LMFDB - Embedded newform 722.2.e.s.99.2

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			99.2
Character	$\chi$	$=$	722.99
Dual form			722.2.e.s.423.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.222978 - 1.26457i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.83108 - 2.37556i) q^{5} +(0.222978 - 1.26457i) q^{6} +(0.221232 - 0.383185i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.26966 - 0.462117i) q^{9} +O(q^{10})$	\(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	$-0.934680\pi$
$3$	−0.222978	−	1.26457i	−0.128736	−	0.730100i	0.850282	−	0.526328i	$-0.176431\pi$
$4$	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	$0.292851\pi$
$13$	−0.849399	+	4.81718i	−0.235581	+	1.33604i	−0.841387	+	0.540433i	$0.818260\pi$
$14$	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	−0.361454	−	0.932390i	$-0.617719\pi$
$29$	−0.210098	+	0.0764694i	−0.0390142	+	0.0142000i	0.322439	+	0.946590i	$0.395497\pi$
$30$	−2.37280	−	4.10980i	−0.433211	−	0.750344i
$31$	1.73993	−	3.01364i	0.312500	−	0.541266i	−0.666403	−	0.745592i	$-0.732167\pi$
$31$	1.73993	−	3.01364i	0.312500	−	0.541266i	0.978903	+	0.204326i	$0.0655002\pi$
$32$	−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	$-0.538004\pi$
$37$	−1.44903			−0.238219			−0.119109	+	0.992881i	$0.538004\pi$
$38$		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	$0.154938\pi$
$41$	1.36569	+	7.74524i	0.213286	+	1.20960i	−0.670571	+	0.741845i	$0.733951\pi$
$42$	−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	−0.0534958	−	0.998568i	$-0.517036\pi$
$53$	−7.61633	−	6.39086i	−1.04618	−	0.877852i	−0.992687	+	0.120716i	$0.961481\pi$
$54$	−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	0.118302	−	0.992978i	$-0.462255\pi$
$59$	−3.29788	−	1.20033i	−0.429347	−	0.156269i	−0.547649	+	0.836708i	$0.684477\pi$
$60$	−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	−0.333524	−	0.942741i	$-0.608238\pi$
$67$	0.138852	−	0.0505379i	0.0169634	−	0.00617418i	0.350488	+	0.936567i	$0.386016\pi$
$68$	−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	−0.992306	−	0.123810i	$-0.960489\pi$
$71$	−8.78585	+	7.37221i	−1.04269	+	0.874920i	−0.0503832	+	0.998730i	$0.516044\pi$
$72$	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	$-0.860952\pi$
$79$	−1.77180	−	10.0484i	−0.199343	−	1.13053i	0.706754	−	0.707459i	$-0.250159\pi$
$80$	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	$-0.842132\pi$
$89$	1.03507	−	5.87019i	0.109717	−	0.622239i	0.989231	−	0.146364i	$-0.0467572\pi$
$90$	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	0.529451	−	0.848340i	$-0.322398\pi$
$97$	3.83842	+	1.39707i	0.389732	+	0.141851i	−0.139719	+	0.990191i	$0.544620\pi$
$98$	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	0.732381	−	0.680895i	$-0.238409\pi$
$103$	−2.26809	−	3.92845i	−0.223482	−	0.387081i	−0.955863	+	0.293813i	$0.905076\pi$
$104$	−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	−0.932439	−	0.361327i	$-0.882324\pi$
$107$	−1.58576	+	2.74661i	−0.153301	+	0.265525i	0.779138	+	0.626852i	$0.215657\pi$
$108$	0.970209	−	5.50233i	0.0933584	−	0.529462i
$109$	5.19464	−	4.35882i	0.497556	−	0.417499i	−0.359169	−	0.933273i	$-0.616940\pi$
$109$	5.19464	−	4.35882i	0.497556	−	0.417499i	0.856725	+	0.515773i	$0.172495\pi$
$110$	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	$-0.343371\pi$
$113$	10.0444			0.944893			0.472447	+	0.881359i	$0.343371\pi$
$114$		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	$0.270345\pi$
$127$	−2.44507	+	13.8667i	−0.216965	+	1.23047i	−0.877464	+	0.479642i	$0.840767\pi$
$128$	−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	$-0.378522\pi$
$151$	9.15317			0.744875			0.372437	+	0.928057i	$0.378522\pi$
$152$		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	0.895439	−	0.445183i	$-0.146861\pi$
$167$	7.91539	+	6.64180i	0.612511	+	0.513958i	−0.282929	+	0.959141i	$0.591306\pi$
$168$	−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	−0.0331648	−	0.999450i	$-0.510559\pi$
$173$	−9.22028	−	3.35591i	−0.701005	−	0.255145i	−0.667840	+	0.744305i	$0.732781\pi$
$174$	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	0.653468	−	0.756955i	$-0.273314\pi$
$179$	−4.39915	−	7.61955i	−0.328808	−	0.569512i	−0.982276	+	0.187442i	$0.939980\pi$
$180$	4.69229	−	1.70786i	0.349743	−	0.127296i
$181$	13.6516	−	4.96878i	1.01472	−	0.369327i	0.219474	−	0.975618i	$-0.429566\pi$
$181$	13.6516	−	4.96878i	1.01472	−	0.369327i	0.795243	+	0.606291i	$0.207344\pi$
$182$	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	$-0.839000\pi$
$193$	−3.03503	−	17.2125i	−0.218466	−	1.23898i	0.656322	−	0.754481i	$-0.272111\pi$
$194$	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	$0.00594499\pi$
$211$	25.8232	+	9.39887i	1.77774	+	0.647045i	0.777915	+	0.628369i	$0.216277\pi$
$212$	−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	−0.992556	−	0.121789i	$-0.961137\pi$
$223$	−15.6048	+	13.0940i	−1.04497	+	0.876837i	−0.0524171	+	0.998625i	$0.516693\pi$
$224$	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	$-0.237158\pi$
$227$	22.1493			1.47010			0.735051	+	0.678011i	$0.237158\pi$
$228$		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	$-0.735307\pi$
$241$	3.29293	−	18.6751i	0.212116	−	1.20297i	0.885841	−	0.463988i	$-0.153582\pi$
$242$	−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	0.431976	−	0.901885i	$-0.357816\pi$
$257$	21.5237	−	7.83398i	1.34261	−	0.488670i	0.910634	+	0.413215i	$0.135594\pi$
$258$	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	$0.162345\pi$
$269$	3.60180	+	20.4268i	0.219606	+	1.24545i	−0.653128	+	0.757248i	$0.726544\pi$
$270$	−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	0.577202	−	0.816601i	$-0.304145\pi$
$281$	−2.12494	−	1.78304i	−0.126763	−	0.106367i	−0.703965	+	0.710234i	$0.748589\pi$
$282$	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	0.854365	−	0.519673i	$-0.173946\pi$
$293$	−0.391435	−	0.677985i	−0.0228679	−	0.0396083i	−0.877233	+	0.480065i	$0.840613\pi$
$294$	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	$0.241657\pi$
$307$	4.89146	+	27.7408i	0.279170	+	1.58325i	−0.446225	+	0.894921i	$0.647232\pi$
$308$	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	−0.999704	−	0.0243404i	$-0.992251\pi$
$317$	−0.925203	+	5.24709i	−0.0519646	+	0.294706i	0.947739	+	0.319046i	$0.103363\pi$
$318$	−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	$-0.975654\pi$
$331$	−10.2740	−	17.7951i	−0.564711	−	0.978108i	0.432366	−	0.901698i	$-0.357679\pi$
$332$	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	−0.876382	−	0.481617i	$-0.840050\pi$
$337$	−10.1749	+	8.53777i	−0.554263	+	0.465082i	0.322118	+	0.946699i	$0.395605\pi$
$338$	−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	−0.829689	−	0.558226i	$-0.811482\pi$
$373$	1.32475	−	2.29454i	0.0685930	−	0.118807i	0.898282	+	0.439419i	$0.144816\pi$
$374$	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	$-0.654519\pi$
$379$	−18.1672			−0.933187			−0.466593	+	0.884472i	$0.654519\pi$
$380$		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	$-0.855536\pi$
$383$	−3.99535	−	22.6588i	−0.204153	−	1.15781i	0.694614	−	0.719383i	$-0.255575\pi$
$384$	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	0.938913	−	0.344155i	$-0.111835\pi$
$401$	28.7748	+	10.4732i	1.43694	+	0.523005i	0.498030	+	0.867160i	$0.334057\pi$
$402$	−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	−0.120747	−	0.992683i	$-0.538529\pi$
$409$	8.59187	−	3.12719i	0.424841	−	0.154629i	0.545587	+	0.838054i	$0.316307\pi$
$410$	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	$-0.754815\pi$
$421$	−5.77473	−	32.7501i	−0.281443	−	1.59614i	0.436278	−	0.899812i	$-0.356296\pi$
$422$	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	$-0.757649\pi$
$431$	3.99242	−	22.6422i	0.192308	−	1.09063i	0.916200	−	0.400721i	$-0.131240\pi$
$432$	4.28005	−	3.59139i	0.205924	−	0.172791i
$433$	−26.5888	−	22.3107i	−1.27778	−	1.07218i	−0.993546	−	0.113427i	$-0.963817\pi$
$433$	−26.5888	−	22.3107i	−1.27778	−	1.07218i	−0.284231	−	0.958756i	$-0.591738\pi$
$434$	−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	−0.649812	−	0.760095i	$-0.725152\pi$
$439$	−34.2817	−	12.4775i	−1.63618	−	0.595519i	−0.986364	+	0.164576i	$0.947374\pi$
$440$	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	−0.950157	−	0.311771i	$-0.899078\pi$
$449$	−4.34551	+	7.52664i	−0.205077	+	0.355204i	0.745080	+	0.666975i	$0.232411\pi$
$450$	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	$-0.532558\pi$
$487$	17.8850	−	30.9777i	0.810445	−	1.40373i	0.912553	−	0.408959i	$-0.134108\pi$
$488$	−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	0.774676	−	0.632358i	$-0.217913\pi$
$509$	6.46251	+	5.42269i	0.286446	+	0.240357i	−0.488230	+	0.872715i	$0.662357\pi$
$510$	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	0.947343	−	0.320221i	$-0.103757\pi$
$521$	4.48183	+	7.76275i	0.196352	+	0.340092i	−0.750991	+	0.660313i	$0.770424\pi$
$522$	−0.283872	+	0.103321i	−0.0124247	+	0.00452223i
$523$	−2.01088	+	0.731900i	−0.0879296	+	0.0320038i	−0.385610	−	0.922662i	$-0.626009\pi$
$523$	−2.01088	+	0.731900i	−0.0879296	+	0.0320038i	0.297681	+	0.954665i	$0.403787\pi$
$524$	−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	0.952621	−	0.304159i	$-0.0983755\pi$
$547$	19.1432	+	16.0630i	0.818504	+	0.686806i	−0.134117	+	0.990965i	$0.542820\pi$
$548$	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	−0.579890	−	0.814694i	$-0.696905\pi$
$563$	9.86122	−	17.0801i	0.415601	−	0.719842i	0.995491	+	0.0948526i	$0.0302380\pi$
$564$	−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	$-0.653666\pi$
$569$	−22.1469			−0.928446			−0.464223	+	0.885718i	$0.653666\pi$
$570$		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	0.0606966	−	0.998156i	$-0.480668\pi$
$599$	18.3264	−	6.67025i	0.748795	−	0.272539i	0.688099	+	0.725617i	$0.258446\pi$
$600$	−5.55899	−	9.62845i	−0.226945	−	0.393080i
$601$	−19.4816	+	33.7431i	−0.794671	+	1.37641i	0.128376	+	0.991726i	$0.459023\pi$
$601$	−19.4816	+	33.7431i	−0.794671	+	1.37641i	−0.923048	+	0.384685i	$0.874310\pi$
$602$	−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	$-0.554925\pi$
$607$	−8.46029			−0.343393			−0.171696	+	0.985150i	$0.554925\pi$
$608$		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	−0.759403	−	0.650620i	$-0.774509\pi$
$641$	−6.34308	+	5.32248i	−0.250537	+	0.210225i	0.508867	+	0.860845i	$0.330065\pi$
$642$	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	$-0.766561\pi$
$659$	4.72698	−	26.8080i	0.184137	−	1.04429i	0.927059	−	0.374915i	$-0.122328\pi$
$660$	14.6492	−	12.2921i	0.570220	−	0.478471i
$661$	6.82412	+	5.72611i	0.265427	+	0.222720i	0.765781	−	0.643101i	$-0.222352\pi$
$661$	6.82412	+	5.72611i	0.265427	+	0.222720i	−0.500354	+	0.865821i	$0.666797\pi$
$662$	−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	$0.0748824\pi$
$673$	17.8505	+	30.9180i	0.688087	+	1.19180i	−0.284370	+	0.958715i	$0.591784\pi$
$674$	−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	$0.343066\pi$
$677$	−13.6924	+	23.7160i	−0.526243	+	0.911480i	−0.999533	+	0.0305727i	$0.990267\pi$
$678$	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	$-0.239555\pi$
$683$	38.1521			1.45985			0.729925	+	0.683528i	$0.239555\pi$
$684$		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	0.844896	−	0.534930i	$-0.179662\pi$
$743$	31.2998	+	11.3922i	1.14828	+	0.417939i	0.303382	+	0.952869i	$0.401884\pi$
$744$	−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	0.0100020	−	0.999950i	$-0.496816\pi$
$751$	18.0984	−	6.58727i	0.660419	−	0.240373i	0.650417	+	0.759577i	$0.274594\pi$
$752$	−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	$-0.813527\pi$
$773$	3.86032	−	21.8929i	0.138846	−	0.787434i	0.972104	−	0.234550i	$-0.0753617\pi$
$774$	−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	0.997372	−	0.0724468i	$-0.0230807\pi$
$787$	12.2298	+	21.1826i	0.435945	+	0.755080i	−0.561427	+	0.827526i	$0.689747\pi$
$788$	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	$-0.764431\pi$
$797$	−41.6933			−1.47685			−0.738426	+	0.674334i	$0.764431\pi$
$798$		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	$0.422407\pi$
$811$	−9.03760	+	51.2548i	−0.317353	+	1.79980i	−0.558710	+	0.829363i	$0.688704\pi$
$812$	−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	−0.668713	−	0.743520i	$-0.733155\pi$
$827$	−20.2181	+	7.35879i	−0.703052	+	0.255890i	−0.0343387	+	0.999410i	$0.510932\pi$
$828$	−6.22153	−	10.7760i	−0.216213	−	0.374492i
$829$	2.82531	−	4.89357i	0.0981269	−	0.169961i	−0.812782	−	0.582567i	$-0.802048\pi$
$829$	2.82531	−	4.89357i	0.0981269	−	0.169961i	0.910909	+	0.412607i	$0.135382\pi$
$830$	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	$0.00344591\pi$
$839$	1.85398	+	10.5144i	0.0640064	+	0.362998i	−0.935935	+	0.352173i	$0.885443\pi$
$840$	−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	−0.335830	−	0.941923i	$-0.609017\pi$
$857$	−35.0869	−	12.7706i	−1.19855	−	0.436235i	−0.862717	+	0.505687i	$0.831239\pi$
$858$	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	0.592659	−	0.805453i	$-0.298078\pi$
$863$	−11.7864	−	20.4146i	−0.401214	−	0.694922i	−0.993873	+	0.110531i	$0.964745\pi$
$864$	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	$0.122551\pi$
$877$	5.45918	+	30.9606i	0.184344	+	1.04546i	−0.742452	+	0.669899i	$0.766337\pi$
$878$	−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	$0.116445\pi$
$887$	−1.96653	+	11.1528i	−0.0660297	+	0.374473i	−0.999860	+	0.0167556i	$0.994666\pi$
$888$	−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	−0.771080	−	0.636739i	$-0.780283\pi$
$907$	−8.36968	+	7.02300i	−0.277911	+	0.233195i	0.493169	+	0.869934i	$0.335838\pi$
$908$	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	$-0.787584\pi$
$911$	−47.4159			−1.57096			−0.785479	+	0.618888i	$0.787584\pi$
$912$		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	−0.0448017	−	0.998996i	$-0.514266\pi$
$941$	17.2711	−	6.28615i	0.563020	−	0.204923i	0.607822	+	0.794073i	$0.292043\pi$
$942$	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	$-0.922546\pi$
$953$	−4.35077	−	24.6744i	−0.140935	−	0.799283i	0.829606	−	0.558349i	$-0.188565\pi$
$954$	−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	$0.0395690\pi$
$971$	57.0903	+	20.7792i	1.83212	+	0.666836i	0.839832	+	0.542846i	$0.182653\pi$
$972$	−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	$-0.955208\pi$
$977$	−19.2706	−	33.3776i	−0.616520	−	1.06784i	0.373595	−	0.927592i	$-0.378125\pi$
$978$	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	−0.546478	−	0.837473i	$-0.684032\pi$
$983$	5.74938	−	4.82430i	0.183377	−	0.153871i	0.729855	+	0.683602i	$0.239587\pi$
$984$	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	$0.0549555\pi$
$991$	3.71991	+	21.0967i	0.118167	+	0.670158i	−0.866966	+	0.498367i	$0.833933\pi$
$992$	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.s.99.2		24
19.2	odd	18		722.2.e.r.415.2		24
19.3	odd	18		722.2.e.r.245.3		24
19.4	even	9		722.2.c.n.653.3		8
19.5	even	9	inner	722.2.e.s.423.2		24
19.6	even	9		722.2.c.n.429.3		8
19.7	even	3	inner	722.2.e.s.595.3		24
19.8	odd	6		722.2.e.r.389.3		24
19.9	even	9		722.2.a.m.1.2	✓	4
19.10	odd	18		722.2.a.n.1.3	yes	4
19.11	even	3	inner	722.2.e.s.389.2		24
19.12	odd	6		722.2.e.r.595.2		24
19.13	odd	18		722.2.c.m.429.2		8
19.14	odd	18		722.2.e.r.423.3		24
19.15	odd	18		722.2.c.m.653.2		8
19.16	even	9	inner	722.2.e.s.245.2		24
19.17	even	9	inner	722.2.e.s.415.3		24
19.18	odd	2		722.2.e.r.99.3		24
57.29	even	18		6498.2.a.bx.1.1		4
57.47	odd	18		6498.2.a.ca.1.1		4
76.47	odd	18		5776.2.a.bv.1.3		4
76.67	even	18		5776.2.a.bt.1.2		4

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