LMFDB - Embedded newform 1050.2.bc.b.943.2

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			943.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.b.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.965926 - 0.258819i) q^{12} +(3.86370 - 3.86370i) q^{13} +(-0.866025 + 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.48356 - 5.53674i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-3.09808 + 5.36603i) q^{19} +(-1.73205 - 2.00000i) q^{21} +(1.93185 - 1.93185i) q^{22} +(0.258819 - 0.0693504i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.73205 + 2.73205i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.63896 - 0.189469i) q^{28} -2.19615i q^{29} +(5.13397 - 2.96410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.707107 + 2.63896i) q^{33} +5.73205 q^{34} -1.00000 q^{36} +(-0.328169 - 1.22474i) q^{37} +(-5.98502 - 1.60368i) q^{38} +(-4.73205 + 2.73205i) q^{39} +4.46410i q^{41} +(1.48356 - 2.19067i) q^{42} +(7.20977 + 7.20977i) q^{43} +(2.36603 + 1.36603i) q^{44} +(0.133975 + 0.232051i) q^{46} +(10.6252 - 2.84701i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.59808 + 6.50000i) q^{49} +(-2.86603 + 4.96410i) q^{51} +(-1.41421 + 5.27792i) q^{52} +(2.26002 - 8.43451i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(4.38134 - 4.38134i) q^{57} +(2.12132 - 0.568406i) q^{58} +(3.73205 + 6.46410i) q^{59} +(-1.56218 - 0.901924i) q^{61} +(4.19187 + 4.19187i) q^{62} +(1.15539 + 2.38014i) q^{63} +1.00000i q^{64} +(-2.36603 + 1.36603i) q^{66} +(-3.86370 - 1.03528i) q^{67} +(1.48356 + 5.53674i) q^{68} -0.267949 q^{69} +14.8564 q^{71} +(-0.258819 - 0.965926i) q^{72} +(7.72741 + 2.07055i) q^{73} +(1.09808 - 0.633975i) q^{74} -6.19615i q^{76} +(0.517638 - 7.20977i) q^{77} +(-3.86370 - 3.86370i) q^{78} +(-13.9641 - 8.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.31199 + 1.15539i) q^{82} +(4.00240 - 4.00240i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-5.09808 + 8.83013i) q^{86} +(-0.568406 + 2.12132i) q^{87} +(-0.707107 + 2.63896i) q^{88} +(-0.232051 + 0.401924i) q^{89} +(14.1962 - 2.73205i) q^{91} +(-0.189469 + 0.189469i) q^{92} +(-5.72620 + 1.53433i) q^{93} +(5.50000 + 9.52628i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(4.94975 + 4.94975i) q^{97} +(-5.60609 + 4.19187i) q^{98} -2.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 4 q^{16} - 4 q^{19} + 4 q^{24} + 24 q^{26} + 48 q^{31} + 32 q^{34} - 8 q^{36} - 24 q^{39} + 12 q^{44} + 8 q^{46} - 16 q^{51} + 4 q^{54} - 4 q^{56} + 16 q^{59} + 36 q^{61} - 12 q^{66} - 16 q^{69} + 8 q^{71} - 12 q^{74} - 84 q^{79} + 4 q^{81} + 20 q^{84} - 20 q^{86} + 12 q^{89} + 72 q^{91} + 44 q^{94}+O(q^{100}) $ 8 * q - 4 * q^11 + 4 * q^16 - 4 * q^19 + 4 * q^24 + 24 * q^26 + 48 * q^31 + 32 * q^34 - 8 * q^36 - 24 * q^39 + 12 * q^44 + 8 * q^46 - 16 * q^51 + 4 * q^54 - 4 * q^56 + 16 * q^59 + 36 * q^61 - 12 * q^66 - 16 * q^69 + 8 * q^71 - 12 * q^74 - 84 * q^79 + 4 * q^81 + 20 * q^84 - 20 * q^86 + 12 * q^89 + 72 * q^91 + 44 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$7$	2.19067	+	1.48356i	0.827996	+	0.560734i
$7$	2.19067	+	1.48356i	0.827996	+	0.560734i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	0.583222	−	0.812313i	$-0.301792\pi$
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	−0.995094	+	0.0989291i	$0.968458\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	3.86370	−	3.86370i	1.07160	−	1.07160i	0.0743676	−	0.997231i	$-0.476306\pi$
$13$	3.86370	−	3.86370i	1.07160	−	1.07160i	0.997231	−	0.0743676i	$-0.0236938\pi$
$14$	−0.866025	+	2.50000i	−0.231455	+	0.668153i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.48356	−	5.53674i	0.359817	−	1.34286i	−0.514496	−	0.857493i	$-0.672021\pi$
$17$	1.48356	−	5.53674i	0.359817	−	1.34286i	0.874313	−	0.485363i	$-0.161312\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	−3.09808	+	5.36603i	−0.710747	+	1.23105i	0.253830	+	0.967249i	$0.418310\pi$
$19$	−3.09808	+	5.36603i	−0.710747	+	1.23105i	−0.964577	+	0.263802i	$0.915024\pi$
$20$		0			0
$21$	−1.73205	−	2.00000i	−0.377964	−	0.436436i
$22$	1.93185	−	1.93185i	0.411872	−	0.411872i
$23$	0.258819	−	0.0693504i	0.0539675	−	0.0144605i	−0.231734	−	0.972779i	$-0.574440\pi$
$23$	0.258819	−	0.0693504i	0.0539675	−	0.0144605i	0.285702	+	0.958319i	$0.407773\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	4.73205	+	2.73205i	0.928032	+	0.535799i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.63896	−	0.189469i	−0.498716	−	0.0358062i
$29$		−	2.19615i		−	0.407815i	−0.978990	−	0.203908i	$-0.934636\pi$
$29$		−	2.19615i		−	0.407815i	0.978990	−	0.203908i	$-0.0653642\pi$
$30$		0			0
$31$	5.13397	−	2.96410i	0.922089	−	0.532368i	0.0377881	−	0.999286i	$-0.487969\pi$
$31$	5.13397	−	2.96410i	0.922089	−	0.532368i	0.884301	+	0.466917i	$0.154635\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.707107	+	2.63896i	0.123091	+	0.459384i
$34$	5.73205			0.983039
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−0.328169	−	1.22474i	−0.0539507	−	0.201347i	0.933690	−	0.358083i	$-0.116569\pi$
$37$	−0.328169	−	1.22474i	−0.0539507	−	0.201347i	−0.987641	+	0.156736i	$0.949903\pi$
$38$	−5.98502	−	1.60368i	−0.970899	−	0.260152i
$39$	−4.73205	+	2.73205i	−0.757735	+	0.437478i
$40$		0			0
$41$			4.46410i			0.697176i	0.937276	+	0.348588i	$0.113339\pi$
$41$			4.46410i			0.697176i	−0.937276	+	0.348588i	$0.886661\pi$
$42$	1.48356	−	2.19067i	0.228919	−	0.338028i
$43$	7.20977	+	7.20977i	1.09948	+	1.09948i	0.994471	+	0.105008i	$0.0334868\pi$
$43$	7.20977	+	7.20977i	1.09948	+	1.09948i	0.105008	+	0.994471i	$0.466513\pi$
$44$	2.36603	+	1.36603i	0.356692	+	0.205936i
$45$		0			0
$46$	0.133975	+	0.232051i	0.0197535	+	0.0342140i
$47$	10.6252	−	2.84701i	1.54984	−	0.415279i	0.620412	−	0.784276i	$-0.286965\pi$
$47$	10.6252	−	2.84701i	1.54984	−	0.415279i	0.929431	+	0.368997i	$0.120299\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	2.59808	+	6.50000i	0.371154	+	0.928571i
$50$		0			0
$51$	−2.86603	+	4.96410i	−0.401324	+	0.695113i
$52$	−1.41421	+	5.27792i	−0.196116	+	0.731915i
$53$	2.26002	−	8.43451i	0.310438	−	1.15857i	−0.617725	−	0.786394i	$-0.711945\pi$
$53$	2.26002	−	8.43451i	0.310438	−	1.15857i	0.928163	−	0.372175i	$-0.121388\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$	4.38134	−	4.38134i	0.580323	−	0.580323i
$58$	2.12132	−	0.568406i	0.278543	−	0.0746354i
$59$	3.73205	+	6.46410i	0.485872	+	0.841554i	0.999868	−	0.0162379i	$-0.00516892\pi$
$59$	3.73205	+	6.46410i	0.485872	+	0.841554i	−0.513997	+	0.857792i	$0.671836\pi$
$60$		0			0
$61$	−1.56218	−	0.901924i	−0.200016	−	0.115480i	0.396647	−	0.917971i	$-0.370174\pi$
$61$	−1.56218	−	0.901924i	−0.200016	−	0.115480i	−0.596663	+	0.802492i	$0.703507\pi$
$62$	4.19187	+	4.19187i	0.532368	+	0.532368i
$63$	1.15539	+	2.38014i	0.145566	+	0.299869i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.36603	+	1.36603i	−0.291238	+	0.168146i
$67$	−3.86370	−	1.03528i	−0.472026	−	0.126479i	0.0149610	−	0.999888i	$-0.495238\pi$
$67$	−3.86370	−	1.03528i	−0.472026	−	0.126479i	−0.486987	+	0.873409i	$0.661904\pi$
$68$	1.48356	+	5.53674i	0.179909	+	0.671428i
$69$	−0.267949			−0.0322573
$70$		0			0
$71$	14.8564			1.76313			0.881566	−	0.472062i	$-0.156490\pi$
$71$	14.8564			1.76313			0.881566	+	0.472062i	$0.156490\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	7.72741	+	2.07055i	0.904425	+	0.242340i	0.680915	−	0.732362i	$-0.261582\pi$
$73$	7.72741	+	2.07055i	0.904425	+	0.242340i	0.223509	+	0.974702i	$0.428249\pi$
$74$	1.09808	−	0.633975i	0.127649	−	0.0736980i
$75$		0			0
$76$		−	6.19615i		−	0.710747i
$77$	0.517638	−	7.20977i	0.0589903	−	0.821629i
$78$	−3.86370	−	3.86370i	−0.437478	−	0.437478i
$79$	−13.9641	−	8.06218i	−1.57108	−	0.907066i	−0.996036	−	0.0889460i	$-0.971650\pi$
$79$	−13.9641	−	8.06218i	−1.57108	−	0.907066i	−0.575048	−	0.818120i	$-0.695017\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−4.31199	+	1.15539i	−0.476180	+	0.127592i
$83$	4.00240	−	4.00240i	0.439321	−	0.439321i	−0.452463	−	0.891783i	$-0.649454\pi$
$83$	4.00240	−	4.00240i	0.439321	−	0.439321i	0.891783	+	0.452463i	$0.149454\pi$
$84$	2.50000	+	0.866025i	0.272772	+	0.0944911i
$85$		0			0
$86$	−5.09808	+	8.83013i	−0.549740	+	0.952177i
$87$	−0.568406	+	2.12132i	−0.0609395	+	0.227429i
$88$	−0.707107	+	2.63896i	−0.0753778	+	0.281314i
$89$	−0.232051	+	0.401924i	−0.0245973	+	0.0426038i	−0.878062	−	0.478547i	$-0.841164\pi$
$89$	−0.232051	+	0.401924i	−0.0245973	+	0.0426038i	0.853465	+	0.521151i	$0.174497\pi$
$90$		0			0
$91$	14.1962	−	2.73205i	1.48816	−	0.286397i
$92$	−0.189469	+	0.189469i	−0.0197535	+	0.0197535i
$93$	−5.72620	+	1.53433i	−0.593780	+	0.159103i
$94$	5.50000	+	9.52628i	0.567282	+	0.982561i
$95$		0			0
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	4.94975	+	4.94975i	0.502571	+	0.502571i	0.912236	−	0.409665i	$-0.134354\pi$
$97$	4.94975	+	4.94975i	0.502571	+	0.502571i	−0.409665	+	0.912236i	$0.634354\pi$
$98$	−5.60609	+	4.19187i	−0.566300	+	0.423443i
$99$		−	2.73205i		−	0.274581i
$100$		0			0
$101$	−8.83013	+	5.09808i	−0.878630	+	0.507278i	−0.870207	−	0.492687i	$-0.836015\pi$
$101$	−8.83013	+	5.09808i	−0.878630	+	0.507278i	−0.00842387	+	0.999965i	$0.502681\pi$
$102$	−5.53674	−	1.48356i	−0.548219	−	0.146895i
$103$	2.75908	+	10.2970i	0.271860	+	1.01460i	0.957917	+	0.287047i	$0.0926735\pi$
$103$	2.75908	+	10.2970i	0.271860	+	1.01460i	−0.686057	+	0.727548i	$0.740660\pi$
$104$	−5.46410			−0.535799
$105$		0			0
$106$	8.73205			0.848132
$107$	−2.58819	−	9.65926i	−0.250210	−	0.933796i	−0.970693	−	0.240323i	$-0.922747\pi$
$107$	−2.58819	−	9.65926i	−0.250210	−	0.933796i	0.720483	−	0.693472i	$-0.243920\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−3.16987	+	1.83013i	−0.303619	+	0.175294i	−0.644067	−	0.764969i	$-0.722754\pi$
$109$	−3.16987	+	1.83013i	−0.303619	+	0.175294i	0.340449	+	0.940263i	$0.389421\pi$
$110$		0			0
$111$			1.26795i			0.120348i
$112$	2.38014	−	1.15539i	0.224902	−	0.109175i
$113$	2.12132	+	2.12132i	0.199557	+	0.199557i	0.799810	−	0.600253i	$-0.204933\pi$
$113$	2.12132	+	2.12132i	0.199557	+	0.199557i	−0.600253	+	0.799810i	$0.704933\pi$
$114$	5.36603	+	3.09808i	0.502574	+	0.290161i
$115$		0			0
$116$	1.09808	+	1.90192i	0.101954	+	0.176589i
$117$	5.27792	−	1.41421i	0.487944	−	0.130744i
$118$	−5.27792	+	5.27792i	−0.485872	+	0.485872i
$119$	11.4641	−	9.92820i	1.05091	−	0.910117i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$	0.466870	−	1.74238i	0.0422684	−	0.157748i
$123$	1.15539	−	4.31199i	0.104178	−	0.388799i
$124$	−2.96410	+	5.13397i	−0.266184	+	0.461045i
$125$		0			0
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	−8.38375	+	8.38375i	−0.743937	+	0.743937i	−0.973333	−	0.229396i	$-0.926325\pi$
$127$	−8.38375	+	8.38375i	−0.743937	+	0.743937i	0.229396	+	0.973333i	$0.426325\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−5.09808	−	8.83013i	−0.448861	−	0.777449i
$130$		0			0
$131$	−3.16987	−	1.83013i	−0.276953	−	0.159899i	0.355090	−	0.934832i	$-0.384450\pi$
$131$	−3.16987	−	1.83013i	−0.276953	−	0.159899i	−0.632043	+	0.774933i	$0.717784\pi$
$132$	−1.93185	−	1.93185i	−0.168146	−	0.168146i
$133$	−14.7477	+	7.15900i	−1.27879	+	0.620764i
$134$		−	4.00000i		−	0.345547i
$135$		0			0
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	−21.1810	−	5.67544i	−1.80962	−	0.484885i	−0.814205	−	0.580577i	$-0.802827\pi$
$137$	−21.1810	−	5.67544i	−1.80962	−	0.484885i	−0.995411	+	0.0956916i	$0.969494\pi$
$138$	−0.0693504	−	0.258819i	−0.00590349	−	0.0220321i
$139$	0.928203			0.0787292			0.0393646	−	0.999225i	$-0.487467\pi$
$139$	0.928203			0.0787292			0.0393646	+	0.999225i	$0.487467\pi$
$140$		0			0
$141$	−11.0000			−0.926367
$142$	3.84512	+	14.3502i	0.322675	+	1.20424i
$143$	−14.4195	−	3.86370i	−1.20582	−	0.323099i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$			8.00000i			0.662085i
$147$	−0.827225	−	6.95095i	−0.0682284	−	0.573305i
$148$	0.896575	+	0.896575i	0.0736980	+	0.0736980i
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.300750	−	0.953703i	$-0.597237\pi$
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.976306	+	0.216394i	$0.930570\pi$
$150$		0			0
$151$	1.46410	+	2.53590i	0.119147	+	0.206368i	0.919430	−	0.393254i	$-0.128651\pi$
$151$	1.46410	+	2.53590i	0.119147	+	0.206368i	−0.800283	+	0.599623i	$0.795317\pi$
$152$	5.98502	−	1.60368i	0.485450	−	0.130076i
$153$	4.05317	−	4.05317i	0.327680	−	0.327680i
$154$	7.09808	−	1.36603i	0.571979	−	0.110077i
$155$		0			0
$156$	2.73205	−	4.73205i	0.218739	−	0.378867i
$157$	−4.46927	+	16.6796i	−0.356687	+	1.33117i	0.521661	+	0.853153i	$0.325312\pi$
$157$	−4.46927	+	16.6796i	−0.356687	+	1.33117i	−0.878348	+	0.478021i	$0.841354\pi$
$158$	4.17329	−	15.5749i	0.332009	−	1.23908i
$159$	−4.36603	+	7.56218i	−0.346248	+	0.599720i
$160$		0			0
$161$	0.669873	+	0.232051i	0.0527934	+	0.0182882i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	11.5911	−	3.10583i	0.907886	−	0.243267i	0.225486	−	0.974246i	$-0.427603\pi$
$163$	11.5911	−	3.10583i	0.907886	−	0.243267i	0.682400	+	0.730979i	$0.260936\pi$
$164$	−2.23205	−	3.86603i	−0.174294	−	0.301886i
$165$		0			0
$166$	4.90192	+	2.83013i	0.380463	+	0.219660i
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.999339	−	0.0363667i	$-0.988422\pi$
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.0363667	−	0.999339i	$-0.511578\pi$
$168$	−0.189469	+	2.63896i	−0.0146178	+	0.203600i
$169$		−	16.8564i		−	1.29665i
$170$		0			0
$171$	−5.36603	+	3.09808i	−0.410350	+	0.236916i
$172$	−9.84873	−	2.63896i	−0.750958	−	0.201219i
$173$	−0.138701	−	0.517638i	−0.0105452	−	0.0393553i	0.960453	−	0.278443i	$-0.0898183\pi$
$173$	−0.138701	−	0.517638i	−0.0105452	−	0.0393553i	−0.970998	+	0.239088i	$0.923152\pi$
$174$	−2.19615			−0.166490
$175$		0			0
$176$	−2.73205			−0.205936
$177$	−1.93185	−	7.20977i	−0.145207	−	0.541919i
$178$	−0.448288	−	0.120118i	−0.0336006	−	0.00900325i
$179$	−6.80385	+	3.92820i	−0.508543	+	0.293608i	−0.732235	−	0.681052i	$-0.761523\pi$
$179$	−6.80385	+	3.92820i	−0.508543	+	0.293608i	0.223691	+	0.974660i	$0.428189\pi$
$180$		0			0
$181$		−	10.1962i		−	0.757874i	−0.925422	−	0.378937i	$-0.876290\pi$
$181$		−	10.1962i		−	0.757874i	0.925422	−	0.378937i	$-0.123710\pi$
$182$	6.31319	+	13.0053i	0.467965	+	0.964019i
$183$	1.27551	+	1.27551i	0.0942886	+	0.0942886i
$184$	−0.232051	−	0.133975i	−0.0171070	−	0.00987674i
$185$		0			0
$186$	−2.96410	−	5.13397i	−0.217338	−	0.376441i
$187$	−15.1266	+	4.05317i	−1.10617	+	0.296397i
$188$	−7.77817	+	7.77817i	−0.567282	+	0.567282i
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$	1.42820	−	2.47372i	0.103341	−	0.178992i	−0.809718	−	0.586819i	$-0.800380\pi$
$191$	1.42820	−	2.47372i	0.103341	−	0.178992i	0.913059	+	0.407827i	$0.133713\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	5.24573	−	19.5773i	0.377596	−	1.40921i	−0.471919	−	0.881642i	$-0.656438\pi$
$193$	5.24573	−	19.5773i	0.377596	−	1.40921i	0.849514	−	0.527565i	$-0.176895\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	−1.31268	+	1.31268i	−0.0935244	+	0.0935244i	−0.752321	−	0.658797i	$-0.771066\pi$
$197$	−1.31268	+	1.31268i	−0.0935244	+	0.0935244i	0.658797	+	0.752321i	$0.271066\pi$
$198$	2.63896	−	0.707107i	0.187543	−	0.0502519i
$199$	9.76795	+	16.9186i	0.692432	+	1.19933i	0.971039	+	0.238922i	$0.0767939\pi$
$199$	9.76795	+	16.9186i	0.692432	+	1.19933i	−0.278607	+	0.960405i	$0.589873\pi$
$200$		0			0
$201$	3.46410	+	2.00000i	0.244339	+	0.141069i
$202$	−7.20977	−	7.20977i	−0.507278	−	0.507278i
$203$	3.25813	−	4.81105i	0.228676	−	0.337669i
$204$		−	5.73205i		−	0.401324i
$205$		0			0
$206$	−9.23205	+	5.33013i	−0.643227	+	0.371368i
$207$	0.258819	+	0.0693504i	0.0179892	+	0.00482018i
$208$	−1.41421	−	5.27792i	−0.0980581	−	0.365958i
$209$	16.9282			1.17095
$210$		0			0
$211$	−2.33975			−0.161075			−0.0805374	−	0.996752i	$-0.525664\pi$
$211$	−2.33975			−0.161075			−0.0805374	+	0.996752i	$0.525664\pi$
$212$	2.26002	+	8.43451i	0.155219	+	0.579285i
$213$	−14.3502	−	3.84512i	−0.983259	−	0.263463i
$214$	8.66025	−	5.00000i	0.592003	−	0.341793i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	15.6443	+	1.12321i	1.06200	+	0.0762484i
$218$	−2.58819	−	2.58819i	−0.175294	−	0.175294i
$219$	−6.92820	−	4.00000i	−0.468165	−	0.270295i
$220$		0			0
$221$	−15.6603	−	27.1244i	−1.05342	−	1.82458i
$222$	−1.22474	+	0.328169i	−0.0821995	+	0.0220253i
$223$	11.1242	−	11.1242i	0.744934	−	0.744934i	−0.228589	−	0.973523i	$-0.573411\pi$
$223$	11.1242	−	11.1242i	0.744934	−	0.744934i	0.973523	+	0.228589i	$0.0734111\pi$
$224$	1.73205	+	2.00000i	0.115728	+	0.133631i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	−7.58871	+	28.3214i	−0.503680	+	1.87976i	−0.0290430	+	0.999578i	$0.509246\pi$
$227$	−7.58871	+	28.3214i	−0.503680	+	1.87976i	−0.474637	+	0.880182i	$0.657421\pi$
$228$	−1.60368	+	5.98502i	−0.106206	+	0.396368i
$229$	11.0981	−	19.2224i	0.733382	−	1.27025i	−0.222048	−	0.975036i	$-0.571274\pi$
$229$	11.0981	−	19.2224i	0.733382	−	1.27025i	0.955430	−	0.295218i	$-0.0953924\pi$
$230$		0			0
$231$	−2.36603	+	6.83013i	−0.155673	+	0.449389i
$232$	−1.55291	+	1.55291i	−0.101954	+	0.101954i
$233$	4.89898	−	1.31268i	0.320943	−	0.0859964i	−0.0947510	−	0.995501i	$-0.530205\pi$
$233$	4.89898	−	1.31268i	0.320943	−	0.0859964i	0.415694	+	0.909505i	$0.363539\pi$
$234$	2.73205	+	4.73205i	0.178600	+	0.309344i
$235$		0			0
$236$	−6.46410	−	3.73205i	−0.420777	−	0.242936i
$237$	11.4016	+	11.4016i	0.740616	+	0.740616i
$238$	12.5570	+	8.50386i	0.813952	+	0.551224i
$239$		−	22.8564i		−	1.47846i	−0.673454	−	0.739229i	$-0.735190\pi$
$239$		−	22.8564i		−	1.47846i	0.673454	−	0.739229i	$-0.264810\pi$
$240$		0			0
$241$	0.803848	−	0.464102i	0.0517804	−	0.0298954i	−0.473886	−	0.880586i	$-0.657149\pi$
$241$	0.803848	−	0.464102i	0.0517804	−	0.0298954i	0.525667	+	0.850691i	$0.323816\pi$
$242$	3.41542	+	0.915158i	0.219551	+	0.0588286i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	1.80385			0.115480
$245$		0			0
$246$	4.46410			0.284621
$247$	8.76268	+	32.7028i	0.557556	+	2.08083i
$248$	−5.72620	−	1.53433i	−0.363614	−	0.0974302i
$249$	−4.90192	+	2.83013i	−0.310647	+	0.179352i
$250$		0			0
$251$			9.85641i			0.622131i	0.950388	+	0.311065i	$0.100686\pi$
$251$			9.85641i			0.622131i	−0.950388	+	0.311065i	$0.899314\pi$
$252$	−2.19067	−	1.48356i	−0.137999	−	0.0934557i
$253$	−0.517638	−	0.517638i	−0.0325436	−	0.0325436i
$254$	−10.2679	−	5.92820i	−0.644268	−	0.371969i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	23.0435	−	6.17449i	1.43742	−	0.385154i	0.545788	−	0.837924i	$-0.316231\pi$
$257$	23.0435	−	6.17449i	1.43742	−	0.385154i	0.891628	+	0.452769i	$0.149564\pi$
$258$	7.20977	−	7.20977i	0.448861	−	0.448861i
$259$	1.09808	−	3.16987i	0.0682311	−	0.196966i
$260$		0			0
$261$	1.09808	−	1.90192i	0.0679692	−	0.117726i
$262$	0.947343	−	3.53553i	0.0585271	−	0.218426i
$263$	−6.86302	+	25.6131i	−0.423192	+	1.57937i	0.344649	+	0.938732i	$0.387998\pi$
$263$	−6.86302	+	25.6131i	−0.423192	+	1.57937i	−0.767840	+	0.640641i	$0.778669\pi$
$264$	1.36603	−	2.36603i	0.0840731	−	0.145619i
$265$		0			0
$266$	−10.7321	−	12.3923i	−0.658024	−	0.759821i
$267$	0.328169	−	0.328169i	0.0200836	−	0.0200836i
$268$	3.86370	−	1.03528i	0.236013	−	0.0632396i
$269$	4.16987	+	7.22243i	0.254242	+	0.440359i	0.964689	−	0.263391i	$-0.0848408\pi$
$269$	4.16987	+	7.22243i	0.254242	+	0.440359i	−0.710448	+	0.703750i	$0.751507\pi$
$270$		0			0
$271$	3.86603	+	2.23205i	0.234844	+	0.135587i	0.612805	−	0.790234i	$-0.290041\pi$
$271$	3.86603	+	2.23205i	0.234844	+	0.135587i	−0.377961	+	0.925822i	$0.623375\pi$
$272$	−4.05317	−	4.05317i	−0.245760	−	0.245760i
$273$	−14.4195	−	1.03528i	−0.872710	−	0.0626578i
$274$		−	21.9282i		−	1.32473i
$275$		0			0
$276$	0.232051	−	0.133975i	0.0139678	−	0.00806432i
$277$	−14.0914	−	3.77577i	−0.846668	−	0.226864i	−0.190696	−	0.981649i	$-0.561074\pi$
$277$	−14.0914	−	3.77577i	−0.846668	−	0.226864i	−0.655972	+	0.754785i	$0.727741\pi$
$278$	0.240237	+	0.896575i	0.0144084	+	0.0537730i
$279$	5.92820			0.354912
$280$		0			0
$281$	−31.9808			−1.90781			−0.953906	−	0.300105i	$-0.902978\pi$
$281$	−31.9808			−1.90781			−0.953906	+	0.300105i	$0.902978\pi$
$282$	−2.84701	−	10.6252i	−0.169537	−	0.632721i
$283$	−16.5409	−	4.43211i	−0.983252	−	0.263462i	−0.268838	−	0.963185i	$-0.586640\pi$
$283$	−16.5409	−	4.43211i	−0.983252	−	0.263462i	−0.714414	+	0.699724i	$0.753306\pi$
$284$	−12.8660	+	7.42820i	−0.763458	+	0.440783i
$285$		0			0
$286$		−	14.9282i		−	0.882723i
$287$	−6.62278	+	9.77938i	−0.390930	+	0.577258i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−13.7321	−	7.92820i	−0.807768	−	0.466365i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	−7.72741	+	2.07055i	−0.452212	+	0.121170i
$293$	11.8313	−	11.8313i	0.691195	−	0.691195i	−0.271300	−	0.962495i	$-0.587454\pi$
$293$	11.8313	−	11.8313i	0.691195	−	0.691195i	0.962495	+	0.271300i	$0.0874536\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$		0			0
$296$	−0.633975	+	1.09808i	−0.0368490	+	0.0638244i
$297$	−0.707107	+	2.63896i	−0.0410305	+	0.153128i
$298$	4.65874	−	17.3867i	0.269874	−	1.00718i
$299$	0.732051	−	1.26795i	0.0423356	−	0.0733274i
$300$		0			0
$301$	5.09808	+	26.4904i	0.293848	+	1.52688i
$302$	−2.07055	+	2.07055i	−0.119147	+	0.119147i
$303$	9.84873	−	2.63896i	0.565795	−	0.151604i
$304$	3.09808	+	5.36603i	0.177687	+	0.307763i
$305$		0			0
$306$	4.96410	+	2.86603i	0.283779	+	0.163840i
$307$	3.58630	+	3.58630i	0.204681	+	0.204681i	0.802002	−	0.597321i	$-0.203768\pi$
$307$	3.58630	+	3.58630i	0.204681	+	0.204681i	−0.597321	+	0.802002i	$0.703768\pi$
$308$	3.15660	+	6.50266i	0.179864	+	0.370524i
$309$		−	10.6603i		−	0.606441i
$310$		0			0
$311$	8.89230	−	5.13397i	0.504236	−	0.291121i	−0.226225	−	0.974075i	$-0.572638\pi$
$311$	8.89230	−	5.13397i	0.504236	−	0.291121i	0.730461	+	0.682954i	$0.239305\pi$
$312$	5.27792	+	1.41421i	0.298803	+	0.0800641i
$313$	2.98571	+	11.1428i	0.168762	+	0.629830i	0.997530	+	0.0702372i	$0.0223756\pi$
$313$	2.98571	+	11.1428i	0.168762	+	0.629830i	−0.828768	+	0.559592i	$0.810958\pi$
$314$	−17.2679			−0.974487
$315$		0			0
$316$	16.1244			0.907066
$317$	−5.74479	−	21.4398i	−0.322659	−	1.20418i	−0.916644	−	0.399705i	$-0.869113\pi$
$317$	−5.74479	−	21.4398i	−0.322659	−	1.20418i	0.593985	−	0.804476i	$-0.297554\pi$
$318$	−8.43451	−	2.26002i	−0.472984	−	0.126736i
$319$	−5.19615	+	3.00000i	−0.290929	+	0.167968i
$320$		0			0
$321$			10.0000i			0.558146i
$322$	−0.0507680	+	0.707107i	−0.00282919	+	0.0394055i
$323$	25.1141	+	25.1141i	1.39738	+	1.39738i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	3.53553	−	0.947343i	0.195515	−	0.0523882i
$328$	3.15660	−	3.15660i	0.174294	−	0.174294i
$329$	27.5000	+	9.52628i	1.51612	+	0.525201i
$330$		0			0
$331$	−7.92820	+	13.7321i	−0.435773	+	0.754782i	−0.997358	−	0.0726373i	$-0.976858\pi$
$331$	−7.92820	+	13.7321i	−0.435773	+	0.754782i	0.561585	+	0.827419i	$0.310192\pi$
$332$	−1.46498	+	5.46739i	−0.0804013	+	0.300062i
$333$	0.328169	−	1.22474i	0.0179836	−	0.0671156i
$334$	9.46410	−	16.3923i	0.517853	−	0.896947i
$335$		0			0
$336$	−2.59808	+	0.500000i	−0.141737	+	0.0272772i
$337$	20.6448	−	20.6448i	1.12459	−	1.12459i	0.133552	−	0.991042i	$-0.457362\pi$
$337$	20.6448	−	20.6448i	1.12459	−	1.12459i	0.991042	−	0.133552i	$-0.0426383\pi$
$338$	16.2820	−	4.36276i	0.885626	−	0.237303i
$339$	−1.50000	−	2.59808i	−0.0814688	−	0.141108i
$340$		0			0
$341$	−14.0263	−	8.09808i	−0.759566	−	0.438535i
$342$	−4.38134	−	4.38134i	−0.236916	−	0.236916i
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$		−	10.1962i		−	0.549740i
$345$		0			0
$346$	0.464102	−	0.267949i	0.0249503	−	0.0144050i
$347$	2.50026	+	0.669942i	0.134221	+	0.0359644i	0.325304	−	0.945609i	$-0.394533\pi$
$347$	2.50026	+	0.669942i	0.134221	+	0.0359644i	−0.191083	+	0.981574i	$0.561200\pi$
$348$	−0.568406	−	2.12132i	−0.0304698	−	0.113715i
$349$	−10.7321			−0.574474			−0.287237	−	0.957860i	$-0.592737\pi$
$349$	−10.7321			−0.574474			−0.287237	+	0.957860i	$0.592737\pi$
$350$		0			0
$351$	−5.46410			−0.291652
$352$	−0.707107	−	2.63896i	−0.0376889	−	0.140657i
$353$	−26.6484	−	7.14042i	−1.41835	−	0.380046i	−0.533453	−	0.845830i	$-0.679106\pi$
$353$	−26.6484	−	7.14042i	−1.41835	−	0.380046i	−0.884899	+	0.465784i	$0.845772\pi$
$354$	6.46410	−	3.73205i	0.343563	−	0.198356i
$355$		0			0
$356$		−	0.464102i		−	0.0245973i
$357$	−13.6431	+	6.62278i	−0.722068	+	0.350515i
$358$	−5.55532	−	5.55532i	−0.293608	−	0.293608i
$359$	18.0000	+	10.3923i	0.950004	+	0.548485i	0.893082	−	0.449894i	$-0.148538\pi$
$359$	18.0000	+	10.3923i	0.950004	+	0.548485i	0.0569216	+	0.998379i	$0.481871\pi$
$360$		0			0
$361$	−9.69615	−	16.7942i	−0.510324	−	0.883907i
$362$	9.84873	−	2.63896i	0.517638	−	0.138701i
$363$	−2.50026	+	2.50026i	−0.131229	+	0.131229i
$364$	−10.9282	+	9.46410i	−0.572793	+	0.496054i
$365$		0			0
$366$	−0.901924	+	1.56218i	−0.0471443	+	0.0816563i
$367$	−0.859411	+	3.20736i	−0.0448609	+	0.167423i	−0.984722	−	0.174134i	$-0.944288\pi$
$367$	−0.859411	+	3.20736i	−0.0448609	+	0.167423i	0.939861	+	0.341557i	$0.110954\pi$
$368$	0.0693504	−	0.258819i	0.00361514	−	0.0134919i
$369$	−2.23205	+	3.86603i	−0.116196	+	0.201257i
$370$		0			0
$371$	17.4641	−	15.1244i	0.906691	−	0.785217i
$372$	4.19187	−	4.19187i	0.217338	−	0.217338i
$373$	−32.7028	+	8.76268i	−1.69329	+	0.453715i	−0.971234	−	0.238125i	$-0.923467\pi$
$373$	−32.7028	+	8.76268i	−1.69329	+	0.453715i	−0.722051	+	0.691840i	$0.756800\pi$
$374$	−7.83013	−	13.5622i	−0.404886	−	0.701284i
$375$		0			0
$376$	−9.52628	−	5.50000i	−0.491280	−	0.283641i
$377$	−8.48528	−	8.48528i	−0.437014	−	0.437014i
$378$	2.38014	−	1.15539i	0.122421	−	0.0594271i
$379$			28.0526i			1.44096i	0.693474	+	0.720482i	$0.256079\pi$
$379$			28.0526i			1.44096i	−0.693474	+	0.720482i	$0.743921\pi$
$380$		0			0
$381$	10.2679	−	5.92820i	0.526043	−	0.303711i
$382$	2.75908	+	0.739292i	0.141167	+	0.0378255i
$383$	−5.05626	−	18.8702i	−0.258363	−	0.964224i	−0.966189	−	0.257836i	$-0.916990\pi$
$383$	−5.05626	−	18.8702i	−0.258363	−	0.964224i	0.707826	−	0.706387i	$-0.249676\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	20.2679			1.03161
$387$	2.63896	+	9.84873i	0.134146	+	0.500639i
$388$	−6.76148	−	1.81173i	−0.343262	−	0.0919768i
$389$	8.95448	−	5.16987i	0.454010	−	0.262123i	−0.255512	−	0.966806i	$-0.582244\pi$
$389$	8.95448	−	5.16987i	0.454010	−	0.262123i	0.709522	+	0.704683i	$0.248911\pi$
$390$		0			0
$391$		−	1.53590i		−	0.0776737i
$392$	2.75908	−	6.43331i	0.139354	−	0.324931i
$393$	2.58819	+	2.58819i	0.130557	+	0.130557i
$394$	−1.60770	−	0.928203i	−0.0809945	−	0.0467622i
$395$		0			0
$396$	1.36603	+	2.36603i	0.0686454	+	0.118897i
$397$	12.1087	−	3.24453i	0.607721	−	0.162838i	0.0581812	−	0.998306i	$-0.481470\pi$
$397$	12.1087	−	3.24453i	0.607721	−	0.162838i	0.549539	+	0.835468i	$0.314803\pi$
$398$	−13.8140	+	13.8140i	−0.692432	+	0.692432i
$399$	16.0981	−	3.09808i	0.805912	−	0.155098i
$400$		0			0
$401$	3.53590	−	6.12436i	0.176574	−	0.305836i	−0.764131	−	0.645062i	$-0.776832\pi$
$401$	3.53590	−	6.12436i	0.176574	−	0.305836i	0.940705	+	0.339226i	$0.110165\pi$
$402$	−1.03528	+	3.86370i	−0.0516349	+	0.192704i
$403$	8.38375	−	31.2886i	0.417624	−	1.55859i
$404$	5.09808	−	8.83013i	0.253639	−	0.439315i
$405$		0			0
$406$	5.49038	+	1.90192i	0.272483	+	0.0943909i
$407$	−2.44949	+	2.44949i	−0.121417	+	0.121417i
$408$	5.53674	−	1.48356i	0.274109	−	0.0734474i
$409$	11.4019	+	19.7487i	0.563789	+	0.976511i	0.997161	+	0.0752960i	$0.0239902\pi$
$409$	11.4019	+	19.7487i	0.563789	+	0.976511i	−0.433372	+	0.901215i	$0.642677\pi$
$410$		0			0
$411$	18.9904	+	10.9641i	0.936726	+	0.540819i
$412$	−7.53794	−	7.53794i	−0.371368	−	0.371368i
$413$	−1.41421	+	19.6975i	−0.0695889	+	0.969248i
$414$			0.267949i			0.0131690i
$415$		0			0
$416$	4.73205	−	2.73205i	0.232008	−	0.133950i
$417$	−0.896575	−	0.240237i	−0.0439055	−	0.0117644i
$418$	4.38134	+	16.3514i	0.214298	+	0.799773i
$419$	−20.5885			−1.00581			−0.502906	−	0.864341i	$-0.667736\pi$
$419$	−20.5885			−1.00581			−0.502906	+	0.864341i	$0.667736\pi$
$420$		0			0
$421$	−9.46410			−0.461252			−0.230626	−	0.973042i	$-0.574077\pi$
$421$	−9.46410			−0.461252			−0.230626	+	0.973042i	$0.574077\pi$
$422$	−0.605571	−	2.26002i	−0.0294787	−	0.110016i
$423$	10.6252	+	2.84701i	0.516614	+	0.138426i
$424$	−7.56218	+	4.36603i	−0.367252	+	0.212033i
$425$		0			0
$426$		−	14.8564i		−	0.719795i
$427$	−2.08416	−	4.29341i	−0.100859	−	0.207773i
$428$	7.07107	+	7.07107i	0.341793	+	0.341793i
$429$	12.9282	+	7.46410i	0.624180	+	0.360370i
$430$		0			0
$431$	3.23205	+	5.59808i	0.155682	+	0.269650i	0.933307	−	0.359079i	$-0.116909\pi$
$431$	3.23205	+	5.59808i	0.155682	+	0.269650i	−0.777625	+	0.628729i	$0.783576\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−4.46927	+	4.46927i	−0.214780	+	0.214780i	−0.806294	−	0.591515i	$-0.798530\pi$
$433$	−4.46927	+	4.46927i	−0.214780	+	0.214780i	0.591515	+	0.806294i	$0.298530\pi$
$434$	2.96410	+	15.4019i	0.142281	+	0.739316i
$435$		0			0
$436$	1.83013	−	3.16987i	0.0876472	−	0.151809i
$437$	−0.429705	+	1.60368i	−0.0205556	+	0.0767145i
$438$	2.07055	−	7.72741i	0.0989348	−	0.369230i
$439$	9.30385	−	16.1147i	0.444048	−	0.769114i	−0.553937	−	0.832559i	$-0.686875\pi$
$439$	9.30385	−	16.1147i	0.444048	−	0.769114i	0.997985	+	0.0634442i	$0.0202085\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$	22.1469	−	22.1469i	1.05342	−	1.05342i
$443$	−22.7153	+	6.08656i	−1.07924	+	0.289181i	−0.754284	−	0.656548i	$-0.772016\pi$
$443$	−22.7153	+	6.08656i	−1.07924	+	0.289181i	−0.324955	+	0.945730i	$0.605349\pi$
$444$	−0.633975	−	1.09808i	−0.0300871	−	0.0521124i
$445$		0			0
$446$	13.6244	+	7.86603i	0.645132	+	0.372467i
$447$	12.7279	+	12.7279i	0.602010	+	0.602010i
$448$	−1.48356	+	2.19067i	−0.0700918	+	0.103499i
$449$			26.2679i			1.23966i	0.784736	+	0.619831i	$0.212799\pi$
$449$			26.2679i			1.23966i	−0.784736	+	0.619831i	$0.787201\pi$
$450$		0			0
$451$	10.5622	−	6.09808i	0.497354	−	0.287147i
$452$	−2.89778	−	0.776457i	−0.136300	−	0.0365215i
$453$	−0.757875	−	2.82843i	−0.0356081	−	0.132891i
$454$	−29.3205			−1.37608
$455$		0			0
$456$	−6.19615			−0.290161
$457$	1.59008	+	5.93426i	0.0743808	+	0.277593i	0.993092	−	0.117337i	$-0.0374357\pi$
$457$	1.59008	+	5.93426i	0.0743808	+	0.277593i	−0.918711	+	0.394930i	$0.870769\pi$
$458$	21.4398	+	5.74479i	1.00182	+	0.268436i
$459$	−4.96410	+	2.86603i	−0.231704	+	0.133775i
$460$		0			0
$461$			15.3205i			0.713547i	0.934191	+	0.356774i	$0.116123\pi$
$461$			15.3205i			0.713547i	−0.934191	+	0.356774i	$0.883877\pi$
$462$	−7.20977	−	0.517638i	−0.335429	−	0.0240827i
$463$	25.0261	+	25.0261i	1.16306	+	1.16306i	0.983801	+	0.179262i	$0.0573710\pi$
$463$	25.0261	+	25.0261i	1.16306	+	1.16306i	0.179262	+	0.983801i	$0.442629\pi$
$464$	−1.90192	−	1.09808i	−0.0882946	−	0.0509769i
$465$		0			0
$466$	2.53590	+	4.39230i	0.117473	+	0.203470i
$467$	−29.0285	+	7.77817i	−1.34328	+	0.359931i	−0.857650	−	0.514233i	$-0.828077\pi$
$467$	−29.0285	+	7.77817i	−1.34328	+	0.359931i	−0.485630	+	0.874164i	$0.661410\pi$
$468$	−3.86370	+	3.86370i	−0.178600	+	0.178600i
$469$	−6.92820	−	8.00000i	−0.319915	−	0.369406i
$470$		0			0
$471$	8.63397	−	14.9545i	0.397833	−	0.689066i
$472$	1.93185	−	7.20977i	0.0889207	−	0.331856i
$473$	7.20977	−	26.9072i	0.331506	−	1.23720i
$474$	−8.06218	+	13.9641i	−0.370308	+	0.641392i
$475$		0			0
$476$	−4.96410	+	14.3301i	−0.227529	+	0.656820i
$477$	6.17449	−	6.17449i	0.282711	−	0.282711i
$478$	22.0776	−	5.91567i	1.00981	−	0.270577i
$479$	15.9904	+	27.6962i	0.730619	+	1.26547i	0.956619	+	0.291342i	$0.0941018\pi$
$479$	15.9904	+	27.6962i	0.730619	+	1.26547i	−0.226000	+	0.974127i	$0.572565\pi$
$480$		0			0
$481$	−6.00000	−	3.46410i	−0.273576	−	0.157949i
$482$	0.656339	+	0.656339i	0.0298954	+	0.0298954i
$483$	−0.586988	−	0.397520i	−0.0267089	−	0.0180878i
$484$			3.53590i			0.160723i
$485$		0			0
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−19.7668	−	5.29650i	−0.895719	−	0.240007i	−0.218542	−	0.975827i	$-0.570130\pi$
$487$	−19.7668	−	5.29650i	−0.895719	−	0.240007i	−0.677177	+	0.735820i	$0.736797\pi$
$488$	0.466870	+	1.74238i	0.0211342	+	0.0788740i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	15.6603			0.706737			0.353369	−	0.935484i	$-0.385036\pi$
$491$	15.6603			0.706737			0.353369	+	0.935484i	$0.385036\pi$
$492$	1.15539	+	4.31199i	0.0520892	+	0.194400i
$493$	−12.1595	−	3.25813i	−0.547637	−	0.146739i
$494$	−29.3205	+	16.9282i	−1.31919	+	0.761636i
$495$		0			0
$496$		−	5.92820i		−	0.266184i
$497$	32.5455	+	22.0404i	1.45986	+	0.988648i
$498$	−4.00240	−	4.00240i	−0.179352	−	0.179352i
$499$	−26.8301	−	15.4904i	−1.20108	−	0.693445i	−0.240286	−	0.970702i	$-0.577241\pi$
$499$	−26.8301	−	15.4904i	−1.20108	−	0.693445i	−0.960796	+	0.277257i	$0.910574\pi$
$500$		0			0
$501$	9.46410	+	16.3923i	0.422825	+	0.732354i
$502$	−9.52056	+	2.55103i	−0.424923	+	0.113858i
$503$	−13.5601	+	13.5601i	−0.604616	+	0.604616i	−0.941534	−	0.336918i	$-0.890616\pi$
$503$	−13.5601	+	13.5601i	−0.604616	+	0.604616i	0.336918	+	0.941534i	$0.390616\pi$
$504$	0.866025	−	2.50000i	0.0385758	−	0.111359i
$505$		0			0
$506$	0.366025	−	0.633975i	0.0162718	−	0.0281836i
$507$	−4.36276	+	16.2820i	−0.193757	+	0.723111i
$508$	3.06866	−	11.4524i	0.136150	−	0.508118i
$509$	−17.0263	+	29.4904i	−0.754677	+	1.30714i	0.190858	+	0.981618i	$0.438873\pi$
$509$	−17.0263	+	29.4904i	−0.754677	+	1.30714i	−0.945535	+	0.325521i	$0.894460\pi$
$510$		0			0
$511$	13.8564	+	16.0000i	0.612971	+	0.707798i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	5.98502	−	1.60368i	0.264245	−	0.0708043i
$514$	11.9282	+	20.6603i	0.526130	+	0.911285i
$515$		0			0
$516$	8.83013	+	5.09808i	0.388725	+	0.224430i
$517$	−21.2504	−	21.2504i	−0.934590	−	0.934590i
$518$	3.34607	+	0.240237i	0.147018	+	0.0105554i
$519$			0.535898i			0.0235233i
$520$		0			0
$521$	−33.3109	+	19.2321i	−1.45938	+	0.842571i	−0.998981	−	0.0451422i	$-0.985626\pi$
$521$	−33.3109	+	19.2321i	−1.45938	+	0.842571i	−0.460396	+	0.887714i	$0.652293\pi$
$522$	2.12132	+	0.568406i	0.0928477	+	0.0248785i
$523$	−0.845807	−	3.15660i	−0.0369846	−	0.138028i	0.944965	−	0.327172i	$-0.106096\pi$
$523$	−0.845807	−	3.15660i	−0.0369846	−	0.138028i	−0.981949	+	0.189143i	$0.939429\pi$
$524$	3.66025			0.159899
$525$		0			0
$526$	−26.5167			−1.15618
$527$	−8.79487	−	32.8229i	−0.383110	−	1.42979i
$528$	2.63896	+	0.707107i	0.114846	+	0.0307729i
$529$	−19.8564	+	11.4641i	−0.863322	+	0.498439i
$530$		0			0
$531$			7.46410i			0.323914i
$532$	9.19239	−	13.5737i	0.398541	−	0.588496i
$533$	17.2480	+	17.2480i	0.747092	+	0.747092i
$534$	0.401924	+	0.232051i	0.0173929	+	0.0100418i
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	7.58871	−	2.03339i	0.327477	−	0.0877472i
$538$	−5.89709	+	5.89709i	−0.254242	+	0.254242i
$539$	11.8301	−	15.0263i	0.509560	−	0.647228i
$540$		0			0
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	−1.15539	+	4.31199i	−0.0496284	+	0.185216i
$543$	−2.63896	+	9.84873i	−0.113249	+	0.422649i
$544$	2.86603	−	4.96410i	0.122880	−	0.212834i
$545$		0			0
$546$	−2.73205	−	14.1962i	−0.116921	−	0.607539i
$547$	15.4920	−	15.4920i	0.662389	−	0.662389i	−0.293554	−	0.955943i	$-0.594838\pi$
$547$	15.4920	−	15.4920i	0.662389	−	0.662389i	0.955943	+	0.293554i	$0.0948379\pi$
$548$	21.1810	−	5.67544i	0.904808	−	0.242443i
$549$	−0.901924	−	1.56218i	−0.0384932	−	0.0666721i
$550$		0			0
$551$	11.7846	+	6.80385i	0.502041	+	0.289854i
$552$	0.189469	+	0.189469i	0.00806432	+	0.00806432i
$553$	−18.6300	−	38.3782i	−0.792228	−	1.63201i
$554$		−	14.5885i		−	0.619804i
$555$		0			0
$556$	−0.803848	+	0.464102i	−0.0340907	+	0.0196823i
$557$	35.0136	+	9.38186i	1.48357	+	0.397522i	0.907561	−	0.419920i	$-0.137942\pi$
$557$	35.0136	+	9.38186i	1.48357	+	0.397522i	0.576011	+	0.817442i	$0.304608\pi$
$558$	1.53433	+	5.72620i	0.0649534	+	0.242410i
$559$	55.7128			2.35640
$560$		0			0
$561$	15.6603			0.661176
$562$	−8.27723	−	30.8910i	−0.349154	−	1.30306i
$563$	−25.0261	−	6.70573i	−1.05473	−	0.282613i	−0.310523	−	0.950566i	$-0.600504\pi$
$563$	−25.0261	−	6.70573i	−1.05473	−	0.282613i	−0.744203	+	0.667953i	$0.767171\pi$
$564$	9.52628	−	5.50000i	0.401129	−	0.231592i
$565$		0			0
$566$		−	17.1244i		−	0.719790i
$567$	−0.189469	+	2.63896i	−0.00795694	+	0.110826i
$568$	−10.5051	−	10.5051i	−0.440783	−	0.440783i
$569$	32.5526	+	18.7942i	1.36467	+	0.787895i	0.990242	−	0.139359i	$-0.0445043\pi$
$569$	32.5526	+	18.7942i	1.36467	+	0.787895i	0.374432	+	0.927254i	$0.377838\pi$
$570$		0			0
$571$	14.1962	+	24.5885i	0.594090	+	1.02899i	0.993675	+	0.112298i	$0.0358212\pi$
$571$	14.1962	+	24.5885i	0.594090	+	1.02899i	−0.399584	+	0.916697i	$0.630845\pi$
$572$	14.4195	−	3.86370i	0.602911	−	0.161550i
$573$	−2.01978	+	2.01978i	−0.0843777	+	0.0843777i
$574$	−11.1603	−	3.86603i	−0.465820	−	0.161365i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	11.9700	−	44.6728i	0.498320	−	1.85975i	−0.0122622	−	0.999925i	$-0.503903\pi$
$577$	11.9700	−	44.6728i	0.498320	−	1.85975i	0.510582	−	0.859829i	$-0.329430\pi$
$578$	4.10394	−	15.3161i	0.170701	−	0.637066i
$579$	−10.1340	+	17.5526i	−0.421154	+	0.729459i
$580$		0			0
$581$	14.7058	−	2.83013i	0.610098	−	0.117413i
$582$	4.94975	−	4.94975i	0.205174	−	0.205174i
$583$	−23.0435	+	6.17449i	−0.954365	+	0.255721i
$584$	−4.00000	−	6.92820i	−0.165521	−	0.286691i
$585$		0			0
$586$	14.4904	+	8.36603i	0.598592	+	0.345597i
$587$	−1.69161	−	1.69161i	−0.0698204	−	0.0698204i	0.671334	−	0.741155i	$-0.265722\pi$
$587$	−1.69161	−	1.69161i	−0.0698204	−	0.0698204i	−0.741155	+	0.671334i	$0.765722\pi$
$588$	4.19187	+	5.60609i	0.172870	+	0.231191i
$589$			36.7321i			1.51352i
$590$		0			0
$591$	1.60770	−	0.928203i	0.0661317	−	0.0381812i
$592$	−1.22474	−	0.328169i	−0.0503367	−	0.0134877i
$593$	7.03888	+	26.2695i	0.289052	+	1.07876i	0.945827	+	0.324671i	$0.105254\pi$
$593$	7.03888	+	26.2695i	0.289052	+	1.07876i	−0.656775	+	0.754087i	$0.728080\pi$
$594$	−2.73205			−0.112097
$595$		0			0
$596$	18.0000			0.737309
$597$	−5.05626	−	18.8702i	−0.206939	−	0.772307i
$598$	1.41421	+	0.378937i	0.0578315	+	0.0154959i
$599$	−26.0429	+	15.0359i	−1.06409	+	0.614350i	−0.926560	−	0.376148i	$-0.877248\pi$
$599$	−26.0429	+	15.0359i	−1.06409	+	0.614350i	−0.137526	+	0.990498i	$0.543915\pi$
$600$		0			0
$601$			28.2487i			1.15229i	0.817348	+	0.576144i	$0.195443\pi$
$601$			28.2487i			1.15229i	−0.817348	+	0.576144i	$0.804557\pi$
$602$	−24.2683	+	11.7806i	−0.989101	+	0.480141i
$603$	−2.82843	−	2.82843i	−0.115182	−	0.115182i
$604$	−2.53590	−	1.46410i	−0.103184	−	0.0595734i
$605$		0			0
$606$	5.09808	+	8.83013i	0.207095	+	0.358699i
$607$	−0.120118	+	0.0321856i	−0.00487545	+	0.00130637i	−0.261256	−	0.965270i	$-0.584137\pi$
$607$	−0.120118	+	0.0321856i	−0.00487545	+	0.00130637i	0.256380	+	0.966576i	$0.417470\pi$
$608$	−4.38134	+	4.38134i	−0.177687	+	0.177687i
$609$	−4.39230	+	3.80385i	−0.177985	+	0.154140i
$610$		0			0
$611$	30.0526	−	52.0526i	1.21580	−	2.10582i
$612$	−1.48356	+	5.53674i	−0.0599695	+	0.223809i
$613$	−6.88160	+	25.6825i	−0.277945	+	1.03731i	0.675897	+	0.736996i	$0.263757\pi$
$613$	−6.88160	+	25.6825i	−0.277945	+	1.03731i	−0.953842	+	0.300309i	$0.902910\pi$
$614$	−2.53590	+	4.39230i	−0.102341	+	0.177259i
$615$		0			0
$616$	−5.46410	+	4.73205i	−0.220155	+	0.190660i
$617$	−21.4398	+	21.4398i	−0.863135	+	0.863135i	−0.991701	−	0.128566i	$-0.958963\pi$
$617$	−21.4398	+	21.4398i	−0.863135	+	0.863135i	0.128566	+	0.991701i	$0.458963\pi$
$618$	10.2970	−	2.75908i	0.414207	−	0.110986i
$619$	12.0981	+	20.9545i	0.486263	+	0.842232i	0.999875	−	0.0157904i	$-0.00502646\pi$
$619$	12.0981	+	20.9545i	0.486263	+	0.842232i	−0.513613	+	0.858022i	$0.671693\pi$
$620$		0			0
$621$	−0.232051	−	0.133975i	−0.00931188	−	0.00537622i
$622$	7.26054	+	7.26054i	0.291121	+	0.291121i
$623$	−1.10463	+	0.536220i	−0.0442559	+	0.0214832i
$624$			5.46410i			0.218739i
$625$		0			0
$626$	−9.99038	+	5.76795i	−0.399296	+	0.230534i
$627$	−16.3514	−	4.38134i	−0.653012	−	0.174974i
$628$	−4.46927	−	16.6796i	−0.178343	−	0.665587i
$629$	−7.26795			−0.289792
$630$		0			0
$631$	−47.5885			−1.89447			−0.947233	−	0.320545i	$-0.896134\pi$
$631$	−47.5885			−1.89447			−0.947233	+	0.320545i	$0.896134\pi$
$632$	4.17329	+	15.5749i	0.166005	+	0.619538i
$633$	2.26002	+	0.605571i	0.0898278	+	0.0240693i
$634$	19.2224	−	11.0981i	0.763420	−	0.440761i
$635$		0			0
$636$		−	8.73205i		−	0.346248i
$637$	35.1523	+	15.0759i	1.39278	+	0.597328i
$638$	−4.24264	−	4.24264i	−0.167968	−	0.167968i
$639$	12.8660	+	7.42820i	0.508972	+	0.293855i
$640$		0			0
$641$	8.33013	+	14.4282i	0.329020	+	0.569880i	0.982318	−	0.187222i	$-0.0599482\pi$
$641$	8.33013	+	14.4282i	0.329020	+	0.569880i	−0.653297	+	0.757101i	$0.726615\pi$
$642$	−9.65926	+	2.58819i	−0.381221	+	0.102148i
$643$	−9.62209	+	9.62209i	−0.379458	+	0.379458i	−0.870907	−	0.491448i	$-0.836468\pi$
$643$	−9.62209	+	9.62209i	−0.379458	+	0.379458i	0.491448	+	0.870907i	$0.336468\pi$
$644$	−0.696152	+	0.133975i	−0.0274322	+	0.00527934i
$645$		0			0
$646$	−17.7583	+	30.7583i	−0.698692	+	1.21017i
$647$	3.24453	−	12.1087i	0.127556	−	0.476044i	−0.872362	−	0.488860i	$-0.837413\pi$
$647$	3.24453	−	12.1087i	0.127556	−	0.476044i	0.999918	+	0.0128160i	$0.00407956\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	10.1962	−	17.6603i	0.400234	−	0.693226i
$650$		0			0
$651$	−14.8205	−	5.13397i	−0.580862	−	0.201216i
$652$	−8.48528	+	8.48528i	−0.332309	+	0.332309i
$653$	45.0518	−	12.0716i	1.76301	−	0.472398i	0.775688	−	0.631117i	$-0.217403\pi$
$653$	45.0518	−	12.0716i	1.76301	−	0.472398i	0.987324	+	0.158719i	$0.0507364\pi$
$654$	1.83013	+	3.16987i	0.0715636	+	0.123952i
$655$		0			0
$656$	3.86603	+	2.23205i	0.150943	+	0.0871469i
$657$	5.65685	+	5.65685i	0.220695	+	0.220695i
$658$	−2.08416	+	29.0285i	−0.0812488	+	1.13165i
$659$			3.80385i			0.148177i	0.997252	+	0.0740884i	$0.0236047\pi$
$659$			3.80385i			0.148177i	−0.997252	+	0.0740884i	$0.976395\pi$
$660$		0			0
$661$	10.5167	−	6.07180i	0.409051	−	0.236166i	−0.281331	−	0.959611i	$-0.590776\pi$
$661$	10.5167	−	6.07180i	0.409051	−	0.236166i	0.690382	+	0.723445i	$0.257443\pi$
$662$	−15.3161	−	4.10394i	−0.595278	−	0.159504i
$663$	8.10634	+	30.2533i	0.314824	+	1.17494i
$664$	−5.66025			−0.219660
$665$		0			0
$666$	1.26795			0.0491320
$667$	−0.152304	−	0.568406i	−0.00589723	−	0.0220088i
$668$	18.2832	+	4.89898i	0.707400	+	0.189547i
$669$	−13.6244	+	7.86603i	−0.526748	+	0.304118i
$670$		0			0
$671$			4.92820i			0.190251i
$672$	−1.15539	−	2.38014i	−0.0445703	−	0.0918159i
$673$	−4.05317	−	4.05317i	−0.156238	−	0.156238i	0.624659	−	0.780897i	$-0.285238\pi$
$673$	−4.05317	−	4.05317i	−0.156238	−	0.156238i	−0.780897	+	0.624659i	$0.785238\pi$
$674$	25.2846	+	14.5981i	0.973927	+	0.562297i
$675$		0			0
$676$	8.42820	+	14.5981i	0.324162	+	0.561464i
$677$	35.5820	−	9.53416i	1.36753	−	0.366428i	0.500952	−	0.865475i	$-0.332983\pi$
$677$	35.5820	−	9.53416i	1.36753	−	0.366428i	0.866575	+	0.499048i	$0.166317\pi$
$678$	2.12132	−	2.12132i	0.0814688	−	0.0814688i
$679$	3.50000	+	18.1865i	0.134318	+	0.697935i
$680$		0			0
$681$	14.6603	−	25.3923i	0.561782	−	0.973035i
$682$	4.19187	−	15.6443i	0.160515	−	0.599051i
$683$	9.83512	−	36.7052i	0.376331	−	1.40448i	−0.475060	−	0.879953i	$-0.657574\pi$
$683$	9.83512	−	36.7052i	0.376331	−	1.40448i	0.851391	−	0.524532i	$-0.175760\pi$
$684$	3.09808	−	5.36603i	0.118458	−	0.205175i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	−15.6950	+	15.6950i	−0.598804	+	0.598804i
$688$	9.84873	−	2.63896i	0.375479	−	0.100609i
$689$	−23.8564	−	41.3205i	−0.908857	−	1.57419i
$690$		0			0
$691$	−32.6147	−	18.8301i	−1.24072	−	0.716332i	−0.271482	−	0.962444i	$-0.587514\pi$
$691$	−32.6147	−	18.8301i	−1.24072	−	0.716332i	−0.969241	+	0.246112i	$0.920847\pi$
$692$	0.378937	+	0.378937i	0.0144050	+	0.0144050i
$693$	4.05317	−	5.98502i	0.153967	−	0.227352i
$694$			2.58846i			0.0982565i
$695$		0			0
$696$	1.90192	−	1.09808i	0.0720922	−	0.0416225i
$697$	24.7166	+	6.62278i	0.936206	+	0.250856i
$698$	−2.77766	−	10.3664i	−0.105136	−	0.392373i
$699$	−5.07180			−0.191833
$700$		0			0
$701$	14.5359			0.549013			0.274507	−	0.961585i	$-0.411485\pi$
$701$	14.5359			0.549013			0.274507	+	0.961585i	$0.411485\pi$
$702$	−1.41421	−	5.27792i	−0.0533761	−	0.199202i
$703$	7.58871	+	2.03339i	0.286213	+	0.0766907i
$704$	2.36603	−	1.36603i	0.0891729	−	0.0514840i
$705$		0			0
$706$		−	27.5885i		−	1.03831i
$707$	−26.9072	−	1.93185i	−1.01195	−	0.0726548i
$708$	5.27792	+	5.27792i	0.198356	+	0.198356i
$709$	−20.0718	−	11.5885i	−0.753812	−	0.435214i	0.0732575	−	0.997313i	$-0.476660\pi$
$709$	−20.0718	−	11.5885i	−0.753812	−	0.435214i	−0.827070	+	0.562099i	$0.809994\pi$
$710$		0			0
$711$	−8.06218	−	13.9641i	−0.302355	−	0.523695i
$712$	0.448288	−	0.120118i	0.0168003	−	0.00450162i
$713$	1.12321	−	1.12321i	0.0420645	−	0.0420645i
$714$	−9.92820	−	11.4641i	−0.371554	−	0.429033i
$715$		0			0
$716$	3.92820	−	6.80385i	0.146804	−	0.254272i
$717$	−5.91567	+	22.0776i	−0.220925	+	0.824503i
$718$	−5.37945	+	20.0764i	−0.200759	+	0.749244i
$719$	15.3301	−	26.5526i	0.571717	−	0.990243i	−0.424673	−	0.905347i	$-0.639611\pi$
$719$	15.3301	−	26.5526i	0.571717	−	0.990243i	0.996390	−	0.0848963i	$-0.0270559\pi$
$720$		0			0
$721$	−9.23205	+	26.6506i	−0.343820	+	0.992522i
$722$	13.7124	−	13.7124i	0.510324	−	0.510324i
$723$	−0.896575	+	0.240237i	−0.0333440	+	0.00893450i
$724$	5.09808	+	8.83013i	0.189469	+	0.328169i
$725$		0			0
$726$	−3.06218	−	1.76795i	−0.113648	−	0.0656147i
$727$	17.0585	+	17.0585i	0.632665	+	0.632665i	0.948736	−	0.316071i	$-0.102364\pi$
$727$	17.0585	+	17.0585i	0.632665	+	0.632665i	−0.316071	+	0.948736i	$0.602364\pi$
$728$	−11.9700	−	8.10634i	−0.443639	−	0.300441i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	50.6147	−	29.2224i	1.87205	−	1.08083i
$732$	−1.74238	−	0.466870i	−0.0644003	−	0.0172560i
$733$	−9.10446	−	33.9783i	−0.336281	−	1.25502i	−0.902474	−	0.430744i	$-0.858251\pi$
$733$	−9.10446	−	33.9783i	−0.336281	−	1.25502i	0.566193	−	0.824273i	$-0.308416\pi$
$734$	−3.32051			−0.122562
$735$		0			0
$736$	0.267949			0.00987674
$737$	2.82843	+	10.5558i	0.104186	+	0.388829i
$738$	−4.31199	−	1.15539i	−0.158727	−	0.0425307i
$739$	−38.6147	+	22.2942i	−1.42047	+	0.820106i	−0.996339	−	0.0854960i	$-0.972753\pi$
$739$	−38.6147	+	22.2942i	−1.42047	+	0.820106i	−0.424128	+	0.905602i	$0.639419\pi$
$740$		0			0
$741$		−	33.8564i		−	1.24375i
$742$	19.1290	+	12.9546i	0.702249	+	0.475577i
$743$	4.60797	+	4.60797i	0.169050	+	0.169050i	0.786562	−	0.617512i	$-0.211859\pi$
$743$	4.60797	+	4.60797i	0.169050	+	0.169050i	−0.617512	+	0.786562i	$0.711859\pi$
$744$	5.13397	+	2.96410i	0.188221	+	0.108669i
$745$		0			0
$746$	−16.9282	−	29.3205i	−0.619786	−	1.07350i
$747$	5.46739	−	1.46498i	0.200041	−	0.0536009i
$748$	11.0735	−	11.0735i	0.404886	−	0.404886i
$749$	8.66025	−	25.0000i	0.316439	−	0.913480i
$750$		0			0
$751$	−0.928203	+	1.60770i	−0.0338706	+	0.0586656i	−0.882464	−	0.470380i	$-0.844117\pi$
$751$	−0.928203	+	1.60770i	−0.0338706	+	0.0586656i	0.848593	+	0.529046i	$0.177450\pi$
$752$	2.84701	−	10.6252i	0.103820	−	0.387461i
$753$	2.55103	−	9.52056i	0.0929645	−	0.346948i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$	1.73205	+	2.00000i	0.0629941	+	0.0727393i
$757$	29.1165	−	29.1165i	1.05826	−	1.05826i	0.0600616	−	0.998195i	$-0.480870\pi$
$757$	29.1165	−	29.1165i	1.05826	−	1.05826i	0.998195	−	0.0600616i	$-0.0191297\pi$
$758$	−27.0967	+	7.26054i	−0.984196	+	0.263715i
$759$	0.366025	+	0.633975i	0.0132859	+	0.0230118i
$760$		0			0
$761$	4.79423	+	2.76795i	0.173791	+	0.100338i	0.584372	−	0.811486i	$-0.301341\pi$
$761$	4.79423	+	2.76795i	0.173791	+	0.100338i	−0.410581	+	0.911824i	$0.634674\pi$
$762$	8.38375	+	8.38375i	0.303711	+	0.303711i
$763$	−9.65926	−	0.693504i	−0.349689	−	0.0251065i
$764$			2.85641i			0.103341i
$765$		0			0
$766$	16.9186	−	9.76795i	0.611293	−	0.352930i
$767$	39.3949	+	10.5558i	1.42247	+	0.381149i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	22.9282			0.826812			0.413406	−	0.910547i	$-0.364339\pi$
$769$	22.9282			0.826812			0.413406	+	0.910547i	$0.364339\pi$
$770$		0			0
$771$	−23.8564			−0.859167
$772$	5.24573	+	19.5773i	0.188798	+	0.704604i
$773$	−26.8565	−	7.19617i	−0.965960	−	0.258828i	−0.258839	−	0.965921i	$-0.583340\pi$
$773$	−26.8565	−	7.19617i	−0.965960	−	0.258828i	−0.707121	+	0.707093i	$0.750006\pi$
$774$	−8.83013	+	5.09808i	−0.317392	+	0.183247i
$775$		0			0
$776$		−	7.00000i		−	0.251285i
$777$	−1.88108	+	2.77766i	−0.0674835	+	0.0996480i
$778$	7.31130	+	7.31130i	0.262123	+	0.262123i
$779$	−23.9545	−	13.8301i	−0.858258	−	0.495516i
$780$		0			0
$781$	−20.2942	−	35.1506i	−0.726185	−	1.25779i
$782$	1.48356	−	0.397520i	0.0530521	−	0.0142153i
$783$	−1.55291	+	1.55291i	−0.0554966	+	0.0554966i
$784$	6.92820	+	1.00000i	0.247436	+	0.0357143i
$785$		0			0
$786$	−1.83013	+	3.16987i	−0.0652785	+	0.113066i
$787$	11.6419	−	43.4481i	0.414988	−	1.54876i	−0.369871	−	0.929083i	$-0.620598\pi$
$787$	11.6419	−	43.4481i	0.414988	−	1.54876i	0.784859	−	0.619674i	$-0.212735\pi$
$788$	0.480473	−	1.79315i	0.0171162	−	0.0638784i
$789$	13.2583	−	22.9641i	0.472009	−	0.817544i
$790$		0			0
$791$	1.50000	+	7.79423i	0.0533339	+	0.277131i
$792$	−1.93185	+	1.93185i	−0.0686454	+	0.0686454i
$793$	−9.52056	+	2.55103i	−0.338085	+	0.0905896i
$794$	6.26795	+	10.8564i	0.222441	+	0.385279i
$795$		0			0
$796$	−16.9186	−	9.76795i	−0.599663	−	0.346216i
$797$	−2.79126	−	2.79126i	−0.0988716	−	0.0988716i	0.655941	−	0.754812i	$-0.272272\pi$
$797$	−2.79126	−	2.79126i	−0.0988716	−	0.0988716i	−0.754812	+	0.655941i	$0.772272\pi$
$798$	7.15900	+	14.7477i	0.253426	+	0.522063i
$799$		−	63.0526i		−	2.23064i
$800$		0			0
$801$	−0.401924	+	0.232051i	−0.0142013	+	0.00819911i
$802$	6.83083	+	1.83032i	0.241205	+	0.0646307i
$803$	−5.65685	−	21.1117i	−0.199626	−	0.745015i
$804$	−4.00000			−0.141069
$805$		0			0
$806$	32.3923			1.14097
$807$	−2.15849	−	8.05558i	−0.0759823	−	0.283570i
$808$	9.84873	+	2.63896i	0.346477	+	0.0928382i
$809$	38.7846	−	22.3923i	1.36359	−	0.787272i	0.373494	−	0.927633i	$-0.378160\pi$
$809$	38.7846	−	22.3923i	1.36359	−	0.787272i	0.990100	+	0.140361i	$0.0448264\pi$
$810$		0			0
$811$			4.78461i			0.168010i	0.996465	+	0.0840052i	$0.0267712\pi$
$811$			4.78461i			0.168010i	−0.996465	+	0.0840052i	$0.973229\pi$
$812$	−0.416102	+	5.79555i	−0.0146023	+	0.203384i
$813$	−3.15660	−	3.15660i	−0.110707	−	0.110707i
$814$	−3.00000	−	1.73205i	−0.105150	−	0.0607083i
$815$		0			0
$816$	2.86603	+	4.96410i	0.100331	+	0.173778i
$817$	−61.0242	+	16.3514i	−2.13497	+	0.572063i
$818$	−16.1248	+	16.1248i	−0.563789	+	0.563789i
$819$	13.6603	+	4.73205i	0.477328	+	0.165351i
$820$		0			0
$821$	−11.2224	+	19.4378i	−0.391666	+	0.678385i	−0.992669	−	0.120861i	$-0.961434\pi$
$821$	−11.2224	+	19.4378i	−0.391666	+	0.678385i	0.601004	+	0.799246i	$0.294768\pi$
$822$	−5.67544	+	21.1810i	−0.197954	+	0.738773i
$823$	−9.93666	+	37.0841i	−0.346370	+	1.29267i	0.544633	+	0.838674i	$0.316669\pi$
$823$	−9.93666	+	37.0841i	−0.346370	+	1.29267i	−0.891003	+	0.453997i	$0.849998\pi$
$824$	5.33013	−	9.23205i	0.185684	−	0.321614i
$825$		0			0
$826$	−19.3923	+	3.73205i	−0.674745	+	0.129855i
$827$	−27.8410	+	27.8410i	−0.968125	+	0.968125i	−0.999507	−	0.0313823i	$-0.990009\pi$
$827$	−27.8410	+	27.8410i	−0.968125	+	0.968125i	0.0313823	+	0.999507i	$0.490009\pi$
$828$	−0.258819	+	0.0693504i	−0.00899458	+	0.00241009i
$829$	−6.85641	−	11.8756i	−0.238133	−	0.412458i	0.722046	−	0.691845i	$-0.243202\pi$
$829$	−6.85641	−	11.8756i	−0.238133	−	0.412458i	−0.960179	+	0.279387i	$0.909869\pi$
$830$		0			0
$831$	12.6340	+	7.29423i	0.438268	+	0.253034i
$832$	3.86370	+	3.86370i	0.133950	+	0.133950i
$833$	39.8432	−	4.74170i	1.38048	−	0.164290i
$834$		−	0.928203i		−	0.0321410i
$835$		0			0
$836$	−14.6603	+	8.46410i	−0.507035	+	0.292737i
$837$	−5.72620	−	1.53433i	−0.197927	−	0.0530343i
$838$	−5.32868	−	19.8869i	−0.184076	−	0.686982i
$839$	0.124356			0.00429323			0.00214662	−	0.999998i	$-0.499317\pi$
$839$	0.124356			0.00429323			0.00214662	+	0.999998i	$0.499317\pi$
$840$		0			0
$841$	24.1769			0.833687
$842$	−2.44949	−	9.14162i	−0.0844150	−	0.315041i
$843$	30.8910	+	8.27723i	1.06394	+	0.285083i
$844$	2.02628	−	1.16987i	0.0697474	−	0.0402687i
$845$		0			0
$846$			11.0000i			0.378188i
$847$	8.41593	−	4.08536i	0.289175	−	0.140375i
$848$	−6.17449	−	6.17449i	−0.212033	−	0.212033i
$849$	14.8301	+	8.56218i	0.508969	+	0.293853i
$850$		0			0
$851$	−0.169873	−	0.294229i	−0.00582317	−	0.0100860i
$852$	14.3502	−	3.84512i	0.491629	−	0.131732i
$853$	22.3872	−	22.3872i	0.766522	−	0.766522i	−0.210970	−	0.977493i	$-0.567662\pi$
$853$	22.3872	−	22.3872i	0.766522	−	0.766522i	0.977493	+	0.210970i	$0.0676623\pi$
$854$	3.60770	−	3.12436i	0.123453	−	0.106913i
$855$		0			0
$856$	−5.00000	+	8.66025i	−0.170896	+	0.296001i
$857$	−10.5930	+	39.5336i	−0.361850	+	1.35044i	0.509791	+	0.860298i	$0.329723\pi$
$857$	−10.5930	+	39.5336i	−0.361850	+	1.35044i	−0.871641	+	0.490144i	$0.836944\pi$
$858$	−3.86370	+	14.4195i	−0.131905	+	0.492275i
$859$	17.9545	−	31.0981i	0.612599	−	1.06105i	−0.378202	−	0.925723i	$-0.623457\pi$
$859$	17.9545	−	31.0981i	0.612599	−	1.06105i	0.990801	−	0.135329i	$-0.0432093\pi$
$860$		0			0
$861$	8.92820	−	7.73205i	0.304272	−	0.263508i
$862$	−4.57081	+	4.57081i	−0.155682	+	0.155682i
$863$	−27.6837	+	7.41782i	−0.942363	+	0.252506i	−0.697119	−	0.716956i	$-0.745535\pi$
$863$	−27.6837	+	7.41782i	−0.942363	+	0.252506i	−0.245245	+	0.969461i	$0.578868\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−5.47372	−	3.16025i	−0.186005	−	0.107390i
$867$	11.2122	+	11.2122i	0.380785	+	0.380785i
$868$	−14.1100	+	6.84941i	−0.478923	+	0.232484i
$869$			44.0526i			1.49438i
$870$		0			0
$871$	−18.9282	+	10.9282i	−0.641358	+	0.370288i
$872$	3.53553	+	0.947343i	0.119728	+	0.0320811i
$873$	1.81173	+	6.76148i	0.0613179	+	0.228841i
$874$	−1.66025			−0.0561589
$875$		0			0
$876$	8.00000			0.270295
$877$	−7.41284	−	27.6651i	−0.250314	−	0.934184i	−0.970638	−	0.240546i	$-0.922673\pi$
$877$	−7.41284	−	27.6651i	−0.250314	−	0.934184i	0.720324	−	0.693638i	$-0.243993\pi$
$878$	17.9737	+	4.81603i	0.606581	+	0.162533i
$879$	−14.4904	+	8.36603i	−0.488748	+	0.282179i
$880$		0			0
$881$			30.3205i			1.02152i	0.859722	+	0.510762i	$0.170637\pi$
$881$			30.3205i			1.02152i	−0.859722	+	0.510762i	$0.829363\pi$
$882$	−6.95095	+	0.827225i	−0.234051	+	0.0278541i
$883$	2.17209	+	2.17209i	0.0730966	+	0.0730966i	0.742710	−	0.669613i	$-0.233540\pi$
$883$	2.17209	+	2.17209i	0.0730966	+	0.0730966i	−0.669613	+	0.742710i	$0.733540\pi$
$884$	27.1244	+	15.6603i	0.912291	+	0.526711i
$885$		0			0
$886$	−11.7583	−	20.3660i	−0.395029	−	0.684210i
$887$	−14.6969	+	3.93803i	−0.493475	+	0.132226i	−0.496970	−	0.867768i	$-0.665554\pi$
$887$	−14.6969	+	3.93803i	−0.493475	+	0.132226i	0.00349516	+	0.999994i	$0.498887\pi$
$888$	0.896575	−	0.896575i	0.0300871	−	0.0300871i
$889$	−30.8038	+	5.92820i	−1.03313	+	0.198826i
$890$		0			0
$891$	1.36603	−	2.36603i	0.0457636	−	0.0792648i
$892$	−4.07175	+	15.1960i	−0.136332	+	0.508800i
$893$	−17.6405	+	65.8353i	−0.590317	+	2.20309i
$894$	−9.00000	+	15.5885i	−0.301005	+	0.521356i
$895$		0			0
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$	−1.03528	+	1.03528i	−0.0345669	+	0.0345669i
$898$	−25.3729	+	6.79865i	−0.846704	+	0.226874i
$899$	−6.50962	−	11.2750i	−0.217108	−	0.376042i
$900$		0			0
$901$	−43.3468	−	25.0263i	−1.44409	−	0.833746i
$902$	8.62398	+	8.62398i	0.287147	+	0.287147i
$903$	1.93185	−	26.9072i	0.0642880	−	0.895416i
$904$		−	3.00000i		−	0.0997785i
$905$		0			0
$906$	2.53590	−	1.46410i	0.0842496	−	0.0486415i
$907$	−14.8864	−	3.98880i	−0.494295	−	0.132446i	0.00305603	−	0.999995i	$-0.499027\pi$
$907$	−14.8864	−	3.98880i	−0.494295	−	0.132446i	−0.497351	+	0.867549i	$0.665694\pi$
$908$	−7.58871	−	28.3214i	−0.251840	−	0.939880i
$909$	−10.1962			−0.338185
$910$		0			0
$911$	5.78461			0.191653			0.0958263	−	0.995398i	$-0.469451\pi$
$911$	5.78461			0.191653			0.0958263	+	0.995398i	$0.469451\pi$
$912$	−1.60368	−	5.98502i	−0.0531032	−	0.198184i
$913$	−14.9372	−	4.00240i	−0.494348	−	0.132460i
$914$	−5.32051	+	3.07180i	−0.175987	+	0.101606i
$915$		0			0
$916$			22.1962i			0.733382i
$917$	−4.22904	−	8.71191i	−0.139655	−	0.287693i
$918$	−4.05317	−	4.05317i	−0.133775	−	0.133775i
$919$	−9.69615	−	5.59808i	−0.319847	−	0.184663i	0.331478	−	0.943463i	$-0.392453\pi$
$919$	−9.69615	−	5.59808i	−0.319847	−	0.184663i	−0.651324	+	0.758800i	$0.725786\pi$
$920$		0			0
$921$	−2.53590	−	4.39230i	−0.0835607	−	0.144731i
$922$	−14.7985	+	3.96524i	−0.487362	+	0.130588i
$923$	57.4007	−	57.4007i	1.88937	−	1.88937i
$924$	−1.36603	−	7.09808i	−0.0449389	−	0.233510i
$925$		0			0
$926$	−17.6962	+	30.6506i	−0.581532	+	1.00724i
$927$	−2.75908	+	10.2970i	−0.0906200	+	0.338198i
$928$	0.568406	−	2.12132i	0.0186588	−	0.0696358i
$929$	−4.87564	+	8.44486i	−0.159965	+	0.277067i	−0.934856	−	0.355028i	$-0.884471\pi$
$929$	−4.87564	+	8.44486i	−0.159965	+	0.277067i	0.774891	+	0.632095i	$0.217805\pi$
$930$		0			0
$931$	−42.9282	−	6.19615i	−1.40692	−	0.203071i
$932$	−3.58630	+	3.58630i	−0.117473	+	0.117473i
$933$	−9.91808	+	2.65754i	−0.324703	+	0.0870040i
$934$	−15.0263	−	26.0263i	−0.491675	−	0.851606i
$935$		0			0
$936$	−4.73205	−	2.73205i	−0.154672	−	0.0892999i
$937$	−5.93426	−	5.93426i	−0.193864	−	0.193864i	0.603500	−	0.797363i	$-0.293772\pi$
$937$	−5.93426	−	5.93426i	−0.193864	−	0.193864i	−0.797363	+	0.603500i	$0.793772\pi$
$938$	5.93426	−	8.76268i	0.193760	−	0.286112i
$939$		−	11.5359i		−	0.376460i
$940$		0			0
$941$	−19.5622	+	11.2942i	−0.637709	+	0.368181i	−0.783731	−	0.621100i	$-0.786686\pi$
$941$	−19.5622	+	11.2942i	−0.637709	+	0.368181i	0.146023	+	0.989281i	$0.453353\pi$
$942$	16.6796	+	4.46927i	0.543449	+	0.145617i
$943$	0.309587	+	1.15539i	0.0100815	+	0.0376248i
$944$	7.46410			0.242936
$945$		0			0
$946$	27.8564			0.905690
$947$	0.582009	+	2.17209i	0.0189128	+	0.0705834i	0.974737	−	0.223355i	$-0.0717008\pi$
$947$	0.582009	+	2.17209i	0.0189128	+	0.0705834i	−0.955825	+	0.293938i	$0.905034\pi$
$948$	−15.5749	−	4.17329i	−0.505850	−	0.135542i
$949$	37.8564	−	21.8564i	1.22887	−	0.709489i
$950$		0			0
$951$			22.1962i			0.719760i
$952$	−15.1266	−	1.08604i	−0.490257	−	0.0351989i
$953$	2.55103	+	2.55103i	0.0826358	+	0.0826358i	0.747217	−	0.664581i	$-0.231390\pi$
$953$	2.55103	+	2.55103i	0.0826358	+	0.0826358i	−0.664581	+	0.747217i	$0.731390\pi$
$954$	7.56218	+	4.36603i	0.244835	+	0.141355i
$955$		0			0
$956$	11.4282	+	19.7942i	0.369615	+	0.640191i
$957$	5.79555	−	1.55291i	0.187344	−	0.0501986i
$958$	−22.6138	+	22.6138i	−0.730619	+	0.730619i
$959$	−37.9808	−	43.8564i	−1.22646	−	1.41620i
$960$		0			0
$961$	2.07180	−	3.58846i	0.0668322	−	0.115757i
$962$	1.79315	−	6.69213i	0.0578135	−	0.215763i
$963$	2.58819	−	9.65926i	0.0834033	−	0.311265i
$964$	−0.464102	+	0.803848i	−0.0149477	+	0.0258902i
$965$		0			0
$966$	0.232051	−	0.669873i	0.00746611	−	0.0215528i
$967$	8.91499	−	8.91499i	0.286687	−	0.286687i	−0.549082	−	0.835769i	$-0.685023\pi$
$967$	8.91499	−	8.91499i	0.286687	−	0.286687i	0.835769	+	0.549082i	$0.185023\pi$
$968$	−3.41542	+	0.915158i	−0.109776	+	0.0294143i
$969$	−17.7583	−	30.7583i	−0.570480	−	0.988100i
$970$		0			0
$971$	−6.97372	−	4.02628i	−0.223797	−	0.129209i	0.383910	−	0.923371i	$-0.374577\pi$
$971$	−6.97372	−	4.02628i	−0.223797	−	0.129209i	−0.607707	+	0.794161i	$0.707911\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	2.03339	+	1.37705i	0.0651874	+	0.0441462i
$974$		−	20.4641i		−	0.655712i
$975$		0			0
$976$	−1.56218	+	0.901924i	−0.0500041	+	0.0288699i
$977$	−58.8843	−	15.7780i	−1.88388	−	0.504783i	−0.999260	−	0.0384628i	$-0.987754\pi$
$977$	−58.8843	−	15.7780i	−1.88388	−	0.504783i	−0.884616	−	0.466320i	$-0.845579\pi$
$978$	−3.10583	−	11.5911i	−0.0993134	−	0.370643i
$979$	1.26795			0.0405238
$980$		0			0
$981$	−3.66025			−0.116863
$982$	4.05317	+	15.1266i	0.129342	+	0.482711i
$983$	7.96764	+	2.13492i	0.254128	+	0.0680935i	0.383634	−	0.923485i	$-0.374672\pi$
$983$	7.96764	+	2.13492i	0.254128	+	0.0680935i	−0.129506	+	0.991579i	$0.541339\pi$
$984$	−3.86603	+	2.23205i	−0.123244	+	0.0711552i
$985$		0			0
$986$		−	12.5885i		−	0.400898i
$987$	−24.0974	−	16.3192i	−0.767028	−	0.519446i
$988$	−23.9401	−	23.9401i	−0.761636	−	0.761636i
$989$	2.36603	+	1.36603i	0.0752352	+	0.0434371i
$990$		0			0
$991$	1.74167	+	3.01666i	0.0553260	+	0.0958274i	0.892362	−	0.451320i	$-0.149047\pi$
$991$	1.74167	+	3.01666i	0.0553260	+	0.0958274i	−0.837036	+	0.547148i	$0.815714\pi$
$992$	5.72620	−	1.53433i	0.181807	−	0.0487151i
$993$	11.2122	−	11.2122i	0.355808	−	0.355808i
$994$	−12.8660	+	37.1410i	−0.408086	+	1.17804i
$995$		0			0
$996$	2.83013	−	4.90192i	0.0896760	−	0.155323i
$997$	−2.62536	+	9.79796i	−0.0831458	+	0.310304i	−0.994957	−	0.100306i	$-0.968018\pi$
$997$	−2.62536	+	9.79796i	−0.0831458	+	0.310304i	0.911811	+	0.410611i	$0.134684\pi$
$998$	8.01841	−	29.9251i	0.253818	−	0.947263i
$999$	−0.633975	+	1.09808i	−0.0200581	+	0.0347416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.b.943.2	yes	8
5.2	odd	4		1050.2.bc.c.607.1	yes	8
5.3	odd	4		1050.2.bc.c.607.2	yes	8
5.4	even	2	inner	1050.2.bc.b.943.1	yes	8
7.3	odd	6		1050.2.bc.c.493.1	yes	8
35.3	even	12	inner	1050.2.bc.b.157.1	✓	8
35.17	even	12	inner	1050.2.bc.b.157.2	yes	8
35.24	odd	6		1050.2.bc.c.493.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.b.157.1	✓	8	35.3	even	12	inner
1050.2.bc.b.157.2	yes	8	35.17	even	12	inner
1050.2.bc.b.943.1	yes	8	5.4	even	2	inner
1050.2.bc.b.943.2	yes	8	1.1	even	1	trivial
1050.2.bc.c.493.1	yes	8	7.3	odd	6
1050.2.bc.c.493.2	yes	8	35.24	odd	6
1050.2.bc.c.607.1	yes	8	5.2	odd	4
1050.2.bc.c.607.2	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.965926 - 0.258819i) q^{12} +(3.86370 - 3.86370i) q^{13} +(-0.866025 + 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.48356 - 5.53674i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-3.09808 + 5.36603i) q^{19} +(-1.73205 - 2.00000i) q^{21} +(1.93185 - 1.93185i) q^{22} +(0.258819 - 0.0693504i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.73205 + 2.73205i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.63896 - 0.189469i) q^{28} -2.19615i q^{29} +(5.13397 - 2.96410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.707107 + 2.63896i) q^{33} +5.73205 q^{34} -1.00000 q^{36} +(-0.328169 - 1.22474i) q^{37} +(-5.98502 - 1.60368i) q^{38} +(-4.73205 + 2.73205i) q^{39} +4.46410i q^{41} +(1.48356 - 2.19067i) q^{42} +(7.20977 + 7.20977i) q^{43} +(2.36603 + 1.36603i) q^{44} +(0.133975 + 0.232051i) q^{46} +(10.6252 - 2.84701i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.59808 + 6.50000i) q^{49} +(-2.86603 + 4.96410i) q^{51} +(-1.41421 + 5.27792i) q^{52} +(2.26002 - 8.43451i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(4.38134 - 4.38134i) q^{57} +(2.12132 - 0.568406i) q^{58} +(3.73205 + 6.46410i) q^{59} +(-1.56218 - 0.901924i) q^{61} +(4.19187 + 4.19187i) q^{62} +(1.15539 + 2.38014i) q^{63} +1.00000i q^{64} +(-2.36603 + 1.36603i) q^{66} +(-3.86370 - 1.03528i) q^{67} +(1.48356 + 5.53674i) q^{68} -0.267949 q^{69} +14.8564 q^{71} +(-0.258819 - 0.965926i) q^{72} +(7.72741 + 2.07055i) q^{73} +(1.09808 - 0.633975i) q^{74} -6.19615i q^{76} +(0.517638 - 7.20977i) q^{77} +(-3.86370 - 3.86370i) q^{78} +(-13.9641 - 8.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.31199 + 1.15539i) q^{82} +(4.00240 - 4.00240i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-5.09808 + 8.83013i) q^{86} +(-0.568406 + 2.12132i) q^{87} +(-0.707107 + 2.63896i) q^{88} +(-0.232051 + 0.401924i) q^{89} +(14.1962 - 2.73205i) q^{91} +(-0.189469 + 0.189469i) q^{92} +(-5.72620 + 1.53433i) q^{93} +(5.50000 + 9.52628i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(4.94975 + 4.94975i) q^{97} +(-5.60609 + 4.19187i) q^{98} -2.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 4 q^{16} - 4 q^{19} + 4 q^{24} + 24 q^{26} + 48 q^{31} + 32 q^{34} - 8 q^{36} - 24 q^{39} + 12 q^{44} + 8 q^{46} - 16 q^{51} + 4 q^{54} - 4 q^{56} + 16 q^{59} + 36 q^{61} - 12 q^{66} - 16 q^{69} + 8 q^{71} - 12 q^{74} - 84 q^{79} + 4 q^{81} + 20 q^{84} - 20 q^{86} + 12 q^{89} + 72 q^{91} + 44 q^{94}+O(q^{100}) \) 8 * q - 4 * q^11 + 4 * q^16 - 4 * q^19 + 4 * q^24 + 24 * q^26 + 48 * q^31 + 32 * q^34 - 8 * q^36 - 24 * q^39 + 12 * q^44 + 8 * q^46 - 16 * q^51 + 4 * q^54 - 4 * q^56 + 16 * q^59 + 36 * q^61 - 12 * q^66 - 16 * q^69 + 8 * q^71 - 12 * q^74 - 84 * q^79 + 4 * q^81 + 20 * q^84 - 20 * q^86 + 12 * q^89 + 72 * q^91 + 44 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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