LMFDB - Embedded newform 475.2.p.e.468.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(107,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("475.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.14096583954457373039394816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 127x^{12} + 13728x^{8} - 304927x^{4} + 5764801 $ x^16 - 127x^12 + 13728x^8 - 304927*x^4 + 5764801
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			468.2
Root			$2.11787 + 0.567482i$ of defining polynomial
Character	$\chi$	$=$	475.468
Dual form			475.2.p.e.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(3.08380 + 0.826301i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59629 + 2.76486i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(6.22896 + 3.59629i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(3.08380 + 0.826301i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59629 + 2.76486i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(6.22896 + 3.59629i) q^{9} -4.19258 q^{11} +(2.25750 + 2.25750i) q^{12} +(-1.08512 - 4.04972i) q^{13} +(0.866025 + 1.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.34129 - 1.43120i) q^{17} +(-5.08592 + 5.08592i) q^{18} +(4.33013 + 0.500000i) q^{19} +(4.78887 - 2.76486i) q^{21} +(1.08512 - 4.04972i) q^{22} +(-1.67303 + 0.448288i) q^{23} +(-8.29457 + 4.78887i) q^{24} +4.19258 q^{26} +(9.46474 + 9.46474i) q^{27} +(1.67303 - 0.448288i) q^{28} +(2.76486 - 4.78887i) q^{29} -2.06561i q^{31} +(-4.82963 + 1.29410i) q^{32} +(-12.9291 - 3.46434i) q^{33} +(2.76486 - 4.78887i) q^{34} +(3.59629 + 6.22896i) q^{36} +(-1.68657 - 1.68657i) q^{37} +(-1.60368 + 4.05317i) q^{38} -13.3852i q^{39} +(3.28887 - 1.89883i) q^{41} +(1.43120 + 5.34129i) q^{42} +(-0.0863323 + 0.322197i) q^{43} +(-3.63088 - 2.09629i) q^{44} -1.73205i q^{46} +(-2.41410 - 9.00956i) q^{47} +(-0.826301 - 3.08380i) q^{48} +4.00000i q^{49} +(-15.2889 - 8.82704i) q^{51} +(1.08512 - 4.04972i) q^{52} +(1.81173 + 6.76148i) q^{53} +(-11.5919 + 6.69258i) q^{54} +5.19615i q^{56} +(12.9401 + 5.11989i) q^{57} +(3.91010 + 3.91010i) q^{58} +(4.66369 + 8.07775i) q^{59} +(-6.28887 + 10.8926i) q^{61} +(1.99523 + 0.534620i) q^{62} +(12.0334 - 3.22435i) q^{63} -7.00000i q^{64} +(6.69258 - 11.5919i) q^{66} +(-10.4033 + 2.78757i) q^{67} +(-3.91010 - 3.91010i) q^{68} -5.52971 q^{69} +(-2.07775 + 1.19959i) q^{71} +(-20.8425 + 5.58473i) q^{72} +(3.22435 - 12.0334i) q^{73} +(2.06561 - 1.19258i) q^{74} +(3.50000 + 2.59808i) q^{76} +(-5.13484 + 5.13484i) q^{77} +(12.9291 + 3.46434i) q^{78} +(5.69650 + 9.86662i) q^{79} +(10.5777 + 18.3212i) q^{81} +(0.982908 + 3.66826i) q^{82} +(5.13484 + 5.13484i) q^{83} +5.52971 q^{84} +(-0.288874 - 0.166781i) q^{86} +(12.4833 - 12.4833i) q^{87} +(8.89381 - 8.89381i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(-6.28887 - 3.63088i) q^{91} +(-1.67303 - 0.448288i) q^{92} +(1.70682 - 6.36993i) q^{93} +9.32738 q^{94} -15.9629 q^{96} +(-1.86158 + 6.94750i) q^{97} +(-3.86370 - 1.03528i) q^{98} +(-26.1154 - 15.0777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^6	$ 16 q - 4 q^{6} - 24 q^{11} - 8 q^{16} + 12 q^{21} + 24 q^{26} + 36 q^{36} - 12 q^{41} - 180 q^{51} - 36 q^{61} + 64 q^{66} + 96 q^{71} + 56 q^{76} + 40 q^{81} + 60 q^{86} - 36 q^{91} - 40 q^{96}+O(q^{100}) $ 16 * q - 4 * q^6 - 24 * q^11 - 8 * q^16 + 12 * q^21 + 24 * q^26 + 36 * q^36 - 12 * q^41 - 180 * q^51 - 36 * q^61 + 64 * q^66 + 96 * q^71 + 56 * q^76 + 40 * q^81 + 60 * q^86 - 36 * q^91 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	0.812035	+	0.583609i	$0.198360\pi$
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	−0.995047	+	0.0994033i	$0.968307\pi$
$3$	3.08380	+	0.826301i	1.78043	+	0.477065i	0.990662	−	0.136339i	$-0.0435336\pi$
$3$	3.08380	+	0.826301i	1.78043	+	0.477065i	0.789769	+	0.613404i	$0.210200\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.59629	+	2.76486i	−0.651683	+	1.12875i
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	−0.436698	−	0.899608i	$-0.643852\pi$
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	0.899608	+	0.436698i	$0.143852\pi$
$8$	−2.12132	+	2.12132i	−0.750000	+	0.750000i
$9$	6.22896	+	3.59629i	2.07632	+	1.19876i
$10$		0			0
$11$	−4.19258			−1.26411			−0.632056	−	0.774923i	$-0.717789\pi$
$11$	−4.19258			−1.26411			−0.632056	+	0.774923i	$0.717789\pi$
$12$	2.25750	+	2.25750i	0.651683	+	0.651683i
$13$	−1.08512	−	4.04972i	−0.300958	−	1.12319i	−0.936369	−	0.351017i	$-0.885836\pi$
$13$	−1.08512	−	4.04972i	−0.300958	−	1.12319i	0.635411	−	0.772174i	$-0.280831\pi$
$14$	0.866025	+	1.50000i	0.231455	+	0.400892i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.34129	−	1.43120i	−1.29545	−	0.347116i	−0.455725	−	0.890121i	$-0.650620\pi$
$17$	−5.34129	−	1.43120i	−1.29545	−	0.347116i	−0.839730	+	0.543005i	$0.817286\pi$
$18$	−5.08592	+	5.08592i	−1.19876	+	1.19876i
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$20$		0			0
$21$	4.78887	−	2.76486i	1.04502	−	0.603341i
$22$	1.08512	−	4.04972i	0.231348	−	0.863404i
$23$	−1.67303	+	0.448288i	−0.348851	+	0.0934745i	−0.428990	−	0.903309i	$-0.641130\pi$
$23$	−1.67303	+	0.448288i	−0.348851	+	0.0934745i	0.0801385	+	0.996784i	$0.474464\pi$
$24$	−8.29457	+	4.78887i	−1.69312	+	0.977525i
$25$		0			0
$26$	4.19258			0.822233
$27$	9.46474	+	9.46474i	1.82149	+	1.82149i
$28$	1.67303	−	0.448288i	0.316173	−	0.0847184i
$29$	2.76486	−	4.78887i	0.513421	−	0.889272i	−0.486458	−	0.873704i	$-0.661711\pi$
$29$	2.76486	−	4.78887i	0.513421	−	0.889272i	0.999879	−	0.0155674i	$-0.00495545\pi$
$30$		0			0
$31$		−	2.06561i		−	0.370995i	−0.982645	−	0.185498i	$-0.940610\pi$
$31$		−	2.06561i		−	0.370995i	0.982645	−	0.185498i	$-0.0593897\pi$
$32$	−4.82963	+	1.29410i	−0.853766	+	0.228766i
$33$	−12.9291	−	3.46434i	−2.25066	−	0.603063i
$34$	2.76486	−	4.78887i	0.474169	−	0.821285i
$35$		0			0
$36$	3.59629	+	6.22896i	0.599382	+	1.03816i
$37$	−1.68657	−	1.68657i	−0.277270	−	0.277270i	0.554748	−	0.832018i	$-0.312815\pi$
$37$	−1.68657	−	1.68657i	−0.277270	−	0.277270i	−0.832018	+	0.554748i	$0.812815\pi$
$38$	−1.60368	+	4.05317i	−0.260152	+	0.657511i
$39$		−	13.3852i		−	2.14334i
$40$		0			0
$41$	3.28887	−	1.89883i	0.513636	−	0.296548i	−0.220691	−	0.975344i	$-0.570831\pi$
$41$	3.28887	−	1.89883i	0.513636	−	0.296548i	0.734327	+	0.678796i	$0.237498\pi$
$42$	1.43120	+	5.34129i	0.220838	+	0.824180i
$43$	−0.0863323	+	0.322197i	−0.0131656	+	0.0491345i	−0.972196	−	0.234168i	$-0.924763\pi$
$43$	−0.0863323	+	0.322197i	−0.0131656	+	0.0491345i	0.959031	+	0.283303i	$0.0914301\pi$
$44$	−3.63088	−	2.09629i	−0.547376	−	0.316028i
$45$		0			0
$46$		−	1.73205i		−	0.255377i
$47$	−2.41410	−	9.00956i	−0.352133	−	1.31418i	−0.884054	−	0.467385i	$-0.845196\pi$
$47$	−2.41410	−	9.00956i	−0.352133	−	1.31418i	0.531921	−	0.846794i	$-0.321470\pi$
$48$	−0.826301	−	3.08380i	−0.119266	−	0.445108i
$49$			4.00000i			0.571429i
$50$		0			0
$51$	−15.2889	−	8.82704i	−2.14087	−	1.23603i
$52$	1.08512	−	4.04972i	0.150479	−	0.561596i
$53$	1.81173	+	6.76148i	0.248861	+	0.928761i	0.971404	+	0.237435i	$0.0763066\pi$
$53$	1.81173	+	6.76148i	0.248861	+	0.928761i	−0.722543	+	0.691326i	$0.757027\pi$
$54$	−11.5919	+	6.69258i	−1.57746	+	0.910745i
$55$		0			0
$56$			5.19615i			0.694365i
$57$	12.9401	+	5.11989i	1.71396	+	0.678146i
$58$	3.91010	+	3.91010i	0.513421	+	0.513421i
$59$	4.66369	+	8.07775i	0.607161	+	1.05163i	0.991706	+	0.128527i	$0.0410249\pi$
$59$	4.66369	+	8.07775i	0.607161	+	1.05163i	−0.384545	+	0.923106i	$0.625642\pi$
$60$		0			0
$61$	−6.28887	+	10.8926i	−0.805208	+	1.39466i	0.110943	+	0.993827i	$0.464613\pi$
$61$	−6.28887	+	10.8926i	−0.805208	+	1.39466i	−0.916151	+	0.400834i	$0.868720\pi$
$62$	1.99523	+	0.534620i	0.253394	+	0.0678968i
$63$	12.0334	−	3.22435i	1.51607	−	0.406229i
$64$		−	7.00000i		−	0.875000i
$65$		0			0
$66$	6.69258	−	11.5919i	0.823800	−	1.42686i
$67$	−10.4033	+	2.78757i	−1.27097	+	0.340555i	−0.830403	−	0.557164i	$-0.811889\pi$
$67$	−10.4033	+	2.78757i	−1.27097	+	0.340555i	−0.440568	+	0.897719i	$0.645223\pi$
$68$	−3.91010	−	3.91010i	−0.474169	−	0.474169i
$69$	−5.52971			−0.665699
$70$		0			0
$71$	−2.07775	+	1.19959i	−0.246583	+	0.142365i	−0.618199	−	0.786022i	$-0.712137\pi$
$71$	−2.07775	+	1.19959i	−0.246583	+	0.142365i	0.371616	+	0.928387i	$0.378804\pi$
$72$	−20.8425	+	5.58473i	−2.45631	+	0.658167i
$73$	3.22435	−	12.0334i	0.377381	−	1.40841i	−0.472453	−	0.881356i	$-0.656631\pi$
$73$	3.22435	−	12.0334i	0.377381	−	1.40841i	0.849834	−	0.527050i	$-0.176702\pi$
$74$	2.06561	−	1.19258i	0.240123	−	0.138635i
$75$		0			0
$76$	3.50000	+	2.59808i	0.401478	+	0.298020i
$77$	−5.13484	+	5.13484i	−0.585170	+	0.585170i
$78$	12.9291	+	3.46434i	1.46393	+	0.392259i
$79$	5.69650	+	9.86662i	0.640906	+	1.11008i	0.985231	+	0.171231i	$0.0547745\pi$
$79$	5.69650	+	9.86662i	0.640906	+	1.11008i	−0.344325	+	0.938851i	$0.611892\pi$
$80$		0			0
$81$	10.5777	+	18.3212i	1.17531	+	2.03569i
$82$	0.982908	+	3.66826i	0.108544	+	0.405092i
$83$	5.13484	+	5.13484i	0.563622	+	0.563622i	0.930334	−	0.366712i	$-0.119517\pi$
$83$	5.13484	+	5.13484i	0.563622	+	0.563622i	−0.366712	+	0.930334i	$0.619517\pi$
$84$	5.52971			0.603341
$85$		0			0
$86$	−0.288874	−	0.166781i	−0.0311500	−	0.0179845i
$87$	12.4833	−	12.4833i	1.33835	−	1.33835i
$88$	8.89381	−	8.89381i	0.948083	−	0.948083i
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	−0.970235	−	0.242166i	$-0.922142\pi$
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	0.694839	+	0.719165i	$0.255475\pi$
$90$		0			0
$91$	−6.28887	−	3.63088i	−0.659253	−	0.380620i
$92$	−1.67303	−	0.448288i	−0.174426	−	0.0467372i
$93$	1.70682	−	6.36993i	0.176989	−	0.660531i
$94$	9.32738			0.962046
$95$		0			0
$96$	−15.9629			−1.62921
$97$	−1.86158	+	6.94750i	−0.189015	+	0.705412i	0.804721	+	0.593653i	$0.202315\pi$
$97$	−1.86158	+	6.94750i	−0.189015	+	0.705412i	−0.993735	+	0.111758i	$0.964352\pi$
$98$	−3.86370	−	1.03528i	−0.390293	−	0.104579i
$99$	−26.1154	−	15.0777i	−2.62470	−	1.51537i
$100$		0			0
$101$	4.19258	−	7.26177i	0.417178	−	0.722573i	−0.578477	−	0.815699i	$-0.696353\pi$
$101$	4.19258	−	7.26177i	0.417178	−	0.722573i	0.995654	+	0.0931262i	$0.0296860\pi$
$102$	12.4833	−	12.4833i	1.23603	−	1.23603i
$103$	−1.68657	+	1.68657i	−0.166182	+	0.166182i	−0.785299	−	0.619117i	$-0.787491\pi$
$103$	−1.68657	+	1.68657i	−0.166182	+	0.166182i	0.619117	+	0.785299i	$0.287491\pi$
$104$	10.8926	+	6.28887i	1.06811	+	0.616675i
$105$		0			0
$106$	−7.00000			−0.679900
$107$	−1.00568	−	1.00568i	−0.0972232	−	0.0972232i	0.656822	−	0.754045i	$-0.271900\pi$
$107$	−1.00568	−	1.00568i	−0.0972232	−	0.0972232i	−0.754045	+	0.656822i	$0.771900\pi$
$108$	3.46434	+	12.9291i	0.333356	+	1.24410i
$109$	−8.12779	−	14.0777i	−0.778501	−	1.34840i	−0.932805	−	0.360380i	$-0.882647\pi$
$109$	−8.12779	−	14.0777i	−0.778501	−	1.34840i	0.154304	−	0.988023i	$-0.450686\pi$
$110$		0			0
$111$	−3.80742	−	6.59464i	−0.361384	−	0.625936i
$112$	−1.67303	−	0.448288i	−0.158087	−	0.0423592i
$113$	6.06538	−	6.06538i	0.570583	−	0.570583i	−0.361708	−	0.932291i	$-0.617806\pi$
$113$	6.06538	−	6.06538i	0.570583	−	0.570583i	0.932291	+	0.361708i	$0.117806\pi$
$114$	−8.29457	+	11.1740i	−0.776858	+	1.04654i
$115$		0			0
$116$	4.78887	−	2.76486i	0.444636	−	0.256711i
$117$	7.80482	−	29.1280i	0.721556	−	2.69288i
$118$	−9.00956	+	2.41410i	−0.829397	+	0.222236i
$119$	−8.29457	+	4.78887i	−0.760362	+	0.438995i
$120$		0			0
$121$	6.57775			0.597977
$122$	−8.89381	−	8.89381i	−0.805208	−	0.805208i
$123$	11.7112	−	3.13801i	1.05597	−	0.282945i
$124$	1.03281	−	1.78887i	0.0927488	−	0.160646i
$125$		0			0
$126$			12.4579i			1.10984i
$127$	9.84528	−	2.63803i	0.873627	−	0.234088i	0.205972	−	0.978558i	$-0.433965\pi$
$127$	9.84528	−	2.63803i	0.873627	−	0.234088i	0.667656	+	0.744470i	$0.267298\pi$
$128$	−2.89778	−	0.776457i	−0.256130	−	0.0686298i
$129$	−0.532463	+	0.922253i	−0.0468807	+	0.0811998i
$130$		0			0
$131$	1.21113	+	2.09773i	0.105817	+	0.183280i	0.914072	−	0.405553i	$-0.132921\pi$
$131$	1.21113	+	2.09773i	0.105817	+	0.183280i	−0.808255	+	0.588833i	$0.799588\pi$
$132$	−9.46474	−	9.46474i	−0.823800	−	0.823800i
$133$	5.91567	−	4.69093i	0.512954	−	0.406755i
$134$		−	10.7703i		−	0.930415i
$135$		0			0
$136$	14.3666	−	8.29457i	1.23193	−	0.711254i
$137$	−0.275623	−	1.02864i	−0.0235481	−	0.0878826i	0.953152	−	0.302492i	$-0.0978187\pi$
$137$	−0.275623	−	1.02864i	−0.0235481	−	0.0878826i	−0.976700	+	0.214610i	$0.931152\pi$
$138$	1.43120	−	5.34129i	0.121831	−	0.454681i
$139$	−0.500344	−	0.288874i	−0.0424386	−	0.0245019i	0.478631	−	0.878016i	$-0.341133\pi$
$139$	−0.500344	−	0.288874i	−0.0424386	−	0.0245019i	−0.521069	+	0.853514i	$0.674467\pi$
$140$		0			0
$141$		−	29.7784i		−	2.50780i
$142$	−0.620952	−	2.31743i	−0.0521092	−	0.194474i
$143$	4.54946	+	16.9788i	0.380445	+	1.41984i
$144$		−	7.19258i		−	0.599382i
$145$		0			0
$146$	10.7889	+	6.22896i	0.892894	+	0.515512i
$147$	−3.30520	+	12.3352i	−0.272609	+	1.01739i
$148$	−0.617326	−	2.30389i	−0.0507439	−	0.189379i
$149$	12.4579	−	7.19258i	1.02059	−	0.589239i	0.106317	−	0.994332i	$-0.466094\pi$
$149$	12.4579	−	7.19258i	1.02059	−	0.589239i	0.914275	+	0.405093i	$0.132761\pi$
$150$		0			0
$151$		−	12.7915i		−	1.04096i	−0.853875	−	0.520478i	$-0.825754\pi$
$151$		−	12.7915i		−	1.04096i	0.853875	−	0.520478i	$-0.174246\pi$
$152$	−10.2462	+	8.12493i	−0.831080	+	0.659019i
$153$	−28.1237	−	28.1237i	−2.27367	−	2.27367i
$154$	−3.63088	−	6.28887i	−0.292585	−	0.506772i
$155$		0			0
$156$	6.69258	−	11.5919i	0.535835	−	0.928094i
$157$	19.3699	+	5.19016i	1.54589	+	0.414220i	0.928163	−	0.372173i	$-0.121387\pi$
$157$	19.3699	+	5.19016i	1.54589	+	0.414220i	0.617727	+	0.786393i	$0.288054\pi$
$158$	−11.0048	+	2.94872i	−0.875494	+	0.234588i
$159$			22.3481i			1.77232i
$160$		0			0
$161$	−1.50000	+	2.59808i	−0.118217	+	0.204757i
$162$	−20.4346	+	5.47544i	−1.60550	+	0.430192i
$163$	3.67423	+	3.67423i	0.287788	+	0.287788i	0.836205	−	0.548417i	$-0.184769\pi$
$163$	3.67423	+	3.67423i	0.287788	+	0.287788i	−0.548417	+	0.836205i	$0.684769\pi$
$164$	3.79766			0.296548
$165$		0			0
$166$	−6.28887	+	3.63088i	−0.488111	+	0.281811i
$167$	−18.9107	+	5.06709i	−1.46335	+	0.392103i	−0.900646	−	0.434555i	$-0.856906\pi$
$167$	−18.9107	+	5.06709i	−1.46335	+	0.392103i	−0.562705	+	0.826658i	$0.690239\pi$
$168$	−4.29359	+	16.0239i	−0.331257	+	1.23627i
$169$	−3.96445	+	2.28887i	−0.304957	+	0.176067i
$170$		0			0
$171$	25.1740	+	18.6869i	1.92511	+	1.42902i
$172$	−0.235864	+	0.235864i	−0.0179845	+	0.0179845i
$173$	6.76148	+	1.81173i	0.514066	+	0.137744i	0.506520	−	0.862228i	$-0.330932\pi$
$173$	6.76148	+	1.81173i	0.514066	+	0.137744i	0.00754550	+	0.999972i	$0.497598\pi$
$174$	8.82704	+	15.2889i	0.669176	+	1.15905i
$175$		0			0
$176$	2.09629	+	3.63088i	0.158014	+	0.273688i
$177$	7.70722	+	28.7638i	0.579310	+	2.16202i
$178$	−3.67423	−	3.67423i	−0.275396	−	0.275396i
$179$	−21.4517			−1.60338			−0.801689	−	0.597741i	$-0.796065\pi$
$179$	−21.4517			−1.60338			−0.801689	+	0.597741i	$0.796065\pi$
$180$		0			0
$181$	−7.78887	−	4.49691i	−0.578942	−	0.334253i	0.181771	−	0.983341i	$-0.441817\pi$
$181$	−7.78887	−	4.49691i	−0.578942	−	0.334253i	−0.760713	+	0.649088i	$0.775151\pi$
$182$	5.13484	−	5.13484i	0.380620	−	0.380620i
$183$	−28.3942	+	28.3942i	−2.09896	+	2.09896i
$184$	2.59808	−	4.50000i	0.191533	−	0.331744i
$185$		0			0
$186$	5.71113	+	3.29732i	0.418760	+	0.241771i
$187$	22.3938	+	6.00041i	1.63760	+	0.438793i
$188$	2.41410	−	9.00956i	0.176067	−	0.657089i
$189$	23.1838			1.68637
$190$		0			0
$191$	15.5777			1.12717			0.563583	−	0.826059i	$-0.309422\pi$
$191$	15.5777			1.12717			0.563583	+	0.826059i	$0.309422\pi$
$192$	5.78411	−	21.5866i	0.417432	−	1.55788i
$193$	−15.0828	−	4.04142i	−1.08568	−	0.290908i	−0.328760	−	0.944413i	$-0.606631\pi$
$193$	−15.0828	−	4.04142i	−1.08568	−	0.290908i	−0.756921	+	0.653506i	$0.773297\pi$
$194$	−6.22896	−	3.59629i	−0.447213	−	0.258199i
$195$		0			0
$196$	−2.00000	+	3.46410i	−0.142857	+	0.247436i
$197$	2.68535	−	2.68535i	0.191324	−	0.191324i	−0.604944	−	0.796268i	$-0.706805\pi$
$197$	2.68535	−	2.68535i	0.191324	−	0.191324i	0.796268	+	0.604944i	$0.206805\pi$
$198$	21.3232	−	21.3232i	1.51537	−	1.51537i
$199$	13.1250	+	7.57775i	0.930410	+	0.537172i	0.886941	−	0.461883i	$-0.152826\pi$
$199$	13.1250	+	7.57775i	0.930410	+	0.537172i	0.0434685	+	0.999055i	$0.486159\pi$
$200$		0			0
$201$	−34.3852			−2.42534
$202$	5.92921	+	5.92921i	0.417178	+	0.417178i
$203$	−2.47890	−	9.25139i	−0.173985	−	0.649321i
$204$	−8.82704	−	15.2889i	−0.618016	−	1.07044i
$205$		0			0
$206$	−1.19258	−	2.06561i	−0.0830912	−	0.143918i
$207$	−12.0334	−	3.22435i	−0.836381	−	0.224108i
$208$	−2.96460	+	2.96460i	−0.205558	+	0.205558i
$209$	−18.1544	−	2.09629i	−1.25577	−	0.145003i
$210$		0			0
$211$	−11.3666	+	6.56252i	−0.782510	+	0.451783i	−0.837319	−	0.546714i	$-0.815878\pi$
$211$	−11.3666	+	6.56252i	−0.782510	+	0.451783i	0.0548088	+	0.998497i	$0.482545\pi$
$212$	−1.81173	+	6.76148i	−0.124430	+	0.464380i
$213$	−7.39857	+	1.98244i	−0.506942	+	0.135835i
$214$	1.23171	−	0.711126i	0.0841978	−	0.0486116i
$215$		0			0
$216$	−40.1555			−2.73224
$217$	−2.52985	−	2.52985i	−0.171737	−	0.171737i
$218$	15.7017	−	4.20725i	1.06345	−	0.284951i
$219$	19.8865	−	34.4444i	1.34380	−	2.32753i
$220$		0			0
$221$			23.1838i			1.55951i
$222$	7.35537	−	1.97086i	0.493660	−	0.132276i
$223$	19.6547	+	5.26647i	1.31618	+	0.352669i	0.847545	−	0.530724i	$-0.178080\pi$
$223$	19.6547	+	5.26647i	1.31618	+	0.352669i	0.468633	+	0.883393i	$0.344747\pi$
$224$	−4.33013	+	7.50000i	−0.289319	+	0.501115i
$225$		0			0
$226$	4.28887	+	7.42855i	0.285292	+	0.494140i
$227$	−3.53553	−	3.53553i	−0.234662	−	0.234662i	0.579974	−	0.814635i	$-0.303063\pi$
$227$	−3.53553	−	3.53553i	−0.234662	−	0.234662i	−0.814635	+	0.579974i	$0.803063\pi$
$228$	8.64650	+	10.9040i	0.572628	+	0.722135i
$229$			21.0000i			1.38772i	0.720110	+	0.693860i	$0.244091\pi$
$229$			21.0000i			1.38772i	−0.720110	+	0.693860i	$0.755909\pi$
$230$		0			0
$231$	−20.0777	+	11.5919i	−1.32102	+	0.762691i
$232$	4.29359	+	16.0239i	0.281888	+	1.05202i
$233$	−7.34527	+	27.4129i	−0.481205	+	1.79588i	0.115371	+	0.993323i	$0.463194\pi$
$233$	−7.34527	+	27.4129i	−0.481205	+	1.79588i	−0.596575	+	0.802557i	$0.703472\pi$
$234$	26.1154	+	15.0777i	1.70722	+	0.985663i
$235$		0			0
$236$			9.32738i			0.607161i
$237$	9.41404	+	35.1337i	0.611508	+	2.28218i
$238$	−2.47890	−	9.25139i	−0.160683	−	0.599679i
$239$		−	9.00000i		−	0.582162i	−0.956698	−	0.291081i	$-0.905985\pi$
$239$		−	9.00000i		−	0.582162i	0.956698	−	0.291081i	$-0.0940149\pi$
$240$		0			0
$241$	−4.21113	−	2.43129i	−0.271262	−	0.156613i	0.358199	−	0.933645i	$-0.383391\pi$
$241$	−4.21113	−	2.43129i	−0.271262	−	0.156613i	−0.629461	+	0.777032i	$0.716724\pi$
$242$	−1.70245	+	6.35362i	−0.109437	+	0.408426i
$243$	7.08780	+	26.4520i	0.454683	+	1.69690i
$244$	−10.8926	+	6.28887i	−0.697330	+	0.402604i
$245$		0			0
$246$			12.1244i			0.773021i
$247$	−2.67385	−	18.0784i	−0.170133	−	1.15030i
$248$	4.38183	+	4.38183i	0.278246	+	0.278246i
$249$	11.5919	+	20.0777i	0.734606	+	1.27238i
$250$		0			0
$251$	1.21113	−	2.09773i	0.0764456	−	0.132408i	−0.825268	−	0.564741i	$-0.808976\pi$
$251$	1.21113	−	2.09773i	0.0764456	−	0.132408i	0.901714	+	0.432333i	$0.142310\pi$
$252$	12.0334	+	3.22435i	0.758035	+	0.203115i
$253$	7.01433	−	1.87948i	0.440987	−	0.118162i
$254$			10.1926i			0.639539i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−11.9990	+	3.21512i	−0.748475	+	0.200553i	−0.612842	−	0.790206i	$-0.709974\pi$
$257$	−11.9990	+	3.21512i	−0.748475	+	0.200553i	−0.135634	+	0.990759i	$0.543307\pi$
$258$	−0.753016	−	0.753016i	−0.0468807	−	0.0468807i
$259$	−4.13123			−0.256702
$260$		0			0
$261$	34.4444	−	19.8865i	2.13205	−	1.23094i
$262$	−2.33972	+	0.626925i	−0.144548	+	0.0387316i
$263$	−4.03459	+	15.0573i	−0.248783	+	0.928472i	0.722660	+	0.691203i	$0.242919\pi$
$263$	−4.03459	+	15.0573i	−0.248783	+	0.928472i	−0.971444	+	0.237269i	$0.923748\pi$
$264$	34.7757	−	20.0777i	2.14030	−	1.23570i
$265$		0			0
$266$	3.00000	+	6.92820i	0.183942	+	0.424795i
$267$	−11.7303	+	11.7303i	−0.717883	+	0.717883i
$268$	−10.4033	−	2.78757i	−0.635485	−	0.170278i
$269$	1.36637	+	2.36662i	0.0833090	+	0.144295i	0.904669	−	0.426114i	$-0.140118\pi$
$269$	1.36637	+	2.36662i	0.0833090	+	0.144295i	−0.821360	+	0.570410i	$0.806784\pi$
$270$		0			0
$271$	1.21113	+	2.09773i	0.0735707	+	0.127428i	0.900464	−	0.434931i	$-0.143227\pi$
$271$	1.21113	+	2.09773i	0.0735707	+	0.127428i	−0.826893	+	0.562359i	$0.809894\pi$
$272$	1.43120	+	5.34129i	0.0867790	+	0.323864i
$273$	−16.3934	−	16.3934i	−0.992174	−	0.992174i
$274$	1.06493			0.0643345
$275$		0			0
$276$	−4.78887	−	2.76486i	−0.288256	−	0.166425i
$277$	−10.7414	+	10.7414i	−0.645389	+	0.645389i	−0.951875	−	0.306486i	$-0.900847\pi$
$277$	−10.7414	+	10.7414i	−0.645389	+	0.645389i	0.306486	+	0.951875i	$0.400847\pi$
$278$	0.408529	−	0.408529i	0.0245019	−	0.0245019i
$279$	7.42855	−	12.8666i	0.444735	−	0.770304i
$280$		0			0
$281$	−5.65549	−	3.26520i	−0.337379	−	0.194786i	0.321734	−	0.946830i	$-0.395734\pi$
$281$	−5.65549	−	3.26520i	−0.337379	−	0.194786i	−0.659112	+	0.752045i	$0.729068\pi$
$282$	28.7638	+	7.70722i	1.71286	+	0.458959i
$283$	3.22435	−	12.0334i	0.191668	−	0.715313i	−0.801437	−	0.598079i	$-0.795931\pi$
$283$	3.22435	−	12.0334i	0.191668	−	0.715313i	0.993104	−	0.117233i	$-0.0374026\pi$
$284$	−2.39918			−0.142365
$285$		0			0
$286$	−17.5777			−1.03939
$287$	1.70245	−	6.35362i	0.100492	−	0.375042i
$288$	−34.7375	−	9.30789i	−2.04693	−	0.548472i
$289$	11.7587	+	6.78887i	0.691687	+	0.399346i
$290$		0			0
$291$	−11.4815	+	19.8865i	−0.673055	+	1.16577i
$292$	8.80908	−	8.80908i	0.515512	−	0.515512i
$293$	1.00568	−	1.00568i	0.0587527	−	0.0587527i	−0.677120	−	0.735873i	$-0.736772\pi$
$293$	1.00568	−	1.00568i	0.0587527	−	0.0587527i	0.735873	+	0.677120i	$0.236772\pi$
$294$	−11.0594	−	6.38516i	−0.644999	−	0.372390i
$295$		0			0
$296$	7.15549			0.415905
$297$	−39.6817	−	39.6817i	−2.30257	−	2.30257i
$298$	3.72315	+	13.8950i	0.215677	+	0.804916i
$299$	3.63088	+	6.28887i	0.209979	+	0.363695i
$300$		0			0
$301$	0.288874	+	0.500344i	0.0166504	+	0.0288393i
$302$	12.3556	+	3.31068i	0.710986	+	0.190508i
$303$	18.9295	−	18.9295i	1.08747	−	1.08747i
$304$	−1.73205	−	4.00000i	−0.0993399	−	0.229416i
$305$		0			0
$306$	34.4444	−	19.8865i	1.96905	−	1.13683i
$307$	1.71205	−	6.38944i	0.0977116	−	0.364665i	−0.899705	−	0.436498i	$-0.856218\pi$
$307$	1.71205	−	6.38944i	0.0977116	−	0.364665i	0.997417	+	0.0718338i	$0.0228851\pi$
$308$	−7.01433	+	1.87948i	−0.399678	+	0.107093i
$309$	−6.59464	+	3.80742i	−0.375156	+	0.216596i
$310$		0			0
$311$	1.77033			0.100386			0.0501931	−	0.998740i	$-0.484016\pi$
$311$	1.77033			0.100386			0.0501931	+	0.998740i	$0.484016\pi$
$312$	28.3942	+	28.3942i	1.60751	+	1.60751i
$313$	−22.3938	+	6.00041i	−1.26577	+	0.339163i	−0.828410	−	0.560122i	$-0.810754\pi$
$313$	−22.3938	+	6.00041i	−1.26577	+	0.339163i	−0.437363	+	0.899285i	$0.644088\pi$
$314$	−10.0266	+	17.3666i	−0.565835	+	0.980055i
$315$		0			0
$316$			11.3930i			0.640906i
$317$	3.86370	−	1.03528i	0.217007	−	0.0581469i	−0.148677	−	0.988886i	$-0.547502\pi$
$317$	3.86370	−	1.03528i	0.217007	−	0.0581469i	0.365685	+	0.930739i	$0.380835\pi$
$318$	−21.5866	−	5.78411i	−1.21052	−	0.324357i
$319$	−11.5919	+	20.0777i	−0.649021	+	1.12414i
$320$		0			0
$321$	−2.27033	−	3.93233i	−0.126717	−	0.219481i
$322$	−2.12132	−	2.12132i	−0.118217	−	0.118217i
$323$	−22.4129	−	8.86791i	−1.24709	−	0.493423i
$324$			21.1555i			1.17531i
$325$		0			0
$326$	−4.50000	+	2.59808i	−0.249232	+	0.143894i
$327$	−13.4320	−	50.1289i	−0.742792	−	2.77214i
$328$	−2.94872	+	11.0048i	−0.162816	+	0.607638i
$329$	−13.9911	−	8.07775i	−0.771353	−	0.445341i
$330$		0			0
$331$		−	17.3205i		−	0.952021i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$		−	17.3205i		−	0.952021i	0.879440	−	0.476011i	$-0.157918\pi$
$332$	1.87948	+	7.01433i	0.103150	+	0.384961i
$333$	−4.44017	−	16.5709i	−0.243320	−	0.908082i
$334$		−	19.5777i		−	1.07125i
$335$		0			0
$336$	−4.78887	−	2.76486i	−0.261254	−	0.150835i
$337$	2.94670	−	10.9972i	0.160517	−	0.599057i	−0.838053	−	0.545589i	$-0.816306\pi$
$337$	2.94670	−	10.9972i	0.160517	−	0.599057i	0.998570	−	0.0534678i	$-0.0170274\pi$
$338$	−1.18481	−	4.42176i	−0.0644451	−	0.240512i
$339$	23.7162	−	13.6926i	1.28809	−	0.743679i
$340$		0			0
$341$			8.66025i			0.468979i
$342$	−24.5657	+	19.4797i	−1.32836	+	1.05334i
$343$	13.4722	+	13.4722i	0.727430	+	0.727430i
$344$	−0.500344	−	0.866621i	−0.0269767	−	0.0467251i
$345$		0			0
$346$	−3.50000	+	6.06218i	−0.188161	+	0.325905i
$347$	19.3699	+	5.19016i	1.03983	+	0.278622i	0.738044	−	0.674752i	$-0.235750\pi$
$347$	19.3699	+	5.19016i	1.03983	+	0.278622i	0.301789	+	0.953375i	$0.402416\pi$
$348$	17.0525	−	4.56921i	0.914111	−	0.244935i
$349$		−	33.3110i		−	1.78310i	−0.452926	−	0.891548i	$-0.649620\pi$
$349$		−	33.3110i		−	1.78310i	0.452926	−	0.891548i	$-0.350380\pi$
$350$		0			0
$351$	28.0592	−	48.6000i	1.49769	−	2.59407i
$352$	20.2486	−	5.42560i	1.07925	−	0.289185i
$353$	6.59545	+	6.59545i	0.351041	+	0.351041i	0.860497	−	0.509456i	$-0.170153\pi$
$353$	6.59545	+	6.59545i	0.351041	+	0.351041i	−0.509456	+	0.860497i	$0.670153\pi$
$354$	−29.7784			−1.58271
$355$		0			0
$356$	−4.50000	+	2.59808i	−0.238500	+	0.137698i
$357$	−29.5358	+	7.91410i	−1.56320	+	0.418859i
$358$	5.55212	−	20.7208i	0.293439	−	1.09513i
$359$	−1.56527	+	0.903709i	−0.0826118	+	0.0476959i	−0.540737	−	0.841192i	$-0.681855\pi$
$359$	−1.56527	+	0.903709i	−0.0826118	+	0.0476959i	0.458125	+	0.888888i	$0.348521\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$	6.35959	−	6.35959i	0.334253	−	0.334253i
$363$	20.2844	+	5.43520i	1.06466	+	0.285274i
$364$	−3.63088	−	6.28887i	−0.190310	−	0.329627i
$365$		0			0
$366$	−20.0777	−	34.7757i	−1.04948	−	1.81775i
$367$	−0.707285	−	2.63962i	−0.0369200	−	0.137787i	0.945006	−	0.327053i	$-0.106056\pi$
$367$	−0.707285	−	2.63962i	−0.0369200	−	0.137787i	−0.981926	+	0.189266i	$0.939389\pi$
$368$	1.22474	+	1.22474i	0.0638442	+	0.0638442i
$369$	27.3150			1.42196
$370$		0			0
$371$	10.5000	+	6.06218i	0.545133	+	0.314733i
$372$	4.66312	−	4.66312i	0.241771	−	0.241771i
$373$	−16.5096	+	16.5096i	−0.854834	+	0.854834i	−0.990724	−	0.135890i	$-0.956611\pi$
$373$	−16.5096	+	16.5096i	−0.854834	+	0.854834i	0.135890	+	0.990724i	$0.456611\pi$
$374$	−11.5919	+	20.0777i	−0.599403	+	1.03820i
$375$		0			0
$376$	24.2332	+	13.9911i	1.24973	+	0.721534i
$377$	−22.3938	−	6.00041i	−1.15334	−	0.309037i
$378$	−6.00041	+	22.3938i	−0.308628	+	1.15181i
$379$	−21.4517			−1.10190			−0.550951	−	0.834538i	$-0.685735\pi$
$379$	−21.4517			−1.10190			−0.550951	+	0.834538i	$0.685735\pi$
$380$		0			0
$381$	32.5407			1.66711
$382$	−4.03182	+	15.0469i	−0.206286	+	0.769869i
$383$	16.4207	+	4.39992i	0.839061	+	0.224826i	0.652663	−	0.757649i	$-0.273652\pi$
$383$	16.4207	+	4.39992i	0.839061	+	0.224826i	0.186398	+	0.982474i	$0.440319\pi$
$384$	−8.29457	−	4.78887i	−0.423281	−	0.244381i
$385$		0			0
$386$	7.80742	−	13.5228i	0.397387	−	0.688295i
$387$	−1.69647	+	1.69647i	−0.0862366	+	0.0862366i
$388$	−5.08592	+	5.08592i	−0.258199	+	0.258199i
$389$	−0.500344	−	0.288874i	−0.0253684	−	0.0146465i	0.487262	−	0.873256i	$-0.337996\pi$
$389$	−0.500344	−	0.288874i	−0.0253684	−	0.0146465i	−0.512631	+	0.858609i	$0.671329\pi$
$390$		0			0
$391$	9.57775			0.484367
$392$	−8.48528	−	8.48528i	−0.428571	−	0.428571i
$393$	2.00151	+	7.46974i	0.100963	+	0.376798i
$394$	1.89883	+	3.28887i	0.0956618	+	0.165691i
$395$		0			0
$396$	−15.0777	−	26.1154i	−0.757685	−	1.31235i
$397$	−7.72077	−	2.06877i	−0.387494	−	0.103829i	0.0598119	−	0.998210i	$-0.480950\pi$
$397$	−7.72077	−	2.06877i	−0.387494	−	0.103829i	−0.447306	+	0.894381i	$0.647617\pi$
$398$	−10.7166	+	10.7166i	−0.537172	+	0.537172i
$399$	22.1189	−	9.57775i	1.10733	−	0.479487i
$400$		0			0
$401$	−31.7332	+	18.3212i	−1.58468	+	0.914917i	−0.590520	+	0.807023i	$0.701077\pi$
$401$	−31.7332	+	18.3212i	−1.58468	+	0.914917i	−0.994162	+	0.107894i	$0.965589\pi$
$402$	8.89954	−	33.2135i	0.443868	−	1.65654i
$403$	−8.36516	+	2.24144i	−0.416698	+	0.111654i
$404$	7.26177	−	4.19258i	0.361286	−	0.208589i
$405$		0			0
$406$	9.57775			0.475336
$407$	7.07107	+	7.07107i	0.350500	+	0.350500i
$408$	51.1576	−	13.7076i	2.53268	−	0.678629i
$409$	−19.7197	+	34.1555i	−0.975076	+	1.68888i	−0.295390	+	0.955377i	$0.595450\pi$
$409$	−19.7197	+	34.1555i	−0.975076	+	1.68888i	−0.679685	+	0.733504i	$0.737884\pi$
$410$		0			0
$411$		−	3.39986i		−	0.167703i
$412$	−2.30389	+	0.617326i	−0.113505	+	0.0304135i
$413$	15.6050	+	4.18135i	0.767872	+	0.205751i
$414$	6.22896	−	10.7889i	0.306137	−	0.530244i
$415$		0			0
$416$	10.4815	+	18.1544i	0.513896	+	0.890093i
$417$	−1.30426	−	1.30426i	−0.0638700	−	0.0638700i
$418$	6.72357	−	16.9933i	0.328861	−	0.831167i
$419$		−	24.0000i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$419$		−	24.0000i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$420$		0			0
$421$	−13.1555	+	7.59533i	−0.641160	+	0.370174i	−0.785061	−	0.619418i	$-0.787368\pi$
$421$	−13.1555	+	7.59533i	−0.641160	+	0.370174i	0.143902	+	0.989592i	$0.454035\pi$
$422$	−3.39701	−	12.6778i	−0.165364	−	0.617147i
$423$	17.3636	−	64.8020i	0.844249	−	3.15078i
$424$	−18.1865	−	10.5000i	−0.883216	−	0.509925i
$425$		0			0
$426$		−	7.65957i		−	0.371107i
$427$	5.63845	+	21.0430i	0.272864	+	1.01834i
$428$	−0.368106	−	1.37379i	−0.0177931	−	0.0664047i
$429$			56.1184i			2.70942i
$430$		0			0
$431$	3.28887	+	1.89883i	0.158419	+	0.0914635i	0.577114	−	0.816664i	$-0.304179\pi$
$431$	3.28887	+	1.89883i	0.158419	+	0.0914635i	−0.418694	+	0.908127i	$0.637512\pi$
$432$	3.46434	−	12.9291i	0.166678	−	0.622050i
$433$	7.60544	+	28.3839i	0.365494	+	1.36404i	0.866750	+	0.498743i	$0.166205\pi$
$433$	7.60544	+	28.3839i	0.365494	+	1.36404i	−0.501256	+	0.865299i	$0.667128\pi$
$434$	3.09842	−	1.78887i	0.148729	−	0.0858687i
$435$		0			0
$436$		−	16.2556i		−	0.778501i
$437$	−7.46859	+	1.10463i	−0.357271	+	0.0528415i
$438$	28.1237	+	28.1237i	1.34380	+	1.34380i
$439$	−3.99656	−	6.92225i	−0.190746	−	0.330381i	0.754752	−	0.656010i	$-0.227757\pi$
$439$	−3.99656	−	6.92225i	−0.190746	−	0.330381i	−0.945498	+	0.325629i	$0.894424\pi$
$440$		0			0
$441$	−14.3852	+	24.9158i	−0.685008	+	1.18647i
$442$	−22.3938	−	6.00041i	−1.06517	−	0.285410i
$443$	27.4129	−	7.34527i	1.30243	−	0.348984i	0.460060	−	0.887888i	$-0.347828\pi$
$443$	27.4129	−	7.34527i	1.30243	−	0.348984i	0.842367	+	0.538904i	$0.181161\pi$
$444$		−	7.61484i		−	0.361384i
$445$		0			0
$446$	−10.1740	+	17.6220i	−0.481755	+	0.834424i
$447$	44.3609	−	11.8865i	2.09820	−	0.562211i
$448$	−8.57321	−	8.57321i	−0.405046	−	0.405046i
$449$	12.7915			0.603667			0.301834	−	0.953361i	$-0.402401\pi$
$449$	12.7915			0.603667			0.301834	+	0.953361i	$0.402401\pi$
$450$		0			0
$451$	−13.7889	+	7.96101i	−0.649293	+	0.374869i
$452$	8.28547	−	2.22008i	0.389716	−	0.104424i
$453$	10.5696	−	39.4463i	0.496604	−	1.85335i
$454$	4.33013	−	2.50000i	0.203223	−	0.117331i
$455$		0			0
$456$	−38.3110	+	16.5891i	−1.79408	+	0.776858i
$457$	10.2697	−	10.2697i	0.480396	−	0.480396i	−0.424862	−	0.905258i	$-0.639677\pi$
$457$	10.2697	−	10.2697i	0.480396	−	0.480396i	0.905258	+	0.424862i	$0.139677\pi$
$458$	−20.2844	−	5.43520i	−0.947830	−	0.253970i
$459$	−37.0081	−	64.0999i	−1.72739	−	2.99193i
$460$		0			0
$461$	1.21113	+	2.09773i	0.0564078	+	0.0977011i	0.892850	−	0.450353i	$-0.148702\pi$
$461$	1.21113	+	2.09773i	0.0564078	+	0.0977011i	−0.836443	+	0.548054i	$0.815369\pi$
$462$	−6.00041	−	22.3938i	−0.279164	−	1.04185i
$463$	−16.1575	−	16.1575i	−0.750905	−	0.750905i	0.223743	−	0.974648i	$-0.428172\pi$
$463$	−16.1575	−	16.1575i	−0.750905	−	0.750905i	−0.974648	+	0.223743i	$0.928172\pi$
$464$	−5.52971			−0.256711
$465$		0			0
$466$	−24.5777	−	14.1900i	−1.13854	−	0.657338i
$467$	1.50603	−	1.50603i	0.0696909	−	0.0696909i	−0.671402	−	0.741093i	$-0.734308\pi$
$467$	1.50603	−	1.50603i	0.0696909	−	0.0696909i	0.741093	+	0.671402i	$0.234308\pi$
$468$	21.3232	−	21.3232i	0.985663	−	0.985663i
$469$	−9.32738	+	16.1555i	−0.430698	+	0.745991i
$470$		0			0
$471$	55.4444	+	32.0108i	2.55474	+	1.47498i
$472$	−27.0287	−	7.24231i	−1.24410	−	0.333354i
$473$	0.361955	−	1.35084i	0.0166427	−	0.0621115i
$474$	−36.3731			−1.67067
$475$		0			0
$476$	−9.57775			−0.438995
$477$	−13.0310	+	48.6325i	−0.596650	+	2.22673i
$478$	8.69333	+	2.32937i	0.397624	+	0.106543i
$479$	12.9261	+	7.46291i	0.590611	+	0.340989i	0.765339	−	0.643628i	$-0.222571\pi$
$479$	12.9261	+	7.46291i	0.590611	+	0.340989i	−0.174728	+	0.984617i	$0.555905\pi$
$480$		0			0
$481$	−5.00000	+	8.66025i	−0.227980	+	0.394874i
$482$	3.43837	−	3.43837i	0.156613	−	0.156613i
$483$	−6.77249	+	6.77249i	−0.308159	+	0.308159i
$484$	5.69650	+	3.28887i	0.258932	+	0.149494i
$485$		0			0
$486$	−27.3852			−1.24222
$487$	−8.92004	−	8.92004i	−0.404205	−	0.404205i	0.475507	−	0.879712i	$-0.342265\pi$
$487$	−8.92004	−	8.92004i	−0.404205	−	0.404205i	−0.879712	+	0.475507i	$0.842265\pi$
$488$	−9.76608	−	36.4475i	−0.442090	−	1.64990i
$489$	8.29457	+	14.3666i	0.375094	+	0.649681i
$490$		0			0
$491$	−0.922253	−	1.59739i	−0.0416207	−	0.0720891i	0.844465	−	0.535611i	$-0.179919\pi$
$491$	−0.922253	−	1.59739i	−0.0416207	−	0.0720891i	−0.886085	+	0.463522i	$0.846585\pi$
$492$	11.7112	+	3.13801i	0.527983	+	0.141473i
$493$	−21.6217	+	21.6217i	−0.973794	+	0.973794i
$494$	18.1544	+	2.09629i	0.816806	+	0.0943166i
$495$		0			0
$496$	−1.78887	+	1.03281i	−0.0803228	+	0.0463744i
$497$	−1.07552	+	4.01390i	−0.0482437	+	0.180048i
$498$	−22.3938	+	6.00041i	−1.00349	+	0.268885i
$499$	3.59876	−	2.07775i	0.161103	−	0.0930127i	−0.417281	−	0.908777i	$-0.637017\pi$
$499$	3.59876	−	2.07775i	0.161103	−	0.0930127i	0.578384	+	0.815765i	$0.303684\pi$
$500$		0			0
$501$	−62.5036			−2.79245
$502$	1.71279	+	1.71279i	0.0764456	+	0.0764456i
$503$	11.0668	−	2.96535i	0.493446	−	0.132218i	−0.00351074	−	0.999994i	$-0.501118\pi$
$503$	11.0668	−	2.96535i	0.493446	−	0.132218i	0.496957	+	0.867775i	$0.334451\pi$
$504$	−18.6869	+	32.3666i	−0.832380	+	1.44172i
$505$		0			0
$506$			7.26177i			0.322825i
$507$	−14.1168	+	3.78260i	−0.626951	+	0.167991i
$508$	9.84528	+	2.63803i	0.436814	+	0.117044i
$509$	8.32669	−	14.4223i	0.369074	−	0.639255i	−0.620347	−	0.784328i	$-0.713008\pi$
$509$	8.32669	−	14.4223i	0.369074	−	0.639255i	0.989421	+	0.145072i	$0.0463415\pi$
$510$		0			0
$511$	−10.7889	−	18.6869i	−0.477272	−	0.826659i
$512$	7.77817	+	7.77817i	0.343750	+	0.343750i
$513$	36.2512	+	45.7159i	1.60053	+	2.01841i
$514$		−	12.4223i		−	0.547922i
$515$		0			0
$516$	−0.922253	+	0.532463i	−0.0405999	+	0.0234404i
$517$	10.1213	+	37.7733i	0.445135	+	1.66127i
$518$	1.06924	−	3.99046i	0.0469797	−	0.175331i
$519$	19.3540	+	11.1740i	0.849546	+	0.490486i
$520$		0			0
$521$		−	33.8454i		−	1.48279i	−0.671066	−	0.741397i	$-0.734163\pi$
$521$		−	33.8454i		−	1.48279i	0.671066	−	0.741397i	$-0.265837\pi$
$522$	10.2940	+	38.4177i	0.450556	+	1.68150i
$523$	8.22277	+	30.6878i	0.359556	+	1.34188i	0.874652	+	0.484751i	$0.161090\pi$
$523$	8.22277	+	30.6878i	0.359556	+	1.34188i	−0.515096	+	0.857132i	$0.672244\pi$
$524$			2.42225i			0.105817i
$525$		0			0
$526$	−13.5000	−	7.79423i	−0.588628	−	0.339845i
$527$	−2.95630	+	11.0330i	−0.128778	+	0.480607i
$528$	3.46434	+	12.9291i	0.150766	+	0.562666i
$529$	−17.3205	+	10.0000i	−0.753066	+	0.434783i
$530$		0			0
$531$			67.0879i			2.91137i
$532$	7.46859	−	1.10463i	0.323804	−	0.0478916i
$533$	−11.2586	−	11.2586i	−0.487663	−	0.487663i
$534$	−8.29457	−	14.3666i	−0.358941	−	0.621704i
$535$		0			0
$536$	16.1555	−	27.9821i	0.697811	−	1.20864i
$537$	−66.1528	−	17.7256i	−2.85470	−	0.764916i
$538$	−2.63962	+	0.707285i	−0.113802	+	0.0304932i
$539$		−	16.7703i		−	0.722349i
$540$		0			0
$541$	−2.36662	+	4.09911i	−0.101749	+	0.176234i	−0.912405	−	0.409288i	$-0.865777\pi$
$541$	−2.36662	+	4.09911i	−0.101749	+	0.176234i	0.810656	+	0.585522i	$0.199111\pi$
$542$	−2.33972	+	0.626925i	−0.100499	+	0.0269287i
$543$	−20.3035	−	20.3035i	−0.871307	−	0.871307i
$544$	27.6486			1.18542
$545$		0			0
$546$	20.0777	−	11.5919i	0.859248	−	0.496087i
$547$	3.42001	−	0.916390i	0.146229	−	0.0391820i	−0.184962	−	0.982746i	$-0.559216\pi$
$547$	3.42001	−	0.916390i	0.146229	−	0.0391820i	0.331191	+	0.943564i	$0.392550\pi$
$548$	0.275623	−	1.02864i	0.0117740	−	0.0439413i
$549$	−78.3463	+	45.2332i	−3.34374	+	1.93051i
$550$		0			0
$551$	14.3666	−	19.3540i	0.612039	−	0.824508i
$552$	11.7303	−	11.7303i	0.499275	−	0.499275i
$553$	19.0608	+	5.10734i	0.810550	+	0.217186i
$554$	−7.59533	−	13.1555i	−0.322695	−	0.558923i
$555$		0			0
$556$	−0.288874	−	0.500344i	−0.0122510	−	0.0212193i
$557$	−5.19016	−	19.3699i	−0.219914	−	0.820731i	−0.984379	−	0.176065i	$-0.943663\pi$
$557$	−5.19016	−	19.3699i	−0.219914	−	0.820731i	0.764464	−	0.644666i	$-0.223004\pi$
$558$	10.5056	+	10.5056i	0.444735	+	0.444735i
$559$	1.39849			0.0591498
$560$		0			0
$561$	64.0999	+	37.0081i	2.70630	+	1.56248i
$562$	4.61769	−	4.61769i	0.194786	−	0.194786i
$563$	−9.60092	+	9.60092i	−0.404630	+	0.404630i	−0.879861	−	0.475231i	$-0.842365\pi$
$563$	−9.60092	+	9.60092i	−0.404630	+	0.404630i	0.475231	+	0.879861i	$0.342365\pi$
$564$	14.8892	−	25.7889i	0.626949	−	1.08591i
$565$		0			0
$566$	10.7889	+	6.22896i	0.453490	+	0.261823i
$567$	35.3938	+	9.48375i	1.48640	+	0.398280i
$568$	1.86286	−	6.95228i	0.0781638	−	0.291711i
$569$	−4.13123			−0.173190			−0.0865950	−	0.996244i	$-0.527599\pi$
$569$	−4.13123			−0.173190			−0.0865950	+	0.996244i	$0.527599\pi$
$570$		0			0
$571$	19.1555			0.801632			0.400816	−	0.916158i	$-0.368727\pi$
$571$	19.1555			0.801632			0.400816	+	0.916158i	$0.368727\pi$
$572$	−4.54946	+	16.9788i	−0.190222	+	0.709919i
$573$	48.0386	+	12.8719i	2.00684	+	0.537732i
$574$	5.69650	+	3.28887i	0.237767	+	0.137275i
$575$		0			0
$576$	25.1740	−	43.6027i	1.04892	−	1.81678i
$577$	7.34847	−	7.34847i	0.305921	−	0.305921i	−0.537404	−	0.843325i	$-0.680595\pi$
$577$	7.34847	−	7.34847i	0.305921	−	0.305921i	0.843325	+	0.537404i	$0.180595\pi$
$578$	−9.60092	+	9.60092i	−0.399346	+	0.399346i
$579$	−43.1728	−	24.9258i	−1.79420	−	1.03588i
$580$		0			0
$581$	12.5777			0.521813
$582$	−16.2372	−	16.2372i	−0.673055	−	0.673055i
$583$	−7.59584	−	28.3481i	−0.314588	−	1.17406i
$584$	18.6869	+	32.3666i	0.773268	+	1.33934i
$585$		0			0
$586$	0.711126	+	1.23171i	0.0293764	+	0.0508813i
$587$	9.39380	+	2.51706i	0.387724	+	0.103890i	0.447415	−	0.894327i	$-0.352345\pi$
$587$	9.39380	+	2.51706i	0.387724	+	0.103890i	−0.0596909	+	0.998217i	$0.519012\pi$
$588$	−9.02999	+	9.02999i	−0.372390	+	0.372390i
$589$	1.03281	−	8.94437i	0.0425561	−	0.368546i
$590$		0			0
$591$	10.5000	−	6.06218i	0.431912	−	0.249365i
$592$	−0.617326	+	2.30389i	−0.0253719	+	0.0946894i
$593$	15.0573	−	4.03459i	0.618329	−	0.165681i	0.0639609	−	0.997952i	$-0.479627\pi$
$593$	15.0573	−	4.03459i	0.618329	−	0.165681i	0.554368	+	0.832272i	$0.312960\pi$
$594$	48.6000	−	28.0592i	1.99408	−	1.15128i
$595$		0			0
$596$	14.3852			0.589239
$597$	34.2135	+	34.2135i	1.40026	+	1.40026i
$598$	−7.01433	+	1.87948i	−0.286837	+	0.0768578i
$599$	20.0854	−	34.7889i	0.820666	−	1.42143i	−0.0845214	−	0.996422i	$-0.526936\pi$
$599$	20.0854	−	34.7889i	0.820666	−	1.42143i	0.905187	−	0.425013i	$-0.139731\pi$
$600$		0			0
$601$		−	25.5830i		−	1.04355i	−0.853083	−	0.521775i	$-0.825270\pi$
$601$		−	25.5830i		−	1.04355i	0.853083	−	0.521775i	$-0.174730\pi$
$602$	−0.558061	+	0.149532i	−0.0227449	+	0.00609447i
$603$	−74.8269	−	20.0498i	−3.04719	−	0.816491i
$604$	6.39574	−	11.0777i	0.260239	−	0.450747i
$605$		0			0
$606$	13.3852	+	23.1838i	0.543735	+	0.941777i
$607$	−11.4499	−	11.4499i	−0.464736	−	0.464736i	0.435468	−	0.900204i	$-0.356583\pi$
$607$	−11.4499	−	11.4499i	−0.464736	−	0.464736i	−0.900204	+	0.435468i	$0.856583\pi$
$608$	−21.5600	+	3.18878i	−0.874372	+	0.129322i
$609$		−	30.5777i		−	1.23907i
$610$		0			0
$611$	−33.8666	+	19.5529i	−1.37010	+	0.791026i
$612$	−10.2940	−	38.4177i	−0.416110	−	1.55294i
$613$	3.86192	−	14.4129i	0.155982	−	0.582132i	−0.843038	−	0.537855i	$-0.819235\pi$
$613$	3.86192	−	14.4129i	0.155982	−	0.582132i	0.999019	−	0.0442769i	$-0.0140984\pi$
$614$	5.72862	+	3.30742i	0.231188	+	0.133477i
$615$		0			0
$616$		−	21.7853i		−	0.877755i
$617$	5.27649	+	19.6921i	0.212424	+	0.792776i	0.987058	+	0.160366i	$0.0512675\pi$
$617$	5.27649	+	19.6921i	0.212424	+	0.792776i	−0.774634	+	0.632410i	$0.782066\pi$
$618$	−1.97086	−	7.35537i	−0.0792798	−	0.295876i
$619$			2.42225i			0.0973586i	0.998814	+	0.0486793i	$0.0155012\pi$
$619$			2.42225i			0.0973586i	−0.998814	+	0.0486793i	$0.984499\pi$
$620$		0			0
$621$	−20.0777	−	11.5919i	−0.805692	−	0.465167i
$622$	−0.458195	+	1.71001i	−0.0183719	+	0.0685650i
$623$	2.32937	+	8.69333i	0.0933243	+	0.348291i
$624$	−11.5919	+	6.69258i	−0.464047	+	0.267918i
$625$		0			0
$626$		−	23.1838i		−	0.926610i
$627$	−54.2524	−	21.4656i	−2.16663	−	0.857252i
$628$	14.1798	+	14.1798i	0.565835	+	0.565835i
$629$	6.59464	+	11.4223i	0.262946	+	0.455435i
$630$		0			0
$631$	0.866621	−	1.50103i	0.0344996	−	0.0597551i	−0.848260	−	0.529580i	$-0.822350\pi$
$631$	0.866621	−	1.50103i	0.0344996	−	0.0597551i	0.882760	+	0.469825i	$0.155683\pi$
$632$	−33.0144	−	8.84617i	−1.31324	−	0.351882i
$633$	−40.4750	+	10.8452i	−1.60874	+	0.431060i
$634$			4.00000i			0.158860i
$635$		0			0
$636$	−11.1740	+	19.3540i	−0.443079	+	0.767436i
$637$	16.1989	−	4.34048i	0.641824	−	0.171976i
$638$	−16.3934	−	16.3934i	−0.649021	−	0.649021i
$639$	−17.2563			−0.682647
$640$		0			0
$641$	−18.8666	+	10.8926i	−0.745187	+	0.430234i	−0.823952	−	0.566659i	$-0.808236\pi$
$641$	−18.8666	+	10.8926i	−0.745187	+	0.430234i	0.0787654	+	0.996893i	$0.474902\pi$
$642$	4.38594	−	1.17521i	0.173099	−	0.0463818i
$643$	−0.723911	+	2.70167i	−0.0285483	+	0.106544i	−0.978730	−	0.205153i	$-0.934231\pi$
$643$	−0.723911	+	2.70167i	−0.0285483	+	0.106544i	0.950182	+	0.311697i	$0.100897\pi$
$644$	−2.59808	+	1.50000i	−0.102379	+	0.0591083i
$645$		0			0
$646$	14.3666	−	19.3540i	0.565247	−	0.761473i
$647$	29.8202	−	29.8202i	1.17235	−	1.17235i	0.190705	−	0.981647i	$-0.438923\pi$
$647$	29.8202	−	29.8202i	1.17235	−	1.17235i	0.981647	−	0.190705i	$-0.0610774\pi$
$648$	−61.3039	−	16.4263i	−2.40825	−	0.645287i
$649$	−19.5529	−	33.8666i	−0.767519	−	1.32938i
$650$		0			0
$651$	−5.71113	−	9.89196i	−0.223837	−	0.387697i
$652$	1.34486	+	5.01910i	0.0526689	+	0.196563i
$653$	−11.4944	−	11.4944i	−0.449812	−	0.449812i	0.445480	−	0.895292i	$-0.353033\pi$
$653$	−11.4944	−	11.4944i	−0.449812	−	0.449812i	−0.895292	+	0.445480i	$0.853033\pi$
$654$	51.8973			2.02934
$655$		0			0
$656$	−3.28887	−	1.89883i	−0.128409	−	0.0741369i
$657$	63.3600	−	63.3600i	2.47191	−	2.47191i
$658$	11.4237	−	11.4237i	0.445341	−	0.445341i
$659$	−13.3239	+	23.0777i	−0.519027	+	0.898981i	0.480728	+	0.876870i	$0.340372\pi$
$659$	−13.3239	+	23.0777i	−0.519027	+	0.898981i	−0.999756	+	0.0221118i	$0.992961\pi$
$660$		0			0
$661$	−26.0221	−	15.0239i	−1.01214	−	0.584361i	−0.100325	−	0.994955i	$-0.531988\pi$
$661$	−26.0221	−	15.0239i	−1.01214	−	0.584361i	−0.911818	+	0.410594i	$0.865321\pi$
$662$	16.7303	+	4.48288i	0.650243	+	0.174232i
$663$	−19.1568	+	71.4941i	−0.743988	+	2.77660i
$664$	−21.7853			−0.845433
$665$		0			0
$666$	17.1555			0.664762
$667$	−2.47890	+	9.25139i	−0.0959835	+	0.358215i
$668$	−18.9107	−	5.06709i	−0.731675	−	0.196052i
$669$	56.2595	+	32.4815i	2.17512	+	1.25581i
$670$		0			0
$671$	26.3666	−	45.6683i	1.01787	−	1.76301i
$672$	−19.5505	+	19.5505i	−0.754177	+	0.754177i
$673$	−0.843283	+	0.843283i	−0.0325062	+	0.0325062i	−0.723173	−	0.690667i	$-0.757317\pi$
$673$	−0.843283	+	0.843283i	−0.0325062	+	0.0325062i	0.690667	+	0.723173i	$0.257317\pi$
$674$	9.85984	+	5.69258i	0.379787	+	0.219270i
$675$		0			0
$676$	−4.57775			−0.176067
$677$	29.8084	+	29.8084i	1.14563	+	1.14563i	0.987402	+	0.158229i	$0.0505784\pi$
$677$	29.8084	+	29.8084i	1.14563	+	1.14563i	0.158229	+	0.987402i	$0.449422\pi$
$678$	7.08780	+	26.4520i	0.272205	+	1.01588i
$679$	6.22896	+	10.7889i	0.239046	+	0.414039i
$680$		0			0
$681$	−7.98146	−	13.8243i	−0.305850	−	0.529748i
$682$	−8.36516	−	2.24144i	−0.320319	−	0.0858291i
$683$	27.7971	−	27.7971i	1.06363	−	1.06363i	0.0657918	−	0.997833i	$-0.479043\pi$
$683$	27.7971	−	27.7971i	1.06363	−	1.06363i	0.997833	−	0.0657918i	$-0.0209573\pi$
$684$	12.4579	+	28.7703i	0.476340	+	1.10006i
$685$		0			0
$686$	−16.5000	+	9.52628i	−0.629973	+	0.363715i
$687$	−17.3523	+	64.7598i	−0.662032	+	2.47074i
$688$	0.322197	−	0.0863323i	0.0122836	−	0.00329139i
$689$	25.4162	−	14.6740i	0.968279	−	0.559036i
$690$		0			0
$691$	37.7332			1.43544			0.717720	−	0.696332i	$-0.245186\pi$
$691$	37.7332			1.43544			0.717720	+	0.696332i	$0.245186\pi$
$692$	4.94975	+	4.94975i	0.188161	+	0.188161i
$693$	−50.4511	+	13.5183i	−1.91648	+	0.513519i
$694$	−10.0266	+	17.3666i	−0.380605	+	0.659228i
$695$		0			0
$696$			52.9622i			2.00753i
$697$	−20.2844	+	5.43520i	−0.768328	+	0.205873i
$698$	32.1759	+	8.62152i	1.21788	+	0.326329i
$699$	−45.3026	+	78.4665i	−1.71350	+	2.96787i
$700$		0			0
$701$	18.2518	+	31.6130i	0.689360	+	1.19401i	0.972045	+	0.234794i	$0.0754417\pi$
$701$	18.2518	+	31.6130i	0.689360	+	1.19401i	−0.282685	+	0.959213i	$0.591225\pi$
$702$	39.6817	+	39.6817i	1.49769	+	1.49769i
$703$	−6.45976	−	8.14633i	−0.243635	−	0.307245i
$704$			29.3481i			1.10610i
$705$		0			0
$706$	−8.07775	+	4.66369i	−0.304010	+	0.175520i
$707$	−3.75897	−	14.0287i	−0.141370	−	0.527602i
$708$	−7.70722	+	28.7638i	−0.289655	+	1.08101i
$709$	30.4456	+	17.5777i	1.14341	+	0.660146i	0.947272	−	0.320431i	$-0.103828\pi$
$709$	30.4456	+	17.5777i	1.14341	+	0.660146i	0.196135	+	0.980577i	$0.437161\pi$
$710$		0			0
$711$			81.9450i			3.07318i
$712$	−4.03459	−	15.0573i	−0.151203	−	0.564296i
$713$	0.925989	+	3.45584i	0.0346786	+	0.129422i
$714$		−	30.5777i		−	1.14434i
$715$		0			0
$716$	−18.5777	−	10.7259i	−0.694283	−	0.400844i
$717$	7.43671	−	27.7542i	0.277729	−	1.03650i
$718$	−0.467794	−	1.74583i	−0.0174579	−	0.0651538i
$719$	21.3171	−	12.3074i	0.794993	−	0.458989i	−0.0467246	−	0.998908i	$-0.514878\pi$
$719$	21.3171	−	12.3074i	0.794993	−	0.458989i	0.841717	+	0.539919i	$0.181545\pi$
$720$		0			0
$721$			4.13123i			0.153855i
$722$	−8.97073	+	16.7489i	−0.333856	+	0.623330i
$723$	−10.9773	−	10.9773i	−0.408249	−	0.408249i
$724$	−4.49691	−	7.78887i	−0.167126	−	0.289471i
$725$		0			0
$726$	−10.5000	+	18.1865i	−0.389692	+	0.674966i
$727$	−27.6731	−	7.41497i	−1.02634	−	0.275006i	−0.293897	−	0.955837i	$-0.594952\pi$
$727$	−27.6731	−	7.41497i	−1.02634	−	0.275006i	−0.732441	+	0.680831i	$0.761619\pi$
$728$	21.0430	−	5.63845i	0.779905	−	0.208975i
$729$			23.9629i			0.887515i
$730$		0			0
$731$	0.922253	−	1.59739i	0.0341108	−	0.0590816i
$732$	−38.7872	+	10.3930i	−1.43362	+	0.384137i
$733$	−14.6969	−	14.6969i	−0.542844	−	0.542844i	0.381518	−	0.924362i	$-0.375402\pi$
$733$	−14.6969	−	14.6969i	−0.542844	−	0.542844i	−0.924362	+	0.381518i	$0.875402\pi$
$734$	2.73274			0.100867
$735$		0			0
$736$	7.50000	−	4.33013i	0.276454	−	0.159611i
$737$	43.6169	−	11.6871i	1.60665	−	0.430500i
$738$	−7.06965	+	26.3843i	−0.260237	+	0.971219i
$739$	44.4366	−	25.6555i	1.63463	−	0.943753i	0.651988	−	0.758230i	$-0.273935\pi$
$739$	44.4366	−	25.6555i	1.63463	−	0.943753i	0.982640	−	0.185523i	$-0.0593979\pi$
$740$		0			0
$741$	6.69258	−	57.9595i	0.245858	−	2.12919i
$742$	−8.57321	+	8.57321i	−0.314733	+	0.314733i
$743$	20.5848	+	5.51569i	0.755184	+	0.202351i	0.615816	−	0.787890i	$-0.288826\pi$
$743$	20.5848	+	5.51569i	0.755184	+	0.202351i	0.139368	+	0.990241i	$0.455493\pi$
$744$	9.89196	+	17.1334i	0.362657	+	0.628140i
$745$		0			0
$746$	−11.6740	−	20.2200i	−0.427417	−	0.740308i
$747$	13.5183	+	50.4511i	0.494610	+	1.84591i
$748$	16.3934	+	16.3934i	0.599403	+	0.599403i
$749$	−2.46341			−0.0900112
$750$		0			0
$751$	12.5777	+	7.26177i	0.458969	+	0.264986i	0.711610	−	0.702574i	$-0.247966\pi$
$751$	12.5777	+	7.26177i	0.458969	+	0.264986i	−0.252642	+	0.967560i	$0.581299\pi$
$752$	−6.59545	+	6.59545i	−0.240511	+	0.240511i
$753$	5.46823	−	5.46823i	0.199273	−	0.199273i
$754$	11.5919	−	20.0777i	0.422152	−	0.731188i
$755$		0			0
$756$	20.0777	+	11.5919i	0.730221	+	0.421593i
$757$	−27.6731	−	7.41497i	−1.00579	−	0.269502i	−0.281923	−	0.959437i	$-0.590972\pi$
$757$	−27.6731	−	7.41497i	−1.00579	−	0.269502i	−0.723871	+	0.689935i	$0.757639\pi$
$758$	5.55212	−	20.7208i	0.201662	−	0.752613i
$759$	23.1838			0.841518
$760$		0			0
$761$	−52.7703			−1.91292			−0.956461	−	0.291859i	$-0.905726\pi$
$761$	−52.7703			−1.91292			−0.956461	+	0.291859i	$0.905726\pi$
$762$	−8.42214	+	31.4319i	−0.305102	+	1.13866i
$763$	−27.1961	−	7.28718i	−0.984566	−	0.263814i
$764$	13.4907	+	7.78887i	0.488077	+	0.281792i
$765$		0			0
$766$	−8.50000	+	14.7224i	−0.307117	+	0.531943i
$767$	27.6520	−	27.6520i	0.998455	−	0.998455i
$768$	38.3774	−	38.3774i	1.38483	−	1.38483i
$769$	9.39162	+	5.42225i	0.338670	+	0.195531i	0.659684	−	0.751543i	$-0.270690\pi$
$769$	9.39162	+	5.42225i	0.338670	+	0.195531i	−0.321014	+	0.947075i	$0.604023\pi$
$770$		0			0
$771$	−39.6591			−1.42829
$772$	−11.0414	−	11.0414i	−0.397387	−	0.397387i
$773$	3.66371	+	13.6732i	0.131775	+	0.491789i	0.999990	−	0.00439751i	$-0.00139978\pi$
$773$	3.66371	+	13.6732i	0.131775	+	0.491789i	−0.868216	+	0.496187i	$0.834733\pi$
$774$	−1.19959	−	2.07775i	−0.0431183	−	0.0746831i
$775$		0			0
$776$	−10.7889	−	18.6869i	−0.387298	−	0.670820i
$777$	−12.7399	−	3.41364i	−0.457040	−	0.122464i
$778$	0.408529	−	0.408529i	0.0146465	−	0.0146465i
$779$	15.1907	−	6.57775i	0.544262	−	0.235672i
$780$		0			0
$781$	8.71113	−	5.02937i	0.311709	−	0.179965i
$782$	−2.47890	+	9.25139i	−0.0886454	+	0.330829i
$783$	71.4941	−	19.1568i	2.55499	−	0.684608i
$784$	3.46410	−	2.00000i	0.123718	−	0.0714286i
$785$		0			0
$786$	−7.73324			−0.275836
$787$	−8.92004	−	8.92004i	−0.317965	−	0.317965i	0.530020	−	0.847985i	$-0.322184\pi$
$787$	−8.92004	−	8.92004i	−0.317965	−	0.317965i	−0.847985	+	0.530020i	$0.822184\pi$
$788$	3.66826	−	0.982908i	0.130676	−	0.0350146i
$789$	−24.8837	+	43.0999i	−0.885884	+	1.53440i
$790$		0			0
$791$		−	14.8571i		−	0.528257i
$792$	87.3839	−	23.4144i	3.10505	−	0.831996i
$793$	50.9364	+	13.6484i	1.80880	+	0.484668i
$794$	3.99656	−	6.92225i	0.141833	−	0.245662i
$795$		0			0
$796$	7.57775	+	13.1250i	0.268586	+	0.465205i
$797$	−6.06538	−	6.06538i	−0.214847	−	0.214847i	0.591476	−	0.806323i	$-0.298546\pi$
$797$	−6.06538	−	6.06538i	−0.214847	−	0.214847i	−0.806323	+	0.591476i	$0.798546\pi$
$798$	3.52661	+	23.8441i	0.124841	+	0.844071i
$799$			51.5777i			1.82469i
$800$		0			0
$801$	−32.3666	+	18.6869i	−1.14362	+	0.660268i
$802$	−9.48375	−	35.3938i	−0.334883	−	1.24980i
$803$	−13.5183	+	50.4511i	−0.477052	+	1.78038i
$804$	−29.7784	−	17.1926i	−1.05020	−	0.606336i
$805$		0			0
$806$		−	8.66025i		−	0.305044i
$807$	2.25806	+	8.42721i	0.0794876	+	0.296652i
$808$	6.51072	+	24.2983i	0.229046	+	0.854813i
$809$		−	42.5777i		−	1.49695i	−0.663161	−	0.748477i	$-0.730785\pi$
$809$		−	42.5777i		−	1.49695i	0.663161	−	0.748477i	$-0.269215\pi$
$810$		0			0
$811$	29.3666	+	16.9548i	1.03120	+	0.595364i	0.917329	−	0.398131i	$-0.130341\pi$
$811$	29.3666	+	16.9548i	1.03120	+	0.595364i	0.113873	+	0.993495i	$0.463674\pi$
$812$	2.47890	−	9.25139i	0.0869925	−	0.324660i
$813$	2.00151	+	7.46974i	0.0701960	+	0.261975i
$814$	−8.66025	+	5.00000i	−0.303542	+	0.175250i
$815$		0			0
$816$			17.6541i			0.618016i
$817$	−0.534928	+	1.35199i	−0.0187148	+	0.0473000i
$818$	−27.8878	−	27.8878i	−0.975076	−	0.975076i
$819$	−26.1154	−	45.2332i	−0.912547	−	1.58058i
$820$		0			0
$821$	−0.577747	+	1.00069i	−0.0201635	+	0.0349242i	−0.875931	−	0.482436i	$-0.839752\pi$
$821$	−0.577747	+	1.00069i	−0.0201635	+	0.0349242i	0.855768	+	0.517360i	$0.173085\pi$
$822$	3.28402	+	0.879949i	0.114543	+	0.0306918i
$823$	−43.4988	+	11.6555i	−1.51627	+	0.406285i	−0.918513	−	0.395390i	$-0.870610\pi$
$823$	−43.4988	+	11.6555i	−1.51627	+	0.406285i	−0.597761	+	0.801674i	$0.703943\pi$
$824$		−	7.15549i		−	0.249273i
$825$		0			0
$826$	−8.07775	+	13.9911i	−0.281061	+	0.486812i
$827$	−24.4485	+	6.55097i	−0.850159	+	0.227799i	−0.657489	−	0.753464i	$-0.728381\pi$
$827$	−24.4485	+	6.55097i	−0.850159	+	0.227799i	−0.192670	+	0.981264i	$0.561715\pi$
$828$	−8.80908	−	8.80908i	−0.306137	−	0.306137i
$829$	44.9691			1.56184			0.780920	−	0.624631i	$-0.214750\pi$
$829$	44.9691			1.56184			0.780920	+	0.624631i	$0.214750\pi$
$830$		0			0
$831$	−42.0000	+	24.2487i	−1.45696	+	0.841178i
$832$	−28.3481	+	7.59584i	−0.982792	+	0.263338i
$833$	5.72478	−	21.3652i	0.198352	−	0.740260i
$834$	1.59739	−	0.922253i	0.0553130	−	0.0319350i
$835$		0			0
$836$	−14.6740	−	10.8926i	−0.507512	−	0.376730i
$837$	19.5505	−	19.5505i	0.675764	−	0.675764i
$838$	23.1822	+	6.21166i	0.800816	+	0.214578i
$839$	10.0266	+	17.3666i	0.346157	+	0.599562i	0.985563	−	0.169307i	$-0.0541530\pi$
$839$	10.0266	+	17.3666i	0.346157	+	0.599562i	−0.639406	+	0.768869i	$0.720820\pi$
$840$		0			0
$841$	−0.788874	−	1.36637i	−0.0272025	−	0.0471162i
$842$	−3.93163	−	14.6730i	−0.135493	−	0.505667i
$843$	−14.7424	−	14.7424i	−0.507754	−	0.507754i
$844$	−13.1250			−0.451783
$845$		0			0
$846$	58.0999	+	33.5440i	1.99751	+	1.15327i
$847$	8.05606	−	8.05606i	0.276810	−	0.276810i
$848$	4.94975	−	4.94975i	0.169975	−	0.169975i
$849$	19.8865	−	34.4444i	0.682502	−	1.18213i
$850$		0			0
$851$	3.57775	+	2.06561i	0.122644	+	0.0708083i
$852$	−7.39857	−	1.98244i	−0.253471	−	0.0679173i
$853$	−0.0863323	+	0.322197i	−0.00295596	+	0.0110318i	−0.967388	−	0.253299i	$-0.918484\pi$
$853$	−0.0863323	+	0.322197i	−0.00295596	+	0.0110318i	0.964432	+	0.264331i	$0.0851510\pi$
$854$	−21.7853			−0.745478
$855$		0			0
$856$	4.26676			0.145835
$857$	−2.11080	+	7.87760i	−0.0721035	+	0.269094i	−0.992561	−	0.121749i	$-0.961150\pi$
$857$	−2.11080	+	7.87760i	−0.0721035	+	0.269094i	0.920457	+	0.390843i	$0.127816\pi$
$858$	−54.2062	−	14.5245i	−1.85057	−	0.495859i
$859$	48.4011	+	27.9444i	1.65142	+	0.953450i	0.976488	+	0.215573i	$0.0691618\pi$
$859$	48.4011	+	27.9444i	1.65142	+	0.953450i	0.674935	+	0.737877i	$0.264172\pi$
$860$		0			0
$861$	10.5000	−	18.1865i	0.357839	−	0.619795i
$862$	−2.68535	+	2.68535i	−0.0914635	+	0.0914635i
$863$	9.08244	−	9.08244i	0.309170	−	0.309170i	−0.535418	−	0.844587i	$-0.679846\pi$
$863$	9.08244	−	9.08244i	0.309170	−	0.309170i	0.844587	+	0.535418i	$0.179846\pi$
$864$	−57.9595	−	33.4629i	−1.97182	−	1.13843i
$865$		0			0
$866$	−29.3852			−0.998549
$867$	30.6517	+	30.6517i	1.04099	+	1.04099i
$868$	−0.925989	−	3.45584i	−0.0314301	−	0.117299i
$869$	−23.8830	−	41.3666i	−0.810176	−	1.40327i
$870$		0			0
$871$	22.5777	+	39.1058i	0.765018	+	1.32505i
$872$	47.1051	+	12.6218i	1.59518	+	0.427427i
$873$	−36.5809	+	36.5809i	−1.23808	+	1.23808i
$874$	0.866025	−	7.50000i	0.0292937	−	0.253691i
$875$		0			0
$876$	34.4444	−	19.8865i	1.16377	−	0.671901i
$877$	−4.81787	+	17.9806i	−0.162688	+	0.607160i	0.835636	+	0.549284i	$0.185099\pi$
$877$	−4.81787	+	17.9806i	−0.162688	+	0.607160i	−0.998324	+	0.0578760i	$0.981567\pi$
$878$	7.72077	−	2.06877i	0.260563	−	0.0698177i
$879$	3.93233	−	2.27033i	0.132634	−	0.0765763i
$880$		0			0
$881$	−12.0371			−0.405540			−0.202770	−	0.979226i	$-0.564994\pi$
$881$	−12.0371			−0.405540			−0.202770	+	0.979226i	$0.564994\pi$
$882$	−20.3437	−	20.3437i	−0.685008	−	0.685008i
$883$	31.4034	−	8.41451i	1.05681	−	0.283171i	0.311745	−	0.950166i	$-0.399086\pi$
$883$	31.4034	−	8.41451i	1.05681	−	0.283171i	0.745062	+	0.666995i	$0.232420\pi$
$884$	−11.5919	+	20.0777i	−0.389878	+	0.675288i
$885$		0			0
$886$			28.3799i			0.953443i
$887$	−14.0810	+	3.77300i	−0.472794	+	0.126685i	−0.487345	−	0.873209i	$-0.662035\pi$
$887$	−14.0810	+	3.77300i	−0.472794	+	0.126685i	0.0145510	+	0.999894i	$0.495368\pi$
$888$	22.0661	+	5.91259i	0.740490	+	0.198414i
$889$	8.82704	−	15.2889i	0.296049	−	0.512772i
$890$		0			0
$891$	−44.3481	−	76.8131i	−1.48572	−	2.57334i
$892$	14.3883	+	14.3883i	0.481755	+	0.481755i
$893$	−5.94860	−	40.2196i	−0.199062	−	1.34590i
$894$			45.9258i			1.53599i
$895$		0			0
$896$	−4.50000	+	2.59808i	−0.150334	+	0.0867956i
$897$	6.00041	+	22.3938i	0.200348	+	0.747708i
$898$	−3.31068	+	12.3556i	−0.110479	+	0.412312i
$899$	−9.89196	−	5.71113i	−0.329915	−	0.190477i
$900$		0			0
$901$		−	38.7080i		−	1.28955i
$902$	−4.12092	−	15.3795i	−0.137212	−	0.512081i
$903$	0.477393	+	1.78166i	0.0158867	+	0.0592898i
$904$			25.7332i			0.855875i
$905$		0			0
$906$	35.3666	+	20.4189i	1.17498	+	0.678373i
$907$	0.607727	−	2.26807i	0.0201792	−	0.0753100i	−0.955102	−	0.296277i	$-0.904255\pi$
$907$	0.607727	−	2.26807i	0.0201792	−	0.0753100i	0.975281	+	0.220967i	$0.0709214\pi$
$908$	−1.29410	−	4.82963i	−0.0429461	−	0.160277i
$909$	52.2308	−	30.1555i	1.73239	−	1.00019i
$910$		0			0
$911$		−	60.2240i		−	1.99531i	−0.0684479	−	0.997655i	$-0.521805\pi$
$911$		−	60.2240i		−	1.99531i	0.0684479	−	0.997655i	$-0.478195\pi$
$912$	−2.03609	−	13.7664i	−0.0674217	−	0.455851i
$913$	−21.5283	−	21.5283i	−0.712481	−	0.712481i
$914$	7.26177	+	12.5777i	0.240198	+	0.416035i
$915$		0			0
$916$	−10.5000	+	18.1865i	−0.346930	+	0.600900i
$917$	4.05251	+	1.08587i	0.133826	+	0.0358585i
$918$	71.4941	−	19.1568i	2.35966	−	0.632268i
$919$		−	0.422253i		−	0.0139288i	−0.999976	−	0.00696442i	$-0.997783\pi$
$919$		−	0.422253i		−	0.0139288i	0.999976	−	0.00696442i	$-0.00221686\pi$
$920$		0			0
$921$	10.5592	−	18.2891i	0.347938	−	0.602646i
$922$	−2.33972	+	0.626925i	−0.0770545	+	0.0206467i
$923$	7.11260	+	7.11260i	0.234114	+	0.234114i
$924$	−23.1838			−0.762691
$925$		0			0
$926$	19.7889	−	11.4251i	0.650303	−	0.375452i
$927$	−16.5709	+	4.44017i	−0.544261	+	0.145834i
$928$	−7.15598	+	26.7065i	−0.234906	+	0.876683i
$929$	−38.4708	+	22.2111i	−1.26219	+	0.728723i	−0.973497	−	0.228700i	$-0.926553\pi$
$929$	−38.4708	+	22.2111i	−1.26219	+	0.728723i	−0.288689	+	0.957423i	$0.593219\pi$
$930$		0			0
$931$	−2.00000	+	17.3205i	−0.0655474	+	0.567657i
$932$	−20.0676	+	20.0676i	−0.657338	+	0.657338i
$933$	5.45934	+	1.46283i	0.178731	+	0.0478908i
$934$	1.06493	+	1.84451i	0.0348454	+	0.0603541i
$935$		0			0
$936$	45.2332	+	78.3463i	1.47849	+	2.56083i
$937$	3.67263	+	13.7065i	0.119980	+	0.447770i	0.999611	−	0.0278855i	$-0.00887739\pi$
$937$	3.67263	+	13.7065i	0.119980	+	0.447770i	−0.879631	+	0.475656i	$0.842211\pi$
$938$	−13.1909	−	13.1909i	−0.430698	−	0.430698i
$939$	−74.0161			−2.41543
$940$		0			0
$941$	−28.5000	−	16.4545i	−0.929073	−	0.536401i	−0.0425550	−	0.999094i	$-0.513550\pi$
$941$	−28.5000	−	16.4545i	−0.929073	−	0.536401i	−0.886518	+	0.462693i	$0.846883\pi$
$942$	−45.2701	+	45.2701i	−1.47498	+	1.47498i
$943$	−4.65117	+	4.65117i	−0.151463	+	0.151463i
$944$	4.66369	−	8.07775i	0.151790	−	0.262908i
$945$		0			0
$946$	1.21113	+	0.699244i	0.0393771	+	0.0227344i
$947$	21.7494	+	5.82774i	0.706761	+	0.189376i	0.594257	−	0.804275i	$-0.297446\pi$
$947$	21.7494	+	5.82774i	0.706761	+	0.189376i	0.112504	+	0.993651i	$0.464113\pi$
$948$	−9.41404	+	35.1337i	−0.305754	+	1.14109i
$949$	−52.2308			−1.69549
$950$		0			0
$951$	12.7703			0.414106
$952$	7.43671	−	27.7542i	0.241025	−	0.899518i
$953$	12.9649	+	3.47393i	0.419974	+	0.112532i	0.462616	−	0.886559i	$-0.346911\pi$
$953$	12.9649	+	3.47393i	0.419974	+	0.112532i	−0.0426419	+	0.999090i	$0.513577\pi$
$954$	−43.6027	−	25.1740i	−1.41169	−	0.815040i
$955$		0			0
$956$	4.50000	−	7.79423i	0.145540	−	0.252083i
$957$	−52.3373	+	52.3373i	−1.69183	+	1.69183i
$958$	−10.5542	+	10.5542i	−0.340989	+	0.340989i
$959$	−1.59739	−	0.922253i	−0.0515824	−	0.0297811i
$960$		0			0
$961$	26.7332			0.862363
$962$	−7.07107	−	7.07107i	−0.227980	−	0.227980i
$963$	−2.64763	−	9.88110i	−0.0853188	−	0.318414i
$964$	−2.43129	−	4.21113i	−0.0783067	−	0.135631i
$965$		0			0
$966$	−4.78887	−	8.29457i	−0.154079	−	0.266873i
$967$	−44.7876	−	12.0008i	−1.44027	−	0.385920i	−0.547644	−	0.836711i	$-0.684475\pi$
$967$	−44.7876	−	12.0008i	−1.44027	−	0.385920i	−0.892629	+	0.450791i	$0.851142\pi$
$968$	−13.9535	+	13.9535i	−0.448483	+	0.448483i
$969$	−61.7892	−	45.8666i	−1.98496	−	1.47345i
$970$		0			0
$971$	20.0777	−	11.5919i	0.644326	−	0.372002i	−0.141953	−	0.989873i	$-0.545338\pi$
$971$	20.0777	−	11.5919i	0.644326	−	0.372002i	0.786279	+	0.617872i	$0.212005\pi$
$972$	−7.08780	+	26.4520i	−0.227341	+	0.848450i
$973$	−0.966590	+	0.258997i	−0.0309875	+	0.00830306i
$974$	10.9248	−	6.30742i	0.350052	−	0.202103i
$975$		0			0
$976$	12.5777			0.402604
$977$	−35.8738	−	35.8738i	−1.14771	−	1.14771i	−0.987003	−	0.160702i	$-0.948624\pi$
$977$	−35.8738	−	35.8738i	−1.14771	−	1.14771i	−0.160702	−	0.987003i	$-0.551376\pi$
$978$	−16.0239	+	4.29359i	−0.512387	+	0.137294i
$979$	10.8926	−	18.8666i	0.348131	−	0.602980i
$980$		0			0
$981$		−	116.920i		−	3.73296i
$982$	1.78166	−	0.477393i	0.0568549	−	0.0152342i
$983$	−4.97983	−	1.33434i	−0.158832	−	0.0425588i	0.178527	−	0.983935i	$-0.442867\pi$
$983$	−4.97983	−	1.33434i	−0.158832	−	0.0425588i	−0.337359	+	0.941376i	$0.609534\pi$
$984$	−18.1865	+	31.5000i	−0.579766	+	1.00418i
$985$		0			0
$986$	−15.2889	−	26.4811i	−0.486897	−	0.843330i
$987$	−36.4710	−	36.4710i	−1.16088	−	1.16088i
$988$	6.72357	−	16.9933i	0.213905	−	0.540628i
$989$		−	0.577747i		−	0.0183713i
$990$		0			0
$991$	3.28887	−	1.89883i	0.104475	−	0.0603184i	−0.446852	−	0.894608i	$-0.647455\pi$
$991$	3.28887	−	1.89883i	0.104475	−	0.0603184i	0.551327	+	0.834289i	$0.314122\pi$
$992$	2.67310	+	9.97615i	0.0848710	+	0.316743i
$993$	14.3120	−	53.4129i	0.454176	−	1.69501i
$994$	−3.59876	−	2.07775i	−0.114146	−	0.0659021i
$995$		0			0
$996$			23.1838i			0.734606i
$997$	10.8286	+	40.4129i	0.342946	+	1.27989i	0.894994	+	0.446078i	$0.147180\pi$
$997$	10.8286	+	40.4129i	0.342946	+	1.27989i	−0.552048	+	0.833812i	$0.686154\pi$
$998$	1.07552	+	4.01390i	0.0340450	+	0.127058i
$999$		−	31.9258i		−	1.01009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.e.468.2	yes	16
5.2	odd	4	inner	475.2.p.e.107.2	✓	16
5.3	odd	4	inner	475.2.p.e.107.3	yes	16
5.4	even	2	inner	475.2.p.e.468.3	yes	16
19.8	odd	6	inner	475.2.p.e.293.2	yes	16
95.8	even	12	inner	475.2.p.e.407.3	yes	16
95.27	even	12	inner	475.2.p.e.407.2	yes	16
95.84	odd	6	inner	475.2.p.e.293.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.p.e.107.2	✓	16	5.2	odd	4	inner
475.2.p.e.107.3	yes	16	5.3	odd	4	inner
475.2.p.e.293.2	yes	16	19.8	odd	6	inner
475.2.p.e.293.3	yes	16	95.84	odd	6	inner
475.2.p.e.407.2	yes	16	95.27	even	12	inner
475.2.p.e.407.3	yes	16	95.8	even	12	inner
475.2.p.e.468.2	yes	16	1.1	even	1	trivial
475.2.p.e.468.3	yes	16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(3.08380 + 0.826301i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59629 + 2.76486i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(6.22896 + 3.59629i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(3.08380 + 0.826301i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59629 + 2.76486i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(6.22896 + 3.59629i) q^{9} -4.19258 q^{11} +(2.25750 + 2.25750i) q^{12} +(-1.08512 - 4.04972i) q^{13} +(0.866025 + 1.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.34129 - 1.43120i) q^{17} +(-5.08592 + 5.08592i) q^{18} +(4.33013 + 0.500000i) q^{19} +(4.78887 - 2.76486i) q^{21} +(1.08512 - 4.04972i) q^{22} +(-1.67303 + 0.448288i) q^{23} +(-8.29457 + 4.78887i) q^{24} +4.19258 q^{26} +(9.46474 + 9.46474i) q^{27} +(1.67303 - 0.448288i) q^{28} +(2.76486 - 4.78887i) q^{29} -2.06561i q^{31} +(-4.82963 + 1.29410i) q^{32} +(-12.9291 - 3.46434i) q^{33} +(2.76486 - 4.78887i) q^{34} +(3.59629 + 6.22896i) q^{36} +(-1.68657 - 1.68657i) q^{37} +(-1.60368 + 4.05317i) q^{38} -13.3852i q^{39} +(3.28887 - 1.89883i) q^{41} +(1.43120 + 5.34129i) q^{42} +(-0.0863323 + 0.322197i) q^{43} +(-3.63088 - 2.09629i) q^{44} -1.73205i q^{46} +(-2.41410 - 9.00956i) q^{47} +(-0.826301 - 3.08380i) q^{48} +4.00000i q^{49} +(-15.2889 - 8.82704i) q^{51} +(1.08512 - 4.04972i) q^{52} +(1.81173 + 6.76148i) q^{53} +(-11.5919 + 6.69258i) q^{54} +5.19615i q^{56} +(12.9401 + 5.11989i) q^{57} +(3.91010 + 3.91010i) q^{58} +(4.66369 + 8.07775i) q^{59} +(-6.28887 + 10.8926i) q^{61} +(1.99523 + 0.534620i) q^{62} +(12.0334 - 3.22435i) q^{63} -7.00000i q^{64} +(6.69258 - 11.5919i) q^{66} +(-10.4033 + 2.78757i) q^{67} +(-3.91010 - 3.91010i) q^{68} -5.52971 q^{69} +(-2.07775 + 1.19959i) q^{71} +(-20.8425 + 5.58473i) q^{72} +(3.22435 - 12.0334i) q^{73} +(2.06561 - 1.19258i) q^{74} +(3.50000 + 2.59808i) q^{76} +(-5.13484 + 5.13484i) q^{77} +(12.9291 + 3.46434i) q^{78} +(5.69650 + 9.86662i) q^{79} +(10.5777 + 18.3212i) q^{81} +(0.982908 + 3.66826i) q^{82} +(5.13484 + 5.13484i) q^{83} +5.52971 q^{84} +(-0.288874 - 0.166781i) q^{86} +(12.4833 - 12.4833i) q^{87} +(8.89381 - 8.89381i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(-6.28887 - 3.63088i) q^{91} +(-1.67303 - 0.448288i) q^{92} +(1.70682 - 6.36993i) q^{93} +9.32738 q^{94} -15.9629 q^{96} +(-1.86158 + 6.94750i) q^{97} +(-3.86370 - 1.03528i) q^{98} +(-26.1154 - 15.0777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^6	\( 16 q - 4 q^{6} - 24 q^{11} - 8 q^{16} + 12 q^{21} + 24 q^{26} + 36 q^{36} - 12 q^{41} - 180 q^{51} - 36 q^{61} + 64 q^{66} + 96 q^{71} + 56 q^{76} + 40 q^{81} + 60 q^{86} - 36 q^{91} - 40 q^{96}+O(q^{100}) \) 16 * q - 4 * q^6 - 24 * q^11 - 8 * q^16 + 12 * q^21 + 24 * q^26 + 36 * q^36 - 12 * q^41 - 180 * q^51 - 36 * q^61 + 64 * q^66 + 96 * q^71 + 56 * q^76 + 40 * q^81 + 60 * q^86 - 36 * q^91 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more