LMFDB - Embedded newform 72.3.j.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, 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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16946 - 1.62246i) q^{2} +(-2.99204 + 0.218346i) q^{3} +(-1.26474 - 3.79479i) q^{4} +(-2.90774 - 5.03636i) q^{5} +(-3.14481 + 5.10981i) q^{6} +(-0.363382 + 0.629396i) q^{7} +(-7.63595 - 2.38585i) q^{8} +(8.90465 - 1.30660i) q^{9} +O(q^{10})$	\(q+(1.16946 - 1.62246i) q^{2} +(-2.99204 + 0.218346i) q^{3} +(-1.26474 - 3.79479i) q^{4} +(-2.90774 - 5.03636i) q^{5} +(-3.14481 + 5.10981i) q^{6} +(-0.363382 + 0.629396i) q^{7} +(-7.63595 - 2.38585i) q^{8} +(8.90465 - 1.30660i) q^{9} +(-11.5718 - 1.17211i) q^{10} +(2.03117 - 3.51809i) q^{11} +(4.61274 + 11.0780i) q^{12} +(13.3457 - 7.70516i) q^{13} +(0.596210 + 1.32562i) q^{14} +(9.79976 + 14.4341i) q^{15} +(-12.8008 + 9.59887i) q^{16} -11.6011i q^{17} +(8.29370 - 15.9754i) q^{18} +35.6847i q^{19} +(-15.4344 + 17.4040i) q^{20} +(0.949829 - 1.96252i) q^{21} +(-3.33259 - 7.40973i) q^{22} +(26.0887 - 15.0623i) q^{23} +(23.3680 + 5.47128i) q^{24} +(-4.40992 + 7.63821i) q^{25} +(3.10595 - 30.6638i) q^{26} +(-26.3578 + 5.85369i) q^{27} +(2.84801 + 0.582934i) q^{28} +(16.7164 - 28.9536i) q^{29} +(34.8791 + 0.980360i) q^{30} +(-17.8105 - 30.8487i) q^{31} +(0.603728 + 31.9943i) q^{32} +(-5.30918 + 10.9698i) q^{33} +(-18.8223 - 13.5669i) q^{34} +4.22648 q^{35} +(-16.2204 - 32.1388i) q^{36} +24.7119i q^{37} +(57.8969 + 41.7317i) q^{38} +(-38.2486 + 25.9682i) q^{39} +(10.1874 + 45.3948i) q^{40} +(-49.7376 + 28.7160i) q^{41} +(-2.07333 - 3.83614i) q^{42} +(-6.79446 - 3.92278i) q^{43} +(-15.9193 - 3.25838i) q^{44} +(-32.4729 - 41.0477i) q^{45} +(6.07162 - 59.9427i) q^{46} +(-4.39286 - 2.53622i) q^{47} +(36.2048 - 31.5152i) q^{48} +(24.2359 + 41.9778i) q^{49} +(7.23546 + 16.0875i) q^{50} +(2.53304 + 34.7109i) q^{51} +(-46.1184 - 40.8992i) q^{52} +28.1114 q^{53} +(-21.3269 + 49.6101i) q^{54} -23.6244 q^{55} +(4.27641 - 3.93906i) q^{56} +(-7.79160 - 106.770i) q^{57} +(-27.4270 - 60.9816i) q^{58} +(-19.8481 - 34.3780i) q^{59} +(42.3802 - 55.4434i) q^{60} +(33.9886 + 19.6234i) q^{61} +(-70.8793 - 7.17940i) q^{62} +(-2.41342 + 6.07935i) q^{63} +(52.6155 + 36.4364i) q^{64} +(-77.6119 - 44.8092i) q^{65} +(11.5891 + 21.4426i) q^{66} +(63.9208 - 36.9047i) q^{67} +(-44.0236 + 14.6724i) q^{68} +(-74.7699 + 50.7635i) q^{69} +(4.94269 - 6.85730i) q^{70} +88.5602i q^{71} +(-71.1128 - 11.2680i) q^{72} +105.069 q^{73} +(40.0941 + 28.8995i) q^{74} +(11.5269 - 23.8167i) q^{75} +(135.416 - 45.1320i) q^{76} +(1.47618 + 2.55682i) q^{77} +(-2.59784 + 92.4255i) q^{78} +(35.5251 - 61.5313i) q^{79} +(85.5649 + 36.5586i) q^{80} +(77.5856 - 23.2696i) q^{81} +(-11.5754 + 114.279i) q^{82} +(18.1858 - 31.4988i) q^{83} +(-8.64865 - 1.12231i) q^{84} +(-58.4271 + 33.7329i) q^{85} +(-14.3104 + 6.43621i) q^{86} +(-43.6942 + 90.2804i) q^{87} +(-23.9035 + 22.0179i) q^{88} +121.817i q^{89} +(-104.574 + 4.68242i) q^{90} +11.1997i q^{91} +(-90.1540 - 79.9513i) q^{92} +(60.0254 + 88.4117i) q^{93} +(-9.25217 + 4.16124i) q^{94} +(179.721 - 103.762i) q^{95} +(-8.79220 - 95.5965i) q^{96} +(-25.3236 + 43.8618i) q^{97} +(96.4501 + 9.76948i) q^{98} +(13.4901 - 33.9812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.16946	−	1.62246i	0.584728	−	0.811229i
$2$	1.16946	−	1.62246i	0.584728	−	0.811229i
$3$	−2.99204	+	0.218346i	−0.997348	+	0.0727819i
$3$	−2.99204	+	0.218346i	−0.997348	+	0.0727819i
$4$	−1.26474	−	3.79479i	−0.316186	−	0.948697i
$5$	−2.90774	−	5.03636i	−0.581548	−	1.00727i	−0.995296	−	0.0968796i	$-0.969114\pi$
$5$	−2.90774	−	5.03636i	−0.581548	−	1.00727i	0.413748	−	0.910392i	$-0.364220\pi$
$6$	−3.14481	+	5.10981i	−0.524135	+	0.851635i
$7$	−0.363382	+	0.629396i	−0.0519117	+	0.0899137i	−0.890814	−	0.454369i	$-0.849865\pi$
$7$	−0.363382	+	0.629396i	−0.0519117	+	0.0899137i	0.838902	+	0.544283i	$0.183198\pi$
$8$	−7.63595	−	2.38585i	−0.954494	−	0.298231i
$9$	8.90465	−	1.30660i	0.989406	−	0.145178i
$10$	−11.5718	−	1.17211i	−1.15718	−	0.117211i
$11$	2.03117	−	3.51809i	0.184652	−	0.319826i	−0.758807	−	0.651315i	$-0.774218\pi$
$11$	2.03117	−	3.51809i	0.184652	−	0.319826i	0.943459	+	0.331489i	$0.107551\pi$
$12$	4.61274	+	11.0780i	0.384395	+	0.923169i
$13$	13.3457	−	7.70516i	1.02659	−	0.592705i	0.110588	−	0.993866i	$-0.464727\pi$
$13$	13.3457	−	7.70516i	1.02659	−	0.592705i	0.916007	+	0.401161i	$0.131393\pi$
$14$	0.596210	+	1.32562i	0.0425864	+	0.0946874i
$15$	9.79976	+	14.4341i	0.653317	+	0.962274i
$16$	−12.8008	+	9.59887i	−0.800053	+	0.599929i
$17$		−	11.6011i		−	0.682416i	−0.939988	−	0.341208i	$-0.889164\pi$
$17$		−	11.6011i		−	0.682416i	0.939988	−	0.341208i	$-0.110836\pi$
$18$	8.29370	−	15.9754i	0.460761	−	0.887524i
$19$			35.6847i			1.87814i	0.343724	+	0.939071i	$0.388312\pi$
$19$			35.6847i			1.87814i	−0.343724	+	0.939071i	$0.611688\pi$
$20$	−15.4344	+	17.4040i	−0.771718	+	0.870198i
$21$	0.949829	−	1.96252i	0.0452300	−	0.0934535i
$22$	−3.33259	−	7.40973i	−0.151481	−	0.336806i
$23$	26.0887	−	15.0623i	1.13429	−	0.654884i	0.189282	−	0.981923i	$-0.439384\pi$
$23$	26.0887	−	15.0623i	1.13429	−	0.654884i	0.945011	+	0.327038i	$0.106051\pi$
$24$	23.3680	+	5.47128i	0.973668	+	0.227970i
$25$	−4.40992	+	7.63821i	−0.176397	+	0.305528i
$26$	3.10595	−	30.6638i	0.119460	−	1.17938i
$27$	−26.3578	+	5.85369i	−0.976215	+	0.216803i
$28$	2.84801	+	0.582934i	0.101715	+	0.0208191i
$29$	16.7164	−	28.9536i	0.576427	−	0.998400i	−0.419458	−	0.907775i	$-0.637780\pi$
$29$	16.7164	−	28.9536i	0.576427	−	0.998400i	0.995885	−	0.0906257i	$-0.0288867\pi$
$30$	34.8791	+	0.980360i	1.16264	+	0.0326787i
$31$	−17.8105	−	30.8487i	−0.574532	−	0.995118i	−0.996092	−	0.0883179i	$-0.971851\pi$
$31$	−17.8105	−	30.8487i	−0.574532	−	0.995118i	0.421561	−	0.906800i	$-0.361482\pi$
$32$	0.603728	+	31.9943i	0.0188665	+	0.999822i
$33$	−5.30918	+	10.9698i	−0.160884	+	0.332417i
$34$	−18.8223	−	13.5669i	−0.553596	−	0.399028i
$35$	4.22648			0.120757
$36$	−16.2204	−	32.1388i	−0.450566	−	0.892743i
$37$			24.7119i			0.667890i	0.942593	+	0.333945i	$0.108380\pi$
$37$			24.7119i			0.667890i	−0.942593	+	0.333945i	$0.891620\pi$
$38$	57.8969	+	41.7317i	1.52360	+	1.09820i
$39$	−38.2486	+	25.9682i	−0.980734	+	0.665850i
$40$	10.1874	+	45.3948i	0.254685	+	1.13487i
$41$	−49.7376	+	28.7160i	−1.21311	+	0.700390i	−0.963436	−	0.267939i	$-0.913657\pi$
$41$	−49.7376	+	28.7160i	−1.21311	+	0.700390i	−0.249676	+	0.968330i	$0.580324\pi$
$42$	−2.07333	−	3.83614i	−0.0493650	−	0.0913368i
$43$	−6.79446	−	3.92278i	−0.158011	−	0.0912276i	0.418910	−	0.908028i	$-0.362412\pi$
$43$	−6.79446	−	3.92278i	−0.158011	−	0.0912276i	−0.576920	+	0.816800i	$0.695746\pi$
$44$	−15.9193	−	3.25838i	−0.361802	−	0.0740541i
$45$	−32.4729	−	41.0477i	−0.721620	−	0.912172i
$46$	6.07162	−	59.9427i	0.131992	−	1.30310i
$47$	−4.39286	−	2.53622i	−0.0934651	−	0.0539621i	0.452539	−	0.891745i	$-0.350518\pi$
$47$	−4.39286	−	2.53622i	−0.0934651	−	0.0539621i	−0.546004	+	0.837783i	$0.683852\pi$
$48$	36.2048	−	31.5152i	0.754267	−	0.656567i
$49$	24.2359	+	41.9778i	0.494610	+	0.856690i
$50$	7.23546	+	16.0875i	0.144709	+	0.321749i
$51$	2.53304	+	34.7109i	0.0496675	+	0.680606i
$52$	−46.1184	−	40.8992i	−0.886892	−	0.786523i
$53$	28.1114			0.530405			0.265202	−	0.964193i	$-0.414561\pi$
$53$	28.1114			0.530405			0.265202	+	0.964193i	$0.414561\pi$
$54$	−21.3269	+	49.6101i	−0.394943	+	0.918705i
$55$	−23.6244			−0.429535
$56$	4.27641	−	3.93906i	0.0763645	−	0.0703404i
$57$	−7.79160	−	106.770i	−0.136695	−	1.87316i
$58$	−27.4270	−	60.9816i	−0.472879	−	1.05141i
$59$	−19.8481	−	34.3780i	−0.336409	−	0.582678i	0.647345	−	0.762197i	$-0.275879\pi$
$59$	−19.8481	−	34.3780i	−0.336409	−	0.582678i	−0.983755	+	0.179519i	$0.942546\pi$
$60$	42.3802	−	55.4434i	0.706337	−	0.924057i
$61$	33.9886	+	19.6234i	0.557191	+	0.321694i	0.752017	−	0.659143i	$-0.229081\pi$
$61$	33.9886	+	19.6234i	0.557191	+	0.321694i	−0.194826	+	0.980838i	$0.562414\pi$
$62$	−70.8793	−	7.17940i	−1.14321	−	0.115797i
$63$	−2.41342	+	6.07935i	−0.0383083	+	0.0964976i
$64$	52.6155	+	36.4364i	0.822117	+	0.569319i
$65$	−77.6119	−	44.8092i	−1.19403	−	0.689373i
$66$	11.5891	+	21.4426i	0.175593	+	0.324888i
$67$	63.9208	−	36.9047i	0.954041	−	0.550816i	0.0597072	−	0.998216i	$-0.480983\pi$
$67$	63.9208	−	36.9047i	0.954041	−	0.550816i	0.894334	+	0.447400i	$0.147650\pi$
$68$	−44.0236	+	14.6724i	−0.647406	+	0.215770i
$69$	−74.7699	+	50.7635i	−1.08362	+	0.735704i
$70$	4.94269	−	6.85730i	0.0706098	−	0.0979614i
$71$			88.5602i			1.24733i	0.781693	+	0.623664i	$0.214357\pi$
$71$			88.5602i			1.24733i	−0.781693	+	0.623664i	$0.785643\pi$
$72$	−71.1128	−	11.2680i	−0.987678	−	0.156500i
$73$	105.069			1.43930			0.719650	−	0.694337i	$-0.244302\pi$
$73$	105.069			1.43930			0.719650	+	0.694337i	$0.244302\pi$
$74$	40.0941	+	28.8995i	0.541812	+	0.390534i
$75$	11.5269	−	23.8167i	0.153692	−	0.317556i
$76$	135.416	−	45.1320i	1.78179	−	0.593842i
$77$	1.47618	+	2.55682i	0.0191712	+	0.0332054i
$78$	−2.59784	+	92.4255i	−0.0333056	+	1.18494i
$79$	35.5251	−	61.5313i	0.449685	−	0.778877i	−0.548680	−	0.836032i	$-0.684870\pi$
$79$	35.5251	−	61.5313i	0.449685	−	0.778877i	0.998365	+	0.0571551i	$0.0182030\pi$
$80$	85.5649	+	36.5586i	1.06956	+	0.456983i
$81$	77.5856	−	23.2696i	0.957847	−	0.287279i
$82$	−11.5754	+	114.279i	−0.141163	+	1.39365i
$83$	18.1858	−	31.4988i	0.219106	−	0.379504i	−0.735429	−	0.677602i	$-0.763019\pi$
$83$	18.1858	−	31.4988i	0.219106	−	0.379504i	0.954535	+	0.298099i	$0.0963525\pi$
$84$	−8.64865	−	1.12231i	−0.102960	−	0.0133609i
$85$	−58.4271	+	33.7329i	−0.687378	+	0.396858i
$86$	−14.3104	+	6.43621i	−0.166400	+	0.0748396i
$87$	−43.6942	+	90.2804i	−0.502232	+	1.03771i
$88$	−23.9035	+	22.0179i	−0.271631	+	0.250203i
$89$			121.817i			1.36873i	0.729141	+	0.684363i	$0.239920\pi$
$89$			121.817i			1.36873i	−0.729141	+	0.684363i	$0.760080\pi$
$90$	−104.574	+	4.68242i	−1.16193	+	0.0520269i
$91$			11.1997i			0.123073i
$92$	−90.1540	−	79.9513i	−0.979934	−	0.869036i
$93$	60.0254	+	88.4117i	0.645435	+	0.950663i
$94$	−9.25217	+	4.16124i	−0.0984273	+	0.0442685i
$95$	179.721	−	103.762i	1.89180	−	1.09223i
$96$	−8.79220	−	95.5965i	−0.0915854	−	0.995797i
$97$	−25.3236	+	43.8618i	−0.261068	+	0.452183i	−0.966526	−	0.256568i	$-0.917408\pi$
$97$	−25.3236	+	43.8618i	−0.261068	+	0.452183i	0.705458	+	0.708752i	$0.250741\pi$
$98$	96.4501	+	9.76948i	0.984185	+	0.0996886i
$99$	13.4901	−	33.9812i	0.136264	−	0.343245i
$100$	34.5628	+	7.07435i	0.345628	+	0.0707435i
$101$	−80.5694	+	139.550i	−0.797717	+	1.38169i	0.123383	+	0.992359i	$0.460626\pi$
$101$	−80.5694	+	139.550i	−0.797717	+	1.38169i	−0.921100	+	0.389327i	$0.872708\pi$
$102$	59.2793	+	36.4831i	0.581170	+	0.357678i
$103$	−47.4976	−	82.2682i	−0.461142	−	0.798721i	0.537877	−	0.843024i	$-0.319227\pi$
$103$	−47.4976	−	82.2682i	−0.461142	−	0.798721i	−0.999018	+	0.0443030i	$0.985893\pi$
$104$	−120.291	+	26.9954i	−1.15664	+	0.259571i
$105$	−12.6458	+	0.922834i	−0.120436	+	0.00878890i
$106$	32.8751	−	45.6096i	0.310142	−	0.430280i
$107$	59.6104			0.557106			0.278553	−	0.960421i	$-0.410145\pi$
$107$	59.6104			0.557106			0.278553	+	0.960421i	$0.410145\pi$
$108$	55.5494	+	92.6189i	0.514346	+	0.857583i
$109$		−	119.342i		−	1.09488i	−0.836846	−	0.547438i	$-0.815603\pi$
$109$		−	119.342i		−	1.09488i	0.836846	−	0.547438i	$-0.184397\pi$
$110$	−27.6278	+	38.3297i	−0.251161	+	0.348452i
$111$	−5.39574	−	73.9392i	−0.0486103	−	0.666119i
$112$	−1.38989	−	11.5449i	−0.0124097	−	0.103079i
$113$	86.6058	−	50.0019i	0.766423	−	0.442495i	−0.0651741	−	0.997874i	$-0.520760\pi$
$113$	86.6058	−	50.0019i	0.766423	−	0.442495i	0.831597	+	0.555379i	$0.187427\pi$
$114$	−182.342	−	112.222i	−1.59949	−	0.984399i
$115$	−151.719	−	87.5948i	−1.31929	−	0.761694i
$116$	−131.015	−	26.8162i	−1.12944	−	0.231174i
$117$	108.772	−	86.0493i	0.929671	−	0.735464i
$118$	−78.9884	−	8.00078i	−0.669393	−	0.0678032i
$119$	7.30167	+	4.21562i	0.0613586	+	0.0354254i
$120$	−40.3929	−	133.599i	−0.336607	−	1.11332i
$121$	52.2487	+	90.4974i	0.431808	+	0.747913i
$122$	71.5863	−	32.1965i	0.586773	−	0.263906i
$123$	142.547	−	96.7795i	1.15892	−	0.786825i
$124$	−94.5385	+	106.603i	−0.762407	+	0.859699i
$125$	−94.0954			−0.752764
$126$	7.04110	+	11.0252i	0.0558817	+	0.0875017i
$127$	−34.1686			−0.269044			−0.134522	−	0.990911i	$-0.542950\pi$
$127$	−34.1686			−0.269044			−0.134522	+	0.990911i	$0.542950\pi$
$128$	120.648	−	42.7556i	0.942563	−	0.334028i
$129$	21.1859	+	10.2536i	0.164231	+	0.0794853i
$130$	−163.465	+	73.5196i	−1.25742	+	0.565535i
$131$	24.7155	+	42.8085i	0.188668	+	0.326783i	0.944806	−	0.327629i	$-0.106250\pi$
$131$	24.7155	+	42.8085i	0.188668	+	0.326783i	−0.756138	+	0.654412i	$0.772916\pi$
$132$	48.3427	+	6.27330i	0.366232	+	0.0475250i
$133$	−22.4598	−	12.9672i	−0.168871	−	0.0974976i
$134$	14.8763	−	146.867i	0.111017	−	1.09602i
$135$	106.123	+	115.726i	0.786096	+	0.857232i
$136$	−27.6784	+	88.5852i	−0.203518	+	0.651362i
$137$	−143.254	−	82.7079i	−1.04565	−	0.603707i	−0.124223	−	0.992254i	$-0.539644\pi$
$137$	−143.254	−	82.7079i	−1.04565	−	0.603707i	−0.921429	+	0.388547i	$0.872977\pi$
$138$	−5.07835	+	180.677i	−0.0367996	+	1.30925i
$139$	18.0427	−	10.4170i	0.129804	−	0.0749421i	−0.433692	−	0.901061i	$-0.642789\pi$
$139$	18.0427	−	10.4170i	0.129804	−	0.0749421i	0.563496	+	0.826119i	$0.309456\pi$
$140$	−5.34542	−	16.0386i	−0.0381816	−	0.114562i
$141$	13.6974	+	6.62932i	0.0971447	+	0.0470164i
$142$	143.685	+	103.567i	1.01187	+	0.729348i
$143$		−	62.6019i		−	0.437776i
$144$	−101.445	+	102.200i	−0.704481	+	0.709723i
$145$	−194.428			−1.34088
$146$	122.873	−	170.470i	0.841599	−	1.16760i
$147$	−81.6806	−	120.308i	−0.555650	−	0.818420i
$148$	93.7765	−	31.2542i	0.633625	−	0.211177i
$149$	26.6261	+	46.1178i	0.178699	+	0.309515i	0.941435	−	0.337194i	$-0.109478\pi$
$149$	26.6261	+	46.1178i	0.178699	+	0.309515i	−0.762736	+	0.646710i	$0.776145\pi$
$150$	−25.1614	−	46.5546i	−0.167743	−	0.310364i
$151$	−101.373	+	175.584i	−0.671347	+	1.16281i	0.306175	+	0.951975i	$0.400951\pi$
$151$	−101.373	+	175.584i	−0.671347	+	1.16281i	−0.977522	+	0.210832i	$0.932383\pi$
$152$	85.1382	−	272.487i	0.560120	−	1.79267i
$153$	−15.1579	−	103.303i	−0.0990716	−	0.675186i
$154$	5.87466	+	0.595047i	0.0381471	+	0.00386394i
$155$	−103.577	+	179.400i	−0.668236	+	1.15742i
$156$	146.918	+	112.302i	0.941785	+	0.719887i
$157$	−72.8570	+	42.0640i	−0.464057	+	0.267924i	−0.713749	−	0.700402i	$-0.753004\pi$
$157$	−72.8570	+	42.0640i	−0.464057	+	0.267924i	0.249691	+	0.968325i	$0.419671\pi$
$158$	−58.2869	−	129.596i	−0.368904	−	0.820229i
$159$	−84.1107	+	6.13801i	−0.528998	+	0.0386038i
$160$	159.379	−	96.0718i	0.996120	−	0.600448i
$161$			21.8935i			0.135985i
$162$	52.9790	−	153.092i	0.327031	−	0.945014i
$163$			107.182i			0.657559i	0.944407	+	0.328780i	$0.106637\pi$
$163$			107.182i			0.657559i	−0.944407	+	0.328780i	$0.893363\pi$
$164$	171.876	+	152.425i	1.04803	+	0.929422i
$165$	70.6854	−	5.15829i	0.428396	−	0.0312624i
$166$	−29.8379	−	66.3422i	−0.179747	−	0.399652i
$167$	−132.530	+	76.5161i	−0.793592	+	0.458180i	−0.841226	−	0.540684i	$-0.818165\pi$
$167$	−132.530	+	76.5161i	−0.793592	+	0.458180i	0.0476337	+	0.998865i	$0.484832\pi$
$168$	−11.9351	+	12.7196i	−0.0710424	+	0.0757118i
$169$	34.2391	−	59.3038i	0.202598	−	0.350910i
$170$	−13.5977	+	134.245i	−0.0799866	+	0.789675i
$171$	46.6256	+	317.760i	0.272664	+	1.85824i
$172$	−6.29289	+	30.7449i	−0.0365866	+	0.178749i
$173$	28.0520	−	48.5876i	0.162151	−	0.280853i	−0.773489	−	0.633810i	$-0.781490\pi$
$173$	28.0520	−	48.5876i	0.162151	−	0.280853i	0.935640	+	0.352957i	$0.114824\pi$
$174$	95.3777	+	176.471i	0.548148	+	1.01420i
$175$	−3.20497	−	5.55117i	−0.0183141	−	0.0317210i
$176$	7.76896	+	64.5314i	0.0441418	+	0.366656i
$177$	66.8928	+	98.5267i	0.377925	+	0.556648i
$178$	197.642	+	142.459i	1.11035	+	0.800333i
$179$	−184.408			−1.03021			−0.515106	−	0.857127i	$-0.672247\pi$
$179$	−184.408			−1.03021			−0.515106	+	0.857127i	$0.672247\pi$
$180$	−114.698	+	175.143i	−0.637209	+	0.973015i
$181$		−	249.415i		−	1.37798i	−0.724769	−	0.688992i	$-0.758054\pi$
$181$		−	249.415i		−	1.37798i	0.724769	−	0.688992i	$-0.241946\pi$
$182$	18.1710	+	13.0975i	0.0998407	+	0.0719645i
$183$	−105.980	−	51.2927i	−0.579127	−	0.280288i
$184$	−235.149	+	52.7715i	−1.27798	+	0.286802i
$185$	124.458	−	71.8559i	0.672746	−	0.388410i
$186$	213.641	+	6.00490i	1.14861	+	0.0322844i
$187$	−40.8136	−	23.5637i	−0.218254	−	0.126009i
$188$	−4.06858	+	19.8776i	−0.0216414	+	0.105732i
$189$	5.89366	−	18.7166i	0.0311834	−	0.0990298i
$190$	41.8264	−	412.935i	0.220139	−	2.17334i
$191$	−33.2377	−	19.1898i	−0.174019	−	0.100470i	0.410460	−	0.911878i	$-0.365368\pi$
$191$	−33.2377	−	19.1898i	−0.174019	−	0.100470i	−0.584480	+	0.811408i	$0.698701\pi$
$192$	−165.383	−	97.5310i	−0.861372	−	0.507974i
$193$	−83.3709	−	144.403i	−0.431974	−	0.748200i	0.565069	−	0.825043i	$-0.308849\pi$
$193$	−83.3709	−	144.403i	−0.431974	−	0.748200i	−0.997043	+	0.0768429i	$0.975516\pi$
$194$	41.5491	+	92.3810i	0.214170	+	0.476191i
$195$	242.002	+	117.125i	1.24104	+	0.600641i
$196$	128.645	−	145.061i	0.656351	−	0.740109i
$197$	188.581			0.957264			0.478632	−	0.878016i	$-0.341133\pi$
$197$	188.581			0.957264			0.478632	+	0.878016i	$0.341133\pi$
$198$	−39.3571	−	61.6267i	−0.198773	−	0.311246i
$199$	−9.63131			−0.0483986			−0.0241993	−	0.999707i	$-0.507704\pi$
$199$	−9.63131			−0.0483986			−0.0241993	+	0.999707i	$0.507704\pi$
$200$	51.8975	−	47.8036i	0.259488	−	0.239018i
$201$	−183.196	+	124.377i	−0.911422	+	0.618792i
$202$	132.192	+	293.919i	0.654417	+	1.45504i
$203$	12.1489	+	21.0424i	0.0598466	+	0.103657i
$204$	128.517	−	53.5127i	0.629985	−	0.262317i
$205$	289.248	+	166.997i	1.41097	+	0.814622i
$206$	−189.023	−	19.1463i	−0.917588	−	0.0929430i
$207$	212.631	−	168.212i	1.02720	−	0.812620i
$208$	−96.8759	+	226.737i	−0.465750	+	1.09008i
$209$	125.542	+	72.4816i	0.600678	+	0.346802i
$210$	−13.2915	+	21.5965i	−0.0632928	+	0.102841i
$211$	108.883	−	62.8637i	0.516034	−	0.297932i	−0.219277	−	0.975663i	$-0.570370\pi$
$211$	108.883	−	62.8637i	0.516034	−	0.297932i	0.735310	+	0.677730i	$0.237036\pi$
$212$	−35.5538	−	106.677i	−0.167706	−	0.503193i
$213$	−19.3367	−	264.976i	−0.0907828	−	1.24402i
$214$	69.7117	−	96.7154i	0.325756	−	0.451941i
$215$			45.6258i			0.212213i
$216$	215.233	+	18.1872i	0.996449	+	0.0842001i
$217$	25.8880			0.119300
$218$	−193.627	−	139.565i	−0.888196	−	0.640205i
$219$	−314.371	+	22.9413i	−1.43548	+	0.104755i
$220$	29.8788	+	89.6498i	0.135813	+	0.407499i
$221$	−89.3881	−	154.825i	−0.404471	−	0.700565i
$222$	−126.273	−	77.7143i	−0.568799	−	0.350064i
$223$	137.654	−	238.424i	0.617282	−	1.06916i	−0.372697	−	0.927953i	$-0.621567\pi$
$223$	137.654	−	238.424i	0.617282	−	1.06916i	0.989980	−	0.141211i	$-0.0450996\pi$
$224$	−20.3565	−	11.2462i	−0.0908771	−	0.0502061i
$225$	−29.2887	+	73.7775i	−0.130172	+	0.327900i
$226$	20.1557	−	198.989i	0.0891847	−	0.880484i
$227$	17.7375	−	30.7223i	0.0781388	−	0.135340i	−0.824308	−	0.566141i	$-0.808436\pi$
$227$	17.7375	−	30.7223i	0.0781388	−	0.135340i	0.902447	+	0.430801i	$0.141769\pi$
$228$	−395.316	+	164.604i	−1.73384	+	0.721949i
$229$	−250.235	+	144.473i	−1.09273	+	0.630888i	−0.934302	−	0.356482i	$-0.883976\pi$
$229$	−250.235	+	144.473i	−1.09273	+	0.630888i	−0.158429	+	0.987370i	$0.550643\pi$
$230$	−319.547	+	143.719i	−1.38934	+	0.624865i
$231$	−4.97506	−	7.32779i	−0.0215371	−	0.0317221i
$232$	−196.724	+	181.206i	−0.847949	+	0.781059i
$233$			53.5754i			0.229937i	0.993369	+	0.114969i	$0.0366768\pi$
$233$			53.5754i			0.229937i	−0.993369	+	0.114969i	$0.963323\pi$
$234$	−12.4079	−	277.108i	−0.0530250	−	1.18422i
$235$			29.4987i			0.125526i
$236$	−105.354	+	118.799i	−0.446417	+	0.503385i
$237$	−92.8576	+	191.861i	−0.391804	+	0.809540i
$238$	15.3787	−	6.91667i	0.0646162	−	0.0290616i
$239$	−155.039	+	89.5120i	−0.648700	+	0.374527i	−0.787958	−	0.615729i	$-0.788862\pi$
$239$	−155.039	+	89.5120i	−0.648700	+	0.374527i	0.139258	+	0.990256i	$0.455528\pi$
$240$	−263.996	−	90.7022i	−1.09998	−	0.377926i
$241$	31.3738	−	54.3410i	0.130182	−	0.225481i	−0.793565	−	0.608486i	$-0.791777\pi$
$241$	31.3738	−	54.3410i	0.130182	−	0.225481i	0.923747	+	0.383004i	$0.125111\pi$
$242$	207.931	+	21.0614i	0.859219	+	0.0870307i
$243$	−227.059	+	86.5642i	−0.934398	+	0.356231i
$244$	31.4796	−	153.798i	0.129015	−	0.630321i
$245$	140.943	−	244.121i	0.575280	−	0.996413i
$246$	9.68175	−	344.456i	0.0393567	−	1.40023i
$247$	274.956	+	476.238i	1.11318	+	1.92809i
$248$	62.3998	+	278.052i	0.251612	+	1.12118i
$249$	−47.5352	+	98.2166i	−0.190904	+	0.394444i
$250$	−110.041	+	152.666i	−0.440162	+	0.610664i
$251$	84.9454			0.338428			0.169214	−	0.985579i	$-0.445877\pi$
$251$	84.9454			0.338428			0.169214	+	0.985579i	$0.445877\pi$
$252$	26.1222	+	1.46961i	0.103660	+	0.00583180i
$253$		−	122.377i		−	0.483702i
$254$	−39.9586	+	55.4371i	−0.157317	+	0.218256i
$255$	167.451	−	113.688i	0.656671	−	0.445834i
$256$	71.7235	−	245.747i	0.280170	−	0.959950i
$257$	27.9325	−	16.1268i	0.108687	−	0.0627503i	−0.444671	−	0.895694i	$-0.646679\pi$
$257$	27.9325	−	16.1268i	0.108687	−	0.0627503i	0.553358	+	0.832944i	$0.313346\pi$
$258$	41.4120	−	22.3820i	0.160512	−	0.0867520i
$259$	−15.5536	−	8.97987i	−0.0600525	−	0.0346713i
$260$	−71.8825	+	351.193i	−0.276471	+	1.35074i
$261$	111.023	−	279.663i	0.425374	−	1.07151i
$262$	98.3587	+	9.96281i	0.375415	+	0.0380260i
$263$	−45.9346	−	26.5204i	−0.174656	−	0.100838i	0.410123	−	0.912030i	$-0.365486\pi$
$263$	−45.9346	−	26.5204i	−0.174656	−	0.100838i	−0.584780	+	0.811192i	$0.698819\pi$
$264$	66.7128	−	71.0977i	0.252700	−	0.269309i
$265$	−81.7408	−	141.579i	−0.308456	−	0.534261i
$266$	−47.3045	+	21.2756i	−0.177836	+	0.0799833i
$267$	−26.5981	−	364.481i	−0.0996185	−	1.36510i
$268$	−220.889	−	195.891i	−0.824212	−	0.730936i
$269$	−86.8402			−0.322826			−0.161413	−	0.986887i	$-0.551605\pi$
$269$	−86.8402			−0.322826			−0.161413	+	0.986887i	$0.551605\pi$
$270$	311.867	−	36.8433i	1.15506	−	0.136457i
$271$	412.202			1.52104			0.760520	−	0.649314i	$-0.224944\pi$
$271$	412.202			1.52104			0.760520	+	0.649314i	$0.224944\pi$
$272$	111.357	+	148.504i	0.409401	+	0.545969i
$273$	−2.44540	−	33.5099i	−0.00895751	−	0.122747i
$274$	−301.720	+	135.701i	−1.10117	+	0.495258i
$275$	17.9146	+	31.0290i	0.0651439	+	0.112833i
$276$	287.202	+	219.533i	1.04059	+	0.795409i
$277$	99.4029	+	57.3903i	0.358855	+	0.207185i	0.668578	−	0.743642i	$-0.266903\pi$
$277$	99.4029	+	57.3903i	0.358855	+	0.207185i	−0.309723	+	0.950827i	$0.600236\pi$
$278$	4.19907	−	41.4557i	0.0151046	−	0.149121i
$279$	−198.903	−	251.425i	−0.712914	−	0.901166i
$280$	−32.2732	−	10.0837i	−0.115262	−	0.0360134i
$281$	317.161	+	183.113i	1.12869	+	0.651647i	0.943604	−	0.331076i	$-0.107412\pi$
$281$	317.161	+	183.113i	1.12869	+	0.651647i	0.185082	+	0.982723i	$0.440745\pi$
$282$	26.7743	−	14.4708i	0.0949443	−	0.0513148i
$283$	−16.7891	+	9.69318i	−0.0593253	+	0.0342515i	−0.529369	−	0.848392i	$-0.677571\pi$
$283$	−16.7891	+	9.69318i	−0.0593253	+	0.0342515i	0.470044	+	0.882643i	$0.344238\pi$
$284$	336.067	−	112.006i	1.18334	−	0.394387i
$285$	−515.077	+	349.701i	−1.80729	+	1.22702i
$286$	−101.569	−	73.2102i	−0.355136	−	0.255980i
$287$		−	41.7395i		−	0.145434i
$288$	47.1797	+	284.109i	0.163818	+	0.986491i
$289$	154.415			0.534309
$290$	−227.375	+	315.451i	−0.784050	+	1.08776i
$291$	66.1923	−	136.766i	0.227465	−	0.469985i
$292$	−132.885	−	398.714i	−0.455086	−	1.36546i
$293$	120.913	+	209.427i	0.412672	+	0.714769i	0.995181	−	0.0980553i	$-0.0312622\pi$
$293$	120.913	+	209.427i	0.412672	+	0.714769i	−0.582509	+	0.812824i	$0.697929\pi$
$294$	−290.716	−	8.17126i	−0.988830	−	0.0277934i
$295$	−115.427	+	199.925i	−0.391276	+	0.677711i
$296$	58.9589	−	188.699i	0.199185	−	0.637497i
$297$	−32.9433	+	104.619i	−0.110920	+	0.352252i
$298$	105.962	+	10.7330i	0.355578	+	0.0360167i
$299$	232.116	−	402.036i	0.776306	−	1.34460i
$300$	−104.958	−	13.6201i	−0.349860	−	0.0454004i
$301$	4.93797	−	2.85094i	0.0164052	−	0.00947156i
$302$	166.326	+	369.812i	0.550748	+	1.22454i
$303$	210.597	−	435.133i	0.695040	−	1.43608i
$304$	−342.533	−	456.794i	−1.12675	−	1.50261i
$305$		−	228.239i		−	0.748323i
$306$	−185.332	−	96.2158i	−0.605661	−	0.314431i
$307$			383.998i			1.25081i	0.780301	+	0.625404i	$0.215066\pi$
$307$			383.998i			1.25081i	−0.780301	+	0.625404i	$0.784934\pi$
$308$	7.83560	−	8.83551i	0.0254403	−	0.0286867i
$309$	160.078	+	235.779i	0.518051	+	0.763040i
$310$	169.941	+	377.849i	0.548195	+	1.21887i
$311$	−409.820	+	236.610i	−1.31775	+	0.760803i	−0.983366	−	0.181635i	$-0.941861\pi$
$311$	−409.820	+	236.610i	−1.31775	+	0.760803i	−0.334383	+	0.942437i	$0.608528\pi$
$312$	354.021	−	107.036i	1.13468	−	0.343065i
$313$	140.084	−	242.632i	0.447552	−	0.775182i	−0.550674	−	0.834720i	$-0.685629\pi$
$313$	140.084	−	242.632i	0.447552	−	0.775182i	0.998226	+	0.0595379i	$0.0189627\pi$
$314$	−16.9560	+	167.399i	−0.0539999	+	0.533119i
$315$	37.6354	−	5.52232i	0.119477	−	0.0175312i
$316$	−278.428	−	56.9890i	−0.881102	−	0.180345i
$317$	−89.4931	+	155.007i	−0.282313	+	0.488980i	−0.971954	−	0.235171i	$-0.924435\pi$
$317$	−89.4931	+	155.007i	−0.282313	+	0.488980i	0.689641	+	0.724151i	$0.257768\pi$
$318$	−88.4051	+	143.644i	−0.278003	+	0.451711i
$319$	−67.9075	−	117.619i	−0.212876	−	0.368712i
$320$	30.5146	−	370.938i	0.0953582	−	1.15918i
$321$	−178.357	+	13.0157i	−0.555629	+	0.0405472i
$322$	35.5214	+	25.6035i	0.110315	+	0.0795141i
$323$	413.981			1.28167
$324$	−186.429	−	264.991i	−0.575399	−	0.817873i
$325$			135.917i			0.418205i
$326$	173.899	+	125.345i	0.533431	+	0.384494i
$327$	26.0577	+	357.075i	0.0796872	+	1.09197i
$328$	448.306	−	100.608i	1.36679	−	0.306731i
$329$	3.19257	−	1.84323i	0.00970387	−	0.00560253i
$330$	74.2943	−	120.716i	0.225134	−	0.365807i
$331$	213.367	+	123.187i	0.644613	+	0.372167i	0.786389	−	0.617731i	$-0.211948\pi$
$331$	213.367	+	123.187i	0.644613	+	0.372167i	−0.141776	+	0.989899i	$0.545281\pi$
$332$	−142.532	−	29.1735i	−0.429312	−	0.0878721i
$333$	32.2886	+	220.051i	0.0969627	+	0.660814i
$334$	−30.8436	+	304.506i	−0.0923462	+	0.911696i
$335$	−371.730	−	214.618i	−1.10964	−	0.640652i
$336$	6.67939	+	34.2393i	0.0198791	+	0.101903i
$337$	−35.3726	−	61.2672i	−0.104963	−	0.181802i	0.808760	−	0.588139i	$-0.200139\pi$
$337$	−35.3726	−	61.2672i	−0.104963	−	0.181802i	−0.913723	+	0.406337i	$0.866806\pi$
$338$	−56.1769	−	124.905i	−0.166204	−	0.369541i
$339$	−248.211	+	168.518i	−0.732185	+	0.497103i
$340$	201.905	+	179.055i	0.593837	+	0.526633i
$341$	−144.704			−0.424353
$342$	570.079	+	295.958i	1.66690	+	0.865374i
$343$	−70.8390			−0.206528
$344$	42.5230	+	46.1647i	0.123613	+	0.134200i
$345$	473.075	+	228.960i	1.37123	+	0.663653i
$346$	−46.0257	−	102.334i	−0.133022	−	0.295764i
$347$	−142.174	−	246.252i	−0.409723	−	0.709661i	0.585136	−	0.810935i	$-0.301041\pi$
$347$	−142.174	−	246.252i	−0.409723	−	0.709661i	−0.994859	+	0.101275i	$0.967708\pi$
$348$	397.857	+	51.6288i	1.14327	+	0.148359i
$349$	441.835	+	255.093i	1.26600	+	0.730927i	0.974229	−	0.225561i	$-0.0724214\pi$
$349$	441.835	+	255.093i	1.26600	+	0.730927i	0.291773	+	0.956488i	$0.405755\pi$
$350$	−12.7546	−	1.29192i	−0.0364418	−	0.00369121i
$351$	−306.661	+	281.213i	−0.873677	+	0.801177i
$352$	113.785	+	62.8618i	0.323253	+	0.178585i
$353$	183.443	+	105.911i	0.519669	+	0.300031i	0.736799	−	0.676112i	$-0.236336\pi$
$353$	183.443	+	105.911i	0.519669	+	0.300031i	−0.217130	+	0.976143i	$0.569670\pi$
$354$	238.084	+	6.69190i	0.672553	+	0.0189037i
$355$	446.021	−	257.510i	1.25640	−	0.725381i
$356$	462.268	−	154.067i	1.29851	−	0.432772i
$357$	−22.7674	−	11.0190i	−0.0637742	−	0.0308656i
$358$	−215.657	+	299.194i	−0.602394	+	0.835738i
$359$		−	9.46105i		−	0.0263539i	−0.999913	−	0.0131769i	$-0.995806\pi$
$359$		−	9.46105i		−	0.0263539i	0.999913	−	0.0131769i	$-0.00419447\pi$
$360$	150.028	+	390.914i	0.416744	+	1.08587i
$361$	−912.397			−2.52742
$362$	−404.665	−	291.680i	−1.11786	−	0.805746i
$363$	−176.090	−	259.364i	−0.485097	−	0.714501i
$364$	42.5004	−	14.1647i	0.116759	−	0.0389140i
$365$	−305.513	−	529.164i	−0.837022	−	1.44977i
$366$	−207.159	+	111.964i	−0.566009	+	0.305912i
$367$	−219.921	+	380.915i	−0.599241	+	1.03792i	0.393693	+	0.919242i	$0.371197\pi$
$367$	−219.921	+	380.915i	−0.599241	+	1.03792i	−0.992933	+	0.118673i	$0.962136\pi$
$368$	−189.377	+	443.233i	−0.514610	+	1.20444i
$369$	−405.375	+	320.693i	−1.09858	+	0.869087i
$370$	28.9651	−	285.960i	0.0782840	−	0.772866i
$371$	−10.2152	+	17.6932i	−0.0275342	+	0.0476907i
$372$	259.587	−	339.602i	0.697815	−	0.912908i
$373$	−420.468	+	242.757i	−1.12726	+	0.650823i	−0.943244	−	0.332100i	$-0.892243\pi$
$373$	−420.468	+	242.757i	−1.12726	+	0.650823i	−0.184015	+	0.982923i	$0.558909\pi$
$374$	−85.9608	+	38.6616i	−0.229842	+	0.103373i
$375$	281.538	−	20.5453i	0.750767	−	0.0547875i
$376$	27.4926	+	29.8471i	0.0731187	+	0.0793807i
$377$		−	515.210i		−	1.36660i
$378$	−23.4746	−	31.4505i	−0.0621021	−	0.0832024i
$379$		−	189.622i		−	0.500321i	−0.968204	−	0.250161i	$-0.919517\pi$
$379$		−	189.622i		−	0.500321i	0.968204	−	0.250161i	$-0.0804834\pi$
$380$	−621.055	−	550.770i	−1.63436	−	1.44940i
$381$	102.234	−	7.46055i	0.268330	−	0.0195815i
$382$	−70.0047	+	31.4852i	−0.183258	+	0.0824219i
$383$	406.033	−	234.423i	1.06014	−	0.612071i	0.134668	−	0.990891i	$-0.457003\pi$
$383$	406.033	−	234.423i	1.06014	−	0.612071i	0.925471	+	0.378819i	$0.123670\pi$
$384$	−351.649	+	154.270i	−0.915752	+	0.401744i
$385$	8.58470	−	14.8691i	0.0222979	−	0.0386211i
$386$	−331.786	−	33.6068i	−0.859549	−	0.0870642i
$387$	−65.6278	−	26.0534i	−0.169581	−	0.0673214i
$388$	198.474	+	40.6239i	0.511531	+	0.104701i
$389$	−34.1349	+	59.1233i	−0.0877503	+	0.151988i	−0.906560	−	0.422077i	$-0.861301\pi$
$389$	−34.1349	+	59.1233i	−0.0877503	+	0.151988i	0.818810	+	0.574065i	$0.194634\pi$
$390$	473.041	−	255.666i	1.21293	−	0.655553i
$391$	−174.739	−	302.657i	−0.446904	−	0.774060i
$392$	−84.9115	−	378.364i	−0.216611	−	0.965214i
$393$	−83.2969	−	122.688i	−0.211951	−	0.312184i
$394$	220.537	−	305.965i	0.559739	−	0.776560i
$395$	−413.191			−1.04605
$396$	−146.013	−	8.21458i	−0.368720	−	0.0207439i
$397$			170.825i			0.430289i	0.976582	+	0.215144i	$0.0690222\pi$
$397$			170.825i			0.430289i	−0.976582	+	0.215144i	$0.930978\pi$
$398$	−11.2634	+	15.6264i	−0.0283000	+	0.0392623i
$399$	70.0321	+	33.8944i	0.175519	+	0.0849483i
$400$	−16.8674	−	140.106i	−0.0421685	−	0.350264i
$401$	−268.522	+	155.031i	−0.669631	+	0.386612i	−0.795937	−	0.605380i	$-0.793021\pi$
$401$	−268.522	+	155.031i	−0.669631	+	0.386612i	0.126306	+	0.991991i	$0.459688\pi$
$402$	−12.4426	+	442.681i	−0.0309517	+	1.10120i
$403$	−475.388	−	274.465i	−1.17962	−	0.681056i
$404$	631.464	+	129.249i	1.56303	+	0.319922i
$405$	−342.793	−	323.087i	−0.846402	−	0.797745i
$406$	48.3481	+	4.89720i	0.119084	+	0.0120621i
$407$	86.9387	+	50.1941i	0.213609	+	0.123327i
$408$	63.4727	−	271.094i	0.155570	−	0.664447i
$409$	−63.7657	−	110.445i	−0.155906	−	0.270038i	0.777482	−	0.628905i	$-0.216496\pi$
$409$	−63.7657	−	110.445i	−0.155906	−	0.270038i	−0.933389	+	0.358867i	$0.883163\pi$
$410$	609.209	−	273.997i	1.48588	−	0.668285i
$411$	446.682	+	216.187i	1.08682	+	0.526002i
$412$	−252.118	+	284.291i	−0.611938	+	0.690028i
$413$	28.8498			0.0698543
$414$	−24.2553	−	541.702i	−0.0585878	−	1.30846i
$415$	−211.519			−0.509684
$416$	254.579	+	422.336i	0.611968	+	1.01523i
$417$	−51.7100	+	35.1075i	−0.124005	+	0.0841907i
$418$	264.414	−	118.922i	0.632569	−	0.284503i
$419$	−38.1531	−	66.0831i	−0.0910575	−	0.157716i	0.816899	−	0.576781i	$-0.195691\pi$
$419$	−38.1531	−	66.0831i	−0.0910575	−	0.157716i	−0.907956	+	0.419065i	$0.862358\pi$
$420$	19.4957	+	46.8211i	0.0464183	+	0.111479i
$421$	−591.625	−	341.575i	−1.40528	−	0.811341i	−0.410356	−	0.911925i	$-0.634596\pi$
$421$	−591.625	−	341.575i	−1.40528	−	0.811341i	−0.994929	+	0.100584i	$0.967929\pi$
$422$	25.3403	−	250.175i	0.0600482	−	0.592831i
$423$	−42.4307	−	16.8444i	−0.100309	−	0.0398214i
$424$	−214.658	−	67.0696i	−0.506268	−	0.158183i
$425$	88.6114	+	51.1598i	0.208497	+	0.120376i
$426$	−452.526	−	278.505i	−1.06227	−	0.653768i
$427$	−24.7017	+	14.2615i	−0.0578495	+	0.0333994i
$428$	−75.3918	−	226.209i	−0.176149	−	0.528525i
$429$	13.6689	+	187.308i	0.0318621	+	0.436615i
$430$	74.0259	+	53.3574i	0.172153	+	0.124087i
$431$		−	16.3619i		−	0.0379627i	−0.999820	−	0.0189814i	$-0.993958\pi$
$431$		−	16.3619i		−	0.0379627i	0.999820	−	0.0189814i	$-0.00604231\pi$
$432$	281.214	−	327.937i	0.650957	−	0.759114i
$433$	618.066			1.42740			0.713702	−	0.700449i	$-0.247017\pi$
$433$	618.066			1.42740			0.713702	+	0.700449i	$0.247017\pi$
$434$	30.2749	−	42.0023i	0.0697579	−	0.0967794i
$435$	581.736	−	42.4524i	1.33732	−	0.0975917i
$436$	−452.876	+	150.936i	−1.03871	+	0.346184i
$437$	537.495	+	930.969i	1.22997	+	2.13036i
$438$	−330.421	+	536.882i	−0.754387	+	1.22576i
$439$	279.199	−	483.587i	0.635989	−	1.10157i	−0.350315	−	0.936632i	$-0.613926\pi$
$439$	279.199	−	483.587i	0.635989	−	1.10157i	0.986305	−	0.164934i	$-0.0527411\pi$
$440$	180.395	+	56.3643i	0.409989	+	0.128101i
$441$	270.660	+	342.131i	0.613743	+	0.775808i
$442$	−355.732	−	36.0323i	−0.804824	−	0.0815211i
$443$	−215.042	+	372.464i	−0.485422	+	0.840775i	−0.999860	−	0.0167523i	$-0.994667\pi$
$443$	−215.042	+	372.464i	−0.485422	+	0.840775i	0.514438	+	0.857528i	$0.328001\pi$
$444$	−273.759	+	113.990i	−0.616575	+	0.256734i
$445$	613.512	−	354.211i	1.37868	−	0.795980i
$446$	−225.852	−	502.164i	−0.506395	−	1.12593i
$447$	−89.7361	−	132.173i	−0.200752	−	0.295688i
$448$	−42.0525	+	19.8756i	−0.0938671	+	0.0443652i
$449$			229.455i			0.511035i	0.966804	+	0.255517i	$0.0822458\pi$
$449$			229.455i			0.511035i	−0.966804	+	0.255517i	$0.917754\pi$
$450$	85.4491	+	133.799i	0.189887	+	0.297332i
$451$			233.308i			0.517313i
$452$	−299.281	−	265.411i	−0.662125	−	0.587193i
$453$	264.976	−	547.489i	0.584936	−	1.20859i
$454$	−29.1024	−	64.7067i	−0.0641021	−	0.142526i
$455$	56.4055	−	32.5658i	0.123968	−	0.0715731i
$456$	−195.241	+	833.881i	−0.428160	+	1.82869i
$457$	−393.037	+	680.760i	−0.860037	+	1.48963i	0.0118556	+	0.999930i	$0.496226\pi$
$457$	−393.037	+	680.760i	−0.860037	+	1.48963i	−0.871892	+	0.489698i	$0.837107\pi$
$458$	−58.2372	+	574.952i	−0.127155	+	1.25535i
$459$	67.9091	+	305.779i	0.147950	+	0.666185i
$460$	−140.519	+	686.525i	−0.305475	+	1.49245i
$461$	219.475	−	380.142i	0.476084	−	0.824602i	−0.523540	−	0.852001i	$-0.675389\pi$
$461$	219.475	−	380.142i	0.476084	−	0.824602i	0.999625	+	0.0273986i	$0.00872235\pi$
$462$	−17.7072	−	0.497702i	−0.0383272	−	0.00107728i
$463$	194.665	+	337.170i	0.420443	+	0.728229i	0.995983	−	0.0895448i	$-0.0285412\pi$
$463$	194.665	+	337.170i	0.420443	+	0.728229i	−0.575539	+	0.817774i	$0.695208\pi$
$464$	63.9381	+	531.089i	0.137798	+	1.14459i
$465$	270.734	−	559.388i	0.582225	−	1.20298i
$466$	86.9239	+	62.6541i	0.186532	+	0.134451i
$467$	−310.283			−0.664417			−0.332209	−	0.943206i	$-0.607794\pi$
$467$	−310.283			−0.664417			−0.332209	+	0.943206i	$0.607794\pi$
$468$	−464.107	−	303.935i	−0.991682	−	0.649433i
$469$			53.6420i			0.114375i
$470$	47.8604	+	34.4974i	0.101831	+	0.0733988i
$471$	208.807	−	141.765i	0.443326	−	0.300988i
$472$	69.5388	+	309.863i	0.147328	+	0.656490i
$473$	−27.6014	+	15.9357i	−0.0583539	+	0.0336906i
$474$	202.694	+	375.031i	0.427624	+	0.791204i
$475$	−272.567	−	157.367i	−0.573825	−	0.331298i
$476$	6.76266	−	33.0400i	0.0142073	−	0.0694117i
$477$	250.323	−	36.7304i	0.524785	−	0.0770029i
$478$	−36.0823	+	356.225i	−0.0754859	+	0.745241i
$479$	534.788	+	308.760i	1.11647	+	0.644593i	0.940497	−	0.339802i	$-0.110360\pi$
$479$	534.788	+	308.760i	1.11647	+	0.644593i	0.175971	+	0.984395i	$0.443694\pi$
$480$	−455.893	+	322.251i	−0.949777	+	0.671355i
$481$	190.409	+	329.799i	0.395862	+	0.685652i
$482$	−51.4758	−	114.452i	−0.106796	−	0.237453i
$483$	−4.78036	−	65.5064i	−0.00989722	−	0.135624i
$484$	277.337	−	312.729i	0.573011	−	0.646134i
$485$	294.538			0.607295
$486$	−125.088	+	469.626i	−0.257384	+	0.966309i
$487$	52.9743			0.108777			0.0543884	−	0.998520i	$-0.482679\pi$
$487$	52.9743			0.108777			0.0543884	+	0.998520i	$0.482679\pi$
$488$	−212.717	−	230.935i	−0.435896	−	0.473227i
$489$	−23.4028	−	320.694i	−0.0478584	−	0.655816i
$490$	−231.249	−	514.164i	−0.471938	−	1.04931i
$491$	455.131	+	788.310i	0.926947	+	1.60552i	0.788399	+	0.615164i	$0.210910\pi$
$491$	455.131	+	788.310i	0.926947	+	1.60552i	0.138548	+	0.990356i	$0.455756\pi$
$492$	−547.543	−	418.534i	−1.11289	−	0.850680i
$493$	−335.893	−	193.928i	−0.681324	−	0.393363i
$494$	1094.23	+	110.835i	2.21503	+	0.224362i
$495$	−210.367	+	30.8677i	−0.424985	+	0.0623589i
$496$	524.102	+	223.929i	1.05666	+	0.451469i
$497$	−55.7395	−	32.1812i	−0.112152	−	0.0647509i
$498$	103.762	+	191.984i	0.208357	+	0.385510i
$499$	92.0144	−	53.1245i	0.184398	−	0.106462i	−0.404960	−	0.914335i	$-0.632714\pi$
$499$	92.0144	−	53.1245i	0.184398	−	0.106462i	0.589357	+	0.807873i	$0.299381\pi$
$500$	119.007	+	357.072i	0.238013	+	0.714145i
$501$	379.828	−	257.877i	0.758140	−	0.514724i
$502$	99.3400	−	137.820i	0.197888	−	0.274543i
$503$		−	452.514i		−	0.899630i	−0.893122	−	0.449815i	$-0.851490\pi$
$503$		−	452.514i		−	0.899630i	0.893122	−	0.449815i	$-0.148510\pi$
$504$	32.9332	−	40.6635i	0.0653436	−	0.0806816i
$505$	937.100			1.85564
$506$	−198.551	−	143.114i	−0.392393	−	0.282834i
$507$	−89.4961	+	184.916i	−0.176521	+	0.364725i
$508$	43.2144	+	129.662i	0.0850678	+	0.255241i
$509$	−282.090	−	488.595i	−0.554205	−	0.959911i	−0.997965	−	0.0637653i	$-0.979689\pi$
$509$	−282.090	−	488.595i	−0.554205	−	0.959911i	0.443760	−	0.896146i	$-0.353644\pi$
$510$	11.3732	−	404.635i	0.0223004	−	0.793402i
$511$	−38.1801	+	66.1300i	−0.0747165	+	0.129413i
$512$	−314.837	−	403.759i	−0.614917	−	0.788592i
$513$	−208.887	−	940.570i	−0.407188	−	1.83347i
$514$	6.50072	−	64.1789i	0.0126473	−	0.124862i
$515$	−276.221	+	478.429i	−0.536352	+	0.928989i
$516$	12.1156	−	93.3640i	0.0234798	−	0.180938i
$517$	−17.8453	+	10.3030i	−0.0345170	+	0.0199284i
$518$	−32.7587	+	14.7335i	−0.0632408	+	0.0284430i
$519$	−73.3241	+	151.501i	−0.141280	+	0.291910i
$520$	485.732	+	527.331i	0.934101	+	1.01410i
$521$		−	246.265i		−	0.472678i	−0.971671	−	0.236339i	$-0.924052\pi$
$521$		−	246.265i		−	0.472678i	0.971671	−	0.236339i	$-0.0759475\pi$
$522$	−323.906	−	507.184i	−0.620509	−	0.971617i
$523$			19.4969i			0.0372789i	0.999826	+	0.0186394i	$0.00593346\pi$
$523$			19.4969i			0.0372789i	−0.999826	+	0.0186394i	$0.994067\pi$
$524$	131.191	−	147.932i	0.250364	−	0.282313i
$525$	10.8015	+	15.9096i	0.0205743	+	0.0303039i
$526$	−96.7467	+	43.5126i	−0.183929	+	0.0827236i
$527$	−357.878	+	206.621i	−0.679084	+	0.392070i
$528$	−37.3352	−	191.384i	−0.0707107	−	0.362470i
$529$	189.248	−	327.788i	0.357747	−	0.619636i
$530$	−325.299	−	32.9497i	−0.613771	−	0.0621692i
$531$	−221.659	−	280.191i	−0.417437	−	0.527666i
$532$	−20.8018	+	101.630i	−0.0391012	+	0.191035i
$533$	−442.523	+	766.472i	−0.830249	+	1.43803i
$534$	−622.460	−	383.090i	−1.16566	−	0.717397i
$535$	−173.332	−	300.219i	−0.323984	−	0.561157i
$536$	−576.145	+	129.297i	−1.07490	+	0.241226i
$537$	551.756	−	40.2646i	1.02748	−	0.0749807i
$538$	−101.556	+	140.895i	−0.188766	+	0.261886i
$539$	196.909			0.365322
$540$	304.939	−	549.078i	0.564701	−	1.01681i
$541$		−	673.728i		−	1.24534i	−0.782485	−	0.622669i	$-0.786048\pi$
$541$		−	673.728i		−	1.24534i	0.782485	−	0.622669i	$-0.213952\pi$
$542$	482.052	−	668.780i	0.889395	−	1.23391i
$543$	54.4587	+	746.260i	0.100292	+	1.37433i
$544$	371.168	−	7.00389i	0.682294	−	0.0128748i
$545$	−601.047	+	347.014i	−1.10284	+	0.636724i
$546$	−57.2282	−	35.2208i	−0.104814	−	0.0645070i
$547$	−445.583	−	257.257i	−0.814594	−	0.470306i	0.0339545	−	0.999423i	$-0.489190\pi$
$547$	−445.583	−	257.257i	−0.814594	−	0.470306i	−0.848549	+	0.529117i	$0.822523\pi$
$548$	−132.679	+	648.224i	−0.242115	+	1.18289i
$549$	328.297	+	130.330i	0.597991	+	0.237394i
$550$	71.2935	+	7.22136i	0.129625	+	0.0131297i
$551$	1033.20	+	596.519i	1.87514	+	1.08261i
$552$	692.053	−	209.238i	1.25372	−	0.379055i
$553$	25.8184	+	44.7187i	0.0466878	+	0.0808657i
$554$	209.361	−	94.1616i	0.377907	−	0.169967i
$555$	−356.695	+	242.171i	−0.642693	+	0.436344i
$556$	−62.3495	−	55.2935i	−0.112139	−	0.0994487i
$557$	−612.943			−1.10044			−0.550218	−	0.835021i	$-0.685455\pi$
$557$	−612.943			−1.10044			−0.550218	+	0.835021i	$0.685455\pi$
$558$	−640.536	+	28.6808i	−1.14791	+	0.0513992i
$559$	−120.903			−0.216284
$560$	−54.1026	+	40.5695i	−0.0966118	+	0.0724455i
$561$	127.261	+	61.5922i	0.226847	+	0.109790i
$562$	667.999	−	300.438i	1.18861	−	0.534587i
$563$	−178.694	−	309.507i	−0.317396	−	0.549746i	0.662548	−	0.749020i	$-0.269475\pi$
$563$	−178.694	−	309.507i	−0.317396	−	0.549746i	−0.979944	+	0.199274i	$0.936142\pi$
$564$	7.83316	−	60.3631i	0.0138886	−	0.107027i
$565$	−503.655	−	290.785i	−0.891424	−	0.514664i
$566$	−3.90731	+	38.5753i	−0.00690338	+	0.0681543i
$567$	−13.5474	+	57.2878i	−0.0238931	+	0.101037i
$568$	211.291	−	676.242i	0.371992	−	1.19057i
$569$	−227.670	−	131.445i	−0.400123	−	0.231011i	0.286414	−	0.958106i	$-0.407537\pi$
$569$	−227.670	−	131.445i	−0.400123	−	0.231011i	−0.686537	+	0.727095i	$0.740870\pi$
$570$	−34.9838	+	1244.65i	−0.0613752	+	2.18360i
$571$	−558.493	+	322.446i	−0.978095	+	0.564704i	−0.901695	−	0.432374i	$-0.857676\pi$
$571$	−558.493	+	322.446i	−0.978095	+	0.564704i	−0.0764009	+	0.997077i	$0.524343\pi$
$572$	−237.561	+	79.1753i	−0.415317	+	0.138418i
$573$	103.639	+	50.1594i	0.180870	+	0.0875382i
$574$	−67.7206	−	48.8126i	−0.117980	−	0.0850393i
$575$			265.695i			0.462078i
$576$	516.130	+	255.706i	0.896059	+	0.443935i
$577$	−497.297			−0.861867			−0.430933	−	0.902384i	$-0.641816\pi$
$577$	−497.297			−0.861867			−0.430933	+	0.902384i	$0.641816\pi$
$578$	180.582	−	250.532i	0.312425	−	0.433447i
$579$	280.979	+	413.855i	0.485284	+	0.714776i
$580$	245.901	+	737.812i	0.423967	+	1.27209i
$581$	13.2168	+	22.8922i	0.0227484	+	0.0394014i
$582$	−144.488	−	267.336i	−0.248260	−	0.459340i
$583$	57.0990	−	98.8984i	0.0979400	−	0.169637i
$584$	−802.301	−	250.678i	−1.37380	−	0.429244i
$585$	−749.654	−	297.603i	−1.28146	−	0.508723i
$586$	481.190	+	48.7399i	0.821143	+	0.0831740i
$587$	272.120	−	471.326i	0.463578	−	0.802940i	−0.535559	−	0.844498i	$-0.679899\pi$
$587$	272.120	−	471.326i	0.463578	−	0.802940i	0.999136	+	0.0415583i	$0.0132322\pi$
$588$	−353.237	+	462.119i	−0.600744	+	0.785916i
$589$	1100.82	−	635.562i	1.86897	−	1.07905i
$590$	189.383	+	421.078i	0.320988	+	0.713692i
$591$	−564.242	+	41.1758i	−0.954725	+	0.0696714i
$592$	−237.206	−	316.334i	−0.400687	−	0.534347i
$593$			629.312i			1.06123i	0.847612	+	0.530617i	$0.178040\pi$
$593$			629.312i			1.06123i	−0.847612	+	0.530617i	$0.821960\pi$
$594$	131.214	+	175.796i	0.220899	+	0.295954i
$595$		−	49.0317i		−	0.0824063i
$596$	141.332	−	159.368i	0.237134	−	0.267395i
$597$	28.8173	−	2.10296i	0.0482702	−	0.00352254i
$598$	−380.838	−	846.762i	−0.636852	−	1.41599i
$599$	82.1059	−	47.4039i	0.137072	−	0.0791384i	−0.429896	−	0.902878i	$-0.641450\pi$
$599$	82.1059	−	47.4039i	0.137072	−	0.0791384i	0.566968	+	0.823740i	$0.308116\pi$
$600$	−144.842	+	154.362i	−0.241403	+	0.257270i
$601$	−10.1162	+	17.5218i	−0.0168323	+	0.0291544i	−0.874319	−	0.485352i	$-0.838691\pi$
$601$	−10.1162	+	17.5218i	−0.0168323	+	0.0291544i	0.857487	+	0.514506i	$0.172025\pi$
$602$	1.14921	−	11.3457i	0.00190899	−	0.0188467i
$603$	520.972	−	412.142i	0.863968	−	0.683486i
$604$	794.516	+	162.622i	1.31542	+	0.269242i
$605$	303.852	−	526.286i	0.502234	−	0.869895i
$606$	−459.701	−	850.553i	−0.758582	−	1.40355i
$607$	−544.261	−	942.688i	−0.896641	−	1.55303i	−0.831760	−	0.555135i	$-0.812666\pi$
$607$	−544.261	−	942.688i	−0.896641	−	1.55303i	−0.0648813	−	0.997893i	$-0.520667\pi$
$608$	−1141.71	+	21.5438i	−1.87781	+	0.0354339i
$609$	−40.9444	−	60.3073i	−0.0672323	−	0.0990267i
$610$	−370.308	−	266.915i	−0.607062	−	0.437566i
$611$	−78.1679			−0.127934
$612$	−372.844	+	188.174i	−0.609222	+	0.307473i
$613$		−	8.79521i		−	0.0143478i	−0.999974	−	0.00717391i	$-0.997716\pi$
$613$		−	8.79521i		−	0.0143478i	0.999974	−	0.00717391i	$-0.00228355\pi$
$614$	623.020	+	449.069i	1.01469	+	0.731382i
$615$	−901.906	−	436.508i	−1.46651	−	0.709768i
$616$	−5.17186	−	23.0457i	−0.00839587	−	0.0374118i
$617$	−437.202	+	252.419i	−0.708593	+	0.409106i	−0.810540	−	0.585684i	$-0.800826\pi$
$617$	−437.202	+	252.419i	−0.708593	+	0.409106i	0.101947	+	0.994790i	$0.467493\pi$
$618$	569.746	+	16.0141i	0.921919	+	0.0259127i
$619$	951.318	+	549.244i	1.53686	+	0.887308i	0.999020	+	0.0442628i	$0.0140939\pi$
$619$	951.318	+	549.244i	1.53686	+	0.887308i	0.537843	+	0.843045i	$0.319239\pi$
$620$	811.782	+	166.156i	1.30933	+	0.267994i
$621$	−599.472	+	549.726i	−0.965333	+	0.885227i
$622$	−95.3772	+	941.620i	−0.153340	+	1.51386i
$623$	−76.6709	−	44.2660i	−0.123067	−	0.0710529i
$624$	240.350	−	699.558i	0.385176	−	1.12109i
$625$	383.853	+	664.853i	0.614165	+	1.06377i
$626$	−229.839	−	511.028i	−0.367154	−	0.816338i
$627$	−391.453	−	189.457i	−0.624326	−	0.302164i
$628$	251.769	+	223.277i	0.400907	+	0.355536i
$629$	286.685			0.455779
$630$	35.0532	−	67.5199i	0.0556400	−	0.107174i
$631$	−131.984			−0.209167			−0.104584	−	0.994516i	$-0.533351\pi$
$631$	−131.984			−0.209167			−0.104584	+	0.994516i	$0.533351\pi$
$632$	−418.072	+	385.092i	−0.661507	+	0.609323i
$633$	−312.057	+	211.865i	−0.492981	+	0.334700i
$634$	146.834	+	326.472i	0.231599	+	0.514941i
$635$	99.3533	+	172.085i	0.156462	+	0.271000i
$636$	129.671	+	311.419i	0.203885	+	0.489653i
$637$	646.892	+	373.483i	1.01553	+	0.586316i
$638$	−270.247	−	27.3735i	−0.423585	−	0.0429051i
$639$	115.713	+	788.598i	0.181084	+	1.23411i
$640$	−566.146	−	483.304i	−0.884603	−	0.755163i
$641$	−564.096	−	325.681i	−0.880025	−	0.508083i	−0.00935827	−	0.999956i	$-0.502979\pi$
$641$	−564.096	−	325.681i	−0.880025	−	0.508083i	−0.870667	+	0.491874i	$0.836312\pi$
$642$	−187.463	+	304.598i	−0.291999	+	0.474452i
$643$	−523.947	+	302.501i	−0.814847	+	0.470452i	−0.848636	−	0.528977i	$-0.822576\pi$
$643$	−523.947	+	302.501i	−0.814847	+	0.470452i	0.0337893	+	0.999429i	$0.489242\pi$
$644$	83.0814	−	27.6897i	0.129008	−	0.0429964i
$645$	−9.96219	−	136.514i	−0.0154453	−	0.211650i
$646$	484.132	−	671.666i	0.749431	−	1.03973i
$647$		−	1266.46i		−	1.95743i	−0.205226	−	0.978715i	$-0.565793\pi$
$647$		−	1266.46i		−	1.95743i	0.205226	−	0.978715i	$-0.434207\pi$
$648$	−647.957	−	7.42176i	−0.999934	−	0.0114533i
$649$	−161.260			−0.248474
$650$	220.519	+	158.949i	0.339260	+	0.244536i
$651$	−77.4581	+	5.65254i	−0.118983	+	0.00868286i
$652$	406.734	−	135.558i	0.623825	−	0.207911i
$653$	132.030	+	228.682i	0.202189	+	0.350202i	0.949234	−	0.314572i	$-0.101861\pi$
$653$	132.030	+	228.682i	0.202189	+	0.350202i	−0.747044	+	0.664774i	$0.768528\pi$
$654$	609.813	+	375.306i	0.932436	+	0.573863i
$655$	143.733	−	248.952i	0.219439	−	0.380080i
$656$	361.042	−	845.014i	0.550369	−	1.28813i
$657$	935.602	−	137.283i	1.42405	−	0.208954i
$658$	0.743006	−	7.33540i	0.00112919	−	0.0111480i
$659$	246.804	−	427.478i	0.374513	−	0.648676i	−0.615741	−	0.787949i	$-0.711143\pi$
$659$	246.804	−	427.478i	0.374513	−	0.648676i	0.990254	+	0.139273i	$0.0444765\pi$
$660$	−108.973	−	261.712i	−0.165111	−	0.396534i
$661$	−1071.29	+	618.508i	−1.62071	+	0.935716i	−0.633977	+	0.773352i	$0.718578\pi$
$661$	−1071.29	+	618.508i	−1.62071	+	0.935716i	−0.986731	+	0.162364i	$0.948088\pi$
$662$	449.390	−	202.117i	0.678837	−	0.305312i
$663$	301.259	+	443.725i	0.454387	+	0.669269i
$664$	−214.017	+	197.135i	−0.322315	+	0.296889i
$665$			150.821i			0.226798i
$666$	394.784	+	204.953i	0.592768	+	0.307738i
$667$		−	1007.15i		−	1.50997i
$668$	457.979	+	406.150i	0.685597	+	0.608008i
$669$	−359.808	+	743.430i	−0.537829	+	1.11126i
$670$	−782.932	+	352.130i	−1.16855	+	0.525567i
$671$	138.073	−	79.7166i	0.205772	−	0.118803i
$672$	63.3630	+	29.2043i	0.0942902	+	0.0434588i
$673$	−263.390	+	456.205i	−0.391367	+	0.677868i	−0.992630	−	0.121184i	$-0.961331\pi$
$673$	−263.390	+	456.205i	−0.391367	+	0.677868i	0.601263	+	0.799051i	$0.294664\pi$
$674$	−140.770	−	14.2587i	−0.208858	−	0.0211553i
$675$	71.5241	−	227.141i	0.105962	−	0.336505i
$676$	−268.349	−	54.9260i	−0.396966	−	0.0812515i
$677$	−179.206	+	310.394i	−0.264706	+	0.458485i	−0.967487	−	0.252922i	$-0.918608\pi$
$677$	−179.206	+	310.394i	−0.264706	+	0.458485i	0.702780	+	0.711407i	$0.251942\pi$
$678$	−16.8584	+	599.786i	−0.0248649	+	0.884640i
$679$	−18.4043	−	31.8772i	−0.0271050	−	0.0469472i
$680$	526.628	−	118.185i	0.774453	−	0.173801i
$681$	−46.3633	+	95.7953i	−0.0680812	+	0.140669i
$682$	−169.225	+	234.777i	−0.248131	+	0.344247i
$683$	−237.803			−0.348175			−0.174087	−	0.984730i	$-0.555697\pi$
$683$	−237.803			−0.348175			−0.174087	+	0.984730i	$0.555697\pi$
$684$	1146.86	−	578.819i	1.67670	−	0.846226i
$685$			961.972i			1.40434i
$686$	−82.8431	+	114.933i	−0.120763	+	0.167541i
$687$	717.170	−	486.909i	1.04392	−	0.708746i
$688$	124.629	−	15.0042i	0.181147	−	0.0218084i
$689$	375.168	−	216.603i	0.544511	−	0.314373i
$690$	924.719	−	499.785i	1.34017	−	0.724326i
$691$	1107.04	+	639.151i	1.60209	+	0.924966i	0.991069	+	0.133349i	$0.0425732\pi$
$691$	1107.04	+	639.151i	1.60209	+	0.924966i	0.611018	+	0.791616i	$0.290760\pi$
$692$	−219.858	−	45.0008i	−0.317714	−	0.0650301i
$693$	16.4856	+	20.8388i	0.0237887	+	0.0300704i
$694$	−565.800	−	57.3102i	−0.815274	−	0.0825796i
$695$	−104.927	−	60.5796i	−0.150974	−	0.0871649i
$696$	549.042	−	585.129i	0.788854	−	0.840702i
$697$	333.136	+	577.009i	0.477957	+	0.827847i
$698$	930.585	−	418.538i	1.33322	−	0.599625i
$699$	−11.6980	−	160.300i	−0.0167353	−	0.229328i
$700$	−17.0121	+	19.1830i	−0.0243030	+	0.0274043i
$701$	−448.586			−0.639923			−0.319962	−	0.947430i	$-0.603670\pi$
$701$	−448.586			−0.639923			−0.319962	+	0.947430i	$0.603670\pi$
$702$	97.6302	+	826.411i	0.139074	+	1.17722i
$703$	−881.837			−1.25439
$704$	235.057	−	111.097i	0.333888	−	0.157809i
$705$	−6.44091	−	88.2613i	−0.00913604	−	0.125193i
$706$	386.365	−	173.771i	0.547259	−	0.246134i
$707$	−58.5550	−	101.420i	−0.0828217	−	0.143451i
$708$	289.286	−	378.455i	0.408596	−	0.534541i
$709$	27.4595	+	15.8537i	0.0387298	+	0.0223607i	0.519240	−	0.854629i	$-0.326215\pi$
$709$	27.4595	+	15.8537i	0.0387298	+	0.0223607i	−0.480510	+	0.876989i	$0.659548\pi$
$710$	103.802	−	1024.80i	0.146200	−	1.44338i
$711$	235.942	−	594.332i	0.331845	−	0.835909i
$712$	290.636	−	930.186i	0.408197	−	1.30644i
$713$	−929.306	−	536.535i	−1.30337	−	0.752504i
$714$	−44.5034	+	24.0528i	−0.0623297	+	0.0336875i
$715$	−315.286	+	182.030i	−0.440959	+	0.254588i
$716$	233.229	+	699.789i	0.325738	+	0.977359i
$717$	444.340	−	301.676i	0.619721	−	0.420748i
$718$	−15.3502	−	11.0643i	−0.0213790	−	0.0154099i
$719$			1090.16i			1.51622i	0.652127	+	0.758110i	$0.273877\pi$
$719$			1090.16i			1.51622i	−0.652127	+	0.758110i	$0.726123\pi$
$720$	809.693	+	213.743i	1.12457	+	0.296865i
$721$	69.0391			0.0957546
$722$	−1067.01	+	1480.33i	−1.47785	+	2.05031i
$723$	−82.0067	+	169.441i	−0.113426	+	0.234358i
$724$	−946.477	+	315.446i	−1.30729	+	0.435699i
$725$	147.436	+	255.366i	0.203360	+	0.352229i
$726$	−626.737	−	17.6159i	−0.863274	−	0.0242644i
$727$	−34.1890	+	59.2171i	−0.0470275	+	0.0814540i	−0.888581	−	0.458720i	$-0.848308\pi$
$727$	−34.1890	+	59.2171i	−0.0470275	+	0.0814540i	0.841553	+	0.540174i	$0.181642\pi$
$728$	26.7207	−	85.5201i	0.0367043	−	0.117473i
$729$	660.469	−	308.581i	0.905993	−	0.423294i
$730$	−1215.83	−	123.152i	−1.66552	−	0.168702i
$731$	−45.5085	+	78.8230i	−0.0622551	+	0.107829i
$732$	−60.6071	+	467.044i	−0.0827966	+	0.638039i
$733$	−212.805	+	122.863i	−0.290321	+	0.167617i	−0.638087	−	0.769965i	$-0.720274\pi$
$733$	−212.805	+	122.863i	−0.290321	+	0.167617i	0.347766	+	0.937582i	$0.386941\pi$
$734$	360.830	+	802.276i	0.491594	+	1.09302i
$735$	−368.406	+	761.196i	−0.501233	+	1.03564i
$736$	497.660	+	825.598i	0.676168	+	1.12174i
$737$		−	299.838i		−	0.406836i
$738$	46.2422	+	1032.74i	0.0626589	+	1.39938i
$739$		−	1019.01i		−	1.37890i	−0.724331	−	0.689452i	$-0.757851\pi$
$739$		−	1019.01i		−	1.37890i	0.724331	−	0.689452i	$-0.242149\pi$
$740$	−430.085	−	381.413i	−0.581197	−	0.515423i
$741$	−926.666	−	1364.89i	−1.25056	−	1.84196i
$742$	16.7603	+	37.2652i	0.0225880	+	0.0502226i
$743$	890.910	−	514.367i	1.19907	−	0.692284i	0.238723	−	0.971088i	$-0.423271\pi$
$743$	890.910	−	514.367i	1.19907	−	0.692284i	0.960348	+	0.278803i	$0.0899378\pi$
$744$	−247.414	−	818.319i	−0.332546	−	1.09989i
$745$	154.844	−	268.197i	0.207844	−	0.359996i
$746$	−97.8553	+	966.085i	−0.131173	+	1.29502i
$747$	120.782	−	304.247i	0.161690	−	0.407292i
$748$	−37.8007	+	184.681i	−0.0505357	+	0.246900i
$749$	−21.6613	+	37.5185i	−0.0289204	+	0.0500915i
$750$	295.912	−	480.810i	0.394549	−	0.641080i
$751$	582.388	+	1008.73i	0.775483	+	1.34318i	0.934522	+	0.355904i	$0.115827\pi$
$751$	582.388	+	1008.73i	0.775483	+	1.34318i	−0.159039	+	0.987272i	$0.550840\pi$
$752$	80.5772	−	9.70072i	0.107150	−	0.0128999i
$753$	−254.160	+	18.5475i	−0.337530	+	0.0246314i
$754$	−835.906	−	602.515i	−1.10863	−	0.799092i
$755$	1179.07			1.56168
$756$	−78.4797	+	1.30652i	−0.103809	+	0.00172820i
$757$			962.868i			1.27195i	0.771709	+	0.635976i	$0.219402\pi$
$757$			962.868i			1.27195i	−0.771709	+	0.635976i	$0.780598\pi$
$758$	−307.653	−	221.754i	−0.405875	−	0.292552i
$759$	26.7204	+	366.156i	0.0352047	+	0.482419i
$760$	−1619.90	+	363.534i	−2.13145	+	0.478334i
$761$	1027.09	−	592.990i	1.34966	−	0.779225i	0.361457	−	0.932389i	$-0.382280\pi$
$761$	1027.09	−	592.990i	1.34966	−	0.779225i	0.988201	+	0.153164i	$0.0489462\pi$
$762$	107.454	−	174.595i	0.141015	−	0.229127i
$763$	75.1131	+	43.3666i	0.0984445	+	0.0568369i
$764$	−30.7841	+	150.400i	−0.0402933	+	0.196859i
$765$	−476.198	+	376.721i	−0.622481	+	0.492445i
$766$	94.4959	−	932.920i	0.123363	−	1.21791i
$767$	−529.776	−	305.866i	−0.690712	−	0.398783i
$768$	−160.942	+	750.947i	−0.209560	+	0.977796i
$769$	−540.055	−	935.403i	−0.702282	−	1.21639i	−0.967663	−	0.252245i	$-0.918831\pi$
$769$	−540.055	−	935.403i	−0.702282	−	1.21639i	0.265381	−	0.964144i	$-0.414502\pi$
$770$	−14.0851	−	31.3171i	−0.0182924	−	0.0406716i
$771$	−80.0540	+	54.3511i	−0.103831	+	0.0704943i
$772$	−442.535	+	499.007i	−0.573232	+	0.646383i
$773$	1304.13			1.68711			0.843553	−	0.537046i	$-0.180460\pi$
$773$	1304.13			1.68711			0.843553	+	0.537046i	$0.180460\pi$
$774$	−119.019	+	76.0101i	−0.153772	+	0.0982043i
$775$	314.171			0.405382
$776$	298.017	−	274.508i	0.384043	−	0.353748i
$777$	48.4977	+	23.4721i	0.0624167	+	0.0302086i
$778$	56.0059	+	124.525i	0.0719870	+	0.160057i
$779$	−1024.72	−	1774.87i	−1.31543	−	2.27840i
$780$	138.394	−	1066.48i	0.177429	−	1.36728i
$781$	311.563	+	179.881i	0.398928	+	0.230321i
$782$	−695.399	−	70.4373i	−0.889257	−	0.0900733i
$783$	−271.121	+	861.006i	−0.346260	+	1.09962i
$784$	−713.180	−	304.715i	−0.909668	−	0.388666i
$785$	423.699	+	244.622i	0.539743	+	0.311621i
$786$	−296.469	−	8.33296i	−0.377187	−	0.0106017i
$787$	76.4534	−	44.1404i	0.0971453	−	0.0560869i	−0.450640	−	0.892706i	$-0.648804\pi$
$787$	76.4534	−	44.1404i	0.0971453	−	0.0560869i	0.547786	+	0.836619i	$0.315471\pi$
$788$	−238.506	−	715.625i	−0.302673	−	0.908154i
$789$	143.229	+	69.3205i	0.181532	+	0.0878587i
$790$	−483.209	+	670.386i	−0.611657	+	0.848589i
$791$			72.6791i			0.0918826i
$792$	−184.084	+	227.294i	−0.232429	+	0.286987i
$793$	604.805			0.762679
$794$	277.156	+	199.772i	0.349063	+	0.251602i
$795$	275.485	+	405.763i	0.346522	+	0.510394i
$796$	12.1811	+	36.5488i	0.0153029	+	0.0459156i
$797$	−527.678	−	913.965i	−0.662080	−	1.14676i	−0.980068	−	0.198662i	$-0.936340\pi$
$797$	−527.678	−	913.965i	−0.662080	−	1.14676i	0.317988	−	0.948095i	$-0.396993\pi$
$798$	136.892	−	73.9861i	0.171543	−	0.0927144i
$799$	−29.4229	+	50.9619i	−0.0368246	+	0.0637821i
$800$	−247.041	−	136.481i	−0.308802	−	0.170601i
$801$	159.166	+	1084.73i	0.198709	+	1.35423i
$802$	−62.4931	+	616.968i	−0.0779215	+	0.769287i
$803$	213.412	−	369.641i	0.265769	−	0.460325i
$804$	703.681	+	537.884i	0.875225	+	0.669010i
$805$	110.264	−	63.6608i	0.136973	−	0.0790817i
$806$	−1001.25	+	450.322i	−1.24225	+	0.558712i
$807$	259.830	−	18.9612i	0.321970	−	0.0234959i
$808$	948.170	−	873.373i	1.17348	−	1.08091i
$809$			635.537i			0.785583i	0.919628	+	0.392792i	$0.128491\pi$
$809$			635.537i			0.785583i	−0.919628	+	0.392792i	$0.871509\pi$
$810$	−925.076	+	178.332i	−1.14207	+	0.220162i
$811$			338.192i			0.417006i	0.978022	+	0.208503i	$0.0668590\pi$
$811$			338.192i			0.417006i	−0.978022	+	0.208503i	$0.933141\pi$
$812$	64.4864	−	72.7156i	0.0794168	−	0.0895513i
$813$	−1233.33	+	90.0025i	−1.51701	+	0.110704i
$814$	183.109	−	82.3546i	0.224949	−	0.101173i
$815$	539.808	−	311.658i	0.662341	−	0.382403i
$816$	−365.611	−	420.015i	−0.448052	−	0.514724i
$817$	139.983	−	242.458i	0.171338	−	0.296767i
$818$	−253.764	−	25.7039i	−0.310225	−	0.0314229i
$819$	14.6335	+	99.7292i	0.0178675	+	0.121769i
$820$	267.896	−	1308.84i	0.326702	−	1.59615i
$821$	360.772	−	624.876i	0.439430	−	0.761116i	−0.558215	−	0.829696i	$-0.688514\pi$
$821$	360.772	−	624.876i	0.439430	−	0.761116i	0.997646	+	0.0685804i	$0.0218470\pi$
$822$	873.129	−	471.902i	1.06220	−	0.574090i
$823$	−426.201	−	738.203i	−0.517863	−	0.896965i	−0.999785	−	0.0207510i	$-0.993394\pi$
$823$	−426.201	−	738.203i	−0.517863	−	0.896965i	0.481921	−	0.876214i	$-0.339939\pi$
$824$	166.410	+	741.518i	0.201954	+	0.899900i
$825$	−60.3762	−	88.9284i	−0.0731833	−	0.107792i
$826$	33.7386	−	46.8077i	0.0408458	−	0.0566679i
$827$	−210.452			−0.254476			−0.127238	−	0.991872i	$-0.540611\pi$
$827$	−210.452			−0.254476			−0.127238	+	0.991872i	$0.540611\pi$
$828$	−907.254	−	594.143i	−1.09572	−	0.717564i
$829$			471.735i			0.569041i	0.958670	+	0.284521i	$0.0918344\pi$
$829$			471.735i			0.569041i	−0.958670	+	0.284521i	$0.908166\pi$
$830$	−247.362	+	343.181i	−0.298027	+	0.413471i
$831$	−309.949	−	150.010i	−0.372983	−	0.180518i
$832$	982.941	+	80.8601i	1.18142	+	0.0971876i
$833$	486.988	−	281.162i	0.584619	−	0.337530i
$834$	−3.51213	+	124.954i	−0.00421119	+	0.149825i
$835$	770.725	+	444.978i	0.923024	+	0.532908i
$836$	116.274	−	568.075i	0.139084	−	0.679516i
$837$	650.024	+	708.846i	0.776612	+	0.846889i
$838$	−151.836	−	15.3795i	−0.181188	−	0.0183526i
$839$	−594.093	−	343.000i	−0.708097	−	0.408820i	0.102259	−	0.994758i	$-0.467393\pi$
$839$	−594.093	−	343.000i	−0.708097	−	0.408820i	−0.810356	+	0.585938i	$0.800726\pi$
$840$	98.7646	+	23.1243i	0.117577	+	0.0275289i
$841$	−138.374	−	239.671i	−0.164535	−	0.284984i
$842$	−1246.07	+	560.430i	−1.47989	+	0.665594i
$843$	−988.941	−	478.631i	−1.17312	−	0.567771i
$844$	−376.264	−	333.682i	−0.445810	−	0.395358i
$845$	−398.234			−0.471282
$846$	−76.9503	+	49.1432i	−0.0909578	+	0.0580889i
$847$	−75.9450			−0.0896635
$848$	−359.850	+	269.838i	−0.424352	+	0.318205i
$849$	48.1172	−	32.6682i	0.0566751	−	0.0384785i
$850$	186.632	−	83.9391i	0.219567	−	0.0987519i
$851$	372.219	+	644.703i	0.437391	+	0.757583i
$852$	−981.072	+	408.506i	−1.15149	+	0.479467i
$853$	−732.848	−	423.110i	−0.859141	−	0.496026i	0.00458321	−	0.999989i	$-0.498541\pi$
$853$	−732.848	−	423.110i	−0.859141	−	0.496026i	−0.863725	+	0.503964i	$0.831874\pi$
$854$	−5.74882	+	56.7558i	−0.00673164	+	0.0664588i
$855$	1464.78	−	1158.79i	1.71319	−	1.35531i
$856$	−455.182	−	142.221i	−0.531755	−	0.166146i
$857$	860.917	+	497.051i	1.00457	+	0.579989i	0.909597	−	0.415491i	$-0.136390\pi$
$857$	860.917	+	497.051i	1.00457	+	0.579989i	0.0949730	+	0.995480i	$0.469724\pi$
$858$	319.884	+	196.871i	0.372825	+	0.229453i
$859$	413.570	−	238.775i	0.481456	−	0.277968i	−0.239567	−	0.970880i	$-0.577006\pi$
$859$	413.570	−	238.775i	0.481456	−	0.277968i	0.721023	+	0.692911i	$0.243672\pi$
$860$	173.140	−	57.7049i	0.201326	−	0.0670987i
$861$	9.11364	+	124.886i	0.0105849	+	0.145048i
$862$	−26.5465	−	19.1346i	−0.0307965	−	0.0221979i
$863$			1244.01i			1.44150i	0.693196	+	0.720749i	$0.256202\pi$
$863$			1244.01i			1.44150i	−0.693196	+	0.720749i	$0.743798\pi$
$864$	−203.198	−	839.766i	−0.235183	−	0.971951i
$865$	−326.272			−0.377194
$866$	722.801	−	1002.79i	0.834644	−	1.15795i
$867$	−462.017	+	33.7159i	−0.532891	+	0.0388880i
$868$	−32.7417	−	98.2397i	−0.0377209	−	0.113179i
$869$	−144.315	−	249.961i	−0.166070	−	0.287642i
$870$	611.437	−	993.488i	0.702802	−	1.14194i
$871$	568.713	−	985.040i	0.652943	−	1.13093i
$872$	−284.731	+	911.286i	−0.326526	+	1.04505i
$873$	−168.188	+	423.662i	−0.192655	+	0.485294i
$874$	2139.04	+	216.664i	2.44741	+	0.247899i
$875$	34.1926	−	59.2233i	0.0390773	−	0.0676838i
$876$	484.656	+	1163.96i	0.553260	+	1.32872i
$877$	1163.95	−	672.007i	1.32719	−	0.766256i	0.342330	−	0.939580i	$-0.388784\pi$
$877$	1163.95	−	672.007i	1.32719	−	0.766256i	0.984865	+	0.173324i	$0.0554507\pi$
$878$	−458.089	−	1018.52i	−0.521741	−	1.16005i
$879$	−407.504	−	600.215i	−0.463600	−	0.682838i
$880$	302.413	−	226.768i	0.343651	−	0.257691i
$881$		−	814.455i		−	0.924467i	−0.886758	−	0.462233i	$-0.847048\pi$
$881$		−	814.455i		−	0.924467i	0.886758	−	0.462233i	$-0.152952\pi$
$882$	871.619	−	39.0278i	0.988231	−	0.0442492i
$883$			363.806i			0.412011i	0.978551	+	0.206006i	$0.0660465\pi$
$883$			363.806i			0.412011i	−0.978551	+	0.206006i	$0.933953\pi$
$884$	−474.474	+	535.023i	−0.536736	+	0.605229i
$885$	301.709	−	623.386i	0.340914	−	0.704391i
$886$	352.824	+	784.476i	0.398222	+	0.885414i
$887$	−624.016	+	360.276i	−0.703513	+	0.406173i	−0.808655	−	0.588284i	$-0.799804\pi$
$887$	−624.016	+	360.276i	−0.703513	+	0.406173i	0.105141	+	0.994457i	$0.466470\pi$
$888$	−135.206	+	577.469i	−0.152259	+	0.650303i
$889$	12.4162	−	21.5056i	0.0139665	−	0.0241907i
$890$	142.782	−	1409.63i	0.160430	−	1.58386i
$891$	75.7248	−	320.217i	0.0849886	−	0.359391i
$892$	−1078.86	−	220.823i	−1.20949	−	0.247559i
$893$	90.5042	−	156.758i	0.101348	−	0.175541i
$894$	−319.387	−	8.97713i	−0.357256	−	0.0100415i
$895$	536.210	+	928.744i	0.599118	+	1.03770i
$896$	−16.9311	+	91.4721i	−0.0188964	+	0.102089i
$897$	−606.717	+	1253.59i	−0.676385	+	1.39754i
$898$	372.281	+	268.337i	0.414567	+	0.298817i
$899$	−1190.91			−1.32470
$900$	317.013	+	17.8349i	0.352237	+	0.0198165i
$901$		−	326.123i		−	0.361956i
$902$	378.533	+	272.844i	0.419659	+	0.302487i
$903$	−14.1521	+	9.60832i	−0.0156724	+	0.0106404i
$904$	−780.614	+	175.184i	−0.863511	+	0.193787i
$905$	−1256.14	+	725.234i	−1.38800	+	0.801364i
$906$	−578.401	−	1070.18i	−0.638412	−	1.18121i
$907$	−311.241	−	179.695i	−0.343155	−	0.198121i	0.318511	−	0.947919i	$-0.396817\pi$
$907$	−311.241	−	179.695i	−0.343155	−	0.198121i	−0.661666	+	0.749798i	$0.730150\pi$
$908$	−139.018	−	28.4543i	−0.153103	−	0.0313374i
$909$	−535.106	+	1347.92i	−0.588676	+	1.48286i
$910$	13.1272	−	129.600i	0.0144255	−	0.142417i
$911$	−1431.05	−	826.217i	−1.57086	−	0.906934i	−0.996064	−	0.0886344i	$-0.971750\pi$
$911$	−1431.05	−	826.217i	−1.57086	−	0.906934i	−0.574792	−	0.818300i	$-0.694917\pi$
$912$	1124.61	+	1291.96i	1.23313	+	1.41662i
$913$	−73.8770	−	127.959i	−0.0809167	−	0.140152i
$914$	644.865	+	1433.80i	0.705541	+	1.56871i
$915$	49.8349	+	682.900i	0.0544643	+	0.746338i
$916$	864.730	+	766.869i	0.944028	+	0.837193i
$917$	−35.9247			−0.0391763
$918$	575.530	+	247.415i	0.626939	+	0.269516i
$919$	1051.67			1.14436			0.572181	−	0.820128i	$-0.306098\pi$
$919$	1051.67			1.14436			0.572181	+	0.820128i	$0.306098\pi$
$920$	949.528	+	1030.85i	1.03210	+	1.12049i
$921$	−83.8442	−	1148.94i	−0.0910361	−	1.24749i
$922$	−360.098	−	800.648i	−0.390562	−	0.868382i
$923$	682.371	+	1181.90i	0.739297	+	1.28050i
$924$	−21.5153	+	28.1471i	−0.0232849	+	0.0304622i
$925$	−188.755	−	108.978i	−0.204059	−	0.117814i
$926$	774.697	+	78.4695i	0.836606	+	0.0847402i
$927$	−530.441	−	670.509i	−0.572212	−	0.723311i
$928$	936.443	+	517.349i	1.00910	+	0.557488i
$929$	−436.589	−	252.065i	−0.469956	−	0.271329i	0.246265	−	0.969202i	$-0.420797\pi$
$929$	−436.589	−	252.065i	−0.469956	−	0.271329i	−0.716221	+	0.697873i	$0.754130\pi$
$930$	−590.971	−	1093.43i	−0.635453	−	1.17574i
$931$	−1497.97	+	864.851i	−1.60899	+	0.928948i
$932$	203.307	−	67.7591i	0.218141	−	0.0727029i
$933$	1174.54	−	797.429i	1.25888	−	0.854693i
$934$	−362.862	+	503.421i	−0.388503	+	0.538995i
$935$			274.069i			0.293122i
$936$	−1035.87	+	397.556i	−1.10670	+	0.424739i
$937$	−360.581			−0.384825			−0.192412	−	0.981314i	$-0.561631\pi$
$937$	−360.581			−0.384825			−0.192412	+	0.981314i	$0.561631\pi$
$938$	87.0319	+	62.7320i	0.0927845	+	0.0668784i
$939$	−366.159	+	756.552i	−0.389946	+	0.805700i
$940$	111.941	−	37.3082i	0.119086	−	0.0396896i
$941$	116.208	+	201.278i	0.123494	+	0.213898i	0.921143	−	0.389224i	$-0.127257\pi$
$941$	116.208	+	201.278i	0.123494	+	0.213898i	−0.797649	+	0.603122i	$0.793923\pi$
$942$	14.1821	−	504.569i	0.0150553	−	0.535636i
$943$	−865.060	+	1498.33i	−0.917349	+	1.58890i
$944$	584.063	+	249.548i	0.618711	+	0.264352i
$945$	−111.401	+	24.7405i	−0.117885	+	0.0261805i
$946$	−6.42366	+	63.4182i	−0.00679034	+	0.0670382i
$947$	−270.427	+	468.394i	−0.285562	+	0.494608i	−0.972745	−	0.231876i	$-0.925514\pi$
$947$	−270.427	+	468.394i	−0.285562	+	0.494608i	0.687183	+	0.726484i	$0.258847\pi$
$948$	845.513	+	109.720i	0.891892	+	0.115738i
$949$	1402.22	−	809.573i	1.47758	−	0.853080i
$950$	−574.076	+	258.195i	−0.604291	+	0.271784i
$951$	233.922	−	483.327i	0.245975	−	0.508230i
$952$	−45.6974	−	49.6109i	−0.0480014	−	0.0521123i
$953$			1654.49i			1.73609i	0.496488	+	0.868044i	$0.334623\pi$
$953$			1654.49i			1.73609i	−0.496488	+	0.868044i	$0.665377\pi$
$954$	233.148	−	449.093i	0.244390	−	0.470747i
$955$			223.196i			0.233713i
$956$	535.764	+	475.132i	0.560423	+	0.497000i
$957$	228.864	+	337.095i	0.239147	+	0.352241i
$958$	1126.36	−	506.590i	1.17574	−	0.528800i
$959$	104.112	−	60.1091i	0.108563	−	0.0626790i
$960$	−10.3084	+	1116.53i	−0.0107380	+	1.16305i
$961$	−153.927	+	266.609i	−0.160173	+	0.277428i
$962$	757.760	+	76.7539i	0.787693	+	0.0797858i
$963$	530.810	−	77.8869i	0.551204	−	0.0808794i
$964$	−245.893	−	50.3295i	−0.255075	−	0.0522091i
$965$	−484.842	+	839.771i	−0.502427	+	0.870229i
$966$	−111.872	−	68.8510i	−0.115809	−	0.0712743i
$967$	564.485	+	977.717i	0.583749	+	1.01108i	0.995030	+	0.0995746i	$0.0317482\pi$
$967$	564.485	+	977.717i	0.583749	+	1.01108i	−0.411281	+	0.911509i	$0.634918\pi$
$968$	−183.056	−	815.691i	−0.189107	−	0.842656i
$969$	−1238.65	+	90.3908i	−1.27827	+	0.0932826i
$970$	344.449	−	477.876i	0.355103	−	0.492655i
$971$	1762.47			1.81511			0.907555	−	0.419933i	$-0.137946\pi$
$971$	1762.47			1.81511			0.907555	+	0.419933i	$0.137946\pi$
$972$	615.664	+	752.158i	0.633399	+	0.773825i
$973$			15.1413i			0.0155615i
$974$	61.9512	−	85.9486i	0.0636049	−	0.0882430i
$975$	−29.6768	−	406.668i	−0.0304377	−	0.417096i
$976$	−623.445	+	75.0569i	−0.638776	+	0.0769026i
$977$	835.276	−	482.247i	0.854939	−	0.493599i	−0.00737503	−	0.999973i	$-0.502348\pi$
$977$	835.276	−	482.247i	0.854939	−	0.493599i	0.862314	+	0.506373i	$0.169014\pi$
$978$	−547.681	−	337.067i	−0.560001	−	0.344650i
$979$	428.561	+	247.430i	0.437754	+	0.252738i
$980$	−1104.65	−	226.100i	−1.12719	−	0.230714i
$981$	−155.932	−	1062.69i	−0.158952	−	1.08328i
$982$	1811.26	+	183.463i	1.84446	+	0.186826i
$983$	−289.032	−	166.872i	−0.294030	−	0.169758i	0.345728	−	0.938335i	$-0.387632\pi$
$983$	−289.032	−	166.872i	−0.294030	−	0.169758i	−0.639758	+	0.768577i	$0.720965\pi$
$984$	−1319.38	+	398.908i	−1.34084	+	0.405394i
$985$	−548.345	−	949.761i	−0.556695	−	0.964224i
$986$	−707.452	+	318.182i	−0.717497	+	0.322700i
$987$	−9.14986	+	6.21212i	−0.00927037	+	0.00629394i
$988$	1459.48	−	1645.72i	1.47720	−	1.66571i
$989$	−236.345			−0.238974
$990$	−195.934	+	377.411i	−0.197913	+	0.381223i
$991$	1203.94			1.21487			0.607435	−	0.794369i	$-0.292198\pi$
$991$	1203.94			1.21487			0.607435	+	0.794369i	$0.292198\pi$
$992$	976.229	−	588.458i	0.984102	−	0.593204i
$993$	−665.301	−	321.994i	−0.669990	−	0.324264i
$994$	−117.398	+	52.8005i	−0.118106	+	0.0531192i
$995$	28.0054	+	48.5067i	0.0281461	+	0.0487505i
$996$	432.831	+	56.1673i	0.434569	+	0.0563929i
$997$	−1018.52	−	588.045i	−1.02159	−	0.589815i	−0.107025	−	0.994256i	$-0.534132\pi$
$997$	−1018.52	−	588.045i	−1.02159	−	0.589815i	−0.914564	+	0.404442i	$0.867466\pi$
$998$	21.4145	−	211.416i	0.0214574	−	0.211840i
$999$	−144.656	−	651.352i	−0.144801	−	0.652004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.16	yes	44
3.2	odd	2		216.3.j.a.197.7		44
4.3	odd	2		288.3.n.a.209.22		44
8.3	odd	2		288.3.n.a.209.1		44
8.5	even	2	inner	72.3.j.a.29.8	yes	44
9.2	odd	6		648.3.h.a.485.44		44
9.4	even	3		216.3.j.a.125.15		44
9.5	odd	6	inner	72.3.j.a.5.8	✓	44
9.7	even	3		648.3.h.a.485.1		44
12.11	even	2		864.3.n.a.305.18		44
24.5	odd	2		216.3.j.a.197.15		44
24.11	even	2		864.3.n.a.305.5		44
36.7	odd	6		2592.3.h.a.1457.36		44
36.11	even	6		2592.3.h.a.1457.9		44
36.23	even	6		288.3.n.a.113.1		44
36.31	odd	6		864.3.n.a.17.5		44
72.5	odd	6	inner	72.3.j.a.5.16	yes	44
72.11	even	6		2592.3.h.a.1457.35		44
72.13	even	6		216.3.j.a.125.7		44
72.29	odd	6		648.3.h.a.485.2		44
72.43	odd	6		2592.3.h.a.1457.10		44
72.59	even	6		288.3.n.a.113.22		44
72.61	even	6		648.3.h.a.485.43		44
72.67	odd	6		864.3.n.a.17.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.8	✓	44	9.5	odd	6	inner
72.3.j.a.5.16	yes	44	72.5	odd	6	inner
72.3.j.a.29.8	yes	44	8.5	even	2	inner
72.3.j.a.29.16	yes	44	1.1	even	1	trivial
216.3.j.a.125.7		44	72.13	even	6
216.3.j.a.125.15		44	9.4	even	3
216.3.j.a.197.7		44	3.2	odd	2
216.3.j.a.197.15		44	24.5	odd	2
288.3.n.a.113.1		44	36.23	even	6
288.3.n.a.113.22		44	72.59	even	6
288.3.n.a.209.1		44	8.3	odd	2
288.3.n.a.209.22		44	4.3	odd	2
648.3.h.a.485.1		44	9.7	even	3
648.3.h.a.485.2		44	72.29	odd	6
648.3.h.a.485.43		44	72.61	even	6
648.3.h.a.485.44		44	9.2	odd	6
864.3.n.a.17.5		44	36.31	odd	6
864.3.n.a.17.18		44	72.67	odd	6
864.3.n.a.305.5		44	24.11	even	2
864.3.n.a.305.18		44	12.11	even	2
2592.3.h.a.1457.9		44	36.11	even	6
2592.3.h.a.1457.10		44	72.43	odd	6
2592.3.h.a.1457.35		44	72.11	even	6
2592.3.h.a.1457.36		44	36.7	odd	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16946 - 1.62246i) q^{2} +(-2.99204 + 0.218346i) q^{3} +(-1.26474 - 3.79479i) q^{4} +(-2.90774 - 5.03636i) q^{5} +(-3.14481 + 5.10981i) q^{6} +(-0.363382 + 0.629396i) q^{7} +(-7.63595 - 2.38585i) q^{8} +(8.90465 - 1.30660i) q^{9} +O(q^{10})\)	\(q+(1.16946 - 1.62246i) q^{2} +(-2.99204 + 0.218346i) q^{3} +(-1.26474 - 3.79479i) q^{4} +(-2.90774 - 5.03636i) q^{5} +(-3.14481 + 5.10981i) q^{6} +(-0.363382 + 0.629396i) q^{7} +(-7.63595 - 2.38585i) q^{8} +(8.90465 - 1.30660i) q^{9} +(-11.5718 - 1.17211i) q^{10} +(2.03117 - 3.51809i) q^{11} +(4.61274 + 11.0780i) q^{12} +(13.3457 - 7.70516i) q^{13} +(0.596210 + 1.32562i) q^{14} +(9.79976 + 14.4341i) q^{15} +(-12.8008 + 9.59887i) q^{16} -11.6011i q^{17} +(8.29370 - 15.9754i) q^{18} +35.6847i q^{19} +(-15.4344 + 17.4040i) q^{20} +(0.949829 - 1.96252i) q^{21} +(-3.33259 - 7.40973i) q^{22} +(26.0887 - 15.0623i) q^{23} +(23.3680 + 5.47128i) q^{24} +(-4.40992 + 7.63821i) q^{25} +(3.10595 - 30.6638i) q^{26} +(-26.3578 + 5.85369i) q^{27} +(2.84801 + 0.582934i) q^{28} +(16.7164 - 28.9536i) q^{29} +(34.8791 + 0.980360i) q^{30} +(-17.8105 - 30.8487i) q^{31} +(0.603728 + 31.9943i) q^{32} +(-5.30918 + 10.9698i) q^{33} +(-18.8223 - 13.5669i) q^{34} +4.22648 q^{35} +(-16.2204 - 32.1388i) q^{36} +24.7119i q^{37} +(57.8969 + 41.7317i) q^{38} +(-38.2486 + 25.9682i) q^{39} +(10.1874 + 45.3948i) q^{40} +(-49.7376 + 28.7160i) q^{41} +(-2.07333 - 3.83614i) q^{42} +(-6.79446 - 3.92278i) q^{43} +(-15.9193 - 3.25838i) q^{44} +(-32.4729 - 41.0477i) q^{45} +(6.07162 - 59.9427i) q^{46} +(-4.39286 - 2.53622i) q^{47} +(36.2048 - 31.5152i) q^{48} +(24.2359 + 41.9778i) q^{49} +(7.23546 + 16.0875i) q^{50} +(2.53304 + 34.7109i) q^{51} +(-46.1184 - 40.8992i) q^{52} +28.1114 q^{53} +(-21.3269 + 49.6101i) q^{54} -23.6244 q^{55} +(4.27641 - 3.93906i) q^{56} +(-7.79160 - 106.770i) q^{57} +(-27.4270 - 60.9816i) q^{58} +(-19.8481 - 34.3780i) q^{59} +(42.3802 - 55.4434i) q^{60} +(33.9886 + 19.6234i) q^{61} +(-70.8793 - 7.17940i) q^{62} +(-2.41342 + 6.07935i) q^{63} +(52.6155 + 36.4364i) q^{64} +(-77.6119 - 44.8092i) q^{65} +(11.5891 + 21.4426i) q^{66} +(63.9208 - 36.9047i) q^{67} +(-44.0236 + 14.6724i) q^{68} +(-74.7699 + 50.7635i) q^{69} +(4.94269 - 6.85730i) q^{70} +88.5602i q^{71} +(-71.1128 - 11.2680i) q^{72} +105.069 q^{73} +(40.0941 + 28.8995i) q^{74} +(11.5269 - 23.8167i) q^{75} +(135.416 - 45.1320i) q^{76} +(1.47618 + 2.55682i) q^{77} +(-2.59784 + 92.4255i) q^{78} +(35.5251 - 61.5313i) q^{79} +(85.5649 + 36.5586i) q^{80} +(77.5856 - 23.2696i) q^{81} +(-11.5754 + 114.279i) q^{82} +(18.1858 - 31.4988i) q^{83} +(-8.64865 - 1.12231i) q^{84} +(-58.4271 + 33.7329i) q^{85} +(-14.3104 + 6.43621i) q^{86} +(-43.6942 + 90.2804i) q^{87} +(-23.9035 + 22.0179i) q^{88} +121.817i q^{89} +(-104.574 + 4.68242i) q^{90} +11.1997i q^{91} +(-90.1540 - 79.9513i) q^{92} +(60.0254 + 88.4117i) q^{93} +(-9.25217 + 4.16124i) q^{94} +(179.721 - 103.762i) q^{95} +(-8.79220 - 95.5965i) q^{96} +(-25.3236 + 43.8618i) q^{97} +(96.4501 + 9.76948i) q^{98} +(13.4901 - 33.9812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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