LMFDB - Embedded newform 1050.2.bc.d.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.d.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-4.05317 - 4.05317i) q^{13} +(2.59808 + 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.93185 + 7.20977i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.13397 + 1.96410i) q^{19} +(0.866025 + 2.50000i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(-5.72620 - 1.53433i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.96410 - 2.86603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.15539 + 2.38014i) q^{28} +6.92820i q^{29} +(6.46410 + 3.73205i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.258819 - 0.965926i) q^{33} -7.46410 q^{34} -1.00000 q^{36} +(-1.01669 + 3.79435i) q^{37} +(-2.19067 + 0.586988i) q^{38} +(4.96410 + 2.86603i) q^{39} +2.26795i q^{41} +(-2.63896 + 0.189469i) q^{42} +(-6.31319 + 6.31319i) q^{43} +(0.866025 - 0.500000i) q^{44} +(2.96410 - 5.13397i) q^{46} +(1.15539 + 0.309587i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-3.73205 - 6.46410i) q^{51} +(1.48356 + 5.53674i) q^{52} +(-0.258819 - 0.965926i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(-1.60368 - 1.60368i) q^{57} +(-6.69213 - 1.79315i) q^{58} +(5.73205 - 9.92820i) q^{59} +(-9.92820 + 5.73205i) q^{61} +(-5.27792 + 5.27792i) q^{62} +(-1.48356 - 2.19067i) q^{63} -1.00000i q^{64} +(0.866025 + 0.500000i) q^{66} +(-1.93185 + 0.517638i) q^{67} +(1.93185 - 7.20977i) q^{68} +5.92820 q^{69} -8.92820 q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.86370 + 1.03528i) q^{73} +(-3.40192 - 1.96410i) q^{74} -2.26795i q^{76} +(2.38014 + 1.15539i) q^{77} +(-4.05317 + 4.05317i) q^{78} +(-2.66025 + 1.53590i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.19067 - 0.586988i) q^{82} +(7.34847 + 7.34847i) q^{83} +(0.500000 - 2.59808i) q^{84} +(-4.46410 - 7.73205i) q^{86} +(-1.79315 - 6.69213i) q^{87} +(0.258819 + 0.965926i) q^{88} +(3.46410 + 6.00000i) q^{89} +(-9.92820 + 11.4641i) q^{91} +(4.19187 + 4.19187i) q^{92} +(-7.20977 - 1.93185i) q^{93} +(-0.598076 + 1.03590i) q^{94} +(0.866025 - 0.500000i) q^{96} +(-2.07055 + 2.07055i) q^{97} +(0.827225 - 6.95095i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 4 q^{16} + 16 q^{19} - 4 q^{24} + 12 q^{26} + 24 q^{31} - 32 q^{34} - 8 q^{36} + 12 q^{39} - 4 q^{46} - 16 q^{51} - 4 q^{54} - 16 q^{56} + 32 q^{59} - 24 q^{61} - 8 q^{69} - 16 q^{71} - 48 q^{74} + 48 q^{79} + 4 q^{81} + 4 q^{84} - 8 q^{86} - 24 q^{91} + 16 q^{94}+O(q^{100}) $ 8 * q - 4 * q^11 + 4 * q^16 + 16 * q^19 - 4 * q^24 + 12 * q^26 + 24 * q^31 - 32 * q^34 - 8 * q^36 + 12 * q^39 - 4 * q^46 - 16 * q^51 - 4 * q^54 - 16 * q^56 + 32 * q^59 - 24 * q^61 - 8 * q^69 - 16 * q^71 - 48 * q^74 + 48 * q^79 + 4 * q^81 + 4 * q^84 - 8 * q^86 - 24 * q^91 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−4.05317	−	4.05317i	−1.12415	−	1.12415i	−0.991111	−	0.133037i	$-0.957527\pi$
$13$	−4.05317	−	4.05317i	−1.12415	−	1.12415i	−0.133037	−	0.991111i	$-0.542473\pi$
$14$	2.59808	+	0.500000i	0.694365	+	0.133631i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.93185	+	7.20977i	0.468543	+	1.74863i	0.644868	+	0.764294i	$0.276912\pi$
$17$	1.93185	+	7.20977i	0.468543	+	1.74863i	−0.176325	+	0.984332i	$0.556421\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	1.13397	+	1.96410i	0.260152	+	0.450596i	0.966282	−	0.257486i	$-0.0828941\pi$
$19$	1.13397	+	1.96410i	0.260152	+	0.450596i	−0.706130	+	0.708082i	$0.749561\pi$
$20$		0			0
$21$	0.866025	+	2.50000i	0.188982	+	0.545545i
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	−5.72620	−	1.53433i	−1.19400	−	0.319930i	−0.393532	−	0.919311i	$-0.628747\pi$
$23$	−5.72620	−	1.53433i	−1.19400	−	0.319930i	−0.800464	+	0.599381i	$0.795414\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	4.96410	−	2.86603i	0.973540	−	0.562074i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.15539	+	2.38014i	−0.218349	+	0.449804i
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	6.46410	+	3.73205i	1.16099	+	0.670296i	0.951540	−	0.307524i	$-0.0995004\pi$
$31$	6.46410	+	3.73205i	1.16099	+	0.670296i	0.209447	+	0.977820i	$0.432834\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.258819	−	0.965926i	0.0450546	−	0.168146i
$34$	−7.46410			−1.28008
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−1.01669	+	3.79435i	−0.167143	+	0.623788i	0.830614	+	0.556849i	$0.187990\pi$
$37$	−1.01669	+	3.79435i	−0.167143	+	0.623788i	−0.997757	+	0.0669387i	$0.978677\pi$
$38$	−2.19067	+	0.586988i	−0.355374	+	0.0952221i
$39$	4.96410	+	2.86603i	0.794892	+	0.458931i
$40$		0			0
$41$			2.26795i			0.354194i	0.984193	+	0.177097i	$0.0566707\pi$
$41$			2.26795i			0.354194i	−0.984193	+	0.177097i	$0.943329\pi$
$42$	−2.63896	+	0.189469i	−0.407200	+	0.0292357i
$43$	−6.31319	+	6.31319i	−0.962753	+	0.962753i	−0.999331	−	0.0365779i	$-0.988354\pi$
$43$	−6.31319	+	6.31319i	−0.962753	+	0.962753i	0.0365779	+	0.999331i	$0.488354\pi$
$44$	0.866025	−	0.500000i	0.130558	−	0.0753778i
$45$		0			0
$46$	2.96410	−	5.13397i	0.437033	−	0.756963i
$47$	1.15539	+	0.309587i	0.168532	+	0.0451579i	0.342098	−	0.939664i	$-0.388862\pi$
$47$	1.15539	+	0.309587i	0.168532	+	0.0451579i	−0.173566	+	0.984822i	$0.555529\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		0			0
$51$	−3.73205	−	6.46410i	−0.522592	−	0.905155i
$52$	1.48356	+	5.53674i	0.205733	+	0.767807i
$53$	−0.258819	−	0.965926i	−0.0355515	−	0.132680i	0.945869	−	0.324548i	$-0.105212\pi$
$53$	−0.258819	−	0.965926i	−0.0355515	−	0.132680i	−0.981421	+	0.191868i	$0.938546\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$	−1.60368	−	1.60368i	−0.212413	−	0.212413i
$58$	−6.69213	−	1.79315i	−0.878720	−	0.235452i
$59$	5.73205	−	9.92820i	0.746249	−	1.29254i	−0.203359	−	0.979104i	$-0.565186\pi$
$59$	5.73205	−	9.92820i	0.746249	−	1.29254i	0.949609	−	0.313438i	$-0.101481\pi$
$60$		0			0
$61$	−9.92820	+	5.73205i	−1.27118	+	0.733914i	−0.975209	−	0.221284i	$-0.928975\pi$
$61$	−9.92820	+	5.73205i	−1.27118	+	0.733914i	−0.295967	+	0.955198i	$0.595642\pi$
$62$	−5.27792	+	5.27792i	−0.670296	+	0.670296i
$63$	−1.48356	−	2.19067i	−0.186911	−	0.275999i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.866025	+	0.500000i	0.106600	+	0.0615457i
$67$	−1.93185	+	0.517638i	−0.236013	+	0.0632396i	−0.374887	−	0.927071i	$-0.622318\pi$
$67$	−1.93185	+	0.517638i	−0.236013	+	0.0632396i	0.138874	+	0.990310i	$0.455652\pi$
$68$	1.93185	−	7.20977i	0.234271	−	0.874313i
$69$	5.92820			0.713672
$70$		0			0
$71$	−8.92820			−1.05958			−0.529791	−	0.848128i	$-0.677730\pi$
$71$	−8.92820			−1.05958			−0.529791	+	0.848128i	$0.677730\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−3.86370	+	1.03528i	−0.452212	+	0.121170i	−0.477734	−	0.878504i	$-0.658542\pi$
$73$	−3.86370	+	1.03528i	−0.452212	+	0.121170i	0.0255221	+	0.999674i	$0.491875\pi$
$74$	−3.40192	−	1.96410i	−0.395466	−	0.228322i
$75$		0			0
$76$		−	2.26795i		−	0.260152i
$77$	2.38014	+	1.15539i	0.271242	+	0.131669i
$78$	−4.05317	+	4.05317i	−0.458931	+	0.458931i
$79$	−2.66025	+	1.53590i	−0.299302	+	0.172802i	−0.642129	−	0.766596i	$-0.721949\pi$
$79$	−2.66025	+	1.53590i	−0.299302	+	0.172802i	0.342827	+	0.939398i	$0.388615\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.19067	−	0.586988i	−0.241919	−	0.0648220i
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	0.984118	−	0.177518i	$-0.0568069\pi$
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	−0.177518	+	0.984118i	$0.556807\pi$
$84$	0.500000	−	2.59808i	0.0545545	−	0.283473i
$85$		0			0
$86$	−4.46410	−	7.73205i	−0.481376	−	0.833768i
$87$	−1.79315	−	6.69213i	−0.192246	−	0.717472i
$88$	0.258819	+	0.965926i	0.0275902	+	0.102968i
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	0.989126	−	0.147073i	$-0.0469852\pi$
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	−0.621932	+	0.783072i	$0.713652\pi$
$90$		0			0
$91$	−9.92820	+	11.4641i	−1.04076	+	1.20176i
$92$	4.19187	+	4.19187i	0.437033	+	0.437033i
$93$	−7.20977	−	1.93185i	−0.747618	−	0.200324i
$94$	−0.598076	+	1.03590i	−0.0616869	+	0.106845i
$95$		0			0
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−2.07055	+	2.07055i	−0.210233	+	0.210233i	−0.804366	−	0.594134i	$-0.797495\pi$
$97$	−2.07055	+	2.07055i	−0.210233	+	0.210233i	0.594134	+	0.804366i	$0.297495\pi$
$98$	0.827225	−	6.95095i	0.0835624	−	0.702152i
$99$			1.00000i			0.100504i
$100$		0			0
$101$	0.928203	+	0.535898i	0.0923597	+	0.0533239i	0.545468	−	0.838131i	$-0.316352\pi$
$101$	0.928203	+	0.535898i	0.0923597	+	0.0533239i	−0.453109	+	0.891455i	$0.649685\pi$
$102$	7.20977	−	1.93185i	0.713873	−	0.191282i
$103$	4.76028	−	17.7656i	0.469044	−	1.75050i	−0.174077	−	0.984732i	$-0.555694\pi$
$103$	4.76028	−	17.7656i	0.469044	−	1.75050i	0.643121	−	0.765765i	$-0.277639\pi$
$104$	−5.73205			−0.562074
$105$		0			0
$106$	1.00000			0.0971286
$107$	−3.86370	+	14.4195i	−0.373518	+	1.39399i	0.481979	+	0.876183i	$0.339918\pi$
$107$	−3.86370	+	14.4195i	−0.373518	+	1.39399i	−0.855498	+	0.517807i	$0.826749\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	−14.6603	−	8.46410i	−1.40420	−	0.810714i	−0.409378	−	0.912365i	$-0.634254\pi$
$109$	−14.6603	−	8.46410i	−1.40420	−	0.810714i	−0.994820	+	0.101651i	$0.967587\pi$
$110$		0			0
$111$		−	3.92820i		−	0.372849i
$112$	2.19067	−	1.48356i	0.206999	−	0.140184i
$113$	−9.14162	+	9.14162i	−0.859971	+	0.859971i	−0.991334	−	0.131363i	$-0.958065\pi$
$113$	−9.14162	+	9.14162i	−0.859971	+	0.859971i	0.131363	+	0.991334i	$0.458065\pi$
$114$	1.96410	−	1.13397i	0.183955	−	0.106206i
$115$		0			0
$116$	3.46410	−	6.00000i	0.321634	−	0.557086i
$117$	−5.53674	−	1.48356i	−0.511871	−	0.137156i
$118$	8.10634	+	8.10634i	0.746249	+	0.746249i
$119$	18.6603	−	6.46410i	1.71058	−	0.592563i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−2.96713	−	11.0735i	−0.268631	−	1.00255i
$123$	−0.586988	−	2.19067i	−0.0529270	−	0.197526i
$124$	−3.73205	−	6.46410i	−0.335148	−	0.580493i
$125$		0			0
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	−3.53553	−	3.53553i	−0.313728	−	0.313728i	0.532624	−	0.846352i	$-0.321206\pi$
$127$	−3.53553	−	3.53553i	−0.313728	−	0.313728i	−0.846352	+	0.532624i	$0.821206\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	4.46410	−	7.73205i	0.393042	−	0.680769i
$130$		0			0
$131$	3.57180	−	2.06218i	0.312069	−	0.180173i	−0.335783	−	0.941939i	$-0.609001\pi$
$131$	3.57180	−	2.06218i	0.312069	−	0.180173i	0.647852	+	0.761766i	$0.275667\pi$
$132$	−0.707107	+	0.707107i	−0.0615457	+	0.0615457i
$133$	4.96833	−	3.36465i	0.430809	−	0.291752i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	6.46410	+	3.73205i	0.554292	+	0.320021i
$137$	18.2832	−	4.89898i	1.56204	−	0.418548i	0.628733	−	0.777621i	$-0.283574\pi$
$137$	18.2832	−	4.89898i	1.56204	−	0.418548i	0.933309	+	0.359073i	$0.116907\pi$
$138$	−1.53433	+	5.72620i	−0.130611	+	0.487447i
$139$	−10.3923			−0.881464			−0.440732	−	0.897639i	$-0.645281\pi$
$139$	−10.3923			−0.881464			−0.440732	+	0.897639i	$0.645281\pi$
$140$		0			0
$141$	−1.19615			−0.100734
$142$	2.31079	−	8.62398i	0.193917	−	0.723708i
$143$	5.53674	−	1.48356i	0.463005	−	0.124062i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$		−	4.00000i		−	0.331042i
$147$	6.43331	−	2.75908i	0.530611	−	0.227565i
$148$	2.77766	−	2.77766i	0.228322	−	0.228322i
$149$	−0.803848	+	0.464102i	−0.0658538	+	0.0380207i	−0.532565	−	0.846389i	$-0.678772\pi$
$149$	−0.803848	+	0.464102i	−0.0658538	+	0.0380207i	0.466712	+	0.884410i	$0.345439\pi$
$150$		0			0
$151$	1.92820	−	3.33975i	0.156915	−	0.271785i	−0.776840	−	0.629698i	$-0.783178\pi$
$151$	1.92820	−	3.33975i	0.156915	−	0.271785i	0.933755	+	0.357914i	$0.116512\pi$
$152$	2.19067	+	0.586988i	0.177687	+	0.0476110i
$153$	5.27792	+	5.27792i	0.426694	+	0.426694i
$154$	−1.73205	+	2.00000i	−0.139573	+	0.161165i
$155$		0			0
$156$	−2.86603	−	4.96410i	−0.229466	−	0.397446i
$157$	1.20616	+	4.50146i	0.0962622	+	0.359256i	0.997208	−	0.0746765i	$-0.0237924\pi$
$157$	1.20616	+	4.50146i	0.0962622	+	0.359256i	−0.900946	+	0.433932i	$0.857126\pi$
$158$	−0.795040	−	2.96713i	−0.0632499	−	0.236052i
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	−2.96410	+	15.4019i	−0.233604	+	1.21384i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.682400	−	0.730979i	$-0.260936\pi$
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.225486	+	0.974246i	$0.427603\pi$
$164$	1.13397	−	1.96410i	0.0885485	−	0.153371i
$165$		0			0
$166$	−9.00000	+	5.19615i	−0.698535	+	0.403300i
$167$	4.81105	−	4.81105i	0.372290	−	0.372290i	−0.496021	−	0.868311i	$-0.665206\pi$
$167$	4.81105	−	4.81105i	0.372290	−	0.372290i	0.868311	+	0.496021i	$0.165206\pi$
$168$	2.38014	+	1.15539i	0.183632	+	0.0891406i
$169$			19.8564i			1.52742i
$170$		0			0
$171$	1.96410	+	1.13397i	0.150199	+	0.0867172i
$172$	8.62398	−	2.31079i	0.657572	−	0.176196i
$173$	−1.96404	+	7.32989i	−0.149323	+	0.557281i	0.850202	+	0.526457i	$0.176480\pi$
$173$	−1.96404	+	7.32989i	−0.149323	+	0.557281i	−0.999525	+	0.0308241i	$0.990187\pi$
$174$	6.92820			0.525226
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−2.96713	+	11.0735i	−0.223023	+	0.832333i
$178$	−6.69213	+	1.79315i	−0.501596	+	0.134402i
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	0.762153	−	0.647397i	$-0.224142\pi$
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	−0.179585	+	0.983742i	$0.557476\pi$
$180$		0			0
$181$			14.3923i			1.06977i	0.844924	+	0.534886i	$0.179645\pi$
$181$			14.3923i			1.06977i	−0.844924	+	0.534886i	$0.820355\pi$
$182$	−8.50386	−	12.5570i	−0.630348	−	0.930789i
$183$	8.10634	−	8.10634i	0.599238	−	0.599238i
$184$	−5.13397	+	2.96410i	−0.378482	+	0.218516i
$185$		0			0
$186$	3.73205	−	6.46410i	0.273647	−	0.473971i
$187$	−7.20977	−	1.93185i	−0.527230	−	0.141271i
$188$	−0.845807	−	0.845807i	−0.0616869	−	0.0616869i
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$		0			0
$191$	−1.46410	−	2.53590i	−0.105939	−	0.183491i	0.808183	−	0.588932i	$-0.200451\pi$
$191$	−1.46410	−	2.53590i	−0.105939	−	0.183491i	−0.914121	+	0.405441i	$0.867118\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	5.89709	+	22.0082i	0.424482	+	1.58419i	0.765052	+	0.643969i	$0.222713\pi$
$193$	5.89709	+	22.0082i	0.424482	+	1.58419i	−0.340570	+	0.940219i	$0.610620\pi$
$194$	−1.46410	−	2.53590i	−0.105116	−	0.182067i
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$	−11.9193	−	11.9193i	−0.849213	−	0.849213i	0.140822	−	0.990035i	$-0.455026\pi$
$197$	−11.9193	−	11.9193i	−0.849213	−	0.849213i	−0.990035	+	0.140822i	$0.955026\pi$
$198$	−0.965926	−	0.258819i	−0.0686454	−	0.0183935i
$199$	6.26795	−	10.8564i	0.444323	−	0.769590i	−0.553682	−	0.832728i	$-0.686778\pi$
$199$	6.26795	−	10.8564i	0.444323	−	0.769590i	0.998005	+	0.0631382i	$0.0201109\pi$
$200$		0			0
$201$	1.73205	−	1.00000i	0.122169	−	0.0705346i
$202$	−0.757875	+	0.757875i	−0.0533239	+	0.0533239i
$203$	18.2832	−	1.31268i	1.28323	−	0.0921319i
$204$			7.46410i			0.522592i
$205$		0			0
$206$	15.9282	+	9.19615i	1.10977	+	0.640726i
$207$	−5.72620	+	1.53433i	−0.397999	+	0.106643i
$208$	1.48356	−	5.53674i	0.102867	−	0.383904i
$209$	−2.26795			−0.156877
$210$		0			0
$211$	−19.7846			−1.36203			−0.681014	−	0.732270i	$-0.738461\pi$
$211$	−19.7846			−1.36203			−0.681014	+	0.732270i	$0.738461\pi$
$212$	−0.258819	+	0.965926i	−0.0177758	+	0.0663401i
$213$	8.62398	−	2.31079i	0.590906	−	0.158333i
$214$	−12.9282	−	7.46410i	−0.883754	−	0.510235i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	8.62398	−	17.7656i	0.585434	−	1.20601i
$218$	11.9700	−	11.9700i	0.810714	−	0.810714i
$219$	3.46410	−	2.00000i	0.234082	−	0.135147i
$220$		0			0
$221$	21.3923	−	37.0526i	1.43900	−	2.49242i
$222$	3.79435	+	1.01669i	0.254660	+	0.0682360i
$223$	−6.59059	−	6.59059i	−0.441339	−	0.441339i	0.451123	−	0.892462i	$-0.351024\pi$
$223$	−6.59059	−	6.59059i	−0.441339	−	0.441339i	−0.892462	+	0.451123i	$0.851024\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$		0			0
$226$	−6.46410	−	11.1962i	−0.429986	−	0.744757i
$227$	−0.896575	−	3.34607i	−0.0595078	−	0.222086i	0.929768	−	0.368146i	$-0.120007\pi$
$227$	−0.896575	−	3.34607i	−0.0595078	−	0.222086i	−0.989276	+	0.146060i	$0.953341\pi$
$228$	0.586988	+	2.19067i	0.0388743	+	0.145081i
$229$	−1.46410	−	2.53590i	−0.0967506	−	0.167577i	0.813587	−	0.581443i	$-0.197512\pi$
$229$	−1.46410	−	2.53590i	−0.0967506	−	0.167577i	−0.910338	+	0.413866i	$0.864178\pi$
$230$		0			0
$231$	−2.59808	−	0.500000i	−0.170941	−	0.0328976i
$232$	4.89898	+	4.89898i	0.321634	+	0.321634i
$233$	1.79315	+	0.480473i	0.117473	+	0.0314769i	0.317077	−	0.948400i	$-0.397299\pi$
$233$	1.79315	+	0.480473i	0.117473	+	0.0314769i	−0.199603	+	0.979877i	$0.563965\pi$
$234$	2.86603	−	4.96410i	0.187358	−	0.324513i
$235$		0			0
$236$	−9.92820	+	5.73205i	−0.646271	+	0.373125i
$237$	2.17209	−	2.17209i	0.141092	−	0.141092i
$238$	1.41421	+	19.6975i	0.0916698	+	1.27680i
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		0			0
$241$	19.2846	+	11.1340i	1.24223	+	0.717202i	0.969548	−	0.244902i	$-0.0787557\pi$
$241$	19.2846	+	11.1340i	1.24223	+	0.717202i	0.272683	+	0.962104i	$0.412089\pi$
$242$	−9.65926	+	2.58819i	−0.620921	+	0.166375i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	11.4641			0.733914
$245$		0			0
$246$	2.26795			0.144599
$247$	3.36465	−	12.5570i	0.214087	−	0.798985i
$248$	7.20977	−	1.93185i	0.457821	−	0.122673i
$249$	−9.00000	−	5.19615i	−0.570352	−	0.329293i
$250$		0			0
$251$		−	7.33975i		−	0.463281i	−0.972801	−	0.231640i	$-0.925591\pi$
$251$		−	7.33975i		−	0.463281i	0.972801	−	0.231640i	$-0.0744092\pi$
$252$	0.189469	+	2.63896i	0.0119354	+	0.166239i
$253$	4.19187	−	4.19187i	0.263541	−	0.263541i
$254$	4.33013	−	2.50000i	0.271696	−	0.156864i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.31079	+	0.619174i	0.144143	+	0.0386230i	0.330169	−	0.943922i	$-0.392894\pi$
$257$	2.31079	+	0.619174i	0.144143	+	0.0386230i	−0.186026	+	0.982545i	$0.559561\pi$
$258$	6.31319	+	6.31319i	0.393042	+	0.393042i
$259$	10.2058	+	1.96410i	0.634156	+	0.122043i
$260$		0			0
$261$	3.46410	+	6.00000i	0.214423	+	0.371391i
$262$	1.06746	+	3.98382i	0.0659480	+	0.246121i
$263$	7.72741	+	28.8391i	0.476492	+	1.77829i	0.615646	+	0.788023i	$0.288895\pi$
$263$	7.72741	+	28.8391i	0.476492	+	1.77829i	−0.139154	+	0.990271i	$0.544438\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$		0			0
$266$	1.96410	+	5.66987i	0.120427	+	0.347642i
$267$	−4.89898	−	4.89898i	−0.299813	−	0.299813i
$268$	1.93185	+	0.517638i	0.118007	+	0.0316198i
$269$	−12.6603	+	21.9282i	−0.771909	+	1.33699i	0.164606	+	0.986359i	$0.447365\pi$
$269$	−12.6603	+	21.9282i	−0.771909	+	1.33699i	−0.936515	+	0.350627i	$0.885969\pi$
$270$		0			0
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	−0.274586	−	0.961563i	$-0.588541\pi$
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	0.695444	+	0.718580i	$0.255208\pi$
$272$	−5.27792	+	5.27792i	−0.320021	+	0.320021i
$273$	6.62278	−	13.6431i	0.400829	−	0.825717i
$274$			18.9282i			1.14349i
$275$		0			0
$276$	−5.13397	−	2.96410i	−0.309029	−	0.178418i
$277$	−21.2504	+	5.69402i	−1.27681	+	0.342120i	−0.832636	−	0.553820i	$-0.813170\pi$
$277$	−21.2504	+	5.69402i	−1.27681	+	0.342120i	−0.444174	+	0.895940i	$0.646503\pi$
$278$	2.68973	−	10.0382i	0.161319	−	0.602051i
$279$	7.46410			0.446864
$280$		0			0
$281$	−27.9282			−1.66606			−0.833028	−	0.553230i	$-0.813395\pi$
$281$	−27.9282			−1.66606			−0.833028	+	0.553230i	$0.813395\pi$
$282$	0.309587	−	1.15539i	0.0184356	−	0.0688027i
$283$	12.1087	−	3.24453i	0.719790	−	0.192867i	0.119712	−	0.992809i	$-0.461803\pi$
$283$	12.1087	−	3.24453i	0.719790	−	0.192867i	0.600078	+	0.799941i	$0.295136\pi$
$284$	7.73205	+	4.46410i	0.458813	+	0.264896i
$285$		0			0
$286$			5.73205i			0.338943i
$287$	5.98502	−	0.429705i	0.353285	−	0.0253647i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−33.5263	+	19.3564i	−1.97213	+	1.13861i
$290$		0			0
$291$	1.46410	−	2.53590i	0.0858272	−	0.148657i
$292$	3.86370	+	1.03528i	0.226106	+	0.0605850i
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	0.741976	−	0.670426i	$-0.233889\pi$
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	−0.670426	+	0.741976i	$0.733889\pi$
$294$	1.00000	+	6.92820i	0.0583212	+	0.404061i
$295$		0			0
$296$	1.96410	+	3.40192i	0.114161	+	0.197733i
$297$	−0.258819	−	0.965926i	−0.0150182	−	0.0560487i
$298$	−0.240237	−	0.896575i	−0.0139165	−	0.0519372i
$299$	16.9904	+	29.4282i	0.982579	+	1.70188i
$300$		0			0
$301$	17.8564	+	15.4641i	1.02923	+	0.891336i
$302$	2.72689	+	2.72689i	0.156915	+	0.156915i
$303$	−1.03528	−	0.277401i	−0.0594751	−	0.0159363i
$304$	−1.13397	+	1.96410i	−0.0650379	+	0.112649i
$305$		0			0
$306$	−6.46410	+	3.73205i	−0.369528	+	0.213347i
$307$	15.8338	−	15.8338i	0.903680	−	0.903680i	−0.0920724	−	0.995752i	$-0.529349\pi$
$307$	15.8338	−	15.8338i	0.903680	−	0.903680i	0.995752	+	0.0920724i	$0.0293491\pi$
$308$	−1.48356	−	2.19067i	−0.0845339	−	0.124825i
$309$			18.3923i			1.04630i
$310$		0			0
$311$	17.7846	+	10.2679i	1.00847	+	0.582242i	0.910744	−	0.412971i	$-0.135509\pi$
$311$	17.7846	+	10.2679i	1.00847	+	0.582242i	0.0977286	+	0.995213i	$0.468842\pi$
$312$	5.53674	−	1.48356i	0.313456	−	0.0839903i
$313$	8.06918	−	30.1146i	0.456097	−	1.70218i	−0.228746	−	0.973486i	$-0.573462\pi$
$313$	8.06918	−	30.1146i	0.456097	−	1.70218i	0.684843	−	0.728691i	$-0.259871\pi$
$314$	−4.66025			−0.262993
$315$		0			0
$316$	3.07180			0.172802
$317$	3.62347	−	13.5230i	0.203514	−	0.759525i	−0.786383	−	0.617739i	$-0.788049\pi$
$317$	3.62347	−	13.5230i	0.203514	−	0.759525i	0.989897	−	0.141786i	$-0.0452845\pi$
$318$	−0.965926	+	0.258819i	−0.0541664	+	0.0145139i
$319$	−6.00000	−	3.46410i	−0.335936	−	0.193952i
$320$		0			0
$321$		−	14.9282i		−	0.833211i
$322$	−14.1100	−	6.84941i	−0.786317	−	0.381703i
$323$	−11.9700	+	11.9700i	−0.666031	+	0.666031i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	16.3514	+	4.38134i	0.904234	+	0.242289i
$328$	1.60368	+	1.60368i	0.0885485	+	0.0885485i
$329$	0.598076	−	3.10770i	0.0329730	−	0.171333i
$330$		0			0
$331$	−12.8923	−	22.3301i	−0.708625	−	1.22737i	−0.965367	−	0.260895i	$-0.915982\pi$
$331$	−12.8923	−	22.3301i	−0.708625	−	1.22737i	0.256742	−	0.966480i	$-0.417351\pi$
$332$	−2.68973	−	10.0382i	−0.147618	−	0.550918i
$333$	1.01669	+	3.79435i	0.0557145	+	0.207929i
$334$	3.40192	+	5.89230i	0.186145	+	0.322413i
$335$		0			0
$336$	−1.73205	+	2.00000i	−0.0944911	+	0.109109i
$337$	7.82894	+	7.82894i	0.426470	+	0.426470i	0.887424	−	0.460954i	$-0.152493\pi$
$337$	7.82894	+	7.82894i	0.426470	+	0.426470i	−0.460954	+	0.887424i	$0.652493\pi$
$338$	−19.1798	−	5.13922i	−1.04324	−	0.279537i
$339$	6.46410	−	11.1962i	0.351082	−	0.608092i
$340$		0			0
$341$	−6.46410	+	3.73205i	−0.350051	+	0.202102i
$342$	−1.60368	+	1.60368i	−0.0867172	+	0.0867172i
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$			8.92820i			0.481376i
$345$		0			0
$346$	−6.57180	−	3.79423i	−0.353302	−	0.203979i
$347$	−2.82843	+	0.757875i	−0.151838	+	0.0406848i	−0.333937	−	0.942595i	$-0.608377\pi$
$347$	−2.82843	+	0.757875i	−0.151838	+	0.0406848i	0.182099	+	0.983280i	$0.441711\pi$
$348$	−1.79315	+	6.69213i	−0.0961230	+	0.358736i
$349$	1.85641			0.0993712			0.0496856	−	0.998765i	$-0.484178\pi$
$349$	1.85641			0.0993712			0.0496856	+	0.998765i	$0.484178\pi$
$350$		0			0
$351$	5.73205			0.305954
$352$	0.258819	−	0.965926i	0.0137951	−	0.0514840i
$353$	−6.69213	+	1.79315i	−0.356186	+	0.0954398i	−0.432475	−	0.901646i	$-0.642360\pi$
$353$	−6.69213	+	1.79315i	−0.356186	+	0.0954398i	0.0762887	+	0.997086i	$0.475693\pi$
$354$	−9.92820	−	5.73205i	−0.527678	−	0.304655i
$355$		0			0
$356$		−	6.92820i		−	0.367194i
$357$	−16.3514	+	11.0735i	−0.865407	+	0.586070i
$358$	−6.36396	+	6.36396i	−0.336346	+	0.336346i
$359$	−4.39230	+	2.53590i	−0.231817	+	0.133840i	−0.611410	−	0.791314i	$-0.709397\pi$
$359$	−4.39230	+	2.53590i	−0.231817	+	0.133840i	0.379593	+	0.925154i	$0.376064\pi$
$360$		0			0
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	−13.9019	−	3.72500i	−0.730668	−	0.195782i
$363$	−7.07107	−	7.07107i	−0.371135	−	0.371135i
$364$	14.3301	−	4.96410i	0.751103	−	0.260190i
$365$		0			0
$366$	5.73205	+	9.92820i	0.299619	+	0.518955i
$367$	7.89829	+	29.4768i	0.412288	+	1.53868i	0.790207	+	0.612840i	$0.209973\pi$
$367$	7.89829	+	29.4768i	0.412288	+	1.53868i	−0.377920	+	0.925838i	$0.623360\pi$
$368$	−1.53433	−	5.72620i	−0.0799826	−	0.298499i
$369$	1.13397	+	1.96410i	0.0590324	+	0.102247i
$370$		0			0
$371$	−2.50000	+	0.866025i	−0.129794	+	0.0449618i
$372$	5.27792	+	5.27792i	0.273647	+	0.273647i
$373$	25.1141	+	6.72930i	1.30036	+	0.348430i	0.841585	−	0.540124i	$-0.181623\pi$
$373$	25.1141	+	6.72930i	1.30036	+	0.348430i	0.458772	+	0.888554i	$0.348289\pi$
$374$	3.73205	−	6.46410i	0.192980	−	0.334251i
$375$		0			0
$376$	1.03590	−	0.598076i	0.0534224	−	0.0308434i
$377$	28.0812	−	28.0812i	1.44626	−	1.44626i
$378$	−2.19067	+	1.48356i	−0.112676	+	0.0763063i
$379$		−	3.92820i		−	0.201778i	−0.994898	−	0.100889i	$-0.967831\pi$
$379$		−	3.92820i		−	0.201778i	0.994898	−	0.100889i	$-0.0321687\pi$
$380$		0			0
$381$	4.33013	+	2.50000i	0.221839	+	0.128079i
$382$	2.82843	−	0.757875i	0.144715	−	0.0387762i
$383$	−5.68904	+	21.2318i	−0.290696	+	1.08489i	0.653879	+	0.756599i	$0.273141\pi$
$383$	−5.68904	+	21.2318i	−0.290696	+	1.08489i	−0.944575	+	0.328294i	$0.893526\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−22.7846			−1.15971
$387$	−2.31079	+	8.62398i	−0.117464	+	0.438382i
$388$	2.82843	−	0.757875i	0.143592	−	0.0384753i
$389$	−31.7321	−	18.3205i	−1.60888	−	0.928887i	−0.989622	−	0.143699i	$-0.954100\pi$
$389$	−31.7321	−	18.3205i	−1.60888	−	0.928887i	−0.619257	−	0.785188i	$-0.712566\pi$
$390$		0			0
$391$		−	44.2487i		−	2.23775i
$392$	−4.19187	+	5.60609i	−0.211722	+	0.283150i
$393$	−2.91636	+	2.91636i	−0.147111	+	0.147111i
$394$	14.5981	−	8.42820i	0.735440	−	0.424607i
$395$		0			0
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−27.8038	−	7.45001i	−1.39543	−	0.373905i	−0.518730	−	0.854938i	$-0.673595\pi$
$397$	−27.8038	−	7.45001i	−1.39543	−	0.373905i	−0.876702	+	0.481033i	$0.840262\pi$
$398$	8.86422	+	8.86422i	0.444323	+	0.444323i
$399$	−3.92820	+	4.53590i	−0.196656	+	0.227079i
$400$		0			0
$401$	−0.964102	−	1.66987i	−0.0481449	−	0.0833895i	0.840949	−	0.541115i	$-0.181998\pi$
$401$	−0.964102	−	1.66987i	−0.0481449	−	0.0833895i	−0.889094	+	0.457725i	$0.848664\pi$
$402$	0.517638	+	1.93185i	0.0258174	+	0.0963520i
$403$	−11.0735	−	41.3268i	−0.551609	−	2.05863i
$404$	−0.535898	−	0.928203i	−0.0266619	−	0.0461798i
$405$		0			0
$406$	−3.46410	+	18.0000i	−0.171920	+	0.893325i
$407$	−2.77766	−	2.77766i	−0.137683	−	0.137683i
$408$	−7.20977	−	1.93185i	−0.356937	−	0.0956409i
$409$	14.3923	−	24.9282i	0.711654	−	1.23262i	−0.252582	−	0.967575i	$-0.581280\pi$
$409$	14.3923	−	24.9282i	0.711654	−	1.23262i	0.964236	−	0.265045i	$-0.0853868\pi$
$410$		0			0
$411$	−16.3923	+	9.46410i	−0.808573	+	0.466830i
$412$	−13.0053	+	13.0053i	−0.640726	+	0.640726i
$413$	−27.2862	−	13.2456i	−1.34266	−	0.651771i
$414$		−	5.92820i		−	0.291355i
$415$		0			0
$416$	4.96410	+	2.86603i	0.243385	+	0.140518i
$417$	10.0382	−	2.68973i	0.491573	−	0.131716i
$418$	0.586988	−	2.19067i	0.0287105	−	0.107149i
$419$	−11.0526			−0.539953			−0.269976	−	0.962867i	$-0.587016\pi$
$419$	−11.0526			−0.539953			−0.269976	+	0.962867i	$0.587016\pi$
$420$		0			0
$421$	−13.8564			−0.675320			−0.337660	−	0.941268i	$-0.609635\pi$
$421$	−13.8564			−0.675320			−0.337660	+	0.941268i	$0.609635\pi$
$422$	5.12063	−	19.1105i	0.249269	−	0.930283i
$423$	1.15539	−	0.309587i	0.0561772	−	0.0150526i
$424$	−0.866025	−	0.500000i	−0.0420579	−	0.0242821i
$425$		0			0
$426$			8.92820i			0.432573i
$427$	17.0077	+	25.1141i	0.823062	+	1.21536i
$428$	10.5558	−	10.5558i	0.510235	−	0.510235i
$429$	−4.96410	+	2.86603i	−0.239669	+	0.138373i
$430$		0			0
$431$	16.8564	−	29.1962i	0.811945	−	1.40633i	−0.0995567	−	0.995032i	$-0.531742\pi$
$431$	16.8564	−	29.1962i	0.811945	−	1.40633i	0.911501	−	0.411297i	$-0.134924\pi$
$432$	−0.965926	−	0.258819i	−0.0464731	−	0.0124524i
$433$	−11.3137	−	11.3137i	−0.543702	−	0.543702i	0.380910	−	0.924612i	$-0.375611\pi$
$433$	−11.3137	−	11.3137i	−0.543702	−	0.543702i	−0.924612	+	0.380910i	$0.875611\pi$
$434$	14.9282	+	12.9282i	0.716577	+	0.620574i
$435$		0			0
$436$	8.46410	+	14.6603i	0.405357	+	0.702099i
$437$	−3.47979	−	12.9867i	−0.166461	−	0.621240i
$438$	1.03528	+	3.86370i	0.0494674	+	0.184615i
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$		0			0
$441$	−5.50000	+	4.33013i	−0.261905	+	0.206197i
$442$	30.2533	+	30.2533i	1.43900	+	1.43900i
$443$	−26.9072	−	7.20977i	−1.27840	−	0.342546i	−0.445157	−	0.895452i	$-0.646852\pi$
$443$	−26.9072	−	7.20977i	−1.27840	−	0.342546i	−0.833244	+	0.552906i	$0.813519\pi$
$444$	−1.96410	+	3.40192i	−0.0932121	+	0.161448i
$445$		0			0
$446$	8.07180	−	4.66025i	0.382211	−	0.220669i
$447$	0.656339	−	0.656339i	0.0310438	−	0.0310438i
$448$	−2.63896	+	0.189469i	−0.124679	+	0.00895155i
$449$		−	13.9282i		−	0.657313i	−0.944450	−	0.328656i	$-0.893404\pi$
$449$		−	13.9282i		−	0.657313i	0.944450	−	0.328656i	$-0.106596\pi$
$450$		0			0
$451$	−1.96410	−	1.13397i	−0.0924859	−	0.0533968i
$452$	12.4877	−	3.34607i	0.587371	−	0.157386i
$453$	−0.998111	+	3.72500i	−0.0468954	+	0.175016i
$454$	3.46410			0.162578
$455$		0			0
$456$	−2.26795			−0.106206
$457$	−4.10394	+	15.3161i	−0.191974	+	0.716458i	0.801055	+	0.598591i	$0.204272\pi$
$457$	−4.10394	+	15.3161i	−0.191974	+	0.716458i	−0.993029	+	0.117867i	$0.962394\pi$
$458$	2.82843	−	0.757875i	0.132164	−	0.0354132i
$459$	−6.46410	−	3.73205i	−0.301718	−	0.174197i
$460$		0			0
$461$			38.6410i			1.79969i	0.436208	+	0.899846i	$0.356321\pi$
$461$			38.6410i			1.79969i	−0.436208	+	0.899846i	$0.643679\pi$
$462$	1.15539	−	2.38014i	0.0537538	−	0.110734i
$463$	−16.0604	+	16.0604i	−0.746389	+	0.746389i	−0.973799	−	0.227410i	$-0.926974\pi$
$463$	−16.0604	+	16.0604i	−0.746389	+	0.746389i	0.227410	+	0.973799i	$0.426974\pi$
$464$	−6.00000	+	3.46410i	−0.278543	+	0.160817i
$465$		0			0
$466$	−0.928203	+	1.60770i	−0.0429982	+	0.0744750i
$467$	−6.17449	−	1.65445i	−0.285721	−	0.0765588i	0.113112	−	0.993582i	$-0.463918\pi$
$467$	−6.17449	−	1.65445i	−0.285721	−	0.0765588i	−0.398833	+	0.917023i	$0.630585\pi$
$468$	4.05317	+	4.05317i	0.187358	+	0.187358i
$469$	1.73205	+	5.00000i	0.0799787	+	0.230879i
$470$		0			0
$471$	−2.33013	−	4.03590i	−0.107367	−	0.185964i
$472$	−2.96713	−	11.0735i	−0.136573	−	0.509698i
$473$	−2.31079	−	8.62398i	−0.106250	−	0.396531i
$474$	1.53590	+	2.66025i	0.0705461	+	0.122190i
$475$		0			0
$476$	−19.3923	−	3.73205i	−0.888845	−	0.171058i
$477$	−0.707107	−	0.707107i	−0.0323762	−	0.0323762i
$478$	23.1822	+	6.21166i	1.06033	+	0.284115i
$479$	14.5359	−	25.1769i	0.664162	−	1.15036i	−0.315350	−	0.948976i	$-0.602122\pi$
$479$	14.5359	−	25.1769i	0.664162	−	1.15036i	0.979512	−	0.201387i	$-0.0645449\pi$
$480$		0			0
$481$	19.5000	−	11.2583i	0.889123	−	0.513336i
$482$	−15.7458	+	15.7458i	−0.717202	+	0.717202i
$483$	−1.12321	−	15.6443i	−0.0511078	−	0.711839i
$484$		−	10.0000i		−	0.454545i
$485$		0			0
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−5.65685	+	1.51575i	−0.256337	+	0.0686852i	−0.384699	−	0.923042i	$-0.625695\pi$
$487$	−5.65685	+	1.51575i	−0.256337	+	0.0686852i	0.128362	+	0.991727i	$0.459028\pi$
$488$	−2.96713	+	11.0735i	−0.134316	+	0.501273i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	−11.7128			−0.528592			−0.264296	−	0.964442i	$-0.585140\pi$
$491$	−11.7128			−0.528592			−0.264296	+	0.964442i	$0.585140\pi$
$492$	−0.586988	+	2.19067i	−0.0264635	+	0.0987631i
$493$	−49.9507	+	13.3843i	−2.24967	+	0.602797i
$494$	11.2583	+	6.50000i	0.506536	+	0.292449i
$495$		0			0
$496$			7.46410i			0.335148i
$497$	1.69161	+	23.5612i	0.0758793	+	1.05686i
$498$	7.34847	−	7.34847i	0.329293	−	0.329293i
$499$	24.2487	−	14.0000i	1.08552	−	0.626726i	0.153141	−	0.988204i	$-0.451061\pi$
$499$	24.2487	−	14.0000i	1.08552	−	0.626726i	0.932381	+	0.361478i	$0.117728\pi$
$500$		0			0
$501$	−3.40192	+	5.89230i	−0.151987	+	0.263249i
$502$	7.08965	+	1.89967i	0.316427	+	0.0847862i
$503$	−9.62209	−	9.62209i	−0.429028	−	0.429028i	0.459269	−	0.888297i	$-0.348111\pi$
$503$	−9.62209	−	9.62209i	−0.429028	−	0.429028i	−0.888297	+	0.459269i	$0.848111\pi$
$504$	−2.59808	−	0.500000i	−0.115728	−	0.0222718i
$505$		0			0
$506$	2.96410	+	5.13397i	0.131770	+	0.228233i
$507$	−5.13922	−	19.1798i	−0.228241	−	0.851806i
$508$	1.29410	+	4.82963i	0.0574162	+	0.214280i
$509$	−5.19615	−	9.00000i	−0.230315	−	0.398918i	0.727586	−	0.686017i	$-0.240642\pi$
$509$	−5.19615	−	9.00000i	−0.230315	−	0.398918i	−0.957901	+	0.287099i	$0.907309\pi$
$510$		0			0
$511$	3.46410	+	10.0000i	0.153243	+	0.442374i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.19067	−	0.586988i	−0.0967205	−	0.0259162i
$514$	−1.19615	+	2.07180i	−0.0527600	+	0.0913830i
$515$		0			0
$516$	−7.73205	+	4.46410i	−0.340385	+	0.196521i
$517$	−0.845807	+	0.845807i	−0.0371986	+	0.0371986i
$518$	−4.53862	+	9.34967i	−0.199416	+	0.410801i
$519$		−	7.58846i		−	0.333096i
$520$		0			0
$521$	27.8205	+	16.0622i	1.21884	+	0.703697i	0.964669	−	0.263463i	$-0.0848647\pi$
$521$	27.8205	+	16.0622i	1.21884	+	0.703697i	0.254169	+	0.967160i	$0.418198\pi$
$522$	−6.69213	+	1.79315i	−0.292907	+	0.0784841i
$523$	−1.59008	+	5.93426i	−0.0695293	+	0.259487i	−0.991937	−	0.126730i	$-0.959552\pi$
$523$	−1.59008	+	5.93426i	−0.0695293	+	0.259487i	0.922408	+	0.386217i	$0.126218\pi$
$524$	−4.12436			−0.180173
$525$		0			0
$526$	−29.8564			−1.30180
$527$	−14.4195	+	53.8144i	−0.628125	+	2.34419i
$528$	0.965926	−	0.258819i	0.0420365	−	0.0112637i
$529$	10.5167	+	6.07180i	0.457246	+	0.263991i
$530$		0			0
$531$		−	11.4641i		−	0.497500i
$532$	−5.98502	+	0.429705i	−0.259484	+	0.0186301i
$533$	9.19239	−	9.19239i	0.398167	−	0.398167i
$534$	6.00000	−	3.46410i	0.259645	−	0.149906i
$535$		0			0
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	−8.69333	−	2.32937i	−0.375145	−	0.100520i
$538$	−17.9043	−	17.9043i	−0.771909	−	0.771909i
$539$	2.59808	−	6.50000i	0.111907	−	0.279975i
$540$		0			0
$541$	−15.4641	−	26.7846i	−0.664854	−	1.15156i	−0.979325	−	0.202293i	$-0.935161\pi$
$541$	−15.4641	−	26.7846i	−0.664854	−	1.15156i	0.314471	−	0.949267i	$-0.398173\pi$
$542$	2.07055	+	7.72741i	0.0889378	+	0.331921i
$543$	−3.72500	−	13.9019i	−0.159855	−	0.596588i
$544$	−3.73205	−	6.46410i	−0.160010	−	0.277146i
$545$		0			0
$546$	11.4641	+	9.92820i	0.490618	+	0.424888i
$547$	−18.1817	−	18.1817i	−0.777394	−	0.777394i	0.201993	−	0.979387i	$-0.435258\pi$
$547$	−18.1817	−	18.1817i	−0.777394	−	0.777394i	−0.979387	+	0.201993i	$0.935258\pi$
$548$	−18.2832	−	4.89898i	−0.781021	−	0.209274i
$549$	−5.73205	+	9.92820i	−0.244638	+	0.423725i
$550$		0			0
$551$	−13.6077	+	7.85641i	−0.579707	+	0.334694i
$552$	4.19187	−	4.19187i	0.178418	−	0.178418i
$553$	4.55721	+	6.72930i	0.193792	+	0.286159i
$554$		−	22.0000i		−	0.934690i
$555$		0			0
$556$	9.00000	+	5.19615i	0.381685	+	0.220366i
$557$	−4.69093	+	1.25693i	−0.198761	+	0.0532579i	−0.356826	−	0.934171i	$-0.616141\pi$
$557$	−4.69093	+	1.25693i	−0.198761	+	0.0532579i	0.158065	+	0.987429i	$0.449474\pi$
$558$	−1.93185	+	7.20977i	−0.0817818	+	0.305214i
$559$	51.1769			2.16455
$560$		0			0
$561$	7.46410			0.315135
$562$	7.22835	−	26.9766i	0.304910	−	1.13794i
$563$	2.31079	−	0.619174i	0.0973881	−	0.0260951i	−0.209796	−	0.977745i	$-0.567280\pi$
$563$	2.31079	−	0.619174i	0.0973881	−	0.0260951i	0.307184	+	0.951650i	$0.400613\pi$
$564$	1.03590	+	0.598076i	0.0436192	+	0.0251836i
$565$		0			0
$566$			12.5359i			0.526923i
$567$	−2.38014	−	1.15539i	−0.0999565	−	0.0485220i
$568$	−6.31319	+	6.31319i	−0.264896	+	0.264896i
$569$	−27.5263	+	15.8923i	−1.15396	+	0.666240i	−0.949849	−	0.312707i	$-0.898764\pi$
$569$	−27.5263	+	15.8923i	−1.15396	+	0.666240i	−0.204112	+	0.978948i	$0.565431\pi$
$570$		0			0
$571$	6.92820	−	12.0000i	0.289936	−	0.502184i	−0.683858	−	0.729615i	$-0.739699\pi$
$571$	6.92820	−	12.0000i	0.289936	−	0.502184i	0.973794	+	0.227431i	$0.0730325\pi$
$572$	−5.53674	−	1.48356i	−0.231503	−	0.0620309i
$573$	2.07055	+	2.07055i	0.0864986	+	0.0864986i
$574$	−1.13397	+	5.89230i	−0.0473312	+	0.245940i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	5.45378	+	20.3538i	0.227044	+	0.847339i	0.981575	+	0.191076i	$0.0611975\pi$
$577$	5.45378	+	20.3538i	0.227044	+	0.847339i	−0.754531	+	0.656264i	$0.772136\pi$
$578$	−10.0196	−	37.3937i	−0.416761	−	1.55537i
$579$	−11.3923	−	19.7321i	−0.473448	−	0.820036i
$580$		0			0
$581$	18.0000	−	20.7846i	0.746766	−	0.862291i
$582$	2.07055	+	2.07055i	0.0858272	+	0.0858272i
$583$	0.965926	+	0.258819i	0.0400046	+	0.0107192i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$		0			0
$586$	−1.50000	+	0.866025i	−0.0619644	+	0.0357752i
$587$	−15.0759	+	15.0759i	−0.622248	+	0.622248i	−0.946106	−	0.323858i	$-0.895020\pi$
$587$	−15.0759	+	15.0759i	−0.622248	+	0.622248i	0.323858	+	0.946106i	$0.395020\pi$
$588$	−6.95095	−	0.827225i	−0.286652	−	0.0341142i
$589$			16.9282i			0.697514i
$590$		0			0
$591$	14.5981	+	8.42820i	0.600485	+	0.346690i
$592$	−3.79435	+	1.01669i	−0.155947	+	0.0417859i
$593$	−10.9719	+	40.9478i	−0.450563	+	1.68153i	0.250250	+	0.968181i	$0.419487\pi$
$593$	−10.9719	+	40.9478i	−0.450563	+	1.68153i	−0.700814	+	0.713344i	$0.747180\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$	0.928203			0.0380207
$597$	−3.24453	+	12.1087i	−0.132790	+	0.495578i
$598$	−32.8229	+	8.79487i	−1.34223	+	0.359649i
$599$	−36.2487	−	20.9282i	−1.48108	−	0.855103i	−0.481312	−	0.876549i	$-0.659840\pi$
$599$	−36.2487	−	20.9282i	−1.48108	−	0.855103i	−0.999770	+	0.0214460i	$0.993173\pi$
$600$		0			0
$601$		−	28.7846i		−	1.17415i	−0.809533	−	0.587074i	$-0.800280\pi$
$601$		−	28.7846i		−	1.17415i	0.809533	−	0.587074i	$-0.199720\pi$
$602$	−19.5588	+	13.2456i	−0.797155	+	0.539849i
$603$	−1.41421	+	1.41421i	−0.0575912	+	0.0575912i
$604$	−3.33975	+	1.92820i	−0.135892	+	0.0784575i
$605$		0			0
$606$	0.535898	−	0.928203i	0.0217694	−	0.0377057i
$607$	−18.4034	−	4.93117i	−0.746969	−	0.200150i	−0.134796	−	0.990873i	$-0.543038\pi$
$607$	−18.4034	−	4.93117i	−0.746969	−	0.200150i	−0.612173	+	0.790724i	$0.709705\pi$
$608$	−1.60368	−	1.60368i	−0.0650379	−	0.0650379i
$609$	−17.3205	+	6.00000i	−0.701862	+	0.243132i
$610$		0			0
$611$	−3.42820	−	5.93782i	−0.138690	−	0.240219i
$612$	−1.93185	−	7.20977i	−0.0780905	−	0.291438i
$613$	4.64016	+	17.3173i	0.187414	+	0.699440i	0.994101	+	0.108460i	$0.0345920\pi$
$613$	4.64016	+	17.3173i	0.187414	+	0.699440i	−0.806686	+	0.590980i	$0.798741\pi$
$614$	11.1962	+	19.3923i	0.451840	+	0.782610i
$615$		0			0
$616$	2.50000	−	0.866025i	0.100728	−	0.0348932i
$617$	2.17209	+	2.17209i	0.0874450	+	0.0874450i	0.749476	−	0.662031i	$-0.230305\pi$
$617$	2.17209	+	2.17209i	0.0874450	+	0.0874450i	−0.662031	+	0.749476i	$0.730305\pi$
$618$	−17.7656	−	4.76028i	−0.714637	−	0.191486i
$619$	5.79423	−	10.0359i	0.232890	−	0.403377i	−0.725768	−	0.687940i	$-0.758515\pi$
$619$	5.79423	−	10.0359i	0.232890	−	0.403377i	0.958657	+	0.284563i	$0.0918485\pi$
$620$		0			0
$621$	5.13397	−	2.96410i	0.206019	−	0.118945i
$622$	−14.5211	+	14.5211i	−0.582242	+	0.582242i
$623$	15.1774	−	10.2784i	0.608070	−	0.411797i
$624$			5.73205i			0.229466i
$625$		0			0
$626$	27.0000	+	15.5885i	1.07914	+	0.623040i
$627$	2.19067	−	0.586988i	0.0874870	−	0.0234421i
$628$	1.20616	−	4.50146i	0.0481311	−	0.179628i
$629$	−29.3205			−1.16909
$630$		0			0
$631$	42.7846			1.70323			0.851614	−	0.524169i	$-0.175624\pi$
$631$	42.7846			1.70323			0.851614	+	0.524169i	$0.175624\pi$
$632$	−0.795040	+	2.96713i	−0.0316250	+	0.118026i
$633$	19.1105	−	5.12063i	0.759573	−	0.203527i
$634$	12.1244	+	7.00000i	0.481520	+	0.278006i
$635$		0			0
$636$		−	1.00000i		−	0.0396526i
$637$	32.1344	+	24.0280i	1.27321	+	0.952025i
$638$	4.89898	−	4.89898i	0.193952	−	0.193952i
$639$	−7.73205	+	4.46410i	−0.305875	+	0.176597i
$640$		0			0
$641$	−15.9641	+	27.6506i	−0.630544	+	1.09213i	0.356897	+	0.934144i	$0.383835\pi$
$641$	−15.9641	+	27.6506i	−0.630544	+	1.09213i	−0.987441	+	0.157991i	$0.949498\pi$
$642$	14.4195	+	3.86370i	0.569094	+	0.152488i
$643$	−29.2180	−	29.2180i	−1.15225	−	1.15225i	−0.986101	−	0.166144i	$-0.946868\pi$
$643$	−29.2180	−	29.2180i	−1.15225	−	1.15225i	−0.166144	−	0.986101i	$-0.553132\pi$
$644$	10.2679	−	11.8564i	0.404614	−	0.467208i
$645$		0			0
$646$	−8.46410	−	14.6603i	−0.333016	−	0.576800i
$647$	−1.14179	−	4.26122i	−0.0448884	−	0.167526i	0.939843	−	0.341607i	$-0.110971\pi$
$647$	−1.14179	−	4.26122i	−0.0448884	−	0.167526i	−0.984731	+	0.174081i	$0.944305\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	5.73205	+	9.92820i	0.225003	+	0.389716i
$650$		0			0
$651$	−3.73205	+	19.3923i	−0.146271	+	0.760044i
$652$	−8.48528	−	8.48528i	−0.332309	−	0.332309i
$653$	23.8707	+	6.39615i	0.934134	+	0.250301i	0.693617	−	0.720344i	$-0.256016\pi$
$653$	23.8707	+	6.39615i	0.934134	+	0.250301i	0.240518	+	0.970645i	$0.422683\pi$
$654$	−8.46410	+	14.6603i	−0.330973	+	0.573261i
$655$		0			0
$656$	−1.96410	+	1.13397i	−0.0766853	+	0.0442743i
$657$	−2.82843	+	2.82843i	−0.110347	+	0.110347i
$658$	2.84701	+	1.38203i	0.110988	+	0.0538771i
$659$			39.7128i			1.54699i	0.633801	+	0.773496i	$0.281494\pi$
$659$			39.7128i			1.54699i	−0.633801	+	0.773496i	$0.718506\pi$
$660$		0			0
$661$	7.85641	+	4.53590i	0.305579	+	0.176426i	0.644946	−	0.764228i	$-0.276880\pi$
$661$	7.85641	+	4.53590i	0.305579	+	0.176426i	−0.339368	+	0.940654i	$0.610213\pi$
$662$	24.9060	−	6.67355i	0.968000	−	0.259375i
$663$	−11.0735	+	41.3268i	−0.430058	+	1.60500i
$664$	10.3923			0.403300
$665$		0			0
$666$	−3.92820			−0.152215
$667$	10.6302	−	39.6723i	0.411602	−	1.53612i
$668$	−6.57201	+	1.76097i	−0.254279	+	0.0681338i
$669$	8.07180	+	4.66025i	0.312074	+	0.180176i
$670$		0			0
$671$		−	11.4641i		−	0.442567i
$672$	−1.48356	−	2.19067i	−0.0572297	−	0.0845070i
$673$	17.5254	−	17.5254i	0.675553	−	0.675553i	−0.283438	−	0.958991i	$-0.591475\pi$
$673$	17.5254	−	17.5254i	0.675553	−	0.675553i	0.958991	+	0.283438i	$0.0914749\pi$
$674$	−9.58846	+	5.53590i	−0.369334	+	0.213235i
$675$		0			0
$676$	9.92820	−	17.1962i	0.381854	−	0.661390i
$677$	48.2777	+	12.9360i	1.85546	+	0.497170i	0.999793	−	0.0203517i	$-0.00647859\pi$
$677$	48.2777	+	12.9360i	1.85546	+	0.497170i	0.855670	+	0.517522i	$0.173145\pi$
$678$	9.14162	+	9.14162i	0.351082	+	0.351082i
$679$	5.85641	+	5.07180i	0.224748	+	0.194638i
$680$		0			0
$681$	1.73205	+	3.00000i	0.0663723	+	0.114960i
$682$	−1.93185	−	7.20977i	−0.0739744	−	0.276076i
$683$	3.66063	+	13.6617i	0.140070	+	0.522749i	0.999925	+	0.0122111i	$0.00388702\pi$
$683$	3.66063	+	13.6617i	0.140070	+	0.522749i	−0.859855	+	0.510538i	$0.829446\pi$
$684$	−1.13397	−	1.96410i	−0.0433586	−	0.0750993i
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	2.07055	+	2.07055i	0.0789965	+	0.0789965i
$688$	−8.62398	−	2.31079i	−0.328786	−	0.0880980i
$689$	−2.86603	+	4.96410i	−0.109187	+	0.189117i
$690$		0			0
$691$	−34.8564	+	20.1244i	−1.32600	+	0.765567i	−0.984678	−	0.174380i	$-0.944208\pi$
$691$	−34.8564	+	20.1244i	−1.32600	+	0.765567i	−0.341322	+	0.939947i	$0.610875\pi$
$692$	5.36585	−	5.36585i	0.203979	−	0.203979i
$693$	2.63896	−	0.189469i	0.100246	−	0.00719732i
$694$		−	2.92820i		−	0.111153i
$695$		0			0
$696$	−6.00000	−	3.46410i	−0.227429	−	0.131306i
$697$	−16.3514	+	4.38134i	−0.619353	+	0.165955i
$698$	−0.480473	+	1.79315i	−0.0181862	+	0.0678718i
$699$	−1.85641			−0.0702157
$700$		0			0
$701$	−4.14359			−0.156501			−0.0782507	−	0.996934i	$-0.524933\pi$
$701$	−4.14359			−0.156501			−0.0782507	+	0.996934i	$0.524933\pi$
$702$	−1.48356	+	5.53674i	−0.0559935	+	0.208971i
$703$	−8.60540	+	2.30581i	−0.324559	+	0.0869653i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$		0			0
$706$		−	6.92820i		−	0.260746i
$707$	1.23835	−	2.55103i	0.0465729	−	0.0959412i
$708$	8.10634	−	8.10634i	0.304655	−	0.304655i
$709$	23.3205	−	13.4641i	0.875820	−	0.505655i	0.00654213	−	0.999979i	$-0.497918\pi$
$709$	23.3205	−	13.4641i	0.875820	−	0.505655i	0.869278	+	0.494324i	$0.164584\pi$
$710$		0			0
$711$	−1.53590	+	2.66025i	−0.0576007	+	0.0997673i
$712$	6.69213	+	1.79315i	0.250798	+	0.0672012i
$713$	−31.2886	−	31.2886i	−1.17177	−	1.17177i
$714$	−6.46410	−	18.6603i	−0.241913	−	0.698342i
$715$		0			0
$716$	−4.50000	−	7.79423i	−0.168173	−	0.291284i
$717$	6.21166	+	23.1822i	0.231979	+	0.865756i
$718$	−1.31268	−	4.89898i	−0.0489887	−	0.182828i
$719$	3.19615	+	5.53590i	0.119196	+	0.206454i	0.919449	−	0.393208i	$-0.128635\pi$
$719$	3.19615	+	5.53590i	0.119196	+	0.206454i	−0.800253	+	0.599662i	$0.795302\pi$
$720$		0			0
$721$	−47.7846	−	9.19615i	−1.77959	−	0.342483i
$722$	9.79796	+	9.79796i	0.364642	+	0.364642i
$723$	−21.5092	−	5.76337i	−0.799935	−	0.214342i
$724$	7.19615	−	12.4641i	0.267443	−	0.463225i
$725$		0			0
$726$	8.66025	−	5.00000i	0.321412	−	0.185567i
$727$	10.8468	−	10.8468i	0.402287	−	0.402287i	−0.476751	−	0.879038i	$-0.658186\pi$
$727$	10.8468	−	10.8468i	0.402287	−	0.402287i	0.879038	+	0.476751i	$0.158186\pi$
$728$	1.08604	+	15.1266i	0.0402515	+	0.560631i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−57.7128	−	33.3205i	−2.13459	−	1.23240i
$732$	−11.0735	+	2.96713i	−0.409287	+	0.109668i
$733$	3.89589	−	14.5397i	0.143898	−	0.537034i	−0.855904	−	0.517135i	$-0.826999\pi$
$733$	3.89589	−	14.5397i	0.143898	−	0.537034i	0.999802	−	0.0198997i	$-0.00633470\pi$
$734$	−30.5167			−1.12639
$735$		0			0
$736$	5.92820			0.218516
$737$	0.517638	−	1.93185i	0.0190674	−	0.0711607i
$738$	−2.19067	+	0.586988i	−0.0806397	+	0.0216073i
$739$	17.2583	+	9.96410i	0.634858	+	0.366535i	0.782631	−	0.622486i	$-0.213877\pi$
$739$	17.2583	+	9.96410i	0.634858	+	0.366535i	−0.147773	+	0.989021i	$0.547211\pi$
$740$		0			0
$741$			13.0000i			0.477567i
$742$	−0.189469	−	2.63896i	−0.00695561	−	0.0968792i
$743$	−5.50455	+	5.50455i	−0.201942	+	0.201942i	−0.800832	−	0.598889i	$-0.795609\pi$
$743$	−5.50455	+	5.50455i	−0.201942	+	0.201942i	0.598889	+	0.800832i	$0.295609\pi$
$744$	−6.46410	+	3.73205i	−0.236985	+	0.136824i
$745$		0			0
$746$	−13.0000	+	22.5167i	−0.475964	+	0.824394i
$747$	10.0382	+	2.68973i	0.367278	+	0.0984119i
$748$	5.27792	+	5.27792i	0.192980	+	0.192980i
$749$	38.7846	+	7.46410i	1.41716	+	0.272732i
$750$		0			0
$751$	6.92820	+	12.0000i	0.252814	+	0.437886i	0.964299	−	0.264814i	$-0.0853107\pi$
$751$	6.92820	+	12.0000i	0.252814	+	0.437886i	−0.711486	+	0.702701i	$0.751977\pi$
$752$	0.309587	+	1.15539i	0.0112895	+	0.0421329i
$753$	1.89967	+	7.08965i	0.0692277	+	0.258361i
$754$	19.8564	+	34.3923i	0.723128	+	1.25249i
$755$		0			0
$756$	−0.866025	−	2.50000i	−0.0314970	−	0.0909241i
$757$	−26.6670	−	26.6670i	−0.969228	−	0.969228i	0.0303124	−	0.999540i	$-0.490350\pi$
$757$	−26.6670	−	26.6670i	−0.969228	−	0.969228i	−0.999540	+	0.0303124i	$0.990350\pi$
$758$	3.79435	+	1.01669i	0.137817	+	0.0369280i
$759$	−2.96410	+	5.13397i	−0.107590	+	0.186351i
$760$		0			0
$761$	41.8923	−	24.1865i	1.51859	−	0.876761i	0.518834	−	0.854875i	$-0.326366\pi$
$761$	41.8923	−	24.1865i	1.51859	−	0.876761i	0.999760	−	0.0218864i	$-0.00696721\pi$
$762$	−3.53553	+	3.53553i	−0.128079	+	0.128079i
$763$	−19.5588	+	40.2915i	−0.708074	+	1.45865i
$764$			2.92820i			0.105939i
$765$		0			0
$766$	−19.0359	−	10.9904i	−0.687795	−	0.397099i
$767$	−63.4737	+	17.0077i	−2.29190	+	0.614113i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−10.8038			−0.389597			−0.194798	−	0.980843i	$-0.562405\pi$
$769$	−10.8038			−0.389597			−0.194798	+	0.980843i	$0.562405\pi$
$770$		0			0
$771$	−2.39230			−0.0861568
$772$	5.89709	−	22.0082i	0.212241	−	0.792094i
$773$	35.1337	−	9.41404i	1.26367	−	0.338600i	0.436068	−	0.899914i	$-0.356371\pi$
$773$	35.1337	−	9.41404i	1.26367	−	0.338600i	0.827603	+	0.561314i	$0.189704\pi$
$774$	−7.73205	−	4.46410i	−0.277923	−	0.160459i
$775$		0			0
$776$			2.92820i			0.105116i
$777$	−10.3664	+	0.744272i	−0.371891	+	0.0267006i
$778$	25.9091	−	25.9091i	0.928887	−	0.928887i
$779$	−4.45448	+	2.57180i	−0.159598	+	0.0921442i
$780$		0			0
$781$	4.46410	−	7.73205i	0.159738	−	0.276675i
$782$	42.7410	+	11.4524i	1.52841	+	0.409537i
$783$	−4.89898	−	4.89898i	−0.175075	−	0.175075i
$784$	−4.33013	−	5.50000i	−0.154647	−	0.196429i
$785$		0			0
$786$	−2.06218	−	3.57180i	−0.0735554	−	0.127402i
$787$	0.619174	+	2.31079i	0.0220712	+	0.0823707i	0.976083	−	0.217398i	$-0.0697570\pi$
$787$	0.619174	+	2.31079i	0.0220712	+	0.0823707i	−0.954012	+	0.299769i	$0.903090\pi$
$788$	4.36276	+	16.2820i	0.155417	+	0.580024i
$789$	−14.9282	−	25.8564i	−0.531458	−	0.920512i
$790$		0			0
$791$	25.8564	+	22.3923i	0.919348	+	0.796179i
$792$	0.707107	+	0.707107i	0.0251259	+	0.0251259i
$793$	63.4737	+	17.0077i	2.25402	+	0.603962i
$794$	14.3923	−	24.9282i	0.510764	−	0.884669i
$795$		0			0
$796$	−10.8564	+	6.26795i	−0.384795	+	0.222162i
$797$	21.1117	−	21.1117i	0.747814	−	0.747814i	−0.226255	−	0.974068i	$-0.572648\pi$
$797$	21.1117	−	21.1117i	0.747814	−	0.747814i	0.974068	+	0.226255i	$0.0726481\pi$
$798$	−3.36465	−	4.96833i	−0.119107	−	0.175877i
$799$			8.92820i			0.315857i
$800$		0			0
$801$	6.00000	+	3.46410i	0.212000	+	0.122398i
$802$	1.86250	−	0.499056i	0.0657672	−	0.0176223i
$803$	1.03528	−	3.86370i	0.0365341	−	0.136347i
$804$	−2.00000			−0.0705346
$805$		0			0
$806$	42.7846			1.50702
$807$	6.55343	−	24.4577i	0.230692	−	0.860953i
$808$	1.03528	−	0.277401i	0.0364209	−	0.00975895i
$809$	22.2058	+	12.8205i	0.780713	+	0.450745i	0.836683	−	0.547687i	$-0.184492\pi$
$809$	22.2058	+	12.8205i	0.780713	+	0.450745i	−0.0559697	+	0.998432i	$0.517825\pi$
$810$		0			0
$811$		−	2.51666i		−	0.0883719i	−0.999023	−	0.0441860i	$-0.985931\pi$
$811$		−	2.51666i		−	0.0883719i	0.999023	−	0.0441860i	$-0.0140694\pi$
$812$	−16.4901	−	8.00481i	−0.578689	−	0.280914i
$813$	−5.65685	+	5.65685i	−0.198395	+	0.198395i
$814$	3.40192	−	1.96410i	0.119237	−	0.0688417i
$815$		0			0
$816$	3.73205	−	6.46410i	0.130648	−	0.226289i
$817$	−19.5588	−	5.24075i	−0.684274	−	0.183351i
$818$	20.3538	+	20.3538i	0.711654	+	0.711654i
$819$	−2.86603	+	14.8923i	−0.100147	+	0.520379i
$820$		0			0
$821$	11.9282	+	20.6603i	0.416297	+	0.721048i	0.995564	−	0.0940904i	$-0.0299943\pi$
$821$	11.9282	+	20.6603i	0.416297	+	0.721048i	−0.579266	+	0.815138i	$0.696661\pi$
$822$	−4.89898	−	18.2832i	−0.170872	−	0.637701i
$823$	−9.24316	−	34.4959i	−0.322196	−	1.20245i	−0.917101	−	0.398656i	$-0.869477\pi$
$823$	−9.24316	−	34.4959i	−0.322196	−	1.20245i	0.594904	−	0.803796i	$-0.297190\pi$
$824$	−9.19615	−	15.9282i	−0.320363	−	0.554885i
$825$		0			0
$826$	19.8564	−	22.9282i	0.690893	−	0.797774i
$827$	31.0112	+	31.0112i	1.07836	+	1.07836i	0.996656	+	0.0817074i	$0.0260373\pi$
$827$	31.0112	+	31.0112i	1.07836	+	1.07836i	0.0817074	+	0.996656i	$0.473963\pi$
$828$	5.72620	+	1.53433i	0.198999	+	0.0533217i
$829$	−8.26795	+	14.3205i	−0.287158	+	0.497372i	−0.973130	−	0.230256i	$-0.926044\pi$
$829$	−8.26795	+	14.3205i	−0.287158	+	0.497372i	0.685972	+	0.727628i	$0.259377\pi$
$830$		0			0
$831$	19.0526	−	11.0000i	0.660926	−	0.381586i
$832$	−4.05317	+	4.05317i	−0.140518	+	0.140518i
$833$	−20.5940	−	48.0189i	−0.713541	−	1.66376i
$834$			10.3923i			0.359856i
$835$		0			0
$836$	1.96410	+	1.13397i	0.0679299	+	0.0392193i
$837$	−7.20977	+	1.93185i	−0.249206	+	0.0667746i
$838$	2.86061	−	10.6760i	0.0988182	−	0.368795i
$839$	−8.53590			−0.294692			−0.147346	−	0.989085i	$-0.547073\pi$
$839$	−8.53590			−0.294692			−0.147346	+	0.989085i	$0.547073\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	3.58630	−	13.3843i	0.123592	−	0.461252i
$843$	26.9766	−	7.22835i	0.929123	−	0.248958i
$844$	17.1340	+	9.89230i	0.589776	+	0.340507i
$845$		0			0
$846$			1.19615i			0.0411246i
$847$	21.9067	−	14.8356i	0.752723	−	0.509759i
$848$	0.707107	−	0.707107i	0.0242821	−	0.0242821i
$849$	−10.8564	+	6.26795i	−0.372591	+	0.215115i
$850$		0			0
$851$	11.6436	−	20.1673i	0.399137	−	0.691326i
$852$	−8.62398	−	2.31079i	−0.295453	−	0.0791663i
$853$	5.56892	+	5.56892i	0.190676	+	0.190676i	0.795988	−	0.605312i	$-0.206952\pi$
$853$	5.56892	+	5.56892i	0.190676	+	0.190676i	−0.605312	+	0.795988i	$0.706952\pi$
$854$	−28.6603	+	9.92820i	−0.980734	+	0.339736i
$855$		0			0
$856$	7.46410	+	12.9282i	0.255118	+	0.441877i
$857$	−4.14110	−	15.4548i	−0.141457	−	0.527926i	−0.999888	−	0.0149958i	$-0.995227\pi$
$857$	−4.14110	−	15.4548i	−0.141457	−	0.527926i	0.858430	−	0.512931i	$-0.171440\pi$
$858$	−1.48356	−	5.53674i	−0.0506480	−	0.189021i
$859$	6.80385	+	11.7846i	0.232144	+	0.402086i	0.958439	−	0.285298i	$-0.0920925\pi$
$859$	6.80385	+	11.7846i	0.232144	+	0.402086i	−0.726295	+	0.687384i	$0.758759\pi$
$860$		0			0
$861$	−5.66987	+	1.96410i	−0.193229	+	0.0669364i
$862$	23.8386	+	23.8386i	0.811945	+	0.811945i
$863$	38.2903	+	10.2598i	1.30342	+	0.349249i	0.842741	−	0.538319i	$-0.180941\pi$
$863$	38.2903	+	10.2598i	1.30342	+	0.349249i	0.460675	+	0.887569i	$0.347607\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	13.8564	−	8.00000i	0.470860	−	0.271851i
$867$	27.3741	−	27.3741i	0.929673	−	0.929673i
$868$	−16.3514	+	11.0735i	−0.555002	+	0.375858i
$869$		−	3.07180i		−	0.104204i
$870$		0			0
$871$	9.92820	+	5.73205i	0.336404	+	0.194223i
$872$	−16.3514	+	4.38134i	−0.553728	+	0.148371i
$873$	−0.757875	+	2.82843i	−0.0256502	+	0.0957278i
$874$	13.4449			0.454779
$875$		0			0
$876$	−4.00000			−0.135147
$877$	1.01669	−	3.79435i	0.0343313	−	0.128126i	−0.946633	−	0.322312i	$-0.895540\pi$
$877$	1.01669	−	3.79435i	0.0343313	−	0.128126i	0.980965	+	0.194186i	$0.0622066\pi$
$878$	19.3185	−	5.17638i	0.651968	−	0.174694i
$879$	−1.50000	−	0.866025i	−0.0505937	−	0.0292103i
$880$		0			0
$881$			36.9090i			1.24349i	0.783218	+	0.621747i	$0.213577\pi$
$881$			36.9090i			1.24349i	−0.783218	+	0.621747i	$0.786423\pi$
$882$	−2.75908	−	6.43331i	−0.0929029	−	0.216621i
$883$	−24.6980	+	24.6980i	−0.831153	+	0.831153i	−0.987675	−	0.156522i	$-0.949972\pi$
$883$	−24.6980	+	24.6980i	−0.831153	+	0.831153i	0.156522	+	0.987675i	$0.449972\pi$
$884$	−37.0526	+	21.3923i	−1.24621	+	0.719501i
$885$		0			0
$886$	13.9282	−	24.1244i	0.467927	−	0.810474i
$887$	−3.34607	−	0.896575i	−0.112350	−	0.0301041i	0.202206	−	0.979343i	$-0.435189\pi$
$887$	−3.34607	−	0.896575i	−0.112350	−	0.0301041i	−0.314556	+	0.949239i	$0.601856\pi$
$888$	−2.77766	−	2.77766i	−0.0932121	−	0.0932121i
$889$	−8.66025	+	10.0000i	−0.290456	+	0.335389i
$890$		0			0
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	2.41233	+	9.00292i	0.0807706	+	0.301440i
$893$	0.702128	+	2.62038i	0.0234958	+	0.0876875i
$894$	0.464102	+	0.803848i	0.0155219	+	0.0268847i
$895$		0			0
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	−24.0280	−	24.0280i	−0.802272	−	0.802272i
$898$	13.4536	+	3.60488i	0.448953	+	0.120297i
$899$	−25.8564	+	44.7846i	−0.862359	+	1.49365i
$900$		0			0
$901$	6.46410	−	3.73205i	0.215350	−	0.124333i
$902$	1.60368	−	1.60368i	0.0533968	−	0.0533968i
$903$	−21.2504	−	10.3156i	−0.707168	−	0.343282i
$904$			12.9282i			0.429986i
$905$		0			0
$906$	−3.33975	−	1.92820i	−0.110956	−	0.0640603i
$907$	2.07055	−	0.554803i	0.0687516	−	0.0184219i	−0.224279	−	0.974525i	$-0.572003\pi$
$907$	2.07055	−	0.554803i	0.0687516	−	0.0184219i	0.293031	+	0.956103i	$0.405336\pi$
$908$	−0.896575	+	3.34607i	−0.0297539	+	0.111043i
$909$	1.07180			0.0355493
$910$		0			0
$911$	−2.28719			−0.0757779			−0.0378889	−	0.999282i	$-0.512063\pi$
$911$	−2.28719			−0.0757779			−0.0378889	+	0.999282i	$0.512063\pi$
$912$	0.586988	−	2.19067i	0.0194371	−	0.0725404i
$913$	−10.0382	+	2.68973i	−0.332216	+	0.0890170i
$914$	−13.7321	−	7.92820i	−0.454216	−	0.262242i
$915$		0			0
$916$			2.92820i			0.0967506i
$917$	−6.11875	−	9.03511i	−0.202059	−	0.298365i
$918$	5.27792	−	5.27792i	0.174197	−	0.174197i
$919$	38.7846	−	22.3923i	1.27939	−	0.738654i	0.302651	−	0.953102i	$-0.402128\pi$
$919$	38.7846	−	22.3923i	1.27939	−	0.738654i	0.976736	+	0.214448i	$0.0687951\pi$
$920$		0			0
$921$	−11.1962	+	19.3923i	−0.368926	+	0.638998i
$922$	−37.3244	−	10.0010i	−1.22921	−	0.329366i
$923$	36.1875	+	36.1875i	1.19113	+	1.19113i
$924$	2.00000	+	1.73205i	0.0657952	+	0.0569803i
$925$		0			0
$926$	−11.3564	−	19.6699i	−0.373195	−	0.646392i
$927$	−4.76028	−	17.7656i	−0.156348	−	0.583499i
$928$	−1.79315	−	6.69213i	−0.0588631	−	0.219680i
$929$	8.06218	+	13.9641i	0.264511	+	0.458147i	0.967436	−	0.253118i	$-0.0814560\pi$
$929$	8.06218	+	13.9641i	0.264511	+	0.458147i	−0.702924	+	0.711265i	$0.748123\pi$
$930$		0			0
$931$	−9.82051	−	12.4737i	−0.321854	−	0.408810i
$932$	−1.31268	−	1.31268i	−0.0429982	−	0.0429982i
$933$	−19.8362	−	5.31508i	−0.649407	−	0.174008i
$934$	3.19615	−	5.53590i	0.104581	−	0.181140i
$935$		0			0
$936$	−4.96410	+	2.86603i	−0.162257	+	0.0936790i
$937$	6.79367	−	6.79367i	0.221939	−	0.221939i	−0.587375	−	0.809315i	$-0.699839\pi$
$937$	6.79367	−	6.79367i	0.221939	−	0.221939i	0.809315	+	0.587375i	$0.199839\pi$
$938$	−5.27792	+	0.378937i	−0.172330	+	0.0123727i
$939$			31.1769i			1.01742i
$940$		0			0
$941$	6.67949	+	3.85641i	0.217745	+	0.125715i	0.604906	−	0.796297i	$-0.293211\pi$
$941$	6.67949	+	3.85641i	0.217745	+	0.125715i	−0.387161	+	0.922012i	$0.626544\pi$
$942$	4.50146	−	1.20616i	0.146665	−	0.0392989i
$943$	3.47979	−	12.9867i	0.113317	−	0.422906i
$944$	11.4641			0.373125
$945$		0			0
$946$	8.92820			0.290281
$947$	−4.69591	+	17.5254i	−0.152596	+	0.569498i	0.846703	+	0.532066i	$0.178584\pi$
$947$	−4.69591	+	17.5254i	−0.152596	+	0.569498i	−0.999299	+	0.0374316i	$0.988082\pi$
$948$	−2.96713	+	0.795040i	−0.0963678	+	0.0258217i
$949$	19.8564	+	11.4641i	0.644566	+	0.372140i
$950$		0			0
$951$			14.0000i			0.453981i
$952$	8.62398	−	17.7656i	0.279505	−	0.575786i
$953$	32.2223	−	32.2223i	1.04378	−	1.04378i	0.0447862	−	0.998997i	$-0.485739\pi$
$953$	32.2223	−	32.2223i	1.04378	−	1.04378i	0.998997	−	0.0447862i	$-0.0142607\pi$
$954$	0.866025	−	0.500000i	0.0280386	−	0.0161881i
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	6.69213	+	1.79315i	0.216326	+	0.0579643i
$958$	20.5569	+	20.5569i	0.664162	+	0.664162i
$959$	−16.3923	−	47.3205i	−0.529335	−	1.52806i
$960$		0			0
$961$	12.3564	+	21.4019i	0.398594	+	0.690385i
$962$	5.82774	+	21.7494i	0.187894	+	0.701230i
$963$	3.86370	+	14.4195i	0.124506	+	0.464663i
$964$	−11.1340	−	19.2846i	−0.358601	−	0.621115i
$965$		0			0
$966$	15.4019	+	2.96410i	0.495549	+	0.0953684i
$967$	21.1117	+	21.1117i	0.678905	+	0.678905i	0.959753	−	0.280847i	$-0.0906154\pi$
$967$	21.1117	+	21.1117i	0.678905	+	0.678905i	−0.280847	+	0.959753i	$0.590615\pi$
$968$	9.65926	+	2.58819i	0.310460	+	0.0831876i
$969$	8.46410	−	14.6603i	0.271906	−	0.470955i
$970$		0			0
$971$	−38.2128	+	22.0622i	−1.22631	+	0.708009i	−0.966255	−	0.257586i	$-0.917073\pi$
$971$	−38.2128	+	22.0622i	−1.22631	+	0.708009i	−0.260052	+	0.965595i	$0.583740\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	1.96902	+	27.4249i	0.0631238	+	0.879201i
$974$		−	5.85641i		−	0.187651i
$975$		0			0
$976$	−9.92820	−	5.73205i	−0.317794	−	0.183478i
$977$	28.9778	−	7.76457i	0.927081	−	0.248411i	0.236472	−	0.971638i	$-0.424009\pi$
$977$	28.9778	−	7.76457i	0.927081	−	0.248411i	0.690610	+	0.723228i	$0.257342\pi$
$978$	3.10583	−	11.5911i	0.0993134	−	0.370643i
$979$	−6.92820			−0.221426
$980$		0			0
$981$	−16.9282			−0.540476
$982$	3.03150	−	11.3137i	0.0967390	−	0.361035i
$983$	54.2120	−	14.5261i	1.72909	−	0.463309i	0.749119	−	0.662435i	$-0.230477\pi$
$983$	54.2120	−	14.5261i	1.72909	−	0.463309i	0.979974	+	0.199126i	$0.0638103\pi$
$984$	−1.96410	−	1.13397i	−0.0626133	−	0.0361498i
$985$		0			0
$986$		−	51.7128i		−	1.64687i
$987$	0.226633	+	3.15660i	0.00721382	+	0.100476i
$988$	−9.19239	+	9.19239i	−0.292449	+	0.292449i
$989$	45.8372	−	26.4641i	1.45754	−	0.841509i
$990$		0			0
$991$	−12.3923	+	21.4641i	−0.393655	+	0.681830i	−0.992928	−	0.118714i	$-0.962123\pi$
$991$	−12.3923	+	21.4641i	−0.393655	+	0.681830i	0.599274	+	0.800544i	$0.295456\pi$
$992$	−7.20977	−	1.93185i	−0.228910	−	0.0613364i
$993$	18.2325	+	18.2325i	0.578590	+	0.578590i
$994$	−23.1962	−	4.46410i	−0.735737	−	0.141593i
$995$		0			0
$996$	5.19615	+	9.00000i	0.164646	+	0.285176i
$997$	0.960947	+	3.58630i	0.0304335	+	0.113579i	0.979472	−	0.201582i	$-0.0646081\pi$
$997$	0.960947	+	3.58630i	0.0304335	+	0.113579i	−0.949038	+	0.315161i	$0.897941\pi$
$998$	7.24693	+	27.0459i	0.229398	+	0.856124i
$999$	−1.96410	−	3.40192i	−0.0621414	−	0.107632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.d.157.1	yes	8
5.2	odd	4		1050.2.bc.a.493.1	✓	8
5.3	odd	4		1050.2.bc.a.493.2	yes	8
5.4	even	2	inner	1050.2.bc.d.157.2	yes	8
7.5	odd	6		1050.2.bc.a.607.2	yes	8
35.12	even	12	inner	1050.2.bc.d.943.2	yes	8
35.19	odd	6		1050.2.bc.a.607.1	yes	8
35.33	even	12	inner	1050.2.bc.d.943.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.a.493.1	✓	8	5.2	odd	4
1050.2.bc.a.493.2	yes	8	5.3	odd	4
1050.2.bc.a.607.1	yes	8	35.19	odd	6
1050.2.bc.a.607.2	yes	8	7.5	odd	6
1050.2.bc.d.157.1	yes	8	1.1	even	1	trivial
1050.2.bc.d.157.2	yes	8	5.4	even	2	inner
1050.2.bc.d.943.1	yes	8	35.33	even	12	inner
1050.2.bc.d.943.2	yes	8	35.12	even	12	inner

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-4.05317 - 4.05317i) q^{13} +(2.59808 + 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.93185 + 7.20977i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.13397 + 1.96410i) q^{19} +(0.866025 + 2.50000i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(-5.72620 - 1.53433i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.96410 - 2.86603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.15539 + 2.38014i) q^{28} +6.92820i q^{29} +(6.46410 + 3.73205i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.258819 - 0.965926i) q^{33} -7.46410 q^{34} -1.00000 q^{36} +(-1.01669 + 3.79435i) q^{37} +(-2.19067 + 0.586988i) q^{38} +(4.96410 + 2.86603i) q^{39} +2.26795i q^{41} +(-2.63896 + 0.189469i) q^{42} +(-6.31319 + 6.31319i) q^{43} +(0.866025 - 0.500000i) q^{44} +(2.96410 - 5.13397i) q^{46} +(1.15539 + 0.309587i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-3.73205 - 6.46410i) q^{51} +(1.48356 + 5.53674i) q^{52} +(-0.258819 - 0.965926i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(-1.60368 - 1.60368i) q^{57} +(-6.69213 - 1.79315i) q^{58} +(5.73205 - 9.92820i) q^{59} +(-9.92820 + 5.73205i) q^{61} +(-5.27792 + 5.27792i) q^{62} +(-1.48356 - 2.19067i) q^{63} -1.00000i q^{64} +(0.866025 + 0.500000i) q^{66} +(-1.93185 + 0.517638i) q^{67} +(1.93185 - 7.20977i) q^{68} +5.92820 q^{69} -8.92820 q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.86370 + 1.03528i) q^{73} +(-3.40192 - 1.96410i) q^{74} -2.26795i q^{76} +(2.38014 + 1.15539i) q^{77} +(-4.05317 + 4.05317i) q^{78} +(-2.66025 + 1.53590i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.19067 - 0.586988i) q^{82} +(7.34847 + 7.34847i) q^{83} +(0.500000 - 2.59808i) q^{84} +(-4.46410 - 7.73205i) q^{86} +(-1.79315 - 6.69213i) q^{87} +(0.258819 + 0.965926i) q^{88} +(3.46410 + 6.00000i) q^{89} +(-9.92820 + 11.4641i) q^{91} +(4.19187 + 4.19187i) q^{92} +(-7.20977 - 1.93185i) q^{93} +(-0.598076 + 1.03590i) q^{94} +(0.866025 - 0.500000i) q^{96} +(-2.07055 + 2.07055i) q^{97} +(0.827225 - 6.95095i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 4 q^{16} + 16 q^{19} - 4 q^{24} + 12 q^{26} + 24 q^{31} - 32 q^{34} - 8 q^{36} + 12 q^{39} - 4 q^{46} - 16 q^{51} - 4 q^{54} - 16 q^{56} + 32 q^{59} - 24 q^{61} - 8 q^{69} - 16 q^{71} - 48 q^{74} + 48 q^{79} + 4 q^{81} + 4 q^{84} - 8 q^{86} - 24 q^{91} + 16 q^{94}+O(q^{100}) \) 8 * q - 4 * q^11 + 4 * q^16 + 16 * q^19 - 4 * q^24 + 12 * q^26 + 24 * q^31 - 32 * q^34 - 8 * q^36 + 12 * q^39 - 4 * q^46 - 16 * q^51 - 4 * q^54 - 16 * q^56 + 32 * q^59 - 24 * q^61 - 8 * q^69 - 16 * q^71 - 48 * q^74 + 48 * q^79 + 4 * q^81 + 4 * q^84 - 8 * q^86 - 24 * q^91 + 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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