LMFDB - Embedded newform 74.5.g.a.45.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			45.6
Character	$\chi$	$=$	74.45
Dual form			74.5.g.a.51.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73205 - 0.732051i) q^{2} +(8.28780 + 4.78497i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-17.4826 + 4.68445i) q^{5} +(-19.1399 - 19.1399i) q^{6} +(-36.2925 + 62.8605i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(5.29180 + 9.16567i) q^{9} +O(q^{10})$	\(q+(-2.73205 - 0.732051i) q^{2} +(8.28780 + 4.78497i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-17.4826 + 4.68445i) q^{5} +(-19.1399 - 19.1399i) q^{6} +(-36.2925 + 62.8605i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(5.29180 + 9.16567i) q^{9} +51.1927 q^{10} -102.318i q^{11} +(38.2797 + 66.3024i) q^{12} +(-128.387 + 34.4011i) q^{13} +(145.170 - 145.170i) q^{14} +(-167.307 - 44.8299i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-36.3083 + 135.504i) q^{17} +(-7.74773 - 28.9149i) q^{18} +(-527.582 + 141.365i) q^{19} +(-139.861 - 37.4756i) q^{20} +(-601.571 + 347.317i) q^{21} +(-74.9021 + 279.538i) q^{22} +(686.570 + 686.570i) q^{23} +(-56.0454 - 209.164i) q^{24} +(-257.568 + 148.707i) q^{25} +375.942 q^{26} -673.880i q^{27} +(-502.884 + 290.340i) q^{28} +(-892.638 + 892.638i) q^{29} +(424.275 + 244.955i) q^{30} +(439.389 - 439.389i) q^{31} +(-46.8513 - 174.851i) q^{32} +(489.589 - 847.993i) q^{33} +(198.392 - 343.625i) q^{34} +(340.021 - 1268.98i) q^{35} +84.6688i q^{36} +(664.189 - 1197.09i) q^{37} +1544.87 q^{38} +(-1228.65 - 329.216i) q^{39} +(354.673 + 204.771i) q^{40} +(876.607 + 506.109i) q^{41} +(1897.78 - 508.508i) q^{42} +(1235.74 + 1235.74i) q^{43} +(409.273 - 708.881i) q^{44} +(-135.451 - 135.451i) q^{45} +(-1373.14 - 2378.35i) q^{46} +2111.90 q^{47} +612.476i q^{48} +(-1433.80 - 2483.41i) q^{49} +(812.550 - 217.722i) q^{50} +(-949.299 + 949.299i) q^{51} +(-1027.09 - 275.208i) q^{52} +(995.706 + 1724.61i) q^{53} +(-493.315 + 1841.07i) q^{54} +(479.305 + 1788.79i) q^{55} +(1586.45 - 425.088i) q^{56} +(-5048.93 - 1352.86i) q^{57} +(3092.19 - 1785.28i) q^{58} +(-392.361 + 1464.31i) q^{59} +(-979.821 - 979.821i) q^{60} +(341.515 + 1274.55i) q^{61} +(-1522.09 + 878.778i) q^{62} -768.212 q^{63} +512.000i q^{64} +(2083.38 - 1202.84i) q^{65} +(-1958.36 + 1958.36i) q^{66} +(-3494.20 - 2017.38i) q^{67} +(-793.568 + 793.568i) q^{68} +(2404.94 + 8975.37i) q^{69} +(-1857.91 + 3218.00i) q^{70} +(1686.23 - 2920.63i) q^{71} +(61.9819 - 231.320i) q^{72} -1548.71i q^{73} +(-2690.93 + 2784.28i) q^{74} -2846.23 q^{75} +(-4220.66 - 1130.92i) q^{76} +(6431.77 + 3713.39i) q^{77} +(3115.73 + 1798.87i) q^{78} +(-2387.54 + 639.741i) q^{79} +(-819.083 - 819.083i) q^{80} +(3653.13 - 6327.41i) q^{81} +(-2024.44 - 2024.44i) q^{82} +(-3359.95 - 5819.61i) q^{83} -5557.07 q^{84} -2539.05i q^{85} +(-2471.48 - 4280.74i) q^{86} +(-11669.3 + 3126.77i) q^{87} +(-1637.09 + 1637.09i) q^{88} +(5076.65 + 1360.29i) q^{89} +(270.901 + 469.215i) q^{90} +(2497.00 - 9318.94i) q^{91} +(2010.42 + 7502.97i) q^{92} +(5744.03 - 1539.11i) q^{93} +(-5769.81 - 1546.02i) q^{94} +(8561.30 - 4942.87i) q^{95} +(448.363 - 1673.31i) q^{96} +(11036.0 + 11036.0i) q^{97} +(2099.22 + 7834.41i) q^{98} +(937.814 - 541.447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−2.73205	−	0.732051i	−0.683013	−	0.183013i
$2$	−2.73205	−	0.732051i	−0.683013	−	0.183013i
$3$	8.28780	+	4.78497i	0.920867	+	0.531663i	0.883912	−	0.467654i	$-0.154901\pi$
$3$	8.28780	+	4.78497i	0.920867	+	0.531663i	0.0369555	+	0.999317i	$0.488234\pi$
$4$	6.92820	+	4.00000i	0.433013	+	0.250000i
$5$	−17.4826	+	4.68445i	−0.699305	+	0.187378i	−0.590919	−	0.806731i	$-0.701235\pi$
$5$	−17.4826	+	4.68445i	−0.699305	+	0.187378i	−0.108386	+	0.994109i	$0.534568\pi$
$6$	−19.1399	−	19.1399i	−0.531663	−	0.531663i
$7$	−36.2925	+	62.8605i	−0.740664	+	1.28287i	0.211529	+	0.977372i	$0.432156\pi$
$7$	−36.2925	+	62.8605i	−0.740664	+	1.28287i	−0.952193	+	0.305496i	$0.901178\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	5.29180	+	9.16567i	0.0653309	+	0.113156i
$10$	51.1927			0.511927
$11$		−	102.318i		−	0.845605i	−0.906222	−	0.422802i	$-0.861046\pi$
$11$		−	102.318i		−	0.845605i	0.906222	−	0.422802i	$-0.138954\pi$
$12$	38.2797	+	66.3024i	0.265831	+	0.460434i
$13$	−128.387	+	34.4011i	−0.759683	+	0.203557i	−0.617809	−	0.786328i	$-0.711980\pi$
$13$	−128.387	+	34.4011i	−0.759683	+	0.203557i	−0.141874	+	0.989885i	$0.545313\pi$
$14$	145.170	−	145.170i	0.740664	−	0.740664i
$15$	−167.307	−	44.8299i	−0.743589	−	0.199244i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−36.3083	+	135.504i	−0.125634	+	0.468873i	−0.999861	−	0.0166439i	$-0.994702\pi$
$17$	−36.3083	+	135.504i	−0.125634	+	0.468873i	0.874227	+	0.485517i	$0.161369\pi$
$18$	−7.74773	−	28.9149i	−0.0239128	−	0.0892436i
$19$	−527.582	+	141.365i	−1.46145	+	0.391594i	−0.899989	−	0.435912i	$-0.856426\pi$
$19$	−527.582	+	141.365i	−1.46145	+	0.391594i	−0.561458	+	0.827505i	$0.689759\pi$
$20$	−139.861	−	37.4756i	−0.349652	−	0.0936891i
$21$	−601.571	+	347.317i	−1.36411	+	0.787567i
$22$	−74.9021	+	279.538i	−0.154756	+	0.577559i
$23$	686.570	+	686.570i	1.29786	+	1.29786i	0.929801	+	0.368062i	$0.119979\pi$
$23$	686.570	+	686.570i	1.29786	+	1.29786i	0.368062	+	0.929801i	$0.380021\pi$
$24$	−56.0454	−	209.164i	−0.0973011	−	0.363133i
$25$	−257.568	+	148.707i	−0.412109	+	0.237931i
$26$	375.942			0.556127
$27$		−	673.880i		−	0.924390i
$28$	−502.884	+	290.340i	−0.641434	+	0.370332i
$29$	−892.638	+	892.638i	−1.06140	+	1.06140i	−0.0634133	+	0.997987i	$0.520199\pi$
$29$	−892.638	+	892.638i	−1.06140	+	1.06140i	−0.997987	+	0.0634133i	$0.979801\pi$
$30$	424.275	+	244.955i	0.471416	+	0.272172i
$31$	439.389	−	439.389i	0.457220	−	0.457220i	−0.440522	−	0.897742i	$-0.645206\pi$
$31$	439.389	−	439.389i	0.457220	−	0.457220i	0.897742	+	0.440522i	$0.145206\pi$
$32$	−46.8513	−	174.851i	−0.0457532	−	0.170753i
$33$	489.589	−	847.993i	0.449577	−	0.778689i
$34$	198.392	−	343.625i	0.171619	−	0.297253i
$35$	340.021	−	1268.98i	0.277569	−	1.03590i
$36$			84.6688i			0.0653309i
$37$	664.189	−	1197.09i	0.485164	−	0.874423i
$37$	664.189	−	1197.09i	0.485164	−	0.874423i
$38$	1544.87			1.06985
$39$	−1228.65	−	329.216i	−0.807791	−	0.216447i
$40$	354.673	+	204.771i	0.221671	+	0.127982i
$41$	876.607	+	506.109i	0.521480	+	0.301076i	0.737540	−	0.675304i	$-0.235987\pi$
$41$	876.607	+	506.109i	0.521480	+	0.301076i	−0.216060	+	0.976380i	$0.569321\pi$
$42$	1897.78	−	508.508i	1.07584	−	0.288270i
$43$	1235.74	+	1235.74i	0.668330	+	0.668330i	0.957329	−	0.288999i	$-0.0933226\pi$
$43$	1235.74	+	1235.74i	0.668330	+	0.668330i	−0.288999	+	0.957329i	$0.593323\pi$
$44$	409.273	−	708.881i	0.211401	−	0.366158i
$45$	−135.451	−	135.451i	−0.0668892	−	0.0668892i
$46$	−1373.14	−	2378.35i	−0.648932	−	1.12398i
$47$	2111.90			0.956043			0.478021	−	0.878348i	$-0.341354\pi$
$47$	2111.90			0.956043			0.478021	+	0.878348i	$0.341354\pi$
$48$			612.476i			0.265831i
$49$	−1433.80	−	2483.41i	−0.597167	−	1.03432i
$50$	812.550	−	217.722i	0.325020	−	0.0870889i
$51$	−949.299	+	949.299i	−0.364975	+	0.364975i
$52$	−1027.09	−	275.208i	−0.379842	−	0.101778i
$53$	995.706	+	1724.61i	0.354470	+	0.613960i	0.987027	−	0.160554i	$-0.0513280\pi$
$53$	995.706	+	1724.61i	0.354470	+	0.613960i	−0.632557	+	0.774514i	$0.717995\pi$
$54$	−493.315	+	1841.07i	−0.169175	+	0.631370i
$55$	479.305	+	1788.79i	0.158448	+	0.591335i
$56$	1586.45	−	425.088i	0.505883	−	0.135551i
$57$	−5048.93	−	1352.86i	−1.55399	−	0.416392i
$58$	3092.19	−	1785.28i	0.919200	−	0.530700i
$59$	−392.361	+	1464.31i	−0.112715	+	0.420658i	−0.999106	−	0.0422798i	$-0.986538\pi$
$59$	−392.361	+	1464.31i	−0.112715	+	0.420658i	0.886391	+	0.462937i	$0.153205\pi$
$60$	−979.821	−	979.821i	−0.272172	−	0.272172i
$61$	341.515	+	1274.55i	0.0917805	+	0.342529i	0.996512	−	0.0834535i	$-0.0265950\pi$
$61$	341.515	+	1274.55i	0.0917805	+	0.342529i	−0.904731	+	0.425983i	$0.859928\pi$
$62$	−1522.09	+	878.778i	−0.395964	+	0.228610i
$63$	−768.212			−0.193553
$64$			512.000i			0.125000i
$65$	2083.38	−	1202.84i	0.493108	−	0.284696i
$66$	−1958.36	+	1958.36i	−0.449577	+	0.449577i
$67$	−3494.20	−	2017.38i	−0.778392	−	0.449405i	0.0574681	−	0.998347i	$-0.481697\pi$
$67$	−3494.20	−	2017.38i	−0.778392	−	0.449405i	−0.835860	+	0.548942i	$0.815031\pi$
$68$	−793.568	+	793.568i	−0.171619	+	0.171619i
$69$	2404.94	+	8975.37i	0.505134	+	1.88519i
$70$	−1857.91	+	3218.00i	−0.379166	+	0.656734i
$71$	1686.23	−	2920.63i	0.334503	−	0.579376i	−0.648886	−	0.760885i	$-0.724765\pi$
$71$	1686.23	−	2920.63i	0.334503	−	0.579376i	0.983389	+	0.181509i	$0.0580983\pi$
$72$	61.9819	−	231.320i	0.0119564	−	0.0446218i
$73$		−	1548.71i		−	0.290620i	−0.989386	−	0.145310i	$-0.953582\pi$
$73$		−	1548.71i		−	0.290620i	0.989386	−	0.145310i	$-0.0464179\pi$
$74$	−2690.93	+	2784.28i	−0.491404	+	0.508451i
$75$	−2846.23			−0.505997
$76$	−4220.66	−	1130.92i	−0.730724	−	0.195797i
$77$	6431.77	+	3713.39i	1.08480	+	0.626309i
$78$	3115.73	+	1798.87i	0.512119	+	0.295672i
$79$	−2387.54	+	639.741i	−0.382558	+	0.102506i	−0.444973	−	0.895544i	$-0.646787\pi$
$79$	−2387.54	+	639.741i	−0.382558	+	0.102506i	0.0624146	+	0.998050i	$0.480120\pi$
$80$	−819.083	−	819.083i	−0.127982	−	0.127982i
$81$	3653.13	−	6327.41i	0.556795	−	0.964397i
$82$	−2024.44	−	2024.44i	−0.301076	−	0.301076i
$83$	−3359.95	−	5819.61i	−0.487727	−	0.844769i	0.512173	−	0.858882i	$-0.328841\pi$
$83$	−3359.95	−	5819.61i	−0.487727	−	0.844769i	−0.999900	+	0.0141137i	$0.995507\pi$
$84$	−5557.07			−0.787567
$85$		−	2539.05i		−	0.351426i
$86$	−2471.48	−	4280.74i	−0.334165	−	0.578791i
$87$	−11669.3	+	3126.77i	−1.54172	+	0.413102i
$88$	−1637.09	+	1637.09i	−0.211401	+	0.211401i
$89$	5076.65	+	1360.29i	0.640911	+	0.171731i	0.564616	−	0.825354i	$-0.309024\pi$
$89$	5076.65	+	1360.29i	0.640911	+	0.171731i	0.0762948	+	0.997085i	$0.475691\pi$
$90$	270.901	+	469.215i	0.0334446	+	0.0579278i
$91$	2497.00	−	9318.94i	0.301534	−	1.12534i
$92$	2010.42	+	7502.97i	0.237525	+	0.886457i
$93$	5744.03	−	1539.11i	0.664126	−	0.177952i
$94$	−5769.81	−	1546.02i	−0.652989	−	0.174968i
$95$	8561.30	−	4942.87i	0.948621	−	0.547686i
$96$	448.363	−	1673.31i	0.0486505	−	0.181566i
$97$	11036.0	+	11036.0i	1.17292	+	1.17292i	0.981510	+	0.191409i	$0.0613058\pi$
$97$	11036.0	+	11036.0i	1.17292	+	1.17292i	0.191409	+	0.981510i	$0.438694\pi$
$98$	2099.22	+	7834.41i	0.218578	+	0.815745i
$99$	937.814	−	541.447i	0.0956856	−	0.0552441i
$100$	−2379.31			−0.237931
$101$			5598.79i			0.548847i	0.961609	+	0.274423i	$0.0884870\pi$
$101$			5598.79i			0.548847i	−0.961609	+	0.274423i	$0.911513\pi$
$102$	3288.47	−	1898.60i	0.316077	−	0.182487i
$103$	−13301.9	+	13301.9i	−1.25383	+	1.25383i	−0.299840	+	0.953990i	$0.596933\pi$
$103$	−13301.9	+	13301.9i	−1.25383	+	1.25383i	−0.953990	+	0.299840i	$0.903067\pi$
$104$	2604.60	+	1503.77i	0.240810	+	0.139032i
$105$	8890.04	−	8890.04i	0.806353	−	0.806353i
$106$	−1457.81	−	5440.64i	−0.129745	−	0.484215i
$107$	−2824.37	+	4891.96i	−0.246692	+	0.427283i	−0.962606	−	0.270906i	$-0.912677\pi$
$107$	−2824.37	+	4891.96i	−0.246692	+	0.427283i	0.715914	+	0.698188i	$0.246010\pi$
$108$	2695.52	−	4668.78i	0.231097	−	0.400273i
$109$	−2273.27	+	8483.95i	−0.191336	+	0.714077i	0.801848	+	0.597527i	$0.203850\pi$
$109$	−2273.27	+	8483.95i	−0.191336	+	0.714077i	−0.993185	+	0.116550i	$0.962817\pi$
$110$		−	5237.94i		−	0.432887i
$111$	11232.7	−	6743.09i	0.911670	−	0.547284i
$112$	−4645.45			−0.370332
$113$	−15027.4	−	4026.58i	−1.17687	−	0.315340i	−0.383184	−	0.923672i	$-0.625172\pi$
$113$	−15027.4	−	4026.58i	−1.17687	−	0.315340i	−0.793683	+	0.608332i	$0.791839\pi$
$114$	12803.6	+	7392.14i	0.985193	+	0.568801i
$115$	−15219.2	−	8786.83i	−1.15079	−	0.664411i
$116$	−9754.93	+	2613.83i	−0.724950	+	0.194250i
$117$	−994.705	−	994.705i	−0.0726645	−	0.0726645i
$118$	2143.90	−	3713.34i	0.153971	−	0.266686i
$119$	−7200.15	−	7200.15i	−0.508449	−	0.508449i
$120$	1959.64	+	3394.20i	0.136086	+	0.235708i
$121$	4172.00			0.284953
$122$		−	3732.15i		−	0.250749i
$123$	4843.43	+	8389.07i	0.320142	+	0.554503i
$124$	4801.73	−	1286.62i	0.312287	−	0.0836771i
$125$	11805.2	−	11805.2i	0.755533	−	0.755533i
$126$	2098.79	+	562.370i	0.132199	+	0.0354226i
$127$	5145.77	+	8912.73i	0.319038	+	0.552590i	0.980288	−	0.197576i	$-0.0633069\pi$
$127$	5145.77	+	8912.73i	0.319038	+	0.552590i	−0.661249	+	0.750166i	$0.729974\pi$
$128$	374.810	−	1398.81i	0.0228766	−	0.0853766i
$129$	4328.60	+	16154.6i	0.260117	+	0.970769i
$130$	−6572.45	+	1761.08i	−0.388902	+	0.104206i
$131$	7233.90	+	1938.32i	0.421531	+	0.112949i	0.463348	−	0.886176i	$-0.346648\pi$
$131$	7233.90	+	1938.32i	0.421531	+	0.112949i	−0.0418169	+	0.999125i	$0.513315\pi$
$132$	6783.94	−	3916.71i	0.389345	−	0.224788i
$133$	10261.0	−	38294.6i	0.580079	−	2.16488i
$134$	8069.51	+	8069.51i	0.449405	+	0.449405i
$135$	3156.76	+	11781.2i	0.173210	+	0.646430i
$136$	2749.00	−	1587.14i	0.148627	−	0.0858097i
$137$	−1833.19			−0.0976713			−0.0488356	−	0.998807i	$-0.515551\pi$
$137$	−1833.19			−0.0976713			−0.0488356	+	0.998807i	$0.515551\pi$
$138$		−	26281.7i		−	1.38005i
$139$	−27223.5	+	15717.5i	−1.40901	+	0.813492i	−0.995293	−	0.0969134i	$-0.969103\pi$
$139$	−27223.5	+	15717.5i	−1.40901	+	0.813492i	−0.413717	+	0.910406i	$0.635770\pi$
$140$	7431.65	−	7431.65i	0.379166	−	0.379166i
$141$	17503.0	+	10105.4i	0.880389	+	0.508293i
$142$	−6744.92	+	6744.92i	−0.334503	+	0.334503i
$143$	3519.85	+	13136.3i	0.172128	+	0.642392i
$144$	−338.675	+	586.603i	−0.0163327	+	0.0282891i
$145$	11424.1	−	19787.2i	0.543359	−	0.941126i
$146$	−1133.74	+	4231.16i	−0.0531871	+	0.198497i
$147$		−	27442.7i		−	1.26997i
$148$	9389.98	−	5636.89i	0.428688	−	0.257345i
$149$	41948.9			1.88951			0.944753	−	0.327783i	$-0.106302\pi$
$149$	41948.9			1.88951			0.944753	+	0.327783i	$0.106302\pi$
$150$	7776.05	+	2083.59i	0.345602	+	0.0926038i
$151$	−34676.4	−	20020.4i	−1.52083	−	0.878050i	−0.999698	−	0.0245728i	$-0.992177\pi$
$151$	−34676.4	−	20020.4i	−1.52083	−	0.878050i	−0.521130	−	0.853478i	$-0.674489\pi$
$152$	10703.2	+	6179.47i	0.463260	+	0.267463i
$153$	−1434.12	+	384.272i	−0.0612637	+	0.0164156i
$154$	−14853.5	−	14853.5i	−0.626309	−	0.626309i
$155$	−5623.37	+	9739.96i	−0.234063	+	0.405409i
$156$	−7195.47	−	7195.47i	−0.295672	−	0.295672i
$157$	−3586.44	−	6211.89i	−0.145500	−	0.252014i	0.784059	−	0.620686i	$-0.213146\pi$
$157$	−3586.44	−	6211.89i	−0.145500	−	0.252014i	−0.929559	+	0.368672i	$0.879813\pi$
$158$	6991.22			0.280052
$159$			19057.7i			0.753834i
$160$	1638.17	+	2837.39i	0.0639908	+	0.110835i
$161$	−68075.5	+	18240.8i	−2.62627	+	0.703706i
$162$	−14612.5	+	14612.5i	−0.556795	+	0.556795i
$163$	−34496.1	−	9243.21i	−1.29836	−	0.347894i	−0.457530	−	0.889194i	$-0.651266\pi$
$163$	−34496.1	−	9243.21i	−1.29836	−	0.347894i	−0.840830	+	0.541300i	$0.817932\pi$
$164$	4048.88	+	7012.86i	0.150538	+	0.260740i
$165$	−4586.91	+	17118.6i	−0.168482	+	0.628782i
$166$	4919.31	+	18359.1i	0.178521	+	0.666248i
$167$	29103.0	−	7798.12i	1.04353	−	0.279613i	0.303954	−	0.952687i	$-0.401693\pi$
$167$	29103.0	−	7798.12i	1.04353	−	0.279613i	0.739575	+	0.673074i	$0.235026\pi$
$168$	15182.2	+	4068.06i	0.537918	+	0.144135i
$169$	−9434.89	+	5447.24i	−0.330342	+	0.190723i
$170$	−1858.72	+	6936.82i	−0.0643154	+	0.240028i
$171$	−4087.57	−	4087.57i	−0.139789	−	0.139789i
$172$	3618.50	+	13504.4i	0.122313	+	0.456478i
$173$	−3054.33	+	1763.42i	−0.102053	+	0.0589201i	−0.550158	−	0.835061i	$-0.685432\pi$
$173$	−3054.33	+	1763.42i	−0.102053	+	0.0589201i	0.448105	+	0.893981i	$0.352099\pi$
$174$	34169.9			1.12861
$175$		−	21587.8i		−	0.704908i
$176$	5671.05	−	3274.18i	0.183079	−	0.105701i
$177$	−10258.5	+	10258.5i	−0.327444	+	0.327444i
$178$	−12873.9	−	7432.74i	−0.406321	−	0.234590i
$179$	−20194.0	+	20194.0i	−0.630256	+	0.630256i	−0.948132	−	0.317876i	$-0.897030\pi$
$179$	−20194.0	+	20194.0i	−0.630256	+	0.630256i	0.317876	+	0.948132i	$0.397030\pi$
$180$	−396.627	−	1480.23i	−0.0122416	−	0.0456862i
$181$	−4460.18	+	7725.25i	−0.136143	+	0.235806i	−0.926033	−	0.377441i	$-0.876804\pi$
$181$	−4460.18	+	7725.25i	−0.136143	+	0.235806i	0.789891	+	0.613248i	$0.210137\pi$
$182$	−13643.9	+	23631.9i	−0.411903	+	0.713437i
$183$	−3268.28	+	12197.4i	−0.0975926	+	0.364220i
$184$		−	21970.2i		−	0.648932i
$185$	−6004.08	+	24039.6i	−0.175430	+	0.702397i
$186$	−16819.7			−0.486174
$187$	13864.5	+	3714.99i	0.396481	+	0.106237i
$188$	14631.7	+	8447.60i	0.413979	+	0.239011i
$189$	42360.5	+	24456.8i	1.18587	+	0.684662i
$190$	−27008.3	+	7236.86i	−0.748154	+	0.200467i
$191$	−17638.2	−	17638.2i	−0.483489	−	0.483489i	0.422755	−	0.906244i	$-0.361063\pi$
$191$	−17638.2	−	17638.2i	−0.483489	−	0.483489i	−0.906244	+	0.422755i	$0.861063\pi$
$192$	−2449.90	+	4243.36i	−0.0664579	+	0.115108i
$193$	−7874.79	−	7874.79i	−0.211410	−	0.211410i	0.593457	−	0.804866i	$-0.297763\pi$
$193$	−7874.79	−	7874.79i	−0.211410	−	0.211410i	−0.804866	+	0.593457i	$0.797763\pi$
$194$	−22072.0	−	38229.8i	−0.586460	−	1.01578i
$195$	23022.2			0.605449
$196$		−	22940.8i		−	0.597167i
$197$	5605.45	+	9708.92i	0.144437	+	0.250172i	0.929163	−	0.369671i	$-0.120530\pi$
$197$	5605.45	+	9708.92i	0.144437	+	0.250172i	−0.784726	+	0.619843i	$0.787196\pi$
$198$	−2958.52	+	792.734i	−0.0754648	+	0.0202207i
$199$	−46663.6	+	46663.6i	−1.17834	+	1.17834i	−0.198179	+	0.980166i	$0.563503\pi$
$199$	−46663.6	+	46663.6i	−1.17834	+	1.17834i	−0.980166	+	0.198179i	$0.936497\pi$
$200$	6500.40	+	1741.78i	0.162510	+	0.0435444i
$201$	−19306.2	−	33439.3i	−0.477864	−	0.827684i
$202$	4098.60	−	15296.2i	0.100446	−	0.374869i
$203$	−23715.6	−	88507.8i	−0.575495	−	2.14778i
$204$	−10374.1	+	2779.74i	−0.249282	+	0.0667950i
$205$	−17696.2	−	4741.69i	−0.421088	−	0.112830i
$206$	46079.1	−	26603.8i	1.08585	−	0.626915i
$207$	−2659.68	+	9926.06i	−0.0620710	+	0.231652i
$208$	−6015.07	−	6015.07i	−0.139032	−	0.139032i
$209$	14464.2	+	53981.3i	0.331133	+	1.23581i
$210$	−30796.0	+	17780.1i	−0.698322	+	0.403177i
$211$	62358.8			1.40066			0.700330	−	0.713819i	$-0.253036\pi$
$211$	62358.8			1.40066			0.700330	+	0.713819i	$0.253036\pi$
$212$			15931.3i			0.354470i
$213$	27950.3	−	16137.1i	0.616065	−	0.355686i
$214$	11297.5	−	11297.5i	0.246692	−	0.246692i
$215$	−27392.8	−	15815.2i	−0.592597	−	0.342136i
$216$	−10782.1	+	10782.1i	−0.231097	+	0.231097i
$217$	11673.7	+	43566.7i	0.247907	+	0.925200i
$218$	12421.4	−	21514.4i	0.261370	−	0.452707i
$219$	7410.53	−	12835.4i	0.154512	−	0.267622i
$220$	−3834.44	+	14310.3i	−0.0792239	+	0.295668i
$221$		−	18646.0i		−	0.381769i
$222$	−35624.5	+	10199.6i	−0.722842	+	0.206955i
$223$	78249.7			1.57352			0.786761	−	0.617257i	$-0.211756\pi$
$223$	78249.7			1.57352			0.786761	+	0.617257i	$0.211756\pi$
$224$	12691.6	+	3400.70i	0.252942	+	0.0677755i
$225$	−2726.00	−	1573.86i	−0.0538469	−	0.0310885i
$226$	38108.0	+	22001.7i	0.746103	+	0.430763i
$227$	−77094.5	+	20657.4i	−1.49614	+	0.400889i	−0.911805	−	0.410624i	$-0.865311\pi$
$227$	−77094.5	+	20657.4i	−1.49614	+	0.400889i	−0.584334	+	0.811513i	$0.698644\pi$
$228$	−29568.6	−	29568.6i	−0.568801	−	0.568801i
$229$	−17268.4	+	29909.7i	−0.329291	+	0.570349i	−0.982371	−	0.186939i	$-0.940143\pi$
$229$	−17268.4	+	29909.7i	−0.329291	+	0.570349i	0.653080	+	0.757289i	$0.273477\pi$
$230$	35147.3	+	35147.3i	0.664411	+	0.664411i
$231$	35536.8	+	61551.6i	0.665970	+	1.15349i
$232$	28564.4			0.530700
$233$		−	20726.5i		−	0.381780i	−0.981611	−	0.190890i	$-0.938863\pi$
$233$		−	20726.5i		−	0.381780i	0.981611	−	0.190890i	$-0.0611374\pi$
$234$	1989.41	+	3445.76i	0.0363323	+	0.0629293i
$235$	−36921.5	+	9893.09i	−0.668565	+	0.179142i
$236$	−8575.59	+	8575.59i	−0.153971	+	0.153971i
$237$	−22848.6	−	6122.27i	−0.406784	−	0.108997i
$238$	14400.3	+	24942.0i	0.254225	+	0.440330i
$239$	27364.6	−	102126.i	0.479064	−	1.78789i	−0.126354	−	0.991985i	$-0.540327\pi$
$239$	27364.6	−	102126.i	0.479064	−	1.78789i	0.605418	−	0.795908i	$-0.293006\pi$
$240$	−2869.11	−	10707.7i	−0.0498110	−	0.185897i
$241$	10794.3	−	2892.33i	0.185850	−	0.0497983i	−0.164694	−	0.986345i	$-0.552664\pi$
$241$	10794.3	−	2892.33i	0.185850	−	0.0497983i	0.350543	+	0.936546i	$0.385997\pi$
$242$	−11398.1	−	3054.11i	−0.194626	−	0.0521500i
$243$	13281.5	−	7668.06i	0.224923	−	0.129859i
$244$	−2732.12	+	10196.4i	−0.0458902	+	0.171265i
$245$	36699.9	+	36699.9i	0.611411	+	0.611411i
$246$	−7091.28	−	26465.0i	−0.117180	−	0.437323i
$247$	62871.3	−	36298.8i	1.03053	−	0.594974i
$248$	−14060.4			−0.228610
$249$		−	64309.1i		−	1.03723i
$250$	−40894.4	+	23610.4i	−0.654311	+	0.377767i
$251$	74907.1	−	74907.1i	1.18898	−	1.18898i	0.211634	−	0.977349i	$-0.432122\pi$
$251$	74907.1	−	74907.1i	1.18898	−	1.18898i	0.977349	−	0.211634i	$-0.0678785\pi$
$252$	−5322.33	−	3072.85i	−0.0838109	−	0.0483882i
$253$	70248.5	−	70248.5i	1.09748	−	1.09748i
$254$	−7533.92	−	28117.0i	−0.116776	−	0.435814i
$255$	12149.3	−	21043.2i	0.186840	−	0.323617i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	14066.2	−	52495.9i	0.212967	−	0.794802i	−0.773906	−	0.633301i	$-0.781700\pi$
$257$	14066.2	−	52495.9i	0.212967	−	0.794802i	0.986872	−	0.161502i	$-0.0516337\pi$
$258$		−	47303.9i		−	0.710652i
$259$	51144.3	+	85196.6i	0.762426	+	1.27006i
$260$	19245.5			0.284696
$261$	−12905.3	−	3457.96i	−0.189447	−	0.0507620i
$262$	−18344.4	−	10591.2i	−0.267240	−	0.154291i
$263$	72524.7	+	41872.2i	1.04852	+	0.605361i	0.922233	−	0.386634i	$-0.126362\pi$
$263$	72524.7	+	41872.2i	1.04852	+	0.605361i	0.126282	+	0.991994i	$0.459696\pi$
$264$	−21401.3	+	5734.46i	−0.307067	+	0.0822782i
$265$	−25486.4	−	25486.4i	−0.362925	−	0.362925i
$266$	−56067.2	+	97111.2i	−0.792402	+	1.37248i
$267$	35565.4	+	35565.4i	0.498890	+	0.498890i
$268$	−16139.0	−	27953.6i	−0.224702	−	0.389196i
$269$	−115991.			−1.60295			−0.801474	−	0.598030i	$-0.795951\pi$
$269$	−115991.			−1.60295			−0.801474	+	0.598030i	$0.795951\pi$
$270$		−	34497.7i		−	0.473220i
$271$	24093.1	+	41730.5i	0.328061	+	0.568218i	0.982127	−	0.188219i	$-0.0602716\pi$
$271$	24093.1	+	41730.5i	0.328061	+	0.568218i	−0.654066	+	0.756437i	$0.726938\pi$
$272$	−8672.27	+	2323.73i	−0.117218	+	0.0314085i
$273$	65285.5	−	65285.5i	0.875975	−	0.875975i
$274$	5008.37	+	1341.99i	0.0667107	+	0.0178751i
$275$	15215.4	+	26353.9i	0.201196	+	0.348481i
$276$	−19239.5	+	71802.9i	−0.252567	+	0.942593i
$277$	−16993.5	−	63420.5i	−0.221474	−	0.826552i	−0.983787	−	0.179343i	$-0.942603\pi$
$277$	−16993.5	−	63420.5i	−0.221474	−	0.826552i	0.762313	−	0.647209i	$-0.224064\pi$
$278$	85881.9	−	23012.0i	1.11125	−	0.297759i
$279$	6352.45	+	1702.13i	0.0816080	+	0.0218668i
$280$	−25744.0	+	14863.3i	−0.328367	+	0.189583i
$281$	−16981.3	+	63375.1i	−0.215059	+	0.802613i	0.771086	+	0.636731i	$0.219714\pi$
$281$	−16981.3	+	63375.1i	−0.215059	+	0.802613i	−0.986146	+	0.165882i	$0.946953\pi$
$282$	−40421.5	−	40421.5i	−0.508293	−	0.508293i
$283$	−36002.6	−	134364.i	−0.449533	−	1.67768i	−0.703682	−	0.710515i	$-0.748462\pi$
$283$	−36002.6	−	134364.i	−0.449533	−	1.67768i	0.254149	−	0.967165i	$-0.418205\pi$
$284$	23365.1	−	13489.8i	0.289688	−	0.167251i
$285$	94605.9			1.16474
$286$		−	38465.7i		−	0.470263i
$287$	−63628.6	+	36736.0i	−0.772482	+	0.445993i
$288$	1354.70	−	1354.70i	0.0163327	−	0.0163327i
$289$	55288.2	+	31920.7i	0.661968	+	0.382187i
$290$	−45696.5	+	45696.5i	−0.543359	+	0.543359i
$291$	38657.3	+	144271.i	0.456505	+	1.70370i
$292$	6194.85	−	10729.8i	0.0726549	−	0.125842i
$293$	10973.3	−	19006.3i	0.127821	−	0.221392i	−0.795011	−	0.606595i	$-0.792535\pi$
$293$	10973.3	−	19006.3i	0.127821	−	0.221392i	0.922832	+	0.385202i	$0.125868\pi$
$294$	−20089.4	+	74974.8i	−0.232420	+	0.867403i
$295$		−	27438.0i		−	0.315288i
$296$	−29780.4	+	8526.34i	−0.339897	+	0.0973149i
$297$	−68950.2			−0.781668
$298$	−114607.	−	30708.7i	−1.29056	−	0.345804i
$299$	−111765.	−	64527.6i	−1.25015	−	0.721777i
$300$	−19719.3	−	11384.9i	−0.219103	−	0.126499i
$301$	−122528.	+	32831.2i	−1.35239	+	0.362371i
$302$	80081.7	+	80081.7i	0.878050	+	0.878050i
$303$	−26790.0	+	46401.6i	−0.291801	+	0.505415i
$304$	−24717.9	−	24717.9i	−0.267463	−	0.267463i
$305$	−11941.2	−	20682.7i	−0.128365	−	0.222335i
$306$	4199.40			0.0448482
$307$			103669.i			1.09995i	0.835180	+	0.549976i	$0.185363\pi$
$307$			103669.i			1.09995i	−0.835180	+	0.549976i	$0.814637\pi$
$308$	29707.1	+	51454.2i	0.313154	+	0.542399i
$309$	−173892.	+	46594.3i	−1.82122	+	0.487996i
$310$	22493.5	−	22493.5i	0.234063	−	0.234063i
$311$	−81554.8	−	21852.6i	−0.843197	−	0.225934i	−0.188734	−	0.982028i	$-0.560438\pi$
$311$	−81554.8	−	21852.6i	−0.843197	−	0.225934i	−0.654463	+	0.756094i	$0.727105\pi$
$312$	14390.9	+	24925.9i	0.147836	+	0.256059i
$313$	−25227.5	+	94150.2i	−0.257505	+	0.961020i	0.709175	+	0.705032i	$0.249067\pi$
$313$	−25227.5	+	94150.2i	−0.257505	+	0.961020i	−0.966680	+	0.255988i	$0.917599\pi$
$314$	5250.91	+	19596.7i	0.0532568	+	0.198757i
$315$	13430.4	−	3598.65i	0.135352	−	0.0362676i
$316$	−19100.4	−	5117.92i	−0.191279	−	0.0512531i
$317$	−4675.51	+	2699.40i	−0.0465275	+	0.0268627i	−0.523083	−	0.852282i	$-0.675218\pi$
$317$	−4675.51	+	2699.40i	−0.0465275	+	0.0268627i	0.476556	+	0.879144i	$0.341885\pi$
$318$	13951.2	−	52066.5i	0.137961	−	0.514878i
$319$	91333.1	+	91333.1i	0.897525	+	0.897525i
$320$	−2398.44	−	8951.10i	−0.0234223	−	0.0874131i
$321$	−46815.7	+	27029.1i	−0.454341	+	0.262314i
$322$	199339.			1.92256
$323$		−	76622.4i		−	0.734430i
$324$	50619.2	−	29225.0i	0.482198	−	0.278397i
$325$	27952.6	−	27952.6i	0.264640	−	0.264640i
$326$	87478.6	+	50505.8i	0.823127	+	0.475233i
$327$	−59435.8	+	59435.8i	−0.555844	+	0.555844i
$328$	−5927.96	−	22123.5i	−0.0551008	−	0.205639i
$329$	−76646.2	+	132755.i	−0.708107	+	1.22648i
$330$	25063.4	−	43411.0i	0.230150	−	0.398632i
$331$	−24537.4	+	91574.7i	−0.223961	+	0.835833i	0.758857	+	0.651257i	$0.225758\pi$
$331$	−24537.4	+	91574.7i	−0.223961	+	0.835833i	−0.982818	+	0.184576i	$0.940909\pi$
$332$		−	53759.3i		−	0.487727i
$333$	14486.8	−	246.999i	0.130643	−	0.00222745i
$334$	−85219.5			−0.763917
$335$	70538.1	+	18900.6i	0.628542	+	0.168417i
$336$	−38500.5	−	22228.3i	−0.341027	−	0.196892i
$337$	−56879.5	−	32839.4i	−0.500836	−	0.289158i	0.228223	−	0.973609i	$-0.426709\pi$
$337$	−56879.5	−	32839.4i	−0.500836	−	0.289158i	−0.729059	+	0.684451i	$0.760042\pi$
$338$	29764.3	−	7975.31i	0.260532	−	0.0698094i
$339$	−105277.	−	105277.i	−0.916083	−	0.916083i
$340$	10156.2	−	17591.1i	0.0878565	−	0.152172i
$341$	−44957.4	−	44957.4i	−0.386628	−	0.386628i
$342$	8175.14	+	14159.8i	0.0698945	+	0.121061i
$343$	33867.8			0.287871
$344$		−	39543.7i		−	0.334165i
$345$	−84089.4	−	145647.i	−0.706485	−	1.22367i
$346$	9635.51	−	2581.83i	0.0804864	−	0.0215663i
$347$	73825.0	−	73825.0i	0.613119	−	0.613119i	−0.330639	−	0.943757i	$-0.607264\pi$
$347$	73825.0	−	73825.0i	0.613119	−	0.613119i	0.943757	+	0.330639i	$0.107264\pi$
$348$	−93354.0	−	25014.1i	−0.770858	−	0.206551i
$349$	37900.0	+	65644.7i	0.311163	+	0.538950i	0.978614	−	0.205703i	$-0.0659482\pi$
$349$	37900.0	+	65644.7i	0.311163	+	0.538950i	−0.667451	+	0.744653i	$0.732615\pi$
$350$	−15803.4	+	58979.0i	−0.129007	+	0.481461i
$351$	23182.2	+	86517.1i	0.188166	+	0.702244i
$352$	−17890.5	+	4793.73i	−0.144390	+	0.0386891i
$353$	34893.5	+	9349.67i	0.280024	+	0.0750321i	0.396097	−	0.918208i	$-0.370364\pi$
$353$	34893.5	+	9349.67i	0.280024	+	0.0750321i	−0.116074	+	0.993241i	$0.537031\pi$
$354$	35536.4	−	20517.0i	0.283574	−	0.163722i
$355$	−15798.1	+	58959.4i	−0.125357	+	0.467839i
$356$	29730.9	+	29730.9i	0.234590	+	0.234590i
$357$	−25221.0	−	94125.9i	−0.197891	−	0.738538i
$358$	69954.1	−	40388.0i	0.545817	−	0.315128i
$359$	−83839.2			−0.650516			−0.325258	−	0.945625i	$-0.605451\pi$
$359$	−83839.2			−0.650516			−0.325258	+	0.945625i	$0.605451\pi$
$360$			4334.42i			0.0334446i
$361$	145498.	−	84003.2i	1.11646	−	0.644587i
$362$	17840.7	−	17840.7i	0.136143	−	0.136143i
$363$	34576.7	+	19962.9i	0.262404	+	0.151499i
$364$	54575.5	−	54575.5i	0.411903	−	0.411903i
$365$	7254.87	+	27075.5i	0.0544558	+	0.203232i
$366$	17858.2	−	30931.3i	0.133314	−	0.230906i
$367$	62813.0	−	108795.i	0.466356	−	0.807752i	−0.532906	−	0.846175i	$-0.678900\pi$
$367$	62813.0	−	108795.i	0.466356	−	0.807752i	0.999262	+	0.0384227i	$0.0122333\pi$
$368$	−16083.3	+	60023.8i	−0.118763	+	0.443229i
$369$			10712.9i			0.0786783i
$370$	34001.6	−	61282.0i	0.248368	−	0.447641i
$371$	−144547.			−1.05017
$372$	45952.2	+	12312.9i	0.332063	+	0.0889761i
$373$	147987.	+	85440.3i	1.06367	+	0.614109i	0.926444	−	0.376432i	$-0.122849\pi$
$373$	147987.	+	85440.3i	1.06367	+	0.614109i	0.137223	+	0.990540i	$0.456182\pi$
$374$	−35159.1	−	20299.1i	−0.251359	−	0.145122i
$375$	154327.	−	41351.7i	1.09743	−	0.294057i
$376$	−33790.4	−	33790.4i	−0.239011	−	0.239011i
$377$	83895.0	−	145310.i	0.590273	−	1.02238i
$378$	−97827.3	−	97827.3i	−0.684662	−	0.684662i
$379$	−84059.3	−	145595.i	−0.585204	−	1.01360i	−0.994850	−	0.101359i	$-0.967681\pi$
$379$	−84059.3	−	145595.i	−0.585204	−	1.01360i	0.409646	−	0.912245i	$-0.365652\pi$
$380$	79085.9			0.547686
$381$			98489.3i			0.678483i
$382$	35276.3	+	61100.4i	0.241744	+	0.418714i
$383$	−17421.5	+	4668.07i	−0.118765	+	0.0318229i	−0.317712	−	0.948187i	$-0.602914\pi$
$383$	−17421.5	+	4668.07i	−0.118765	+	0.0318229i	0.198947	+	0.980010i	$0.436248\pi$
$384$	9799.61	−	9799.61i	0.0664579	−	0.0664579i
$385$	−129839.	−	34790.4i	−0.875962	−	0.234713i
$386$	15749.6	+	27279.1i	0.105705	+	0.183086i
$387$	−4787.10	+	17865.7i	−0.0319632	+	0.119288i
$388$	32315.7	+	120604.i	0.214659	+	0.801119i
$389$	175773.	−	47098.1i	1.16159	−	0.311246i	0.373988	−	0.927434i	$-0.377990\pi$
$389$	175773.	−	47098.1i	1.16159	−	0.311246i	0.787600	+	0.616187i	$0.211324\pi$
$390$	−62897.9	−	16853.4i	−0.413530	−	0.110805i
$391$	−117961.	+	68105.0i	−0.771589	+	0.445477i
$392$	−16793.8	+	62675.3i	−0.109289	+	0.407872i
$393$	50678.4	+	50678.4i	0.328124	+	0.328124i
$394$	−8206.94	−	30628.7i	−0.0528675	−	0.197304i
$395$	38743.7	−	22368.7i	0.248317	−	0.143366i
$396$	8663.16			0.0552441
$397$			161561.i			1.02507i	0.858666	+	0.512536i	$0.171294\pi$
$397$			161561.i			1.02507i	−0.858666	+	0.512536i	$0.828706\pi$
$398$	161648.	−	93327.2i	1.02048	−	0.589172i
$399$	268280.	−	268280.i	1.68516	−	1.68516i
$400$	−16484.4	−	9517.25i	−0.103027	−	0.0594828i
$401$	73656.6	−	73656.6i	0.458061	−	0.458061i	−0.439958	−	0.898018i	$-0.645007\pi$
$401$	73656.6	−	73656.6i	0.458061	−	0.458061i	0.898018	+	0.439958i	$0.145007\pi$
$402$	28266.2	+	105491.i	0.174910	+	0.652774i
$403$	−41296.1	+	71527.0i	−0.254273	+	0.440413i
$404$	−22395.1	+	38789.5i	−0.137212	+	0.237658i
$405$	−34225.8	+	127733.i	−0.208662	+	0.778738i
$406$			259169.i			1.57228i
$407$	−122484.	−	67958.6i	−0.739416	−	0.410257i
$408$	30377.6			0.182487
$409$	22432.7	+	6010.81i	0.134102	+	0.0359324i	0.325246	−	0.945630i	$-0.394553\pi$
$409$	22432.7	+	6010.81i	0.134102	+	0.0359324i	−0.191144	+	0.981562i	$0.561220\pi$
$410$	44875.9	+	25909.1i	0.266959	+	0.154129i
$411$	−15193.1	−	8771.76i	−0.0899423	−	0.0519282i
$412$	−145366.	+	38950.6i	−0.856381	+	0.229467i
$413$	−77807.5	−	77807.5i	−0.456164	−	0.456164i
$414$	14532.8	−	25171.5i	0.0847905	−	0.146862i
$415$	86002.5	+	86002.5i	0.499361	+	0.499361i
$416$	12030.1	+	20836.8i	0.0695159	+	0.120405i
$417$	−300830.			−1.73001
$418$		−	158068.i		−	0.904673i
$419$	59939.4	+	103818.i	0.341417	+	0.591351i	0.984696	−	0.174281i	$-0.0557600\pi$
$419$	59939.4	+	103818.i	0.341417	+	0.591351i	−0.643279	+	0.765631i	$0.722427\pi$
$420$	97152.2	−	26031.9i	0.550750	−	0.147573i
$421$	−119336.	+	119336.i	−0.673299	+	0.673299i	−0.958475	−	0.285176i	$-0.907948\pi$
$421$	−119336.	+	119336.i	−0.673299	+	0.673299i	0.285176	+	0.958475i	$0.407948\pi$
$422$	−170367.	−	45649.8i	−0.956669	−	0.256339i
$423$	11175.7	+	19357.0i	0.0624591	+	0.108182i
$424$	11662.5	−	43525.1i	0.0648725	−	0.242107i
$425$	−10798.6	−	40300.9i	−0.0597845	−	0.223119i
$426$	−88174.7	+	23626.3i	−0.485875	+	0.130190i
$427$	−92513.5	−	24788.9i	−0.507399	−	0.135957i
$428$	−39135.7	+	22595.0i	−0.213641	+	0.123346i
$429$	−33684.8	+	125713.i	−0.183029	+	0.683072i
$430$	63260.9	+	63260.9i	0.342136	+	0.342136i
$431$	44293.1	+	165304.i	0.238441	+	0.889876i	0.976567	+	0.215213i	$0.0690444\pi$
$431$	44293.1	+	165304.i	0.238441	+	0.889876i	−0.738126	+	0.674663i	$0.764289\pi$
$432$	37350.2	−	21564.2i	0.200136	−	0.115549i
$433$	265556.			1.41638			0.708192	−	0.706020i	$-0.249511\pi$
$433$	265556.			1.41638			0.708192	+	0.706020i	$0.249511\pi$
$434$		−	127572.i		−	0.677293i
$435$	189362.	−	109328.i	1.00072	−	0.577768i
$436$	−49685.5	+	49685.5i	−0.261370	+	0.261370i
$437$	−459279.	−	265165.i	−2.40499	−	1.38852i
$438$	−29642.1	+	29642.1i	−0.154512	+	0.154512i
$439$	37654.4	+	140528.i	0.195383	+	0.729180i	0.992167	+	0.124916i	$0.0398661\pi$
$439$	37654.4	+	140528.i	0.195383	+	0.729180i	−0.796784	+	0.604264i	$0.793467\pi$
$440$	20951.8	−	36289.5i	0.108222	−	0.187446i
$441$	15174.7	−	26283.4i	0.0780268	−	0.135146i
$442$	−13649.8	+	50941.7i	−0.0698685	+	0.260753i
$443$		−	291905.i		−	1.48742i	−0.668501	−	0.743711i	$-0.733064\pi$
$443$		−	291905.i		−	1.48742i	0.668501	−	0.743711i	$-0.266936\pi$
$444$	104795.	−	1786.74i	0.531586	−	0.00906348i
$445$	−95125.4			−0.480371
$446$	−213782.	−	57282.8i	−1.07474	−	0.287975i
$447$	347664.	+	200724.i	1.73998	+	1.00458i
$448$	−32184.6	−	18581.8i	−0.160358	−	0.0925830i
$449$	236386.	−	63339.5i	1.17254	−	0.314182i	0.380579	−	0.924748i	$-0.375725\pi$
$449$	236386.	−	63339.5i	1.17254	−	0.314182i	0.791965	+	0.610566i	$0.209058\pi$
$450$	6295.42	+	6295.42i	0.0310885	+	0.0310885i
$451$	51784.2	−	89692.8i	0.254592	−	0.440966i
$452$	−88006.6	−	88006.6i	−0.430763	−	0.430763i
$453$	−191594.	−	331851.i	−0.933654	−	1.61714i
$454$	225748.			1.09525
$455$			174617.i			0.843457i
$456$	59137.1	+	102429.i	0.284401	+	0.492596i
$457$	44335.2	−	11879.6i	0.212284	−	0.0568812i	−0.151110	−	0.988517i	$-0.548285\pi$
$457$	44335.2	−	11879.6i	0.212284	−	0.0568812i	0.363394	+	0.931636i	$0.381618\pi$
$458$	69073.5	−	69073.5i	0.329291	−	0.329291i
$459$	91313.6	+	24467.4i	0.433421	+	0.116135i
$460$	−70294.7	−	121754.i	−0.332205	−	0.575397i
$461$	−93701.0	+	349697.i	−0.440902	+	1.64547i	0.285632	+	0.958339i	$0.407796\pi$
$461$	−93701.0	+	349697.i	−0.440902	+	1.64547i	−0.726535	+	0.687130i	$0.758870\pi$
$462$	−52029.6	−	194177.i	−0.243762	−	0.909733i
$463$	236666.	−	63414.3i	1.10401	−	0.295819i	0.339614	−	0.940565i	$-0.389704\pi$
$463$	236666.	−	63414.3i	1.10401	−	0.295819i	0.764397	+	0.644746i	$0.223037\pi$
$464$	−78039.4	−	20910.6i	−0.362475	−	0.0971249i
$465$	−93210.8	+	53815.3i	−0.431082	+	0.248886i
$466$	−15172.8	+	56625.8i	−0.0698706	+	0.260761i
$467$	154729.	+	154729.i	0.709477	+	0.709477i	0.966425	−	0.256948i	$-0.0827170\pi$
$467$	154729.	+	154729.i	0.709477	+	0.709477i	−0.256948	+	0.966425i	$0.582717\pi$
$468$	−2912.70	−	10870.3i	−0.0132985	−	0.0496308i
$469$	253627.	−	146432.i	1.15305	−	0.665716i
$470$	108114.			0.489424
$471$		−	68643.9i		−	0.309428i
$472$	29706.7	−	17151.2i	0.133343	−	0.0769857i
$473$	126439.	−	126439.i	0.565143	−	0.565143i
$474$	57941.8	+	33452.7i	0.257891	+	0.148893i
$475$	114866.	−	114866.i	0.509103	−	0.509103i
$476$	−21083.5	−	78684.7i	−0.0930527	−	0.347277i
$477$	−10538.2	+	18252.6i	−0.0463157	+	0.0802211i
$478$	−149523.	+	258982.i	−0.654414	+	1.13348i
$479$	−86636.4	+	323332.i	−0.377598	+	1.40921i	0.471914	+	0.881645i	$0.343563\pi$
$479$	−86636.4	+	323332.i	−0.377598	+	1.40921i	−0.849512	+	0.527570i	$0.823103\pi$
$480$			31354.3i			0.136086i
$481$	−44091.9	+	176538.i	−0.190576	+	0.763043i
$482$	−31608.0			−0.136051
$483$	−651478.	−	174563.i	−2.79258	−	0.748269i
$484$	28904.4	+	16688.0i	0.123388	+	0.0712382i
$485$	−244636.	−	141241.i	−1.04001	−	0.600449i
$486$	−41899.0	+	11226.8i	−0.177391	+	0.0475318i
$487$	248817.	+	248817.i	1.04911	+	1.04911i	0.998730	+	0.0503816i	$0.0160438\pi$
$487$	248817.	+	248817.i	1.04911	+	1.04911i	0.0503816	+	0.998730i	$0.483956\pi$
$488$	14928.6	−	25857.1i	0.0626872	−	0.108577i
$489$	−241669.	−	241669.i	−1.01065	−	1.01065i
$490$	−73399.9	−	127132.i	−0.305706	−	0.529497i
$491$	−281769.			−1.16877			−0.584386	−	0.811476i	$-0.698665\pi$
$491$	−281769.			−1.16877			−0.584386	+	0.811476i	$0.698665\pi$
$492$			77494.9i			0.320142i
$493$	−88546.1	−	153366.i	−0.364314	−	0.631010i
$494$	−198340.	+	53145.1i	−0.812750	+	0.217776i
$495$	−13859.1	+	13859.1i	−0.0565618	+	0.0565618i
$496$	38413.8	+	10293.0i	0.156144	+	0.0418386i
$497$	122395.	+	211994.i	0.495509	+	0.858246i
$498$	−47077.5	+	175696.i	−0.189826	+	0.708439i
$499$	−105760.	−	394700.i	−0.424735	−	1.58513i	−0.764500	−	0.644623i	$-0.777014\pi$
$499$	−105760.	−	394700.i	−0.424735	−	1.58513i	0.339765	−	0.940510i	$-0.389652\pi$
$500$	129010.	−	34568.0i	0.516039	−	0.138272i
$501$	278514.	+	74627.5i	1.10961	+	0.297320i
$502$	−259486.	+	149814.i	−1.02969	+	0.594491i
$503$	−86561.1	+	323050.i	−0.342126	+	1.27683i	0.553807	+	0.832645i	$0.313175\pi$
$503$	−86561.1	+	323050.i	−0.342126	+	1.27683i	−0.895933	+	0.444188i	$0.853492\pi$
$504$	12291.4	+	12291.4i	0.0483882	+	0.0483882i
$505$	−26227.3	−	97881.4i	−0.102842	−	0.383811i
$506$	−243348.	+	140497.i	−0.950445	+	0.548740i
$507$	−104259.			−0.405601
$508$			82332.3i			0.319038i
$509$	−280589.	+	161998.i	−1.08302	+	0.625280i	−0.931709	−	0.363206i	$-0.881682\pi$
$509$	−280589.	+	161998.i	−1.08302	+	0.625280i	−0.151309	+	0.988487i	$0.548349\pi$
$510$	−48597.1	+	48597.1i	−0.186840	+	0.186840i
$511$	97352.9	+	56206.7i	0.372827	+	0.215252i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	95263.3	+	355527.i	0.361985	+	1.35095i
$514$	−76859.3	+	133124.i	−0.290918	+	0.503884i
$515$	170240.	−	294864.i	0.641869	−	1.11175i
$516$	−34628.8	+	129237.i	−0.130058	+	0.485385i
$517$		−	216086.i		−	0.808434i
$518$	−77360.6	−	270202.i	−0.288310	−	1.00700i
$519$	−33751.6			−0.125303
$520$	−52579.6	−	14088.7i	−0.194451	−	0.0521030i
$521$	459470.	+	265275.i	1.69271	+	0.977285i	0.952319	+	0.305105i	$0.0986916\pi$
$521$	459470.	+	265275.i	1.69271	+	0.977285i	0.740388	+	0.672180i	$0.234642\pi$
$522$	32726.5	+	18894.6i	0.120104	+	0.0693422i
$523$	258320.	−	69216.7i	0.944398	−	0.253051i	0.246415	−	0.969165i	$-0.420748\pi$
$523$	258320.	−	69216.7i	0.944398	−	0.253051i	0.697984	+	0.716114i	$0.254081\pi$
$524$	42364.6	+	42364.6i	0.154291	+	0.154291i
$525$	103297.	−	178916.i	0.374774	−	0.649127i
$526$	−167489.	−	167489.i	−0.605361	−	0.605361i
$527$	43585.6	+	75492.5i	0.156936	+	0.271821i
$528$	62667.4			0.224788
$529$			662915.i			2.36890i
$530$	50972.8	+	88287.5i	0.181463	+	0.314302i
$531$	−15497.7	+	4152.59i	−0.0549639	+	0.0147275i
$532$	224269.	−	224269.i	0.792402	−	0.792402i
$533$	−129955.	−	34821.4i	−0.457445	−	0.122572i
$534$	−71130.8	−	123202.i	−0.249445	−	0.432052i
$535$	26461.3	−	98754.9i	0.0924493	−	0.345025i
$536$	23629.2	+	88185.3i	0.0822468	+	0.306949i
$537$	−263992.	+	70736.4i	−0.915465	+	0.245298i
$538$	316893.	+	84911.3i	1.09483	+	0.293360i
$539$	−254098.	+	146703.i	−0.874628	+	0.504967i
$540$	−25254.1	+	94249.5i	−0.0866052	+	0.323215i
$541$	−165201.	−	165201.i	−0.564440	−	0.564440i	0.366125	−	0.930566i	$-0.380684\pi$
$541$	−165201.	−	165201.i	−0.564440	−	0.564440i	−0.930566	+	0.366125i	$0.880684\pi$
$542$	−35274.8	−	131647.i	−0.120079	−	0.448139i
$543$	−73930.1	+	42683.6i	−0.250739	+	0.144764i
$544$	25394.2			0.0858097
$545$		−	158971.i		−	0.535210i
$546$	−226156.	+	130571.i	−0.758616	+	0.437987i
$547$	−3798.88	+	3798.88i	−0.0126964	+	0.0126964i	−0.713426	−	0.700730i	$-0.752858\pi$
$547$	−3798.88	+	3798.88i	−0.0126964	+	0.0126964i	0.700730	+	0.713426i	$0.252858\pi$
$548$	−12700.7	−	7332.77i	−0.0422929	−	0.0244178i
$549$	−9874.89	+	9874.89i	−0.0327633	+	0.0327633i
$550$	−22276.9	−	83138.6i	−0.0736427	−	0.274838i
$551$	344752.	−	597128.i	1.13554	−	1.96682i
$552$	105127.	−	182085.i	0.345013	−	0.597580i
$553$	46435.6	−	173300.i	0.151845	−	0.566694i
$554$			185708.i			0.605078i
$555$	−164789.	+	170506.i	−0.534986	+	0.553545i
$556$	−251480.			−0.813492
$557$	456838.	+	122409.i	1.47249	+	0.394552i	0.903783	−	0.427990i	$-0.140778\pi$
$557$	456838.	+	122409.i	1.47249	+	0.394552i	0.568704	+	0.822542i	$0.307445\pi$
$558$	−16109.2	−	9300.63i	−0.0517374	−	0.0298706i
$559$	−201163.	−	116142.i	−0.643762	−	0.371676i
$560$	81214.5	−	21761.4i	0.258975	−	0.0693921i
$561$	97130.5	+	97130.5i	0.308624	+	0.308624i
$562$	92787.6	−	160713.i	0.293777	−	0.508836i
$563$	−104456.	−	104456.i	−0.329547	−	0.329547i	0.522867	−	0.852414i	$-0.324862\pi$
$563$	−104456.	−	104456.i	−0.329547	−	0.329547i	−0.852414	+	0.522867i	$0.824862\pi$
$564$	80842.9	+	140024.i	0.254146	+	0.440194i
$565$	281581.			0.882076
$566$			393444.i			1.22815i
$567$	265163.	+	459275.i	0.824796	+	1.42859i
$568$	−73709.8	+	19750.5i	−0.228470	+	0.0612183i
$569$	306476.	−	306476.i	0.946612	−	0.946612i	−0.0520335	−	0.998645i	$-0.516570\pi$
$569$	306476.	−	306476.i	0.946612	−	0.946612i	0.998645	+	0.0520335i	$0.0165703\pi$
$570$	−258468.	−	69256.3i	−0.795531	−	0.213162i
$571$	−147284.	−	255103.i	−0.451735	−	0.782427i	0.546759	−	0.837290i	$-0.315861\pi$
$571$	−147284.	−	255103.i	−0.451735	−	0.782427i	−0.998494	+	0.0548627i	$0.982528\pi$
$572$	−28158.8	+	105090.i	−0.0860642	+	0.321196i
$573$	−61783.6	−	230580.i	−0.188176	−	0.702282i
$574$	200729.	−	53785.2i	0.609238	−	0.163245i
$575$	−278936.	−	74740.7i	−0.843663	−	0.226059i
$576$	−4692.82	+	2709.40i	−0.0141445	+	0.00816636i
$577$	−54992.2	+	205234.i	−0.165177	+	0.616448i	0.832841	+	0.553513i	$0.186713\pi$
$577$	−54992.2	+	205234.i	−0.165177	+	0.616448i	−0.998018	+	0.0629357i	$0.979954\pi$
$578$	−127683.	−	127683.i	−0.382187	−	0.382187i
$579$	−27584.1	−	102945.i	−0.0822815	−	0.307079i
$580$	158297.	−	91393.0i	0.470563	−	0.271680i
$581$	487765.			1.44497
$582$		−	422455.i		−	1.24720i
$583$	176459.	−	101879.i	0.519167	−	0.299741i
$584$	−24779.4	+	24779.4i	−0.0726549	+	0.0726549i
$585$	22049.7	+	12730.4i	0.0644304	+	0.0371989i
$586$	−43893.2	+	43893.2i	−0.127821	+	0.127821i
$587$	−83728.0	−	312477.i	−0.242994	−	0.906864i	−0.974381	−	0.224902i	$-0.927794\pi$
$587$	−83728.0	−	312477.i	−0.242994	−	0.906864i	0.731388	−	0.681962i	$-0.238873\pi$
$588$	109771.	−	190128.i	0.317491	−	0.549911i
$589$	−169699.	+	293928.i	−0.489159	+	0.847248i
$590$	−20086.0	+	74961.9i	−0.0577017	+	0.215346i
$591$			107287.i			0.307167i
$592$	87603.3	−	1493.63i	0.249964	−	0.00426185i
$593$	−328329.			−0.933683			−0.466841	−	0.884341i	$-0.654608\pi$
$593$	−328329.			−0.933683			−0.466841	+	0.884341i	$0.654608\pi$
$594$	188375.	+	50475.0i	0.533889	+	0.143055i
$595$	159606.	+	92148.7i	0.450833	+	0.260289i
$596$	290631.	+	167796.i	0.818180	+	0.472376i
$597$	−610023.	+	163455.i	−1.71158	+	0.458617i
$598$	258110.	+	258110.i	0.721777	+	0.721777i
$599$	187920.	−	325486.i	0.523743	−	0.907150i	−0.475875	−	0.879513i	$-0.657868\pi$
$599$	187920.	−	325486.i	0.523743	−	0.907150i	0.999618	−	0.0276368i	$-0.00879820\pi$
$600$	45539.7	+	45539.7i	0.126499	+	0.126499i
$601$	117824.	+	204077.i	0.326200	+	0.564994i	0.981754	−	0.190153i	$-0.0608985\pi$
$601$	117824.	+	204077.i	0.326200	+	0.564994i	−0.655555	+	0.755148i	$0.727565\pi$
$602$	358786.			0.990016
$603$		−	42702.3i		−	0.117440i
$604$	−160163.	−	277411.i	−0.439025	−	0.760414i
$605$	−72937.4	+	19543.5i	−0.199269	+	0.0533940i
$606$	107160.	−	107160.i	0.291801	−	0.291801i
$607$	47042.2	+	12604.9i	0.127676	+	0.0342108i	0.322091	−	0.946709i	$-0.395614\pi$
$607$	47042.2	+	12604.9i	0.127676	+	0.0342108i	−0.194415	+	0.980919i	$0.562281\pi$
$608$	49435.8	+	85625.3i	0.133732	+	0.231630i
$609$	226957.	−	847014.i	0.611939	−	2.28379i
$610$	17483.1	+	65247.7i	0.0469849	+	0.175350i
$611$	−271139.	+	72651.6i	−0.726290	+	0.194609i
$612$	−11473.0	−	3074.18i	−0.0306319	−	0.00820778i
$613$	205696.	−	118759.i	0.547401	−	0.316042i	−0.200672	−	0.979658i	$-0.564313\pi$
$613$	205696.	−	118759.i	0.547401	−	0.316042i	0.748073	+	0.663616i	$0.230979\pi$
$614$	75891.3	−	283230.i	0.201305	−	0.751281i
$615$	−123974.	−	123974.i	−0.327779	−	0.327779i
$616$	−43494.2	−	162323.i	−0.114622	−	0.427777i
$617$	87837.3	−	50712.9i	0.230732	−	0.133213i	−0.380177	−	0.924914i	$-0.624137\pi$
$617$	87837.3	−	50712.9i	0.230732	−	0.133213i	0.610910	+	0.791700i	$0.290804\pi$
$618$	509192.			1.33323
$619$			66828.7i			0.174414i	0.996190	+	0.0872071i	$0.0277942\pi$
$619$			66828.7i			0.174414i	−0.996190	+	0.0872071i	$0.972206\pi$
$620$	−77919.7	+	44987.0i	−0.202705	+	0.117032i
$621$	462666.	−	462666.i	1.19973	−	1.19973i
$622$	206815.	+	119405.i	0.534565	+	0.308631i
$623$	−269753.	+	269753.i	−0.695008	+	0.695008i
$624$	−21069.8	−	78633.6i	−0.0541117	−	0.201948i
$625$	−58143.1	+	100707.i	−0.148846	+	0.257809i
$626$	137845.	−	238755.i	0.351758	−	0.609262i
$627$	−138422.	+	516597.i	−0.352103	+	1.31406i
$628$		−	57383.0i		−	0.145500i
$629$	138095.	+	133465.i	0.349040	+	0.337337i
$630$	−39326.8			−0.0990849
$631$	−509606.	−	136549.i	−1.27990	−	0.342948i	−0.446084	−	0.894991i	$-0.647182\pi$
$631$	−509606.	−	136549.i	−1.27990	−	0.342948i	−0.833816	+	0.552043i	$0.813849\pi$
$632$	48436.6	+	27964.9i	0.121266	+	0.0700130i
$633$	516818.	+	298385.i	1.28982	+	0.744679i
$634$	14749.8	−	3952.20i	0.0366951	−	0.00983243i
$635$	−131713.	−	131713.i	−0.326648	−	0.326648i
$636$	−76230.7	+	132035.i	−0.188458	+	0.326420i
$637$	269512.	+	269512.i	0.664201	+	0.664201i
$638$	−182666.	−	316387.i	−0.448763	−	0.777280i
$639$	35692.8			0.0874135
$640$			26210.6i			0.0639908i
$641$	186200.	+	322508.i	0.453173	+	0.784919i	0.998581	−	0.0532520i	$-0.0169587\pi$
$641$	186200.	+	322508.i	0.453173	+	0.784919i	−0.545408	+	0.838171i	$0.683625\pi$
$642$	147690.	−	39573.3i	0.358327	−	0.0960135i
$643$	−298628.	+	298628.i	−0.722285	+	0.722285i	−0.969070	−	0.246785i	$-0.920626\pi$
$643$	−298628.	+	298628.i	−0.722285	+	0.722285i	0.246785	+	0.969070i	$0.420626\pi$
$644$	−544604.	−	145926.i	−1.31313	−	0.351853i
$645$	−151351.	−	262147.i	−0.363802	−	0.630123i
$646$	−56091.5	+	209336.i	−0.134410	+	0.501625i
$647$	−49301.6	−	183996.i	−0.117775	−	0.439541i	0.881705	−	0.471801i	$-0.156396\pi$
$647$	−49301.6	−	183996.i	−0.117775	−	0.439541i	−0.999480	+	0.0322603i	$0.989729\pi$
$648$	−159689.	+	42788.4i	−0.380298	+	0.101900i
$649$	149825.	+	40145.6i	0.355710	+	0.0953122i
$650$	−96830.6	+	55905.2i	−0.229185	+	0.132320i
$651$	−111716.	+	416931.i	−0.263605	+	0.983789i
$652$	−202023.	−	202023.i	−0.475233	−	0.475233i
$653$	33910.6	+	126556.i	0.0795261	+	0.296795i	0.994221	−	0.107349i	$-0.0342361\pi$
$653$	33910.6	+	126556.i	0.0795261	+	0.296795i	−0.914695	+	0.404144i	$0.867569\pi$
$654$	205892.	−	118872.i	0.481375	−	0.277922i
$655$	−135547.			−0.315943
$656$			64782.0i			0.150538i
$657$	14195.0	−	8195.48i	0.0328855	−	0.0189864i
$658$	306585.	−	306585.i	0.708107	−	0.708107i
$659$	−241916.	−	139670.i	−0.557048	−	0.321612i	0.194912	−	0.980821i	$-0.437558\pi$
$659$	−241916.	−	139670.i	−0.557048	−	0.321612i	−0.751960	+	0.659209i	$0.770891\pi$
$660$	−100253.	+	100253.i	−0.230150	+	0.230150i
$661$	−145356.	−	542475.i	−0.332682	−	1.24159i	−0.906360	−	0.422506i	$-0.861151\pi$
$661$	−145356.	−	542475.i	−0.332682	−	1.24159i	0.573678	−	0.819081i	$-0.305516\pi$
$662$	134075.	−	232224.i	0.305936	−	0.529897i
$663$	89220.3	−	154534.i	0.202972	−	0.351558i
$664$	−39354.5	+	146873.i	−0.0892603	+	0.333124i
$665$			717557.i			1.62261i
$666$	−39759.6	−	9930.29i	−0.0896383	−	0.0223879i
$667$	−1.22572e6			−2.75511
$668$	232824.	+	62385.0i	0.521765	+	0.139806i
$669$	648518.	+	374422.i	1.44901	+	0.836584i
$670$	−178877.	−	103275.i	−0.398480	−	0.230062i
$671$	130410.	−	34943.2i	0.289644	−	0.0776100i
$672$	88913.2	+	88913.2i	0.196892	+	0.196892i
$673$	158202.	−	274013.i	0.349286	−	0.604981i	−0.636837	−	0.770999i	$-0.719758\pi$
$673$	158202.	−	274013.i	0.349286	−	0.604981i	0.986123	+	0.166018i	$0.0530908\pi$
$674$	131357.	+	131357.i	0.289158	+	0.289158i
$675$	100211.	+	173570.i	0.219941	+	0.380949i
$676$	−87155.8			−0.190723
$677$			796725.i			1.73833i	0.494526	+	0.869163i	$0.335342\pi$
$677$			796725.i			1.73833i	−0.494526	+	0.869163i	$0.664658\pi$
$678$	210554.	+	364691.i	0.458041	+	0.793351i
$679$	−1.09425e6	+	293204.i	−2.37344	+	0.635961i
$680$	−40624.8	+	40624.8i	−0.0878565	+	0.0878565i
$681$	−737789.	−	197690.i	−1.59088	−	0.426276i
$682$	89914.9	+	155737.i	0.193314	+	0.334829i
$683$	19115.5	−	71339.9i	0.0409773	−	0.152929i	−0.942406	−	0.334472i	$-0.891442\pi$
$683$	19115.5	−	71339.9i	0.0409773	−	0.152929i	0.983383	+	0.181542i	$0.0581089\pi$
$684$	−11969.2	−	44669.8i	−0.0255832	−	0.0954776i
$685$	32049.0	−	8587.50i	0.0683020	−	0.0183015i
$686$	−92528.5	−	24792.9i	−0.196620	−	0.0526841i
$687$	−286234.	+	165257.i	−0.606467	+	0.350144i
$688$	−28948.0	+	108036.i	−0.0611564	+	0.228239i
$689$	−187164.	−	187164.i	−0.394260	−	0.394260i
$690$	123115.	+	459473.i	0.258591	+	0.965077i
$691$	410049.	−	236742.i	0.858775	−	0.495814i	−0.00482708	−	0.999988i	$-0.501537\pi$
$691$	410049.	−	236742.i	0.858775	−	0.495814i	0.863602	+	0.504175i	$0.168203\pi$
$692$	−28214.7			−0.0589201
$693$			78602.0i			0.163669i
$694$	−255737.	+	147650.i	−0.530977	+	0.306559i
$695$	402310.	−	402310.i	0.832897	−	0.832897i
$696$	236736.	+	136680.i	0.488705	+	0.282154i
$697$	−100408.	+	100408.i	−0.206682	+	0.206682i
$698$	−55489.4	−	207089.i	−0.113894	−	0.425056i
$699$	99175.5	−	171777.i	0.202978	−	0.351569i
$700$	86351.3	−	149565.i	0.176227	−	0.305234i
$701$	−114518.	+	427386.i	−0.233044	+	0.869730i	0.745977	+	0.665971i	$0.231983\pi$
$701$	−114518.	+	427386.i	−0.233044	+	0.869730i	−0.979021	+	0.203759i	$0.934684\pi$
$702$		−	253340.i		−	0.514078i
$703$	−181188.	+	725455.i	−0.366623	+	1.46791i
$704$	52386.9			0.105701
$705$	−353336.	−	94676.2i	−0.710903	−	0.190486i
$706$	−88486.3	−	51087.6i	−0.177528	−	0.102496i
$707$	−351943.	−	203194.i	−0.704098	−	0.406511i
$708$	−112107.	+	30038.9i	−0.223648	+	0.0599263i
$709$	−303158.	−	303158.i	−0.603082	−	0.603082i	0.338047	−	0.941129i	$-0.390234\pi$
$709$	−303158.	−	303158.i	−0.603082	−	0.603082i	−0.941129	+	0.338047i	$0.890234\pi$
$710$	86322.5	−	149515.i	0.171241	−	0.296598i
$711$	−18498.1	−	18498.1i	−0.0365921	−	0.0365921i
$712$	−59461.9	−	102991.i	−0.117295	−	0.203161i
$713$	603342.			1.18682
$714$			275620.i			0.540647i
$715$	−123072.	−	213168.i	−0.240740	−	0.416975i
$716$	−220684.	+	59132.2i	−0.430473	+	0.115345i
$717$	715463.	−	715463.i	1.39171	−	1.39171i
$718$	229053.	+	61374.5i	0.444311	+	0.119053i
$719$	391419.	+	677958.i	0.757154	+	1.31143i	0.944296	+	0.329096i	$0.106744\pi$
$719$	391419.	+	677958.i	0.757154	+	1.31143i	−0.187142	+	0.982333i	$0.559923\pi$
$720$	3173.02	−	11841.9i	0.00612079	−	0.0228431i
$721$	−353404.	−	1.31892e6i	−0.679831	−	2.53716i
$722$	−459002.	+	122989.i	−0.880522	+	0.235935i
$723$	103301.	+	27679.4i	0.197619	+	0.0529518i
$724$	−61802.0	+	35681.4i	−0.117903	+	0.0680714i
$725$	97173.5	−	362657.i	0.184872	−	0.689953i
$726$	−79851.4	−	79851.4i	−0.151499	−	0.151499i
$727$	264520.	+	987201.i	0.500483	+	1.86783i	0.496855	+	0.867833i	$0.334488\pi$
$727$	264520.	+	987201.i	0.500483	+	1.86783i	0.00362734	+	0.999993i	$0.498845\pi$
$728$	−189055.	+	109151.i	−0.356719	+	0.205952i
$729$	−445041.			−0.837424
$730$		−	79282.7i		−	0.148776i
$731$	−212316.	+	122581.i	−0.397327	+	0.229397i
$732$	−71432.8	+	71432.8i	−0.133314	+	0.133314i
$733$	−246276.	−	142188.i	−0.458368	−	0.264639i	0.252990	−	0.967469i	$-0.418586\pi$
$733$	−246276.	−	142188.i	−0.458368	−	0.264639i	−0.711358	+	0.702830i	$0.751919\pi$
$734$	−251252.	+	251252.i	−0.466356	+	0.466356i
$735$	128554.	+	479770.i	0.237964	+	0.888093i
$736$	87880.9	−	152214.i	0.162233	−	0.280996i
$737$	−206414.	+	357520.i	−0.380019	+	0.658212i
$738$	7842.40	−	29268.2i	0.0143991	−	0.0537383i
$739$		−	590831.i		−	1.08187i	−0.841065	−	0.540934i	$-0.818071\pi$
$739$		−	590831.i		−	1.08187i	0.841065	−	0.540934i	$-0.181929\pi$
$740$	−137756.	+	142535.i	−0.251563	+	0.260290i
$741$	694754.			1.26530
$742$	394909.	+	105816.i	0.717281	+	0.192195i
$743$	−48940.7	−	28255.9i	−0.0886529	−	0.0511838i	0.455018	−	0.890482i	$-0.349633\pi$
$743$	−48940.7	−	28255.9i	−0.0886529	−	0.0511838i	−0.543671	+	0.839298i	$0.682966\pi$
$744$	−116530.	−	67278.7i	−0.210520	−	0.121544i
$745$	−733377.	+	196508.i	−1.32134	+	0.354052i
$746$	−341761.	−	341761.i	−0.614109	−	0.614109i
$747$	35560.4	−	61592.4i	0.0637273	−	0.110379i
$748$	81196.4	+	81196.4i	0.145122	+	0.145122i
$749$	−205007.	−	355083.i	−0.365431	−	0.632946i
$750$	−451900.			−0.803378
$751$		−	625070.i		−	1.10828i	−0.832424	−	0.554139i	$-0.813047\pi$
$751$		−	625070.i		−	1.10828i	0.832424	−	0.554139i	$-0.186953\pi$
$752$	67580.8	+	117053.i	0.119505	+	0.206989i
$753$	979244.	−	262388.i	1.72703	−	0.462757i
$754$	−335580.	+	335580.i	−0.590273	+	0.590273i
$755$	700019.	+	187569.i	1.22805	+	0.329055i
$756$	195655.	+	338884.i	0.342331	+	0.592935i
$757$	−234907.	+	876684.i	−0.409924	+	1.52986i	0.384865	+	0.922973i	$0.374248\pi$
$757$	−234907.	+	876684.i	−0.409924	+	1.52986i	−0.794789	+	0.606885i	$0.792419\pi$
$758$	123071.	+	459309.i	0.214200	+	0.799404i
$759$	918343.	−	246069.i	1.59412	−	0.427144i
$760$	−216067.	−	57894.9i	−0.374077	−	0.100234i
$761$	100001.	−	57735.5i	0.172677	−	0.0996951i	−0.411171	−	0.911558i	$-0.634880\pi$
$761$	100001.	−	57735.5i	0.172677	−	0.0996951i	0.583848	+	0.811863i	$0.301547\pi$
$762$	72099.1	−	269078.i	0.124171	−	0.463412i
$763$	−450803.	−	450803.i	−0.774351	−	0.774351i
$764$	−51648.1	−	192753.i	−0.0884846	−	0.330229i
$765$	23272.1	−	13436.2i	0.0397661	−	0.0229590i
$766$	51013.7			0.0869419
$767$		−	201495.i		−	0.342511i
$768$	−33946.8	+	19599.2i	−0.0575542	+	0.0332289i
$769$	−41224.0	+	41224.0i	−0.0697105	+	0.0697105i	−0.741102	−	0.671392i	$-0.765697\pi$
$769$	−41224.0	+	41224.0i	−0.0697105	+	0.0697105i	0.671392	+	0.741102i	$0.265697\pi$
$770$	329260.	+	190098.i	0.555337	+	0.320624i
$771$	367769.	−	367769.i	0.618681	−	0.618681i
$772$	−23059.0	−	86057.3i	−0.0386906	−	0.144395i
$773$	−114279.	+	197938.i	−0.191253	+	0.331260i	−0.945666	−	0.325140i	$-0.894589\pi$
$773$	−114279.	+	197938.i	−0.191253	+	0.331260i	0.754413	+	0.656401i	$0.227922\pi$
$774$	26157.2	−	45305.6i	0.0436626	−	0.0756258i
$775$	−47832.3	+	178513.i	−0.0796376	+	0.297212i
$776$		−	353152.i		−	0.586460i
$777$	16211.3	+	950816.i	0.0268520	+	1.57491i
$778$	−514698.			−0.850341
$779$	−534029.	−	143093.i	−0.880014	−	0.235799i
$780$	159503.	+	92088.9i	0.262167	+	0.151362i
$781$	−298834.	−	172532.i	−0.489923	−	0.282857i
$782$	372132.	−	99712.6i	0.608533	−	0.163056i
$783$	601531.	+	601531.i	0.981148	+	0.981148i
$784$	91763.0	−	158938.i	0.149292	−	0.258581i
$785$	91799.6	+	91799.6i	0.148971	+	0.148971i
$786$	−101357.	−	175555.i	−0.164062	−	0.284163i
$787$	923559.			1.49113			0.745564	−	0.666434i	$-0.232180\pi$
$787$	923559.			1.49113			0.745564	+	0.666434i	$0.232180\pi$
$788$			89687.1i			0.144437i
$789$	400714.	+	694057.i	0.643695	+	1.11491i
$790$	−122225.	+	32750.0i	−0.195842	+	0.0524756i
$791$	798496.	−	798496.i	1.27620	−	1.27620i
$792$	−23668.2	−	6341.87i	−0.0377324	−	0.0101104i
$793$	−87691.9	−	151887.i	−0.139448	−	0.241531i
$794$	118271.	−	441392.i	0.187601	−	0.700138i
$795$	−89274.8	−	333178.i	−0.141252	−	0.527160i
$796$	−509950.	+	136641.i	−0.804824	+	0.215652i
$797$	655934.	+	175757.i	1.03263	+	0.276692i	0.735055	−	0.678008i	$-0.237156\pi$
$797$	655934.	+	175757.i	1.03263	+	0.276692i	0.297572	+	0.954699i	$0.403823\pi$
$798$	−929348.	+	536559.i	−1.45939	+	0.842582i
$799$	−76679.4	+	286171.i	−0.120112	+	0.448263i
$800$	38069.0	+	38069.0i	0.0594828	+	0.0594828i
$801$	14396.7	+	53729.3i	0.0224387	+	0.0837425i
$802$	−255154.	+	147313.i	−0.396692	+	0.229030i
$803$	−158461.			−0.245749
$804$		−	308899.i		−	0.477864i
$805$	1.10469e6	−	637793.i	1.70470	−	0.984210i
$806$	165185.	−	165185.i	0.254273	−	0.254273i
$807$	−961310.	−	555013.i	−1.47610	−	0.852228i
$808$	89580.6	−	89580.6i	0.137212	−	0.137212i
$809$	129613.	+	483722.i	0.198039	+	0.739093i	0.991459	+	0.130418i	$0.0416319\pi$
$809$	129613.	+	483722.i	0.198039	+	0.739093i	−0.793420	+	0.608675i	$0.791701\pi$
$810$	187013.	−	323917.i	0.285038	−	0.493700i
$811$	348012.	−	602774.i	0.529118	−	0.916459i	−0.470306	−	0.882504i	$-0.655856\pi$
$811$	348012.	−	602774.i	0.529118	−	0.916459i	0.999423	−	0.0339550i	$-0.0108103\pi$
$812$	189725.	−	708062.i	0.287748	−	1.07389i
$813$			461139.i			0.697671i
$814$	284882.	+	275331.i	0.429949	+	0.415533i
$815$	646382.			0.973137
$816$	−82993.0	−	22237.9i	−0.124641	−	0.0333975i
$817$	−826647.	−	477265.i	−1.23844	−	0.715015i
$818$	−56887.0	−	32843.7i	−0.0850171	−	0.0490846i
$819$	98628.0	−	26427.3i	0.147039	−	0.0393990i
$820$	−103636.	−	103636.i	−0.154129	−	0.154129i
$821$	−587541.	+	1.01765e6i	−0.871670	+	1.50978i	−0.0114010	+	0.999935i	$0.503629\pi$
$821$	−587541.	+	1.01765e6i	−0.871670	+	1.50978i	−0.860269	+	0.509841i	$0.829704\pi$
$822$	35087.0	+	35087.0i	0.0519282	+	0.0519282i
$823$	−626063.	−	1.08437e6i	−0.924312	−	1.60096i	−0.792664	−	0.609658i	$-0.791307\pi$
$823$	−626063.	−	1.08437e6i	−0.924312	−	1.60096i	−0.131648	−	0.991297i	$-0.542027\pi$
$824$	425660.			0.626915
$825$			291221.i			0.427873i
$826$	155615.	+	269533.i	0.228082	+	0.395050i
$827$	267880.	−	71778.1i	0.391678	−	0.104950i	−0.0576049	−	0.998339i	$-0.518346\pi$
$827$	267880.	−	71778.1i	0.391678	−	0.104950i	0.449282	+	0.893390i	$0.351680\pi$
$828$	−58131.0	+	58131.0i	−0.0847905	+	0.0847905i
$829$	−34920.7	−	9356.98i	−0.0508129	−	0.0136153i	0.233323	−	0.972399i	$-0.425040\pi$
$829$	−34920.7	−	9356.98i	−0.0508129	−	0.0136153i	−0.284136	+	0.958784i	$0.591707\pi$
$830$	−172005.	−	297921.i	−0.249681	−	0.432459i
$831$	162626.	−	606930.i	0.235499	−	0.878894i
$832$	−17613.3	−	65733.9i	−0.0254446	−	0.0949604i
$833$	388571.	−	104117.i	0.559990	−	0.150049i
$834$	821884.	+	220223.i	1.18162	+	0.316615i
$835$	−472267.	+	272663.i	−0.677352	+	0.391069i
$836$	−115714.	+	431850.i	−0.165567	+	0.617903i
$837$	−296095.	−	296095.i	−0.422650	−	0.422650i
$838$	−87757.4	−	327515.i	−0.124967	−	0.466384i
$839$	−153305.	+	88510.5i	−0.217787	+	0.125739i	−0.604925	−	0.796282i	$-0.706797\pi$
$839$	−153305.	+	88510.5i	−0.217787	+	0.125739i	0.387138	+	0.922022i	$0.373464\pi$
$840$	−284481.			−0.403177
$841$		−	886324.i		−	1.25314i
$842$	413393.	−	238672.i	0.583094	−	0.336649i
$843$	−443986.	+	443986.i	−0.624761	+	0.624761i
$844$	432035.	+	249435.i	0.606504	+	0.350165i
$845$	139429.	−	139429.i	0.195272	−	0.195272i
$846$	−16362.4	−	61065.4i	−0.0228616	−	0.0853207i
$847$	−151412.	+	262254.i	−0.211054	+	0.365557i
$848$	−63725.2	+	110375.i	−0.0886175	+	0.153490i
$849$	344543.	−	1.28585e6i	0.478000	−	1.78392i
$850$			118009.i			0.163334i
$851$	1.27789e6	−	365870.i	1.76456	−	0.505205i
$852$	258194.			0.355686
$853$	−194483.	−	52111.5i	−0.267290	−	0.0716202i	0.122685	−	0.992446i	$-0.460850\pi$
$853$	−194483.	−	52111.5i	−0.267290	−	0.0716202i	−0.389975	+	0.920825i	$0.627516\pi$
$854$	234605.	+	135449.i	0.321678	+	0.185721i
$855$	90609.4	+	52313.4i	0.123948	+	0.0715617i
$856$	123461.	−	33081.4i	0.168494	−	0.0451477i
$857$	−50015.9	−	50015.9i	−0.0680999	−	0.0680999i	0.672237	−	0.740336i	$-0.265334\pi$
$857$	−50015.9	−	50015.9i	−0.0680999	−	0.0680999i	−0.740336	+	0.672237i	$0.765334\pi$
$858$	184057.	−	318796.i	0.250022	−	0.433050i
$859$	263501.	+	263501.i	0.357105	+	0.357105i	0.862745	−	0.505640i	$-0.168744\pi$
$859$	263501.	+	263501.i	0.357105	+	0.357105i	−0.505640	+	0.862745i	$0.668744\pi$
$860$	−126522.	−	219142.i	−0.171068	−	0.296298i
$861$	−703122.			−0.948472
$862$		−	484044.i		−	0.651434i
$863$	301192.	+	521680.i	0.404410	+	0.700458i	0.994253	−	0.107060i	$-0.0341436\pi$
$863$	301192.	+	521680.i	0.404410	+	0.700458i	−0.589843	+	0.807518i	$0.700810\pi$
$864$	−117829.	+	31572.1i	−0.157842	+	0.0422938i
$865$	45137.1	−	45137.1i	0.0603256	−	0.0603256i
$866$	−725513.	−	194401.i	−0.967408	−	0.259216i
$867$	305479.	+	529104.i	0.406390	+	0.703887i
$868$	−93389.4	+	348534.i	−0.123953	+	0.462600i
$869$	65457.1	+	244289.i	0.0866796	+	0.323493i
$870$	−597380.	+	160067.i	−0.789246	+	0.211478i
$871$	518008.	+	138800.i	0.682811	+	0.182959i
$872$	172116.	−	99370.9i	0.226353	−	0.130685i
$873$	−42752.0	+	159553.i	−0.0560955	+	0.209351i
$874$	1.06066e6	+	1.06066e6i	1.38852	+	1.38852i
$875$	313641.	+	1.17052e6i	0.409653	+	1.52885i
$876$	102683.	−	59284.3i	0.133811	−	0.0772558i
$877$	418158.			0.543677			0.271839	−	0.962343i	$-0.412368\pi$
$877$	418158.			0.543677			0.271839	+	0.962343i	$0.412368\pi$
$878$		−	411495.i		−	0.533797i
$879$	181889.	−	105014.i	0.235412	−	0.135915i
$880$	−83807.0	+	83807.0i	−0.108222	+	0.108222i
$881$	252820.	+	145966.i	0.325731	+	0.188061i	0.653944	−	0.756543i	$-0.273113\pi$
$881$	252820.	+	145966.i	0.325731	+	0.188061i	−0.328213	+	0.944604i	$0.606446\pi$
$882$	−60699.0	+	60699.0i	−0.0780268	+	0.0780268i
$883$	130671.	+	487671.i	0.167594	+	0.625469i	0.997695	+	0.0678564i	$0.0216160\pi$
$883$	130671.	+	487671.i	0.167594	+	0.625469i	−0.830101	+	0.557613i	$0.811717\pi$
$884$	74583.8	−	129183.i	0.0954421	−	0.165311i
$885$	131290.	−	227400.i	0.167627	−	0.290339i
$886$	−213689.	+	797500.i	−0.272217	+	1.01593i
$887$		−	302503.i		−	0.384488i	−0.981347	−	0.192244i	$-0.938424\pi$
$887$		−	302503.i		−	0.384488i	0.981347	−	0.192244i	$-0.0615764\pi$
$888$	−287612.	−	71833.6i	−0.364738	−	0.0910965i
$889$	−747012.			−0.945200
$890$	259887.	+	69636.6i	0.328099	+	0.0879139i
$891$	−647408.	−	373781.i	−0.815498	−	0.470828i
$892$	542130.	+	312999.i	0.681355	+	0.393381i
$893$	−1.11420e6	+	298549.i	−1.39721	+	0.374380i
$894$	−802897.	−	802897.i	−1.00458	−	1.00458i
$895$	258446.	−	447642.i	0.322645	−	0.558837i
$896$	74327.1	+	74327.1i	0.0925830	+	0.0925830i
$897$	−617524.	−	1.06958e6i	−0.767484	−	1.32932i
$898$	−692186.			−0.858362
$899$			784430.i			0.970588i
$900$	−12590.8	−	21808.0i	−0.0155443	−	0.0269234i
$901$	−269845.	+	72304.7i	−0.332403	+	0.0890670i
$902$	−207137.	+	207137.i	−0.254592	+	0.254592i
$903$	−1.17258e6	−	314192.i	−1.43803	−	0.385318i
$904$	176013.	+	304864.i	0.215382	+	0.373052i
$905$	41787.0	−	155951.i	0.0510204	−	0.190411i
$906$	280513.	+	1.04689e6i	0.341741	+	1.27539i
$907$	330404.	−	88531.4i	0.401634	−	0.107617i	−0.0523469	−	0.998629i	$-0.516670\pi$
$907$	330404.	−	88531.4i	0.401634	−	0.107617i	0.453981	+	0.891012i	$0.350003\pi$
$908$	−616756.	−	165259.i	−0.748069	−	0.200445i
$909$	−51316.6	+	29627.7i	−0.0621055	+	0.0358566i
$910$	127828.	−	477062.i	0.154363	−	0.576092i
$911$	262310.	+	262310.i	0.316066	+	0.316066i	0.847254	−	0.531188i	$-0.178254\pi$
$911$	262310.	+	262310.i	0.316066	+	0.316066i	−0.531188	+	0.847254i	$0.678254\pi$
$912$	−86582.8	−	323131.i	−0.104098	−	0.388499i
$913$	−595452.	+	343784.i	−0.714340	+	0.412424i
$914$	−129823.			−0.155402
$915$		−	228552.i		−	0.272988i
$916$	−239278.	+	138147.i	−0.285175	+	0.164646i
$917$	−384380.	+	384380.i	−0.457112	+	0.457112i
$918$	−231562.	−	133692.i	−0.274778	−	0.158643i
$919$	383862.	−	383862.i	0.454511	−	0.454511i	−0.442337	−	0.896849i	$-0.645851\pi$
$919$	383862.	−	383862.i	0.454511	−	0.454511i	0.896849	+	0.442337i	$0.145851\pi$
$920$	102919.	+	384097.i	0.121596	+	0.453801i
$921$	−496054.	+	859192.i	−0.584804	+	1.01291i
$922$	511992.	−	886795.i	0.602284	−	1.04319i
$923$	−116016.	+	432978.i	−0.136181	+	0.508233i
$924$			568590.i			0.665970i
$925$	6941.02	+	407101.i	0.00811222	+	0.475793i
$926$	−693005.			−0.808192
$927$	−192311.	−	51529.7i	−0.223793	−	0.0599650i
$928$	197900.	+	114258.i	0.229800	+	0.132675i
$929$	−108139.	−	62433.9i	−0.125300	−	0.0723418i	0.436040	−	0.899927i	$-0.356381\pi$
$929$	−108139.	−	62433.9i	−0.125300	−	0.0723418i	−0.561340	+	0.827585i	$0.689714\pi$
$930$	294052.	−	78791.0i	0.339984	−	0.0910984i
$931$	1.10751e6	+	1.10751e6i	1.27776	+	1.27776i
$932$	82905.9	−	143597.i	0.0954451	−	0.165316i
$933$	−571347.	−	571347.i	−0.656352	−	0.656352i
$934$	−309458.	−	535997.i	−0.354738	−	0.614425i
$935$	−259791.			−0.297167
$936$			31830.5i			0.0363323i
$937$	173846.	+	301111.i	0.198010	+	0.342963i	0.947883	−	0.318618i	$-0.103219\pi$
$937$	173846.	+	301111.i	0.198010	+	0.342963i	−0.749873	+	0.661582i	$0.769886\pi$
$938$	−800117.	+	214391.i	−0.909385	+	0.243669i
$939$	−659586.	+	659586.i	−0.748066	+	0.748066i
$940$	−295372.	−	79144.7i	−0.334283	−	0.0895708i
$941$	−244739.	−	423900.i	−0.276391	−	0.478723i	0.694094	−	0.719884i	$-0.255805\pi$
$941$	−244739.	−	423900.i	−0.276391	−	0.478723i	−0.970485	+	0.241161i	$0.922472\pi$
$942$	−50250.8	+	187539.i	−0.0566293	+	0.211344i
$943$	254373.	+	949331.i	0.286053	+	1.06757i
$944$	−93715.8	+	25111.1i	−0.105164	+	0.0281787i
$945$	−855139.	−	229134.i	−0.957575	−	0.256582i
$946$	−437997.	+	252878.i	−0.489428	+	0.282571i
$947$	247142.	−	922348.i	0.275580	−	1.02848i	−0.679872	−	0.733331i	$-0.737965\pi$
$947$	247142.	−	922348.i	0.275580	−	1.02848i	0.955452	−	0.295147i	$-0.0953686\pi$
$948$	−133811.	−	133811.i	−0.148893	−	0.148893i
$949$	53277.3	+	198834.i	0.0591575	+	0.220779i
$950$	−397909.	+	229733.i	−0.440896	+	0.254552i
$951$	−51666.2			−0.0571276
$952$			230405.i			0.254225i
$953$	1.43087e6	−	826116.i	1.57549	−	0.909610i	0.580014	−	0.814607i	$-0.303047\pi$
$953$	1.43087e6	−	826116.i	1.57549	−	0.909610i	0.995477	−	0.0950031i	$-0.0302861\pi$
$954$	42152.6	−	42152.6i	0.0463157	−	0.0463157i
$955$	390986.	+	225736.i	0.428701	+	0.247511i
$956$	598093.	−	598093.i	0.654414	−	0.654414i
$957$	319925.	+	1.19398e6i	0.349321	+	1.30368i
$958$	473390.	−	819936.i	0.515808	−	0.893406i
$959$	66531.2	−	115235.i	0.0723416	−	0.125299i
$960$	22952.9	−	85661.4i	0.0249055	−	0.0929486i
$961$			537396.i			0.581899i
$962$	249697.	−	450034.i	0.269813	−	0.486290i
$963$	−59784.1			−0.0644664
$964$	86354.7	+	23138.7i	0.0929249	+	0.0248991i
$965$	174561.	+	100783.i	0.187453	+	0.108226i
$966$	1.65208e6	+	953830.i	1.77042	+	1.02215i
$967$	−999074.	+	267701.i	−1.06843	+	0.286284i	−0.749847	−	0.661612i	$-0.769873\pi$
$967$	−999074.	+	267701.i	−1.06843	+	0.286284i	−0.318580	+	0.947896i	$0.603206\pi$
$968$	−66751.9	−	66751.9i	−0.0712382	−	0.0712382i
$969$	366635.	−	635031.i	0.390469	−	0.676313i
$970$	564962.	+	564962.i	0.600449	+	0.600449i
$971$	−203757.	−	352918.i	−0.216110	−	0.374314i	0.737505	−	0.675341i	$-0.236004\pi$
$971$	−203757.	−	352918.i	−0.216110	−	0.374314i	−0.953615	+	0.301028i	$0.902670\pi$
$972$	122689.			0.129859
$973$		−	2.28171e6i		−	2.41010i
$974$	−497634.	−	861927.i	−0.524556	−	0.908557i
$975$	365418.	−	97913.4i	0.384397	−	0.102999i
$976$	−59714.4	+	59714.4i	−0.0626872	+	0.0626872i
$977$	−775552.	−	207809.i	−0.812497	−	0.217708i	−0.171434	−	0.985196i	$-0.554840\pi$
$977$	−775552.	−	207809.i	−0.812497	−	0.217708i	−0.641064	+	0.767488i	$0.721507\pi$
$978$	483337.	+	837165.i	0.505327	+	0.875252i
$979$	139182.	−	519434.i	0.145217	−	0.541957i
$980$	107465.	+	401064.i	0.111896	+	0.417601i
$981$	−89790.8	+	24059.4i	−0.0933026	+	0.0250004i
$982$	769807.	+	206269.i	0.798287	+	0.213900i
$983$	757657.	−	437434.i	0.784090	−	0.452694i	−0.0537881	−	0.998552i	$-0.517130\pi$
$983$	757657.	−	437434.i	0.784090	−	0.452694i	0.837878	+	0.545858i	$0.183796\pi$
$984$	56730.2	−	211720.i	0.0585901	−	0.218661i
$985$	−143479.	−	143479.i	−0.147882	−	0.147882i
$986$	129640.	+	483825.i	0.133348	+	0.497662i
$987$	−1.27046e6	+	733499.i	−1.30414	+	0.752948i
$988$	580781.			0.594974
$989$			1.69685e6i			1.73480i
$990$	48009.2	−	27718.1i	0.0489840	−	0.0282809i
$991$	−390656.	+	390656.i	−0.397784	+	0.397784i	−0.877451	−	0.479667i	$-0.840758\pi$
$991$	−390656.	+	390656.i	−0.397784	+	0.397784i	0.479667	+	0.877451i	$0.340758\pi$
$992$	−97413.6	−	56241.8i	−0.0989911	−	0.0571525i
$993$	−641543.	+	641543.i	−0.650619	+	0.650619i
$994$	−179199.	−	668779.i	−0.181369	−	0.676877i
$995$	597209.	−	1.03440e6i	0.603226	−	1.04482i
$996$	257236.	−	445546.i	0.259307	−	0.449132i
$997$	8899.16	−	33212.1i	0.00895280	−	0.0334123i	−0.961305	−	0.275486i	$-0.911161\pi$
$997$	8899.16	−	33212.1i	0.00895280	−	0.0334123i	0.970258	+	0.242074i	$0.0778277\pi$
$998$			1.15576e6i			1.16040i
$999$	−806692.	−	447584.i	−0.808308	−	0.448481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.g.a.45.6	✓	28
37.14	odd	12	inner	74.5.g.a.51.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.g.a.45.6	✓	28	1.1	even	1	trivial
74.5.g.a.51.6	yes	28	37.14	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73205 - 0.732051i) q^{2} +(8.28780 + 4.78497i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-17.4826 + 4.68445i) q^{5} +(-19.1399 - 19.1399i) q^{6} +(-36.2925 + 62.8605i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(5.29180 + 9.16567i) q^{9} +O(q^{10})\)	\(q+(-2.73205 - 0.732051i) q^{2} +(8.28780 + 4.78497i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-17.4826 + 4.68445i) q^{5} +(-19.1399 - 19.1399i) q^{6} +(-36.2925 + 62.8605i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(5.29180 + 9.16567i) q^{9} +51.1927 q^{10} -102.318i q^{11} +(38.2797 + 66.3024i) q^{12} +(-128.387 + 34.4011i) q^{13} +(145.170 - 145.170i) q^{14} +(-167.307 - 44.8299i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-36.3083 + 135.504i) q^{17} +(-7.74773 - 28.9149i) q^{18} +(-527.582 + 141.365i) q^{19} +(-139.861 - 37.4756i) q^{20} +(-601.571 + 347.317i) q^{21} +(-74.9021 + 279.538i) q^{22} +(686.570 + 686.570i) q^{23} +(-56.0454 - 209.164i) q^{24} +(-257.568 + 148.707i) q^{25} +375.942 q^{26} -673.880i q^{27} +(-502.884 + 290.340i) q^{28} +(-892.638 + 892.638i) q^{29} +(424.275 + 244.955i) q^{30} +(439.389 - 439.389i) q^{31} +(-46.8513 - 174.851i) q^{32} +(489.589 - 847.993i) q^{33} +(198.392 - 343.625i) q^{34} +(340.021 - 1268.98i) q^{35} +84.6688i q^{36} +(664.189 - 1197.09i) q^{37} +1544.87 q^{38} +(-1228.65 - 329.216i) q^{39} +(354.673 + 204.771i) q^{40} +(876.607 + 506.109i) q^{41} +(1897.78 - 508.508i) q^{42} +(1235.74 + 1235.74i) q^{43} +(409.273 - 708.881i) q^{44} +(-135.451 - 135.451i) q^{45} +(-1373.14 - 2378.35i) q^{46} +2111.90 q^{47} +612.476i q^{48} +(-1433.80 - 2483.41i) q^{49} +(812.550 - 217.722i) q^{50} +(-949.299 + 949.299i) q^{51} +(-1027.09 - 275.208i) q^{52} +(995.706 + 1724.61i) q^{53} +(-493.315 + 1841.07i) q^{54} +(479.305 + 1788.79i) q^{55} +(1586.45 - 425.088i) q^{56} +(-5048.93 - 1352.86i) q^{57} +(3092.19 - 1785.28i) q^{58} +(-392.361 + 1464.31i) q^{59} +(-979.821 - 979.821i) q^{60} +(341.515 + 1274.55i) q^{61} +(-1522.09 + 878.778i) q^{62} -768.212 q^{63} +512.000i q^{64} +(2083.38 - 1202.84i) q^{65} +(-1958.36 + 1958.36i) q^{66} +(-3494.20 - 2017.38i) q^{67} +(-793.568 + 793.568i) q^{68} +(2404.94 + 8975.37i) q^{69} +(-1857.91 + 3218.00i) q^{70} +(1686.23 - 2920.63i) q^{71} +(61.9819 - 231.320i) q^{72} -1548.71i q^{73} +(-2690.93 + 2784.28i) q^{74} -2846.23 q^{75} +(-4220.66 - 1130.92i) q^{76} +(6431.77 + 3713.39i) q^{77} +(3115.73 + 1798.87i) q^{78} +(-2387.54 + 639.741i) q^{79} +(-819.083 - 819.083i) q^{80} +(3653.13 - 6327.41i) q^{81} +(-2024.44 - 2024.44i) q^{82} +(-3359.95 - 5819.61i) q^{83} -5557.07 q^{84} -2539.05i q^{85} +(-2471.48 - 4280.74i) q^{86} +(-11669.3 + 3126.77i) q^{87} +(-1637.09 + 1637.09i) q^{88} +(5076.65 + 1360.29i) q^{89} +(270.901 + 469.215i) q^{90} +(2497.00 - 9318.94i) q^{91} +(2010.42 + 7502.97i) q^{92} +(5744.03 - 1539.11i) q^{93} +(-5769.81 - 1546.02i) q^{94} +(8561.30 - 4942.87i) q^{95} +(448.363 - 1673.31i) q^{96} +(11036.0 + 11036.0i) q^{97} +(2099.22 + 7834.41i) q^{98} +(937.814 - 541.447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

Introduction

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