LMFDB - Embedded newform 1050.2.bc.c.607.2

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			607.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.c.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(3.86370 + 3.86370i) q^{13} +(0.866025 - 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-5.53674 - 1.48356i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(3.09808 - 5.36603i) q^{19} +(-1.73205 - 2.00000i) q^{21} +(-1.93185 - 1.93185i) q^{22} +(0.0693504 + 0.258819i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.73205 + 2.73205i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.189469 - 2.63896i) q^{28} +2.19615i q^{29} +(5.13397 - 2.96410i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.63896 + 0.707107i) q^{33} -5.73205 q^{34} -1.00000 q^{36} +(-1.22474 + 0.328169i) q^{37} +(1.60368 - 5.98502i) q^{38} +(4.73205 - 2.73205i) q^{39} +4.46410i q^{41} +(-2.19067 - 1.48356i) q^{42} +(-7.20977 + 7.20977i) q^{43} +(-2.36603 - 1.36603i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-2.84701 - 10.6252i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.59808 - 6.50000i) q^{49} +(-2.86603 + 4.96410i) q^{51} +(5.27792 + 1.41421i) q^{52} +(8.43451 + 2.26002i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(-4.38134 - 4.38134i) q^{57} +(0.568406 + 2.12132i) q^{58} +(-3.73205 - 6.46410i) q^{59} +(-1.56218 - 0.901924i) q^{61} +(4.19187 - 4.19187i) q^{62} +(-2.38014 + 1.15539i) q^{63} -1.00000i q^{64} +(-2.36603 + 1.36603i) q^{66} +(-1.03528 + 3.86370i) q^{67} +(-5.53674 + 1.48356i) q^{68} +0.267949 q^{69} +14.8564 q^{71} +(-0.965926 + 0.258819i) q^{72} +(-2.07055 + 7.72741i) q^{73} +(-1.09808 + 0.633975i) q^{74} -6.19615i q^{76} +(-7.20977 - 0.517638i) q^{77} +(3.86370 - 3.86370i) q^{78} +(13.9641 + 8.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.15539 + 4.31199i) q^{82} +(4.00240 + 4.00240i) q^{83} +(-2.50000 - 0.866025i) q^{84} +(-5.09808 + 8.83013i) q^{86} +(2.12132 + 0.568406i) q^{87} +(-2.63896 - 0.707107i) q^{88} +(0.232051 - 0.401924i) q^{89} +(14.1962 - 2.73205i) q^{91} +(0.189469 + 0.189469i) q^{92} +(-1.53433 - 5.72620i) q^{93} +(-5.50000 - 9.52628i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(4.94975 - 4.94975i) q^{97} +(-4.19187 - 5.60609i) 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	1.48356	−	2.19067i	0.560734	−	0.827996i
$7$	1.48356	−	2.19067i	0.560734	−	0.827996i
$8$	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	$0.968458\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	3.86370	+	3.86370i	1.07160	+	1.07160i	0.997231	+	0.0743676i	$0.0236938\pi$
$13$	3.86370	+	3.86370i	1.07160	+	1.07160i	0.0743676	+	0.997231i	$0.476306\pi$
$14$	0.866025	−	2.50000i	0.231455	−	0.668153i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−5.53674	−	1.48356i	−1.34286	−	0.359817i	−0.485363	−	0.874313i	$-0.661312\pi$
$17$	−5.53674	−	1.48356i	−1.34286	−	0.359817i	−0.857493	+	0.514496i	$0.827979\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	3.09808	−	5.36603i	0.710747	−	1.23105i	−0.253830	−	0.967249i	$-0.581690\pi$
$19$	3.09808	−	5.36603i	0.710747	−	1.23105i	0.964577	−	0.263802i	$-0.0849764\pi$
$20$		0			0
$21$	−1.73205	−	2.00000i	−0.377964	−	0.436436i
$22$	−1.93185	−	1.93185i	−0.411872	−	0.411872i
$23$	0.0693504	+	0.258819i	0.0144605	+	0.0539675i	0.972779	−	0.231734i	$-0.0744400\pi$
$23$	0.0693504	+	0.258819i	0.0144605	+	0.0539675i	−0.958319	+	0.285702i	$0.907773\pi$
$24$	−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
$28$	0.189469	−	2.63896i	0.0358062	−	0.498716i
$29$			2.19615i			0.407815i	0.978990	+	0.203908i	$0.0653642\pi$
$29$			2.19615i			0.407815i	−0.978990	+	0.203908i	$0.934636\pi$
$30$		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	$0.154635\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−2.63896	+	0.707107i	−0.459384	+	0.123091i
$34$	−5.73205			−0.983039
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−1.22474	+	0.328169i	−0.201347	+	0.0539507i	−0.358083	−	0.933690i	$-0.616569\pi$
$37$	−1.22474	+	0.328169i	−0.201347	+	0.0539507i	0.156736	+	0.987641i	$0.449903\pi$
$38$	1.60368	−	5.98502i	0.260152	−	0.970899i
$39$	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	$0.886661\pi$
$42$	−2.19067	−	1.48356i	−0.338028	−	0.228919i
$43$	−7.20977	+	7.20977i	−1.09948	+	1.09948i	−0.105008	+	0.994471i	$0.533487\pi$
$43$	−7.20977	+	7.20977i	−1.09948	+	1.09948i	−0.994471	+	0.105008i	$0.966513\pi$
$44$	−2.36603	−	1.36603i	−0.356692	−	0.205936i
$45$		0			0
$46$	0.133975	+	0.232051i	0.0197535	+	0.0342140i
$47$	−2.84701	−	10.6252i	−0.415279	−	1.54984i	−0.784276	−	0.620412i	$-0.786965\pi$
$47$	−2.84701	−	10.6252i	−0.415279	−	1.54984i	0.368997	−	0.929431i	$-0.379701\pi$
$48$	−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
$52$	5.27792	+	1.41421i	0.731915	+	0.196116i
$53$	8.43451	+	2.26002i	1.15857	+	0.310438i	0.786394	−	0.617725i	$-0.211945\pi$
$53$	8.43451	+	2.26002i	1.15857	+	0.310438i	0.372175	+	0.928163i	$0.378612\pi$
$54$	−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
$58$	0.568406	+	2.12132i	0.0746354	+	0.278543i
$59$	−3.73205	−	6.46410i	−0.485872	−	0.841554i	0.513997	−	0.857792i	$-0.328164\pi$
$59$	−3.73205	−	6.46410i	−0.485872	−	0.841554i	−0.999868	+	0.0162379i	$0.994831\pi$
$60$		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
$63$	−2.38014	+	1.15539i	−0.299869	+	0.145566i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.36603	+	1.36603i	−0.291238	+	0.168146i
$67$	−1.03528	+	3.86370i	−0.126479	+	0.472026i	−0.999888	−	0.0149610i	$-0.995238\pi$
$67$	−1.03528	+	3.86370i	−0.126479	+	0.472026i	0.873409	+	0.486987i	$0.161904\pi$
$68$	−5.53674	+	1.48356i	−0.671428	+	0.179909i
$69$	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	$0.156490\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−2.07055	+	7.72741i	−0.242340	+	0.904425i	0.732362	+	0.680915i	$0.238418\pi$
$73$	−2.07055	+	7.72741i	−0.242340	+	0.904425i	−0.974702	+	0.223509i	$0.928249\pi$
$74$	−1.09808	+	0.633975i	−0.127649	+	0.0736980i
$75$		0			0
$76$		−	6.19615i		−	0.710747i
$77$	−7.20977	−	0.517638i	−0.821629	−	0.0589903i
$78$	3.86370	−	3.86370i	0.437478	−	0.437478i
$79$	13.9641	+	8.06218i	1.57108	+	0.907066i	0.996036	+	0.0889460i	$0.0283499\pi$
$79$	13.9641	+	8.06218i	1.57108	+	0.907066i	0.575048	+	0.818120i	$0.304983\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.15539	+	4.31199i	0.127592	+	0.476180i
$83$	4.00240	+	4.00240i	0.439321	+	0.439321i	0.891783	−	0.452463i	$-0.149454\pi$
$83$	4.00240	+	4.00240i	0.439321	+	0.439321i	−0.452463	+	0.891783i	$0.649454\pi$
$84$	−2.50000	−	0.866025i	−0.272772	−	0.0944911i
$85$		0			0
$86$	−5.09808	+	8.83013i	−0.549740	+	0.952177i
$87$	2.12132	+	0.568406i	0.227429	+	0.0609395i
$88$	−2.63896	−	0.707107i	−0.281314	−	0.0753778i
$89$	0.232051	−	0.401924i	0.0245973	−	0.0426038i	−0.853465	−	0.521151i	$-0.825503\pi$
$89$	0.232051	−	0.401924i	0.0245973	−	0.0426038i	0.878062	+	0.478547i	$0.158836\pi$
$90$		0			0
$91$	14.1962	−	2.73205i	1.48816	−	0.286397i
$92$	0.189469	+	0.189469i	0.0197535	+	0.0197535i
$93$	−1.53433	−	5.72620i	−0.159103	−	0.593780i
$94$	−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	−0.409665	−	0.912236i	$-0.634354\pi$
$97$	4.94975	−	4.94975i	0.502571	−	0.502571i	0.912236	+	0.409665i	$0.134354\pi$
$98$	−4.19187	−	5.60609i	−0.423443	−	0.566300i
$99$			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	$0.502681\pi$
$102$	−1.48356	+	5.53674i	−0.146895	+	0.548219i
$103$	−10.2970	+	2.75908i	−1.01460	+	0.271860i	−0.727548	−	0.686057i	$-0.759340\pi$
$103$	−10.2970	+	2.75908i	−1.01460	+	0.271860i	−0.287047	+	0.957917i	$0.592674\pi$
$104$	5.46410			0.535799
$105$		0			0
$106$	8.73205			0.848132
$107$	−9.65926	+	2.58819i	−0.933796	+	0.250210i	−0.693472	−	0.720483i	$-0.743920\pi$
$107$	−9.65926	+	2.58819i	−0.933796	+	0.250210i	−0.240323	+	0.970693i	$0.577253\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	3.16987	−	1.83013i	0.303619	−	0.175294i	−0.340449	−	0.940263i	$-0.610579\pi$
$109$	3.16987	−	1.83013i	0.303619	−	0.175294i	0.644067	+	0.764969i	$0.277246\pi$
$110$		0			0
$111$			1.26795i			0.120348i
$112$	−1.15539	−	2.38014i	−0.109175	−	0.224902i
$113$	−2.12132	+	2.12132i	−0.199557	+	0.199557i	−0.799810	−	0.600253i	$-0.795067\pi$
$113$	−2.12132	+	2.12132i	−0.199557	+	0.199557i	0.600253	+	0.799810i	$0.295067\pi$
$114$	−5.36603	−	3.09808i	−0.502574	−	0.290161i
$115$		0			0
$116$	1.09808	+	1.90192i	0.101954	+	0.176589i
$117$	−1.41421	−	5.27792i	−0.130744	−	0.487944i
$118$	−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
$122$	−1.74238	−	0.466870i	−0.157748	−	0.0422684i
$123$	4.31199	+	1.15539i	0.388799	+	0.104178i
$124$	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	$-0.0736751\pi$
$127$	8.38375	+	8.38375i	0.743937	+	0.743937i	−0.229396	+	0.973333i	$0.573675\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	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
$133$	−7.15900	−	14.7477i	−0.620764	−	1.27879i
$134$			4.00000i			0.345547i
$135$		0			0
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	−5.67544	+	21.1810i	−0.484885	+	1.80962i	0.0956916	+	0.995411i	$0.469494\pi$
$137$	−5.67544	+	21.1810i	−0.484885	+	1.80962i	−0.580577	+	0.814205i	$0.697173\pi$
$138$	0.258819	−	0.0693504i	0.0220321	−	0.00590349i
$139$	−0.928203			−0.0787292			−0.0393646	−	0.999225i	$-0.512533\pi$
$139$	−0.928203			−0.0787292			−0.0393646	+	0.999225i	$0.512533\pi$
$140$		0			0
$141$	−11.0000			−0.926367
$142$	14.3502	−	3.84512i	1.20424	−	0.322675i
$143$	3.86370	−	14.4195i	0.323099	−	1.20582i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$			8.00000i			0.662085i
$147$	−6.95095	+	0.827225i	−0.573305	+	0.0682284i
$148$	−0.896575	+	0.896575i	−0.0736980	+	0.0736980i
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.976306	−	0.216394i	$-0.0694297\pi$
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.300750	+	0.953703i	$0.402763\pi$
$150$		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	$0.795317\pi$
$152$	−1.60368	−	5.98502i	−0.130076	−	0.485450i
$153$	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
$157$	16.6796	+	4.46927i	1.33117	+	0.356687i	0.853153	−	0.521661i	$-0.174688\pi$
$157$	16.6796	+	4.46927i	1.33117	+	0.356687i	0.478021	+	0.878348i	$0.341354\pi$
$158$	15.5749	+	4.17329i	1.23908	+	0.332009i
$159$	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
$163$	3.10583	+	11.5911i	0.243267	+	0.907886i	0.974246	+	0.225486i	$0.0723970\pi$
$163$	3.10583	+	11.5911i	0.243267	+	0.907886i	−0.730979	+	0.682400i	$0.760936\pi$
$164$	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	−0.0363667	+	0.999339i	$0.511578\pi$
$167$	−13.3843	+	13.3843i	−1.03571	+	1.03571i	−0.999339	+	0.0363667i	$0.988422\pi$
$168$	−2.63896	−	0.189469i	−0.203600	−	0.0146178i
$169$			16.8564i			1.29665i
$170$		0			0
$171$	−5.36603	+	3.09808i	−0.410350	+	0.236916i
$172$	−2.63896	+	9.84873i	−0.201219	+	0.750958i
$173$	0.517638	−	0.138701i	0.0393553	−	0.0105452i	−0.239088	−	0.970998i	$-0.576848\pi$
$173$	0.517638	−	0.138701i	0.0393553	−	0.0105452i	0.278443	+	0.960453i	$0.410182\pi$
$174$	2.19615			0.166490
$175$		0			0
$176$	−2.73205			−0.205936
$177$	−7.20977	+	1.93185i	−0.541919	+	0.145207i
$178$	0.120118	−	0.448288i	0.00900325	−	0.0336006i
$179$	6.80385	−	3.92820i	0.508543	−	0.293608i	−0.223691	−	0.974660i	$-0.571811\pi$
$179$	6.80385	−	3.92820i	0.508543	−	0.293608i	0.732235	+	0.681052i	$0.238477\pi$
$180$		0			0
$181$		−	10.1962i		−	0.757874i	−0.925422	−	0.378937i	$-0.876290\pi$
$181$		−	10.1962i		−	0.757874i	0.925422	−	0.378937i	$-0.123710\pi$
$182$	13.0053	−	6.31319i	0.964019	−	0.467965i
$183$	−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
$187$	4.05317	+	15.1266i	0.296397	+	1.10617i
$188$	−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	$0.133713\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	19.5773	+	5.24573i	1.40921	+	0.377596i	0.881642	−	0.471919i	$-0.156438\pi$
$193$	19.5773	+	5.24573i	1.40921	+	0.377596i	0.527565	+	0.849514i	$0.323105\pi$
$194$	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	$-0.228934\pi$
$197$	1.31268	+	1.31268i	0.0935244	+	0.0935244i	−0.658797	+	0.752321i	$0.728934\pi$
$198$	0.707107	+	2.63896i	0.0502519	+	0.187543i
$199$	−9.76795	−	16.9186i	−0.692432	−	1.19933i	−0.971039	−	0.238922i	$-0.923206\pi$
$199$	−9.76795	−	16.9186i	−0.692432	−	1.19933i	0.278607	−	0.960405i	$-0.410127\pi$
$200$		0			0
$201$	3.46410	+	2.00000i	0.244339	+	0.141069i
$202$	−7.20977	+	7.20977i	−0.507278	+	0.507278i
$203$	4.81105	+	3.25813i	0.337669	+	0.228676i
$204$			5.73205i			0.401324i
$205$		0			0
$206$	−9.23205	+	5.33013i	−0.643227	+	0.371368i
$207$	0.0693504	−	0.258819i	0.00482018	−	0.0179892i
$208$	5.27792	−	1.41421i	0.365958	−	0.0980581i
$209$	−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	$0.525664\pi$
$212$	8.43451	−	2.26002i	0.579285	−	0.155219i
$213$	3.84512	−	14.3502i	0.263463	−	0.983259i
$214$	−8.66025	+	5.00000i	−0.592003	+	0.341793i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	1.12321	−	15.6443i	0.0762484	−	1.06200i
$218$	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
$222$	0.328169	+	1.22474i	0.0220253	+	0.0821995i
$223$	11.1242	+	11.1242i	0.744934	+	0.744934i	0.973523	−	0.228589i	$-0.0734111\pi$
$223$	11.1242	+	11.1242i	0.744934	+	0.744934i	−0.228589	+	0.973523i	$0.573411\pi$
$224$	−1.73205	−	2.00000i	−0.115728	−	0.133631i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	28.3214	+	7.58871i	1.87976	+	0.503680i	0.999578	+	0.0290430i	$0.00924596\pi$
$227$	28.3214	+	7.58871i	1.87976	+	0.503680i	0.880182	+	0.474637i	$0.157421\pi$
$228$	−5.98502	−	1.60368i	−0.396368	−	0.106206i
$229$	−11.0981	+	19.2224i	−0.733382	+	1.27025i	0.222048	+	0.975036i	$0.428726\pi$
$229$	−11.0981	+	19.2224i	−0.733382	+	1.27025i	−0.955430	+	0.295218i	$0.904608\pi$
$230$		0			0
$231$	−2.36603	+	6.83013i	−0.155673	+	0.449389i
$232$	1.55291	+	1.55291i	0.101954	+	0.101954i
$233$	1.31268	+	4.89898i	0.0859964	+	0.320943i	0.995501	−	0.0947510i	$-0.0302055\pi$
$233$	1.31268	+	4.89898i	0.0859964	+	0.320943i	−0.909505	+	0.415694i	$0.863539\pi$
$234$	−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
$238$	−8.50386	+	12.5570i	−0.551224	+	0.813952i
$239$			22.8564i			1.47846i	0.673454	+	0.739229i	$0.264810\pi$
$239$			22.8564i			1.47846i	−0.673454	+	0.739229i	$0.735190\pi$
$240$		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	$0.323816\pi$
$242$	0.915158	−	3.41542i	0.0588286	−	0.219551i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−1.80385			−0.115480
$245$		0			0
$246$	4.46410			0.284621
$247$	32.7028	−	8.76268i	2.08083	−	0.557556i
$248$	1.53433	−	5.72620i	0.0974302	−	0.363614i
$249$	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	$0.899314\pi$
$252$	−1.48356	+	2.19067i	−0.0934557	+	0.137999i
$253$	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
$257$	−6.17449	−	23.0435i	−0.385154	−	1.43742i	−0.837924	−	0.545788i	$-0.816231\pi$
$257$	−6.17449	−	23.0435i	−0.385154	−	1.43742i	0.452769	−	0.891628i	$-0.350436\pi$
$258$	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
$262$	−3.53553	−	0.947343i	−0.218426	−	0.0585271i
$263$	−25.6131	−	6.86302i	−1.57937	−	0.423192i	−0.640641	−	0.767840i	$-0.721331\pi$
$263$	−25.6131	−	6.86302i	−1.57937	−	0.423192i	−0.938732	+	0.344649i	$0.887998\pi$
$264$	−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
$268$	1.03528	+	3.86370i	0.0632396	+	0.236013i
$269$	−4.16987	−	7.22243i	−0.254242	−	0.440359i	0.710448	−	0.703750i	$-0.248493\pi$
$269$	−4.16987	−	7.22243i	−0.254242	−	0.440359i	−0.964689	+	0.263391i	$0.915159\pi$
$270$		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
$273$	1.03528	−	14.4195i	0.0626578	−	0.872710i
$274$			21.9282i			1.32473i
$275$		0			0
$276$	0.232051	−	0.133975i	0.0139678	−	0.00806432i
$277$	−3.77577	+	14.0914i	−0.226864	+	0.846668i	0.754785	+	0.655972i	$0.227741\pi$
$277$	−3.77577	+	14.0914i	−0.226864	+	0.846668i	−0.981649	+	0.190696i	$0.938926\pi$
$278$	−0.896575	+	0.240237i	−0.0537730	+	0.0144084i
$279$	−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	$0.902978\pi$
$282$	−10.6252	+	2.84701i	−0.632721	+	0.169537i
$283$	4.43211	−	16.5409i	0.263462	−	0.983252i	−0.699724	−	0.714414i	$-0.746694\pi$
$283$	4.43211	−	16.5409i	0.263462	−	0.983252i	0.963185	−	0.268838i	$-0.0866398\pi$
$284$	12.8660	−	7.42820i	0.763458	−	0.440783i
$285$		0			0
$286$		−	14.9282i		−	0.882723i
$287$	9.77938	+	6.62278i	0.577258	+	0.390930i
$288$	−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
$292$	2.07055	+	7.72741i	0.121170	+	0.452212i
$293$	11.8313	+	11.8313i	0.691195	+	0.691195i	0.962495	−	0.271300i	$-0.0874536\pi$
$293$	11.8313	+	11.8313i	0.691195	+	0.691195i	−0.271300	+	0.962495i	$0.587454\pi$
$294$	−6.50000	+	2.59808i	−0.379088	+	0.151523i
$295$		0			0
$296$	−0.633975	+	1.09808i	−0.0368490	+	0.0638244i
$297$	2.63896	+	0.707107i	0.153128	+	0.0410305i
$298$	17.3867	+	4.65874i	1.00718	+	0.269874i
$299$	−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
$303$	2.63896	+	9.84873i	0.151604	+	0.565795i
$304$	−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	−0.597321	−	0.802002i	$-0.703768\pi$
$307$	3.58630	−	3.58630i	0.204681	−	0.204681i	0.802002	+	0.597321i	$0.203768\pi$
$308$	−6.50266	+	3.15660i	−0.370524	+	0.179864i
$309$			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	$0.239305\pi$
$312$	1.41421	−	5.27792i	0.0800641	−	0.298803i
$313$	−11.1428	+	2.98571i	−0.629830	+	0.168762i	−0.559592	−	0.828768i	$-0.689042\pi$
$313$	−11.1428	+	2.98571i	−0.629830	+	0.168762i	−0.0702372	+	0.997530i	$0.522376\pi$
$314$	17.2679			0.974487
$315$		0			0
$316$	16.1244			0.907066
$317$	−21.4398	+	5.74479i	−1.20418	+	0.322659i	−0.804476	−	0.593985i	$-0.797554\pi$
$317$	−21.4398	+	5.74479i	−1.20418	+	0.322659i	−0.399705	+	0.916644i	$0.630887\pi$
$318$	2.26002	−	8.43451i	0.126736	−	0.472984i
$319$	5.19615	−	3.00000i	0.290929	−	0.167968i
$320$		0			0
$321$			10.0000i			0.558146i
$322$	0.707107	+	0.0507680i	0.0394055	+	0.00282919i
$323$	−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
$327$	−0.947343	−	3.53553i	−0.0523882	−	0.195515i
$328$	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	$0.310192\pi$
$332$	5.46739	+	1.46498i	0.300062	+	0.0804013i
$333$	1.22474	+	0.328169i	0.0671156	+	0.0179836i
$334$	−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	−0.991042	−	0.133552i	$-0.957362\pi$
$337$	−20.6448	−	20.6448i	−1.12459	−	1.12459i	−0.133552	−	0.991042i	$-0.542638\pi$
$338$	4.36276	+	16.2820i	0.237303	+	0.885626i
$339$	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
$343$	−18.0938	−	3.95164i	−0.976972	−	0.213368i
$344$			10.1962i			0.549740i
$345$		0			0
$346$	0.464102	−	0.267949i	0.0249503	−	0.0144050i
$347$	0.669942	−	2.50026i	0.0359644	−	0.134221i	−0.945609	−	0.325304i	$-0.894533\pi$
$347$	0.669942	−	2.50026i	0.0359644	−	0.134221i	0.981574	+	0.191083i	$0.0612000\pi$
$348$	2.12132	−	0.568406i	0.113715	−	0.0304698i
$349$	10.7321			0.574474			0.287237	−	0.957860i	$-0.407263\pi$
$349$	10.7321			0.574474			0.287237	+	0.957860i	$0.407263\pi$
$350$		0			0
$351$	−5.46410			−0.291652
$352$	−2.63896	+	0.707107i	−0.140657	+	0.0376889i
$353$	7.14042	−	26.6484i	0.380046	−	1.41835i	−0.465784	−	0.884899i	$-0.654228\pi$
$353$	7.14042	−	26.6484i	0.380046	−	1.41835i	0.845830	−	0.533453i	$-0.179106\pi$
$354$	−6.46410	+	3.73205i	−0.343563	+	0.198356i
$355$		0			0
$356$		−	0.464102i		−	0.0245973i
$357$	6.62278	+	13.6431i	0.350515	+	0.722068i
$358$	5.55532	−	5.55532i	0.293608	−	0.293608i
$359$	−18.0000	−	10.3923i	−0.950004	−	0.548485i	−0.0569216	−	0.998379i	$-0.518129\pi$
$359$	−18.0000	−	10.3923i	−0.950004	−	0.548485i	−0.893082	+	0.449894i	$0.851462\pi$
$360$		0			0
$361$	−9.69615	−	16.7942i	−0.510324	−	0.883907i
$362$	−2.63896	−	9.84873i	−0.138701	−	0.517638i
$363$	−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
$367$	3.20736	+	0.859411i	0.167423	+	0.0448609i	0.341557	−	0.939861i	$-0.389046\pi$
$367$	3.20736	+	0.859411i	0.167423	+	0.0448609i	−0.174134	+	0.984722i	$0.555712\pi$
$368$	0.258819	+	0.0693504i	0.0134919	+	0.00361514i
$369$	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
$373$	−8.76268	−	32.7028i	−0.453715	−	1.69329i	−0.691840	−	0.722051i	$-0.743200\pi$
$373$	−8.76268	−	32.7028i	−0.453715	−	1.69329i	0.238125	−	0.971234i	$-0.423467\pi$
$374$	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
$378$	1.15539	+	2.38014i	0.0594271	+	0.122421i
$379$		−	28.0526i		−	1.44096i	−0.693474	−	0.720482i	$-0.743921\pi$
$379$		−	28.0526i		−	1.44096i	0.693474	−	0.720482i	$-0.256079\pi$
$380$		0			0
$381$	10.2679	−	5.92820i	0.526043	−	0.303711i
$382$	0.739292	−	2.75908i	0.0378255	−	0.141167i
$383$	18.8702	−	5.05626i	0.964224	−	0.258363i	0.257836	−	0.966189i	$-0.416990\pi$
$383$	18.8702	−	5.05626i	0.964224	−	0.258363i	0.706387	+	0.707826i	$0.250324\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	20.2679			1.03161
$387$	9.84873	−	2.63896i	0.500639	−	0.134146i
$388$	1.81173	−	6.76148i	0.0919768	−	0.343262i
$389$	−8.95448	+	5.16987i	−0.454010	+	0.262123i	−0.709522	−	0.704683i	$-0.751089\pi$
$389$	−8.95448	+	5.16987i	−0.454010	+	0.262123i	0.255512	+	0.966806i	$0.417756\pi$
$390$		0			0
$391$		−	1.53590i		−	0.0776737i
$392$	−6.43331	−	2.75908i	−0.324931	−	0.139354i
$393$	−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
$397$	−3.24453	−	12.1087i	−0.162838	−	0.607721i	−0.998306	−	0.0581812i	$-0.981470\pi$
$397$	−3.24453	−	12.1087i	−0.162838	−	0.607721i	0.835468	−	0.549539i	$-0.185197\pi$
$398$	−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	$0.110165\pi$
$402$	3.86370	+	1.03528i	0.192704	+	0.0516349i
$403$	31.2886	+	8.38375i	1.55859	+	0.417624i
$404$	−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
$408$	1.48356	+	5.53674i	0.0734474	+	0.274109i
$409$	−11.4019	−	19.7487i	−0.563789	−	0.976511i	−0.997161	−	0.0752960i	$-0.976010\pi$
$409$	−11.4019	−	19.7487i	−0.563789	−	0.976511i	0.433372	−	0.901215i	$-0.357323\pi$
$410$		0			0
$411$	18.9904	+	10.9641i	0.936726	+	0.540819i
$412$	−7.53794	+	7.53794i	−0.371368	+	0.371368i
$413$	−19.6975	−	1.41421i	−0.969248	−	0.0695889i
$414$		−	0.267949i		−	0.0131690i
$415$		0			0
$416$	4.73205	−	2.73205i	0.232008	−	0.133950i
$417$	−0.240237	+	0.896575i	−0.0117644	+	0.0439055i
$418$	−16.3514	+	4.38134i	−0.799773	+	0.214298i
$419$	20.5885			1.00581			0.502906	−	0.864341i	$-0.332264\pi$
$419$	20.5885			1.00581			0.502906	+	0.864341i	$0.332264\pi$
$420$		0			0
$421$	−9.46410			−0.461252			−0.230626	−	0.973042i	$-0.574077\pi$
$421$	−9.46410			−0.461252			−0.230626	+	0.973042i	$0.574077\pi$
$422$	−2.26002	+	0.605571i	−0.110016	+	0.0294787i
$423$	−2.84701	+	10.6252i	−0.138426	+	0.516614i
$424$	7.56218	−	4.36603i	0.367252	−	0.212033i
$425$		0			0
$426$		−	14.8564i		−	0.719795i
$427$	−4.29341	+	2.08416i	−0.207773	+	0.100859i
$428$	−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	$0.783576\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−4.46927	−	4.46927i	−0.214780	−	0.214780i	0.591515	−	0.806294i	$-0.298530\pi$
$433$	−4.46927	−	4.46927i	−0.214780	−	0.214780i	−0.806294	+	0.591515i	$0.798530\pi$
$434$	−2.96410	−	15.4019i	−0.142281	−	0.739316i
$435$		0			0
$436$	1.83013	−	3.16987i	0.0876472	−	0.151809i
$437$	1.60368	+	0.429705i	0.0767145	+	0.0205556i
$438$	7.72741	+	2.07055i	0.369230	+	0.0989348i
$439$	−9.30385	+	16.1147i	−0.444048	+	0.769114i	−0.997985	−	0.0634442i	$-0.979792\pi$
$439$	−9.30385	+	16.1147i	−0.444048	+	0.769114i	0.553937	+	0.832559i	$0.313125\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$	−22.1469	−	22.1469i	−1.05342	−	1.05342i
$443$	−6.08656	−	22.7153i	−0.289181	−	1.07924i	−0.945730	−	0.324955i	$-0.894651\pi$
$443$	−6.08656	−	22.7153i	−0.289181	−	1.07924i	0.656548	−	0.754284i	$-0.272016\pi$
$444$	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
$448$	−2.19067	−	1.48356i	−0.103499	−	0.0700918i
$449$		−	26.2679i		−	1.23966i	−0.784736	−	0.619831i	$-0.787201\pi$
$449$		−	26.2679i		−	1.23966i	0.784736	−	0.619831i	$-0.212799\pi$
$450$		0			0
$451$	10.5622	−	6.09808i	0.497354	−	0.287147i
$452$	−0.776457	+	2.89778i	−0.0365215	+	0.136300i
$453$	2.82843	−	0.757875i	0.132891	−	0.0356081i
$454$	29.3205			1.37608
$455$		0			0
$456$	−6.19615			−0.290161
$457$	5.93426	−	1.59008i	0.277593	−	0.0743808i	−0.117337	−	0.993092i	$-0.537436\pi$
$457$	5.93426	−	1.59008i	0.277593	−	0.0743808i	0.394930	+	0.918711i	$0.370769\pi$
$458$	−5.74479	+	21.4398i	−0.268436	+	1.00182i
$459$	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	$0.883877\pi$
$462$	−0.517638	+	7.20977i	−0.0240827	+	0.335429i
$463$	−25.0261	+	25.0261i	−1.16306	+	1.16306i	−0.179262	+	0.983801i	$0.557371\pi$
$463$	−25.0261	+	25.0261i	−1.16306	+	1.16306i	−0.983801	+	0.179262i	$0.942629\pi$
$464$	1.90192	+	1.09808i	0.0882946	+	0.0509769i
$465$		0			0
$466$	2.53590	+	4.39230i	0.117473	+	0.203470i
$467$	7.77817	+	29.0285i	0.359931	+	1.34328i	0.874164	+	0.485630i	$0.161410\pi$
$467$	7.77817	+	29.0285i	0.359931	+	1.34328i	−0.514233	+	0.857650i	$0.671923\pi$
$468$	−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
$472$	−7.20977	−	1.93185i	−0.331856	−	0.0889207i
$473$	26.9072	+	7.20977i	1.23720	+	0.331506i
$474$	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
$478$	5.91567	+	22.0776i	0.270577	+	1.00981i
$479$	−15.9904	−	27.6962i	−0.730619	−	1.26547i	−0.956619	−	0.291342i	$-0.905898\pi$
$479$	−15.9904	−	27.6962i	−0.730619	−	1.26547i	0.226000	−	0.974127i	$-0.427435\pi$
$480$		0			0
$481$	−6.00000	−	3.46410i	−0.273576	−	0.157949i
$482$	0.656339	−	0.656339i	0.0298954	−	0.0298954i
$483$	0.397520	−	0.586988i	0.0180878	−	0.0267089i
$484$		−	3.53590i		−	0.160723i
$485$		0			0
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−5.29650	+	19.7668i	−0.240007	+	0.895719i	0.735820	+	0.677177i	$0.236797\pi$
$487$	−5.29650	+	19.7668i	−0.240007	+	0.895719i	−0.975827	+	0.218542i	$0.929870\pi$
$488$	−1.74238	+	0.466870i	−0.0788740	+	0.0211342i
$489$	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	$0.385036\pi$
$492$	4.31199	−	1.15539i	0.194400	−	0.0520892i
$493$	3.25813	−	12.1595i	0.146739	−	0.547637i
$494$	29.3205	−	16.9282i	1.31919	−	0.761636i
$495$		0			0
$496$		−	5.92820i		−	0.266184i
$497$	22.0404	−	32.5455i	0.988648	−	1.45986i
$498$	4.00240	−	4.00240i	0.179352	−	0.179352i
$499$	26.8301	+	15.4904i	1.20108	+	0.693445i	0.960796	−	0.277257i	$-0.0894255\pi$
$499$	26.8301	+	15.4904i	1.20108	+	0.693445i	0.240286	+	0.970702i	$0.422759\pi$
$500$		0			0
$501$	9.46410	+	16.3923i	0.422825	+	0.732354i
$502$	2.55103	+	9.52056i	0.113858	+	0.424923i
$503$	−13.5601	−	13.5601i	−0.604616	−	0.604616i	0.336918	−	0.941534i	$-0.390616\pi$
$503$	−13.5601	−	13.5601i	−0.604616	−	0.604616i	−0.941534	+	0.336918i	$0.890616\pi$
$504$	−0.866025	+	2.50000i	−0.0385758	+	0.111359i
$505$		0			0
$506$	0.366025	−	0.633975i	0.0162718	−	0.0281836i
$507$	16.2820	+	4.36276i	0.723111	+	0.193757i
$508$	11.4524	+	3.06866i	0.508118	+	0.136150i
$509$	17.0263	−	29.4904i	0.754677	−	1.30714i	−0.190858	−	0.981618i	$-0.561127\pi$
$509$	17.0263	−	29.4904i	0.754677	−	1.30714i	0.945535	−	0.325521i	$-0.105540\pi$
$510$		0			0
$511$	13.8564	+	16.0000i	0.612971	+	0.707798i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.60368	+	5.98502i	0.0708043	+	0.264245i
$514$	−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
$518$	−0.240237	+	3.34607i	−0.0105554	+	0.147018i
$519$		−	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	$0.652293\pi$
$522$	0.568406	−	2.12132i	0.0248785	−	0.0928477i
$523$	3.15660	−	0.845807i	0.138028	−	0.0369846i	−0.189143	−	0.981949i	$-0.560571\pi$
$523$	3.15660	−	0.845807i	0.138028	−	0.0369846i	0.327172	+	0.944965i	$0.393904\pi$
$524$	−3.66025			−0.159899
$525$		0			0
$526$	−26.5167			−1.15618
$527$	−32.8229	+	8.79487i	−1.42979	+	0.383110i
$528$	−0.707107	+	2.63896i	−0.0307729	+	0.114846i
$529$	19.8564	−	11.4641i	0.863322	−	0.498439i
$530$		0			0
$531$			7.46410i			0.323914i
$532$	−13.5737	−	9.19239i	−0.588496	−	0.398541i
$533$	−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
$537$	−2.03339	−	7.58871i	−0.0877472	−	0.327477i
$538$	−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	$0.166667\pi$
$542$	4.31199	+	1.15539i	0.185216	+	0.0496284i
$543$	−9.84873	−	2.63896i	−0.422649	−	0.113249i
$544$	−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	$-0.405162\pi$
$547$	−15.4920	−	15.4920i	−0.662389	−	0.662389i	−0.955943	+	0.293554i	$0.905162\pi$
$548$	5.67544	+	21.1810i	0.242443	+	0.904808i
$549$	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
$553$	38.3782	−	18.6300i	1.63201	−	0.792228i
$554$			14.5885i			0.619804i
$555$		0			0
$556$	−0.803848	+	0.464102i	−0.0340907	+	0.0196823i
$557$	9.38186	−	35.0136i	0.397522	−	1.48357i	−0.419920	−	0.907561i	$-0.637942\pi$
$557$	9.38186	−	35.0136i	0.397522	−	1.48357i	0.817442	−	0.576011i	$-0.195392\pi$
$558$	−5.72620	+	1.53433i	−0.242410	+	0.0649534i
$559$	−55.7128			−2.35640
$560$		0			0
$561$	15.6603			0.661176
$562$	−30.8910	+	8.27723i	−1.30306	+	0.349154i
$563$	6.70573	−	25.0261i	0.282613	−	1.05473i	−0.667953	−	0.744203i	$-0.732829\pi$
$563$	6.70573	−	25.0261i	0.282613	−	1.05473i	0.950566	−	0.310523i	$-0.100504\pi$
$564$	−9.52628	+	5.50000i	−0.401129	+	0.231592i
$565$		0			0
$566$		−	17.1244i		−	0.719790i
$567$	2.63896	+	0.189469i	0.110826	+	0.00795694i
$568$	10.5051	−	10.5051i	0.440783	−	0.440783i
$569$	−32.5526	−	18.7942i	−1.36467	−	0.787895i	−0.374432	−	0.927254i	$-0.622162\pi$
$569$	−32.5526	−	18.7942i	−1.36467	−	0.787895i	−0.990242	+	0.139359i	$0.955496\pi$
$570$		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	$0.630845\pi$
$572$	−3.86370	−	14.4195i	−0.161550	−	0.602911i
$573$	−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
$577$	−44.6728	−	11.9700i	−1.85975	−	0.498320i	−0.859829	−	0.510582i	$-0.829430\pi$
$577$	−44.6728	−	11.9700i	−1.85975	−	0.498320i	−0.999925	+	0.0122622i	$0.996097\pi$
$578$	15.3161	+	4.10394i	0.637066	+	0.170701i
$579$	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
$583$	−6.17449	−	23.0435i	−0.255721	−	0.954365i
$584$	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	−0.741155	−	0.671334i	$-0.765722\pi$
$587$	−1.69161	+	1.69161i	−0.0698204	+	0.0698204i	0.671334	+	0.741155i	$0.265722\pi$
$588$	−5.60609	+	4.19187i	−0.231191	+	0.172870i
$589$		−	36.7321i		−	1.51352i
$590$		0			0
$591$	1.60770	−	0.928203i	0.0661317	−	0.0381812i
$592$	−0.328169	+	1.22474i	−0.0134877	+	0.0503367i
$593$	−26.2695	+	7.03888i	−1.07876	+	0.289052i	−0.754087	−	0.656775i	$-0.771920\pi$
$593$	−26.2695	+	7.03888i	−1.07876	+	0.289052i	−0.324671	+	0.945827i	$0.605254\pi$
$594$	2.73205			0.112097
$595$		0			0
$596$	18.0000			0.737309
$597$	−18.8702	+	5.05626i	−0.772307	+	0.206939i
$598$	−0.378937	+	1.41421i	−0.0154959	+	0.0578315i
$599$	26.0429	−	15.0359i	1.06409	−	0.614350i	0.137526	−	0.990498i	$-0.456085\pi$
$599$	26.0429	−	15.0359i	1.06409	−	0.614350i	0.926560	+	0.376148i	$0.122752\pi$
$600$		0			0
$601$			28.2487i			1.15229i	0.817348	+	0.576144i	$0.195443\pi$
$601$			28.2487i			1.15229i	−0.817348	+	0.576144i	$0.804557\pi$
$602$	11.7806	+	24.2683i	0.480141	+	0.989101i
$603$	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
$607$	0.0321856	+	0.120118i	0.00130637	+	0.00487545i	0.966576	−	0.256380i	$-0.0825300\pi$
$607$	0.0321856	+	0.120118i	0.00130637	+	0.00487545i	−0.965270	+	0.261256i	$0.915863\pi$
$608$	−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
$612$	5.53674	+	1.48356i	0.223809	+	0.0599695i
$613$	−25.6825	−	6.88160i	−1.03731	−	0.277945i	−0.300309	−	0.953842i	$-0.597090\pi$
$613$	−25.6825	−	6.88160i	−1.03731	−	0.277945i	−0.736996	+	0.675897i	$0.763757\pi$
$614$	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	$-0.0410373\pi$
$617$	21.4398	+	21.4398i	0.863135	+	0.863135i	−0.128566	+	0.991701i	$0.541037\pi$
$618$	2.75908	+	10.2970i	0.110986	+	0.414207i
$619$	−12.0981	−	20.9545i	−0.486263	−	0.842232i	0.513613	−	0.858022i	$-0.328307\pi$
$619$	−12.0981	−	20.9545i	−0.486263	−	0.842232i	−0.999875	+	0.0157904i	$0.994974\pi$
$620$		0			0
$621$	−0.232051	−	0.133975i	−0.00931188	−	0.00537622i
$622$	7.26054	−	7.26054i	0.291121	−	0.291121i
$623$	−0.536220	−	1.10463i	−0.0214832	−	0.0442559i
$624$		−	5.46410i		−	0.218739i
$625$		0			0
$626$	−9.99038	+	5.76795i	−0.399296	+	0.230534i
$627$	−4.38134	+	16.3514i	−0.174974	+	0.653012i
$628$	16.6796	−	4.46927i	0.665587	−	0.178343i
$629$	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	$0.896134\pi$
$632$	15.5749	−	4.17329i	0.619538	−	0.166005i
$633$	−0.605571	+	2.26002i	−0.0240693	+	0.0898278i
$634$	−19.2224	+	11.0981i	−0.763420	+	0.440761i
$635$		0			0
$636$		−	8.73205i		−	0.346248i
$637$	15.0759	−	35.1523i	0.597328	−	1.39278i
$638$	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	$0.726615\pi$
$642$	2.58819	+	9.65926i	0.102148	+	0.381221i
$643$	−9.62209	−	9.62209i	−0.379458	−	0.379458i	0.491448	−	0.870907i	$-0.336468\pi$
$643$	−9.62209	−	9.62209i	−0.379458	−	0.379458i	−0.870907	+	0.491448i	$0.836468\pi$
$644$	0.696152	−	0.133975i	0.0274322	−	0.00527934i
$645$		0			0
$646$	−17.7583	+	30.7583i	−0.698692	+	1.21017i
$647$	−12.1087	−	3.24453i	−0.476044	−	0.127556i	0.0128160	−	0.999918i	$-0.495920\pi$
$647$	−12.1087	−	3.24453i	−0.476044	−	0.127556i	−0.488860	+	0.872362i	$0.662587\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−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
$653$	12.0716	+	45.0518i	0.472398	+	1.76301i	0.631117	+	0.775688i	$0.282597\pi$
$653$	12.0716	+	45.0518i	0.472398	+	1.76301i	−0.158719	+	0.987324i	$0.550736\pi$
$654$	−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
$658$	−29.0285	−	2.08416i	−1.13165	−	0.0812488i
$659$		−	3.80385i		−	0.148177i	−0.997252	−	0.0740884i	$-0.976395\pi$
$659$		−	3.80385i		−	0.148177i	0.997252	−	0.0740884i	$-0.0236047\pi$
$660$		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	$0.257443\pi$
$662$	−4.10394	+	15.3161i	−0.159504	+	0.595278i
$663$	−30.2533	+	8.10634i	−1.17494	+	0.314824i
$664$	5.66025			0.219660
$665$		0			0
$666$	1.26795			0.0491320
$667$	−0.568406	+	0.152304i	−0.0220088	+	0.00589723i
$668$	−4.89898	+	18.2832i	−0.189547	+	0.707400i
$669$	13.6244	−	7.86603i	0.526748	−	0.304118i
$670$		0			0
$671$			4.92820i			0.190251i
$672$	−2.38014	+	1.15539i	−0.0918159	+	0.0445703i
$673$	4.05317	−	4.05317i	0.156238	−	0.156238i	−0.624659	−	0.780897i	$-0.714762\pi$
$673$	4.05317	−	4.05317i	0.156238	−	0.156238i	0.780897	+	0.624659i	$0.214762\pi$
$674$	−25.2846	−	14.5981i	−0.973927	−	0.562297i
$675$		0			0
$676$	8.42820	+	14.5981i	0.324162	+	0.561464i
$677$	−9.53416	−	35.5820i	−0.366428	−	1.36753i	−0.865475	−	0.500952i	$-0.832983\pi$
$677$	−9.53416	−	35.5820i	−0.366428	−	1.36753i	0.499048	−	0.866575i	$-0.333683\pi$
$678$	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
$682$	−15.6443	−	4.19187i	−0.599051	−	0.160515i
$683$	36.7052	+	9.83512i	1.40448	+	0.376331i	0.879953	−	0.475060i	$-0.157574\pi$
$683$	36.7052	+	9.83512i	1.40448	+	0.376331i	0.524532	+	0.851391i	$0.324240\pi$
$684$	−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
$688$	2.63896	+	9.84873i	0.100609	+	0.375479i
$689$	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
$693$	5.98502	+	4.05317i	0.227352	+	0.153967i
$694$		−	2.58846i		−	0.0982565i
$695$		0			0
$696$	1.90192	−	1.09808i	0.0720922	−	0.0416225i
$697$	6.62278	−	24.7166i	0.250856	−	0.936206i
$698$	10.3664	−	2.77766i	0.392373	−	0.105136i
$699$	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	$0.411485\pi$
$702$	−5.27792	+	1.41421i	−0.199202	+	0.0533761i
$703$	−2.03339	+	7.58871i	−0.0766907	+	0.286213i
$704$	−2.36603	+	1.36603i	−0.0891729	+	0.0514840i
$705$		0			0
$706$		−	27.5885i		−	1.03831i
$707$	−1.93185	+	26.9072i	−0.0726548	+	1.01195i
$708$	−5.27792	+	5.27792i	−0.198356	+	0.198356i
$709$	20.0718	+	11.5885i	0.753812	+	0.435214i	0.827070	−	0.562099i	$-0.190006\pi$
$709$	20.0718	+	11.5885i	0.753812	+	0.435214i	−0.0732575	+	0.997313i	$0.523340\pi$
$710$		0			0
$711$	−8.06218	−	13.9641i	−0.302355	−	0.523695i
$712$	−0.120118	−	0.448288i	−0.00450162	−	0.0168003i
$713$	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
$717$	22.0776	+	5.91567i	0.824503	+	0.220925i
$718$	−20.0764	−	5.37945i	−0.749244	−	0.200759i
$719$	−15.3301	+	26.5526i	−0.571717	+	0.990243i	0.424673	+	0.905347i	$0.360389\pi$
$719$	−15.3301	+	26.5526i	−0.571717	+	0.990243i	−0.996390	+	0.0848963i	$0.972944\pi$
$720$		0			0
$721$	−9.23205	+	26.6506i	−0.343820	+	0.992522i
$722$	−13.7124	−	13.7124i	−0.510324	−	0.510324i
$723$	−0.240237	−	0.896575i	−0.00893450	−	0.0333440i
$724$	−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	−0.316071	−	0.948736i	$-0.602364\pi$
$727$	17.0585	−	17.0585i	0.632665	−	0.632665i	0.948736	+	0.316071i	$0.102364\pi$
$728$	8.10634	−	11.9700i	0.300441	−	0.443639i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	50.6147	−	29.2224i	1.87205	−	1.08083i
$732$	−0.466870	+	1.74238i	−0.0172560	+	0.0644003i
$733$	33.9783	−	9.10446i	1.25502	−	0.336281i	0.430744	−	0.902474i	$-0.358251\pi$
$733$	33.9783	−	9.10446i	1.25502	−	0.336281i	0.824273	+	0.566193i	$0.191584\pi$
$734$	3.32051			0.122562
$735$		0			0
$736$	0.267949			0.00987674
$737$	10.5558	−	2.82843i	0.388829	−	0.104186i
$738$	1.15539	−	4.31199i	0.0425307	−	0.158727i
$739$	38.6147	−	22.2942i	1.42047	−	0.820106i	0.424128	−	0.905602i	$-0.360581\pi$
$739$	38.6147	−	22.2942i	1.42047	−	0.820106i	0.996339	+	0.0854960i	$0.0272475\pi$
$740$		0			0
$741$		−	33.8564i		−	1.24375i
$742$	12.9546	−	19.1290i	0.475577	−	0.702249i
$743$	−4.60797	+	4.60797i	−0.169050	+	0.169050i	−0.786562	−	0.617512i	$-0.788141\pi$
$743$	−4.60797	+	4.60797i	−0.169050	+	0.169050i	0.617512	+	0.786562i	$0.288141\pi$
$744$	−5.13397	−	2.96410i	−0.188221	−	0.108669i
$745$		0			0
$746$	−16.9282	−	29.3205i	−0.619786	−	1.07350i
$747$	−1.46498	−	5.46739i	−0.0536009	−	0.200041i
$748$	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	$0.177450\pi$
$752$	−10.6252	−	2.84701i	−0.387461	−	0.103820i
$753$	9.52056	+	2.55103i	0.346948	+	0.0929645i
$754$	−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	−0.998195	−	0.0600616i	$-0.980870\pi$
$757$	−29.1165	−	29.1165i	−1.05826	−	1.05826i	−0.0600616	−	0.998195i	$-0.519130\pi$
$758$	−7.26054	−	27.0967i	−0.263715	−	0.984196i
$759$	−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
$763$	0.693504	−	9.65926i	0.0251065	−	0.349689i
$764$		−	2.85641i		−	0.103341i
$765$		0			0
$766$	16.9186	−	9.76795i	0.611293	−	0.352930i
$767$	10.5558	−	39.3949i	0.381149	−	1.42247i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	−22.9282			−0.826812			−0.413406	−	0.910547i	$-0.635661\pi$
$769$	−22.9282			−0.826812			−0.413406	+	0.910547i	$0.635661\pi$
$770$		0			0
$771$	−23.8564			−0.859167
$772$	19.5773	−	5.24573i	0.704604	−	0.188798i
$773$	7.19617	−	26.8565i	0.258828	−	0.965960i	−0.707093	−	0.707121i	$-0.749994\pi$
$773$	7.19617	−	26.8565i	0.258828	−	0.965960i	0.965921	−	0.258839i	$-0.0833397\pi$
$774$	8.83013	−	5.09808i	0.317392	−	0.183247i
$775$		0			0
$776$		−	7.00000i		−	0.251285i
$777$	2.77766	+	1.88108i	0.0996480	+	0.0674835i
$778$	−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
$782$	−0.397520	−	1.48356i	−0.0142153	−	0.0530521i
$783$	−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
$787$	−43.4481	−	11.6419i	−1.54876	−	0.414988i	−0.619674	−	0.784859i	$-0.712735\pi$
$787$	−43.4481	−	11.6419i	−1.54876	−	0.414988i	−0.929083	+	0.369871i	$0.879402\pi$
$788$	1.79315	+	0.480473i	0.0638784	+	0.0171162i
$789$	−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
$793$	−2.55103	−	9.52056i	−0.0905896	−	0.338085i
$794$	−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	−0.754812	−	0.655941i	$-0.772272\pi$
$797$	−2.79126	+	2.79126i	−0.0988716	+	0.0988716i	0.655941	+	0.754812i	$0.272272\pi$
$798$	−14.7477	+	7.15900i	−0.522063	+	0.253426i
$799$			63.0526i			2.23064i
$800$		0			0
$801$	−0.401924	+	0.232051i	−0.0142013	+	0.00819911i
$802$	1.83032	−	6.83083i	0.0646307	−	0.241205i
$803$	21.1117	−	5.65685i	0.745015	−	0.199626i
$804$	4.00000			0.141069
$805$		0			0
$806$	32.3923			1.14097
$807$	−8.05558	+	2.15849i	−0.283570	+	0.0759823i
$808$	−2.63896	+	9.84873i	−0.0928382	+	0.346477i
$809$	−38.7846	+	22.3923i	−1.36359	+	0.787272i	−0.990100	−	0.140361i	$-0.955174\pi$
$809$	−38.7846	+	22.3923i	−1.36359	+	0.787272i	−0.373494	+	0.927633i	$0.621840\pi$
$810$		0			0
$811$			4.78461i			0.168010i	0.996465	+	0.0840052i	$0.0267712\pi$
$811$			4.78461i			0.168010i	−0.996465	+	0.0840052i	$0.973229\pi$
$812$	5.79555	+	0.416102i	0.203384	+	0.0146023i
$813$	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
$817$	16.3514	+	61.0242i	0.572063	+	2.13497i
$818$	−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	$0.294768\pi$
$822$	21.1810	+	5.67544i	0.738773	+	0.197954i
$823$	−37.0841	−	9.93666i	−1.29267	−	0.346370i	−0.453997	−	0.891003i	$-0.650002\pi$
$823$	−37.0841	−	9.93666i	−1.29267	−	0.346370i	−0.838674	+	0.544633i	$0.816669\pi$
$824$	−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	$-0.00999094\pi$
$827$	27.8410	+	27.8410i	0.968125	+	0.968125i	−0.0313823	+	0.999507i	$0.509991\pi$
$828$	−0.0693504	−	0.258819i	−0.00241009	−	0.00899458i
$829$	6.85641	+	11.8756i	0.238133	+	0.412458i	0.960179	−	0.279387i	$-0.0901313\pi$
$829$	6.85641	+	11.8756i	0.238133	+	0.412458i	−0.722046	+	0.691845i	$0.756798\pi$
$830$		0			0
$831$	12.6340	+	7.29423i	0.438268	+	0.253034i
$832$	3.86370	−	3.86370i	0.133950	−	0.133950i
$833$	4.74170	+	39.8432i	0.164290	+	1.38048i
$834$			0.928203i			0.0321410i
$835$		0			0
$836$	−14.6603	+	8.46410i	−0.507035	+	0.292737i
$837$	−1.53433	+	5.72620i	−0.0530343	+	0.197927i
$838$	19.8869	−	5.32868i	0.686982	−	0.184076i
$839$	−0.124356			−0.00429323			−0.00214662	−	0.999998i	$-0.500683\pi$
$839$	−0.124356			−0.00429323			−0.00214662	+	0.999998i	$0.500683\pi$
$840$		0			0
$841$	24.1769			0.833687
$842$	−9.14162	+	2.44949i	−0.315041	+	0.0844150i
$843$	−8.27723	+	30.8910i	−0.285083	+	1.06394i
$844$	−2.02628	+	1.16987i	−0.0697474	+	0.0402687i
$845$		0			0
$846$			11.0000i			0.378188i
$847$	−4.08536	−	8.41593i	−0.140375	−	0.289175i
$848$	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
$852$	−3.84512	−	14.3502i	−0.131732	−	0.491629i
$853$	22.3872	+	22.3872i	0.766522	+	0.766522i	0.977493	−	0.210970i	$-0.0676623\pi$
$853$	22.3872	+	22.3872i	0.766522	+	0.766522i	−0.210970	+	0.977493i	$0.567662\pi$
$854$	−3.60770	+	3.12436i	−0.123453	+	0.106913i
$855$		0			0
$856$	−5.00000	+	8.66025i	−0.170896	+	0.296001i
$857$	39.5336	+	10.5930i	1.35044	+	0.361850i	0.860298	−	0.509791i	$-0.170277\pi$
$857$	39.5336	+	10.5930i	1.35044	+	0.361850i	0.490144	+	0.871641i	$0.336944\pi$
$858$	−14.4195	−	3.86370i	−0.492275	−	0.131905i
$859$	−17.9545	+	31.0981i	−0.612599	+	1.06105i	0.378202	+	0.925723i	$0.376543\pi$
$859$	−17.9545	+	31.0981i	−0.612599	+	1.06105i	−0.990801	+	0.135329i	$0.956791\pi$
$860$		0			0
$861$	8.92820	−	7.73205i	0.304272	−	0.263508i
$862$	4.57081	+	4.57081i	0.155682	+	0.155682i
$863$	−7.41782	−	27.6837i	−0.252506	−	0.942363i	−0.969461	−	0.245245i	$-0.921132\pi$
$863$	−7.41782	−	27.6837i	−0.252506	−	0.942363i	0.716956	−	0.697119i	$-0.245535\pi$
$864$	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
$868$	−6.84941	−	14.1100i	−0.232484	−	0.478923i
$869$		−	44.0526i		−	1.49438i
$870$		0			0
$871$	−18.9282	+	10.9282i	−0.641358	+	0.370288i
$872$	0.947343	−	3.53553i	0.0320811	−	0.119728i
$873$	−6.76148	+	1.81173i	−0.228841	+	0.0613179i
$874$	1.66025			0.0561589
$875$		0			0
$876$	8.00000			0.270295
$877$	−27.6651	+	7.41284i	−0.934184	+	0.250314i	−0.693638	−	0.720324i	$-0.743993\pi$
$877$	−27.6651	+	7.41284i	−0.934184	+	0.250314i	−0.240546	+	0.970638i	$0.577327\pi$
$878$	−4.81603	+	17.9737i	−0.162533	+	0.606581i
$879$	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	$0.829363\pi$
$882$	0.827225	+	6.95095i	0.0278541	+	0.234051i
$883$	−2.17209	+	2.17209i	−0.0730966	+	0.0730966i	−0.742710	−	0.669613i	$-0.766460\pi$
$883$	−2.17209	+	2.17209i	−0.0730966	+	0.0730966i	0.669613	+	0.742710i	$0.266460\pi$
$884$	−27.1244	−	15.6603i	−0.912291	−	0.526711i
$885$		0			0
$886$	−11.7583	−	20.3660i	−0.395029	−	0.684210i
$887$	3.93803	+	14.6969i	0.132226	+	0.493475i	0.999994	−	0.00349516i	$-0.00111254\pi$
$887$	3.93803	+	14.6969i	0.132226	+	0.493475i	−0.867768	+	0.496970i	$0.834446\pi$
$888$	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
$892$	15.1960	+	4.07175i	0.508800	+	0.136332i
$893$	−65.8353	−	17.6405i	−2.20309	−	0.590317i
$894$	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
$898$	−6.79865	−	25.3729i	−0.226874	−	0.846704i
$899$	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
$903$	26.9072	+	1.93185i	0.895416	+	0.0642880i
$904$			3.00000i			0.0997785i
$905$		0			0
$906$	2.53590	−	1.46410i	0.0842496	−	0.0486415i
$907$	−3.98880	+	14.8864i	−0.132446	+	0.494295i	−0.999995	−	0.00305603i	$-0.999027\pi$
$907$	−3.98880	+	14.8864i	−0.132446	+	0.494295i	0.867549	+	0.497351i	$0.165694\pi$
$908$	28.3214	−	7.58871i	0.939880	−	0.251840i
$909$	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	$0.469451\pi$
$912$	−5.98502	+	1.60368i	−0.198184	+	0.0531032i
$913$	4.00240	−	14.9372i	0.132460	−	0.494348i
$914$	5.32051	−	3.07180i	0.175987	−	0.101606i
$915$		0			0
$916$			22.1962i			0.733382i
$917$	−8.71191	+	4.22904i	−0.287693	+	0.139655i
$918$	4.05317	−	4.05317i	0.133775	−	0.133775i
$919$	9.69615	+	5.59808i	0.319847	+	0.184663i	0.651324	−	0.758800i	$-0.274214\pi$
$919$	9.69615	+	5.59808i	0.319847	+	0.184663i	−0.331478	+	0.943463i	$0.607547\pi$
$920$		0			0
$921$	−2.53590	−	4.39230i	−0.0835607	−	0.144731i
$922$	3.96524	+	14.7985i	0.130588	+	0.487362i
$923$	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
$927$	10.2970	+	2.75908i	0.338198	+	0.0906200i
$928$	2.12132	+	0.568406i	0.0696358	+	0.0186588i
$929$	4.87564	−	8.44486i	0.159965	−	0.277067i	−0.774891	−	0.632095i	$-0.782195\pi$
$929$	4.87564	−	8.44486i	0.159965	−	0.277067i	0.934856	+	0.355028i	$0.115529\pi$
$930$		0			0
$931$	−42.9282	−	6.19615i	−1.40692	−	0.203071i
$932$	3.58630	+	3.58630i	0.117473	+	0.117473i
$933$	−2.65754	−	9.91808i	−0.0870040	−	0.324703i
$934$	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	−0.797363	−	0.603500i	$-0.793772\pi$
$937$	−5.93426	+	5.93426i	−0.193864	+	0.193864i	0.603500	+	0.797363i	$0.293772\pi$
$938$	8.76268	+	5.93426i	0.286112	+	0.193760i
$939$			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	$0.453353\pi$
$942$	4.46927	−	16.6796i	0.145617	−	0.543449i
$943$	−1.15539	+	0.309587i	−0.0376248	+	0.0100815i
$944$	−7.46410			−0.242936
$945$		0			0
$946$	27.8564			0.905690
$947$	2.17209	−	0.582009i	0.0705834	−	0.0189128i	−0.223355	−	0.974737i	$-0.571701\pi$
$947$	2.17209	−	0.582009i	0.0705834	−	0.0189128i	0.293938	+	0.955825i	$0.405034\pi$
$948$	4.17329	−	15.5749i	0.135542	−	0.505850i
$949$	−37.8564	+	21.8564i	−1.22887	+	0.709489i
$950$		0			0
$951$			22.1962i			0.719760i
$952$	−1.08604	+	15.1266i	−0.0351989	+	0.490257i
$953$	−2.55103	+	2.55103i	−0.0826358	+	0.0826358i	−0.747217	−	0.664581i	$-0.768610\pi$
$953$	−2.55103	+	2.55103i	−0.0826358	+	0.0826358i	0.664581	+	0.747217i	$0.268610\pi$
$954$	−7.56218	−	4.36603i	−0.244835	−	0.141355i
$955$		0			0
$956$	11.4282	+	19.7942i	0.369615	+	0.640191i
$957$	−1.55291	−	5.79555i	−0.0501986	−	0.187344i
$958$	−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
$962$	−6.69213	−	1.79315i	−0.215763	−	0.0578135i
$963$	9.65926	+	2.58819i	0.311265	+	0.0834033i
$964$	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	$-0.314977\pi$
$967$	−8.91499	−	8.91499i	−0.286687	−	0.286687i	−0.835769	+	0.549082i	$0.814977\pi$
$968$	−0.915158	−	3.41542i	−0.0294143	−	0.109776i
$969$	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
$973$	−1.37705	+	2.03339i	−0.0441462	+	0.0651874i
$974$			20.4641i			0.655712i
$975$		0			0
$976$	−1.56218	+	0.901924i	−0.0500041	+	0.0288699i
$977$	−15.7780	+	58.8843i	−0.504783	+	1.88388i	−0.0384628	+	0.999260i	$0.512246\pi$
$977$	−15.7780	+	58.8843i	−0.504783	+	1.88388i	−0.466320	+	0.884616i	$0.654421\pi$
$978$	11.5911	−	3.10583i	0.370643	−	0.0993134i
$979$	−1.26795			−0.0405238
$980$		0			0
$981$	−3.66025			−0.116863
$982$	15.1266	−	4.05317i	0.482711	−	0.129342i
$983$	−2.13492	+	7.96764i	−0.0680935	+	0.254128i	−0.991579	−	0.129506i	$-0.958661\pi$
$983$	−2.13492	+	7.96764i	−0.0680935	+	0.254128i	0.923485	+	0.383634i	$0.125328\pi$
$984$	3.86603	−	2.23205i	0.123244	−	0.0711552i
$985$		0			0
$986$		−	12.5885i		−	0.400898i
$987$	−16.3192	+	24.0974i	−0.519446	+	0.767028i
$988$	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	$0.815714\pi$
$992$	−1.53433	−	5.72620i	−0.0487151	−	0.181807i
$993$	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
$997$	9.79796	+	2.62536i	0.310304	+	0.0831458i	0.410611	−	0.911811i	$-0.365316\pi$
$997$	9.79796	+	2.62536i	0.310304	+	0.0831458i	−0.100306	+	0.994957i	$0.531982\pi$
$998$	29.9251	+	8.01841i	0.947263	+	0.253818i
$999$	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.c.607.2	yes	8
5.2	odd	4		1050.2.bc.b.943.2	yes	8
5.3	odd	4		1050.2.bc.b.943.1	yes	8
5.4	even	2	inner	1050.2.bc.c.607.1	yes	8
7.3	odd	6		1050.2.bc.b.157.1	✓	8
35.3	even	12	inner	1050.2.bc.c.493.2	yes	8
35.17	even	12	inner	1050.2.bc.c.493.1	yes	8
35.24	odd	6		1050.2.bc.b.157.2	yes	8

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

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)

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

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Database

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