LMFDB - Embedded newform 72.7.p.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.99998 + 0.0188688i) q^{2} +(-26.9864 - 0.858100i) q^{3} +(63.9993 - 0.301900i) q^{4} +(186.544 - 107.701i) q^{5} +(215.906 + 6.35558i) q^{6} +(13.1755 + 7.60688i) q^{7} +(-511.987 + 3.62278i) q^{8} +(727.527 + 46.3140i) q^{9} +O(q^{10})$	\(q+(-7.99998 + 0.0188688i) q^{2} +(-26.9864 - 0.858100i) q^{3} +(63.9993 - 0.301900i) q^{4} +(186.544 - 107.701i) q^{5} +(215.906 + 6.35558i) q^{6} +(13.1755 + 7.60688i) q^{7} +(-511.987 + 3.62278i) q^{8} +(727.527 + 46.3140i) q^{9} +(-1490.31 + 865.125i) q^{10} +(-455.881 + 789.610i) q^{11} +(-1727.37 - 46.7706i) q^{12} +(-778.170 + 449.277i) q^{13} +(-105.547 - 60.6062i) q^{14} +(-5126.55 + 2746.38i) q^{15} +(4095.82 - 38.6428i) q^{16} +4242.51 q^{17} +(-5821.08 - 356.783i) q^{18} +28.7969 q^{19} +(11906.1 - 6949.10i) q^{20} +(-349.031 - 216.588i) q^{21} +(3632.14 - 6325.46i) q^{22} +(5967.04 - 3445.07i) q^{23} +(13819.8 + 341.571i) q^{24} +(15386.5 - 26650.2i) q^{25} +(6216.87 - 3608.89i) q^{26} +(-19593.6 - 1874.14i) q^{27} +(845.519 + 482.857i) q^{28} +(23978.8 + 13844.2i) q^{29} +(40960.5 - 22067.7i) q^{30} +(-14953.5 + 8633.39i) q^{31} +(-32765.7 + 386.424i) q^{32} +(12980.1 - 20917.5i) q^{33} +(-33940.0 + 80.0510i) q^{34} +3277.07 q^{35} +(46575.2 + 2744.42i) q^{36} -85544.0i q^{37} +(-230.375 + 0.543364i) q^{38} +(21385.5 - 11456.6i) q^{39} +(-95117.7 + 55817.3i) q^{40} +(47013.9 + 81430.5i) q^{41} +(2796.33 + 1726.11i) q^{42} +(68396.1 - 118466. i) q^{43} +(-28937.7 + 50672.1i) q^{44} +(140704. - 69715.8i) q^{45} +(-47671.2 + 27673.1i) q^{46} +(163062. + 94144.0i) q^{47} +(-110564. - 2471.79i) q^{48} +(-58708.8 - 101687. i) q^{49} +(-122589. + 213491. i) q^{50} +(-114490. - 3640.50i) q^{51} +(-49666.7 + 28988.3i) q^{52} -157958. i q^{53} +(156784. + 14623.4i) q^{54} +196396. i q^{55} +(-6773.24 - 3846.89i) q^{56} +(-777.125 - 24.7107i) q^{57} +(-192091. - 110301. i) q^{58} +(-107927. - 186934. i) q^{59} +(-327266. + 177314. i) q^{60} +(104128. + 60118.3i) q^{61} +(119465. - 69349.1i) q^{62} +(9233.23 + 6144.42i) q^{63} +(262118. - 3709.64i) q^{64} +(-96775.1 + 167619. i) q^{65} +(-103446. + 167584. i) q^{66} +(5099.06 + 8831.83i) q^{67} +(271517. - 1280.81i) q^{68} +(-163985. + 87849.7i) q^{69} +(-26216.5 + 61.8344i) q^{70} -196713. i q^{71} +(-372652. - 21076.5i) q^{72} -622581. q^{73} +(1614.11 + 684350. i) q^{74} +(-438094. + 705989. i) q^{75} +(1842.98 - 8.69379i) q^{76} +(-12012.9 + 6935.67i) q^{77} +(-170867. + 92056.0i) q^{78} +(297865. + 171972. i) q^{79} +(759887. - 448332. i) q^{80} +(527151. + 67389.4i) q^{81} +(-377647. - 650555. i) q^{82} +(308605. - 534520. i) q^{83} +(-22403.1 - 13756.1i) q^{84} +(791412. - 456922. i) q^{85} +(-544932. + 949012. i) q^{86} +(-635222. - 394181. i) q^{87} +(230545. - 405922. i) q^{88} +1.21369e6 q^{89} +(-1.12431e6 + 560380. i) q^{90} -13670.4 q^{91} +(380846. - 222284. i) q^{92} +(410948. - 220152. i) q^{93} +(-1.30627e6 - 750073. i) q^{94} +(5371.88 - 3101.46i) q^{95} +(884559. + 17688.1i) q^{96} +(654810. - 1.13416e6i) q^{97} +(471588. + 812383. i) q^{98} +(-368236. + 553349. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) $ 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−7.99998	+	0.0188688i	−0.999997	+	0.00235860i
$2$	−7.99998	+	0.0188688i	−0.999997	+	0.00235860i
$3$	−26.9864	−	0.858100i	−0.999495	−	0.0317815i
$3$	−26.9864	−	0.858100i	−0.999495	−	0.0317815i
$4$	63.9993	−	0.301900i	0.999989	−	0.00471719i
$5$	186.544	−	107.701i	1.49235	−	0.861608i	0.492387	−	0.870376i	$-0.336125\pi$
$5$	186.544	−	107.701i	1.49235	−	0.861608i	0.999962	+	0.00876862i	$0.00279117\pi$
$6$	215.906	+	6.35558i	0.999567	+	0.0294240i
$7$	13.1755	+	7.60688i	0.0384125	+	0.0221775i	0.519083	−	0.854724i	$-0.326273\pi$
$7$	13.1755	+	7.60688i	0.0384125	+	0.0221775i	−0.480671	+	0.876901i	$0.659607\pi$
$8$	−511.987	+	3.62278i	−0.999975	+	0.00707575i
$9$	727.527	+	46.3140i	0.997980	+	0.0635309i
$10$	−1490.31	+	865.125i	−1.49031	+	0.865125i
$11$	−455.881	+	789.610i	−0.342510	+	0.593246i	−0.984898	−	0.173134i	$-0.944611\pi$
$11$	−455.881	+	789.610i	−0.342510	+	0.593246i	0.642388	+	0.766380i	$0.277944\pi$
$12$	−1727.37	−	46.7706i	−0.999634	−	0.0270663i
$13$	−778.170	+	449.277i	−0.354197	+	0.204496i	−0.666532	−	0.745476i	$-0.732222\pi$
$13$	−778.170	+	449.277i	−0.354197	+	0.204496i	0.312335	+	0.949972i	$0.398889\pi$
$14$	−105.547	−	60.6062i	−0.0384647	−	0.0220868i
$15$	−5126.55	+	2746.38i	−1.51898	+	0.813743i
$16$	4095.82	−	38.6428i	0.999955	−	0.00943427i
$17$	4242.51			0.863527			0.431763	−	0.901987i	$-0.357892\pi$
$17$	4242.51			0.863527			0.431763	+	0.901987i	$0.357892\pi$
$18$	−5821.08	−	356.783i	−0.998127	−	0.0611769i
$19$	28.7969			0.00419842			0.00209921	−	0.999998i	$-0.499332\pi$
$19$	28.7969			0.00419842			0.00209921	+	0.999998i	$0.499332\pi$
$20$	11906.1	−	6949.10i	1.48827	−	0.868638i
$21$	−349.031	−	216.588i	−0.0376883	−	0.0233871i
$22$	3632.14	−	6325.46i	0.341110	−	0.594052i
$23$	5967.04	−	3445.07i	0.490428	−	0.283149i	−0.234324	−	0.972159i	$-0.575288\pi$
$23$	5967.04	−	3445.07i	0.490428	−	0.283149i	0.724752	+	0.689010i	$0.241954\pi$
$24$	13819.8	+	341.571i	0.999695	+	0.0247085i
$25$	15386.5	−	26650.2i	0.984736	−	1.70561i
$26$	6216.87	−	3608.89i	0.353713	−	0.205330i
$27$	−19593.6	−	1874.14i	−0.995457	−	0.0952161i
$28$	845.519	+	482.857i	0.0385167	+	0.0219960i
$29$	23978.8	+	13844.2i	0.983183	+	0.567641i	0.903230	−	0.429158i	$-0.141190\pi$
$29$	23978.8	+	13844.2i	0.983183	+	0.567641i	0.0799533	+	0.996799i	$0.474523\pi$
$30$	40960.5	−	22067.7i	1.51705	−	0.817324i
$31$	−14953.5	+	8633.39i	−0.501946	+	0.289799i	−0.729517	−	0.683963i	$-0.760255\pi$
$31$	−14953.5	+	8633.39i	−0.501946	+	0.289799i	0.227571	+	0.973762i	$0.426922\pi$
$32$	−32765.7	+	386.424i	−0.999930	+	0.0117927i
$33$	12980.1	−	20917.5i	0.361192	−	0.582060i
$34$	−33940.0	+	80.0510i	−0.863524	+	0.00203671i
$35$	3277.07			0.0764332
$36$	46575.2	+	2744.42i	0.998268	+	0.0588225i
$37$		−	85544.0i		−	1.68882i	−0.535694	−	0.844412i	$-0.679950\pi$
$37$		−	85544.0i		−	1.68882i	0.535694	−	0.844412i	$-0.320050\pi$
$38$	−230.375	+	0.543364i	−0.00419840	+	9.90238e-6i
$39$	21385.5	−	11456.6i	0.360517	−	0.193135i
$40$	−95117.7	+	55817.3i	−1.48621	+	0.872146i
$41$	47013.9	+	81430.5i	0.682142	+	1.18151i	0.974326	+	0.225143i	$0.0722849\pi$
$41$	47013.9	+	81430.5i	0.682142	+	1.18151i	−0.292184	+	0.956362i	$0.594382\pi$
$42$	2796.33	+	1726.11i	0.0377433	+	0.0232981i
$43$	68396.1	−	118466.i	0.860253	−	1.49000i	−0.0114322	−	0.999935i	$-0.503639\pi$
$43$	68396.1	−	118466.i	0.860253	−	1.49000i	0.871685	−	0.490067i	$-0.163028\pi$
$44$	−28937.7	+	50672.1i	−0.339708	+	0.594855i
$45$	140704.	−	69715.8i	1.54407	−	0.765057i
$46$	−47671.2	+	27673.1i	−0.489759	+	0.284305i
$47$	163062.	+	94144.0i	1.57058	+	0.906774i	0.996098	+	0.0882566i	$0.0281295\pi$
$47$	163062.	+	94144.0i	1.57058	+	0.906774i	0.574481	+	0.818518i	$0.305204\pi$
$48$	−110564.	−	2471.79i	−0.999750	−	0.0223506i
$49$	−58708.8	−	101687.i	−0.499016	−	0.864322i
$50$	−122589.	+	213491.i	−0.980710	+	1.70793i
$51$	−114490.	−	3640.50i	−0.863090	−	0.0274442i
$52$	−49666.7	+	28988.3i	−0.353228	+	0.206164i
$53$		−	157958.i		−	1.06100i	−0.847686	−	0.530499i	$-0.822005\pi$
$53$		−	157958.i		−	1.06100i	0.847686	−	0.530499i	$-0.177995\pi$
$54$	156784.	+	14623.4i	0.995678	+	0.0928679i
$55$			196396.i			1.18044i
$56$	−6773.24	−	3846.89i	−0.0385685	−	0.0219051i
$57$	−777.125	−	24.7107i	−0.00419630	−	0.000133432i
$58$	−192091.	−	110301.i	−0.984519	−	0.565320i
$59$	−107927.	−	186934.i	−0.525500	−	0.910192i	−0.999559	−	0.0296992i	$-0.990545\pi$
$59$	−107927.	−	186934.i	−0.525500	−	0.910192i	0.474059	−	0.880493i	$-0.342788\pi$
$60$	−327266.	+	177314.i	−1.51512	+	0.820900i
$61$	104128.	+	60118.3i	0.458752	+	0.264860i	0.711519	−	0.702667i	$-0.248007\pi$
$61$	104128.	+	60118.3i	0.458752	+	0.264860i	−0.252768	+	0.967527i	$0.581341\pi$
$62$	119465.	−	69349.1i	0.501261	−	0.290982i
$63$	9233.23	+	6144.42i	0.0369260	+	0.0245731i
$64$	262118.	−	3709.64i	0.999900	−	0.0141511i
$65$	−96775.1	+	167619.i	−0.352390	+	0.610357i
$66$	−103446.	+	167584.i	−0.359818	+	0.582911i
$67$	5099.06	+	8831.83i	0.0169538	+	0.0293648i	0.874378	−	0.485246i	$-0.161270\pi$
$67$	5099.06	+	8831.83i	0.0169538	+	0.0293648i	−0.857424	+	0.514611i	$0.827937\pi$
$68$	271517.	−	1280.81i	0.863517	−	0.00407342i
$69$	−163985.	+	87849.7i	−0.499180	+	0.267419i
$70$	−26216.5	+	61.8344i	−0.0764330	+	0.000180275i
$71$		−	196713.i		−	0.549614i	−0.961499	−	0.274807i	$-0.911386\pi$
$71$		−	196713.i		−	0.549614i	0.961499	−	0.274807i	$-0.0886140\pi$
$72$	−372652.	−	21076.5i	−0.998404	−	0.0564678i
$73$	−622581.			−1.60040			−0.800198	−	0.599736i	$-0.795272\pi$
$73$	−622581.			−1.60040			−0.800198	+	0.599736i	$0.795272\pi$
$74$	1614.11	+	684350.i	0.00398326	+	1.68882i
$75$	−438094.	+	705989.i	−1.03845	+	1.67345i
$76$	1842.98	−	8.69379i	0.00419837	−	1.98047e-5i
$77$	−12012.9	+	6935.67i	−0.0263134	+	0.0151920i
$78$	−170867.	+	92056.0i	−0.360060	+	0.193985i
$79$	297865.	+	171972.i	0.604140	+	0.348800i	0.770669	−	0.637236i	$-0.219922\pi$
$79$	297865.	+	171972.i	0.604140	+	0.348800i	−0.166528	+	0.986037i	$0.553256\pi$
$80$	759887.	−	448332.i	1.48415	−	0.875649i
$81$	527151.	+	67389.4i	0.991928	+	0.126805i
$82$	−377647.	−	650555.i	−0.684927	−	1.17989i
$83$	308605.	−	534520.i	0.539720	−	0.934823i	−0.459198	−	0.888334i	$-0.651863\pi$
$83$	308605.	−	534520.i	0.539720	−	0.934823i	0.998919	−	0.0464894i	$-0.0148034\pi$
$84$	−22403.1	−	13756.1i	−0.0377982	−	0.0232090i
$85$	791412.	−	456922.i	1.28868	−	0.744021i
$86$	−544932.	+	949012.i	−0.856736	+	1.49203i
$87$	−635222.	−	394181.i	−0.964646	−	0.598601i
$88$	230545.	−	405922.i	0.338304	−	0.595654i
$89$	1.21369e6			1.72162			0.860812	−	0.508923i	$-0.169956\pi$
$89$	1.21369e6			1.72162			0.860812	+	0.508923i	$0.169956\pi$
$90$	−1.12431e6	+	560380.i	−1.54226	+	0.768697i
$91$	−13670.4			−0.0181408
$92$	380846.	−	222284.i	0.489087	−	0.285459i
$93$	410948.	−	220152.i	0.510903	−	0.273700i
$94$	−1.30627e6	−	750073.i	−1.57271	−	0.903067i
$95$	5371.88	−	3101.46i	0.00626550	−	0.00361739i
$96$	884559.	+	17688.1i	0.999800	+	0.0199925i
$97$	654810.	−	1.13416e6i	0.717464	−	1.24268i	−0.244538	−	0.969640i	$-0.578636\pi$
$97$	654810.	−	1.13416e6i	0.717464	−	1.24268i	0.962002	−	0.273044i	$-0.0880305\pi$
$98$	471588.	+	812383.i	0.501054	+	0.863142i
$99$	−368236.	+	553349.i	−0.379508	+	0.570287i
$100$	976679.	−	1.71024e6i	0.976679	−	1.71024i
$101$	−586995.	−	338902.i	−0.569732	−	0.328935i	0.187310	−	0.982301i	$-0.440023\pi$
$101$	−586995.	−	338902.i	−0.569732	−	0.328935i	−0.757042	+	0.653366i	$0.773356\pi$
$102$	915985.	+	26963.6i	0.863153	+	0.0254084i
$103$	−195278.	+	112744.i	−0.178707	+	0.103176i	−0.586685	−	0.809815i	$-0.699567\pi$
$103$	−195278.	+	112744.i	−0.178707	+	0.103176i	0.407978	+	0.912992i	$0.366234\pi$
$104$	396786.	−	232843.i	0.352741	−	0.206997i
$105$	−88436.3	−	2812.06i	−0.0763946	−	0.00242916i
$106$	2980.48	+	1.26366e6i	0.00250247	+	1.06099i
$107$	−628477.			−0.513025			−0.256512	−	0.966541i	$-0.582573\pi$
$107$	−628477.			−0.513025			−0.256512	+	0.966541i	$0.582573\pi$
$108$	−1.25454e6	−	114028.i	−0.995895	−	0.0905193i
$109$			437704.i			0.337987i	0.985617	+	0.168994i	$0.0540518\pi$
$109$			437704.i			0.337987i	−0.985617	+	0.168994i	$0.945948\pi$
$110$	−3705.75	−	1.57116e6i	−0.00278418	−	1.18044i
$111$	−73405.4	+	2.30852e6i	−0.0536734	+	1.68797i
$112$	54258.4	+	30647.2i	0.0386201	+	0.0218141i
$113$	−221852.	−	384258.i	−0.153754	−	0.266310i	0.778850	−	0.627210i	$-0.215803\pi$
$113$	−221852.	−	384258.i	−0.153754	−	0.266310i	−0.932605	+	0.360899i	$0.882470\pi$
$114$	6217.45	+	183.021i	0.00419660	+	0.000123534i
$115$	742076.	−	1.28531e6i	0.487927	−	0.845114i
$116$	1.53881e6	+	878779.i	0.985850	+	0.562997i
$117$	−586948.	+	290821.i	−0.366473	+	0.181580i
$118$	866938.	+	1.49343e6i	0.527645	+	0.908950i
$119$	55897.1	+	32272.2i	0.0331702	+	0.0191508i
$120$	2.61478e6	−	1.42469e6i	1.51318	−	0.824471i
$121$	470125.	+	814280.i	0.265373	+	0.459640i
$122$	−834155.	−	478980.i	−0.459375	−	0.263778i
$123$	−1.19886e6	−	2.23786e6i	−0.644248	−	1.20259i
$124$	−954405.	+	557045.i	−0.500573	+	0.292163i
$125$		−	3.26291e6i		−	1.67061i
$126$	−73981.6	−	48981.0i	−0.0369838	−	0.0244859i
$127$			3.19698e6i			1.56073i	0.625322	+	0.780367i	$0.284968\pi$
$127$			3.19698e6i			1.56073i	−0.625322	+	0.780367i	$0.715032\pi$
$128$	−2.09687e6	+	34622.9i	−0.999864	+	0.0165095i
$129$	−1.94742e6	+	3.13826e6i	−0.907173	+	1.46191i
$130$	771036.	−	1.34278e6i	0.350949	−	0.611187i
$131$	1.17524e6	+	2.03558e6i	0.522773	+	0.905469i	0.999649	+	0.0264982i	$0.00843562\pi$
$131$	1.17524e6	+	2.03558e6i	0.522773	+	0.905469i	−0.476876	+	0.878970i	$0.658231\pi$
$132$	824405.	−	1.34262e6i	0.358442	−	0.583758i
$133$	379.414	+	219.055i	0.000161272	+	9.31103e-5i
$134$	−40959.0	−	70558.3i	−0.0170230	−	0.0293247i
$135$	−3.85690e6	+	1.76064e6i	−1.56761	+	0.715598i
$136$	−2.17211e6	+	15369.7i	−0.863505	+	0.00611010i
$137$	−836488.	+	1.44884e6i	−0.325311	+	0.563454i	−0.981575	−	0.191076i	$-0.938802\pi$
$137$	−836488.	+	1.44884e6i	−0.325311	+	0.563454i	0.656265	+	0.754531i	$0.272136\pi$
$138$	1.31022e6	−	705890.i	0.498547	−	0.268596i
$139$	−1.09955e6	−	1.90448e6i	−0.409423	−	0.709141i	0.585402	−	0.810743i	$-0.300937\pi$
$139$	−1.09955e6	−	1.90448e6i	−0.409423	−	0.709141i	−0.994825	+	0.101602i	$0.967603\pi$
$140$	209730.	−	989.348i	0.0764323	−	0.000360550i
$141$	−4.31967e6	−	2.68053e6i	−1.54097	−	0.956232i
$142$	3711.74	+	1.57370e6i	0.00129632	+	0.549613i
$143$		−	819268.i		−	0.280168i
$144$	2.98161e6	+	161580.i	0.998535	+	0.0541128i
$145$	5.96413e6			1.95634
$146$	4.98064e6	−	11747.4i	1.60039	−	0.00377469i
$147$	1.49708e6	+	2.79453e6i	0.471295	+	0.879744i
$148$	−25825.7	−	5.47476e6i	−0.00796650	−	1.68881i
$149$	2.65081e6	−	1.53045e6i	0.801347	−	0.462658i	−0.0425952	−	0.999092i	$-0.513563\pi$
$149$	2.65081e6	−	1.53045e6i	0.801347	−	0.462658i	0.843942	+	0.536435i	$0.180229\pi$
$150$	3.49142e6	−	5.65616e6i	1.03450	−	1.67590i
$151$	−1.24984e6	−	721593.i	−0.363013	−	0.209586i	0.307389	−	0.951584i	$-0.400545\pi$
$151$	−1.24984e6	−	721593.i	−0.363013	−	0.209586i	−0.670402	+	0.741999i	$0.733878\pi$
$152$	−14743.7	+	104.325i	−0.00419831	+	2.97069e-5i
$153$	3.08654e6	+	196487.i	0.861782	+	0.0548606i
$154$	95972.3	−	55711.9i	0.0262775	−	0.0152541i
$155$	−1.85965e6	+	3.22101e6i	−0.499386	+	0.864961i
$156$	1.36520e6	−	739670.i	0.359602	−	0.194834i
$157$	273632.	−	157981.i	0.0707079	−	0.0408232i	−0.464229	−	0.885715i	$-0.653669\pi$
$157$	273632.	−	157981.i	0.0707079	−	0.0408232i	0.534937	+	0.844892i	$0.320335\pi$
$158$	−2.38616e6	−	1.37015e6i	−0.604961	−	0.347375i
$159$	−135544.	+	4.26272e6i	−0.0337201	+	1.06046i
$160$	−6.07062e6	+	3.60099e6i	−1.48208	+	0.879147i
$161$	104825.			0.0251181
$162$	−4.21847e6	−	529167.i	−0.992224	−	0.124465i
$163$	−1.56845e6			−0.362166			−0.181083	−	0.983468i	$-0.557960\pi$
$163$	−1.56845e6			−0.362166			−0.181083	+	0.983468i	$0.557960\pi$
$164$	3.03344e6	+	5.19730e6i	0.687708	+	1.17827i
$165$	168527.	−	5.30000e6i	0.0375161	−	1.17984i
$166$	−2.45875e6	+	4.28197e6i	−0.537514	+	0.936094i
$167$	−2.77069e6	+	1.59966e6i	−0.594892	+	0.343461i	−0.767029	−	0.641612i	$-0.778266\pi$
$167$	−2.77069e6	+	1.59966e6i	−0.594892	+	0.343461i	0.172137	+	0.985073i	$0.444933\pi$
$168$	179484.	+	109626.i	0.0378528	+	0.0231198i
$169$	−2.00971e6	+	3.48091e6i	−0.416363	+	0.721162i
$170$	−6.32266e6	+	3.67030e6i	−1.28692	+	0.747059i
$171$	20950.6	+	1333.70i	0.00418994	+	0.000266729i
$172$	4.34154e6	−	7.60236e6i	0.853215	−	1.49404i
$173$	180905.	+	104446.i	0.0349392	+	0.0201721i	0.517368	−	0.855763i	$-0.326912\pi$
$173$	180905.	+	104446.i	0.0349392	+	0.0201721i	−0.482429	+	0.875935i	$0.660245\pi$
$174$	5.08920e6	+	3.14145e6i	0.966055	+	0.596324i
$175$	405450.	−	234086.i	0.0756524	−	0.0436779i
$176$	−1.83669e6	+	3.25171e6i	−0.336898	+	0.596450i
$177$	2.75214e6	+	5.13729e6i	0.496307	+	0.926433i
$178$	−9.70951e6	+	22900.9i	−1.72162	+	0.00406062i
$179$	−1.04983e7			−1.83045			−0.915225	−	0.402943i	$-0.867987\pi$
$179$	−1.04983e7			−1.83045			−0.915225	+	0.402943i	$0.867987\pi$
$180$	8.98388e6	−	4.50424e6i	1.54045	−	0.772332i
$181$			8.75736e6i			1.47685i	0.674333	+	0.738427i	$0.264431\pi$
$181$			8.75736e6i			1.47685i	−0.674333	+	0.738427i	$0.735569\pi$
$182$	109363.	−	257.944i	0.0181407	−	4.27869e-5i
$183$	−2.75844e6	−	1.71173e6i	−0.450102	−	0.279306i
$184$	−3.04257e6	+	1.78545e6i	−0.488413	+	0.286612i
$185$	−9.21317e6	−	1.59577e7i	−1.45510	−	2.52031i
$186$	−3.28342e6	+	1.76897e6i	−0.510256	+	0.274904i
$187$	−1.93408e6	+	3.34992e6i	−0.295767	+	0.512283i
$188$	1.04643e7	+	5.97592e6i	1.57484	+	0.899355i
$189$	−243899.	−	173739.i	−0.0361264	−	0.0257342i
$190$	−42916.4	+	24913.0i	−0.00625695	+	0.00363216i
$191$	9.06334e6	+	5.23272e6i	1.30073	+	0.750978i	0.980530	−	0.196371i	$-0.0629156\pi$
$191$	9.06334e6	+	5.23272e6i	1.30073	+	0.750978i	0.320203	+	0.947349i	$0.396249\pi$
$192$	−7.07679e6	−	124814.i	−0.999845	−	0.0176343i
$193$	−365313.	−	632741.i	−0.0508152	−	0.0880145i	0.839499	−	0.543361i	$-0.182849\pi$
$193$	−365313.	−	632741.i	−0.0508152	−	0.0880145i	−0.890314	+	0.455347i	$0.849515\pi$
$194$	−5.21706e6	+	9.08564e6i	−0.714531	+	1.24437i
$195$	2.75544e6	−	4.44039e6i	0.371610	−	0.598849i
$196$	−3.78802e6	−	6.49014e6i	−0.503088	−	0.861958i
$197$		−	1.82759e6i		−	0.239046i	−0.992831	−	0.119523i	$-0.961864\pi$
$197$		−	1.82759e6i		−	0.239046i	0.992831	−	0.119523i	$-0.0381365\pi$
$198$	2.93544e6	−	4.43373e6i	0.378162	−	0.571181i
$199$		−	6.64556e6i		−	0.843281i	−0.906763	−	0.421640i	$-0.861454\pi$
$199$		−	6.64556e6i		−	0.843281i	0.906763	−	0.421640i	$-0.138546\pi$
$200$	−7.78114e6	+	1.37003e7i	−0.972643	+	1.71254i
$201$	−130027.	−	242715.i	−0.0160119	−	0.0298887i
$202$	4.70234e6	+	2.70013e6i	0.570506	+	0.327590i
$203$	210622.	+	364808.i	0.0251777	+	0.0436090i
$204$	−7.32836e6	−	198425.i	−0.863210	−	0.0233725i
$205$	1.75403e7	+	1.01269e7i	2.03599	+	1.17548i
$206$	1.56009e6	−	905632.i	0.178463	−	0.103598i
$207$	4.50074e6	−	2.23003e6i	0.507426	−	0.251420i
$208$	−3.16988e6	+	1.87023e6i	−0.352252	+	0.207828i
$209$	−13128.0	+	22738.3i	−0.00143800	+	0.00249069i
$210$	707541.	+	20827.7i	0.0764001	+	0.00224897i
$211$	−1.69456e6	−	2.93506e6i	−0.180388	−	0.312442i	0.761624	−	0.648019i	$-0.224402\pi$
$211$	−1.69456e6	−	2.93506e6i	−0.180388	−	0.312442i	−0.942013	+	0.335577i	$0.891069\pi$
$212$	−47687.6	−	1.01092e7i	−0.00500493	−	1.06099i
$213$	−168799.	+	5.30857e6i	−0.0174676	+	0.549337i
$214$	5.02780e6	−	11858.6i	0.513023	−	0.00121002i
$215$		−	2.94653e7i		−	2.96480i
$216$	1.00384e7	+	888551.i	0.996105	+	0.0881701i
$217$	−262693.			−0.0257080
$218$	−8258.94	−	3.50162e6i	−0.000797177	−	0.337986i
$219$	1.68012e7	+	534237.i	1.59959	+	0.0508630i
$220$	59291.8	+	1.25692e7i	0.00556835	+	1.18043i
$221$	−3.30139e6	+	1.90606e6i	−0.305858	+	0.176587i
$222$	543682.	−	1.84695e7i	0.0496920	−	1.68809i
$223$	1.14030e7	+	6.58351e6i	1.02826	+	0.593667i	0.916486	−	0.400067i	$-0.131013\pi$
$223$	1.14030e7	+	6.58351e6i	1.02826	+	0.593667i	0.111775	+	0.993734i	$0.464346\pi$
$224$	−434644.	−	244153.i	−0.0386714	−	0.0217230i
$225$	1.24284e7	−	1.86761e7i	1.09111	−	1.63961i
$226$	1.78206e6	+	3.06987e6i	0.154382	+	0.265947i
$227$	9.03108e6	−	1.56423e7i	0.772080	−	1.33728i	−0.164341	−	0.986404i	$-0.552550\pi$
$227$	9.03108e6	−	1.56423e7i	0.772080	−	1.33728i	0.936421	−	0.350878i	$-0.114117\pi$
$228$	−49742.9	−	1346.85i	−0.00419688	−	0.000113636i
$229$	1.33189e6	−	768968.i	0.110908	−	0.0640327i	−0.443520	−	0.896264i	$-0.646270\pi$
$229$	1.33189e6	−	768968.i	0.110908	−	0.0640327i	0.554428	+	0.832232i	$0.312937\pi$
$230$	−5.91234e6	+	1.02965e7i	−0.485932	+	0.846262i
$231$	330137.	−	176860.i	0.0267829	−	0.0143481i
$232$	−1.23270e7	−	7.00118e6i	−0.987175	−	0.560670i
$233$	−1.16139e7			−0.918141			−0.459071	−	0.888400i	$-0.651817\pi$
$233$	−1.16139e7			−0.918141			−0.459071	+	0.888400i	$0.651817\pi$
$234$	4.69008e6	−	2.33764e6i	0.366044	−	0.182444i
$235$	4.05576e7			3.12514
$236$	−6.96366e6	−	1.19311e7i	−0.529787	−	0.907703i
$237$	−7.89071e6	−	4.89650e6i	−0.592750	−	0.367825i
$238$	−447785.	−	257122.i	−0.0332153	−	0.0190726i
$239$	1.92064e7	−	1.10888e7i	1.40687	−	0.812255i	0.411782	−	0.911282i	$-0.364907\pi$
$239$	1.92064e7	−	1.10888e7i	1.40687	−	0.812255i	0.995085	+	0.0990276i	$0.0315732\pi$
$240$	−2.08913e7	+	1.14468e7i	−1.51123	+	0.828038i
$241$	−9.02214e6	+	1.56268e7i	−0.644553	+	1.11640i	0.339852	+	0.940479i	$0.389623\pi$
$241$	−9.02214e6	+	1.56268e7i	−0.644553	+	1.11640i	−0.984405	+	0.175919i	$0.943710\pi$
$242$	−3.77635e6	−	6.50535e6i	−0.266457	−	0.459013i
$243$	−1.41681e7	−	2.27094e6i	−0.987397	−	0.158266i
$244$	6.68226e6	+	3.81609e6i	0.459996	+	0.262693i
$245$	−2.19035e7	−	1.26460e7i	−1.48941	−	0.859913i
$246$	9.63307e6	+	1.78802e7i	0.647082	+	1.20106i
$247$	−22408.9	+	12937.8i	−0.00148707	+	0.000858558i
$248$	7.62471e6	−	4.47436e6i	0.499883	−	0.293343i
$249$	−8.78680e6	+	1.41599e7i	−0.569158	+	0.917198i
$250$	61567.2	+	2.61032e7i	0.00394030	+	1.67060i
$251$	−3.52408e6			−0.222856			−0.111428	−	0.993772i	$-0.535543\pi$
$251$	−3.52408e6			−0.222856			−0.111428	+	0.993772i	$0.535543\pi$
$252$	592775.	+	390451.i	0.0370415	+	0.0243986i
$253$			6.28218e6i			0.387926i
$254$	−60323.2	−	2.55758e7i	−0.00368115	−	1.56073i
$255$	−2.17494e7	+	1.16516e7i	−1.31168	+	0.702689i
$256$	1.67742e7	−	316547.i	0.999822	−	0.0188677i
$257$	3.28185e6	+	5.68433e6i	0.193339	+	0.334873i	0.946355	−	0.323130i	$-0.104735\pi$
$257$	3.28185e6	+	5.68433e6i	0.193339	+	0.334873i	−0.753016	+	0.658002i	$0.771402\pi$
$258$	1.55201e7	−	2.51428e7i	0.903722	−	1.46404i
$259$	650723.	−	1.12709e6i	0.0374539	−	0.0648720i
$260$	−6.14293e6	+	1.07567e7i	−0.349507	+	0.612013i
$261$	1.68041e7	+	1.11826e7i	0.945134	+	0.628957i
$262$	−9.44030e6	−	1.62624e7i	−0.524907	−	0.904233i
$263$	1.70023e7	+	9.81626e6i	0.934630	+	0.539609i	0.888273	−	0.459316i	$-0.151906\pi$
$263$	1.70023e7	+	9.81626e6i	0.934630	+	0.539609i	0.0463568	+	0.998925i	$0.485239\pi$
$264$	−6.56989e6	+	1.07565e7i	−0.357064	+	0.584602i
$265$	−1.70123e7	−	2.94661e7i	−0.914164	−	1.58338i
$266$	−3039.44	−	1745.27i	−0.000161491	−	9.27297e-5i
$267$	−3.27531e7	−	1.04147e6i	−1.72075	−	0.0547158i
$268$	329003.	+	563692.i	0.0170921	+	0.0292845i
$269$			3.22256e7i			1.65556i	0.561054	+	0.827779i	$0.310396\pi$
$269$			3.22256e7i			1.65556i	−0.561054	+	0.827779i	$0.689604\pi$
$270$	3.08219e7	−	1.41578e7i	1.56591	−	0.719293i
$271$		−	2.69528e7i		−	1.35424i	−0.735872	−	0.677121i	$-0.763228\pi$
$271$		−	2.69528e7i		−	1.35424i	0.735872	−	0.677121i	$-0.236772\pi$
$272$	1.73765e7	−	163942.i	0.863488	−	0.00814674i
$273$	368914.	+	11730.6i	0.0181316	+	0.000576541i
$274$	6.66455e6	−	1.16065e7i	0.323981	−	0.564220i
$275$	1.40288e7	+	2.42987e7i	0.674565	+	1.16838i
$276$	−1.04684e7	+	5.67182e6i	−0.497913	+	0.269771i
$277$	5.26729e6	+	3.04107e6i	0.247826	+	0.143083i	0.618769	−	0.785573i	$-0.287632\pi$
$277$	5.26729e6	+	3.04107e6i	0.247826	+	0.143083i	−0.370942	+	0.928656i	$0.620965\pi$
$278$	8.83234e6	+	1.52151e7i	0.411094	+	0.708173i
$279$	−1.12789e7	+	5.58847e6i	−0.519343	+	0.257324i
$280$	−1.67782e6	+	11872.1i	−0.0764313	+	0.000540822i
$281$	−5.64305e6	+	9.77404e6i	−0.254328	+	0.440509i	−0.964713	−	0.263304i	$-0.915188\pi$
$281$	−5.64305e6	+	9.77404e6i	−0.254328	+	0.440509i	0.710385	+	0.703814i	$0.248521\pi$
$282$	3.46079e7	+	2.13627e7i	1.54322	+	0.952594i
$283$	−4.95534e6	−	8.58290e6i	−0.218632	−	0.378682i	0.735758	−	0.677245i	$-0.236826\pi$
$283$	−4.95534e6	−	8.58290e6i	−0.218632	−	0.378682i	−0.954390	+	0.298563i	$0.903493\pi$
$284$	−59387.6	−	1.25895e7i	−0.00259263	−	0.549608i
$285$	−147629.	+	79087.5i	−0.00637730	+	0.00341643i
$286$	15458.6	+	6.55412e6i	0.000660803	+	0.280167i
$287$			1.43052e6i			0.0605128i
$288$	−2.38559e7	−	1.23638e6i	−0.998660	−	0.0517575i
$289$	−6.13871e6			−0.254322
$290$	−4.77129e7	+	112536.i	−1.95633	+	0.00461421i
$291$	−1.86442e7	+	3.00451e7i	−0.756596	+	1.21925i
$292$	−3.98448e7	+	187957.i	−1.60038	+	0.00754937i
$293$	−1.97515e7	+	1.14035e7i	−0.785229	+	0.453352i	−0.838280	−	0.545240i	$-0.816439\pi$
$293$	−1.97515e7	+	1.14035e7i	−0.785229	+	0.453352i	0.0530513	+	0.998592i	$0.483105\pi$
$294$	−1.20293e7	−	2.23279e7i	−0.473368	−	0.878630i
$295$	−4.02660e7	−	2.32476e7i	−1.56846	−	0.905549i
$296$	309907.	+	4.37974e7i	0.0119497	+	1.68878i
$297$	1.04122e7	−	1.46169e7i	0.397441	−	0.557938i
$298$	−2.11776e7	+	1.22936e7i	−0.800253	+	0.464546i
$299$	−3.09558e6	+	5.36171e6i	−0.115805	+	0.200581i
$300$	−2.78246e7	+	4.53150e7i	−1.03054	+	1.67833i
$301$	1.80231e6	−	1.04056e6i	0.0660890	−	0.0381565i
$302$	1.00123e7	+	5.74914e6i	0.363506	+	0.208729i
$303$	1.55501e7	+	9.64943e6i	0.558990	+	0.346876i
$304$	117947.	−	1112.79i	0.00419823	−	3.96090e-5i
$305$	2.58992e7			0.912823
$306$	−2.46960e7	−	1.51366e6i	−0.861909	−	0.0528278i
$307$	1.29420e7			0.447288			0.223644	−	0.974671i	$-0.428205\pi$
$307$	1.29420e7			0.447288			0.223644	+	0.974671i	$0.428205\pi$
$308$	−766725.	+	447505.i	−0.0262414	+	0.0153160i
$309$	5.36658e6	−	2.87497e6i	0.181896	−	0.0974447i
$310$	1.48164e7	−	2.58031e7i	0.497344	−	0.866137i
$311$	2.08091e7	−	1.20141e7i	0.691786	−	0.399403i	−0.112495	−	0.993652i	$-0.535884\pi$
$311$	2.08091e7	−	1.20141e7i	0.691786	−	0.399403i	0.804281	+	0.594249i	$0.202551\pi$
$312$	−1.09076e7	+	5.94311e6i	−0.359141	+	0.195681i
$313$	−1.19817e7	+	2.07530e7i	−0.390739	+	0.676779i	−0.992547	−	0.121861i	$-0.961114\pi$
$313$	−1.19817e7	+	2.07530e7i	−0.390739	+	0.676779i	0.601808	+	0.798640i	$0.294447\pi$
$314$	−2.18607e6	+	1.26901e6i	−0.0706114	+	0.0409899i
$315$	2.38416e6	+	151774.i	0.0762788	+	0.00485587i
$316$	1.91150e7	+	1.09162e7i	0.605779	+	0.345947i
$317$	−1.16437e7	−	6.72249e6i	−0.365522	−	0.211034i	0.305979	−	0.952038i	$-0.401016\pi$
$317$	−1.16437e7	−	6.72249e6i	−0.365522	−	0.211034i	−0.671500	+	0.741004i	$0.734350\pi$
$318$	1.00392e6	−	3.41042e7i	0.0312188	−	1.06054i
$319$	−2.18630e7	+	1.26226e7i	−0.673501	+	0.388846i
$320$	4.84968e7	−	2.89223e7i	1.48001	−	0.882640i
$321$	1.69603e7	+	539297.i	0.512766	+	0.0163047i
$322$	−838598.	+	1977.92i	−0.0251181	+	5.92436e-5i
$323$	122171.			0.00362544
$324$	3.37576e7	+	4.15373e6i	0.992515	+	0.122125i
$325$			2.76512e7i			0.805497i
$326$	1.25476e7	−	29594.8i	0.362165	−	0.000854205i
$327$	375594.	−	1.18120e7i	0.0107417	−	0.337817i
$328$	−2.43655e7	−	4.15211e7i	−0.690485	−	1.17665i
$329$	1.43228e6	+	2.48079e6i	0.0402199	+	0.0696630i
$330$	−1.24821e6	+	4.24031e7i	−0.0347332	+	1.17993i
$331$	2.36486e6	−	4.09606e6i	0.0652111	−	0.112949i	−0.831577	−	0.555410i	$-0.812561\pi$
$331$	2.36486e6	−	4.09606e6i	0.0652111	−	0.112949i	0.896788	+	0.442461i	$0.145895\pi$
$332$	1.95891e7	−	3.43020e7i	0.535305	−	0.937359i
$333$	3.96189e6	−	6.22356e7i	0.107292	−	1.68541i
$334$	2.21353e7	−	1.28495e7i	0.594080	−	0.344863i
$335$	1.90239e6	+	1.09835e6i	0.0506018	+	0.0292150i
$336$	−1.43794e6	−	873617.i	−0.0379073	−	0.0230305i
$337$	5.09199e6	+	8.81958e6i	0.133045	+	0.230440i	0.924849	−	0.380335i	$-0.124191\pi$
$337$	5.09199e6	+	8.81958e6i	0.133045	+	0.230440i	−0.791804	+	0.610775i	$0.790858\pi$
$338$	1.60119e7	−	2.78851e7i	0.414661	−	0.722142i
$339$	5.65724e6	+	1.05601e7i	0.145213	+	0.271062i
$340$	5.05119e7	−	2.94816e7i	1.28516	−	0.750092i
$341$		−	1.57432e7i		−	0.397036i
$342$	−167629.	−	10274.3i	−0.00419055	−	0.000256846i
$343$		−	3.57624e6i		−	0.0886227i
$344$	−3.45888e7	+	6.09006e7i	−0.849688	+	1.49605i
$345$	−2.11288e7	+	3.40491e7i	−0.514539	+	0.829180i
$346$	−1.44921e6	−	832149.i	−0.0349867	−	0.0200897i
$347$	3.08128e7	+	5.33694e7i	0.737468	+	1.27733i	0.953632	+	0.300975i	$0.0973120\pi$
$347$	3.08128e7	+	5.33694e7i	0.737468	+	1.27733i	−0.216164	+	0.976357i	$0.569355\pi$
$348$	−4.07728e7	−	2.50355e7i	−0.967459	−	0.594044i
$349$	1.96498e7	+	1.13448e7i	0.462256	+	0.266883i	0.712992	−	0.701172i	$-0.247339\pi$
$349$	1.96498e7	+	1.13448e7i	0.462256	+	0.266883i	−0.250737	+	0.968055i	$0.580673\pi$
$350$	−3.23917e6	+	1.88034e6i	−0.0755492	+	0.0438562i
$351$	1.60891e7	−	7.34454e6i	0.372059	−	0.169841i
$352$	1.46322e7	−	2.60483e7i	0.335491	−	0.597243i
$353$	3.01862e7	−	5.22841e7i	0.686254	−	1.18863i	−0.286787	−	0.957994i	$-0.592587\pi$
$353$	3.01862e7	−	5.22841e7i	0.686254	−	1.18863i	0.973041	−	0.230632i	$-0.0740794\pi$
$354$	−2.21140e7	−	4.10463e7i	−0.498491	−	0.925260i
$355$	−2.11862e7	−	3.66955e7i	−0.473552	−	0.820216i
$356$	7.76754e7	−	366413.i	1.72160	−	0.00812122i
$357$	−1.48077e6	−	918875.i	−0.0325448	−	0.0201954i
$358$	8.39858e7	−	198089.i	1.83045	−	0.00431730i
$359$			5.14955e7i			1.11298i	0.830855	+	0.556488i	$0.187852\pi$
$359$			5.14955e7i			1.11298i	−0.830855	+	0.556488i	$0.812148\pi$
$360$	−7.17859e7	+	3.62033e7i	−1.53862	+	0.775963i
$361$	−4.70451e7			−0.999982
$362$	−165241.	−	7.00587e7i	−0.00348331	−	1.47685i
$363$	−1.19882e7	−	2.23779e7i	−0.250631	−	0.467842i
$364$	−874894.	+	4127.08i	−0.0181406	+	8.55735e-5i
$365$	−1.16139e8	+	6.70526e7i	−2.38835	+	1.37891i
$366$	2.20998e7	+	1.36417e7i	0.450760	+	0.278244i
$367$	−7.70104e7	−	4.44620e7i	−1.55794	−	0.899478i	−0.997454	−	0.0713151i	$-0.977280\pi$
$367$	−7.70104e7	−	4.44620e7i	−1.55794	−	0.899478i	−0.560488	−	0.828163i	$-0.689386\pi$
$368$	2.43068e7	−	1.43410e7i	0.487735	−	0.287763i
$369$	3.04325e7	+	6.14203e7i	0.605702	+	1.22246i
$370$	7.40063e7	+	1.27487e8i	1.46104	+	2.51688i
$371$	1.20157e6	−	2.08118e6i	0.0235303	−	0.0407556i
$372$	2.62339e7	−	1.42137e7i	0.509606	−	0.276107i
$373$	−3.69305e7	+	2.13219e7i	−0.711638	+	0.410864i	−0.811667	−	0.584120i	$-0.801440\pi$
$373$	−3.69305e7	+	2.13219e7i	−0.711638	+	0.410864i	0.100029	+	0.994984i	$0.468106\pi$
$374$	1.54094e7	−	2.68358e7i	0.294558	−	0.512979i
$375$	−2.79990e6	+	8.80540e7i	−0.0530945	+	1.66977i
$376$	−8.38268e7	−	4.76098e7i	−1.57696	−	0.895639i
$377$	−2.48795e7			−0.464320
$378$	1.95446e6	+	1.38530e6i	0.0361870	+	0.0256489i
$379$	−3.34409e7			−0.614271			−0.307135	−	0.951666i	$-0.599370\pi$
$379$	−3.34409e7			−0.614271			−0.307135	+	0.951666i	$0.599370\pi$
$380$	342860.	−	200113.i	0.00624837	−	0.00364690i
$381$	2.74333e6	−	8.62749e7i	0.0496025	−	1.55995i
$382$	−7.26052e7	−	4.16906e7i	−1.30250	−	0.747908i
$383$	−4.20692e7	+	2.42886e7i	−0.748803	+	0.432322i	−0.825261	−	0.564751i	$-0.808972\pi$
$383$	−4.20692e7	+	2.42886e7i	−0.748803	+	0.432322i	0.0764582	+	0.997073i	$0.475639\pi$
$384$	5.66165e7	+	864977.i	0.999883	+	0.0152760i
$385$	−1.49396e6	+	2.58761e6i	−0.0261792	+	0.0453436i
$386$	2.93444e6	+	5.05502e6i	0.0510227	+	0.0878944i
$387$	5.52467e7	−	8.30192e7i	0.953176	−	1.43234i
$388$	4.15650e7	−	7.27834e7i	0.711594	−	1.24605i
$389$	4.72641e7	+	2.72879e7i	0.802938	+	0.463577i	0.844498	−	0.535559i	$-0.179899\pi$
$389$	4.72641e7	+	2.72879e7i	0.802938	+	0.463577i	−0.0415592	+	0.999136i	$0.513233\pi$
$390$	−2.19597e7	+	3.55750e7i	−0.370197	+	0.599724i
$391$	2.53152e7	−	1.46157e7i	0.423498	−	0.244507i
$392$	3.04265e7	+	5.18495e7i	0.505120	+	0.860769i
$393$	−2.99687e7	−	5.59413e7i	−0.493731	−	0.921626i
$394$	34484.5	+	1.46207e7i	0.000563813	+	0.239045i
$395$	7.40863e7			1.20212
$396$	−2.33998e7	+	3.55251e7i	−0.376814	+	0.572071i
$397$			3.89199e7i			0.622013i	0.950408	+	0.311007i	$0.100666\pi$
$397$			3.89199e7i			0.622013i	−0.950408	+	0.311007i	$0.899334\pi$
$398$	125394.	+	5.31643e7i	0.00198896	+	0.843278i
$399$	−10051.0	−	6237.07i	−0.000158231	−	9.81887e-5i
$400$	6.19905e7	−	1.09749e8i	0.968601	−	1.71483i
$401$	−1.22548e7	−	2.12259e7i	−0.190052	−	0.329180i	0.755215	−	0.655477i	$-0.227532\pi$
$401$	−1.22548e7	−	2.12259e7i	−0.190052	−	0.329180i	−0.945267	+	0.326297i	$0.894199\pi$
$402$	1.04479e6	+	1.93926e6i	0.0160824	+	0.0298509i
$403$	7.75757e6	−	1.34365e7i	0.118525	−	0.205291i
$404$	−3.76696e7	−	2.15123e7i	−0.571277	−	0.326244i
$405$	1.05595e8	−	4.42036e7i	1.58956	−	0.665415i
$406$	−1.69186e6	−	2.91448e6i	−0.0252805	−	0.0435495i
$407$	6.75464e7	+	3.89979e7i	1.00189	+	0.578440i
$408$	5.86305e7	+	1.44912e6i	0.863263	+	0.0213365i
$409$	4.19294e7	+	7.26238e7i	0.612842	+	1.06147i	0.990759	+	0.135634i	$0.0433071\pi$
$409$	4.19294e7	+	7.26238e7i	0.612842	+	1.06147i	−0.377917	+	0.925839i	$0.623360\pi$
$410$	−1.40513e8	−	8.06839e7i	−2.03875	−	1.17067i
$411$	2.38170e7	−	3.83811e7i	0.343054	−	0.552831i
$412$	−1.24636e7	+	7.27447e6i	−0.178218	+	0.104018i
$413$		−	3.28394e6i		−	0.0466170i
$414$	−3.59638e7	+	1.79251e7i	−0.506832	+	0.252616i
$415$		−	1.32948e8i		−	1.86011i
$416$	2.53237e7	−	1.50216e7i	0.351761	−	0.208658i
$417$	2.80387e7	+	5.23386e7i	0.386678	+	0.721795i
$418$	104595.	−	182154.i	0.00143212	−	0.00249408i
$419$	3.22522e7	+	5.58625e7i	0.438447	+	0.759413i	0.997570	−	0.0696717i	$-0.0221952\pi$
$419$	3.22522e7	+	5.58625e7i	0.438447	+	0.759413i	−0.559122	+	0.829085i	$0.688862\pi$
$420$	−5.66071e6	−	153271.i	−0.0764052	−	0.00206877i
$421$	−8.07801e7	−	4.66384e7i	−1.08258	−	0.625025i	−0.150985	−	0.988536i	$-0.548245\pi$
$421$	−8.07801e7	−	4.66384e7i	−1.08258	−	0.625025i	−0.931590	+	0.363511i	$0.881578\pi$
$422$	1.36118e7	+	2.34484e7i	0.181125	+	0.312016i
$423$	1.14272e8	+	7.60444e7i	1.50980	+	1.00472i
$424$	572248.	+	8.08726e7i	0.00750735	+	1.06097i
$425$	6.52773e7	−	1.13064e8i	0.850346	−	1.47284i
$426$	1.25023e6	−	4.24716e7i	0.0161718	−	0.549376i
$427$	914624.	+	1.58418e6i	0.0117479	+	0.0203479i
$428$	−4.02221e7	+	189737.i	−0.513019	+	0.00242003i
$429$	−703014.	+	2.21091e7i	−0.00890414	+	0.280026i
$430$	555975.	+	2.35722e8i	0.00699278	+	2.96479i
$431$		−	7.21688e7i		−	0.901401i	−0.892675	−	0.450700i	$-0.851174\pi$
$431$		−	7.21688e7i		−	0.901401i	0.892675	−	0.450700i	$-0.148826\pi$
$432$	−8.03241e7	−	6.91898e6i	−0.996311	−	0.0858204i
$433$	4.33248e7			0.533670			0.266835	−	0.963742i	$-0.414022\pi$
$433$	4.33248e7			0.533670			0.266835	+	0.963742i	$0.414022\pi$
$434$	2.10154e6	−	4956.69i	0.0257080	−	6.06349e-5i
$435$	−1.60950e8	−	5.11782e6i	−1.95535	−	0.0621753i
$436$	132143.	+	2.80127e7i	0.00159435	+	0.337984i
$437$	171833.	−	99207.6i	0.00205902	−	0.00118878i
$438$	−1.34419e8	−	3.95687e6i	−1.59970	−	0.0470901i
$439$	1.32007e7	+	7.62144e6i	0.156029	+	0.0900831i	0.575981	−	0.817463i	$-0.304620\pi$
$439$	1.32007e7	+	7.62144e6i	0.156029	+	0.0900831i	−0.419953	+	0.907546i	$0.637953\pi$
$440$	−711498.	−	1.00552e8i	−0.00835249	−	1.18041i
$441$	−3.80027e7	−	7.66988e7i	−0.443097	−	0.894279i
$442$	2.63751e7	−	1.53107e7i	0.305441	−	0.177308i
$443$	−5.54789e7	+	9.60923e7i	−0.638141	+	1.10529i	0.347699	+	0.937606i	$0.386963\pi$
$443$	−5.54789e7	+	9.60923e7i	−0.638141	+	1.10529i	−0.985840	+	0.167687i	$0.946370\pi$
$444$	−4.00095e6	+	1.47766e8i	−0.0457103	+	1.68821i
$445$	2.26406e8	−	1.30716e8i	2.56926	−	1.48336i
$446$	−9.13477e7	−	5.24527e7i	−1.02966	−	0.591240i
$447$	−7.28491e7	+	3.90266e7i	−0.815646	+	0.436956i
$448$	3.48175e6	+	1.94502e6i	0.0387225	+	0.0216317i
$449$	−4.75431e7			−0.525229			−0.262615	−	0.964901i	$-0.584585\pi$
$449$	−4.75431e7			−0.525229			−0.262615	+	0.964901i	$0.584585\pi$
$450$	−9.90743e7	+	1.49643e8i	−1.08724	+	1.64218i
$451$	−8.57311e7			−0.934563
$452$	−1.43144e7	−	2.45253e7i	−0.155009	−	0.265582i
$453$	3.31093e7	+	2.05456e7i	0.356168	+	0.221017i
$454$	−7.19533e7	+	1.25308e8i	−0.768924	+	1.33910i
$455$	−2.55012e6	+	1.47231e6i	−0.0270724	+	0.0156302i
$456$	397967.	+	9836.19i	0.00419713	+	0.000103737i
$457$	2.95199e6	−	5.11299e6i	0.0309290	−	0.0535706i	−0.850147	−	0.526546i	$-0.823487\pi$
$457$	2.95199e6	−	5.11299e6i	0.0309290	−	0.0535706i	0.881076	+	0.472975i	$0.156820\pi$
$458$	−1.06406e7	+	6.17686e6i	−0.110757	+	0.0642941i
$459$	−8.31259e7	−	7.95104e6i	−0.859603	−	0.0822216i
$460$	4.71043e7	−	8.24831e7i	0.483935	−	0.847406i
$461$	6.49950e7	+	3.75249e7i	0.663403	+	0.383016i	0.793572	−	0.608476i	$-0.208219\pi$
$461$	6.49950e7	+	3.75249e7i	0.663403	+	0.383016i	−0.130169	+	0.991492i	$0.541552\pi$
$462$	−2.63775e6	+	1.42111e6i	−0.0267490	+	0.0144112i
$463$	−7.50074e7	+	4.33056e7i	−0.755721	+	0.436316i	−0.827757	−	0.561086i	$-0.810384\pi$
$463$	−7.50074e7	+	4.33056e7i	−0.755721	+	0.436316i	0.0720365	+	0.997402i	$0.477050\pi$
$464$	9.87480e7	+	5.57767e7i	0.988494	+	0.558340i
$465$	5.29491e7	−	8.53275e7i	0.526623	−	0.848653i
$466$	9.29107e7	−	219140.i	0.918138	−	0.00216553i
$467$	−9.04330e7			−0.887925			−0.443962	−	0.896045i	$-0.646428\pi$
$467$	−9.04330e7			−0.887925			−0.443962	+	0.896045i	$0.646428\pi$
$468$	−3.74764e7	+	1.87895e7i	−0.365612	+	0.183307i
$469$			155152.i			0.00150397i
$470$	−3.24460e8	+	765273.i	−3.12513	+	0.00737094i
$471$	−7.51989e6	+	4.02854e6i	−0.0719696	+	0.0385554i
$472$	5.59343e7	+	9.53170e7i	0.531927	+	0.906451i
$473$	6.23610e7	+	1.08012e8i	0.589291	+	1.02068i
$474$	6.32179e7	+	3.90230e7i	0.593616	+	0.366426i
$475$	443084.	−	767444.i	0.00413433	−	0.00716087i
$476$	3.58712e6	+	2.04852e6i	0.0332602	+	0.0189942i
$477$	7.31568e6	−	1.14919e8i	0.0674061	−	1.05885i
$478$	−1.53442e8	+	8.90729e7i	−1.40495	+	0.815571i
$479$	1.27717e8	+	7.37376e7i	1.16210	+	0.670938i	0.951806	−	0.306700i	$-0.0992250\pi$
$479$	1.27717e8	+	7.37376e7i	1.16210	+	0.670938i	0.210293	+	0.977638i	$0.432558\pi$
$480$	1.66914e8	−	9.19683e7i	1.50928	−	0.831600i
$481$	3.84329e7	+	6.65678e7i	0.345357	+	0.598176i
$482$	7.18821e7	−	1.25184e8i	0.641918	−	1.11792i
$483$	−2.82885e6	−	89950.4i	−0.0251054	−	0.000798292i
$484$	3.03335e7	+	5.19714e7i	0.267538	+	0.458383i
$485$		−	2.82095e8i		−	2.47269i
$486$	1.13387e8	+	1.79002e7i	0.987767	+	0.155937i
$487$			2.70075e7i			0.233829i	0.993142	+	0.116914i	$0.0373003\pi$
$487$			2.70075e7i			0.233829i	−0.993142	+	0.116914i	$0.962700\pi$
$488$	−5.35299e7	−	3.04025e7i	−0.460614	−	0.261608i
$489$	4.23268e7	+	1.34589e6i	0.361983	+	0.0115102i
$490$	1.75466e8	+	1.00754e8i	1.49144	+	0.856397i
$491$	−1.02452e8	−	1.77451e8i	−0.865514	−	1.49911i	−0.866536	−	0.499114i	$-0.833659\pi$
$491$	−1.02452e8	−	1.77451e8i	−0.865514	−	1.49911i	0.00102273	−	0.999999i	$-0.499674\pi$
$492$	−7.74017e7	−	1.42859e8i	−0.649913	−	1.19954i
$493$	1.01730e8	+	5.87341e7i	0.849005	+	0.490173i
$494$	179027.	−	103925.i	0.00148504	−	0.000862063i
$495$	−9.09586e6	+	1.42883e8i	−0.0749943	+	1.17805i
$496$	−6.09131e7	+	3.59386e7i	−0.499190	+	0.294521i
$497$	1.49637e6	−	2.59179e6i	0.0121891	−	0.0211121i
$498$	7.00270e7	−	1.13445e8i	0.566993	−	0.918538i
$499$	5.49600e7	+	9.51936e7i	0.442329	+	0.766136i	0.997862	−	0.0653584i	$-0.0208191\pi$
$499$	5.49600e7	+	9.51936e7i	0.442329	+	0.766136i	−0.555533	+	0.831495i	$0.687486\pi$
$500$	−985072.	−	2.08824e8i	−0.00788058	−	1.67059i
$501$	7.61434e7	−	4.07914e7i	0.605507	−	0.324381i
$502$	2.81926e7	−	66495.2i	0.222856	−	0.000525629i
$503$			9.58390e7i			0.753075i	0.926401	+	0.376537i	$0.122885\pi$
$503$			9.58390e7i			0.753075i	−0.926401	+	0.376537i	$0.877115\pi$
$504$	−4.74956e6	−	3.11241e6i	−0.0370989	−	0.0243112i
$505$	−1.46000e8			−1.13365
$506$	−118537.	−	5.02573e7i	−0.000914962	−	0.387925i
$507$	5.72216e7	−	9.22126e7i	0.439072	−	0.707565i
$508$	965168.	+	2.04604e8i	0.00736227	+	1.56072i
$509$	−1.82881e8	+	1.05586e8i	−1.38680	+	0.800670i	−0.992953	−	0.118505i	$-0.962190\pi$
$509$	−1.82881e8	+	1.05586e8i	−1.38680	+	0.800670i	−0.393848	+	0.919176i	$0.628856\pi$
$510$	1.73775e8	−	9.36225e7i	1.31002	−	0.705781i
$511$	−8.20282e6	−	4.73590e6i	−0.0614753	−	0.0354928i
$512$	−1.34187e8	+	2.84888e6i	−0.999775	+	0.0212258i
$513$	−564235.	−	53969.4i	−0.00417934	−	0.000399757i
$514$	−2.63620e7	−	4.54126e7i	−0.194128	−	0.334416i
$515$	−2.42852e7	+	4.20632e7i	−0.177795	+	0.307950i
$516$	−1.23686e8	+	2.01435e8i	−0.900266	+	1.46617i
$517$	−1.48674e8	+	8.58370e7i	−1.07588	+	0.621159i
$518$	−5.18450e6	+	9.02893e6i	−0.0373008	+	0.0649602i
$519$	−4.79235e6	−	2.97384e6i	−0.0342804	−	0.0212724i
$520$	4.89404e7	−	8.61696e7i	0.348062	−	0.612835i
$521$	−1.27128e8			−0.898936			−0.449468	−	0.893296i	$-0.648386\pi$
$521$	−1.27128e8			−0.898936			−0.449468	+	0.893296i	$0.648386\pi$
$522$	−1.34643e8	−	8.91434e7i	−0.946615	−	0.626726i
$523$	1.83504e8			1.28275			0.641373	−	0.767230i	$-0.278365\pi$
$523$	1.83504e8			1.28275			0.641373	+	0.767230i	$0.278365\pi$
$524$	7.58291e7	+	1.29921e8i	0.527038	+	0.902993i
$525$	−1.11425e7	+	5.96922e6i	−0.0770023	+	0.0412515i
$526$	−1.36203e8	−	7.82091e7i	−0.935900	−	0.537403i
$527$	−6.34402e7	+	3.66272e7i	−0.433444	+	0.250249i
$528$	5.23560e7	−	8.61759e7i	0.355684	−	0.585442i
$529$	−5.02809e7	+	8.70890e7i	−0.339653	+	0.588297i
$530$	1.36654e8	+	2.35407e8i	0.917896	+	1.58122i
$531$	−6.98619e7	−	1.40998e8i	−0.466613	−	0.941739i
$532$	24348.4	+	13904.8i	0.000161709	+	9.23485e-5i
$533$	−7.31697e7	−	4.22445e7i	−0.483225	−	0.278990i
$534$	2.62044e8	+	7.71372e6i	1.72088	+	0.0506571i
$535$	−1.17238e8	+	6.76876e7i	−0.765612	+	0.442026i
$536$	−2.64265e6	−	4.50331e6i	−0.0171611	−	0.0292441i
$537$	2.83310e8	+	9.00855e6i	1.82953	+	0.0581744i
$538$	−608059.	−	2.57804e8i	−0.00390480	−	1.65555i
$539$	1.07057e8			0.683673
$540$	−2.46307e8	+	1.13844e8i	−1.56421	+	0.722984i
$541$		−	1.69485e8i		−	1.07038i	−0.844731	−	0.535191i	$-0.820240\pi$
$541$		−	1.69485e8i		−	1.07038i	0.844731	−	0.535191i	$-0.179760\pi$
$542$	508567.	+	2.15622e8i	0.00319411	+	1.35424i
$543$	7.51470e6	−	2.36329e8i	0.0469366	−	1.47611i
$544$	−1.39009e8	+	1.63941e6i	−0.863467	+	0.0101833i
$545$	4.71411e7	+	8.16508e7i	0.291213	+	0.504395i
$546$	−2.95152e6	−	86883.2i	−0.0181329	−	0.000533775i
$547$	4.06533e6	−	7.04136e6i	0.0248390	−	0.0430224i	−0.853339	−	0.521357i	$-0.825426\pi$
$547$	4.06533e6	−	7.04136e6i	0.0248390	−	0.0430224i	0.878178	+	0.478335i	$0.158759\pi$
$548$	−5.30973e7	+	9.29773e7i	−0.322649	+	0.564983i
$549$	7.29716e7	+	4.85603e7i	0.440998	+	0.293470i
$550$	−1.12689e8	−	1.94124e8i	−0.677319	−	1.16679i
$551$	690517.	+	398670.i	0.00412781	+	0.00238319i
$552$	8.36399e7	−	4.55720e7i	0.497275	−	0.270945i
$553$	2.61634e6	+	4.53164e6i	0.0154710	+	0.0267966i
$554$	−4.21955e7	−	2.42291e7i	−0.248163	−	0.142498i
$555$	2.34937e8	+	4.38546e8i	1.37427	+	2.56529i
$556$	−7.09456e7	−	1.21554e8i	−0.412763	−	0.707202i
$557$			2.58878e8i			1.49806i	0.662535	+	0.749031i	$0.269481\pi$
$557$			2.58878e8i			1.49806i	−0.662535	+	0.749031i	$0.730519\pi$
$558$	9.01256e7	−	4.49205e7i	0.518735	−	0.258548i
$559$			1.22915e8i			0.703671i
$560$	1.34223e7	−	126635.i	0.0764298	−	0.000721091i
$561$	5.50683e7	−	8.87426e7i	0.311899	−	0.502625i
$562$	4.49598e7	−	7.82986e7i	0.253289	−	0.441108i
$563$	−1.33706e8	−	2.31585e8i	−0.749247	−	1.29773i	−0.948184	−	0.317722i	$-0.897082\pi$
$563$	−1.33706e8	−	2.31585e8i	−0.749247	−	1.29773i	0.198937	−	0.980012i	$-0.436251\pi$
$564$	−2.77265e8	−	1.70248e8i	−1.54546	−	0.948952i
$565$	−8.27700e7	−	4.77873e7i	−0.458910	−	0.264952i
$566$	3.98046e7	+	6.85695e7i	0.219525	+	0.378166i
$567$	6.43285e6	+	4.89786e6i	0.0352902	+	0.0268694i
$568$	712648.	+	1.00715e8i	0.00388893	+	0.549600i
$569$	−3.20601e6	+	5.55298e6i	−0.0174032	+	0.0301432i	−0.874596	−	0.484853i	$-0.838873\pi$
$569$	−3.20601e6	+	5.55298e6i	−0.0174032	+	0.0301432i	0.857193	+	0.514996i	$0.172207\pi$
$570$	1.17954e6	−	635483.i	0.00636923	−	0.00343147i
$571$	3.13721e7	+	5.43381e7i	0.168514	+	0.291874i	0.937897	−	0.346913i	$-0.112770\pi$
$571$	3.13721e7	+	5.43381e7i	0.168514	+	0.291874i	−0.769384	+	0.638787i	$0.779437\pi$
$572$	−247337.	−	5.24326e7i	−0.00132160	−	0.280164i
$573$	−2.40096e8	−	1.48989e8i	−1.27621	−	0.791938i
$574$	−26992.1	−	1.14441e7i	−0.000142725	−	0.0605126i
$575$		−	2.12030e8i		−	1.11531i
$576$	1.90870e8	+	9.44086e6i	0.998779	+	0.0494020i
$577$	−1.46226e8			−0.761195			−0.380597	−	0.924741i	$-0.624282\pi$
$577$	−1.46226e8			−0.761195			−0.380597	+	0.924741i	$0.624282\pi$
$578$	4.91096e7	−	115830.i	0.254321	−	0.000599844i
$579$	9.31552e6	+	1.73889e7i	0.0479923	+	0.0895850i
$580$	3.81700e8	−	1.80057e6i	1.95631	−	0.00922840i
$581$	8.13205e6	−	4.69504e6i	0.0414641	−	0.0239393i
$582$	1.48586e8	−	2.40712e8i	0.753718	−	1.22104i
$583$	1.24725e8	+	7.20102e7i	0.629432	+	0.363403i
$584$	3.18754e8	−	2.25548e6i	1.60036	−	0.0113240i
$585$	−7.81696e7	+	1.17466e8i	−0.390455	+	0.586737i
$586$	1.57796e8	−	9.16005e7i	0.784157	−	0.455203i
$587$	1.36631e8	−	2.36652e8i	0.675515	−	1.17003i	−0.300803	−	0.953686i	$-0.597255\pi$
$587$	1.36631e8	−	2.36652e8i	0.675515	−	1.17003i	0.976318	−	0.216340i	$-0.0694120\pi$
$588$	9.66556e7	+	1.78396e8i	0.475439	+	0.877512i
$589$	−430614.	+	248615.i	−0.00210738	+	0.00121670i
$590$	3.22566e8	+	1.85221e8i	1.57059	+	0.901847i
$591$	−1.56826e6	+	4.93201e7i	−0.00759723	+	0.238925i
$592$	−3.30566e6	−	3.50373e8i	−0.0159328	−	1.68875i
$593$	−1.10924e8			−0.531939			−0.265969	−	0.963981i	$-0.585692\pi$
$593$	−1.10924e8			−0.531939			−0.265969	+	0.963981i	$0.585692\pi$
$594$	−8.30214e7	+	1.17131e8i	−0.396124	+	0.558874i
$595$	1.39030e7			0.0660021
$596$	1.69188e8	−	9.87479e7i	0.799155	−	0.466433i
$597$	−5.70255e6	+	1.79339e8i	−0.0268007	+	0.842855i
$598$	2.46634e7	−	4.29519e7i	0.115332	−	0.200853i
$599$	7.23362e7	−	4.17634e7i	0.336570	−	0.194319i	−0.322184	−	0.946677i	$-0.604417\pi$
$599$	7.23362e7	−	4.17634e7i	0.336570	−	0.194319i	0.658754	+	0.752358i	$0.271084\pi$
$600$	2.21741e8	−	3.63044e8i	1.02658	−	1.68076i
$601$	1.20264e8	−	2.08304e8i	0.554004	−	0.959563i	−0.443976	−	0.896038i	$-0.646433\pi$
$601$	1.20264e8	−	2.08304e8i	0.554004	−	0.959563i	0.997980	−	0.0635244i	$-0.0202341\pi$
$602$	−1.43988e7	+	8.35848e6i	−0.0659988	+	0.0383123i
$603$	3.30067e6	+	6.66156e6i	0.0150539	+	0.0303825i
$604$	−8.02064e7	−	4.58041e7i	−0.363997	−	0.207871i
$605$	1.75397e8	+	1.01266e8i	0.792058	+	0.457295i
$606$	−1.24582e8	−	7.69018e7i	−0.559806	−	0.345556i
$607$	−1.17355e7	+	6.77548e6i	−0.0524728	+	0.0302952i	−0.526007	−	0.850480i	$-0.676311\pi$
$607$	−1.17355e7	+	6.77548e6i	−0.0524728	+	0.0302952i	0.473534	+	0.880775i	$0.342978\pi$
$608$	−943552.	+	11127.8i	−0.00419812	+	4.95108e-5i
$609$	−5.37088e6	−	1.00256e7i	−0.0237790	−	0.0443872i
$610$	−2.07193e8	+	488686.i	−0.912820	+	0.00215298i
$611$	−1.69187e8			−0.741725
$612$	1.97596e8	+	1.16432e7i	0.862031	+	0.0507948i
$613$			4.03260e8i			1.75067i	0.483518	+	0.875335i	$0.339359\pi$
$613$			4.03260e8i			1.75067i	−0.483518	+	0.875335i	$0.660641\pi$
$614$	−1.03536e8	+	244200.i	−0.447286	+	0.00105497i
$615$	−4.64659e8	−	2.88339e8i	−1.99760	−	1.23959i
$616$	6.12534e6	−	3.59449e6i	0.0262052	−	0.0153778i
$617$	−1.36300e7	−	2.36079e7i	−0.0580284	−	0.100508i	0.835552	−	0.549412i	$-0.185148\pi$
$617$	−1.36300e7	−	2.36079e7i	−0.0580284	−	0.100508i	−0.893580	+	0.448903i	$0.851815\pi$
$618$	−4.28783e7	+	2.31010e7i	−0.181665	+	0.0978735i
$619$	−2.34463e7	+	4.06102e7i	−0.0988559	+	0.171223i	−0.911211	−	0.411939i	$-0.864852\pi$
$619$	−2.34463e7	+	4.06102e7i	−0.0988559	+	0.171223i	0.812355	+	0.583163i	$0.198185\pi$
$620$	−1.18044e8	+	2.06704e8i	−0.495300	+	0.867307i
$621$	−1.23372e8	+	5.63182e7i	−0.515161	+	0.235166i
$622$	−1.66246e8	+	9.65054e7i	−0.690842	+	0.401034i
$623$	1.59910e7	+	9.23240e6i	0.0661319	+	0.0381813i
$624$	8.71484e7	−	4.77505e7i	0.358679	−	0.196528i
$625$	−1.11004e8	−	1.92265e8i	−0.454674	−	0.787518i
$626$	9.54620e7	−	1.66249e8i	0.389141	−	0.677699i
$627$	373788.	−	602360.i	0.00151643	−	0.00244373i
$628$	1.74645e7	−	1.01933e7i	0.0705145	−	0.0411563i
$629$		−	3.62921e8i		−	1.45834i
$630$	−1.90761e7	−	1.16921e6i	−0.0762900	−	0.00467594i
$631$		−	3.49337e8i		−	1.39046i	−0.718790	−	0.695228i	$-0.755304\pi$
$631$		−	3.49337e8i		−	1.39046i	0.718790	−	0.695228i	$-0.244696\pi$
$632$	−1.53126e8	−	8.69685e7i	−0.606593	−	0.344517i
$633$	4.32113e7	+	8.06606e7i	0.170367	+	0.318017i
$634$	9.32762e7	+	5.35601e7i	0.366018	+	0.210171i
$635$	3.44318e8	+	5.96376e8i	1.34474	+	2.32916i
$636$	−7.38780e6	+	2.72852e8i	−0.0287173	+	1.06061i
$637$	9.13708e7	+	5.27530e7i	0.353500	+	0.204093i
$638$	1.74666e8	−	1.01393e8i	0.672582	−	0.390433i
$639$	9.11057e6	−	1.43114e8i	0.0349175	−	0.548504i
$640$	−3.87428e8	+	2.32293e8i	−1.47792	+	0.886128i
$641$	6.32768e6	−	1.09599e7i	0.0240254	−	0.0416132i	−0.853763	−	0.520662i	$-0.825685\pi$
$641$	6.32768e6	−	1.09599e7i	0.0240254	−	0.0416132i	0.877788	+	0.479049i	$0.159018\pi$
$642$	−1.35692e8	−	3.99434e6i	−0.512803	−	0.0150952i
$643$	−1.08022e8	−	1.87100e8i	−0.406330	−	0.703785i	0.588145	−	0.808756i	$-0.299858\pi$
$643$	−1.08022e8	−	1.87100e8i	−0.406330	−	0.703785i	−0.994475	+	0.104971i	$0.966525\pi$
$644$	6.70873e6	−	31646.7i	0.0251178	−	0.000118487i
$645$	−2.52842e7	+	7.95162e8i	−0.0942258	+	2.96330i
$646$	−977367.	+	2305.22i	−0.00362543	+	8.55097e-6i
$647$		−	4.99885e8i		−	1.84568i	−0.385180	−	0.922841i	$-0.625861\pi$
$647$		−	4.99885e8i		−	1.84568i	0.385180	−	0.922841i	$-0.374139\pi$
$648$	−2.70139e8	−	3.25928e7i	−0.992800	−	0.119783i
$649$	1.96807e8			0.719957
$650$	−521745.	−	2.21209e8i	−0.00189984	−	0.805494i
$651$	7.08912e6	+	225417.i	0.0256950	+	0.000817039i
$652$	−1.00380e8	+	473515.i	−0.362162	+	0.00170841i
$653$	−1.71642e8	+	9.90978e7i	−0.616432	+	0.355897i	−0.775479	−	0.631374i	$-0.782491\pi$
$653$	−1.71642e8	+	9.90978e7i	−0.616432	+	0.355897i	0.159047	+	0.987271i	$0.449158\pi$
$654$	−2.78186e6	+	9.45030e7i	−0.00994494	+	0.337841i
$655$	4.38467e8	+	2.53149e8i	1.56032	+	0.900850i
$656$	1.95707e8	+	3.31708e8i	0.693259	+	1.17502i
$657$	−4.52945e8	−	2.88342e7i	−1.59716	−	0.101675i
$658$	−1.15051e7	−	1.98192e7i	−0.0403841	−	0.0695679i
$659$	−1.12179e8	+	1.94299e8i	−0.391971	+	0.678914i	−0.992709	−	0.120532i	$-0.961540\pi$
$659$	−1.12179e8	+	1.94299e8i	−0.391971	+	0.678914i	0.600738	+	0.799446i	$0.294873\pi$
$660$	9.18554e6	−	3.39247e8i	0.0319502	−	1.18001i
$661$	−4.20415e7	+	2.42727e7i	−0.145571	+	0.0840453i	−0.571016	−	0.820939i	$-0.693451\pi$
$661$	−4.20415e7	+	2.42727e7i	−0.145571	+	0.0840453i	0.425446	+	0.904984i	$0.360117\pi$
$662$	−1.88415e7	+	3.28130e7i	−0.0649445	+	0.113102i
$663$	9.07281e7	−	4.86047e7i	0.311316	−	0.166778i
$664$	−1.56065e8	+	2.74785e8i	−0.533092	+	0.938619i
$665$	94369.7			0.000320898
$666$	−3.05207e7	+	4.97958e8i	−0.103317	+	1.68566i
$667$	1.90777e8			0.642908
$668$	−1.76839e8	+	1.03213e8i	−0.593265	+	0.346263i
$669$	−3.02075e8	−	1.87450e8i	−1.00887	−	0.626046i
$670$	−1.52398e7	−	8.75086e6i	−0.0506706	−	0.0290955i
$671$	−9.49399e7	+	5.48136e7i	−0.314254	+	0.181435i
$672$	1.15200e7	+	6.96178e6i	0.0379615	+	0.0229410i
$673$	1.81862e8	−	3.14995e8i	0.596620	−	1.03338i	−0.396696	−	0.917950i	$-0.629843\pi$
$673$	1.81862e8	−	3.14995e8i	0.596620	−	1.03338i	0.993316	−	0.115426i	$-0.0368233\pi$
$674$	−4.09022e7	−	7.04604e7i	−0.133588	−	0.230126i
$675$	−3.51423e8	+	4.93336e8i	−1.14266	+	1.60410i
$676$	−1.27569e8	+	2.23383e8i	−0.412957	+	0.723118i
$677$	3.13711e8	+	1.81121e8i	1.01103	+	0.583717i	0.911493	−	0.411317i	$-0.134931\pi$
$677$	3.13711e8	+	1.81121e8i	1.01103	+	0.583717i	0.0995356	+	0.995034i	$0.468264\pi$
$678$	−4.54570e7	−	8.43739e7i	−0.145852	−	0.270719i
$679$	1.72549e7	−	9.96212e6i	0.0551192	−	0.0318231i
$680$	−4.03538e8	+	2.36805e8i	−1.28339	+	0.753121i
$681$	−2.57139e8	+	4.14379e8i	−0.814191	+	1.31207i
$682$	297056.	+	1.25945e8i	0.000936450	+	0.397035i
$683$	7.37635e7			0.231515			0.115758	−	0.993277i	$-0.463070\pi$
$683$	7.37635e7			0.231515			0.115758	+	0.993277i	$0.463070\pi$
$684$	1.34122e6	+	79031.0i	0.00419115	+	0.000246961i
$685$			3.60362e8i			1.12116i
$686$	67479.4	+	2.86099e7i	0.000209025	+	0.0886224i
$687$	−3.66028e7	+	1.96088e7i	−0.112887	+	0.0604755i
$688$	2.75560e8	−	4.87856e8i	0.846157	−	1.49805i
$689$	7.09669e7	+	1.22918e8i	0.216969	+	0.375802i
$690$	1.68388e8	−	2.72791e8i	0.512582	−	0.830391i
$691$	5.89719e7	−	1.02142e8i	0.178736	−	0.309579i	−0.762712	−	0.646738i	$-0.776133\pi$
$691$	5.89719e7	−	1.02142e8i	0.178736	−	0.309579i	0.941448	+	0.337159i	$0.109466\pi$
$692$	1.16093e7	+	6.62983e6i	0.0350339	+	0.0200071i
$693$	−9.06095e6	+	4.48952e6i	−0.0272254	+	0.0134896i
$694$	−2.47509e8	−	4.26372e8i	−0.740478	−	1.27559i
$695$	−4.10229e8	−	2.36846e8i	−1.22200	−	0.705523i
$696$	3.26654e8	+	1.99514e8i	0.968857	+	0.591761i
$697$	1.99457e8	+	3.45469e8i	0.589048	+	1.02026i
$698$	−1.57412e8	−	9.03876e7i	−0.462884	−	0.265792i
$699$	3.13416e8	+	9.96587e6i	0.917677	+	0.0291799i
$700$	2.58778e7	−	1.51038e7i	0.0754455	−	0.0440343i
$701$		−	2.20454e8i		−	0.639976i	−0.947422	−	0.319988i	$-0.896321\pi$
$701$		−	2.20454e8i		−	0.639976i	0.947422	−	0.319988i	$-0.103679\pi$
$702$	−1.28574e8	+	5.90597e7i	−0.371657	+	0.170718i
$703$		−	2.46341e6i		−	0.00709039i
$704$	−1.16565e8	+	2.08662e8i	−0.334081	+	0.598033i
$705$	−1.09450e9	−	3.48025e7i	−3.12356	−	0.0993215i
$706$	−2.40503e8	+	4.18841e8i	−0.683448	+	1.19024i
$707$	−5.15597e6	−	8.93040e6i	−0.0145899	−	0.0252704i
$708$	1.77686e8	+	3.27952e8i	0.500672	+	0.924082i
$709$	−5.16049e8	−	2.97941e8i	−1.44795	−	0.835971i	−0.449586	−	0.893237i	$-0.648428\pi$
$709$	−5.16049e8	−	2.97941e8i	−1.44795	−	0.835971i	−0.998359	+	0.0572656i	$0.981762\pi$
$710$	1.70181e8	+	2.93164e8i	0.475485	+	0.819097i
$711$	2.08740e8	+	1.38910e8i	0.580760	+	0.386477i
$712$	−6.21395e8	+	4.39694e6i	−1.72158	+	0.0121818i
$713$	−5.94853e7	+	1.03032e8i	−0.164112	+	0.284251i
$714$	1.18634e7	+	7.32304e6i	0.0325924	+	0.0201186i
$715$	−8.82359e7	−	1.52829e8i	−0.241395	−	0.418108i
$716$	−6.71881e8	+	3.16942e6i	−1.83043	+	0.00863458i
$717$	−5.27827e8	+	2.82766e8i	−1.43197	+	0.767132i
$718$	−971659.	−	4.11963e8i	−0.00262507	−	1.11297i
$719$			7.81707e7i			0.210309i	0.994456	+	0.105154i	$0.0335337\pi$
$719$			7.81707e7i			0.210309i	−0.994456	+	0.105154i	$0.966466\pi$
$720$	5.73602e8	−	2.90980e8i	1.53679	−	0.779590i
$721$	−3.43051e6			−0.00915278
$722$	3.76359e8	−	887684.i	0.999980	−	0.00235856i
$723$	2.56884e8	−	4.13969e8i	0.679708	−	1.09535i
$724$	2.64385e6	+	5.60465e8i	0.00696660	+	1.47684i
$725$	7.37901e8	−	4.26027e8i	1.93635	−	1.11795i
$726$	9.63277e7	+	1.78796e8i	0.251734	+	0.467249i
$727$	1.79553e8	+	1.03665e8i	0.467292	+	0.269791i	0.715106	−	0.699016i	$-0.246379\pi$
$727$	1.79553e8	+	1.03665e8i	0.467292	+	0.269791i	−0.247813	+	0.968808i	$0.579712\pi$
$728$	6.99906e6	−	49524.8i	0.0181403	−	0.000128360i
$729$	3.80396e8	+	7.34421e7i	0.981868	+	0.189567i
$730$	9.27841e8	−	5.38611e8i	2.38509	−	1.38454i
$731$	2.90171e8	−	5.02591e8i	0.742851	−	1.28666i
$732$	−1.77055e8	−	1.08716e8i	−0.451415	−	0.277180i
$733$	4.72439e8	−	2.72763e8i	1.19959	−	0.692585i	0.239127	−	0.970988i	$-0.423139\pi$
$733$	4.72439e8	−	2.72763e8i	1.19959	−	0.692585i	0.960464	+	0.278404i	$0.0898053\pi$
$734$	6.16920e8	+	3.54242e8i	1.56006	+	0.895801i
$735$	5.80244e8	+	3.60064e8i	1.46133	+	0.906814i
$736$	−1.94183e8	+	1.15186e8i	−0.487055	+	0.288913i
$737$	−9.29827e6			−0.0232274
$738$	−2.44619e8	−	4.90787e8i	−0.608584	−	1.22102i
$739$	−5.11564e8			−1.26755			−0.633777	−	0.773515i	$-0.718497\pi$
$739$	−5.11564e8			−1.26755			−0.633777	+	0.773515i	$0.718497\pi$
$740$	−5.94454e8	−	1.01850e9i	−1.46698	−	2.51342i
$741$	615837.	−	329915.i	0.00151360	−	0.000810863i
$742$	−9.57325e6	+	1.66720e7i	−0.0234341	+	0.0408110i
$743$	−2.78630e8	+	1.60867e8i	−0.679300	+	0.392194i	−0.799591	−	0.600545i	$-0.794950\pi$
$743$	−2.78630e8	+	1.60867e8i	−0.679300	+	0.392194i	0.120291	+	0.992739i	$0.461617\pi$
$744$	−2.09603e8	+	1.14204e8i	−0.508953	+	0.277308i
$745$	3.29661e8	−	5.70990e8i	0.797259	−	1.38089i
$746$	2.95041e8	−	1.71271e8i	0.710667	−	0.412542i
$747$	2.49274e8	−	3.74585e8i	0.598020	−	0.898646i
$748$	−1.22768e8	+	2.14977e8i	−0.293347	+	0.513673i
$749$	−8.28050e6	−	4.78075e6i	−0.0197066	−	0.0113776i
$750$	2.07377e7	−	7.04483e8i	0.0491560	−	1.66989i
$751$	4.26413e8	−	2.46190e8i	1.00672	−	0.581232i	0.0964932	−	0.995334i	$-0.469237\pi$
$751$	4.26413e8	−	2.46190e8i	1.00672	−	0.581232i	0.910231	+	0.414101i	$0.135904\pi$
$752$	6.71511e8	+	3.79296e8i	1.57906	+	0.891917i
$753$	9.51022e7	+	3.02402e6i	0.222744	+	0.00708271i
$754$	1.99035e8	−	469446.i	0.464319	−	0.00109515i
$755$	−3.10865e8			−0.722322
$756$	−1.56618e7	−	1.10455e7i	−0.0362473	−	0.0255635i
$757$		−	1.07130e8i		−	0.246958i	−0.992347	−	0.123479i	$-0.960595\pi$
$757$		−	1.07130e8i		−	0.246958i	0.992347	−	0.123479i	$-0.0394051\pi$
$758$	2.67526e8	−	630989.i	0.614269	−	0.00144882i
$759$	5.39074e6	−	1.69533e8i	0.0123289	−	0.387730i
$760$	−2.73910e6	+	1.60737e6i	−0.00623975	+	0.00366163i
$761$	−2.07308e8	−	3.59068e8i	−0.470394	−	0.814746i	0.529033	−	0.848601i	$-0.322555\pi$
$761$	−2.07308e8	−	3.59068e8i	−0.470394	−	0.814746i	−0.999427	+	0.0338551i	$0.989222\pi$
$762$	−2.03187e7	+	6.90249e8i	−0.0459230	+	1.56006i
$763$	−3.32956e6	+	5.76696e6i	−0.00749571	+	0.0129830i
$764$	5.81627e8	+	3.32154e8i	1.30426	+	0.744834i
$765$	5.96936e8	−	2.95770e8i	1.33335	−	0.660647i
$766$	3.36094e8	−	1.95102e8i	0.747781	−	0.434087i
$767$	1.67971e8	+	9.69778e7i	0.372261	+	0.214925i
$768$	−4.52947e8	−	5.85151e6i	−0.999917	−	0.0129177i
$769$	1.45874e7	+	2.52661e7i	0.0320773	+	0.0555595i	0.881618	−	0.471963i	$-0.156454\pi$
$769$	1.45874e7	+	2.52661e7i	0.0320773	+	0.0555595i	−0.849541	+	0.527522i	$0.823121\pi$
$770$	1.19028e7	−	2.07290e7i	0.0260721	−	0.0454053i
$771$	−8.36874e7	−	1.56215e8i	−0.182598	−	0.340848i
$772$	−2.35708e7	−	4.03847e7i	−0.0512298	−	0.0877738i
$773$		−	3.74367e7i		−	0.0810511i	−0.999179	−	0.0405256i	$-0.987097\pi$
$773$		−	3.74367e7i		−	0.0810511i	0.999179	−	0.0405256i	$-0.0129032\pi$
$774$	−4.40406e8	+	6.65194e8i	−0.949795	+	1.43458i
$775$			5.31351e8i			1.14150i
$776$	−3.31145e8	+	5.83050e8i	−0.708653	+	1.24773i
$777$	−1.85278e7	+	2.98575e7i	−0.0394967	+	0.0636489i
$778$	−3.78626e8	−	2.17411e8i	−0.804030	−	0.461682i
$779$	1.35386e6	+	2.34495e6i	0.00286392	+	0.00496045i
$780$	1.75006e8	−	2.85014e8i	0.368781	−	0.600596i
$781$	1.55326e8	+	8.96778e7i	0.326056	+	0.188249i
$782$	−2.02245e8	+	1.17403e8i	−0.422920	+	0.245505i
$783$	−4.43885e8	−	3.16197e8i	−0.924667	−	0.658677i
$784$	−2.44390e8	−	4.14221e8i	−0.507148	−	0.859575i
$785$	3.40295e7	−	5.89408e7i	0.0703472	−	0.121845i
$786$	2.40805e8	+	4.46963e8i	0.495904	+	0.920459i
$787$	−1.32434e8	−	2.29382e8i	−0.271690	−	0.470582i	0.697604	−	0.716483i	$-0.254249\pi$
$787$	−1.32434e8	−	2.29382e8i	−0.271690	−	0.470582i	−0.969295	+	0.245902i	$0.920916\pi$
$788$	−551751.	−	1.16965e8i	−0.00112762	−	0.239043i
$789$	−4.50406e8	−	2.79495e8i	−0.917008	−	0.569040i
$790$	−5.92689e8	+	1.39792e6i	−1.20211	+	0.00283531i
$791$		−	6.75039e6i		−	0.0136395i
$792$	1.86528e8	−	2.84642e8i	0.375463	−	0.572958i
$793$	−1.08039e8			−0.216651
$794$	−734371.	−	3.11358e8i	−0.00146708	−	0.622012i
$795$	4.33814e8	+	8.09781e8i	0.863380	+	1.61163i
$796$	−2.00629e6	−	4.25311e8i	−0.00397791	−	0.843271i
$797$	8.17715e8	−	4.72108e8i	1.61520	−	0.932538i	0.627065	−	0.778967i	$-0.284256\pi$
$797$	8.17715e8	−	4.72108e8i	1.61520	−	0.932538i	0.988138	−	0.153571i	$-0.0490773\pi$
$798$	80525.7	+	49706.7i	0.000158462	+	9.78153e-5i
$799$	6.91793e8	+	3.99407e8i	1.35624	+	0.783024i
$800$	−4.93851e8	+	8.79159e8i	−0.964554	+	1.71711i
$801$	8.82994e8	+	5.62109e7i	1.71815	+	0.109376i
$802$	9.84387e7	+	1.69576e8i	0.190828	+	0.328731i
$803$	2.83823e8	−	4.91596e8i	0.548152	−	0.949428i
$804$	−8.39488e6	−	1.54943e7i	−0.0161527	−	0.0298129i
$805$	1.95544e7	−	1.12898e7i	0.0374850	−	0.0216420i
$806$	−6.18068e7	+	1.07638e8i	−0.118041	+	0.205570i
$807$	2.76528e7	−	8.69652e8i	0.0526161	−	1.65472i
$808$	3.01762e8	+	1.71387e8i	0.572045	+	0.324895i
$809$	8.09797e8			1.52943			0.764717	−	0.644366i	$-0.222879\pi$
$809$	8.09797e8			1.52943			0.764717	+	0.644366i	$0.222879\pi$
$810$	−8.43920e8	+	3.55620e8i	−1.58798	+	0.669163i
$811$	−5.38557e7			−0.100965			−0.0504823	−	0.998725i	$-0.516076\pi$
$811$	−5.38557e7			−0.100965			−0.0504823	+	0.998725i	$0.516076\pi$
$812$	1.35898e7	+	2.32839e7i	0.0253831	+	0.0434898i
$813$	−2.31282e7	+	7.27358e8i	−0.0430398	+	1.35356i
$814$	−5.41106e8	−	3.10708e8i	−1.00325	−	0.576075i
$815$	−2.92584e8	+	1.68924e8i	−0.540478	+	0.312045i
$816$	−4.69070e8	−	1.04866e7i	−0.863311	−	0.0193003i
$817$	1.96960e6	−	3.41144e6i	0.00361170	−	0.00625565i
$818$	−3.36804e8	−	5.80198e8i	−0.615344	−	1.06002i
$819$	−9.94557e6	−	633130.i	−0.0181041	−	0.00115250i
$820$	1.12562e9	+	6.42818e8i	2.04151	+	1.16586i
$821$	−1.67172e8	−	9.65169e7i	−0.302089	−	0.174411i	0.341292	−	0.939957i	$-0.389135\pi$
$821$	−1.67172e8	−	9.65169e7i	−0.302089	−	0.174411i	−0.643381	+	0.765546i	$0.722469\pi$
$822$	−1.89811e8	+	3.07498e8i	−0.341749	+	0.553639i
$823$	−1.75227e8	+	1.01167e8i	−0.314341	+	0.181485i	−0.648867	−	0.760902i	$-0.724757\pi$
$823$	−1.75227e8	+	1.01167e8i	−0.314341	+	0.181485i	0.334527	+	0.942386i	$0.391424\pi$
$824$	9.95713e7	−	5.84308e7i	0.177972	−	0.104438i
$825$	−3.57737e8	−	6.67771e8i	−0.637091	−	1.18923i
$826$	61964.0	+	2.62714e7i	0.000109951	+	0.0466169i
$827$	−7.78210e8			−1.37588			−0.687939	−	0.725768i	$-0.741485\pi$
$827$	−7.78210e8			−1.37588			−0.687939	+	0.725768i	$0.741485\pi$
$828$	2.87371e8	−	1.44079e8i	0.506235	−	0.253810i
$829$		−	1.43762e8i		−	0.252336i	−0.992009	−	0.126168i	$-0.959732\pi$
$829$		−	1.43762e8i		−	0.252336i	0.992009	−	0.126168i	$-0.0402679\pi$
$830$	2.50857e6	+	1.06358e9i	0.00438725	+	1.86010i
$831$	−1.39535e8	−	8.65872e7i	−0.243154	−	0.150887i
$832$	−2.02306e8	+	1.20650e8i	−0.351267	+	0.209487i
$833$	−2.49072e8	−	4.31406e8i	−0.430914	−	0.746365i
$834$	−2.25297e8	−	4.18178e8i	−0.388380	−	0.720881i
$835$	−3.44569e8	+	5.96811e8i	−0.591857	+	1.02513i
$836$	−833317.	+	1.45920e6i	−0.00142624	+	0.00249745i
$837$	3.09172e8	−	1.41134e8i	0.527259	−	0.240689i
$838$	−2.59071e8	−	4.46290e8i	−0.440237	−	0.758377i
$839$	4.37358e7	+	2.52509e7i	0.0740544	+	0.0427553i	0.536570	−	0.843856i	$-0.319720\pi$
$839$	4.37358e7	+	2.52509e7i	0.0740544	+	0.0427553i	−0.462516	+	0.886611i	$0.653053\pi$
$840$	4.52884e7	+	1.11935e6i	0.0764098	+	0.00188855i
$841$	8.59117e7	+	1.48803e8i	0.144432	+	0.250164i
$842$	6.47119e8	+	3.71582e8i	1.08405	+	0.622470i
$843$	1.60672e8	−	2.58924e8i	0.268200	−	0.432204i
$844$	−1.09336e8	−	1.87330e8i	−0.181860	−	0.311587i
$845$			8.65789e8i			1.43497i
$846$	−9.15609e8	−	6.06197e8i	−1.51216	−	1.00116i
$847$			1.43047e7i			0.0235412i
$848$	−6.10394e6	−	6.46968e8i	−0.0100097	−	1.06095i
$849$	1.26362e8	+	2.35874e8i	0.206487	+	0.385439i
$850$	−5.20084e8	+	9.05738e8i	−0.846869	+	1.47484i
$851$	−2.94705e8	−	5.10445e8i	−0.478189	−	0.828247i
$852$	−9.20039e6	+	3.39795e8i	−0.0148760	+	0.549413i
$853$	−7.94602e8	−	4.58764e8i	−1.28027	−	0.739166i	−0.303375	−	0.952871i	$-0.598113\pi$
$853$	−7.94602e8	−	4.58764e8i	−1.28027	−	0.739166i	−0.976898	+	0.213706i	$0.931447\pi$
$854$	−7.34687e6	−	1.26561e7i	−0.0117958	−	0.0203201i
$855$	4.05183e6	−	2.00760e6i	0.00648266	−	0.00321203i
$856$	3.21772e8	−	2.27684e6i	0.513012	−	0.00363003i
$857$	−3.89257e8	+	6.74213e8i	−0.618435	+	1.07116i	0.371336	+	0.928498i	$0.378900\pi$
$857$	−3.89257e8	+	6.74213e8i	−0.618435	+	1.07116i	−0.989771	+	0.142662i	$0.954434\pi$
$858$	5.20692e6	−	1.76885e8i	0.00824365	−	0.280046i
$859$	4.74249e8	+	8.21424e8i	0.748216	+	1.29595i	0.948677	+	0.316247i	$0.102423\pi$
$859$	4.74249e8	+	8.21424e8i	0.748216	+	1.29595i	−0.200460	+	0.979702i	$0.564244\pi$
$860$	−8.89558e6	−	1.88576e9i	−0.0139855	−	2.96477i
$861$	1.22753e6	−	3.86044e7i	0.00192319	−	0.0604822i
$862$	1.36174e6	+	5.77349e8i	0.00212604	+	0.901398i
$863$			4.40010e8i			0.684590i	0.939593	+	0.342295i	$0.111204\pi$
$863$			4.40010e8i			0.684590i	−0.939593	+	0.342295i	$0.888796\pi$
$864$	6.42722e8	+	5.38360e7i	0.996510	+	0.0834703i
$865$	4.49956e7			0.0695219
$866$	−3.46597e8	+	817487.i	−0.533669	+	0.00125871i
$867$	1.65661e8	+	5.26763e6i	0.254193	+	0.00808273i
$868$	−1.68121e7	+	79306.9i	−0.0257077	+	0.000121270i
$869$	−2.71582e8	+	1.56798e8i	−0.413849	+	0.238936i
$870$	1.28769e9	+	3.79055e7i	1.95549	+	0.0575632i
$871$	−7.93588e6	−	4.58178e6i	−0.0120099	−	0.00693394i
$872$	−1.58570e6	−	2.24099e8i	−0.00239151	−	0.337979i
$873$	5.28920e8	−	7.94808e8i	0.794963	−	1.19459i
$874$	−1.37278e6	+	796901.i	−0.00205621	+	0.00119363i
$875$	2.48205e7	−	4.29904e7i	0.0370499	−	0.0641723i
$876$	1.07543e9	+	2.91185e7i	1.59981	+	0.0433169i
$877$	1.23290e8	−	7.11818e7i	0.182781	−	0.105529i	−0.405818	−	0.913954i	$-0.633013\pi$
$877$	1.23290e8	−	7.11818e7i	0.182781	−	0.105529i	0.588599	+	0.808425i	$0.299680\pi$
$878$	−1.05749e8	−	6.07223e7i	−0.156241	−	0.0897149i
$879$	5.42805e8	−	2.90790e8i	0.799240	−	0.428167i
$880$	7.58926e6	+	8.04400e8i	0.0111366	+	1.18039i
$881$	−6.92935e8			−1.01336			−0.506681	−	0.862134i	$-0.669128\pi$
$881$	−6.92935e8			−1.01336			−0.506681	+	0.862134i	$0.669128\pi$
$882$	3.05468e8	+	6.12872e8i	0.445205	+	0.893231i
$883$	−4.51890e8			−0.656373			−0.328186	−	0.944613i	$-0.606437\pi$
$883$	−4.51890e8			−0.656373			−0.328186	+	0.944613i	$0.606437\pi$
$884$	−2.10711e8	+	1.22983e8i	−0.305022	+	0.178028i
$885$	1.06668e9	+	6.61920e8i	1.53889	+	0.954940i
$886$	4.42017e8	−	7.69783e8i	0.635533	−	1.10680i
$887$	−6.09733e8	+	3.52029e8i	−0.873713	+	0.504438i	−0.868580	−	0.495549i	$-0.834967\pi$
$887$	−6.09733e8	+	3.52029e8i	−0.873713	+	0.504438i	−0.00513250	+	0.999987i	$0.501634\pi$
$888$	2.92193e7	−	1.18220e9i	0.0417284	−	1.68831i
$889$	−2.43190e7	+	4.21218e7i	−0.0346132	+	0.0599517i
$890$	−1.80878e9	+	1.05000e9i	−2.56576	+	1.48942i
$891$	−2.93530e8	+	3.85522e8i	−0.414972	+	0.545025i
$892$	7.31769e8	+	4.17897e8i	1.03105	+	0.588810i
$893$	4.69569e6	+	2.71106e6i	0.00659395	+	0.00380702i
$894$	5.82055e8	−	3.13586e8i	0.814613	−	0.438879i
$895$	−1.95838e9	+	1.13067e9i	−2.73167	+	1.57713i
$896$	−2.78906e7	−	1.54944e7i	−0.0387734	−	0.0215403i
$897$	8.81394e7	−	1.42037e8i	0.122122	−	0.196799i
$898$	3.80344e8	−	897082.i	0.525228	−	0.00123881i
$899$	−4.78089e8			−0.658006
$900$	7.89769e8	−	1.19901e9i	1.08336	−	1.64473i
$901$		−	6.70139e8i		−	0.916200i
$902$	6.85847e8	−	1.61764e6i	0.934561	−	0.00220426i
$903$	−4.95306e7	+	2.65344e7i	−0.0672683	+	0.0360368i
$904$	1.14977e8	+	1.95932e8i	0.155635	+	0.265216i
$905$	9.43177e8	+	1.63363e9i	1.27247	+	2.20398i
$906$	−2.65261e8	−	1.63740e8i	−0.356689	−	0.220176i
$907$	−2.41795e8	+	4.18801e8i	−0.324060	+	0.561289i	−0.981322	−	0.192374i	$-0.938381\pi$
$907$	−2.41795e8	+	4.18801e8i	−0.324060	+	0.561289i	0.657262	+	0.753663i	$0.271715\pi$
$908$	5.73261e8	−	1.00382e9i	0.765763	−	1.34091i
$909$	−4.11359e8	−	2.73746e8i	−0.547683	−	0.364466i
$910$	2.03731e7	−	1.18266e7i	0.0270354	−	0.0156941i
$911$	−6.38833e8	−	3.68831e8i	−0.844953	−	0.487834i	0.0139918	−	0.999902i	$-0.495546\pi$
$911$	−6.38833e8	−	3.68831e8i	−0.844953	−	0.487834i	−0.858945	+	0.512068i	$0.828879\pi$
$912$	−3.18392e6	−	71180.1i	−0.00419737	−	9.38370e-5i
$913$	2.81375e8	+	4.87355e8i	0.369720	+	0.640373i
$914$	−2.35194e7	+	4.09595e7i	−0.0308026	+	0.0536434i
$915$	−6.98925e8	−	2.22241e7i	−0.912362	−	0.0290109i
$916$	8.50080e7	−	4.96155e7i	0.110605	−	0.0645552i
$917$			3.57596e7i			0.0463751i
$918$	6.65155e8	+	6.20397e7i	0.859795	+	0.0801939i
$919$		−	6.06795e7i		−	0.0781799i	−0.999236	−	0.0390900i	$-0.987554\pi$
$919$		−	6.06795e7i		−	0.0781799i	0.999236	−	0.0390900i	$-0.0124459\pi$
$920$	−3.75277e8	+	6.60752e8i	−0.481935	+	0.848545i
$921$	−3.49258e8	−	1.11055e7i	−0.447062	−	0.0142155i
$922$	−5.20667e8	−	2.98972e8i	−0.664305	−	0.381450i
$923$	8.83786e7	+	1.53076e8i	0.112394	+	0.194672i
$924$	2.10751e7	−	1.14186e7i	0.0267149	−	0.0144743i
$925$	−2.27977e9	−	1.31622e9i	−2.88048	−	1.66305i
$926$	5.99241e8	−	3.47859e8i	0.754690	−	0.438097i
$927$	−1.47292e8	+	7.29800e7i	−0.184901	+	0.0916146i
$928$	−7.91034e8	−	4.44349e8i	−0.989809	−	0.556007i
$929$	−5.21195e8	+	9.02736e8i	−0.650059	+	1.12594i	0.333049	+	0.942910i	$0.391923\pi$
$929$	−5.21195e8	+	9.02736e8i	−0.650059	+	1.12594i	−0.983108	+	0.183026i	$0.941411\pi$
$930$	−4.21982e8	+	6.83617e8i	−0.524620	+	0.849893i
$931$	−1.69063e6	−	2.92826e6i	−0.00209508	−	0.00362878i
$932$	−7.43280e8	+	3.50623e6i	−0.918131	+	0.00433104i
$933$	−5.71871e8	+	3.06361e8i	−0.704130	+	0.377215i
$934$	7.23462e8	−	1.70636e6i	0.887922	−	0.00209426i
$935$			8.33209e8i			1.01934i
$936$	2.99456e8	−	1.51023e8i	0.365179	−	0.184169i
$937$	−6.95539e8			−0.845479			−0.422740	−	0.906251i	$-0.638931\pi$
$937$	−6.95539e8			−0.845479			−0.422740	+	0.906251i	$0.638931\pi$
$938$	−2927.53	−	1.24121e6i	−3.54726e−6	−	0.00150396i
$939$	3.41151e8	−	5.49765e8i	0.412050	−	0.664019i
$940$	2.59566e9	−	1.22443e7i	3.12510	−	0.0147418i
$941$	−1.54943e8	+	8.94564e7i	−0.185953	+	0.107360i	−0.590087	−	0.807340i	$-0.700906\pi$
$941$	−1.54943e8	+	8.94564e7i	−0.185953	+	0.107360i	0.404134	+	0.914700i	$0.367573\pi$
$942$	6.00829e7	−	3.23701e7i	0.0718784	−	0.0387250i
$943$	5.61068e8	+	3.23933e8i	0.669084	+	0.386296i
$944$	−4.49271e8	−	7.61478e8i	−0.534063	−	0.905194i
$945$	−6.42096e7	−	6.14169e6i	−0.0760859	−	0.00727767i
$946$	−5.00925e8	−	8.62921e8i	−0.591697	−	1.01929i
$947$	−1.32653e8	+	2.29762e8i	−0.156195	+	0.270538i	−0.933494	−	0.358594i	$-0.883256\pi$
$947$	−1.32653e8	+	2.29762e8i	−0.156195	+	0.270538i	0.777298	+	0.629132i	$0.216590\pi$
$948$	−5.06478e8	−	3.10990e8i	−0.594478	−	0.365025i
$949$	4.84474e8	−	2.79711e8i	0.566855	−	0.327274i
$950$	−3.53018e6	+	6.14790e6i	−0.00411743	+	0.00717060i
$951$	3.08452e8	+	1.91407e8i	0.358630	+	0.222544i
$952$	−2.87355e7	−	1.63205e7i	−0.0333049	−	0.0189157i
$953$	2.87222e8			0.331848			0.165924	−	0.986139i	$-0.446939\pi$
$953$	2.87222e8			0.331848			0.165924	+	0.986139i	$0.446939\pi$
$954$	−5.63569e7	+	9.19487e8i	−0.0649085	+	1.05901i
$955$	2.25428e9			2.58820
$956$	1.22585e9	−	7.15476e8i	1.40302	−	0.818882i
$957$	6.00835e8	−	3.21878e8i	0.685519	−	0.367245i
$958$	−1.02313e9	−	5.87489e8i	−1.16368	−	0.668195i
$959$	−2.20423e7	+	1.27261e7i	−0.0249920	+	0.0144291i
$960$	−1.33357e9	+	7.38894e8i	−1.50731	+	0.835157i
$961$	−2.94681e8	+	5.10402e8i	−0.332033	+	0.575099i
$962$	−3.08719e8	−	5.31816e8i	−0.346767	−	0.597360i
$963$	−4.57234e8	−	2.91073e7i	−0.511988	−	0.0325929i
$964$	−5.72693e8	+	1.00283e9i	−0.639279	+	1.11943i
$965$	−1.36294e8	−	7.86892e7i	−0.151668	−	0.0875656i
$966$	2.26324e7	+	666224.i	0.0251073	+	0.000739076i
$967$	4.93560e8	−	2.84957e8i	0.545834	−	0.315137i	−0.201606	−	0.979467i	$-0.564616\pi$
$967$	4.93560e8	−	2.84957e8i	0.545834	−	0.315137i	0.747440	+	0.664329i	$0.231283\pi$
$968$	−2.43648e8	−	4.15198e8i	−0.268619	−	0.457751i
$969$	−3.29696e6	−	104835.i	−0.00362361	−	0.000115222i
$970$	5.32279e6	+	2.25675e9i	0.00583209	+	2.47268i
$971$	1.29879e9			1.41867			0.709335	−	0.704871i	$-0.248995\pi$
$971$	1.29879e9			1.41867			0.709335	+	0.704871i	$0.248995\pi$
$972$	−9.07431e8	−	1.41061e8i	−0.988132	−	0.153606i
$973$		−	3.34567e7i		−	0.0363199i
$974$	−509600.	−	2.16060e8i	−0.000551509	−	0.233828i
$975$	2.37275e7	−	7.46205e8i	0.0255999	−	0.805090i
$976$	4.28812e8	+	2.42210e8i	0.461230	+	0.260521i
$977$	7.21394e7	+	1.24949e8i	0.0773551	+	0.133983i	0.902108	−	0.431510i	$-0.142019\pi$
$977$	7.21394e7	+	1.24949e8i	0.0773551	+	0.133983i	−0.824753	+	0.565493i	$0.808686\pi$
$978$	−3.38639e8	−	9.96842e6i	−0.362010	−	0.0106564i
$979$	−5.53300e8	+	9.58343e8i	−0.589674	+	1.02135i
$980$	−1.40563e9	−	8.02721e8i	−1.49345	−	0.852877i
$981$	−2.02718e7	+	3.18441e8i	−0.0214726	+	0.337305i
$982$	8.22958e8	+	1.41767e9i	0.869047	+	1.49707i
$983$	9.49643e8	+	5.48277e8i	0.999769	+	0.577217i	0.908180	−	0.418580i	$-0.137472\pi$
$983$	9.49643e8	+	5.48277e8i	0.999769	+	0.577217i	0.0915893	+	0.995797i	$0.470805\pi$
$984$	6.21908e8	+	1.14141e9i	0.652741	+	1.19800i
$985$	−1.96834e8	−	3.40926e8i	−0.205964	−	0.356740i
$986$	−8.14949e8	−	4.67952e8i	−0.850158	−	0.488169i
$987$	−3.65234e7	−	6.81765e7i	−0.0379856	−	0.0709060i
$988$	−1.43025e6	+	834775.i	−0.00148300	+	0.000865563i
$989$		−	9.42519e8i		−	0.974319i
$990$	7.00707e7	−	1.14323e9i	0.0722155	−	1.17823i
$991$		−	1.53202e9i		−	1.57414i	−0.616865	−	0.787069i	$-0.711598\pi$
$991$		−	1.53202e9i		−	1.57414i	0.616865	−	0.787069i	$-0.288402\pi$
$992$	4.86625e8	−	2.88658e8i	0.498494	−	0.295698i
$993$	−6.73338e7	+	1.08508e8i	−0.0687678	+	0.110819i
$994$	−1.19220e7	+	2.07625e7i	−0.0121392	+	0.0211408i
$995$	−7.15733e8	−	1.23969e9i	−0.726577	−	1.25847i
$996$	−5.58074e8	+	9.08878e8i	−0.564825	+	0.919872i
$997$	8.19402e8	+	4.73082e8i	0.826821	+	0.477365i	0.852763	−	0.522298i	$-0.174925\pi$
$997$	8.19402e8	+	4.73082e8i	0.826821	+	0.477365i	−0.0259418	+	0.999663i	$0.508258\pi$
$998$	−4.41475e8	−	7.60509e8i	−0.444135	−	0.765091i
$999$	−1.60321e8	+	1.67611e9i	−0.160803	+	1.68115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.1	✓	136
8.3	odd	2	inner	72.7.p.b.43.46	yes	136
9.4	even	3	inner	72.7.p.b.67.46	yes	136
72.67	odd	6	inner	72.7.p.b.67.1	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.1	✓	136	1.1	even	1	trivial
72.7.p.b.43.46	yes	136	8.3	odd	2	inner
72.7.p.b.67.1	yes	136	72.67	odd	6	inner
72.7.p.b.67.46	yes	136	9.4	even	3	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.99998 + 0.0188688i) q^{2} +(-26.9864 - 0.858100i) q^{3} +(63.9993 - 0.301900i) q^{4} +(186.544 - 107.701i) q^{5} +(215.906 + 6.35558i) q^{6} +(13.1755 + 7.60688i) q^{7} +(-511.987 + 3.62278i) q^{8} +(727.527 + 46.3140i) q^{9} +O(q^{10})\)	\(q+(-7.99998 + 0.0188688i) q^{2} +(-26.9864 - 0.858100i) q^{3} +(63.9993 - 0.301900i) q^{4} +(186.544 - 107.701i) q^{5} +(215.906 + 6.35558i) q^{6} +(13.1755 + 7.60688i) q^{7} +(-511.987 + 3.62278i) q^{8} +(727.527 + 46.3140i) q^{9} +(-1490.31 + 865.125i) q^{10} +(-455.881 + 789.610i) q^{11} +(-1727.37 - 46.7706i) q^{12} +(-778.170 + 449.277i) q^{13} +(-105.547 - 60.6062i) q^{14} +(-5126.55 + 2746.38i) q^{15} +(4095.82 - 38.6428i) q^{16} +4242.51 q^{17} +(-5821.08 - 356.783i) q^{18} +28.7969 q^{19} +(11906.1 - 6949.10i) q^{20} +(-349.031 - 216.588i) q^{21} +(3632.14 - 6325.46i) q^{22} +(5967.04 - 3445.07i) q^{23} +(13819.8 + 341.571i) q^{24} +(15386.5 - 26650.2i) q^{25} +(6216.87 - 3608.89i) q^{26} +(-19593.6 - 1874.14i) q^{27} +(845.519 + 482.857i) q^{28} +(23978.8 + 13844.2i) q^{29} +(40960.5 - 22067.7i) q^{30} +(-14953.5 + 8633.39i) q^{31} +(-32765.7 + 386.424i) q^{32} +(12980.1 - 20917.5i) q^{33} +(-33940.0 + 80.0510i) q^{34} +3277.07 q^{35} +(46575.2 + 2744.42i) q^{36} -85544.0i q^{37} +(-230.375 + 0.543364i) q^{38} +(21385.5 - 11456.6i) q^{39} +(-95117.7 + 55817.3i) q^{40} +(47013.9 + 81430.5i) q^{41} +(2796.33 + 1726.11i) q^{42} +(68396.1 - 118466. i) q^{43} +(-28937.7 + 50672.1i) q^{44} +(140704. - 69715.8i) q^{45} +(-47671.2 + 27673.1i) q^{46} +(163062. + 94144.0i) q^{47} +(-110564. - 2471.79i) q^{48} +(-58708.8 - 101687. i) q^{49} +(-122589. + 213491. i) q^{50} +(-114490. - 3640.50i) q^{51} +(-49666.7 + 28988.3i) q^{52} -157958. i q^{53} +(156784. + 14623.4i) q^{54} +196396. i q^{55} +(-6773.24 - 3846.89i) q^{56} +(-777.125 - 24.7107i) q^{57} +(-192091. - 110301. i) q^{58} +(-107927. - 186934. i) q^{59} +(-327266. + 177314. i) q^{60} +(104128. + 60118.3i) q^{61} +(119465. - 69349.1i) q^{62} +(9233.23 + 6144.42i) q^{63} +(262118. - 3709.64i) q^{64} +(-96775.1 + 167619. i) q^{65} +(-103446. + 167584. i) q^{66} +(5099.06 + 8831.83i) q^{67} +(271517. - 1280.81i) q^{68} +(-163985. + 87849.7i) q^{69} +(-26216.5 + 61.8344i) q^{70} -196713. i q^{71} +(-372652. - 21076.5i) q^{72} -622581. q^{73} +(1614.11 + 684350. i) q^{74} +(-438094. + 705989. i) q^{75} +(1842.98 - 8.69379i) q^{76} +(-12012.9 + 6935.67i) q^{77} +(-170867. + 92056.0i) q^{78} +(297865. + 171972. i) q^{79} +(759887. - 448332. i) q^{80} +(527151. + 67389.4i) q^{81} +(-377647. - 650555. i) q^{82} +(308605. - 534520. i) q^{83} +(-22403.1 - 13756.1i) q^{84} +(791412. - 456922. i) q^{85} +(-544932. + 949012. i) q^{86} +(-635222. - 394181. i) q^{87} +(230545. - 405922. i) q^{88} +1.21369e6 q^{89} +(-1.12431e6 + 560380. i) q^{90} -13670.4 q^{91} +(380846. - 222284. i) q^{92} +(410948. - 220152. i) q^{93} +(-1.30627e6 - 750073. i) q^{94} +(5371.88 - 3101.46i) q^{95} +(884559. + 17688.1i) q^{96} +(654810. - 1.13416e6i) q^{97} +(471588. + 812383. i) q^{98} +(-368236. + 553349. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Introduction

L-functions

Modular forms

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Database

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