LMFDB - Embedded newform 1050.3.f.d.601.1

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			601.1
Root			$0.854122 + 1.47938i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.d.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.06258 + 3.49930i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.06258 + 3.49930i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -17.5400 q^{11} -3.46410i q^{12} +17.6164i q^{13} +(8.57378 - 4.94876i) q^{14} +4.00000 q^{16} +14.0819i q^{17} +4.24264 q^{18} -16.6057i q^{19} +(6.06097 + 10.5007i) q^{21} +24.8054 q^{22} -15.5368 q^{23} +4.89898i q^{24} -24.9133i q^{26} +5.19615i q^{27} +(-12.1252 + 6.99861i) q^{28} +36.9225 q^{29} -54.2245i q^{31} -5.65685 q^{32} +30.3802i q^{33} -19.9147i q^{34} -6.00000 q^{36} +45.0739 q^{37} +23.4840i q^{38} +30.5124 q^{39} -1.20567i q^{41} +(-8.57151 - 14.8502i) q^{42} +50.7479 q^{43} -35.0801 q^{44} +21.9724 q^{46} -91.7612i q^{47} -6.92820i q^{48} +(24.5098 - 42.4296i) q^{49} +24.3905 q^{51} +35.2327i q^{52} -51.5658 q^{53} -7.34847i q^{54} +(17.1476 - 9.89752i) q^{56} -28.7619 q^{57} -52.2163 q^{58} -14.8313i q^{59} +91.2041i q^{61} +76.6850i q^{62} +(18.1877 - 10.4979i) q^{63} +8.00000 q^{64} -42.9641i q^{66} -5.61477 q^{67} +28.1637i q^{68} +26.9106i q^{69} +80.8420 q^{71} +8.48528 q^{72} +91.0434i q^{73} -63.7442 q^{74} -33.2114i q^{76} +(106.338 - 61.3779i) q^{77} -43.1511 q^{78} -28.5067 q^{79} +9.00000 q^{81} +1.70508i q^{82} +50.3930i q^{83} +(12.1219 + 21.0014i) q^{84} -71.7683 q^{86} -63.9516i q^{87} +49.6107 q^{88} -76.5302i q^{89} +(-61.6450 - 106.801i) q^{91} -31.0736 q^{92} -93.9196 q^{93} +129.770i q^{94} +9.79796i q^{96} -125.356i q^{97} +(-34.6620 + 60.0045i) q^{98} +52.6201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9}+O(q^{10}) $ 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9	$ 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9} - 16 q^{11} + 8 q^{14} + 48 q^{16} - 6 q^{21} + 48 q^{22} + 20 q^{28} + 48 q^{29} - 72 q^{36} - 64 q^{37} - 12 q^{39} - 24 q^{42} + 108 q^{43} - 32 q^{44} + 80 q^{46} + 118 q^{49} + 72 q^{51} - 176 q^{53} + 16 q^{56} + 132 q^{57} - 128 q^{58} - 30 q^{63} + 96 q^{64} + 4 q^{67} + 248 q^{71} - 64 q^{74} + 396 q^{77} - 48 q^{78} - 208 q^{79} + 108 q^{81} - 12 q^{84} + 128 q^{86} + 96 q^{88} - 158 q^{91} - 252 q^{93} + 240 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 + 10 * q^7 - 36 * q^9 - 16 * q^11 + 8 * q^14 + 48 * q^16 - 6 * q^21 + 48 * q^22 + 20 * q^28 + 48 * q^29 - 72 * q^36 - 64 * q^37 - 12 * q^39 - 24 * q^42 + 108 * q^43 - 32 * q^44 + 80 * q^46 + 118 * q^49 + 72 * q^51 - 176 * q^53 + 16 * q^56 + 132 * q^57 - 128 * q^58 - 30 * q^63 + 96 * q^64 + 4 * q^67 + 248 * q^71 - 64 * q^74 + 396 * q^77 - 48 * q^78 - 208 * q^79 + 108 * q^81 - 12 * q^84 + 128 * q^86 + 96 * q^88 - 158 * q^91 - 252 * q^93 + 240 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.06258	+	3.49930i	−0.866083	+	0.499900i
$7$	−6.06258	+	3.49930i	−0.866083	+	0.499900i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−17.5400			−1.59455			−0.797275	−	0.603617i	$-0.793726\pi$
$11$	−17.5400			−1.59455			−0.797275	+	0.603617i	$0.793726\pi$
$12$		−	3.46410i		−	0.288675i
$13$			17.6164i			1.35510i	0.735475	+	0.677552i	$0.236959\pi$
$13$			17.6164i			1.35510i	−0.735475	+	0.677552i	$0.763041\pi$
$14$	8.57378	−	4.94876i	0.612413	−	0.353483i
$15$		0			0
$16$	4.00000			0.250000
$17$			14.0819i			0.828344i	0.910199	+	0.414172i	$0.135929\pi$
$17$			14.0819i			0.828344i	−0.910199	+	0.414172i	$0.864071\pi$
$18$	4.24264			0.235702
$19$		−	16.6057i		−	0.873983i	−0.899466	−	0.436992i	$-0.856044\pi$
$19$		−	16.6057i		−	0.873983i	0.899466	−	0.436992i	$-0.143956\pi$
$20$		0			0
$21$	6.06097	+	10.5007i	0.288618	+	0.500033i
$22$	24.8054			1.12752
$23$	−15.5368			−0.675514			−0.337757	−	0.941233i	$-0.609668\pi$
$23$	−15.5368			−0.675514			−0.337757	+	0.941233i	$0.609668\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$		−	24.9133i		−	0.958203i
$27$			5.19615i			0.192450i
$28$	−12.1252	+	6.99861i	−0.433041	+	0.249950i
$29$	36.9225			1.27319			0.636594	−	0.771199i	$-0.280343\pi$
$29$	36.9225			1.27319			0.636594	+	0.771199i	$0.280343\pi$
$30$		0			0
$31$		−	54.2245i		−	1.74918i	−0.484865	−	0.874589i	$-0.661131\pi$
$31$		−	54.2245i		−	1.74918i	0.484865	−	0.874589i	$-0.338869\pi$
$32$	−5.65685			−0.176777
$33$			30.3802i			0.920613i
$34$		−	19.9147i		−	0.585728i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	45.0739			1.21821			0.609107	−	0.793088i	$-0.291528\pi$
$37$	45.0739			1.21821			0.609107	+	0.793088i	$0.291528\pi$
$38$			23.4840i			0.618000i
$39$	30.5124			0.782370
$40$		0			0
$41$		−	1.20567i		−	0.0294067i	−0.999892	−	0.0147034i	$-0.995320\pi$
$41$		−	1.20567i		−	0.0294067i	0.999892	−	0.0147034i	$-0.00468039\pi$
$42$	−8.57151	−	14.8502i	−0.204084	−	0.353577i
$43$	50.7479			1.18018			0.590091	−	0.807336i	$-0.299092\pi$
$43$	50.7479			1.18018			0.590091	+	0.807336i	$0.299092\pi$
$44$	−35.0801			−0.797275
$45$		0			0
$46$	21.9724			0.477661
$47$		−	91.7612i		−	1.95237i	−0.216949	−	0.976183i	$-0.569611\pi$
$47$		−	91.7612i		−	1.95237i	0.216949	−	0.976183i	$-0.430389\pi$
$48$		−	6.92820i		−	0.144338i
$49$	24.5098	−	42.4296i	0.500199	−	0.865910i
$50$		0			0
$51$	24.3905			0.478245
$52$			35.2327i			0.677552i
$53$	−51.5658			−0.972939			−0.486470	−	0.873697i	$-0.661716\pi$
$53$	−51.5658			−0.972939			−0.486470	+	0.873697i	$0.661716\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	17.1476	−	9.89752i	0.306207	−	0.176742i
$57$	−28.7619			−0.504595
$58$	−52.2163			−0.900281
$59$		−	14.8313i		−	0.251378i	−0.992070	−	0.125689i	$-0.959886\pi$
$59$		−	14.8313i		−	0.251378i	0.992070	−	0.125689i	$-0.0401142\pi$
$60$		0			0
$61$			91.2041i			1.49515i	0.664178	+	0.747575i	$0.268782\pi$
$61$			91.2041i			1.49515i	−0.664178	+	0.747575i	$0.731218\pi$
$62$			76.6850i			1.23686i
$63$	18.1877	−	10.4979i	0.288694	−	0.166633i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	42.9641i		−	0.650972i
$67$	−5.61477			−0.0838025			−0.0419013	−	0.999122i	$-0.513341\pi$
$67$	−5.61477			−0.0838025			−0.0419013	+	0.999122i	$0.513341\pi$
$68$			28.1637i			0.414172i
$69$			26.9106i			0.390008i
$70$		0			0
$71$	80.8420			1.13862			0.569310	−	0.822123i	$-0.307210\pi$
$71$	80.8420			1.13862			0.569310	+	0.822123i	$0.307210\pi$
$72$	8.48528			0.117851
$73$			91.0434i			1.24717i	0.781756	+	0.623585i	$0.214324\pi$
$73$			91.0434i			1.24717i	−0.781756	+	0.623585i	$0.785676\pi$
$74$	−63.7442			−0.861408
$75$		0			0
$76$		−	33.2114i		−	0.436992i
$77$	106.338	−	61.3779i	1.38101	−	0.797116i
$78$	−43.1511			−0.553219
$79$	−28.5067			−0.360845			−0.180422	−	0.983589i	$-0.557746\pi$
$79$	−28.5067			−0.360845			−0.180422	+	0.983589i	$0.557746\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			1.70508i			0.0207937i
$83$			50.3930i			0.607145i	0.952808	+	0.303573i	$0.0981795\pi$
$83$			50.3930i			0.607145i	−0.952808	+	0.303573i	$0.901821\pi$
$84$	12.1219	+	21.0014i	0.144309	+	0.250017i
$85$		0			0
$86$	−71.7683			−0.834515
$87$		−	63.9516i		−	0.735076i
$88$	49.6107			0.563758
$89$		−	76.5302i		−	0.859890i	−0.902855	−	0.429945i	$-0.858533\pi$
$89$		−	76.5302i		−	0.859890i	0.902855	−	0.429945i	$-0.141467\pi$
$90$		0			0
$91$	−61.6450	−	106.801i	−0.677417	−	1.17363i
$92$	−31.0736			−0.337757
$93$	−93.9196			−1.00989
$94$			129.770i			1.38053i
$95$		0			0
$96$			9.79796i			0.102062i
$97$		−	125.356i		−	1.29233i	−0.763198	−	0.646164i	$-0.776372\pi$
$97$		−	125.356i		−	1.29233i	0.763198	−	0.646164i	$-0.223628\pi$
$98$	−34.6620	+	60.0045i	−0.353694	+	0.612291i
$99$	52.6201			0.531516
$100$		0			0
$101$		−	133.915i		−	1.32589i	−0.748667	−	0.662946i	$-0.769306\pi$
$101$		−	133.915i		−	1.32589i	0.748667	−	0.662946i	$-0.230694\pi$
$102$	−34.4934			−0.338170
$103$			71.1180i			0.690466i	0.938517	+	0.345233i	$0.112200\pi$
$103$			71.1180i			0.690466i	−0.938517	+	0.345233i	$0.887800\pi$
$104$		−	49.8266i		−	0.479102i
$105$		0			0
$106$	72.9250			0.687972
$107$	−9.18582			−0.0858488			−0.0429244	−	0.999078i	$-0.513667\pi$
$107$	−9.18582			−0.0858488			−0.0429244	+	0.999078i	$0.513667\pi$
$108$			10.3923i			0.0962250i
$109$	110.684			1.01545			0.507726	−	0.861519i	$-0.330486\pi$
$109$	110.684			1.01545			0.507726	+	0.861519i	$0.330486\pi$
$110$		0			0
$111$		−	78.0703i		−	0.703336i
$112$	−24.2503	+	13.9972i	−0.216521	+	0.124975i
$113$	−168.521			−1.49134			−0.745668	−	0.666317i	$-0.767870\pi$
$113$	−168.521			−1.49134			−0.745668	+	0.666317i	$0.767870\pi$
$114$	40.6755			0.356802
$115$		0			0
$116$	73.8450			0.636594
$117$		−	52.8491i		−	0.451701i
$118$			20.9747i			0.177751i
$119$	−49.2767	−	85.3723i	−0.414090	−	0.717415i
$120$		0			0
$121$	186.653			1.54259
$122$		−	128.982i		−	1.05723i
$123$	−2.08829			−0.0169780
$124$		−	108.449i		−	0.874589i
$125$		0			0
$126$	−25.7213	+	14.8463i	−0.204138	+	0.117828i
$127$	98.7378			0.777463			0.388731	−	0.921351i	$-0.372913\pi$
$127$	98.7378			0.777463			0.388731	+	0.921351i	$0.372913\pi$
$128$	−11.3137			−0.0883883
$129$		−	87.8979i		−	0.681379i
$130$		0			0
$131$		−	5.20765i		−	0.0397531i	−0.999802	−	0.0198765i	$-0.993673\pi$
$131$		−	5.20765i		−	0.0397531i	0.999802	−	0.0198765i	$-0.00632732\pi$
$132$			60.7605i			0.460307i
$133$	58.1083	+	100.673i	0.436905	+	0.756942i
$134$	7.94048			0.0592573
$135$		0			0
$136$		−	39.8295i		−	0.292864i
$137$	4.91235			0.0358566			0.0179283	−	0.999839i	$-0.494293\pi$
$137$	4.91235			0.0358566			0.0179283	+	0.999839i	$0.494293\pi$
$138$		−	38.0573i		−	0.275777i
$139$		−	13.5723i		−	0.0976424i	−0.998808	−	0.0488212i	$-0.984454\pi$
$139$		−	13.5723i		−	0.0976424i	0.998808	−	0.0488212i	$-0.0155465\pi$
$140$		0			0
$141$	−158.935			−1.12720
$142$	−114.328			−0.805126
$143$		−	308.992i		−	2.16078i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	128.755i		−	0.881882i
$147$	−73.4902	−	42.4521i	−0.499934	−	0.288790i
$148$	90.1479			0.609107
$149$	−154.960			−1.04000			−0.520001	−	0.854165i	$-0.674069\pi$
$149$	−154.960			−1.04000			−0.520001	+	0.854165i	$0.674069\pi$
$150$		0			0
$151$	197.940			1.31086			0.655432	−	0.755254i	$-0.272487\pi$
$151$	197.940			1.31086			0.655432	+	0.755254i	$0.272487\pi$
$152$			46.9680i			0.309000i
$153$		−	42.2456i		−	0.276115i
$154$	−150.384	+	86.8015i	−0.976523	+	0.563646i
$155$		0			0
$156$	61.0248			0.391185
$157$		−	189.082i		−	1.20434i	−0.798367	−	0.602171i	$-0.794303\pi$
$157$		−	189.082i		−	1.20434i	0.798367	−	0.602171i	$-0.205697\pi$
$158$	40.3146			0.255156
$159$			89.3146i			0.561727i
$160$		0			0
$161$	94.1932	−	54.3681i	0.585051	−	0.337690i
$162$	−12.7279			−0.0785674
$163$	269.128			1.65109			0.825545	−	0.564336i	$-0.190868\pi$
$163$	269.128			1.65109			0.825545	+	0.564336i	$0.190868\pi$
$164$		−	2.41135i		−	0.0147034i
$165$		0			0
$166$		−	71.2665i		−	0.429316i
$167$			125.338i			0.750526i	0.926918	+	0.375263i	$0.122448\pi$
$167$			125.338i			0.750526i	−0.926918	+	0.375263i	$0.877552\pi$
$168$	−17.1430	−	29.7005i	−0.102042	−	0.176788i
$169$	−141.336			−0.836308
$170$		0			0
$171$			49.8171i			0.291328i
$172$	101.496			0.590091
$173$		−	196.074i		−	1.13338i	−0.823932	−	0.566688i	$-0.808224\pi$
$173$		−	196.074i		−	1.13338i	0.823932	−	0.566688i	$-0.191776\pi$
$174$			90.4412i			0.519777i
$175$		0			0
$176$	−70.1602			−0.398637
$177$	−25.6886			−0.145133
$178$			108.230i			0.608034i
$179$	255.467			1.42719			0.713596	−	0.700557i	$-0.247065\pi$
$179$	255.467			1.42719			0.713596	+	0.700557i	$0.247065\pi$
$180$		0			0
$181$			253.527i			1.40070i	0.713799	+	0.700351i	$0.246973\pi$
$181$			253.527i			1.40070i	−0.713799	+	0.700351i	$0.753027\pi$
$182$	87.1792	+	151.039i	0.479006	+	0.829884i
$183$	157.970			0.863225
$184$	43.9448			0.238830
$185$		0			0
$186$	132.822			0.714099
$187$		−	246.996i		−	1.32084i
$188$		−	183.522i		−	0.976183i
$189$	−18.1829	−	31.5021i	−0.0962059	−	0.166678i
$190$		0			0
$191$	−286.274			−1.49882			−0.749410	−	0.662107i	$-0.769663\pi$
$191$	−286.274			−1.49882			−0.749410	+	0.662107i	$0.769663\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	198.340			1.02767			0.513834	−	0.857889i	$-0.328225\pi$
$193$	198.340			1.02767			0.513834	+	0.857889i	$0.328225\pi$
$194$			177.280i			0.913814i
$195$		0			0
$196$	49.0195	−	84.8592i	0.250099	−	0.432955i
$197$	253.374			1.28616			0.643080	−	0.765799i	$-0.277656\pi$
$197$	253.374			1.28616			0.643080	+	0.765799i	$0.277656\pi$
$198$	−74.4161			−0.375839
$199$		−	203.091i		−	1.02056i	−0.860009	−	0.510278i	$-0.829542\pi$
$199$		−	203.091i		−	1.02056i	0.860009	−	0.510278i	$-0.170458\pi$
$200$		0			0
$201$			9.72507i			0.0483834i
$202$			189.384i			0.937547i
$203$	−223.845	+	129.203i	−1.10269	+	0.636468i
$204$	48.7810			0.239122
$205$		0			0
$206$		−	100.576i		−	0.488233i
$207$	46.6105			0.225171
$208$			70.4654i			0.338776i
$209$			291.264i			1.39361i
$210$		0			0
$211$	39.9211			0.189200			0.0945998	−	0.995515i	$-0.469843\pi$
$211$	39.9211			0.189200			0.0945998	+	0.995515i	$0.469843\pi$
$212$	−103.132			−0.486470
$213$		−	140.022i		−	0.657382i
$214$	12.9907			0.0607043
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	189.748	+	328.740i	0.874415	+	1.51493i
$218$	−156.531			−0.718033
$219$	157.692			0.720054
$220$		0			0
$221$	−248.071			−1.12249
$222$			110.408i			0.497334i
$223$		−	220.520i		−	0.988880i	−0.869212	−	0.494440i	$-0.835373\pi$
$223$		−	220.520i		−	0.988880i	0.869212	−	0.494440i	$-0.164627\pi$
$224$	34.2951	−	19.7950i	0.153103	−	0.0883708i
$225$		0			0
$226$	238.325			1.05453
$227$		−	287.672i		−	1.26728i	−0.773629	−	0.633639i	$-0.781560\pi$
$227$		−	287.672i		−	1.26728i	0.773629	−	0.633639i	$-0.218440\pi$
$228$	−57.5238			−0.252297
$229$		−	167.481i		−	0.731358i	−0.930741	−	0.365679i	$-0.880837\pi$
$229$		−	167.481i		−	0.731358i	0.930741	−	0.365679i	$-0.119163\pi$
$230$		0			0
$231$	−106.310	−	184.183i	−0.460215	−	0.797327i
$232$	−104.433			−0.450140
$233$	−11.6077			−0.0498185			−0.0249092	−	0.999690i	$-0.507930\pi$
$233$	−11.6077			−0.0498185			−0.0249092	+	0.999690i	$0.507930\pi$
$234$			74.7399i			0.319401i
$235$		0			0
$236$		−	29.6626i		−	0.125689i
$237$			49.3751i			0.208334i
$238$	69.6877	+	120.735i	0.292806	+	0.507289i
$239$	−17.5810			−0.0735608			−0.0367804	−	0.999323i	$-0.511710\pi$
$239$	−17.5810			−0.0735608			−0.0367804	+	0.999323i	$0.511710\pi$
$240$		0			0
$241$		−	46.5601i		−	0.193196i	−0.995323	−	0.0965978i	$-0.969204\pi$
$241$		−	46.5601i		−	0.193196i	0.995323	−	0.0965978i	$-0.0307960\pi$
$242$	−263.967			−1.09077
$243$		−	15.5885i		−	0.0641500i
$244$			182.408i			0.747575i
$245$		0			0
$246$	2.95329			0.0120052
$247$	292.532			1.18434
$248$			153.370i			0.618428i
$249$	87.2833			0.350535
$250$		0			0
$251$			227.785i			0.907510i	0.891126	+	0.453755i	$0.149916\pi$
$251$			227.785i			0.907510i	−0.891126	+	0.453755i	$0.850084\pi$
$252$	36.3755	−	20.9958i	0.144347	−	0.0833167i
$253$	272.516			1.07714
$254$	−139.636			−0.549749
$255$		0			0
$256$	16.0000			0.0625000
$257$			91.2755i			0.355158i	0.984107	+	0.177579i	$0.0568265\pi$
$257$			91.2755i			0.355158i	−0.984107	+	0.177579i	$0.943174\pi$
$258$			124.306i			0.481808i
$259$	−273.264	+	157.727i	−1.05507	+	0.608986i
$260$		0			0
$261$	−110.767			−0.424396
$262$			7.36474i			0.0281097i
$263$	−108.528			−0.412653			−0.206326	−	0.978483i	$-0.566151\pi$
$263$	−108.528			−0.412653			−0.206326	+	0.978483i	$0.566151\pi$
$264$		−	85.9283i		−	0.325486i
$265$		0			0
$266$	−82.1776	−	142.374i	−0.308938	−	0.535239i
$267$	−132.554			−0.496458
$268$	−11.2295			−0.0419013
$269$		−	351.607i		−	1.30709i	−0.756888	−	0.653545i	$-0.773281\pi$
$269$		−	351.607i		−	1.30709i	0.756888	−	0.653545i	$-0.226719\pi$
$270$		0			0
$271$			387.665i			1.43050i	0.698869	+	0.715250i	$0.253687\pi$
$271$			387.665i			1.43050i	−0.698869	+	0.715250i	$0.746313\pi$
$272$			56.3274i			0.207086i
$273$	−184.984	+	106.772i	−0.677597	+	0.391107i
$274$	−6.94711			−0.0253544
$275$		0			0
$276$			53.8211i			0.195004i
$277$	−503.195			−1.81659			−0.908293	−	0.418334i	$-0.862614\pi$
$277$	−503.195			−1.81659			−0.908293	+	0.418334i	$0.862614\pi$
$278$			19.1941i			0.0690436i
$279$			162.674i			0.583059i
$280$		0			0
$281$	106.871			0.380323			0.190161	−	0.981753i	$-0.439099\pi$
$281$	106.871			0.380323			0.190161	+	0.981753i	$0.439099\pi$
$282$	224.768			0.797050
$283$		−	85.3646i		−	0.301642i	−0.988561	−	0.150821i	$-0.951808\pi$
$283$		−	85.3646i		−	0.301642i	0.988561	−	0.150821i	$-0.0481916\pi$
$284$	161.684			0.569310
$285$		0			0
$286$			436.980i			1.52790i
$287$	4.21902	+	7.30950i	0.0147004	+	0.0254686i
$288$	16.9706			0.0589256
$289$	90.7015			0.313846
$290$		0			0
$291$	−217.123			−0.746126
$292$			182.087i			0.623585i
$293$		−	155.961i		−	0.532289i	−0.963933	−	0.266145i	$-0.914250\pi$
$293$		−	155.961i		−	0.532289i	0.963933	−	0.266145i	$-0.0857499\pi$
$294$	103.931	+	60.0364i	0.353506	+	0.204205i
$295$		0			0
$296$	−127.488			−0.430704
$297$		−	91.1407i		−	0.306871i
$298$	219.147			0.735393
$299$		−	273.702i		−	0.915392i
$300$		0			0
$301$	−307.663	+	177.582i	−1.02214	+	0.589974i
$302$	−279.930			−0.926921
$303$	−231.948			−0.765504
$304$		−	66.4227i		−	0.218496i
$305$		0			0
$306$			59.7442i			0.195243i
$307$			495.927i			1.61540i	0.589595	+	0.807699i	$0.299287\pi$
$307$			495.927i			1.61540i	−0.589595	+	0.807699i	$0.700713\pi$
$308$	212.676	−	122.756i	0.690506	−	0.398558i
$309$	123.180			0.398641
$310$		0			0
$311$			270.262i			0.869008i	0.900670	+	0.434504i	$0.143076\pi$
$311$			270.262i			0.869008i	−0.900670	+	0.434504i	$0.856924\pi$
$312$	−86.3022			−0.276610
$313$		−	23.6843i		−	0.0756688i	−0.999284	−	0.0378344i	$-0.987954\pi$
$313$		−	23.6843i		−	0.0756688i	0.999284	−	0.0378344i	$-0.0120459\pi$
$314$			267.402i			0.851598i
$315$		0			0
$316$	−57.0135			−0.180422
$317$	−3.53825			−0.0111617			−0.00558083	−	0.999984i	$-0.501776\pi$
$317$	−3.53825			−0.0111617			−0.00558083	+	0.999984i	$0.501776\pi$
$318$		−	126.310i		−	0.397201i
$319$	−647.622			−2.03016
$320$		0			0
$321$			15.9103i			0.0495648i
$322$	−133.209	+	76.8880i	−0.413694	+	0.238783i
$323$	233.839			0.723959
$324$	18.0000			0.0555556
$325$		0			0
$326$	−380.604			−1.16750
$327$		−	191.711i		−	0.586272i
$328$			3.41016i			0.0103968i
$329$	321.100	+	556.310i	0.975989	+	1.69091i
$330$		0			0
$331$	−341.340			−1.03124			−0.515619	−	0.856818i	$-0.672438\pi$
$331$	−341.340			−1.03124			−0.515619	+	0.856818i	$0.672438\pi$
$332$			100.786i			0.303573i
$333$	−135.222			−0.406071
$334$		−	177.254i		−	0.530702i
$335$		0			0
$336$	24.2439	+	42.0028i	0.0721544	+	0.125008i
$337$	92.5173			0.274532			0.137266	−	0.990534i	$-0.456168\pi$
$337$	92.5173			0.274532			0.137266	+	0.990534i	$0.456168\pi$
$338$	199.879			0.591359
$339$			291.887i			0.861024i
$340$		0			0
$341$			951.100i			2.78915i
$342$		−	70.4520i		−	0.206000i
$343$	−0.118226	+	343.000i	−0.000344681	+	1.00000i
$344$	−143.537			−0.417258
$345$		0			0
$346$			277.291i			0.801418i
$347$	354.217			1.02080			0.510399	−	0.859938i	$-0.329498\pi$
$347$	354.217			1.02080			0.510399	+	0.859938i	$0.329498\pi$
$348$		−	127.903i		−	0.367538i
$349$		−	149.606i		−	0.428670i	−0.976760	−	0.214335i	$-0.931242\pi$
$349$		−	149.606i		−	0.428670i	0.976760	−	0.214335i	$-0.0687584\pi$
$350$		0			0
$351$	−91.5373			−0.260790
$352$	99.2214			0.281879
$353$			326.247i			0.924213i	0.886824	+	0.462107i	$0.152906\pi$
$353$			326.247i			0.924213i	−0.886824	+	0.462107i	$0.847094\pi$
$354$	36.3292			0.102625
$355$		0			0
$356$		−	153.060i		−	0.429945i
$357$	−147.869	+	85.3497i	−0.414200	+	0.239075i
$358$	−361.285			−1.00918
$359$	−296.371			−0.825545			−0.412772	−	0.910834i	$-0.635439\pi$
$359$	−296.371			−0.825545			−0.412772	+	0.910834i	$0.635439\pi$
$360$		0			0
$361$	85.2512			0.236153
$362$		−	358.541i		−	0.990445i
$363$		−	323.292i		−	0.890613i
$364$	−123.290	−	213.601i	−0.338709	−	0.586816i
$365$		0			0
$366$	−223.404			−0.610392
$367$			284.903i			0.776303i	0.921596	+	0.388151i	$0.126886\pi$
$367$			284.903i			0.776303i	−0.921596	+	0.388151i	$0.873114\pi$
$368$	−62.1473			−0.168879
$369$			3.61702i			0.00980223i
$370$		0			0
$371$	312.622	−	180.444i	0.842646	−	0.486373i
$372$	−187.839			−0.504944
$373$	−163.961			−0.439573			−0.219787	−	0.975548i	$-0.570536\pi$
$373$	−163.961			−0.439573			−0.219787	+	0.975548i	$0.570536\pi$
$374$			349.305i			0.933972i
$375$		0			0
$376$			259.540i			0.690266i
$377$			650.440i			1.72530i
$378$	25.7145	+	44.5507i	0.0680278	+	0.117859i
$379$	−178.496			−0.470966			−0.235483	−	0.971878i	$-0.575667\pi$
$379$	−178.496			−0.470966			−0.235483	+	0.971878i	$0.575667\pi$
$380$		0			0
$381$		−	171.019i		−	0.448868i
$382$	404.853			1.05983
$383$		−	522.144i		−	1.36330i	−0.731678	−	0.681650i	$-0.761263\pi$
$383$		−	522.144i		−	1.36330i	0.731678	−	0.681650i	$-0.238737\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−280.495			−0.726672
$387$	−152.244			−0.393394
$388$		−	250.712i		−	0.646164i
$389$	582.959			1.49861			0.749305	−	0.662225i	$-0.230388\pi$
$389$	582.959			1.49861			0.749305	+	0.662225i	$0.230388\pi$
$390$		0			0
$391$		−	218.787i		−	0.559558i
$392$	−69.3240	+	120.009i	−0.176847	+	0.306146i
$393$	−9.01992			−0.0229515
$394$	−358.324			−0.909453
$395$		0			0
$396$	105.240			0.265758
$397$		−	431.754i		−	1.08754i	−0.839234	−	0.543770i	$-0.816996\pi$
$397$		−	431.754i		−	1.08754i	0.839234	−	0.543770i	$-0.183004\pi$
$398$			287.214i			0.721643i
$399$	174.371	−	100.647i	0.437021	−	0.252247i
$400$		0			0
$401$	261.939			0.653216			0.326608	−	0.945160i	$-0.394094\pi$
$401$	261.939			0.653216			0.326608	+	0.945160i	$0.394094\pi$
$402$		−	13.7533i		−	0.0342122i
$403$	955.238			2.37032
$404$		−	267.830i		−	0.662946i
$405$		0			0
$406$	316.565	−	182.721i	0.779718	−	0.450051i
$407$	−790.598			−1.94250
$408$	−68.9867			−0.169085
$409$		−	443.220i		−	1.08367i	−0.840485	−	0.541834i	$-0.817730\pi$
$409$		−	443.220i		−	1.08367i	0.840485	−	0.541834i	$-0.182270\pi$
$410$		0			0
$411$		−	8.50844i		−	0.0207018i
$412$			142.236i			0.345233i
$413$	51.8993	+	89.9161i	0.125664	+	0.217714i
$414$	−65.9172			−0.159220
$415$		0			0
$416$		−	99.6532i		−	0.239551i
$417$	−23.5079			−0.0563739
$418$		−	411.910i		−	0.985431i
$419$			255.406i			0.609561i	0.952423	+	0.304781i	$0.0985832\pi$
$419$			255.406i			0.609561i	−0.952423	+	0.304781i	$0.901417\pi$
$420$		0			0
$421$	317.879			0.755057			0.377529	−	0.925998i	$-0.376774\pi$
$421$	317.879			0.755057			0.377529	+	0.925998i	$0.376774\pi$
$422$	−56.4570			−0.133784
$423$			275.284i			0.650789i
$424$	145.850			0.343986
$425$		0			0
$426$			198.022i			0.464840i
$427$	−319.151	−	552.932i	−0.747426	−	1.29492i
$428$	−18.3716			−0.0429244
$429$	−535.189			−1.24753
$430$		0			0
$431$	83.1442			0.192910			0.0964550	−	0.995337i	$-0.469250\pi$
$431$	83.1442			0.192910			0.0964550	+	0.995337i	$0.469250\pi$
$432$			20.7846i			0.0481125i
$433$			501.302i			1.15774i	0.815419	+	0.578871i	$0.196506\pi$
$433$			501.302i			1.15774i	−0.815419	+	0.578871i	$0.803494\pi$
$434$	−268.344	−	464.909i	−0.618305	−	1.07122i
$435$		0			0
$436$	221.369			0.507726
$437$			258.000i			0.590388i
$438$	−223.010			−0.509155
$439$			10.1601i			0.0231438i	0.999933	+	0.0115719i	$0.00368354\pi$
$439$			10.1601i			0.0231438i	−0.999933	+	0.0115719i	$0.996316\pi$
$440$		0			0
$441$	−73.5293	+	127.289i	−0.166733	+	0.288637i
$442$	350.825			0.793722
$443$	−201.289			−0.454377			−0.227189	−	0.973851i	$-0.572953\pi$
$443$	−201.289			−0.454377			−0.227189	+	0.973851i	$0.572953\pi$
$444$		−	156.141i		−	0.351668i
$445$		0			0
$446$			311.863i			0.699244i
$447$			268.399i			0.600446i
$448$	−48.5006	+	27.9944i	−0.108260	+	0.0624876i
$449$	602.966			1.34291			0.671454	−	0.741046i	$-0.265670\pi$
$449$	602.966			1.34291			0.671454	+	0.741046i	$0.265670\pi$
$450$		0			0
$451$			21.1476i			0.0468904i
$452$	−337.042			−0.745668
$453$		−	342.843i		−	0.756828i
$454$			406.830i			0.896101i
$455$		0			0
$456$	81.3509			0.178401
$457$	−233.942			−0.511909			−0.255955	−	0.966689i	$-0.582390\pi$
$457$	−233.942			−0.511909			−0.255955	+	0.966689i	$0.582390\pi$
$458$			236.854i			0.517148i
$459$	−73.1714			−0.159415
$460$		0			0
$461$			536.813i			1.16445i	0.813027	+	0.582226i	$0.197818\pi$
$461$			536.813i			1.16445i	−0.813027	+	0.582226i	$0.802182\pi$
$462$	150.345	+	260.474i	0.325421	+	0.563796i
$463$	−23.5707			−0.0509087			−0.0254543	−	0.999676i	$-0.508103\pi$
$463$	−23.5707			−0.0509087			−0.0254543	+	0.999676i	$0.508103\pi$
$464$	147.690			0.318297
$465$		0			0
$466$	16.4158			0.0352270
$467$		−	716.108i		−	1.53342i	−0.641993	−	0.766711i	$-0.721892\pi$
$467$		−	716.108i		−	1.53342i	0.641993	−	0.766711i	$-0.278108\pi$
$468$		−	105.698i		−	0.225851i
$469$	34.0400	−	19.6478i	0.0725799	−	0.0418929i
$470$		0			0
$471$	−327.499			−0.695327
$472$			41.9493i			0.0888757i
$473$	−890.119			−1.88186
$474$		−	69.8270i		−	0.147314i
$475$		0			0
$476$	−98.5533	−	170.745i	−0.207045	−	0.358707i
$477$	154.697			0.324313
$478$	24.8633			0.0520153
$479$			484.826i			1.01216i	0.862486	+	0.506082i	$0.168907\pi$
$479$			484.826i			1.01216i	−0.862486	+	0.506082i	$0.831093\pi$
$480$		0			0
$481$			794.038i			1.65081i
$482$			65.8460i			0.136610i
$483$	−94.1682	−	163.147i	−0.194965	−	0.337779i
$484$	373.306			0.771293
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	−104.620			−0.214825			−0.107413	−	0.994215i	$-0.534257\pi$
$487$	−104.620			−0.214825			−0.107413	+	0.994215i	$0.534257\pi$
$488$		−	257.964i		−	0.528615i
$489$		−	466.143i		−	0.953257i
$490$		0			0
$491$	31.7002			0.0645624			0.0322812	−	0.999479i	$-0.489723\pi$
$491$	31.7002			0.0645624			0.0322812	+	0.999479i	$0.489723\pi$
$492$	−4.17658			−0.00848898
$493$			519.937i			1.05464i
$494$	−413.702			−0.837454
$495$		0			0
$496$		−	216.898i		−	0.437294i
$497$	−490.111	+	282.891i	−0.986139	+	0.569197i
$498$	−123.437			−0.247866
$499$	527.582			1.05728			0.528639	−	0.848847i	$-0.322702\pi$
$499$	527.582			1.05728			0.528639	+	0.848847i	$0.322702\pi$
$500$		0			0
$501$	217.091			0.433316
$502$		−	322.137i		−	0.641706i
$503$		−	635.097i		−	1.26262i	−0.775531	−	0.631309i	$-0.782518\pi$
$503$		−	635.097i		−	1.26262i	0.775531	−	0.631309i	$-0.217482\pi$
$504$	−51.4427	+	29.6926i	−0.102069	+	0.0589138i
$505$		0			0
$506$	−385.397			−0.761653
$507$			244.801i			0.482843i
$508$	197.476			0.388731
$509$		−	376.147i		−	0.738992i	−0.929232	−	0.369496i	$-0.879530\pi$
$509$		−	376.147i		−	0.738992i	0.929232	−	0.369496i	$-0.120470\pi$
$510$		0			0
$511$	−318.588	−	551.958i	−0.623461	−	1.08015i
$512$	−22.6274			−0.0441942
$513$	86.2857			0.168198
$514$		−	129.083i		−	0.251134i
$515$		0			0
$516$		−	175.796i		−	0.340689i
$517$			1609.49i			3.11314i
$518$	386.454	−	223.060i	0.746050	−	0.430618i
$519$	−339.610			−0.654355
$520$		0			0
$521$		−	375.330i		−	0.720403i	−0.932875	−	0.360201i	$-0.882708\pi$
$521$		−	375.330i		−	0.720403i	0.932875	−	0.360201i	$-0.117292\pi$
$522$	156.649			0.300094
$523$		−	375.647i		−	0.718255i	−0.933288	−	0.359128i	$-0.883074\pi$
$523$		−	375.647i		−	0.718255i	0.933288	−	0.359128i	$-0.116926\pi$
$524$		−	10.4153i		−	0.0198765i
$525$		0			0
$526$	153.481			0.291790
$527$	763.582			1.44892
$528$			121.521i			0.230153i
$529$	−287.607			−0.543681
$530$		0			0
$531$			44.4940i			0.0837928i
$532$	116.217	+	201.347i	0.218452	+	0.378471i
$533$	21.2396			0.0398492
$534$	187.460			0.351049
$535$		0			0
$536$	15.8810			0.0296287
$537$		−	442.482i		−	0.823990i
$538$			497.247i			0.924252i
$539$	−429.902	+	744.217i	−0.797592	+	1.38074i
$540$		0			0
$541$	−252.515			−0.466755			−0.233378	−	0.972386i	$-0.574978\pi$
$541$	−252.515			−0.466755			−0.233378	+	0.972386i	$0.574978\pi$
$542$		−	548.241i		−	1.01152i
$543$	439.122			0.808695
$544$		−	79.6590i		−	0.146432i
$545$		0			0
$546$	261.607	−	150.999i	0.479134	−	0.276554i
$547$	619.645			1.13281			0.566403	−	0.824129i	$-0.308335\pi$
$547$	619.645			1.13281			0.566403	+	0.824129i	$0.308335\pi$
$548$	9.82470			0.0179283
$549$		−	273.612i		−	0.498383i
$550$		0			0
$551$		−	613.123i		−	1.11275i
$552$		−	76.1146i		−	0.137889i
$553$	172.824	−	99.7538i	0.312522	−	0.180387i
$554$	711.625			1.28452
$555$		0			0
$556$		−	27.1446i		−	0.0488212i
$557$	−243.944			−0.437960			−0.218980	−	0.975729i	$-0.570273\pi$
$557$	−243.944			−0.437960			−0.218980	+	0.975729i	$0.570273\pi$
$558$		−	230.055i		−	0.412285i
$559$			893.992i			1.59927i
$560$		0			0
$561$	−427.810			−0.762585
$562$	−151.138			−0.268929
$563$		−	754.322i		−	1.33983i	−0.742440	−	0.669913i	$-0.766332\pi$
$563$		−	754.322i		−	1.33983i	0.742440	−	0.669913i	$-0.233668\pi$
$564$	−317.870			−0.563599
$565$		0			0
$566$			120.724i			0.213293i
$567$	−54.5632	+	31.4937i	−0.0962314	+	0.0555445i
$568$	−228.656			−0.402563
$569$	755.833			1.32835			0.664176	−	0.747576i	$-0.268782\pi$
$569$	755.833			1.32835			0.664176	+	0.747576i	$0.268782\pi$
$570$		0			0
$571$	−517.669			−0.906601			−0.453300	−	0.891358i	$-0.649753\pi$
$571$	−517.669			−0.906601			−0.453300	+	0.891358i	$0.649753\pi$
$572$		−	617.983i		−	1.08039i
$573$			495.842i			0.865344i
$574$	−5.96660	−	10.3372i	−0.0103948	−	0.0180090i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	451.476i		−	0.782455i	−0.920294	−	0.391227i	$-0.872051\pi$
$577$		−	451.476i		−	0.782455i	0.920294	−	0.391227i	$-0.127949\pi$
$578$	−128.271			−0.221923
$579$		−	343.535i		−	0.593325i
$580$		0			0
$581$	−176.341	−	305.512i	−0.303512	−	0.525838i
$582$	307.058			0.527591
$583$	904.466			1.55140
$584$		−	257.510i		−	0.440941i
$585$		0			0
$586$			220.562i			0.376385i
$587$			145.909i			0.248568i	0.992247	+	0.124284i	$0.0396634\pi$
$587$			145.909i			0.248568i	−0.992247	+	0.124284i	$0.960337\pi$
$588$	−146.980	−	84.9043i	−0.249967	−	0.144395i
$589$	−900.435			−1.52875
$590$		0			0
$591$		−	438.856i		−	0.742565i
$592$	180.296			0.304554
$593$			920.404i			1.55211i	0.630663	+	0.776057i	$0.282783\pi$
$593$			920.404i			1.55211i	−0.630663	+	0.776057i	$0.717217\pi$
$594$			128.892i			0.216991i
$595$		0			0
$596$	−309.921			−0.520001
$597$	−351.764			−0.589219
$598$			387.073i			0.647280i
$599$	458.821			0.765979			0.382989	−	0.923753i	$-0.374895\pi$
$599$	458.821			0.765979			0.382989	+	0.923753i	$0.374895\pi$
$600$		0			0
$601$		−	936.167i		−	1.55768i	−0.627222	−	0.778841i	$-0.715808\pi$
$601$		−	936.167i		−	1.55768i	0.627222	−	0.778841i	$-0.284192\pi$
$602$	435.101	−	251.139i	0.722759	−	0.417175i
$603$	16.8443			0.0279342
$604$	395.881			0.655432
$605$		0			0
$606$	328.024			0.541293
$607$		−	851.306i		−	1.40248i	−0.712925	−	0.701240i	$-0.752630\pi$
$607$		−	851.306i		−	1.40248i	0.712925	−	0.701240i	$-0.247370\pi$
$608$			93.9359i			0.154500i
$609$	223.786	+	387.712i	0.367465	+	0.636637i
$610$		0			0
$611$	1616.50			2.64566
$612$		−	84.4911i		−	0.138057i
$613$	−769.065			−1.25459			−0.627296	−	0.778781i	$-0.715838\pi$
$613$	−769.065			−1.25459			−0.627296	+	0.778781i	$0.715838\pi$
$614$		−	701.347i		−	1.14226i
$615$		0			0
$616$	−300.769	+	173.603i	−0.488261	+	0.281823i
$617$	−326.419			−0.529042			−0.264521	−	0.964380i	$-0.585214\pi$
$617$	−326.419			−0.529042			−0.264521	+	0.964380i	$0.585214\pi$
$618$	−174.203			−0.281882
$619$		−	256.214i		−	0.413917i	−0.978350	−	0.206958i	$-0.933644\pi$
$619$		−	256.214i		−	0.413917i	0.978350	−	0.206958i	$-0.0663564\pi$
$620$		0			0
$621$		−	80.7317i		−	0.130003i
$622$		−	382.208i		−	0.614482i
$623$	267.802	+	463.970i	0.429859	+	0.744736i
$624$	122.050			0.195592
$625$		0			0
$626$			33.4947i			0.0535059i
$627$	504.485			0.804601
$628$		−	378.163i		−	0.602171i
$629$			634.724i			1.00910i
$630$		0			0
$631$	1195.94			1.89531			0.947655	−	0.319297i	$-0.103447\pi$
$631$	1195.94			1.89531			0.947655	+	0.319297i	$0.103447\pi$
$632$	80.6293			0.127578
$633$		−	69.1454i		−	0.109234i
$634$	5.00384			0.00789249
$635$		0			0
$636$			178.629i			0.280863i
$637$	747.455	+	431.773i	1.17340	+	0.677822i
$638$	915.875			1.43554
$639$	−242.526			−0.379540
$640$		0			0
$641$	922.133			1.43858			0.719292	−	0.694707i	$-0.244466\pi$
$641$	922.133			1.43858			0.719292	+	0.694707i	$0.244466\pi$
$642$		−	22.5006i		−	0.0350476i
$643$			113.572i			0.176628i	0.996093	+	0.0883140i	$0.0281479\pi$
$643$			113.572i			0.176628i	−0.996093	+	0.0883140i	$0.971852\pi$
$644$	188.386	−	108.736i	0.292526	−	0.168845i
$645$		0			0
$646$	−330.698			−0.511916
$647$			345.510i			0.534019i	0.963694	+	0.267010i	$0.0860355\pi$
$647$			345.510i			0.534019i	−0.963694	+	0.267010i	$0.913964\pi$
$648$	−25.4558			−0.0392837
$649$			260.142i			0.400835i
$650$		0			0
$651$	569.395	−	328.653i	0.874647	−	0.504844i
$652$	538.255			0.825545
$653$	584.964			0.895810			0.447905	−	0.894081i	$-0.352170\pi$
$653$	584.964			0.895810			0.447905	+	0.894081i	$0.352170\pi$
$654$			271.120i			0.414557i
$655$		0			0
$656$		−	4.82270i		−	0.00735168i
$657$		−	273.130i		−	0.415723i
$658$	−454.104	−	786.740i	−0.690128	−	1.19565i
$659$	−1144.54			−1.73678			−0.868389	−	0.495884i	$-0.834844\pi$
$659$	−1144.54			−1.73678			−0.868389	+	0.495884i	$0.834844\pi$
$660$		0			0
$661$		−	462.966i		−	0.700402i	−0.936674	−	0.350201i	$-0.886113\pi$
$661$		−	462.966i		−	0.700402i	0.936674	−	0.350201i	$-0.113887\pi$
$662$	482.728			0.729196
$663$			429.671i			0.648072i
$664$		−	142.533i		−	0.214658i
$665$		0			0
$666$	191.232			0.287136
$667$	−573.658			−0.860057
$668$			250.676i			0.375263i
$669$	−381.952			−0.570930
$670$		0			0
$671$		−	1599.72i		−	2.38409i
$672$	−34.2860	−	59.4009i	−0.0510209	−	0.0883942i
$673$	−529.399			−0.786625			−0.393312	−	0.919405i	$-0.628671\pi$
$673$	−529.399			−0.786625			−0.393312	+	0.919405i	$0.628671\pi$
$674$	−130.839			−0.194124
$675$		0			0
$676$	−282.672			−0.418154
$677$		−	1079.35i		−	1.59431i	−0.603776	−	0.797154i	$-0.706338\pi$
$677$		−	1079.35i		−	1.59431i	0.603776	−	0.797154i	$-0.293662\pi$
$678$		−	412.791i		−	0.608836i
$679$	438.658	+	759.980i	0.646036	+	1.11926i
$680$		0			0
$681$	−498.263			−0.731664
$682$		−	1345.06i		−	1.97223i
$683$	−661.804			−0.968966			−0.484483	−	0.874801i	$-0.660992\pi$
$683$	−661.804			−0.968966			−0.484483	+	0.874801i	$0.660992\pi$
$684$			99.6341i			0.145664i
$685$		0			0
$686$	0.167196	−	485.075i	0.000243726	−	0.707107i
$687$	−290.085			−0.422250
$688$	202.991			0.295046
$689$		−	908.401i		−	1.31843i
$690$		0			0
$691$		−	987.850i		−	1.42959i	−0.699332	−	0.714797i	$-0.746519\pi$
$691$		−	987.850i		−	1.42959i	0.699332	−	0.714797i	$-0.253481\pi$
$692$		−	392.148i		−	0.566688i
$693$	−319.014	+	184.134i	−0.460337	+	0.265705i
$694$	−500.938			−0.721813
$695$		0			0
$696$			180.882i			0.259889i
$697$	16.9781			0.0243589
$698$			211.574i			0.303115i
$699$			20.1051i			0.0287627i
$700$		0			0
$701$	−747.087			−1.06574			−0.532872	−	0.846196i	$-0.678887\pi$
$701$	−747.087			−1.06574			−0.532872	+	0.846196i	$0.678887\pi$
$702$	129.453			0.184406
$703$		−	748.483i		−	1.06470i
$704$	−140.320			−0.199319
$705$		0			0
$706$		−	461.383i		−	0.653517i
$707$	468.609	+	811.871i	0.662814	+	1.14833i
$708$	−51.3772			−0.0725667
$709$	169.799			0.239491			0.119746	−	0.992805i	$-0.461792\pi$
$709$	169.799			0.239491			0.119746	+	0.992805i	$0.461792\pi$
$710$		0			0
$711$	85.5202			0.120282
$712$			216.460i			0.304017i
$713$			842.477i			1.18159i
$714$	209.119	−	120.703i	0.292883	−	0.169051i
$715$		0			0
$716$	510.935			0.713596
$717$			30.4512i			0.0424704i
$718$	419.131			0.583748
$719$			1213.73i			1.68808i	0.536277	+	0.844042i	$0.319830\pi$
$719$			1213.73i			1.68808i	−0.536277	+	0.844042i	$0.680170\pi$
$720$		0			0
$721$	−248.863	−	431.159i	−0.345164	−	0.598001i
$722$	−120.563			−0.166985
$723$	−80.6445			−0.111542
$724$			507.054i			0.700351i
$725$		0			0
$726$			457.205i			0.629758i
$727$			372.922i			0.512960i	0.966550	+	0.256480i	$0.0825628\pi$
$727$			372.922i			0.512960i	−0.966550	+	0.256480i	$0.917437\pi$
$728$	174.358	+	302.078i	0.239503	+	0.414942i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			714.624i			0.977597i
$732$	315.940			0.431613
$733$			421.740i			0.575362i	0.957726	+	0.287681i	$0.0928843\pi$
$733$			421.740i			0.575362i	−0.957726	+	0.287681i	$0.907116\pi$
$734$		−	402.914i		−	0.548929i
$735$		0			0
$736$	87.8895			0.119415
$737$	98.4833			0.133627
$738$		−	5.11525i		−	0.00693123i
$739$	271.839			0.367847			0.183923	−	0.982941i	$-0.441120\pi$
$739$	271.839			0.367847			0.183923	+	0.982941i	$0.441120\pi$
$740$		0			0
$741$		−	506.680i		−	0.683778i
$742$	−442.114	+	255.187i	−0.595841	+	0.343918i
$743$	68.6075			0.0923385			0.0461693	−	0.998934i	$-0.485299\pi$
$743$	68.6075			0.0923385			0.0461693	+	0.998934i	$0.485299\pi$
$744$	265.645			0.357049
$745$		0			0
$746$	231.876			0.310825
$747$		−	151.179i		−	0.202382i
$748$		−	493.992i		−	0.660418i
$749$	55.6898	−	32.1440i	0.0743522	−	0.0429159i
$750$		0			0
$751$	1404.74			1.87049			0.935246	−	0.353999i	$-0.115179\pi$
$751$	1404.74			1.87049			0.935246	+	0.353999i	$0.115179\pi$
$752$		−	367.045i		−	0.488091i
$753$	394.535			0.523951
$754$		−	919.860i		−	1.21997i
$755$		0			0
$756$	−36.3658	−	63.0042i	−0.0481029	−	0.0833389i
$757$	551.876			0.729031			0.364515	−	0.931197i	$-0.381235\pi$
$757$	551.876			0.729031			0.364515	+	0.931197i	$0.381235\pi$
$758$	252.432			0.333023
$759$		−	472.012i		−	0.621887i
$760$		0			0
$761$			664.607i			0.873334i	0.899623	+	0.436667i	$0.143841\pi$
$761$			664.607i			0.873334i	−0.899623	+	0.436667i	$0.856159\pi$
$762$			241.857i			0.317398i
$763$	−671.032	+	387.318i	−0.879466	+	0.507625i
$764$	−572.549			−0.749410
$765$		0			0
$766$			738.423i			0.963999i
$767$	261.274			0.340644
$768$		−	27.7128i		−	0.0360844i
$769$		−	428.695i		−	0.557471i	−0.960368	−	0.278735i	$-0.910085\pi$
$769$		−	428.695i		−	0.557471i	0.960368	−	0.278735i	$-0.0899152\pi$
$770$		0			0
$771$	158.094			0.205050
$772$	396.680			0.513834
$773$			1082.57i			1.40047i	0.713910	+	0.700237i	$0.246922\pi$
$773$			1082.57i			1.40047i	−0.713910	+	0.700237i	$0.753078\pi$
$774$	215.305			0.278172
$775$		0			0
$776$			354.560i			0.456907i
$777$	273.192	+	473.308i	0.351598	+	0.609148i
$778$	−824.429			−1.05968
$779$	−20.0211			−0.0257010
$780$		0			0
$781$	−1417.97			−1.81558
$782$			309.412i			0.395667i
$783$			191.855i			0.245025i
$784$	98.0390	−	169.718i	0.125050	−	0.216478i
$785$		0			0
$786$	12.7561			0.0162291
$787$		−	391.950i		−	0.498030i	−0.968500	−	0.249015i	$-0.919893\pi$
$787$		−	391.950i		−	0.498030i	0.968500	−	0.249015i	$-0.0801069\pi$
$788$	506.747			0.643080
$789$			187.976i			0.238245i
$790$		0			0
$791$	1021.67	−	589.706i	1.29162	−	0.745520i
$792$	−148.832			−0.187919
$793$	−1606.68			−2.02608
$794$			610.592i			0.769007i
$795$		0			0
$796$		−	406.182i		−	0.510278i
$797$			518.451i			0.650504i	0.945627	+	0.325252i	$0.105449\pi$
$797$			518.451i			0.650504i	−0.945627	+	0.325252i	$0.894551\pi$
$798$	−246.598	+	142.336i	−0.309020	+	0.178366i
$799$	1292.17			1.61723
$800$		0			0
$801$			229.591i			0.286630i
$802$	−370.438			−0.461893
$803$		−	1596.90i		−	1.98867i
$804$			19.4501i			0.0241917i
$805$		0			0
$806$	−1350.91			−1.67607
$807$	−609.001			−0.754648
$808$			378.769i			0.468773i
$809$	−244.444			−0.302155			−0.151078	−	0.988522i	$-0.548274\pi$
$809$	−244.444			−0.302155			−0.151078	+	0.988522i	$0.548274\pi$
$810$		0			0
$811$		−	179.191i		−	0.220951i	−0.993879	−	0.110476i	$-0.964763\pi$
$811$		−	179.191i		−	0.220951i	0.993879	−	0.110476i	$-0.0352374\pi$
$812$	−447.691	+	258.406i	−0.551344	+	0.318234i
$813$	671.456			0.825899
$814$	1118.08			1.37356
$815$		0			0
$816$	97.5619			0.119561
$817$		−	842.703i		−	1.03146i
$818$			626.808i			0.766269i
$819$	184.935	+	320.402i	0.225806	+	0.391211i
$820$		0			0
$821$	907.336			1.10516			0.552579	−	0.833460i	$-0.313644\pi$
$821$	907.336			1.10516			0.552579	+	0.833460i	$0.313644\pi$
$822$			12.0328i			0.0146384i
$823$	−946.853			−1.15049			−0.575245	−	0.817981i	$-0.695093\pi$
$823$	−946.853			−1.15049			−0.575245	+	0.817981i	$0.695093\pi$
$824$		−	201.152i		−	0.244117i
$825$		0			0
$826$	−73.3967	−	127.161i	−0.0888580	−	0.153947i
$827$	1016.38			1.22899			0.614497	−	0.788919i	$-0.289359\pi$
$827$	1016.38			1.22899			0.614497	+	0.788919i	$0.289359\pi$
$828$	93.2209			0.112586
$829$		−	1222.70i		−	1.47491i	−0.675394	−	0.737457i	$-0.736027\pi$
$829$		−	1222.70i		−	1.47491i	0.675394	−	0.737457i	$-0.263973\pi$
$830$		0			0
$831$			871.558i			1.04881i
$832$			140.931i			0.169388i
$833$	597.488	+	345.143i	0.717272	+	0.414337i
$834$	33.2452			0.0398624
$835$		0			0
$836$			582.529i			0.696805i
$837$	281.759			0.336629
$838$		−	361.199i		−	0.431025i
$839$		−	1149.98i		−	1.37066i	−0.728235	−	0.685328i	$-0.759659\pi$
$839$		−	1149.98i		−	1.37066i	0.728235	−	0.685328i	$-0.240341\pi$
$840$		0			0
$841$	522.269			0.621010
$842$	−449.549			−0.533906
$843$		−	185.105i		−	0.219579i
$844$	79.8422			0.0945998
$845$		0			0
$846$		−	389.310i		−	0.460177i
$847$	−1131.60	+	653.155i	−1.33601	+	0.771140i
$848$	−206.263			−0.243235
$849$	−147.856			−0.174153
$850$		0			0
$851$	−700.306			−0.822921
$852$		−	280.045i		−	0.328691i
$853$			340.841i			0.399579i	0.979839	+	0.199789i	$0.0640258\pi$
$853$			340.841i			0.399579i	−0.979839	+	0.199789i	$0.935974\pi$
$854$	451.348	+	781.964i	0.528510	+	0.915649i
$855$		0			0
$856$	25.9814			0.0303521
$857$		−	154.862i		−	0.180702i	−0.995910	−	0.0903511i	$-0.971201\pi$
$857$		−	154.862i		−	0.180702i	0.995910	−	0.0903511i	$-0.0287989\pi$
$858$	756.872			0.882135
$859$		−	1186.43i		−	1.38118i	−0.723246	−	0.690590i	$-0.757351\pi$
$859$		−	1186.43i		−	1.38118i	0.723246	−	0.690590i	$-0.242649\pi$
$860$		0			0
$861$	12.6604	−	7.30756i	0.0147043	−	0.00848729i
$862$	−117.584			−0.136408
$863$	−25.3901			−0.0294207			−0.0147104	−	0.999892i	$-0.504683\pi$
$863$	−25.3901			−0.0294207			−0.0147104	+	0.999892i	$0.504683\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$		−	708.948i		−	0.818647i
$867$		−	157.100i		−	0.181199i
$868$	379.496	+	657.481i	0.437207	+	0.757466i
$869$	500.009			0.575385
$870$		0			0
$871$		−	98.9118i		−	0.113561i
$872$	−313.062			−0.359017
$873$			376.068i			0.430776i
$874$		−	364.867i		−	0.417467i
$875$		0			0
$876$	315.384			0.360027
$877$	−1270.43			−1.44861			−0.724304	−	0.689481i	$-0.757839\pi$
$877$	−1270.43			−1.44861			−0.724304	+	0.689481i	$0.757839\pi$
$878$		−	14.3686i		−	0.0163652i
$879$	−270.132			−0.307317
$880$		0			0
$881$		−	20.8647i		−	0.0236830i	−0.999930	−	0.0118415i	$-0.996231\pi$
$881$		−	20.8647i		−	0.0236830i	0.999930	−	0.0118415i	$-0.00376935\pi$
$882$	103.986	−	180.014i	0.117898	−	0.204097i
$883$	−850.321			−0.962990			−0.481495	−	0.876449i	$-0.659906\pi$
$883$	−850.321			−0.962990			−0.481495	+	0.876449i	$0.659906\pi$
$884$	−496.142			−0.561246
$885$		0			0
$886$	284.666			0.321293
$887$		−	347.058i		−	0.391272i	−0.980677	−	0.195636i	$-0.937323\pi$
$887$		−	347.058i		−	0.391272i	0.980677	−	0.195636i	$-0.0626771\pi$
$888$			220.816i			0.248667i
$889$	−598.606	+	345.513i	−0.673347	+	0.388654i
$890$		0			0
$891$	−157.860			−0.177172
$892$		−	441.040i		−	0.494440i
$893$	−1523.76			−1.70634
$894$		−	379.574i		−	0.424579i
$895$		0			0
$896$	68.5903	−	39.5901i	0.0765516	−	0.0441854i
$897$	−474.066			−0.528502
$898$	−852.722			−0.949579
$899$		−	2002.10i		−	2.22703i
$900$		0			0
$901$		−	726.142i		−	0.805929i
$902$		−	29.9072i		−	0.0331565i
$903$	307.581	+	532.888i	0.340622	+	0.590130i
$904$	476.650			0.527267
$905$		0			0
$906$			484.853i			0.535158i
$907$	−808.517			−0.891419			−0.445710	−	0.895178i	$-0.647049\pi$
$907$	−808.517			−0.891419			−0.445710	+	0.895178i	$0.647049\pi$
$908$		−	575.344i		−	0.633639i
$909$			401.745i			0.441964i
$910$		0			0
$911$	290.542			0.318926			0.159463	−	0.987204i	$-0.449024\pi$
$911$	290.542			0.318926			0.159463	+	0.987204i	$0.449024\pi$
$912$	−115.048			−0.126149
$913$		−	883.896i		−	0.968123i
$914$	330.845			0.361974
$915$		0			0
$916$		−	334.962i		−	0.365679i
$917$	18.2232	+	31.5718i	0.0198726	+	0.0344295i
$918$	103.480			0.112723
$919$	−632.051			−0.687759			−0.343880	−	0.939014i	$-0.611741\pi$
$919$	−632.051			−0.687759			−0.343880	+	0.939014i	$0.611741\pi$
$920$		0			0
$921$	858.971			0.932651
$922$		−	759.168i		−	0.823392i
$923$			1424.14i			1.54295i
$924$	−212.619	−	368.365i	−0.230108	−	0.398664i
$925$		0			0
$926$	33.3340			0.0359979
$927$		−	213.354i		−	0.230155i
$928$	−208.865			−0.225070
$929$		−	39.3251i		−	0.0423306i	−0.999776	−	0.0211653i	$-0.993262\pi$
$929$		−	39.3251i		−	0.0423306i	0.999776	−	0.0211653i	$-0.00673762\pi$
$930$		0			0
$931$	−704.573	−	407.001i	−0.756791	−	0.437166i
$932$	−23.2154			−0.0249092
$933$	468.107			0.501722
$934$			1012.73i			1.08429i
$935$		0			0
$936$			149.480i			0.159701i
$937$		−	1178.92i		−	1.25818i	−0.777331	−	0.629092i	$-0.783427\pi$
$937$		−	1178.92i		−	1.25818i	0.777331	−	0.629092i	$-0.216573\pi$
$938$	−48.1398	+	27.7862i	−0.0513218	+	0.0296228i
$939$	−41.0225			−0.0436874
$940$		0			0
$941$		−	818.442i		−	0.869758i	−0.900489	−	0.434879i	$-0.856791\pi$
$941$		−	818.442i		−	0.869758i	0.900489	−	0.434879i	$-0.143209\pi$
$942$	463.154			0.491671
$943$			18.7324i			0.0198646i
$944$		−	59.3253i		−	0.0628446i
$945$		0			0
$946$	1258.82			1.33068
$947$	1154.06			1.21865			0.609324	−	0.792921i	$-0.291441\pi$
$947$	1154.06			1.21865			0.609324	+	0.792921i	$0.291441\pi$
$948$			98.7503i			0.104167i
$949$	−1603.85			−1.69005
$950$		0			0
$951$			6.12843i			0.00644419i
$952$	139.375	+	241.469i	0.146403	+	0.253644i
$953$	−534.547			−0.560910			−0.280455	−	0.959867i	$-0.590485\pi$
$953$	−534.547			−0.560910			−0.280455	+	0.959867i	$0.590485\pi$
$954$	−218.775			−0.229324
$955$		0			0
$956$	−35.1621			−0.0367804
$957$			1121.71i			1.17211i
$958$		−	685.648i		−	0.715708i
$959$	−29.7815	+	17.1898i	−0.0310548	+	0.0179247i
$960$		0			0
$961$	−1979.30			−2.05962
$962$		−	1122.94i		−	1.16730i
$963$	27.5575			0.0286163
$964$		−	93.1203i		−	0.0965978i
$965$		0			0
$966$	133.174	+	230.725i	0.137861	+	0.238846i
$967$	−88.4962			−0.0915163			−0.0457581	−	0.998953i	$-0.514570\pi$
$967$	−88.4962			−0.0915163			−0.0457581	+	0.998953i	$0.514570\pi$
$968$	−527.934			−0.545387
$969$		−	405.021i		−	0.417978i
$970$		0			0
$971$			1732.09i			1.78382i	0.452216	+	0.891908i	$0.350634\pi$
$971$			1732.09i			1.78382i	−0.452216	+	0.891908i	$0.649366\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	47.4936	+	82.2831i	0.0488115	+	0.0845664i
$974$	147.955			0.151904
$975$		0			0
$976$			364.817i			0.373787i
$977$	−83.2486			−0.0852084			−0.0426042	−	0.999092i	$-0.513565\pi$
$977$	−83.2486			−0.0852084			−0.0426042	+	0.999092i	$0.513565\pi$
$978$			659.225i			0.674055i
$979$			1342.34i			1.37114i
$980$		0			0
$981$	−332.053			−0.338484
$982$	−44.8308			−0.0456525
$983$		−	1409.80i		−	1.43418i	−0.696978	−	0.717092i	$-0.745473\pi$
$983$		−	1409.80i		−	1.43418i	0.696978	−	0.717092i	$-0.254527\pi$
$984$	5.90658			0.00600262
$985$		0			0
$986$		−	735.302i		−	0.745742i
$987$	963.556	−	556.162i	0.976248	−	0.563487i
$988$	585.063			0.592169
$989$	−788.460			−0.797230
$990$		0			0
$991$	480.699			0.485064			0.242532	−	0.970143i	$-0.422022\pi$
$991$	480.699			0.485064			0.242532	+	0.970143i	$0.422022\pi$
$992$			306.740i			0.309214i
$993$			591.218i			0.595386i
$994$	693.122	−	400.068i	0.697306	−	0.402483i
$995$		0			0
$996$	174.567			0.175268
$997$			1588.98i			1.59376i	0.604136	+	0.796881i	$0.293518\pi$
$997$			1588.98i			1.59376i	−0.604136	+	0.796881i	$0.706482\pi$
$998$	−746.114			−0.747609
$999$			234.211i			0.234445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.d.601.1	yes	12
5.2	odd	4		1050.3.h.c.349.5		24
5.3	odd	4		1050.3.h.c.349.22		24
5.4	even	2		1050.3.f.c.601.12	yes	12
7.6	odd	2	inner	1050.3.f.d.601.4	yes	12
35.13	even	4		1050.3.h.c.349.6		24
35.27	even	4		1050.3.h.c.349.21		24
35.34	odd	2		1050.3.f.c.601.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.9	✓	12	35.34	odd	2
1050.3.f.c.601.12	yes	12	5.4	even	2
1050.3.f.d.601.1	yes	12	1.1	even	1	trivial
1050.3.f.d.601.4	yes	12	7.6	odd	2	inner
1050.3.h.c.349.5		24	5.2	odd	4
1050.3.h.c.349.6		24	35.13	even	4
1050.3.h.c.349.21		24	35.27	even	4
1050.3.h.c.349.22		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.06258 + 3.49930i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.06258 + 3.49930i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -17.5400 q^{11} -3.46410i q^{12} +17.6164i q^{13} +(8.57378 - 4.94876i) q^{14} +4.00000 q^{16} +14.0819i q^{17} +4.24264 q^{18} -16.6057i q^{19} +(6.06097 + 10.5007i) q^{21} +24.8054 q^{22} -15.5368 q^{23} +4.89898i q^{24} -24.9133i q^{26} +5.19615i q^{27} +(-12.1252 + 6.99861i) q^{28} +36.9225 q^{29} -54.2245i q^{31} -5.65685 q^{32} +30.3802i q^{33} -19.9147i q^{34} -6.00000 q^{36} +45.0739 q^{37} +23.4840i q^{38} +30.5124 q^{39} -1.20567i q^{41} +(-8.57151 - 14.8502i) q^{42} +50.7479 q^{43} -35.0801 q^{44} +21.9724 q^{46} -91.7612i q^{47} -6.92820i q^{48} +(24.5098 - 42.4296i) q^{49} +24.3905 q^{51} +35.2327i q^{52} -51.5658 q^{53} -7.34847i q^{54} +(17.1476 - 9.89752i) q^{56} -28.7619 q^{57} -52.2163 q^{58} -14.8313i q^{59} +91.2041i q^{61} +76.6850i q^{62} +(18.1877 - 10.4979i) q^{63} +8.00000 q^{64} -42.9641i q^{66} -5.61477 q^{67} +28.1637i q^{68} +26.9106i q^{69} +80.8420 q^{71} +8.48528 q^{72} +91.0434i q^{73} -63.7442 q^{74} -33.2114i q^{76} +(106.338 - 61.3779i) q^{77} -43.1511 q^{78} -28.5067 q^{79} +9.00000 q^{81} +1.70508i q^{82} +50.3930i q^{83} +(12.1219 + 21.0014i) q^{84} -71.7683 q^{86} -63.9516i q^{87} +49.6107 q^{88} -76.5302i q^{89} +(-61.6450 - 106.801i) q^{91} -31.0736 q^{92} -93.9196 q^{93} +129.770i q^{94} +9.79796i q^{96} -125.356i q^{97} +(-34.6620 + 60.0045i) q^{98} +52.6201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9}+O(q^{10}) \) 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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