LMFDB - Embedded newform 1050.3.f.c.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:	$12$
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			601.7
Root			$-3.88205 + 6.72390i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.c.601.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-5.11242 + 4.78154i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-5.11242 + 4.78154i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +10.3587 q^{11} -3.46410i q^{12} +0.605169i q^{13} +(-7.23005 + 6.76212i) q^{14} +4.00000 q^{16} -5.49382i q^{17} -4.24264 q^{18} -33.2186i q^{19} +(8.28188 + 8.85497i) q^{21} +14.6495 q^{22} +14.4299 q^{23} -4.89898i q^{24} +0.855838i q^{26} +5.19615i q^{27} +(-10.2248 + 9.56309i) q^{28} +42.0972 q^{29} +0.540656i q^{31} +5.65685 q^{32} -17.9418i q^{33} -7.76943i q^{34} -6.00000 q^{36} +13.6996 q^{37} -46.9782i q^{38} +1.04818 q^{39} -13.7668i q^{41} +(11.7123 + 12.5228i) q^{42} +82.3938 q^{43} +20.7175 q^{44} +20.4069 q^{46} +53.0228i q^{47} -6.92820i q^{48} +(3.27369 - 48.8905i) q^{49} -9.51557 q^{51} +1.21034i q^{52} +19.4291 q^{53} +7.34847i q^{54} +(-14.4601 + 13.5242i) q^{56} -57.5364 q^{57} +59.5344 q^{58} -29.4240i q^{59} -74.7188i q^{61} +0.764604i q^{62} +(15.3373 - 14.3446i) q^{63} +8.00000 q^{64} -25.3736i q^{66} -12.1937 q^{67} -10.9876i q^{68} -24.9933i q^{69} +42.3945 q^{71} -8.48528 q^{72} -66.9179i q^{73} +19.3742 q^{74} -66.4373i q^{76} +(-52.9582 + 49.5307i) q^{77} +1.48236 q^{78} -27.0962 q^{79} +9.00000 q^{81} -19.4693i q^{82} -126.850i q^{83} +(16.5638 + 17.7099i) q^{84} +116.522 q^{86} -72.9145i q^{87} +29.2989 q^{88} +30.1856i q^{89} +(-2.89364 - 3.09388i) q^{91} +28.8597 q^{92} +0.936444 q^{93} +74.9856i q^{94} -9.79796i q^{96} +164.602i q^{97} +(4.62970 - 69.1416i) q^{98} -31.0762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−5.11242	+	4.78154i	−0.730346	+	0.683078i
$7$	−5.11242	+	4.78154i	−0.730346	+	0.683078i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	10.3587			0.941702			0.470851	−	0.882213i	$-0.343947\pi$
$11$	10.3587			0.941702			0.470851	+	0.882213i	$0.343947\pi$
$12$		−	3.46410i		−	0.288675i
$13$			0.605169i			0.0465515i	0.999729	+	0.0232757i	$0.00740956\pi$
$13$			0.605169i			0.0465515i	−0.999729	+	0.0232757i	$0.992590\pi$
$14$	−7.23005	+	6.76212i	−0.516432	+	0.483009i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	5.49382i		−	0.323166i	−0.986859	−	0.161583i	$-0.948340\pi$
$17$		−	5.49382i		−	0.323166i	0.986859	−	0.161583i	$-0.0516599\pi$
$18$	−4.24264			−0.235702
$19$		−	33.2186i		−	1.74835i	−0.485612	−	0.874175i	$-0.661403\pi$
$19$		−	33.2186i		−	1.74835i	0.485612	−	0.874175i	$-0.338597\pi$
$20$		0			0
$21$	8.28188	+	8.85497i	0.394375	+	0.421665i
$22$	14.6495			0.665884
$23$	14.4299			0.627385			0.313693	−	0.949525i	$-0.398434\pi$
$23$	14.4299			0.627385			0.313693	+	0.949525i	$0.398434\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$			0.855838i			0.0329169i
$27$			5.19615i			0.192450i
$28$	−10.2248	+	9.56309i	−0.365173	+	0.341539i
$29$	42.0972			1.45163			0.725814	−	0.687891i	$-0.241464\pi$
$29$	42.0972			1.45163			0.725814	+	0.687891i	$0.241464\pi$
$30$		0			0
$31$			0.540656i			0.0174405i	0.999962	+	0.00872026i	$0.00277578\pi$
$31$			0.540656i			0.0174405i	−0.999962	+	0.00872026i	$0.997224\pi$
$32$	5.65685			0.176777
$33$		−	17.9418i		−	0.543692i
$34$		−	7.76943i		−	0.228513i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	13.6996			0.370260			0.185130	−	0.982714i	$-0.440729\pi$
$37$	13.6996			0.370260			0.185130	+	0.982714i	$0.440729\pi$
$38$		−	46.9782i		−	1.23627i
$39$	1.04818			0.0268765
$40$		0			0
$41$		−	13.7668i		−	0.335777i	−0.985806	−	0.167888i	$-0.946305\pi$
$41$		−	13.7668i		−	0.335777i	0.985806	−	0.167888i	$-0.0536948\pi$
$42$	11.7123	+	12.5228i	0.278865	+	0.298162i
$43$	82.3938			1.91614			0.958068	−	0.286541i	$-0.0925056\pi$
$43$	82.3938			1.91614			0.958068	+	0.286541i	$0.0925056\pi$
$44$	20.7175			0.470851
$45$		0			0
$46$	20.4069			0.443628
$47$			53.0228i			1.12814i	0.825725	+	0.564072i	$0.190766\pi$
$47$			53.0228i			1.12814i	−0.825725	+	0.564072i	$0.809234\pi$
$48$		−	6.92820i		−	0.144338i
$49$	3.27369	−	48.8905i	0.0668101	−	0.997766i
$50$		0			0
$51$	−9.51557			−0.186580
$52$			1.21034i			0.0232757i
$53$	19.4291			0.366587			0.183294	−	0.983058i	$-0.441324\pi$
$53$	19.4291			0.366587			0.183294	+	0.983058i	$0.441324\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	−14.4601	+	13.5242i	−0.258216	+	0.241504i
$57$	−57.5364			−1.00941
$58$	59.5344			1.02646
$59$		−	29.4240i		−	0.498713i	−0.968412	−	0.249356i	$-0.919781\pi$
$59$		−	29.4240i		−	0.498713i	0.968412	−	0.249356i	$-0.0802190\pi$
$60$		0			0
$61$		−	74.7188i		−	1.22490i	−0.790510	−	0.612449i	$-0.790185\pi$
$61$		−	74.7188i		−	1.22490i	0.790510	−	0.612449i	$-0.209815\pi$
$62$			0.764604i			0.0123323i
$63$	15.3373	−	14.3446i	0.243449	−	0.227693i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	25.3736i		−	0.384448i
$67$	−12.1937			−0.181996			−0.0909981	−	0.995851i	$-0.529006\pi$
$67$	−12.1937			−0.181996			−0.0909981	+	0.995851i	$0.529006\pi$
$68$		−	10.9876i		−	0.161583i
$69$		−	24.9933i		−	0.362221i
$70$		0			0
$71$	42.3945			0.597105			0.298553	−	0.954393i	$-0.403496\pi$
$71$	42.3945			0.597105			0.298553	+	0.954393i	$0.403496\pi$
$72$	−8.48528			−0.117851
$73$		−	66.9179i		−	0.916683i	−0.888776	−	0.458342i	$-0.848444\pi$
$73$		−	66.9179i		−	0.916683i	0.888776	−	0.458342i	$-0.151556\pi$
$74$	19.3742			0.261813
$75$		0			0
$76$		−	66.4373i		−	0.874175i
$77$	−52.9582	+	49.5307i	−0.687768	+	0.643256i
$78$	1.48236			0.0190046
$79$	−27.0962			−0.342990			−0.171495	−	0.985185i	$-0.554860\pi$
$79$	−27.0962			−0.342990			−0.171495	+	0.985185i	$0.554860\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	19.4693i		−	0.237430i
$83$		−	126.850i		−	1.52831i	−0.645031	−	0.764156i	$-0.723156\pi$
$83$		−	126.850i		−	1.52831i	0.645031	−	0.764156i	$-0.276844\pi$
$84$	16.5638	+	17.7099i	0.197188	+	0.210833i
$85$		0			0
$86$	116.522			1.35491
$87$		−	72.9145i		−	0.838097i
$88$	29.2989			0.332942
$89$			30.1856i			0.339164i	0.985516	+	0.169582i	$0.0542417\pi$
$89$			30.1856i			0.339164i	−0.985516	+	0.169582i	$0.945758\pi$
$90$		0			0
$91$	−2.89364	−	3.09388i	−0.0317983	−	0.0339987i
$92$	28.8597			0.313693
$93$	0.936444			0.0100693
$94$			74.9856i			0.797719i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$			164.602i			1.69693i	0.529251	+	0.848465i	$0.322473\pi$
$97$			164.602i			1.69693i	−0.529251	+	0.848465i	$0.677527\pi$
$98$	4.62970	−	69.1416i	0.0472419	−	0.705527i
$99$	−31.0762			−0.313901
$100$		0			0
$101$		−	19.5033i		−	0.193102i	−0.995328	−	0.0965508i	$-0.969219\pi$
$101$		−	19.5033i		−	0.193102i	0.995328	−	0.0965508i	$-0.0307810\pi$
$102$	−13.4570			−0.131932
$103$			108.949i			1.05775i	0.848699	+	0.528877i	$0.177387\pi$
$103$			108.949i			1.05775i	−0.848699	+	0.528877i	$0.822613\pi$
$104$			1.71168i			0.0164584i
$105$		0			0
$106$	27.4769			0.259216
$107$	−120.784			−1.12882			−0.564409	−	0.825495i	$-0.690896\pi$
$107$	−120.784			−1.12882			−0.564409	+	0.825495i	$0.690896\pi$
$108$			10.3923i			0.0962250i
$109$	123.855			1.13628			0.568141	−	0.822931i	$-0.307663\pi$
$109$	123.855			1.13628			0.568141	+	0.822931i	$0.307663\pi$
$110$		0			0
$111$		−	23.7284i		−	0.213770i
$112$	−20.4497	+	19.1262i	−0.182586	+	0.170769i
$113$	−201.420			−1.78248			−0.891239	−	0.453534i	$-0.850163\pi$
$113$	−201.420			−1.78248			−0.891239	+	0.453534i	$0.850163\pi$
$114$	−81.3687			−0.713761
$115$		0			0
$116$	84.1944			0.725814
$117$		−	1.81551i		−	0.0155172i
$118$		−	41.6119i		−	0.352643i
$119$	26.2689	+	28.0867i	0.220747	+	0.236023i
$120$		0			0
$121$	−13.6968			−0.113196
$122$		−	105.668i		−	0.866133i
$123$	−23.8449			−0.193861
$124$			1.08131i			0.00872026i
$125$		0			0
$126$	21.6902	−	20.2864i	0.172144	−	0.161003i
$127$	−213.378			−1.68014			−0.840071	−	0.542476i	$-0.817487\pi$
$127$	−213.378			−1.68014			−0.840071	+	0.542476i	$0.817487\pi$
$128$	11.3137			0.0883883
$129$		−	142.710i		−	1.10628i
$130$		0			0
$131$		−	139.162i		−	1.06231i	−0.847276	−	0.531153i	$-0.821759\pi$
$131$		−	139.162i		−	1.06231i	0.847276	−	0.531153i	$-0.178241\pi$
$132$		−	35.8837i		−	0.271846i
$133$	158.836	+	169.828i	1.19426	+	1.27690i
$134$	−17.2446			−0.128691
$135$		0			0
$136$		−	15.5389i		−	0.114256i
$137$	18.2823			0.133448			0.0667238	−	0.997771i	$-0.478745\pi$
$137$	18.2823			0.133448			0.0667238	+	0.997771i	$0.478745\pi$
$138$		−	35.3458i		−	0.256129i
$139$			38.7265i			0.278608i	0.990250	+	0.139304i	$0.0444865\pi$
$139$			38.7265i			0.278608i	−0.990250	+	0.139304i	$0.955513\pi$
$140$		0			0
$141$	91.8382			0.651335
$142$	59.9548			0.422217
$143$			6.26878i			0.0438376i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	94.6362i		−	0.648193i
$147$	−84.6809	−	5.67021i	−0.576060	−	0.0385728i
$148$	27.3992			0.185130
$149$	−20.1135			−0.134990			−0.0674950	−	0.997720i	$-0.521501\pi$
$149$	−20.1135			−0.134990			−0.0674950	+	0.997720i	$0.521501\pi$
$150$		0			0
$151$	11.3257			0.0750047			0.0375023	−	0.999297i	$-0.488060\pi$
$151$	11.3257			0.0750047			0.0375023	+	0.999297i	$0.488060\pi$
$152$		−	93.9565i		−	0.618135i
$153$			16.4814i			0.107722i
$154$	−74.8942	+	70.0470i	−0.486326	+	0.454851i
$155$		0			0
$156$	2.09637			0.0134382
$157$			108.422i			0.690589i	0.938494	+	0.345294i	$0.112221\pi$
$157$			108.422i			0.690589i	−0.938494	+	0.345294i	$0.887779\pi$
$158$	−38.3198			−0.242531
$159$		−	33.6522i		−	0.211649i
$160$		0			0
$161$	−73.7715	+	68.9970i	−0.458208	+	0.428553i
$162$	12.7279			0.0785674
$163$	82.1443			0.503953			0.251976	−	0.967733i	$-0.418919\pi$
$163$	82.1443			0.503953			0.251976	+	0.967733i	$0.418919\pi$
$164$		−	27.5337i		−	0.167888i
$165$		0			0
$166$		−	179.393i		−	1.08068i
$167$			314.645i			1.88410i	0.335472	+	0.942050i	$0.391104\pi$
$167$			314.645i			1.88410i	−0.335472	+	0.942050i	$0.608896\pi$
$168$	23.4247	+	25.0456i	0.139433	+	0.149081i
$169$	168.634			0.997833
$170$		0			0
$171$			99.6559i			0.582783i
$172$	164.788			0.958068
$173$		−	188.637i		−	1.09039i	−0.838311	−	0.545193i	$-0.816456\pi$
$173$		−	188.637i		−	1.09039i	0.838311	−	0.545193i	$-0.183544\pi$
$174$		−	103.117i		−	0.592624i
$175$		0			0
$176$	41.4349			0.235426
$177$	−50.9639			−0.287932
$178$			42.6889i			0.239825i
$179$	254.112			1.41962			0.709810	−	0.704393i	$-0.248781\pi$
$179$	254.112			1.41962			0.709810	+	0.704393i	$0.248781\pi$
$180$		0			0
$181$		−	138.747i		−	0.766560i	−0.923632	−	0.383280i	$-0.874794\pi$
$181$		−	138.747i		−	0.766560i	0.923632	−	0.383280i	$-0.125206\pi$
$182$	−4.09223	−	4.37540i	−0.0224848	−	0.0240407i
$183$	−129.417			−0.707195
$184$	40.8138			0.221814
$185$		0			0
$186$	1.32433			0.00712007
$187$		−	56.9089i		−	0.304326i
$188$			106.046i			0.564072i
$189$	−24.8456	−	26.5649i	−0.131458	−	0.140555i
$190$		0			0
$191$	178.907			0.936685			0.468342	−	0.883547i	$-0.344851\pi$
$191$	178.907			0.936685			0.468342	+	0.883547i	$0.344851\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−3.65902			−0.0189587			−0.00947933	−	0.999955i	$-0.503017\pi$
$193$	−3.65902			−0.0189587			−0.00947933	+	0.999955i	$0.503017\pi$
$194$			232.783i			1.19991i
$195$		0			0
$196$	6.54739	−	97.7810i	0.0334051	−	0.498883i
$197$	201.822			1.02447			0.512237	−	0.858844i	$-0.328817\pi$
$197$	201.822			1.02447			0.512237	+	0.858844i	$0.328817\pi$
$198$	−43.9484			−0.221961
$199$			97.5792i			0.490348i	0.969479	+	0.245174i	$0.0788451\pi$
$199$			97.5792i			0.490348i	−0.969479	+	0.245174i	$0.921155\pi$
$200$		0			0
$201$			21.1202i			0.105076i
$202$		−	27.5818i		−	0.136543i
$203$	−215.219	+	201.290i	−1.06019	+	0.991574i
$204$	−19.0311			−0.0932899
$205$		0			0
$206$			154.077i			0.747945i
$207$	−43.2896			−0.209128
$208$			2.42068i			0.0116379i
$209$		−	344.103i		−	1.64642i
$210$		0			0
$211$	−104.122			−0.493469			−0.246734	−	0.969083i	$-0.579357\pi$
$211$	−104.122			−0.493469			−0.246734	+	0.969083i	$0.579357\pi$
$212$	38.8582			0.183294
$213$		−	73.4294i		−	0.344739i
$214$	−170.814			−0.798196
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−2.58517	−	2.76406i	−0.0119132	−	0.0127376i
$218$	175.157			0.803473
$219$	−115.905			−0.529247
$220$		0			0
$221$	3.32469			0.0150438
$222$		−	33.5571i		−	0.151158i
$223$			255.861i			1.14736i	0.819080	+	0.573679i	$0.194484\pi$
$223$			255.861i			1.14736i	−0.819080	+	0.573679i	$0.805516\pi$
$224$	−28.9202	+	27.0485i	−0.129108	+	0.120752i
$225$		0			0
$226$	−284.851			−1.26040
$227$			102.642i			0.452168i	0.974108	+	0.226084i	$0.0725924\pi$
$227$			102.642i			0.452168i	−0.974108	+	0.226084i	$0.927408\pi$
$228$	−115.073			−0.504705
$229$			254.063i			1.10945i	0.832035	+	0.554723i	$0.187176\pi$
$229$			254.063i			1.10945i	−0.832035	+	0.554723i	$0.812824\pi$
$230$		0			0
$231$	85.7897	+	91.7262i	0.371384	+	0.397083i
$232$	119.069			0.513228
$233$	−87.3948			−0.375085			−0.187543	−	0.982256i	$-0.560052\pi$
$233$	−87.3948			−0.375085			−0.187543	+	0.982256i	$0.560052\pi$
$234$		−	2.56751i		−	0.0109723i
$235$		0			0
$236$		−	58.8481i		−	0.249356i
$237$			46.9320i			0.198025i
$238$	37.1499	+	39.7206i	0.156092	+	0.166893i
$239$	−238.165			−0.996505			−0.498253	−	0.867032i	$-0.666025\pi$
$239$	−238.165			−0.996505			−0.498253	+	0.867032i	$0.666025\pi$
$240$		0			0
$241$			235.615i			0.977655i	0.872381	+	0.488827i	$0.162575\pi$
$241$			235.615i			0.977655i	−0.872381	+	0.488827i	$0.837425\pi$
$242$	−19.3702			−0.0800420
$243$		−	15.5885i		−	0.0641500i
$244$		−	149.438i		−	0.612449i
$245$		0			0
$246$	−33.7217			−0.137080
$247$	20.1029			0.0813882
$248$			1.52921i			0.00616616i
$249$	−219.710			−0.882371
$250$		0			0
$251$			281.571i			1.12180i	0.827884	+	0.560899i	$0.189544\pi$
$251$			281.571i			1.12180i	−0.827884	+	0.560899i	$0.810456\pi$
$252$	30.6745	−	28.6893i	0.121724	−	0.113846i
$253$	149.475			0.590810
$254$	−301.762			−1.18804
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	253.540i		−	0.986539i	−0.869877	−	0.493269i	$-0.835802\pi$
$257$		−	253.540i		−	0.986539i	0.869877	−	0.493269i	$-0.164198\pi$
$258$		−	201.823i		−	0.782259i
$259$	−70.0382	+	65.5053i	−0.270418	+	0.252916i
$260$		0			0
$261$	−126.292			−0.483876
$262$		−	196.805i		−	0.751163i
$263$	−264.972			−1.00750			−0.503749	−	0.863850i	$-0.668046\pi$
$263$	−264.972			−1.00750			−0.503749	+	0.863850i	$0.668046\pi$
$264$		−	50.7472i		−	0.192224i
$265$		0			0
$266$	224.628	+	240.173i	0.844468	+	0.902904i
$267$	52.2830			0.195816
$268$	−24.3875			−0.0909981
$269$			189.680i			0.705130i	0.935787	+	0.352565i	$0.114690\pi$
$269$			189.680i			0.705130i	−0.935787	+	0.352565i	$0.885310\pi$
$270$		0			0
$271$		−	286.595i		−	1.05755i	−0.848763	−	0.528773i	$-0.822652\pi$
$271$		−	286.595i		−	1.05755i	0.848763	−	0.528773i	$-0.177348\pi$
$272$		−	21.9753i		−	0.0807914i
$273$	−5.35875	+	5.01193i	−0.0196291	+	0.0183587i
$274$	25.8551			0.0943617
$275$		0			0
$276$		−	49.9865i		−	0.181111i
$277$	82.5341			0.297957			0.148979	−	0.988840i	$-0.452401\pi$
$277$	82.5341			0.297957			0.148979	+	0.988840i	$0.452401\pi$
$278$			54.7676i			0.197006i
$279$		−	1.62197i		−	0.00581351i
$280$		0			0
$281$	−384.926			−1.36984			−0.684922	−	0.728617i	$-0.740164\pi$
$281$	−384.926			−1.36984			−0.684922	+	0.728617i	$0.740164\pi$
$282$	129.879			0.460563
$283$			514.332i			1.81743i	0.417419	+	0.908714i	$0.362935\pi$
$283$			514.332i			1.81743i	−0.417419	+	0.908714i	$0.637065\pi$
$284$	84.7889			0.298553
$285$		0			0
$286$			8.86539i			0.0309979i
$287$	65.8268	+	70.3819i	0.229362	+	0.245233i
$288$	−16.9706			−0.0589256
$289$	258.818			0.895564
$290$		0			0
$291$	285.099			0.979723
$292$		−	133.836i		−	0.458342i
$293$		−	431.273i		−	1.47192i	−0.677023	−	0.735962i	$-0.736730\pi$
$293$		−	431.273i		−	1.47192i	0.677023	−	0.735962i	$-0.263270\pi$
$294$	−119.757	−	8.01888i	−0.407336	−	0.0272751i
$295$		0			0
$296$	38.7484			0.130907
$297$			53.8255i			0.181231i
$298$	−28.4448			−0.0954524
$299$			8.73251i			0.0292057i
$300$		0			0
$301$	−421.232	+	393.970i	−1.39944	+	1.30887i
$302$	16.0170			0.0530363
$303$	−33.7806			−0.111487
$304$		−	132.875i		−	0.437087i
$305$		0			0
$306$			23.3083i			0.0761709i
$307$			341.103i			1.11108i	0.831489	+	0.555542i	$0.187489\pi$
$307$			341.103i			1.11108i	−0.831489	+	0.555542i	$0.812511\pi$
$308$	−105.916	+	99.0614i	−0.343884	+	0.321628i
$309$	188.705			0.610694
$310$		0			0
$311$			545.710i			1.75469i	0.479857	+	0.877347i	$0.340689\pi$
$311$			545.710i			1.75469i	−0.479857	+	0.877347i	$0.659311\pi$
$312$	2.96471			0.00950228
$313$			98.7397i			0.315462i	0.987482	+	0.157731i	$0.0504179\pi$
$313$			98.7397i			0.315462i	−0.987482	+	0.157731i	$0.949582\pi$
$314$			153.332i			0.488320i
$315$		0			0
$316$	−54.1924			−0.171495
$317$	−165.058			−0.520689			−0.260344	−	0.965516i	$-0.583836\pi$
$317$	−165.058			−0.520689			−0.260344	+	0.965516i	$0.583836\pi$
$318$		−	47.5914i		−	0.149659i
$319$	436.073			1.36700
$320$		0			0
$321$			209.203i			0.651724i
$322$	−104.329	+	97.5765i	−0.324002	+	0.303033i
$323$	−182.497			−0.565006
$324$	18.0000			0.0555556
$325$		0			0
$326$	116.170			0.356349
$327$		−	214.523i		−	0.656033i
$328$		−	38.9385i		−	0.118715i
$329$	−253.531	−	271.075i	−0.770610	−	0.823936i
$330$		0			0
$331$	−230.662			−0.696863			−0.348431	−	0.937334i	$-0.613286\pi$
$331$	−230.662			−0.696863			−0.348431	+	0.937334i	$0.613286\pi$
$332$		−	253.700i		−	0.764156i
$333$	−41.0988			−0.123420
$334$			444.975i			1.33226i
$335$		0			0
$336$	33.1275	+	35.4199i	0.0985938	+	0.105416i
$337$	144.633			0.429179			0.214590	−	0.976704i	$-0.431159\pi$
$337$	144.633			0.429179			0.214590	+	0.976704i	$0.431159\pi$
$338$	238.484			0.705574
$339$			348.870i			1.02911i
$340$		0			0
$341$			5.60051i			0.0164238i
$342$			140.935i			0.412090i
$343$	217.036	+	265.602i	0.632757	+	0.774351i
$344$	233.045			0.677456
$345$		0			0
$346$		−	266.773i		−	0.771019i
$347$	162.310			0.467751			0.233875	−	0.972267i	$-0.424859\pi$
$347$	162.310			0.467751			0.233875	+	0.972267i	$0.424859\pi$
$348$		−	145.829i		−	0.419049i
$349$		−	313.404i		−	0.898006i	−0.893530	−	0.449003i	$-0.851779\pi$
$349$		−	313.404i		−	0.898006i	0.893530	−	0.449003i	$-0.148221\pi$
$350$		0			0
$351$	−3.14455			−0.00895883
$352$	58.5978			0.166471
$353$		−	343.028i		−	0.971752i	−0.874028	−	0.485876i	$-0.838501\pi$
$353$		−	343.028i		−	0.971752i	0.874028	−	0.485876i	$-0.161499\pi$
$354$	−72.0739			−0.203599
$355$		0			0
$356$			60.3712i			0.169582i
$357$	48.6476	−	45.4991i	0.136268	−	0.127448i
$358$	359.369			1.00382
$359$	−357.293			−0.995244			−0.497622	−	0.867394i	$-0.665793\pi$
$359$	−357.293			−0.995244			−0.497622	+	0.867394i	$0.665793\pi$
$360$		0			0
$361$	−742.478			−2.05672
$362$		−	196.218i		−	0.542040i
$363$			23.7235i			0.0653540i
$364$	−5.78728	−	6.18776i	−0.0158991	−	0.0169993i
$365$		0			0
$366$	−183.023			−0.500062
$367$		−	617.139i		−	1.68158i	−0.541363	−	0.840789i	$-0.682091\pi$
$367$		−	617.139i		−	1.68158i	0.541363	−	0.840789i	$-0.317909\pi$
$368$	57.7195			0.156846
$369$			41.3005i			0.111926i
$370$		0			0
$371$	−99.3298	+	92.9011i	−0.267735	+	0.250407i
$372$	1.87289			0.00503465
$373$	338.873			0.908506			0.454253	−	0.890873i	$-0.349906\pi$
$373$	338.873			0.908506			0.454253	+	0.890873i	$0.349906\pi$
$374$		−	80.4814i		−	0.215191i
$375$		0			0
$376$			149.971i			0.398859i
$377$			25.4759i			0.0675754i
$378$	−35.1370	−	37.5685i	−0.0929551	−	0.0993875i
$379$	−211.631			−0.558392			−0.279196	−	0.960234i	$-0.590068\pi$
$379$	−211.631			−0.558392			−0.279196	+	0.960234i	$0.590068\pi$
$380$		0			0
$381$			369.582i			0.970031i
$382$	253.012			0.662336
$383$		−	238.751i		−	0.623370i	−0.950185	−	0.311685i	$-0.899107\pi$
$383$		−	238.751i		−	0.623370i	0.950185	−	0.311685i	$-0.100893\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−5.17464			−0.0134058
$387$	−247.182			−0.638712
$388$			329.204i			0.848465i
$389$	−21.7723			−0.0559700			−0.0279850	−	0.999608i	$-0.508909\pi$
$389$	−21.7723			−0.0559700			−0.0279850	+	0.999608i	$0.508909\pi$
$390$		0			0
$391$		−	79.2750i		−	0.202749i
$392$	9.25941	−	138.283i	0.0236209	−	0.352763i
$393$	−241.036			−0.613322
$394$	285.419			0.724413
$395$		0			0
$396$	−62.1524			−0.156950
$397$		−	552.917i		−	1.39274i	−0.717684	−	0.696369i	$-0.754798\pi$
$397$		−	552.917i		−	1.39274i	0.717684	−	0.696369i	$-0.245202\pi$
$398$			137.998i			0.346728i
$399$	294.150	−	275.113i	0.737218	−	0.689505i
$400$		0			0
$401$	−636.205			−1.58655			−0.793273	−	0.608866i	$-0.791625\pi$
$401$	−636.205			−1.58655			−0.793273	+	0.608866i	$0.791625\pi$
$402$			29.8685i			0.0742997i
$403$	−0.327188			−0.000811882
$404$		−	39.0065i		−	0.0965508i
$405$		0			0
$406$	−304.365	+	284.666i	−0.749667	+	0.701149i
$407$	141.911			0.348675
$408$	−26.9141			−0.0659659
$409$			358.386i			0.876249i	0.898914	+	0.438124i	$0.144357\pi$
$409$			358.386i			0.876249i	−0.898914	+	0.438124i	$0.855643\pi$
$410$		0			0
$411$		−	31.6659i		−	0.0770460i
$412$			217.897i			0.528877i
$413$	140.692	+	150.428i	0.340659	+	0.364233i
$414$	−61.2207			−0.147876
$415$		0			0
$416$			3.42335i			0.00822921i
$417$	67.0763			0.160854
$418$		−	486.635i		−	1.16420i
$419$		−	391.544i		−	0.934472i	−0.884133	−	0.467236i	$-0.845250\pi$
$419$		−	391.544i		−	0.934472i	0.884133	−	0.467236i	$-0.154750\pi$
$420$		0			0
$421$	472.677			1.12275			0.561374	−	0.827563i	$-0.310273\pi$
$421$	472.677			1.12275			0.561374	+	0.827563i	$0.310273\pi$
$422$	−147.251			−0.348935
$423$		−	159.068i		−	0.376048i
$424$	54.9538			0.129608
$425$		0			0
$426$		−	103.845i		−	0.243767i
$427$	357.271	+	381.994i	0.836700	+	0.894599i
$428$	−241.567			−0.564409
$429$	10.8578			0.0253097
$430$		0			0
$431$	−671.160			−1.55721			−0.778607	−	0.627511i	$-0.784074\pi$
$431$	−671.160			−1.55721			−0.778607	+	0.627511i	$0.784074\pi$
$432$			20.7846i			0.0481125i
$433$			113.211i			0.261456i	0.991418	+	0.130728i	$0.0417315\pi$
$433$			113.211i			0.261456i	−0.991418	+	0.130728i	$0.958268\pi$
$434$	−3.65599	−	3.90898i	−0.00842393	−	0.00900686i
$435$		0			0
$436$	247.710			0.568141
$437$		−	479.340i		−	1.09689i
$438$	−163.915			−0.374234
$439$			603.089i			1.37378i	0.726762	+	0.686890i	$0.241024\pi$
$439$			603.089i			1.37378i	−0.726762	+	0.686890i	$0.758976\pi$
$440$		0			0
$441$	−9.82108	+	146.672i	−0.0222700	+	0.332589i
$442$	4.70182			0.0106376
$443$	−853.722			−1.92714			−0.963569	−	0.267459i	$-0.913816\pi$
$443$	−853.722			−1.92714			−0.963569	+	0.267459i	$0.913816\pi$
$444$		−	47.4569i		−	0.106885i
$445$		0			0
$446$			361.842i			0.811305i
$447$			34.8376i			0.0779366i
$448$	−40.8994	+	38.2523i	−0.0912932	+	0.0853847i
$449$	−232.558			−0.517946			−0.258973	−	0.965885i	$-0.583384\pi$
$449$	−232.558			−0.517946			−0.258973	+	0.965885i	$0.583384\pi$
$450$		0			0
$451$		−	142.607i		−	0.316202i
$452$	−402.840			−0.891239
$453$		−	19.6167i		−	0.0433040i
$454$			145.158i			0.319731i
$455$		0			0
$456$	−162.737			−0.356880
$457$	389.899			0.853170			0.426585	−	0.904448i	$-0.359717\pi$
$457$	389.899			0.853170			0.426585	+	0.904448i	$0.359717\pi$
$458$			359.299i			0.784496i
$459$	28.5467			0.0621932
$460$		0			0
$461$		−	599.713i		−	1.30090i	−0.759551	−	0.650448i	$-0.774581\pi$
$461$		−	599.713i		−	1.30090i	0.759551	−	0.650448i	$-0.225419\pi$
$462$	121.325	+	129.721i	0.262608	+	0.280780i
$463$	−211.263			−0.456292			−0.228146	−	0.973627i	$-0.573266\pi$
$463$	−211.263			−0.456292			−0.228146	+	0.973627i	$0.573266\pi$
$464$	168.389			0.362907
$465$		0			0
$466$	−123.595			−0.265225
$467$		−	796.828i		−	1.70627i	−0.521690	−	0.853135i	$-0.674698\pi$
$467$		−	796.828i		−	1.70627i	0.521690	−	0.853135i	$-0.325302\pi$
$468$		−	3.63101i		−	0.00775858i
$469$	62.3396	−	58.3049i	0.132920	−	0.124318i
$470$		0			0
$471$	187.793			0.398712
$472$		−	83.2238i		−	0.176322i
$473$	853.495			1.80443
$474$			66.3719i			0.140025i
$475$		0			0
$476$	52.5378	+	56.1734i	0.110374	+	0.118011i
$477$	−58.2873			−0.122196
$478$	−336.816			−0.704636
$479$			522.525i			1.09087i	0.838154	+	0.545433i	$0.183635\pi$
$479$			522.525i			1.09087i	−0.838154	+	0.545433i	$0.816365\pi$
$480$		0			0
$481$			8.29058i			0.0172361i
$482$			333.210i			0.691306i
$483$	119.506	+	127.776i	0.247425	+	0.264547i
$484$	−27.3935			−0.0565982
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$	216.781			0.445135			0.222568	−	0.974917i	$-0.428556\pi$
$487$	216.781			0.445135			0.222568	+	0.974917i	$0.428556\pi$
$488$		−	211.337i		−	0.433067i
$489$		−	142.278i		−	0.290957i
$490$		0			0
$491$	451.246			0.919035			0.459517	−	0.888169i	$-0.348022\pi$
$491$	451.246			0.919035			0.459517	+	0.888169i	$0.348022\pi$
$492$	−47.6897			−0.0969304
$493$		−	231.274i		−	0.469116i
$494$	28.4298			0.0575501
$495$		0			0
$496$			2.16263i			0.00436013i
$497$	−216.738	+	202.711i	−0.436093	+	0.407869i
$498$	−310.718			−0.623931
$499$	347.296			0.695984			0.347992	−	0.937498i	$-0.386864\pi$
$499$	347.296			0.695984			0.347992	+	0.937498i	$0.386864\pi$
$500$		0			0
$501$	544.981			1.08779
$502$			398.202i			0.793231i
$503$			684.193i			1.36022i	0.733108	+	0.680112i	$0.238069\pi$
$503$			684.193i			1.36022i	−0.733108	+	0.680112i	$0.761931\pi$
$504$	43.3803	−	40.5727i	0.0860721	−	0.0805015i
$505$		0			0
$506$	211.390			0.417766
$507$		−	292.082i		−	0.576099i
$508$	−426.756			−0.840071
$509$		−	577.464i		−	1.13451i	−0.823543	−	0.567253i	$-0.808006\pi$
$509$		−	577.464i		−	1.13451i	0.823543	−	0.567253i	$-0.191994\pi$
$510$		0			0
$511$	319.971	+	342.112i	0.626166	+	0.669496i
$512$	22.6274			0.0441942
$513$	172.609			0.336470
$514$		−	358.560i		−	0.697588i
$515$		0			0
$516$		−	285.421i		−	0.553141i
$517$			549.249i			1.06238i
$518$	−99.0490	+	92.6385i	−0.191214	+	0.178839i
$519$	−326.728			−0.629534
$520$		0			0
$521$		−	871.106i		−	1.67199i	−0.548738	−	0.835994i	$-0.684891\pi$
$521$		−	871.106i		−	1.67199i	0.548738	−	0.835994i	$-0.315109\pi$
$522$	−178.603			−0.342152
$523$		−	108.067i		−	0.206629i	−0.994649	−	0.103315i	$-0.967055\pi$
$523$		−	108.067i		−	0.206629i	0.994649	−	0.103315i	$-0.0329449\pi$
$524$		−	278.324i		−	0.531153i
$525$		0			0
$526$	−374.727			−0.712408
$527$	2.97027			0.00563618
$528$		−	71.7674i		−	0.135923i
$529$	−320.779			−0.606388
$530$		0			0
$531$			88.2721i			0.166238i
$532$	317.673	+	339.655i	0.597129	+	0.638450i
$533$	8.33127			0.0156309
$534$	73.9393			0.138463
$535$		0			0
$536$	−34.4891			−0.0643454
$537$		−	440.135i		−	0.819618i
$538$			268.248i			0.498602i
$539$	33.9113	−	506.444i	0.0629152	−	0.939598i
$540$		0			0
$541$	608.803			1.12533			0.562664	−	0.826685i	$-0.309776\pi$
$541$	608.803			1.12533			0.562664	+	0.826685i	$0.309776\pi$
$542$		−	405.306i		−	0.747797i
$543$	−240.318			−0.442574
$544$		−	31.0777i		−	0.0571281i
$545$		0			0
$546$	−7.57842	+	7.08794i	−0.0138799	+	0.0129816i
$547$	−1020.16			−1.86502			−0.932508	−	0.361150i	$-0.882384\pi$
$547$	−1020.16			−1.86502			−0.932508	+	0.361150i	$0.882384\pi$
$548$	36.5646			0.0667238
$549$			224.156i			0.408299i
$550$		0			0
$551$		−	1398.41i		−	2.53795i
$552$		−	70.6916i		−	0.128065i
$553$	138.527	−	129.562i	0.250501	−	0.234289i
$554$	116.721			0.210687
$555$		0			0
$556$			77.4531i			0.139304i
$557$	162.089			0.291003			0.145502	−	0.989358i	$-0.453520\pi$
$557$	162.089			0.291003			0.145502	+	0.989358i	$0.453520\pi$
$558$		−	2.29381i		−	0.00411077i
$559$			49.8622i			0.0891989i
$560$		0			0
$561$	−98.5692			−0.175703
$562$	−544.368			−0.968626
$563$			273.813i			0.486347i	0.969983	+	0.243173i	$0.0781884\pi$
$563$			273.813i			0.486347i	−0.969983	+	0.243173i	$0.921812\pi$
$564$	183.676			0.325667
$565$		0			0
$566$			727.375i			1.28512i
$567$	−46.0118	+	43.0339i	−0.0811495	+	0.0758975i
$568$	119.910			0.211109
$569$	−618.238			−1.08653			−0.543267	−	0.839560i	$-0.682813\pi$
$569$	−618.238			−1.08653			−0.543267	+	0.839560i	$0.682813\pi$
$570$		0			0
$571$	602.897			1.05586			0.527931	−	0.849287i	$-0.322968\pi$
$571$	602.897			1.05586			0.527931	+	0.849287i	$0.322968\pi$
$572$			12.5376i			0.0219188i
$573$		−	309.876i		−	0.540795i
$574$	93.0931	+	99.5350i	0.162183	+	0.173406i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$			491.145i			0.851204i	0.904911	+	0.425602i	$0.139938\pi$
$577$			491.145i			0.851204i	−0.904911	+	0.425602i	$0.860062\pi$
$578$	366.024			0.633259
$579$			6.33761i			0.0109458i
$580$		0			0
$581$	606.538	+	648.510i	1.04396	+	1.11620i
$582$	403.192			0.692769
$583$	201.261			0.345216
$584$		−	189.272i		−	0.324096i
$585$		0			0
$586$		−	609.913i		−	1.04081i
$587$			990.289i			1.68703i	0.537102	+	0.843517i	$0.319519\pi$
$587$			990.289i			1.68703i	−0.537102	+	0.843517i	$0.680481\pi$
$588$	−169.362	−	11.3404i	−0.288030	−	0.0192864i
$589$	17.9599			0.0304921
$590$		0			0
$591$		−	349.565i		−	0.591481i
$592$	54.7985			0.0925650
$593$		−	10.4613i		−	0.0176414i	−0.999961	−	0.00882070i	$-0.997192\pi$
$593$		−	10.4613i		−	0.0176414i	0.999961	−	0.00882070i	$-0.00280775\pi$
$594$			76.1208i			0.128149i
$595$		0			0
$596$	−40.2270			−0.0674950
$597$	169.012			0.283102
$598$			12.3496i			0.0206516i
$599$	−592.559			−0.989248			−0.494624	−	0.869107i	$-0.664694\pi$
$599$	−592.559			−0.989248			−0.494624	+	0.869107i	$0.664694\pi$
$600$		0			0
$601$			595.499i			0.990846i	0.868652	+	0.495423i	$0.164987\pi$
$601$			595.499i			0.990846i	−0.868652	+	0.495423i	$0.835013\pi$
$602$	−595.712	+	557.157i	−0.989555	+	0.925510i
$603$	36.5812			0.0606654
$604$	22.6514			0.0375023
$605$		0			0
$606$	−47.7730			−0.0788334
$607$		−	621.260i		−	1.02349i	−0.859136	−	0.511747i	$-0.828999\pi$
$607$		−	621.260i		−	1.02349i	0.859136	−	0.511747i	$-0.171001\pi$
$608$		−	187.913i		−	0.309067i
$609$	348.644	+	372.769i	0.572485	+	0.612101i
$610$		0			0
$611$	−32.0878			−0.0525168
$612$			32.9629i			0.0538609i
$613$	−332.564			−0.542519			−0.271259	−	0.962506i	$-0.587440\pi$
$613$	−332.564			−0.542519			−0.271259	+	0.962506i	$0.587440\pi$
$614$			482.392i			0.785654i
$615$		0			0
$616$	−149.788	+	140.094i	−0.243163	+	0.227425i
$617$	366.977			0.594776			0.297388	−	0.954757i	$-0.403884\pi$
$617$	366.977			0.594776			0.297388	+	0.954757i	$0.403884\pi$
$618$	266.869			0.431826
$619$			1123.84i			1.81557i	0.419439	+	0.907783i	$0.362227\pi$
$619$			1123.84i			1.81557i	−0.419439	+	0.907783i	$0.637773\pi$
$620$		0			0
$621$			74.9798i			0.120740i
$622$			771.750i			1.24076i
$623$	−144.334	−	154.321i	−0.231675	−	0.247707i
$624$	4.19273			0.00671912
$625$		0			0
$626$			139.639i			0.223066i
$627$	−596.003			−0.950564
$628$			216.845i			0.345294i
$629$		−	75.2632i		−	0.119655i
$630$		0			0
$631$	782.201			1.23962			0.619810	−	0.784752i	$-0.287210\pi$
$631$	782.201			1.23962			0.619810	+	0.784752i	$0.287210\pi$
$632$	−76.6397			−0.121265
$633$			180.344i			0.284904i
$634$	−233.428			−0.368183
$635$		0			0
$636$		−	67.3044i		−	0.105825i
$637$	29.5870	+	1.98114i	0.0464474	+	0.00311011i
$638$	616.701			0.966616
$639$	−127.183			−0.199035
$640$		0			0
$641$	6.16909			0.00962416			0.00481208	−	0.999988i	$-0.498468\pi$
$641$	6.16909			0.00962416			0.00481208	+	0.999988i	$0.498468\pi$
$642$			295.858i			0.460838i
$643$		−	82.5062i		−	0.128315i	−0.997940	−	0.0641573i	$-0.979564\pi$
$643$		−	82.5062i		−	0.128315i	0.997940	−	0.0641573i	$-0.0204359\pi$
$644$	−147.543	+	137.994i	−0.229104	+	0.214276i
$645$		0			0
$646$	−258.090			−0.399520
$647$			863.567i			1.33472i	0.744733	+	0.667362i	$0.232577\pi$
$647$			863.567i			1.33472i	−0.744733	+	0.667362i	$0.767423\pi$
$648$	25.4558			0.0392837
$649$		−	304.796i		−	0.469639i
$650$		0			0
$651$	−4.78750	+	4.47765i	−0.00735407	+	0.00687811i
$652$	164.289			0.251976
$653$	−172.088			−0.263535			−0.131767	−	0.991281i	$-0.542065\pi$
$653$	−172.088			−0.263535			−0.131767	+	0.991281i	$0.542065\pi$
$654$		−	303.381i		−	0.463885i
$655$		0			0
$656$		−	55.0674i		−	0.0839442i
$657$			200.754i			0.305561i
$658$	−358.547	−	383.358i	−0.544904	−	0.582611i
$659$	170.542			0.258789			0.129394	−	0.991593i	$-0.458697\pi$
$659$	170.542			0.258789			0.129394	+	0.991593i	$0.458697\pi$
$660$		0			0
$661$			53.4631i			0.0808822i	0.999182	+	0.0404411i	$0.0128763\pi$
$661$			53.4631i			0.0808822i	−0.999182	+	0.0404411i	$0.987124\pi$
$662$	−326.205			−0.492756
$663$		−	5.75853i		−	0.00868556i
$664$		−	358.786i		−	0.540340i
$665$		0			0
$666$	−58.1225			−0.0872711
$667$	607.457			0.910730
$668$			629.290i			0.942050i
$669$	443.164			0.662427
$670$		0			0
$671$		−	773.991i		−	1.15349i
$672$	46.8494	+	50.0913i	0.0697163	+	0.0745406i
$673$	1215.31			1.80581			0.902907	−	0.429836i	$-0.141429\pi$
$673$	1215.31			1.80581			0.902907	+	0.429836i	$0.141429\pi$
$674$	204.542			0.303475
$675$		0			0
$676$	337.268			0.498916
$677$		−	1161.52i		−	1.71569i	−0.513907	−	0.857846i	$-0.671802\pi$
$677$		−	1161.52i		−	1.71569i	0.513907	−	0.857846i	$-0.328198\pi$
$678$			493.376i			0.727694i
$679$	−787.053	−	841.516i	−1.15914	−	1.23935i
$680$		0			0
$681$	177.781			0.261059
$682$			7.92032i			0.0116134i
$683$	724.141			1.06024			0.530118	−	0.847924i	$-0.322148\pi$
$683$	724.141			1.06024			0.530118	+	0.847924i	$0.322148\pi$
$684$			199.312i			0.291392i
$685$		0			0
$686$	306.935	+	375.618i	0.447427	+	0.547549i
$687$	440.050			0.640539
$688$	329.575			0.479034
$689$			11.7579i			0.0170652i
$690$		0			0
$691$		−	1084.92i		−	1.57007i	−0.619450	−	0.785036i	$-0.712644\pi$
$691$		−	1084.92i		−	1.57007i	0.619450	−	0.785036i	$-0.287356\pi$
$692$		−	377.273i		−	0.545193i
$693$	158.875	−	148.592i	0.229256	−	0.214419i
$694$	229.540			0.330750
$695$		0			0
$696$		−	206.233i		−	0.296312i
$697$	−75.6325			−0.108511
$698$		−	443.220i		−	0.634986i
$699$			151.372i			0.216556i
$700$		0			0
$701$	−405.283			−0.578150			−0.289075	−	0.957307i	$-0.593348\pi$
$701$	−405.283			−0.578150			−0.289075	+	0.957307i	$0.593348\pi$
$702$	−4.44707			−0.00633485
$703$		−	455.083i		−	0.647344i
$704$	82.8698			0.117713
$705$		0			0
$706$		−	485.115i		−	0.687132i
$707$	93.2557	+	99.7089i	0.131903	+	0.141031i
$708$	−101.928			−0.143966
$709$	906.179			1.27811			0.639055	−	0.769161i	$-0.279326\pi$
$709$	906.179			1.27811			0.639055	+	0.769161i	$0.279326\pi$
$710$		0			0
$711$	81.2886			0.114330
$712$			85.3777i			0.119913i
$713$			7.80160i			0.0109419i
$714$	68.7981	−	64.3454i	0.0963558	−	0.0901197i
$715$		0			0
$716$	508.224			0.709810
$717$			412.514i			0.575333i
$718$	−505.288			−0.703744
$719$			1374.58i			1.91180i	0.293693	+	0.955900i	$0.405116\pi$
$719$			1374.58i			1.91180i	−0.293693	+	0.955900i	$0.594884\pi$
$720$		0			0
$721$	−520.943	−	556.991i	−0.722528	−	0.772526i
$722$	−1050.02			−1.45432
$723$	408.097			0.564449
$724$		−	277.495i		−	0.383280i
$725$		0			0
$726$			33.5501i			0.0462122i
$727$			203.600i			0.280055i	0.990148	+	0.140028i	$0.0447192\pi$
$727$			203.600i			0.280055i	−0.990148	+	0.140028i	$0.955281\pi$
$728$	−8.18445	−	8.75081i	−0.0112424	−	0.0120203i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	452.657i		−	0.619229i
$732$	−258.833			−0.353597
$733$		−	841.642i		−	1.14822i	−0.818780	−	0.574108i	$-0.805349\pi$
$733$		−	841.642i		−	1.14822i	0.818780	−	0.574108i	$-0.194651\pi$
$734$		−	872.767i		−	1.18906i
$735$		0			0
$736$	81.6276			0.110907
$737$	−126.312			−0.171386
$738$			58.4078i			0.0791433i
$739$	−1251.55			−1.69358			−0.846788	−	0.531930i	$-0.821467\pi$
$739$	−1251.55			−1.69358			−0.846788	+	0.531930i	$0.821467\pi$
$740$		0			0
$741$		−	34.8192i		−	0.0469895i
$742$	−140.474	+	131.382i	−0.189317	+	0.177065i
$743$	−83.5814			−0.112492			−0.0562459	−	0.998417i	$-0.517913\pi$
$743$	−83.5814			−0.112492			−0.0562459	+	0.998417i	$0.517913\pi$
$744$	2.64866			0.00356003
$745$		0			0
$746$	479.239			0.642411
$747$			380.550i			0.509437i
$748$		−	113.818i		−	0.152163i
$749$	617.497	−	577.532i	0.824428	−	0.771071i
$750$		0			0
$751$	1364.04			1.81630			0.908152	−	0.418641i	$-0.137493\pi$
$751$	1364.04			1.81630			0.908152	+	0.418641i	$0.137493\pi$
$752$			212.091i			0.282036i
$753$	487.696			0.647670
$754$			36.0284i			0.0477830i
$755$		0			0
$756$	−49.6913	−	53.1298i	−0.0657292	−	0.0702776i
$757$	−193.941			−0.256196			−0.128098	−	0.991761i	$-0.540887\pi$
$757$	−193.941			−0.256196			−0.128098	+	0.991761i	$0.540887\pi$
$758$	−299.291			−0.394843
$759$		−	258.898i		−	0.341105i
$760$		0			0
$761$		−	698.879i		−	0.918369i	−0.888341	−	0.459185i	$-0.848142\pi$
$761$		−	698.879i		−	0.918369i	0.888341	−	0.459185i	$-0.151858\pi$
$762$			522.667i			0.685915i
$763$	−633.198	+	592.217i	−0.829879	+	0.776169i
$764$	357.814			0.468342
$765$		0			0
$766$		−	337.645i		−	0.440789i
$767$	17.8065			0.0232158
$768$		−	27.7128i		−	0.0360844i
$769$		−	335.359i		−	0.436097i	−0.975938	−	0.218049i	$-0.930031\pi$
$769$		−	335.359i		−	0.436097i	0.975938	−	0.218049i	$-0.0699691\pi$
$770$		0			0
$771$	−439.145			−0.569578
$772$	−7.31805			−0.00947933
$773$		−	1276.11i		−	1.65085i	−0.564511	−	0.825426i	$-0.690935\pi$
$773$		−	1276.11i		−	1.65085i	0.564511	−	0.825426i	$-0.309065\pi$
$774$	−349.567			−0.451638
$775$		0			0
$776$			465.565i			0.599955i
$777$	113.459	+	121.310i	0.146021	+	0.156126i
$778$	−30.7907			−0.0395767
$779$	−457.316			−0.587055
$780$		0			0
$781$	439.153			0.562295
$782$		−	112.112i		−	0.143365i
$783$			218.743i			0.279366i
$784$	13.0948	−	195.562i	0.0167025	−	0.249441i
$785$		0			0
$786$	−340.876			−0.433684
$787$			415.510i			0.527967i	0.964527	+	0.263983i	$0.0850364\pi$
$787$			415.510i			0.527967i	−0.964527	+	0.263983i	$0.914964\pi$
$788$	403.643			0.512237
$789$			458.945i			0.581679i
$790$		0			0
$791$	1029.74	−	963.098i	1.30183	−	1.21757i
$792$	−87.8967			−0.110981
$793$	45.2175			0.0570208
$794$		−	781.943i		−	0.984814i
$795$		0			0
$796$			195.158i			0.245174i
$797$			1337.78i			1.67852i	0.543731	+	0.839259i	$0.317011\pi$
$797$			1337.78i			1.67852i	−0.543731	+	0.839259i	$0.682989\pi$
$798$	415.991	−	389.068i	0.521292	−	0.487554i
$799$	291.297			0.364578
$800$		0			0
$801$		−	90.5568i		−	0.113055i
$802$	−899.730			−1.12186
$803$		−	693.184i		−	0.863243i
$804$			42.2404i			0.0525378i
$805$		0			0
$806$	−0.462714			−0.000574087
$807$	328.535			0.407107
$808$		−	55.1635i		−	0.0682717i
$809$	754.137			0.932184			0.466092	−	0.884736i	$-0.345662\pi$
$809$	754.137			0.932184			0.466092	+	0.884736i	$0.345662\pi$
$810$		0			0
$811$			509.569i			0.628321i	0.949370	+	0.314161i	$0.101723\pi$
$811$			509.569i			0.628321i	−0.949370	+	0.314161i	$0.898277\pi$
$812$	−430.437	+	402.579i	−0.530095	+	0.495787i
$813$	−496.397			−0.610574
$814$	200.692			0.246550
$815$		0			0
$816$	−38.0623			−0.0466449
$817$		−	2737.01i		−	3.35007i
$818$			506.834i			0.619602i
$819$	8.68092	+	9.28163i	0.0105994	+	0.0113329i
$820$		0			0
$821$	−508.671			−0.619575			−0.309787	−	0.950806i	$-0.600258\pi$
$821$	−508.671			−0.619575			−0.309787	+	0.950806i	$0.600258\pi$
$822$		−	44.7824i		−	0.0544797i
$823$	−717.806			−0.872182			−0.436091	−	0.899903i	$-0.643637\pi$
$823$	−717.806			−0.872182			−0.436091	+	0.899903i	$0.643637\pi$
$824$			308.153i			0.373972i
$825$		0			0
$826$	198.969	+	212.737i	0.240883	+	0.257551i
$827$	444.662			0.537681			0.268841	−	0.963185i	$-0.413360\pi$
$827$	444.662			0.537681			0.268841	+	0.963185i	$0.413360\pi$
$828$	−86.5792			−0.104564
$829$			250.314i			0.301947i	0.988538	+	0.150973i	$0.0482407\pi$
$829$			250.314i			0.301947i	−0.988538	+	0.150973i	$0.951759\pi$
$830$		0			0
$831$		−	142.953i		−	0.172026i
$832$			4.84135i			0.00581893i
$833$	−268.595	−	17.9851i	−0.322444	−	0.0215907i
$834$	94.8602			0.113741
$835$		0			0
$836$		−	688.206i		−	0.823212i
$837$	−2.80933			−0.00335643
$838$		−	553.726i		−	0.660771i
$839$			1026.45i			1.22343i	0.791080	+	0.611713i	$0.209519\pi$
$839$			1026.45i			1.22343i	−0.791080	+	0.611713i	$0.790481\pi$
$840$		0			0
$841$	931.173			1.10722
$842$	668.466			0.793902
$843$			666.711i			0.790880i
$844$	−208.244			−0.246734
$845$		0			0
$846$		−	224.957i		−	0.265906i
$847$	70.0236	−	65.4917i	0.0826725	−	0.0773219i
$848$	77.7165			0.0916468
$849$	890.849			1.04929
$850$		0			0
$851$	197.684			0.232296
$852$		−	146.859i		−	0.172369i
$853$		−	840.837i		−	0.985740i	−0.870103	−	0.492870i	$-0.835948\pi$
$853$		−	840.837i		−	0.985740i	0.870103	−	0.492870i	$-0.164052\pi$
$854$	505.257	+	540.221i	0.591636	+	0.632577i
$855$		0			0
$856$	−341.628			−0.399098
$857$		−	860.502i		−	1.00409i	−0.864843	−	0.502043i	$-0.832582\pi$
$857$		−	860.502i		−	1.00409i	0.864843	−	0.502043i	$-0.167418\pi$
$858$	15.3553			0.0178966
$859$		−	1163.93i		−	1.35498i	−0.735532	−	0.677490i	$-0.763068\pi$
$859$		−	1163.93i		−	1.35498i	0.735532	−	0.677490i	$-0.236932\pi$
$860$		0			0
$861$	121.905	−	114.015i	0.141585	−	0.132422i
$862$	−949.163			−1.10112
$863$	−704.504			−0.816343			−0.408172	−	0.912905i	$-0.633833\pi$
$863$	−704.504			−0.816343			−0.408172	+	0.912905i	$0.633833\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$			160.104i			0.184878i
$867$		−	448.286i		−	0.517054i
$868$	−5.17034	−	5.52813i	−0.00595662	−	0.00636881i
$869$	−280.682			−0.322995
$870$		0			0
$871$		−	7.37928i		−	0.00847219i
$872$	350.314			0.401736
$873$		−	493.807i		−	0.565643i
$874$		−	677.890i		−	0.775618i
$875$		0			0
$876$	−231.810			−0.264624
$877$	−570.744			−0.650792			−0.325396	−	0.945578i	$-0.605498\pi$
$877$	−570.744			−0.650792			−0.325396	+	0.945578i	$0.605498\pi$
$878$			852.897i			0.971409i
$879$	−746.988			−0.849815
$880$		0			0
$881$			1241.29i			1.40895i	0.709728	+	0.704476i	$0.248818\pi$
$881$			1241.29i			1.40895i	−0.709728	+	0.704476i	$0.751182\pi$
$882$	−13.8891	+	207.425i	−0.0157473	+	0.235176i
$883$	−907.346			−1.02757			−0.513786	−	0.857918i	$-0.671758\pi$
$883$	−907.346			−1.02757			−0.513786	+	0.857918i	$0.671758\pi$
$884$	6.64937			0.00752191
$885$		0			0
$886$	−1207.35			−1.36269
$887$			132.595i			0.149487i	0.997203	+	0.0747437i	$0.0238139\pi$
$887$			132.595i			0.149487i	−0.997203	+	0.0747437i	$0.976186\pi$
$888$		−	67.1141i		−	0.0755790i
$889$	1090.88	−	1020.28i	1.22708	−	1.14767i
$890$		0			0
$891$	93.2285			0.104634
$892$			511.722i			0.573679i
$893$	1761.35			1.97239
$894$			49.2679i			0.0551095i
$895$		0			0
$896$	−57.8404	+	54.0970i	−0.0645541	+	0.0603761i
$897$	15.1251			0.0168619
$898$	−328.887			−0.366243
$899$			22.7601i			0.0253171i
$900$		0			0
$901$		−	106.740i		−	0.118468i
$902$		−	201.677i		−	0.223588i
$903$	682.375	+	729.595i	0.755676	+	0.807968i
$904$	−569.702			−0.630201
$905$		0			0
$906$		−	27.7422i		−	0.0306205i
$907$	−1309.04			−1.44326			−0.721632	−	0.692277i	$-0.756608\pi$
$907$	−1309.04			−1.44326			−0.721632	+	0.692277i	$0.756608\pi$
$908$			205.284i			0.226084i
$909$			58.5098i			0.0643672i
$910$		0			0
$911$	−1252.86			−1.37525			−0.687627	−	0.726064i	$-0.741348\pi$
$911$	−1252.86			−1.37525			−0.687627	+	0.726064i	$0.741348\pi$
$912$	−230.145			−0.252352
$913$		−	1314.00i		−	1.43922i
$914$	551.400			0.603282
$915$		0			0
$916$			508.126i			0.554723i
$917$	665.409	+	711.455i	0.725637	+	0.775850i
$918$	40.3711			0.0439773
$919$	−329.889			−0.358966			−0.179483	−	0.983761i	$-0.557442\pi$
$919$	−329.889			−0.358966			−0.179483	+	0.983761i	$0.557442\pi$
$920$		0			0
$921$	590.807			0.641484
$922$		−	848.122i		−	0.919872i
$923$			25.6558i			0.0277961i
$924$	171.579	+	183.452i	0.185692	+	0.198542i
$925$		0			0
$926$	−298.771			−0.322647
$927$		−	326.846i		−	0.352585i
$928$	238.138			0.256614
$929$			12.0040i			0.0129214i	0.999979	+	0.00646072i	$0.00205653\pi$
$929$			12.0040i			0.0129214i	−0.999979	+	0.00646072i	$0.997943\pi$
$930$		0			0
$931$	−1624.08	−	108.748i	−1.74444	−	0.116807i
$932$	−174.790			−0.187543
$933$	945.197			1.01307
$934$		−	1126.89i		−	1.20652i
$935$		0			0
$936$		−	5.13503i		−	0.00548614i
$937$		−	300.461i		−	0.320663i	−0.987063	−	0.160331i	$-0.948744\pi$
$937$		−	300.461i		−	0.320663i	0.987063	−	0.160331i	$-0.0512563\pi$
$938$	88.1615	−	82.4556i	0.0939888	−	0.0879058i
$939$	171.022			0.182132
$940$		0			0
$941$			494.625i			0.525637i	0.964845	+	0.262819i	$0.0846521\pi$
$941$			494.625i			0.525637i	−0.964845	+	0.262819i	$0.915348\pi$
$942$	265.580			0.281932
$943$		−	198.654i		−	0.210661i
$944$		−	117.696i		−	0.124678i
$945$		0			0
$946$	1207.02			1.27592
$947$	337.631			0.356527			0.178263	−	0.983983i	$-0.442952\pi$
$947$	337.631			0.356527			0.178263	+	0.983983i	$0.442952\pi$
$948$			93.8640i			0.0990127i
$949$	40.4966			0.0426729
$950$		0			0
$951$			285.889i			0.300620i
$952$	74.2997	+	79.4412i	0.0780459	+	0.0834466i
$953$	635.279			0.666610			0.333305	−	0.942819i	$-0.391836\pi$
$953$	635.279			0.666610			0.333305	+	0.942819i	$0.391836\pi$
$954$	−82.4308			−0.0864054
$955$		0			0
$956$	−476.330			−0.498253
$957$		−	755.301i		−	0.789238i
$958$			738.962i			0.771359i
$959$	−93.4669	+	87.4177i	−0.0974629	+	0.0911551i
$960$		0			0
$961$	960.708			0.999696
$962$			11.7247i			0.0121878i
$963$	362.351			0.376273
$964$			471.230i			0.488827i
$965$		0			0
$966$	169.007	+	180.703i	0.174956	+	0.187063i
$967$	−489.313			−0.506011			−0.253006	−	0.967465i	$-0.581419\pi$
$967$	−489.313			−0.506011			−0.253006	+	0.967465i	$0.581419\pi$
$968$	−38.7403			−0.0400210
$969$			316.094i			0.326207i
$970$		0			0
$971$		−	621.040i		−	0.639588i	−0.947487	−	0.319794i	$-0.896386\pi$
$971$		−	621.040i		−	0.639588i	0.947487	−	0.319794i	$-0.103614\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−185.173	−	197.986i	−0.190311	−	0.203480i
$974$	306.574			0.314758
$975$		0			0
$976$		−	298.875i		−	0.306224i
$977$	1475.20			1.50993			0.754963	−	0.655768i	$-0.227655\pi$
$977$	1475.20			1.50993			0.754963	+	0.655768i	$0.227655\pi$
$978$		−	201.212i		−	0.205738i
$979$			312.684i			0.319392i
$980$		0			0
$981$	−371.564			−0.378761
$982$	638.158			0.649856
$983$		−	343.366i		−	0.349304i	−0.984630	−	0.174652i	$-0.944120\pi$
$983$		−	343.366i		−	0.349304i	0.984630	−	0.174652i	$-0.0558801\pi$
$984$	−67.4435			−0.0685401
$985$		0			0
$986$		−	327.071i		−	0.331715i
$987$	−469.515	+	439.128i	−0.475700	+	0.444912i
$988$	40.2058			0.0406941
$989$	1188.93			1.20216
$990$		0			0
$991$	−1389.23			−1.40184			−0.700921	−	0.713239i	$-0.747228\pi$
$991$	−1389.23			−1.40184			−0.700921	+	0.713239i	$0.747228\pi$
$992$			3.05841i			0.00308308i
$993$			399.518i			0.402334i
$994$	−306.514	+	286.677i	−0.308364	+	0.288407i
$995$		0			0
$996$	−439.421			−0.441186
$997$		−	347.412i		−	0.348458i	−0.984705	−	0.174229i	$-0.944257\pi$
$997$		−	347.412i		−	0.348458i	0.984705	−	0.174229i	$-0.0557432\pi$
$998$	491.151			0.492135
$999$			71.1853i			0.0712565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.c.601.7	✓	12
5.2	odd	4		1050.3.h.c.349.2		24
5.3	odd	4		1050.3.h.c.349.23		24
5.4	even	2		1050.3.f.d.601.6	yes	12
7.6	odd	2	inner	1050.3.f.c.601.10	yes	12
35.13	even	4		1050.3.h.c.349.1		24
35.27	even	4		1050.3.h.c.349.24		24
35.34	odd	2		1050.3.f.d.601.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.7	✓	12	1.1	even	1	trivial
1050.3.f.c.601.10	yes	12	7.6	odd	2	inner
1050.3.f.d.601.3	yes	12	35.34	odd	2
1050.3.f.d.601.6	yes	12	5.4	even	2
1050.3.h.c.349.1		24	35.13	even	4
1050.3.h.c.349.2		24	5.2	odd	4
1050.3.h.c.349.23		24	5.3	odd	4
1050.3.h.c.349.24		24	35.27	even	4

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-5.11242 + 4.78154i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-5.11242 + 4.78154i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +10.3587 q^{11} -3.46410i q^{12} +0.605169i q^{13} +(-7.23005 + 6.76212i) q^{14} +4.00000 q^{16} -5.49382i q^{17} -4.24264 q^{18} -33.2186i q^{19} +(8.28188 + 8.85497i) q^{21} +14.6495 q^{22} +14.4299 q^{23} -4.89898i q^{24} +0.855838i q^{26} +5.19615i q^{27} +(-10.2248 + 9.56309i) q^{28} +42.0972 q^{29} +0.540656i q^{31} +5.65685 q^{32} -17.9418i q^{33} -7.76943i q^{34} -6.00000 q^{36} +13.6996 q^{37} -46.9782i q^{38} +1.04818 q^{39} -13.7668i q^{41} +(11.7123 + 12.5228i) q^{42} +82.3938 q^{43} +20.7175 q^{44} +20.4069 q^{46} +53.0228i q^{47} -6.92820i q^{48} +(3.27369 - 48.8905i) q^{49} -9.51557 q^{51} +1.21034i q^{52} +19.4291 q^{53} +7.34847i q^{54} +(-14.4601 + 13.5242i) q^{56} -57.5364 q^{57} +59.5344 q^{58} -29.4240i q^{59} -74.7188i q^{61} +0.764604i q^{62} +(15.3373 - 14.3446i) q^{63} +8.00000 q^{64} -25.3736i q^{66} -12.1937 q^{67} -10.9876i q^{68} -24.9933i q^{69} +42.3945 q^{71} -8.48528 q^{72} -66.9179i q^{73} +19.3742 q^{74} -66.4373i q^{76} +(-52.9582 + 49.5307i) q^{77} +1.48236 q^{78} -27.0962 q^{79} +9.00000 q^{81} -19.4693i q^{82} -126.850i q^{83} +(16.5638 + 17.7099i) q^{84} +116.522 q^{86} -72.9145i q^{87} +29.2989 q^{88} +30.1856i q^{89} +(-2.89364 - 3.09388i) q^{91} +28.8597 q^{92} +0.936444 q^{93} +74.9856i q^{94} -9.79796i q^{96} +164.602i q^{97} +(4.62970 - 69.1416i) q^{98} -31.0762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 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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