LMFDB - Embedded newform 945.2.k.c.856.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [945,2,Mod(361,945)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(945, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("945.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.k (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.1
Character	$\chi$	$=$	945.856
Dual form			945.2.k.c.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34882 - 2.33623i) q^{2} +(-2.63865 + 4.57028i) q^{4} -1.00000 q^{5} +(-2.16746 + 1.51728i) q^{7} +8.84100 q^{8} +(1.34882 + 2.33623i) q^{10} +3.92366 q^{11} +(0.993996 + 1.72165i) q^{13} +(6.46823 + 3.01714i) q^{14} +(-6.64765 - 11.5141i) q^{16} +(-2.23716 - 3.87488i) q^{17} +(0.0804749 - 0.139387i) q^{19} +(2.63865 - 4.57028i) q^{20} +(-5.29232 - 9.16657i) q^{22} -6.22371 q^{23} +1.00000 q^{25} +(2.68145 - 4.64441i) q^{26} +(-1.21521 - 13.9094i) q^{28} +(0.384982 - 0.666809i) q^{29} +(4.01507 - 6.95430i) q^{31} +(-9.09202 + 15.7478i) q^{32} +(-6.03507 + 10.4530i) q^{34} +(2.16746 - 1.51728i) q^{35} +(-3.50272 + 6.06689i) q^{37} -0.434186 q^{38} -8.84100 q^{40} +(-1.42108 - 2.46138i) q^{41} +(-1.53771 + 2.66340i) q^{43} +(-10.3532 + 17.9322i) q^{44} +(8.39468 + 14.5400i) q^{46} +(-2.83830 - 4.91609i) q^{47} +(2.39574 - 6.57727i) q^{49} +(-1.34882 - 2.33623i) q^{50} -10.4912 q^{52} +(-5.50814 - 9.54037i) q^{53} -3.92366 q^{55} +(-19.1625 + 13.4143i) q^{56} -2.07709 q^{58} +(-1.68281 + 2.91472i) q^{59} +(3.44816 + 5.97239i) q^{61} -21.6625 q^{62} +22.4635 q^{64} +(-0.993996 - 1.72165i) q^{65} +(-5.04488 + 8.73799i) q^{67} +23.6123 q^{68} +(-6.46823 - 3.01714i) q^{70} -6.78242 q^{71} +(-7.20971 - 12.4876i) q^{73} +18.8982 q^{74} +(0.424690 + 0.735585i) q^{76} +(-8.50436 + 5.95327i) q^{77} +(-5.65914 - 9.80192i) q^{79} +(6.64765 + 11.5141i) q^{80} +(-3.83357 + 6.63994i) q^{82} +(2.40898 - 4.17248i) q^{83} +(2.23716 + 3.87488i) q^{85} +8.29642 q^{86} +34.6891 q^{88} +(-5.16019 + 8.93770i) q^{89} +(-4.76667 - 2.22344i) q^{91} +(16.4222 - 28.4441i) q^{92} +(-7.65674 + 13.2619i) q^{94} +(-0.0804749 + 0.139387i) q^{95} +(6.51896 - 11.2912i) q^{97} +(-18.5974 + 3.27456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) $ 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.34882	−	2.33623i	−0.953762	−	1.65196i	−0.737175	−	0.675702i	$-0.763841\pi$
$2$	−1.34882	−	2.33623i	−0.953762	−	1.65196i	−0.216587	−	0.976263i	$-0.569493\pi$
$3$		0			0
$3$		0			0
$4$	−2.63865	+	4.57028i	−1.31933	+	2.28514i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.16746	+	1.51728i	−0.819222	+	0.573477i
$7$	−2.16746	+	1.51728i	−0.819222	+	0.573477i
$8$	8.84100			3.12577
$9$		0			0
$10$	1.34882	+	2.33623i	0.426536	+	0.738781i
$11$	3.92366			1.18303			0.591514	−	0.806295i	$-0.298531\pi$
$11$	3.92366			1.18303			0.591514	+	0.806295i	$0.298531\pi$
$12$		0			0
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	0.970308	−	0.241874i	$-0.0777620\pi$
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	−0.694623	+	0.719374i	$0.744429\pi$
$14$	6.46823	+	3.01714i	1.72871	+	0.806365i
$15$		0			0
$16$	−6.64765	−	11.5141i	−1.66191	−	2.87852i
$17$	−2.23716	−	3.87488i	−0.542591	−	0.939795i	−0.998754	−	0.0498992i	$-0.984110\pi$
$17$	−2.23716	−	3.87488i	−0.542591	−	0.939795i	0.456163	−	0.889896i	$-0.349223\pi$
$18$		0			0
$19$	0.0804749	−	0.139387i	0.0184622	−	0.0319775i	−0.856647	−	0.515904i	$-0.827456\pi$
$19$	0.0804749	−	0.139387i	0.0184622	−	0.0319775i	0.875109	+	0.483926i	$0.160790\pi$
$20$	2.63865	−	4.57028i	0.590020	−	1.02195i
$21$		0			0
$22$	−5.29232	−	9.16657i	−1.12833	−	1.95432i
$23$	−6.22371			−1.29773			−0.648866	−	0.760903i	$-0.724757\pi$
$23$	−6.22371			−1.29773			−0.648866	+	0.760903i	$0.724757\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.68145	−	4.64441i	0.525876	−	0.910843i
$27$		0			0
$28$	−1.21521	−	13.9094i	−0.229654	−	2.62864i
$29$	0.384982	−	0.666809i	0.0714894	−	0.123823i	−0.828065	−	0.560632i	$-0.810558\pi$
$29$	0.384982	−	0.666809i	0.0714894	−	0.123823i	0.899554	+	0.436809i	$0.143891\pi$
$30$		0			0
$31$	4.01507	−	6.95430i	0.721127	−	1.24903i	−0.239421	−	0.970916i	$-0.576958\pi$
$31$	4.01507	−	6.95430i	0.721127	−	1.24903i	0.960548	−	0.278113i	$-0.0897091\pi$
$32$	−9.09202	+	15.7478i	−1.60726	+	2.78385i
$33$		0			0
$34$	−6.03507	+	10.4530i	−1.03501	+	1.79268i
$35$	2.16746	−	1.51728i	0.366367	−	0.256467i
$36$		0			0
$37$	−3.50272	+	6.06689i	−0.575843	+	0.997390i	0.420106	+	0.907475i	$0.361993\pi$
$37$	−3.50272	+	6.06689i	−0.575843	+	0.997390i	−0.995949	+	0.0899150i	$0.971340\pi$
$38$	−0.434186			−0.0704342
$39$		0			0
$40$	−8.84100			−1.39789
$41$	−1.42108	−	2.46138i	−0.221935	−	0.384404i	0.733460	−	0.679732i	$-0.237904\pi$
$41$	−1.42108	−	2.46138i	−0.221935	−	0.384404i	−0.955396	+	0.295329i	$0.904571\pi$
$42$		0			0
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	−0.959127	−	0.282976i	$-0.908678\pi$
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	0.724628	+	0.689140i	$0.242012\pi$
$44$	−10.3532	+	17.9322i	−1.56080	+	2.70338i
$45$		0			0
$46$	8.39468	+	14.5400i	1.23773	+	2.14381i
$47$	−2.83830	−	4.91609i	−0.414009	−	0.717085i	0.581315	−	0.813679i	$-0.302538\pi$
$47$	−2.83830	−	4.91609i	−0.414009	−	0.717085i	−0.995324	+	0.0965940i	$0.969205\pi$
$48$		0			0
$49$	2.39574	−	6.57727i	0.342249	−	0.939609i
$50$	−1.34882	−	2.33623i	−0.190752	−	0.330393i
$51$		0			0
$52$	−10.4912			−1.45487
$53$	−5.50814	−	9.54037i	−0.756601	−	1.31047i	−0.944575	−	0.328297i	$-0.893525\pi$
$53$	−5.50814	−	9.54037i	−0.756601	−	1.31047i	0.187974	−	0.982174i	$-0.439808\pi$
$54$		0			0
$55$	−3.92366			−0.529066
$56$	−19.1625	+	13.4143i	−2.56070	+	1.79255i
$57$		0			0
$58$	−2.07709			−0.272736
$59$	−1.68281	+	2.91472i	−0.219084	+	0.379464i	−0.954528	−	0.298121i	$-0.903640\pi$
$59$	−1.68281	+	2.91472i	−0.219084	+	0.379464i	0.735444	+	0.677585i	$0.236973\pi$
$60$		0			0
$61$	3.44816	+	5.97239i	0.441492	+	0.764686i	0.997800	−	0.0662898i	$-0.0211162\pi$
$61$	3.44816	+	5.97239i	0.441492	+	0.764686i	−0.556309	+	0.830976i	$0.687783\pi$
$62$	−21.6625			−2.75114
$63$		0			0
$64$	22.4635			2.80794
$65$	−0.993996	−	1.72165i	−0.123290	−	0.213545i
$66$		0			0
$67$	−5.04488	+	8.73799i	−0.616330	+	1.06752i	0.373819	+	0.927502i	$0.378048\pi$
$67$	−5.04488	+	8.73799i	−0.616330	+	1.06752i	−0.990150	+	0.140014i	$0.955285\pi$
$68$	23.6123			2.86342
$69$		0			0
$70$	−6.46823	−	3.01714i	−0.773101	−	0.360617i
$71$	−6.78242			−0.804925			−0.402463	−	0.915436i	$-0.631846\pi$
$71$	−6.78242			−0.804925			−0.402463	+	0.915436i	$0.631846\pi$
$72$		0			0
$73$	−7.20971	−	12.4876i	−0.843833	−	1.46156i	−0.886631	−	0.462477i	$-0.846961\pi$
$73$	−7.20971	−	12.4876i	−0.843833	−	1.46156i	0.0427985	−	0.999084i	$-0.486373\pi$
$74$	18.8982			2.19687
$75$		0			0
$76$	0.424690	+	0.735585i	0.0487153	+	0.0843774i
$77$	−8.50436	+	5.95327i	−0.969162	+	0.678439i
$78$		0			0
$79$	−5.65914	−	9.80192i	−0.636703	−	1.10280i	−0.986152	−	0.165846i	$-0.946964\pi$
$79$	−5.65914	−	9.80192i	−0.636703	−	1.10280i	0.349449	−	0.936955i	$-0.386369\pi$
$80$	6.64765	+	11.5141i	0.743230	+	1.28731i
$81$		0			0
$82$	−3.83357	+	6.63994i	−0.423347	+	0.733259i
$83$	2.40898	−	4.17248i	0.264420	−	0.457989i	−0.702991	−	0.711198i	$-0.748153\pi$
$83$	2.40898	−	4.17248i	0.264420	−	0.457989i	0.967412	+	0.253209i	$0.0814861\pi$
$84$		0			0
$85$	2.23716	+	3.87488i	0.242654	+	0.420289i
$86$	8.29642			0.894626
$87$		0			0
$88$	34.6891			3.69787
$89$	−5.16019	+	8.93770i	−0.546979	+	0.947395i	0.451501	+	0.892271i	$0.350889\pi$
$89$	−5.16019	+	8.93770i	−0.546979	+	0.947395i	−0.998480	+	0.0551241i	$0.982445\pi$
$90$		0			0
$91$	−4.76667	−	2.22344i	−0.499682	−	0.233080i
$92$	16.4222	−	28.4441i	1.71213	−	2.96550i
$93$		0			0
$94$	−7.65674	+	13.2619i	−0.789733	+	1.36786i
$95$	−0.0804749	+	0.139387i	−0.00825655	+	0.0143008i
$96$		0			0
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	−0.318216	−	0.948018i	$-0.603084\pi$
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	0.980116	−	0.198426i	$-0.0635828\pi$
$98$	−18.5974	+	3.27456i	−1.87863	+	0.330781i
$99$		0			0
$100$	−2.63865	+	4.57028i	−0.263865	+	0.457028i
$101$	1.92974			0.192016			0.0960079	−	0.995381i	$-0.469393\pi$
$101$	1.92974			0.192016			0.0960079	+	0.995381i	$0.469393\pi$
$102$		0			0
$103$	1.54457			0.152191			0.0760957	−	0.997101i	$-0.475755\pi$
$103$	1.54457			0.152191			0.0760957	+	0.997101i	$0.475755\pi$
$104$	8.78792	+	15.2211i	0.861727	+	1.49255i
$105$		0			0
$106$	−14.8590	+	25.7366i	−1.44323	+	2.49976i
$107$	0.350836	−	0.607665i	0.0339166	−	0.0587452i	−0.848569	−	0.529085i	$-0.822535\pi$
$107$	0.350836	−	0.607665i	0.0339166	−	0.0587452i	0.882485	+	0.470340i	$0.155869\pi$
$108$		0			0
$109$	−6.34253	−	10.9856i	−0.607504	−	1.05223i	−0.991650	−	0.128956i	$-0.958837\pi$
$109$	−6.34253	−	10.9856i	−0.607504	−	1.05223i	0.384146	−	0.923272i	$-0.374496\pi$
$110$	5.29232	+	9.16657i	0.504603	+	0.873998i
$111$		0			0
$112$	31.8785	+	14.8699i	3.01224	+	1.40508i
$113$	−3.27999	−	5.68110i	−0.308555	−	0.534433i	0.669491	−	0.742820i	$-0.266512\pi$
$113$	−3.27999	−	5.68110i	−0.308555	−	0.534433i	−0.978047	+	0.208387i	$0.933179\pi$
$114$		0			0
$115$	6.22371			0.580364
$116$	2.03167	+	3.51895i	0.188636	+	0.326726i
$117$		0			0
$118$	9.07927			0.835815
$119$	10.7282	+	5.00424i	0.983453	+	0.458738i
$120$		0			0
$121$	4.39509			0.399553
$122$	9.30192	−	16.1114i	0.842156	−	1.45866i
$123$		0			0
$124$	21.1887	+	36.6999i	1.90280	+	3.29575i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.28822			0.557989			0.278994	−	0.960293i	$-0.409999\pi$
$127$	6.28822			0.557989			0.278994	+	0.960293i	$0.409999\pi$
$128$	−12.1153	−	20.9843i	−1.07085	−	1.85477i
$129$		0			0
$130$	−2.68145	+	4.64441i	−0.235179	+	0.407342i
$131$	9.66738			0.844643			0.422321	−	0.906446i	$-0.361215\pi$
$131$	9.66738			0.844643			0.422321	+	0.906446i	$0.361215\pi$
$132$		0			0
$133$	0.0370622	+	0.424217i	0.00321370	+	0.0367843i
$134$	27.2186			2.35133
$135$		0			0
$136$	−19.7787	−	34.2578i	−1.69601	−	2.93758i
$137$	3.29165			0.281224			0.140612	−	0.990065i	$-0.455093\pi$
$137$	3.29165			0.281224			0.140612	+	0.990065i	$0.455093\pi$
$138$		0			0
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	0.999297	−	0.0374890i	$-0.0119359\pi$
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	−0.532115	+	0.846672i	$0.678603\pi$
$140$	1.21521	+	13.9094i	0.102704	+	1.17556i
$141$		0			0
$142$	9.14829	+	15.8453i	0.767708	+	1.32971i
$143$	3.90010	+	6.75517i	0.326143	+	0.564896i
$144$		0			0
$145$	−0.384982	+	0.666809i	−0.0319710	+	0.0553755i
$146$	−19.4493	+	33.6871i	−1.60963	+	2.78796i
$147$		0			0
$148$	−18.4849	−	32.0168i	−1.51945	−	2.63176i
$149$	−16.2101			−1.32798			−0.663992	−	0.747740i	$-0.731139\pi$
$149$	−16.2101			−1.32798			−0.663992	+	0.747740i	$0.731139\pi$
$150$		0			0
$151$	−19.1653			−1.55965			−0.779827	−	0.625996i	$-0.784693\pi$
$151$	−19.1653			−1.55965			−0.779827	+	0.625996i	$0.784693\pi$
$152$	0.711479	−	1.23232i	0.0577086	−	0.0999542i
$153$		0			0
$154$	25.3791	+	11.8382i	2.04511	+	0.953952i
$155$	−4.01507	+	6.95430i	−0.322498	+	0.558583i
$156$		0			0
$157$	3.60535	−	6.24465i	0.287738	−	0.498377i	−0.685531	−	0.728043i	$-0.740430\pi$
$157$	3.60535	−	6.24465i	0.287738	−	0.498377i	0.973270	+	0.229666i	$0.0737633\pi$
$158$	−15.2664	+	26.4421i	−1.21453	+	2.10362i
$159$		0			0
$160$	9.09202	−	15.7478i	0.718787	−	1.24498i
$161$	13.4896	−	9.44309i	1.06313	−	0.744219i
$162$		0			0
$163$	4.40268	−	7.62567i	0.344845	−	0.597288i	−0.640481	−	0.767974i	$-0.721265\pi$
$163$	4.40268	−	7.62567i	0.344845	−	0.597288i	0.985326	+	0.170686i	$0.0545983\pi$
$164$	14.9989			1.17122
$165$		0			0
$166$	−12.9972			−1.00878
$167$	−0.470408	−	0.814771i	−0.0364013	−	0.0630488i	0.847251	−	0.531193i	$-0.178256\pi$
$167$	−0.470408	−	0.814771i	−0.0364013	−	0.0630488i	−0.883652	+	0.468144i	$0.844923\pi$
$168$		0			0
$169$	4.52394	−	7.83570i	0.347996	−	0.602746i
$170$	6.03507	−	10.4530i	0.462869	−	0.801712i
$171$		0			0
$172$	−8.11498	−	14.0556i	−0.618762	−	1.07173i
$173$	−4.76243	−	8.24877i	−0.362081	−	0.627142i	0.626222	−	0.779645i	$-0.284600\pi$
$173$	−4.76243	−	8.24877i	−0.362081	−	0.627142i	−0.988303	+	0.152502i	$0.951267\pi$
$174$		0			0
$175$	−2.16746	+	1.51728i	−0.163844	+	0.114695i
$176$	−26.0831	−	45.1773i	−1.96609	−	3.40537i
$177$		0			0
$178$	27.8407			2.08675
$179$	−11.9714	−	20.7351i	−0.894784	−	1.54981i	−0.834071	−	0.551657i	$-0.813996\pi$
$179$	−11.9714	−	20.7351i	−0.894784	−	1.54981i	−0.0607130	−	0.998155i	$-0.519337\pi$
$180$		0			0
$181$	−2.51843			−0.187193			−0.0935967	−	0.995610i	$-0.529836\pi$
$181$	−2.51843			−0.187193			−0.0935967	+	0.995610i	$0.529836\pi$
$182$	1.23492	+	14.1351i	0.0915387	+	1.04776i
$183$		0			0
$184$	−55.0238			−4.05641
$185$	3.50272	−	6.06689i	0.257525	−	0.446046i
$186$		0			0
$187$	−8.77785	−	15.2037i	−0.641900	−	1.11180i
$188$	29.9572			2.18485
$189$		0			0
$190$	0.434186			0.0314991
$191$	−4.70573	−	8.15057i	−0.340495	−	0.589755i	0.644030	−	0.765000i	$-0.277261\pi$
$191$	−4.70573	−	8.15057i	−0.340495	−	0.589755i	−0.984525	+	0.175246i	$0.943928\pi$
$192$		0			0
$193$	−3.77743	+	6.54271i	−0.271906	+	0.470954i	−0.969350	−	0.245685i	$-0.920987\pi$
$193$	−3.77743	+	6.54271i	−0.271906	+	0.470954i	0.697444	+	0.716639i	$0.254321\pi$
$194$	−35.1717			−2.52518
$195$		0			0
$196$	23.7384	+	28.3043i	1.69560	+	2.02174i
$197$	−21.1556			−1.50727			−0.753637	−	0.657291i	$-0.771702\pi$
$197$	−21.1556			−1.50727			−0.753637	+	0.657291i	$0.771702\pi$
$198$		0			0
$199$	−0.0783738	−	0.135747i	−0.00555577	−	0.00962288i	0.863234	−	0.504804i	$-0.168435\pi$
$199$	−0.0783738	−	0.135747i	−0.00555577	−	0.00962288i	−0.868790	+	0.495181i	$0.835102\pi$
$200$	8.84100			0.625153
$201$		0			0
$202$	−2.60287	−	4.50831i	−0.183138	−	0.317203i
$203$	0.177301	+	2.02940i	0.0124441	+	0.142436i
$204$		0			0
$205$	1.42108	+	2.46138i	0.0992526	+	0.171910i
$206$	−2.08336	−	3.60848i	−0.145154	−	0.251415i
$207$		0			0
$208$	13.2155	−	22.8899i	0.916329	−	1.58713i
$209$	0.315756	−	0.546905i	0.0218413	−	0.0378302i
$210$		0			0
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	0.931870	−	0.362794i	$-0.118177\pi$
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	−0.780123	+	0.625626i	$0.784844\pi$
$212$	58.1362			3.99281
$213$		0			0
$214$	−1.89286			−0.129393
$215$	1.53771	−	2.66340i	0.104871	−	0.181642i
$216$		0			0
$217$	1.84911	+	21.1651i	0.125526	+	1.43678i
$218$	−17.1099	+	29.6352i	−1.15883	+	2.00715i
$219$		0			0
$220$	10.3532	−	17.9322i	0.698010	−	1.20899i
$221$	4.44746	−	7.70322i	0.299168	−	0.518175i
$222$		0			0
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	−0.947337	−	0.320237i	$-0.896237\pi$
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	0.751002	+	0.660300i	$0.229571\pi$
$224$	−4.18727	−	47.9279i	−0.279774	−	3.20232i
$225$		0			0
$226$	−8.84825	+	15.3256i	−0.588577	+	1.01944i
$227$	11.6794			0.775190			0.387595	−	0.921830i	$-0.373306\pi$
$227$	11.6794			0.775190			0.387595	+	0.921830i	$0.373306\pi$
$228$		0			0
$229$	−17.0028			−1.12358			−0.561790	−	0.827280i	$-0.689887\pi$
$229$	−17.0028			−1.12358			−0.561790	+	0.827280i	$0.689887\pi$
$230$	−8.39468	−	14.5400i	−0.553529	−	0.958740i
$231$		0			0
$232$	3.40363	−	5.89526i	0.223459	−	0.387043i
$233$	−0.351193	+	0.608285i	−0.0230074	+	0.0398501i	−0.877300	−	0.479943i	$-0.840657\pi$
$233$	−0.351193	+	0.608285i	−0.0230074	+	0.0398501i	0.854292	+	0.519793i	$0.173991\pi$
$234$		0			0
$235$	2.83830	+	4.91609i	0.185150	+	0.320690i
$236$	−8.88071	−	15.3818i	−0.578085	−	1.00127i
$237$		0			0
$238$	−2.77941	−	31.8134i	−0.180162	−	2.06216i
$239$	1.37629	+	2.38380i	0.0890246	+	0.154195i	0.907099	−	0.420917i	$-0.138292\pi$
$239$	1.37629	+	2.38380i	0.0890246	+	0.154195i	−0.818074	+	0.575112i	$0.804958\pi$
$240$		0			0
$241$	15.2330			0.981243			0.490622	−	0.871373i	$-0.336770\pi$
$241$	15.2330			0.981243			0.490622	+	0.871373i	$0.336770\pi$
$242$	−5.92820	−	10.2679i	−0.381079	−	0.660048i
$243$		0			0
$244$	−36.3940			−2.32988
$245$	−2.39574	+	6.57727i	−0.153058	+	0.420206i
$246$		0			0
$247$	0.319967			0.0203590
$248$	35.4972	−	61.4830i	2.25408	−	3.90417i
$249$		0			0
$250$	1.34882	+	2.33623i	0.0853071	+	0.147756i
$251$	15.2671			0.963651			0.481825	−	0.876267i	$-0.339974\pi$
$251$	15.2671			0.963651			0.481825	+	0.876267i	$0.339974\pi$
$252$		0			0
$253$	−24.4197			−1.53525
$254$	−8.48169	−	14.6907i	−0.532189	−	0.921778i
$255$		0			0
$256$	−10.2193	+	17.7003i	−0.638704	+	1.10627i
$257$	−28.5573			−1.78136			−0.890678	−	0.454635i	$-0.849770\pi$
$257$	−28.5573			−1.78136			−0.890678	+	0.454635i	$0.849770\pi$
$258$		0			0
$259$	−1.61315	−	18.4643i	−0.100237	−	1.14732i
$260$	10.4912			0.650639
$261$		0			0
$262$	−13.0396	−	22.5852i	−0.805589	−	1.39532i
$263$	13.7018			0.844892			0.422446	−	0.906388i	$-0.361172\pi$
$263$	13.7018			0.844892			0.422446	+	0.906388i	$0.361172\pi$
$264$		0			0
$265$	5.50814	+	9.54037i	0.338362	+	0.586060i
$266$	0.941079	−	0.658780i	0.0577013	−	0.0403924i
$267$		0			0
$268$	−26.6234	−	46.1130i	−1.62628	−	2.81680i
$269$	9.33523	+	16.1691i	0.569179	+	0.985847i	0.996647	+	0.0818164i	$0.0260721\pi$
$269$	9.33523	+	16.1691i	0.569179	+	0.985847i	−0.427469	+	0.904030i	$0.640595\pi$
$270$		0			0
$271$	12.3195	−	21.3380i	0.748356	−	1.29619i	−0.200254	−	0.979744i	$-0.564177\pi$
$271$	12.3195	−	21.3380i	0.748356	−	1.29619i	0.948610	−	0.316447i	$-0.102490\pi$
$272$	−29.7437	+	51.5177i	−1.80348	+	3.12372i
$273$		0			0
$274$	−4.43985	−	7.69004i	−0.268221	−	0.464573i
$275$	3.92366			0.236605
$276$		0			0
$277$	−14.7577			−0.886703			−0.443352	−	0.896348i	$-0.646211\pi$
$277$	−14.7577			−0.886703			−0.443352	+	0.896348i	$0.646211\pi$
$278$	14.8586	−	25.7359i	0.891161	−	1.54354i
$279$		0			0
$280$	19.1625	−	13.4143i	1.14518	−	0.801655i
$281$	6.43418	−	11.1443i	0.383831	−	0.664815i	−0.607775	−	0.794109i	$-0.707938\pi$
$281$	6.43418	−	11.1443i	0.383831	−	0.664815i	0.991606	+	0.129294i	$0.0412712\pi$
$282$		0			0
$283$	−6.31761	+	10.9424i	−0.375543	+	0.650459i	−0.990408	−	0.138173i	$-0.955877\pi$
$283$	−6.31761	+	10.9424i	−0.375543	+	0.650459i	0.614865	+	0.788632i	$0.289210\pi$
$284$	17.8964	−	30.9975i	1.06196	−	1.83937i
$285$		0			0
$286$	10.5211	−	18.2231i	0.622125	−	1.07755i
$287$	6.81473	+	3.17877i	0.402261	+	0.187637i
$288$		0			0
$289$	−1.50977	+	2.61501i	−0.0888103	+	0.153824i
$290$	2.07709			0.121971
$291$		0			0
$292$	76.0956			4.45316
$293$	5.42891	+	9.40315i	0.317160	+	0.549338i	0.979894	−	0.199517i	$-0.0639374\pi$
$293$	5.42891	+	9.40315i	0.317160	+	0.549338i	−0.662734	+	0.748855i	$0.730604\pi$
$294$		0			0
$295$	1.68281	−	2.91472i	0.0979772	−	0.169701i
$296$	−30.9676	+	53.6374i	−1.79995	+	3.11761i
$297$		0			0
$298$	21.8646	+	37.8705i	1.26658	+	2.19378i
$299$	−6.18634	−	10.7151i	−0.357765	−	0.619667i
$300$		0			0
$301$	−0.708184	−	8.10594i	−0.0408191	−	0.467219i
$302$	25.8507	+	44.7747i	1.48754	+	2.57649i
$303$		0			0
$304$	−2.13988			−0.122730
$305$	−3.44816	−	5.97239i	−0.197441	−	0.341978i
$306$		0			0
$307$	11.8223			0.674737			0.337368	−	0.941373i	$-0.390463\pi$
$307$	11.8223			0.674737			0.337368	+	0.941373i	$0.390463\pi$
$308$	−4.76808	−	54.5759i	−0.271687	−	3.10975i
$309$		0			0
$310$	21.6625			1.23035
$311$	−9.73145	+	16.8554i	−0.551820	+	0.955780i	0.446324	+	0.894872i	$0.352733\pi$
$311$	−9.73145	+	16.8554i	−0.551820	+	0.955780i	−0.998143	+	0.0609083i	$0.980600\pi$
$312$		0			0
$313$	−7.09490	−	12.2887i	−0.401027	−	0.694600i	0.592823	−	0.805333i	$-0.298013\pi$
$313$	−7.09490	−	12.2887i	−0.401027	−	0.694600i	−0.993850	+	0.110733i	$0.964680\pi$
$314$	−19.4519			−1.09774
$315$		0			0
$316$	59.7300			3.36007
$317$	−3.87392	−	6.70982i	−0.217581	−	0.376861i	0.736487	−	0.676452i	$-0.236483\pi$
$317$	−3.87392	−	6.70982i	−0.217581	−	0.376861i	−0.954068	+	0.299591i	$0.903150\pi$
$318$		0			0
$319$	1.51054	−	2.61633i	0.0845739	−	0.146486i
$320$	−22.4635			−1.25575
$321$		0			0
$322$	−40.2563	−	18.7778i	−2.24340	−	1.04645i
$323$	−0.720141			−0.0400697
$324$		0			0
$325$	0.993996	+	1.72165i	0.0551370	+	0.0955000i
$326$	−23.7538			−1.31560
$327$		0			0
$328$	−12.5638	−	21.7611i	−0.693719	−	1.20156i
$329$	13.6110	+	6.34891i	0.750397	+	0.350027i
$330$		0			0
$331$	13.9027	+	24.0803i	0.764164	+	1.32357i	0.940687	+	0.339275i	$0.110182\pi$
$331$	13.9027	+	24.0803i	0.764164	+	1.32357i	−0.176523	+	0.984296i	$0.556485\pi$
$332$	12.7129	+	22.0194i	0.697712	+	1.20847i
$333$		0			0
$334$	−1.26899	+	2.19796i	−0.0694363	+	0.120267i
$335$	5.04488	−	8.73799i	0.275631	−	0.477407i
$336$		0			0
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	0.904801	−	0.425834i	$-0.140019\pi$
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	−0.821184	+	0.570664i	$0.806686\pi$
$338$	−24.4080			−1.32762
$339$		0			0
$340$	−23.6123			−1.28056
$341$	15.7538	−	27.2863i	0.853113	−	1.47764i
$342$		0			0
$343$	4.78686	+	17.8909i	0.258466	+	0.966020i
$344$	−13.5949	+	23.5471i	−0.732990	+	1.26958i
$345$		0			0
$346$	−12.8474	+	22.2523i	−0.690678	+	1.19629i
$347$	−13.3050	+	23.0449i	−0.714247	+	1.23711i	0.249002	+	0.968503i	$0.419898\pi$
$347$	−13.3050	+	23.0449i	−0.714247	+	1.23711i	−0.963249	+	0.268610i	$0.913436\pi$
$348$		0			0
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	0.475931	+	0.879482i	$0.342111\pi$
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	−0.999620	+	0.0275725i	$0.991222\pi$
$350$	6.46823	+	3.01714i	0.345741	+	0.161273i
$351$		0			0
$352$	−35.6740	+	61.7891i	−1.90143	+	3.29337i
$353$	7.48500			0.398386			0.199193	−	0.979960i	$-0.436168\pi$
$353$	7.48500			0.398386			0.199193	+	0.979960i	$0.436168\pi$
$354$		0			0
$355$	6.78242			0.359974
$356$	−27.2319	−	47.1670i	−1.44329	−	2.49984i
$357$		0			0
$358$	−32.2946	+	55.9359i	−1.70682	+	2.95630i
$359$	1.89571	−	3.28347i	0.100052	−	0.173295i	−0.811654	−	0.584139i	$-0.801432\pi$
$359$	1.89571	−	3.28347i	0.100052	−	0.173295i	0.911706	+	0.410844i	$0.134766\pi$
$360$		0			0
$361$	9.48705	+	16.4320i	0.499318	+	0.864845i
$362$	3.39692	+	5.88363i	0.178538	+	0.309237i
$363$		0			0
$364$	22.7393	−	15.9181i	1.19186	−	0.834335i
$365$	7.20971	+	12.4876i	0.377373	+	0.653630i
$366$		0			0
$367$	32.4384			1.69327			0.846634	−	0.532175i	$-0.178625\pi$
$367$	32.4384			1.69327			0.846634	+	0.532175i	$0.178625\pi$
$368$	41.3730	+	71.6602i	2.15672	+	3.73555i
$369$		0			0
$370$	−18.8982			−0.982471
$371$	26.4140	+	12.3210i	1.37135	+	0.639673i
$372$		0			0
$373$	8.11950			0.420412			0.210206	−	0.977657i	$-0.432587\pi$
$373$	8.11950			0.420412			0.210206	+	0.977657i	$0.432587\pi$
$374$	−23.6795	+	41.0142i	−1.22444	+	2.12079i
$375$		0			0
$376$	−25.0935	−	43.4631i	−1.29410	−	2.24144i
$377$	1.53068			0.0788342
$378$		0			0
$379$	22.3585			1.14848			0.574240	−	0.818687i	$-0.305298\pi$
$379$	22.3585			1.14848			0.574240	+	0.818687i	$0.305298\pi$
$380$	−0.424690	−	0.735585i	−0.0217862	−	0.0377347i
$381$		0			0
$382$	−12.6944	+	21.9874i	−0.649503	+	1.12497i
$383$	−1.93040			−0.0986387			−0.0493194	−	0.998783i	$-0.515705\pi$
$383$	−1.93040			−0.0986387			−0.0493194	+	0.998783i	$0.515705\pi$
$384$		0			0
$385$	8.50436	−	5.95327i	0.433422	−	0.303407i
$386$	20.3804			1.03733
$387$		0			0
$388$	34.4025	+	59.5869i	1.74652	+	3.02506i
$389$	−30.9899			−1.57125			−0.785625	−	0.618704i	$-0.787658\pi$
$389$	−30.9899			−1.57125			−0.785625	+	0.618704i	$0.787658\pi$
$390$		0			0
$391$	13.9234	+	24.1161i	0.704138	+	1.21960i
$392$	21.1808	−	58.1496i	1.06979	−	2.93700i
$393$		0			0
$394$	28.5352	+	49.4244i	1.43758	+	2.48996i
$395$	5.65914	+	9.80192i	0.284742	+	0.493188i
$396$		0			0
$397$	8.46510	−	14.6620i	0.424851	−	0.735864i	−0.571555	−	0.820563i	$-0.693660\pi$
$397$	8.46510	−	14.6620i	0.424851	−	0.735864i	0.996407	+	0.0846997i	$0.0269931\pi$
$398$	−0.211425	+	0.366199i	−0.0105978	+	0.0183559i
$399$		0			0
$400$	−6.64765	−	11.5141i	−0.332383	−	0.575704i
$401$	16.8343			0.840665			0.420332	−	0.907370i	$-0.361913\pi$
$401$	16.8343			0.840665			0.420332	+	0.907370i	$0.361913\pi$
$402$		0			0
$403$	15.9638			0.795216
$404$	−5.09190	+	8.81943i	−0.253331	+	0.438783i
$405$		0			0
$406$	4.50201	−	3.15153i	0.223431	−	0.156408i
$407$	−13.7435	+	23.8044i	−0.681238	+	1.17994i
$408$		0			0
$409$	5.95910	−	10.3215i	0.294659	−	0.510364i	−0.680247	−	0.732983i	$-0.738127\pi$
$409$	5.95910	−	10.3215i	0.294659	−	0.510364i	0.974905	+	0.222619i	$0.0714607\pi$
$410$	3.83357	−	6.63994i	0.189327	−	0.327924i
$411$		0			0
$412$	−4.07559	+	7.05913i	−0.200790	+	0.347778i
$413$	−0.775008	−	8.87082i	−0.0381357	−	0.436505i
$414$		0			0
$415$	−2.40898	+	4.17248i	−0.118252	+	0.204819i
$416$	−36.1497			−1.77239
$417$		0			0
$418$	−1.70360			−0.0833256
$419$	−5.83768	−	10.1112i	−0.285189	−	0.493962i	0.687466	−	0.726217i	$-0.258723\pi$
$419$	−5.83768	−	10.1112i	−0.285189	−	0.493962i	−0.972655	+	0.232254i	$0.925390\pi$
$420$		0			0
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	−0.912444	−	0.409202i	$-0.865807\pi$
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	0.810601	+	0.585599i	$0.199140\pi$
$422$	5.94627	−	10.2992i	0.289460	−	0.501359i
$423$		0			0
$424$	−48.6974	−	84.3464i	−2.36496	−	4.09623i
$425$	−2.23716	−	3.87488i	−0.108518	−	0.187959i
$426$		0			0
$427$	−16.5355	−	7.71308i	−0.800209	−	0.373262i
$428$	1.85147	+	3.20683i	0.0894940	+	0.155008i
$429$		0			0
$430$	−8.29642			−0.400089
$431$	4.48625	+	7.77041i	0.216095	+	0.374288i	0.953611	−	0.301042i	$-0.0973346\pi$
$431$	4.48625	+	7.77041i	0.216095	+	0.374288i	−0.737516	+	0.675330i	$0.764001\pi$
$432$		0			0
$433$	9.18475			0.441391			0.220696	−	0.975343i	$-0.429167\pi$
$433$	9.18475			0.441391			0.220696	+	0.975343i	$0.429167\pi$
$434$	46.9525	−	32.8680i	2.25379	−	1.57771i
$435$		0			0
$436$	66.9429			3.20598
$437$	−0.500852	+	0.867501i	−0.0239590	+	0.0414982i
$438$		0			0
$439$	−16.0846	−	27.8593i	−0.767674	−	1.32965i	−0.938821	−	0.344405i	$-0.888081\pi$
$439$	−16.0846	−	27.8593i	−0.767674	−	1.32965i	0.171148	−	0.985245i	$-0.445253\pi$
$440$	−34.6891			−1.65374
$441$		0			0
$442$	−23.9953			−1.14134
$443$	11.5386	+	19.9854i	0.548214	+	0.949534i	0.998397	+	0.0565981i	$0.0180254\pi$
$443$	11.5386	+	19.9854i	0.548214	+	0.949534i	−0.450183	+	0.892936i	$0.648641\pi$
$444$		0			0
$445$	5.16019	−	8.93770i	0.244616	−	0.423688i
$446$	15.8185			0.749029
$447$		0			0
$448$	−48.6887	+	34.0834i	−2.30033	+	1.61029i
$449$	−25.7100			−1.21333			−0.606664	−	0.794958i	$-0.707493\pi$
$449$	−25.7100			−1.21333			−0.606664	+	0.794958i	$0.707493\pi$
$450$		0			0
$451$	−5.57583	−	9.65763i	−0.262556	−	0.454760i
$452$	34.6190			1.62834
$453$		0			0
$454$	−15.7535	−	27.2858i	−0.739347	−	1.28059i
$455$	4.76667	+	2.22344i	0.223465	+	0.104236i
$456$		0			0
$457$	−8.76619	−	15.1835i	−0.410065	−	0.710253i	0.584832	−	0.811155i	$-0.301161\pi$
$457$	−8.76619	−	15.1835i	−0.410065	−	0.710253i	−0.994896	+	0.100902i	$0.967827\pi$
$458$	22.9338	+	39.7226i	1.07163	+	1.85611i
$459$		0			0
$460$	−16.4222	+	28.4441i	−0.765688	+	1.32621i
$461$	−13.7588	+	23.8310i	−0.640811	+	1.10992i	0.344440	+	0.938808i	$0.388069\pi$
$461$	−13.7588	+	23.8310i	−0.640811	+	1.10992i	−0.985252	+	0.171110i	$0.945265\pi$
$462$		0			0
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	0.999043	−	0.0437411i	$-0.0139277\pi$
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	−0.537402	+	0.843326i	$0.680594\pi$
$464$	−10.2369			−0.475237
$465$		0			0
$466$	1.89479			0.0877746
$467$	12.7739	−	22.1250i	0.591106	−	1.02382i	−0.402978	−	0.915210i	$-0.632025\pi$
$467$	12.7739	−	22.1250i	0.591106	−	1.02382i	0.994084	−	0.108615i	$-0.0346417\pi$
$468$		0			0
$469$	−2.32339	−	26.5937i	−0.107284	−	1.22798i
$470$	7.65674	−	13.2619i	0.353179	−	0.611724i
$471$		0			0
$472$	−14.8778	+	25.7690i	−0.684804	+	1.18612i
$473$	−6.03346	+	10.4503i	−0.277419	+	0.480504i
$474$		0			0
$475$	0.0804749	−	0.139387i	0.00369244	−	0.00639550i
$476$	−51.1787	+	35.8265i	−2.34577	+	1.64210i
$477$		0			0
$478$	3.71274	−	6.43065i	0.169817	−	0.294131i
$479$	0.190231			0.00869185			0.00434593	−	0.999991i	$-0.498617\pi$
$479$	0.190231			0.00869185			0.00434593	+	0.999991i	$0.498617\pi$
$480$		0			0
$481$	−13.9268			−0.635005
$482$	−20.5466	−	35.5878i	−0.935873	−	1.62098i
$483$		0			0
$484$	−11.5971	+	20.0868i	−0.527141	+	0.913035i
$485$	−6.51896	+	11.2912i	−0.296011	+	0.512705i
$486$		0			0
$487$	2.65585	+	4.60007i	0.120348	+	0.208449i	0.919905	−	0.392141i	$-0.128266\pi$
$487$	2.65585	+	4.60007i	0.120348	+	0.208449i	−0.799557	+	0.600590i	$0.794932\pi$
$488$	30.4852	+	52.8019i	1.38000	+	2.39023i
$489$		0			0
$490$	18.5974	−	3.27456i	0.840147	−	0.147930i
$491$	10.1203	+	17.5288i	0.456721	+	0.791065i	0.998785	−	0.0492725i	$-0.0156903\pi$
$491$	10.1203	+	17.5288i	0.456721	+	0.791065i	−0.542064	+	0.840337i	$0.682357\pi$
$492$		0			0
$493$	−3.44507			−0.155158
$494$	−0.431579	−	0.747517i	−0.0194177	−	0.0336324i
$495$		0			0
$496$	−106.763			−4.79381
$497$	14.7006	−	10.2908i	0.659412	−	0.461606i
$498$		0			0
$499$	−2.42997			−0.108780			−0.0543902	−	0.998520i	$-0.517321\pi$
$499$	−2.42997			−0.108780			−0.0543902	+	0.998520i	$0.517321\pi$
$500$	2.63865	−	4.57028i	0.118004	−	0.204389i
$501$		0			0
$502$	−20.5926	−	35.6675i	−0.919094	−	1.59192i
$503$	−11.8338			−0.527644			−0.263822	−	0.964571i	$-0.584983\pi$
$503$	−11.8338			−0.527644			−0.263822	+	0.964571i	$0.584983\pi$
$504$		0			0
$505$	−1.92974			−0.0858721
$506$	32.9379	+	57.0500i	1.46427	+	2.53618i
$507$		0			0
$508$	−16.5924	+	28.7389i	−0.736169	+	1.27508i
$509$	16.1165			0.714351			0.357176	−	0.934037i	$-0.383740\pi$
$509$	16.1165			0.714351			0.357176	+	0.934037i	$0.383740\pi$
$510$		0			0
$511$	34.5739	+	16.1272i	1.52946	+	0.713424i
$512$	6.67474			0.294985
$513$		0			0
$514$	38.5188	+	66.7164i	1.69899	+	2.94274i
$515$	−1.54457			−0.0680620
$516$		0			0
$517$	−11.1365	−	19.2890i	−0.489784	−	0.848331i
$518$	−40.9610	+	28.6738i	−1.79972	+	1.25985i
$519$		0			0
$520$	−8.78792	−	15.2211i	−0.385376	−	0.667491i
$521$	−14.6673	−	25.4044i	−0.642584	−	1.11299i	−0.984854	−	0.173386i	$-0.944529\pi$
$521$	−14.6673	−	25.4044i	−0.642584	−	1.11299i	0.342270	−	0.939602i	$-0.388804\pi$
$522$		0			0
$523$	−2.13586	+	3.69941i	−0.0933945	+	0.161764i	−0.908937	−	0.416933i	$-0.863105\pi$
$523$	−2.13586	+	3.69941i	−0.0933945	+	0.161764i	0.815543	+	0.578697i	$0.196438\pi$
$524$	−25.5088	+	44.1826i	−1.11436	+	1.93013i
$525$		0			0
$526$	−18.4814	−	32.0107i	−0.805826	−	1.39573i
$527$	−35.9294			−1.56511
$528$		0			0
$529$	15.7345			0.684110
$530$	14.8590	−	25.7366i	0.645434	−	1.11792i
$531$		0			0
$532$	−2.03658	−	0.949977i	−0.0882971	−	0.0411867i
$533$	2.82510	−	4.89321i	0.122369	−	0.211948i
$534$		0			0
$535$	−0.350836	+	0.607665i	−0.0151680	+	0.0262717i
$536$	−44.6018	+	77.2526i	−1.92650	+	3.33680i
$537$		0			0
$538$	25.1831	−	43.6185i	1.08572	−	1.88053i
$539$	9.40007	−	25.8069i	0.404890	−	1.11158i
$540$		0			0
$541$	−13.6460	+	23.6356i	−0.586688	+	1.01617i	0.407975	+	0.912993i	$0.366235\pi$
$541$	−13.6460	+	23.6356i	−0.586688	+	1.01617i	−0.994663	+	0.103180i	$0.967098\pi$
$542$	−66.4673			−2.85502
$543$		0			0
$544$	81.3613			3.48833
$545$	6.34253	+	10.9856i	0.271684	+	0.470571i
$546$		0			0
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	−0.758468	−	0.651711i	$-0.774052\pi$
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	0.943632	+	0.330997i	$0.107385\pi$
$548$	−8.68550	+	15.0437i	−0.371026	+	0.642636i
$549$		0			0
$550$	−5.29232	−	9.16657i	−0.225665	−	0.390864i
$551$	−0.0619628	−	0.107323i	−0.00263971	−	0.00457210i
$552$		0			0
$553$	27.1382	+	12.6588i	1.15403	+	0.538305i
$554$	19.9055	+	34.4774i	0.845704	+	1.46480i
$555$		0			0
$556$	−58.1347			−2.46546
$557$	21.6429	+	37.4865i	0.917037	+	1.58835i	0.803891	+	0.594777i	$0.202759\pi$
$557$	21.6429	+	37.4865i	0.917037	+	1.58835i	0.113146	+	0.993578i	$0.463907\pi$
$558$		0			0
$559$	−6.11393			−0.258592
$560$	−31.8785	−	14.8699i	−1.34711	−	0.628369i
$561$		0			0
$562$	−34.7143			−1.46433
$563$	16.9386	−	29.3385i	0.713876	−	1.23647i	−0.249515	−	0.968371i	$-0.580271\pi$
$563$	16.9386	−	29.3385i	0.713876	−	1.23647i	0.963391	−	0.268099i	$-0.0863954\pi$
$564$		0			0
$565$	3.27999	+	5.68110i	0.137990	+	0.239006i
$566$	34.0853			1.43271
$567$		0			0
$568$	−59.9634			−2.51601
$569$	16.3249	+	28.2755i	0.684374	+	1.18537i	0.973633	+	0.228120i	$0.0732579\pi$
$569$	16.3249	+	28.2755i	0.684374	+	1.18537i	−0.289259	+	0.957251i	$0.593409\pi$
$570$		0			0
$571$	−0.585599	+	1.01429i	−0.0245065	+	0.0424466i	−0.878019	−	0.478627i	$-0.841135\pi$
$571$	−0.585599	+	1.01429i	−0.0245065	+	0.0424466i	0.853512	+	0.521073i	$0.174468\pi$
$572$	−41.1640			−1.72115
$573$		0			0
$574$	−1.76553	−	20.2084i	−0.0736917	−	0.843482i
$575$	−6.22371			−0.259546
$576$		0			0
$577$	0.527159	+	0.913066i	0.0219459	+	0.0380114i	0.876790	−	0.480874i	$-0.159681\pi$
$577$	0.527159	+	0.913066i	0.0219459	+	0.0380114i	−0.854844	+	0.518885i	$0.826347\pi$
$578$	8.14568			0.338816
$579$		0			0
$580$	−2.03167	−	3.51895i	−0.0843604	−	0.146117i
$581$	1.10944	+	12.6988i	0.0460274	+	0.526834i
$582$		0			0
$583$	−21.6120	−	37.4331i	−0.895079	−	1.55032i
$584$	−63.7411	−	110.403i	−2.63762	−	4.56850i
$585$		0			0
$586$	14.6453	−	25.3664i	0.604991	−	1.04788i
$587$	11.9179	−	20.6425i	0.491906	−	0.852006i	−0.508051	−	0.861327i	$-0.669634\pi$
$587$	11.9179	−	20.6425i	0.491906	−	0.852006i	0.999957	+	0.00932152i	$0.00296717\pi$
$588$		0			0
$589$	−0.646224	−	1.11929i	−0.0266272	−	0.0461197i
$590$	−9.07927			−0.373788
$591$		0			0
$592$	93.1394			3.82801
$593$	−3.25508	+	5.63796i	−0.133670	+	0.231523i	−0.925089	−	0.379751i	$-0.876010\pi$
$593$	−3.25508	+	5.63796i	−0.133670	+	0.231523i	0.791419	+	0.611275i	$0.209343\pi$
$594$		0			0
$595$	−10.7282	−	5.00424i	−0.439814	−	0.205154i
$596$	42.7728	−	74.0847i	1.75204	−	3.03463i
$597$		0			0
$598$	−16.6886	+	28.9054i	−0.682446	+	1.18203i
$599$	8.49145	−	14.7076i	0.346951	−	0.600937i	−0.638755	−	0.769410i	$-0.720550\pi$
$599$	8.49145	−	14.7076i	0.346951	−	0.600937i	0.985706	+	0.168473i	$0.0538836\pi$
$600$		0			0
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	0.467726	+	0.883874i	$0.345073\pi$
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	−0.999320	+	0.0368744i	$0.988260\pi$
$602$	−17.9821	+	12.5880i	−0.732897	+	0.513047i
$603$		0			0
$604$	50.5706	−	87.5909i	2.05769	−	3.56402i
$605$	−4.39509			−0.178686
$606$		0			0
$607$	−19.5786			−0.794670			−0.397335	−	0.917674i	$-0.630065\pi$
$607$	−19.5786			−0.794670			−0.397335	+	0.917674i	$0.630065\pi$
$608$	1.46336	+	2.53461i	0.0593471	+	0.102792i
$609$		0			0
$610$	−9.30192	+	16.1114i	−0.376624	+	0.652331i
$611$	5.64252	−	9.77314i	0.228272	−	0.395379i
$612$		0			0
$613$	−19.4227	−	33.6411i	−0.784475	−	1.35875i	−0.929312	−	0.369295i	$-0.879599\pi$
$613$	−19.4227	−	33.6411i	−0.784475	−	1.35875i	0.144837	−	0.989456i	$-0.453734\pi$
$614$	−15.9463	−	27.6197i	−0.643539	−	1.11464i
$615$		0			0
$616$	−75.1871	+	52.6329i	−3.02937	+	2.12064i
$617$	−16.5821	−	28.7211i	−0.667571	−	1.15627i	−0.978581	−	0.205861i	$-0.934001\pi$
$617$	−16.5821	−	28.7211i	−0.667571	−	1.15627i	0.311010	−	0.950407i	$-0.399333\pi$
$618$		0			0
$619$	29.8135			1.19830			0.599152	−	0.800635i	$-0.295504\pi$
$619$	29.8135			1.19830			0.599152	+	0.800635i	$0.295504\pi$
$620$	−21.1887	−	36.6999i	−0.850960	−	1.47391i
$621$		0			0
$622$	52.5040			2.10522
$623$	−2.37649	−	27.2015i	−0.0952120	−	1.08981i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−19.1395	+	33.1507i	−0.764970	+	1.32497i
$627$		0			0
$628$	19.0265	+	32.9549i	0.759241	+	1.31504i
$629$	31.3446			1.24979
$630$		0			0
$631$	8.52204			0.339257			0.169629	−	0.985508i	$-0.445743\pi$
$631$	8.52204			0.339257			0.169629	+	0.985508i	$0.445743\pi$
$632$	−50.0325	−	86.6588i	−1.99018	−	3.44710i
$633$		0			0
$634$	−10.4505	+	18.1007i	−0.415041	+	0.718872i
$635$	−6.28822			−0.249540
$636$		0			0
$637$	13.7051	−	2.41314i	0.543016	−	0.0956122i
$638$	−8.14980			−0.322654
$639$		0			0
$640$	12.1153	+	20.9843i	0.478899	+	0.829477i
$641$	−1.54670			−0.0610909			−0.0305455	−	0.999533i	$-0.509724\pi$
$641$	−1.54670			−0.0610909			−0.0305455	+	0.999533i	$0.509724\pi$
$642$		0			0
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	0.789130	−	0.614226i	$-0.210532\pi$
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	−0.926500	+	0.376294i	$0.877198\pi$
$644$	7.56313	+	86.5683i	0.298029	+	3.41127i
$645$		0			0
$646$	0.971343	+	1.68242i	0.0382170	+	0.0661938i
$647$	23.3064	+	40.3678i	0.916268	+	1.58702i	0.805034	+	0.593229i	$0.202147\pi$
$647$	23.3064	+	40.3678i	0.916268	+	1.58702i	0.111234	+	0.993794i	$0.464520\pi$
$648$		0			0
$649$	−6.60278	+	11.4364i	−0.259182	+	0.448916i
$650$	2.68145	−	4.64441i	0.105175	−	0.182169i
$651$		0			0
$652$	23.2343	+	40.2429i	0.909924	+	1.57603i
$653$	22.2475			0.870614			0.435307	−	0.900282i	$-0.356640\pi$
$653$	22.2475			0.870614			0.435307	+	0.900282i	$0.356640\pi$
$654$		0			0
$655$	−9.66738			−0.377736
$656$	−18.8937	+	32.7249i	−0.737675	+	1.27769i
$657$		0			0
$658$	−3.52626	−	40.3619i	−0.137468	−	1.57347i
$659$	−4.70312	+	8.14605i	−0.183208	+	0.317325i	−0.942971	−	0.332875i	$-0.891981\pi$
$659$	−4.70312	+	8.14605i	−0.183208	+	0.317325i	0.759763	+	0.650200i	$0.225315\pi$
$660$		0			0
$661$	8.49414	−	14.7123i	0.330384	−	0.572241i	−0.652203	−	0.758044i	$-0.726155\pi$
$661$	8.49414	−	14.7123i	0.330384	−	0.572241i	0.982587	+	0.185803i	$0.0594886\pi$
$662$	37.5047	−	64.9601i	1.45766	−	2.52474i
$663$		0			0
$664$	21.2978	−	36.8889i	0.826516	−	1.43157i
$665$	−0.0370622	−	0.424217i	−0.00143721	−	0.0164504i
$666$		0			0
$667$	−2.39602	+	4.15002i	−0.0927741	+	0.160690i
$668$	4.96497			0.192100
$669$		0			0
$670$	−27.2186			−1.05155
$671$	13.5294	+	23.4336i	0.522297	+	0.904644i
$672$		0			0
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	−0.607649	−	0.794206i	$-0.707887\pi$
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	0.991627	+	0.129136i	$0.0412205\pi$
$674$	4.14091	−	7.17227i	0.159502	−	0.276265i
$675$		0			0
$676$	23.8742	+	41.3514i	0.918239	+	1.59044i
$677$	16.7021	+	28.9289i	0.641914	+	1.11183i	0.985005	+	0.172526i	$0.0551928\pi$
$677$	16.7021	+	28.9289i	0.641914	+	1.11183i	−0.343091	+	0.939302i	$0.611474\pi$
$678$		0			0
$679$	3.00226	+	34.3642i	0.115216	+	1.31878i
$680$	19.7787	+	34.2578i	0.758480	+	1.31373i
$681$		0			0
$682$	−84.9961			−3.25467
$683$	7.65577	+	13.2602i	0.292940	+	0.507387i	0.974504	−	0.224372i	$-0.0720331\pi$
$683$	7.65577	+	13.2602i	0.292940	+	0.507387i	−0.681564	+	0.731759i	$0.738700\pi$
$684$		0			0
$685$	−3.29165			−0.125767
$686$	35.3407	−	35.3150i	1.34932	−	1.34833i
$687$		0			0
$688$	40.8888			1.55887
$689$	10.9501	−	18.9662i	0.417167	−	0.722554i
$690$		0			0
$691$	4.77665	+	8.27339i	0.181712	+	0.314735i	0.942464	−	0.334309i	$-0.108503\pi$
$691$	4.77665	+	8.27339i	0.181712	+	0.314735i	−0.760752	+	0.649043i	$0.775169\pi$
$692$	50.2656			1.91081
$693$		0			0
$694$	71.7842			2.72489
$695$	−5.50800	−	9.54013i	−0.208930	−	0.361878i
$696$		0			0
$697$	−6.35837	+	11.0130i	−0.240840	+	0.417148i
$698$	52.7838			1.99790
$699$		0			0
$700$	−1.21521	−	13.9094i	−0.0459307	−	0.525728i
$701$	−39.6830			−1.49881			−0.749403	−	0.662114i	$-0.769660\pi$
$701$	−39.6830			−1.49881			−0.749403	+	0.662114i	$0.769660\pi$
$702$		0			0
$703$	0.563762	+	0.976464i	0.0212627	+	0.0368280i
$704$	88.1392			3.32187
$705$		0			0
$706$	−10.0959	−	17.4867i	−0.379966	−	0.658120i
$707$	−4.18262	+	2.92794i	−0.157304	+	0.110117i
$708$		0			0
$709$	8.24428	+	14.2795i	0.309620	+	0.536278i	0.978279	−	0.207291i	$-0.0664647\pi$
$709$	8.24428	+	14.2795i	0.309620	+	0.536278i	−0.668659	+	0.743569i	$0.733131\pi$
$710$	−9.14829	−	15.8453i	−0.343329	−	0.594664i
$711$		0			0
$712$	−45.6212	+	79.0183i	−1.70973	+	2.96134i
$713$	−24.9886	+	43.2815i	−0.935831	+	1.62091i
$714$		0			0
$715$	−3.90010	−	6.75517i	−0.145855	−	0.252629i
$716$	126.353			4.72205
$717$		0			0
$718$	−10.2279			−0.381703
$719$	−13.3872	+	23.1873i	−0.499259	+	0.864742i	−1.00000		0.000855526i	$-0.999728\pi$
$719$	−13.3872	+	23.1873i	−0.499259	+	0.864742i	0.500741	+	0.865597i	$0.333061\pi$
$720$		0			0
$721$	−3.34780	+	2.34355i	−0.124678	+	0.0872782i
$722$	25.5927	−	44.3279i	0.952462	−	1.64971i
$723$		0			0
$724$	6.64526	−	11.5099i	0.246969	−	0.427763i
$725$	0.384982	−	0.666809i	0.0142979	−	0.0247647i
$726$		0			0
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	0.113378	+	0.993552i	$0.463833\pi$
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	−0.917130	+	0.398587i	$0.869501\pi$
$728$	−42.1421	−	19.6574i	−1.56189	−	0.728553i
$729$		0			0
$730$	19.4493	−	33.6871i	0.719849	−	1.24682i
$731$	13.7605			0.508949
$732$		0			0
$733$	−18.3671			−0.678406			−0.339203	−	0.940713i	$-0.610157\pi$
$733$	−18.3671			−0.678406			−0.339203	+	0.940713i	$0.610157\pi$
$734$	−43.7536	−	75.7835i	−1.61498	−	2.79722i
$735$		0			0
$736$	56.5861	−	98.0100i	2.08579	−	3.61270i
$737$	−19.7944	+	34.2849i	−0.729135	+	1.26290i
$738$		0			0
$739$	−15.5586	−	26.9484i	−0.572334	−	0.991312i	−0.996326	−	0.0856457i	$-0.972705\pi$
$739$	−15.5586	−	26.9484i	−0.572334	−	0.991312i	0.423992	−	0.905666i	$-0.360629\pi$
$740$	18.4849	+	32.0168i	0.679519	+	1.17696i
$741$		0			0
$742$	−6.84322	−	78.3281i	−0.251222	−	2.87552i
$743$	2.83876	+	4.91687i	0.104144	+	0.180382i	0.913388	−	0.407090i	$-0.133456\pi$
$743$	2.83876	+	4.91687i	0.104144	+	0.180382i	−0.809244	+	0.587472i	$0.800123\pi$
$744$		0			0
$745$	16.2101			0.593892
$746$	−10.9518	−	18.9690i	−0.400973	−	0.694506i
$747$		0			0
$748$	92.6467			3.38750
$749$	0.161575	+	1.84940i	0.00590382	+	0.0675757i
$750$		0			0
$751$	19.6756			0.717972			0.358986	−	0.933343i	$-0.383123\pi$
$751$	19.6756			0.717972			0.358986	+	0.933343i	$0.383123\pi$
$752$	−37.7361	+	65.3609i	−1.37609	+	2.38347i
$753$		0			0
$754$	−2.06462	−	3.57603i	−0.0751891	−	0.130231i
$755$	19.1653			0.697498
$756$		0			0
$757$	−15.9595			−0.580056			−0.290028	−	0.957018i	$-0.593665\pi$
$757$	−15.9595			−0.580056			−0.290028	+	0.957018i	$0.593665\pi$
$758$	−30.1577	−	52.2346i	−1.09538	−	1.89725i
$759$		0			0
$760$	−0.711479	+	1.23232i	−0.0258081	+	0.0447009i
$761$	11.0211			0.399515			0.199757	−	0.979845i	$-0.435985\pi$
$761$	11.0211			0.399515			0.199757	+	0.979845i	$0.435985\pi$
$762$		0			0
$763$	30.4153	+	14.1874i	1.10111	+	0.513619i
$764$	49.6672			1.79689
$765$		0			0
$766$	2.60377	+	4.50985i	0.0940779	+	0.162948i
$767$	−6.69084			−0.241592
$768$		0			0
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	−0.976560	−	0.215245i	$-0.930945\pi$
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	0.301873	−	0.953348i	$-0.402388\pi$
$770$	−25.3791	−	11.8382i	−0.914600	−	0.426620i
$771$		0			0
$772$	−19.9347	−	34.5278i	−0.717464	−	1.24268i
$773$	−3.56136	−	6.16845i	−0.128093	−	0.221864i	0.794845	−	0.606813i	$-0.207552\pi$
$773$	−3.56136	−	6.16845i	−0.128093	−	0.221864i	−0.922938	+	0.384949i	$0.874219\pi$
$774$		0			0
$775$	4.01507	−	6.95430i	0.144225	−	0.249806i
$776$	57.6341	−	99.8252i	2.06894	−	3.58352i
$777$		0			0
$778$	41.7999	+	72.3995i	1.49860	+	2.59565i
$779$	−0.457445			−0.0163897
$780$		0			0
$781$	−26.6119			−0.952249
$782$	37.5605	−	65.0567i	1.34316	−	2.32642i
$783$		0			0
$784$	−91.6572	+	16.1386i	−3.27347	+	0.576380i
$785$	−3.60535	+	6.24465i	−0.128680	+	0.222881i
$786$		0			0
$787$	4.57800	−	7.92933i	0.163188	−	0.282650i	−0.772822	−	0.634622i	$-0.781156\pi$
$787$	4.57800	−	7.92933i	0.163188	−	0.282650i	0.936010	+	0.351973i	$0.114489\pi$
$788$	55.8222	−	96.6870i	1.98859	−	3.44433i
$789$		0			0
$790$	15.2664	−	26.4421i	0.543153	−	0.940768i
$791$	15.7290	+	7.33690i	0.559260	+	0.260870i
$792$		0			0
$793$	−6.85491	+	11.8731i	−0.243425	+	0.421625i
$794$	−45.6717			−1.62083
$795$		0			0
$796$	0.827204			0.0293195
$797$	21.7602	+	37.6897i	0.770785	+	1.33504i	0.937133	+	0.348972i	$0.113469\pi$
$797$	21.7602	+	37.6897i	0.770785	+	1.33504i	−0.166348	+	0.986067i	$0.553198\pi$
$798$		0			0
$799$	−12.6995	+	21.9961i	−0.449275	+	0.778168i
$800$	−9.09202	+	15.7478i	−0.321452	+	0.556770i
$801$		0			0
$802$	−22.7065	−	39.3288i	−0.801795	−	1.38875i
$803$	−28.2884	−	48.9970i	−0.998277	−	1.72907i
$804$		0			0
$805$	−13.4896	+	9.44309i	−0.475447	+	0.332825i
$806$	−21.5324	−	37.2952i	−0.758447	−	1.31367i
$807$		0			0
$808$	17.0608			0.600197
$809$	−17.9148	−	31.0293i	−0.629850	−	1.09093i	−0.987581	−	0.157108i	$-0.949783\pi$
$809$	−17.9148	−	31.0293i	−0.629850	−	1.09093i	0.357731	−	0.933825i	$-0.383550\pi$
$810$		0			0
$811$	21.5972			0.758379			0.379190	−	0.925319i	$-0.376203\pi$
$811$	21.5972			0.758379			0.379190	+	0.925319i	$0.376203\pi$
$812$	−9.74278	−	4.54457i	−0.341904	−	0.159483i
$813$		0			0
$814$	74.1501			2.59896
$815$	−4.40268	+	7.62567i	−0.154219	+	0.267115i
$816$		0			0
$817$	0.247495	+	0.428674i	0.00865875	+	0.0149974i
$818$	−32.1511			−1.12414
$819$		0			0
$820$	−14.9989			−0.523786
$821$	−12.7736	−	22.1246i	−0.445803	−	0.772154i	0.552304	−	0.833643i	$-0.313749\pi$
$821$	−12.7736	−	22.1246i	−0.445803	−	0.772154i	−0.998108	+	0.0614883i	$0.980415\pi$
$822$		0			0
$823$	−20.4120	+	35.3546i	−0.711518	+	1.23239i	0.252769	+	0.967527i	$0.418659\pi$
$823$	−20.4120	+	35.3546i	−0.711518	+	1.23239i	−0.964287	+	0.264859i	$0.914675\pi$
$824$	13.6556			0.475715
$825$		0			0
$826$	−19.6789	+	13.7758i	−0.684718	+	0.479320i
$827$	2.26313			0.0786968			0.0393484	−	0.999226i	$-0.487472\pi$
$827$	2.26313			0.0786968			0.0393484	+	0.999226i	$0.487472\pi$
$828$		0			0
$829$	−0.766415	−	1.32747i	−0.0266187	−	0.0461049i	0.852409	−	0.522875i	$-0.175141\pi$
$829$	−0.766415	−	1.32747i	−0.0266187	−	0.0461049i	−0.879028	+	0.476770i	$0.841807\pi$
$830$	12.9972			0.451138
$831$		0			0
$832$	22.3287	+	38.6744i	0.774107	+	1.34079i
$833$	−30.8457	+	5.43120i	−1.06874	+	0.188180i
$834$		0			0
$835$	0.470408	+	0.814771i	0.0162791	+	0.0281963i
$836$	1.66634	+	2.88618i	0.0576315	+	0.0998208i
$837$		0			0
$838$	−15.7480	+	27.2763i	−0.544006	+	0.942245i
$839$	10.1354	−	17.5550i	0.349911	−	0.606064i	−0.636322	−	0.771424i	$-0.719545\pi$
$839$	10.1354	−	17.5550i	0.349911	−	0.606064i	0.986233	+	0.165359i	$0.0528783\pi$
$840$		0			0
$841$	14.2036	+	24.6013i	0.489779	+	0.848321i
$842$	11.2742			0.388534
$843$		0			0
$844$	−23.2649			−0.800811
$845$	−4.52394	+	7.83570i	−0.155628	+	0.269556i
$846$		0			0
$847$	−9.52616	+	6.66856i	−0.327323	+	0.229135i
$848$	−73.2324	+	126.842i	−2.51481	+	4.35578i
$849$		0			0
$850$	−6.03507	+	10.4530i	−0.207001	+	0.358537i
$851$	21.7999	−	37.7585i	0.747291	−	1.29435i
$852$		0			0
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	−0.242070	−	0.970259i	$-0.577826\pi$
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	0.961304	−	0.275490i	$-0.0888402\pi$
$854$	4.28394	+	49.0343i	0.146593	+	1.67792i
$855$		0			0
$856$	3.10174	−	5.37237i	0.106015	−	0.183624i
$857$	−51.5059			−1.75941			−0.879703	−	0.475523i	$-0.842259\pi$
$857$	−51.5059			−1.75941			−0.879703	+	0.475523i	$0.842259\pi$
$858$		0			0
$859$	−20.9322			−0.714198			−0.357099	−	0.934067i	$-0.616234\pi$
$859$	−20.9322			−0.714198			−0.357099	+	0.934067i	$0.616234\pi$
$860$	8.11498	+	14.0556i	0.276719	+	0.479291i
$861$		0			0
$862$	12.1023	−	20.9618i	0.412207	−	0.713963i
$863$	2.54430	−	4.40686i	0.0866090	−	0.150011i	−0.819467	−	0.573127i	$-0.805730\pi$
$863$	2.54430	−	4.40686i	0.0866090	−	0.150011i	0.906076	+	0.423116i	$0.139064\pi$
$864$		0			0
$865$	4.76243	+	8.24877i	0.161927	+	0.280467i
$866$	−12.3886	−	21.4577i	−0.420982	−	0.729162i
$867$		0			0
$868$	−101.610	−	47.3964i	−3.44886	−	1.60874i
$869$	−22.2045	−	38.4594i	−0.753237	−	1.30464i
$870$		0			0
$871$	−20.0584			−0.679652
$872$	−56.0743	−	97.1236i	−1.89892	−	3.28902i
$873$		0			0
$874$	2.70224			0.0914048
$875$	2.16746	−	1.51728i	0.0732734	−	0.0512933i
$876$		0			0
$877$	5.75163			0.194219			0.0971094	−	0.995274i	$-0.469040\pi$
$877$	5.75163			0.194219			0.0971094	+	0.995274i	$0.469040\pi$
$878$	−43.3904	+	75.1545i	−1.46436	+	2.53634i
$879$		0			0
$880$	26.0831	+	45.1773i	0.879262	+	1.52293i
$881$	−38.0306			−1.28129			−0.640643	−	0.767839i	$-0.721332\pi$
$881$	−38.0306			−1.28129			−0.640643	+	0.767839i	$0.721332\pi$
$882$		0			0
$883$	−43.8909			−1.47705			−0.738523	−	0.674228i	$-0.764476\pi$
$883$	−43.8909			−1.47705			−0.738523	+	0.674228i	$0.764476\pi$
$884$	23.4706	+	40.6522i	0.789401	+	1.36728i
$885$		0			0
$886$	31.1270	−	53.9135i	1.04573	−	1.81126i
$887$	−3.66354			−0.123010			−0.0615049	−	0.998107i	$-0.519590\pi$
$887$	−3.66354			−0.123010			−0.0615049	+	0.998107i	$0.519590\pi$
$888$		0			0
$889$	−13.6294	+	9.54096i	−0.457117	+	0.319994i
$890$	−27.8407			−0.933223
$891$		0			0
$892$	−15.4726	−	26.7993i	−0.518061	−	0.897307i
$893$	−0.913649			−0.0305741
$894$		0			0
$895$	11.9714	+	20.7351i	0.400160	+	0.693097i
$896$	58.0984	+	27.1003i	1.94093	+	0.905358i
$897$		0			0
$898$	34.6782	+	60.0644i	1.15723	+	2.00438i
$899$	−3.09146	−	5.35457i	−0.103106	−	0.178585i
$900$		0			0
$901$	−24.6452	+	42.6867i	−0.821050	+	1.42210i
$902$	−15.0416	+	26.0529i	−0.500832	+	0.867466i
$903$		0			0
$904$	−28.9984	−	50.2267i	−0.964472	−	1.67051i
$905$	2.51843			0.0837154
$906$		0			0
$907$	34.9389			1.16013			0.580063	−	0.814571i	$-0.303028\pi$
$907$	34.9389			1.16013			0.580063	+	0.814571i	$0.303028\pi$
$908$	−30.8179	+	53.3782i	−1.02273	+	1.77142i
$909$		0			0
$910$	−1.23492	−	14.1351i	−0.0409373	−	0.468573i
$911$	5.69235	−	9.85944i	0.188596	−	0.326658i	−0.756186	−	0.654356i	$-0.772940\pi$
$911$	5.69235	−	9.85944i	0.188596	−	0.326658i	0.944782	+	0.327699i	$0.106273\pi$
$912$		0			0
$913$	9.45202	−	16.3714i	0.312816	−	0.541814i
$914$	−23.6481	+	40.9597i	−0.782209	+	1.35483i
$915$		0			0
$916$	44.8646	−	77.7077i	1.48237	−	2.56754i
$917$	−20.9536	+	14.6681i	−0.691950	+	0.484383i
$918$		0			0
$919$	−17.6042	+	30.4913i	−0.580708	+	1.00582i	0.414688	+	0.909964i	$0.363891\pi$
$919$	−17.6042	+	30.4913i	−0.580708	+	1.00582i	−0.995396	+	0.0958515i	$0.969443\pi$
$920$	55.0238			1.81408
$921$		0			0
$922$	74.2328			2.44473
$923$	−6.74170	−	11.6770i	−0.221906	−	0.384352i
$924$		0			0
$925$	−3.50272	+	6.06689i	−0.115169	+	0.199478i
$926$	26.7966	−	46.4131i	0.880591	−	1.52523i
$927$		0			0
$928$	7.00054	+	12.1253i	0.229804	+	0.398032i
$929$	20.6589	+	35.7823i	0.677797	+	1.17398i	0.975643	+	0.219365i	$0.0703986\pi$
$929$	20.6589	+	35.7823i	0.677797	+	1.17398i	−0.297846	+	0.954614i	$0.596268\pi$
$930$		0			0
$931$	−0.723986	−	0.863239i	−0.0237277	−	0.0282915i
$932$	−1.85335	−	3.21010i	−0.0607086	−	0.105150i
$933$		0			0
$934$	−68.9190			−2.25510
$935$	8.77785	+	15.2037i	0.287066	+	0.497214i
$936$		0			0
$937$	−37.0566			−1.21059			−0.605293	−	0.796003i	$-0.706944\pi$
$937$	−37.0566			−1.21059			−0.605293	+	0.796003i	$0.706944\pi$
$938$	−58.9952	+	41.2982i	−1.92626	+	1.34843i
$939$		0			0
$940$	−29.9572			−0.977095
$941$	15.0482	−	26.0642i	0.490556	−	0.849668i	−0.509385	−	0.860539i	$-0.670127\pi$
$941$	15.0482	−	26.0642i	0.490556	−	0.849668i	0.999941	+	0.0108709i	$0.00346037\pi$
$942$		0			0
$943$	8.84439	+	15.3189i	0.288013	+	0.498853i
$944$	44.7470			1.45639
$945$		0			0
$946$	32.5523			1.05837
$947$	29.2879	+	50.7282i	0.951730	+	1.64844i	0.741681	+	0.670753i	$0.234029\pi$
$947$	29.2879	+	50.7282i	0.951730	+	1.64844i	0.210049	+	0.977691i	$0.432638\pi$
$948$		0			0
$949$	14.3328	−	24.8252i	0.465264	−	0.805860i
$950$	−0.434186			−0.0140868
$951$		0			0
$952$	94.8481	+	44.2425i	3.07405	+	1.43391i
$953$	−33.7935			−1.09468			−0.547340	−	0.836910i	$-0.684359\pi$
$953$	−33.7935			−1.09468			−0.547340	+	0.836910i	$0.684359\pi$
$954$		0			0
$955$	4.70573	+	8.15057i	0.152274	+	0.263746i
$956$	−14.5262			−0.469810
$957$		0			0
$958$	−0.256587	−	0.444422i	−0.00828996	−	0.0143586i
$959$	−7.13450	+	4.99434i	−0.230385	+	0.161276i
$960$		0			0
$961$	−16.7415	−	28.9972i	−0.540050	−	0.935393i
$962$	18.7847	+	32.5361i	0.605644	+	1.04901i
$963$		0			0
$964$	−40.1945	+	69.6190i	−1.29458	+	2.24228i
$965$	3.77743	−	6.54271i	0.121600	−	0.210617i
$966$		0			0
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	0.911772	−	0.410697i	$-0.134715\pi$
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	−0.811560	+	0.584269i	$0.801381\pi$
$968$	38.8570			1.24891
$969$		0			0
$970$	35.1717			1.12929
$971$	−14.8809	+	25.7744i	−0.477550	+	0.827141i	−0.999669	−	0.0257316i	$-0.991808\pi$
$971$	−14.8809	+	25.7744i	−0.477550	+	0.827141i	0.522119	+	0.852873i	$0.325142\pi$
$972$		0			0
$973$	−26.4134	−	12.3207i	−0.846773	−	0.394982i
$974$	7.16455	−	12.4094i	0.229567	−	0.397621i
$975$		0			0
$976$	45.8443	−	79.4047i	1.46744	−	2.54168i
$977$	−18.6758	+	32.3475i	−0.597492	+	1.03489i	0.395697	+	0.918381i	$0.370503\pi$
$977$	−18.6758	+	32.3475i	−0.597492	+	1.03489i	−0.993190	+	0.116506i	$0.962830\pi$
$978$		0			0
$979$	−20.2468	+	35.0685i	−0.647091	+	1.12079i
$980$	−23.7384	−	28.3043i	−0.758295	−	0.904148i
$981$		0			0
$982$	27.3009	−	47.2866i	0.871208	−	1.50898i
$983$	17.8494			0.569307			0.284653	−	0.958631i	$-0.408122\pi$
$983$	17.8494			0.569307			0.284653	+	0.958631i	$0.408122\pi$
$984$		0			0
$985$	21.1556			0.674074
$986$	4.64679	+	8.04848i	0.147984	+	0.256316i
$987$		0			0
$988$	−0.844281	+	1.46234i	−0.0268602	+	0.0465231i
$989$	9.57028	−	16.5762i	0.304317	−	0.527093i
$990$		0			0
$991$	−13.4638	−	23.3199i	−0.427691	−	0.740782i	0.568977	−	0.822354i	$-0.307339\pi$
$991$	−13.4638	−	23.3199i	−0.427691	−	0.740782i	−0.996667	+	0.0815716i	$0.974006\pi$
$992$	73.0102	+	126.457i	2.31808	+	4.01502i
$993$		0			0
$994$	−43.8702	−	20.4635i	−1.39148	−	0.649064i
$995$	0.0783738	+	0.135747i	0.00248462	+	0.00430348i
$996$		0			0
$997$	−38.7198			−1.22627			−0.613135	−	0.789978i	$-0.710092\pi$
$997$	−38.7198			−1.22627			−0.613135	+	0.789978i	$0.710092\pi$
$998$	3.27760	+	5.67697i	0.103751	+	0.179701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.k.c.856.1		36
3.2	odd	2		315.2.k.c.16.18	✓	36
7.4	even	3		945.2.l.c.46.18		36
9.4	even	3		945.2.l.c.226.18		36
9.5	odd	6		315.2.l.c.121.1	yes	36
21.11	odd	6		315.2.l.c.151.1	yes	36
63.4	even	3	inner	945.2.k.c.361.1		36
63.32	odd	6		315.2.k.c.256.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.18	✓	36	3.2	odd	2
315.2.k.c.256.18	yes	36	63.32	odd	6
315.2.l.c.121.1	yes	36	9.5	odd	6
315.2.l.c.151.1	yes	36	21.11	odd	6
945.2.k.c.361.1		36	63.4	even	3	inner
945.2.k.c.856.1		36	1.1	even	1	trivial
945.2.l.c.46.18		36	7.4	even	3
945.2.l.c.226.18		36	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34882 - 2.33623i) q^{2} +(-2.63865 + 4.57028i) q^{4} -1.00000 q^{5} +(-2.16746 + 1.51728i) q^{7} +8.84100 q^{8} +(1.34882 + 2.33623i) q^{10} +3.92366 q^{11} +(0.993996 + 1.72165i) q^{13} +(6.46823 + 3.01714i) q^{14} +(-6.64765 - 11.5141i) q^{16} +(-2.23716 - 3.87488i) q^{17} +(0.0804749 - 0.139387i) q^{19} +(2.63865 - 4.57028i) q^{20} +(-5.29232 - 9.16657i) q^{22} -6.22371 q^{23} +1.00000 q^{25} +(2.68145 - 4.64441i) q^{26} +(-1.21521 - 13.9094i) q^{28} +(0.384982 - 0.666809i) q^{29} +(4.01507 - 6.95430i) q^{31} +(-9.09202 + 15.7478i) q^{32} +(-6.03507 + 10.4530i) q^{34} +(2.16746 - 1.51728i) q^{35} +(-3.50272 + 6.06689i) q^{37} -0.434186 q^{38} -8.84100 q^{40} +(-1.42108 - 2.46138i) q^{41} +(-1.53771 + 2.66340i) q^{43} +(-10.3532 + 17.9322i) q^{44} +(8.39468 + 14.5400i) q^{46} +(-2.83830 - 4.91609i) q^{47} +(2.39574 - 6.57727i) q^{49} +(-1.34882 - 2.33623i) q^{50} -10.4912 q^{52} +(-5.50814 - 9.54037i) q^{53} -3.92366 q^{55} +(-19.1625 + 13.4143i) q^{56} -2.07709 q^{58} +(-1.68281 + 2.91472i) q^{59} +(3.44816 + 5.97239i) q^{61} -21.6625 q^{62} +22.4635 q^{64} +(-0.993996 - 1.72165i) q^{65} +(-5.04488 + 8.73799i) q^{67} +23.6123 q^{68} +(-6.46823 - 3.01714i) q^{70} -6.78242 q^{71} +(-7.20971 - 12.4876i) q^{73} +18.8982 q^{74} +(0.424690 + 0.735585i) q^{76} +(-8.50436 + 5.95327i) q^{77} +(-5.65914 - 9.80192i) q^{79} +(6.64765 + 11.5141i) q^{80} +(-3.83357 + 6.63994i) q^{82} +(2.40898 - 4.17248i) q^{83} +(2.23716 + 3.87488i) q^{85} +8.29642 q^{86} +34.6891 q^{88} +(-5.16019 + 8.93770i) q^{89} +(-4.76667 - 2.22344i) q^{91} +(16.4222 - 28.4441i) q^{92} +(-7.65674 + 13.2619i) q^{94} +(-0.0804749 + 0.139387i) q^{95} +(6.51896 - 11.2912i) q^{97} +(-18.5974 + 3.27456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) \) 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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