LMFDB - Embedded newform 1050.3.f.d.601.2

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			601.2
Root			$4.23503 + 7.33529i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.d.601.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(2.03595 - 6.69738i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(2.03595 - 6.69738i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -5.30397 q^{11} -3.46410i q^{12} -15.0546i q^{13} +(-2.87926 + 9.47153i) q^{14} +4.00000 q^{16} +1.80427i q^{17} +4.24264 q^{18} -7.35835i q^{19} +(-11.6002 - 3.52636i) q^{21} +7.50095 q^{22} +15.8246 q^{23} +4.89898i q^{24} +21.2904i q^{26} +5.19615i q^{27} +(4.07189 - 13.3948i) q^{28} -44.3922 q^{29} -6.10279i q^{31} -5.65685 q^{32} +9.18674i q^{33} -2.55162i q^{34} -6.00000 q^{36} -36.0606 q^{37} +10.4063i q^{38} -26.0753 q^{39} +18.8619i q^{41} +(16.4052 + 4.98703i) q^{42} +36.0186 q^{43} -10.6079 q^{44} -22.3793 q^{46} -26.7314i q^{47} -6.92820i q^{48} +(-40.7099 - 27.2710i) q^{49} +3.12509 q^{51} -30.1092i q^{52} +80.7350 q^{53} -7.34847i q^{54} +(-5.75852 + 18.9431i) q^{56} -12.7450 q^{57} +62.7801 q^{58} +38.7017i q^{59} +25.5365i q^{61} +8.63065i q^{62} +(-6.10784 + 20.0921i) q^{63} +8.00000 q^{64} -12.9920i q^{66} -90.4318 q^{67} +3.60854i q^{68} -27.4089i q^{69} -41.4375 q^{71} +8.48528 q^{72} -106.712i q^{73} +50.9974 q^{74} -14.7167i q^{76} +(-10.7986 + 35.5227i) q^{77} +36.8761 q^{78} -16.1960 q^{79} +9.00000 q^{81} -26.6748i q^{82} +34.7857i q^{83} +(-23.2004 - 7.05272i) q^{84} -50.9379 q^{86} +76.8896i q^{87} +15.0019 q^{88} +58.7705i q^{89} +(-100.826 - 30.6503i) q^{91} +31.6491 q^{92} -10.5703 q^{93} +37.8039i q^{94} +9.79796i q^{96} +140.734i q^{97} +(57.5724 + 38.5670i) q^{98} +15.9119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.03595	−	6.69738i	0.290849	−	0.956769i
$7$	2.03595	−	6.69738i	0.290849	−	0.956769i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−5.30397			−0.482179			−0.241090	−	0.970503i	$-0.577505\pi$
$11$	−5.30397			−0.482179			−0.241090	+	0.970503i	$0.577505\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	15.0546i		−	1.15805i	−0.815311	−	0.579023i	$-0.803434\pi$
$13$		−	15.0546i		−	1.15805i	0.815311	−	0.579023i	$-0.196566\pi$
$14$	−2.87926	+	9.47153i	−0.205662	+	0.676538i
$15$		0			0
$16$	4.00000			0.250000
$17$			1.80427i			0.106133i	0.998591	+	0.0530667i	$0.0168996\pi$
$17$			1.80427i			0.106133i	−0.998591	+	0.0530667i	$0.983100\pi$
$18$	4.24264			0.235702
$19$		−	7.35835i		−	0.387282i	−0.981073	−	0.193641i	$-0.937970\pi$
$19$		−	7.35835i		−	0.387282i	0.981073	−	0.193641i	$-0.0620296\pi$
$20$		0			0
$21$	−11.6002	−	3.52636i	−0.552391	−	0.167922i
$22$	7.50095			0.340952
$23$	15.8246			0.688024			0.344012	−	0.938965i	$-0.388214\pi$
$23$	15.8246			0.688024			0.344012	+	0.938965i	$0.388214\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$			21.2904i			0.818862i
$27$			5.19615i			0.192450i
$28$	4.07189	−	13.3948i	0.145425	−	0.478384i
$29$	−44.3922			−1.53077			−0.765384	−	0.643574i	$-0.777451\pi$
$29$	−44.3922			−1.53077			−0.765384	+	0.643574i	$0.777451\pi$
$30$		0			0
$31$		−	6.10279i		−	0.196864i	−0.995144	−	0.0984322i	$-0.968617\pi$
$31$		−	6.10279i		−	0.196864i	0.995144	−	0.0984322i	$-0.0313827\pi$
$32$	−5.65685			−0.176777
$33$			9.18674i			0.278386i
$34$		−	2.55162i		−	0.0750477i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−36.0606			−0.974611			−0.487305	−	0.873232i	$-0.662020\pi$
$37$	−36.0606			−0.974611			−0.487305	+	0.873232i	$0.662020\pi$
$38$			10.4063i			0.273849i
$39$	−26.0753			−0.668598
$40$		0			0
$41$			18.8619i			0.460047i	0.973185	+	0.230024i	$0.0738803\pi$
$41$			18.8619i			0.460047i	−0.973185	+	0.230024i	$0.926120\pi$
$42$	16.4052	+	4.98703i	0.390599	+	0.118739i
$43$	36.0186			0.837641			0.418820	−	0.908069i	$-0.362444\pi$
$43$	36.0186			0.837641			0.418820	+	0.908069i	$0.362444\pi$
$44$	−10.6079			−0.241090
$45$		0			0
$46$	−22.3793			−0.486506
$47$		−	26.7314i		−	0.568753i	−0.958713	−	0.284376i	$-0.908213\pi$
$47$		−	26.7314i		−	0.568753i	0.958713	−	0.284376i	$-0.0917866\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−40.7099	−	27.2710i	−0.830813	−	0.556551i
$50$		0			0
$51$	3.12509			0.0612762
$52$		−	30.1092i		−	0.579023i
$53$	80.7350			1.52330			0.761651	−	0.647987i	$-0.224389\pi$
$53$	80.7350			1.52330			0.761651	+	0.647987i	$0.224389\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−5.75852	+	18.9431i	−0.102831	+	0.338269i
$57$	−12.7450			−0.223597
$58$	62.7801			1.08242
$59$			38.7017i			0.655961i	0.944684	+	0.327981i	$0.106368\pi$
$59$			38.7017i			0.655961i	−0.944684	+	0.327981i	$0.893632\pi$
$60$		0			0
$61$			25.5365i			0.418630i	0.977848	+	0.209315i	$0.0671235\pi$
$61$			25.5365i			0.418630i	−0.977848	+	0.209315i	$0.932877\pi$
$62$			8.63065i			0.139204i
$63$	−6.10784	+	20.0921i	−0.0969498	+	0.318923i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	12.9920i		−	0.196849i
$67$	−90.4318			−1.34973			−0.674864	−	0.737942i	$-0.735798\pi$
$67$	−90.4318			−1.34973			−0.674864	+	0.737942i	$0.735798\pi$
$68$			3.60854i			0.0530667i
$69$		−	27.4089i		−	0.397231i
$70$		0			0
$71$	−41.4375			−0.583626			−0.291813	−	0.956475i	$-0.594259\pi$
$71$	−41.4375			−0.583626			−0.291813	+	0.956475i	$0.594259\pi$
$72$	8.48528			0.117851
$73$		−	106.712i		−	1.46181i	−0.682481	−	0.730903i	$-0.739099\pi$
$73$		−	106.712i		−	1.46181i	0.682481	−	0.730903i	$-0.260901\pi$
$74$	50.9974			0.689154
$75$		0			0
$76$		−	14.7167i		−	0.193641i
$77$	−10.7986	+	35.5227i	−0.140241	+	0.461334i
$78$	36.8761			0.472770
$79$	−16.1960			−0.205013			−0.102507	−	0.994732i	$-0.532686\pi$
$79$	−16.1960			−0.205013			−0.102507	+	0.994732i	$0.532686\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	26.6748i		−	0.325302i
$83$			34.7857i			0.419105i	0.977797	+	0.209552i	$0.0672006\pi$
$83$			34.7857i			0.419105i	−0.977797	+	0.209552i	$0.932799\pi$
$84$	−23.2004	−	7.05272i	−0.276195	−	0.0839610i
$85$		0			0
$86$	−50.9379			−0.592302
$87$			76.8896i			0.883789i
$88$	15.0019			0.170476
$89$			58.7705i			0.660342i	0.943921	+	0.330171i	$0.107106\pi$
$89$			58.7705i			0.660342i	−0.943921	+	0.330171i	$0.892894\pi$
$90$		0			0
$91$	−100.826	−	30.6503i	−1.10798	−	0.336817i
$92$	31.6491			0.344012
$93$	−10.5703			−0.113660
$94$			37.8039i			0.402169i
$95$		0			0
$96$			9.79796i			0.102062i
$97$			140.734i			1.45087i	0.688293	+	0.725433i	$0.258360\pi$
$97$			140.734i			1.45087i	−0.688293	+	0.725433i	$0.741640\pi$
$98$	57.5724	+	38.5670i	0.587474	+	0.393541i
$99$	15.9119			0.160726
$100$		0			0
$101$		−	96.7964i		−	0.958380i	−0.877711	−	0.479190i	$-0.840930\pi$
$101$		−	96.7964i		−	0.958380i	0.877711	−	0.479190i	$-0.159070\pi$
$102$	−4.41954			−0.0433288
$103$		−	102.523i		−	0.995374i	−0.867357	−	0.497687i	$-0.834183\pi$
$103$		−	102.523i		−	0.995374i	0.867357	−	0.497687i	$-0.165817\pi$
$104$			42.5808i			0.409431i
$105$		0			0
$106$	−114.177			−1.07714
$107$	−139.632			−1.30497			−0.652487	−	0.757800i	$-0.726274\pi$
$107$	−139.632			−1.30497			−0.652487	+	0.757800i	$0.726274\pi$
$108$			10.3923i			0.0962250i
$109$	−27.3238			−0.250677			−0.125338	−	0.992114i	$-0.540002\pi$
$109$	−27.3238			−0.250677			−0.125338	+	0.992114i	$0.540002\pi$
$110$		0			0
$111$			62.4588i			0.562692i
$112$	8.14378	−	26.7895i	0.0727123	−	0.239192i
$113$	46.4392			0.410966			0.205483	−	0.978661i	$-0.434123\pi$
$113$	46.4392			0.410966			0.205483	+	0.978661i	$0.434123\pi$
$114$	18.0242			0.158107
$115$		0			0
$116$	−88.7845			−0.765384
$117$			45.1638i			0.386015i
$118$		−	54.7325i		−	0.463835i
$119$	12.0839	+	3.67339i	0.101545	+	0.0308688i
$120$		0			0
$121$	−92.8679			−0.767503
$122$		−	36.1140i		−	0.296016i
$123$	32.6698			0.265608
$124$		−	12.2056i		−	0.0984322i
$125$		0			0
$126$	8.63779	−	28.4146i	0.0685538	−	0.225513i
$127$	−60.7189			−0.478101			−0.239051	−	0.971007i	$-0.576836\pi$
$127$	−60.7189			−0.478101			−0.239051	+	0.971007i	$0.576836\pi$
$128$	−11.3137			−0.0883883
$129$		−	62.3860i		−	0.483612i
$130$		0			0
$131$			202.250i			1.54389i	0.635688	+	0.771946i	$0.280717\pi$
$131$			202.250i			1.54389i	−0.635688	+	0.771946i	$0.719283\pi$
$132$			18.3735i			0.139193i
$133$	−49.2817	−	14.9812i	−0.370539	−	0.112641i
$134$	127.890			0.954402
$135$		0			0
$136$		−	5.10324i		−	0.0375238i
$137$	−118.169			−0.862548			−0.431274	−	0.902221i	$-0.641936\pi$
$137$	−118.169			−0.862548			−0.431274	+	0.902221i	$0.641936\pi$
$138$			38.7621i			0.280885i
$139$			256.027i			1.84192i	0.389658	+	0.920959i	$0.372593\pi$
$139$			256.027i			1.84192i	−0.389658	+	0.920959i	$0.627407\pi$
$140$		0			0
$141$	−46.3001			−0.328370
$142$	58.6014			0.412686
$143$			79.8491i			0.558385i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$			150.913i			1.03365i
$147$	−47.2348	+	70.5115i	−0.321325	+	0.479670i
$148$	−72.1212			−0.487305
$149$	−264.538			−1.77543			−0.887713	−	0.460398i	$-0.847707\pi$
$149$	−264.538			−1.77543			−0.887713	+	0.460398i	$0.847707\pi$
$150$		0			0
$151$	12.8709			0.0852377			0.0426188	−	0.999091i	$-0.486430\pi$
$151$	12.8709			0.0852377			0.0426188	+	0.999091i	$0.486430\pi$
$152$			20.8126i			0.136925i
$153$		−	5.41281i		−	0.0353778i
$154$	15.2715	−	50.2367i	0.0991657	−	0.326212i
$155$		0			0
$156$	−52.1507			−0.334299
$157$		−	203.635i		−	1.29704i	−0.761200	−	0.648518i	$-0.775389\pi$
$157$		−	203.635i		−	1.29704i	0.761200	−	0.648518i	$-0.224611\pi$
$158$	22.9047			0.144966
$159$		−	139.837i		−	0.879479i
$160$		0			0
$161$	32.2179	−	105.983i	0.200111	−	0.658280i
$162$	−12.7279			−0.0785674
$163$	−261.841			−1.60639			−0.803194	−	0.595718i	$-0.796868\pi$
$163$	−261.841			−1.60639			−0.803194	+	0.595718i	$0.796868\pi$
$164$			37.7239i			0.230024i
$165$		0			0
$166$		−	49.1944i		−	0.296352i
$167$			90.7037i			0.543136i	0.962419	+	0.271568i	$0.0875422\pi$
$167$			90.7037i			0.543136i	−0.962419	+	0.271568i	$0.912458\pi$
$168$	32.8103	+	9.97405i	0.195300	+	0.0593694i
$169$	−57.6409			−0.341070
$170$		0			0
$171$			22.0750i			0.129094i
$172$	72.0371			0.418820
$173$			248.626i			1.43714i	0.695452	+	0.718572i	$0.255204\pi$
$173$			248.626i			1.43714i	−0.695452	+	0.718572i	$0.744796\pi$
$174$		−	108.738i		−	0.624933i
$175$		0			0
$176$	−21.2159			−0.120545
$177$	67.0333			0.378719
$178$		−	83.1140i		−	0.466933i
$179$	138.861			0.775761			0.387880	−	0.921710i	$-0.373207\pi$
$179$	138.861			0.775761			0.387880	+	0.921710i	$0.373207\pi$
$180$		0			0
$181$		−	148.488i		−	0.820375i	−0.912001	−	0.410187i	$-0.865463\pi$
$181$		−	148.488i		−	0.820375i	0.912001	−	0.410187i	$-0.134537\pi$
$182$	142.590	+	43.3461i	0.783462	+	0.238166i
$183$	44.2304			0.241696
$184$	−44.7586			−0.243253
$185$		0			0
$186$	14.9487			0.0803695
$187$		−	9.56979i		−	0.0511753i
$188$		−	53.4628i		−	0.284376i
$189$	34.8006	+	10.5791i	0.184130	+	0.0559740i
$190$		0			0
$191$	−46.0781			−0.241247			−0.120623	−	0.992698i	$-0.538489\pi$
$191$	−46.0781			−0.241247			−0.120623	+	0.992698i	$0.538489\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−26.4406			−0.136998			−0.0684991	−	0.997651i	$-0.521821\pi$
$193$	−26.4406			−0.136998			−0.0684991	+	0.997651i	$0.521821\pi$
$194$		−	199.028i		−	1.02592i
$195$		0			0
$196$	−81.4197	−	54.5420i	−0.415407	−	0.278276i
$197$	−286.547			−1.45455			−0.727277	−	0.686345i	$-0.759214\pi$
$197$	−286.547			−1.45455			−0.727277	+	0.686345i	$0.759214\pi$
$198$	−22.5028			−0.113651
$199$		−	34.4563i		−	0.173147i	−0.996245	−	0.0865737i	$-0.972408\pi$
$199$		−	34.4563i		−	0.173147i	0.996245	−	0.0865737i	$-0.0275918\pi$
$200$		0			0
$201$			156.632i			0.779266i
$202$			136.891i			0.677677i
$203$	−90.3802	+	297.312i	−0.445223	+	1.46459i
$204$	6.25017			0.0306381
$205$		0			0
$206$			144.990i			0.703835i
$207$	−47.4737			−0.229341
$208$		−	60.2184i		−	0.289511i
$209$			39.0285i			0.186739i
$210$		0			0
$211$	121.627			0.576432			0.288216	−	0.957565i	$-0.406938\pi$
$211$	121.627			0.576432			0.288216	+	0.957565i	$0.406938\pi$
$212$	161.470			0.761651
$213$			71.7718i			0.336957i
$214$	197.470			0.922756
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−40.8727	−	12.4250i	−0.188354	−	0.0572579i
$218$	38.6416			0.177255
$219$	−184.830			−0.843974
$220$		0			0
$221$	27.1625			0.122907
$222$		−	88.3301i		−	0.397883i
$223$		−	302.025i		−	1.35437i	−0.735811	−	0.677187i	$-0.763199\pi$
$223$		−	302.025i		−	1.35437i	0.735811	−	0.677187i	$-0.236801\pi$
$224$	−11.5170	+	37.8861i	−0.0514154	+	0.169134i
$225$		0			0
$226$	−65.6749			−0.290597
$227$		−	159.784i		−	0.703892i	−0.936020	−	0.351946i	$-0.885520\pi$
$227$		−	159.784i		−	0.703892i	0.936020	−	0.351946i	$-0.114480\pi$
$228$	−25.4901			−0.111799
$229$			46.0123i			0.200927i	0.994941	+	0.100463i	$0.0320325\pi$
$229$			46.0123i			0.200927i	−0.994941	+	0.100463i	$0.967967\pi$
$230$		0			0
$231$	61.5271	+	18.7037i	0.266351	+	0.0809684i
$232$	125.560			0.541208
$233$	97.3113			0.417645			0.208822	−	0.977954i	$-0.433037\pi$
$233$	97.3113			0.417645			0.208822	+	0.977954i	$0.433037\pi$
$234$		−	63.8712i		−	0.272954i
$235$		0			0
$236$			77.4034i			0.327981i
$237$			28.0524i			0.118364i
$238$	−17.0892	−	5.19496i	−0.0718033	−	0.0218276i
$239$	124.280			0.520000			0.260000	−	0.965609i	$-0.416278\pi$
$239$	124.280			0.520000			0.260000	+	0.965609i	$0.416278\pi$
$240$		0			0
$241$		−	332.949i		−	1.38153i	−0.723078	−	0.690766i	$-0.757273\pi$
$241$		−	332.949i		−	1.38153i	0.723078	−	0.690766i	$-0.242727\pi$
$242$	131.335			0.542707
$243$		−	15.5885i		−	0.0641500i
$244$			51.0729i			0.209315i
$245$		0			0
$246$	−46.2021			−0.187813
$247$	−110.777			−0.448490
$248$			17.2613i			0.0696020i
$249$	60.2506			0.241970
$250$		0			0
$251$			154.118i			0.614018i	0.951707	+	0.307009i	$0.0993281\pi$
$251$			154.118i			0.614018i	−0.951707	+	0.307009i	$0.900672\pi$
$252$	−12.2157	+	40.1843i	−0.0484749	+	0.159461i
$253$	−83.9329			−0.331751
$254$	85.8695			0.338069
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	410.364i		−	1.59675i	−0.602164	−	0.798373i	$-0.705694\pi$
$257$		−	410.364i		−	1.59675i	0.602164	−	0.798373i	$-0.294306\pi$
$258$			88.2271i			0.341965i
$259$	−73.4174	+	241.512i	−0.283465	+	0.932477i
$260$		0			0
$261$	133.177			0.510256
$262$		−	286.025i		−	1.09170i
$263$	−342.998			−1.30418			−0.652088	−	0.758143i	$-0.726107\pi$
$263$	−342.998			−1.30418			−0.652088	+	0.758143i	$0.726107\pi$
$264$		−	25.9840i		−	0.0984244i
$265$		0			0
$266$	69.6948	+	21.1866i	0.262011	+	0.0796489i
$267$	101.793			0.381249
$268$	−180.864			−0.674864
$269$		−	238.076i		−	0.885042i	−0.896758	−	0.442521i	$-0.854084\pi$
$269$		−	238.076i		−	0.885042i	0.896758	−	0.442521i	$-0.145916\pi$
$270$		0			0
$271$			32.6454i			0.120463i	0.998184	+	0.0602313i	$0.0191838\pi$
$271$			32.6454i			0.120463i	−0.998184	+	0.0602313i	$0.980816\pi$
$272$			7.21707i			0.0265334i
$273$	−53.0879	+	174.636i	−0.194461	+	0.639694i
$274$	167.116			0.609914
$275$		0			0
$276$		−	54.8179i		−	0.198615i
$277$	−230.271			−0.831301			−0.415651	−	0.909524i	$-0.636446\pi$
$277$	−230.271			−0.831301			−0.415651	+	0.909524i	$0.636446\pi$
$278$		−	362.076i		−	1.30243i
$279$			18.3084i			0.0656214i
$280$		0			0
$281$	486.859			1.73260			0.866298	−	0.499528i	$-0.166493\pi$
$281$	486.859			1.73260			0.866298	+	0.499528i	$0.166493\pi$
$282$	65.4783			0.232192
$283$		−	324.645i		−	1.14716i	−0.819151	−	0.573578i	$-0.805555\pi$
$283$		−	324.645i		−	1.14716i	0.819151	−	0.573578i	$-0.194445\pi$
$284$	−82.8749			−0.291813
$285$		0			0
$286$		−	112.924i		−	0.394838i
$287$	126.326	+	38.4019i	0.440159	+	0.133804i
$288$	16.9706			0.0589256
$289$	285.745			0.988736
$290$		0			0
$291$	243.758			0.837658
$292$		−	213.424i		−	0.730903i
$293$			128.334i			0.438000i	0.975725	+	0.219000i	$0.0702795\pi$
$293$			128.334i			0.438000i	−0.975725	+	0.219000i	$0.929721\pi$
$294$	66.8001	−	99.7184i	0.227211	−	0.339178i
$295$		0			0
$296$	101.995			0.344577
$297$		−	27.5602i		−	0.0927954i
$298$	374.114			1.25542
$299$		−	238.232i		−	0.796763i
$300$		0			0
$301$	73.3318	−	241.230i	0.243627	−	0.801429i
$302$	−18.2022			−0.0602721
$303$	−167.656			−0.553321
$304$		−	29.4334i		−	0.0968204i
$305$		0			0
$306$			7.65486i			0.0250159i
$307$			290.110i			0.944983i	0.881335	+	0.472492i	$0.156645\pi$
$307$			290.110i			0.944983i	−0.881335	+	0.472492i	$0.843355\pi$
$308$	−21.5972	+	71.0454i	−0.0701207	+	0.230667i
$309$	−177.576			−0.574679
$310$		0			0
$311$		−	76.1670i		−	0.244910i	−0.992474	−	0.122455i	$-0.960923\pi$
$311$		−	76.1670i		−	0.244910i	0.992474	−	0.122455i	$-0.0390767\pi$
$312$	73.7522			0.236385
$313$		−	527.145i		−	1.68417i	−0.539344	−	0.842085i	$-0.681328\pi$
$313$		−	527.145i		−	1.68417i	0.539344	−	0.842085i	$-0.318672\pi$
$314$			287.983i			0.917142i
$315$		0			0
$316$	−32.3921			−0.102507
$317$	488.328			1.54047			0.770233	−	0.637763i	$-0.220140\pi$
$317$	488.328			1.54047			0.770233	+	0.637763i	$0.220140\pi$
$318$			197.760i			0.621886i
$319$	235.455			0.738104
$320$		0			0
$321$			241.850i			0.753427i
$322$	−45.5630	+	149.883i	−0.141500	+	0.465474i
$323$	13.2764			0.0411035
$324$	18.0000			0.0555556
$325$		0			0
$326$	370.299			1.13589
$327$			47.3261i			0.144728i
$328$		−	53.3496i		−	0.162651i
$329$	−179.030	−	54.4236i	−0.544165	−	0.165421i
$330$		0			0
$331$	519.849			1.57054			0.785271	−	0.619152i	$-0.212524\pi$
$331$	519.849			1.57054			0.785271	+	0.619152i	$0.212524\pi$
$332$			69.5714i			0.209552i
$333$	108.182			0.324870
$334$		−	128.274i		−	0.384055i
$335$		0			0
$336$	−46.4008	−	14.1054i	−0.138098	−	0.0419805i
$337$	460.233			1.36568			0.682838	−	0.730570i	$-0.260745\pi$
$337$	460.233			1.36568			0.682838	+	0.730570i	$0.260745\pi$
$338$	81.5165			0.241173
$339$		−	80.4350i		−	0.237271i
$340$		0			0
$341$			32.3690i			0.0949238i
$342$		−	31.2188i		−	0.0912831i
$343$	−265.527	+	217.127i	−0.774132	+	0.633024i
$344$	−101.876			−0.296151
$345$		0			0
$346$		−	351.610i		−	1.01621i
$347$	−5.51518			−0.0158939			−0.00794695	−	0.999968i	$-0.502530\pi$
$347$	−5.51518			−0.0158939			−0.00794695	+	0.999968i	$0.502530\pi$
$348$			153.779i			0.441894i
$349$			563.892i			1.61574i	0.589364	+	0.807868i	$0.299378\pi$
$349$			563.892i			1.61574i	−0.589364	+	0.807868i	$0.700622\pi$
$350$		0			0
$351$	78.2260			0.222866
$352$	30.0038			0.0852380
$353$			274.152i			0.776633i	0.921526	+	0.388317i	$0.126943\pi$
$353$			274.152i			0.776633i	−0.921526	+	0.388317i	$0.873057\pi$
$354$	−94.7994			−0.267795
$355$		0			0
$356$			117.541i			0.330171i
$357$	6.36250	−	20.9299i	0.0178221	−	0.0586271i
$358$	−196.379			−0.548546
$359$	−65.4883			−0.182419			−0.0912093	−	0.995832i	$-0.529073\pi$
$359$	−65.4883			−0.182419			−0.0912093	+	0.995832i	$0.529073\pi$
$360$		0			0
$361$	306.855			0.850013
$362$			209.993i			0.580092i
$363$			160.852i			0.443118i
$364$	−201.653	−	61.3007i	−0.553991	−	0.168408i
$365$		0			0
$366$	−62.5513			−0.170905
$367$			159.838i			0.435526i	0.976002	+	0.217763i	$0.0698760\pi$
$367$			159.838i			0.435526i	−0.976002	+	0.217763i	$0.930124\pi$
$368$	63.2982			0.172006
$369$		−	56.5858i		−	0.153349i
$370$		0			0
$371$	164.372	−	540.713i	0.443051	−	1.45745i
$372$	−21.1407			−0.0568298
$373$	470.755			1.26208			0.631039	−	0.775751i	$-0.282629\pi$
$373$	470.755			1.26208			0.631039	+	0.775751i	$0.282629\pi$
$374$			13.5337i			0.0361864i
$375$		0			0
$376$			75.6078i			0.201085i
$377$			668.307i			1.77270i
$378$	−49.2155	−	14.9611i	−0.130200	−	0.0395796i
$379$	61.4701			0.162190			0.0810951	−	0.996706i	$-0.474158\pi$
$379$	61.4701			0.162190			0.0810951	+	0.996706i	$0.474158\pi$
$380$		0			0
$381$			105.168i			0.276032i
$382$	65.1643			0.170587
$383$			120.113i			0.313611i	0.987629	+	0.156806i	$0.0501196\pi$
$383$			120.113i			0.313611i	−0.987629	+	0.156806i	$0.949880\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	37.3927			0.0968723
$387$	−108.056			−0.279214
$388$			281.468i			0.725433i
$389$	309.597			0.795879			0.397939	−	0.917412i	$-0.369725\pi$
$389$	309.597			0.795879			0.397939	+	0.917412i	$0.369725\pi$
$390$		0			0
$391$			28.5517i			0.0730224i
$392$	115.145	+	77.1341i	0.293737	+	0.196771i
$393$	350.307			0.891367
$394$	405.239			1.02852
$395$		0			0
$396$	31.8238			0.0803632
$397$		−	754.188i		−	1.89972i	−0.312680	−	0.949858i	$-0.601227\pi$
$397$		−	754.188i		−	1.89972i	0.312680	−	0.949858i	$-0.398773\pi$
$398$			48.7286i			0.122434i
$399$	−25.9482	+	85.3584i	−0.0650331	+	0.213931i
$400$		0			0
$401$	235.697			0.587774			0.293887	−	0.955840i	$-0.405051\pi$
$401$	235.697			0.587774			0.293887	+	0.955840i	$0.405051\pi$
$402$		−	221.512i		−	0.551024i
$403$	−91.8751			−0.227978
$404$		−	193.593i		−	0.479190i
$405$		0			0
$406$	127.817	−	420.462i	0.314820	−	1.03562i
$407$	191.264			0.469937
$408$	−8.83908			−0.0216644
$409$		−	81.3407i		−	0.198877i	−0.995044	−	0.0994385i	$-0.968295\pi$
$409$		−	81.3407i		−	0.198877i	0.995044	−	0.0994385i	$-0.0317047\pi$
$410$		0			0
$411$			204.675i			0.497993i
$412$		−	205.047i		−	0.497687i
$413$	259.200	+	78.7946i	0.627603	+	0.190786i
$414$	67.1379			0.162169
$415$		0			0
$416$			85.1617i			0.204716i
$417$	443.451			1.06343
$418$		−	55.1946i		−	0.132044i
$419$		−	213.030i		−	0.508424i	−0.967149	−	0.254212i	$-0.918184\pi$
$419$		−	213.030i		−	0.508424i	0.967149	−	0.254212i	$-0.0818161\pi$
$420$		0			0
$421$	416.836			0.990108			0.495054	−	0.868862i	$-0.335148\pi$
$421$	416.836			0.990108			0.495054	+	0.868862i	$0.335148\pi$
$422$	−172.007			−0.407599
$423$			80.1942i			0.189584i
$424$	−228.353			−0.538569
$425$		0			0
$426$		−	101.501i		−	0.238264i
$427$	171.027	+	51.9908i	0.400533	+	0.121758i
$428$	−279.265			−0.652487
$429$	138.303			0.322384
$430$		0			0
$431$	−331.912			−0.770096			−0.385048	−	0.922896i	$-0.625815\pi$
$431$	−331.912			−0.770096			−0.385048	+	0.922896i	$0.625815\pi$
$432$			20.7846i			0.0481125i
$433$		−	304.120i		−	0.702356i	−0.936309	−	0.351178i	$-0.885781\pi$
$433$		−	304.120i		−	0.702356i	0.936309	−	0.351178i	$-0.114219\pi$
$434$	57.8028	+	17.5715i	0.133186	+	0.0404874i
$435$		0			0
$436$	−54.6475			−0.125338
$437$		−	116.443i		−	0.266459i
$438$	261.390			0.596780
$439$		−	24.3758i		−	0.0555258i	−0.999615	−	0.0277629i	$-0.991162\pi$
$439$		−	24.3758i		−	0.0555258i	0.999615	−	0.0277629i	$-0.00883834\pi$
$440$		0			0
$441$	122.130	+	81.8130i	0.276938	+	0.185517i
$442$	−38.4136			−0.0869087
$443$	30.3119			0.0684241			0.0342121	−	0.999415i	$-0.489108\pi$
$443$	30.3119			0.0684241			0.0342121	+	0.999415i	$0.489108\pi$
$444$			124.918i			0.281346i
$445$		0			0
$446$			427.128i			0.957687i
$447$			458.194i			1.02504i
$448$	16.2876	−	53.5791i	0.0363562	−	0.119596i
$449$	−550.099			−1.22517			−0.612583	−	0.790407i	$-0.709869\pi$
$449$	−550.099			−1.22517			−0.612583	+	0.790407i	$0.709869\pi$
$450$		0			0
$451$		−	100.043i		−	0.221825i
$452$	92.8783			0.205483
$453$		−	22.2930i		−	0.0492120i
$454$			225.968i			0.497727i
$455$		0			0
$456$	36.0484			0.0790535
$457$	477.234			1.04428			0.522138	−	0.852861i	$-0.325135\pi$
$457$	477.234			1.04428			0.522138	+	0.852861i	$0.325135\pi$
$458$		−	65.0712i		−	0.142077i
$459$	−9.37526			−0.0204254
$460$		0			0
$461$		−	860.755i		−	1.86715i	−0.358386	−	0.933574i	$-0.616673\pi$
$461$		−	860.755i		−	1.86715i	0.358386	−	0.933574i	$-0.383327\pi$
$462$	−87.0125	−	26.4510i	−0.188339	−	0.0572533i
$463$	−774.505			−1.67280			−0.836398	−	0.548122i	$-0.815343\pi$
$463$	−774.505			−1.67280			−0.836398	+	0.548122i	$0.815343\pi$
$464$	−177.569			−0.382692
$465$		0			0
$466$	−137.619			−0.295320
$467$		−	769.862i		−	1.64853i	−0.566207	−	0.824263i	$-0.691590\pi$
$467$		−	769.862i		−	1.64853i	0.566207	−	0.824263i	$-0.308410\pi$
$468$			90.3276i			0.193008i
$469$	−184.114	+	605.656i	−0.392568	+	1.29138i
$470$		0			0
$471$	−352.705			−0.748844
$472$		−	109.465i		−	0.231917i
$473$	−191.041			−0.403893
$474$		−	39.6720i		−	0.0836962i
$475$		0			0
$476$	24.1678	+	7.34679i	0.0507726	+	0.0154344i
$477$	−242.205			−0.507767
$478$	−175.758			−0.367695
$479$		−	724.734i		−	1.51302i	−0.653985	−	0.756508i	$-0.726904\pi$
$479$		−	724.734i		−	1.51302i	0.653985	−	0.756508i	$-0.273096\pi$
$480$		0			0
$481$			542.878i			1.12864i
$482$			470.861i			0.976891i
$483$	−183.568	−	55.8031i	−0.380058	−	0.115534i
$484$	−185.736			−0.383752
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	−58.9904			−0.121130			−0.0605651	−	0.998164i	$-0.519290\pi$
$487$	−58.9904			−0.121130			−0.0605651	+	0.998164i	$0.519290\pi$
$488$		−	72.2280i		−	0.148008i
$489$			453.522i			0.927448i
$490$		0			0
$491$	−574.652			−1.17037			−0.585185	−	0.810900i	$-0.698978\pi$
$491$	−574.652			−1.17037			−0.585185	+	0.810900i	$0.698978\pi$
$492$	65.3396			0.132804
$493$		−	80.0955i		−	0.162466i
$494$	156.662			0.317130
$495$		0			0
$496$		−	24.4112i		−	0.0492161i
$497$	−84.3644	+	277.523i	−0.169747	+	0.558396i
$498$	−85.2072			−0.171099
$499$	282.439			0.566010			0.283005	−	0.959118i	$-0.408669\pi$
$499$	282.439			0.566010			0.283005	+	0.959118i	$0.408669\pi$
$500$		0			0
$501$	157.103			0.313580
$502$		−	217.956i		−	0.434176i
$503$			87.4043i			0.173766i	0.996219	+	0.0868830i	$0.0276906\pi$
$503$			87.4043i			0.173766i	−0.996219	+	0.0868830i	$0.972309\pi$
$504$	17.2756	−	56.8292i	0.0342769	−	0.112756i
$505$		0			0
$506$	118.699			0.234583
$507$			99.8370i			0.196917i
$508$	−121.438			−0.239051
$509$		−	632.350i		−	1.24234i	−0.783677	−	0.621169i	$-0.786658\pi$
$509$		−	632.350i		−	1.24234i	0.783677	−	0.621169i	$-0.213342\pi$
$510$		0			0
$511$	−714.690	−	217.260i	−1.39861	−	0.425165i
$512$	−22.6274			−0.0441942
$513$	38.2351			0.0745324
$514$			580.342i			1.12907i
$515$		0			0
$516$		−	124.772i		−	0.241806i
$517$			141.782i			0.274241i
$518$	103.828	−	341.549i	0.200440	−	0.659361i
$519$	430.633			0.829736
$520$		0			0
$521$		−	637.695i		−	1.22398i	−0.790864	−	0.611992i	$-0.790369\pi$
$521$		−	637.695i		−	1.22398i	0.790864	−	0.611992i	$-0.209631\pi$
$522$	−188.340			−0.360805
$523$		−	315.243i		−	0.602759i	−0.953504	−	0.301380i	$-0.902553\pi$
$523$		−	315.243i		−	0.602759i	0.953504	−	0.301380i	$-0.0974471\pi$
$524$			404.500i			0.771946i
$525$		0			0
$526$	485.073			0.922192
$527$	11.0111			0.0208939
$528$			36.7470i			0.0695965i
$529$	−278.584			−0.526623
$530$		0			0
$531$		−	116.105i		−	0.218654i
$532$	−98.5634	−	29.9624i	−0.185269	−	0.0563203i
$533$	283.959			0.532756
$534$	−143.958			−0.269584
$535$		0			0
$536$	255.780			0.477201
$537$		−	240.515i		−	0.447886i
$538$			336.691i			0.625819i
$539$	215.924	+	144.645i	0.400601	+	0.268357i
$540$		0			0
$541$	−273.034			−0.504684			−0.252342	−	0.967638i	$-0.581201\pi$
$541$	−273.034			−0.504684			−0.252342	+	0.967638i	$0.581201\pi$
$542$		−	46.1675i		−	0.0851800i
$543$	−257.188			−0.473644
$544$		−	10.2065i		−	0.0187619i
$545$		0			0
$546$	75.0777	−	246.973i	0.137505	−	0.452332i
$547$	31.9994			0.0584998			0.0292499	−	0.999572i	$-0.490688\pi$
$547$	31.9994			0.0584998			0.0292499	+	0.999572i	$0.490688\pi$
$548$	−236.338			−0.431274
$549$		−	76.6094i		−	0.139543i
$550$		0			0
$551$			326.654i			0.592838i
$552$			77.5242i			0.140442i
$553$	−32.9742	+	108.471i	−0.0596279	+	0.196150i
$554$	325.652			0.587819
$555$		0			0
$556$			512.053i			0.920959i
$557$	134.429			0.241344			0.120672	−	0.992692i	$-0.461495\pi$
$557$	134.429			0.241344			0.120672	+	0.992692i	$0.461495\pi$
$558$		−	25.8920i		−	0.0464014i
$559$		−	542.245i		−	0.970027i
$560$		0			0
$561$	−16.5754			−0.0295461
$562$	−688.523			−1.22513
$563$			138.895i			0.246706i	0.992363	+	0.123353i	$0.0393647\pi$
$563$			138.895i			0.246706i	−0.992363	+	0.123353i	$0.960635\pi$
$564$	−92.6002			−0.164185
$565$		0			0
$566$			459.118i			0.811162i
$567$	18.3235	−	60.2764i	0.0323166	−	0.106308i
$568$	117.203			0.206343
$569$	−247.938			−0.435744			−0.217872	−	0.975977i	$-0.569912\pi$
$569$	−247.938			−0.435744			−0.217872	+	0.975977i	$0.569912\pi$
$570$		0			0
$571$	−1085.67			−1.90134			−0.950672	−	0.310197i	$-0.899605\pi$
$571$	−1085.67			−1.90134			−0.950672	+	0.310197i	$0.899605\pi$
$572$			159.698i			0.279193i
$573$			79.8096i			0.139284i
$574$	−178.651	−	54.3084i	−0.311239	−	0.0946140i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	155.146i		−	0.268884i	−0.990921	−	0.134442i	$-0.957076\pi$
$577$		−	155.146i		−	0.268884i	0.990921	−	0.134442i	$-0.0429242\pi$
$578$	−404.104			−0.699142
$579$			45.7965i			0.0790959i
$580$		0			0
$581$	232.973	+	70.8217i	0.400986	+	0.121896i
$582$	−344.726			−0.592313
$583$	−428.216			−0.734504
$584$			301.827i			0.516827i
$585$		0			0
$586$		−	181.492i		−	0.309713i
$587$			938.218i			1.59833i	0.601113	+	0.799164i	$0.294724\pi$
$587$			938.218i			1.59833i	−0.601113	+	0.799164i	$0.705276\pi$
$588$	−94.4695	+	141.023i	−0.160662	+	0.239835i
$589$	−44.9065			−0.0762419
$590$		0			0
$591$			496.314i			0.839787i
$592$	−144.242			−0.243653
$593$		−	736.439i		−	1.24189i	−0.783856	−	0.620943i	$-0.786750\pi$
$593$		−	736.439i		−	1.24189i	0.783856	−	0.620943i	$-0.213250\pi$
$594$			38.9761i			0.0656163i
$595$		0			0
$596$	−529.077			−0.887713
$597$	−59.6801			−0.0999667
$598$			336.911i			0.563397i
$599$	385.386			0.643383			0.321692	−	0.946845i	$-0.395749\pi$
$599$	385.386			0.643383			0.321692	+	0.946845i	$0.395749\pi$
$600$		0			0
$601$			965.914i			1.60718i	0.595184	+	0.803589i	$0.297079\pi$
$601$			965.914i			1.60718i	−0.595184	+	0.803589i	$0.702921\pi$
$602$	−103.707	+	341.151i	−0.172271	+	0.566696i
$603$	271.295			0.449909
$604$	25.7418			0.0426188
$605$		0			0
$606$	237.102			0.391257
$607$		−	1162.16i		−	1.91460i	−0.289103	−	0.957298i	$-0.593357\pi$
$607$		−	1162.16i		−	1.91460i	0.289103	−	0.957298i	$-0.406643\pi$
$608$			41.6251i			0.0684623i
$609$	514.959	+	156.543i	0.845582	+	0.257049i
$610$		0			0
$611$	−402.430			−0.658642
$612$		−	10.8256i		−	0.0176889i
$613$	709.805			1.15792			0.578960	−	0.815356i	$-0.303459\pi$
$613$	709.805			1.15792			0.578960	+	0.815356i	$0.303459\pi$
$614$		−	410.277i		−	0.668204i
$615$		0			0
$616$	30.5430	−	100.473i	0.0495828	−	0.163106i
$617$	−326.387			−0.528990			−0.264495	−	0.964387i	$-0.585205\pi$
$617$	−326.387			−0.528990			−0.264495	+	0.964387i	$0.585205\pi$
$618$	251.130			0.406360
$619$		−	340.928i		−	0.550772i	−0.961334	−	0.275386i	$-0.911194\pi$
$619$		−	340.928i		−	0.550772i	0.961334	−	0.275386i	$-0.0888056\pi$
$620$		0			0
$621$			82.2268i			0.132410i
$622$			107.716i			0.173177i
$623$	393.608	+	119.653i	0.631795	+	0.192060i
$624$	−104.301			−0.167150
$625$		0			0
$626$			745.496i			1.19089i
$627$	67.5993			0.107814
$628$		−	407.269i		−	0.648518i
$629$		−	65.0630i		−	0.103439i
$630$		0			0
$631$	−64.3589			−0.101995			−0.0509975	−	0.998699i	$-0.516240\pi$
$631$	−64.3589			−0.101995			−0.0509975	+	0.998699i	$0.516240\pi$
$632$	45.8093			0.0724831
$633$		−	210.664i		−	0.332803i
$634$	−690.600			−1.08927
$635$		0			0
$636$		−	279.674i		−	0.439739i
$637$	−410.554	+	612.870i	−0.644512	+	0.962120i
$638$	−332.984			−0.521918
$639$	124.312			0.194542
$640$		0			0
$641$	−621.739			−0.969952			−0.484976	−	0.874527i	$-0.661172\pi$
$641$	−621.739			−0.969952			−0.484976	+	0.874527i	$0.661172\pi$
$642$		−	342.028i		−	0.532754i
$643$			396.767i			0.617056i	0.951215	+	0.308528i	$0.0998363\pi$
$643$			396.767i			0.617056i	−0.951215	+	0.308528i	$0.900164\pi$
$644$	64.4358	−	211.966i	0.100056	−	0.329140i
$645$		0			0
$646$	−18.7757			−0.0290646
$647$		−	564.262i		−	0.872121i	−0.899917	−	0.436060i	$-0.856373\pi$
$647$		−	564.262i		−	0.872121i	0.899917	−	0.436060i	$-0.143627\pi$
$648$	−25.4558			−0.0392837
$649$		−	205.273i		−	0.316291i
$650$		0			0
$651$	−21.5207	+	70.7937i	−0.0330578	+	0.108746i
$652$	−523.682			−0.803194
$653$	804.359			1.23179			0.615895	−	0.787828i	$-0.288794\pi$
$653$	804.359			1.23179			0.615895	+	0.787828i	$0.288794\pi$
$654$		−	66.9293i		−	0.102338i
$655$		0			0
$656$			75.4477i			0.115012i
$657$			320.136i			0.487269i
$658$	253.187	+	76.9667i	0.384783	+	0.116971i
$659$	229.717			0.348584			0.174292	−	0.984694i	$-0.444236\pi$
$659$	229.717			0.348584			0.174292	+	0.984694i	$0.444236\pi$
$660$		0			0
$661$			411.750i			0.622920i	0.950259	+	0.311460i	$0.100818\pi$
$661$			411.750i			0.622920i	−0.950259	+	0.311460i	$0.899182\pi$
$662$	−735.178			−1.11054
$663$		−	47.0469i		−	0.0709606i
$664$		−	98.3888i		−	0.148176i
$665$		0			0
$666$	−152.992			−0.229718
$667$	−702.487			−1.05320
$668$			181.407i			0.271568i
$669$	−523.123			−0.781948
$670$		0			0
$671$		−	135.445i		−	0.201855i
$672$	65.6207	+	19.9481i	0.0976498	+	0.0296847i
$673$	905.399			1.34532			0.672659	−	0.739952i	$-0.265152\pi$
$673$	905.399			1.34532			0.672659	+	0.739952i	$0.265152\pi$
$674$	−650.868			−0.965679
$675$		0			0
$676$	−115.282			−0.170535
$677$		−	632.507i		−	0.934279i	−0.884184	−	0.467139i	$-0.845285\pi$
$677$		−	632.507i		−	0.934279i	0.884184	−	0.467139i	$-0.154715\pi$
$678$			113.752i			0.167776i
$679$	942.549	+	286.527i	1.38814	+	0.421983i
$680$		0			0
$681$	−276.753			−0.406392
$682$		−	45.7767i		−	0.0671213i
$683$	−1050.88			−1.53862			−0.769310	−	0.638876i	$-0.779400\pi$
$683$	−1050.88			−1.53862			−0.769310	+	0.638876i	$0.779400\pi$
$684$			44.1501i			0.0645469i
$685$		0			0
$686$	375.512	−	307.064i	0.547394	−	0.447615i
$687$	79.6956			0.116005
$688$	144.074			0.209410
$689$		−	1215.43i		−	1.76405i
$690$		0			0
$691$			1353.15i			1.95825i	0.203270	+	0.979123i	$0.434843\pi$
$691$			1353.15i			1.95825i	−0.203270	+	0.979123i	$0.565157\pi$
$692$			497.252i			0.718572i
$693$	32.3958	−	106.568i	0.0467472	−	0.153778i
$694$	7.79965			0.0112387
$695$		0			0
$696$		−	217.477i		−	0.312467i
$697$	−34.0320			−0.0488264
$698$		−	797.463i		−	1.14250i
$699$		−	168.548i		−	0.241127i
$700$		0			0
$701$	−1124.26			−1.60379			−0.801897	−	0.597462i	$-0.796176\pi$
$701$	−1124.26			−1.60379			−0.801897	+	0.597462i	$0.796176\pi$
$702$	−110.628			−0.157590
$703$			265.347i			0.377449i
$704$	−42.4318			−0.0602724
$705$		0			0
$706$		−	387.709i		−	0.549163i
$707$	−648.283	−	197.072i	−0.916949	−	0.278744i
$708$	134.067			0.189360
$709$	270.618			0.381689			0.190845	−	0.981620i	$-0.438877\pi$
$709$	270.618			0.381689			0.190845	+	0.981620i	$0.438877\pi$
$710$		0			0
$711$	48.5881			0.0683377
$712$		−	166.228i		−	0.233466i
$713$		−	96.5740i		−	0.135447i
$714$	−8.99794	+	29.5993i	−0.0126022	+	0.0414556i
$715$		0			0
$716$	277.722			0.387880
$717$		−	215.259i		−	0.300222i
$718$	92.6144			0.128989
$719$			865.721i			1.20406i	0.798473	+	0.602031i	$0.205642\pi$
$719$			865.721i			1.20406i	−0.798473	+	0.602031i	$0.794358\pi$
$720$		0			0
$721$	−686.639	−	208.732i	−0.952342	−	0.289504i
$722$	−433.958			−0.601050
$723$	−576.685			−0.797628
$724$		−	296.976i		−	0.410187i
$725$		0			0
$726$		−	227.479i		−	0.313332i
$727$			747.526i			1.02823i	0.857720	+	0.514117i	$0.171880\pi$
$727$			747.526i			1.02823i	−0.857720	+	0.514117i	$0.828120\pi$
$728$	285.180	+	86.6922i	0.391731	+	0.119083i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			64.9872i			0.0889017i
$732$	88.4609			0.120848
$733$			506.845i			0.691467i	0.938333	+	0.345733i	$0.112370\pi$
$733$			506.845i			0.691467i	−0.938333	+	0.345733i	$0.887630\pi$
$734$		−	226.045i		−	0.307963i
$735$		0			0
$736$	−89.5172			−0.121627
$737$	479.647			0.650811
$738$			80.0244i			0.108434i
$739$	−350.632			−0.474468			−0.237234	−	0.971453i	$-0.576241\pi$
$739$	−350.632			−0.474468			−0.237234	+	0.971453i	$0.576241\pi$
$740$		0			0
$741$			191.871i			0.258936i
$742$	−232.457	+	764.684i	−0.313285	+	1.03057i
$743$	958.163			1.28959			0.644793	−	0.764357i	$-0.276944\pi$
$743$	958.163			1.28959			0.644793	+	0.764357i	$0.276944\pi$
$744$	29.8975			0.0401848
$745$		0			0
$746$	−665.749			−0.892424
$747$		−	104.357i		−	0.139702i
$748$		−	19.1396i		−	0.0255877i
$749$	−284.284	+	935.171i	−0.379551	+	1.24856i
$750$		0			0
$751$	−457.638			−0.609371			−0.304686	−	0.952453i	$-0.598551\pi$
$751$	−457.638			−0.609371			−0.304686	+	0.952453i	$0.598551\pi$
$752$		−	106.926i		−	0.142188i
$753$	266.941			0.354503
$754$		−	945.129i		−	1.25349i
$755$		0			0
$756$	69.6012	+	21.1582i	0.0920651	+	0.0279870i
$757$	1273.11			1.68179			0.840893	−	0.541201i	$-0.182030\pi$
$757$	1273.11			1.68179			0.840893	+	0.541201i	$0.182030\pi$
$758$	−86.9319			−0.114686
$759$			145.376i			0.191536i
$760$		0			0
$761$			103.915i			0.136551i	0.997667	+	0.0682754i	$0.0217496\pi$
$761$			103.915i			0.136551i	−0.997667	+	0.0682754i	$0.978250\pi$
$762$		−	148.730i		−	0.195184i
$763$	−55.6297	+	182.998i	−0.0729091	+	0.239840i
$764$	−92.1562			−0.120623
$765$		0			0
$766$		−	169.866i		−	0.221757i
$767$	582.639			0.759633
$768$		−	27.7128i		−	0.0360844i
$769$			433.921i			0.564266i	0.959375	+	0.282133i	$0.0910420\pi$
$769$			433.921i			0.564266i	−0.959375	+	0.282133i	$0.908958\pi$
$770$		0			0
$771$	−710.771			−0.921881
$772$	−52.8813			−0.0684991
$773$		−	1220.86i		−	1.57937i	−0.613510	−	0.789687i	$-0.710243\pi$
$773$		−	1220.86i		−	1.57937i	0.613510	−	0.789687i	$-0.289757\pi$
$774$	152.814			0.197434
$775$		0			0
$776$		−	398.056i		−	0.512958i
$777$	418.310	+	127.163i	0.538366	+	0.163659i
$778$	−437.836			−0.562771
$779$	138.793			0.178168
$780$		0			0
$781$	219.783			0.281412
$782$		−	40.3783i		−	0.0516346i
$783$		−	230.669i		−	0.294596i
$784$	−162.839	−	109.084i	−0.207703	−	0.139138i
$785$		0			0
$786$	−495.409			−0.630292
$787$			866.849i			1.10146i	0.834683	+	0.550730i	$0.185651\pi$
$787$			866.849i			1.10146i	−0.834683	+	0.550730i	$0.814349\pi$
$788$	−573.094			−0.727277
$789$			594.091i			0.752967i
$790$		0			0
$791$	94.5476	−	311.021i	0.119529	−	0.393199i
$792$	−45.0057			−0.0568253
$793$	384.441			0.484793
$794$			1066.58i			1.34330i
$795$		0			0
$796$		−	68.9127i		−	0.0865737i
$797$		−	915.806i		−	1.14907i	−0.818481	−	0.574533i	$-0.805184\pi$
$797$		−	915.806i		−	1.14907i	0.818481	−	0.574533i	$-0.194816\pi$
$798$	36.6963	−	120.715i	0.0459853	−	0.151272i
$799$	48.2306			0.0603637
$800$		0			0
$801$		−	176.311i		−	0.220114i
$802$	−333.326			−0.415619
$803$			565.996i			0.704852i
$804$			313.265i			0.389633i
$805$		0			0
$806$	129.931			0.161205
$807$	−412.360			−0.510979
$808$			273.782i			0.338839i
$809$	−693.212			−0.856875			−0.428437	−	0.903571i	$-0.640936\pi$
$809$	−693.212			−0.856875			−0.428437	+	0.903571i	$0.640936\pi$
$810$		0			0
$811$		−	1165.31i		−	1.43688i	−0.695591	−	0.718438i	$-0.744857\pi$
$811$		−	1165.31i		−	1.43688i	0.695591	−	0.718438i	$-0.255143\pi$
$812$	−180.760	+	594.624i	−0.222611	+	0.732295i
$813$	56.5435			0.0695492
$814$	−270.489			−0.332296
$815$		0			0
$816$	12.5003			0.0153190
$817$		−	265.037i		−	0.324403i
$818$			115.033i			0.140627i
$819$	302.479	+	91.9510i	0.369327	+	0.112272i
$820$		0			0
$821$	−392.977			−0.478657			−0.239329	−	0.970939i	$-0.576927\pi$
$821$	−392.977			−0.478657			−0.239329	+	0.970939i	$0.576927\pi$
$822$		−	289.454i		−	0.352134i
$823$	1430.26			1.73786			0.868932	−	0.494931i	$-0.164807\pi$
$823$	1430.26			1.73786			0.868932	+	0.494931i	$0.164807\pi$
$824$			289.980i			0.351918i
$825$		0			0
$826$	−366.564	−	111.432i	−0.443782	−	0.134906i
$827$	−667.082			−0.806629			−0.403314	−	0.915062i	$-0.632142\pi$
$827$	−667.082			−0.806629			−0.403314	+	0.915062i	$0.632142\pi$
$828$	−94.9473			−0.114671
$829$		−	851.079i		−	1.02663i	−0.858199	−	0.513317i	$-0.828417\pi$
$829$		−	851.079i		−	1.02663i	0.858199	−	0.513317i	$-0.171583\pi$
$830$		0			0
$831$			398.840i			0.479952i
$832$		−	120.437i		−	0.144756i
$833$	49.2042	−	73.4515i	0.0590687	−	0.0881771i
$834$	−627.135			−0.751960
$835$		0			0
$836$			78.0569i			0.0933695i
$837$	31.7110			0.0378866
$838$			301.269i			0.359510i
$839$			1401.61i			1.67057i	0.549815	+	0.835287i	$0.314698\pi$
$839$			1401.61i			1.67057i	−0.549815	+	0.835287i	$0.685302\pi$
$840$		0			0
$841$	1129.67			1.34325
$842$	−589.494			−0.700112
$843$		−	843.265i		−	1.00031i
$844$	243.254			0.288216
$845$		0			0
$846$		−	113.412i		−	0.134056i
$847$	−189.074	+	621.972i	−0.223228	+	0.734323i
$848$	322.940			0.380826
$849$	−562.302			−0.662311
$850$		0			0
$851$	−570.643			−0.670556
$852$			143.544i			0.168478i
$853$			390.367i			0.457640i	0.973469	+	0.228820i	$0.0734867\pi$
$853$			390.367i			0.457640i	−0.973469	+	0.228820i	$0.926513\pi$
$854$	−241.869	−	73.5261i	−0.283219	−	0.0860962i
$855$		0			0
$856$	394.940			0.461378
$857$			1123.67i			1.31117i	0.755124	+	0.655583i	$0.227577\pi$
$857$			1123.67i			1.31117i	−0.755124	+	0.655583i	$0.772423\pi$
$858$	−195.590			−0.227960
$859$		−	774.660i		−	0.901816i	−0.892571	−	0.450908i	$-0.851100\pi$
$859$		−	774.660i		−	0.901816i	0.892571	−	0.450908i	$-0.148900\pi$
$860$		0			0
$861$	66.5140	−	218.802i	0.0772520	−	0.254126i
$862$	469.394			0.544540
$863$	596.376			0.691050			0.345525	−	0.938409i	$-0.387701\pi$
$863$	596.376			0.691050			0.345525	+	0.938409i	$0.387701\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			430.091i			0.496641i
$867$		−	494.924i		−	0.570847i
$868$	−81.7455	−	24.8499i	−0.0941768	−	0.0286289i
$869$	85.9033			0.0988530
$870$		0			0
$871$			1361.41i			1.56305i
$872$	77.2832			0.0886276
$873$		−	422.202i		−	0.483622i
$874$			164.675i			0.188415i
$875$		0			0
$876$	−369.661			−0.421987
$877$	−481.187			−0.548674			−0.274337	−	0.961634i	$-0.588458\pi$
$877$	−481.187			−0.548674			−0.274337	+	0.961634i	$0.588458\pi$
$878$			34.4726i			0.0392627i
$879$	222.281			0.252879
$880$		0			0
$881$		−	1098.21i		−	1.24655i	−0.782004	−	0.623273i	$-0.785803\pi$
$881$		−	1098.21i		−	1.24655i	0.782004	−	0.623273i	$-0.214197\pi$
$882$	−172.717	−	115.701i	−0.195825	−	0.131180i
$883$	−930.631			−1.05394			−0.526971	−	0.849883i	$-0.676672\pi$
$883$	−930.631			−1.05394			−0.526971	+	0.849883i	$0.676672\pi$
$884$	54.3251			0.0614537
$885$		0			0
$886$	−42.8675			−0.0483832
$887$		−	1762.36i		−	1.98688i	−0.114343	−	0.993441i	$-0.536476\pi$
$887$		−	1762.36i		−	1.98688i	0.114343	−	0.993441i	$-0.463524\pi$
$888$		−	176.660i		−	0.198942i
$889$	−123.620	+	406.657i	−0.139055	+	0.457432i
$890$		0			0
$891$	−47.7357			−0.0535754
$892$		−	604.051i		−	0.677187i
$893$	−196.699			−0.220268
$894$		−	647.984i		−	0.724814i
$895$		0			0
$896$	−23.0341	+	75.7722i	−0.0257077	+	0.0845672i
$897$	−412.630			−0.460012
$898$	777.958			0.866323
$899$			270.917i			0.301353i
$900$		0			0
$901$			145.668i			0.161673i
$902$			141.482i			0.156854i
$903$	−417.823	−	127.014i	−0.462705	−	0.140658i
$904$	−131.350			−0.145298
$905$		0			0
$906$			31.5271i			0.0347981i
$907$	135.202			0.149065			0.0745327	−	0.997219i	$-0.476253\pi$
$907$	135.202			0.149065			0.0745327	+	0.997219i	$0.476253\pi$
$908$		−	319.567i		−	0.351946i
$909$			290.389i			0.319460i
$910$		0			0
$911$	−995.115			−1.09233			−0.546166	−	0.837677i	$-0.683913\pi$
$911$	−995.115			−1.09233			−0.546166	+	0.837677i	$0.683913\pi$
$912$	−50.9801			−0.0558993
$913$		−	184.502i		−	0.202083i
$914$	−674.911			−0.738414
$915$		0			0
$916$			92.0245i			0.100463i
$917$	1354.55	+	411.770i	1.47715	+	0.449040i
$918$	13.2586			0.0144429
$919$	514.989			0.560380			0.280190	−	0.959945i	$-0.409603\pi$
$919$	514.989			0.560380			0.280190	+	0.959945i	$0.409603\pi$
$920$		0			0
$921$	502.485			0.545586
$922$			1217.29i			1.32027i
$923$			623.824i			0.675866i
$924$	123.054	+	37.4074i	0.133176	+	0.0404842i
$925$		0			0
$926$	1095.32			1.18285
$927$			307.570i			0.331791i
$928$	251.120			0.270604
$929$		−	865.807i		−	0.931977i	−0.884791	−	0.465989i	$-0.845699\pi$
$929$		−	865.807i		−	0.931977i	0.884791	−	0.465989i	$-0.154301\pi$
$930$		0			0
$931$	−200.670	+	299.557i	−0.215542	+	0.321759i
$932$	194.623			0.208822
$933$	−131.925			−0.141399
$934$			1088.75i			1.16568i
$935$		0			0
$936$		−	127.742i		−	0.136477i
$937$			1000.06i			1.06730i	0.845706	+	0.533649i	$0.179180\pi$
$937$			1000.06i			1.06730i	−0.845706	+	0.533649i	$0.820820\pi$
$938$	260.377	−	856.527i	0.277587	−	0.913142i
$939$	−913.043			−0.972356
$940$		0			0
$941$			776.370i			0.825048i	0.910947	+	0.412524i	$0.135353\pi$
$941$			776.370i			0.825048i	−0.910947	+	0.412524i	$0.864647\pi$
$942$	498.801			0.529512
$943$			298.482i			0.316523i
$944$			154.807i			0.163990i
$945$		0			0
$946$	270.173			0.285595
$947$	−472.690			−0.499144			−0.249572	−	0.968356i	$-0.580290\pi$
$947$	−472.690			−0.499144			−0.249572	+	0.968356i	$0.580290\pi$
$948$			56.1047i			0.0591822i
$949$	−1606.50			−1.69284
$950$		0			0
$951$		−	845.808i		−	0.889388i
$952$	−34.1784	−	10.3899i	−0.0359016	−	0.0109138i
$953$	104.665			0.109827			0.0549133	−	0.998491i	$-0.482512\pi$
$953$	104.665			0.109827			0.0549133	+	0.998491i	$0.482512\pi$
$954$	342.530			0.359046
$955$		0			0
$956$	248.560			0.260000
$957$		−	407.820i		−	0.426144i
$958$			1024.93i			1.06986i
$959$	−240.586	+	791.424i	−0.250872	+	0.825259i
$960$		0			0
$961$	923.756			0.961244
$962$		−	767.745i		−	0.798072i
$963$	418.897			0.434992
$964$		−	665.899i		−	0.690766i
$965$		0			0
$966$	259.604	+	78.9175i	0.268742	+	0.0816951i
$967$	1463.91			1.51386			0.756931	−	0.653495i	$-0.226698\pi$
$967$	1463.91			1.51386			0.756931	+	0.653495i	$0.226698\pi$
$968$	262.670			0.271353
$969$		−	22.9955i		−	0.0237311i
$970$		0			0
$971$		−	101.826i		−	0.104867i	−0.998624	−	0.0524333i	$-0.983302\pi$
$971$		−	101.826i		−	0.104867i	0.998624	−	0.0524333i	$-0.0166977\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1714.71	+	521.256i	1.76229	+	0.535721i
$974$	83.4250			0.0856520
$975$		0			0
$976$			102.146i			0.104658i
$977$	69.4893			0.0711252			0.0355626	−	0.999367i	$-0.488678\pi$
$977$	69.4893			0.0711252			0.0355626	+	0.999367i	$0.488678\pi$
$978$		−	641.377i		−	0.655805i
$979$		−	311.717i		−	0.318403i
$980$		0			0
$981$	81.9713			0.0835589
$982$	812.681			0.827577
$983$			166.731i			0.169614i	0.996397	+	0.0848070i	$0.0270274\pi$
$983$			166.731i			0.169614i	−0.996397	+	0.0848070i	$0.972973\pi$
$984$	−92.4042			−0.0939067
$985$		0			0
$986$			113.272i			0.114881i
$987$	−94.2645	+	310.090i	−0.0955061	+	0.314174i
$988$	−221.554			−0.224245
$989$	569.978			0.576317
$990$		0			0
$991$	−990.392			−0.999387			−0.499693	−	0.866202i	$-0.666554\pi$
$991$	−990.392			−0.999387			−0.499693	+	0.866202i	$0.666554\pi$
$992$			34.5226i			0.0348010i
$993$		−	900.405i		−	0.906753i
$994$	119.309	−	392.476i	0.120030	−	0.394845i
$995$		0			0
$996$	120.501			0.120985
$997$			567.448i			0.569156i	0.958653	+	0.284578i	$0.0918534\pi$
$997$			567.448i			0.569156i	−0.958653	+	0.284578i	$0.908147\pi$
$998$	−399.429			−0.400230
$999$		−	187.376i		−	0.187564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.d.601.2	yes	12
5.2	odd	4		1050.3.h.c.349.7		24
5.3	odd	4		1050.3.h.c.349.20		24
5.4	even	2		1050.3.f.c.601.11	yes	12
7.6	odd	2	inner	1050.3.f.d.601.5	yes	12
35.13	even	4		1050.3.h.c.349.8		24
35.27	even	4		1050.3.h.c.349.19		24
35.34	odd	2		1050.3.f.c.601.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.8	✓	12	35.34	odd	2
1050.3.f.c.601.11	yes	12	5.4	even	2
1050.3.f.d.601.2	yes	12	1.1	even	1	trivial
1050.3.f.d.601.5	yes	12	7.6	odd	2	inner
1050.3.h.c.349.7		24	5.2	odd	4
1050.3.h.c.349.8		24	35.13	even	4
1050.3.h.c.349.19		24	35.27	even	4
1050.3.h.c.349.20		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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(2.03595 - 6.69738i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(2.03595 - 6.69738i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -5.30397 q^{11} -3.46410i q^{12} -15.0546i q^{13} +(-2.87926 + 9.47153i) q^{14} +4.00000 q^{16} +1.80427i q^{17} +4.24264 q^{18} -7.35835i q^{19} +(-11.6002 - 3.52636i) q^{21} +7.50095 q^{22} +15.8246 q^{23} +4.89898i q^{24} +21.2904i q^{26} +5.19615i q^{27} +(4.07189 - 13.3948i) q^{28} -44.3922 q^{29} -6.10279i q^{31} -5.65685 q^{32} +9.18674i q^{33} -2.55162i q^{34} -6.00000 q^{36} -36.0606 q^{37} +10.4063i q^{38} -26.0753 q^{39} +18.8619i q^{41} +(16.4052 + 4.98703i) q^{42} +36.0186 q^{43} -10.6079 q^{44} -22.3793 q^{46} -26.7314i q^{47} -6.92820i q^{48} +(-40.7099 - 27.2710i) q^{49} +3.12509 q^{51} -30.1092i q^{52} +80.7350 q^{53} -7.34847i q^{54} +(-5.75852 + 18.9431i) q^{56} -12.7450 q^{57} +62.7801 q^{58} +38.7017i q^{59} +25.5365i q^{61} +8.63065i q^{62} +(-6.10784 + 20.0921i) q^{63} +8.00000 q^{64} -12.9920i q^{66} -90.4318 q^{67} +3.60854i q^{68} -27.4089i q^{69} -41.4375 q^{71} +8.48528 q^{72} -106.712i q^{73} +50.9974 q^{74} -14.7167i q^{76} +(-10.7986 + 35.5227i) q^{77} +36.8761 q^{78} -16.1960 q^{79} +9.00000 q^{81} -26.6748i q^{82} +34.7857i q^{83} +(-23.2004 - 7.05272i) q^{84} -50.9379 q^{86} +76.8896i q^{87} +15.0019 q^{88} +58.7705i q^{89} +(-100.826 - 30.6503i) q^{91} +31.6491 q^{92} -10.5703 q^{93} +37.8039i q^{94} +9.79796i q^{96} +140.734i q^{97} +(57.5724 + 38.5670i) q^{98} +15.9119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 10 q^{7} - 36 q^{9}+O(q^{10}) \) 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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