LMFDB - Embedded newform 74.5.g.a.29.2

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			29.2
Character	$\chi$	$=$	74.29
Dual form			74.5.g.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.732051 - 2.73205i) q^{2} +(-12.4198 - 7.17059i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(11.3964 + 42.5318i) q^{5} +(-28.6824 + 28.6824i) q^{6} +(6.42196 - 11.1232i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(62.3348 + 107.967i) q^{9} +O(q^{10})$	\(q+(0.732051 - 2.73205i) q^{2} +(-12.4198 - 7.17059i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(11.3964 + 42.5318i) q^{5} +(-28.6824 + 28.6824i) q^{6} +(6.42196 - 11.1232i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(62.3348 + 107.967i) q^{9} +124.542 q^{10} -116.105i q^{11} +(57.3647 + 99.3586i) q^{12} +(28.9334 + 107.981i) q^{13} +(-25.6879 - 25.6879i) q^{14} +(163.437 - 609.956i) q^{15} +(32.0000 + 55.4256i) q^{16} +(501.141 + 134.280i) q^{17} +(340.604 - 91.2644i) q^{18} +(76.0134 + 283.686i) q^{19} +(91.1708 - 340.254i) q^{20} +(-159.519 + 92.0986i) q^{21} +(-317.205 - 84.9949i) q^{22} +(-416.700 + 416.700i) q^{23} +(313.447 - 83.9878i) q^{24} +(-1137.81 + 656.914i) q^{25} +316.190 q^{26} -626.273i q^{27} +(-88.9854 + 51.3757i) q^{28} +(629.268 + 629.268i) q^{29} +(-1546.79 - 893.037i) q^{30} +(556.172 + 556.172i) q^{31} +(174.851 - 46.8513i) q^{32} +(-832.543 + 1442.01i) q^{33} +(733.721 - 1270.84i) q^{34} +(546.275 + 146.374i) q^{35} -997.356i q^{36} +(-530.192 - 1262.16i) q^{37} +830.690 q^{38} +(414.939 - 1548.57i) q^{39} +(-862.850 - 498.167i) q^{40} +(1372.33 + 792.313i) q^{41} +(134.842 + 503.236i) q^{42} +(-753.477 + 753.477i) q^{43} +(-464.421 + 804.401i) q^{44} +(-3881.64 + 3881.64i) q^{45} +(833.400 + 1443.49i) q^{46} -58.2936 q^{47} -917.836i q^{48} +(1118.02 + 1936.46i) q^{49} +(961.788 + 3589.44i) q^{50} +(-5261.21 - 5261.21i) q^{51} +(231.467 - 863.847i) q^{52} +(-1894.64 - 3281.62i) q^{53} +(-1711.01 - 458.464i) q^{54} +(4938.16 - 1323.18i) q^{55} +(75.2193 + 280.722i) q^{56} +(1090.12 - 4068.39i) q^{57} +(2179.85 - 1258.54i) q^{58} +(-3913.81 - 1048.70i) q^{59} +(-3572.15 + 3572.15i) q^{60} +(-5014.41 + 1343.61i) q^{61} +(1926.64 - 1112.34i) q^{62} +1601.25 q^{63} -512.000i q^{64} +(-4262.88 + 2461.18i) q^{65} +(3330.17 + 3330.17i) q^{66} +(7024.07 + 4055.35i) q^{67} +(-2934.88 - 2934.88i) q^{68} +(8163.33 - 2187.36i) q^{69} +(799.802 - 1385.30i) q^{70} +(-849.084 + 1470.66i) q^{71} +(-2724.83 - 730.116i) q^{72} -4435.14i q^{73} +(-3836.42 + 524.545i) q^{74} +18841.8 q^{75} +(608.108 - 2269.49i) q^{76} +(-1291.46 - 745.624i) q^{77} +(-3927.03 - 2267.27i) q^{78} +(2480.61 + 9257.76i) q^{79} +(-1992.67 + 1992.67i) q^{80} +(558.369 - 967.124i) q^{81} +(3169.25 - 3169.25i) q^{82} +(-2498.63 - 4327.76i) q^{83} +1473.58 q^{84} +22844.7i q^{85} +(1506.95 + 2610.12i) q^{86} +(-3303.18 - 12327.6i) q^{87} +(1857.68 + 1857.68i) q^{88} +(1361.09 - 5079.66i) q^{89} +(7763.27 + 13446.4i) q^{90} +(1386.90 + 371.618i) q^{91} +(4553.78 - 1220.18i) q^{92} +(-2919.48 - 10895.6i) q^{93} +(-42.6739 + 159.261i) q^{94} +(-11199.4 + 6465.97i) q^{95} +(-2507.57 - 671.902i) q^{96} +(10038.9 - 10038.9i) q^{97} +(6108.96 - 1636.89i) q^{98} +(12535.5 - 7237.39i) 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$3$	−12.4198	−	7.17059i	−1.37998	−	0.796732i	−0.387824	−	0.921733i	$-0.626773\pi$
$3$	−12.4198	−	7.17059i	−1.37998	−	0.796732i	−0.992157	+	0.125001i	$0.960107\pi$
$4$	−6.92820	−	4.00000i	−0.433013	−	0.250000i
$5$	11.3964	+	42.5318i	0.455854	+	1.70127i	0.685565	+	0.728011i	$0.259555\pi$
$5$	11.3964	+	42.5318i	0.455854	+	1.70127i	−0.229711	+	0.973259i	$0.573778\pi$
$6$	−28.6824	+	28.6824i	−0.796732	+	0.796732i
$7$	6.42196	−	11.1232i	0.131061	−	0.227003i	−0.793025	−	0.609189i	$-0.791495\pi$
$7$	6.42196	−	11.1232i	0.131061	−	0.227003i	0.924086	+	0.382185i	$0.124828\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	62.3348	+	107.967i	0.769565	+	1.33293i
$10$	124.542			1.24542
$11$		−	116.105i		−	0.959547i	−0.877392	−	0.479774i	$-0.840719\pi$
$11$		−	116.105i		−	0.959547i	0.877392	−	0.479774i	$-0.159281\pi$
$12$	57.3647	+	99.3586i	0.398366	+	0.689991i
$13$	28.9334	+	107.981i	0.171203	+	0.638940i	0.997167	+	0.0752168i	$0.0239649\pi$
$13$	28.9334	+	107.981i	0.171203	+	0.638940i	−0.825964	+	0.563723i	$0.809368\pi$
$14$	−25.6879	−	25.6879i	−0.131061	−	0.131061i
$15$	163.437	−	609.956i	0.726387	−	2.71091i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	501.141	+	134.280i	1.73405	+	0.464637i	0.981110	−	0.193451i	$-0.0619682\pi$
$17$	501.141	+	134.280i	1.73405	+	0.464637i	0.752940	+	0.658089i	$0.228635\pi$
$18$	340.604	−	91.2644i	1.05125	−	0.281680i
$19$	76.0134	+	283.686i	0.210564	+	0.785834i	0.987681	+	0.156479i	$0.0500143\pi$
$19$	76.0134	+	283.686i	0.210564	+	0.785834i	−0.777118	+	0.629355i	$0.783319\pi$
$20$	91.1708	−	340.254i	0.227927	−	0.850635i
$21$	−159.519	+	92.0986i	−0.361722	+	0.208840i
$22$	−317.205	−	84.9949i	−0.655383	−	0.175609i
$23$	−416.700	+	416.700i	−0.787713	+	0.787713i	−0.981119	−	0.193406i	$-0.938047\pi$
$23$	−416.700	+	416.700i	−0.787713	+	0.787713i	0.193406	+	0.981119i	$0.438047\pi$
$24$	313.447	−	83.9878i	0.544178	−	0.145812i
$25$	−1137.81	+	656.914i	−1.82049	+	1.05106i
$26$	316.190			0.467737
$27$		−	626.273i		−	0.859085i
$28$	−88.9854	+	51.3757i	−0.113502	+	0.0655303i
$29$	629.268	+	629.268i	0.748238	+	0.748238i	0.974148	−	0.225911i	$-0.0725357\pi$
$29$	629.268	+	629.268i	0.748238	+	0.748238i	−0.225911	+	0.974148i	$0.572536\pi$
$30$	−1546.79	−	893.037i	−1.71865	−	0.992264i
$31$	556.172	+	556.172i	0.578743	+	0.578743i	0.934557	−	0.355814i	$-0.115796\pi$
$31$	556.172	+	556.172i	0.578743	+	0.578743i	−0.355814	+	0.934557i	$0.615796\pi$
$32$	174.851	−	46.8513i	0.170753	−	0.0457532i
$33$	−832.543	+	1442.01i	−0.764502	+	1.32416i
$34$	733.721	−	1270.84i	0.634706	−	1.09934i
$35$	546.275	+	146.374i	0.445939	+	0.119489i
$36$		−	997.356i		−	0.769565i
$37$	−530.192	−	1262.16i	−0.387285	−	0.921960i
$37$	−530.192	−	1262.16i	−0.387285	−	0.921960i
$38$	830.690			0.575270
$39$	414.939	−	1548.57i	0.272807	−	1.01813i
$40$	−862.850	−	498.167i	−0.539281	−	0.311354i
$41$	1372.33	+	792.313i	0.816375	+	0.471334i	0.849165	−	0.528128i	$-0.177106\pi$
$41$	1372.33	+	792.313i	0.816375	+	0.471334i	−0.0327899	+	0.999462i	$0.510439\pi$
$42$	134.842	+	503.236i	0.0764409	+	0.285281i
$43$	−753.477	+	753.477i	−0.407505	+	0.407505i	−0.880868	−	0.473363i	$-0.843040\pi$
$43$	−753.477	+	753.477i	−0.407505	+	0.407505i	0.473363	+	0.880868i	$0.343040\pi$
$44$	−464.421	+	804.401i	−0.239887	+	0.415496i
$45$	−3881.64	+	3881.64i	−1.91686	+	1.91686i
$46$	833.400	+	1443.49i	0.393857	+	0.682180i
$47$	−58.2936			−0.0263891			−0.0131946	−	0.999913i	$-0.504200\pi$
$47$	−58.2936			−0.0263891			−0.0131946	+	0.999913i	$0.504200\pi$
$48$		−	917.836i		−	0.398366i
$49$	1118.02	+	1936.46i	0.465646	+	0.806523i
$50$	961.788	+	3589.44i	0.384715	+	1.43578i
$51$	−5261.21	−	5261.21i	−2.02276	−	2.02276i
$52$	231.467	−	863.847i	0.0856017	−	0.319470i
$53$	−1894.64	−	3281.62i	−0.674490	−	1.16825i	−0.976618	−	0.214984i	$-0.931030\pi$
$53$	−1894.64	−	3281.62i	−0.674490	−	1.16825i	0.302127	−	0.953268i	$-0.402303\pi$
$54$	−1711.01	−	458.464i	−0.586766	−	0.157223i
$55$	4938.16	−	1323.18i	1.63245	−	0.437413i
$56$	75.2193	+	280.722i	0.0239857	+	0.0895160i
$57$	1090.12	−	4068.39i	0.335526	−	1.25220i
$58$	2179.85	−	1258.54i	0.647993	−	0.374119i
$59$	−3913.81	−	1048.70i	−1.12433	−	0.301265i	−0.351698	−	0.936113i	$-0.614396\pi$
$59$	−3913.81	−	1048.70i	−1.12433	−	0.301265i	−0.772636	+	0.634849i	$0.781062\pi$
$60$	−3572.15	+	3572.15i	−0.992264	+	0.992264i
$61$	−5014.41	+	1343.61i	−1.34760	+	0.361088i	−0.859248	−	0.511560i	$-0.829068\pi$
$61$	−5014.41	+	1343.61i	−1.34760	+	0.361088i	−0.488350	+	0.872648i	$0.662401\pi$
$62$	1926.64	−	1112.34i	0.501206	−	0.289372i
$63$	1601.25			0.403438
$64$		−	512.000i		−	0.125000i
$65$	−4262.88	+	2461.18i	−1.00897	+	0.582527i
$66$	3330.17	+	3330.17i	0.764502	+	0.764502i
$67$	7024.07	+	4055.35i	1.56473	+	0.903397i	0.996767	+	0.0803431i	$0.0256016\pi$
$67$	7024.07	+	4055.35i	1.56473	+	0.903397i	0.567963	+	0.823054i	$0.307732\pi$
$68$	−2934.88	−	2934.88i	−0.634706	−	0.634706i
$69$	8163.33	−	2187.36i	1.71463	−	0.459433i
$70$	799.802	−	1385.30i	0.163225	−	0.282714i
$71$	−849.084	+	1470.66i	−0.168436	+	0.291739i	−0.937870	−	0.346987i	$-0.887205\pi$
$71$	−849.084	+	1470.66i	−0.168436	+	0.291739i	0.769434	+	0.638726i	$0.220538\pi$
$72$	−2724.83	−	730.116i	−0.525623	−	0.140840i
$73$		−	4435.14i		−	0.832265i	−0.909304	−	0.416133i	$-0.863385\pi$
$73$		−	4435.14i		−	0.832265i	0.909304	−	0.416133i	$-0.136615\pi$
$74$	−3836.42	+	524.545i	−0.700589	+	0.0957898i
$75$	18841.8			3.34966
$76$	608.108	−	2269.49i	0.105282	−	0.392917i
$77$	−1291.46	−	745.624i	−0.217821	−	0.125759i
$78$	−3927.03	−	2267.27i	−0.645468	−	0.372661i
$79$	2480.61	+	9257.76i	0.397470	+	1.48338i	0.817533	+	0.575882i	$0.195341\pi$
$79$	2480.61	+	9257.76i	0.397470	+	1.48338i	−0.420063	+	0.907495i	$0.637992\pi$
$80$	−1992.67	+	1992.67i	−0.311354	+	0.311354i
$81$	558.369	−	967.124i	0.0851043	−	0.147405i
$82$	3169.25	−	3169.25i	0.471334	−	0.471334i
$83$	−2498.63	−	4327.76i	−0.362699	−	0.628213i	0.625705	−	0.780060i	$-0.284811\pi$
$83$	−2498.63	−	4327.76i	−0.362699	−	0.628213i	−0.988404	+	0.151847i	$0.951478\pi$
$84$	1473.58			0.208840
$85$			22844.7i			3.16189i
$86$	1506.95	+	2610.12i	0.203753	+	0.352910i
$87$	−3303.18	−	12327.6i	−0.436409	−	1.62870i
$88$	1857.68	+	1857.68i	0.239887	+	0.239887i
$89$	1361.09	−	5079.66i	0.171833	−	0.641291i	−0.825236	−	0.564788i	$-0.808958\pi$
$89$	1361.09	−	5079.66i	0.171833	−	0.641291i	0.997069	−	0.0765027i	$-0.0243754\pi$
$90$	7763.27	+	13446.4i	0.958429	+	1.66005i
$91$	1386.90	+	371.618i	0.167480	+	0.0448760i
$92$	4553.78	−	1220.18i	0.538018	−	0.144162i
$93$	−2919.48	−	10895.6i	−0.337551	−	1.25976i
$94$	−42.6739	+	159.261i	−0.00482955	+	0.0180241i
$95$	−11199.4	+	6465.97i	−1.24093	+	0.716451i
$96$	−2507.57	−	671.902i	−0.272089	−	0.0729061i
$97$	10038.9	−	10038.9i	1.06695	−	1.06695i	0.0693574	−	0.997592i	$-0.477905\pi$
$97$	10038.9	−	10038.9i	1.06695	−	1.06695i	0.997592	−	0.0693574i	$-0.0220949\pi$
$98$	6108.96	−	1636.89i	0.636085	−	0.170438i
$99$	12535.5	−	7237.39i	1.27901	−	0.738434i
$100$	10510.6			1.05106
$101$			11990.1i			1.17538i	0.809084	+	0.587692i	$0.199963\pi$
$101$			11990.1i			1.17538i	−0.809084	+	0.587692i	$0.800037\pi$
$102$	−18225.4	+	10522.4i	−1.75177	+	1.01138i
$103$	−1487.26	−	1487.26i	−0.140189	−	0.140189i	0.633530	−	0.773718i	$-0.281606\pi$
$103$	−1487.26	−	1487.26i	−0.140189	−	0.140189i	−0.773718	+	0.633530i	$0.781606\pi$
$104$	−2190.63	−	1264.76i	−0.202536	−	0.116934i
$105$	−5735.05	−	5735.05i	−0.520186	−	0.520186i
$106$	−10352.5	+	2773.95i	−0.921371	+	0.246881i
$107$	−1311.64	+	2271.83i	−0.114564	+	0.198430i	−0.917605	−	0.397493i	$-0.869880\pi$
$107$	−1311.64	+	2271.83i	−0.114564	+	0.198430i	0.803041	+	0.595923i	$0.203214\pi$
$108$	−2505.09	+	4338.95i	−0.214771	+	0.371995i
$109$	−4767.40	−	1277.42i	−0.401263	−	0.107518i	0.0525429	−	0.998619i	$-0.483267\pi$
$109$	−4767.40	−	1277.42i	−0.401263	−	0.107518i	−0.453806	+	0.891101i	$0.649934\pi$
$110$		−	14459.9i		−	1.19504i
$111$	−2465.56	+	19477.7i	−0.200110	+	1.58085i
$112$	822.011			0.0655303
$113$	2578.19	−	9621.93i	0.201910	−	0.753538i	−0.788459	−	0.615087i	$-0.789121\pi$
$113$	2578.19	−	9621.93i	0.201910	−	0.753538i	0.990369	−	0.138451i	$-0.0442124\pi$
$114$	−10317.0	−	5956.54i	−0.793862	−	0.458337i
$115$	−22471.9	−	12974.1i	−1.69920	−	0.981031i
$116$	−1842.62	−	6876.77i	−0.136937	−	0.511056i
$117$	−9854.81	+	9854.81i	−0.719908	+	0.719908i
$118$	−5730.21	+	9925.02i	−0.411535	+	0.712799i
$119$	4711.93	−	4711.93i	0.332740	−	0.332740i
$120$	7144.30	+	12374.3i	0.496132	+	0.859325i
$121$	1160.58			0.0792691
$122$			14683.2i			0.986510i
$123$	−11362.7	−	19680.8i	−0.751055	−	1.30086i
$124$	−1628.59	−	6077.96i	−0.105917	−	0.395289i
$125$	−21446.9	−	21446.9i	−1.37260	−	1.37260i
$126$	1172.19	−	4374.69i	0.0738343	−	0.275554i
$127$	9036.76	+	15652.1i	0.560280	+	0.970434i	0.997472	+	0.0710656i	$0.0226400\pi$
$127$	9036.76	+	15652.1i	0.560280	+	0.970434i	−0.437191	+	0.899369i	$0.644027\pi$
$128$	−1398.81	−	374.810i	−0.0853766	−	0.0228766i
$129$	14760.9	−	3955.18i	0.887022	−	0.237677i
$130$	3603.41	+	13448.1i	0.213220	+	0.795746i
$131$	−2676.97	+	9990.59i	−0.155991	+	0.582168i	0.843027	+	0.537871i	$0.180771\pi$
$131$	−2676.97	+	9990.59i	−0.155991	+	0.582168i	−0.999018	+	0.0442968i	$0.985895\pi$
$132$	11536.1	−	6660.34i	0.662078	−	0.382251i
$133$	3643.64	+	976.311i	0.205984	+	0.0551931i
$134$	16221.4	−	16221.4i	0.903397	−	0.903397i
$135$	26636.5	−	7137.23i	1.46154	−	0.391617i
$136$	−10166.7	+	5869.76i	−0.549672	+	0.317353i
$137$	−20258.4			−1.07935			−0.539677	−	0.841872i	$-0.681454\pi$
$137$	−20258.4			−1.07935			−0.539677	+	0.841872i	$0.681454\pi$
$138$		−	23903.9i		−	1.25519i
$139$	17822.2	−	10289.6i	0.922426	−	0.532563i	0.0380175	−	0.999277i	$-0.487896\pi$
$139$	17822.2	−	10289.6i	0.922426	−	0.532563i	0.884408	+	0.466714i	$0.154562\pi$
$140$	−3199.21	−	3199.21i	−0.163225	−	0.163225i
$141$	723.997	+	418.000i	0.0364165	+	0.0210251i
$142$	3396.34	+	3396.34i	0.168436	+	0.168436i
$143$	12537.1	−	3359.32i	0.613093	−	0.164278i
$144$	−3989.43	+	6909.89i	−0.192391	+	0.333231i
$145$	−19592.5	+	33935.2i	−0.931867	+	1.61404i
$146$	−12117.0	−	3246.75i	−0.568448	−	0.152315i
$147$		−	32067.4i		−	1.48398i
$148$	−1375.37	+	10865.3i	−0.0627910	+	0.496042i
$149$	8415.51			0.379060			0.189530	−	0.981875i	$-0.439304\pi$
$149$	8415.51			0.379060			0.189530	+	0.981875i	$0.439304\pi$
$150$	13793.2	−	51476.9i	0.613030	−	2.28786i
$151$	−23646.4	−	13652.3i	−1.03708	−	0.598758i	−0.118074	−	0.993005i	$-0.537672\pi$
$151$	−23646.4	−	13652.3i	−1.03708	−	0.598758i	−0.919005	+	0.394247i	$0.871005\pi$
$152$	−5755.19	−	3322.76i	−0.249099	−	0.143818i
$153$	16740.7	+	62477.0i	0.715137	+	2.66893i
$154$	−2982.49	+	2982.49i	−0.125759	+	0.125759i
$155$	−17316.6	+	29993.3i	−0.720776	+	1.24842i
$156$	−9069.08	+	9069.08i	−0.372661	+	0.372661i
$157$	8379.29	+	14513.4i	0.339944	+	0.588801i	0.984422	−	0.175822i	$-0.0562584\pi$
$157$	8379.29	+	14513.4i	0.339944	+	0.588801i	−0.644478	+	0.764623i	$0.722925\pi$
$158$	27108.6			1.08591
$159$			54342.9i			2.14955i
$160$	3985.33	+	6902.80i	0.155677	+	0.269641i
$161$	1958.99	+	7311.06i	0.0755755	+	0.282052i
$162$	−2233.48	−	2233.48i	−0.0851043	−	0.0851043i
$163$	5333.68	−	19905.6i	0.200748	−	0.749203i	−0.789955	−	0.613165i	$-0.789896\pi$
$163$	5333.68	−	19905.6i	0.200748	−	0.749203i	0.990704	−	0.136039i	$-0.0434371\pi$
$164$	−6338.50	−	10978.6i	−0.235667	−	0.408187i
$165$	−70819.0	−	18975.9i	−2.60125	−	0.697003i
$166$	−13652.8	+	3658.25i	−0.495456	+	0.132757i
$167$	−9491.45	−	35422.6i	−0.340329	−	1.27013i	−0.897975	−	0.440047i	$-0.854962\pi$
$167$	−9491.45	−	35422.6i	−0.340329	−	1.27013i	0.557645	−	0.830079i	$-0.311705\pi$
$168$	1078.73	−	4025.89i	0.0382204	−	0.142641i
$169$	13911.8	−	8032.00i	0.487092	−	0.281222i
$170$	62412.9	+	16723.5i	2.15961	+	0.578667i
$171$	−25890.4	+	25890.4i	−0.885416	+	0.885416i
$172$	8234.15	−	2206.33i	0.278331	−	0.0745786i
$173$	−6878.00	+	3971.01i	−0.229811	+	0.132681i	−0.610485	−	0.792028i	$-0.709025\pi$
$173$	−6878.00	+	3971.01i	−0.229811	+	0.132681i	0.380674	+	0.924709i	$0.375692\pi$
$174$	−36097.8			−1.19229
$175$			16874.7i			0.551011i
$176$	6435.20	−	3715.37i	0.207748	−	0.119943i
$177$	41089.0	+	41089.0i	1.31153	+	1.31153i
$178$	−12881.5	−	7437.14i	−0.406562	−	0.234729i
$179$	8973.82	+	8973.82i	0.280073	+	0.280073i	0.833138	−	0.553065i	$-0.186542\pi$
$179$	8973.82	+	8973.82i	0.280073	+	0.280073i	−0.553065	+	0.833138i	$0.686542\pi$
$180$	42419.3	−	11366.2i	1.30924	−	0.350809i
$181$	−31151.0	+	53955.1i	−0.950857	+	1.64693i	−0.207280	+	0.978282i	$0.566461\pi$
$181$	−31151.0	+	53955.1i	−0.950857	+	1.64693i	−0.743577	+	0.668650i	$0.766872\pi$
$182$	2030.56	−	3517.03i	0.0613018	−	0.106178i
$183$	71912.6	+	19268.9i	2.14735	+	0.575381i
$184$		−	13334.4i		−	0.393857i
$185$	47639.8	−	36934.1i	1.39196	−	1.07915i
$186$	−31904.7			−0.922207
$187$	15590.6	−	58185.0i	0.445841	−	1.66390i
$188$	403.870	+	233.174i	0.0114268	+	0.00659729i
$189$	−6966.14	−	4021.90i	−0.195015	−	0.112592i
$190$	9466.84	+	35330.7i	0.262239	+	0.978690i
$191$	22712.1	−	22712.1i	0.622575	−	0.622575i	−0.323614	−	0.946189i	$-0.604898\pi$
$191$	22712.1	−	22712.1i	0.622575	−	0.622575i	0.946189	+	0.323614i	$0.104898\pi$
$192$	−3671.34	+	6358.95i	−0.0995916	+	0.172498i
$193$	32518.0	−	32518.0i	0.872991	−	0.872991i	−0.119806	−	0.992797i	$-0.538227\pi$
$193$	32518.0	−	32518.0i	0.872991	−	0.872991i	0.992797	+	0.119806i	$0.0382274\pi$
$194$	−20077.9	−	34775.9i	−0.533475	−	0.924005i
$195$	70592.3			1.85647
$196$		−	17888.3i		−	0.465646i
$197$	−16739.0	−	28992.9i	−0.431318	−	0.747065i	0.565669	−	0.824632i	$-0.308618\pi$
$197$	−16739.0	−	28992.9i	−0.431318	−	0.747065i	−0.996987	+	0.0775674i	$0.975285\pi$
$198$	−10596.3	−	39545.8i	−0.270286	−	1.00872i
$199$	26054.4	+	26054.4i	0.657923	+	0.657923i	0.954888	−	0.296965i	$-0.0959745\pi$
$199$	26054.4	+	26054.4i	0.657923	+	0.657923i	−0.296965	+	0.954888i	$0.595974\pi$
$200$	7694.31	−	28715.5i	0.192358	−	0.717889i
$201$	−58158.5	−	100734.i	−1.43953	−	2.49334i
$202$	32757.6	+	8777.36i	0.802803	+	0.215110i
$203$	11040.6	−	2958.32i	0.267917	−	0.0717881i
$204$	15405.9	+	57495.6i	0.370192	+	1.38157i
$205$	−18059.0	+	67396.9i	−0.429719	+	1.60373i
$206$	−5152.03	+	2974.53i	−0.121407	+	0.0700945i
$207$	−70964.8	−	19015.0i	−1.65616	−	0.443767i
$208$	−5059.04	+	5059.04i	−0.116934	+	0.116934i
$209$	32937.4	−	8825.56i	0.754045	−	0.202046i
$210$	−19866.8	+	11470.1i	−0.450494	+	0.260093i
$211$	31308.2			0.703222			0.351611	−	0.936146i	$-0.385634\pi$
$211$	31308.2			0.703222			0.351611	+	0.936146i	$0.385634\pi$
$212$			30314.3i			0.674490i
$213$	21091.0	−	12176.9i	0.464876	−	0.268396i
$214$	5246.57	+	5246.57i	0.114564	+	0.114564i
$215$	−40633.6	−	23459.8i	−0.879039	−	0.507514i
$216$	10020.4	+	10020.4i	0.214771	+	0.214771i
$217$	9758.12	−	2614.68i	0.207227	−	0.0555263i
$218$	−6979.96	+	12089.7i	−0.146872	+	0.254390i
$219$	−31802.6	+	55083.7i	−0.663093	+	1.14851i
$220$	−39505.3	−	10585.4i	−0.816225	−	0.218707i
$221$			57998.8i			1.18750i
$222$	51409.0	+	20994.7i	1.04312	+	0.425994i
$223$	52715.7			1.06006			0.530030	−	0.847979i	$-0.322181\pi$
$223$	52715.7			1.06006			0.530030	+	0.847979i	$0.322181\pi$
$224$	601.754	−	2245.78i	0.0119929	−	0.0447580i
$225$	−141850.	−	81897.1i	−2.80197	−	1.61772i
$226$	−24400.2	−	14087.5i	−0.477724	−	0.275814i
$227$	−8511.26	−	31764.5i	−0.165174	−	0.616438i	−0.998018	−	0.0629303i	$-0.979955\pi$
$227$	−8511.26	−	31764.5i	−0.165174	−	0.616438i	0.832844	−	0.553508i	$-0.186711\pi$
$228$	−23826.2	+	23826.2i	−0.458337	+	0.458337i
$229$	−20946.4	+	36280.3i	−0.399428	+	0.691830i	−0.993655	−	0.112467i	$-0.964125\pi$
$229$	−20946.4	+	36280.3i	−0.399428	+	0.691830i	0.594227	+	0.804297i	$0.297458\pi$
$230$	−51896.5	+	51896.5i	−0.981031	+	0.981031i
$231$	10693.1	+	18521.0i	0.200392	+	0.347089i
$232$	−20136.6			−0.374119
$233$			54089.5i			0.996326i	0.867083	+	0.498163i	$0.165992\pi$
$233$			54089.5i			0.996326i	−0.867083	+	0.498163i	$0.834008\pi$
$234$	19709.6	+	34138.1i	0.359954	+	0.623458i
$235$	−664.334	−	2479.33i	−0.0120296	−	0.0448951i
$236$	22920.9	+	22920.9i	0.411535	+	0.411535i
$237$	35574.9	−	132767.i	0.633354	−	2.36371i
$238$	−9423.86	−	16322.6i	−0.166370	−	0.288161i
$239$	−77889.4	−	20870.4i	−1.36359	−	0.365372i	−0.498454	−	0.866916i	$-0.666099\pi$
$239$	−77889.4	−	20870.4i	−1.36359	−	0.365372i	−0.865132	+	0.501544i	$0.832765\pi$
$240$	39037.2	−	10460.0i	0.677729	−	0.181597i
$241$	−4223.66	−	15762.9i	−0.0727202	−	0.271396i	0.919986	−	0.391950i	$-0.128199\pi$
$241$	−4223.66	−	15762.9i	−0.0727202	−	0.271396i	−0.992707	+	0.120554i	$0.961533\pi$
$242$	849.602	−	3170.76i	0.0145072	−	0.0541418i
$243$	−57801.5	+	33371.7i	−0.978874	+	0.565153i
$244$	40115.3	+	10748.9i	0.673799	+	0.180544i
$245$	−69619.8	+	69619.8i	−1.15985	+	1.15985i
$246$	−62087.0	+	16636.2i	−1.02596	+	0.274905i
$247$	−28433.3	+	16416.0i	−0.466052	+	0.269075i
$248$	−17797.5			−0.289372
$249$			71666.7i			1.15590i
$250$	−74294.3	+	42893.8i	−1.18871	+	0.686301i
$251$	−46328.6	−	46328.6i	−0.735363	−	0.735363i	0.236314	−	0.971677i	$-0.424061\pi$
$251$	−46328.6	−	46328.6i	−0.735363	−	0.735363i	−0.971677	+	0.236314i	$0.924061\pi$
$252$	−11093.8	−	6404.99i	−0.174694	−	0.100860i
$253$	48381.1	+	48381.1i	0.755848	+	0.755848i
$254$	49377.8	−	13230.7i	0.765357	−	0.205077i
$255$	163810.	−	283727.i	2.51918	−	4.36336i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−28401.7	−	7610.22i	−0.430010	−	0.115221i	0.0373210	−	0.999303i	$-0.488118\pi$
$257$	−28401.7	−	7610.22i	−0.430010	−	0.115221i	−0.467331	+	0.884083i	$0.654784\pi$
$258$		−	43223.0i		−	0.649345i
$259$	−17444.1	−	2208.15i	−0.260046	−	0.0329177i
$260$	39378.8			0.582527
$261$	−28714.9	+	107165.i	−0.421528	+	1.57316i
$262$	25335.1	+	14627.2i	0.369080	+	0.213088i
$263$	−41108.1	−	23733.8i	−0.594313	−	0.343127i	0.172488	−	0.985012i	$-0.444819\pi$
$263$	−41108.1	−	23733.8i	−0.594313	−	0.343127i	−0.766801	+	0.641885i	$0.778153\pi$
$264$	−9751.42	−	36392.8i	−0.139914	−	0.522165i
$265$	117981.	−	117981.i	1.68004	−	1.68004i
$266$	5334.66	−	9239.91i	0.0753952	−	0.130588i
$267$	−53328.7	+	53328.7i	−0.748064	+	0.748064i
$268$	−32442.8	−	56192.6i	−0.451699	−	0.782365i
$269$	48197.1			0.666065			0.333033	−	0.942915i	$-0.391928\pi$
$269$	48197.1			0.666065			0.333033	+	0.942915i	$0.391928\pi$
$270$		−	77997.1i		−	1.06992i
$271$	43985.7	+	76185.5i	0.598926	+	1.03737i	0.992980	+	0.118283i	$0.0377389\pi$
$271$	43985.7	+	76185.5i	0.598926	+	1.03737i	−0.394054	+	0.919087i	$0.628928\pi$
$272$	8593.93	+	32073.0i	0.116159	+	0.433513i
$273$	−14560.3	−	14560.3i	−0.195365	−	0.195365i
$274$	−14830.2	+	55347.0i	−0.197536	+	0.737213i
$275$	76271.1	+	132105.i	1.00854	+	1.74685i
$276$	−65306.7	−	17498.9i	−0.857313	−	0.229716i
$277$	−72840.7	+	19517.6i	−0.949324	+	0.254371i	−0.700075	−	0.714069i	$-0.746850\pi$
$277$	−72840.7	+	19517.6i	−0.949324	+	0.254371i	−0.249249	+	0.968440i	$0.580184\pi$
$278$	−15065.1	−	56223.7i	−0.194931	−	0.727494i
$279$	−25379.4	+	94717.1i	−0.326041	+	1.21680i
$280$	−11082.4	+	6398.42i	−0.141357	+	0.0816124i
$281$	119831.	+	32108.7i	1.51760	+	0.406640i	0.918951	−	0.394372i	$-0.129038\pi$
$281$	119831.	+	32108.7i	1.51760	+	0.406640i	0.598649	+	0.801012i	$0.295705\pi$
$282$	1672.00	−	1672.00i	0.0210251	−	0.0210251i
$283$	−22714.6	+	6086.35i	−0.283617	+	0.0759948i	−0.397823	−	0.917462i	$-0.630234\pi$
$283$	−22714.6	+	6086.35i	−0.283617	+	0.0759948i	0.114206	+	0.993457i	$0.463567\pi$
$284$	11765.3	−	6792.67i	0.145870	−	0.0842178i
$285$	185459.			2.28328
$286$		−	36711.3i		−	0.448815i
$287$	17626.1	−	10176.4i	0.213989	−	0.123547i
$288$	15957.7	+	15957.7i	0.192391	+	0.192391i
$289$	160779.	+	92826.0i	1.92502	+	1.11141i
$290$	78370.0	+	78370.0i	0.931867	+	0.931867i
$291$	−196667.	+	52696.7i	−2.32244	+	0.622297i
$292$	−17740.6	+	30727.6i	−0.208066	+	0.360381i
$293$	47090.0	−	81562.2i	0.548521	−	0.950066i	−0.449855	−	0.893102i	$-0.648524\pi$
$293$	47090.0	−	81562.2i	0.548521	−	0.950066i	0.998376	−	0.0569647i	$-0.0181423\pi$
$294$	−87609.7	−	23474.9i	−1.01358	−	0.271588i
$295$		−	178413.i		−	2.05013i
$296$	28677.7	+	11711.5i	0.327311	+	0.133669i
$297$	−72713.6			−0.824333
$298$	6160.58	−	22991.6i	0.0693728	−	0.258903i
$299$	−57052.2	−	32939.1i	−0.638161	−	0.368442i
$300$	−130540.	−	75367.4i	−1.45045	−	0.837415i
$301$	3542.25	+	13219.9i	0.0390972	+	0.145913i
$302$	−54609.1	+	54609.1i	−0.598758	+	0.598758i
$303$	85976.1	−	148915.i	0.936467	−	1.62201i
$304$	−13291.0	+	13291.0i	−0.143818	+	0.143818i
$305$	−114292.	−	197960.i	−1.22862	−	2.12803i
$306$	182945.			1.95379
$307$			133438.i			1.41580i	0.706313	+	0.707899i	$0.250357\pi$
$307$			133438.i			1.41580i	−0.706313	+	0.707899i	$0.749643\pi$
$308$	5964.99	+	10331.7i	0.0628794	+	0.108910i
$309$	7807.00	+	29136.1i	0.0817650	+	0.305151i
$310$	69266.6	+	69266.6i	0.720776	+	0.720776i
$311$	22407.9	−	83627.3i	0.231675	−	0.864624i	−0.747944	−	0.663762i	$-0.768959\pi$
$311$	22407.9	−	83627.3i	0.231675	−	0.864624i	0.979619	−	0.200862i	$-0.0643744\pi$
$312$	18138.2	+	31416.2i	0.186330	+	0.322734i
$313$	−129678.	−	34747.2i	−1.32367	−	0.354675i	−0.473317	−	0.880892i	$-0.656943\pi$
$313$	−129678.	−	34747.2i	−1.32367	−	0.354675i	−0.850350	+	0.526217i	$0.823610\pi$
$314$	45785.3	−	12268.1i	0.464373	−	0.124428i
$315$	18248.4	+	68103.8i	0.183909	+	0.686358i
$316$	19844.9	−	74062.1i	0.198735	−	0.741689i
$317$	−208.710	+	120.499i	−0.00207695	+	0.00119913i	−0.501038	−	0.865425i	$-0.667048\pi$
$317$	−208.710	+	120.499i	−0.00207695	+	0.00119913i	0.498961	+	0.866624i	$0.333715\pi$
$318$	148467.	+	39781.7i	1.46817	+	0.393396i
$319$	73061.3	−	73061.3i	0.717969	−	0.717969i
$320$	21776.3	−	5834.93i	0.212659	−	0.0569818i
$321$	32580.7	−	18810.5i	0.316192	−	0.182553i
$322$	21408.3			0.206476
$323$			152374.i			1.46051i
$324$	−7736.99	+	4466.95i	−0.0737025	+	0.0425521i
$325$	−103855.	−	103855.i	−0.983240	−	0.983240i
$326$	−50478.5	−	29143.8i	−0.474976	−	0.274227i
$327$	50050.5	+	50050.5i	0.468072	+	0.468072i
$328$	−34634.2	+	9280.21i	−0.321927	+	0.0862602i
$329$	−374.360	+	648.410i	−0.00345857	+	0.00599043i
$330$	−103686.	+	179590.i	−0.952124	+	1.64913i
$331$	−125081.	−	33515.4i	−1.14166	−	0.305906i	−0.362041	−	0.932162i	$-0.617920\pi$
$331$	−125081.	−	33515.4i	−1.14166	−	0.305906i	−0.779618	+	0.626256i	$0.784587\pi$
$332$			39978.1i			0.362699i
$333$	103223.	−	135920.i	0.930864	−	1.22573i
$334$	−103724.			−0.929797
$335$	−92432.4	+	344962.i	−0.823635	+	3.07385i
$336$	−10209.2	−	5894.31i	−0.0904305	−	0.0522101i
$337$	54667.4	+	31562.3i	0.481359	+	0.277913i	0.720983	−	0.692953i	$-0.243691\pi$
$337$	54667.4	+	31562.3i	0.481359	+	0.277913i	−0.239624	+	0.970866i	$0.577024\pi$
$338$	−11759.7	−	43887.6i	−0.102935	−	0.384157i
$339$	−101016.	+	101016.i	−0.879000	+	0.879000i
$340$	91378.8	−	158273.i	0.790474	−	1.36914i
$341$	64574.5	−	64574.5i	0.555331	−	0.555331i
$342$	51780.9	+	89687.1i	0.442708	+	0.766793i
$343$	59557.7			0.506232
$344$		−	24111.3i		−	0.203753i
$345$	186064.	+	322273.i	1.56324	+	2.70761i
$346$	5813.97	+	21698.0i	0.0485647	+	0.181246i
$347$	24526.3	+	24526.3i	0.203692	+	0.203692i	0.801580	−	0.597888i	$-0.203993\pi$
$347$	24526.3	+	24526.3i	0.203692	+	0.203692i	−0.597888	+	0.801580i	$0.703993\pi$
$348$	−26425.4	+	98621.0i	−0.218204	+	0.814349i
$349$	−86628.5	−	150045.i	−0.711230	−	1.23189i	−0.964396	−	0.264463i	$-0.914805\pi$
$349$	−86628.5	−	150045.i	−0.711230	−	1.23189i	0.253166	−	0.967423i	$-0.418528\pi$
$350$	46102.6	+	12353.1i	0.376347	+	0.100842i
$351$	67625.5	−	18120.2i	0.548904	−	0.147078i
$352$	−5439.67	−	20301.1i	−0.0439023	−	0.163846i
$353$	33574.0	−	125300.i	0.269435	−	1.00554i	−0.690045	−	0.723766i	$-0.742409\pi$
$353$	33574.0	−	125300.i	0.269435	−	1.00554i	0.959480	−	0.281777i	$-0.0909239\pi$
$354$	142337.	−	82178.0i	1.13582	−	0.655766i
$355$	−72226.1	−	19352.9i	−0.573109	−	0.153564i
$356$	−29748.6	+	29748.6i	−0.234729	+	0.234729i
$357$	−92308.6	+	24734.0i	−0.724279	+	0.194070i
$358$	31086.2	−	17947.6i	0.242550	−	0.140036i
$359$	−24962.2			−0.193684			−0.0968421	−	0.995300i	$-0.530874\pi$
$359$	−24962.2			−0.193684			−0.0968421	+	0.995300i	$0.530874\pi$
$360$		−	124212.i		−	0.958429i
$361$	38161.6	−	22032.6i	0.292828	−	0.169064i
$362$	124604.	+	124604.i	0.950857	+	0.950857i
$363$	−14414.2	−	8322.03i	−0.109390	−	0.0631562i
$364$	−8122.24	−	8122.24i	−0.0613018	−	0.0613018i
$365$	188634.	−	50544.4i	1.41591	−	0.379391i
$366$	105287.	−	182363.i	0.785985	−	1.36137i
$367$	13470.9	−	23332.3i	0.100015	−	0.173231i	−0.811676	−	0.584108i	$-0.801444\pi$
$367$	13470.9	−	23332.3i	0.100015	−	0.173231i	0.911691	+	0.410878i	$0.134778\pi$
$368$	−36430.3	−	9761.46i	−0.269009	−	0.0720808i
$369$			197555.i			1.45089i
$370$	−66031.0	−	157192.i	−0.482330	−	1.14822i
$371$	−48669.3			−0.353596
$372$	−23355.8	+	87165.2i	−0.168776	+	0.629879i
$373$	63125.0	+	36445.2i	0.453716	+	0.261953i	0.709398	−	0.704808i	$-0.248967\pi$
$373$	63125.0	+	36445.2i	0.453716	+	0.261953i	−0.255683	+	0.966761i	$0.582300\pi$
$374$	−147551.	−	85188.8i	−1.05487	−	0.609031i
$375$	112580.	+	420154.i	0.800569	+	2.98776i
$376$	932.698	−	932.698i	0.00659729	−	0.00659729i
$377$	−49742.0	+	86155.7i	−0.349978	+	0.606180i
$378$	−16087.6	+	16087.6i	−0.112592	+	0.112592i
$379$	−90490.4	−	156734.i	−0.629976	−	1.09115i	−0.987556	−	0.157268i	$-0.949731\pi$
$379$	−90490.4	−	156734.i	−0.629976	−	1.09115i	0.357579	−	0.933883i	$-0.383602\pi$
$380$	103456.			0.716451
$381$		−	259196.i		−	1.78557i
$382$	−45424.3	−	78677.2i	−0.311287	−	0.539165i
$383$	−8815.07	−	32898.3i	−0.0600936	−	0.224272i	0.929348	−	0.369205i	$-0.120370\pi$
$383$	−8815.07	−	32898.3i	−0.0600936	−	0.224272i	−0.989441	+	0.144933i	$0.953703\pi$
$384$	14685.4	+	14685.4i	0.0995916	+	0.0995916i
$385$	16994.8	−	63425.4i	0.114655	−	0.427899i
$386$	−65036.1	−	112646.i	−0.436495	−	0.756032i
$387$	−128318.	−	34382.8i	−0.856776	−	0.229572i
$388$	−109707.	+	29396.0i	−0.728740	+	0.195265i
$389$	−10372.0	−	38708.8i	−0.0685430	−	0.255806i	0.923149	−	0.384443i	$-0.125606\pi$
$389$	−10372.0	−	38708.8i	−0.0685430	−	0.255806i	−0.991692	+	0.128637i	$0.958940\pi$
$390$	51677.2	−	192862.i	0.339758	−	1.26799i
$391$	−264780.	+	152871.i	−1.73193	+	0.999933i
$392$	−48871.7	−	13095.1i	−0.318042	−	0.0852192i
$393$	104886.	−	104886.i	0.679098	−	0.679098i
$394$	−91463.8	+	24507.6i	−0.589192	+	0.157873i
$395$	−365479.	+	211009.i	−2.34244	+	1.35241i
$396$	−115798.			−0.738434
$397$		−	200596.i		−	1.27274i	−0.771382	−	0.636372i	$-0.780434\pi$
$397$		−	200596.i		−	1.27274i	0.771382	−	0.636372i	$-0.219566\pi$
$398$	90255.2	−	52108.8i	0.569778	−	0.328962i
$399$	−38252.7	−	38252.7i	−0.240279	−	0.240279i
$400$	−72819.7	−	42042.5i	−0.455123	−	0.262765i
$401$	57086.9	+	57086.9i	0.355016	+	0.355016i	0.861972	−	0.506956i	$-0.169229\pi$
$401$	57086.9	+	57086.9i	0.355016	+	0.355016i	−0.506956	+	0.861972i	$0.669229\pi$
$402$	−317784.	+	85150.0i	−1.96644	+	0.526905i
$403$	−43964.0	+	76147.9i	−0.270699	+	0.468865i
$404$	47960.4	−	83069.9i	0.293846	−	0.508957i
$405$	47496.8	+	12726.7i	0.289571	+	0.0775902i
$406$		−	32329.1i		−	0.196129i
$407$	−146544.	+	61558.1i	−0.884664	+	0.371618i
$408$	168359.			1.01138
$409$	27545.1	−	102800.i	0.164664	−	0.614533i	−0.833419	−	0.552641i	$-0.813620\pi$
$409$	27545.1	−	102800.i	0.164664	−	0.614533i	0.998083	−	0.0618916i	$-0.0197133\pi$
$410$	170912.	+	98675.9i	1.01673	+	0.587007i
$411$	251606.	+	145265.i	1.48949	+	0.859957i
$412$	4355.01	+	16253.1i	0.0256564	+	0.0957508i
$413$	−36799.2	+	36799.2i	−0.215744	+	0.215744i
$414$	−103900.	+	179959.i	−0.606196	+	1.04996i
$415$	155592.	−	155592.i	0.903423	−	0.903423i
$416$	10118.1	+	17525.0i	0.0584671	+	0.101268i
$417$	−295131.			−1.69724
$418$		−	96447.5i		−	0.551999i
$419$	31934.2	+	55311.6i	0.181898	+	0.315056i	0.942527	−	0.334131i	$-0.108443\pi$
$419$	31934.2	+	55311.6i	0.181898	+	0.315056i	−0.760629	+	0.649187i	$0.775109\pi$
$420$	16793.4	+	62673.8i	0.0952007	+	0.355294i
$421$	27945.5	+	27945.5i	0.157669	+	0.157669i	0.781533	−	0.623864i	$-0.214438\pi$
$421$	27945.5	+	27945.5i	0.157669	+	0.157669i	−0.623864	+	0.781533i	$0.714438\pi$
$422$	22919.2	−	85535.5i	0.128699	−	0.480310i
$423$	−3633.72	−	6293.79i	−0.0203082	−	0.0351748i
$424$	82820.2	+	22191.6i	0.460685	+	0.123440i
$425$	−658412.	+	176421.i	−3.64519	+	0.976725i
$426$	−17828.2	−	66535.7i	−0.0982398	−	0.366636i
$427$	−17257.2	+	64404.8i	−0.0946487	+	0.353234i
$428$	18174.6	−	10493.1i	0.0992152	−	0.0572819i
$429$	−179797.	−	48176.6i	−0.976942	−	0.261771i
$430$	−93839.3	+	93839.3i	−0.507514	+	0.507514i
$431$	41795.3	−	11199.0i	0.224995	−	0.0602873i	−0.144560	−	0.989496i	$-0.546177\pi$
$431$	41795.3	−	11199.0i	0.224995	−	0.0602873i	0.369555	+	0.929209i	$0.379510\pi$
$432$	34711.6	−	20040.7i	0.185997	−	0.107386i
$433$	79871.2			0.426005			0.213002	−	0.977052i	$-0.431676\pi$
$433$	79871.2			0.426005			0.213002	+	0.977052i	$0.431676\pi$
$434$		−	28573.7i		−	0.151701i
$435$	486671.	−	280980.i	2.57192	−	1.48490i
$436$	27919.9	+	27919.9i	0.146872	+	0.146872i
$437$	−149887.	−	86537.2i	−0.784875	−	0.453148i
$438$	127210.	+	127210.i	0.663093	+	0.663093i
$439$	96535.4	−	25866.6i	0.500908	−	0.134218i	0.000486404	−	1.00000i	$-0.499845\pi$
$439$	96535.4	−	25866.6i	0.500908	−	0.134218i	0.500421	+	0.865782i	$0.333179\pi$
$440$	−57839.7	+	100181.i	−0.298759	+	0.517466i
$441$	−139383.	+	241418.i	−0.716690	+	1.24134i
$442$	158456.	+	42458.0i	0.811079	+	0.217328i
$443$		−	240502.i		−	1.22550i	−0.790278	−	0.612748i	$-0.790064\pi$
$443$		−	240502.i		−	1.22550i	0.790278	−	0.612748i	$-0.209936\pi$
$444$	94992.5	−	125083.i	0.481863	−	0.634500i
$445$	231559.			1.16934
$446$	38590.6	−	144022.i	0.194004	−	0.724034i
$447$	−104519.	−	60344.2i	−0.523095	−	0.302009i
$448$	−5695.06	−	3288.05i	−0.0283754	−	0.0163826i
$449$	32901.3	+	122789.i	0.163200	+	0.609071i	0.998263	+	0.0589167i	$0.0187646\pi$
$449$	32901.3	+	122789.i	0.163200	+	0.609071i	−0.835063	+	0.550155i	$0.814569\pi$
$450$	−327589.	+	327589.i	−1.61772	+	1.61772i
$451$	91991.7	−	159334.i	0.452268	−	0.783350i
$452$	−56349.9	+	56349.9i	−0.275814	+	0.275814i
$453$	195790.	+	339118.i	0.954099	+	1.65255i
$454$	−93012.8			−0.451264
$455$			63222.3i			0.305385i
$456$	47652.3	+	82536.3i	0.229168	+	0.396931i
$457$	−42900.7	−	160108.i	−0.205415	−	0.766619i	−0.989323	−	0.145742i	$-0.953443\pi$
$457$	−42900.7	−	160108.i	−0.205415	−	0.766619i	0.783908	−	0.620877i	$-0.213224\pi$
$458$	83785.7	+	83785.7i	0.399428	+	0.399428i
$459$	84096.0	−	313851.i	0.399163	−	1.48970i
$460$	103793.	+	179775.i	0.490515	+	0.849598i
$461$	−171527.	−	45960.4i	−0.807105	−	0.216263i	−0.168404	−	0.985718i	$-0.553861\pi$
$461$	−171527.	−	45960.4i	−0.807105	−	0.216263i	−0.638701	+	0.769455i	$0.720528\pi$
$462$	58428.3	−	15655.8i	0.273741	−	0.0733486i
$463$	−27205.5	−	101532.i	−0.126910	−	0.473634i	0.872991	−	0.487737i	$-0.162177\pi$
$463$	−27205.5	−	101532.i	−0.126910	−	0.473634i	−0.999901	+	0.0141029i	$0.995511\pi$
$464$	−14741.0	+	55014.1i	−0.0684685	+	0.255528i
$465$	430140.	−	248341.i	1.98931	−	1.14853i
$466$	147775.	+	39596.3i	0.680503	+	0.182340i
$467$	206813.	−	206813.i	0.948295	−	0.948295i	−0.0504321	−	0.998727i	$-0.516060\pi$
$467$	206813.	−	206813.i	0.948295	−	0.948295i	0.998727	+	0.0504321i	$0.0160599\pi$
$468$	107695.	−	28856.9i	0.491706	−	0.131752i
$469$	90216.7	−	52086.6i	0.410149	−	0.236799i
$470$	−7259.98			−0.0328655
$471$		−	240338.i		−	1.08338i
$472$	79400.2	−	45841.7i	0.356400	−	0.205767i
$473$	87482.6	+	87482.6i	0.391020	+	0.391020i
$474$	−336684.	−	194385.i	−1.49853	−	0.865178i
$475$	−272846.	−	272846.i	−1.20929	−	1.20929i
$476$	−51492.9	+	13797.5i	−0.227265	+	0.0608956i
$477$	236204.	−	409118.i	1.03813	−	1.79809i
$478$	−114038.	+	197520.i	−0.499107	+	0.864479i
$479$	398538.	+	106788.i	1.73700	+	0.465427i	0.981776	−	0.190042i	$-0.0608625\pi$
$479$	398538.	+	106788.i	1.73700	+	0.465427i	0.755222	+	0.655469i	$0.227529\pi$
$480$		−	114309.i		−	0.496132i
$481$	120949.	−	93769.3i	0.522773	−	0.405294i
$482$	−46157.1			−0.198675
$483$	28094.3	−	104849.i	0.120427	−	0.449439i
$484$	−8040.72	−	4642.31i	−0.0343245	−	0.0198173i
$485$	541380.	+	312566.i	2.30154	+	1.32880i
$486$	48859.6	+	182347.i	0.206860	+	0.772014i
$487$	−248814.	+	248814.i	−1.04910	+	1.04910i	−0.0503711	+	0.998731i	$0.516040\pi$
$487$	−248814.	+	248814.i	−1.04910	+	1.04910i	−0.998731	+	0.0503711i	$0.983960\pi$
$488$	58732.9	−	101728.i	0.246628	−	0.427171i
$489$	−208978.	+	208978.i	−0.873943	+	0.873943i
$490$	139240.	+	241170.i	0.579923	+	1.00446i
$491$	−421783.			−1.74955			−0.874774	−	0.484532i	$-0.838990\pi$
$491$	−421783.			−1.74955			−0.874774	+	0.484532i	$0.838990\pi$
$492$			181803.i			0.751055i
$493$	230853.	+	399850.i	0.949822	+	1.64514i
$494$	24034.7	+	89698.7i	0.0984883	+	0.367563i
$495$	450678.	+	450678.i	1.83932	+	1.83932i
$496$	−13028.7	+	48623.7i	−0.0529587	+	0.197644i
$497$	10905.6	+	18889.0i	0.0441505	+	0.0764709i
$498$	195797.	+	52463.7i	0.789492	+	0.211544i
$499$	−63426.3	+	16995.0i	−0.254723	+	0.0682528i	−0.383921	−	0.923366i	$-0.625426\pi$
$499$	−63426.3	+	16995.0i	−0.254723	+	0.0682528i	0.129198	+	0.991619i	$0.458760\pi$
$500$	62800.9	+	234376.i	0.251204	+	0.937505i
$501$	−136119.	+	508001.i	−0.542303	+	2.02390i
$502$	−160487.	+	92657.2i	−0.636843	+	0.367681i
$503$	27387.4	+	7338.43i	0.108247	+	0.0290046i	0.312536	−	0.949906i	$-0.398822\pi$
$503$	27387.4	+	7338.43i	0.108247	+	0.0290046i	−0.204289	+	0.978911i	$0.565488\pi$
$504$	−25619.9	+	25619.9i	−0.100860	+	0.100860i
$505$	−509960.	+	136643.i	−1.99965	+	0.535804i
$506$	167597.	−	96762.1i	0.654584	−	0.377924i
$507$	−230377.			−0.896236
$508$		−	144588.i		−	0.560280i
$509$	30456.8	−	17584.2i	0.117557	−	0.0678715i	−0.440069	−	0.897964i	$-0.645046\pi$
$509$	30456.8	−	17584.2i	0.117557	−	0.0678715i	0.557626	+	0.830093i	$0.311713\pi$
$510$	−655240.	−	655240.i	−2.51918	−	2.51918i
$511$	−49332.8	−	28482.3i	−0.188927	−	0.109077i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	177665.	−	47605.2i	0.675098	−	0.180892i
$514$	−41583.0	+	72023.9i	−0.157394	+	0.272615i
$515$	46306.6	−	80205.4i	0.174594	−	0.302405i
$516$	−118087.	−	31641.4i	−0.443511	−	0.118838i
$517$			6768.19i			0.0253216i
$518$	−18802.8	+	46041.8i	−0.0700749	+	0.171590i
$519$	113898.			0.422846
$520$	28827.3	−	107585.i	0.106610	−	0.397873i
$521$	−67431.0	−	38931.3i	−0.248418	−	0.143424i	0.370621	−	0.928784i	$-0.379145\pi$
$521$	−67431.0	−	38931.3i	−0.248418	−	0.143424i	−0.619040	+	0.785360i	$0.712478\pi$
$522$	271761.	+	156901.i	0.997345	+	0.575817i
$523$	−94518.2	−	352747.i	−0.345551	−	1.28961i	−0.891967	−	0.452100i	$-0.850675\pi$
$523$	−94518.2	−	352747.i	−0.345551	−	1.28961i	0.546416	−	0.837514i	$-0.315992\pi$
$524$	58508.9	−	58508.9i	0.213088	−	0.213088i
$525$	121002.	−	209581.i	0.439008	−	0.760384i
$526$	−94935.0	+	94935.0i	−0.343127	+	0.343127i
$527$	204038.	+	353403.i	0.734664	+	1.27248i
$528$	−106566.			−0.382251
$529$		−	67437.2i		−	0.240984i
$530$	−235962.	−	408698.i	−0.840021	−	1.45496i
$531$	−130741.	−	487933.i	−0.463685	−	1.73050i
$532$	−21338.7	−	21338.7i	−0.0753952	−	0.0753952i
$533$	−45848.6	+	171109.i	−0.161388	+	0.602309i
$534$	106657.	+	184736.i	0.374032	+	0.647842i
$535$	−111573.	−	29895.9i	−0.389808	−	0.104449i
$536$	−177271.	+	47499.6i	−0.617032	+	0.165333i
$537$	−47105.7	−	175801.i	−0.163352	−	0.609639i
$538$	35282.7	−	131677.i	0.121898	−	0.454931i
$539$	224833.	−	129808.i	0.773897	−	0.446810i
$540$	−213092.	−	57097.8i	−0.730768	−	0.195809i
$541$	−16081.3	+	16081.3i	−0.0549448	+	0.0549448i	−0.734045	−	0.679101i	$-0.762370\pi$
$541$	−16081.3	+	16081.3i	−0.0549448	+	0.0549448i	0.679101	+	0.734045i	$0.262370\pi$
$542$	240342.	−	64399.6i	0.818148	−	0.219222i
$543$	773781.	−	446742.i	2.62433	−	1.51516i
$544$	93916.2			0.317353
$545$		−	217324.i		−	0.731669i
$546$	−50438.4	+	29120.6i	−0.169191	+	0.0976823i
$547$	167720.	+	167720.i	0.560544	+	0.560544i	0.929462	−	0.368918i	$-0.120272\pi$
$547$	167720.	+	167720.i	0.560544	+	0.560544i	−0.368918	+	0.929462i	$0.620272\pi$
$548$	140354.	+	81033.6i	0.467374	+	0.269839i
$549$	−457638.	−	457638.i	−1.51837	−	1.51837i
$550$	416753.	−	111669.i	1.37770	−	0.369153i
$551$	−130682.	+	226347.i	−0.430439	+	0.745542i
$552$	−95615.6	+	165611.i	−0.313798	+	0.543515i
$553$	118906.	+	31860.8i	0.388824	+	0.104185i
$554$			213292.i			0.694953i
$555$	−856517.	+	117110.i	−2.78067	+	0.380195i
$556$	−164634.			−0.532563
$557$	−43645.3	+	162887.i	−0.140678	+	0.525019i	0.859231	+	0.511587i	$0.170942\pi$
$557$	−43645.3	+	162887.i	−0.140678	+	0.525019i	−0.999910	+	0.0134319i	$0.995724\pi$
$558$	240193.	+	138675.i	0.771422	+	0.445381i
$559$	−103162.	−	59560.5i	−0.330138	−	0.190605i
$560$	9367.93	+	34961.6i	0.0298722	+	0.111485i
$561$	−610854.	+	610854.i	−1.94094	+	1.94094i
$562$	175445.	−	303880.i	0.555480	−	0.962120i
$563$	284102.	−	284102.i	0.896310	−	0.896310i	−0.0987978	−	0.995108i	$-0.531500\pi$
$563$	284102.	−	284102.i	0.896310	−	0.896310i	0.995108	+	0.0987978i	$0.0314997\pi$
$564$	−3344.00	−	5791.97i	−0.0105125	−	0.0182083i
$565$	438620.			1.37401
$566$			66512.9i			0.207622i
$567$	−7171.65	−	12421.7i	−0.0223076	−	0.0386379i
$568$	−9945.16	−	37115.9i	−0.0308259	−	0.115044i
$569$	24828.2	+	24828.2i	0.0766867	+	0.0766867i	0.744410	−	0.667723i	$-0.232731\pi$
$569$	24828.2	+	24828.2i	0.0766867	+	0.0766867i	−0.667723	+	0.744410i	$0.732731\pi$
$570$	135766.	−	506684.i	0.417869	−	1.55951i
$571$	251600.	+	435783.i	0.771681	+	1.33659i	0.936641	+	0.350291i	$0.113917\pi$
$571$	251600.	+	435783.i	0.771681	+	1.33659i	−0.164960	+	0.986300i	$0.552749\pi$
$572$	−100297.	−	26874.5i	−0.306547	−	0.0821389i
$573$	−444940.	+	119221.i	−1.35517	+	0.363116i
$574$	−14899.3	−	55604.9i	−0.0452212	−	0.168768i
$575$	200389.	−	747861.i	0.606091	−	2.26196i
$576$	55279.1	−	31915.4i	0.166616	−	0.0961956i
$577$	80446.3	+	21555.5i	0.241632	+	0.0647451i	0.377602	−	0.925968i	$-0.376749\pi$
$577$	80446.3	+	21555.5i	0.241632	+	0.0647451i	−0.135971	+	0.990713i	$0.543415\pi$
$578$	371304.	−	371304.i	1.11141	−	1.11141i
$579$	−637042.	+	170695.i	−1.90025	+	0.509171i
$580$	271482.	−	156740.i	0.807021	−	0.465934i
$581$	−64184.6			−0.190142
$582$			575880.i			1.70015i
$583$	−381013.	+	219978.i	−1.12099	+	0.647205i
$584$	70962.3	+	70962.3i	0.208066	+	0.208066i
$585$	−531451.	−	306834.i	−1.55293	−	0.896585i
$586$	−188360.	−	188360.i	−0.548521	−	0.548521i
$587$	417363.	−	111832.i	1.21126	−	0.324556i	0.404004	−	0.914757i	$-0.367618\pi$
$587$	417363.	−	111832.i	1.21126	−	0.324556i	0.807256	+	0.590201i	$0.200952\pi$
$588$	−128269.	+	222169.i	−0.370995	+	0.642583i
$589$	−115502.	+	200055.i	−0.332934	+	0.576658i
$590$	−487432.	−	130607.i	−1.40026	−	0.375200i
$591$			480115.i			1.37458i
$592$	52990.0	−	69775.5i	0.151200	−	0.199095i
$593$	488787.			1.38999			0.694993	−	0.719016i	$-0.255407\pi$
$593$	488787.			1.38999			0.694993	+	0.719016i	$0.255407\pi$
$594$	−53230.0	+	198657.i	−0.150863	+	0.563030i
$595$	254105.	+	146708.i	0.717761	+	0.414400i
$596$	−58304.3	−	33662.0i	−0.164138	−	0.0947650i
$597$	−136766.	−	510417.i	−0.383733	−	1.43211i
$598$	−131756.	+	131756.i	−0.368442	+	0.368442i
$599$	218664.	−	378737.i	0.609429	−	1.05556i	−0.381905	−	0.924202i	$-0.624732\pi$
$599$	218664.	−	378737.i	0.609429	−	1.05556i	0.991335	−	0.131361i	$-0.0419348\pi$
$600$	−301469.	+	301469.i	−0.837415	+	0.837415i
$601$	141041.	+	244291.i	0.390479	+	0.676330i	0.992513	−	0.122141i	$-0.0389761\pi$
$601$	141041.	+	244291.i	0.390479	+	0.676330i	−0.602034	+	0.798471i	$0.705643\pi$
$602$	38710.4			0.106816
$603$			1.01116e6i			2.78089i
$604$	109218.	+	189171.i	0.299379	+	0.518539i
$605$	13226.4	+	49361.4i	0.0361351	+	0.134858i
$606$	−343904.	−	343904.i	−0.936467	−	0.936467i
$607$	−108246.	+	403979.i	−0.293788	+	1.09643i	0.648387	+	0.761311i	$0.275444\pi$
$607$	−108246.	+	403979.i	−0.293788	+	1.09643i	−0.942175	+	0.335121i	$0.891223\pi$
$608$	26582.1	+	46041.5i	0.0719088	+	0.124550i
$609$	−158335.	−	42425.8i	−0.426916	−	0.114392i
$610$	−624503.	+	167335.i	−1.67832	+	0.449705i
$611$	−1686.63	−	6294.60i	−0.00451791	−	0.0168611i
$612$	133925.	−	499816.i	0.357569	−	1.33446i
$613$	−304350.	+	175717.i	−0.809939	+	0.467619i	−0.846935	−	0.531697i	$-0.821555\pi$
$613$	−304350.	+	175717.i	−0.809939	+	0.467619i	0.0369954	+	0.999315i	$0.488221\pi$
$614$	364558.	+	97683.1i	0.967008	+	0.259109i
$615$	707565.	−	707565.i	1.87075	−	1.87075i
$616$	32593.3	−	8733.35i	0.0858948	−	0.0230154i
$617$	−413405.	+	238680.i	−1.08594	+	0.626967i	−0.932492	−	0.361189i	$-0.882371\pi$
$617$	−413405.	+	238680.i	−1.08594	+	0.626967i	−0.153447	+	0.988157i	$0.549037\pi$
$618$	85316.5			0.223386
$619$			316130.i			0.825059i	0.910944	+	0.412529i	$0.135355\pi$
$619$			316130.i			0.825059i	−0.910944	+	0.412529i	$0.864645\pi$
$620$	239947.	−	138533.i	0.624211	−	0.360388i
$621$	260968.	+	260968.i	0.676712	+	0.676712i
$622$	−212070.	−	122439.i	−0.548150	−	0.316474i
$623$	−47761.1	−	47761.1i	−0.123055	−	0.123055i
$624$	99108.7	−	26556.1i	0.254532	−	0.0682017i
$625$	257188.	−	445462.i	0.658400	−	1.14038i
$626$	−189862.	+	328851.i	−0.484496	+	0.839171i
$627$	−472362.	−	126569.i	−1.20154	−	0.321953i
$628$		−	134069.i		−	0.339944i
$629$	−96217.4	−	703716.i	−0.243194	−	1.77867i
$630$	199422.			0.502449
$631$	−36745.7	+	137137.i	−0.0922887	+	0.344426i	−0.996594	−	0.0824594i	$-0.973723\pi$
$631$	−36745.7	+	137137.i	−0.0922887	+	0.344426i	0.904306	+	0.426885i	$0.140389\pi$
$632$	−187814.	−	108434.i	−0.470212	−	0.271477i
$633$	−388842.	−	224498.i	−0.970433	−	0.560280i
$634$	176.423	+	658.418i	0.000438910	+	0.00163804i
$635$	−562727.	+	562727.i	−1.39556	+	1.39556i
$636$	217371.	−	376498.i	0.537388	−	0.930784i
$637$	−176753.	+	176753.i	−0.435600	+	0.435600i
$638$	−146123.	−	253092.i	−0.358985	−	0.621780i
$639$	−211710.			−0.518489
$640$		−	63765.3i		−	0.155677i
$641$	−159617.	−	276465.i	−0.388475	−	0.672859i	0.603769	−	0.797159i	$-0.293665\pi$
$641$	−159617.	−	276465.i	−0.388475	−	0.672859i	−0.992245	+	0.124300i	$0.960331\pi$
$642$	−27540.5	−	102782.i	−0.0668192	−	0.249373i
$643$	−323.568	−	323.568i	−0.000782607	−	0.000782607i	0.706715	−	0.707498i	$-0.250176\pi$
$643$	−323.568	−	323.568i	−0.000782607	−	0.000782607i	−0.707498	+	0.706715i	$0.750176\pi$
$644$	15671.9	−	58488.5i	0.0377878	−	0.141026i
$645$	336442.	+	582734.i	0.808705	+	1.40072i
$646$	416293.	+	111545.i	0.997548	+	0.267292i
$647$	497884.	−	133408.i	1.18938	−	0.318693i	0.390737	−	0.920502i	$-0.372220\pi$
$647$	497884.	−	133408.i	1.18938	−	0.318693i	0.798640	+	0.601810i	$0.205553\pi$
$648$	6540.07	+	24407.9i	0.0155752	+	0.0581273i
$649$	−121760.	+	454414.i	−0.289078	+	1.07885i
$650$	−359763.	+	207709.i	−0.851511	+	0.491620i
$651$	−139943.	−	37497.6i	−0.330209	−	0.0884792i
$652$	−116575.	+	116575.i	−0.274227	+	0.274227i
$653$	296061.	−	79329.3i	0.694312	−	0.186040i	0.105630	−	0.994405i	$-0.466314\pi$
$653$	296061.	−	79329.3i	0.694312	−	0.186040i	0.588681	+	0.808365i	$0.299647\pi$
$654$	173380.	−	100101.i	0.405362	−	0.234036i
$655$	−455425.			−1.06153
$656$			101416.i			0.235667i
$657$	478849.	−	276464.i	1.10935	−	0.640482i
$658$	1497.44	+	1497.44i	0.00345857	+	0.00345857i
$659$	−157427.	−	90890.4i	−0.362500	−	0.209289i	0.307677	−	0.951491i	$-0.400448\pi$
$659$	−157427.	−	90890.4i	−0.362500	−	0.209289i	−0.670177	+	0.742201i	$0.733782\pi$
$660$	414745.	+	414745.i	0.952124	+	0.952124i
$661$	418602.	−	112164.i	0.958072	−	0.256715i	0.254288	−	0.967128i	$-0.418159\pi$
$661$	418602.	−	112164.i	0.958072	−	0.256715i	0.703784	+	0.710414i	$0.251492\pi$
$662$	−183132.	+	317193.i	−0.417876	+	0.723783i
$663$	415885.	−	720335.i	0.946121	−	1.63873i
$664$	109222.	+	29266.0i	0.247728	+	0.0663785i
$665$			166097.i			0.375594i
$666$	−295776.	−	381510.i	−0.666829	−	0.860116i
$667$	−524432.			−1.17879
$668$	−75931.6	+	283381.i	−0.170165	+	0.635063i
$669$	−654720.	−	378003.i	−1.46286	−	0.844584i
$670$	874790.	+	505060.i	1.94874	+	1.12511i
$671$	156000.	+	582199.i	0.346481	+	1.29308i
$672$	−23577.2	+	23577.2i	−0.0522101	+	0.0522101i
$673$	−152927.	+	264877.i	−0.337640	+	0.584809i	−0.983988	−	0.178233i	$-0.942962\pi$
$673$	−152927.	+	264877.i	−0.337640	+	0.584809i	0.646349	+	0.763042i	$0.276295\pi$
$674$	126249.	−	126249.i	0.277913	−	0.277913i
$675$	411407.	+	712578.i	0.902951	+	1.56396i
$676$	−128512.			−0.281222
$677$		−	98874.0i		−	0.215727i	−0.994166	−	0.107864i	$-0.965599\pi$
$677$		−	98874.0i		−	0.215727i	0.994166	−	0.107864i	$-0.0344010\pi$
$678$	202031.	+	349928.i	0.439500	+	0.761237i
$679$	−47195.0	−	176134.i	−0.102366	−	0.382036i
$680$	−365515.	−	365515.i	−0.790474	−	0.790474i
$681$	−122062.	+	455540.i	−0.263199	+	0.982273i
$682$	−129149.	−	223693.i	−0.277666	−	0.480931i
$683$	−57625.8	−	15440.8i	−0.123531	−	0.0331000i	0.196524	−	0.980499i	$-0.437035\pi$
$683$	−57625.8	−	15440.8i	−0.123531	−	0.0331000i	−0.320055	+	0.947399i	$0.603701\pi$
$684$	282936.	−	75812.5i	0.604750	−	0.162042i
$685$	−230872.	−	861626.i	−0.492028	−	1.83627i
$686$	43599.3	−	162715.i	0.0926469	−	0.345763i
$687$	520302.	−	300396.i	1.10241	−	0.636475i
$688$	−65873.2	−	17650.7i	−0.139166	−	0.0372893i
$689$	299534.	−	299534.i	0.630968	−	0.630968i
$690$	1.01667e6	−	272417.i	2.13542	−	0.572185i
$691$	293430.	−	169412.i	0.614537	−	0.354803i	−0.160202	−	0.987084i	$-0.551214\pi$
$691$	293430.	−	169412.i	0.614537	−	0.354803i	0.774739	+	0.632281i	$0.217881\pi$
$692$	63536.2			0.132681
$693$		−	185913.i		−	0.387118i
$694$	84961.6	−	49052.6i	0.176402	−	0.101846i
$695$	640745.	+	640745.i	1.32652	+	1.32652i
$696$	250093.	+	144391.i	0.516277	+	0.298073i
$697$	581336.	+	581336.i	1.19664	+	1.19664i
$698$	−473347.	+	126833.i	−0.971558	+	0.260328i
$699$	387854.	−	671783.i	0.793805	−	1.37491i
$700$	67498.8	−	116911.i	0.137753	−	0.238595i
$701$	−546293.	−	146379.i	−1.11170	−	0.297880i	−0.344183	−	0.938903i	$-0.611844\pi$
$701$	−546293.	−	146379.i	−1.11170	−	0.297880i	−0.767522	+	0.641022i	$0.778511\pi$
$702$		−	198021.i		−	0.401825i
$703$	317756.	−	246350.i	0.642960	−	0.498473i
$704$	−59445.9			−0.119943
$705$	−9527.34	+	35556.5i	−0.0191687	+	0.0715387i
$706$	−317747.	−	183452.i	−0.637489	−	0.368054i
$707$	133368.	+	77000.0i	0.266816	+	0.154047i
$708$	−120317.	−	449029.i	−0.240027	−	0.895794i
$709$	305093.	−	305093.i	0.606933	−	0.606933i	−0.335211	−	0.942143i	$-0.608807\pi$
$709$	305093.	−	305093.i	0.606933	−	0.606933i	0.942143	+	0.335211i	$0.108807\pi$
$710$	−105746.	+	183158.i	−0.209772	+	0.363337i
$711$	−844904.	+	844904.i	−1.67135	+	1.67135i
$712$	59497.2	+	103052.i	0.117364	+	0.203281i
$713$	−463514.			−0.911767
$714$			270298.i			0.530209i
$715$	285755.	+	494943.i	0.558962	+	0.968151i
$716$	−26277.2	−	98067.7i	−0.0512569	−	0.191293i
$717$	817720.	+	817720.i	1.59062	+	1.59062i
$718$	−18273.6	+	68198.0i	−0.0354467	+	0.132289i
$719$	−189202.	−	327707.i	−0.365988	−	0.633910i	0.622946	−	0.782265i	$-0.285936\pi$
$719$	−189202.	−	327707.i	−0.365988	−	0.633910i	−0.988934	+	0.148355i	$0.952602\pi$
$720$	−339355.	−	90929.8i	−0.654619	−	0.175405i
$721$	−26094.3	+	6991.93i	−0.0501966	+	0.0134501i
$722$	−32258.0	−	120388.i	−0.0618817	−	0.230946i
$723$	−60572.3	+	226059.i	−0.115877	+	0.432459i
$724$	431641.	−	249208.i	0.823466	−	0.475428i
$725$	−1.12936e6	−	302611.i	−2.14860	−	0.575717i
$726$	−33288.1	+	33288.1i	−0.0631562	+	0.0631562i
$727$	−284060.	+	76113.6i	−0.537453	+	0.144010i	−0.517328	−	0.855787i	$-0.673073\pi$
$727$	−284060.	+	76113.6i	−0.537453	+	0.144010i	−0.0201254	+	0.999797i	$0.506407\pi$
$728$	−28136.3	+	16244.5i	−0.0530889	+	0.0306509i
$729$	866724.			1.63089
$730$		−	552360.i		−	1.03652i
$731$	−478775.	+	276421.i	−0.895977	+	0.517292i
$732$	−421149.	−	421149.i	−0.785985	−	0.785985i
$733$	−376903.	−	217605.i	−0.701491	−	0.405006i	0.106411	−	0.994322i	$-0.466064\pi$
$733$	−376903.	−	217605.i	−0.701491	−	0.405006i	−0.807903	+	0.589316i	$0.799397\pi$
$734$	−53883.6	−	53883.6i	−0.100015	−	0.100015i
$735$	1.36388e6	−	365451.i	2.52465	−	0.676479i
$736$	−53337.6	+	92383.5i	−0.0984641	+	0.170545i
$737$	470847.	−	815532.i	0.866852	−	1.50143i
$738$	539729.	+	144620.i	0.990976	+	0.265531i
$739$		−	52403.6i		−	0.0959561i	−0.998848	−	0.0479780i	$-0.984722\pi$
$739$		−	52403.6i		−	0.0959561i	0.998848	−	0.0479780i	$-0.0152778\pi$
$740$	−477794.	+	65327.7i	−0.872524	+	0.119298i
$741$	470850.			0.857523
$742$	−35628.4	+	132967.i	−0.0647126	+	0.241511i
$743$	188619.	+	108899.i	0.341671	+	0.197264i	0.661011	−	0.750376i	$-0.270128\pi$
$743$	188619.	+	108899.i	0.341671	+	0.197264i	−0.319340	+	0.947640i	$0.603461\pi$
$744$	221042.	+	127619.i	0.399327	+	0.230552i
$745$	95906.1	+	357926.i	0.172796	+	0.644883i
$746$	145781.	−	145781.i	0.261953	−	0.261953i
$747$	311504.	−	539540.i	0.558241	−	0.966902i
$748$	−340755.	+	340755.i	−0.609031	+	0.609031i
$749$	16846.6	+	29179.2i	0.0300296	+	0.0520128i
$750$	1.23030e6			2.18719
$751$			743989.i			1.31913i	0.751649	+	0.659563i	$0.229259\pi$
$751$			743989.i			1.31913i	−0.751649	+	0.659563i	$0.770741\pi$
$752$	−1865.40	−	3230.96i	−0.00329864	−	0.00571342i
$753$	243190.	+	907597.i	0.428899	+	1.60067i
$754$	198968.	+	198968.i	0.349978	+	0.349978i
$755$	311172.	−	1.16131e6i	0.545892	−	2.03730i
$756$	32175.2	+	55729.1i	0.0562961	+	0.0975076i
$757$	881800.	+	236278.i	1.53879	+	0.412317i	0.925874	−	0.377834i	$-0.123331\pi$
$757$	881800.	+	236278.i	1.53879	+	0.412317i	0.612913	+	0.790150i	$0.289998\pi$
$758$	−494449.	+	132487.i	−0.860564	+	0.230587i
$759$	−253964.	−	947806.i	−0.440847	−	1.64526i
$760$	75734.7	−	282646.i	0.131120	−	0.489345i
$761$	595874.	−	344028.i	1.02893	−	0.594052i	0.112251	−	0.993680i	$-0.464194\pi$
$761$	595874.	−	344028.i	1.02893	−	0.594052i	0.916678	+	0.399628i	$0.130861\pi$
$762$	−708136.	−	189744.i	−1.21957	−	0.326783i
$763$	−44825.1	+	44825.1i	−0.0769967	+	0.0769967i
$764$	−248203.	+	66505.8i	−0.425226	+	0.113939i
$765$	−2.46647e6	+	1.42402e6i	−4.21457	+	2.43328i
$766$	−96332.9			−0.164179
$767$		−	452959.i		−	0.769960i
$768$	50871.6	−	29370.7i	0.0862488	−	0.0497958i
$769$	−452328.	−	452328.i	−0.764894	−	0.764894i	0.212309	−	0.977203i	$-0.431902\pi$
$769$	−452328.	−	452328.i	−0.764894	−	0.764894i	−0.977203	+	0.212309i	$0.931902\pi$
$770$	−160840.	−	92861.2i	−0.271277	−	0.156622i
$771$	298175.	+	298175.i	0.501605	+	0.501605i
$772$	−355364.	+	95219.4i	−0.596264	+	0.159768i
$773$	−156741.	+	271483.i	−0.262315	+	0.454343i	−0.966857	−	0.255320i	$-0.917819\pi$
$773$	−156741.	+	271483.i	−0.262315	+	0.454343i	0.704542	+	0.709663i	$0.251153\pi$
$774$	−187871.	+	325403.i	−0.313602	+	0.543174i
$775$	−998174.	−	267460.i	−1.66189	−	0.445303i
$776$			321246.i			0.533475i
$777$	200819.	+	152510.i	0.332632	+	0.252613i
$778$	−113347.			−0.187263
$779$	−120453.	+	449536.i	−0.198492	+	0.740781i
$780$	−489078.	−	282369.i	−0.803876	−	0.464118i
$781$	170751.	+	98583.1i	0.279937	+	0.161622i
$782$	223818.	+	835301.i	0.366001	+	1.36593i
$783$	394093.	−	394093.i	0.642800	−	0.642800i
$784$	−71553.1	+	123934.i	−0.116412	+	0.201631i
$785$	−521785.	+	521785.i	−0.846745	+	0.846745i
$786$	−209772.	−	363336.i	−0.339549	−	0.588116i
$787$	903858.			1.45932			0.729661	−	0.683810i	$-0.239678\pi$
$787$	903858.			1.45932			0.729661	+	0.683810i	$0.239678\pi$
$788$			267824.i			0.431318i
$789$	340370.	+	589538.i	0.546761	+	0.947017i
$790$	308939.	+	1.15298e6i	0.495015	+	1.84742i
$791$	−90469.3	−	90469.3i	−0.144593	−	0.144593i
$792$	−84770.2	+	316367.i	−0.135143	+	0.504360i
$793$	−290168.	−	502585.i	−0.461427	−	0.799215i
$794$	−548038.	−	146846.i	−0.869300	−	0.232928i
$795$	−2.31130e6	+	619310.i	−3.65697	+	0.979883i
$796$	−76292.6	−	284728.i	−0.120408	−	0.449370i
$797$	−40570.1	+	151410.i	−0.0638690	+	0.238362i	−0.990480	−	0.137660i	$-0.956042\pi$
$797$	−40570.1	+	151410.i	−0.0638690	+	0.238362i	0.926611	+	0.376022i	$0.122708\pi$
$798$	−132511.	+	76505.4i	−0.208088	+	0.120140i
$799$	−29213.3	−	7827.68i	−0.0457601	−	0.0122614i
$800$	−168170.	+	168170.i	−0.262765	+	0.262765i
$801$	633279.	−	169687.i	0.987030	−	0.264474i
$802$	197755.	−	114174.i	0.307453	−	0.177508i
$803$	−514943.			−0.798598
$804$			930536.i			1.43953i
$805$	−288627.	+	166639.i	−0.445395	+	0.257149i
$806$	175856.	+	175856.i	0.270699	+	0.270699i
$807$	−598600.	−	345602.i	−0.919157	−	0.530676i
$808$	−191842.	−	191842.i	−0.293846	−	0.293846i
$809$	−939846.	+	251831.i	−1.43602	+	0.384780i	−0.891137	−	0.453734i	$-0.850092\pi$
$809$	−939846.	+	251831.i	−1.43602	+	0.384780i	−0.544880	+	0.838514i	$0.683425\pi$
$810$	69540.2	−	120447.i	0.105990	−	0.183580i
$811$	−21948.9	+	38016.7i	−0.0333712	+	0.0578006i	−0.882229	−	0.470821i	$-0.843958\pi$
$811$	−21948.9	+	38016.7i	−0.0333712	+	0.0578006i	0.848857	+	0.528622i	$0.177291\pi$
$812$	−88324.7	−	23666.5i	−0.133958	−	0.0358941i
$813$		−	1.26161e6i		−	1.90873i
$814$	60902.4	+	445429.i	0.0919148	+	0.672248i
$815$	907404.			1.36611
$816$	123247.	−	459965.i	0.185096	−	0.690787i
$817$	−271025.	−	156477.i	−0.406037	−	0.234426i
$818$	−260689.	−	150509.i	−0.389598	−	0.224935i
$819$	46329.5	+	172904.i	0.0690700	+	0.257773i
$820$	394704.	−	394704.i	0.587007	−	0.587007i
$821$	43145.0	−	74729.4i	0.0640095	−	0.110868i	−0.832245	−	0.554409i	$-0.812945\pi$
$821$	43145.0	−	74729.4i	0.0640095	−	0.110868i	0.896254	+	0.443541i	$0.146278\pi$
$822$	581059.	−	581059.i	0.859957	−	0.859957i
$823$	−557966.	−	966426.i	−0.823774	−	1.42682i	−0.902852	−	0.429950i	$-0.858531\pi$
$823$	−557966.	−	966426.i	−0.823774	−	1.42682i	0.0790782	−	0.996868i	$-0.474802\pi$
$824$	47592.5			0.0700945
$825$		−	2.18764e6i		−	3.21416i
$826$	73598.4	+	127476.i	0.107872	+	0.186840i
$827$	−141929.	−	529687.i	−0.207520	−	0.774477i	−0.988666	−	0.150128i	$-0.952031\pi$
$827$	−141929.	−	529687.i	−0.207520	−	0.774477i	0.781146	−	0.624348i	$-0.214635\pi$
$828$	415599.	+	415599.i	0.606196	+	0.606196i
$829$	−296689.	+	1.10726e6i	−0.431710	+	1.61116i	0.317109	+	0.948389i	$0.397288\pi$
$829$	−296689.	+	1.10726e6i	−0.431710	+	1.61116i	−0.748819	+	0.662774i	$0.769379\pi$
$830$	−311184.	−	538986.i	−0.451711	−	0.782387i
$831$	1.04462e6	+	279905.i	1.51271	+	0.405331i
$832$	55286.2	−	14813.9i	0.0798675	−	0.0214004i
$833$	300255.	+	1.12057e6i	0.432713	+	1.61491i
$834$	−216051.	+	806314.i	−0.310616	+	1.15924i
$835$	1.39842e6	−	807376.i	2.00569	−	1.15798i
$836$	−263499.	−	70604.5i	−0.377022	−	0.101023i
$837$	348316.	−	348316.i	0.497190	−	0.497190i
$838$	174492.	−	46754.9i	0.248477	−	0.0665792i
$839$	735951.	−	424901.i	1.04550	−	0.603621i	0.124115	−	0.992268i	$-0.460391\pi$
$839$	735951.	−	424901.i	1.04550	−	0.603621i	0.921387	+	0.388647i	$0.127057\pi$
$840$	183522.			0.260093
$841$			84674.9i			0.119719i
$842$	96806.0	−	55891.0i	0.136546	−	0.0788347i
$843$	−1.25804e6	−	1.25804e6i	−1.77028	−	1.77028i
$844$	−216909.	−	125233.i	−0.304504	−	0.175806i
$845$	500159.	+	500159.i	0.700478	+	0.700478i
$846$	−19855.0	+	5320.13i	−0.0277415	+	0.00743330i
$847$	7453.19	−	12909.3i	0.0103890	−	0.0179944i
$848$	121257.	−	210024.i	0.168623	−	0.292063i
$849$	325754.	+	87285.5i	0.451933	+	0.121095i
$850$			1.92796e6i			2.66846i
$851$	746875.	+	305013.i	1.03131	+	0.421171i
$852$	−194830.			−0.268396
$853$	−41509.5	+	154916.i	−0.0570492	+	0.212911i	−0.988566	−	0.150787i	$-0.951819\pi$
$853$	−41509.5	+	154916.i	−0.0570492	+	0.212911i	0.931517	+	0.363698i	$0.118486\pi$
$854$	163324.	+	94295.1i	0.223941	+	0.129293i
$855$	−1.39622e6	−	806110.i	−1.90995	−	1.10271i
$856$	−15363.0	−	57335.5i	−0.0209666	−	0.0782486i
$857$	574043.	−	574043.i	0.781597	−	0.781597i	−0.198503	−	0.980100i	$-0.563608\pi$
$857$	574043.	−	574043.i	0.781597	−	0.781597i	0.980100	+	0.198503i	$0.0636081\pi$
$858$	−263242.	+	455948.i	−0.357586	+	0.619357i
$859$	791961.	−	791961.i	1.07329	−	1.07329i	0.0761977	−	0.997093i	$-0.475722\pi$
$859$	791961.	−	791961.i	1.07329	−	1.07329i	0.997093	−	0.0761977i	$-0.0242780\pi$
$860$	187679.	+	325069.i	0.253757	+	0.439520i
$861$	−291884.			−0.393734
$862$		−	122385.i		−	0.164708i
$863$	−63820.2	−	110540.i	−0.0856913	−	0.148422i	0.819994	−	0.572372i	$-0.193977\pi$
$863$	−63820.2	−	110540.i	−0.0856913	−	0.148422i	−0.905686	+	0.423950i	$0.860643\pi$
$864$	−29341.7	−	109505.i	−0.0393059	−	0.146691i
$865$	−247278.	−	247278.i	−0.330487	−	0.330487i
$866$	58469.8	−	218212.i	0.0779642	−	0.290967i
$867$	−1.33123e6	−	2.30577e6i	−1.77099	−	3.06745i
$868$	−78064.9	−	20917.4i	−0.103614	−	0.0277632i
$869$	1.07487e6	−	288012.i	1.42337	−	0.381391i
$870$	−411383.	−	1.53530e6i	−0.543510	−	2.02841i
$871$	−234670.	+	875801.i	−0.309330	+	1.15443i
$872$	96717.2	−	55839.7i	0.127195	−	0.0734362i
$873$	1.70965e6	+	458098.i	2.24325	+	0.601077i
$874$	−346149.	+	346149.i	−0.453148	+	0.453148i
$875$	−376289.	+	100826.i	−0.491480	+	0.131692i
$876$	440670.	−	254421.i	0.574255	−	0.331546i
$877$	390802.			0.508109			0.254055	−	0.967190i	$-0.418236\pi$
$877$	390802.			0.508109			0.254055	+	0.967190i	$0.418236\pi$
$878$		−	282675.i		−	0.366690i
$879$	−1.16970e6	+	675326.i	−1.51390	+	0.874049i
$880$	231359.	+	231359.i	0.298759	+	0.298759i
$881$	−194891.	−	112521.i	−0.251097	−	0.144971i	0.369170	−	0.929362i	$-0.379642\pi$
$881$	−194891.	−	112521.i	−0.251097	−	0.144971i	−0.620266	+	0.784391i	$0.712975\pi$
$882$	557531.	+	557531.i	0.716690	+	0.716690i
$883$	551829.	−	147862.i	0.707755	−	0.189642i	0.113053	−	0.993589i	$-0.463937\pi$
$883$	551829.	−	147862.i	0.707755	−	0.189642i	0.594702	+	0.803946i	$0.297270\pi$
$884$	231995.	−	401827.i	0.296875	−	0.514203i
$885$	−1.27932e6	+	2.21585e6i	−1.63340	+	2.82914i
$886$	−657065.	−	176060.i	−0.837029	−	0.224281i
$887$			423925.i			0.538817i	0.963026	+	0.269409i	$0.0868282\pi$
$887$			423925.i			0.538817i	−0.963026	+	0.269409i	$0.913172\pi$
$888$	−272193.	−	351091.i	−0.345185	−	0.445240i
$889$	232135.			0.293723
$890$	169513.	−	632630.i	0.214004	−	0.798674i
$891$	−112288.	−	64829.6i	−0.141442	−	0.0816616i
$892$	−365225.	−	210863.i	−0.459019	−	0.265015i
$893$	−4431.10	−	16537.1i	−0.00555659	−	0.0207375i
$894$	−241377.	+	241377.i	−0.302009	+	0.302009i
$895$	−279404.	+	483941.i	−0.348807	+	0.604152i
$896$	−13152.2	+	13152.2i	−0.0163826	+	0.0163826i
$897$	472386.	+	818196.i	0.587100	+	1.01689i
$898$	359552.			0.445871
$899$			699962.i			0.866075i
$900$	655177.	+	1.13480e6i	0.808860	+	1.40099i
$901$	−508826.	−	1.89897e6i	−0.626787	−	2.33920i
$902$	−367967.	−	367967.i	−0.452268	−	0.452268i
$903$	50800.1	−	189588.i	0.0623001	−	0.232507i
$904$	112700.	+	195202.i	0.137907	+	0.238862i
$905$	−2.64981e6	−	710016.i	−3.23533	−	0.866904i
$906$	1.06982e6	−	286656.i	1.30332	−	0.349225i
$907$	401027.	+	1.49665e6i	0.487482	+	1.81931i	0.568613	+	0.822605i	$0.307480\pi$
$907$	401027.	+	1.49665e6i	0.487482	+	1.81931i	−0.0811309	+	0.996703i	$0.525853\pi$
$908$	−68090.1	+	254116.i	−0.0825871	+	0.308219i
$909$	−1.29454e6	+	747400.i	−1.56670	+	0.904535i
$910$	172727.	+	46282.0i	0.208582	+	0.0558893i
$911$	704696.	−	704696.i	0.849112	−	0.849112i	−0.140911	−	0.990022i	$-0.545003\pi$
$911$	704696.	−	704696.i	0.849112	−	0.849112i	0.990022	+	0.140911i	$0.0450030\pi$
$912$	260377.	−	69767.9i	0.313050	−	0.0838814i
$913$	−502476.	+	290104.i	−0.602800	+	0.348027i
$914$	−468828.			−0.561204
$915$			3.27816e6i			3.91551i
$916$	290242.	−	167571.i	0.345915	−	0.199714i
$917$	93935.6	+	93935.6i	0.111710	+	0.111710i
$918$	−795894.	−	459509.i	−0.944430	−	0.545267i
$919$	−256802.	−	256802.i	−0.304065	−	0.304065i	0.538537	−	0.842602i	$-0.318977\pi$
$919$	−256802.	−	256802.i	−0.304065	−	0.304065i	−0.842602	+	0.538537i	$0.818977\pi$
$920$	567136.	−	151964.i	0.670056	−	0.179541i
$921$	956827.	−	1.65727e6i	1.12801	−	1.95378i
$922$	−251132.	+	434974.i	−0.295421	+	0.511684i
$923$	−183370.	−	49133.8i	−0.215241	−	0.0576735i
$924$		−	171090.i		−	0.200392i
$925$	1.43239e6	+	1.08781e6i	1.67409	+	1.27136i
$926$	−297308.			−0.346724
$927$	67867.2	−	253284.i	0.0789769	−	0.294746i
$928$	139510.	+	80546.3i	0.161998	+	0.0935297i
$929$	909376.	+	525028.i	1.05369	+	0.608347i	0.923679	−	0.383166i	$-0.125166\pi$
$929$	909376.	+	525028.i	1.05369	+	0.608347i	0.130008	+	0.991513i	$0.458500\pi$
$930$	−363597.	−	1.35696e6i	−0.420392	−	1.56892i
$931$	−464363.	+	464363.i	−0.535745	+	0.535745i
$932$	216358.	−	374743.i	0.249082	−	0.431422i
$933$	−877959.	+	877959.i	−1.00858	+	1.00858i
$934$	−413626.	−	716421.i	−0.474148	−	0.821248i
$935$	2.65239e6			3.03399
$936$		−	315354.i		−	0.359954i
$937$	−435065.	−	753554.i	−0.495535	−	0.858292i	0.504451	−	0.863440i	$-0.331695\pi$
$937$	−435065.	−	753554.i	−0.495535	−	0.858292i	−0.999987	+	0.00514776i	$0.998361\pi$
$938$	−76260.1	−	284607.i	−0.0866746	−	0.323474i
$939$	1.36142e6	+	1.36142e6i	1.54405	+	1.54405i
$940$	−5314.68	+	19834.6i	−0.00601480	+	0.0224475i
$941$	−180851.	−	313244.i	−0.204241	−	0.353755i	0.745650	−	0.666338i	$-0.232139\pi$
$941$	−180851.	−	313244.i	−0.204241	−	0.353755i	−0.949891	+	0.312583i	$0.898806\pi$
$942$	−656615.	−	175940.i	−0.739962	−	0.198272i
$943$	−902006.	+	241692.i	−1.01435	+	0.271793i
$944$	−67116.9	−	250484.i	−0.0753161	−	0.281084i
$945$	91670.0	−	342117.i	0.102651	−	0.383099i
$946$	303049.	−	174965.i	0.338634	−	0.195510i
$947$	378542.	+	101430.i	0.422098	+	0.113101i	0.463615	−	0.886037i	$-0.346552\pi$
$947$	378542.	+	101430.i	0.422098	+	0.113101i	−0.0415164	+	0.999138i	$0.513219\pi$
$948$	−777539.	+	777539.i	−0.865178	+	0.865178i
$949$	478910.	−	128324.i	0.531768	−	0.142487i
$950$	−945166.	+	545692.i	−1.04728	+	0.604645i
$951$	3456.19			0.00382153
$952$			150782.i			0.166370i
$953$	10801.1	−	6236.04i	0.0118928	−	0.00686630i	−0.494042	−	0.869438i	$-0.664481\pi$
$953$	10801.1	−	6236.04i	0.0118928	−	0.00686630i	0.505935	+	0.862572i	$0.331148\pi$
$954$	−944817.	−	944817.i	−1.03813	−	1.03813i
$955$	1.22482e6	+	707152.i	1.34297	+	0.775365i
$956$	456152.	+	456152.i	0.499107	+	0.499107i
$957$	−1.43130e6	+	383516.i	−1.56281	+	0.418755i
$958$	583501.	−	1.01065e6i	0.635785	−	1.10121i
$959$	−130099.	+	225338.i	−0.141461	+	0.245017i
$960$	−312297.	−	83679.8i	−0.338864	−	0.0907984i
$961$		−	304866.i		−	0.330113i
$962$	−167642.	−	399083.i	−0.181147	−	0.431235i
$963$	−327043.			−0.352657
$964$	−33789.3	+	126103.i	−0.0363601	+	0.135698i
$965$	1.75364e6	+	1.01246e6i	1.88315	+	1.08724i
$966$	−265887.	−	153510.i	−0.284933	−	0.164506i
$967$	116414.	+	434465.i	0.124496	+	0.464624i	0.999821	−	0.0189101i	$-0.00601963\pi$
$967$	116414.	+	434465.i	0.124496	+	0.464624i	−0.875326	+	0.483534i	$0.839353\pi$
$968$	−18569.3	+	18569.3i	−0.0198173	+	0.0198173i
$969$	1.09261e6	−	1.89245e6i	1.16364	−	2.01548i
$970$	1.25026e6	−	1.25026e6i	1.32880	−	1.32880i
$971$	888811.	+	1.53947e6i	0.942695	+	1.63280i	0.760302	+	0.649570i	$0.225051\pi$
$971$	888811.	+	1.53947e6i	0.942695	+	1.63280i	0.182393	+	0.983226i	$0.441616\pi$
$972$	533948.			0.565153
$973$		−	264319.i		−	0.279192i
$974$	497629.	+	861918.i	0.524551	+	0.908549i
$975$	545158.	+	2.03456e6i	0.573473	+	2.14023i
$976$	−234931.	−	234931.i	−0.246628	−	0.246628i
$977$	−91322.1	+	340819.i	−0.0956724	+	0.357054i	−0.997121	−	0.0758329i	$-0.975838\pi$
$977$	−91322.1	+	340819.i	−0.0956724	+	0.357054i	0.901448	+	0.432887i	$0.142505\pi$
$978$	417956.	+	723922.i	0.436972	+	0.756857i
$979$	−589775.	−	158030.i	−0.615349	−	0.164882i
$980$	760819.	−	203861.i	0.792190	−	0.212267i
$981$	−159256.	−	594350.i	−0.165484	−	0.617596i
$982$	−308766.	+	1.15233e6i	−0.320189	+	1.19496i
$983$	−704183.	+	406560.i	−0.728749	+	0.420744i	−0.817964	−	0.575269i	$-0.804897\pi$
$983$	−704183.	+	406560.i	−0.728749	+	0.420744i	0.0892151	+	0.996012i	$0.471564\pi$
$984$	496696.	+	133089.i	0.512980	+	0.137453i
$985$	1.04235e6	−	1.04235e6i	1.07434	−	1.07434i
$986$	1.26141e6	−	337993.i	1.29748	−	0.347659i
$987$	9298.96	−	5368.76i	0.00954553	−	0.00551112i
$988$	262656.			0.269075
$989$		−	627948.i		−	0.641994i
$990$	1.56120e6	−	901357.i	1.59289	−	0.919658i
$991$	−923115.	−	923115.i	−0.939958	−	0.939958i	0.0583386	−	0.998297i	$-0.481420\pi$
$991$	−923115.	−	923115.i	−0.939958	−	0.939958i	−0.998297	+	0.0583386i	$0.981420\pi$
$992$	123305.	+	71190.0i	0.125302	+	0.0723429i
$993$	1.31316e6	+	1.31316e6i	1.33174	+	1.33174i
$994$	59589.2	−	15966.9i	0.0603107	−	0.0161602i
$995$	−811215.	+	1.40507e6i	−0.819388	+	1.41922i
$996$	286667.	−	496522.i	0.288974	−	0.500518i
$997$	−1.33469e6	−	357630.i	−1.34274	−	0.359786i	−0.485289	−	0.874354i	$-0.661286\pi$
$997$	−1.33469e6	−	357630.i	−1.34274	−	0.359786i	−0.857450	+	0.514568i	$0.827952\pi$
$998$			185725.i			0.186470i
$999$	−790459.	+	332045.i	−0.792042	+	0.332710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.g.a.29.2	yes	28
37.23	odd	12	inner	74.5.g.a.23.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.g.a.23.2	✓	28	37.23	odd	12	inner
74.5.g.a.29.2	yes	28	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.732051 - 2.73205i) q^{2} +(-12.4198 - 7.17059i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(11.3964 + 42.5318i) q^{5} +(-28.6824 + 28.6824i) q^{6} +(6.42196 - 11.1232i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(62.3348 + 107.967i) q^{9} +O(q^{10})\)	\(q+(0.732051 - 2.73205i) q^{2} +(-12.4198 - 7.17059i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(11.3964 + 42.5318i) q^{5} +(-28.6824 + 28.6824i) q^{6} +(6.42196 - 11.1232i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(62.3348 + 107.967i) q^{9} +124.542 q^{10} -116.105i q^{11} +(57.3647 + 99.3586i) q^{12} +(28.9334 + 107.981i) q^{13} +(-25.6879 - 25.6879i) q^{14} +(163.437 - 609.956i) q^{15} +(32.0000 + 55.4256i) q^{16} +(501.141 + 134.280i) q^{17} +(340.604 - 91.2644i) q^{18} +(76.0134 + 283.686i) q^{19} +(91.1708 - 340.254i) q^{20} +(-159.519 + 92.0986i) q^{21} +(-317.205 - 84.9949i) q^{22} +(-416.700 + 416.700i) q^{23} +(313.447 - 83.9878i) q^{24} +(-1137.81 + 656.914i) q^{25} +316.190 q^{26} -626.273i q^{27} +(-88.9854 + 51.3757i) q^{28} +(629.268 + 629.268i) q^{29} +(-1546.79 - 893.037i) q^{30} +(556.172 + 556.172i) q^{31} +(174.851 - 46.8513i) q^{32} +(-832.543 + 1442.01i) q^{33} +(733.721 - 1270.84i) q^{34} +(546.275 + 146.374i) q^{35} -997.356i q^{36} +(-530.192 - 1262.16i) q^{37} +830.690 q^{38} +(414.939 - 1548.57i) q^{39} +(-862.850 - 498.167i) q^{40} +(1372.33 + 792.313i) q^{41} +(134.842 + 503.236i) q^{42} +(-753.477 + 753.477i) q^{43} +(-464.421 + 804.401i) q^{44} +(-3881.64 + 3881.64i) q^{45} +(833.400 + 1443.49i) q^{46} -58.2936 q^{47} -917.836i q^{48} +(1118.02 + 1936.46i) q^{49} +(961.788 + 3589.44i) q^{50} +(-5261.21 - 5261.21i) q^{51} +(231.467 - 863.847i) q^{52} +(-1894.64 - 3281.62i) q^{53} +(-1711.01 - 458.464i) q^{54} +(4938.16 - 1323.18i) q^{55} +(75.2193 + 280.722i) q^{56} +(1090.12 - 4068.39i) q^{57} +(2179.85 - 1258.54i) q^{58} +(-3913.81 - 1048.70i) q^{59} +(-3572.15 + 3572.15i) q^{60} +(-5014.41 + 1343.61i) q^{61} +(1926.64 - 1112.34i) q^{62} +1601.25 q^{63} -512.000i q^{64} +(-4262.88 + 2461.18i) q^{65} +(3330.17 + 3330.17i) q^{66} +(7024.07 + 4055.35i) q^{67} +(-2934.88 - 2934.88i) q^{68} +(8163.33 - 2187.36i) q^{69} +(799.802 - 1385.30i) q^{70} +(-849.084 + 1470.66i) q^{71} +(-2724.83 - 730.116i) q^{72} -4435.14i q^{73} +(-3836.42 + 524.545i) q^{74} +18841.8 q^{75} +(608.108 - 2269.49i) q^{76} +(-1291.46 - 745.624i) q^{77} +(-3927.03 - 2267.27i) q^{78} +(2480.61 + 9257.76i) q^{79} +(-1992.67 + 1992.67i) q^{80} +(558.369 - 967.124i) q^{81} +(3169.25 - 3169.25i) q^{82} +(-2498.63 - 4327.76i) q^{83} +1473.58 q^{84} +22844.7i q^{85} +(1506.95 + 2610.12i) q^{86} +(-3303.18 - 12327.6i) q^{87} +(1857.68 + 1857.68i) q^{88} +(1361.09 - 5079.66i) q^{89} +(7763.27 + 13446.4i) q^{90} +(1386.90 + 371.618i) q^{91} +(4553.78 - 1220.18i) q^{92} +(-2919.48 - 10895.6i) q^{93} +(-42.6739 + 159.261i) q^{94} +(-11199.4 + 6465.97i) q^{95} +(-2507.57 - 671.902i) q^{96} +(10038.9 - 10038.9i) q^{97} +(6108.96 - 1636.89i) q^{98} +(12535.5 - 7237.39i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more