LMFDB - Embedded newform 7.5.d.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,5,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	7.d (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:	$0.723589741587$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$2.34521 - 4.06202i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.5.d.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34521 - 2.32997i) q^{2} +(-5.53562 + 3.19599i) q^{3} +(4.38083 + 7.58782i) q^{4} +(-21.5712 - 12.4542i) q^{5} +17.1971i q^{6} +(32.8329 - 36.3731i) q^{7} +66.6192 q^{8} +(-20.0712 + 34.7644i) q^{9} +O(q^{10})$	\(q+(1.34521 - 2.32997i) q^{2} +(-5.53562 + 3.19599i) q^{3} +(4.38083 + 7.58782i) q^{4} +(-21.5712 - 12.4542i) q^{5} +17.1971i q^{6} +(32.8329 - 36.3731i) q^{7} +66.6192 q^{8} +(-20.0712 + 34.7644i) q^{9} +(-58.0356 + 33.5069i) q^{10} +(-54.3685 - 94.1691i) q^{11} +(-48.5013 - 28.0022i) q^{12} +234.980i q^{13} +(-40.5810 - 125.429i) q^{14} +159.214 q^{15} +(19.5233 - 33.8154i) q^{16} +(177.711 - 102.602i) q^{17} +(54.0000 + 93.5307i) q^{18} +(-99.8181 - 57.6300i) q^{19} -218.238i q^{20} +(-65.5025 + 306.281i) q^{21} -292.548 q^{22} +(-23.6535 + 40.9691i) q^{23} +(-368.779 + 212.914i) q^{24} +(-2.28753 - 3.96211i) q^{25} +(547.496 + 316.097i) q^{26} -774.341i q^{27} +(419.828 + 89.7860i) q^{28} -872.329 q^{29} +(214.176 - 370.963i) q^{30} +(700.467 - 404.415i) q^{31} +(480.427 + 832.125i) q^{32} +(601.927 + 347.523i) q^{33} -552.082i q^{34} +(-1161.24 + 375.706i) q^{35} -351.715 q^{36} +(-311.402 + 539.363i) q^{37} +(-268.552 + 155.049i) q^{38} +(-750.995 - 1300.76i) q^{39} +(-1437.06 - 829.686i) q^{40} +1723.39i q^{41} +(625.511 + 564.631i) q^{42} +2259.65 q^{43} +(476.359 - 825.078i) q^{44} +(865.924 - 499.941i) q^{45} +(63.6378 + 110.224i) q^{46} +(930.162 + 537.029i) q^{47} +249.586i q^{48} +(-245.000 - 2388.47i) q^{49} -12.3088 q^{50} +(-655.828 + 1135.93i) q^{51} +(-1782.99 + 1029.41i) q^{52} +(-330.129 - 571.801i) q^{53} +(-1804.19 - 1041.65i) q^{54} +2708.46i q^{55} +(2187.30 - 2423.14i) q^{56} +736.740 q^{57} +(-1173.46 + 2032.50i) q^{58} +(-2527.50 + 1459.25i) q^{59} +(697.489 + 1208.09i) q^{60} +(-1759.05 - 1015.59i) q^{61} -2176.09i q^{62} +(605.491 + 1871.47i) q^{63} +3209.85 q^{64} +(2926.48 - 5068.81i) q^{65} +(1619.44 - 934.981i) q^{66} +(-435.034 - 753.502i) q^{67} +(1557.05 + 898.961i) q^{68} -302.386i q^{69} +(-686.730 + 3211.06i) q^{70} -3718.32 q^{71} +(-1337.13 + 2315.98i) q^{72} +(3217.19 - 1857.45i) q^{73} +(837.800 + 1451.11i) q^{74} +(25.3258 + 14.6218i) q^{75} -1009.87i q^{76} +(-5210.29 - 1114.29i) q^{77} -4040.98 q^{78} +(-1204.33 + 2085.96i) q^{79} +(-842.285 + 486.293i) q^{80} +(849.019 + 1470.54i) q^{81} +(4015.44 + 2318.31i) q^{82} -2663.90i q^{83} +(-2610.96 + 844.746i) q^{84} -5111.27 q^{85} +(3039.69 - 5264.90i) q^{86} +(4828.89 - 2787.96i) q^{87} +(-3621.99 - 6273.46i) q^{88} +(11142.9 + 6433.35i) q^{89} -2690.10i q^{90} +(8546.95 + 7715.08i) q^{91} -414.488 q^{92} +(-2585.01 + 4477.38i) q^{93} +(2502.52 - 1444.83i) q^{94} +(1435.47 + 2486.30i) q^{95} +(-5318.93 - 3070.89i) q^{96} -9161.84i q^{97} +(-5894.63 - 2642.14i) q^{98} +4364.98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9} - 204 q^{10} - 58 q^{11} - 588 q^{12} + 560 q^{14} + 468 q^{15} - 72 q^{16} - 246 q^{17} + 216 q^{18} + 642 q^{19} - 1050 q^{21} - 1264 q^{22} + 290 q^{23} + 720 q^{24} - 572 q^{25} + 1008 q^{26} - 28 q^{28} - 2176 q^{29} - 72 q^{30} + 3618 q^{31} + 1584 q^{32} + 2070 q^{33} - 2478 q^{35} - 1632 q^{36} - 270 q^{37} - 6168 q^{38} - 1428 q^{39} - 1752 q^{40} + 6048 q^{42} + 2472 q^{43} + 2412 q^{44} + 1944 q^{45} + 2384 q^{46} - 1542 q^{47} - 980 q^{49} + 7568 q^{50} - 4734 q^{51} - 3192 q^{52} - 4510 q^{53} - 11016 q^{54} - 1232 q^{56} + 11052 q^{57} - 904 q^{58} + 2526 q^{59} - 756 q^{60} - 282 q^{61} - 336 q^{63} - 5472 q^{64} + 5796 q^{65} - 2556 q^{66} - 1318 q^{67} + 20412 q^{68} + 3360 q^{70} - 10408 q^{71} - 1296 q^{72} + 5214 q^{73} + 4036 q^{74} - 9636 q^{75} - 8890 q^{77} - 9072 q^{78} - 8110 q^{79} - 3144 q^{80} + 9306 q^{81} - 4032 q^{82} + 588 q^{84} - 15492 q^{85} + 12928 q^{86} + 5976 q^{87} - 2912 q^{88} + 33990 q^{89} + 17640 q^{91} - 20232 q^{92} + 7446 q^{93} + 27768 q^{94} + 6558 q^{95} - 37828 q^{98} + 10368 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9 - 204 * q^10 - 58 * q^11 - 588 * q^12 + 560 * q^14 + 468 * q^15 - 72 * q^16 - 246 * q^17 + 216 * q^18 + 642 * q^19 - 1050 * q^21 - 1264 * q^22 + 290 * q^23 + 720 * q^24 - 572 * q^25 + 1008 * q^26 - 28 * q^28 - 2176 * q^29 - 72 * q^30 + 3618 * q^31 + 1584 * q^32 + 2070 * q^33 - 2478 * q^35 - 1632 * q^36 - 270 * q^37 - 6168 * q^38 - 1428 * q^39 - 1752 * q^40 + 6048 * q^42 + 2472 * q^43 + 2412 * q^44 + 1944 * q^45 + 2384 * q^46 - 1542 * q^47 - 980 * q^49 + 7568 * q^50 - 4734 * q^51 - 3192 * q^52 - 4510 * q^53 - 11016 * q^54 - 1232 * q^56 + 11052 * q^57 - 904 * q^58 + 2526 * q^59 - 756 * q^60 - 282 * q^61 - 336 * q^63 - 5472 * q^64 + 5796 * q^65 - 2556 * q^66 - 1318 * q^67 + 20412 * q^68 + 3360 * q^70 - 10408 * q^71 - 1296 * q^72 + 5214 * q^73 + 4036 * q^74 - 9636 * q^75 - 8890 * q^77 - 9072 * q^78 - 8110 * q^79 - 3144 * q^80 + 9306 * q^81 - 4032 * q^82 + 588 * q^84 - 15492 * q^85 + 12928 * q^86 + 5976 * q^87 - 2912 * q^88 + 33990 * q^89 + 17640 * q^91 - 20232 * q^92 + 7446 * q^93 + 27768 * q^94 + 6558 * q^95 - 37828 * q^98 + 10368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.34521	−	2.32997i	0.336302	−	0.582492i	−0.647432	−	0.762123i	$-0.724157\pi$
$2$	1.34521	−	2.32997i	0.336302	−	0.582492i	0.983734	+	0.179631i	$0.0574904\pi$
$3$	−5.53562	+	3.19599i	−0.615069	+	0.355110i	−0.774947	−	0.632026i	$-0.782223\pi$
$3$	−5.53562	+	3.19599i	−0.615069	+	0.355110i	0.159878	+	0.987137i	$0.448890\pi$
$4$	4.38083	+	7.58782i	0.273802	+	0.474239i
$5$	−21.5712	−	12.4542i	−0.862850	−	0.498167i	0.00211572	−	0.999998i	$-0.499327\pi$
$5$	−21.5712	−	12.4542i	−0.862850	−	0.498167i	−0.864966	+	0.501831i	$0.832660\pi$
$6$			17.1971i			0.477697i
$7$	32.8329	−	36.3731i	0.670059	−	0.742307i
$7$	32.8329	−	36.3731i	0.670059	−	0.742307i
$8$	66.6192			1.04092
$9$	−20.0712	+	34.7644i	−0.247793	+	0.429190i
$10$	−58.0356	+	33.5069i	−0.580356	+	0.335069i
$11$	−54.3685	−	94.1691i	−0.449327	−	0.778257i	0.549016	−	0.835812i	$-0.315003\pi$
$11$	−54.3685	−	94.1691i	−0.449327	−	0.778257i	−0.998342	+	0.0575554i	$0.981669\pi$
$12$	−48.5013	−	28.0022i	−0.336814	−	0.194460i
$13$			234.980i			1.39041i	0.718809	+	0.695207i	$0.244687\pi$
$13$			234.980i			1.39041i	−0.718809	+	0.695207i	$0.755313\pi$
$14$	−40.5810	−	125.429i	−0.207046	−	0.639944i
$15$	159.214			0.707617
$16$	19.5233	−	33.8154i	0.0762630	−	0.132091i
$17$	177.711	−	102.602i	0.614918	−	0.355023i	−0.159970	−	0.987122i	$-0.551140\pi$
$17$	177.711	−	102.602i	0.614918	−	0.355023i	0.774888	+	0.632099i	$0.217806\pi$
$18$	54.0000	+	93.5307i	0.166667	+	0.288675i
$19$	−99.8181	−	57.6300i	−0.276504	−	0.159640i	0.355335	−	0.934739i	$-0.384367\pi$
$19$	−99.8181	−	57.6300i	−0.276504	−	0.159640i	−0.631840	+	0.775099i	$0.717700\pi$
$20$		−	218.238i		−	0.545596i
$21$	−65.5025	+	306.281i	−0.148532	+	0.694516i
$22$	−292.548			−0.604438
$23$	−23.6535	+	40.9691i	−0.0447137	+	0.0774463i	−0.887516	−	0.460777i	$-0.847571\pi$
$23$	−23.6535	+	40.9691i	−0.0447137	+	0.0774463i	0.842802	+	0.538223i	$0.180904\pi$
$24$	−368.779	+	212.914i	−0.640241	+	0.369643i
$25$	−2.28753	−	3.96211i	−0.00366004	−	0.00633938i
$26$	547.496	+	316.097i	0.809906	+	0.467599i
$27$		−	774.341i		−	1.06220i
$28$	419.828	+	89.7860i	0.535495	+	0.114523i
$29$	−872.329			−1.03725			−0.518626	−	0.855001i	$-0.673556\pi$
$29$	−872.329			−1.03725			−0.518626	+	0.855001i	$0.673556\pi$
$30$	214.176	−	370.963i	0.237973	−	0.412181i
$31$	700.467	−	404.415i	0.728894	−	0.420827i	−0.0891236	−	0.996021i	$-0.528407\pi$
$31$	700.467	−	404.415i	0.728894	−	0.420827i	0.818017	+	0.575194i	$0.195073\pi$
$32$	480.427	+	832.125i	0.469167	+	0.812622i
$33$	601.927	+	347.523i	0.552734	+	0.319121i
$34$		−	552.082i		−	0.477580i
$35$	−1161.24	+	375.706i	−0.947953	+	0.306699i
$36$	−351.715			−0.271385
$37$	−311.402	+	539.363i	−0.227466	+	0.393984i	−0.957057	−	0.289901i	$-0.906378\pi$
$37$	−311.402	+	539.363i	−0.227466	+	0.393984i	0.729590	+	0.683885i	$0.239711\pi$
$38$	−268.552	+	155.049i	−0.185978	+	0.107374i
$39$	−750.995	−	1300.76i	−0.493751	−	0.855201i
$40$	−1437.06	−	829.686i	−0.898162	−	0.518554i
$41$			1723.39i			1.02521i	0.858623	+	0.512607i	$0.171320\pi$
$41$			1723.39i			1.02521i	−0.858623	+	0.512607i	$0.828680\pi$
$42$	625.511	+	564.631i	0.354598	+	0.320086i
$43$	2259.65			1.22209			0.611045	−	0.791596i	$-0.290749\pi$
$43$	2259.65			1.22209			0.611045	+	0.791596i	$0.290749\pi$
$44$	476.359	−	825.078i	0.246053	−	0.426176i
$45$	865.924	−	499.941i	0.427617	−	0.246885i
$46$	63.6378	+	110.224i	0.0300746	+	0.0520907i
$47$	930.162	+	537.029i	0.421078	+	0.243110i	0.695538	−	0.718489i	$-0.255166\pi$
$47$	930.162	+	537.029i	0.421078	+	0.243110i	−0.274460	+	0.961598i	$0.588499\pi$
$48$			249.586i			0.108327i
$49$	−245.000	−	2388.47i	−0.102041	−	0.994780i
$50$	−12.3088			−0.00492352
$51$	−655.828	+	1135.93i	−0.252145	+	0.436727i
$52$	−1782.99	+	1029.41i	−0.659389	+	0.380698i
$53$	−330.129	−	571.801i	−0.117526	−	0.203560i	0.801261	−	0.598315i	$-0.204163\pi$
$53$	−330.129	−	571.801i	−0.117526	−	0.203560i	−0.918787	+	0.394755i	$0.870830\pi$
$54$	−1804.19	−	1041.65i	−0.618721	−	0.357219i
$55$			2708.46i			0.895358i
$56$	2187.30	−	2423.14i	0.697481	−	0.772686i
$57$	736.740			0.226759
$58$	−1173.46	+	2032.50i	−0.348830	+	0.604191i
$59$	−2527.50	+	1459.25i	−0.726083	+	0.419204i	−0.816987	−	0.576655i	$-0.804358\pi$
$59$	−2527.50	+	1459.25i	−0.726083	+	0.419204i	0.0909045	+	0.995860i	$0.471024\pi$
$60$	697.489	+	1208.09i	0.193747	+	0.335579i
$61$	−1759.05	−	1015.59i	−0.472736	−	0.272934i	0.244648	−	0.969612i	$-0.421327\pi$
$61$	−1759.05	−	1015.59i	−0.472736	−	0.272934i	−0.717384	+	0.696678i	$0.754661\pi$
$62$		−	2176.09i		−	0.566100i
$63$	605.491	+	1871.47i	0.152555	+	0.471522i
$64$	3209.85			0.783654
$65$	2926.48	−	5068.81i	0.692658	−	1.19972i
$66$	1619.44	−	934.981i	0.371771	−	0.214642i
$67$	−435.034	−	753.502i	−0.0969112	−	0.167855i	0.813493	−	0.581574i	$-0.197563\pi$
$67$	−435.034	−	753.502i	−0.0969112	−	0.167855i	−0.910405	+	0.413719i	$0.864230\pi$
$68$	1557.05	+	898.961i	0.336731	+	0.194412i
$69$		−	302.386i		−	0.0635131i
$70$	−686.730	+	3211.06i	−0.140149	+	0.655319i
$71$	−3718.32			−0.737615			−0.368808	−	0.929506i	$-0.620234\pi$
$71$	−3718.32			−0.737615			−0.368808	+	0.929506i	$0.620234\pi$
$72$	−1337.13	+	2315.98i	−0.257934	+	0.446755i
$73$	3217.19	−	1857.45i	0.603714	−	0.348554i	−0.166788	−	0.985993i	$-0.553339\pi$
$73$	3217.19	−	1857.45i	0.603714	−	0.348554i	0.770501	+	0.637439i	$0.220006\pi$
$74$	837.800	+	1451.11i	0.152995	+	0.264995i
$75$	25.3258	+	14.6218i	0.00450236	+	0.00259944i
$76$		−	1009.87i		−	0.174839i
$77$	−5210.29	−	1114.29i	−0.878781	−	0.187940i
$78$	−4040.98			−0.664197
$79$	−1204.33	+	2085.96i	−0.192971	+	0.334236i	−0.946233	−	0.323484i	$-0.895146\pi$
$79$	−1204.33	+	2085.96i	−0.192971	+	0.334236i	0.753262	+	0.657720i	$0.228479\pi$
$80$	−842.285	+	486.293i	−0.131607	+	0.0759834i
$81$	849.019	+	1470.54i	0.129404	+	0.224134i
$82$	4015.44	+	2318.31i	0.597180	+	0.344782i
$83$		−	2663.90i		−	0.386689i	−0.981131	−	0.193345i	$-0.938066\pi$
$83$		−	2663.90i		−	0.386689i	0.981131	−	0.193345i	$-0.0619336\pi$
$84$	−2610.96	+	844.746i	−0.370035	+	0.119720i
$85$	−5111.27			−0.707442
$86$	3039.69	−	5264.90i	0.410991	−	0.711858i
$87$	4828.89	−	2787.96i	0.637982	−	0.368339i
$88$	−3621.99	−	6273.46i	−0.467715	−	0.810106i
$89$	11142.9	+	6433.35i	1.40675	+	0.812190i	0.995074	−	0.0991390i	$-0.0316088\pi$
$89$	11142.9	+	6433.35i	1.40675	+	0.812190i	0.411680	+	0.911329i	$0.364942\pi$
$90$		−	2690.10i		−	0.332111i
$91$	8546.95	+	7715.08i	1.03212	+	0.931660i
$92$	−414.488			−0.0489707
$93$	−2585.01	+	4477.38i	−0.298880	+	0.517676i
$94$	2502.52	−	1444.83i	0.283219	−	0.163516i
$95$	1435.47	+	2486.30i	0.159055	+	0.275490i
$96$	−5318.93	−	3070.89i	−0.577141	−	0.333213i
$97$		−	9161.84i		−	0.973731i	−0.873477	−	0.486866i	$-0.838140\pi$
$97$		−	9161.84i		−	0.973731i	0.873477	−	0.486866i	$-0.161860\pi$
$98$	−5894.63	−	2642.14i	−0.613768	−	0.275109i
$99$	4364.98			0.445360
$100$	20.0425	−	34.7147i	0.00200425	−	0.00347147i
$101$	−14903.3	+	8604.41i	−1.46096	+	0.843487i	−0.999056	−	0.0434412i	$-0.986168\pi$
$101$	−14903.3	+	8604.41i	−1.46096	+	0.843487i	−0.461907	+	0.886928i	$0.652835\pi$
$102$	1764.45	+	3056.12i	0.169593	+	0.293745i
$103$	−16238.7	−	9375.42i	−1.53065	−	0.883723i	−0.999332	−	0.0365529i	$-0.988362\pi$
$103$	−16238.7	−	9375.42i	−1.53065	−	0.883723i	−0.531322	−	0.847170i	$-0.678304\pi$
$104$			15654.2i			1.44732i
$105$	5227.45	−	5791.09i	0.474145	−	0.525269i
$106$	−1776.37			−0.158096
$107$	1364.36	−	2363.14i	0.119168	−	0.206406i	−0.800270	−	0.599640i	$-0.795310\pi$
$107$	1364.36	−	2363.14i	0.119168	−	0.206406i	0.919438	+	0.393234i	$0.128644\pi$
$108$	5875.56	−	3392.26i	0.503735	−	0.290832i
$109$	5763.31	+	9982.34i	0.485086	+	0.840194i	0.999853	−	0.0171363i	$-0.00545491\pi$
$109$	5763.31	+	9982.34i	0.485086	+	0.840194i	−0.514767	+	0.857330i	$0.672122\pi$
$110$	6310.62	+	3643.44i	0.521539	+	0.301111i
$111$		−	3980.95i		−	0.323103i
$112$	−588.962	−	1820.38i	−0.0469517	−	0.145120i
$113$	9209.52			0.721241			0.360620	−	0.932713i	$-0.382565\pi$
$113$	9209.52			0.721241			0.360620	+	0.932713i	$0.382565\pi$
$114$	991.069	−	1716.58i	0.0762595	−	0.132085i
$115$	1020.47	−	589.170i	0.0771623	−	0.0445497i
$116$	−3821.53	−	6619.08i	−0.284002	−	0.491905i
$117$	−8168.95	−	4716.34i	−0.596753	−	0.344535i
$118$			7851.98i			0.563917i
$119$	2102.84	−	9832.61i	0.148495	−	0.694344i
$120$	10606.7			0.736575
$121$	1408.63	−	2439.81i	0.0962110	−	0.166642i
$122$	−4732.57	+	2732.35i	−0.317964	+	0.183577i
$123$	−5507.93	−	9540.02i	−0.364064	−	0.630578i
$124$	6137.26	+	3543.35i	0.399145	+	0.230447i
$125$			15681.7i			1.00363i
$126$	5174.98	+	1106.74i	0.325962	+	0.0697116i
$127$	5887.06			0.364998			0.182499	−	0.983206i	$-0.441581\pi$
$127$	5887.06			0.364998			0.182499	+	0.983206i	$0.441581\pi$
$128$	−3368.93	+	5835.16i	−0.205623	+	0.356150i
$129$	−12508.5	+	7221.81i	−0.751670	+	0.433977i
$130$	−7873.45	−	13637.2i	−0.465885	−	0.806936i
$131$	−7340.79	−	4238.21i	−0.427760	−	0.246967i	0.270632	−	0.962683i	$-0.412767\pi$
$131$	−7340.79	−	4238.21i	−0.427760	−	0.246967i	−0.698392	+	0.715715i	$0.746101\pi$
$132$			6089.76i			0.349504i
$133$	−5373.50	+	1738.53i	−0.303776	+	0.0982831i
$134$	−2340.85			−0.130366
$135$	−9643.77	+	16703.5i	−0.529151	+	0.916516i
$136$	11839.0	−	6835.23i	0.640083	−	0.369552i
$137$	2364.48	+	4095.40i	0.125978	+	0.218200i	0.922115	−	0.386916i	$-0.126460\pi$
$137$	2364.48	+	4095.40i	0.125978	+	0.218200i	−0.796137	+	0.605117i	$0.793127\pi$
$138$	−704.550	−	406.772i	−0.0369959	−	0.0213596i
$139$		−	15901.3i		−	0.823007i	−0.911408	−	0.411503i	$-0.865004\pi$
$139$		−	15901.3i		−	0.823007i	0.911408	−	0.411503i	$-0.134996\pi$
$140$	−7938.00	−	7165.40i	−0.405000	−	0.365582i
$141$	−6865.37			−0.345323
$142$	−5001.91	+	8663.57i	−0.248061	+	0.429655i
$143$	22127.9	−	12775.5i	1.08210	−	0.624751i
$144$	783.715	+	1357.43i	0.0377949	+	0.0654627i
$145$	18817.2	+	10864.1i	0.894993	+	0.516724i
$146$		−	9994.60i		−	0.468878i
$147$	8989.75	+	12438.6i	0.416019	+	0.575623i
$148$	−5456.79			−0.249123
$149$	21900.9	−	37933.4i	0.986482	−	1.70864i	0.351324	−	0.936254i	$-0.385731\pi$
$149$	21900.9	−	37933.4i	0.986482	−	1.70864i	0.635157	−	0.772383i	$-0.280935\pi$
$150$	68.1369	−	39.3388i	0.00302831	−	0.00174839i
$151$	14386.4	+	24918.0i	0.630956	+	1.09285i	0.987357	+	0.158515i	$0.0506706\pi$
$151$	14386.4	+	24918.0i	0.630956	+	1.09285i	−0.356400	+	0.934333i	$0.615996\pi$
$152$	−6649.80	−	3839.26i	−0.287820	−	0.166173i
$153$			8237.37i			0.351889i
$154$	−9605.20	+	10640.9i	−0.405009	+	0.448679i
$155$	−20146.6			−0.838568
$156$	6579.96	−	11396.8i	0.270380	−	0.468312i
$157$	−20200.5	+	11662.8i	−0.819528	+	0.473154i	−0.850254	−	0.526373i	$-0.823551\pi$
$157$	−20200.5	+	11662.8i	−0.819528	+	0.473154i	0.0307259	+	0.999528i	$0.490218\pi$
$158$	3240.15	+	5612.11i	0.129793	+	0.224808i
$159$	3654.94	+	2110.18i	0.144573	+	0.0834691i
$160$		−	23933.3i		−	0.934894i
$161$	713.558	+	2205.49i	0.0275282	+	0.0850849i
$162$	4568.43			0.174075
$163$	−8062.41	+	13964.5i	−0.303452	+	0.525594i	−0.976915	−	0.213627i	$-0.931472\pi$
$163$	−8062.41	+	13964.5i	−0.303452	+	0.525594i	0.673464	+	0.739220i	$0.264806\pi$
$164$	−13076.7	+	7549.86i	−0.486197	+	0.280706i
$165$	−8656.22	−	14993.0i	−0.317951	−	0.550707i
$166$	−6206.81	−	3583.50i	−0.225243	−	0.130044i
$167$		−	22132.2i		−	0.793580i	−0.917909	−	0.396790i	$-0.870124\pi$
$167$		−	22132.2i		−	0.793580i	0.917909	−	0.396790i	$-0.129876\pi$
$168$	−4363.72	+	20404.2i	−0.154610	+	0.722938i
$169$	−26654.6			−0.933253
$170$	−6875.72	+	11909.1i	−0.237914	+	0.412079i
$171$	4006.95	−	2313.41i	0.137032	−	0.0791153i
$172$	9899.13	+	17145.8i	0.334611	+	0.579563i
$173$	30654.9	+	17698.6i	1.02426	+	0.591354i	0.915334	−	0.402696i	$-0.131927\pi$
$173$	30654.9	+	17698.6i	1.02426	+	0.591354i	0.108922	+	0.994050i	$0.465260\pi$
$174$		−	15001.5i		−	0.495493i
$175$	−219.220	−	46.8833i	−0.00715822	−	0.00153088i
$176$	−4245.82			−0.137068
$177$	9327.51	−	16155.7i	0.297728	−	0.515679i
$178$	29979.0	−	17308.4i	0.946188	−	0.546282i
$179$	−3968.42	−	6873.50i	−0.123854	−	0.214522i	0.797430	−	0.603411i	$-0.206192\pi$
$179$	−3968.42	−	6873.50i	−0.123854	−	0.214522i	−0.921285	+	0.388889i	$0.872859\pi$
$180$	7586.93	+	4380.32i	0.234165	+	0.135195i
$181$			10575.9i			0.322820i	0.986887	+	0.161410i	$0.0516041\pi$
$181$			10575.9i			0.322820i	−0.986887	+	0.161410i	$0.948396\pi$
$182$	29473.3	−	9535.73i	0.889787	−	0.287880i
$183$	12983.2			0.387687
$184$	−1575.78	+	2729.33i	−0.0465435	+	0.0806158i
$185$	13434.6	−	7756.49i	0.392539	−	0.226632i
$186$	6954.76	+	12046.0i	0.201028	+	0.348191i
$187$	−19323.8	−	11156.6i	−0.552598	−	0.319043i
$188$			9410.54i			0.266256i
$189$	−28165.2	−	25423.9i	−0.788476	−	0.711735i
$190$	7724.01			0.213961
$191$	−25531.5	+	44221.9i	−0.699858	+	1.21219i	0.268657	+	0.963236i	$0.413420\pi$
$191$	−25531.5	+	44221.9i	−0.699858	+	1.21219i	−0.968515	+	0.248954i	$0.919913\pi$
$192$	−17768.5	+	10258.6i	−0.482001	+	0.278284i
$193$	−27700.5	−	47978.6i	−0.743657	−	1.28805i	−0.950820	−	0.309745i	$-0.899756\pi$
$193$	−27700.5	−	47978.6i	−0.743657	−	1.28805i	0.207163	−	0.978306i	$-0.433577\pi$
$194$	−21346.8	−	12324.6i	−0.567191	−	0.327468i
$195$			37412.1i			0.983881i
$196$	17050.0	−	12322.5i	0.443825	−	0.320765i
$197$	22045.4			0.568049			0.284025	−	0.958817i	$-0.408330\pi$
$197$	22045.4			0.568049			0.284025	+	0.958817i	$0.408330\pi$
$198$	5871.80	−	10170.3i	0.149776	−	0.259419i
$199$	1751.61	−	1011.29i	0.0442314	−	0.0255370i	−0.477721	−	0.878511i	$-0.658537\pi$
$199$	1751.61	−	1011.29i	0.0442314	−	0.0255370i	0.521953	+	0.852974i	$0.325204\pi$
$200$	−152.393	−	263.953i	−0.00380983	−	0.00659882i
$201$	4816.37	+	2780.73i	0.119214	+	0.0688284i
$202$			46298.9i			1.13467i
$203$	−28641.1	+	31729.3i	−0.695021	+	0.769960i
$204$	−11492.3			−0.276151
$205$	21463.3	−	37175.6i	0.510728	−	0.884607i
$206$	−43688.9	+	25223.8i	−1.02952	+	0.594396i
$207$	−949.511	−	1644.60i	−0.0221595	−	0.0383813i
$208$	7945.94	+	4587.59i	0.183662	+	0.106037i
$209$			12533.0i			0.286922i
$210$	−6461.05	−	19970.0i	−0.146509	−	0.452835i
$211$	70036.9			1.57312			0.786560	−	0.617514i	$-0.211860\pi$
$211$	70036.9			1.57312			0.786560	+	0.617514i	$0.211860\pi$
$212$	2892.48	−	5009.93i	0.0643575	−	0.111470i
$213$	20583.2	−	11883.7i	0.453685	−	0.261935i
$214$	−3670.69	−	6357.83i	−0.0801531	−	0.138829i
$215$	−48743.4	−	28142.0i	−1.05448	−	0.608805i
$216$		−	51586.0i		−	1.10567i
$217$	8288.56	−	38756.2i	0.176019	−	0.823042i
$218$	31011.4			0.652542
$219$	−11872.8	+	20564.2i	−0.247550	+	0.428770i
$220$	−20551.3	+	11865.3i	−0.424614	+	0.245151i
$221$	24109.3	+	41758.6i	0.493629	+	0.854991i
$222$	−9275.49	−	5355.21i	−0.188205	−	0.108660i
$223$			51085.3i			1.02727i	0.858008	+	0.513637i	$0.171702\pi$
$223$			51085.3i			1.02727i	−0.858008	+	0.513637i	$0.828298\pi$
$224$	46040.8	+	9846.46i	0.917585	+	0.196238i
$225$	183.654			0.00362774
$226$	12388.7	−	21457.9i	0.242555	−	0.420117i
$227$	44548.4	−	25720.0i	0.864530	−	0.499137i	−0.000996727	−	1.00000i	$-0.500317\pi$
$227$	44548.4	−	25720.0i	0.864530	−	0.499137i	0.865527	+	0.500863i	$0.166984\pi$
$228$	3227.54	+	5590.26i	0.0620871	+	0.107538i
$229$	1659.99	+	958.398i	0.0316545	+	0.0182757i	0.515744	−	0.856743i	$-0.327516\pi$
$229$	1659.99	+	958.398i	0.0316545	+	0.0182757i	−0.484089	+	0.875019i	$0.660849\pi$
$230$		−	3170.22i		−	0.0599286i
$231$	32403.5	−	10483.8i	0.607251	−	0.196469i
$232$	−58113.8			−1.07970
$233$	−36002.4	+	62358.1i	−0.663163	+	1.14863i	0.316617	+	0.948553i	$0.397453\pi$
$233$	−36002.4	+	62358.1i	−0.663163	+	1.14863i	−0.979780	+	0.200078i	$0.935880\pi$
$234$	−21977.9	+	12688.9i	−0.401378	+	0.231736i
$235$	−13376.5	−	23168.8i	−0.242218	−	0.419534i
$236$	−22145.1	−	12785.5i	−0.397606	−	0.229558i
$237$		−	15396.2i		−	0.274104i
$238$	−20080.9	−	18126.5i	−0.354511	−	0.320007i
$239$	−31098.1			−0.544425			−0.272212	−	0.962237i	$-0.587755\pi$
$239$	−31098.1			−0.544425			−0.272212	+	0.962237i	$0.587755\pi$
$240$	3108.38	−	5383.88i	0.0539650	−	0.0934701i
$241$	−70827.4	+	40892.2i	−1.21946	+	0.704055i	−0.964802	−	0.262977i	$-0.915296\pi$
$241$	−70827.4	+	40892.2i	−1.21946	+	0.704055i	−0.254656	+	0.967032i	$0.581962\pi$
$242$	−3789.79	−	6564.10i	−0.0647119	−	0.112084i
$243$	44918.8	+	25933.9i	0.760705	+	0.439193i
$244$		−	17796.5i		−	0.298920i
$245$	−24461.4	+	54573.5i	−0.407520	+	0.909179i
$246$	−29637.3			−0.489742
$247$	13541.9	−	23455.3i	0.221966	−	0.384456i
$248$	46664.5	−	26941.8i	0.758723	−	0.438049i
$249$	8513.82	+	14746.4i	0.137317	+	0.237841i
$250$	36537.8	+	21095.1i	0.584604	+	0.337522i
$251$		−	118566.i		−	1.88196i	−0.338456	−	0.940982i	$-0.609905\pi$
$251$		−	118566.i		−	1.88196i	0.338456	−	0.940982i	$-0.390095\pi$
$252$	−11547.8	+	12793.0i	−0.181844	+	0.201451i
$253$	5144.03			0.0803642
$254$	7919.32	−	13716.7i	0.122750	−	0.212609i
$255$	28294.1	−	16335.6i	0.435126	−	0.251220i
$256$	34742.6	+	60175.9i	0.530130	+	0.918212i
$257$	31423.9	+	18142.6i	0.475767	+	0.274684i	0.718651	−	0.695371i	$-0.244760\pi$
$257$	31423.9	+	18142.6i	0.475767	+	0.274684i	−0.242884	+	0.970055i	$0.578093\pi$
$258$			38859.4i			0.583789i
$259$	9394.08	+	29035.5i	0.140041	+	0.432842i
$260$	51281.7			0.758605
$261$	17508.7	−	30326.0i	0.257024	−	0.445179i
$262$	−19749.8	+	11402.5i	−0.287713	+	0.166111i
$263$	−65657.8	−	113723.i	−0.949237	−	1.64413i	−0.747037	−	0.664783i	$-0.768524\pi$
$263$	−65657.8	−	113723.i	−0.949237	−	1.64413i	−0.202200	−	0.979344i	$-0.564809\pi$
$264$	40099.9	+	23151.7i	0.575355	+	0.332181i
$265$			16445.9i			0.234189i
$266$	−3177.75	+	14858.8i	−0.0449114	+	0.210000i
$267$	−82243.8			−1.15367
$268$	3811.62	−	6601.93i	0.0530690	−	0.0919181i
$269$	81091.0	−	46817.9i	1.12065	−	0.647005i	0.179080	−	0.983835i	$-0.442688\pi$
$269$	81091.0	−	46817.9i	1.12065	−	0.647005i	0.941566	+	0.336830i	$0.109355\pi$
$270$	25945.8	+	44939.4i	0.355909	+	0.616452i
$271$	−15686.7	−	9056.73i	−0.213596	−	0.123320i	0.389385	−	0.921075i	$-0.372687\pi$
$271$	−15686.7	−	9056.73i	−0.213596	−	0.123320i	−0.602982	+	0.797755i	$0.706021\pi$
$272$		−	8012.50i		−	0.108300i
$273$	−71970.0	−	15391.8i	−0.965665	−	0.206521i
$274$	12722.9			0.169466
$275$	−248.739	+	430.829i	−0.00328911	+	0.00569691i
$276$	2294.45	−	1324.70i	0.0301204	−	0.0173900i
$277$	29527.9	+	51143.8i	0.384834	+	0.666552i	0.991746	−	0.128217i	$-0.0409255\pi$
$277$	29527.9	+	51143.8i	0.384834	+	0.666552i	−0.606912	+	0.794769i	$0.707592\pi$
$278$	−37049.6	−	21390.6i	−0.479395	−	0.276779i
$279$			32468.4i			0.417112i
$280$	−77361.0	+	25029.2i	−0.986748	+	0.319250i
$281$	−91604.1			−1.16012			−0.580059	−	0.814574i	$-0.696971\pi$
$281$	−91604.1			−1.16012			−0.580059	+	0.814574i	$0.696971\pi$
$282$	−9235.34	+	15996.1i	−0.116133	+	0.201148i
$283$	10085.9	−	5823.09i	0.125933	−	0.0727077i	−0.435710	−	0.900087i	$-0.643503\pi$
$283$	10085.9	−	5823.09i	0.125933	−	0.0727077i	0.561643	+	0.827379i	$0.310169\pi$
$284$	−16289.3	−	28213.9i	−0.201961	−	0.349806i
$285$	−15892.4	−	9175.49i	−0.195659	−	0.112964i
$286$		−	68742.9i		−	0.840419i
$287$	62684.8	+	56583.8i	0.761025	+	0.686955i
$288$	−38571.1			−0.465026
$289$	−20706.3	+	35864.4i	−0.247918	+	0.429406i
$290$	50626.2	−	29229.0i	0.601976	−	0.347551i
$291$	29281.2	+	50716.5i	0.345782	+	0.598912i
$292$	28187.9	+	16274.3i	0.330596	+	0.190870i
$293$			21920.3i			0.255336i	0.991817	+	0.127668i	$0.0407492\pi$
$293$			21920.3i			0.255336i	−0.991817	+	0.127668i	$0.959251\pi$
$294$	41074.7	−	4213.29i	0.475204	−	0.0487446i
$295$	72695.0			0.835334
$296$	−20745.3	+	35931.9i	−0.236775	+	0.410107i
$297$	−72919.0	+	42099.8i	−0.826662	+	0.477273i
$298$	−58922.5	−	102057.i	−0.663512	−	1.14924i
$299$	−9626.92	−	5558.11i	−0.107683	−	0.0621705i
$300$			256.223i			0.00284693i
$301$	74190.7	−	82190.2i	0.818873	−	0.907167i
$302$	77411.0			0.848767
$303$	54999.3	−	95261.6i	0.599062	−	1.03761i
$304$	−3897.56	+	2250.26i	−0.0421741	+	0.0243492i
$305$	25296.6	+	43815.0i	0.271933	+	0.471002i
$306$	19192.8	+	11081.0i	0.204973	+	0.118341i
$307$		−	18472.4i		−	0.195995i	−0.995187	−	0.0979977i	$-0.968756\pi$
$307$		−	18472.4i		−	0.195995i	0.995187	−	0.0979977i	$-0.0312438\pi$
$308$	−14370.4	−	44416.3i	−0.151484	−	0.468211i
$309$	119855.			1.25528
$310$	−27101.4	+	46940.9i	−0.282012	+	0.488459i
$311$	−146238.	+	84430.6i	−1.51196	+	0.872929i	−0.512055	+	0.858953i	$0.671116\pi$
$311$	−146238.	+	84430.6i	−1.51196	+	0.872929i	−0.999902	+	0.0139764i	$0.995551\pi$
$312$	−50030.7	−	86655.6i	−0.513957	−	0.890200i
$313$	12640.9	+	7298.25i	0.129030	+	0.0744955i	0.563126	−	0.826371i	$-0.309599\pi$
$313$	12640.9	+	7298.25i	0.129030	+	0.0744955i	−0.434096	+	0.900867i	$0.642932\pi$
$314$			62755.5i			0.636491i
$315$	10246.4	−	47910.8i	0.103264	−	0.482850i
$316$	−21103.9			−0.211343
$317$	−2738.78	+	4743.71i	−0.0272545	+	0.0472062i	−0.879331	−	0.476211i	$-0.842010\pi$
$317$	−2738.78	+	4743.71i	−0.0272545	+	0.0472062i	0.852076	+	0.523417i	$0.175343\pi$
$318$	9833.32	−	5677.27i	0.0972402	−	0.0561417i
$319$	47427.3	+	82146.4i	0.466065	+	0.807248i
$320$	−69240.4	−	39976.0i	−0.676176	−	0.390390i
$321$			17441.9i			0.169272i
$322$	6098.60	+	1304.27i	0.0588191	+	0.0125793i
$323$	−23651.7			−0.226703
$324$	−7438.82	+	12884.4i	−0.0708621	+	0.122737i
$325$	931.018	−	537.523i	0.00881437	−	0.00508898i
$326$	21691.2	+	37570.3i	0.204103	+	0.353516i
$327$	−63807.0	−	36839.0i	−0.596723	−	0.344518i
$328$			114811.i			1.06717i
$329$	50073.3	−	16200.6i	0.462609	−	0.149672i
$330$	−46577.6			−0.427710
$331$	24215.3	−	41942.2i	0.221021	−	0.382820i	−0.734097	−	0.679045i	$-0.762394\pi$
$331$	24215.3	−	41942.2i	0.221021	−	0.382820i	0.955118	+	0.296224i	$0.0957276\pi$
$332$	20213.2	−	11670.1i	0.183383	−	0.105876i
$333$	−12500.4	−	21651.4i	−0.112729	−	0.195253i
$334$	−51567.2	−	29772.4i	−0.462254	−	0.266883i
$335$			21672.0i			0.193112i
$336$	9078.20	+	8194.63i	0.0804120	+	0.0725856i
$337$	−42519.2			−0.374391			−0.187196	−	0.982323i	$-0.559940\pi$
$337$	−42519.2			−0.374391			−0.187196	+	0.982323i	$0.559940\pi$
$338$	−35856.0	+	62104.5i	−0.313855	+	0.543613i
$339$	−50980.5	+	29433.6i	−0.443613	+	0.256120i
$340$	−22391.6	−	38783.4i	−0.193699	−	0.335497i
$341$	−76166.7	−	43974.9i	−0.655023	−	0.378178i
$342$		−	12448.1i		−	0.106427i
$343$	−94919.9	−	69508.9i	−0.806806	−	0.590816i
$344$	150536.			1.27210
$345$	−3765.97	+	6522.84i	−0.0316401	+	0.0548023i
$346$	82474.5	−	47616.7i	0.688918	−	0.397747i
$347$	42622.3	+	73824.0i	0.353979	+	0.613110i	0.986943	−	0.161071i	$-0.0514949\pi$
$347$	42622.3	+	73824.0i	0.353979	+	0.613110i	−0.632963	+	0.774182i	$0.718162\pi$
$348$	42309.1	+	24427.2i	0.349361	+	0.201704i
$349$		−	61875.9i		−	0.508008i	−0.967203	−	0.254004i	$-0.918252\pi$
$349$		−	61875.9i		−	0.508008i	0.967203	−	0.254004i	$-0.0817477\pi$
$350$	−404.134	+	447.709i	−0.00329905	+	0.00365477i
$351$	181955.			1.47689
$352$	52240.3	−	90482.8i	0.421619	−	0.730265i
$353$	65034.9	−	37547.9i	0.521912	−	0.301326i	−0.215805	−	0.976437i	$-0.569237\pi$
$353$	65034.9	−	37547.9i	0.521912	−	0.301326i	0.737716	+	0.675111i	$0.235904\pi$
$354$	−25094.9	−	43465.6i	−0.200253	−	0.346848i
$355$	80208.8	+	46308.6i	0.636451	+	0.367455i
$356$			112734.i			0.889516i
$357$	19784.4	+	61150.3i	0.155234	+	0.479802i
$358$	−21353.4			−0.166610
$359$	−40601.7	+	70324.1i	−0.315032	+	0.545652i	−0.979444	−	0.201715i	$-0.935349\pi$
$359$	−40601.7	+	70324.1i	−0.315032	+	0.545652i	0.664412	+	0.747366i	$0.268682\pi$
$360$	57687.1	−	33305.7i	0.445117	−	0.256988i
$361$	−58518.1	−	101356.i	−0.449030	−	0.777743i
$362$	24641.5	+	14226.8i	0.188040	+	0.108565i
$363$			18007.8i			0.136662i
$364$	−21097.9	+	98651.2i	−0.159234	+	0.744560i
$365$	−92531.7			−0.694552
$366$	17465.2	−	30250.6i	0.130380	−	0.225825i
$367$	−52701.5	+	30427.2i	−0.391283	+	0.225907i	−0.682716	−	0.730684i	$-0.739201\pi$
$367$	−52701.5	+	30427.2i	−0.391283	+	0.225907i	0.291433	+	0.956591i	$0.405868\pi$
$368$	923.591	+	1599.71i	0.00681999	+	0.0118126i
$369$	−59912.5	−	34590.5i	−0.440012	−	0.254041i
$370$		−	41736.4i		−	0.304868i
$371$	−31637.3	−	6766.07i	−0.229853	−	0.0491574i
$372$	−45298.0			−0.327336
$373$	−2508.99	+	4345.69i	−0.0180335	+	0.0312350i	−0.874901	−	0.484301i	$-0.839074\pi$
$373$	−2508.99	+	4345.69i	−0.0180335	+	0.0312350i	0.856868	+	0.515536i	$0.172407\pi$
$374$	−51989.0	+	30015.9i	−0.371680	+	0.214589i
$375$	−50118.5	−	86807.8i	−0.356398	−	0.617300i
$376$	61966.6	+	35776.4i	0.438311	+	0.253059i
$377$		−	204980.i		−	1.44221i
$378$	−97124.8	+	31423.6i	−0.679746	+	0.219924i
$379$	−267609.			−1.86304			−0.931520	−	0.363691i	$-0.881517\pi$
$379$	−267609.			−1.86304			−0.931520	+	0.363691i	$0.881517\pi$
$380$	−12577.1	+	21784.1i	−0.0870989	+	0.150860i
$381$	−32588.5	+	18815.0i	−0.224499	+	0.129615i
$382$	68690.4	+	118975.i	0.470727	+	0.815324i
$383$	222428.	+	128419.i	1.51632	+	0.875449i	0.999816	+	0.0191663i	$0.00610121\pi$
$383$	222428.	+	128419.i	1.51632	+	0.875449i	0.516507	+	0.856283i	$0.327232\pi$
$384$		−	43068.3i		−	0.292076i
$385$	98515.0	+	88926.6i	0.664631	+	0.599943i
$386$	−149052.			−1.00037
$387$	−45353.9	+	78555.3i	−0.302826	+	0.524510i
$388$	69518.4	−	40136.5i	0.461781	−	0.266610i
$389$	22017.4	+	38135.2i	0.145501	+	0.252015i	0.929560	−	0.368671i	$-0.120187\pi$
$389$	22017.4	+	38135.2i	0.145501	+	0.252015i	−0.784059	+	0.620687i	$0.786854\pi$
$390$	87168.9	+	50327.0i	0.573103	+	0.330881i
$391$			9707.56i			0.0634975i
$392$	−16321.7	−	159118.i	−0.106217	−	1.03549i
$393$	54181.2			0.350803
$394$	29655.7	−	51365.1i	0.191036	−	0.330884i
$395$	51957.9	−	29997.9i	0.333010	−	0.192263i
$396$	19122.2	+	33120.7i	0.121941	+	0.211207i
$397$	−45928.2	−	26516.7i	−0.291406	−	0.168243i	0.347170	−	0.937802i	$-0.387143\pi$
$397$	−45928.2	−	26516.7i	−0.291406	−	0.168243i	−0.638576	+	0.769559i	$0.720476\pi$
$398$		−	5441.58i		−	0.0343526i
$399$	24189.3	−	26797.5i	0.151942	−	0.168325i
$400$	−178.641			−0.00111650
$401$	101739.	−	176217.i	0.632702	−	1.09587i	−0.354296	−	0.935133i	$-0.615279\pi$
$401$	101739.	−	176217.i	0.632702	−	1.09587i	0.986997	−	0.160738i	$-0.0513873\pi$
$402$	12958.0	−	7481.33i	0.0801839	−	0.0462942i
$403$	95029.4	+	164596.i	0.585124	+	1.01346i
$404$	−130578.	−	75389.0i	−0.800029	−	0.461897i
$405$		−	42295.3i		−	0.257859i
$406$	35400.0	+	109415.i	0.214759	+	0.663783i
$407$	67721.8			0.408827
$408$	−43690.7	+	75674.6i	−0.262464	+	0.454600i
$409$	158124.	−	91293.1i	0.945262	−	0.545747i	0.0536557	−	0.998559i	$-0.482913\pi$
$409$	158124.	−	91293.1i	0.945262	−	0.545747i	0.891606	+	0.452813i	$0.149579\pi$
$410$	−57745.3	−	100018.i	−0.343518	−	0.594990i
$411$	−26177.7	−	15113.7i	−0.154970	−	0.0894721i
$412$		−	164289.i		−	0.967861i
$413$	−29907.6	+	139844.i	−0.175340	+	0.819869i
$414$	−5109.16			−0.0298091
$415$	−33176.7	+	57463.7i	−0.192636	+	0.333655i
$416$	−195533.	+	112891.i	−1.12988	+	0.652337i
$417$	50820.5	+	88023.7i	0.292258	+	0.506206i
$418$	29201.6	+	16859.5i	0.167130	+	0.0964924i
$419$		−	88028.9i		−	0.501415i	−0.968063	−	0.250707i	$-0.919337\pi$
$419$		−	88028.9i		−	0.501415i	0.968063	−	0.250707i	$-0.0806632\pi$
$420$	66842.4	+	14295.2i	0.378925	+	0.0810384i
$421$	9478.51			0.0534781			0.0267390	−	0.999642i	$-0.491488\pi$
$421$	9478.51			0.0534781			0.0267390	+	0.999642i	$0.491488\pi$
$422$	94214.2	−	163184.i	0.529043	−	0.916330i
$423$	−37339.0	+	21557.7i	−0.208681	+	0.120482i
$424$	−21992.9	−	38092.9i	−0.122335	−	0.211891i
$425$	−813.038	−	469.408i	−0.00450125	−	0.00259880i
$426$		−	63944.3i		−	0.352357i
$427$	−94694.8	+	30637.3i	−0.519362	+	0.168033i
$428$	23908.1			0.130514
$429$	−81661.0	+	141441.i	−0.443711	+	0.768530i
$430$	−131140.	+	75713.7i	−0.709248	+	0.409484i
$431$	2374.01	+	4111.90i	0.0127799	+	0.0221354i	0.872345	−	0.488891i	$-0.162599\pi$
$431$	2374.01	+	4111.90i	0.0127799	+	0.0221354i	−0.859565	+	0.511027i	$0.829265\pi$
$432$	−26184.7	−	15117.7i	−0.140307	−	0.0810063i
$433$			202469.i			1.07990i	0.841698	+	0.539949i	$0.181556\pi$
$433$			202469.i			1.07990i	−0.841698	+	0.539949i	$0.818444\pi$
$434$	−79151.0	−	71447.3i	−0.420220	−	0.379321i
$435$	−138887.			−0.733977
$436$	−50496.2	+	87461.9i	−0.265635	+	0.460093i
$437$	4722.10	−	2726.30i	0.0247270	−	0.0142762i
$438$	31942.7	+	55326.3i	0.166503	+	0.288392i
$439$	−161616.	−	93308.9i	−0.838599	−	0.484165i	0.0181886	−	0.999835i	$-0.494210\pi$
$439$	−161616.	−	93308.9i	−0.838599	−	0.484165i	−0.856788	+	0.515669i	$0.827543\pi$
$440$			180435.i			0.932000i
$441$	87951.1	+	39422.2i	0.452235	+	0.202705i
$442$	129728.			0.664034
$443$	161125.	−	279077.i	0.821023	−	1.42205i	−0.0838984	−	0.996474i	$-0.526737\pi$
$443$	161125.	−	279077.i	0.821023	−	1.42205i	0.904921	−	0.425579i	$-0.139930\pi$
$444$	30206.7	−	17439.9i	0.153228	−	0.0884662i
$445$	−160244.	−	277551.i	−0.809211	−	1.40160i
$446$	119027.	+	68720.4i	0.598379	+	0.345474i
$447$			279980.i			1.40124i
$448$	105389.	−	116752.i	0.525095	−	0.581712i
$449$	161215.			0.799674			0.399837	−	0.916586i	$-0.369067\pi$
$449$	161215.			0.799674			0.399837	+	0.916586i	$0.369067\pi$
$450$	247.053	−	427.908i	0.00122001	−	0.00211313i
$451$	162290.	−	93698.0i	0.797880	−	0.460656i
$452$	40345.4	+	69880.2i	0.197477	+	0.342040i
$453$	−159276.	−	91957.9i	−0.776164	−	0.448118i
$454$		−	138395.i		−	0.671442i
$455$	−88283.4	−	272869.i	−0.426438	−	1.31805i
$456$	49081.0			0.236039
$457$	−191544.	+	331764.i	−0.917141	+	1.58853i	−0.113405	+	0.993549i	$0.536176\pi$
$457$	−191544.	+	331764.i	−0.917141	+	1.58853i	−0.803736	+	0.594986i	$0.797158\pi$
$458$	4466.08	−	2578.49i	0.0212910	−	0.0122923i
$459$	−79448.7	−	137609.i	−0.377104	−	0.653163i
$460$	8941.03	+	5162.11i	0.0422544	+	0.0243956i
$461$			221916.i			1.04421i	0.852883	+	0.522103i	$0.174852\pi$
$461$			221916.i			1.04421i	−0.852883	+	0.522103i	$0.825148\pi$
$462$	19162.6	−	89602.0i	0.0897783	−	0.419792i
$463$	260981.			1.21744			0.608720	−	0.793385i	$-0.291683\pi$
$463$	260981.			1.21744			0.608720	+	0.793385i	$0.291683\pi$
$464$	−17030.8	+	29498.2i	−0.0791040	+	0.137012i
$465$	111524.	−	64388.4i	0.515777	−	0.297784i
$466$	96861.5	+	167769.i	0.446046	+	0.772574i
$467$	261408.	+	150924.i	1.19863	+	0.692029i	0.960250	−	0.279143i	$-0.0900503\pi$
$467$	261408.	+	150924.i	1.19863	+	0.692029i	0.238380	+	0.971172i	$0.423384\pi$
$468$		−	82646.0i		−	0.377338i
$469$	−41690.6	−	8916.12i	−0.189536	−	0.0405350i
$470$	−71976.7			−0.325834
$471$	74548.4	−	129122.i	0.336044	−	0.582046i
$472$	−168380.	+	97214.0i	−0.755798	+	0.436360i
$473$	−122854.	−	212789.i	−0.549118	−	0.951100i
$474$	−35872.5	−	20711.0i	−0.159663	−	0.0921817i
$475$			527.321i			0.00233716i
$476$	83820.3	−	27119.0i	0.369943	−	0.119691i
$477$	26504.4			0.116488
$478$	−41833.4	+	72457.5i	−0.183091	+	0.317123i
$479$	−150194.	+	86714.3i	−0.654607	+	0.377937i	−0.790219	−	0.612825i	$-0.790033\pi$
$479$	−150194.	+	86714.3i	−0.654607	+	0.377937i	0.135612	+	0.990762i	$0.456700\pi$
$480$	76490.7	+	132486.i	0.331991	+	0.575025i
$481$	−126740.	−	73173.2i	−0.547800	−	0.316273i
$482$			220034.i			0.947100i
$483$	−10998.7	−	9928.21i	−0.0471463	−	0.0425576i
$484$	24683.8			0.105371
$485$	−114103.	+	197632.i	−0.485080	+	0.840184i
$486$	120850.	−	69773.0i	0.511653	−	0.295403i
$487$	−123046.	−	213122.i	−0.518812	−	0.898609i	−0.999761	−	0.0218604i	$-0.993041\pi$
$487$	−123046.	−	213122.i	−0.518812	−	0.898609i	0.480949	−	0.876749i	$-0.340292\pi$
$488$	−117186.	−	67657.6i	−0.492082	−	0.284104i
$489$		−	103070.i		−	0.431035i
$490$	94248.8	+	130407.i	0.392540	+	0.543136i
$491$	−264510.			−1.09718			−0.548591	−	0.836091i	$-0.684835\pi$
$491$	−264510.			−1.09718			−0.548591	+	0.836091i	$0.684835\pi$
$492$	48258.6	−	83586.4i	0.199363	−	0.345307i
$493$	−155023.	+	89502.4i	−0.637825	+	0.368248i
$494$	−36433.3	−	63104.4i	−0.149295	−	0.258586i
$495$	−94158.0	−	54362.1i	−0.384279	−	0.221864i
$496$		−	31582.1i		−	0.128374i
$497$	−122083.	+	135247.i	−0.494246	+	0.547537i
$498$	45811.4			0.184720
$499$	99962.3	−	173140.i	0.401453	−	0.695338i	−0.592448	−	0.805609i	$-0.701839\pi$
$499$	99962.3	−	173140.i	0.401453	−	0.695338i	0.993902	+	0.110271i	$0.0351719\pi$
$500$	−118990.	+	68698.7i	−0.475959	+	0.274795i
$501$	70734.3	+	122515.i	0.281809	+	0.488107i
$502$	−276254.	−	159495.i	−1.09623	−	0.632908i
$503$			8534.43i			0.0337317i	0.999858	+	0.0168659i	$0.00536883\pi$
$503$			8534.43i			0.0337317i	−0.999858	+	0.0168659i	$0.994631\pi$
$504$	40337.3	+	124676.i	0.158798	+	0.490819i
$505$	428643.			1.68079
$506$	6919.79	−	11985.4i	0.0270266	−	0.0468115i
$507$	147550.	−	85188.1i	0.574015	−	0.331408i
$508$	25790.2	+	44670.0i	0.0999373	+	0.173096i
$509$	333893.	+	192773.i	1.28876	+	0.744064i	0.978433	−	0.206566i	$-0.0662289\pi$
$509$	333893.	+	192773.i	1.28876	+	0.744064i	0.310325	+	0.950631i	$0.399562\pi$
$510$		−	87899.0i		−	0.337943i
$511$	38068.7	−	178004.i	0.145790	−	0.681693i
$512$	79138.3			0.301888
$513$	−44625.3	+	77293.3i	−0.169569	+	0.293702i
$514$	84543.4	−	48811.2i	0.320003	−	0.184754i
$515$	233526.	+	404479.i	0.880483	+	1.52504i
$516$	−109596.	−	63275.1i	−0.411618	−	0.237648i
$517$		−	116790.i		−	0.436943i
$518$	80288.8	+	17170.9i	0.299223	+	0.0639931i
$519$	−226259.			−0.839984
$520$	194960.	−	337680.i	0.721005	−	1.24882i
$521$	57523.3	−	33211.1i	0.211918	−	0.122351i	−0.390284	−	0.920694i	$-0.627623\pi$
$521$	57523.3	−	33211.1i	0.211918	−	0.122351i	0.602202	+	0.798343i	$0.294290\pi$
$522$	−47105.8	−	81589.6i	−0.172875	−	0.299429i
$523$	238995.	+	137984.i	0.873748	+	0.504459i	0.868592	−	0.495528i	$-0.165025\pi$
$523$	238995.	+	137984.i	0.873748	+	0.504459i	0.00515609	+	0.999987i	$0.498359\pi$
$524$		−	74267.5i		−	0.270481i
$525$	1363.36	−	441.099i	0.00494643	−	0.00160036i
$526$	−353293.			−1.27692
$527$	82987.2	−	143738.i	0.298806	−	0.517548i
$528$	23503.3	−	13569.6i	0.0843063	−	0.0486743i
$529$	138802.	+	240411.i	0.496001	+	0.859100i
$530$	38318.5	+	22123.2i	0.136413	+	0.0787583i
$531$		−	117156.i		−	0.415504i
$532$	−36732.0	−	33156.9i	−0.129784	−	0.117152i
$533$	−404961.			−1.42547
$534$	−110635.	+	191626.i	−0.387981	+	0.672002i
$535$	−58861.9	+	33983.9i	−0.205649	+	0.118731i
$536$	−28981.6	−	50197.7i	−0.100877	−	0.174725i
$537$	43935.4	+	25366.1i	0.152358	+	0.0879640i
$538$		−	251919.i		−	0.870356i
$539$	−211599.	+	152929.i	−0.728345	+	0.526395i
$540$	−168991.			−0.579530
$541$	−73123.9	+	126654.i	−0.249842	+	0.432738i	−0.963482	−	0.267774i	$-0.913712\pi$
$541$	−73123.9	+	126654.i	−0.249842	+	0.432738i	0.713640	+	0.700512i	$0.247045\pi$
$542$	−42203.8	+	24366.4i	−0.143666	+	0.0829454i
$543$	−33800.5	−	58544.2i	−0.114637	−	0.198556i
$544$	170755.	+	98585.3i	0.576999	+	0.333130i
$545$		−	287109.i		−	0.966615i
$546$	−132677.	+	146983.i	−0.445052	+	0.493039i
$547$	14872.2			0.0497050			0.0248525	−	0.999691i	$-0.492088\pi$
$547$	14872.2			0.0497050			0.0248525	+	0.999691i	$0.492088\pi$
$548$	−20716.8	+	35882.5i	−0.0689860	+	0.119487i
$549$	70612.6	−	40768.2i	0.234281	−	0.135262i
$550$	669.211	+	1159.11i	0.00221227	+	0.00383176i
$551$	87074.2	+	50272.3i	0.286805	+	0.165587i
$552$		−	20144.7i		−	0.0661124i
$553$	36331.2	+	112294.i	0.118804	+	0.367202i
$554$	158885.			0.517681
$555$	−49579.4	+	85874.1i	−0.160959	+	0.278789i
$556$	120656.	−	69661.0i	0.390302	−	0.225341i
$557$	−109394.	−	189476.i	−0.352600	−	0.610721i	0.634104	−	0.773248i	$-0.281369\pi$
$557$	−109394.	−	189476.i	−0.352600	−	0.610721i	−0.986704	+	0.162526i	$0.948036\pi$
$558$	75650.4	+	43676.8i	0.242965	+	0.140276i
$559$			530972.i			1.69921i
$560$	−9966.68	+	46602.9i	−0.0317815	+	0.148606i
$561$	142626.			0.453181
$562$	−123227.	+	213435.i	−0.390150	+	0.675760i
$563$	−131884.	+	76143.4i	−0.416079	+	0.240224i	−0.693399	−	0.720554i	$-0.743887\pi$
$563$	−131884.	+	76143.4i	−0.416079	+	0.240224i	0.277319	+	0.960778i	$0.410554\pi$
$564$	−30076.0	−	52093.2i	−0.0945501	−	0.163766i
$565$	−198661.	−	114697.i	−0.622323	−	0.359298i
$566$		−	31333.0i		−	0.0978070i
$567$	81364.0	+	17400.8i	0.253085	+	0.0541257i
$568$	−247711.			−0.767802
$569$	232673.	−	403002.i	0.718657	−	1.24475i	−0.242875	−	0.970058i	$-0.578090\pi$
$569$	232673.	−	403002.i	0.718657	−	1.24475i	0.961532	−	0.274693i	$-0.0885762\pi$
$570$	−42757.2	+	24685.9i	−0.131601	+	0.0759799i
$571$	−278804.	−	482902.i	−0.855118	−	1.48111i	−0.876535	−	0.481338i	$-0.840151\pi$
$571$	−278804.	−	482902.i	−0.855118	−	1.48111i	0.0214168	−	0.999771i	$-0.493182\pi$
$572$	193877.	+	111935.i	0.592562	+	0.342116i
$573$		−	326394.i		−	0.994108i
$574$	216163.	−	69936.7i	0.656080	−	0.212267i
$575$	216.432			0.000654616
$576$	−64425.6	+	111588.i	−0.194184	+	0.336337i
$577$	364388.	−	210380.i	1.09449	−	0.631905i	0.159723	−	0.987162i	$-0.448940\pi$
$577$	364388.	−	210380.i	1.09449	−	0.631905i	0.934769	+	0.355257i	$0.115607\pi$
$578$	55708.6	+	96490.1i	0.166750	+	0.288820i
$579$	306679.	+	177061.i	0.914801	+	0.528160i
$580$			190376.i			0.565921i
$581$	−96894.3	−	87463.7i	−0.287042	−	0.259105i
$582$	157557.			0.465149
$583$	−35897.3	+	62175.9i	−0.105615	+	0.182930i
$584$	214326.	−	123741.i	0.628420	−	0.362819i
$585$	117476.	+	203475.i	0.343272	+	0.594564i
$586$	51073.7	+	29487.4i	0.148731	+	0.0858700i
$587$		−	223137.i		−	0.647584i	−0.946128	−	0.323792i	$-0.895042\pi$
$587$		−	223137.i		−	0.647584i	0.946128	−	0.323792i	$-0.104958\pi$
$588$	−54999.6	+	122704.i	−0.159076	+	0.354899i
$589$	−93225.7			−0.268723
$590$	97789.8	−	169377.i	0.280925	−	0.486576i
$591$	−122035.	+	70457.0i	−0.349390	+	0.201720i
$592$	12159.2	+	21060.3i	0.0346945	+	0.0600927i
$593$	−545091.	−	314708.i	−1.55010	−	0.894950i	−0.998133	−	0.0610840i	$-0.980544\pi$
$593$	−545091.	−	314708.i	−1.55010	−	0.894950i	−0.551967	−	0.833866i	$-0.686122\pi$
$594$			226532.i			0.642032i
$595$	−167818.	+	185913.i	−0.474028	+	0.525140i
$596$	383776.			1.08040
$597$	−6464.16	+	11196.2i	−0.0181369	+	0.0314140i
$598$	−25900.4	+	14953.6i	−0.0724277	+	0.0418161i
$599$	221078.	+	382919.i	0.616158	+	1.06722i	0.990180	+	0.139797i	$0.0446451\pi$
$599$	221078.	+	382919.i	0.616158	+	1.06722i	−0.374022	+	0.927420i	$0.622022\pi$
$600$	1687.18	+	974.095i	0.00468662	+	0.00270582i
$601$			243251.i			0.673449i	0.941603	+	0.336725i	$0.109319\pi$
$601$			243251.i			0.673449i	−0.941603	+	0.336725i	$0.890681\pi$
$602$	−91698.7	−	283425.i	−0.253029	−	0.782069i
$603$	34926.7			0.0960557
$604$	−126049.	+	218323.i	−0.345514	+	0.598448i
$605$	−60771.6	+	35086.5i	−0.166031	+	0.0958582i
$606$	−147971.	−	256293.i	−0.402932	−	0.697898i
$607$	−370728.	−	214040.i	−1.00619	−	0.580922i	−0.0961135	−	0.995370i	$-0.530641\pi$
$607$	−370728.	−	214040.i	−1.00619	−	0.580922i	−0.910073	+	0.414448i	$0.863975\pi$
$608$		−	110748.i		−	0.299591i
$609$	57139.8	−	267178.i	0.154065	−	0.720388i
$610$	136117.			0.365807
$611$	−126191.	+	218569.i	−0.338023	+	0.585473i
$612$	−62503.7	+	36086.5i	−0.166879	+	0.0963479i
$613$	151423.	+	262272.i	0.402968	+	0.697961i	0.994083	−	0.108626i	$-0.0346452\pi$
$613$	151423.	+	262272.i	0.402968	+	0.697961i	−0.591114	+	0.806588i	$0.701312\pi$
$614$	−43040.1	−	24849.2i	−0.114166	−	0.0659137i
$615$			274387.i			0.725459i
$616$	−347106.	−	74233.3i	−0.914745	−	0.195631i
$617$	−298440.			−0.783947			−0.391974	−	0.919976i	$-0.628208\pi$
$617$	−298440.			−0.783947			−0.391974	+	0.919976i	$0.628208\pi$
$618$	161230.	−	279259.i	0.422152	−	0.731189i
$619$	−483872.	+	279363.i	−1.26284	+	0.729102i	−0.973623	−	0.228161i	$-0.926729\pi$
$619$	−483872.	+	279363.i	−1.26284	+	0.729102i	−0.289218	+	0.957263i	$0.593395\pi$
$620$	−88258.8	−	152869.i	−0.229602	−	0.397682i
$621$	31724.1	+	18315.9i	0.0822632	+	0.0474947i
$622$			454307.i			1.17427i
$623$	599854.	−	194076.i	1.54550	−	0.500028i
$624$	−58647.7			−0.150620
$625$	193872.	−	335797.i	0.496313	−	0.859640i
$626$	34009.4	−	19635.3i	0.0867860	−	0.0501059i
$627$	−40055.5	−	69378.2i	−0.101889	−	0.176477i
$628$	−176990.	−	102185.i	−0.448777	−	0.259101i
$629$			127801.i			0.323023i
$630$	−97847.2	−	88323.8i	−0.246529	−	0.222534i
$631$	569114.			1.42936			0.714678	−	0.699454i	$-0.246573\pi$
$631$	569114.			1.42936			0.714678	+	0.699454i	$0.246573\pi$
$632$	−80231.6	+	138965.i	−0.200868	+	0.347914i
$633$	−387698.	+	223837.i	−0.967578	+	0.558631i
$634$	7368.46	+	12762.5i	0.0183315	+	0.0317511i
$635$	−126991.	−	73318.4i	−0.314939	−	0.181830i
$636$			36977.4i			0.0914160i
$637$	561242.	−	57570.1i	1.38316	−	0.141879i
$638$	255198.			0.626954
$639$	74631.3	−	129265.i	0.182776	−	0.316577i
$640$	145344.	−	83914.4i	0.354844	−	0.204869i
$641$	−135617.	−	234895.i	−0.330063	−	0.571686i	0.652461	−	0.757823i	$-0.273737\pi$
$641$	−135617.	−	234895.i	−0.330063	−	0.571686i	−0.982524	+	0.186136i	$0.940403\pi$
$642$	40639.2	+	23463.0i	0.0985995	+	0.0569264i
$643$		−	623039.i		−	1.50693i	−0.657488	−	0.753465i	$-0.728381\pi$
$643$		−	623039.i		−	1.50693i	0.657488	−	0.753465i	$-0.271619\pi$
$644$	−13608.9	+	15076.2i	−0.0328133	+	0.0363514i
$645$	359767.			0.864772
$646$	−31816.5	+	55107.8i	−0.0762407	+	0.132053i
$647$	34724.5	−	20048.2i	0.0829521	−	0.0478924i	−0.457950	−	0.888978i	$-0.651416\pi$
$647$	34724.5	−	20048.2i	0.0829521	−	0.0478924i	0.540902	+	0.841085i	$0.318083\pi$
$648$	56560.9	+	97966.4i	0.134700	+	0.233307i
$649$	274832.	+	158675.i	0.652497	+	0.376719i
$650$		−	2892.32i		−	0.00684573i
$651$	77982.4	+	241030.i	0.184007	+	0.568734i
$652$	−141280.			−0.332343
$653$	−283098.	+	490339.i	−0.663911	+	1.14993i	0.315668	+	0.948870i	$0.397771\pi$
$653$	−283098.	+	490339.i	−0.663911	+	1.14993i	−0.979579	+	0.201058i	$0.935562\pi$
$654$	−171667.	+	99112.2i	−0.401358	+	0.231724i
$655$	105567.	+	182847.i	0.246062	+	0.426192i
$656$	58277.0	+	33646.2i	0.135422	+	0.0781860i
$657$			149125.i			0.345477i
$658$	29612.1	−	138462.i	0.0683939	−	0.319801i
$659$	45784.3			0.105426			0.0527128	−	0.998610i	$-0.483213\pi$
$659$	45784.3			0.105426			0.0527128	+	0.998610i	$0.483213\pi$
$660$	75842.9	−	131364.i	0.174111	−	0.301570i
$661$	261218.	−	150814.i	0.597862	−	0.345176i	−0.170338	−	0.985386i	$-0.554486\pi$
$661$	261218.	−	150814.i	0.597862	−	0.345176i	0.768200	+	0.640210i	$0.221153\pi$
$662$	−65149.3	−	112842.i	−0.148660	−	0.257487i
$663$	−266920.	−	154107.i	−0.607232	−	0.350586i
$664$		−	177467.i		−	0.402514i
$665$	137565.	+	29420.2i	0.311075	+	0.0665276i
$666$	−67262.7			−0.151644
$667$	20633.7	−	35738.5i	0.0463793	−	0.0803314i
$668$	167935.	−	96957.3i	0.376347	−	0.217284i
$669$	−163268.	−	282789.i	−0.364796	−	0.631845i
$670$	50495.0	+	29153.3i	0.112486	+	0.0649438i
$671$			220864.i			0.490546i
$672$	−286334.	+	92639.7i	−0.634065	+	0.205144i
$673$	−602232.			−1.32964			−0.664820	−	0.747004i	$-0.731492\pi$
$673$	−602232.			−1.32964			−0.664820	+	0.747004i	$0.731492\pi$
$674$	−57197.2	+	99068.5i	−0.125908	+	0.218080i
$675$	−3068.03	+	1771.33i	−0.00673367	+	0.00388769i
$676$	−116770.	−	202251.i	−0.255527	−	0.442585i
$677$	−123836.	−	71496.5i	−0.270189	−	0.155994i	0.358784	−	0.933420i	$-0.383191\pi$
$677$	−123836.	−	71496.5i	−0.270189	−	0.155994i	−0.628974	+	0.777427i	$0.716525\pi$
$678$			158377.i			0.344535i
$679$	−333244.	−	300810.i	−0.722808	−	0.652458i
$680$	−340509.			−0.736394
$681$	−164402.	+	284753.i	−0.354497	+	0.614007i
$682$	−204920.	+	118311.i	−0.440571	+	0.254364i
$683$	235237.	+	407443.i	0.504272	+	0.873424i	0.999988	+	0.00493953i	$0.00157231\pi$
$683$	235237.	+	407443.i	0.504272	+	0.873424i	−0.495716	+	0.868485i	$0.665094\pi$
$684$	35107.5	+	20269.3i	0.0750391	+	0.0433239i
$685$		−	117790.i		−	0.251032i
$686$	−289641.	+	127657.i	−0.615476	+	0.271266i
$687$	−12252.1			−0.0259596
$688$	44115.8	−	76410.8i	0.0932003	−	0.161428i
$689$	134362.	−	77573.8i	0.283033	−	0.163409i
$690$	10132.0	+	17549.2i	0.0212813	+	0.0368602i
$691$	407498.	+	235269.i	0.853434	+	0.492730i	0.861808	−	0.507235i	$-0.169332\pi$
$691$	407498.	+	235269.i	0.853434	+	0.492730i	−0.00837428	+	0.999965i	$0.502666\pi$
$692$			310139.i			0.647656i
$693$	143315.	−	158768.i	0.298418	−	0.330594i
$694$	229344.			0.476176
$695$	−198038.	+	343011.i	−0.409994	+	0.710131i
$696$	321696.	−	185731.i	0.664091	−	0.383413i
$697$	176822.	+	306265.i	0.363975	+	0.630423i
$698$	−144169.	−	83236.0i	−0.295911	−	0.170844i
$699$		−	460254.i		−	0.941984i
$700$	−604.625	−	1868.79i	−0.00123393	−	0.00381386i
$701$	234109.			0.476410			0.238205	−	0.971215i	$-0.423441\pi$
$701$	234109.			0.476410			0.238205	+	0.971215i	$0.423441\pi$
$702$	244767.	−	423949.i	0.496682	−	0.860279i
$703$	62167.0	−	35892.1i	0.125791	−	0.0726254i
$704$	−174515.	−	302268.i	−0.352117	−	0.609884i
$705$	148095.	+	85502.4i	0.297962	+	0.172028i
$706$		−	202039.i		−	0.405346i
$707$	−176349.	+	824586.i	−0.352805	+	1.64967i
$708$	163449.			0.326074
$709$	423080.	−	732797.i	0.841648	−	1.45778i	−0.0468526	−	0.998902i	$-0.514919\pi$
$709$	423080.	−	732797.i	0.841648	−	1.45778i	0.888501	−	0.458875i	$-0.151748\pi$
$710$	215795.	−	124589.i	0.428080	−	0.247152i
$711$	−48344.9	−	83735.8i	−0.0956338	−	0.165643i
$712$	742330.	+	428585.i	1.46432	+	0.845428i
$713$			38263.3i			0.0752669i
$714$	169092.	+	36162.8i	0.331686	+	0.0709358i
$715$	−636434.			−1.24492
$716$	34770.0	−	60223.3i	0.0678232	−	0.117473i
$717$	172147.	−	99389.3i	0.334859	−	0.193331i
$718$	109235.	+	189201.i	0.211892	+	0.367007i
$719$	−477068.	−	275435.i	−0.922831	−	0.532797i	−0.0382937	−	0.999267i	$-0.512192\pi$
$719$	−477068.	−	275435.i	−0.922831	−	0.532797i	−0.884537	+	0.466470i	$0.845526\pi$
$720$		−	39042.1i		−	0.0753126i
$721$	−874177.	+	282829.i	−1.68162	+	0.544068i
$722$	−314876.			−0.604039
$723$	261382.	−	452728.i	0.500034	−	0.866085i
$724$	−80248.0	+	46331.2i	−0.153094	+	0.0883886i
$725$	1995.48	+	3456.27i	0.00379639	+	0.00657554i
$726$	41957.7	+	24224.3i	0.0796046	+	0.0459597i
$727$		−	689036.i		−	1.30369i	−0.758354	−	0.651843i	$-0.773996\pi$
$727$		−	689036.i		−	1.30369i	0.758354	−	0.651843i	$-0.226004\pi$
$728$	569390.	+	513972.i	1.07435	+	0.969788i
$729$	−469079.			−0.882656
$730$	−124474.	+	215596.i	−0.233579	+	0.404571i
$731$	401564.	−	231843.i	0.751485	−	0.433870i
$732$	56877.4	+	98514.6i	0.106149	+	0.183856i
$733$	410255.	+	236861.i	0.763565	+	0.440845i	0.830574	−	0.556908i	$-0.188012\pi$
$733$	410255.	+	236861.i	0.763565	+	0.440845i	−0.0670091	+	0.997752i	$0.521346\pi$
$734$			163724.i			0.303892i
$735$	−39007.4	−	380277.i	−0.0722058	−	0.703923i
$736$	−45455.2			−0.0839128
$737$	−47304.4	+	81933.6i	−0.0870896	+	0.150844i
$738$	−161190.	+	93062.9i	−0.295954	+	0.170869i
$739$	−212053.	−	367286.i	−0.388289	−	0.672536i	0.603931	−	0.797037i	$-0.293600\pi$
$739$	−212053.	−	367286.i	−0.388289	−	0.672536i	−0.992220	+	0.124501i	$0.960267\pi$
$740$	117710.	+	67959.8i	0.214956	+	0.124105i
$741$			173119.i			0.315289i
$742$	−58323.4	+	64612.0i	−0.105934	+	0.117356i
$743$	787035.			1.42566			0.712830	−	0.701336i	$-0.247413\pi$
$743$	787035.			1.42566			0.712830	+	0.701336i	$0.247413\pi$
$744$	−172211.	+	298279.i	−0.311112	+	0.538861i
$745$	−944859.	+	545514.i	−1.70237	+	0.982865i
$746$	6750.22	+	11691.7i	0.0121294	+	0.0210088i
$747$	92609.0	+	53467.9i	0.165963	+	0.0958190i
$748$		−	195501.i		−	0.349418i
$749$	−41158.7	−	127215.i	−0.0733666	−	0.226764i
$750$	−269679.			−0.479430
$751$	−301872.	+	522857.i	−0.535233	+	0.927050i	0.463919	+	0.885877i	$0.346443\pi$
$751$	−301872.	+	522857.i	−0.535233	+	0.927050i	−0.999152	+	0.0411727i	$0.986891\pi$
$752$	36319.7	−	20969.2i	0.0642254	−	0.0370805i
$753$	378935.	+	656335.i	0.668305	+	1.15754i
$754$	−477597.	−	275741.i	−0.840076	−	0.485018i
$755$		−	716684.i		−	1.25729i
$756$	69525.0	−	325090.i	0.121646	−	0.568801i
$757$	−143178.			−0.249854			−0.124927	−	0.992166i	$-0.539870\pi$
$757$	−143178.			−0.249854			−0.124927	+	0.992166i	$0.539870\pi$
$758$	−359990.	+	623520.i	−0.626544	+	1.08521i
$759$	−28475.4	+	16440.3i	−0.0494295	+	0.0285382i
$760$	95629.6	+	165635.i	0.165564	+	0.286765i
$761$	−107912.	−	62303.1i	−0.186338	−	0.107582i	0.403929	−	0.914790i	$-0.367644\pi$
$761$	−107912.	−	62303.1i	−0.186338	−	0.107582i	−0.590267	+	0.807208i	$0.700978\pi$
$762$			101240.i			0.174359i
$763$	552315.	+	118120.i	0.948719	+	0.202897i
$764$	−447397.			−0.766490
$765$	102590.	−	177690.i	0.175299	−	0.303627i
$766$	598424.	−	345500.i	1.01988	−	0.588831i
$767$	−342895.	−	593911.i	−0.582868	−	1.00956i
$768$	−384644.	−	222074.i	−0.652133	−	0.376509i
$769$			465468.i			0.787114i	0.919300	+	0.393557i	$0.128756\pi$
$769$			465468.i			0.787114i	−0.919300	+	0.393557i	$0.871244\pi$
$770$	339719.	−	109912.i	0.572979	−	0.185380i
$771$	−231935.			−0.390173
$772$	242702.	−	420372.i	0.407229	−	0.705342i
$773$	−194582.	+	112342.i	−0.325645	+	0.188011i	−0.653906	−	0.756576i	$-0.726871\pi$
$773$	−194582.	+	112342.i	−0.325645	+	0.188011i	0.328261	+	0.944587i	$0.393537\pi$
$774$	122021.	+	211346.i	0.203682	+	0.352787i
$775$	−3204.67	−	1850.22i	−0.00533557	−	0.00308049i
$776$		−	610354.i		−	1.01358i
$777$	−144799.	−	130706.i	−0.239842	−	0.216498i
$778$	118472.			0.195729
$779$	99318.7	−	172025.i	0.163665	−	0.283476i
$780$	−283876.	+	163896.i	−0.466594	+	0.269388i
$781$	202160.	+	350151.i	0.331430	+	0.574054i
$782$	22618.3	+	13058.7i	0.0369868	+	0.0213543i
$783$			675480.i			1.10177i
$784$	−85550.2	−	38346.1i	−0.139184	−	0.0623862i
$785$	581001.			0.942839
$786$	72884.9	−	126240.i	0.117976	−	0.204340i
$787$	671212.	−	387525.i	1.08370	−	0.625677i	0.151811	−	0.988410i	$-0.451490\pi$
$787$	671212.	−	387525.i	1.08370	−	0.625677i	0.931893	+	0.362733i	$0.118156\pi$
$788$	96577.3	+	167277.i	0.155533	+	0.269391i
$789$	726914.	+	419684.i	1.16769	+	0.674168i
$790$		−	161414.i		−	0.258634i
$791$	302375.	−	334979.i	0.483274	−	0.535382i
$792$	290791.			0.463587
$793$	238643.	−	413342.i	0.379492	−	0.657299i
$794$	−123566.	+	71340.9i	−0.196001	+	0.113161i
$795$	−52561.1	−	91038.5i	−0.0831630	−	0.144043i
$796$	15347.0	+	8860.59i	0.0242213	+	0.0139842i
$797$			515563.i			0.811643i	0.913952	+	0.405821i	$0.133015\pi$
$797$			515563.i			0.811643i	−0.913952	+	0.405821i	$0.866985\pi$
$798$	−29897.7	−	92408.6i	−0.0469496	−	0.145113i
$799$	220400.			0.345238
$800$	2197.98	−	3807.02i	0.00343435	−	0.00594846i
$801$	−447304.	+	258251.i	−0.697168	+	0.402510i
$802$	−273720.	−	474097.i	−0.425558	−	0.737087i
$803$	−349828.	−	201973.i	−0.542529	−	0.313229i
$804$			48727.7i			0.0753814i
$805$	12075.2	−	56461.9i	0.0186338	−	0.0871291i
$806$	511337.			0.787114
$807$	−299260.	+	518333.i	−0.459516	+	0.795906i
$808$	−992844.	+	573219.i	−1.52075	+	0.878007i
$809$	−348953.	−	604405.i	−0.533175	−	0.923487i	−0.999249	−	0.0387410i	$-0.987665\pi$
$809$	−348953.	−	604405.i	−0.533175	−	0.923487i	0.466074	−	0.884746i	$-0.345668\pi$
$810$	−98546.7	−	56896.0i	−0.150201	−	0.0867184i
$811$			1.19753e6i			1.82072i	0.413815	+	0.910361i	$0.364196\pi$
$811$			1.19753e6i			1.82072i	−0.413815	+	0.910361i	$0.635804\pi$
$812$	−366228.	−	78323.0i	−0.555443	−	0.118789i
$813$	115781.			0.175169
$814$	91099.9	−	157790.i	0.137489	−	0.238139i
$815$	347832.	−	200821.i	0.523667	−	0.302339i
$816$	25607.9	+	44354.2i	0.0384586	+	0.0666123i
$817$	−225553.	−	130223.i	−0.337913	−	0.195094i
$818$		−	491233.i		−	0.734143i
$819$	−439758.	+	142278.i	−0.655611	+	0.212115i
$820$	376109.			0.559353
$821$	32217.0	−	55801.5i	0.0477968	−	0.0827866i	−0.841137	−	0.540822i	$-0.818113\pi$
$821$	32217.0	−	55801.5i	0.0477968	−	0.0827866i	0.888934	+	0.458035i	$0.151447\pi$
$822$	−70429.0	+	40662.2i	−0.104234	+	0.0601793i
$823$	−20809.3	−	36042.8i	−0.0307226	−	0.0532131i	0.850255	−	0.526371i	$-0.176448\pi$
$823$	−20809.3	−	36042.8i	−0.0307226	−	0.0532131i	−0.880978	+	0.473157i	$0.843114\pi$
$824$	−1.08181e6	−	624583.i	−1.59329	−	0.919889i
$825$		−	3179.87i		−	0.00467199i
$826$	285601.	+	257803.i	0.418600	+	0.377858i
$827$	99598.7			0.145627			0.0728136	−	0.997346i	$-0.476802\pi$
$827$	99598.7			0.145627			0.0728136	+	0.997346i	$0.476802\pi$
$828$	8319.30	−	14409.4i	0.0121346	−	0.0210178i
$829$	51566.3	−	29771.8i	0.0750338	−	0.0433208i	−0.462014	−	0.886873i	$-0.652873\pi$
$829$	51566.3	−	29771.8i	0.0750338	−	0.0433208i	0.537047	+	0.843552i	$0.319540\pi$
$830$	89259.1	+	154601.i	0.129568	+	0.224418i
$831$	−326911.	−	188742.i	−0.473399	−	0.273317i
$832$			754250.i			1.08960i
$833$	−288600.	−	399320.i	−0.415916	−	0.575481i
$834$	273457.			0.393148
$835$	−275638.	+	477418.i	−0.395335	+	0.684741i
$836$	−95098.4	+	54905.1i	−0.136070	+	0.0785598i
$837$	−313155.	−	542400.i	−0.447001	−	0.774228i
$838$	−205104.	−	118417.i	−0.292070	−	0.168627i
$839$			783896.i			1.11361i	0.830642	+	0.556807i	$0.187974\pi$
$839$			783896.i			1.11361i	−0.830642	+	0.556807i	$0.812026\pi$
$840$	348248.	−	385798.i	0.493549	−	0.546766i
$841$	53677.1			0.0758921
$842$	12750.6	−	22084.6i	0.0179848	−	0.0311505i
$843$	507086.	−	292766.i	0.713553	−	0.411970i
$844$	306820.	+	531428.i	0.430723	+	0.746035i
$845$	574974.	+	331961.i	0.805257	+	0.464916i
$846$			115998.i			0.162073i
$847$	−42494.1	−	131342.i	−0.0592328	−	0.183078i
$848$	−25780.9			−0.0358514
$849$	−37221.1	+	64468.8i	−0.0516385	+	0.0894405i
$850$	−2187.41	+	1262.90i	−0.00302756	+	0.00174796i
$851$	−14731.5	−	25515.7i	−0.0203417	−	0.0352329i
$852$	180343.	+	104121.i	0.248439	+	0.143437i
$853$		−	671061.i		−	0.922282i	−0.887327	−	0.461141i	$-0.847440\pi$
$853$		−	671061.i		−	0.922282i	0.887327	−	0.461141i	$-0.152560\pi$
$854$	−56000.1	+	261849.i	−0.0767845	+	0.359034i
$855$	−115246.			−0.157650
$856$	90892.5	−	157430.i	0.124045	−	0.214853i
$857$	581900.	−	335960.i	0.792295	−	0.457432i	−0.0484749	−	0.998824i	$-0.515436\pi$
$857$	581900.	−	335960.i	0.792295	−	0.457432i	0.840770	+	0.541393i	$0.182103\pi$
$858$	219702.	+	380535.i	0.298442	+	0.516916i
$859$	132493.	+	76494.7i	0.179558	+	0.103668i	0.587085	−	0.809525i	$-0.300275\pi$
$859$	132493.	+	76494.7i	0.179558	+	0.103668i	−0.407527	+	0.913193i	$0.633609\pi$
$860$		−	493141.i		−	0.666768i
$861$	−527841.	−	112886.i	−0.712028	−	0.152277i
$862$	12774.1			0.0171916
$863$	2510.28	−	4347.92i	0.00337054	−	0.00583795i	−0.864335	−	0.502916i	$-0.832260\pi$
$863$	2510.28	−	4347.92i	0.00337054	−	0.00583795i	0.867706	+	0.497078i	$0.165594\pi$
$864$	644349.	−	372015.i	0.863164	−	0.498348i
$865$	−440844.	−	763563.i	−0.589186	−	1.02050i
$866$	471746.	+	272363.i	0.629032	+	0.363172i
$867$		−	264709.i		−	0.352152i
$868$	330386.	−	106892.i	0.438513	−	0.141876i
$869$	261911.			0.346828
$870$	−186832.	+	323602.i	−0.246838	+	0.427536i
$871$	177058.	−	102224.i	0.233388	−	0.134747i
$872$	383947.	+	665015.i	0.504938	+	0.874578i
$873$	318506.	+	183890.i	0.417916	+	0.241284i
$874$		−	14669.8i		−	0.0192044i
$875$	570390.	+	514875.i	0.744999	+	0.672489i
$876$	−208050.			−0.271119
$877$	100827.	−	174638.i	0.131093	−	0.227060i	−0.793005	−	0.609215i	$-0.791485\pi$
$877$	100827.	−	174638.i	0.131093	−	0.227060i	0.924098	+	0.382155i	$0.124818\pi$
$878$	−434813.	+	251040.i	−0.564045	+	0.325652i
$879$	−70057.3	−	121343.i	−0.0906725	−	0.157049i
$880$	91587.6	+	52878.1i	0.118269	+	0.0682827i
$881$			36596.7i			0.0471509i	0.999722	+	0.0235754i	$0.00750499\pi$
$881$			36596.7i			0.0471509i	−0.999722	+	0.0235754i	$0.992495\pi$
$882$	210165.	−	151892.i	0.270162	−	0.195253i
$883$	−1.08259e6			−1.38849			−0.694243	−	0.719741i	$-0.744261\pi$
$883$	−1.08259e6			−1.38849			−0.694243	+	0.719741i	$0.744261\pi$
$884$	−211238.	+	365875.i	−0.270313	+	0.468196i
$885$	−402412.	+	232333.i	−0.513788	+	0.296636i
$886$	−433493.	−	750832.i	−0.552223	−	0.956479i
$887$	−771378.	−	445355.i	−0.980437	−	0.566056i	−0.0780352	−	0.996951i	$-0.524865\pi$
$887$	−771378.	−	445355.i	−0.980437	−	0.566056i	−0.902402	+	0.430895i	$0.858198\pi$
$888$		−	265208.i		−	0.336326i
$889$	193289.	−	214130.i	0.244571	−	0.270941i
$890$	−862246.			−1.08856
$891$	92319.8	−	159903.i	0.116289	−	0.201419i
$892$	−387626.	+	223796.i	−0.487173	+	0.281270i
$893$	−61898.0	−	107210.i	−0.0776200	−	0.134442i
$894$	652345.	+	376632.i	0.816211	+	0.471240i
$895$			197693.i			0.246801i
$896$	101631.	+	314124.i	0.126593	+	0.391277i
$897$	71054.7			0.0883096
$898$	216868.	−	375626.i	0.268932	−	0.465804i
$899$	−611038.	+	352783.i	−0.756047	+	0.436504i
$900$	804.558	+	1393.53i	0.000993281	+	0.00172041i
$901$	−117335.	−	67743.6i	−0.144537	−	0.0834485i
$902$		−	504173.i		−	0.619679i
$903$	−148013.	+	692087.i	−0.181519	+	0.848761i
$904$	613531.			0.750757
$905$	131714.	−	228135.i	0.160818	−	0.278545i
$906$	−428518.	+	247405.i	−0.522051	+	0.301406i
$907$	612167.	+	1.06030e6i	0.744141	+	1.28889i	0.950595	+	0.310434i	$0.100474\pi$
$907$	612167.	+	1.06030e6i	0.744141	+	1.28889i	−0.206454	+	0.978456i	$0.566192\pi$
$908$	390318.	+	225350.i	0.473420	+	0.273329i
$909$		−	690805.i		−	0.836042i
$910$	−754536.	−	161368.i	−0.911165	−	0.194865i
$911$	−140064.			−0.168768			−0.0843841	−	0.996433i	$-0.526892\pi$
$911$	−140064.			−0.168768			−0.0843841	+	0.996433i	$0.526892\pi$
$912$	14383.6	−	24913.2i	0.0172933	−	0.0299529i
$913$	−250857.	+	144832.i	−0.300944	+	0.173750i
$914$	515333.	+	892583.i	0.616873	+	1.06845i
$915$	−280065.	−	161696.i	−0.334516	−	0.193133i
$916$			16794.3i			0.0200157i
$917$	−395176.	+	127854.i	−0.469951	+	0.152047i
$918$	−427500.			−0.507283
$919$	−298659.	+	517293.i	−0.353626	+	0.612499i	−0.986882	−	0.161444i	$-0.948385\pi$
$919$	−298659.	+	517293.i	−0.353626	+	0.612499i	0.633256	+	0.773943i	$0.281718\pi$
$920$	67983.0	−	39250.0i	0.0803202	−	0.0463729i
$921$	59037.6	+	102256.i	0.0696000	+	0.120551i
$922$	517056.	+	298523.i	0.608242	+	0.351168i
$923$		−	873731.i		−	1.02559i
$924$	221503.	+	199945.i	0.259439	+	0.234188i
$925$	2849.36			0.00333015
$926$	351074.	−	608078.i	0.409427	−	0.709149i
$927$	651862.	−	376353.i	0.758571	−	0.437961i
$928$	−419091.	−	725887.i	−0.486645	−	0.842894i
$929$	983557.	+	567857.i	1.13964	+	0.657972i	0.946342	−	0.323168i	$-0.104748\pi$
$929$	983557.	+	567857.i	1.13964	+	0.657972i	0.193299	+	0.981140i	$0.438081\pi$
$930$		−	346463.i		−	0.400582i
$931$	−113192.	+	252532.i	−0.130592	+	0.291351i
$932$	−630883.			−0.726301
$933$	539679.	−	934752.i	0.619972	−	1.07382i
$934$	703296.	−	406048.i	0.806203	−	0.465461i
$935$	277892.	+	481323.i	0.317873	+	0.550572i
$936$	−544208.	−	314199.i	−0.621174	−	0.358635i
$937$		−	553396.i		−	0.630314i	−0.949039	−	0.315157i	$-0.897943\pi$
$937$		−	553396.i		−	0.630314i	0.949039	−	0.315157i	$-0.102057\pi$
$938$	−76856.8	+	85143.8i	−0.0873528	+	0.0967714i
$939$	−93300.6			−0.105816
$940$	117200.	−	202997.i	0.132640	−	0.229739i
$941$	469222.	−	270906.i	0.529907	−	0.305942i	−0.211072	−	0.977471i	$-0.567695\pi$
$941$	469222.	−	270906.i	0.529907	−	0.305942i	0.740979	+	0.671529i	$0.234362\pi$
$942$	−200566.	−	347391.i	−0.226025	−	0.391486i
$943$	−70605.6	−	40764.2i	−0.0793991	−	0.0458411i
$944$			113958.i			0.127879i
$945$	290925.	+	899198.i	0.325774	+	1.00691i
$946$	−661055.			−0.738678
$947$	−499150.	+	864554.i	−0.556585	+	0.964033i	0.441193	+	0.897412i	$0.354555\pi$
$947$	−499150.	+	864554.i	−0.556585	+	0.964033i	−0.997778	+	0.0666213i	$0.978778\pi$
$948$	116823.	−	67447.9i	0.129991	−	0.0750502i
$949$	436463.	+	755976.i	0.484635	+	0.839412i
$950$	1228.64	+	709.356i	0.00136137	+	0.000785990i
$951$		−	35012.5i		−	0.0387135i
$952$	140090.	−	655040.i	0.154572	−	0.722760i
$953$	−326477.			−0.359473			−0.179736	−	0.983715i	$-0.557525\pi$
$953$	−326477.			−0.359473			−0.179736	+	0.983715i	$0.557525\pi$
$954$	35654.0	−	61754.5i	0.0391752	−	0.0678534i
$955$	1.10149e6	−	635948.i	1.20775	−	0.697292i
$956$	−136235.	−	235967.i	−0.149065	−	0.258187i
$957$	−525079.	−	303154.i	−0.573325	−	0.331009i
$958$			466595.i			0.508404i
$959$	226595.	+	48460.5i	0.246384	+	0.0526927i
$960$	511052.			0.554526
$961$	−134658.	+	233234.i	−0.145809	+	0.252549i
$962$	−340982.	+	196866.i	−0.368453	+	0.212726i
$963$	54768.8	+	94862.3i	0.0590582	+	0.102292i
$964$	−620565.	−	358284.i	−0.667780	−	0.385543i
$965$			1.37994e6i			1.48186i
$966$	−37928.0	+	12271.1i	−0.0406448	+	0.0131501i
$967$	1.62506e6			1.73787			0.868936	−	0.494925i	$-0.164804\pi$
$967$	1.62506e6			1.73787			0.868936	+	0.494925i	$0.164804\pi$
$968$	93841.4	−	162538.i	0.100148	−	0.173462i
$969$	130927.	−	75590.8i	0.139438	−	0.0805047i
$970$	306985.	+	531713.i	0.326267	+	0.565111i
$971$	567659.	+	327738.i	0.602073	+	0.347607i	0.769857	−	0.638217i	$-0.220328\pi$
$971$	567659.	+	327738.i	0.602073	+	0.347607i	−0.167784	+	0.985824i	$0.553661\pi$
$972$			454448.i			0.481008i
$973$	−578380.	−	522086.i	−0.610924	−	0.551463i
$974$	−662091.			−0.697910
$975$	−3435.84	+	5951.05i	−0.00361430	+	0.00626015i
$976$	−68685.0	+	39655.3i	−0.0721045	+	0.0416295i
$977$	−296119.	−	512894.i	−0.310226	−	0.537327i	0.668185	−	0.743995i	$-0.267071\pi$
$977$	−296119.	−	512894.i	−0.310226	−	0.537327i	−0.978411	+	0.206668i	$0.933738\pi$
$978$	−240149.	−	138650.i	−0.251075	−	0.144958i
$979$		−	1.39909e6i		−	1.45975i
$980$	−521255.	+	53468.4i	−0.542748	+	0.0556731i
$981$	−462707.			−0.480804
$982$	−355820.	+	616299.i	−0.368984	+	0.639099i
$983$	−1.18731e6	+	685496.i	−1.22874	+	0.709411i	−0.966765	−	0.255665i	$-0.917706\pi$
$983$	−1.18731e6	+	685496.i	−1.22874	+	0.709411i	−0.261970	+	0.965076i	$0.584372\pi$
$984$	−366934.	−	635548.i	−0.378964	−	0.656384i
$985$	−475547.	−	274557.i	−0.490141	−	0.282983i
$986$			481597.i			0.495370i
$987$	−225410.	+	249714.i	−0.231387	+	0.256336i
$988$	237299.			0.243099
$989$	−53448.6	+	92575.7i	−0.0546441	+	0.0946464i
$990$	−253324.	+	146257.i	−0.258468	+	0.149226i
$991$	−759233.	−	1.31503e6i	−0.773086	−	1.33902i	−0.935864	−	0.352361i	$-0.885379\pi$
$991$	−759233.	−	1.31503e6i	−0.773086	−	1.33902i	0.162779	−	0.986663i	$-0.447954\pi$
$992$	673047.	+	388584.i	0.683946	+	0.394877i
$993$			309568.i			0.313948i
$994$	150893.	+	466385.i	0.152720	+	0.472032i
$995$	−50379.1			−0.0508867
$996$	−74595.2	+	129203.i	−0.0751956	+	0.130243i
$997$	−1.19152e6	+	687927.i	−1.19871	+	0.692073i	−0.960266	−	0.279085i	$-0.909969\pi$
$997$	−1.19152e6	+	687927.i	−1.19871	+	0.692073i	−0.238439	+	0.971158i	$0.576636\pi$
$998$	−268940.	−	465818.i	−0.270019	−	0.467687i
$999$	417651.	+	241131.i	0.418488	+	0.241614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.5.d.a.5.2	yes	4
3.2	odd	2		63.5.m.d.19.1		4
4.3	odd	2		112.5.s.a.33.2		4
5.2	odd	4		175.5.j.a.124.3		8
5.3	odd	4		175.5.j.a.124.2		8
5.4	even	2		175.5.i.a.26.1		4
7.2	even	3		49.5.b.a.48.1		4
7.3	odd	6	inner	7.5.d.a.3.2	✓	4
7.4	even	3		49.5.d.b.31.2		4
7.5	odd	6		49.5.b.a.48.2		4
7.6	odd	2		49.5.d.b.19.2		4
21.2	odd	6		441.5.d.d.244.3		4
21.5	even	6		441.5.d.d.244.4		4
21.17	even	6		63.5.m.d.10.1		4
28.3	even	6		112.5.s.a.17.2		4
28.19	even	6		784.5.c.c.97.2		4
28.23	odd	6		784.5.c.c.97.3		4
35.3	even	12		175.5.j.a.24.3		8
35.17	even	12		175.5.j.a.24.2		8
35.24	odd	6		175.5.i.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.5.d.a.3.2	✓	4	7.3	odd	6	inner
7.5.d.a.5.2	yes	4	1.1	even	1	trivial
49.5.b.a.48.1		4	7.2	even	3
49.5.b.a.48.2		4	7.5	odd	6
49.5.d.b.19.2		4	7.6	odd	2
49.5.d.b.31.2		4	7.4	even	3
63.5.m.d.10.1		4	21.17	even	6
63.5.m.d.19.1		4	3.2	odd	2
112.5.s.a.17.2		4	28.3	even	6
112.5.s.a.33.2		4	4.3	odd	2
175.5.i.a.26.1		4	5.4	even	2
175.5.i.a.101.1		4	35.24	odd	6
175.5.j.a.24.2		8	35.17	even	12
175.5.j.a.24.3		8	35.3	even	12
175.5.j.a.124.2		8	5.3	odd	4
175.5.j.a.124.3		8	5.2	odd	4
441.5.d.d.244.3		4	21.2	odd	6
441.5.d.d.244.4		4	21.5	even	6
784.5.c.c.97.2		4	28.19	even	6
784.5.c.c.97.3		4	28.23	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34521 - 2.32997i) q^{2} +(-5.53562 + 3.19599i) q^{3} +(4.38083 + 7.58782i) q^{4} +(-21.5712 - 12.4542i) q^{5} +17.1971i q^{6} +(32.8329 - 36.3731i) q^{7} +66.6192 q^{8} +(-20.0712 + 34.7644i) q^{9} +O(q^{10})\)	\(q+(1.34521 - 2.32997i) q^{2} +(-5.53562 + 3.19599i) q^{3} +(4.38083 + 7.58782i) q^{4} +(-21.5712 - 12.4542i) q^{5} +17.1971i q^{6} +(32.8329 - 36.3731i) q^{7} +66.6192 q^{8} +(-20.0712 + 34.7644i) q^{9} +(-58.0356 + 33.5069i) q^{10} +(-54.3685 - 94.1691i) q^{11} +(-48.5013 - 28.0022i) q^{12} +234.980i q^{13} +(-40.5810 - 125.429i) q^{14} +159.214 q^{15} +(19.5233 - 33.8154i) q^{16} +(177.711 - 102.602i) q^{17} +(54.0000 + 93.5307i) q^{18} +(-99.8181 - 57.6300i) q^{19} -218.238i q^{20} +(-65.5025 + 306.281i) q^{21} -292.548 q^{22} +(-23.6535 + 40.9691i) q^{23} +(-368.779 + 212.914i) q^{24} +(-2.28753 - 3.96211i) q^{25} +(547.496 + 316.097i) q^{26} -774.341i q^{27} +(419.828 + 89.7860i) q^{28} -872.329 q^{29} +(214.176 - 370.963i) q^{30} +(700.467 - 404.415i) q^{31} +(480.427 + 832.125i) q^{32} +(601.927 + 347.523i) q^{33} -552.082i q^{34} +(-1161.24 + 375.706i) q^{35} -351.715 q^{36} +(-311.402 + 539.363i) q^{37} +(-268.552 + 155.049i) q^{38} +(-750.995 - 1300.76i) q^{39} +(-1437.06 - 829.686i) q^{40} +1723.39i q^{41} +(625.511 + 564.631i) q^{42} +2259.65 q^{43} +(476.359 - 825.078i) q^{44} +(865.924 - 499.941i) q^{45} +(63.6378 + 110.224i) q^{46} +(930.162 + 537.029i) q^{47} +249.586i q^{48} +(-245.000 - 2388.47i) q^{49} -12.3088 q^{50} +(-655.828 + 1135.93i) q^{51} +(-1782.99 + 1029.41i) q^{52} +(-330.129 - 571.801i) q^{53} +(-1804.19 - 1041.65i) q^{54} +2708.46i q^{55} +(2187.30 - 2423.14i) q^{56} +736.740 q^{57} +(-1173.46 + 2032.50i) q^{58} +(-2527.50 + 1459.25i) q^{59} +(697.489 + 1208.09i) q^{60} +(-1759.05 - 1015.59i) q^{61} -2176.09i q^{62} +(605.491 + 1871.47i) q^{63} +3209.85 q^{64} +(2926.48 - 5068.81i) q^{65} +(1619.44 - 934.981i) q^{66} +(-435.034 - 753.502i) q^{67} +(1557.05 + 898.961i) q^{68} -302.386i q^{69} +(-686.730 + 3211.06i) q^{70} -3718.32 q^{71} +(-1337.13 + 2315.98i) q^{72} +(3217.19 - 1857.45i) q^{73} +(837.800 + 1451.11i) q^{74} +(25.3258 + 14.6218i) q^{75} -1009.87i q^{76} +(-5210.29 - 1114.29i) q^{77} -4040.98 q^{78} +(-1204.33 + 2085.96i) q^{79} +(-842.285 + 486.293i) q^{80} +(849.019 + 1470.54i) q^{81} +(4015.44 + 2318.31i) q^{82} -2663.90i q^{83} +(-2610.96 + 844.746i) q^{84} -5111.27 q^{85} +(3039.69 - 5264.90i) q^{86} +(4828.89 - 2787.96i) q^{87} +(-3621.99 - 6273.46i) q^{88} +(11142.9 + 6433.35i) q^{89} -2690.10i q^{90} +(8546.95 + 7715.08i) q^{91} -414.488 q^{92} +(-2585.01 + 4477.38i) q^{93} +(2502.52 - 1444.83i) q^{94} +(1435.47 + 2486.30i) q^{95} +(-5318.93 - 3070.89i) q^{96} -9161.84i q^{97} +(-5894.63 - 2642.14i) q^{98} +4364.98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9} - 204 q^{10} - 58 q^{11} - 588 q^{12} + 560 q^{14} + 468 q^{15} - 72 q^{16} - 246 q^{17} + 216 q^{18} + 642 q^{19} - 1050 q^{21} - 1264 q^{22} + 290 q^{23} + 720 q^{24} - 572 q^{25} + 1008 q^{26} - 28 q^{28} - 2176 q^{29} - 72 q^{30} + 3618 q^{31} + 1584 q^{32} + 2070 q^{33} - 2478 q^{35} - 1632 q^{36} - 270 q^{37} - 6168 q^{38} - 1428 q^{39} - 1752 q^{40} + 6048 q^{42} + 2472 q^{43} + 2412 q^{44} + 1944 q^{45} + 2384 q^{46} - 1542 q^{47} - 980 q^{49} + 7568 q^{50} - 4734 q^{51} - 3192 q^{52} - 4510 q^{53} - 11016 q^{54} - 1232 q^{56} + 11052 q^{57} - 904 q^{58} + 2526 q^{59} - 756 q^{60} - 282 q^{61} - 336 q^{63} - 5472 q^{64} + 5796 q^{65} - 2556 q^{66} - 1318 q^{67} + 20412 q^{68} + 3360 q^{70} - 10408 q^{71} - 1296 q^{72} + 5214 q^{73} + 4036 q^{74} - 9636 q^{75} - 8890 q^{77} - 9072 q^{78} - 8110 q^{79} - 3144 q^{80} + 9306 q^{81} - 4032 q^{82} + 588 q^{84} - 15492 q^{85} + 12928 q^{86} + 5976 q^{87} - 2912 q^{88} + 33990 q^{89} + 17640 q^{91} - 20232 q^{92} + 7446 q^{93} + 27768 q^{94} + 6558 q^{95} - 37828 q^{98} + 10368 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9 - 204 * q^10 - 58 * q^11 - 588 * q^12 + 560 * q^14 + 468 * q^15 - 72 * q^16 - 246 * q^17 + 216 * q^18 + 642 * q^19 - 1050 * q^21 - 1264 * q^22 + 290 * q^23 + 720 * q^24 - 572 * q^25 + 1008 * q^26 - 28 * q^28 - 2176 * q^29 - 72 * q^30 + 3618 * q^31 + 1584 * q^32 + 2070 * q^33 - 2478 * q^35 - 1632 * q^36 - 270 * q^37 - 6168 * q^38 - 1428 * q^39 - 1752 * q^40 + 6048 * q^42 + 2472 * q^43 + 2412 * q^44 + 1944 * q^45 + 2384 * q^46 - 1542 * q^47 - 980 * q^49 + 7568 * q^50 - 4734 * q^51 - 3192 * q^52 - 4510 * q^53 - 11016 * q^54 - 1232 * q^56 + 11052 * q^57 - 904 * q^58 + 2526 * q^59 - 756 * q^60 - 282 * q^61 - 336 * q^63 - 5472 * q^64 + 5796 * q^65 - 2556 * q^66 - 1318 * q^67 + 20412 * q^68 + 3360 * q^70 - 10408 * q^71 - 1296 * q^72 + 5214 * q^73 + 4036 * q^74 - 9636 * q^75 - 8890 * q^77 - 9072 * q^78 - 8110 * q^79 - 3144 * q^80 + 9306 * q^81 - 4032 * q^82 + 588 * q^84 - 15492 * q^85 + 12928 * q^86 + 5976 * q^87 - 2912 * q^88 + 33990 * q^89 + 17640 * q^91 - 20232 * q^92 + 7446 * q^93 + 27768 * q^94 + 6558 * q^95 - 37828 * q^98 + 10368 * q^99

Introduction

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