+	10.8553i	−0.0951477	+	0.0143589i
$757$	−47.2357			−0.0623985			−0.0311992	−	0.999513i	$-0.509933\pi$
$757$	−47.2357			−0.0623985			−0.0311992	+	0.999513i	$0.509933\pi$
$758$	−627.909			−0.828376
$759$			507.094i			0.668108i
$760$		0			0
$761$		−	64.6316i		−	0.0849299i	−0.999098	−	0.0424649i	$-0.986479\pi$
$761$		−	64.6316i		−	0.0849299i	0.999098	−	0.0424649i	$-0.0135211\pi$
$762$			116.393i			0.152746i
$763$	211.720	+	1402.94i	0.277484	+	1.83872i
$764$	376.286			0.492520
$765$		0			0
$766$		−	821.615i		−	1.07260i
$767$	111.727			0.145668
$768$			27.7128i			0.0360844i
$769$		−	931.435i		−	1.21123i	−0.795758	−	0.605615i	$-0.792927\pi$
$769$		−	931.435i		−	1.21123i	0.795758	−	0.605615i	$-0.207073\pi$
$770$		0			0
$771$	113.920			0.147757
$772$	−20.4744			−0.0265213
$773$		−	1232.95i		−	1.59501i	−0.603309	−	0.797507i	$-0.706152\pi$
$773$		−	1232.95i		−	1.59501i	0.603309	−	0.797507i	$-0.293848\pi$
$774$	110.235			0.142423
$775$		0			0
$776$		−	82.8019i		−	0.106703i
$777$	−731.724	+	110.426i	−0.941729	+	0.142118i
$778$	−780.858			−1.00367
$779$	−627.305			−0.805270
$780$		0			0
$781$	−1731.38			−2.21688
$782$			512.047i			0.654792i
$783$			276.908i			0.353650i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$		0			0
$786$	33.8436			0.0430580
$787$			545.472i			0.693103i	0.938031	+	0.346552i	$0.112647\pi$
$787$			545.472i			0.693103i	−0.938031	+	0.346552i	$0.887353\pi$
$788$	−437.662			−0.555408
$789$			266.816i			0.338170i
$790$		0			0
$791$	176.549	+	1169.88i	0.223198	+	1.47899i
$792$	135.446			0.171018
$793$	569.387			0.718017
$794$			239.038i			0.301056i
$795$		0			0
$796$			221.730i			0.278556i
$797$		−	46.3471i		−	0.0581519i	−0.999577	−	0.0290759i	$-0.990744\pi$
$797$		−	46.3471i		−	0.0581519i	0.999577	−	0.0290759i	$-0.00925646\pi$
$798$	75.2011	+	498.311i	0.0942369	+	0.624450i
$799$	−204.160			−0.255519
$800$		0			0
$801$			400.055i			0.499444i
$802$	81.9586			0.102193
$803$		−	1174.22i		−	1.46230i
$804$			63.1683i			0.0785675i
$805$		0			0
$806$	−328.735			−0.407860
$807$	−179.684			−0.222657
$808$			165.136i			0.204376i
$809$	−996.788			−1.23212			−0.616062	−	0.787698i	$-0.711273\pi$
$809$	−996.788			−1.23212			−0.616062	+	0.787698i	$0.711273\pi$
$810$		0			0
$811$		−	524.649i		−	0.646917i	−0.946242	−	0.323458i	$-0.895154\pi$
$811$		−	524.649i		−	0.646917i	0.946242	−	0.323458i	$-0.104846\pi$
$812$	111.331	+	737.720i	0.137107	+	0.908522i
$813$	−92.1400			−0.113333
$814$	1377.83			1.69266
$815$		0			0
$816$	136.769			0.167610
$817$		−	763.662i		−	0.934715i
$818$			616.735i			0.753955i
$819$	−128.733	+	19.4273i	−0.157183	+	0.0237207i
$820$		0			0
$821$	89.8739			0.109469			0.0547344	−	0.998501i	$-0.482569\pi$
$821$	89.8739			0.109469			0.0547344	+	0.998501i	$0.482569\pi$
$822$		−	277.726i		−	0.337866i
$823$	601.322			0.730647			0.365323	−	0.930881i	$-0.380958\pi$
$823$	601.322			0.730647			0.365323	+	0.930881i	$0.380958\pi$
$824$		−	291.315i		−	0.353538i
$825$		0			0
$826$	−176.410	+	26.6223i	−0.213571	+	0.0322304i
$827$	−742.670			−0.898029			−0.449014	−	0.893525i	$-0.648225\pi$
$827$	−742.670			−0.898029			−0.449014	+	0.893525i	$0.648225\pi$
$828$	110.047			0.132907
$829$		−	1323.55i		−	1.59657i	−0.602282	−	0.798283i	$-0.705742\pi$
$829$		−	1323.55i		−	1.59657i	0.602282	−	0.798283i	$-0.294258\pi$
$830$		0			0
$831$		−	392.709i		−	0.472574i
$832$			49.5963i			0.0596109i
$833$	285.455	+	924.229i	0.342684	+	1.10952i
$834$	−312.015			−0.374119
$835$		0			0
$836$		−	938.313i		−	1.12238i
$837$	194.829			0.232771
$838$		−	1176.44i		−	1.40386i
$839$		−	206.287i		−	0.245872i	−0.992415	−	0.122936i	$-0.960769\pi$
$839$		−	206.287i		−	0.245872i	0.992415	−	0.122936i	$-0.0392310\pi$
$840$		0			0
$841$	1998.92			2.37684
$842$	53.9335			0.0640540
$843$		−	595.420i		−	0.706311i
$844$	233.647			0.276833
$845$		0			0
$846$			43.8771i			0.0518642i
$847$	−139.763	−	926.125i	−0.165010	−	1.09342i
$848$	258.930			0.305342
$849$	−226.291			−0.266539
$850$		0			0
$851$	1119.45			1.31545
$852$			375.735i			0.441004i
$853$			1220.74i			1.43112i	0.698554	+	0.715558i	$0.253827\pi$
$853$			1220.74i			1.43112i	−0.698554	+	0.715558i	$0.746173\pi$
$854$	−899.025	+	135.674i	−1.05272	+	0.158868i
$855$		0			0
$856$	166.338			0.194320
$857$			1031.50i			1.20362i	0.798641	+	0.601808i	$0.205553\pi$
$857$			1031.50i			1.20362i	−0.798641	+	0.601808i	$0.794447\pi$
$858$	242.402			0.282520
$859$		−	263.066i		−	0.306247i	−0.988207	−	0.153124i	$-0.951067\pi$
$859$		−	263.066i		−	0.306247i	0.988207	−	0.153124i	$-0.0489333\pi$
$860$		0			0
$861$	38.6149	+	255.877i	0.0448489	+	0.297186i
$862$	−192.187			−0.222954
$863$	−811.835			−0.940713			−0.470356	−	0.882477i	$-0.655875\pi$
$863$	−811.835			−0.940713			−0.470356	+	0.882477i	$0.655875\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$		−	188.649i		−	0.217840i
$867$		−	174.427i		−	0.201185i
$868$	519.051	−	78.3310i	0.597985	−	0.0902431i
$869$	912.902			1.05052
$870$		0			0
$871$			113.049i			0.129792i
$872$	−573.292			−0.657445
$873$			87.8247i			0.100601i
$874$		−	762.357i		−	0.872262i
$875$		0			0
$876$	−254.824			−0.290895
$877$	−1294.40			−1.47595			−0.737973	−	0.674830i	$-0.764217\pi$
$877$	−1294.40			−1.47595			−0.737973	+	0.674830i	$0.764217\pi$
$878$			533.936i			0.608127i
$879$	−237.379			−0.270055
$880$		0			0
$881$		−	1592.39i		−	1.80748i	−0.428084	−	0.903739i	$-0.640811\pi$
$881$		−	1592.39i		−	1.80748i	0.428084	−	0.903739i	$-0.359189\pi$
$882$	198.631	−	61.3488i	0.225205	−	0.0695565i
$883$	−760.044			−0.860752			−0.430376	−	0.902650i	$-0.641619\pi$
$883$	−760.044			−0.860752			−0.430376	+	0.902650i	$0.641619\pi$
$884$	244.770			0.276889
$885$		0			0
$886$	310.509			0.350462
$887$			219.050i			0.246956i	0.992347	+	0.123478i	$0.0394049\pi$
$887$			219.050i			0.246956i	−0.992347	+	0.123478i	$0.960595\pi$
$888$		−	299.009i		−	0.336722i
$889$	−49.6343	−	328.896i	−0.0558316	−	0.369961i
$890$		0			0
$891$	−143.663			−0.161237
$892$		−	171.402i		−	0.192155i
$893$	303.962			0.340383
$894$			568.774i			0.636212i
$895$		0			0
$896$	−11.8178	−	78.3093i	−0.0131895	−	0.0873987i
$897$	196.946			0.219560
$898$	156.651			0.174444
$899$		−	1998.14i		−	2.22262i
$900$		0			0
$901$		−	1277.88i		−	1.41829i
$902$		−	481.813i		−	0.534161i
$903$	−311.497	+	47.0086i	−0.344958	+	0.0520582i
$904$	−478.056			−0.528823
$905$		0			0
$906$		−	273.731i		−	0.302131i
$907$	41.6200			0.0458875			0.0229438	−	0.999737i	$-0.492696\pi$
$907$	41.6200			0.0458875			0.0229438	+	0.999737i	$0.492696\pi$
$908$		−	226.779i		−	0.249757i
$909$		−	175.153i		−	0.192688i
$910$		0			0
$911$	−522.703			−0.573769			−0.286884	−	0.957965i	$-0.592620\pi$
$911$	−522.703			−0.573769			−0.286884	+	0.957965i	$0.592620\pi$
$912$	−203.628			−0.223276
$913$			576.889i			0.631861i
$914$	−806.461			−0.882343
$915$		0			0
$916$			98.4062i			0.107430i
$917$	−95.6333	+	14.4322i	−0.104289	+	0.0157385i
$918$	−145.066			−0.158024
$919$	−1356.85			−1.47644			−0.738222	−	0.674557i	$-0.764334\pi$
$919$	−1356.85			−1.47644			−0.738222	+	0.674557i	$0.764334\pi$
$920$		0			0
$921$	−238.233			−0.258668
$922$			415.053i			0.450166i
$923$			672.435i			0.728532i
$924$	−382.736	+	57.7595i	−0.414217	+	0.0625103i
$925$		0			0
$926$	−895.562			−0.967130
$927$			308.987i			0.333319i
$928$	−301.459			−0.324848
$929$			274.165i			0.295118i	0.989053	+	0.147559i	$0.0471416\pi$
$929$			274.165i			0.295118i	−0.989053	+	0.147559i	$0.952858\pi$
$930$		0			0
$931$	−424.998	−	1376.03i	−0.456496	−	1.47801i
$932$	230.823			0.247665
$933$	−977.785			−1.04800
$934$			650.164i			0.696107i
$935$		0			0
$936$		−	52.6048i		−	0.0562017i
$937$		−	938.107i		−	1.00118i	−0.865684	−	0.500591i	$-0.833116\pi$
$937$		−	938.107i		−	1.00118i	0.865684	−	0.500591i	$-0.166884\pi$
$938$	−26.9374	−	178.497i	−0.0287179	−	0.190296i
$939$	993.596			1.05814
$940$		0			0
$941$			595.662i			0.633010i	0.948591	+	0.316505i	$0.102509\pi$
$941$			595.662i			0.633010i	−0.948591	+	0.316505i	$0.897491\pi$
$942$	−648.221			−0.688133
$943$		−	391.462i		−	0.415124i
$944$		−	72.0874i		−	0.0763638i
$945$		0			0
$946$	586.544			0.620026
$947$	114.789			0.121213			0.0606067	−	0.998162i	$-0.480696\pi$
$947$	114.789			0.121213			0.0606067	+	0.998162i	$0.480696\pi$
$948$		−	198.113i		−	0.208980i
$949$	−456.046			−0.480555
$950$		0			0
$951$			112.110i			0.117886i
$952$	−386.475	+	58.3237i	−0.405961	+	0.0612644i
$953$	−349.928			−0.367186			−0.183593	−	0.983002i	$-0.558773\pi$
$953$	−349.928			−0.367186			−0.183593	+	0.983002i	$0.558773\pi$
$954$	−274.637			−0.287879
$955$		0			0
$956$	304.983			0.319020
$957$			1473.38i			1.53958i
$958$			328.506i			0.342908i
$959$	118.433	+	784.782i	0.123496	+	0.818334i
$960$		0			0
$961$	−444.867			−0.462921
$962$		−	535.122i		−	0.556259i
$963$	−176.428			−0.183206
$964$		−	830.223i		−	0.861227i
$965$		0			0
$966$	−310.964	+	46.9282i	−0.321909	+	0.0485800i
$967$	−246.460			−0.254871			−0.127436	−	0.991847i	$-0.540675\pi$
$967$	−246.460			−0.254871			−0.127436	+	0.991847i	$0.540675\pi$
$968$	378.448			0.390959
$969$			1004.95i			1.03710i
$970$		0			0
$971$			1064.63i			1.09642i	0.836339	+	0.548212i	$0.184691\pi$
$971$			1064.63i			1.09642i	−0.836339	+	0.548212i	$0.815309\pi$
$972$			31.1769i			0.0320750i
$973$	881.674	−	133.055i	0.906140	−	0.136747i
$974$	431.261			0.442773
$975$		0			0
$976$		−	367.374i		−	0.376408i
$977$	−344.273			−0.352377			−0.176189	−	0.984356i	$-0.556377\pi$
$977$	−344.273			−0.352377			−0.176189	+	0.984356i	$0.556377\pi$
$978$		−	130.912i		−	0.133857i
$979$			2128.62i			2.17428i
$980$		0			0
$981$	608.068			0.619845
$982$	−943.245			−0.960535
$983$		−	25.5898i		−	0.0260324i	−0.999915	−	0.0130162i	$-0.995857\pi$
$983$		−	25.5898i		−	0.0260324i	0.999915	−	0.0130162i	$-0.00414329\pi$
$984$	−104.561			−0.106261
$985$		0			0
$986$			1487.77i			1.50890i
$987$	−18.7109	−	123.985i	−0.0189573	−	0.125619i
$988$	−364.423			−0.368849
$989$	476.553			0.481854
$990$		0			0
$991$	406.270			0.409960			0.204980	−	0.978766i	$-0.434287\pi$
$991$	406.270			0.409960			0.204980	+	0.978766i	$0.434287\pi$
$992$			212.103i			0.213814i
$993$			218.937i			0.220480i
$994$	−160.228	−	1061.73i	−0.161195	−	1.06814i
$995$		0			0
$996$	125.193			0.125696
$997$			557.561i			0.559239i	0.960111	+	0.279620i	$0.0902083\pi$
$997$			557.561i			0.559239i	−0.960111	+	0.279620i	$0.909792\pi$
$998$	1362.58			1.36531
$999$			317.147i			0.317464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.b.601.7		8
5.2	odd	4		1050.3.h.b.349.16		16
5.3	odd	4		1050.3.h.b.349.1		16
5.4	even	2		210.3.f.a.181.2	✓	8
7.6	odd	2	inner	1050.3.f.b.601.5		8
15.14	odd	2		630.3.f.c.181.6		8
20.19	odd	2		1680.3.s.a.1441.8		8
35.13	even	4		1050.3.h.b.349.8		16
35.27	even	4		1050.3.h.b.349.9		16
35.34	odd	2		210.3.f.a.181.3	yes	8
105.104	even	2		630.3.f.c.181.8		8
140.139	even	2		1680.3.s.a.1441.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.2	✓	8	5.4	even	2
210.3.f.a.181.3	yes	8	35.34	odd	2
630.3.f.c.181.6		8	15.14	odd	2
630.3.f.c.181.8		8	105.104	even	2
1050.3.f.b.601.5		8	7.6	odd	2	inner
1050.3.f.b.601.7		8	1.1	even	1	trivial
1050.3.h.b.349.1		16	5.3	odd	4
1050.3.h.b.349.8		16	35.13	even	4
1050.3.h.b.349.9		16	35.27	even	4
1050.3.h.b.349.16		16	5.2	odd	4
1680.3.s.a.1441.2		8	140.139	even	2
1680.3.s.a.1441.8		8	20.19	odd	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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -15.9625 q^{11} +3.46410i q^{12} +6.19954i q^{13} +(-1.47723 - 9.78866i) q^{14} +4.00000 q^{16} -19.7410i q^{17} -4.24264 q^{18} +29.3912i q^{19} +(11.9886 - 1.80922i) q^{21} -22.5744 q^{22} -18.3412 q^{23} +4.89898i q^{24} +8.76747i q^{26} -5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} -53.2909 q^{29} +37.4949i q^{31} +5.65685 q^{32} -27.6479i q^{33} -27.9179i q^{34} -6.00000 q^{36} -61.0349 q^{37} +41.5654i q^{38} -10.7379 q^{39} +21.3433i q^{41} +(16.9545 - 2.55863i) q^{42} -25.9827 q^{43} -31.9250 q^{44} -25.9383 q^{46} -10.3419i q^{47} +6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} +34.1924 q^{51} +12.3991i q^{52} +64.7326 q^{53} -7.34847i q^{54} +(-2.95445 - 19.5773i) q^{56} -50.9070 q^{57} -75.3647 q^{58} -18.0219i q^{59} -91.8436i q^{61} +53.0258i q^{62} +(3.13367 + 20.7649i) q^{63} +8.00000 q^{64} -39.1000i q^{66} +18.2351 q^{67} -39.4819i q^{68} -31.7678i q^{69} +108.465 q^{71} -8.48528 q^{72} +73.5614i q^{73} -86.3164 q^{74} +58.7823i q^{76} +(16.6737 + 110.486i) q^{77} -15.1857 q^{78} -57.1904 q^{79} +9.00000 q^{81} +30.1840i q^{82} -36.1402i q^{83} +(23.9772 - 3.61845i) q^{84} -36.7451 q^{86} -92.3026i q^{87} -45.1488 q^{88} -133.352i q^{89} +(42.9109 - 6.47576i) q^{91} -36.6823 q^{92} -64.9431 q^{93} -14.6257i q^{94} +9.79796i q^{96} -29.2749i q^{97} +(-66.2104 + 20.4496i) q^{98} +47.8875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 24 * q^9	\( 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * q^99

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