LMFDB - Embedded newform 1050.3.f.d.601.6

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			601.6
Root			$-3.88205 + 6.72390i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.d.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(5.11242 - 4.78154i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(5.11242 - 4.78154i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +10.3587 q^{11} +3.46410i q^{12} -0.605169i q^{13} +(-7.23005 + 6.76212i) q^{14} +4.00000 q^{16} +5.49382i q^{17} +4.24264 q^{18} -33.2186i q^{19} +(8.28188 + 8.85497i) q^{21} -14.6495 q^{22} -14.4299 q^{23} -4.89898i q^{24} +0.855838i q^{26} -5.19615i q^{27} +(10.2248 - 9.56309i) q^{28} +42.0972 q^{29} +0.540656i q^{31} -5.65685 q^{32} +17.9418i q^{33} -7.76943i q^{34} -6.00000 q^{36} -13.6996 q^{37} +46.9782i q^{38} +1.04818 q^{39} -13.7668i q^{41} +(-11.7123 - 12.5228i) q^{42} -82.3938 q^{43} +20.7175 q^{44} +20.4069 q^{46} -53.0228i q^{47} +6.92820i q^{48} +(3.27369 - 48.8905i) q^{49} -9.51557 q^{51} -1.21034i q^{52} -19.4291 q^{53} +7.34847i q^{54} +(-14.4601 + 13.5242i) q^{56} +57.5364 q^{57} -59.5344 q^{58} -29.4240i q^{59} -74.7188i q^{61} -0.764604i q^{62} +(-15.3373 + 14.3446i) q^{63} +8.00000 q^{64} -25.3736i q^{66} +12.1937 q^{67} +10.9876i q^{68} -24.9933i q^{69} +42.3945 q^{71} +8.48528 q^{72} +66.9179i q^{73} +19.3742 q^{74} -66.4373i q^{76} +(52.9582 - 49.5307i) q^{77} -1.48236 q^{78} -27.0962 q^{79} +9.00000 q^{81} +19.4693i q^{82} +126.850i q^{83} +(16.5638 + 17.7099i) q^{84} +116.522 q^{86} +72.9145i q^{87} -29.2989 q^{88} +30.1856i q^{89} +(-2.89364 - 3.09388i) q^{91} -28.8597 q^{92} -0.936444 q^{93} +74.9856i q^{94} -9.79796i q^{96} -164.602i q^{97} +(-4.62970 + 69.1416i) q^{98} -31.0762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.992590\pi$
$13$		−	0.605169i		−	0.0465515i	0.999729	−	0.0232757i	$-0.00740956\pi$
$14$	−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	$0.0516599\pi$
$17$			5.49382i			0.323166i	−0.986859	+	0.161583i	$0.948340\pi$
$18$	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	$-0.601566\pi$
$23$	−14.4299			−0.627385			−0.313693	+	0.949525i	$0.601566\pi$
$24$		−	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	$-0.559271\pi$
$37$	−13.6996			−0.370260			−0.185130	+	0.982714i	$0.559271\pi$
$38$			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	$-0.907494\pi$
$43$	−82.3938			−1.91614			−0.958068	+	0.286541i	$0.907494\pi$
$44$	20.7175			0.470851
$45$		0			0
$46$	20.4069			0.443628
$47$		−	53.0228i		−	1.12814i	−0.825725	−	0.564072i	$-0.809234\pi$
$47$		−	53.0228i		−	1.12814i	0.825725	−	0.564072i	$-0.190766\pi$
$48$			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	$-0.558676\pi$
$53$	−19.4291			−0.366587			−0.183294	+	0.983058i	$0.558676\pi$
$54$			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	$-0.470994\pi$
$67$	12.1937			0.181996			0.0909981	+	0.995851i	$0.470994\pi$
$68$			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	$0.151556\pi$
$73$			66.9179i			0.916683i	−0.888776	+	0.458342i	$0.848444\pi$
$74$	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	$0.276844\pi$
$83$			126.850i			1.52831i	−0.645031	+	0.764156i	$0.723156\pi$
$84$	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	$-0.677527\pi$
$97$		−	164.602i		−	1.69693i	0.529251	−	0.848465i	$-0.322473\pi$
$98$	−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	$-0.822613\pi$
$103$		−	108.949i		−	1.05775i	0.848699	−	0.528877i	$-0.177387\pi$
$104$			1.71168i			0.0164584i
$105$		0			0
$106$	27.4769			0.259216
$107$	120.784			1.12882			0.564409	−	0.825495i	$-0.309104\pi$
$107$	120.784			1.12882			0.564409	+	0.825495i	$0.309104\pi$
$108$		−	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	$-0.149837\pi$
$113$	201.420			1.78248			0.891239	+	0.453534i	$0.149837\pi$
$114$	−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	$-0.182513\pi$
$127$	213.378			1.68014			0.840071	+	0.542476i	$0.182513\pi$
$128$	−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	$-0.521255\pi$
$137$	−18.2823			−0.133448			−0.0667238	+	0.997771i	$0.521255\pi$
$138$			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	$-0.887779\pi$
$157$		−	108.422i		−	0.690589i	0.938494	−	0.345294i	$-0.112221\pi$
$158$	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	$-0.581081\pi$
$163$	−82.1443			−0.503953			−0.251976	+	0.967733i	$0.581081\pi$
$164$		−	27.5337i		−	0.167888i
$165$		0			0
$166$		−	179.393i		−	1.08068i
$167$		−	314.645i		−	1.88410i	−0.335472	−	0.942050i	$-0.608896\pi$
$167$		−	314.645i		−	1.88410i	0.335472	−	0.942050i	$-0.391104\pi$
$168$	−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	$0.183544\pi$
$173$			188.637i			1.09039i	−0.838311	+	0.545193i	$0.816456\pi$
$174$		−	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	$-0.496983\pi$
$193$	3.65902			0.0189587			0.00947933	+	0.999955i	$0.496983\pi$
$194$			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	$-0.671183\pi$
$197$	−201.822			−1.02447			−0.512237	+	0.858844i	$0.671183\pi$
$198$	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	$-0.805516\pi$
$223$		−	255.861i		−	1.14736i	0.819080	−	0.573679i	$-0.194484\pi$
$224$	−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	$-0.927408\pi$
$227$		−	102.642i		−	0.452168i	0.974108	−	0.226084i	$-0.0725924\pi$
$228$	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	$-0.439948\pi$
$233$	87.3948			0.375085			0.187543	+	0.982256i	$0.439948\pi$
$234$		−	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	$0.164198\pi$
$257$			253.540i			0.986539i	−0.869877	+	0.493269i	$0.835802\pi$
$258$			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	$-0.331954\pi$
$263$	264.972			1.00750			0.503749	+	0.863850i	$0.331954\pi$
$264$		−	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	$-0.547599\pi$
$277$	−82.5341			−0.297957			−0.148979	+	0.988840i	$0.547599\pi$
$278$		−	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	$-0.637065\pi$
$283$		−	514.332i		−	1.81743i	0.417419	−	0.908714i	$-0.362935\pi$
$284$	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	$0.263270\pi$
$293$			431.273i			1.47192i	−0.677023	+	0.735962i	$0.736730\pi$
$294$	−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	$-0.812511\pi$
$307$		−	341.103i		−	1.11108i	0.831489	−	0.555542i	$-0.187489\pi$
$308$	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	$-0.949582\pi$
$313$		−	98.7397i		−	0.315462i	0.987482	−	0.157731i	$-0.0504179\pi$
$314$			153.332i			0.488320i
$315$		0			0
$316$	−54.1924			−0.171495
$317$	165.058			0.520689			0.260344	−	0.965516i	$-0.416164\pi$
$317$	165.058			0.520689			0.260344	+	0.965516i	$0.416164\pi$
$318$			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	$-0.568841\pi$
$337$	−144.633			−0.429179			−0.214590	+	0.976704i	$0.568841\pi$
$338$	−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	$-0.575141\pi$
$347$	−162.310			−0.467751			−0.233875	+	0.972267i	$0.575141\pi$
$348$			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	$0.161499\pi$
$353$			343.028i			0.971752i	−0.874028	+	0.485876i	$0.838501\pi$
$354$	−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	$0.317909\pi$
$367$			617.139i			1.68158i	−0.541363	+	0.840789i	$0.682091\pi$
$368$	−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	$-0.650094\pi$
$373$	−338.873			−0.908506			−0.454253	+	0.890873i	$0.650094\pi$
$374$		−	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	$0.100893\pi$
$383$			238.751i			0.623370i	−0.950185	+	0.311685i	$0.899107\pi$
$384$		−	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	$0.245202\pi$
$397$			552.917i			1.39274i	−0.717684	+	0.696369i	$0.754798\pi$
$398$		−	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	$-0.958268\pi$
$433$		−	113.211i		−	0.261456i	0.991418	−	0.130728i	$-0.0417315\pi$
$434$	−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	$-0.0861840\pi$
$443$	853.722			1.92714			0.963569	+	0.267459i	$0.0861840\pi$
$444$		−	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	$-0.640283\pi$
$457$	−389.899			−0.853170			−0.426585	+	0.904448i	$0.640283\pi$
$458$		−	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	$-0.426734\pi$
$463$	211.263			0.456292			0.228146	+	0.973627i	$0.426734\pi$
$464$	168.389			0.362907
$465$		0			0
$466$	−123.595			−0.265225
$467$			796.828i			1.70627i	0.521690	+	0.853135i	$0.325302\pi$
$467$			796.828i			1.70627i	−0.521690	+	0.853135i	$0.674698\pi$
$468$			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	$-0.571444\pi$
$487$	−216.781			−0.445135			−0.222568	+	0.974917i	$0.571444\pi$
$488$			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	$-0.761931\pi$
$503$		−	684.193i		−	1.36022i	0.733108	−	0.680112i	$-0.238069\pi$
$504$	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	$0.0329449\pi$
$523$			108.067i			0.206629i	−0.994649	+	0.103315i	$0.967055\pi$
$524$		−	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	$-0.117616\pi$
$547$	1020.16			1.86502			0.932508	+	0.361150i	$0.117616\pi$
$548$	−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	$-0.546480\pi$
$557$	−162.089			−0.291003			−0.145502	+	0.989358i	$0.546480\pi$
$558$			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	$-0.921812\pi$
$563$		−	273.813i		−	0.486347i	0.969983	−	0.243173i	$-0.0781884\pi$
$564$	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	$-0.860062\pi$
$577$		−	491.145i		−	0.851204i	0.904911	−	0.425602i	$-0.139938\pi$
$578$	−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	$-0.680481\pi$
$587$		−	990.289i		−	1.68703i	0.537102	−	0.843517i	$-0.319519\pi$
$588$	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	$0.00280775\pi$
$593$			10.4613i			0.0176414i	−0.999961	+	0.00882070i	$0.997192\pi$
$594$			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	$0.171001\pi$
$607$			621.260i			1.02349i	−0.859136	+	0.511747i	$0.828999\pi$
$608$			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	$-0.412560\pi$
$613$	332.564			0.542519			0.271259	+	0.962506i	$0.412560\pi$
$614$			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	$-0.596116\pi$
$617$	−366.977			−0.594776			−0.297388	+	0.954757i	$0.596116\pi$
$618$	−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	$0.0204359\pi$
$643$			82.5062i			0.128315i	−0.997940	+	0.0641573i	$0.979564\pi$
$644$	−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	$-0.767423\pi$
$647$		−	863.567i		−	1.33472i	0.744733	−	0.667362i	$-0.232577\pi$
$648$	−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	$-0.457935\pi$
$653$	172.088			0.263535			0.131767	+	0.991281i	$0.457935\pi$
$654$		−	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	$-0.858571\pi$
$673$	−1215.31			−1.80581			−0.902907	+	0.429836i	$0.858571\pi$
$674$	204.542			0.303475
$675$		0			0
$676$	337.268			0.498916
$677$			1161.52i			1.71569i	0.513907	+	0.857846i	$0.328198\pi$
$677$			1161.52i			1.71569i	−0.513907	+	0.857846i	$0.671802\pi$
$678$		−	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	$-0.677852\pi$
$683$	−724.141			−1.06024			−0.530118	+	0.847924i	$0.677852\pi$
$684$			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	$-0.955281\pi$
$727$		−	203.600i		−	0.280055i	0.990148	−	0.140028i	$-0.0447192\pi$
$728$	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	$0.194651\pi$
$733$			841.642i			1.14822i	−0.818780	+	0.574108i	$0.805349\pi$
$734$		−	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	$-0.482087\pi$
$743$	83.5814			0.112492			0.0562459	+	0.998417i	$0.482087\pi$
$744$	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	$-0.459113\pi$
$757$	193.941			0.256196			0.128098	+	0.991761i	$0.459113\pi$
$758$	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	$0.309065\pi$
$773$			1276.11i			1.65085i	−0.564511	+	0.825426i	$0.690935\pi$
$774$	−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	$-0.914964\pi$
$787$		−	415.510i		−	0.527967i	0.964527	−	0.263983i	$-0.0850364\pi$
$788$	−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	$-0.682989\pi$
$797$		−	1337.78i		−	1.67852i	0.543731	−	0.839259i	$-0.317011\pi$
$798$	−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	$-0.356363\pi$
$823$	717.806			0.872182			0.436091	+	0.899903i	$0.356363\pi$
$824$			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	$-0.586640\pi$
$827$	−444.662			−0.537681			−0.268841	+	0.963185i	$0.586640\pi$
$828$	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	$0.164052\pi$
$853$			840.837i			0.985740i	−0.870103	+	0.492870i	$0.835948\pi$
$854$	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	$0.167418\pi$
$857$			860.502i			1.00409i	−0.864843	+	0.502043i	$0.832582\pi$
$858$	−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	$-0.366167\pi$
$863$	704.504			0.816343			0.408172	+	0.912905i	$0.366167\pi$
$864$			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	$-0.394502\pi$
$877$	570.744			0.650792			0.325396	+	0.945578i	$0.394502\pi$
$878$		−	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	$-0.328242\pi$
$883$	907.346			1.02757			0.513786	+	0.857918i	$0.328242\pi$
$884$	6.64937			0.00752191
$885$		0			0
$886$	−1207.35			−1.36269
$887$		−	132.595i		−	0.149487i	−0.997203	−	0.0747437i	$-0.976186\pi$
$887$		−	132.595i		−	0.149487i	0.997203	−	0.0747437i	$-0.0238139\pi$
$888$			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	$-0.243392\pi$
$907$	1309.04			1.44326			0.721632	+	0.692277i	$0.243392\pi$
$908$		−	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	$0.0512563\pi$
$937$			300.461i			0.320663i	−0.987063	+	0.160331i	$0.948744\pi$
$938$	−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	$-0.557048\pi$
$947$	−337.631			−0.356527			−0.178263	+	0.983983i	$0.557048\pi$
$948$		−	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	$-0.608164\pi$
$953$	−635.279			−0.666610			−0.333305	+	0.942819i	$0.608164\pi$
$954$	−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	$-0.418581\pi$
$967$	489.313			0.506011			0.253006	+	0.967465i	$0.418581\pi$
$968$	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	$-0.772345\pi$
$977$	−1475.20			−1.50993			−0.754963	+	0.655768i	$0.772345\pi$
$978$			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	$0.0558801\pi$
$983$			343.366i			0.349304i	−0.984630	+	0.174652i	$0.944120\pi$
$984$	−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	$0.0557432\pi$
$997$			347.412i			0.348458i	−0.984705	+	0.174229i	$0.944257\pi$
$998$	−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.d.601.6	yes	12
5.2	odd	4		1050.3.h.c.349.23		24
5.3	odd	4		1050.3.h.c.349.2		24
5.4	even	2		1050.3.f.c.601.7	✓	12
7.6	odd	2	inner	1050.3.f.d.601.3	yes	12
35.13	even	4		1050.3.h.c.349.24		24
35.27	even	4		1050.3.h.c.349.1		24
35.34	odd	2		1050.3.f.c.601.10	yes	12

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

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