LMFDB - Embedded newform 1050.2.bc.d.157.2

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			157.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.d.943.2

$q$-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	$0.0424728\pi$
$13$	4.05317	+	4.05317i	1.12415	+	1.12415i	0.133037	+	0.991111i	$0.457527\pi$
$14$	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	$-0.723088\pi$
$17$	−1.93185	−	7.20977i	−0.468543	−	1.74863i	0.176325	−	0.984332i	$-0.443579\pi$
$18$	−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	0.800464	−	0.599381i	$-0.204586\pi$
$23$	5.72620	+	1.53433i	1.19400	+	0.319930i	0.393532	+	0.919311i	$0.371253\pi$
$24$	−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	$-0.812010\pi$
$37$	1.01669	−	3.79435i	0.167143	−	0.623788i	0.997757	−	0.0669387i	$-0.0213232\pi$
$38$	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	−0.0365779	−	0.999331i	$-0.511646\pi$
$43$	6.31319	−	6.31319i	0.962753	−	0.962753i	0.999331	+	0.0365779i	$0.0116457\pi$
$44$	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	0.173566	−	0.984822i	$-0.444471\pi$
$47$	−1.15539	−	0.309587i	−0.168532	−	0.0451579i	−0.342098	+	0.939664i	$0.611138\pi$
$48$	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	0.981421	−	0.191868i	$-0.0614545\pi$
$53$	0.258819	+	0.965926i	0.0355515	+	0.132680i	−0.945869	+	0.324548i	$0.894788\pi$
$54$	−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	−0.138874	−	0.990310i	$-0.544348\pi$
$67$	1.93185	−	0.517638i	0.236013	−	0.0632396i	0.374887	+	0.927071i	$0.377682\pi$
$68$	−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	−0.0255221	−	0.999674i	$-0.508125\pi$
$73$	3.86370	−	1.03528i	0.452212	−	0.121170i	0.477734	+	0.878504i	$0.341458\pi$
$74$	−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	0.177518	−	0.984118i	$-0.443193\pi$
$83$	−7.34847	−	7.34847i	−0.806599	−	0.806599i	−0.984118	+	0.177518i	$0.943193\pi$
$84$	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	−0.594134	−	0.804366i	$-0.702505\pi$
$97$	2.07055	−	2.07055i	0.210233	−	0.210233i	0.804366	+	0.594134i	$0.202505\pi$
$98$	−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	$0.444306\pi$
$103$	−4.76028	+	17.7656i	−0.469044	+	1.75050i	−0.643121	+	0.765765i	$0.722361\pi$
$104$	−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	$-0.660082\pi$
$107$	3.86370	−	14.4195i	0.373518	−	1.39399i	0.855498	−	0.517807i	$-0.173251\pi$
$108$	−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	−0.131363	−	0.991334i	$-0.541935\pi$
$113$	9.14162	−	9.14162i	0.859971	−	0.859971i	0.991334	+	0.131363i	$0.0419354\pi$
$114$	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	0.846352	−	0.532624i	$-0.178794\pi$
$127$	3.53553	+	3.53553i	0.313728	+	0.313728i	−0.532624	+	0.846352i	$0.678794\pi$
$128$	−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	−0.933309	−	0.359073i	$-0.883093\pi$
$137$	−18.2832	+	4.89898i	−1.56204	+	0.418548i	−0.628733	+	0.777621i	$0.716426\pi$
$138$	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	0.900946	−	0.433932i	$-0.142874\pi$
$157$	−1.20616	−	4.50146i	−0.0962622	−	0.359256i	−0.997208	+	0.0746765i	$0.976208\pi$
$158$	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	−0.225486	−	0.974246i	$-0.572397\pi$
$163$	−11.5911	−	3.10583i	−0.907886	−	0.243267i	−0.682400	+	0.730979i	$0.739064\pi$
$164$	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	−0.868311	−	0.496021i	$-0.834794\pi$
$167$	−4.81105	+	4.81105i	−0.372290	+	0.372290i	0.496021	+	0.868311i	$0.334794\pi$
$168$	−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	$-0.823520\pi$
$173$	1.96404	−	7.32989i	0.149323	−	0.557281i	0.999525	−	0.0308241i	$-0.00981317\pi$
$174$	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	$-0.777287\pi$
$193$	−5.89709	−	22.0082i	−0.424482	−	1.58419i	0.340570	−	0.940219i	$-0.389380\pi$
$194$	−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	0.990035	−	0.140822i	$-0.0449744\pi$
$197$	11.9193	+	11.9193i	0.849213	+	0.849213i	−0.140822	+	0.990035i	$0.544974\pi$
$198$	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	0.892462	−	0.451123i	$-0.148976\pi$
$223$	6.59059	+	6.59059i	0.441339	+	0.441339i	−0.451123	+	0.892462i	$0.648976\pi$
$224$	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	0.989276	−	0.146060i	$-0.0466593\pi$
$227$	0.896575	+	3.34607i	0.0595078	+	0.222086i	−0.929768	+	0.368146i	$0.879993\pi$
$228$	−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	0.199603	−	0.979877i	$-0.436035\pi$
$233$	−1.79315	−	0.480473i	−0.117473	−	0.0314769i	−0.317077	+	0.948400i	$0.602701\pi$
$234$	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	0.186026	−	0.982545i	$-0.440439\pi$
$257$	−2.31079	−	0.619174i	−0.144143	−	0.0386230i	−0.330169	+	0.943922i	$0.607106\pi$
$258$	−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	$-0.711105\pi$
$263$	−7.72741	−	28.8391i	−0.476492	−	1.77829i	0.139154	−	0.990271i	$-0.455562\pi$
$264$	−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	0.444174	−	0.895940i	$-0.353497\pi$
$277$	21.2504	−	5.69402i	1.27681	−	0.342120i	0.832636	+	0.553820i	$0.186830\pi$
$278$	−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	−0.600078	−	0.799941i	$-0.704864\pi$
$283$	−12.1087	+	3.24453i	−0.719790	+	0.192867i	−0.119712	+	0.992809i	$0.538197\pi$
$284$	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	0.670426	−	0.741976i	$-0.266111\pi$
$293$	−1.22474	−	1.22474i	−0.0715504	−	0.0715504i	−0.741976	+	0.670426i	$0.766111\pi$
$294$	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	−0.995752	−	0.0920724i	$-0.970651\pi$
$307$	−15.8338	+	15.8338i	−0.903680	+	0.903680i	0.0920724	+	0.995752i	$0.470651\pi$
$308$	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	$0.426538\pi$
$313$	−8.06918	+	30.1146i	−0.456097	+	1.70218i	−0.684843	+	0.728691i	$0.740129\pi$
$314$	−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	$0.211951\pi$
$317$	−3.62347	+	13.5230i	−0.203514	+	0.759525i	−0.989897	+	0.141786i	$0.954715\pi$
$318$	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	0.460954	−	0.887424i	$-0.347507\pi$
$337$	−7.82894	−	7.82894i	−0.426470	−	0.426470i	−0.887424	+	0.460954i	$0.847507\pi$
$338$	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	−0.182099	−	0.983280i	$-0.558289\pi$
$347$	2.82843	−	0.757875i	0.151838	−	0.0406848i	0.333937	+	0.942595i	$0.391623\pi$
$348$	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	−0.0762887	−	0.997086i	$-0.524307\pi$
$353$	6.69213	−	1.79315i	0.356186	−	0.0954398i	0.432475	+	0.901646i	$0.357640\pi$
$354$	−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	$-0.790027\pi$
$367$	−7.89829	−	29.4768i	−0.412288	−	1.53868i	0.377920	−	0.925838i	$-0.376640\pi$
$368$	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	−0.458772	−	0.888554i	$-0.651711\pi$
$373$	−25.1141	−	6.72930i	−1.30036	−	0.348430i	−0.841585	+	0.540124i	$0.818377\pi$
$374$	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	$-0.726859\pi$
$383$	5.68904	−	21.2318i	0.290696	−	1.08489i	0.944575	−	0.328294i	$-0.106474\pi$
$384$	−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	0.876702	−	0.481033i	$-0.159738\pi$
$397$	27.8038	+	7.45001i	1.39543	+	0.373905i	0.518730	+	0.854938i	$0.326405\pi$
$398$	−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	0.924612	−	0.380910i	$-0.124389\pi$
$433$	11.3137	+	11.3137i	0.543702	+	0.543702i	−0.380910	+	0.924612i	$0.624389\pi$
$434$	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	0.833244	−	0.552906i	$-0.186481\pi$
$443$	26.9072	+	7.20977i	1.27840	+	0.342546i	0.445157	+	0.895452i	$0.353148\pi$
$444$	−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	$-0.795728\pi$
$457$	4.10394	−	15.3161i	0.191974	−	0.716458i	0.993029	−	0.117867i	$-0.0376057\pi$
$458$	−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	−0.227410	−	0.973799i	$-0.573026\pi$
$463$	16.0604	−	16.0604i	0.746389	−	0.746389i	0.973799	+	0.227410i	$0.0730257\pi$
$464$	−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	0.398833	−	0.917023i	$-0.369415\pi$
$467$	6.17449	+	1.65445i	0.285721	+	0.0765588i	−0.113112	+	0.993582i	$0.536082\pi$
$468$	−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	−0.128362	−	0.991727i	$-0.540972\pi$
$487$	5.65685	−	1.51575i	0.256337	−	0.0686852i	0.384699	+	0.923042i	$0.374305\pi$
$488$	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	0.888297	−	0.459269i	$-0.151889\pi$
$503$	9.62209	+	9.62209i	0.429028	+	0.429028i	−0.459269	+	0.888297i	$0.651889\pi$
$504$	−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	−0.922408	−	0.386217i	$-0.873782\pi$
$523$	1.59008	−	5.93426i	0.0695293	−	0.259487i	0.991937	+	0.126730i	$0.0404482\pi$
$524$	−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	0.979387	−	0.201993i	$-0.0647419\pi$
$547$	18.1817	+	18.1817i	0.777394	+	0.777394i	−0.201993	+	0.979387i	$0.564742\pi$
$548$	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	−0.158065	−	0.987429i	$-0.550526\pi$
$557$	4.69093	−	1.25693i	0.198761	−	0.0532579i	0.356826	+	0.934171i	$0.383859\pi$
$558$	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	−0.307184	−	0.951650i	$-0.599387\pi$
$563$	−2.31079	+	0.619174i	−0.0973881	+	0.0260951i	0.209796	+	0.977745i	$0.432720\pi$
$564$	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	$-0.938802\pi$
$577$	−5.45378	−	20.3538i	−0.227044	−	0.847339i	0.754531	−	0.656264i	$-0.227864\pi$
$578$	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	−0.323858	−	0.946106i	$-0.604980\pi$
$587$	15.0759	−	15.0759i	0.622248	−	0.622248i	0.946106	+	0.323858i	$0.104980\pi$
$588$	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	$-0.580513\pi$
$593$	10.9719	−	40.9478i	0.450563	−	1.68153i	0.700814	−	0.713344i	$-0.252820\pi$
$594$	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	0.612173	−	0.790724i	$-0.290295\pi$
$607$	18.4034	+	4.93117i	0.746969	+	0.200150i	0.134796	+	0.990873i	$0.456962\pi$
$608$	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	$-0.965408\pi$
$613$	−4.64016	−	17.3173i	−0.187414	−	0.699440i	0.806686	−	0.590980i	$-0.201259\pi$
$614$	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	0.662031	−	0.749476i	$-0.269695\pi$
$617$	−2.17209	−	2.17209i	−0.0874450	−	0.0874450i	−0.749476	+	0.662031i	$0.769695\pi$
$618$	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	$0.0531318\pi$
$643$	29.2180	+	29.2180i	1.15225	+	1.15225i	0.166144	+	0.986101i	$0.446868\pi$
$644$	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	0.984731	−	0.174081i	$-0.0556955\pi$
$647$	1.14179	+	4.26122i	0.0448884	+	0.167526i	−0.939843	+	0.341607i	$0.889029\pi$
$648$	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	−0.240518	−	0.970645i	$-0.577317\pi$
$653$	−23.8707	−	6.39615i	−0.934134	−	0.250301i	−0.693617	+	0.720344i	$0.743984\pi$
$654$	−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	−0.958991	−	0.283438i	$-0.908525\pi$
$673$	−17.5254	+	17.5254i	−0.675553	+	0.675553i	0.283438	+	0.958991i	$0.408525\pi$
$674$	−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	−0.855670	−	0.517522i	$-0.826855\pi$
$677$	−48.2777	−	12.9360i	−1.85546	−	0.497170i	−0.999793	+	0.0203517i	$0.993521\pi$
$678$	−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	$-0.996113\pi$
$683$	−3.66063	−	13.6617i	−0.140070	−	0.522749i	0.859855	−	0.510538i	$-0.170554\pi$
$684$	−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	−0.879038	−	0.476751i	$-0.841814\pi$
$727$	−10.8468	+	10.8468i	−0.402287	+	0.402287i	0.476751	+	0.879038i	$0.341814\pi$
$728$	−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	$0.173001\pi$
$733$	−3.89589	+	14.5397i	−0.143898	+	0.537034i	−0.999802	+	0.0198997i	$0.993665\pi$
$734$	−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	−0.598889	−	0.800832i	$-0.704391\pi$
$743$	5.50455	−	5.50455i	0.201942	−	0.201942i	0.800832	+	0.598889i	$0.204391\pi$
$744$	−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	0.999540	−	0.0303124i	$-0.00965021\pi$
$757$	26.6670	+	26.6670i	0.969228	+	0.969228i	−0.0303124	+	0.999540i	$0.509650\pi$
$758$	−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	−0.827603	−	0.561314i	$-0.810296\pi$
$773$	−35.1337	+	9.41404i	−1.26367	+	0.338600i	−0.436068	+	0.899914i	$0.643629\pi$
$774$	−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	0.954012	−	0.299769i	$-0.0969096\pi$
$787$	−0.619174	−	2.31079i	−0.0220712	−	0.0823707i	−0.976083	+	0.217398i	$0.930243\pi$
$788$	−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	−0.974068	−	0.226255i	$-0.927352\pi$
$797$	−21.1117	+	21.1117i	−0.747814	+	0.747814i	0.226255	+	0.974068i	$0.427352\pi$
$798$	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	$0.130523\pi$
$823$	9.24316	+	34.4959i	0.322196	+	1.20245i	−0.594904	+	0.803796i	$0.702810\pi$
$824$	−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	$-0.973963\pi$
$827$	−31.0112	−	31.0112i	−1.07836	−	1.07836i	−0.0817074	−	0.996656i	$-0.526037\pi$
$828$	−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	0.605312	−	0.795988i	$-0.293048\pi$
$853$	−5.56892	−	5.56892i	−0.190676	−	0.190676i	−0.795988	+	0.605312i	$0.793048\pi$
$854$	−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	$0.00477350\pi$
$857$	4.14110	+	15.4548i	0.141457	+	0.527926i	−0.858430	+	0.512931i	$0.828560\pi$
$858$	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	−0.460675	−	0.887569i	$-0.652393\pi$
$863$	−38.2903	−	10.2598i	−1.30342	−	0.349249i	−0.842741	+	0.538319i	$0.819059\pi$
$864$	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	−0.980965	−	0.194186i	$-0.937793\pi$
$877$	−1.01669	+	3.79435i	−0.0343313	+	0.128126i	0.946633	+	0.322312i	$0.104460\pi$
$878$	−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	−0.156522	−	0.987675i	$-0.550028\pi$
$883$	24.6980	−	24.6980i	0.831153	−	0.831153i	0.987675	+	0.156522i	$0.0500281\pi$
$884$	−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	0.314556	−	0.949239i	$-0.398144\pi$
$887$	3.34607	+	0.896575i	0.112350	+	0.0301041i	−0.202206	+	0.979343i	$0.564811\pi$
$888$	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	−0.293031	−	0.956103i	$-0.594664\pi$
$907$	−2.07055	+	0.554803i	−0.0687516	+	0.0184219i	0.224279	+	0.974525i	$0.427997\pi$
$908$	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	−0.809315	−	0.587375i	$-0.800161\pi$
$937$	−6.79367	+	6.79367i	−0.221939	+	0.221939i	0.587375	+	0.809315i	$0.300161\pi$
$938$	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	$-0.821416\pi$
$947$	4.69591	−	17.5254i	0.152596	−	0.569498i	0.999299	−	0.0374316i	$-0.0119176\pi$
$948$	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	$0.514261\pi$
$953$	−32.2223	+	32.2223i	−1.04378	+	1.04378i	−0.998997	+	0.0447862i	$0.985739\pi$
$954$	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	0.280847	−	0.959753i	$-0.409385\pi$
$967$	−21.1117	−	21.1117i	−0.678905	−	0.678905i	−0.959753	+	0.280847i	$0.909385\pi$
$968$	−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	−0.690610	−	0.723228i	$-0.742658\pi$
$977$	−28.9778	+	7.76457i	−0.927081	+	0.248411i	−0.236472	+	0.971638i	$0.575991\pi$
$978$	−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	−0.979974	−	0.199126i	$-0.936190\pi$
$983$	−54.2120	+	14.5261i	−1.72909	+	0.463309i	−0.749119	+	0.662435i	$0.769523\pi$
$984$	−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	0.949038	−	0.315161i	$-0.102059\pi$
$997$	−0.960947	−	3.58630i	−0.0304335	−	0.113579i	−0.979472	+	0.201582i	$0.935392\pi$
$998$	−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.157.2	yes	8
5.2	odd	4		1050.2.bc.a.493.2	yes	8
5.3	odd	4		1050.2.bc.a.493.1	✓	8
5.4	even	2	inner	1050.2.bc.d.157.1	yes	8
7.5	odd	6		1050.2.bc.a.607.1	yes	8
35.12	even	12	inner	1050.2.bc.d.943.1	yes	8
35.19	odd	6		1050.2.bc.a.607.2	yes	8
35.33	even	12	inner	1050.2.bc.d.943.2	yes	8

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