LMFDB - Embedded newform 1050.3.f.d.601.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 $ x^12 - 2x^11 + 103x^10 + 14x^9 + 7600x^8 + 1474x^7 + 229961x^6 + 442438x^5 + 4765612x^4 + 4021754x^3 + 21002899x^2 - 8701742*x + 69739201
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.10
Root			$-1.37625 + 2.38373i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.d.601.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.84490 - 1.46536i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.84490 - 1.46536i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -5.87800 q^{11} +3.46410i q^{12} -2.06416i q^{13} +(-9.68016 - 2.07233i) q^{14} +4.00000 q^{16} -2.59754i q^{17} -4.24264 q^{18} -14.3990i q^{19} +(2.53808 - 11.8557i) q^{21} -8.31274 q^{22} +4.73565 q^{23} +4.89898i q^{24} -2.91916i q^{26} -5.19615i q^{27} +(-13.6898 - 2.93072i) q^{28} -16.1571 q^{29} -48.3772i q^{31} +5.65685 q^{32} -10.1810i q^{33} -3.67347i q^{34} -6.00000 q^{36} -46.3013 q^{37} -20.3632i q^{38} +3.57522 q^{39} -74.7122i q^{41} +(3.58939 - 16.7665i) q^{42} +10.4038 q^{43} -11.7560 q^{44} +6.69723 q^{46} -35.0672i q^{47} +6.92820i q^{48} +(44.7054 + 20.0605i) q^{49} +4.49907 q^{51} -4.12831i q^{52} -39.9926 q^{53} -7.34847i q^{54} +(-19.3603 - 4.14467i) q^{56} +24.9397 q^{57} -22.8495 q^{58} +60.1573i q^{59} -73.1619i q^{61} -68.4156i q^{62} +(20.5347 + 4.39608i) q^{63} +8.00000 q^{64} -14.3981i q^{66} -39.5941 q^{67} -5.19507i q^{68} +8.20239i q^{69} -39.3463 q^{71} -8.48528 q^{72} -11.8315i q^{73} -65.4800 q^{74} -28.7979i q^{76} +(40.2343 + 8.61339i) q^{77} +5.05613 q^{78} +41.2398 q^{79} +9.00000 q^{81} -105.659i q^{82} +126.222i q^{83} +(5.07616 - 23.7114i) q^{84} +14.7133 q^{86} -27.9849i q^{87} -16.6255 q^{88} -92.1225i q^{89} +(-3.02473 + 14.1290i) q^{91} +9.47131 q^{92} +83.7917 q^{93} -49.5925i q^{94} +9.79796i q^{96} -4.26795i q^{97} +(63.2230 + 28.3698i) q^{98} +17.6340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9}+O(q^{10}) $ 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9	$ 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9} - 16 q^{11} + 8 q^{14} + 48 q^{16} - 6 q^{21} + 48 q^{22} + 20 q^{28} + 48 q^{29} - 72 q^{36} - 64 q^{37} - 12 q^{39} - 24 q^{42} + 108 q^{43} - 32 q^{44} + 80 q^{46} + 118 q^{49} + 72 q^{51} - 176 q^{53} + 16 q^{56} + 132 q^{57} - 128 q^{58} - 30 q^{63} + 96 q^{64} + 4 q^{67} + 248 q^{71} - 64 q^{74} + 396 q^{77} - 48 q^{78} - 208 q^{79} + 108 q^{81} - 12 q^{84} + 128 q^{86} + 96 q^{88} - 158 q^{91} - 252 q^{93} + 240 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9 - 16 * q^11 + 8 * q^14 + 48 * q^16 - 6 * q^21 + 48 * q^22 + 20 * q^28 + 48 * q^29 - 72 * q^36 - 64 * q^37 - 12 * q^39 - 24 * q^42 + 108 * q^43 - 32 * q^44 + 80 * q^46 + 118 * q^49 + 72 * q^51 - 176 * q^53 + 16 * q^56 + 132 * q^57 - 128 * q^58 - 30 * q^63 + 96 * q^64 + 4 * q^67 + 248 * q^71 - 64 * q^74 + 396 * q^77 - 48 * q^78 - 208 * q^79 + 108 * q^81 - 12 * q^84 + 128 * q^86 + 96 * q^88 - 158 * q^91 - 252 * q^93 + 240 * q^98 + 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
$7$	−6.84490	−	1.46536i	−0.977844	−	0.209337i
$7$	−6.84490	−	1.46536i	−0.977844	−	0.209337i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−5.87800			−0.534363			−0.267182	−	0.963646i	$-0.586092\pi$
$11$	−5.87800			−0.534363			−0.267182	+	0.963646i	$0.586092\pi$
$12$			3.46410i			0.288675i
$13$		−	2.06416i		−	0.158781i	−0.996844	−	0.0793906i	$-0.974703\pi$
$13$		−	2.06416i		−	0.158781i	0.996844	−	0.0793906i	$-0.0252974\pi$
$14$	−9.68016	−	2.07233i	−0.691440	−	0.148024i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	2.59754i		−	0.152796i	−0.997077	−	0.0763982i	$-0.975658\pi$
$17$		−	2.59754i		−	0.152796i	0.997077	−	0.0763982i	$-0.0243420\pi$
$18$	−4.24264			−0.235702
$19$		−	14.3990i		−	0.757840i	−0.925429	−	0.378920i	$-0.876296\pi$
$19$		−	14.3990i		−	0.757840i	0.925429	−	0.378920i	$-0.123704\pi$
$20$		0			0
$21$	2.53808	−	11.8557i	0.120861	−	0.564558i
$22$	−8.31274			−0.377852
$23$	4.73565			0.205898			0.102949	−	0.994687i	$-0.467172\pi$
$23$	4.73565			0.205898			0.102949	+	0.994687i	$0.467172\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$		−	2.91916i		−	0.112275i
$27$		−	5.19615i		−	0.192450i
$28$	−13.6898	−	2.93072i	−0.488922	−	0.104669i
$29$	−16.1571			−0.557140			−0.278570	−	0.960416i	$-0.589860\pi$
$29$	−16.1571			−0.557140			−0.278570	+	0.960416i	$0.589860\pi$
$30$		0			0
$31$		−	48.3772i		−	1.56055i	−0.625434	−	0.780277i	$-0.715078\pi$
$31$		−	48.3772i		−	1.56055i	0.625434	−	0.780277i	$-0.284922\pi$
$32$	5.65685			0.176777
$33$		−	10.1810i		−	0.308515i
$34$		−	3.67347i		−	0.108043i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−46.3013			−1.25139			−0.625694	−	0.780069i	$-0.715184\pi$
$37$	−46.3013			−1.25139			−0.625694	+	0.780069i	$0.715184\pi$
$38$		−	20.3632i		−	0.535874i
$39$	3.57522			0.0916724
$40$		0			0
$41$		−	74.7122i		−	1.82225i	−0.412132	−	0.911124i	$-0.635216\pi$
$41$		−	74.7122i		−	1.82225i	0.412132	−	0.911124i	$-0.364784\pi$
$42$	3.58939	−	16.7665i	0.0854616	−	0.399203i
$43$	10.4038			0.241950			0.120975	−	0.992656i	$-0.461398\pi$
$43$	10.4038			0.241950			0.120975	+	0.992656i	$0.461398\pi$
$44$	−11.7560			−0.267182
$45$		0			0
$46$	6.69723			0.145592
$47$		−	35.0672i		−	0.746111i	−0.927809	−	0.373055i	$-0.878310\pi$
$47$		−	35.0672i		−	0.746111i	0.927809	−	0.373055i	$-0.121690\pi$
$48$			6.92820i			0.144338i
$49$	44.7054	+	20.0605i	0.912356	+	0.409398i
$50$		0			0
$51$	4.49907			0.0882170
$52$		−	4.12831i		−	0.0793906i
$53$	−39.9926			−0.754578			−0.377289	−	0.926096i	$-0.623144\pi$
$53$	−39.9926			−0.754578			−0.377289	+	0.926096i	$0.623144\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−19.3603	−	4.14467i	−0.345720	−	0.0740119i
$57$	24.9397			0.437539
$58$	−22.8495			−0.393958
$59$			60.1573i			1.01962i	0.860288	+	0.509808i	$0.170284\pi$
$59$			60.1573i			1.01962i	−0.860288	+	0.509808i	$0.829716\pi$
$60$		0			0
$61$		−	73.1619i		−	1.19938i	−0.800234	−	0.599688i	$-0.795291\pi$
$61$		−	73.1619i		−	1.19938i	0.800234	−	0.599688i	$-0.204709\pi$
$62$		−	68.4156i		−	1.10348i
$63$	20.5347	+	4.39608i	0.325948	+	0.0697791i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	14.3981i		−	0.218153i
$67$	−39.5941			−0.590956			−0.295478	−	0.955350i	$-0.595479\pi$
$67$	−39.5941			−0.590956			−0.295478	+	0.955350i	$0.595479\pi$
$68$		−	5.19507i		−	0.0763982i
$69$			8.20239i			0.118875i
$70$		0			0
$71$	−39.3463			−0.554173			−0.277087	−	0.960845i	$-0.589369\pi$
$71$	−39.3463			−0.554173			−0.277087	+	0.960845i	$0.589369\pi$
$72$	−8.48528			−0.117851
$73$		−	11.8315i		−	0.162075i	−0.996711	−	0.0810377i	$-0.974177\pi$
$73$		−	11.8315i		−	0.162075i	0.996711	−	0.0810377i	$-0.0258234\pi$
$74$	−65.4800			−0.884864
$75$		0			0
$76$		−	28.7979i		−	0.378920i
$77$	40.2343	+	8.61339i	0.522524	+	0.111862i
$78$	5.05613			0.0648222
$79$	41.2398			0.522023			0.261012	−	0.965336i	$-0.415944\pi$
$79$	41.2398			0.522023			0.261012	+	0.965336i	$0.415944\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	105.659i		−	1.28852i
$83$			126.222i			1.52075i	0.649485	+	0.760374i	$0.274984\pi$
$83$			126.222i			1.52075i	−0.649485	+	0.760374i	$0.725016\pi$
$84$	5.07616	−	23.7114i	0.0604304	−	0.282279i
$85$		0			0
$86$	14.7133			0.171084
$87$		−	27.9849i		−	0.321665i
$88$	−16.6255			−0.188926
$89$		−	92.1225i		−	1.03508i	−0.855658	−	0.517542i	$-0.826847\pi$
$89$		−	92.1225i		−	1.03508i	0.855658	−	0.517542i	$-0.173153\pi$
$90$		0			0
$91$	−3.02473	+	14.1290i	−0.0332388	+	0.155263i
$92$	9.47131			0.102949
$93$	83.7917			0.900986
$94$		−	49.5925i		−	0.527580i
$95$		0			0
$96$			9.79796i			0.102062i
$97$		−	4.26795i		−	0.0439995i	−0.999758	−	0.0219997i	$-0.992997\pi$
$97$		−	4.26795i		−	0.0439995i	0.999758	−	0.0219997i	$-0.00700330\pi$
$98$	63.2230	+	28.3698i	0.645133	+	0.289488i
$99$	17.6340			0.178121
$100$		0			0
$101$		−	90.7089i		−	0.898108i	−0.893505	−	0.449054i	$-0.851761\pi$
$101$		−	90.7089i		−	0.898108i	0.893505	−	0.449054i	$-0.148239\pi$
$102$	6.36264			0.0623788
$103$			136.976i			1.32986i	0.746904	+	0.664932i	$0.231540\pi$
$103$			136.976i			1.32986i	−0.746904	+	0.664932i	$0.768460\pi$
$104$		−	5.83832i		−	0.0561377i
$105$		0			0
$106$	−56.5581			−0.533567
$107$	23.3746			0.218454			0.109227	−	0.994017i	$-0.465162\pi$
$107$	23.3746			0.218454			0.109227	+	0.994017i	$0.465162\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−25.6873			−0.235663			−0.117832	−	0.993034i	$-0.537594\pi$
$109$	−25.6873			−0.235663			−0.117832	+	0.993034i	$0.537594\pi$
$110$		0			0
$111$		−	80.1962i		−	0.722489i
$112$	−27.3796	−	5.86144i	−0.244461	−	0.0523343i
$113$	2.51092			0.0222205			0.0111103	−	0.999938i	$-0.496463\pi$
$113$	2.51092			0.0222205			0.0111103	+	0.999938i	$0.496463\pi$
$114$	35.2701			0.309387
$115$		0			0
$116$	−32.3141			−0.278570
$117$			6.19247i			0.0529271i
$118$			85.0753i			0.720977i
$119$	−3.80633	+	17.7799i	−0.0319860	+	0.149411i
$120$		0			0
$121$	−86.4491			−0.714456
$122$		−	103.467i		−	0.848087i
$123$	129.405			1.05208
$124$		−	96.7543i		−	0.780277i
$125$		0			0
$126$	29.0405	+	6.21700i	0.230480	+	0.0493413i
$127$	−19.5421			−0.153875			−0.0769375	−	0.997036i	$-0.524514\pi$
$127$	−19.5421			−0.153875			−0.0769375	+	0.997036i	$0.524514\pi$
$128$	11.3137			0.0883883
$129$			18.0200i			0.139690i
$130$		0			0
$131$		−	45.5826i		−	0.347959i	−0.984749	−	0.173980i	$-0.944337\pi$
$131$		−	45.5826i		−	0.347959i	0.984749	−	0.173980i	$-0.0556627\pi$
$132$		−	20.3620i		−	0.154257i
$133$	−21.0997	+	98.5595i	−0.158644	+	0.741049i
$134$	−55.9945			−0.417869
$135$		0			0
$136$		−	7.34694i		−	0.0540217i
$137$	177.239			1.29372			0.646859	−	0.762610i	$-0.276082\pi$
$137$	177.239			1.29372			0.646859	+	0.762610i	$0.276082\pi$
$138$			11.5999i			0.0840575i
$139$		−	33.1908i		−	0.238783i	−0.992847	−	0.119391i	$-0.961906\pi$
$139$		−	33.1908i		−	0.238783i	0.992847	−	0.119391i	$-0.0380944\pi$
$140$		0			0
$141$	60.7382			0.430767
$142$	−55.6441			−0.391860
$143$			12.1331i			0.0848469i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	16.7323i		−	0.114605i
$147$	−34.7458	+	77.4321i	−0.236366	+	0.526749i
$148$	−92.6026			−0.625694
$149$	−43.9593			−0.295029			−0.147514	−	0.989060i	$-0.547127\pi$
$149$	−43.9593			−0.295029			−0.147514	+	0.989060i	$0.547127\pi$
$150$		0			0
$151$	−182.752			−1.21028			−0.605139	−	0.796120i	$-0.706882\pi$
$151$	−182.752			−1.21028			−0.605139	+	0.796120i	$0.706882\pi$
$152$		−	40.7264i		−	0.267937i
$153$			7.79261i			0.0509321i
$154$	56.8999	+	12.1812i	0.369480	+	0.0790985i
$155$		0			0
$156$	7.15045			0.0458362
$157$			50.4042i			0.321046i	0.987032	+	0.160523i	$0.0513180\pi$
$157$			50.4042i			0.321046i	−0.987032	+	0.160523i	$0.948682\pi$
$158$	58.3219			0.369126
$159$		−	69.2693i		−	0.435656i
$160$		0			0
$161$	−32.4151	−	6.93944i	−0.201336	−	0.0431021i
$162$	12.7279			0.0785674
$163$	−101.758			−0.624281			−0.312140	−	0.950036i	$-0.601046\pi$
$163$	−101.758			−0.624281			−0.312140	+	0.950036i	$0.601046\pi$
$164$		−	149.424i		−	0.911124i
$165$		0			0
$166$			178.505i			1.07533i
$167$			129.715i			0.776738i	0.921504	+	0.388369i	$0.126961\pi$
$167$			129.715i			0.776738i	−0.921504	+	0.388369i	$0.873039\pi$
$168$	7.17877	−	33.5330i	0.0427308	−	0.199601i
$169$	164.739			0.974789
$170$		0			0
$171$			43.1969i			0.252613i
$172$	20.8077			0.120975
$173$			80.2634i			0.463950i	0.972722	+	0.231975i	$0.0745188\pi$
$173$			80.2634i			0.463950i	−0.972722	+	0.231975i	$0.925481\pi$
$174$		−	39.5766i		−	0.227452i
$175$		0			0
$176$	−23.5120			−0.133591
$177$	−104.196			−0.588676
$178$		−	130.281i		−	0.731915i
$179$	−145.799			−0.814519			−0.407260	−	0.913312i	$-0.633516\pi$
$179$	−145.799			−0.814519			−0.407260	+	0.913312i	$0.633516\pi$
$180$		0			0
$181$		−	323.062i		−	1.78487i	−0.451175	−	0.892435i	$-0.648995\pi$
$181$		−	323.062i		−	1.78487i	0.451175	−	0.892435i	$-0.351005\pi$
$182$	−4.27762	+	19.9814i	−0.0235034	+	0.109788i
$183$	126.720			0.692460
$184$	13.3945			0.0727959
$185$		0			0
$186$	118.499			0.637093
$187$			15.2683i			0.0816488i
$188$		−	70.1344i		−	0.373055i
$189$	−7.61424	+	35.5672i	−0.0402870	+	0.188186i
$190$		0			0
$191$	309.035			1.61799			0.808993	−	0.587818i	$-0.200013\pi$
$191$	309.035			1.61799			0.808993	+	0.587818i	$0.200013\pi$
$192$			13.8564i			0.0721688i
$193$	−353.480			−1.83150			−0.915752	−	0.401743i	$-0.868404\pi$
$193$	−353.480			−1.83150			−0.915752	+	0.401743i	$0.868404\pi$
$194$		−	6.03579i		−	0.0311123i
$195$		0			0
$196$	89.4109	+	40.1210i	0.456178	+	0.204699i
$197$	136.303			0.691892			0.345946	−	0.938254i	$-0.387558\pi$
$197$	136.303			0.691892			0.345946	+	0.938254i	$0.387558\pi$
$198$	24.9382			0.125951
$199$			62.4881i			0.314011i	0.987598	+	0.157005i	$0.0501840\pi$
$199$			62.4881i			0.314011i	−0.987598	+	0.157005i	$0.949816\pi$
$200$		0			0
$201$		−	68.5789i		−	0.341189i
$202$		−	128.282i		−	0.635058i
$203$	110.594	+	23.6759i	0.544796	+	0.116630i
$204$	8.99813			0.0441085
$205$		0			0
$206$			193.713i			0.940356i
$207$	−14.2070			−0.0686327
$208$		−	8.25663i		−	0.0396953i
$209$			84.6371i			0.404962i
$210$		0			0
$211$	−188.967			−0.895579			−0.447790	−	0.894139i	$-0.647789\pi$
$211$	−188.967			−0.895579			−0.447790	+	0.894139i	$0.647789\pi$
$212$	−79.9853			−0.377289
$213$		−	68.1498i		−	0.319952i
$214$	33.0566			0.154470
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−70.8900	+	331.137i	−0.326682	+	1.52598i
$218$	−36.3273			−0.166639
$219$	20.4928			0.0935742
$220$		0			0
$221$	−5.36172			−0.0242612
$222$		−	113.415i		−	0.510877i
$223$			264.391i			1.18561i	0.805346	+	0.592805i	$0.201980\pi$
$223$			264.391i			1.18561i	−0.805346	+	0.592805i	$0.798020\pi$
$224$	−38.7206	−	8.28933i	−0.172860	−	0.0370059i
$225$		0			0
$226$	3.55098			0.0157123
$227$			24.7955i			0.109231i	0.998507	+	0.0546157i	$0.0173934\pi$
$227$			24.7955i			0.109231i	−0.998507	+	0.0546157i	$0.982607\pi$
$228$	49.8795			0.218770
$229$		−	131.811i		−	0.575595i	−0.957691	−	0.287798i	$-0.907077\pi$
$229$		−	131.811i		−	0.575595i	0.957691	−	0.287798i	$-0.0929230\pi$
$230$		0			0
$231$	−14.9188	+	69.6879i	−0.0645836	+	0.301679i
$232$	−45.6991			−0.196979
$233$	145.909			0.626217			0.313109	−	0.949717i	$-0.398630\pi$
$233$	145.909			0.626217			0.313109	+	0.949717i	$0.398630\pi$
$234$			8.75747i			0.0374251i
$235$		0			0
$236$			120.315i			0.509808i
$237$			71.4295i			0.301390i
$238$	−5.38296	+	25.1446i	−0.0226175	+	0.105649i
$239$	−411.485			−1.72169			−0.860847	−	0.508864i	$-0.830066\pi$
$239$	−411.485			−1.72169			−0.860847	+	0.508864i	$0.830066\pi$
$240$		0			0
$241$			381.587i			1.58335i	0.610943	+	0.791675i	$0.290791\pi$
$241$			381.587i			1.58335i	−0.610943	+	0.791675i	$0.709209\pi$
$242$	−122.258			−0.505196
$243$			15.5885i			0.0641500i
$244$		−	146.324i		−	0.599688i
$245$		0			0
$246$	183.007			0.743930
$247$	−29.7217			−0.120331
$248$		−	136.831i		−	0.551739i
$249$	−218.623			−0.878004
$250$		0			0
$251$		−	236.750i		−	0.943229i	−0.881805	−	0.471614i	$-0.843671\pi$
$251$		−	236.750i		−	0.943229i	0.881805	−	0.471614i	$-0.156329\pi$
$252$	41.0694	+	8.79216i	0.162974	+	0.0348895i
$253$	−27.8362			−0.110024
$254$	−27.6367			−0.108806
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	187.550i		−	0.729768i	−0.931053	−	0.364884i	$-0.881109\pi$
$257$		−	187.550i		−	0.729768i	0.931053	−	0.364884i	$-0.118891\pi$
$258$			25.4841i			0.0987756i
$259$	316.928	+	67.8481i	1.22366	+	0.261962i
$260$		0			0
$261$	48.4712			0.185713
$262$		−	64.4636i		−	0.246044i
$263$	−167.502			−0.636890			−0.318445	−	0.947941i	$-0.603161\pi$
$263$	−167.502			−0.636890			−0.318445	+	0.947941i	$0.603161\pi$
$264$		−	28.7962i		−	0.109076i
$265$		0			0
$266$	−29.8394	+	139.384i	−0.112178	+	0.524001i
$267$	159.561			0.597606
$268$	−79.1881			−0.295478
$269$			373.386i			1.38805i	0.719950	+	0.694026i	$0.244165\pi$
$269$			373.386i			1.38805i	−0.719950	+	0.694026i	$0.755835\pi$
$270$		0			0
$271$			395.308i			1.45870i	0.684141	+	0.729350i	$0.260177\pi$
$271$			395.308i			1.45870i	−0.684141	+	0.729350i	$0.739823\pi$
$272$		−	10.3901i		−	0.0381991i
$273$	−24.4721	−	5.23899i	−0.0896413	−	0.0191904i
$274$	250.654			0.914796
$275$		0			0
$276$			16.4048i			0.0594376i
$277$	−50.0168			−0.180566			−0.0902830	−	0.995916i	$-0.528777\pi$
$277$	−50.0168			−0.180566			−0.0902830	+	0.995916i	$0.528777\pi$
$278$		−	46.9389i		−	0.168845i
$279$			145.132i			0.520185i
$280$		0			0
$281$	414.869			1.47640			0.738201	−	0.674580i	$-0.235675\pi$
$281$	414.869			1.47640			0.738201	+	0.674580i	$0.235675\pi$
$282$	85.8968			0.304598
$283$		−	40.4964i		−	0.143097i	−0.997437	−	0.0715484i	$-0.977206\pi$
$283$		−	40.4964i		−	0.143097i	0.997437	−	0.0715484i	$-0.0227940\pi$
$284$	−78.6926			−0.277087
$285$		0			0
$286$			17.1588i			0.0599958i
$287$	−109.480	+	511.398i	−0.381464	+	1.78187i
$288$	−16.9706			−0.0589256
$289$	282.253			0.976653
$290$		0			0
$291$	7.39230			0.0254031
$292$		−	23.6630i		−	0.0810377i
$293$		−	23.5736i		−	0.0804560i	−0.999191	−	0.0402280i	$-0.987192\pi$
$293$		−	23.5736i		−	0.0804560i	0.999191	−	0.0402280i	$-0.0128084\pi$
$294$	−49.1380	+	109.506i	−0.167136	+	0.372468i
$295$		0			0
$296$	−130.960			−0.442432
$297$			30.5430i			0.102838i
$298$	−62.1679			−0.208617
$299$		−	9.77513i		−	0.0326927i
$300$		0			0
$301$	−71.2133	−	15.2454i	−0.236589	−	0.0506491i
$302$	−258.450			−0.855796
$303$	157.112			0.518523
$304$		−	57.5958i		−	0.189460i
$305$		0			0
$306$			11.0204i			0.0360144i
$307$			313.711i			1.02186i	0.859622	+	0.510930i	$0.170699\pi$
$307$			313.711i			1.02186i	−0.859622	+	0.510930i	$0.829301\pi$
$308$	80.4687	+	17.2268i	0.261262	+	0.0559311i
$309$	−237.249			−0.767798
$310$		0			0
$311$			341.192i			1.09708i	0.836125	+	0.548539i	$0.184816\pi$
$311$			341.192i			1.09708i	−0.836125	+	0.548539i	$0.815184\pi$
$312$	10.1123			0.0324111
$313$		−	508.988i		−	1.62616i	−0.582151	−	0.813081i	$-0.697789\pi$
$313$		−	508.988i		−	1.62616i	0.582151	−	0.813081i	$-0.302211\pi$
$314$			71.2823i			0.227014i
$315$		0			0
$316$	82.4797			0.261012
$317$	355.980			1.12297			0.561483	−	0.827488i	$-0.310231\pi$
$317$	355.980			1.12297			0.561483	+	0.827488i	$0.310231\pi$
$318$		−	97.9616i		−	0.308055i
$319$	94.9712			0.297715
$320$		0			0
$321$			40.4860i			0.126124i
$322$	−45.8419	−	9.81385i	−0.142366	−	0.0304778i
$323$	−37.4018			−0.115795
$324$	18.0000			0.0555556
$325$		0			0
$326$	−143.907			−0.441433
$327$		−	44.4917i		−	0.136060i
$328$		−	211.318i		−	0.644262i
$329$	−51.3861	+	240.032i	−0.156189	+	0.729579i
$330$		0			0
$331$	−568.964			−1.71892			−0.859462	−	0.511199i	$-0.829201\pi$
$331$	−568.964			−1.71892			−0.859462	+	0.511199i	$0.829201\pi$
$332$			252.444i			0.760374i
$333$	138.904			0.417129
$334$			183.445i			0.549237i
$335$		0			0
$336$	10.1523	−	47.4229i	0.0302152	−	0.141140i
$337$	−292.641			−0.868372			−0.434186	−	0.900823i	$-0.642964\pi$
$337$	−292.641			−0.868372			−0.434186	+	0.900823i	$0.642964\pi$
$338$	232.976			0.689280
$339$			4.34904i			0.0128290i
$340$		0			0
$341$			284.361i			0.833903i
$342$			61.0896i			0.178625i
$343$	−276.609	−	202.822i	−0.806439	−	0.591317i
$344$	29.4265			0.0855422
$345$		0			0
$346$			113.510i			0.328063i
$347$	175.594			0.506036			0.253018	−	0.967462i	$-0.418577\pi$
$347$	175.594			0.506036			0.253018	+	0.967462i	$0.418577\pi$
$348$		−	55.9697i		−	0.160833i
$349$			451.738i			1.29438i	0.762329	+	0.647190i	$0.224056\pi$
$349$			451.738i			1.29438i	−0.762329	+	0.647190i	$0.775944\pi$
$350$		0			0
$351$	−10.7257			−0.0305575
$352$	−33.2510			−0.0944630
$353$		−	539.172i		−	1.52740i	−0.645571	−	0.763700i	$-0.723381\pi$
$353$		−	539.172i		−	1.52740i	0.645571	−	0.763700i	$-0.276619\pi$
$354$	−147.355			−0.416256
$355$		0			0
$356$		−	184.245i		−	0.517542i
$357$	−30.7957	−	6.59275i	−0.0862624	−	0.0184671i
$358$	−206.191			−0.575952
$359$	166.475			0.463720			0.231860	−	0.972749i	$-0.425519\pi$
$359$	166.475			0.463720			0.231860	+	0.972749i	$0.425519\pi$
$360$		0			0
$361$	153.670			0.425678
$362$		−	456.878i		−	1.26209i
$363$		−	149.734i		−	0.412491i
$364$	−6.04947	+	28.2579i	−0.0166194	+	0.0776316i
$365$		0			0
$366$	179.209			0.489643
$367$			129.246i			0.352169i	0.984375	+	0.176084i	$0.0563432\pi$
$367$			129.246i			0.352169i	−0.984375	+	0.176084i	$0.943657\pi$
$368$	18.9426			0.0514745
$369$			224.137i			0.607416i
$370$		0			0
$371$	273.746	+	58.6036i	0.737859	+	0.157961i
$372$	167.583			0.450493
$373$	−423.280			−1.13480			−0.567399	−	0.823443i	$-0.692050\pi$
$373$	−423.280			−1.13480			−0.567399	+	0.823443i	$0.692050\pi$
$374$			21.5927i			0.0577344i
$375$		0			0
$376$		−	99.1850i		−	0.263790i
$377$			33.3507i			0.0884634i
$378$	−10.7682	+	50.2996i	−0.0284872	+	0.133068i
$379$	30.5074			0.0804944			0.0402472	−	0.999190i	$-0.487185\pi$
$379$	30.5074			0.0804944			0.0402472	+	0.999190i	$0.487185\pi$
$380$		0			0
$381$		−	33.8479i		−	0.0888398i
$382$	437.042			1.14409
$383$		−	367.882i		−	0.960529i	−0.877124	−	0.480264i	$-0.840541\pi$
$383$		−	367.882i		−	0.960529i	0.877124	−	0.480264i	$-0.159459\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−499.897			−1.29507
$387$	−31.2115			−0.0806500
$388$		−	8.53590i		−	0.0219997i
$389$	583.606			1.50027			0.750136	−	0.661283i	$-0.229988\pi$
$389$	583.606			1.50027			0.750136	+	0.661283i	$0.229988\pi$
$390$		0			0
$391$		−	12.3010i		−	0.0314605i
$392$	126.446	+	56.7397i	0.322567	+	0.144744i
$393$	78.9515			0.200894
$394$	192.761			0.489241
$395$		0			0
$396$	35.2680			0.0890606
$397$		−	618.783i		−	1.55865i	−0.626622	−	0.779323i	$-0.715563\pi$
$397$		−	618.783i		−	1.55865i	0.626622	−	0.779323i	$-0.284437\pi$
$398$			88.3715i			0.222039i
$399$	−170.710	−	36.5457i	−0.427845	−	0.0915932i
$400$		0			0
$401$	577.546			1.44026			0.720132	−	0.693837i	$-0.244081\pi$
$401$	577.546			1.44026			0.720132	+	0.693837i	$0.244081\pi$
$402$		−	96.9852i		−	0.241257i
$403$	−99.8580			−0.247787
$404$		−	181.418i		−	0.449054i
$405$		0			0
$406$	156.403	+	33.4828i	0.385229	+	0.0824700i
$407$	272.159			0.668696
$408$	12.7253			0.0311894
$409$			488.227i			1.19371i	0.802349	+	0.596855i	$0.203583\pi$
$409$			488.227i			1.19371i	−0.802349	+	0.596855i	$0.796417\pi$
$410$		0			0
$411$			306.987i			0.746928i
$412$			273.952i			0.664932i
$413$	88.1522	−	411.771i	0.213444	−	0.997025i
$414$	−20.0917			−0.0485306
$415$		0			0
$416$		−	11.6766i		−	0.0280688i
$417$	57.4882			0.137861
$418$			119.695i			0.286351i
$419$			131.348i			0.313481i	0.987640	+	0.156740i	$0.0500986\pi$
$419$			131.348i			0.313481i	−0.987640	+	0.156740i	$0.949901\pi$
$420$		0			0
$421$	−556.789			−1.32254			−0.661270	−	0.750148i	$-0.729982\pi$
$421$	−556.789			−1.32254			−0.661270	+	0.750148i	$0.729982\pi$
$422$	−267.240			−0.633270
$423$			105.202i			0.248704i
$424$	−113.116			−0.266784
$425$		0			0
$426$		−	96.3784i		−	0.226240i
$427$	−107.209	+	500.787i	−0.251074	+	1.17280i
$428$	46.7492			0.109227
$429$	−21.0152			−0.0489864
$430$		0			0
$431$	−167.379			−0.388351			−0.194175	−	0.980967i	$-0.562203\pi$
$431$	−167.379			−0.388351			−0.194175	+	0.980967i	$0.562203\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			57.5429i			0.132894i	0.997790	+	0.0664468i	$0.0211663\pi$
$433$			57.5429i			0.132894i	−0.997790	+	0.0664468i	$0.978834\pi$
$434$	−100.254	+	468.299i	−0.230999	+	1.07903i
$435$		0			0
$436$	−51.3746			−0.117832
$437$		−	68.1885i		−	0.156038i
$438$	28.9811			0.0661670
$439$		−	838.459i		−	1.90993i	−0.296719	−	0.954965i	$-0.595893\pi$
$439$		−	838.459i		−	1.90993i	0.296719	−	0.954965i	$-0.404107\pi$
$440$		0			0
$441$	−134.116	−	60.1815i	−0.304119	−	0.136466i
$442$	−7.58262			−0.0171553
$443$	435.742			0.983616			0.491808	−	0.870704i	$-0.336336\pi$
$443$	435.742			0.983616			0.491808	+	0.870704i	$0.336336\pi$
$444$		−	160.392i		−	0.361244i
$445$		0			0
$446$			373.905i			0.838353i
$447$		−	76.1398i		−	0.170335i
$448$	−54.7592	−	11.7229i	−0.122230	−	0.0261672i
$449$	612.776			1.36476			0.682378	−	0.730999i	$-0.260946\pi$
$449$	612.776			1.36476			0.682378	+	0.730999i	$0.260946\pi$
$450$		0			0
$451$			439.158i			0.973743i
$452$	5.02184			0.0111103
$453$		−	316.536i		−	0.698754i
$454$			35.0662i			0.0772382i
$455$		0			0
$456$	70.5402			0.154693
$457$	−3.25143			−0.00711473			−0.00355736	−	0.999994i	$-0.501132\pi$
$457$	−3.25143			−0.00711473			−0.00355736	+	0.999994i	$0.501132\pi$
$458$		−	186.409i		−	0.407007i
$459$	−13.4972			−0.0294057
$460$		0			0
$461$		−	662.733i		−	1.43760i	−0.695218	−	0.718799i	$-0.744692\pi$
$461$		−	662.733i		−	1.43760i	0.695218	−	0.718799i	$-0.255308\pi$
$462$	−21.0984	+	98.5536i	−0.0456675	+	0.213319i
$463$	193.306			0.417507			0.208754	−	0.977968i	$-0.433059\pi$
$463$	193.306			0.417507			0.208754	+	0.977968i	$0.433059\pi$
$464$	−64.6283			−0.139285
$465$		0			0
$466$	206.346			0.442802
$467$		−	353.116i		−	0.756138i	−0.925777	−	0.378069i	$-0.876588\pi$
$467$		−	353.116i		−	0.756138i	0.925777	−	0.378069i	$-0.123412\pi$
$468$			12.3849i			0.0264635i
$469$	271.018	+	58.0196i	0.577863	+	0.123709i
$470$		0			0
$471$	−87.3026			−0.185356
$472$			170.151i			0.360489i
$473$	−61.1538			−0.129289
$474$			101.017i			0.213115i
$475$		0			0
$476$	−7.61266	+	35.5598i	−0.0159930	+	0.0747054i
$477$	119.978			0.251526
$478$	−581.927			−1.21742
$479$		−	608.762i		−	1.27090i	−0.772141	−	0.635451i	$-0.780814\pi$
$479$		−	608.762i		−	1.27090i	0.772141	−	0.635451i	$-0.219186\pi$
$480$		0			0
$481$			95.5732i			0.198697i
$482$			539.646i			1.11960i
$483$	12.0195	−	56.1446i	0.0248850	−	0.116241i
$484$	−172.898			−0.357228
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	185.222			0.380333			0.190167	−	0.981752i	$-0.439097\pi$
$487$	185.222			0.380333			0.190167	+	0.981752i	$0.439097\pi$
$488$		−	206.933i		−	0.424044i
$489$		−	176.250i		−	0.360429i
$490$		0			0
$491$	924.656			1.88321			0.941605	−	0.336720i	$-0.109317\pi$
$491$	924.656			1.88321			0.941605	+	0.336720i	$0.109317\pi$
$492$	258.811			0.526038
$493$			41.9686i			0.0851290i
$494$	−42.0328			−0.0850867
$495$		0			0
$496$		−	193.509i		−	0.390138i
$497$	269.322	+	57.6565i	0.541895	+	0.116009i
$498$	−309.180			−0.620843
$499$	−644.190			−1.29096			−0.645481	−	0.763776i	$-0.723343\pi$
$499$	−644.190			−1.29096			−0.645481	+	0.763776i	$0.723343\pi$
$500$		0			0
$501$	−224.674			−0.448450
$502$		−	334.816i		−	0.666963i
$503$			774.419i			1.53960i	0.638285	+	0.769800i	$0.279644\pi$
$503$			774.419i			1.53960i	−0.638285	+	0.769800i	$0.720356\pi$
$504$	58.0809	+	12.4340i	0.115240	+	0.0246706i
$505$		0			0
$506$	−39.3663			−0.0777990
$507$			285.337i			0.562794i
$508$	−39.0842			−0.0769375
$509$		−	675.381i		−	1.32688i	−0.748231	−	0.663439i	$-0.769096\pi$
$509$		−	675.381i		−	1.32688i	0.748231	−	0.663439i	$-0.230904\pi$
$510$		0			0
$511$	−17.3374	+	80.9855i	−0.0339284	+	0.158484i
$512$	22.6274			0.0441942
$513$	−74.8192			−0.145846
$514$		−	265.236i		−	0.516024i
$515$		0			0
$516$			36.0400i			0.0698449i
$517$			206.125i			0.398694i
$518$	448.204	+	95.9517i	0.865259	+	0.185235i
$519$	−139.020			−0.267862
$520$		0			0
$521$			572.162i			1.09820i	0.835757	+	0.549100i	$0.185029\pi$
$521$			572.162i			1.09820i	−0.835757	+	0.549100i	$0.814971\pi$
$522$	68.5486			0.131319
$523$			85.2596i			0.163020i	0.996673	+	0.0815102i	$0.0259743\pi$
$523$			85.2596i			0.163020i	−0.996673	+	0.0815102i	$0.974026\pi$
$524$		−	91.1653i		−	0.173980i
$525$		0			0
$526$	−236.884			−0.450349
$527$	−125.661			−0.238447
$528$		−	40.7240i		−	0.0771287i
$529$	−506.574			−0.957606
$530$		0			0
$531$		−	180.472i		−	0.339872i
$532$	−42.1993	+	197.119i	−0.0793221	+	0.370524i
$533$	−154.218			−0.289339
$534$	225.653			0.422571
$535$		0			0
$536$	−111.989			−0.208935
$537$		−	252.531i		−	0.470263i
$538$			528.048i			0.981501i
$539$	−262.778	−	117.916i	−0.487530	−	0.218767i
$540$		0			0
$541$	−347.233			−0.641836			−0.320918	−	0.947107i	$-0.603991\pi$
$541$	−347.233			−0.641836			−0.320918	+	0.947107i	$0.603991\pi$
$542$			559.049i			1.03146i
$543$	559.559			1.03050
$544$		−	14.6939i		−	0.0270108i
$545$		0			0
$546$	−34.6087	−	7.40905i	−0.0633859	−	0.0135697i
$547$	−593.025			−1.08414			−0.542070	−	0.840333i	$-0.682359\pi$
$547$	−593.025			−1.08414			−0.542070	+	0.840333i	$0.682359\pi$
$548$	354.479			0.646859
$549$			219.486i			0.399792i
$550$		0			0
$551$			232.645i			0.422223i
$552$			23.1999i			0.0420288i
$553$	−282.283	−	60.4312i	−0.510457	−	0.109279i
$554$	−70.7344			−0.127679
$555$		0			0
$556$		−	66.3817i		−	0.119391i
$557$	−836.159			−1.50118			−0.750591	−	0.660767i	$-0.770231\pi$
$557$	−836.159			−1.50118			−0.750591	+	0.660767i	$0.770231\pi$
$558$			205.247i			0.367826i
$559$		−	21.4752i		−	0.0384171i
$560$		0			0
$561$	−26.4455			−0.0471399
$562$	586.714			1.04397
$563$			894.630i			1.58904i	0.607238	+	0.794520i	$0.292278\pi$
$563$			894.630i			1.58904i	−0.607238	+	0.794520i	$0.707722\pi$
$564$	121.476			0.215384
$565$		0			0
$566$		−	57.2706i		−	0.101185i
$567$	−61.6041	−	13.1882i	−0.108649	−	0.0232597i
$568$	−111.288			−0.195930
$569$	559.583			0.983450			0.491725	−	0.870751i	$-0.336367\pi$
$569$	559.583			0.983450			0.491725	+	0.870751i	$0.336367\pi$
$570$		0			0
$571$	439.360			0.769457			0.384729	−	0.923030i	$-0.374295\pi$
$571$	439.360			0.769457			0.384729	+	0.923030i	$0.374295\pi$
$572$			24.2662i			0.0424235i
$573$			535.265i			0.934145i
$574$	−154.828	+	723.226i	−0.269736	+	1.25998i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	704.688i		−	1.22130i	−0.791902	−	0.610648i	$-0.790909\pi$
$577$		−	704.688i		−	1.22130i	0.791902	−	0.610648i	$-0.209091\pi$
$578$	399.166			0.690598
$579$		−	612.246i		−	1.05742i
$580$		0			0
$581$	184.961	−	863.978i	0.318349	−	1.48705i
$582$	10.4543			0.0179627
$583$	235.077			0.403219
$584$		−	33.4645i		−	0.0573023i
$585$		0			0
$586$		−	33.3381i		−	0.0568910i
$587$			144.103i			0.245491i	0.992438	+	0.122746i	$0.0391699\pi$
$587$			144.103i			0.245491i	−0.992438	+	0.122746i	$0.960830\pi$
$588$	−69.4916	+	154.864i	−0.118183	+	0.263374i
$589$	−696.581			−1.18265
$590$		0			0
$591$			236.083i			0.399464i
$592$	−185.205			−0.312847
$593$		−	612.101i		−	1.03221i	−0.856525	−	0.516105i	$-0.827381\pi$
$593$		−	612.101i		−	1.03221i	0.856525	−	0.516105i	$-0.172619\pi$
$594$			43.1943i			0.0727177i
$595$		0			0
$596$	−87.9186			−0.147514
$597$	−108.233			−0.181294
$598$		−	13.8241i		−	0.0231173i
$599$	435.517			0.727074			0.363537	−	0.931580i	$-0.381569\pi$
$599$	435.517			0.727074			0.363537	+	0.931580i	$0.381569\pi$
$600$		0			0
$601$		−	412.897i		−	0.687017i	−0.939150	−	0.343508i	$-0.888385\pi$
$601$		−	412.897i		−	0.687017i	0.939150	−	0.343508i	$-0.111615\pi$
$602$	−100.711	−	21.5602i	−0.167294	−	0.0358143i
$603$	118.782			0.196985
$604$	−365.504			−0.605139
$605$		0			0
$606$	222.190			0.366651
$607$		−	868.480i		−	1.43077i	−0.698728	−	0.715387i	$-0.746250\pi$
$607$		−	868.480i		−	1.43077i	0.698728	−	0.715387i	$-0.253750\pi$
$608$		−	81.4528i		−	0.133968i
$609$	−41.0079	+	191.554i	−0.0673365	+	0.314538i
$610$		0			0
$611$	−72.3842			−0.118468
$612$			15.5852i			0.0254661i
$613$	−320.085			−0.522161			−0.261080	−	0.965317i	$-0.584079\pi$
$613$	−320.085			−0.522161			−0.261080	+	0.965317i	$0.584079\pi$
$614$			443.654i			0.722564i
$615$		0			0
$616$	113.800	+	24.3623i	0.184740	+	0.0395492i
$617$	−287.002			−0.465157			−0.232578	−	0.972578i	$-0.574716\pi$
$617$	−287.002			−0.465157			−0.232578	+	0.972578i	$0.574716\pi$
$618$	−335.521			−0.542915
$619$		−	461.836i		−	0.746100i	−0.927811	−	0.373050i	$-0.878312\pi$
$619$		−	461.836i		−	0.746100i	0.927811	−	0.373050i	$-0.121688\pi$
$620$		0			0
$621$		−	24.6072i		−	0.0396251i
$622$			482.518i			0.775752i
$623$	−134.993	+	630.570i	−0.216682	+	1.01215i
$624$	14.3009			0.0229181
$625$		0			0
$626$		−	719.818i		−	1.14987i
$627$	−146.596			−0.233805
$628$			100.808i			0.160523i
$629$			120.269i			0.191207i
$630$		0			0
$631$	−13.3642			−0.0211794			−0.0105897	−	0.999944i	$-0.503371\pi$
$631$	−13.3642			−0.0211794			−0.0105897	+	0.999944i	$0.503371\pi$
$632$	116.644			0.184563
$633$		−	327.301i		−	0.517063i
$634$	503.432			0.794057
$635$		0			0
$636$		−	138.539i		−	0.217828i
$637$	41.4080	−	92.2790i	0.0650047	−	0.144865i
$638$	134.310			0.210517
$639$	118.039			0.184724
$640$		0			0
$641$	−248.329			−0.387408			−0.193704	−	0.981060i	$-0.562050\pi$
$641$	−248.329			−0.387408			−0.193704	+	0.981060i	$0.562050\pi$
$642$			57.2558i			0.0891835i
$643$			1084.03i			1.68590i	0.537991	+	0.842950i	$0.319183\pi$
$643$			1084.03i			1.68590i	−0.537991	+	0.842950i	$0.680817\pi$
$644$	−64.8302	−	13.8789i	−0.100668	−	0.0215511i
$645$		0			0
$646$	−52.8942			−0.0818795
$647$		−	1131.40i		−	1.74868i	−0.485312	−	0.874341i	$-0.661294\pi$
$647$		−	1131.40i		−	1.74868i	0.485312	−	0.874341i	$-0.338706\pi$
$648$	25.4558			0.0392837
$649$		−	353.605i		−	0.544845i
$650$		0			0
$651$	−573.546	−	122.785i	−0.881023	−	0.188610i
$652$	−203.515			−0.312140
$653$	239.818			0.367256			0.183628	−	0.982996i	$-0.441216\pi$
$653$	239.818			0.367256			0.183628	+	0.982996i	$0.441216\pi$
$654$		−	62.9207i		−	0.0962091i
$655$		0			0
$656$		−	298.849i		−	0.455562i
$657$			35.4945i			0.0540251i
$658$	−72.6709	+	339.456i	−0.110442	+	0.515891i
$659$	340.662			0.516938			0.258469	−	0.966020i	$-0.416782\pi$
$659$	340.662			0.516938			0.258469	+	0.966020i	$0.416782\pi$
$660$		0			0
$661$		−	88.1855i		−	0.133412i	−0.997773	−	0.0667061i	$-0.978751\pi$
$661$		−	88.1855i		−	0.133412i	0.997773	−	0.0667061i	$-0.0212490\pi$
$662$	−804.637			−1.21546
$663$		−	9.28678i		−	0.0140072i
$664$			357.010i			0.537666i
$665$		0			0
$666$	196.440			0.294955
$667$	−76.5143			−0.114714
$668$			259.431i			0.388369i
$669$	−457.939			−0.684512
$670$		0			0
$671$			430.046i			0.640903i
$672$	14.3575	−	67.0661i	0.0213654	−	0.0998007i
$673$	1258.19			1.86952			0.934759	−	0.355283i	$-0.115616\pi$
$673$	1258.19			1.86952			0.934759	+	0.355283i	$0.115616\pi$
$674$	−413.857			−0.614032
$675$		0			0
$676$	329.479			0.487394
$677$		−	1194.41i		−	1.76427i	−0.470999	−	0.882134i	$-0.656107\pi$
$677$		−	1194.41i		−	1.76427i	0.470999	−	0.882134i	$-0.343893\pi$
$678$			6.15047i			0.00907149i
$679$	−6.25408	+	29.2137i	−0.00921073	+	0.0430246i
$680$		0			0
$681$	−42.9471			−0.0630647
$682$			402.147i			0.589658i
$683$	−890.365			−1.30361			−0.651804	−	0.758387i	$-0.725988\pi$
$683$	−890.365			−1.30361			−0.651804	+	0.758387i	$0.725988\pi$
$684$			86.3938i			0.126307i
$685$		0			0
$686$	−391.184	−	286.833i	−0.570239	−	0.418124i
$687$	228.304			0.332320
$688$	41.6154			0.0604875
$689$			82.5511i			0.119813i
$690$		0			0
$691$			328.636i			0.475595i	0.971315	+	0.237798i	$0.0764255\pi$
$691$			328.636i			0.475595i	−0.971315	+	0.237798i	$0.923575\pi$
$692$			160.527i			0.231975i
$693$	−120.703	−	25.8402i	−0.174175	−	0.0372874i
$694$	248.328			0.357821
$695$		0			0
$696$		−	79.1531i		−	0.113726i
$697$	−194.068			−0.278433
$698$			638.855i			0.915265i
$699$			252.721i			0.361547i
$700$		0			0
$701$	144.549			0.206204			0.103102	−	0.994671i	$-0.467123\pi$
$701$	144.549			0.206204			0.103102	+	0.994671i	$0.467123\pi$
$702$	−15.1684			−0.0216074
$703$			666.691i			0.948351i
$704$	−47.0240			−0.0667954
$705$		0			0
$706$		−	762.505i		−	1.08004i
$707$	−132.921	+	620.894i	−0.188007	+	0.878209i
$708$	−208.391			−0.294338
$709$	−1014.70			−1.43117			−0.715585	−	0.698526i	$-0.753840\pi$
$709$	−1014.70			−1.43117			−0.715585	+	0.698526i	$0.753840\pi$
$710$		0			0
$711$	−123.719			−0.174008
$712$		−	260.562i		−	0.365958i
$713$		−	229.098i		−	0.321315i
$714$	−43.5517	−	9.32356i	−0.0609967	−	0.0130582i
$715$		0			0
$716$	−291.598			−0.407260
$717$		−	712.713i		−	0.994020i
$718$	235.432			0.327899
$719$		−	1364.28i		−	1.89747i	−0.316076	−	0.948734i	$-0.602365\pi$
$719$		−	1364.28i		−	1.89747i	0.316076	−	0.948734i	$-0.397635\pi$
$720$		0			0
$721$	200.719	−	937.588i	0.278390	−	1.30040i
$722$	217.322			0.301000
$723$	−660.928			−0.914147
$724$		−	646.123i		−	0.892435i
$725$		0			0
$726$		−	211.756i		−	0.291675i
$727$		−	121.107i		−	0.166584i	−0.996525	−	0.0832922i	$-0.973457\pi$
$727$		−	121.107i		−	0.166584i	0.996525	−	0.0832922i	$-0.0265435\pi$
$728$	−8.55524	+	39.9627i	−0.0117517	+	0.0548938i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	27.0244i		−	0.0369690i
$732$	253.440			0.346230
$733$		−	1064.94i		−	1.45285i	−0.687245	−	0.726426i	$-0.741180\pi$
$733$		−	1064.94i		−	1.45285i	0.687245	−	0.726426i	$-0.258820\pi$
$734$			182.781i			0.249021i
$735$		0			0
$736$	26.7889			0.0363980
$737$	232.734			0.315785
$738$			316.977i			0.429508i
$739$	658.565			0.891156			0.445578	−	0.895243i	$-0.352998\pi$
$739$	658.565			0.891156			0.445578	+	0.895243i	$0.352998\pi$
$740$		0			0
$741$		−	51.4795i		−	0.0694730i
$742$	387.135	+	82.8781i	0.521745	+	0.111695i
$743$	−844.054			−1.13601			−0.568004	−	0.823026i	$-0.692284\pi$
$743$	−844.054			−1.13601			−0.568004	+	0.823026i	$0.692284\pi$
$744$	236.999			0.318547
$745$		0			0
$746$	−598.608			−0.802424
$747$		−	378.666i		−	0.506916i
$748$			30.5366i			0.0408244i
$749$	−159.997	−	34.2522i	−0.213614	−	0.0457305i
$750$		0			0
$751$	802.681			1.06882			0.534408	−	0.845227i	$-0.320535\pi$
$751$	802.681			1.06882			0.534408	+	0.845227i	$0.320535\pi$
$752$		−	140.269i		−	0.186528i
$753$	410.064			0.544573
$754$			47.1650i			0.0625531i
$755$		0			0
$756$	−15.2285	+	71.1343i	−0.0201435	+	0.0940930i
$757$	207.749			0.274437			0.137219	−	0.990541i	$-0.456184\pi$
$757$	207.749			0.274437			0.137219	+	0.990541i	$0.456184\pi$
$758$	43.1440			0.0569182
$759$		−	48.2136i		−	0.0635226i
$760$		0			0
$761$		−	135.451i		−	0.177991i	−0.996032	−	0.0889956i	$-0.971634\pi$
$761$		−	135.451i		−	0.177991i	0.996032	−	0.0889956i	$-0.0283657\pi$
$762$		−	47.8682i		−	0.0628192i
$763$	175.827	+	37.6411i	0.230442	+	0.0493331i
$764$	618.071			0.808993
$765$		0			0
$766$		−	520.264i		−	0.679196i
$767$	124.174			0.161896
$768$			27.7128i			0.0360844i
$769$		−	12.5945i		−	0.0163778i	−0.999966	−	0.00818890i	$-0.997393\pi$
$769$		−	12.5945i		−	0.0163778i	0.999966	−	0.00818890i	$-0.00260664\pi$
$770$		0			0
$771$	324.847			0.421332
$772$	−706.961			−0.915752
$773$			614.951i			0.795538i	0.917486	+	0.397769i	$0.130215\pi$
$773$			614.951i			0.795538i	−0.917486	+	0.397769i	$0.869785\pi$
$774$	−44.1398			−0.0570281
$775$		0			0
$776$		−	12.0716i		−	0.0155562i
$777$	−117.516	+	548.936i	−0.151244	+	0.706481i
$778$	825.343			1.06085
$779$	−1075.78			−1.38097
$780$		0			0
$781$	231.278			0.296130
$782$		−	17.3963i		−	0.0222459i
$783$			83.9546i			0.107222i
$784$	178.822	+	80.2420i	0.228089	+	0.102350i
$785$		0			0
$786$	111.654			0.142054
$787$		−	783.038i		−	0.994966i	−0.867474	−	0.497483i	$-0.834258\pi$
$787$		−	783.038i		−	0.994966i	0.867474	−	0.497483i	$-0.165742\pi$
$788$	272.605			0.345946
$789$		−	290.122i		−	0.367708i
$790$		0			0
$791$	−17.1870	−	3.67940i	−0.0217282	−	0.00465158i
$792$	49.8765			0.0629753
$793$	−151.018			−0.190438
$794$		−	875.091i		−	1.10213i
$795$		0			0
$796$			124.976i			0.157005i
$797$			50.5740i			0.0634554i	0.999497	+	0.0317277i	$0.0101009\pi$
$797$			50.5740i			0.0634554i	−0.999497	+	0.0317277i	$0.989899\pi$
$798$	−241.421	−	51.6834i	−0.302532	−	0.0647662i
$799$	−91.0884			−0.114003
$800$		0			0
$801$			276.367i			0.345028i
$802$	816.773			1.01842
$803$			69.5455i			0.0866071i
$804$		−	137.158i		−	0.170594i
$805$		0			0
$806$	−141.221			−0.175212
$807$	−646.724			−0.801393
$808$		−	256.563i		−	0.317529i
$809$	908.730			1.12328			0.561638	−	0.827383i	$-0.310172\pi$
$809$	908.730			1.12328			0.561638	+	0.827383i	$0.310172\pi$
$810$		0			0
$811$		−	195.796i		−	0.241426i	−0.992687	−	0.120713i	$-0.961482\pi$
$811$		−	195.796i		−	0.241426i	0.992687	−	0.120713i	$-0.0385181\pi$
$812$	221.187	+	47.3518i	0.272398	+	0.0583151i
$813$	−684.693			−0.842181
$814$	384.891			0.472839
$815$		0			0
$816$	17.9963			0.0220542
$817$		−	149.805i		−	0.183359i
$818$			690.458i			0.844080i
$819$	9.07420	−	42.3869i	0.0110796	−	0.0517544i
$820$		0			0
$821$	−239.589			−0.291826			−0.145913	−	0.989297i	$-0.546612\pi$
$821$	−239.589			−0.291826			−0.145913	+	0.989297i	$0.546612\pi$
$822$			434.146i			0.528158i
$823$	1493.19			1.81432			0.907162	−	0.420781i	$-0.138244\pi$
$823$	1493.19			1.81432			0.907162	+	0.420781i	$0.138244\pi$
$824$			387.427i			0.470178i
$825$		0			0
$826$	124.666	−	582.332i	0.150927	−	0.705003i
$827$	1031.14			1.24685			0.623424	−	0.781884i	$-0.285741\pi$
$827$	1031.14			1.24685			0.623424	+	0.781884i	$0.285741\pi$
$828$	−28.4139			−0.0343163
$829$		−	113.418i		−	0.136814i	−0.997658	−	0.0684068i	$-0.978208\pi$
$829$		−	113.418i		−	0.136814i	0.997658	−	0.0684068i	$-0.0217916\pi$
$830$		0			0
$831$		−	86.6316i		−	0.104250i
$832$		−	16.5133i		−	0.0198477i
$833$	52.1079	−	116.124i	0.0625545	−	0.139405i
$834$	81.3006			0.0974827
$835$		0			0
$836$			169.274i			0.202481i
$837$	−251.375			−0.300329
$838$			185.755i			0.221664i
$839$			252.998i			0.301548i	0.988568	+	0.150774i	$0.0481765\pi$
$839$			252.998i			0.301548i	−0.988568	+	0.150774i	$0.951823\pi$
$840$		0			0
$841$	−579.949			−0.689595
$842$	−787.419			−0.935177
$843$			718.575i			0.852402i
$844$	−377.934			−0.447790
$845$		0			0
$846$			148.778i			0.175860i
$847$	591.736	+	126.679i	0.698626	+	0.149562i
$848$	−159.971			−0.188645
$849$	70.1418			0.0826170
$850$		0			0
$851$	−219.267			−0.257658
$852$		−	136.300i		−	0.159976i
$853$		−	911.188i		−	1.06822i	−0.845416	−	0.534108i	$-0.820648\pi$
$853$		−	911.188i		−	1.06822i	0.845416	−	0.534108i	$-0.179352\pi$
$854$	−151.616	+	708.219i	−0.177536	+	0.829296i
$855$		0			0
$856$	66.1133			0.0772352
$857$		−	638.434i		−	0.744963i	−0.928040	−	0.372482i	$-0.878507\pi$
$857$		−	638.434i		−	0.744963i	0.928040	−	0.372482i	$-0.121493\pi$
$858$	−29.7199			−0.0346386
$859$		−	644.249i		−	0.749999i	−0.927025	−	0.374999i	$-0.877643\pi$
$859$		−	644.249i		−	0.749999i	0.927025	−	0.374999i	$-0.122357\pi$
$860$		0			0
$861$	−885.767	−	189.625i	−1.02877	−	0.220239i
$862$	−236.710			−0.274605
$863$	−623.500			−0.722480			−0.361240	−	0.932473i	$-0.617647\pi$
$863$	−623.500			−0.722480			−0.361240	+	0.932473i	$0.617647\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			81.3779i			0.0939699i
$867$			488.876i			0.563871i
$868$	−141.780	+	662.274i	−0.163341	+	0.762989i
$869$	−242.408			−0.278950
$870$		0			0
$871$			81.7283i			0.0938328i
$872$	−72.6546			−0.0833195
$873$			12.8038i			0.0146665i
$874$		−	96.4331i		−	0.110335i
$875$		0			0
$876$	40.9855			0.0467871
$877$	204.837			0.233566			0.116783	−	0.993157i	$-0.462742\pi$
$877$	204.837			0.233566			0.116783	+	0.993157i	$0.462742\pi$
$878$		−	1185.76i		−	1.35052i
$879$	40.8307			0.0464513
$880$		0			0
$881$		−	1294.76i		−	1.46964i	−0.678260	−	0.734822i	$-0.737266\pi$
$881$		−	1294.76i		−	1.46964i	0.678260	−	0.734822i	$-0.262734\pi$
$882$	−189.669	−	85.1095i	−0.215044	−	0.0964960i
$883$	1600.29			1.81233			0.906165	−	0.422925i	$-0.138997\pi$
$883$	1600.29			1.81233			0.906165	+	0.422925i	$0.138997\pi$
$884$	−10.7234			−0.0121306
$885$		0			0
$886$	616.232			0.695521
$887$		−	822.386i		−	0.927154i	−0.886057	−	0.463577i	$-0.846566\pi$
$887$		−	822.386i		−	0.927154i	0.886057	−	0.463577i	$-0.153434\pi$
$888$		−	226.829i		−	0.255438i
$889$	133.764	+	28.6362i	0.150466	+	0.0322118i
$890$		0			0
$891$	−52.9020			−0.0593737
$892$			528.782i			0.592805i
$893$	−504.931			−0.565433
$894$		−	107.678i		−	0.120445i
$895$		0			0
$896$	−77.4413	−	16.5787i	−0.0864300	−	0.0185030i
$897$	16.9310			0.0188752
$898$	866.596			0.965028
$899$			781.633i			0.869447i
$900$		0			0
$901$			103.882i			0.115297i
$902$			621.063i			0.688540i
$903$	26.4058	−	123.345i	0.0292423	−	0.136595i
$904$	7.10195			0.00785614
$905$		0			0
$906$		−	447.649i		−	0.494094i
$907$	803.919			0.886350			0.443175	−	0.896435i	$-0.353852\pi$
$907$	803.919			0.886350			0.443175	+	0.896435i	$0.353852\pi$
$908$			49.5910i			0.0546157i
$909$			272.127i			0.299369i
$910$		0			0
$911$	−604.804			−0.663891			−0.331945	−	0.943299i	$-0.607705\pi$
$911$	−604.804			−0.663891			−0.331945	+	0.943299i	$0.607705\pi$
$912$	99.7589			0.109385
$913$		−	741.933i		−	0.812632i
$914$	−4.59822			−0.00503087
$915$		0			0
$916$		−	263.623i		−	0.287798i
$917$	−66.7950	+	312.009i	−0.0728408	+	0.340250i
$918$	−19.0879			−0.0207929
$919$	152.377			0.165807			0.0829035	−	0.996558i	$-0.473581\pi$
$919$	152.377			0.165807			0.0829035	+	0.996558i	$0.473581\pi$
$920$		0			0
$921$	−543.363			−0.589971
$922$		−	937.246i		−	1.01654i
$923$			81.2169i			0.0879923i
$924$	−29.8376	+	139.376i	−0.0322918	+	0.150840i
$925$		0			0
$926$	273.376			0.295222
$927$		−	410.928i		−	0.443288i
$928$	−91.3982			−0.0984894
$929$		−	756.423i		−	0.814233i	−0.913376	−	0.407117i	$-0.866534\pi$
$929$		−	756.423i		−	0.814233i	0.913376	−	0.407117i	$-0.133466\pi$
$930$		0			0
$931$	288.850	−	643.712i	0.310258	−	0.691420i
$932$	291.817			0.313109
$933$	−590.961			−0.633399
$934$		−	499.382i		−	0.534670i
$935$		0			0
$936$			17.5149i			0.0187126i
$937$			62.9589i			0.0671920i	0.999435	+	0.0335960i	$0.0106960\pi$
$937$			62.9589i			0.0671920i	−0.999435	+	0.0335960i	$0.989304\pi$
$938$	383.277	+	82.0521i	0.408611	+	0.0874755i
$939$	881.594			0.938865
$940$		0			0
$941$		−	513.455i		−	0.545648i	−0.962064	−	0.272824i	$-0.912042\pi$
$941$		−	513.455i		−	0.545648i	0.962064	−	0.272824i	$-0.0879577\pi$
$942$	−123.465			−0.131066
$943$		−	353.811i		−	0.375197i
$944$			240.629i			0.254904i
$945$		0			0
$946$	−86.4845			−0.0914212
$947$	1612.21			1.70243			0.851217	−	0.524813i	$-0.175865\pi$
$947$	1612.21			1.70243			0.851217	+	0.524813i	$0.175865\pi$
$948$			142.859i			0.150695i
$949$	−24.4221			−0.0257345
$950$		0			0
$951$			616.576i			0.648345i
$952$	−10.7659	+	50.2891i	−0.0113087	+	0.0528247i
$953$	−1350.65			−1.41726			−0.708629	−	0.705582i	$-0.750686\pi$
$953$	−1350.65			−1.41726			−0.708629	+	0.705582i	$0.750686\pi$
$954$	169.674			0.177856
$955$		0			0
$956$	−822.970			−0.860847
$957$			164.495i			0.171886i
$958$		−	860.920i		−	0.898664i
$959$	−1213.19	−	259.719i	−1.26505	−	0.270823i
$960$		0			0
$961$	−1379.35			−1.43533
$962$			135.161i			0.140500i
$963$	−70.1237			−0.0728180
$964$			763.174i			0.791675i
$965$		0			0
$966$	16.9981	−	79.4004i	0.0175964	−	0.0821951i
$967$	−936.177			−0.968125			−0.484063	−	0.875033i	$-0.660839\pi$
$967$	−936.177			−0.968125			−0.484063	+	0.875033i	$0.660839\pi$
$968$	−244.515			−0.252598
$969$		−	64.7819i		−	0.0668544i
$970$		0			0
$971$			135.578i			0.139627i	0.997560	+	0.0698133i	$0.0222404\pi$
$971$			135.578i			0.139627i	−0.997560	+	0.0698133i	$0.977760\pi$
$972$			31.1769i			0.0320750i
$973$	−48.6365	+	227.188i	−0.0499862	+	0.233492i
$974$	261.944			0.268936
$975$		0			0
$976$		−	292.648i		−	0.299844i
$977$	−1726.37			−1.76701			−0.883506	−	0.468420i	$-0.844823\pi$
$977$	−1726.37			−1.76701			−0.883506	+	0.468420i	$0.844823\pi$
$978$		−	249.255i		−	0.254861i
$979$			541.496i			0.553111i
$980$		0			0
$981$	77.0619			0.0785544
$982$	1307.66			1.33163
$983$			73.5367i			0.0748085i	0.999300	+	0.0374042i	$0.0119089\pi$
$983$			73.5367i			0.0748085i	−0.999300	+	0.0374042i	$0.988091\pi$
$984$	366.013			0.371965
$985$		0			0
$986$			59.3525i			0.0601953i
$987$	−415.747	−	89.0033i	−0.421223	−	0.0901756i
$988$	−59.4434			−0.0601654
$989$	49.2690			0.0498170
$990$		0			0
$991$	1809.34			1.82578			0.912888	−	0.408209i	$-0.133847\pi$
$991$	1809.34			1.82578			0.912888	+	0.408209i	$0.133847\pi$
$992$		−	273.663i		−	0.275870i
$993$		−	985.474i		−	0.992421i
$994$	380.878	+	81.5386i	0.383178	+	0.0820308i
$995$		0			0
$996$	−437.246			−0.439002
$997$		−	1094.62i		−	1.09792i	−0.835850	−	0.548958i	$-0.815025\pi$
$997$		−	1094.62i		−	1.09792i	0.835850	−	0.548958i	$-0.184975\pi$
$998$	−911.023			−0.912849
$999$			240.589i			0.240830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.d.601.10	yes	12
5.2	odd	4		1050.3.h.c.349.18		24
5.3	odd	4		1050.3.h.c.349.9		24
5.4	even	2		1050.3.f.c.601.3	✓	12
7.6	odd	2	inner	1050.3.f.d.601.7	yes	12
35.13	even	4		1050.3.h.c.349.17		24
35.27	even	4		1050.3.h.c.349.10		24
35.34	odd	2		1050.3.f.c.601.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.3	✓	12	5.4	even	2
1050.3.f.c.601.6	yes	12	35.34	odd	2
1050.3.f.d.601.7	yes	12	7.6	odd	2	inner
1050.3.f.d.601.10	yes	12	1.1	even	1	trivial
1050.3.h.c.349.9		24	5.3	odd	4
1050.3.h.c.349.10		24	35.27	even	4
1050.3.h.c.349.17		24	35.13	even	4
1050.3.h.c.349.18		24	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.84490 - 1.46536i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.84490 - 1.46536i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -5.87800 q^{11} +3.46410i q^{12} -2.06416i q^{13} +(-9.68016 - 2.07233i) q^{14} +4.00000 q^{16} -2.59754i q^{17} -4.24264 q^{18} -14.3990i q^{19} +(2.53808 - 11.8557i) q^{21} -8.31274 q^{22} +4.73565 q^{23} +4.89898i q^{24} -2.91916i q^{26} -5.19615i q^{27} +(-13.6898 - 2.93072i) q^{28} -16.1571 q^{29} -48.3772i q^{31} +5.65685 q^{32} -10.1810i q^{33} -3.67347i q^{34} -6.00000 q^{36} -46.3013 q^{37} -20.3632i q^{38} +3.57522 q^{39} -74.7122i q^{41} +(3.58939 - 16.7665i) q^{42} +10.4038 q^{43} -11.7560 q^{44} +6.69723 q^{46} -35.0672i q^{47} +6.92820i q^{48} +(44.7054 + 20.0605i) q^{49} +4.49907 q^{51} -4.12831i q^{52} -39.9926 q^{53} -7.34847i q^{54} +(-19.3603 - 4.14467i) q^{56} +24.9397 q^{57} -22.8495 q^{58} +60.1573i q^{59} -73.1619i q^{61} -68.4156i q^{62} +(20.5347 + 4.39608i) q^{63} +8.00000 q^{64} -14.3981i q^{66} -39.5941 q^{67} -5.19507i q^{68} +8.20239i q^{69} -39.3463 q^{71} -8.48528 q^{72} -11.8315i q^{73} -65.4800 q^{74} -28.7979i q^{76} +(40.2343 + 8.61339i) q^{77} +5.05613 q^{78} +41.2398 q^{79} +9.00000 q^{81} -105.659i q^{82} +126.222i q^{83} +(5.07616 - 23.7114i) q^{84} +14.7133 q^{86} -27.9849i q^{87} -16.6255 q^{88} -92.1225i q^{89} +(-3.02473 + 14.1290i) q^{91} +9.47131 q^{92} +83.7917 q^{93} -49.5925i q^{94} +9.79796i q^{96} -4.26795i q^{97} +(63.2230 + 28.3698i) q^{98} +17.6340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9}+O(q^{10}) \) 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9	\( 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9} - 16 q^{11} + 8 q^{14} + 48 q^{16} - 6 q^{21} + 48 q^{22} + 20 q^{28} + 48 q^{29} - 72 q^{36} - 64 q^{37} - 12 q^{39} - 24 q^{42} + 108 q^{43} - 32 q^{44} + 80 q^{46} + 118 q^{49} + 72 q^{51} - 176 q^{53} + 16 q^{56} + 132 q^{57} - 128 q^{58} - 30 q^{63} + 96 q^{64} + 4 q^{67} + 248 q^{71} - 64 q^{74} + 396 q^{77} - 48 q^{78} - 208 q^{79} + 108 q^{81} - 12 q^{84} + 128 q^{86} + 96 q^{88} - 158 q^{91} - 252 q^{93} + 240 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9 - 16 * q^11 + 8 * q^14 + 48 * q^16 - 6 * q^21 + 48 * q^22 + 20 * q^28 + 48 * q^29 - 72 * q^36 - 64 * q^37 - 12 * q^39 - 24 * q^42 + 108 * q^43 - 32 * q^44 + 80 * q^46 + 118 * q^49 + 72 * q^51 - 176 * q^53 + 16 * q^56 + 132 * q^57 - 128 * q^58 - 30 * q^63 + 96 * q^64 + 4 * q^67 + 248 * q^71 - 64 * q^74 + 396 * q^77 - 48 * q^78 - 208 * q^79 + 108 * q^81 - 12 * q^84 + 128 * q^86 + 96 * q^88 - 158 * q^91 - 252 * q^93 + 240 * q^98 + 48 * q^99

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