LMFDB - Embedded newform 722.2.e.r.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.3
Character	$\chi$	$=$	722.99
Dual form			722.2.e.r.423.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.222978 + 1.26457i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.83108 - 2.37556i) q^{5} +(0.222978 - 1.26457i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26966 - 0.462117i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.222978 + 1.26457i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.83108 - 2.37556i) q^{5} +(0.222978 - 1.26457i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26966 - 0.462117i) q^{9} +(-3.47284 + 1.26401i) q^{10} +(2.01484 + 3.48980i) q^{11} +(-0.642040 + 1.11205i) q^{12} +(0.849399 - 4.81718i) q^{13} +(-0.338947 + 0.284410i) q^{14} +(3.63534 + 3.05041i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.250797 - 0.0912828i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.533894 + 0.194322i) q^{21} +(-0.699745 - 3.96845i) q^{22} +(-7.05473 - 5.91962i) q^{23} +(0.983662 - 0.825390i) q^{24} +(1.50350 - 8.52679i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(2.79360 + 4.83866i) q^{27} +(0.415780 - 0.151331i) q^{28} +(0.210098 - 0.0764694i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(-1.73993 + 3.01364i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.96383 + 3.32605i) q^{33} +(0.204452 + 0.171556i) q^{34} +(-0.283953 - 1.61038i) q^{35} +(1.26966 + 0.462117i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-3.47284 - 1.26401i) q^{40} +(-1.36569 - 7.74524i) q^{41} +(-0.435234 - 0.365205i) q^{42} +(-4.31683 + 3.62225i) q^{43} +(-0.699745 + 3.96845i) q^{44} +(2.49672 - 4.32444i) q^{45} +(4.60465 + 7.97549i) q^{46} +(-2.06608 + 0.751992i) q^{47} +(-1.20664 + 0.439181i) q^{48} +(3.40211 + 5.89263i) q^{49} +(-4.32916 + 7.49833i) q^{50} +(0.0595113 - 0.337505i) q^{51} +(3.74710 - 3.14419i) q^{52} +(7.61633 + 6.39086i) q^{53} +(-0.970209 - 5.50233i) q^{54} +(13.9944 + 5.09355i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(3.29788 + 1.20033i) q^{59} +(0.824064 + 4.67350i) q^{60} +(3.12512 + 2.62228i) q^{61} +(2.66572 - 2.23681i) q^{62} +(0.103812 - 0.588748i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.03879 - 15.6556i) q^{65} +(4.86236 - 1.76976i) q^{66} +(-0.138852 + 0.0505379i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(5.91273 - 10.2412i) q^{69} +(-0.283953 + 1.61038i) q^{70} +(8.78585 - 7.37221i) q^{71} +(-1.03503 - 0.868497i) q^{72} +(0.246973 + 1.40065i) q^{73} +(-1.36164 - 0.495597i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-5.90227 - 2.14825i) q^{78} +(1.77180 + 10.0484i) q^{79} +(2.83108 + 2.37556i) q^{80} +(-2.39082 + 2.00614i) q^{81} +(-1.36569 + 7.74524i) q^{82} +(1.64439 - 2.84817i) q^{83} +(0.284079 + 0.492039i) q^{84} +(-0.926876 + 0.337355i) q^{85} +(5.29537 - 1.92736i) q^{86} +(0.143548 + 0.248633i) q^{87} +(2.01484 - 3.48980i) q^{88} +(-1.03507 + 5.87019i) q^{89} +(-3.82519 + 3.20972i) q^{90} +(-1.65795 - 1.39119i) q^{91} +(-1.59918 - 9.06939i) q^{92} +(-4.19893 - 1.52828i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-3.83842 - 1.39707i) q^{97} +(-1.18154 - 6.70085i) q^{98} +(4.17085 + 3.49976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 - 12 * q^8	$ 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.222978	+	1.26457i	0.128736	+	0.730100i	0.979018	+	0.203773i	$0.0653204\pi$
$3$	0.222978	+	1.26457i	0.128736	+	0.730100i	−0.850282	+	0.526328i	$0.823569\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	2.83108	−	2.37556i	1.26610	−	1.06238i	0.271095	−	0.962553i	$-0.412614\pi$
$5$	2.83108	−	2.37556i	1.26610	−	1.06238i	0.995004	−	0.0998307i	$-0.0318301\pi$
$6$	0.222978	−	1.26457i	0.0910304	−	0.516259i
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	−0.821184	−	0.570664i	$-0.806686\pi$
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	0.904801	+	0.425834i	$0.140019\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.26966	−	0.462117i	0.423219	−	0.154039i
$10$	−3.47284	+	1.26401i	−1.09821	+	0.399715i
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	0.991652	+	0.128946i	$0.0411593\pi$
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625507\pi$
$12$	−0.642040	+	1.11205i	−0.185341	+	0.321020i
$13$	0.849399	−	4.81718i	0.235581	−	1.33604i	−0.605806	−	0.795612i	$-0.707149\pi$
$13$	0.849399	−	4.81718i	0.235581	−	1.33604i	0.841387	−	0.540433i	$-0.181740\pi$
$14$	−0.338947	+	0.284410i	−0.0905873	+	0.0760118i
$15$	3.63534	+	3.05041i	0.938640	+	0.787612i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.250797	−	0.0912828i	−0.0608273	−	0.0221393i	0.311427	−	0.950270i	$-0.399193\pi$
$17$	−0.250797	−	0.0912828i	−0.0608273	−	0.0221393i	−0.372255	+	0.928131i	$0.621415\pi$
$18$	−1.35114			−0.318467
$19$		0			0
$19$		0			0
$20$	3.69572			0.826388
$21$	0.533894	+	0.194322i	0.116505	+	0.0424044i
$22$	−0.699745	−	3.96845i	−0.149186	−	0.846077i
$23$	−7.05473	−	5.91962i	−1.47101	−	1.23433i	−0.915188	−	0.403028i	$-0.867958\pi$
$23$	−7.05473	−	5.91962i	−1.47101	−	1.23433i	−0.555826	−	0.831299i	$-0.687598\pi$
$24$	0.983662	−	0.825390i	0.200789	−	0.168482i
$25$	1.50350	−	8.52679i	0.300701	−	1.70536i
$26$	−2.44575	+	4.23616i	−0.479650	+	0.830779i
$27$	2.79360	+	4.83866i	0.537629	+	0.931201i
$28$	0.415780	−	0.151331i	0.0785750	−	0.0285990i
$29$	0.210098	−	0.0764694i	0.0390142	−	0.0142000i	−0.322439	−	0.946590i	$-0.604503\pi$
$29$	0.210098	−	0.0764694i	0.0390142	−	0.0142000i	0.361454	+	0.932390i	$0.382281\pi$
$30$	−2.37280	−	4.10980i	−0.433211	−	0.750344i
$31$	−1.73993	+	3.01364i	−0.312500	+	0.541266i	−0.978903	−	0.204326i	$-0.934500\pi$
$31$	−1.73993	+	3.01364i	−0.312500	+	0.541266i	0.666403	+	0.745592i	$0.267833\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−3.96383	+	3.32605i	−0.690015	+	0.578991i
$34$	0.204452	+	0.171556i	0.0350632	+	0.0294215i
$35$	−0.283953	−	1.61038i	−0.0479968	−	0.272203i
$36$	1.26966	+	0.462117i	0.211610	+	0.0770196i
$37$	1.44903			0.238219			0.119109	−	0.992881i	$-0.461996\pi$
$37$	1.44903			0.238219			0.119109	+	0.992881i	$0.461996\pi$
$38$		0			0
$39$	6.28106			1.00577
$40$	−3.47284	−	1.26401i	−0.549104	−	0.199858i
$41$	−1.36569	−	7.74524i	−0.213286	−	1.20960i	−0.883857	−	0.467758i	$-0.845062\pi$
$41$	−1.36569	−	7.74524i	−0.213286	−	1.20960i	0.670571	−	0.741845i	$-0.266049\pi$
$42$	−0.435234	−	0.365205i	−0.0671581	−	0.0563524i
$43$	−4.31683	+	3.62225i	−0.658310	+	0.552388i	−0.909580	−	0.415529i	$-0.863596\pi$
$43$	−4.31683	+	3.62225i	−0.658310	+	0.552388i	0.251270	+	0.967917i	$0.419152\pi$
$44$	−0.699745	+	3.96845i	−0.105491	+	0.598267i
$45$	2.49672	−	4.32444i	0.372189	−	0.644650i
$46$	4.60465	+	7.97549i	0.678919	+	1.17592i
$47$	−2.06608	+	0.751992i	−0.301369	+	0.109689i	−0.488279	−	0.872688i	$-0.662375\pi$
$47$	−2.06608	+	0.751992i	−0.301369	+	0.109689i	0.186910	+	0.982377i	$0.440153\pi$
$48$	−1.20664	+	0.439181i	−0.174163	+	0.0633903i
$49$	3.40211	+	5.89263i	0.486016	+	0.841805i
$50$	−4.32916	+	7.49833i	−0.612236	+	1.06042i
$51$	0.0595113	−	0.337505i	0.00833324	−	0.0472602i
$52$	3.74710	−	3.14419i	0.519629	−	0.436021i
$53$	7.61633	+	6.39086i	1.04618	+	0.877852i	0.992687	−	0.120716i	$-0.0385192\pi$
$53$	7.61633	+	6.39086i	1.04618	+	0.877852i	0.0534958	+	0.998568i	$0.482964\pi$
$54$	−0.970209	−	5.50233i	−0.132029	−	0.748772i
$55$	13.9944	+	5.09355i	1.88700	+	0.686814i
$56$	−0.442463			−0.0591267
$57$		0			0
$58$	−0.223582			−0.0293577
$59$	3.29788	+	1.20033i	0.429347	+	0.156269i	0.547649	−	0.836708i	$-0.315523\pi$
$59$	3.29788	+	1.20033i	0.429347	+	0.156269i	−0.118302	+	0.992978i	$0.537745\pi$
$60$	0.824064	+	4.67350i	0.106386	+	0.603346i
$61$	3.12512	+	2.62228i	0.400130	+	0.335749i	0.820544	−	0.571583i	$-0.193671\pi$
$61$	3.12512	+	2.62228i	0.400130	+	0.335749i	−0.420414	+	0.907332i	$0.638115\pi$
$62$	2.66572	−	2.23681i	0.338547	−	0.284075i
$63$	0.103812	−	0.588748i	0.0130791	−	0.0741753i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−9.03879	−	15.6556i	−1.12112	−	1.94184i
$66$	4.86236	−	1.76976i	0.598515	−	0.217842i
$67$	−0.138852	+	0.0505379i	−0.0169634	+	0.00617418i	−0.350488	−	0.936567i	$-0.613984\pi$
$67$	−0.138852	+	0.0505379i	−0.0169634	+	0.00617418i	0.333524	+	0.942741i	$0.391762\pi$
$68$	−0.133446	−	0.231136i	−0.0161828	−	0.0280294i
$69$	5.91273	−	10.2412i	0.711810	−	1.23289i
$70$	−0.283953	+	1.61038i	−0.0339389	+	0.192477i
$71$	8.78585	−	7.37221i	1.04269	−	0.874920i	0.0503832	−	0.998730i	$-0.483956\pi$
$71$	8.78585	−	7.37221i	1.04269	−	0.874920i	0.992306	+	0.123810i	$0.0395113\pi$
$72$	−1.03503	−	0.868497i	−0.121980	−	0.102353i
$73$	0.246973	+	1.40065i	0.0289060	+	0.163934i	0.995844	−	0.0910787i	$-0.0290315\pi$
$73$	0.246973	+	1.40065i	0.0289060	+	0.163934i	−0.966938	+	0.255013i	$0.917920\pi$
$74$	−1.36164	−	0.495597i	−0.158288	−	0.0576120i
$75$	11.1180			1.28379
$76$		0			0
$77$	1.78298			0.203190
$78$	−5.90227	−	2.14825i	−0.668300	−	0.243241i
$79$	1.77180	+	10.0484i	0.199343	+	1.13053i	0.906097	+	0.423070i	$0.139048\pi$
$79$	1.77180	+	10.0484i	0.199343	+	1.13053i	−0.706754	+	0.707459i	$0.749841\pi$
$80$	2.83108	+	2.37556i	0.316525	+	0.265596i
$81$	−2.39082	+	2.00614i	−0.265647	+	0.222904i
$82$	−1.36569	+	7.74524i	−0.150816	+	0.855319i
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	−0.761554	−	0.648101i	$-0.775563\pi$
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	0.942049	+	0.335475i	$0.108897\pi$
$84$	0.284079	+	0.492039i	0.0309956	+	0.0536859i
$85$	−0.926876	+	0.337355i	−0.100534	+	0.0365913i
$86$	5.29537	−	1.92736i	0.571015	−	0.207832i
$87$	0.143548	+	0.248633i	0.0153900	+	0.0266562i
$88$	2.01484	−	3.48980i	0.214782	−	0.372014i
$89$	−1.03507	+	5.87019i	−0.109717	+	0.622239i	0.879513	+	0.475874i	$0.157868\pi$
$89$	−1.03507	+	5.87019i	−0.109717	+	0.622239i	−0.989231	+	0.146364i	$0.953243\pi$
$90$	−3.82519	+	3.20972i	−0.403211	+	0.338334i
$91$	−1.65795	−	1.39119i	−0.173801	−	0.145836i
$92$	−1.59918	−	9.06939i	−0.166726	−	0.945549i
$93$	−4.19893	−	1.52828i	−0.435409	−	0.158476i
$94$	2.19868			0.226776
$95$		0			0
$96$	1.28408			0.131056
$97$	−3.83842	−	1.39707i	−0.389732	−	0.141851i	0.139719	−	0.990191i	$-0.455380\pi$
$97$	−3.83842	−	1.39707i	−0.389732	−	0.141851i	−0.529451	+	0.848340i	$0.677602\pi$
$98$	−1.18154	−	6.70085i	−0.119354	−	0.676889i
$99$	4.17085	+	3.49976i	0.419186	+	0.351739i
$100$	6.63266	−	5.56547i	0.663266	−	0.556547i
$101$	0.0738486	−	0.418817i	0.00734822	−	0.0416738i	−0.980913	−	0.194446i	$-0.937709\pi$
$101$	0.0738486	−	0.418817i	0.00734822	−	0.0416738i	0.988261	+	0.152772i	$0.0488201\pi$
$102$	−0.171356	+	0.296797i	−0.0169668	+	0.0293873i
$103$	2.26809	+	3.92845i	0.223482	+	0.387081i	0.955863	−	0.293813i	$-0.0949244\pi$
$103$	2.26809	+	3.92845i	0.223482	+	0.387081i	−0.732381	+	0.680895i	$0.761591\pi$
$104$	−4.59650	+	1.67299i	−0.450724	+	0.164050i
$105$	1.97312	−	0.718157i	0.192557	−	0.0700850i
$106$	−4.97120	−	8.61038i	−0.482846	−	0.836314i
$107$	1.58576	−	2.74661i	0.153301	−	0.265525i	−0.779138	−	0.626852i	$-0.784343\pi$
$107$	1.58576	−	2.74661i	0.153301	−	0.265525i	0.932439	+	0.361327i	$0.117676\pi$
$108$	−0.970209	+	5.50233i	−0.0933584	+	0.529462i
$109$	−5.19464	+	4.35882i	−0.497556	+	0.417499i	−0.856725	−	0.515773i	$-0.827505\pi$
$109$	−5.19464	+	4.35882i	−0.497556	+	0.417499i	0.359169	+	0.933273i	$0.383060\pi$
$110$	−11.4083	−	9.57273i	−1.08774	−	0.912724i
$111$	0.323101	+	1.83240i	0.0306674	+	0.173924i
$112$	0.415780	+	0.151331i	0.0392875	+	0.0142995i
$113$	−10.0444			−0.944893			−0.472447	−	0.881359i	$-0.656629\pi$
$113$	−10.0444			−0.944893			−0.472447	+	0.881359i	$0.656629\pi$
$114$		0			0
$115$	−34.0350			−3.17378
$116$	0.210098	+	0.0764694i	0.0195071	+	0.00710001i
$117$	−1.14766	−	6.50869i	−0.106101	−	0.601728i
$118$	−2.68845	−	2.25588i	−0.247492	−	0.207671i
$119$	−0.0904625	+	0.0759070i	−0.00829268	+	0.00695839i
$120$	0.824064	−	4.67350i	0.0752264	−	0.426630i
$121$	−2.61913	+	4.53647i	−0.238103	+	0.412406i
$122$	−2.03977	−	3.53299i	−0.184672	−	0.319862i
$123$	9.48989	−	3.45404i	0.855674	−	0.311440i
$124$	−3.26999	+	1.19018i	−0.293654	+	0.106881i
$125$	−6.76007	−	11.7088i	−0.604639	−	1.04727i
$126$	−0.298915	+	0.517736i	−0.0266295	+	0.0461236i
$127$	2.44507	−	13.8667i	0.216965	−	1.23047i	−0.660500	−	0.750826i	$-0.729655\pi$
$127$	2.44507	−	13.8667i	0.216965	−	1.23047i	0.877464	−	0.479642i	$-0.159233\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−5.54315	−	4.65125i	−0.488047	−	0.409520i
$130$	3.13914	+	17.8029i	0.275321	+	1.56142i
$131$	−14.8861	−	5.41811i	−1.30061	−	0.473383i	−0.403414	−	0.915018i	$-0.632176\pi$
$131$	−14.8861	−	5.41811i	−1.30061	−	0.473383i	−0.897195	+	0.441635i	$0.854399\pi$
$132$	−5.17442			−0.450375
$133$		0			0
$134$	0.147763			0.0127648
$135$	19.4035	+	7.06229i	1.66999	+	0.607825i
$136$	0.0463455	+	0.262838i	0.00397409	+	0.0225382i
$137$	1.69099	+	1.41891i	0.144471	+	0.121226i	0.712159	−	0.702018i	$-0.247717\pi$
$137$	1.69099	+	1.41891i	0.144471	+	0.121226i	−0.567688	+	0.823244i	$0.692162\pi$
$138$	−9.05883	+	7.60127i	−0.771139	+	0.647063i
$139$	−2.96321	+	16.8052i	−0.251336	+	1.42540i	0.553969	+	0.832537i	$0.313113\pi$
$139$	−2.96321	+	16.8052i	−0.251336	+	1.42540i	−0.805305	+	0.592861i	$0.797998\pi$
$140$	0.817610	−	1.41614i	0.0691007	−	0.119686i
$141$	−1.41164	−	2.44503i	−0.118881	−	0.205909i
$142$	−10.7774	+	3.92267i	−0.904423	+	0.329183i
$143$	18.5224	−	6.74160i	1.54892	−	0.563761i
$144$	0.675571	+	1.17012i	0.0562975	+	0.0975102i
$145$	0.413147	−	0.715592i	0.0343100	−	0.0594267i
$146$	0.246973	−	1.40065i	0.0204396	−	0.115919i
$147$	−6.69306	+	5.61614i	−0.552034	+	0.463211i
$148$	1.11002	+	0.931417i	0.0912431	+	0.0765620i
$149$	2.35220	+	13.3400i	0.192699	+	1.09285i	0.915657	+	0.401961i	$0.131671\pi$
$149$	2.35220	+	13.3400i	0.192699	+	1.09285i	−0.722957	+	0.690893i	$0.757218\pi$
$150$	−10.4475	−	3.80257i	−0.853033	−	0.310479i
$151$	−9.15317			−0.744875			−0.372437	−	0.928057i	$-0.621478\pi$
$151$	−9.15317			−0.744875			−0.372437	+	0.928057i	$0.621478\pi$
$152$		0			0
$153$	−0.360610			−0.0291536
$154$	−1.67546	−	0.609816i	−0.135012	−	0.0491404i
$155$	2.23321	+	12.6652i	0.179376	+	1.01729i
$156$	4.81157	+	4.03739i	0.385234	+	0.323250i
$157$	−12.5557	+	10.5355i	−1.00205	+	0.840822i	−0.987268	−	0.159069i	$-0.949151\pi$
$157$	−12.5557	+	10.5355i	−1.00205	+	0.840822i	−0.0147852	+	0.999891i	$0.504706\pi$
$158$	1.77180	−	10.0484i	0.140957	−	0.799405i
$159$	−6.38342	+	11.0564i	−0.506238	+	0.876830i
$160$	−1.84786	−	3.20059i	−0.146086	−	0.253028i
$161$	−3.82904	+	1.39366i	−0.301771	+	0.109836i
$162$	2.93278	−	1.06744i	0.230421	−	0.0838663i
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	0.998938	+	0.0460652i	$0.0146682\pi$
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	−0.459576	+	0.888139i	$0.651998\pi$
$164$	3.93236	−	6.81105i	0.307066	−	0.531854i
$165$	−3.32071	+	18.8327i	−0.258517	+	1.46612i
$166$	−2.51935	+	2.11399i	−0.195540	+	0.164077i
$167$	−7.91539	−	6.64180i	−0.612511	−	0.513958i	0.282929	−	0.959141i	$-0.408694\pi$
$167$	−7.91539	−	6.64180i	−0.612511	−	0.513958i	−0.895439	+	0.445183i	$0.853139\pi$
$168$	−0.0986596	−	0.559526i	−0.00761175	−	0.0431684i
$169$	−10.2677	−	3.73715i	−0.789825	−	0.287473i
$170$	0.986361			0.0756504
$171$		0			0
$172$	−5.63522			−0.429682
$173$	9.22028	+	3.35591i	0.701005	+	0.255145i	0.667840	−	0.744305i	$-0.267219\pi$
$173$	9.22028	+	3.35591i	0.701005	+	0.255145i	0.0331648	+	0.999450i	$0.489441\pi$
$174$	−0.0498538	−	0.282735i	−0.00377940	−	0.0214341i
$175$	−2.93471	−	2.46252i	−0.221843	−	0.186149i
$176$	−3.08691	+	2.59022i	−0.232684	+	0.195245i
$177$	−0.782547	+	4.43804i	−0.0588198	+	0.333584i
$178$	2.98037	−	5.16216i	0.223388	−	0.386920i
$179$	4.39915	+	7.61955i	0.328808	+	0.569512i	0.982276	−	0.187442i	$-0.0600197\pi$
$179$	4.39915	+	7.61955i	0.328808	+	0.569512i	−0.653468	+	0.756955i	$0.726686\pi$
$180$	4.69229	−	1.70786i	0.349743	−	0.127296i
$181$	−13.6516	+	4.96878i	−1.01472	+	0.369327i	−0.795243	−	0.606291i	$-0.792656\pi$
$181$	−13.6516	+	4.96878i	−1.01472	+	0.369327i	−0.219474	+	0.975618i	$0.570434\pi$
$182$	1.08215	+	1.87434i	0.0802145	+	0.138936i
$183$	−2.61923	+	4.53664i	−0.193619	+	0.335358i
$184$	−1.59918	+	9.06939i	−0.117893	+	0.668604i
$185$	4.10232	−	3.44225i	0.301609	−	0.253080i
$186$	3.42300	+	2.87224i	0.250986	+	0.210603i
$187$	−0.186757	−	1.05915i	−0.0136570	−	0.0774529i
$188$	−2.06608	−	0.751992i	−0.150685	−	0.0548447i
$189$	2.47214			0.179821
$190$		0			0
$191$	12.7302			0.921122			0.460561	−	0.887628i	$-0.347648\pi$
$191$	12.7302			0.921122			0.460561	+	0.887628i	$0.347648\pi$
$192$	−1.20664	−	0.439181i	−0.0870817	−	0.0316952i
$193$	3.03503	+	17.2125i	0.218466	+	1.23898i	0.874789	+	0.484504i	$0.161000\pi$
$193$	3.03503	+	17.2125i	0.218466	+	1.23898i	−0.656322	+	0.754481i	$0.727889\pi$
$194$	3.12911	+	2.62563i	0.224657	+	0.188509i
$195$	17.7822	−	14.9210i	1.27341	−	1.06852i
$196$	−1.18154	+	6.70085i	−0.0843958	+	0.478632i
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.0144872	−	0.999895i	$-0.495388\pi$
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.858691	−	0.512494i	$-0.171278\pi$
$198$	−2.72233	−	4.71521i	−0.193467	−	0.335095i
$199$	−15.4731	+	5.63174i	−1.09686	+	0.399223i	−0.826157	−	0.563440i	$-0.809477\pi$
$199$	−15.4731	+	5.63174i	−1.09686	+	0.399223i	−0.270700	+	0.962664i	$0.587255\pi$
$200$	−8.13617	+	2.96132i	−0.575314	+	0.209397i
$201$	−0.0948696	−	0.164319i	−0.00669159	−	0.0115902i
$202$	−0.212639	+	0.368301i	−0.0149612	+	0.0259136i
$203$	0.0171784	−	0.0974238i	0.00120569	−	0.00683781i
$204$	0.262532	−	0.220291i	0.0183809	−	0.0154234i
$205$	−22.2657	−	18.6831i	−1.55510	−	1.30489i
$206$	−0.787699	−	4.46727i	−0.0548816	−	0.311249i
$207$	−11.6927	−	4.25578i	−0.812696	−	0.295797i
$208$	4.89149			0.339164
$209$		0			0
$210$	−2.09975			−0.144897
$211$	−25.8232	−	9.39887i	−1.77774	−	0.647045i	−0.999826	−	0.0186757i	$-0.994055\pi$
$211$	−25.8232	−	9.39887i	−1.77774	−	0.647045i	−0.777915	−	0.628369i	$-0.783723\pi$
$212$	1.72648	+	9.79136i	0.118575	+	0.672473i
$213$	11.2817	+	9.46650i	0.773012	+	0.648634i
$214$	−2.42952	+	2.03861i	−0.166079	+	0.139356i
$215$	−3.61643	+	20.5098i	−0.246638	+	1.39876i
$216$	2.79360	−	4.83866i	0.190081	−	0.329229i
$217$	0.769854	+	1.33343i	0.0522611	+	0.0905189i
$218$	6.37217	−	2.31928i	0.431578	−	0.157081i
$219$	−1.71616	+	0.624629i	−0.115967	+	0.0422085i
$220$	7.44627	+	12.8973i	0.502027	+	0.869536i
$221$	−0.652752	+	1.13060i	−0.0439089	+	0.0760524i
$222$	0.323101	−	1.83240i	0.0216851	−	0.122983i
$223$	15.6048	−	13.0940i	1.04497	−	0.876837i	0.0524171	−	0.998625i	$-0.483307\pi$
$223$	15.6048	−	13.0940i	1.04497	−	0.876837i	0.992556	+	0.121789i	$0.0388630\pi$
$224$	−0.338947	−	0.284410i	−0.0226468	−	0.0190029i
$225$	−2.03144	−	11.5209i	−0.135430	−	0.768060i
$226$	9.43860	+	3.43537i	0.627847	+	0.228517i
$227$	−22.1493			−1.47010			−0.735051	−	0.678011i	$-0.762842\pi$
$227$	−22.1493			−1.47010			−0.735051	+	0.678011i	$0.762842\pi$
$228$		0			0
$229$	12.7148			0.840216			0.420108	−	0.907474i	$-0.361992\pi$
$229$	12.7148			0.840216			0.420108	+	0.907474i	$0.361992\pi$
$230$	31.9824	+	11.6406i	2.10886	+	0.767561i
$231$	0.397566	+	2.25471i	0.0261579	+	0.148349i
$232$	−0.171273	−	0.143715i	−0.0112447	−	0.00943538i
$233$	−6.65062	+	5.58053i	−0.435696	+	0.365593i	−0.834096	−	0.551619i	$-0.814010\pi$
$233$	−6.65062	+	5.58053i	−0.435696	+	0.365593i	0.398400	+	0.917212i	$0.369566\pi$
$234$	−1.14766	+	6.50869i	−0.0750247	+	0.425486i
$235$	−4.06285	+	7.03706i	−0.265031	+	0.459047i
$236$	1.75476	+	3.03934i	0.114225	+	0.197844i
$237$	−12.3118	+	4.48113i	−0.799737	+	0.291081i
$238$	0.110969	−	0.0403893i	0.00719303	−	0.00261805i
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	−0.965787	−	0.259336i	$-0.916496\pi$
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	0.258302	−	0.966064i	$-0.416837\pi$
$240$	−2.37280	+	4.10980i	−0.153163	+	0.265287i
$241$	−3.29293	+	18.6751i	−0.212116	+	1.20297i	0.673725	+	0.738982i	$0.264693\pi$
$241$	−3.29293	+	18.6751i	−0.212116	+	1.20297i	−0.885841	+	0.463988i	$0.846418\pi$
$242$	4.01274	−	3.36709i	0.257949	−	0.216445i
$243$	9.77015	+	8.19813i	0.626755	+	0.525910i
$244$	0.708406	+	4.01757i	0.0453511	+	0.257199i
$245$	23.6300	+	8.60061i	1.50966	+	0.549473i
$246$	−10.0989			−0.643884
$247$		0			0
$248$	3.47985			0.220971
$249$	3.96837	+	1.44437i	0.251485	+	0.0915332i
$250$	2.34775	+	13.3147i	0.148485	+	0.842098i
$251$	2.22364	+	1.86586i	0.140355	+	0.117772i	0.710262	−	0.703937i	$-0.248576\pi$
$251$	2.22364	+	1.86586i	0.140355	+	0.117772i	−0.569907	+	0.821709i	$0.693021\pi$
$252$	0.457965	−	0.384278i	0.0288491	−	0.0242072i
$253$	6.44416	−	36.5467i	0.405141	−	2.29767i
$254$	−7.04029	+	12.1941i	−0.441747	+	0.765129i
$255$	−0.633283	−	1.09688i	−0.0396577	−	0.0686892i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−21.5237	+	7.83398i	−1.34261	+	0.488670i	−0.910634	−	0.413215i	$-0.864406\pi$
$257$	−21.5237	+	7.83398i	−1.34261	+	0.488670i	−0.431976	+	0.901885i	$0.642184\pi$
$258$	3.61803	+	6.26662i	0.225249	+	0.390143i
$259$	0.320571	−	0.555245i	0.0199193	−	0.0345013i
$260$	3.13914	−	17.8029i	0.194681	−	1.10409i
$261$	0.231415	−	0.194180i	0.0143242	−	0.0120194i
$262$	12.1353	+	10.1827i	0.749721	+	0.629091i
$263$	−0.879070	−	4.98545i	−0.0542058	−	0.307416i	0.945636	−	0.325228i	$-0.105441\pi$
$263$	−0.879070	−	4.98545i	−0.0542058	−	0.307416i	−0.999841	+	0.0178119i	$0.994330\pi$
$264$	4.86236	+	1.76976i	0.299258	+	0.108921i
$265$	36.7443			2.25719
$266$		0			0
$267$	−7.65407			−0.468421
$268$	−0.138852	−	0.0505379i	−0.00848172	−	0.00308709i
$269$	−3.60180	−	20.4268i	−0.219606	−	1.24545i	−0.872733	−	0.488197i	$-0.837655\pi$
$269$	−3.60180	−	20.4268i	−0.219606	−	1.24545i	0.653128	−	0.757248i	$-0.273456\pi$
$270$	−15.8179	−	13.2728i	−0.962644	−	0.807754i
$271$	4.82202	−	4.04616i	0.292917	−	0.245786i	−0.484472	−	0.874807i	$-0.660988\pi$
$271$	4.82202	−	4.04616i	0.292917	−	0.245786i	0.777389	+	0.629020i	$0.216544\pi$
$272$	0.0463455	−	0.262838i	0.00281011	−	0.0159369i
$273$	1.38957	−	2.40681i	0.0841006	−	0.145667i
$274$	−1.10372	−	1.91169i	−0.0666780	−	0.115490i
$275$	32.7861	−	11.9332i	1.97708	−	0.719597i
$276$	11.1123	−	4.04455i	0.668882	−	0.243453i
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	0.737869	−	0.674944i	$-0.235832\pi$
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	−0.953453	+	0.301541i	$0.902499\pi$
$278$	8.53222	−	14.7782i	0.511729	−	0.886340i
$279$	−0.816454	+	4.63034i	−0.0488798	+	0.277211i
$280$	−1.25265	+	1.05110i	−0.0748602	+	0.0628152i
$281$	2.12494	+	1.78304i	0.126763	+	0.106367i	0.703965	−	0.710234i	$-0.251411\pi$
$281$	2.12494	+	1.78304i	0.126763	+	0.106367i	−0.577202	+	0.816601i	$0.695855\pi$
$282$	0.490257	+	2.78039i	0.0291944	+	0.165570i
$283$	−7.28131	−	2.65018i	−0.432829	−	0.157537i	0.116412	−	0.993201i	$-0.462861\pi$
$283$	−7.28131	−	2.65018i	−0.432829	−	0.157537i	−0.549241	+	0.835664i	$0.685083\pi$
$284$	11.4691			0.680567
$285$		0			0
$286$	−19.7111			−1.16554
$287$	−3.26999	−	1.19018i	−0.193022	−	0.0702541i
$288$	−0.234623	−	1.33061i	−0.0138253	−	0.0784072i
$289$	−12.9682	−	10.8816i	−0.762835	−	0.640094i
$290$	−0.632978	+	0.531132i	−0.0371698	+	0.0311891i
$291$	0.910811	−	5.16547i	0.0533927	−	0.302805i
$292$	−0.711130	+	1.23171i	−0.0416157	+	0.0720806i
$293$	0.391435	+	0.677985i	0.0228679	+	0.0396083i	0.877233	−	0.480065i	$-0.159387\pi$
$293$	0.391435	+	0.677985i	0.0228679	+	0.0396083i	−0.854365	+	0.519673i	$0.826054\pi$
$294$	8.21025	−	2.98829i	0.478831	−	0.174280i
$295$	12.1880	−	4.43607i	0.709614	−	0.258278i
$296$	−0.724514	−	1.25490i	−0.0421115	−	0.0729393i
$297$	−11.2573	+	19.4982i	−0.653215	+	1.13140i
$298$	2.35220	−	13.3400i	0.136259	−	0.772764i
$299$	−34.5082	+	28.9558i	−1.99566	+	1.67456i
$300$	8.51686	+	7.14650i	0.491721	+	0.412603i
$301$	0.432971	+	2.45550i	0.0249560	+	0.141533i
$302$	8.60117	+	3.13057i	0.494942	+	0.180144i
$303$	0.546090			0.0313720
$304$		0			0
$305$	15.0769			0.863298
$306$	0.338863	+	0.123336i	0.0193715	+	0.00705064i
$307$	−4.89146	−	27.7408i	−0.279170	−	1.58325i	−0.725395	−	0.688332i	$-0.758343\pi$
$307$	−4.89146	−	27.7408i	−0.279170	−	1.58325i	0.446225	−	0.894921i	$-0.352768\pi$
$308$	1.36584	+	1.14608i	0.0778262	+	0.0653039i
$309$	−4.46207	+	3.74412i	−0.253838	+	0.212995i
$310$	2.23321	−	12.6652i	0.126838	−	0.719333i
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	−0.915639	−	0.402003i	$-0.868314\pi$
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$312$	−3.14053	−	5.43956i	−0.177798	−	0.307954i
$313$	−28.5552	+	10.3932i	−1.61403	+	0.587460i	−0.982232	−	0.187670i	$-0.939906\pi$
$313$	−28.5552	+	10.3932i	−1.61403	+	0.587460i	−0.631801	+	0.775130i	$0.717684\pi$
$314$	15.4018	−	5.60581i	0.869175	−	0.316354i
$315$	−1.10471	−	1.91341i	−0.0622432	−	0.107808i
$316$	−5.10169	+	8.83638i	−0.286992	+	0.497085i
$317$	0.925203	−	5.24709i	0.0519646	−	0.294706i	−0.947739	−	0.319046i	$-0.896637\pi$
$317$	0.925203	−	5.24709i	0.0519646	−	0.294706i	0.999704	+	0.0243404i	$0.00774857\pi$
$318$	9.77996	−	8.20636i	0.548433	−	0.460190i
$319$	0.690176	+	0.579126i	0.0386424	+	0.0324248i
$320$	0.641755	+	3.63957i	0.0358752	+	0.203458i
$321$	3.82687	+	1.39287i	0.213595	+	0.0777423i
$322$	4.07478			0.227079
$323$		0			0
$324$	−3.12099			−0.173389
$325$	−39.7980	−	14.4853i	−2.20760	−	0.803499i
$326$	−2.39153	−	13.5630i	−0.132454	−	0.751186i
$327$	−6.67033	−	5.59707i	−0.368870	−	0.309519i
$328$	−6.02473	+	5.05535i	−0.332660	+	0.279135i
$329$	−0.168931	+	0.958055i	−0.00931347	+	0.0528193i
$330$	9.56159	−	16.5612i	0.526348	−	0.911662i
$331$	10.2740	+	17.7951i	0.564711	+	0.978108i	0.997077	+	0.0764094i	$0.0243456\pi$
$331$	10.2740	+	17.7951i	0.564711	+	0.978108i	−0.432366	+	0.901698i	$0.642321\pi$
$332$	3.09044	−	1.12483i	0.169610	−	0.0617330i
$333$	1.83977	−	0.669621i	0.100819	−	0.0366950i
$334$	5.16640	+	8.94847i	0.282693	+	0.489638i
$335$	−0.273045	+	0.472928i	−0.0149180	+	0.0258388i
$336$	−0.0986596	+	0.559526i	−0.00538232	+	0.0305247i
$337$	10.1749	−	8.53777i	0.554263	−	0.465082i	−0.322118	−	0.946699i	$-0.604395\pi$
$337$	10.1749	−	8.53777i	0.554263	−	0.465082i	0.876382	+	0.481617i	$0.159950\pi$
$338$	8.37033	+	7.02354i	0.455286	+	0.382030i
$339$	−2.23967	−	12.7018i	−0.121642	−	0.689867i
$340$	−0.926876	−	0.337355i	−0.0502669	−	0.0182957i
$341$	−14.0227			−0.759370
$342$		0			0
$343$	6.10787			0.329794
$344$	5.29537	+	1.92736i	0.285507	+	0.103916i
$345$	−7.58905	−	43.0396i	−0.408581	−	2.31718i
$346$	−7.51644	−	6.30704i	−0.404086	−	0.339069i
$347$	23.0904	−	19.3751i	1.23956	−	1.04011i	0.241997	−	0.970277i	$-0.422198\pi$
$347$	23.0904	−	19.3751i	1.23956	−	1.04011i	0.997559	−	0.0698336i	$-0.0222468\pi$
$348$	−0.0498538	+	0.282735i	−0.00267244	+	0.0151562i
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.170232	+	0.985404i	$0.554452\pi$
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.768269	+	0.640127i	$0.778882\pi$
$350$	1.91550	+	3.31774i	0.102388	+	0.177341i
$351$	25.6816	−	9.34734i	1.37078	−	0.498924i
$352$	3.78665	−	1.37823i	0.201829	−	0.0734599i
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	0.627661	−	0.778487i	$-0.284012\pi$
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	−0.988020	+	0.154327i	$0.950679\pi$
$354$	2.25325	−	3.90275i	0.119759	−	0.207429i
$355$	7.36036	−	41.7427i	0.390647	−	2.21547i
$356$	−4.56620	+	3.83149i	−0.242008	+	0.203069i
$357$	−0.116161	−	0.0974706i	−0.00614789	−	0.00515869i
$358$	−1.52781	−	8.66464i	−0.0807472	−	0.457940i
$359$	22.0896	+	8.03994i	1.16584	+	0.424332i	0.851181	−	0.524872i	$-0.175887\pi$
$359$	22.0896	+	8.03994i	1.16584	+	0.424332i	0.314661	+	0.949204i	$0.398109\pi$
$360$	−4.99344			−0.263177
$361$		0			0
$362$	14.5278			0.763562
$363$	−6.32069	−	2.30054i	−0.331750	−	0.120747i
$364$	−0.375828	−	2.13143i	−0.0196987	−	0.111717i
$365$	4.02654	+	3.37867i	0.210759	+	0.176847i
$366$	4.01290	−	3.36722i	0.209757	−	0.176007i
$367$	−2.20410	+	12.5000i	−0.115053	+	0.652497i	0.871671	+	0.490091i	$0.163037\pi$
$367$	−2.20410	+	12.5000i	−0.115053	+	0.652497i	−0.986724	+	0.162406i	$0.948075\pi$
$368$	4.60465	−	7.97549i	0.240034	−	0.415751i
$369$	−5.31318	−	9.20269i	−0.276593	−	0.479073i
$370$	−5.03224	+	1.83159i	−0.261614	+	0.0952196i
$371$	4.13385	−	1.50460i	0.214619	−	0.0781149i
$372$	−2.23420	−	3.86975i	−0.115838	−	0.200637i
$373$	−1.32475	+	2.29454i	−0.0685930	+	0.118807i	−0.898282	−	0.439419i	$-0.855184\pi$
$373$	−1.32475	+	2.29454i	−0.0685930	+	0.118807i	0.829689	+	0.558226i	$0.188518\pi$
$374$	−0.186757	+	1.05915i	−0.00965698	+	0.0547675i
$375$	13.2992	−	11.1594i	0.686770	−	0.576269i
$376$	1.68429	+	1.41328i	0.0868604	+	0.0728845i
$377$	−0.189910	−	1.07703i	−0.00978086	−	0.0554700i
$378$	−2.32305	−	0.845520i	−0.119485	−	0.0434889i
$379$	18.1672			0.933187			0.466593	−	0.884472i	$-0.345481\pi$
$379$	18.1672			0.933187			0.466593	+	0.884472i	$0.345481\pi$
$380$		0			0
$381$	18.0806			0.926297
$382$	−11.9624	−	4.35397i	−0.612052	−	0.222769i
$383$	3.99535	+	22.6588i	0.204153	+	1.15781i	0.898767	+	0.438426i	$0.144464\pi$
$383$	3.99535	+	22.6588i	0.204153	+	1.15781i	−0.694614	+	0.719383i	$0.744425\pi$
$384$	0.983662	+	0.825390i	0.0501973	+	0.0421205i
$385$	5.04777	−	4.23559i	0.257258	−	0.215865i
$386$	3.03503	−	17.2125i	0.154479	−	0.876095i
$387$	−3.80699	+	6.59390i	−0.193520	+	0.335187i
$388$	−2.04238	−	3.53750i	−0.103686	−	0.179590i
$389$	15.5713	−	5.66749i	0.789496	−	0.287353i	0.0843694	−	0.996435i	$-0.473112\pi$
$389$	15.5713	−	5.66749i	0.789496	−	0.287353i	0.705126	+	0.709082i	$0.250890\pi$
$390$	−21.8131	+	7.93932i	−1.10455	+	0.402023i
$391$	1.22895	+	2.12860i	0.0621506	+	0.107648i
$392$	3.40211	−	5.89263i	0.171833	−	0.297623i
$393$	3.53231	−	20.0327i	0.178181	−	1.01052i
$394$	−18.7767	+	15.7555i	−0.945958	+	0.793753i
$395$	28.8866	+	24.2388i	1.45344	+	1.21958i
$396$	0.945455	+	5.36194i	0.0475109	+	0.269448i
$397$	16.7217	+	6.08619i	0.839236	+	0.305457i	0.725644	−	0.688070i	$-0.241542\pi$
$397$	16.7217	+	6.08619i	0.839236	+	0.305457i	0.113592	+	0.993527i	$0.463764\pi$
$398$	16.4661			0.825371
$399$		0			0
$400$	8.65833			0.432916
$401$	−28.7748	−	10.4732i	−1.43694	−	0.523005i	−0.498030	−	0.867160i	$-0.665943\pi$
$401$	−28.7748	−	10.4732i	−1.43694	−	0.523005i	−0.938913	+	0.344155i	$0.888165\pi$
$402$	0.0329479	+	0.186857i	0.00164329	+	0.00931956i
$403$	13.0394	+	10.9413i	0.649537	+	0.545026i
$404$	0.325781	−	0.273363i	0.0162082	−	0.0136003i
$405$	−2.00291	+	11.3591i	−0.0995255	+	0.564437i
$406$	−0.0494633	+	0.0856730i	−0.00245482	+	0.00425188i
$407$	2.91955	+	5.05682i	0.144717	+	0.250657i
$408$	−0.322044	+	0.117214i	−0.0159435	+	0.00580297i
$409$	−8.59187	+	3.12719i	−0.424841	+	0.154629i	−0.545587	−	0.838054i	$-0.683693\pi$
$409$	−8.59187	+	3.12719i	−0.424841	+	0.154629i	0.120747	+	0.992683i	$0.461471\pi$
$410$	14.5329	+	25.1717i	0.717729	+	1.24314i
$411$	−1.41726	+	2.45477i	−0.0699083	+	0.121085i
$412$	−0.787699	+	4.46727i	−0.0388072	+	0.220086i
$413$	1.18954	−	0.998144i	0.0585335	−	0.0491155i
$414$	9.53194	+	7.99825i	0.468469	+	0.393092i
$415$	−2.11059	−	11.9697i	−0.103605	−	0.587572i
$416$	−4.59650	−	1.67299i	−0.225362	−	0.0820250i
$417$	−21.9121			−1.07304
$418$		0			0
$419$	12.6157			0.616315			0.308158	−	0.951335i	$-0.400288\pi$
$419$	12.6157			0.616315			0.308158	+	0.951335i	$0.400288\pi$
$420$	1.97312	+	0.718157i	0.0962785	+	0.0350425i
$421$	5.77473	+	32.7501i	0.281443	+	1.59614i	0.717721	+	0.696331i	$0.245185\pi$
$421$	5.77473	+	32.7501i	0.281443	+	1.59614i	−0.436278	+	0.899812i	$0.643704\pi$
$422$	21.0512	+	17.6641i	1.02476	+	0.859875i
$423$	−2.27571	+	1.90955i	−0.110649	+	0.0928453i
$424$	1.72648	−	9.79136i	0.0838453	−	0.475510i
$425$	−1.15542	+	2.00125i	−0.0560463	+	0.0970750i
$426$	−7.36363	−	12.7542i	−0.356769	−	0.617942i
$427$	1.69619	−	0.617364i	0.0820845	−	0.0298763i
$428$	2.98025	−	1.08472i	0.144056	−	0.0524320i
$429$	12.6553	+	21.9196i	0.611004	+	1.05829i
$430$	10.4131	−	18.0360i	0.502164	−	0.869773i
$431$	−3.99242	+	22.6422i	−0.192308	+	1.09063i	0.723892	+	0.689914i	$0.242351\pi$
$431$	−3.99242	+	22.6422i	−0.192308	+	1.09063i	−0.916200	+	0.400721i	$0.868760\pi$
$432$	−4.28005	+	3.59139i	−0.205924	+	0.172791i
$433$	26.5888	+	22.3107i	1.27778	+	1.07218i	0.993546	+	0.113427i	$0.0361827\pi$
$433$	26.5888	+	22.3107i	1.27778	+	1.07218i	0.284231	+	0.958756i	$0.408262\pi$
$434$	−0.267367	−	1.51632i	−0.0128340	−	0.0727855i
$435$	0.997039	+	0.362893i	0.0478044	+	0.0173994i
$436$	−6.78112			−0.324757
$437$		0			0
$438$	1.82629			0.0872637
$439$	34.2817	+	12.4775i	1.63618	+	0.595519i	0.986364	−	0.164576i	$-0.0526255\pi$
$439$	34.2817	+	12.4775i	1.63618	+	0.595519i	0.649812	+	0.760095i	$0.274848\pi$
$440$	−2.58606	−	14.6663i	−0.123286	−	0.699187i
$441$	7.04261	+	5.90945i	0.335362	+	0.281402i
$442$	1.00007	−	0.839162i	0.0475687	−	0.0399149i
$443$	2.04181	−	11.5797i	0.0970091	−	0.550166i	−0.897104	−	0.441819i	$-0.854333\pi$
$443$	2.04181	−	11.5797i	0.0970091	−	0.550166i	0.994113	−	0.108347i	$-0.0345557\pi$
$444$	−0.930333	+	1.61138i	−0.0441517	+	0.0764729i
$445$	11.0146	+	19.0779i	0.522143	+	0.904378i
$446$	−19.1421	+	6.96715i	−0.906404	+	0.329904i
$447$	−16.3449	+	5.94904i	−0.773085	+	0.281380i
$448$	0.221232	+	0.383185i	0.0104522	+	0.0181038i
$449$	4.34551	−	7.52664i	0.205077	−	0.355204i	−0.745080	−	0.666975i	$-0.767589\pi$
$449$	4.34551	−	7.52664i	0.205077	−	0.355204i	0.950157	+	0.311771i	$0.100922\pi$
$450$	−2.03144	+	11.5209i	−0.0957632	+	0.543100i
$451$	24.2777	−	20.3714i	1.14319	−	0.959251i
$452$	−7.69442	−	6.45638i	−0.361915	−	0.303683i
$453$	−2.04096	−	11.5748i	−0.0958925	−	0.543833i
$454$	20.8136	+	7.57552i	0.976829	+	0.355537i
$455$	−7.99866			−0.374983
$456$		0			0
$457$	−13.0286			−0.609454			−0.304727	−	0.952440i	$-0.598565\pi$
$457$	−13.0286			−0.609454			−0.304727	+	0.952440i	$0.598565\pi$
$458$	−11.9480	−	4.34871i	−0.558292	−	0.203202i
$459$	−0.258942	−	1.46853i	−0.0120864	−	0.0685452i
$460$	−26.0723	−	21.8773i	−1.21563	−	1.02003i
$461$	6.92703	−	5.81247i	0.322624	−	0.270714i	−0.467062	−	0.884224i	$-0.654688\pi$
$461$	6.92703	−	5.81247i	0.322624	−	0.270714i	0.789686	+	0.613511i	$0.210243\pi$
$462$	0.397566	−	2.25471i	0.0184964	−	0.104899i
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	−0.583313	−	0.812248i	$-0.698244\pi$
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	0.995083	+	0.0990396i	$0.0315771\pi$
$464$	0.111791	+	0.193627i	0.00518976	+	0.00898892i
$465$	−15.5181	+	5.64811i	−0.719632	+	0.261925i
$466$	8.15819	−	2.96934i	0.377921	−	0.137552i
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	0.942653	−	0.333775i	$-0.108323\pi$
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	−0.760384	+	0.649474i	$0.774989\pi$
$468$	3.30455	−	5.72364i	0.152753	−	0.264576i
$469$	−0.0113531	+	0.0643864i	−0.000524236	+	0.00297309i
$470$	6.22464	−	5.22310i	0.287121	−	0.240923i
$471$	−16.1225	−	13.5284i	−0.742885	−	0.623355i
$472$	−0.609423	−	3.45621i	−0.0280510	−	0.159085i
$473$	−21.3386	−	7.76662i	−0.981151	−	0.357110i
$474$	13.1019			0.601792
$475$		0			0
$476$	−0.118090			−0.00541266
$477$	12.6234	+	4.59456i	0.577988	+	0.210370i
$478$	3.79854	+	21.5426i	0.173741	+	0.985334i
$479$	−23.1191	−	19.3992i	−1.05634	−	0.886373i	−0.0625925	−	0.998039i	$-0.519937\pi$
$479$	−23.1191	−	19.3992i	−1.05634	−	0.886373i	−0.993746	+	0.111666i	$0.964381\pi$
$480$	3.63534	−	3.05041i	0.165930	−	0.139231i
$481$	1.23080	−	6.98023i	0.0561198	−	0.318271i
$482$	9.48160	−	16.4226i	0.431875	−	0.748030i
$483$	−2.61617	−	4.53134i	−0.119040	−	0.206183i
$484$	−4.92235	+	1.79159i	−0.223743	+	0.0814359i
$485$	−14.1857	+	5.16317i	−0.644140	+	0.234448i
$486$	−6.37701	−	11.0453i	−0.289267	−	0.501025i
$487$	−17.8850	+	30.9777i	−0.810445	+	1.40373i	0.102107	+	0.994773i	$0.467442\pi$
$487$	−17.8850	+	30.9777i	−0.810445	+	1.40373i	−0.912553	+	0.408959i	$0.865892\pi$
$488$	0.708406	−	4.01757i	0.0320680	−	0.181867i
$489$	−13.5472	+	11.3675i	−0.612627	+	0.514055i
$490$	−19.2633	−	16.1639i	−0.870229	−	0.730209i
$491$	−3.17301	−	17.9950i	−0.143196	−	0.812104i	−0.968798	−	0.247852i	$-0.920275\pi$
$491$	−3.17301	−	17.9950i	−0.143196	−	0.812104i	0.825602	−	0.564253i	$-0.190836\pi$
$492$	9.48989	+	3.45404i	0.427837	+	0.155720i
$493$	−0.0596724			−0.00268751
$494$		0			0
$495$	20.1219			0.904413
$496$	−3.26999	−	1.19018i	−0.146827	−	0.0534407i
$497$	−0.881207	−	4.99757i	−0.0395275	−	0.224172i
$498$	−3.23505	−	2.71453i	−0.144966	−	0.121641i
$499$	13.5574	−	11.3760i	0.606914	−	0.509262i	−0.286745	−	0.958007i	$-0.592573\pi$
$499$	13.5574	−	11.3760i	0.606914	−	0.509262i	0.893660	+	0.448745i	$0.148129\pi$
$500$	2.34775	−	13.3147i	0.104995	−	0.595454i
$501$	6.63407	−	11.4905i	0.296388	−	0.513360i
$502$	−1.45138	−	2.51386i	−0.0647782	−	0.112199i
$503$	9.57570	−	3.48527i	0.426959	−	0.155401i	−0.119598	−	0.992822i	$-0.538160\pi$
$503$	9.57570	−	3.48527i	0.426959	−	0.155401i	0.546557	+	0.837422i	$0.315938\pi$
$504$	−0.561777	+	0.204470i	−0.0250235	+	0.00910782i
$505$	−0.785853	−	1.36114i	−0.0349700	−	0.0605698i
$506$	−18.5552	+	32.1386i	−0.824881	+	1.42874i
$507$	2.43641	−	13.8176i	0.108205	−	0.613660i
$508$	10.7864	−	9.05083i	0.478567	−	0.401566i
$509$	−6.46251	−	5.42269i	−0.286446	−	0.240357i	0.488230	−	0.872715i	$-0.337643\pi$
$509$	−6.46251	−	5.42269i	−0.286446	−	0.240357i	−0.774676	+	0.632358i	$0.782087\pi$
$510$	0.219937	+	1.24732i	0.00973897	+	0.0552324i
$511$	0.591347	+	0.215233i	0.0261596	+	0.00952133i
$512$	1.00000			0.0441942
$513$		0			0
$514$	22.9050			1.01030
$515$	15.7534	+	5.73378i	0.694179	+	0.252660i
$516$	−1.25653	−	7.12614i	−0.0553156	−	0.313711i
$517$	−6.78712	−	5.69507i	−0.298497	−	0.250469i
$518$	−0.491143	+	0.412118i	−0.0215796	+	0.0181074i
$519$	−2.18786	+	12.4080i	−0.0960365	+	0.544650i
$520$	−9.03879	+	15.6556i	−0.396377	+	0.686545i
$521$	−4.48183	−	7.76275i	−0.196352	−	0.340092i	0.750991	−	0.660313i	$-0.229576\pi$
$521$	−4.48183	−	7.76275i	−0.196352	−	0.340092i	−0.947343	+	0.320221i	$0.896243\pi$
$522$	−0.283872	+	0.103321i	−0.0124247	+	0.00452223i
$523$	2.01088	−	0.731900i	0.0879296	−	0.0320038i	−0.297681	−	0.954665i	$-0.596213\pi$
$523$	2.01088	−	0.731900i	0.0879296	−	0.0320038i	0.385610	+	0.922662i	$0.373991\pi$
$524$	−7.92075	−	13.7191i	−0.346020	−	0.599324i
$525$	2.45965	−	4.26024i	0.107348	−	0.185932i
$526$	−0.879070	+	4.98545i	−0.0383293	+	0.217376i
$527$	0.711462	−	0.596988i	0.0309918	−	0.0260052i
$528$	−3.96383	−	3.32605i	−0.172504	−	0.144748i
$529$	10.7334	+	60.8722i	0.466670	+	2.64662i
$530$	−34.5284	−	12.5673i	−1.49982	−	0.545889i
$531$	4.74186			0.205779
$532$		0			0
$533$	−38.4702			−1.66633
$534$	7.19247	+	2.61785i	0.311249	+	0.113285i
$535$	−2.03533	−	11.5429i	−0.0879951	−	0.499045i
$536$	0.113193	+	0.0949801i	0.00488919	+	0.00410252i
$537$	−8.65455	+	7.26203i	−0.373472	+	0.313380i
$538$	−3.60180	+	20.4268i	−0.155285	+	0.880663i
$539$	−13.7094	+	23.7454i	−0.590506	+	1.02279i
$540$	10.3244	+	17.8823i	0.444290	+	0.769533i
$541$	11.0053	−	4.00559i	0.473153	−	0.172214i	−0.0944272	−	0.995532i	$-0.530102\pi$
$541$	11.0053	−	4.00559i	0.473153	−	0.172214i	0.567580	+	0.823318i	$0.307880\pi$
$542$	−5.91508	+	2.15291i	−0.254075	+	0.0924756i
$543$	−9.32739	−	16.1555i	−0.400277	−	0.693299i
$544$	−0.133446	+	0.231136i	−0.00572147	+	0.00990988i
$545$	−4.35181	+	24.6804i	−0.186411	+	1.05719i
$546$	−2.12895	+	1.78640i	−0.0911104	+	0.0764507i
$547$	−19.1432	−	16.0630i	−0.818504	−	0.686806i	0.134117	−	0.990965i	$-0.457180\pi$
$547$	−19.1432	−	16.0630i	−0.818504	−	0.686806i	−0.952621	+	0.304159i	$0.901625\pi$
$548$	0.383317	+	2.17390i	0.0163745	+	0.0928644i
$549$	5.17963	+	1.88523i	0.221061	+	0.0804597i
$550$	−34.8902			−1.48772
$551$		0			0
$552$	−11.8255			−0.503325
$553$	4.24236	+	1.54409i	0.180403	+	0.0656615i
$554$	1.24611	+	7.06706i	0.0529423	+	0.300251i
$555$	5.26770	+	4.42013i	0.223602	+	0.187624i
$556$	−13.0721	+	10.9688i	−0.554381	+	0.465181i
$557$	1.59681	−	9.05596i	0.0676590	−	0.383713i	−0.932109	−	0.362178i	$-0.882033\pi$
$557$	1.59681	−	9.05596i	0.0676590	−	0.383713i	0.999768	−	0.0215356i	$-0.00685552\pi$
$558$	2.35089	−	4.07185i	0.0995209	−	0.172375i
$559$	13.7823	+	23.8717i	0.582930	+	1.00966i
$560$	1.53660	−	0.559278i	0.0649334	−	0.0236338i
$561$	1.29773	−	0.472335i	0.0547902	−	0.0199420i
$562$	−1.38696	−	2.40228i	−0.0585052	−	0.101334i
$563$	−9.86122	+	17.0801i	−0.415601	+	0.719842i	−0.995491	−	0.0948526i	$-0.969762\pi$
$563$	−9.86122	+	17.0801i	−0.415601	+	0.719842i	0.579890	+	0.814694i	$0.303095\pi$
$564$	0.490257	−	2.78039i	0.0206435	−	0.117075i
$565$	−28.4364	+	23.8610i	−1.19633	+	1.00384i
$566$	5.93578	+	4.98071i	0.249499	+	0.209355i
$567$	0.239795	+	1.35995i	0.0100705	+	0.0571124i
$568$	−10.7774	−	3.92267i	−0.452212	−	0.164592i
$569$	22.1469			0.928446			0.464223	−	0.885718i	$-0.346334\pi$
$569$	22.1469			0.928446			0.464223	+	0.885718i	$0.346334\pi$
$570$		0			0
$571$	−3.02145			−0.126444			−0.0632218	−	0.998000i	$-0.520138\pi$
$571$	−3.02145			−0.126444			−0.0632218	+	0.998000i	$0.520138\pi$
$572$	18.5224	+	6.74160i	0.774460	+	0.281880i
$573$	2.83855	+	16.0982i	0.118582	+	0.672512i
$574$	2.66572	+	2.23681i	0.111265	+	0.0933625i
$575$	−61.0822	+	51.2540i	−2.54730	+	2.13744i
$576$	−0.234623	+	1.33061i	−0.00977597	+	0.0554423i
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	−0.889059	−	0.457792i	$-0.848641\pi$
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	0.840989	+	0.541052i	$0.181974\pi$
$578$	8.46438	+	14.6607i	0.352072	+	0.609807i
$579$	−21.0897	+	7.67603i	−0.876459	+	0.319005i
$580$	0.776463	−	0.282609i	0.0322409	−	0.0117347i
$581$	−0.727582	−	1.26021i	−0.0301852	−	0.0522823i
$582$	−2.62258	+	4.54243i	−0.108709	+	0.188290i
$583$	−6.95715	+	39.4560i	−0.288136	+	1.63410i
$584$	1.08951	−	0.914211i	0.0450844	−	0.0378303i
$585$	−18.7109	−	15.7003i	−0.773601	−	0.649128i
$586$	−0.135944	−	0.770977i	−0.00561579	−	0.0318487i
$587$	−26.3950	−	9.60701i	−1.08944	−	0.396524i	−0.266027	−	0.963966i	$-0.585711\pi$
$587$	−26.3950	−	9.60701i	−1.08944	−	0.396524i	−0.823413	+	0.567442i	$0.807933\pi$
$588$	−8.73716			−0.360315
$589$		0			0
$590$	−12.9702			−0.533975
$591$	29.5763	+	10.7649i	1.21661	+	0.442808i
$592$	0.251621	+	1.42701i	0.0103416	+	0.0586499i
$593$	−9.26446	−	7.77381i	−0.380446	−	0.319232i	0.432432	−	0.901667i	$-0.357656\pi$
$593$	−9.26446	−	7.77381i	−0.380446	−	0.319232i	−0.812877	+	0.582435i	$0.802100\pi$
$594$	17.2472	−	14.4721i	0.707661	−	0.593798i
$595$	−0.0757851	+	0.429798i	−0.00310688	+	0.0176200i
$596$	−6.77288	+	11.7310i	−0.277428	+	0.480519i
$597$	−10.5719	−	18.3110i	−0.432679	−	0.749421i
$598$	42.3305	−	15.4071i	1.73102	−	0.630041i
$599$	−18.3264	+	6.67025i	−0.748795	+	0.272539i	−0.688099	−	0.725617i	$-0.741554\pi$
$599$	−18.3264	+	6.67025i	−0.748795	+	0.272539i	−0.0606966	+	0.998156i	$0.519332\pi$
$600$	−5.55899	−	9.62845i	−0.226945	−	0.393080i
$601$	19.4816	−	33.7431i	0.794671	−	1.37641i	−0.128376	−	0.991726i	$-0.540977\pi$
$601$	19.4816	−	33.7431i	0.794671	−	1.37641i	0.923048	−	0.384685i	$-0.125690\pi$
$602$	0.432971	−	2.45550i	0.0176466	−	0.100079i
$603$	−0.152940	+	0.128332i	−0.00622818	+	0.00522607i
$604$	−7.01174	−	5.88355i	−0.285304	−	0.239398i
$605$	3.36168	+	19.0650i	0.136672	+	0.775103i
$606$	−0.513157	−	0.186774i	−0.0208456	−	0.00758716i
$607$	8.46029			0.343393			0.171696	−	0.985150i	$-0.445075\pi$
$607$	8.46029			0.343393			0.171696	+	0.985150i	$0.445075\pi$
$608$		0			0
$609$	0.127030			0.00514750
$610$	−14.1676	−	5.15659i	−0.573630	−	0.208784i
$611$	1.86755	+	10.5914i	0.0755532	+	0.428483i
$612$	−0.276243	−	0.231796i	−0.0111665	−	0.00936978i
$613$	−2.23296	+	1.87368i	−0.0901885	+	0.0756772i	−0.686767	−	0.726877i	$-0.740971\pi$
$613$	−2.23296	+	1.87368i	−0.0901885	+	0.0756772i	0.596579	+	0.802555i	$0.296526\pi$
$614$	−4.89146	+	27.7408i	−0.197403	+	1.11953i
$615$	18.6614	−	32.3225i	0.752500	−	1.30337i
$616$	−0.891491	−	1.54411i	−0.0359192	−	0.0622139i
$617$	2.83698	−	1.03258i	0.114213	−	0.0415700i	−0.284282	−	0.958741i	$-0.591755\pi$
$617$	2.83698	−	1.03258i	0.114213	−	0.0415700i	0.398494	+	0.917171i	$0.369533\pi$
$618$	5.47354	−	1.99220i	0.220178	−	0.0801382i
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	0.902794	−	0.430074i	$-0.141512\pi$
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	−0.823852	+	0.566806i	$0.808179\pi$
$620$	−6.43028	+	11.1376i	−0.258246	+	0.447295i
$621$	8.93494	−	50.6726i	0.358547	−	2.03342i
$622$	2.96327	−	2.48648i	0.118816	−	0.0996986i
$623$	2.02038	+	1.69530i	0.0809446	+	0.0679206i
$624$	1.09069	+	6.18564i	0.0436627	+	0.247624i
$625$	−6.27245	−	2.28299i	−0.250898	−	0.0913194i
$626$	30.3878			1.21454
$627$		0			0
$628$	−16.3903			−0.654043
$629$	−0.363412	−	0.132271i	−0.0144902	−	0.00527400i
$630$	0.383661	+	2.17585i	0.0152854	+	0.0866878i
$631$	7.76517	+	6.51575i	0.309127	+	0.259388i	0.784131	−	0.620595i	$-0.213109\pi$
$631$	7.76517	+	6.51575i	0.309127	+	0.259388i	−0.475004	+	0.879983i	$0.657553\pi$
$632$	7.81624	−	6.55861i	0.310913	−	0.260887i
$633$	6.12754	−	34.7510i	0.243548	−	1.38123i
$634$	−2.66402	+	4.61421i	−0.105802	+	0.183254i
$635$	−26.0189	−	45.0661i	−1.03253	−	1.78839i
$636$	−11.9969	+	4.36652i	−0.475708	+	0.173144i
$637$	31.2756	−	11.3834i	1.23918	−	0.451026i
$638$	−0.450480	−	0.780255i	−0.0178347	−	0.0308906i
$639$	7.74820	−	13.4203i	0.306514	−	0.530898i
$640$	0.641755	−	3.63957i	0.0253676	−	0.143867i
$641$	6.34308	−	5.32248i	0.250537	−	0.210225i	−0.508867	−	0.860845i	$-0.669935\pi$
$641$	6.34308	−	5.32248i	0.250537	−	0.210225i	0.759403	+	0.650620i	$0.225491\pi$
$642$	−3.11970	−	2.61774i	−0.123125	−	0.103314i
$643$	6.39964	+	36.2942i	0.252377	+	1.43130i	0.802716	+	0.596361i	$0.203387\pi$
$643$	6.39964	+	36.2942i	0.252377	+	1.43130i	−0.550339	+	0.834941i	$0.685502\pi$
$644$	−3.82904	−	1.39366i	−0.150885	−	0.0549178i
$645$	−26.7425			−1.05298
$646$		0			0
$647$	−20.1901			−0.793753			−0.396876	−	0.917872i	$-0.629906\pi$
$647$	−20.1901			−0.793753			−0.396876	+	0.917872i	$0.629906\pi$
$648$	2.93278	+	1.06744i	0.115210	+	0.0419331i
$649$	2.45577	+	13.9274i	0.0963976	+	0.546698i
$650$	32.4436	+	27.2234i	1.27254	+	1.06779i
$651$	−1.51455	+	1.27086i	−0.0593600	+	0.0498089i
$652$	−2.39153	+	13.5630i	−0.0936594	+	0.531169i
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	−0.565757	−	0.824572i	$-0.691416\pi$
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	0.996979	+	0.0776744i	$0.0247495\pi$
$654$	4.35375	+	7.54091i	0.170245	+	0.294873i
$655$	−55.0150	+	20.0238i	−2.14961	+	0.782395i
$656$	7.39042	−	2.68989i	0.288548	−	0.105023i
$657$	0.960837	+	1.66422i	0.0374858	+	0.0649273i
$658$	0.486417	−	0.842500i	0.0189625	−	0.0328441i
$659$	−4.72698	+	26.8080i	−0.184137	+	1.04429i	0.742922	+	0.669378i	$0.233439\pi$
$659$	−4.72698	+	26.8080i	−0.184137	+	1.04429i	−0.927059	+	0.374915i	$0.877672\pi$
$660$	−14.6492	+	12.2921i	−0.570220	+	0.478471i
$661$	−6.82412	−	5.72611i	−0.265427	−	0.222720i	0.500354	−	0.865821i	$-0.333203\pi$
$661$	−6.82412	−	5.72611i	−0.265427	−	0.222720i	−0.765781	+	0.643101i	$0.777648\pi$
$662$	−3.56813	−	20.2359i	−0.138679	−	0.786489i
$663$	−1.57527	−	0.573353i	−0.0611786	−	0.0222672i
$664$	−3.28878			−0.127629
$665$		0			0
$666$	−1.95784			−0.0758648
$667$	−1.93486	−	0.704230i	−0.0749179	−	0.0272679i
$668$	−1.79427	−	10.1758i	−0.0694225	−	0.393714i
$669$	20.0378	+	16.8137i	0.774705	+	0.650055i
$670$	0.418329	−	0.351020i	0.0161615	−	0.0135611i
$671$	−2.85464	+	16.1895i	−0.110202	+	0.624989i
$672$	0.284079	−	0.492039i	0.0109586	−	0.0189808i
$673$	−17.8505	−	30.9180i	−0.688087	−	1.19180i	−0.972456	−	0.233086i	$-0.925118\pi$
$673$	−17.8505	−	30.9180i	−0.688087	−	1.19180i	0.284370	−	0.958715i	$-0.408216\pi$
$674$	−12.4814	+	4.54285i	−0.480765	+	0.174984i
$675$	45.4585	−	16.5455i	1.74970	−	0.636838i
$676$	−5.46334	−	9.46279i	−0.210129	−	0.363953i
$677$	13.6924	−	23.7160i	0.526243	−	0.911480i	−0.473290	−	0.880907i	$-0.656934\pi$
$677$	13.6924	−	23.7160i	0.526243	−	0.911480i	0.999533	−	0.0305727i	$-0.00973312\pi$
$678$	−2.23967	+	12.7018i	−0.0860140	+	0.487810i
$679$	−1.38452	+	1.16175i	−0.0531328	+	0.0445837i
$680$	0.755596	+	0.634021i	0.0289758	+	0.0243136i
$681$	−4.93881	−	28.0094i	−0.189256	−	1.07332i
$682$	13.1770	+	4.79603i	0.504573	+	0.183650i
$683$	−38.1521			−1.45985			−0.729925	−	0.683528i	$-0.760445\pi$
$683$	−38.1521			−1.45985			−0.729925	+	0.683528i	$0.760445\pi$
$684$		0			0
$685$	8.15806			0.311703
$686$	−5.73952	−	2.08901i	−0.219136	−	0.0797589i
$687$	2.83511	+	16.0787i	0.108166	+	0.613442i
$688$	−4.31683	−	3.62225i	−0.164578	−	0.138097i
$689$	37.2552	−	31.2608i	1.41931	−	1.19094i
$690$	−7.58905	+	43.0396i	−0.288910	+	1.63849i
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	−0.462590	−	0.886572i	$-0.653080\pi$
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	0.999089	−	0.0426714i	$-0.0135868\pi$
$692$	4.90601	+	8.49745i	0.186498	+	0.323025i
$693$	2.26378	−	0.823948i	0.0859938	−	0.0312992i
$694$	−28.3245	+	10.3093i	−1.07518	+	0.391335i
$695$	31.5327	+	54.6162i	1.19610	+	2.07171i
$696$	0.143548	−	0.248633i	0.00544118	−	0.00942440i
$697$	−0.364494	+	2.06715i	−0.0138062	+	0.0782989i
$698$	26.8616	−	22.5395i	1.01673	−	0.853134i
$699$	−8.53992	−	7.16584i	−0.323009	−	0.271037i
$700$	−0.665245	−	3.77279i	−0.0251439	−	0.142598i
$701$	−40.0448	−	14.5751i	−1.51247	−	0.550495i	−0.553217	−	0.833037i	$-0.686600\pi$
$701$	−40.0448	−	14.5751i	−1.51247	−	0.550495i	−0.959255	+	0.282543i	$0.908822\pi$
$702$	−27.3298			−1.03150
$703$		0			0
$704$	−4.02967			−0.151874
$705$	−9.80478	−	3.56865i	−0.369270	−	0.134403i
$706$	2.35138	+	13.3353i	0.0884954	+	0.501882i
$707$	−0.144146	−	0.120953i	−0.00542118	−	0.00454891i
$708$	−3.45219	+	2.89673i	−0.129741	+	0.108866i
$709$	−3.93993	+	22.3445i	−0.147967	+	0.839164i	0.816969	+	0.576681i	$0.195653\pi$
$709$	−3.93993	+	22.3445i	−0.147967	+	0.839164i	−0.964937	+	0.262483i	$0.915459\pi$
$710$	−21.1933	+	36.7079i	−0.795371	+	1.37762i
$711$	6.89310	+	11.9392i	0.258511	+	0.447755i
$712$	5.60127	−	2.03870i	0.209916	−	0.0764033i
$713$	30.1143	−	10.9607i	1.12779	−	0.410482i
$714$	0.0758187	+	0.131322i	0.00283744	+	0.00491460i
$715$	36.4233	−	63.0871i	1.36216	−	2.35932i
$716$	−1.52781	+	8.66464i	−0.0570969	+	0.323813i
$717$	21.5175	−	18.0553i	0.803586	−	0.674289i
$718$	−18.0076	−	15.1102i	−0.672037	−	0.563906i
$719$	−6.56953	−	37.2577i	−0.245002	−	1.38948i	−0.820488	−	0.571664i	$-0.806298\pi$
$719$	−6.56953	−	37.2577i	−0.245002	−	1.38948i	0.575486	−	0.817812i	$-0.304813\pi$
$720$	4.69229	+	1.70786i	0.174871	+	0.0636480i
$721$	2.00709			0.0747481
$722$		0			0
$723$	−24.3503			−0.905596
$724$	−13.6516	−	4.96878i	−0.507358	−	0.184663i
$725$	−0.336156	−	1.90643i	−0.0124845	−	0.0708031i
$726$	5.15268	+	4.32361i	0.191234	+	0.160464i
$727$	−14.9687	+	12.5603i	−0.555160	+	0.465835i	−0.876684	−	0.481067i	$-0.840249\pi$
$727$	−14.9687	+	12.5603i	−0.555160	+	0.465835i	0.321524	+	0.946901i	$0.395805\pi$
$728$	−0.375828	+	2.13143i	−0.0139291	+	0.0789959i
$729$	−12.8701	+	22.2916i	−0.476670	+	0.825616i
$730$	−2.62814	−	4.55206i	−0.0972717	−	0.168479i
$731$	1.41330	−	0.514399i	0.0522727	−	0.0190257i
$732$	−4.92254	+	1.79166i	−0.181942	+	0.0662216i
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	−0.983503	−	0.180894i	$-0.942101\pi$
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	0.335092	−	0.942185i	$-0.391232\pi$
$734$	6.34644	−	10.9924i	0.234251	−	0.405735i
$735$	−5.60712	+	31.7995i	−0.206822	+	1.17294i
$736$	−7.05473	+	5.91962i	−0.260041	+	0.218200i
$737$	−0.456130	−	0.382739i	−0.0168018	−	0.0140984i
$738$	1.84525	+	10.4649i	0.0679245	+	0.385219i
$739$	15.2958	+	5.56722i	0.562666	+	0.204794i	0.607665	−	0.794193i	$-0.292106\pi$
$739$	15.2958	+	5.56722i	0.562666	+	0.204794i	−0.0449992	+	0.998987i	$0.514329\pi$
$740$	5.35520			0.196861
$741$		0			0
$742$	−4.39915			−0.161498
$743$	−31.2998	−	11.3922i	−1.14828	−	0.417939i	−0.303382	−	0.952869i	$-0.598116\pi$
$743$	−31.2998	−	11.3922i	−1.14828	−	0.417939i	−0.844896	+	0.534930i	$0.820338\pi$
$744$	0.775931	+	4.40052i	0.0284470	+	0.161331i
$745$	38.3492	+	32.1788i	1.40501	+	1.17894i
$746$	2.02964	−	1.70307i	0.0743103	−	0.0623537i
$747$	0.771624	−	4.37610i	0.0282322	−	0.160113i
$748$	0.537746	−	0.931403i	0.0196619	−	0.0340555i
$749$	−0.701639	−	1.21528i	−0.0256373	−	0.0444052i
$750$	−16.3139	+	5.93779i	−0.595701	+	0.216817i
$751$	−18.0984	+	6.58727i	−0.660419	+	0.240373i	−0.650417	−	0.759577i	$-0.725406\pi$
$751$	−18.0984	+	6.58727i	−0.660419	+	0.240373i	−0.0100020	+	0.999950i	$0.503184\pi$
$752$	−1.09934	−	1.90411i	−0.0400888	−	0.0694358i
$753$	−1.86368	+	3.22800i	−0.0679164	+	0.117635i
$754$	−0.189910	+	1.07703i	−0.00691611	+	0.0392232i
$755$	−25.9134	+	21.7439i	−0.943085	+	0.791343i
$756$	1.89377	+	1.58906i	0.0688756	+	0.0577935i
$757$	−4.15808	−	23.5816i	−0.151128	−	0.857089i	−0.962241	−	0.272200i	$-0.912249\pi$
$757$	−4.15808	−	23.5816i	−0.151128	−	0.857089i	0.811113	−	0.584890i	$-0.198862\pi$
$758$	−17.0716	−	6.21355i	−0.620068	−	0.225686i
$759$	47.6528			1.72969
$760$		0			0
$761$	−44.7968			−1.62388			−0.811941	−	0.583739i	$-0.801589\pi$
$761$	−44.7968			−1.62388			−0.811941	+	0.583739i	$0.801589\pi$
$762$	−16.9902	−	6.18393i	−0.615490	−	0.224020i
$763$	0.521013	+	2.95481i	0.0188620	+	0.106971i
$764$	9.75187	+	8.18279i	0.352810	+	0.296043i
$765$	−1.02092	+	0.856651i	−0.0369113	+	0.0309723i
$766$	3.99535	−	22.6588i	0.144358	−	0.818695i
$767$	8.58341	−	14.8669i	0.309929	−	0.536813i
$768$	−0.642040	−	1.11205i	−0.0231676	−	0.0401275i
$769$	29.8228	−	10.8546i	1.07544	−	0.391427i	0.257229	−	0.966350i	$-0.417190\pi$
$769$	29.8228	−	10.8546i	1.07544	−	0.391427i	0.818207	+	0.574924i	$0.194968\pi$
$770$	−6.19201	+	2.25371i	−0.223145	+	0.0812180i
$771$	−14.7059	−	25.4714i	−0.529621	−	0.917330i
$772$	−8.73903	+	15.1364i	−0.314525	+	0.544772i
$773$	−3.86032	+	21.8929i	−0.138846	+	0.787434i	0.833258	+	0.552884i	$0.186473\pi$
$773$	−3.86032	+	21.8929i	−0.138846	+	0.787434i	−0.972104	+	0.234550i	$0.924638\pi$
$774$	5.83264	−	4.89417i	0.209650	−	0.175917i
$775$	23.0807	+	19.3670i	0.829083	+	0.695683i
$776$	0.709311	+	4.02270i	0.0254628	+	0.144407i
$777$	0.773627	+	0.281577i	0.0277537	+	0.0101015i
$778$	−16.5706			−0.594086
$779$		0			0
$780$	23.2130			0.831160
$781$	43.4296	+	15.8071i	1.55403	+	0.565622i
$782$	−0.426809	−	2.42056i	−0.0152627	−	0.0865589i
$783$	0.956940	+	0.802968i	0.0341983	+	0.0286957i
$784$	−5.21234	+	4.37367i	−0.186155	+	0.156203i
$785$	−10.5185	+	59.6536i	−0.375423	+	2.12913i
$786$	−10.1709	+	17.6165i	−0.362783	+	0.628358i
$787$	−12.2298	−	21.1826i	−0.435945	−	0.755080i	0.561427	−	0.827526i	$-0.310253\pi$
$787$	−12.2298	−	21.1826i	−0.435945	−	0.755080i	−0.997372	+	0.0724468i	$0.976919\pi$
$788$	23.0331	−	8.38335i	0.820519	−	0.298645i
$789$	6.10845	−	2.22329i	0.217466	−	0.0791513i
$790$	−18.8544	−	32.6568i	−0.670810	−	1.16188i
$791$	−2.22213	+	3.84884i	−0.0790098	+	0.136849i
$792$	0.945455	−	5.36194i	0.0335953	−	0.190528i
$793$	15.2865	−	12.8269i	0.542839	−	0.455496i
$794$	−13.6316	−	11.4383i	−0.483768	−	0.405930i
$795$	8.19318	+	46.4658i	0.290582	+	1.64797i
$796$	−15.4731	−	5.63174i	−0.548429	−	0.199612i
$797$	41.6933			1.47685			0.738426	−	0.674334i	$-0.235569\pi$
$797$	41.6933			1.47685			0.738426	+	0.674334i	$0.235569\pi$
$798$		0			0
$799$	0.586812			0.0207599
$800$	−8.13617	−	2.96132i	−0.287657	−	0.104699i
$801$	1.39853	+	7.93145i	0.0494146	+	0.280244i
$802$	23.4574	+	19.6831i	0.828310	+	0.695034i
$803$	−4.39039	+	3.68397i	−0.154933	+	0.130005i
$804$	0.0329479	−	0.186857i	0.00116198	−	0.00658993i
$805$	−7.52962	+	13.0417i	−0.265384	+	0.459659i
$806$	−8.51084	−	14.7412i	−0.299781	−	0.519237i
$807$	25.0280	−	9.10946i	0.881029	−	0.320668i
$808$	−0.399630	+	0.145453i	−0.0140589	+	0.00511703i
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	0.866303	+	0.499519i	$0.166490\pi$
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	−0.000555336		1.00000i	$0.500177\pi$
$810$	5.76716	−	9.98901i	0.202637	−	0.350978i
$811$	9.03760	−	51.2548i	0.317353	−	1.79980i	−0.241357	−	0.970436i	$-0.577593\pi$
$811$	9.03760	−	51.2548i	0.317353	−	1.79980i	0.558710	−	0.829363i	$-0.311296\pi$
$812$	0.0757822	−	0.0635888i	0.00265944	−	0.00223153i
$813$	6.19186	+	5.19558i	0.217158	+	0.182217i
$814$	−1.01395	−	5.75040i	−0.0355389	−	0.201551i
$815$	47.8288	+	17.4083i	1.67537	+	0.609785i
$816$	0.342712			0.0119973
$817$		0			0
$818$	9.14328			0.319687
$819$	−2.74793	−	1.00016i	−0.0960203	−	0.0349485i
$820$	−5.04722	−	28.6242i	−0.176257	−	0.999601i
$821$	−32.3717	−	27.1631i	−1.12978	−	0.947998i	−0.130723	−	0.991419i	$-0.541730\pi$
$821$	−32.3717	−	27.1631i	−1.12978	−	0.947998i	−0.999057	+	0.0434212i	$0.986174\pi$
$822$	2.17137	−	1.82200i	0.0757352	−	0.0635494i
$823$	5.63959	−	31.9837i	0.196584	−	1.11488i	−0.713561	−	0.700593i	$-0.752919\pi$
$823$	5.63959	−	31.9837i	0.196584	−	1.11488i	0.910145	−	0.414290i	$-0.135970\pi$
$824$	2.26809	−	3.92845i	0.0790127	−	0.136854i
$825$	22.4009	+	38.7995i	0.779899	+	1.35083i
$826$	−1.45919	+	0.531101i	−0.0507717	+	0.0184794i
$827$	20.2181	−	7.35879i	0.703052	−	0.255890i	0.0343387	−	0.999410i	$-0.489068\pi$
$827$	20.2181	−	7.35879i	0.703052	−	0.255890i	0.668713	+	0.743520i	$0.266845\pi$
$828$	−6.22153	−	10.7760i	−0.216213	−	0.374492i
$829$	−2.82531	+	4.89357i	−0.0981269	+	0.169961i	−0.910909	−	0.412607i	$-0.864618\pi$
$829$	−2.82531	+	4.89357i	−0.0981269	+	0.169961i	0.812782	+	0.582567i	$0.197952\pi$
$830$	−2.11059	+	11.9697i	−0.0732596	+	0.415476i
$831$	7.05883	−	5.92307i	0.244868	−	0.205469i
$832$	3.74710	+	3.14419i	0.129907	+	0.109005i
$833$	−0.315345	−	1.78841i	−0.0109261	−	0.0619648i
$834$	20.5906	+	7.49438i	0.712995	+	0.259509i
$835$	−38.1871			−1.32152
$836$		0			0
$837$	−19.4427			−0.672037
$838$	−11.8548	−	4.31481i	−0.409519	−	0.149053i
$839$	−1.85398	−	10.5144i	−0.0640064	−	0.362998i	−0.999941	−	0.0108254i	$-0.996554\pi$
$839$	−1.85398	−	10.5144i	−0.0640064	−	0.362998i	0.935935	−	0.352173i	$-0.114557\pi$
$840$	−1.60850	−	1.34969i	−0.0554986	−	0.0465689i
$841$	−22.1770	+	18.6087i	−0.764724	+	0.641680i
$842$	5.77473	−	32.7501i	0.199010	−	1.12864i
$843$	−1.78096	+	3.08471i	−0.0613395	+	0.106243i
$844$	−13.7402	−	23.7988i	−0.472958	−	0.819187i
$845$	−37.9466	+	13.8114i	−1.30540	+	0.475128i
$846$	2.79157	−	1.01605i	0.0959761	−	0.0349324i
$847$	1.15887	+	2.00722i	0.0398192	+	0.0689689i
$848$	−4.97120	+	8.61038i	−0.170712	+	0.295682i
$849$	1.72777	−	9.79867i	0.0592969	−	0.336289i
$850$	1.77021	−	1.48538i	0.0607178	−	0.0509482i
$851$	−10.2225	−	8.57770i	−0.350423	−	0.294040i
$852$	2.55736	+	14.5035i	0.0876137	+	0.496882i
$853$	−9.64743	−	3.51138i	−0.330322	−	0.120227i	0.171535	−	0.985178i	$-0.445127\pi$
$853$	−9.64743	−	3.51138i	−0.330322	−	0.120227i	−0.501857	+	0.864951i	$0.667350\pi$
$854$	−1.80505			−0.0617676
$855$		0			0
$856$	−3.17151			−0.108400
$857$	35.0869	+	12.7706i	1.19855	+	0.436235i	0.862717	−	0.505687i	$-0.168761\pi$
$857$	35.0869	+	12.7706i	1.19855	+	0.436235i	0.335830	+	0.941923i	$0.390983\pi$
$858$	−4.39514	−	24.9261i	−0.150048	−	0.850963i
$859$	−18.6064	−	15.6127i	−0.634844	−	0.532697i	0.267586	−	0.963534i	$-0.413774\pi$
$859$	−18.6064	−	15.6127i	−0.634844	−	0.532697i	−0.902430	+	0.430837i	$0.858218\pi$
$860$	−15.9538	+	13.3868i	−0.544019	+	0.456486i
$861$	0.775931	−	4.40052i	0.0264436	−	0.149969i
$862$	11.4957	−	19.9112i	0.391546	−	0.678178i
$863$	11.7864	+	20.4146i	0.401214	+	0.694922i	0.993873	−	0.110531i	$-0.0352552\pi$
$863$	11.7864	+	20.4146i	0.401214	+	0.694922i	−0.592659	+	0.805453i	$0.701922\pi$
$864$	5.25026	−	1.91094i	0.178617	−	0.0650114i
$865$	34.0755	−	12.4025i	1.15860	−	0.421697i
$866$	−17.3546	−	30.0591i	−0.589734	−	1.02145i
$867$	10.8689	−	18.8256i	0.369128	−	0.639349i
$868$	−0.267367	+	1.51632i	−0.00907504	+	0.0514671i
$869$	−31.4969	+	26.4290i	−1.06846	+	0.896543i
$870$	−0.812794	−	0.682015i	−0.0275563	−	0.0231225i
$871$	0.125510	+	0.711800i	0.00425273	+	0.0241184i
$872$	6.37217	+	2.31928i	0.215789	+	0.0785407i
$873$	−5.51908			−0.186793
$874$		0			0
$875$	−5.98217			−0.202234
$876$	−1.71616	−	0.624629i	−0.0579835	−	0.0211043i
$877$	−5.45918	−	30.9606i	−0.184344	−	1.04546i	−0.926796	−	0.375565i	$-0.877449\pi$
$877$	−5.45918	−	30.9606i	−0.184344	−	1.04546i	0.742452	−	0.669899i	$-0.233663\pi$
$878$	−27.9467	−	23.4501i	−0.943155	−	0.791401i
$879$	−0.770079	+	0.646173i	−0.0259741	+	0.0217949i
$880$	−2.58606	+	14.6663i	−0.0871761	+	0.494400i
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	−0.263776	−	0.964584i	$-0.584968\pi$
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	0.967242	−	0.253855i	$-0.0816985\pi$
$882$	−4.59673	−	7.96178i	−0.154780	−	0.268087i
$883$	−0.510291	+	0.185731i	−0.0171727	+	0.00625034i	−0.350592	−	0.936528i	$-0.614020\pi$
$883$	−0.510291	+	0.185731i	−0.0171727	+	0.00625034i	0.333420	+	0.942779i	$0.391797\pi$
$884$	−1.22677	+	0.446509i	−0.0412608	+	0.0150177i
$885$	8.32739	+	14.4235i	0.279922	+	0.484839i
$886$	−5.87915	+	10.1830i	−0.197514	+	0.342104i
$887$	1.96653	−	11.1528i	0.0660297	−	0.374473i	−0.933830	−	0.357717i	$-0.883555\pi$
$887$	1.96653	−	11.1528i	0.0660297	−	0.374473i	0.999860	−	0.0167556i	$-0.00533371\pi$
$888$	1.42535	−	1.19601i	0.0478317	−	0.0401356i
$889$	−4.77257	−	4.00466i	−0.160067	−	0.134312i
$890$	−3.82534	−	21.6946i	−0.128226	−	0.727203i
$891$	−11.8181	−	4.30145i	−0.395922	−	0.144104i
$892$	20.3706			0.682058
$893$		0			0
$894$	17.3938			0.581737
$895$	30.5551	+	11.1211i	1.02134	+	0.371739i
$896$	−0.0768330	−	0.435741i	−0.00256681	−	0.0145571i
$897$	−44.3112	−	37.1815i	−1.47951	−	1.24145i
$898$	−6.65771	+	5.58648i	−0.222171	+	0.186423i
$899$	−0.135104	+	0.766211i	−0.00450596	+	0.0255546i
$900$	5.84931	−	10.1313i	0.194977	−	0.337710i
$901$	−1.32678	−	2.29805i	−0.0442014	−	0.0765591i
$902$	−29.7810	+	10.8394i	−0.991598	+	0.360912i
$903$	−3.00861	+	1.09504i	−0.100120	+	0.0364408i
$904$	5.02218	+	8.69866i	0.167035	+	0.289313i
$905$	−26.8452	+	46.4973i	−0.892366	+	1.54562i
$906$	−2.04096	+	11.5748i	−0.0678062	+	0.384548i
$907$	8.36968	−	7.02300i	0.277911	−	0.233195i	−0.493169	−	0.869934i	$-0.664162\pi$
$907$	8.36968	−	7.02300i	0.277911	−	0.233195i	0.771080	+	0.636739i	$0.219717\pi$
$908$	−16.9674	−	14.2373i	−0.563082	−	0.472482i
$909$	−0.0997799	−	0.565880i	−0.00330949	−	0.0187691i
$910$	7.51629	+	2.73570i	0.249162	+	0.0906877i
$911$	47.4159			1.57096			0.785479	−	0.618888i	$-0.212416\pi$
$911$	47.4159			1.57096			0.785479	+	0.618888i	$0.212416\pi$
$912$		0			0
$913$	13.2527			0.438600
$914$	12.2429	+	4.45605i	0.404959	+	0.147393i
$915$	3.36181	+	19.0658i	0.111138	+	0.630295i
$916$	9.74008	+	8.17290i	0.321821	+	0.270040i
$917$	−5.36942	+	4.50548i	−0.177314	+	0.148784i
$918$	−0.258942	+	1.46853i	−0.00854636	+	0.0484688i
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	−0.905090	−	0.425221i	$-0.860197\pi$
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	0.820797	+	0.571220i	$0.193530\pi$
$920$	17.0175	+	29.4752i	0.561050	+	0.971767i
$921$	33.9896	−	12.3712i	1.11999	−	0.407645i
$922$	−8.49726	+	3.09275i	−0.279842	+	0.101854i
$923$	−28.0505	−	48.5850i	−0.923295	−	1.59919i
$924$	−1.14475	+	1.98276i	−0.0376594	+	0.0652279i
$925$	2.17862	−	12.3556i	0.0716325	−	0.406248i
$926$	−13.5747	+	11.3905i	−0.446092	+	0.374316i
$927$	4.69510	+	3.93966i	0.154207	+	0.129395i
$928$	−0.0388245	−	0.220185i	−0.00127448	−	0.00722792i
$929$	40.2604	+	14.6536i	1.32090	+	0.480769i	0.903747	−	0.428067i	$-0.140805\pi$
$929$	40.2604	+	14.6536i	1.32090	+	0.480769i	0.417154	+	0.908836i	$0.363028\pi$
$930$	16.5140			0.541514
$931$		0			0
$932$	−8.68176			−0.284381
$933$	−4.66761	−	1.69887i	−0.152811	−	0.0556185i
$934$	−1.36795	−	7.75804i	−0.0447607	−	0.253851i
$935$	−3.04481	−	2.55490i	−0.0995758	−	0.0835540i
$936$	−5.06286	+	4.24824i	−0.165485	+	0.138858i
$937$	−0.638825	+	3.62296i	−0.0208695	+	0.118357i	−0.993463	−	0.114156i	$-0.963584\pi$
$937$	−0.638825	+	3.62296i	−0.0208695	+	0.118357i	0.972593	+	0.232513i	$0.0746948\pi$
$938$	0.0326898	−	0.0566205i	0.00106736	−	0.00184872i
$939$	−19.5102	−	33.7926i	−0.636690	−	1.10278i
$940$	−7.63566	+	2.77915i	−0.249048	+	0.0906459i
$941$	−17.2711	+	6.28615i	−0.563020	+	0.204923i	−0.607822	−	0.794073i	$-0.707957\pi$
$941$	−17.2711	+	6.28615i	−0.563020	+	0.204923i	0.0448017	+	0.998996i	$0.485734\pi$
$942$	10.5232	+	18.2267i	0.342865	+	0.593859i
$943$	−36.2143	+	62.7250i	−1.17930	+	2.04261i
$944$	−0.609423	+	3.45621i	−0.0198350	+	0.112490i
$945$	6.99882	−	5.87271i	0.227672	−	0.191039i
$946$	17.3954	+	14.5965i	0.565573	+	0.474572i
$947$	8.11962	+	46.0486i	0.263852	+	1.49638i	0.772284	+	0.635277i	$0.219114\pi$
$947$	8.11962	+	46.0486i	0.263852	+	1.49638i	−0.508432	+	0.861102i	$0.669775\pi$
$948$	−12.3118	−	4.48113i	−0.399869	−	0.145540i
$949$	6.95697			0.225833
$950$		0			0
$951$	6.84162			0.221855
$952$	0.110969	+	0.0403893i	0.00359652	+	0.00130902i
$953$	4.35077	+	24.6744i	0.140935	+	0.799283i	0.970541	+	0.240934i	$0.0774538\pi$
$953$	4.35077	+	24.6744i	0.140935	+	0.799283i	−0.829606	+	0.558349i	$0.811435\pi$
$954$	−10.2907	−	8.63495i	−0.333175	−	0.279567i
$955$	36.0401	−	30.2413i	1.16623	−	0.978585i
$956$	3.79854	−	21.5426i	0.122853	−	0.696737i
$957$	−0.578452	+	1.00191i	−0.0186987	+	0.0323871i
$958$	15.0899	+	26.1365i	0.487533	+	0.844432i
$959$	0.917807	−	0.334054i	0.0296375	−	0.0107872i
$960$	−4.45940	+	1.62309i	−0.143926	+	0.0523850i
$961$	9.44531	+	16.3598i	0.304687	+	0.527734i
$962$	−3.54395	+	6.13831i	−0.114262	+	0.197907i
$963$	0.744111	−	4.22006i	0.0239786	−	0.135990i
$964$	−14.5267	+	12.1893i	−0.467872	+	0.392591i
$965$	49.4818	+	41.5202i	1.59288	+	1.33658i
$966$	0.908586	+	5.15285i	0.0292333	+	0.165790i
$967$	−6.67771	−	2.43049i	−0.214741	−	0.0781592i	0.232410	−	0.972618i	$-0.425339\pi$
$967$	−6.67771	−	2.43049i	−0.214741	−	0.0781592i	−0.447151	+	0.894459i	$0.647561\pi$
$968$	5.23826			0.168364
$969$		0			0
$970$	15.0961			0.484707
$971$	−57.0903	−	20.7792i	−1.83212	−	0.666836i	−0.992284	−	0.123990i	$-0.960431\pi$
$971$	−57.0903	−	20.7792i	−1.83212	−	0.666836i	−0.839832	−	0.542846i	$-0.817347\pi$
$972$	2.21471	+	12.5603i	0.0710369	+	0.402871i
$973$	5.78394	+	4.85330i	0.185424	+	0.155590i
$974$	27.4014	−	22.9925i	0.877996	−	0.736726i
$975$	9.44359	−	53.5573i	0.302437	−	1.71521i
$976$	−2.03977	+	3.53299i	−0.0652916	+	0.113088i
$977$	19.2706	+	33.3776i	0.616520	+	1.06784i	0.990116	+	0.140253i	$0.0447915\pi$
$977$	19.2706	+	33.3776i	0.616520	+	1.06784i	−0.373595	+	0.927592i	$0.621875\pi$
$978$	16.6181	−	6.04851i	0.531390	−	0.193410i
$979$	−22.5713	+	8.21527i	−0.721381	+	0.262561i
$980$	12.5732	+	21.7775i	0.401638	+	0.695657i
$981$	−4.58112	+	7.93474i	−0.146264	+	0.253337i
$982$	−3.17301	+	17.9950i	−0.101255	+	0.574244i
$983$	−5.74938	+	4.82430i	−0.183377	+	0.153871i	−0.729855	−	0.683602i	$-0.760413\pi$
$983$	−5.74938	+	4.82430i	−0.183377	+	0.153871i	0.546478	+	0.837473i	$0.315968\pi$
$984$	−7.73623	−	6.49146i	−0.246622	−	0.206940i
$985$	−15.7302	−	89.2105i	−0.501207	−	2.84248i
$986$	0.0560737	+	0.0204091i	0.00178575	+	0.000649960i
$987$	−1.24920			−0.0397624
$988$		0			0
$989$	51.8964			1.65021
$990$	−18.9084	−	6.88210i	−0.600949	−	0.218727i
$991$	−3.71991	−	21.0967i	−0.118167	−	0.670158i	−0.985133	−	0.171791i	$-0.945044\pi$
$991$	−3.71991	−	21.0967i	−0.118167	−	0.670158i	0.866966	−	0.498367i	$-0.166067\pi$
$992$	2.66572	+	2.23681i	0.0846368	+	0.0710187i
$993$	−20.2123	+	16.9601i	−0.641418	+	0.538214i
$994$	−0.881207	+	4.99757i	−0.0279502	+	0.158513i
$995$	−30.4270	+	52.7012i	−0.964602	+	1.67074i
$996$	2.11153	+	3.65727i	0.0669063	+	0.115885i
$997$	38.5279	−	14.0230i	1.22019	−	0.444113i	0.349963	−	0.936763i	$-0.386194\pi$
$997$	38.5279	−	14.0230i	1.22019	−	0.444113i	0.870227	+	0.492650i	$0.163972\pi$
$998$	−16.6307	+	6.05307i	−0.526434	+	0.191606i
$999$	4.04801	+	7.01136i	0.128073	+	0.221830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.r.99.3		24
19.2	odd	18		722.2.e.s.415.3		24
19.3	odd	18		722.2.e.s.245.2		24
19.4	even	9		722.2.c.m.653.2		8
19.5	even	9	inner	722.2.e.r.423.3		24
19.6	even	9		722.2.c.m.429.2		8
19.7	even	3	inner	722.2.e.r.595.2		24
19.8	odd	6		722.2.e.s.389.2		24
19.9	even	9		722.2.a.n.1.3	yes	4
19.10	odd	18		722.2.a.m.1.2	✓	4
19.11	even	3	inner	722.2.e.r.389.3		24
19.12	odd	6		722.2.e.s.595.3		24
19.13	odd	18		722.2.c.n.429.3		8
19.14	odd	18		722.2.e.s.423.2		24
19.15	odd	18		722.2.c.n.653.3		8
19.16	even	9	inner	722.2.e.r.245.3		24
19.17	even	9	inner	722.2.e.r.415.2		24
19.18	odd	2		722.2.e.s.99.2		24
57.29	even	18		6498.2.a.ca.1.1		4
57.47	odd	18		6498.2.a.bx.1.1		4
76.47	odd	18		5776.2.a.bt.1.2		4
76.67	even	18		5776.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.10	odd	18
722.2.a.n.1.3	yes	4	19.9	even	9
722.2.c.m.429.2		8	19.6	even	9
722.2.c.m.653.2		8	19.4	even	9
722.2.c.n.429.3		8	19.13	odd	18
722.2.c.n.653.3		8	19.15	odd	18
722.2.e.r.99.3		24	1.1	even	1	trivial
722.2.e.r.245.3		24	19.16	even	9	inner
722.2.e.r.389.3		24	19.11	even	3	inner
722.2.e.r.415.2		24	19.17	even	9	inner
722.2.e.r.423.3		24	19.5	even	9	inner
722.2.e.r.595.2		24	19.7	even	3	inner
722.2.e.s.99.2		24	19.18	odd	2
722.2.e.s.245.2		24	19.3	odd	18
722.2.e.s.389.2		24	19.8	odd	6
722.2.e.s.415.3		24	19.2	odd	18
722.2.e.s.423.2		24	19.14	odd	18
722.2.e.s.595.3		24	19.12	odd	6
5776.2.a.bt.1.2		4	76.47	odd	18
5776.2.a.bv.1.3		4	76.67	even	18
6498.2.a.bx.1.1		4	57.47	odd	18
6498.2.a.ca.1.1		4	57.29	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.222978 + 1.26457i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.83108 - 2.37556i) q^{5} +(0.222978 - 1.26457i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26966 - 0.462117i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.222978 + 1.26457i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.83108 - 2.37556i) q^{5} +(0.222978 - 1.26457i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26966 - 0.462117i) q^{9} +(-3.47284 + 1.26401i) q^{10} +(2.01484 + 3.48980i) q^{11} +(-0.642040 + 1.11205i) q^{12} +(0.849399 - 4.81718i) q^{13} +(-0.338947 + 0.284410i) q^{14} +(3.63534 + 3.05041i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.250797 - 0.0912828i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.533894 + 0.194322i) q^{21} +(-0.699745 - 3.96845i) q^{22} +(-7.05473 - 5.91962i) q^{23} +(0.983662 - 0.825390i) q^{24} +(1.50350 - 8.52679i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(2.79360 + 4.83866i) q^{27} +(0.415780 - 0.151331i) q^{28} +(0.210098 - 0.0764694i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(-1.73993 + 3.01364i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.96383 + 3.32605i) q^{33} +(0.204452 + 0.171556i) q^{34} +(-0.283953 - 1.61038i) q^{35} +(1.26966 + 0.462117i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-3.47284 - 1.26401i) q^{40} +(-1.36569 - 7.74524i) q^{41} +(-0.435234 - 0.365205i) q^{42} +(-4.31683 + 3.62225i) q^{43} +(-0.699745 + 3.96845i) q^{44} +(2.49672 - 4.32444i) q^{45} +(4.60465 + 7.97549i) q^{46} +(-2.06608 + 0.751992i) q^{47} +(-1.20664 + 0.439181i) q^{48} +(3.40211 + 5.89263i) q^{49} +(-4.32916 + 7.49833i) q^{50} +(0.0595113 - 0.337505i) q^{51} +(3.74710 - 3.14419i) q^{52} +(7.61633 + 6.39086i) q^{53} +(-0.970209 - 5.50233i) q^{54} +(13.9944 + 5.09355i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(3.29788 + 1.20033i) q^{59} +(0.824064 + 4.67350i) q^{60} +(3.12512 + 2.62228i) q^{61} +(2.66572 - 2.23681i) q^{62} +(0.103812 - 0.588748i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.03879 - 15.6556i) q^{65} +(4.86236 - 1.76976i) q^{66} +(-0.138852 + 0.0505379i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(5.91273 - 10.2412i) q^{69} +(-0.283953 + 1.61038i) q^{70} +(8.78585 - 7.37221i) q^{71} +(-1.03503 - 0.868497i) q^{72} +(0.246973 + 1.40065i) q^{73} +(-1.36164 - 0.495597i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-5.90227 - 2.14825i) q^{78} +(1.77180 + 10.0484i) q^{79} +(2.83108 + 2.37556i) q^{80} +(-2.39082 + 2.00614i) q^{81} +(-1.36569 + 7.74524i) q^{82} +(1.64439 - 2.84817i) q^{83} +(0.284079 + 0.492039i) q^{84} +(-0.926876 + 0.337355i) q^{85} +(5.29537 - 1.92736i) q^{86} +(0.143548 + 0.248633i) q^{87} +(2.01484 - 3.48980i) q^{88} +(-1.03507 + 5.87019i) q^{89} +(-3.82519 + 3.20972i) q^{90} +(-1.65795 - 1.39119i) q^{91} +(-1.59918 - 9.06939i) q^{92} +(-4.19893 - 1.52828i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-3.83842 - 1.39707i) q^{97} +(-1.18154 - 6.70085i) q^{98} +(4.17085 + 3.49976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 - 12 * q^8	\( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

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