LMFDB - Embedded newform 845.2.m.d.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$1.12824 - 0.651388i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.d.316.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12824 - 0.651388i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.151388 + 0.262211i) q^{4} -1.00000i q^{5} +(-1.12824 - 0.651388i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +(-0.651388 - 1.12824i) q^{10} +(4.85455 - 2.80278i) q^{11} +0.302776 q^{12} -1.30278 q^{14} +(-0.866025 + 0.500000i) q^{15} +(1.65139 + 2.86029i) q^{16} +(0.197224 - 0.341603i) q^{17} -2.60555i q^{18} +(-1.39045 - 0.802776i) q^{19} +(0.262211 + 0.151388i) q^{20} +1.00000i q^{21} +(3.65139 - 6.32439i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(2.59808 - 1.50000i) q^{24} -1.00000 q^{25} -5.00000 q^{27} +(0.262211 - 0.151388i) q^{28} +(-4.10555 - 7.11102i) q^{29} +(-0.651388 + 1.12824i) q^{30} -4.00000i q^{31} +(-1.46984 - 0.848612i) q^{32} +(-4.85455 - 2.80278i) q^{33} -0.513878i q^{34} +(-0.500000 + 0.866025i) q^{35} +(0.302776 + 0.524423i) q^{36} +(3.12250 - 1.80278i) q^{37} -2.09167 q^{38} +3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(0.651388 + 1.12824i) q^{42} +(2.10555 - 3.64692i) q^{43} +1.69722i q^{44} +(-1.73205 - 1.00000i) q^{45} +(-3.38471 - 1.95416i) q^{46} +5.21110i q^{47} +(1.65139 - 2.86029i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(-1.12824 + 0.651388i) q^{50} -0.394449 q^{51} +11.2111 q^{53} +(-5.64118 + 3.25694i) q^{54} +(-2.80278 - 4.85455i) q^{55} +(1.50000 - 2.59808i) q^{56} +1.60555i q^{57} +(-9.26407 - 5.34861i) q^{58} +(9.36750 + 5.40833i) q^{59} -0.302776i q^{60} +(0.500000 - 0.866025i) q^{61} +(-2.60555 - 4.51295i) q^{62} +(-1.73205 + 1.00000i) q^{63} -8.81665 q^{64} -7.30278 q^{66} +(-6.06218 + 3.50000i) q^{67} +(0.0597147 + 0.103429i) q^{68} +(-1.50000 + 2.59808i) q^{69} +1.30278i q^{70} +(14.5636 + 8.40833i) q^{71} +(5.19615 + 3.00000i) q^{72} +15.2111i q^{73} +(2.34861 - 4.06792i) q^{74} +(0.500000 + 0.866025i) q^{75} +(0.420994 - 0.243061i) q^{76} -5.60555 q^{77} -9.21110 q^{79} +(2.86029 - 1.65139i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.95416 - 3.38471i) q^{82} +5.21110i q^{83} +(-0.262211 - 0.151388i) q^{84} +(-0.341603 - 0.197224i) q^{85} -5.48612i q^{86} +(-4.10555 + 7.11102i) q^{87} +(8.40833 + 14.5636i) q^{88} +(-7.11102 + 4.10555i) q^{89} -2.60555 q^{90} +0.908327 q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.39445 + 5.87936i) q^{94} +(-0.802776 + 1.39045i) q^{95} +1.69722i q^{96} +(13.5148 + 7.80278i) q^{97} +(-6.76942 - 3.90833i) q^{98} -11.2111i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 6 q^{4} + 8 q^{9} + 2 q^{10} - 12 q^{12} + 4 q^{14} + 6 q^{16} + 16 q^{17} + 22 q^{22} - 12 q^{23} - 8 q^{25} - 40 q^{27} - 4 q^{29} + 2 q^{30} - 4 q^{35} - 12 q^{36} - 60 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 6 * q^4 + 8 * q^9 + 2 * q^10 - 12 * q^12 + 4 * q^14 + 6 * q^16 + 16 * q^17 + 22 * q^22 - 12 * q^23 - 8 * q^25 - 40 * q^27 - 4 * q^29 + 2 * q^30 - 4 * q^35 - 12 * q^36 - 60 * q^38 + 24 * q^40 - 2 * q^42 - 12 * q^43 + 6 * q^48 - 24 * q^49 - 32 * q^51 + 32 * q^53 - 8 * q^55 + 12 * q^56 + 4 * q^61 + 8 * q^62 + 16 * q^64 - 44 * q^66 - 50 * q^68 - 12 * q^69 + 26 * q^74 + 4 * q^75 - 16 * q^77 - 16 * q^79 - 4 * q^81 - 6 * q^82 - 4 * q^87 + 24 * q^88 + 8 * q^90 - 36 * q^92 + 56 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.12824	−	0.651388i	0.797784	−	0.460601i	−0.0449118	−	0.998991i	$-0.514301\pi$
$2$	1.12824	−	0.651388i	0.797784	−	0.460601i	0.842696	+	0.538390i	$0.180967\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.151388	+	0.262211i	−0.0756939	+	0.131106i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.12824	−	0.651388i	−0.460601	−	0.265928i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$			3.00000i			1.06066i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−0.651388	−	1.12824i	−0.205987	−	0.356780i
$11$	4.85455	−	2.80278i	1.46370	−	0.845069i	0.464522	−	0.885562i	$-0.346226\pi$
$11$	4.85455	−	2.80278i	1.46370	−	0.845069i	0.999180	+	0.0404929i	$0.0128928\pi$
$12$	0.302776			0.0874038
$13$		0			0
$13$		0			0
$14$	−1.30278			−0.348181
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	0.197224	−	0.341603i	0.0478339	−	0.0828508i	−0.841117	−	0.540853i	$-0.818102\pi$
$17$	0.197224	−	0.341603i	0.0478339	−	0.0828508i	0.888951	+	0.458002i	$0.151435\pi$
$18$		−	2.60555i		−	0.614134i
$19$	−1.39045	−	0.802776i	−0.318991	−	0.184169i	0.331952	−	0.943296i	$-0.392293\pi$
$19$	−1.39045	−	0.802776i	−0.318991	−	0.184169i	−0.650943	+	0.759127i	$0.725626\pi$
$20$	0.262211	+	0.151388i	0.0586323	+	0.0338513i
$21$			1.00000i			0.218218i
$22$	3.65139	−	6.32439i	0.778478	−	1.34836i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	2.59808	−	1.50000i	0.530330	−	0.306186i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	0.262211	−	0.151388i	0.0495533	−	0.0286096i
$29$	−4.10555	−	7.11102i	−0.762382	−	1.32048i	−0.941620	−	0.336678i	$-0.890697\pi$
$29$	−4.10555	−	7.11102i	−0.762382	−	1.32048i	0.179238	−	0.983806i	$-0.442637\pi$
$30$	−0.651388	+	1.12824i	−0.118927	+	0.205987i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	−1.46984	−	0.848612i	−0.259833	−	0.150015i
$33$	−4.85455	−	2.80278i	−0.845069	−	0.487901i
$34$		−	0.513878i		−	0.0881294i
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	0.302776	+	0.524423i	0.0504626	+	0.0874038i
$37$	3.12250	−	1.80278i	0.513336	−	0.296374i	−0.220868	−	0.975304i	$-0.570889\pi$
$37$	3.12250	−	1.80278i	0.513336	−	0.296374i	0.734204	+	0.678929i	$0.237556\pi$
$38$	−2.09167			−0.339314
$39$		0			0
$40$	3.00000			0.474342
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	0.651388	+	1.12824i	0.100511	+	0.174091i
$43$	2.10555	−	3.64692i	0.321094	−	0.556150i	−0.659620	−	0.751599i	$-0.729283\pi$
$43$	2.10555	−	3.64692i	0.321094	−	0.556150i	0.980714	+	0.195449i	$0.0626163\pi$
$44$			1.69722i			0.255866i
$45$	−1.73205	−	1.00000i	−0.258199	−	0.149071i
$46$	−3.38471	−	1.95416i	−0.499048	−	0.288126i
$47$			5.21110i			0.760117i	0.924962	+	0.380059i	$0.124096\pi$
$47$			5.21110i			0.760117i	−0.924962	+	0.380059i	$0.875904\pi$
$48$	1.65139	−	2.86029i	0.238357	−	0.412847i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$	−1.12824	+	0.651388i	−0.159557	+	0.0921201i
$51$	−0.394449			−0.0552339
$52$		0			0
$53$	11.2111			1.53996			0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111			1.53996			0.769982	+	0.638066i	$0.220265\pi$
$54$	−5.64118	+	3.25694i	−0.767668	+	0.443213i
$55$	−2.80278	−	4.85455i	−0.377926	−	0.654587i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$			1.60555i			0.212660i
$58$	−9.26407	−	5.34861i	−1.21643	−	0.702307i
$59$	9.36750	+	5.40833i	1.21954	+	0.704104i	0.964820	−	0.262910i	$-0.0846821\pi$
$59$	9.36750	+	5.40833i	1.21954	+	0.704104i	0.254724	+	0.967014i	$0.418015\pi$
$60$		−	0.302776i		−	0.0390882i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−2.60555	−	4.51295i	−0.330905	−	0.573145i
$63$	−1.73205	+	1.00000i	−0.218218	+	0.125988i
$64$	−8.81665			−1.10208
$65$		0			0
$66$	−7.30278			−0.898910
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	0.0597147	+	0.103429i	0.00724147	+	0.0125426i
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$			1.30278i			0.155711i
$71$	14.5636	+	8.40833i	1.72839	+	0.997885i	0.896697	+	0.442645i	$0.145960\pi$
$71$	14.5636	+	8.40833i	1.72839	+	0.997885i	0.831690	+	0.555240i	$0.187374\pi$
$72$	5.19615	+	3.00000i	0.612372	+	0.353553i
$73$			15.2111i			1.78032i	0.455643	+	0.890162i	$0.349409\pi$
$73$			15.2111i			1.78032i	−0.455643	+	0.890162i	$0.650591\pi$
$74$	2.34861	−	4.06792i	0.273021	−	0.472886i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	0.420994	−	0.243061i	0.0482913	−	0.0278810i
$77$	−5.60555			−0.638812
$78$		0			0
$79$	−9.21110			−1.03633			−0.518165	−	0.855281i	$-0.673385\pi$
$79$	−9.21110			−1.03633			−0.518165	+	0.855281i	$0.673385\pi$
$80$	2.86029	−	1.65139i	0.319790	−	0.184631i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.95416	−	3.38471i	0.215801	−	0.373779i
$83$			5.21110i			0.571993i	0.958231	+	0.285996i	$0.0923245\pi$
$83$			5.21110i			0.571993i	−0.958231	+	0.285996i	$0.907675\pi$
$84$	−0.262211	−	0.151388i	−0.0286096	−	0.0165178i
$85$	−0.341603	−	0.197224i	−0.0370520	−	0.0213920i
$86$		−	5.48612i		−	0.591584i
$87$	−4.10555	+	7.11102i	−0.440161	+	0.762382i
$88$	8.40833	+	14.5636i	0.896331	+	1.55249i
$89$	−7.11102	+	4.10555i	−0.753767	+	0.435188i	−0.827053	−	0.562123i	$-0.809985\pi$
$89$	−7.11102	+	4.10555i	−0.753767	+	0.435188i	0.0732864	+	0.997311i	$0.476651\pi$
$90$	−2.60555			−0.274649
$91$		0			0
$92$	0.908327			0.0946996
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	3.39445	+	5.87936i	0.350111	+	0.606409i
$95$	−0.802776	+	1.39045i	−0.0823630	+	0.142657i
$96$			1.69722i			0.173222i
$97$	13.5148	+	7.80278i	1.37222	+	0.792252i	0.991207	−	0.132318i	$-0.0422419\pi$
$97$	13.5148	+	7.80278i	1.37222	+	0.792252i	0.381013	+	0.924570i	$0.375575\pi$
$98$	−6.76942	−	3.90833i	−0.683815	−	0.394801i
$99$		−	11.2111i		−	1.12676i
$100$	0.151388	−	0.262211i	0.0151388	−	0.0262211i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−0.445032	+	0.256939i	−0.0440647	+	0.0254408i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$	12.6488	−	7.30278i	1.22856	−	0.709308i
$107$	4.10555	+	7.11102i	0.396899	+	0.687449i	0.993342	−	0.115207i	$-0.0367531\pi$
$107$	4.10555	+	7.11102i	0.396899	+	0.687449i	−0.596443	+	0.802656i	$0.703420\pi$
$108$	0.756939	−	1.31106i	0.0728365	−	0.126157i
$109$		−	4.78890i		−	0.458693i	−0.973345	−	0.229347i	$-0.926341\pi$
$109$		−	4.78890i		−	0.458693i	0.973345	−	0.229347i	$-0.0736589\pi$
$110$	−6.32439	−	3.65139i	−0.603007	−	0.348146i
$111$	−3.12250	−	1.80278i	−0.296374	−	0.171112i
$112$		−	3.30278i		−	0.312083i
$113$	−2.80278	+	4.85455i	−0.263663	+	0.456678i	−0.967212	−	0.253969i	$-0.918264\pi$
$113$	−2.80278	+	4.85455i	−0.263663	+	0.456678i	0.703550	+	0.710646i	$0.251597\pi$
$114$	1.04584	+	1.81144i	0.0979516	+	0.169657i
$115$	−2.59808	+	1.50000i	−0.242272	+	0.139876i
$116$	2.48612			0.230831
$117$		0			0
$118$	14.0917			1.29724
$119$	−0.341603	+	0.197224i	−0.0313147	+	0.0180795i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	10.2111	−	17.6861i	0.928282	−	1.60783i
$122$		−	1.30278i		−	0.117948i
$123$	−2.59808	−	1.50000i	−0.234261	−	0.135250i
$124$	1.04885	+	0.605551i	0.0941891	+	0.0543801i
$125$			1.00000i			0.0894427i
$126$	−1.30278	+	2.25647i	−0.116060	+	0.201023i
$127$	5.10555	+	8.84307i	0.453044	+	0.784696i	0.998573	−	0.0533960i	$-0.0170046\pi$
$127$	5.10555	+	8.84307i	0.453044	+	0.784696i	−0.545529	+	0.838092i	$0.683671\pi$
$128$	−7.00759	+	4.04584i	−0.619390	+	0.357605i
$129$	−4.21110			−0.370767
$130$		0			0
$131$	−6.78890			−0.593149			−0.296574	−	0.955010i	$-0.595844\pi$
$131$	−6.78890			−0.593149			−0.296574	+	0.955010i	$0.595844\pi$
$132$	1.46984	−	0.848612i	0.127933	−	0.0738622i
$133$	0.802776	+	1.39045i	0.0696095	+	0.120567i
$134$	−4.55971	+	7.89766i	−0.393899	+	0.682254i
$135$			5.00000i			0.430331i
$136$	1.02481	+	0.591673i	0.0878765	+	0.0507355i
$137$	4.85455	+	2.80278i	0.414752	+	0.239457i	0.692830	−	0.721101i	$-0.256364\pi$
$137$	4.85455	+	2.80278i	0.414752	+	0.239457i	−0.278077	+	0.960559i	$0.589697\pi$
$138$			3.90833i			0.332699i
$139$	−6.80278	+	11.7828i	−0.577004	+	0.999400i	0.418817	+	0.908071i	$0.362445\pi$
$139$	−6.80278	+	11.7828i	−0.577004	+	0.999400i	−0.995821	+	0.0913293i	$0.970888\pi$
$140$	−0.151388	−	0.262211i	−0.0127946	−	0.0221609i
$141$	4.51295	−	2.60555i	0.380059	−	0.219427i
$142$	21.9083			1.83851
$143$		0			0
$144$	6.60555			0.550463
$145$	−7.11102	+	4.10555i	−0.590538	+	0.340947i
$146$	9.90833	+	17.1617i	0.820019	+	1.42031i
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$			1.09167i			0.0897350i
$149$	−2.59808	−	1.50000i	−0.212843	−	0.122885i	0.389789	−	0.920904i	$-0.372548\pi$
$149$	−2.59808	−	1.50000i	−0.212843	−	0.122885i	−0.602632	+	0.798019i	$0.705881\pi$
$150$	1.12824	+	0.651388i	0.0921201	+	0.0531856i
$151$		−	13.2111i		−	1.07510i	−0.843231	−	0.537552i	$-0.819349\pi$
$151$		−	13.2111i		−	1.07510i	0.843231	−	0.537552i	$-0.180651\pi$
$152$	2.40833	−	4.17134i	0.195341	−	0.338341i
$153$	−0.394449	−	0.683205i	−0.0318893	−	0.0552339i
$154$	−6.32439	+	3.65139i	−0.509634	+	0.294237i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−3.21110			−0.256274			−0.128137	−	0.991756i	$-0.540900\pi$
$157$	−3.21110			−0.256274			−0.128137	+	0.991756i	$0.540900\pi$
$158$	−10.3923	+	6.00000i	−0.826767	+	0.477334i
$159$	−5.60555	−	9.70910i	−0.444549	−	0.769982i
$160$	−0.848612	+	1.46984i	−0.0670887	+	0.116201i
$161$			3.00000i			0.236433i
$162$	−1.12824	−	0.651388i	−0.0886427	−	0.0511779i
$163$	−15.7713	−	9.10555i	−1.23530	−	0.713202i	−0.267172	−	0.963649i	$-0.586089\pi$
$163$	−15.7713	−	9.10555i	−1.23530	−	0.713202i	−0.968130	+	0.250447i	$0.919422\pi$
$164$			0.908327i			0.0709284i
$165$	−2.80278	+	4.85455i	−0.218196	+	0.377926i
$166$	3.39445	+	5.87936i	0.263460	+	0.456327i
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	−0.770274	−	0.637713i	$-0.779881\pi$
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	0.167139	+	0.985933i	$0.446547\pi$
$168$	−3.00000			−0.231455
$169$		0			0
$170$	−0.513878			−0.0394127
$171$	−2.78090	+	1.60555i	−0.212660	+	0.122780i
$172$	0.637510	+	1.10420i	0.0486097	+	0.0841944i
$173$	−8.40833	+	14.5636i	−0.639273	+	1.10725i	0.346319	+	0.938117i	$0.387431\pi$
$173$	−8.40833	+	14.5636i	−0.639273	+	1.10725i	−0.985593	+	0.169137i	$0.945902\pi$
$174$			10.6972i			0.810954i
$175$	0.866025	+	0.500000i	0.0654654	+	0.0377964i
$176$	16.0335	+	9.25694i	1.20857	+	0.697768i
$177$		−	10.8167i		−	0.813029i
$178$	−5.34861	+	9.26407i	−0.400895	+	0.694371i
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	0.887290	−	0.461212i	$-0.152585\pi$
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	−0.843066	+	0.537810i	$0.819252\pi$
$180$	0.524423	−	0.302776i	0.0390882	−	0.0225676i
$181$	25.6333			1.90531			0.952654	−	0.304055i	$-0.0983408\pi$
$181$	25.6333			1.90531			0.952654	+	0.304055i	$0.0983408\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	7.79423	−	4.50000i	0.574598	−	0.331744i
$185$	−1.80278	−	3.12250i	−0.132543	−	0.229571i
$186$	−2.60555	+	4.51295i	−0.191048	+	0.330905i
$187$		−	2.21110i		−	0.161692i
$188$	−1.36641	−	0.788897i	−0.0996557	−	0.0575363i
$189$	4.33013	+	2.50000i	0.314970	+	0.181848i
$190$			2.09167i			0.151746i
$191$	2.40833	−	4.17134i	0.174260	−	0.301828i	−0.765645	−	0.643264i	$-0.777580\pi$
$191$	2.40833	−	4.17134i	0.174260	−	0.301828i	0.939905	+	0.341436i	$0.110913\pi$
$192$	4.40833	+	7.63545i	0.318144	+	0.551041i
$193$	−7.26981	+	4.19722i	−0.523292	+	0.302123i	−0.738281	−	0.674494i	$-0.764362\pi$
$193$	−7.26981	+	4.19722i	−0.523292	+	0.302123i	0.214988	+	0.976617i	$0.431029\pi$
$194$	20.3305			1.45965
$195$		0			0
$196$	1.81665			0.129761
$197$	19.7598	−	11.4083i	1.40783	−	0.812810i	0.412649	−	0.910890i	$-0.364604\pi$
$197$	19.7598	−	11.4083i	1.40783	−	0.812810i	0.995178	+	0.0980804i	$0.0312702\pi$
$198$	−7.30278	−	12.6488i	−0.518986	−	0.898910i
$199$	−4.40833	+	7.63545i	−0.312498	+	0.541262i	−0.978902	−	0.204328i	$-0.934499\pi$
$199$	−4.40833	+	7.63545i	−0.312498	+	0.541262i	0.666404	+	0.745590i	$0.267832\pi$
$200$		−	3.00000i		−	0.212132i
$201$	6.06218	+	3.50000i	0.427593	+	0.246871i
$202$	−10.1541	−	5.86249i	−0.714442	−	0.412483i
$203$			8.21110i			0.576306i
$204$	0.0597147	−	0.103429i	0.00418087	−	0.00724147i
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$	4.51295	−	2.60555i	0.314432	−	0.181537i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$	1.12824	−	0.651388i	0.0778557	−	0.0449500i
$211$	8.19722	+	14.1980i	0.564320	+	0.977431i	0.997113	+	0.0759376i	$0.0241950\pi$
$211$	8.19722	+	14.1980i	0.564320	+	0.977431i	−0.432792	+	0.901494i	$0.642472\pi$
$212$	−1.69722	+	2.93968i	−0.116566	+	0.201898i
$213$		−	16.8167i		−	1.15226i
$214$	9.26407	+	5.34861i	0.633279	+	0.365624i
$215$	−3.64692	−	2.10555i	−0.248718	−	0.143597i
$216$		−	15.0000i		−	1.02062i
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	−3.11943	−	5.40301i	−0.211274	−	0.365938i
$219$	13.1732	−	7.60555i	0.890162	−	0.513936i
$220$	1.69722			0.114427
$221$		0			0
$222$	−4.69722			−0.315257
$223$	8.84307	−	5.10555i	0.592176	−	0.341893i	−0.173781	−	0.984784i	$-0.555599\pi$
$223$	8.84307	−	5.10555i	0.592176	−	0.341893i	0.765957	+	0.642891i	$0.222265\pi$
$224$	0.848612	+	1.46984i	0.0567003	+	0.0982078i
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$			7.30278i			0.485773i
$227$	−1.23167	−	0.711103i	−0.0817485	−	0.0471975i	0.458569	−	0.888659i	$-0.348362\pi$
$227$	−1.23167	−	0.711103i	−0.0817485	−	0.0471975i	−0.540317	+	0.841462i	$0.681696\pi$
$228$	−0.420994	−	0.243061i	−0.0278810	−	0.0160971i
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$	−1.95416	+	3.38471i	−0.128854	+	0.223181i
$231$	2.80278	+	4.85455i	0.184409	+	0.319406i
$232$	21.3331	−	12.3167i	1.40058	−	0.808628i
$233$	−0.788897			−0.0516824			−0.0258412	−	0.999666i	$-0.508226\pi$
$233$	−0.788897			−0.0516824			−0.0258412	+	0.999666i	$0.508226\pi$
$234$		0			0
$235$	5.21110			0.339935
$236$	−2.83625	+	1.63751i	−0.184624	+	0.106593i
$237$	4.60555	+	7.97705i	0.299163	+	0.518165i
$238$	−0.256939	+	0.445032i	−0.0166549	+	0.0288471i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−2.86029	−	1.65139i	−0.184631	−	0.106597i
$241$	14.0392	+	8.10555i	0.904346	+	0.522124i	0.878608	−	0.477544i	$-0.158473\pi$
$241$	14.0392	+	8.10555i	0.904346	+	0.522124i	0.0257384	+	0.999669i	$0.491806\pi$
$242$		−	26.6056i		−	1.71027i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	0.151388	+	0.262211i	0.00969161	+	0.0167864i
$245$	−5.19615	+	3.00000i	−0.331970	+	0.191663i
$246$	−3.90833			−0.249186
$247$		0			0
$248$	12.0000			0.762001
$249$	4.51295	−	2.60555i	0.285996	−	0.165120i
$250$	0.651388	+	1.12824i	0.0411974	+	0.0713560i
$251$	−14.4083	+	24.9560i	−0.909446	+	1.57521i	−0.0946094	+	0.995514i	$0.530160\pi$
$251$	−14.4083	+	24.9560i	−0.909446	+	1.57521i	−0.814836	+	0.579691i	$0.803173\pi$
$252$		−	0.605551i		−	0.0381461i
$253$	−14.5636	−	8.40833i	−0.915609	−	0.528627i
$254$	11.5205	+	6.65139i	0.722863	+	0.417345i
$255$			0.394449i			0.0247013i
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	−11.8028	−	20.4430i	−0.736237	−	1.27520i	−0.954179	−	0.299238i	$-0.903268\pi$
$257$	−11.8028	−	20.4430i	−0.736237	−	1.27520i	0.217942	−	0.975962i	$-0.430066\pi$
$258$	−4.75112	+	2.74306i	−0.295792	+	0.170776i
$259$	−3.60555			−0.224038
$260$		0			0
$261$	−16.4222			−1.01651
$262$	−7.65948	+	4.42221i	−0.473204	+	0.273205i
$263$	−13.1056	−	22.6995i	−0.808123	−	1.39971i	−0.914162	−	0.405348i	$-0.867150\pi$
$263$	−13.1056	−	22.6995i	−0.808123	−	1.39971i	0.106040	−	0.994362i	$-0.466183\pi$
$264$	8.40833	−	14.5636i	0.517497	−	0.896331i
$265$		−	11.2111i		−	0.688693i
$266$	1.81144	+	1.04584i	0.111067	+	0.0641244i
$267$	7.11102	+	4.10555i	0.435188	+	0.251256i
$268$		−	2.11943i		−	0.129465i
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	3.25694	+	5.64118i	0.198211	+	0.343312i
$271$	−0.707243	+	0.408327i	−0.0429620	+	0.0248041i	−0.521327	−	0.853357i	$-0.674563\pi$
$271$	−0.707243	+	0.408327i	−0.0429620	+	0.0248041i	0.478365	+	0.878161i	$0.341230\pi$
$272$	1.30278			0.0789924
$273$		0			0
$274$	7.30278			0.441177
$275$	−4.85455	+	2.80278i	−0.292740	+	0.169014i
$276$	−0.454163	−	0.786634i	−0.0273374	−	0.0473498i
$277$	10.1972	−	17.6621i	0.612692	−	1.06121i	−0.378093	−	0.925768i	$-0.623420\pi$
$277$	10.1972	−	17.6621i	0.612692	−	1.06121i	0.990785	−	0.135446i	$-0.0432466\pi$
$278$			17.7250i			1.06307i
$279$	−6.92820	−	4.00000i	−0.414781	−	0.239474i
$280$	−2.59808	−	1.50000i	−0.155265	−	0.0896421i
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	3.39445	−	5.87936i	0.202136	−	0.350111i
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	0.930714	−	0.365748i	$-0.119187\pi$
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	−0.782104	+	0.623148i	$0.785854\pi$
$284$	−4.40952	+	2.54584i	−0.261657	+	0.151068i
$285$	1.60555			0.0951046
$286$		0			0
$287$	−3.00000			−0.177084
$288$	−2.93968	+	1.69722i	−0.173222	+	0.100010i
$289$	8.42221	+	14.5877i	0.495424	+	0.858099i
$290$	−5.34861	+	9.26407i	−0.314081	+	0.544005i
$291$		−	15.6056i		−	0.914814i
$292$	−3.98852	−	2.30278i	−0.233411	−	0.134760i
$293$	15.2469	+	8.80278i	0.890731	+	0.514264i	0.874181	−	0.485599i	$-0.161399\pi$
$293$	15.2469	+	8.80278i	0.890731	+	0.514264i	0.0165493	+	0.999863i	$0.494732\pi$
$294$			7.81665i			0.455877i
$295$	5.40833	−	9.36750i	0.314885	−	0.545397i
$296$	5.40833	+	9.36750i	0.314353	+	0.544475i
$297$	−24.2727	+	14.0139i	−1.40845	+	0.813168i
$298$	−3.90833			−0.226403
$299$		0			0
$300$	−0.302776			−0.0174808
$301$	−3.64692	+	2.10555i	−0.210205	+	0.121362i
$302$	−8.60555	−	14.9053i	−0.495194	−	0.857701i
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$		−	5.30278i		−	0.304135i
$305$	−0.866025	−	0.500000i	−0.0495885	−	0.0286299i
$306$	−0.890063	−	0.513878i	−0.0508815	−	0.0293765i
$307$			16.0000i			0.913168i	0.889680	+	0.456584i	$0.150927\pi$
$307$			16.0000i			0.913168i	−0.889680	+	0.456584i	$0.849073\pi$
$308$	0.848612	−	1.46984i	0.0483542	−	0.0837519i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$	−4.51295	+	2.60555i	−0.256318	+	0.147985i
$311$	−5.21110			−0.295495			−0.147747	−	0.989025i	$-0.547202\pi$
$311$	−5.21110			−0.295495			−0.147747	+	0.989025i	$0.547202\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−3.62288	+	2.09167i	−0.204451	+	0.118040i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	1.39445	−	2.41526i	0.0784439	−	0.135869i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−12.6488	−	7.30278i	−0.709308	−	0.409519i
$319$	−39.8612	−	23.0139i	−2.23180	−	1.28853i
$320$			8.81665i			0.492866i
$321$	4.10555	−	7.11102i	0.229150	−	0.396899i
$322$	1.95416	+	3.38471i	0.108901	+	0.188623i
$323$	−0.548461	+	0.316654i	−0.0305172	+	0.0176191i
$324$	0.302776			0.0168209
$325$		0			0
$326$	−23.7250			−1.31401
$327$	−4.14731	+	2.39445i	−0.229347	+	0.132413i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	2.60555	−	4.51295i	0.143649	−	0.248807i
$330$			7.30278i			0.402005i
$331$	22.5407	+	13.0139i	1.23895	+	0.715307i	0.968879	−	0.247533i	$-0.0796200\pi$
$331$	22.5407	+	13.0139i	1.23895	+	0.715307i	0.270069	+	0.962841i	$0.412953\pi$
$332$	−1.36641	−	0.788897i	−0.0749915	−	0.0432964i
$333$		−	7.21110i		−	0.395166i
$334$	−5.86249	+	10.1541i	−0.320781	+	0.555609i
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$	−2.86029	+	1.65139i	−0.156041	+	0.0900906i
$337$	−17.6333			−0.960547			−0.480274	−	0.877119i	$-0.659463\pi$
$337$	−17.6333			−0.960547			−0.480274	+	0.877119i	$0.659463\pi$
$338$		0			0
$339$	5.60555			0.304452
$340$	0.103429	−	0.0597147i	0.00560922	−	0.00323849i
$341$	−11.2111	−	19.4182i	−0.607115	−	1.05155i
$342$	−2.09167	+	3.62288i	−0.113105	+	0.195903i
$343$			13.0000i			0.701934i
$344$	10.9408	+	6.31665i	0.589887	+	0.340571i
$345$	2.59808	+	1.50000i	0.139876	+	0.0807573i
$346$			21.9083i			1.17780i
$347$	−10.1056	+	17.5033i	−0.542494	+	0.939628i	0.456266	+	0.889844i	$0.349187\pi$
$347$	−10.1056	+	17.5033i	−0.542494	+	0.939628i	−0.998760	+	0.0497842i	$0.984147\pi$
$348$	−1.24306	−	2.15304i	−0.0666351	−	0.115415i
$349$	15.7713	−	9.10555i	0.844217	−	0.487409i	−0.0144783	−	0.999895i	$-0.504609\pi$
$349$	15.7713	−	9.10555i	0.844217	−	0.487409i	0.858695	+	0.512486i	$0.171275\pi$
$350$	1.30278			0.0696363
$351$		0			0
$352$	−9.51388			−0.507091
$353$	−4.17134	+	2.40833i	−0.222018	+	0.128182i	−0.606884	−	0.794790i	$-0.707581\pi$
$353$	−4.17134	+	2.40833i	−0.222018	+	0.128182i	0.384866	+	0.922972i	$0.374248\pi$
$354$	−7.04584	−	12.2037i	−0.374482	−	0.648622i
$355$	8.40833	−	14.5636i	0.446268	−	0.772958i
$356$		−	2.48612i		−	0.131764i
$357$	0.341603	+	0.197224i	0.0180795	+	0.0104382i
$358$	1.33509	+	0.770817i	0.0705619	+	0.0407390i
$359$			10.4222i			0.550063i	0.961435	+	0.275031i	$0.0886883\pi$
$359$			10.4222i			0.550063i	−0.961435	+	0.275031i	$0.911312\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	−8.21110	−	14.2220i	−0.432163	−	0.748529i
$362$	28.9204	−	16.6972i	1.52002	−	0.877587i
$363$	−20.4222			−1.07189
$364$		0			0
$365$	15.2111			0.796185
$366$	−1.12824	+	0.651388i	−0.0589739	+	0.0340486i
$367$	8.71110	+	15.0881i	0.454716	+	0.787591i	0.998672	−	0.0515228i	$-0.0164075\pi$
$367$	8.71110	+	15.0881i	0.454716	+	0.787591i	−0.543956	+	0.839114i	$0.683074\pi$
$368$	4.95416	−	8.58086i	0.258254	−	0.447308i
$369$		−	6.00000i		−	0.312348i
$370$	−4.06792	−	2.34861i	−0.211481	−	0.122099i
$371$	−9.70910	−	5.60555i	−0.504071	−	0.291026i
$372$		−	1.21110i		−	0.0627927i
$373$	13.8028	−	23.9071i	0.714681	−	1.23786i	−0.248402	−	0.968657i	$-0.579905\pi$
$373$	13.8028	−	23.9071i	0.714681	−	1.23786i	0.963083	−	0.269206i	$-0.0867613\pi$
$374$	−1.44029	−	2.49465i	−0.0744754	−	0.128995i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$	−15.6333			−0.806226
$377$		0			0
$378$	6.51388			0.335038
$379$	2.07365	−	1.19722i	0.106516	−	0.0614973i	−0.445795	−	0.895135i	$-0.647079\pi$
$379$	2.07365	−	1.19722i	0.106516	−	0.0614973i	0.552312	+	0.833638i	$0.313746\pi$
$380$	−0.243061	−	0.420994i	−0.0124688	−	0.0215965i
$381$	5.10555	−	8.84307i	0.261565	−	0.453044i
$382$		−	6.27502i		−	0.321058i
$383$	−16.1369	−	9.31665i	−0.824558	−	0.476059i	0.0274277	−	0.999624i	$-0.491268\pi$
$383$	−16.1369	−	9.31665i	−0.824558	−	0.476059i	−0.851986	+	0.523565i	$0.824602\pi$
$384$	7.00759	+	4.04584i	0.357605	+	0.206463i
$385$			5.60555i			0.285685i
$386$	−5.46804	+	9.47093i	−0.278316	+	0.482057i
$387$	−4.21110	−	7.29384i	−0.214062	−	0.370767i
$388$	−4.09195	+	2.36249i	−0.207737	+	0.119937i
$389$	0.788897			0.0399987			0.0199993	−	0.999800i	$-0.493634\pi$
$389$	0.788897			0.0399987			0.0199993	+	0.999800i	$0.493634\pi$
$390$		0			0
$391$	−1.18335			−0.0598444
$392$	15.5885	−	9.00000i	0.787336	−	0.454569i
$393$	3.39445	+	5.87936i	0.171227	+	0.296574i
$394$	14.8625	−	25.7426i	0.748761	−	1.29689i
$395$			9.21110i			0.463461i
$396$	2.93968	+	1.69722i	0.147724	+	0.0852887i
$397$	−12.1484	−	7.01388i	−0.609710	−	0.352016i	0.163142	−	0.986603i	$-0.447837\pi$
$397$	−12.1484	−	7.01388i	−0.609710	−	0.352016i	−0.772852	+	0.634586i	$0.781171\pi$
$398$			11.4861i			0.575747i
$399$	0.802776	−	1.39045i	0.0401890	−	0.0696095i
$400$	−1.65139	−	2.86029i	−0.0825694	−	0.143014i
$401$	1.91487	−	1.10555i	0.0956241	−	0.0552086i	−0.451425	−	0.892309i	$-0.649084\pi$
$401$	1.91487	−	1.10555i	0.0956241	−	0.0552086i	0.547049	+	0.837100i	$0.315751\pi$
$402$	9.11943			0.454836
$403$		0			0
$404$	2.72498			0.135573
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	5.34861	+	9.26407i	0.265447	+	0.459768i
$407$	10.1056	−	17.5033i	0.500914	−	0.867608i
$408$		−	1.18335i		−	0.0585844i
$409$	5.37897	+	3.10555i	0.265973	+	0.153560i	0.627056	−	0.778974i	$-0.284260\pi$
$409$	5.37897	+	3.10555i	0.265973	+	0.153560i	−0.361083	+	0.932534i	$0.617593\pi$
$410$	−3.38471	−	1.95416i	−0.167159	−	0.0965093i
$411$		−	5.60555i		−	0.276501i
$412$	−0.605551	+	1.04885i	−0.0298334	+	0.0516729i
$413$	−5.40833	−	9.36750i	−0.266126	−	0.460944i
$414$	−6.76942	+	3.90833i	−0.332699	+	0.192084i
$415$	5.21110			0.255803
$416$		0			0
$417$	13.6056			0.666267
$418$	−10.1541	+	5.86249i	−0.496655	+	0.286744i
$419$	16.6194	+	28.7857i	0.811912	+	1.40627i	0.911524	+	0.411247i	$0.134907\pi$
$419$	16.6194	+	28.7857i	0.811912	+	1.40627i	−0.0996117	+	0.995026i	$0.531760\pi$
$420$	−0.151388	+	0.262211i	−0.00738697	+	0.0127946i
$421$			3.57779i			0.174371i	0.996192	+	0.0871855i	$0.0277873\pi$
$421$			3.57779i			0.174371i	−0.996192	+	0.0871855i	$0.972213\pi$
$422$	18.4968	+	10.6791i	0.900411	+	0.519853i
$423$	9.02589	+	5.21110i	0.438854	+	0.253372i
$424$			33.6333i			1.63338i
$425$	−0.197224	+	0.341603i	−0.00956679	+	0.0165702i
$426$	−10.9542	−	18.9732i	−0.530731	−	0.919253i
$427$	−0.866025	+	0.500000i	−0.0419099	+	0.0241967i
$428$	−2.48612			−0.120171
$429$		0			0
$430$	−5.48612			−0.264564
$431$	−18.3934	+	10.6194i	−0.885978	+	0.511520i	−0.872625	−	0.488391i	$-0.837584\pi$
$431$	−18.3934	+	10.6194i	−0.885978	+	0.511520i	−0.0133535	+	0.999911i	$0.504251\pi$
$432$	−8.25694	−	14.3014i	−0.397262	−	0.688078i
$433$	−1.80278	+	3.12250i	−0.0866359	+	0.150058i	−0.906087	−	0.423091i	$-0.860945\pi$
$433$	−1.80278	+	3.12250i	−0.0866359	+	0.150058i	0.819451	+	0.573149i	$0.194278\pi$
$434$			5.21110i			0.250141i
$435$	7.11102	+	4.10555i	0.340947	+	0.196846i
$436$	1.25570	+	0.724981i	0.0601373	+	0.0347203i
$437$			4.81665i			0.230412i
$438$	9.90833	−	17.1617i	0.473438	−	0.820019i
$439$	11.6194	+	20.1254i	0.554565	+	0.960535i	0.997937	+	0.0641973i	$0.0204487\pi$
$439$	11.6194	+	20.1254i	0.554565	+	0.960535i	−0.443372	+	0.896338i	$0.646218\pi$
$440$	14.5636	−	8.40833i	0.694295	−	0.400851i
$441$	−12.0000			−0.571429
$442$		0			0
$443$	−22.4222			−1.06531			−0.532656	−	0.846332i	$-0.678806\pi$
$443$	−22.4222			−1.06531			−0.532656	+	0.846332i	$0.678806\pi$
$444$	0.945417	−	0.545837i	0.0448675	−	0.0259043i
$445$	4.10555	+	7.11102i	0.194622	+	0.337095i
$446$	6.65139	−	11.5205i	0.314952	−	0.545513i
$447$			3.00000i			0.141895i
$448$	7.63545	+	4.40833i	0.360741	+	0.208274i
$449$	−10.9408	−	6.31665i	−0.516327	−	0.298101i	0.219104	−	0.975702i	$-0.429687\pi$
$449$	−10.9408	−	6.31665i	−0.516327	−	0.298101i	−0.735430	+	0.677600i	$0.763020\pi$
$450$			2.60555i			0.122827i
$451$	8.40833	−	14.5636i	0.395933	−	0.685775i
$452$	−0.848612	−	1.46984i	−0.0399154	−	0.0691354i
$453$	−11.4412	+	6.60555i	−0.537552	+	0.310356i
$454$	−1.85281			−0.0869569
$455$		0			0
$456$	−4.81665			−0.225560
$457$	−4.48891	+	2.59167i	−0.209982	+	0.121233i	−0.601303	−	0.799021i	$-0.705352\pi$
$457$	−4.48891	+	2.59167i	−0.209982	+	0.121233i	0.391321	+	0.920254i	$0.372018\pi$
$458$	−9.11943	−	15.7953i	−0.426123	−	0.738067i
$459$	−0.986122	+	1.70801i	−0.0460282	+	0.0797232i
$460$		−	0.908327i		−	0.0423510i
$461$	−18.8697	−	10.8944i	−0.878851	−	0.507405i	−0.00857184	−	0.999963i	$-0.502729\pi$
$461$	−18.8697	−	10.8944i	−0.878851	−	0.507405i	−0.870280	+	0.492558i	$0.836062\pi$
$462$	6.32439	+	3.65139i	0.294237	+	0.169878i
$463$			5.57779i			0.259222i	0.991565	+	0.129611i	$0.0413729\pi$
$463$			5.57779i			0.259222i	−0.991565	+	0.129611i	$0.958627\pi$
$464$	13.5597	−	23.4861i	0.629494	−	1.09032i
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$	−0.890063	+	0.513878i	−0.0412314	+	0.0238049i
$467$	−17.2111			−0.796435			−0.398217	−	0.917291i	$-0.630371\pi$
$467$	−17.2111			−0.796435			−0.398217	+	0.917291i	$0.630371\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	5.87936	−	3.39445i	0.271195	−	0.156574i
$471$	1.60555	+	2.78090i	0.0739799	+	0.128137i
$472$	−16.2250	+	28.1025i	−0.746815	+	1.29352i
$473$		−	23.6056i		−	1.08538i
$474$	10.3923	+	6.00000i	0.477334	+	0.275589i
$475$	1.39045	+	0.802776i	0.0637981	+	0.0368339i
$476$		−	0.119429i		−	0.00547404i
$477$	11.2111	−	19.4182i	0.513321	−	0.889098i
$478$		0			0
$479$	6.22096	−	3.59167i	0.284243	−	0.164108i	−0.351100	−	0.936338i	$-0.614192\pi$
$479$	6.22096	−	3.59167i	0.284243	−	0.164108i	0.635343	+	0.772230i	$0.280859\pi$
$480$	1.69722			0.0774673
$481$		0			0
$482$	21.1194			0.961964
$483$	2.59808	−	1.50000i	0.118217	−	0.0682524i
$484$	3.09167	+	5.35493i	0.140531	+	0.243406i
$485$	7.80278	−	13.5148i	0.354306	−	0.613676i
$486$			20.8444i			0.945522i
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	0.519493	−	0.854475i	$-0.326121\pi$
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	−0.480250	+	0.877132i	$0.659454\pi$
$488$	2.59808	+	1.50000i	0.117609	+	0.0679018i
$489$			18.2111i			0.823535i
$490$	−3.90833	+	6.76942i	−0.176560	+	0.305811i
$491$	2.40833	+	4.17134i	0.108686	+	0.188250i	0.915238	−	0.402913i	$-0.132002\pi$
$491$	2.40833	+	4.17134i	0.108686	+	0.188250i	−0.806552	+	0.591163i	$0.798669\pi$
$492$	0.786634	−	0.454163i	0.0354642	−	0.0204753i
$493$	−3.23886			−0.145871
$494$		0			0
$495$	−11.2111			−0.503902
$496$	11.4412	−	6.60555i	0.513723	−	0.296598i
$497$	−8.40833	−	14.5636i	−0.377165	−	0.653269i
$498$	3.39445	−	5.87936i	0.152109	−	0.263460i
$499$		−	26.4222i		−	1.18282i	−0.806371	−	0.591410i	$-0.798571\pi$
$499$		−	26.4222i		−	1.18282i	0.806371	−	0.591410i	$-0.201429\pi$
$500$	−0.262211	−	0.151388i	−0.0117265	−	0.00677027i
$501$	7.79423	+	4.50000i	0.348220	+	0.201045i
$502$			37.5416i			1.67557i
$503$	−1.50000	+	2.59808i	−0.0668817	+	0.115842i	−0.897527	−	0.440959i	$-0.854638\pi$
$503$	−1.50000	+	2.59808i	−0.0668817	+	0.115842i	0.830645	+	0.556802i	$0.187972\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	−7.79423	+	4.50000i	−0.346839	+	0.200247i
$506$	−21.9083			−0.973944
$507$		0			0
$508$	−3.09167			−0.137171
$509$	2.59808	−	1.50000i	0.115158	−	0.0664863i	−0.441315	−	0.897352i	$-0.645488\pi$
$509$	2.59808	−	1.50000i	0.115158	−	0.0664863i	0.556473	+	0.830866i	$0.312154\pi$
$510$	0.256939	+	0.445032i	0.0113775	+	0.0197063i
$511$	7.60555	−	13.1732i	0.336450	−	0.582748i
$512$		−	25.4222i		−	1.12351i
$513$	6.95224	+	4.01388i	0.306949	+	0.177217i
$514$	−26.6327	−	15.3764i	−1.17472	−	0.678223i
$515$		−	4.00000i		−	0.176261i
$516$	0.637510	−	1.10420i	0.0280648	−	0.0486097i
$517$	14.6056	+	25.2976i	0.642351	+	1.11259i
$518$	−4.06792	+	2.34861i	−0.178734	+	0.103192i
$519$	16.8167			0.738169
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−18.5281	+	10.6972i	−0.810954	+	0.468205i
$523$	−13.7111	−	23.7483i	−0.599545	−	1.03844i	−0.992888	−	0.119050i	$-0.962015\pi$
$523$	−13.7111	−	23.7483i	−0.599545	−	1.03844i	0.393344	−	0.919392i	$-0.371318\pi$
$524$	1.02776	−	1.78013i	0.0448977	−	0.0777652i
$525$		−	1.00000i		−	0.0436436i
$526$	−29.5723	−	17.0736i	−1.28941	−	0.744444i
$527$	−1.36641	−	0.788897i	−0.0595218	−	0.0343649i
$528$		−	18.5139i		−	0.805713i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−7.30278	−	12.6488i	−0.317212	−	0.549428i
$531$	18.7350	−	10.8167i	0.813029	−	0.469403i
$532$	−0.486122			−0.0210761
$533$		0			0
$534$	10.6972			0.462914
$535$	7.11102	−	4.10555i	0.307436	−	0.177498i
$536$	−10.5000	−	18.1865i	−0.453531	−	0.785539i
$537$	0.591673	−	1.02481i	0.0255326	−	0.0442237i
$538$		−	11.7250i		−	0.505500i
$539$	−29.1273	−	16.8167i	−1.25460	−	0.724345i
$540$	−1.31106	−	0.756939i	−0.0564189	−	0.0325735i
$541$		−	17.6333i		−	0.758115i	−0.925373	−	0.379058i	$-0.876248\pi$
$541$		−	17.6333i		−	0.758115i	0.925373	−	0.379058i	$-0.123752\pi$
$542$	−0.531958	+	0.921379i	−0.0228496	+	0.0395766i
$543$	−12.8167	−	22.1991i	−0.550015	−	0.952654i
$544$	−0.579776	+	0.334734i	−0.0248577	+	0.0143516i
$545$	−4.78890			−0.205134
$546$		0			0
$547$	−24.8444			−1.06227			−0.531135	−	0.847287i	$-0.678234\pi$
$547$	−24.8444			−1.06227			−0.531135	+	0.847287i	$0.678234\pi$
$548$	−1.46984	+	0.848612i	−0.0627884	+	0.0362509i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−3.65139	+	6.32439i	−0.155696	+	0.269673i
$551$			13.1833i			0.561629i
$552$	−7.79423	−	4.50000i	−0.331744	−	0.191533i
$553$	7.97705	+	4.60555i	0.339219	+	0.195848i
$554$		−	26.5694i		−	1.12883i
$555$	−1.80278	+	3.12250i	−0.0765236	+	0.132543i
$556$	−2.05971	−	3.56753i	−0.0873514	−	0.151297i
$557$	−4.85455	+	2.80278i	−0.205694	+	0.118757i	−0.599309	−	0.800518i	$-0.704558\pi$
$557$	−4.85455	+	2.80278i	−0.205694	+	0.118757i	0.393615	+	0.919276i	$0.371224\pi$
$558$	−10.4222			−0.441207
$559$		0			0
$560$	−3.30278			−0.139568
$561$	−1.91487	+	1.10555i	−0.0808459	+	0.0466764i
$562$	3.90833	+	6.76942i	0.164863	+	0.285551i
$563$	−9.71110	+	16.8201i	−0.409274	+	0.708884i	−0.994809	−	0.101764i	$-0.967551\pi$
$563$	−9.71110	+	16.8201i	−0.409274	+	0.708884i	0.585534	+	0.810648i	$0.300885\pi$
$564$			1.57779i			0.0664372i
$565$	4.85455	+	2.80278i	0.204232	+	0.117914i
$566$	5.64118	+	3.25694i	0.237117	+	0.136899i
$567$			1.00000i			0.0419961i
$568$	−25.2250	+	43.6909i	−1.05842	+	1.83323i
$569$	0.711103	+	1.23167i	0.0298110	+	0.0516341i	0.880546	−	0.473961i	$-0.157176\pi$
$569$	0.711103	+	1.23167i	0.0298110	+	0.0516341i	−0.850735	+	0.525595i	$0.823843\pi$
$570$	1.81144	−	1.04584i	0.0758730	−	0.0438053i
$571$	36.8444			1.54189			0.770945	−	0.636901i	$-0.219784\pi$
$571$	36.8444			1.54189			0.770945	+	0.636901i	$0.219784\pi$
$572$		0			0
$573$	−4.81665			−0.201219
$574$	−3.38471	+	1.95416i	−0.141275	+	0.0815652i
$575$	1.50000	+	2.59808i	0.0625543	+	0.108347i
$576$	−8.81665	+	15.2709i	−0.367361	+	0.636287i
$577$			29.6333i			1.23365i	0.787100	+	0.616825i	$0.211582\pi$
$577$			29.6333i			1.23365i	−0.787100	+	0.616825i	$0.788418\pi$
$578$	19.0045	+	10.9722i	0.790482	+	0.456385i
$579$	7.26981	+	4.19722i	0.302123	+	0.174431i
$580$		−	2.48612i		−	0.103231i
$581$	2.60555	−	4.51295i	0.108096	−	0.187229i
$582$	−10.1653	−	17.6068i	−0.421364	−	0.729824i
$583$	54.4249	−	31.4222i	2.25405	−	1.30137i
$584$	−45.6333			−1.88832
$585$		0			0
$586$	22.9361			0.947481
$587$	−3.96449	+	2.28890i	−0.163632	+	0.0944729i	−0.579580	−	0.814916i	$-0.696783\pi$
$587$	−3.96449	+	2.28890i	−0.163632	+	0.0944729i	0.415948	+	0.909389i	$0.363450\pi$
$588$	−0.908327	−	1.57327i	−0.0374588	−	0.0648805i
$589$	−3.21110	+	5.56179i	−0.132311	+	0.229170i
$590$		−	14.0917i		−	0.580145i
$591$	−19.7598	−	11.4083i	−0.812810	−	0.469276i
$592$	10.3129	+	5.95416i	0.423858	+	0.244715i
$593$		−	35.2111i		−	1.44595i	−0.690876	−	0.722973i	$-0.742775\pi$
$593$		−	35.2111i		−	1.44595i	0.690876	−	0.722973i	$-0.257225\pi$
$594$	−18.2569	+	31.6219i	−0.749091	+	1.29746i
$595$	0.197224	+	0.341603i	0.00808541	+	0.0140043i
$596$	0.786634	−	0.454163i	0.0322218	−	0.0186033i
$597$	8.81665			0.360842
$598$		0			0
$599$	−6.78890			−0.277387			−0.138693	−	0.990335i	$-0.544290\pi$
$599$	−6.78890			−0.277387			−0.138693	+	0.990335i	$0.544290\pi$
$600$	−2.59808	+	1.50000i	−0.106066	+	0.0612372i
$601$	−14.1056	−	24.4315i	−0.575377	−	0.996583i	−0.996001	−	0.0893475i	$-0.971522\pi$
$601$	−14.1056	−	24.4315i	−0.575377	−	0.996583i	0.420623	−	0.907235i	$-0.361811\pi$
$602$	−2.74306	+	4.75112i	−0.111799	+	0.193641i
$603$			14.0000i			0.570124i
$604$	3.46410	+	2.00000i	0.140952	+	0.0813788i
$605$	−17.6861	−	10.2111i	−0.719044	−	0.415140i
$606$			11.7250i			0.476295i
$607$	9.89445	−	17.1377i	0.401603	−	0.695597i	−0.592316	−	0.805706i	$-0.701786\pi$
$607$	9.89445	−	17.1377i	0.401603	−	0.695597i	0.993920	+	0.110108i	$0.0351197\pi$
$608$	1.36249	+	2.35990i	0.0552563	+	0.0957067i
$609$	7.11102	−	4.10555i	0.288153	−	0.166365i
$610$	−1.30278			−0.0527478
$611$		0			0
$612$	0.238859			0.00965530
$613$	1.39045	−	0.802776i	0.0561597	−	0.0324238i	−0.471657	−	0.881782i	$-0.656344\pi$
$613$	1.39045	−	0.802776i	0.0561597	−	0.0324238i	0.527817	+	0.849358i	$0.323011\pi$
$614$	10.4222	+	18.0518i	0.420606	+	0.728511i
$615$	−1.50000	+	2.59808i	−0.0604858	+	0.104765i
$616$		−	16.8167i		−	0.677562i
$617$	−22.9063	−	13.2250i	−0.922174	−	0.532418i	−0.0378463	−	0.999284i	$-0.512050\pi$
$617$	−22.9063	−	13.2250i	−0.922174	−	0.532418i	−0.884328	+	0.466866i	$0.845383\pi$
$618$	−4.51295	−	2.60555i	−0.181537	−	0.104811i
$619$			14.4222i			0.579677i	0.957076	+	0.289839i	$0.0936017\pi$
$619$			14.4222i			0.579677i	−0.957076	+	0.289839i	$0.906398\pi$
$620$	0.605551	−	1.04885i	0.0243195	−	0.0421227i
$621$	7.50000	+	12.9904i	0.300965	+	0.521286i
$622$	−5.87936	+	3.39445i	−0.235741	+	0.136105i
$623$	8.21110			0.328971
$624$		0			0
$625$	1.00000			0.0400000
$626$	15.7953	−	9.11943i	0.631308	−	0.364486i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	0.486122	−	0.841988i	0.0193984	−	0.0335990i
$629$		−	1.42221i		−	0.0567070i
$630$	2.25647	+	1.30278i	0.0899001	+	0.0519038i
$631$	0.0240377	+	0.0138782i	0.000956927	+	0.000552482i	0.500478	−	0.865749i	$-0.333157\pi$
$631$	0.0240377	+	0.0138782i	0.000956927	+	0.000552482i	−0.499521	+	0.866302i	$0.666491\pi$
$632$		−	27.6333i		−	1.09919i
$633$	8.19722	−	14.1980i	0.325810	−	0.564320i
$634$	3.90833	+	6.76942i	0.155219	+	0.268848i
$635$	8.84307	−	5.10555i	0.350927	−	0.202608i
$636$	3.39445			0.134599
$637$		0			0
$638$	−59.9638			−2.37399
$639$	29.1273	−	16.8167i	1.15226	−	0.665257i
$640$	4.04584	+	7.00759i	0.159926	+	0.276999i
$641$	−9.71110	+	16.8201i	−0.383565	+	0.664355i	−0.991569	−	0.129579i	$-0.958637\pi$
$641$	−9.71110	+	16.8201i	−0.383565	+	0.664355i	0.608004	+	0.793934i	$0.291971\pi$
$642$		−	10.6972i		−	0.422186i
$643$	35.1895	+	20.3167i	1.38774	+	0.801211i	0.993060	−	0.117609i	$-0.0375230\pi$
$643$	35.1895	+	20.3167i	1.38774	+	0.801211i	0.394678	+	0.918820i	$0.370856\pi$
$644$	−0.786634	−	0.454163i	−0.0309977	−	0.0178965i
$645$			4.21110i			0.165812i
$646$	−0.412529	+	0.714521i	−0.0162307	+	0.0281125i
$647$	5.28890	+	9.16064i	0.207928	+	0.360142i	0.951062	−	0.309001i	$-0.0999947\pi$
$647$	5.28890	+	9.16064i	0.207928	+	0.360142i	−0.743134	+	0.669143i	$0.766661\pi$
$648$	2.59808	−	1.50000i	0.102062	−	0.0589256i
$649$	60.6333			2.38007
$650$		0			0
$651$	4.00000			0.156772
$652$	4.77516	−	2.75694i	0.187010	−	0.107970i
$653$	14.4083	+	24.9560i	0.563841	+	0.976602i	0.997156	+	0.0753594i	$0.0240104\pi$
$653$	14.4083	+	24.9560i	0.563841	+	0.976602i	−0.433315	+	0.901243i	$0.642656\pi$
$654$	−3.11943	+	5.40301i	−0.121979	+	0.211274i
$655$			6.78890i			0.265264i
$656$	8.58086	+	4.95416i	0.335026	+	0.193428i
$657$	26.3464	+	15.2111i	1.02787	+	0.593442i
$658$		−	6.78890i		−	0.264659i
$659$	6.59167	−	11.4171i	0.256775	−	0.444748i	−0.708601	−	0.705609i	$-0.750673\pi$
$659$	6.59167	−	11.4171i	0.256775	−	0.444748i	0.965376	+	0.260862i	$0.0840067\pi$
$660$	−0.848612	−	1.46984i	−0.0330322	−	0.0572134i
$661$	−33.4574	+	19.3167i	−1.30134	+	0.751331i	−0.980634	−	0.195847i	$-0.937254\pi$
$661$	−33.4574	+	19.3167i	−1.30134	+	0.751331i	−0.320709	+	0.947178i	$0.603921\pi$
$662$	33.9083			1.31788
$663$		0			0
$664$	−15.6333			−0.606690
$665$	1.39045	−	0.802776i	0.0539193	−	0.0311303i
$666$	−4.69722	−	8.13583i	−0.182014	−	0.315257i
$667$	−12.3167	+	21.3331i	−0.476903	+	0.826020i
$668$		−	2.72498i		−	0.105433i
$669$	−8.84307	−	5.10555i	−0.341893	−	0.197392i
$670$	7.89766	+	4.55971i	0.305113	+	0.176157i
$671$		−	5.60555i		−	0.216400i
$672$	0.848612	−	1.46984i	0.0327359	−	0.0567003i
$673$	−5.19722	−	9.00186i	−0.200338	−	0.346996i	0.748299	−	0.663361i	$-0.230871\pi$
$673$	−5.19722	−	9.00186i	−0.200338	−	0.346996i	−0.948637	+	0.316365i	$0.897537\pi$
$674$	−19.8945	+	11.4861i	−0.766309	+	0.442429i
$675$	5.00000			0.192450
$676$		0			0
$677$	33.6333			1.29263			0.646317	−	0.763069i	$-0.276309\pi$
$677$	33.6333			1.29263			0.646317	+	0.763069i	$0.276309\pi$
$678$	6.32439	−	3.65139i	0.242887	−	0.140231i
$679$	−7.80278	−	13.5148i	−0.299443	−	0.518651i
$680$	0.591673	−	1.02481i	0.0226896	−	0.0392996i
$681$			1.42221i			0.0544990i
$682$	−25.2976	−	14.6056i	−0.968694	−	0.559275i
$683$	18.8697	+	10.8944i	0.722030	+	0.416864i	0.815500	−	0.578758i	$-0.196462\pi$
$683$	18.8697	+	10.8944i	0.722030	+	0.416864i	−0.0934691	+	0.995622i	$0.529796\pi$
$684$		−	0.972244i		−	0.0371747i
$685$	2.80278	−	4.85455i	0.107089	−	0.185483i
$686$	8.46804	+	14.6671i	0.323311	+	0.559992i
$687$	−12.1244	+	7.00000i	−0.462573	+	0.267067i
$688$	13.9083			0.530250
$689$		0			0
$690$	3.90833			0.148787
$691$	5.22019	−	3.01388i	0.198585	−	0.114653i	−0.397410	−	0.917641i	$-0.630091\pi$
$691$	5.22019	−	3.01388i	0.198585	−	0.114653i	0.595995	+	0.802988i	$0.296758\pi$
$692$	−2.54584	−	4.40952i	−0.0967782	−	0.167625i
$693$	−5.60555	+	9.70910i	−0.212937	+	0.368818i
$694$			26.3305i			0.999493i
$695$	11.7828	+	6.80278i	0.446945	+	0.258044i
$696$	−21.3331	−	12.3167i	−0.808628	−	0.466862i
$697$		−	1.18335i		−	0.0448224i
$698$	11.8625	−	20.5464i	0.449002	−	0.777694i
$699$	0.394449	+	0.683205i	0.0149194	+	0.0258412i
$700$	−0.262211	+	0.151388i	−0.00991066	+	0.00572192i
$701$	7.57779			0.286209			0.143105	−	0.989708i	$-0.454291\pi$
$701$	7.57779			0.286209			0.143105	+	0.989708i	$0.454291\pi$
$702$		0			0
$703$	−5.78890			−0.218332
$704$	−42.8009	+	24.7111i	−1.61312	+	0.931335i
$705$	−2.60555	−	4.51295i	−0.0981307	−	0.169967i
$706$	−3.13751	+	5.43433i	−0.118082	+	0.204524i
$707$			9.00000i			0.338480i
$708$	2.83625	+	1.63751i	0.106593	+	0.0615414i
$709$	37.9704	+	21.9222i	1.42601	+	0.823306i	0.996803	−	0.0799016i	$-0.0254606\pi$
$709$	37.9704	+	21.9222i	1.42601	+	0.823306i	0.429205	+	0.903207i	$0.358794\pi$
$710$		−	21.9083i		−	0.822205i
$711$	−9.21110	+	15.9541i	−0.345443	+	0.598325i
$712$	−12.3167	−	21.3331i	−0.461586	−	0.799491i
$713$	−10.3923	+	6.00000i	−0.389195	+	0.224702i
$714$	0.513878			0.0192314
$715$		0			0
$716$	−0.358288			−0.0133899
$717$		0			0
$718$	6.78890	+	11.7587i	0.253359	+	0.438831i
$719$	−9.19722	+	15.9301i	−0.342999	+	0.594091i	−0.984988	−	0.172622i	$-0.944776\pi$
$719$	−9.19722	+	15.9301i	−0.342999	+	0.594091i	0.641989	+	0.766713i	$0.278109\pi$
$720$		−	6.60555i		−	0.246174i
$721$	−3.46410	−	2.00000i	−0.129010	−	0.0744839i
$722$	−18.5281	−	10.6972i	−0.689546	−	0.398109i
$723$		−	16.2111i		−	0.602897i
$724$	−3.88057	+	6.72135i	−0.144220	+	0.249797i
$725$	4.10555	+	7.11102i	0.152476	+	0.264097i
$726$	−23.0411	+	13.3028i	−0.855135	+	0.493712i
$727$	−42.4222			−1.57335			−0.786676	−	0.617366i	$-0.788200\pi$
$727$	−42.4222			−1.57335			−0.786676	+	0.617366i	$0.788200\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	17.1617	−	9.90833i	0.635184	−	0.366724i
$731$	−0.830532	−	1.43852i	−0.0307183	−	0.0532057i
$732$	0.151388	−	0.262211i	0.00559545	−	0.00969161i
$733$			10.8444i			0.400547i	0.979740	+	0.200274i	$0.0641831\pi$
$733$			10.8444i			0.400547i	−0.979740	+	0.200274i	$0.935817\pi$
$734$	19.6564	+	11.3486i	0.725530	+	0.418885i
$735$	5.19615	+	3.00000i	0.191663	+	0.110657i
$736$			5.09167i			0.187682i
$737$	−19.6194	+	33.9818i	−0.722691	+	1.25174i
$738$	−3.90833	−	6.76942i	−0.143868	−	0.249186i
$739$	24.5903	−	14.1972i	0.904569	−	0.522253i	0.0258895	−	0.999665i	$-0.491758\pi$
$739$	24.5903	−	14.1972i	0.904569	−	0.522253i	0.878680	+	0.477411i	$0.158425\pi$
$740$	1.09167			0.0401307
$741$		0			0
$742$	−14.6056			−0.536187
$743$	−5.74461	+	3.31665i	−0.210749	+	0.121676i	−0.601660	−	0.798753i	$-0.705494\pi$
$743$	−5.74461	+	3.31665i	−0.210749	+	0.121676i	0.390910	+	0.920429i	$0.372160\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$		−	35.9638i		−	1.31673i
$747$	9.02589	+	5.21110i	0.330240	+	0.190664i
$748$	0.579776	+	0.334734i	0.0211987	+	0.0122391i
$749$		−	8.21110i		−	0.300027i
$750$	0.651388	−	1.12824i	0.0237853	−	0.0411974i
$751$	−9.22498	−	15.9781i	−0.336624	−	0.583050i	0.647171	−	0.762345i	$-0.275952\pi$
$751$	−9.22498	−	15.9781i	−0.336624	−	0.583050i	−0.983795	+	0.179294i	$0.942619\pi$
$752$	−14.9053	+	8.60555i	−0.543539	+	0.313812i
$753$	28.8167			1.05014
$754$		0			0
$755$	−13.2111			−0.480801
$756$	−1.31106	+	0.756939i	−0.0476827	+	0.0275296i
$757$	10.4083	+	18.0278i	0.378297	+	0.655230i	0.990815	−	0.135227i	$-0.0431764\pi$
$757$	10.4083	+	18.0278i	0.378297	+	0.655230i	−0.612518	+	0.790457i	$0.709843\pi$
$758$	1.55971	−	2.70151i	0.0566514	−	0.0981231i
$759$			16.8167i			0.610406i
$760$	−4.17134	−	2.40833i	−0.151311	−	0.0873592i
$761$	−21.3331	−	12.3167i	−0.773323	−	0.446478i	0.0607356	−	0.998154i	$-0.480655\pi$
$761$	−21.3331	−	12.3167i	−0.773323	−	0.446478i	−0.834059	+	0.551676i	$0.813989\pi$
$762$		−	13.3028i		−	0.481909i
$763$	−2.39445	+	4.14731i	−0.0866849	+	0.150143i
$764$	0.729183	+	1.26298i	0.0263809	+	0.0456931i
$765$	−0.683205	+	0.394449i	−0.0247013	+	0.0142613i
$766$	−24.2750			−0.877092
$767$		0			0
$768$	−7.09167			−0.255899
$769$	9.52628	−	5.50000i	0.343526	−	0.198335i	−0.318304	−	0.947989i	$-0.603113\pi$
$769$	9.52628	−	5.50000i	0.343526	−	0.198335i	0.661830	+	0.749654i	$0.269780\pi$
$770$	3.65139	+	6.32439i	0.131587	+	0.227915i
$771$	−11.8028	+	20.4430i	−0.425067	+	0.736237i
$772$		−	2.54163i		−	0.0914754i
$773$	−25.6392	−	14.8028i	−0.922176	−	0.532419i	−0.0378477	−	0.999284i	$-0.512050\pi$
$773$	−25.6392	−	14.8028i	−0.922176	−	0.532419i	−0.884329	+	0.466865i	$0.845384\pi$
$774$	−9.50224	−	5.48612i	−0.341551	−	0.197195i
$775$			4.00000i			0.143684i
$776$	−23.4083	+	40.5444i	−0.840310	+	1.45546i
$777$	1.80278	+	3.12250i	0.0646742	+	0.112019i
$778$	0.890063	−	0.513878i	0.0319103	−	0.0184234i
$779$	−4.81665			−0.172575
$780$		0			0
$781$	94.2666			3.37312
$782$	−1.33509	+	0.770817i	−0.0477429	+	0.0275644i
$783$	20.5278	+	35.5551i	0.733602	+	1.27064i
$784$	9.90833	−	17.1617i	0.353869	−	0.612919i
$785$			3.21110i			0.114609i
$786$	7.65948	+	4.42221i	0.273205	+	0.157735i
$787$	−24.7972	−	14.3167i	−0.883924	−	0.510334i	−0.0119736	−	0.999928i	$-0.503811\pi$
$787$	−24.7972	−	14.3167i	−0.883924	−	0.510334i	−0.871950	+	0.489595i	$0.837145\pi$
$788$			6.90833i			0.246099i
$789$	−13.1056	+	22.6995i	−0.466570	+	0.808123i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$	4.85455	−	2.80278i	0.172608	−	0.0996552i
$792$	33.6333			1.19511
$793$		0			0
$794$	−18.2750			−0.648556
$795$	−9.70910	+	5.60555i	−0.344346	+	0.198808i
$796$	−1.33473	−	2.31183i	−0.0473084	−	0.0819405i
$797$	25.2250	−	43.6909i	0.893515	−	1.54761i	0.0578825	−	0.998323i	$-0.481565\pi$
$797$	25.2250	−	43.6909i	0.893515	−	1.54761i	0.835632	−	0.549289i	$-0.185102\pi$
$798$		−	2.09167i		−	0.0740444i
$799$	1.78013	+	1.02776i	0.0629763	+	0.0363594i
$800$	1.46984	+	0.848612i	0.0519667	+	0.0300030i
$801$			16.4222i			0.580250i
$802$	1.44029	−	2.49465i	0.0508582	−	0.0880891i
$803$	42.6333	+	73.8431i	1.50450	+	2.60586i
$804$	−1.83548	+	1.05971i	−0.0647324	+	0.0373733i
$805$	3.00000			0.105736
$806$		0			0
$807$	−9.00000			−0.316815
$808$	23.3827	−	13.5000i	0.822600	−	0.474928i
$809$	−8.52776	−	14.7705i	−0.299820	−	0.519303i	0.676275	−	0.736650i	$-0.263593\pi$
$809$	−8.52776	−	14.7705i	−0.299820	−	0.519303i	−0.976095	+	0.217346i	$0.930260\pi$
$810$	−0.651388	+	1.12824i	−0.0228874	+	0.0396422i
$811$		−	17.5778i		−	0.617240i	−0.951185	−	0.308620i	$-0.900133\pi$
$811$		−	17.5778i		−	0.617240i	0.951185	−	0.308620i	$-0.0998671\pi$
$812$	−2.15304	−	1.24306i	−0.0755571	−	0.0436229i
$813$	0.707243	+	0.408327i	0.0248041	+	0.0143207i
$814$		−	26.3305i		−	0.922885i
$815$	−9.10555	+	15.7713i	−0.318954	+	0.552444i
$816$	−0.651388	−	1.12824i	−0.0228031	−	0.0394962i
$817$	−5.85532	+	3.38057i	−0.204852	+	0.118271i
$818$	8.09167			0.282919
$819$		0			0
$820$	0.908327			0.0317202
$821$	−6.42782	+	3.71110i	−0.224332	+	0.129518i	−0.607955	−	0.793972i	$-0.708010\pi$
$821$	−6.42782	+	3.71110i	−0.224332	+	0.129518i	0.383622	+	0.923490i	$0.374676\pi$
$822$	−3.65139	−	6.32439i	−0.127357	−	0.220588i
$823$	13.3167	−	23.0651i	0.464189	−	0.804000i	−0.534975	−	0.844868i	$-0.679679\pi$
$823$	13.3167	−	23.0651i	0.464189	−	0.804000i	0.999165	+	0.0408682i	$0.0130124\pi$
$824$			12.0000i			0.418040i
$825$	4.85455	+	2.80278i	0.169014	+	0.0975801i
$826$	−12.2037	−	7.04584i	−0.424623	−	0.245156i
$827$			13.5778i			0.472146i	0.971735	+	0.236073i	$0.0758605\pi$
$827$			13.5778i			0.472146i	−0.971735	+	0.236073i	$0.924140\pi$
$828$	0.908327	−	1.57327i	0.0315665	−	0.0546749i
$829$	0.288897	+	0.500385i	0.0100338	+	0.0173791i	0.870999	−	0.491285i	$-0.163473\pi$
$829$	0.288897	+	0.500385i	0.0100338	+	0.0173791i	−0.860965	+	0.508664i	$0.830139\pi$
$830$	5.87936	−	3.39445i	0.204075	−	0.117823i
$831$	−20.3944			−0.707476
$832$		0			0
$833$	−2.36669			−0.0820010
$834$	15.3503	−	8.86249i	0.531537	−	0.306883i
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	1.36249	−	2.35990i	0.0471227	−	0.0816189i
$837$			20.0000i			0.691301i
$838$	37.5013	+	21.6514i	1.29546	+	0.747935i
$839$	13.8804	+	8.01388i	0.479206	+	0.276670i	0.720086	−	0.693885i	$-0.244103\pi$
$839$	13.8804	+	8.01388i	0.479206	+	0.276670i	−0.240879	+	0.970555i	$0.577436\pi$
$840$			3.00000i			0.103510i
$841$	−19.2111	+	33.2746i	−0.662452	+	1.14740i
$842$	2.33053	+	4.03660i	0.0803154	+	0.139110i
$843$	5.19615	−	3.00000i	0.178965	−	0.103325i
$844$	−4.96384			−0.170862
$845$		0			0
$846$	13.5778			0.466814
$847$	−17.6861	+	10.2111i	−0.607703	+	0.350858i
$848$	18.5139	+	32.0670i	0.635769	+	1.10118i
$849$	2.50000	−	4.33013i	0.0857998	−	0.148610i
$850$			0.513878i			0.0176259i
$851$	−9.36750	−	5.40833i	−0.321114	−	0.185395i
$852$	4.40952	+	2.54584i	0.151068	+	0.0872189i
$853$		−	32.7889i		−	1.12267i	−0.827589	−	0.561335i	$-0.810288\pi$
$853$		−	32.7889i		−	1.12267i	0.827589	−	0.561335i	$-0.189712\pi$
$854$	−0.651388	+	1.12824i	−0.0222900	+	0.0386075i
$855$	1.60555	+	2.78090i	0.0549087	+	0.0951046i
$856$	−21.3331	+	12.3167i	−0.729149	+	0.420975i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	25.2111			0.860192			0.430096	−	0.902783i	$-0.358480\pi$
$859$	25.2111			0.860192			0.430096	+	0.902783i	$0.358480\pi$
$860$	1.10420	−	0.637510i	0.0376529	−	0.0217389i
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$	−13.8347	+	23.9625i	−0.471213	+	0.816165i
$863$			36.0000i			1.22545i	0.790295	+	0.612727i	$0.209928\pi$
$863$			36.0000i			1.22545i	−0.790295	+	0.612727i	$0.790072\pi$
$864$	7.34920	+	4.24306i	0.250025	+	0.144352i
$865$	14.5636	+	8.40833i	0.495179	+	0.285892i
$866$			4.69722i			0.159618i
$867$	8.42221	−	14.5877i	0.286033	−	0.495424i
$868$	−0.605551	−	1.04885i	−0.0205537	−	0.0356001i
$869$	−44.7158	+	25.8167i	−1.51688	+	0.875770i
$870$	10.6972			0.362670
$871$		0			0
$872$	14.3667			0.486518
$873$	27.0296	−	15.6056i	0.914814	−	0.528168i
$874$	3.13751	+	5.43433i	0.106128	+	0.183819i
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$			4.60555i			0.155607i
$877$	32.9330	+	19.0139i	1.11207	+	0.642053i	0.939364	−	0.342921i	$-0.111416\pi$
$877$	32.9330	+	19.0139i	1.11207	+	0.642053i	0.172704	+	0.984974i	$0.444750\pi$
$878$	26.2189	+	15.1375i	0.884846	+	0.510866i
$879$		−	17.6056i		−	0.593821i
$880$	9.25694	−	16.0335i	0.312051	−	0.540489i
$881$	17.9222	+	31.0422i	0.603814	+	1.04584i	0.992238	+	0.124356i	$0.0396865\pi$
$881$	17.9222	+	31.0422i	0.603814	+	1.04584i	−0.388423	+	0.921481i	$0.626980\pi$
$882$	−13.5388	+	7.81665i	−0.455877	+	0.263200i
$883$	31.6333			1.06455			0.532273	−	0.846573i	$-0.321338\pi$
$883$	31.6333			1.06455			0.532273	+	0.846573i	$0.321338\pi$
$884$		0			0
$885$	−10.8167			−0.363598
$886$	−25.2976	+	14.6056i	−0.849888	+	0.490683i
$887$	−17.5278	−	30.3590i	−0.588524	−	1.01935i	−0.994426	−	0.105437i	$-0.966376\pi$
$887$	−17.5278	−	30.3590i	−0.588524	−	1.01935i	0.405901	−	0.913917i	$-0.366958\pi$
$888$	5.40833	−	9.36750i	0.181492	−	0.314353i
$889$		−	10.2111i		−	0.342469i
$890$	9.26407	+	5.34861i	0.310532	+	0.179286i
$891$	−4.85455	−	2.80278i	−0.162634	−	0.0938965i
$892$			3.09167i			0.103517i
$893$	4.18335	−	7.24577i	0.139990	−	0.242470i
$894$	1.95416	+	3.38471i	0.0653570	+	0.113202i
$895$	1.02481	−	0.591673i	0.0342555	−	0.0197775i
$896$	8.09167			0.270324
$897$		0			0
$898$	−16.4584			−0.549223
$899$	−28.4441	+	16.4222i	−0.948664	+	0.547711i
$900$	−0.302776	−	0.524423i	−0.0100925	−	0.0174808i
$901$	2.21110	−	3.82974i	0.0736625	−	0.127587i
$902$		−	21.9083i		−	0.729467i
$903$	3.64692	+	2.10555i	0.121362	+	0.0700684i
$904$	−14.5636	−	8.40833i	−0.484380	−	0.279657i
$905$		−	25.6333i		−	0.852080i
$906$	−8.60555	+	14.9053i	−0.285900	+	0.495194i
$907$	24.1333	+	41.8001i	0.801333	+	1.38795i	0.918739	+	0.394866i	$0.129209\pi$
$907$	24.1333	+	41.8001i	0.801333	+	1.38795i	−0.117405	+	0.993084i	$0.537458\pi$
$908$	0.372918	−	0.215305i	0.0123757	−	0.00714513i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−4.59234	+	2.65139i	−0.152068	+	0.0877962i
$913$	14.6056	+	25.2976i	0.483373	+	0.837227i
$914$	−3.37637	+	5.84804i	−0.111680	+	0.193436i
$915$			1.00000i			0.0330590i
$916$	3.67096	+	2.11943i	0.121292	+	0.0700279i
$917$	5.87936	+	3.39445i	0.194153	+	0.112095i
$918$			2.56939i			0.0848025i
$919$	8.59167	−	14.8812i	0.283413	−	0.490886i	−0.688810	−	0.724942i	$-0.741867\pi$
$919$	8.59167	−	14.8812i	0.283413	−	0.490886i	0.972223	+	0.234056i	$0.0751999\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	13.8564	−	8.00000i	0.456584	−	0.263609i
$922$	−28.3860			−0.934845
$923$		0			0
$924$	−1.69722			−0.0558346
$925$	−3.12250	+	1.80278i	−0.102667	+	0.0592749i
$926$	3.63331	+	6.29307i	0.119398	+	0.206803i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$			13.9361i			0.457474i
$929$	−11.6240	−	6.71110i	−0.381370	−	0.220184i	0.297044	−	0.954864i	$-0.403999\pi$
$929$	−11.6240	−	6.71110i	−0.381370	−	0.220184i	−0.678414	+	0.734680i	$0.737332\pi$
$930$	4.51295	+	2.60555i	0.147985	+	0.0854394i
$931$			9.63331i			0.315719i
$932$	0.119429	−	0.206858i	0.00391204	−	0.00677586i
$933$	2.60555	+	4.51295i	0.0853019	+	0.147747i
$934$	−19.4182	+	11.2111i	−0.635383	+	0.366838i
$935$	−2.21110			−0.0723108
$936$		0			0
$937$	−46.4777			−1.51836			−0.759180	−	0.650880i	$-0.774400\pi$
$937$	−46.4777			−1.51836			−0.759180	+	0.650880i	$0.774400\pi$
$938$	7.89766	−	4.55971i	0.257868	−	0.148880i
$939$	−7.00000	−	12.1244i	−0.228436	−	0.395663i
$940$	−0.788897	+	1.36641i	−0.0257310	+	0.0445674i
$941$			33.6333i			1.09641i	0.836343	+	0.548207i	$0.184689\pi$
$941$			33.6333i			1.09641i	−0.836343	+	0.548207i	$0.815311\pi$
$942$	3.62288	+	2.09167i	0.118040	+	0.0681504i
$943$	−7.79423	−	4.50000i	−0.253815	−	0.146540i
$944$			35.7250i			1.16275i
$945$	2.50000	−	4.33013i	0.0813250	−	0.140859i
$946$	−15.3764	−	26.6327i	−0.499929	−	0.865902i
$947$	−21.3331	+	12.3167i	−0.693232	+	0.400237i	−0.804822	−	0.593517i	$-0.797739\pi$
$947$	−21.3331	+	12.3167i	−0.693232	+	0.400237i	0.111590	+	0.993754i	$0.464406\pi$
$948$	−2.78890			−0.0905792
$949$		0			0
$950$	2.09167			0.0678628
$951$	5.19615	−	3.00000i	0.168497	−	0.0972817i
$952$	−0.591673	−	1.02481i	−0.0191762	−	0.0332142i
$953$	25.2250	−	43.6909i	0.817117	−	1.41529i	−0.0906803	−	0.995880i	$-0.528904\pi$
$953$	25.2250	−	43.6909i	0.817117	−	1.41529i	0.907798	−	0.419409i	$-0.137763\pi$
$954$		−	29.2111i		−	0.945744i
$955$	−4.17134	−	2.40833i	−0.134982	−	0.0779316i
$956$		0			0
$957$			46.0278i			1.48787i
$958$	4.67914	−	8.10452i	0.151176	−	0.261845i
$959$	−2.80278	−	4.85455i	−0.0905063	−	0.156762i
$960$	7.63545	−	4.40833i	0.246433	−	0.142278i
$961$	15.0000			0.483871
$962$		0			0
$963$	16.4222			0.529198
$964$	−4.25074	+	2.45416i	−0.136907	+	0.0790433i
$965$	4.19722	+	7.26981i	0.135113	+	0.234023i
$966$	1.95416	−	3.38471i	0.0628742	−	0.108901i
$967$			56.4777i			1.81620i	0.418752	+	0.908100i	$0.362468\pi$
$967$			56.4777i			1.81620i	−0.418752	+	0.908100i	$0.637532\pi$
$968$	53.0584	+	30.6333i	1.70536	+	0.984592i
$969$	0.548461	+	0.316654i	0.0176191	+	0.0101724i
$970$		−	20.3305i		−	0.652774i
$971$	3.98612	−	6.90417i	0.127921	−	0.221565i	−0.794950	−	0.606675i	$-0.792503\pi$
$971$	3.98612	−	6.90417i	0.127921	−	0.221565i	0.922871	+	0.385110i	$0.125836\pi$
$972$	−2.42221	−	4.19538i	−0.0776923	−	0.134567i
$973$	11.7828	−	6.80278i	0.377738	−	0.218087i
$974$	1.30278			0.0417436
$975$		0			0
$976$	3.30278			0.105719
$977$	6.22096	−	3.59167i	0.199026	−	0.114908i	−0.397175	−	0.917743i	$-0.630009\pi$
$977$	6.22096	−	3.59167i	0.199026	−	0.114908i	0.596201	+	0.802835i	$0.296676\pi$
$978$	11.8625	+	20.5464i	0.379321	+	0.657003i
$979$	−23.0139	+	39.8612i	−0.735527	+	1.27397i
$980$		−	1.81665i		−	0.0580309i
$981$	−8.29461	−	4.78890i	−0.264827	−	0.152898i
$982$	5.43433	+	3.13751i	0.173416	+	0.100122i
$983$			10.4222i			0.332417i	0.986091	+	0.166208i	$0.0531524\pi$
$983$			10.4222i			0.332417i	−0.986091	+	0.166208i	$0.946848\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	−11.4083	−	19.7598i	−0.363500	−	0.629600i
$986$	−3.65420	+	2.10975i	−0.116373	+	0.0671882i
$987$	−5.21110			−0.165871
$988$		0			0
$989$	−12.6333			−0.401716
$990$	−12.6488	+	7.30278i	−0.402005	+	0.232097i
$991$	−1.98612	−	3.44006i	−0.0630912	−	0.109277i	0.832754	−	0.553642i	$-0.186763\pi$
$991$	−1.98612	−	3.44006i	−0.0630912	−	0.109277i	−0.895846	+	0.444365i	$0.853429\pi$
$992$	−3.39445	+	5.87936i	−0.107774	+	0.186670i
$993$		−	26.0278i		−	0.825966i
$994$	−18.9732	−	10.9542i	−0.601792	−	0.347445i
$995$	7.63545	+	4.40833i	0.242060	+	0.139753i
$996$			1.57779i			0.0499943i
$997$	−23.2250	+	40.2268i	−0.735543	+	1.27400i	0.218942	+	0.975738i	$0.429739\pi$
$997$	−23.2250	+	40.2268i	−0.735543	+	1.27400i	−0.954485	+	0.298259i	$0.903594\pi$
$998$	−17.2111	−	29.8105i	−0.544808	−	0.943635i
$999$	−15.6125	+	9.01388i	−0.493957	+	0.285186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.d.361.3		8
13.2	odd	12		845.2.a.c.1.2		2
13.3	even	3		845.2.c.d.506.3		4
13.4	even	6	inner	845.2.m.d.316.3		8
13.5	odd	4		65.2.e.b.16.1	✓	4
13.6	odd	12		65.2.e.b.61.1	yes	4
13.7	odd	12		845.2.e.d.191.2		4
13.8	odd	4		845.2.e.d.146.2		4
13.9	even	3	inner	845.2.m.d.316.2		8
13.10	even	6		845.2.c.d.506.2		4
13.11	odd	12		845.2.a.f.1.1		2
13.12	even	2	inner	845.2.m.d.361.2		8
39.2	even	12		7605.2.a.bg.1.1		2
39.5	even	4		585.2.j.d.406.2		4
39.11	even	12		7605.2.a.bb.1.2		2
39.32	even	12		585.2.j.d.451.2		4
52.19	even	12		1040.2.q.o.321.1		4
52.31	even	4		1040.2.q.o.81.1		4
65.18	even	4		325.2.o.b.224.2		8
65.19	odd	12		325.2.e.a.126.2		4
65.24	odd	12		4225.2.a.t.1.2		2
65.32	even	12		325.2.o.b.74.2		8
65.44	odd	4		325.2.e.a.276.2		4
65.54	odd	12		4225.2.a.x.1.1		2
65.57	even	4		325.2.o.b.224.3		8
65.58	even	12		325.2.o.b.74.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	13.5	odd	4
65.2.e.b.61.1	yes	4	13.6	odd	12
325.2.e.a.126.2		4	65.19	odd	12
325.2.e.a.276.2		4	65.44	odd	4
325.2.o.b.74.2		8	65.32	even	12
325.2.o.b.74.3		8	65.58	even	12
325.2.o.b.224.2		8	65.18	even	4
325.2.o.b.224.3		8	65.57	even	4
585.2.j.d.406.2		4	39.5	even	4
585.2.j.d.451.2		4	39.32	even	12
845.2.a.c.1.2		2	13.2	odd	12
845.2.a.f.1.1		2	13.11	odd	12
845.2.c.d.506.2		4	13.10	even	6
845.2.c.d.506.3		4	13.3	even	3
845.2.e.d.146.2		4	13.8	odd	4
845.2.e.d.191.2		4	13.7	odd	12
845.2.m.d.316.2		8	13.9	even	3	inner
845.2.m.d.316.3		8	13.4	even	6	inner
845.2.m.d.361.2		8	13.12	even	2	inner
845.2.m.d.361.3		8	1.1	even	1	trivial
1040.2.q.o.81.1		4	52.31	even	4
1040.2.q.o.321.1		4	52.19	even	12
4225.2.a.t.1.2		2	65.24	odd	12
4225.2.a.x.1.1		2	65.54	odd	12
7605.2.a.bb.1.2		2	39.11	even	12
7605.2.a.bg.1.1		2	39.2	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12824 - 0.651388i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.151388 + 0.262211i) q^{4} -1.00000i q^{5} +(-1.12824 - 0.651388i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +(-0.651388 - 1.12824i) q^{10} +(4.85455 - 2.80278i) q^{11} +0.302776 q^{12} -1.30278 q^{14} +(-0.866025 + 0.500000i) q^{15} +(1.65139 + 2.86029i) q^{16} +(0.197224 - 0.341603i) q^{17} -2.60555i q^{18} +(-1.39045 - 0.802776i) q^{19} +(0.262211 + 0.151388i) q^{20} +1.00000i q^{21} +(3.65139 - 6.32439i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(2.59808 - 1.50000i) q^{24} -1.00000 q^{25} -5.00000 q^{27} +(0.262211 - 0.151388i) q^{28} +(-4.10555 - 7.11102i) q^{29} +(-0.651388 + 1.12824i) q^{30} -4.00000i q^{31} +(-1.46984 - 0.848612i) q^{32} +(-4.85455 - 2.80278i) q^{33} -0.513878i q^{34} +(-0.500000 + 0.866025i) q^{35} +(0.302776 + 0.524423i) q^{36} +(3.12250 - 1.80278i) q^{37} -2.09167 q^{38} +3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(0.651388 + 1.12824i) q^{42} +(2.10555 - 3.64692i) q^{43} +1.69722i q^{44} +(-1.73205 - 1.00000i) q^{45} +(-3.38471 - 1.95416i) q^{46} +5.21110i q^{47} +(1.65139 - 2.86029i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(-1.12824 + 0.651388i) q^{50} -0.394449 q^{51} +11.2111 q^{53} +(-5.64118 + 3.25694i) q^{54} +(-2.80278 - 4.85455i) q^{55} +(1.50000 - 2.59808i) q^{56} +1.60555i q^{57} +(-9.26407 - 5.34861i) q^{58} +(9.36750 + 5.40833i) q^{59} -0.302776i q^{60} +(0.500000 - 0.866025i) q^{61} +(-2.60555 - 4.51295i) q^{62} +(-1.73205 + 1.00000i) q^{63} -8.81665 q^{64} -7.30278 q^{66} +(-6.06218 + 3.50000i) q^{67} +(0.0597147 + 0.103429i) q^{68} +(-1.50000 + 2.59808i) q^{69} +1.30278i q^{70} +(14.5636 + 8.40833i) q^{71} +(5.19615 + 3.00000i) q^{72} +15.2111i q^{73} +(2.34861 - 4.06792i) q^{74} +(0.500000 + 0.866025i) q^{75} +(0.420994 - 0.243061i) q^{76} -5.60555 q^{77} -9.21110 q^{79} +(2.86029 - 1.65139i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.95416 - 3.38471i) q^{82} +5.21110i q^{83} +(-0.262211 - 0.151388i) q^{84} +(-0.341603 - 0.197224i) q^{85} -5.48612i q^{86} +(-4.10555 + 7.11102i) q^{87} +(8.40833 + 14.5636i) q^{88} +(-7.11102 + 4.10555i) q^{89} -2.60555 q^{90} +0.908327 q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.39445 + 5.87936i) q^{94} +(-0.802776 + 1.39045i) q^{95} +1.69722i q^{96} +(13.5148 + 7.80278i) q^{97} +(-6.76942 - 3.90833i) q^{98} -11.2111i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 6 q^{4} + 8 q^{9} + 2 q^{10} - 12 q^{12} + 4 q^{14} + 6 q^{16} + 16 q^{17} + 22 q^{22} - 12 q^{23} - 8 q^{25} - 40 q^{27} - 4 q^{29} + 2 q^{30} - 4 q^{35} - 12 q^{36} - 60 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 6 * q^4 + 8 * q^9 + 2 * q^10 - 12 * q^12 + 4 * q^14 + 6 * q^16 + 16 * q^17 + 22 * q^22 - 12 * q^23 - 8 * q^25 - 40 * q^27 - 4 * q^29 + 2 * q^30 - 4 * q^35 - 12 * q^36 - 60 * q^38 + 24 * q^40 - 2 * q^42 - 12 * q^43 + 6 * q^48 - 24 * q^49 - 32 * q^51 + 32 * q^53 - 8 * q^55 + 12 * q^56 + 4 * q^61 + 8 * q^62 + 16 * q^64 - 44 * q^66 - 50 * q^68 - 12 * q^69 + 26 * q^74 + 4 * q^75 - 16 * q^77 - 16 * q^79 - 4 * q^81 - 6 * q^82 - 4 * q^87 + 24 * q^88 + 8 * q^90 - 36 * q^92 + 56 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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