LMFDB - Embedded newform 21.7.h.a.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88516 + 1.66575i) q^{2} +(16.8223 - 21.1189i) q^{3} +(-26.4506 - 45.8137i) q^{4} +(-166.359 - 96.0474i) q^{5} +(83.7139 - 32.9098i) q^{6} +(157.090 + 304.913i) q^{7} -389.456i q^{8} +(-163.020 - 710.539i) q^{9} +O(q^{10})$	\(q+(2.88516 + 1.66575i) q^{2} +(16.8223 - 21.1189i) q^{3} +(-26.4506 - 45.8137i) q^{4} +(-166.359 - 96.0474i) q^{5} +(83.7139 - 32.9098i) q^{6} +(157.090 + 304.913i) q^{7} -389.456i q^{8} +(-163.020 - 710.539i) q^{9} +(-319.982 - 554.224i) q^{10} +(750.813 - 433.482i) q^{11} +(-1412.50 - 212.085i) q^{12} +3412.13 q^{13} +(-54.6774 + 1141.39i) q^{14} +(-4826.96 + 1897.59i) q^{15} +(-1044.10 + 1808.44i) q^{16} +(2065.25 - 1192.37i) q^{17} +(713.242 - 2321.57i) q^{18} +(-1295.70 + 2244.22i) q^{19} +10162.0i q^{20} +(9082.05 + 1811.76i) q^{21} +2888.29 q^{22} +(-6492.91 - 3748.68i) q^{23} +(-8224.89 - 6551.55i) q^{24} +(10637.7 + 18425.1i) q^{25} +(9844.55 + 5683.75i) q^{26} +(-17748.2 - 8510.11i) q^{27} +(9814.06 - 15262.0i) q^{28} -24538.1i q^{29} +(-17087.5 - 2565.66i) q^{30} +(10218.4 + 17698.7i) q^{31} +(-27610.6 + 15941.0i) q^{32} +(3475.73 - 23148.5i) q^{33} +7944.77 q^{34} +(3152.71 - 65813.1i) q^{35} +(-28240.5 + 26262.7i) q^{36} +(33989.3 - 58871.2i) q^{37} +(-7476.62 + 4316.63i) q^{38} +(57400.0 - 72060.6i) q^{39} +(-37406.2 + 64789.5i) q^{40} +87649.0i q^{41} +(23185.2 + 20355.6i) q^{42} +11230.1 q^{43} +(-39718.8 - 22931.7i) q^{44} +(-41125.7 + 133862. i) q^{45} +(-12488.7 - 21631.1i) q^{46} +(105944. + 61166.8i) q^{47} +(20628.1 + 52472.4i) q^{48} +(-68294.4 + 95797.5i) q^{49} +70879.0i q^{50} +(9560.63 - 63674.4i) q^{51} +(-90252.8 - 156322. i) q^{52} +(145009. - 83721.1i) q^{53} +(-37030.7 - 54117.1i) q^{54} -166539. q^{55} +(118750. - 61179.6i) q^{56} +(25598.9 + 65116.9i) q^{57} +(40874.3 - 70796.4i) q^{58} +(-139071. + 80292.8i) q^{59} +(214611. + 170949. i) q^{60} +(19933.4 - 34525.7i) q^{61} +68084.8i q^{62} +(191044. - 161325. i) q^{63} +27430.2 q^{64} +(-567639. - 327726. i) q^{65} +(48587.7 - 60997.6i) q^{66} +(36908.0 + 63926.6i) q^{67} +(-109254. - 63077.9i) q^{68} +(-188394. + 74061.9i) q^{69} +(118724. - 184630. i) q^{70} -9292.90i q^{71} +(-276723. + 63488.9i) q^{72} +(-78094.7 - 135264. i) q^{73} +(196129. - 113235. i) q^{74} +(568069. + 85294.9i) q^{75} +137088. q^{76} +(250119. + 160836. i) q^{77} +(285643. - 112293. i) q^{78} +(-116864. + 202414. i) q^{79} +(347391. - 200566. i) q^{80} +(-478290. + 231663. i) q^{81} +(-146001. + 252881. i) q^{82} +872261. i q^{83} +(-157222. - 464005. i) q^{84} -458097. q^{85} +(32400.8 + 18706.6i) q^{86} +(-518219. - 412788. i) q^{87} +(-168822. - 292408. i) q^{88} +(-182193. - 105189. i) q^{89} +(-341635. + 317709. i) q^{90} +(536012. + 1.04040e6i) q^{91} +396619. i q^{92} +(545674. + 81932.4i) q^{93} +(203777. + 352952. i) q^{94} +(431104. - 248898. i) q^{95} +(-127817. + 851272. i) q^{96} +1.18735e6 q^{97} +(-356615. + 162630. i) q^{98} +(-430403. - 462816. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.88516	+	1.66575i	0.360645	+	0.208219i	0.669364	−	0.742935i	$-0.266567\pi$
$2$	2.88516	+	1.66575i	0.360645	+	0.208219i	−0.308719	+	0.951153i	$0.599900\pi$
$3$	16.8223	−	21.1189i	0.623049	−	0.782183i
$3$	16.8223	−	21.1189i	0.623049	−	0.782183i
$4$	−26.4506	−	45.8137i	−0.413290	−	0.715839i
$5$	−166.359	−	96.0474i	−1.33087	−	0.768379i	−0.345439	−	0.938441i	$-0.612270\pi$
$5$	−166.359	−	96.0474i	−1.33087	−	0.768379i	−0.985433	+	0.170062i	$0.945603\pi$
$6$	83.7139	−	32.9098i	0.387564	−	0.152360i
$7$	157.090	+	304.913i	0.457989	+	0.888958i
$7$	157.090	+	304.913i	0.457989	+	0.888958i
$8$		−	389.456i		−	0.760656i
$9$	−163.020	−	710.539i	−0.223621	−	0.974676i
$10$	−319.982	−	554.224i	−0.319982	−	0.554224i
$11$	750.813	−	433.482i	0.564097	−	0.325681i	−0.190692	−	0.981650i	$-0.561073\pi$
$11$	750.813	−	433.482i	0.564097	−	0.325681i	0.754788	+	0.655969i	$0.227740\pi$
$12$	−1412.50	−	212.085i	−0.817417	−	0.122734i
$13$	3412.13			1.55309			0.776543	−	0.630064i	$-0.216971\pi$
$13$	3412.13			1.55309			0.776543	+	0.630064i	$0.216971\pi$
$14$	−54.6774	+	1141.39i	−0.0199262	+	0.415960i
$15$	−4826.96	+	1897.59i	−1.43021	+	0.562248i
$16$	−1044.10	+	1808.44i	−0.254908	+	0.441513i
$17$	2065.25	−	1192.37i	0.420364	−	0.242697i	−0.274869	−	0.961482i	$-0.588634\pi$
$17$	2065.25	−	1192.37i	0.420364	−	0.242697i	0.695233	+	0.718784i	$0.255301\pi$
$18$	713.242	−	2321.57i	0.122298	−	0.398074i
$19$	−1295.70	+	2244.22i	−0.188906	+	0.327194i	−0.944886	−	0.327401i	$-0.893827\pi$
$19$	−1295.70	+	2244.22i	−0.188906	+	0.327194i	0.755980	+	0.654595i	$0.227161\pi$
$20$			10162.0i			1.27025i
$21$	9082.05	+	1811.76i	0.980677	+	0.195633i
$22$	2888.29			0.271252
$23$	−6492.91	−	3748.68i	−0.533649	−	0.308103i	0.208852	−	0.977947i	$-0.433027\pi$
$23$	−6492.91	−	3748.68i	−0.533649	−	0.308103i	−0.742501	+	0.669845i	$0.766361\pi$
$24$	−8224.89	−	6551.55i	−0.594972	−	0.473925i
$25$	10637.7	+	18425.1i	0.680813	+	1.17920i
$26$	9844.55	+	5683.75i	0.560113	+	0.323381i
$27$	−17748.2	−	8510.11i	−0.901702	−	0.432358i
$28$	9814.06	−	15262.0i	0.447069	−	0.695244i
$29$		−	24538.1i		−	1.00611i	−0.864253	−	0.503057i	$-0.832209\pi$
$29$		−	24538.1i		−	1.00611i	0.864253	−	0.503057i	$-0.167791\pi$
$30$	−17087.5	−	2565.66i	−0.632869	−	0.0950246i
$31$	10218.4	+	17698.7i	0.343001	+	0.594096i	0.984989	−	0.172619i	$-0.0552231\pi$
$31$	10218.4	+	17698.7i	0.343001	+	0.594096i	−0.641987	+	0.766715i	$0.721890\pi$
$32$	−27610.6	+	15941.0i	−0.842609	+	0.486481i
$33$	3475.73	−	23148.5i	0.0967172	−	0.644142i
$34$	7944.77			0.202136
$35$	3152.71	−	65813.1i	0.0735326	−	1.53500i
$36$	−28240.5	+	26262.7i	−0.605291	+	0.562901i
$37$	33989.3	−	58871.2i	0.671023	−	1.16225i	−0.306591	−	0.951841i	$-0.599188\pi$
$37$	33989.3	−	58871.2i	0.671023	−	1.16225i	0.977614	−	0.210405i	$-0.0674782\pi$
$38$	−7476.62	+	4316.63i	−0.136256	+	0.0786673i
$39$	57400.0	−	72060.6i	0.967649	−	1.21480i
$40$	−37406.2	+	64789.5i	−0.584472	+	1.01234i
$41$			87649.0i			1.27173i	0.771800	+	0.635866i	$0.219357\pi$
$41$			87649.0i			1.27173i	−0.771800	+	0.635866i	$0.780643\pi$
$42$	23185.2	+	20355.6i	0.312942	+	0.274749i
$43$	11230.1			0.141247			0.0706236	−	0.997503i	$-0.477501\pi$
$43$	11230.1			0.141247			0.0706236	+	0.997503i	$0.477501\pi$
$44$	−39718.8	−	22931.7i	−0.466271	−	0.269202i
$45$	−41125.7	+	133862.i	−0.451310	+	1.46899i
$46$	−12488.7	−	21631.1i	−0.128305	−	0.222231i
$47$	105944.	+	61166.8i	1.02043	+	0.589145i	0.914228	−	0.405200i	$-0.132798\pi$
$47$	105944.	+	61166.8i	1.02043	+	0.589145i	0.106200	+	0.994345i	$0.466132\pi$
$48$	20628.1	+	52472.4i	0.186524	+	0.474468i
$49$	−68294.4	+	95797.5i	−0.580493	+	0.814265i
$50$			70879.0i			0.567032i
$51$	9560.63	−	63674.4i	0.0720736	−	0.480014i
$52$	−90252.8	−	156322.i	−0.641875	−	1.11176i
$53$	145009.	−	83721.1i	0.974021	−	0.562351i	0.0735610	−	0.997291i	$-0.476564\pi$
$53$	145009.	−	83721.1i	0.974021	−	0.562351i	0.900460	+	0.434940i	$0.143230\pi$
$54$	−37030.7	−	54117.1i	−0.235169	−	0.343679i
$55$	−166539.			−1.00099
$56$	118750.	−	61179.6i	0.676191	−	0.348372i
$57$	25598.9	+	65116.9i	0.138228	+	0.351617i
$58$	40874.3	−	70796.4i	0.209492	−	0.362850i
$59$	−139071.	+	80292.8i	−0.677144	+	0.390949i	−0.798778	−	0.601626i	$-0.794520\pi$
$59$	−139071.	+	80292.8i	−0.677144	+	0.390949i	0.121634	+	0.992575i	$0.461187\pi$
$60$	214611.	+	170949.i	0.993571	+	0.791430i
$61$	19933.4	−	34525.7i	0.0878198	−	0.152108i	−0.818769	−	0.574122i	$-0.805343\pi$
$61$	19933.4	−	34525.7i	0.0878198	−	0.152108i	0.906589	+	0.422014i	$0.138677\pi$
$62$			68084.8i			0.285677i
$63$	191044.	−	161325.i	0.764031	−	0.645180i
$64$	27430.2			0.104638
$65$	−567639.	−	327726.i	−2.06696	−	1.19336i
$66$	48587.7	−	60997.6i	0.169003	−	0.212168i
$67$	36908.0	+	63926.6i	0.122715	+	0.212548i	0.920837	−	0.389947i	$-0.127507\pi$
$67$	36908.0	+	63926.6i	0.122715	+	0.212548i	−0.798123	+	0.602495i	$0.794173\pi$
$68$	−109254.	−	63077.9i	−0.347465	−	0.200609i
$69$	−188394.	+	74061.9i	−0.573482	+	0.225449i
$70$	118724.	−	184630.i	0.346134	−	0.538279i
$71$		−	9292.90i		−	0.0259643i	−0.999916	−	0.0129821i	$-0.995868\pi$
$71$		−	9292.90i		−	0.0259643i	0.999916	−	0.0129821i	$-0.00413246\pi$
$72$	−276723.	+	63488.9i	−0.741393	+	0.170098i
$73$	−78094.7	−	135264.i	−0.200749	−	0.347707i	0.748021	−	0.663675i	$-0.231004\pi$
$73$	−78094.7	−	135264.i	−0.200749	−	0.347707i	−0.948770	+	0.315968i	$0.897671\pi$
$74$	196129.	−	113235.i	0.484002	−	0.279439i
$75$	568069.	+	85294.9i	1.34653	+	0.202180i
$76$	137088.			0.312291
$77$	250119.	+	160836.i	0.547867	+	0.352300i
$78$	285643.	−	112293.i	0.601921	−	0.236629i
$79$	−116864.	+	202414.i	−0.237027	+	0.410543i	−0.959860	−	0.280480i	$-0.909506\pi$
$79$	−116864.	+	202414.i	−0.237027	+	0.410543i	0.722833	+	0.691023i	$0.242840\pi$
$80$	347391.	−	200566.i	0.678499	−	0.391731i
$81$	−478290.	+	231663.i	−0.899988	+	0.435916i
$82$	−146001.	+	252881.i	−0.264798	+	0.458644i
$83$			872261.i			1.52550i	0.646693	+	0.762750i	$0.276151\pi$
$83$			872261.i			1.52550i	−0.646693	+	0.762750i	$0.723849\pi$
$84$	−157222.	−	464005.i	−0.265262	−	0.782861i
$85$	−458097.			−0.745935
$86$	32400.8	+	18706.6i	0.0509401	+	0.0294103i
$87$	−518219.	−	412788.i	−0.786965	−	0.626858i
$88$	−168822.	−	292408.i	−0.247731	−	0.429083i
$89$	−182193.	−	105189.i	−0.258441	−	0.149211i	0.365182	−	0.930936i	$-0.381007\pi$
$89$	−182193.	−	105189.i	−0.258441	−	0.149211i	−0.623623	+	0.781725i	$0.714340\pi$
$90$	−341635.	+	317709.i	−0.468635	+	0.435815i
$91$	536012.	+	1.04040e6i	0.711296	+	1.38063i
$92$			396619.i			0.509343i
$93$	545674.	+	81932.4i	0.678398	+	0.101861i
$94$	203777.	+	352952.i	0.245342	+	0.424944i
$95$	431104.	−	248898.i	0.502818	−	0.290302i
$96$	−127817.	+	851272.i	−0.144470	+	0.962176i
$97$	1.18735e6			1.30096			0.650479	−	0.759524i	$-0.274568\pi$
$97$	1.18735e6			1.30096			0.650479	+	0.759524i	$0.274568\pi$
$98$	−356615.	+	162630.i	−0.378897	+	0.172791i
$99$	−430403.	−	462816.i	−0.443578	−	0.476982i
$100$	562747.	−	974706.i	0.562747	−	0.974706i
$101$	−198035.	+	114336.i	−0.192211	+	0.110973i	−0.593017	−	0.805190i	$-0.702063\pi$
$101$	−198035.	+	114336.i	−0.192211	+	0.110973i	0.400806	+	0.916163i	$0.368730\pi$
$102$	133649.	−	167785.i	0.125941	−	0.158108i
$103$	26909.7	−	46608.9i	0.0246262	−	0.0426538i	−0.853450	−	0.521175i	$-0.825494\pi$
$103$	26909.7	−	46608.9i	0.0246262	−	0.0426538i	0.878076	+	0.478521i	$0.158827\pi$
$104$		−	1.32887e6i		−	1.18136i
$105$	−1.33687e6	−	1.17371e6i	−1.15484	−	1.01389i
$106$	557833.			0.468368
$107$	340687.	+	196696.i	0.278102	+	0.160562i	0.632564	−	0.774508i	$-0.282003\pi$
$107$	340687.	+	196696.i	0.278102	+	0.160562i	−0.354462	+	0.935071i	$0.615336\pi$
$108$	79570.0	+	1.03821e6i	0.0631653	+	0.824163i
$109$	−100478.	−	174032.i	−0.0775871	−	0.134385i	0.824621	−	0.565685i	$-0.191388\pi$
$109$	−100478.	−	174032.i	−0.0775871	−	0.134385i	−0.902208	+	0.431300i	$0.858055\pi$
$110$	−480492.	−	277412.i	−0.361001	−	0.208424i
$111$	−671519.	−	1.70817e6i	−0.491009	−	1.24900i
$112$	−715433.	−	34272.1i	−0.509231	−	0.0243942i
$113$		−	1.17250e6i		−	0.812599i	−0.913740	−	0.406299i	$-0.866819\pi$
$113$		−	1.17250e6i		−	0.812599i	0.913740	−	0.406299i	$-0.133181\pi$
$114$	−34611.4	+	230514.i	−0.0233617	+	0.155590i
$115$	720103.	+	1.24725e6i	0.473479	+	0.820090i
$116$	−1.12418e6	+	649047.i	−0.720216	+	0.415817i
$117$	−556244.	−	2.42445e6i	−0.347302	−	1.51376i
$118$	−534990.			−0.325612
$119$	688000.	+	442411.i	0.408270	+	0.262534i
$120$	739026.	+	1.87989e6i	0.427677	+	1.08790i
$121$	−509968.	+	883290.i	−0.287863	+	0.498594i
$122$	115022.	−	66408.1i	0.0633436	−	0.0365714i
$123$	1.85105e6	+	1.47446e6i	0.994727	+	0.792351i
$124$	540563.	−	936282.i	0.283518	−	0.491068i
$125$		−	1.08542e6i		−	0.555733i
$126$	819919.	−	147219.i	0.409882	−	0.0735957i
$127$	−1.58681e6			−0.774667			−0.387334	−	0.921940i	$-0.626604\pi$
$127$	−1.58681e6			−0.774667			−0.387334	+	0.921940i	$0.626604\pi$
$128$	1.84622e6	+	1.06592e6i	0.880346	+	0.508268i
$129$	188917.	−	237169.i	0.0880039	−	0.110481i
$130$	−1.09182e6	−	1.89109e6i	−0.496959	−	0.860759i
$131$	1.12008e6	+	646680.i	0.498237	+	0.287657i	0.727985	−	0.685593i	$-0.240457\pi$
$131$	1.12008e6	+	646680.i	0.498237	+	0.287657i	−0.229748	+	0.973250i	$0.573790\pi$
$132$	−1.15246e6	+	453056.i	−0.501075	+	0.196984i
$133$	−887834.	−	42530.9i	−0.377378	−	0.0180779i
$134$			245918.i			0.102206i
$135$	2.13520e6	+	3.12040e6i	0.867834	+	1.26826i
$136$	−464376.	−	804323.i	−0.184609	−	0.319752i
$137$	−3.98018e6	+	2.29796e6i	−1.54790	+	0.893678i	−0.549593	+	0.835433i	$0.685217\pi$
$137$	−3.98018e6	+	2.29796e6i	−1.54790	+	0.893678i	−0.998302	+	0.0582450i	$0.981450\pi$
$138$	−666915.	−	100137.i	−0.253766	−	0.0381027i
$139$	3.55130e6			1.32234			0.661169	−	0.750237i	$-0.270061\pi$
$139$	3.55130e6			1.32234			0.661169	+	0.750237i	$0.270061\pi$
$140$	−3.09853e6	+	1.59636e6i	−1.12920	+	0.581762i
$141$	3.07400e6	−	1.20846e6i	1.09660	−	0.431096i
$142$	15479.6	−	26811.5i	0.00540624	−	0.00936389i
$143$	2.56187e6	−	1.47910e6i	0.876091	−	0.505811i
$144$	1.45517e6	+	447064.i	0.487335	+	0.149721i
$145$	−2.35682e6	+	4.08214e6i	−0.773077	+	1.33901i
$146$		−	520344.i		−	0.167198i
$147$	874273.	+	3.05384e6i	0.275229	+	0.961379i
$148$	−3.59615e6			−1.10931
$149$	2.03237e6	+	1.17339e6i	0.614391	+	0.354719i	0.774682	−	0.632351i	$-0.217910\pi$
$149$	2.03237e6	+	1.17339e6i	0.614391	+	0.354719i	−0.160291	+	0.987070i	$0.551243\pi$
$150$	1.49689e6	+	1.19235e6i	0.443523	+	0.353288i
$151$	−2.36893e6	−	4.10311e6i	−0.688053	−	1.19174i	−0.972467	−	0.233041i	$-0.925132\pi$
$151$	−2.36893e6	−	4.10311e6i	−0.688053	−	1.19174i	0.284414	−	0.958702i	$-0.408201\pi$
$152$	874026.	+	504619.i	0.248882	+	0.143692i
$153$	−1.18390e6	−	1.27306e6i	−0.330554	−	0.355447i
$154$	453721.	+	880675.i	0.124230	+	0.241131i
$155$		−	3.92579e6i		−	1.05422i
$156$	−4.81963e6	−	723661.i	−1.26952	−	0.190617i
$157$	−2.81197e6	−	4.87048e6i	−0.726627	−	1.25856i	−0.958301	−	0.285762i	$-0.907753\pi$
$157$	−2.81197e6	−	4.87048e6i	−0.726627	−	1.25856i	0.231673	−	0.972794i	$-0.425580\pi$
$158$	−674341.	+	389331.i	−0.170965	+	0.0987069i
$159$	671289.	−	4.47083e6i	0.167001	−	1.11223i
$160$	6.12437e6			1.49521
$161$	123049.	−	2.56865e6i	0.0294849	−	0.615499i
$162$	−1.76584e6	−	128325.i	−0.415342	−	0.0301833i
$163$	870496.	−	1.50774e6i	0.201004	−	0.348148i	−0.747848	−	0.663869i	$-0.768913\pi$
$163$	870496.	−	1.50774e6i	0.201004	−	0.348148i	0.948852	+	0.315721i	$0.102246\pi$
$164$	4.01553e6	−	2.31837e6i	0.910356	−	0.525594i
$165$	−2.80158e6	+	3.51713e6i	−0.623664	+	0.782955i
$166$	−1.45297e6	+	2.51661e6i	−0.317637	+	0.550164i
$167$			2.55870e6i			0.549377i	0.961533	+	0.274689i	$0.0885748\pi$
$167$			2.55870e6i			0.549377i	−0.961533	+	0.274689i	$0.911425\pi$
$168$	705600.	−	3.53706e6i	0.148809	−	0.745958i
$169$	6.81583e6			1.41208
$170$	−1.32168e6	−	763075.i	−0.269018	−	0.155317i
$171$	1.80583e6	+	554795.i	0.361151	+	0.110954i
$172$	−297044.	−	514495.i	−0.0583761	−	0.101110i
$173$	−5.23650e6	−	3.02330e6i	−1.01135	−	0.583905i	−0.0997657	−	0.995011i	$-0.531809\pi$
$173$	−5.23650e6	−	3.02330e6i	−1.01135	−	0.583905i	−0.911588	+	0.411106i	$0.865143\pi$
$174$	−807544.	−	2.05418e6i	−0.153292	−	0.389934i
$175$	−3.94695e6	+	6.13797e6i	−0.736458	+	1.14528i
$176$			1.81040e6i			0.332074i
$177$	−643801.	+	4.28775e6i	−0.116100	+	0.773231i
$178$	−350437.	−	606974.i	−0.0621369	−	0.107624i
$179$	5.14190e6	−	2.96868e6i	0.896530	−	0.517612i	0.0204569	−	0.999791i	$-0.493488\pi$
$179$	5.14190e6	−	2.96868e6i	0.896530	−	0.517612i	0.876073	+	0.482179i	$0.160155\pi$
$180$	7.22052e6	−	1.65661e6i	1.23809	−	0.284055i
$181$	−1.58959e6			−0.268070			−0.134035	−	0.990977i	$-0.542794\pi$
$181$	−1.58959e6			−0.268070			−0.134035	+	0.990977i	$0.542794\pi$
$182$	−186567.	+	3.89459e6i	−0.0309471	+	0.646022i
$183$	−393820.	−	1.00178e6i	−0.0642606	−	0.163462i
$184$	−1.45995e6	+	2.52870e6i	−0.234360	+	0.405923i
$185$	−1.13089e7	+	6.52917e6i	−1.78609	+	1.03120i
$186$	1.43788e6	+	1.14534e6i	0.223452	+	0.177991i
$187$	1.03374e6	−	1.79050e6i	0.158084	−	0.273810i
$188$		−	6.47158e6i		−	0.973950i
$189$	−193227.	−	6.74850e6i	−0.0286208	−	0.999590i
$190$	1.65840e6			0.241785
$191$	2.04587e6	+	1.18118e6i	0.293615	+	0.169519i	0.639571	−	0.768732i	$-0.279112\pi$
$191$	2.04587e6	+	1.18118e6i	0.293615	+	0.169519i	−0.345956	+	0.938251i	$0.612445\pi$
$192$	461439.	−	579296.i	0.0651945	−	0.0818459i
$193$	1.66782e6	+	2.88875e6i	0.231994	+	0.401826i	0.958395	−	0.285446i	$-0.0921417\pi$
$193$	1.66782e6	+	2.88875e6i	0.231994	+	0.401826i	−0.726401	+	0.687271i	$0.758808\pi$
$194$	3.42569e6	+	1.97783e6i	0.469184	+	0.270884i
$195$	−1.64702e7	+	6.47481e6i	−2.22124	+	0.873220i
$196$	6.19527e6	+	594922.i	0.822795	+	0.0790118i
$197$			1.43025e7i			1.87074i	0.353665	+	0.935372i	$0.384935\pi$
$197$			1.43025e7i			1.87074i	−0.353665	+	0.935372i	$0.615065\pi$
$198$	−470847.	−	2.05224e6i	−0.0606575	−	0.264382i
$199$	2.45397e6	+	4.25039e6i	0.311393	+	0.539349i	0.978664	−	0.205466i	$-0.0658710\pi$
$199$	2.45397e6	+	4.25039e6i	0.311393	+	0.539349i	−0.667271	+	0.744815i	$0.732538\pi$
$200$	7.17574e6	−	4.14292e6i	0.896968	−	0.517865i
$201$	1.97094e6	+	295934.i	0.242709	+	0.0364424i
$202$	−761819.			−0.0924267
$203$	7.48198e6	−	3.85469e6i	0.894393	−	0.460789i
$204$	−3.17004e6	+	1.24621e6i	−0.373400	+	0.146792i
$205$	8.41846e6	−	1.45812e7i	0.977172	−	1.69251i
$206$	155278.	−	89649.5i	0.0177626	−	0.0102553i
$207$	−1.60511e6	+	5.22457e6i	−0.180965	+	0.589033i
$208$	−3.56261e6	+	6.17062e6i	−0.395893	+	0.685708i
$209$			2.24666e6i			0.246092i
$210$	−1.90197e6	−	5.61322e6i	−0.205374	−	0.606114i
$211$	−7.32393e6			−0.779645			−0.389822	−	0.920890i	$-0.627464\pi$
$211$	−7.32393e6			−0.779645			−0.389822	+	0.920890i	$0.627464\pi$
$212$	−7.67115e6	−	4.42894e6i	−0.805106	−	0.464828i
$213$	−196256.	−	156328.i	−0.0203088	−	0.0161770i
$214$	655291.	+	1.13500e6i	0.0668641	+	0.115812i
$215$	−1.86823e6	−	1.07863e6i	−0.187982	−	0.108531i
$216$	−3.31431e6	+	6.91214e6i	−0.328876	+	0.685885i
$217$	−3.79136e6	+	5.89600e6i	−0.371036	+	0.577003i
$218$		−	669481.i		−	0.0646203i
$219$	−4.17036e6	−	626176.i	−0.397047	−	0.0596161i
$220$	4.40506e6	+	7.62978e6i	0.413698	+	0.716546i
$221$	7.04690e6	−	4.06853e6i	0.652862	−	0.376930i
$222$	907939.	−	6.04692e6i	0.0829846	−	0.552682i
$223$	2.18380e7			1.96924			0.984619	−	0.174714i	$-0.0559000\pi$
$223$	2.18380e7			1.96924			0.984619	+	0.174714i	$0.0559000\pi$
$224$	−9.19797e6	−	5.91465e6i	−0.818367	−	0.526242i
$225$	1.13576e7	−	1.05622e7i	0.997098	−	0.927267i
$226$	1.95308e6	−	3.38284e6i	0.169198	−	0.293060i
$227$	−1.45374e7	+	8.39317e6i	−1.24282	+	0.717544i	−0.969668	−	0.244426i	$-0.921400\pi$
$227$	−1.45374e7	+	8.39317e6i	−1.24282	+	0.717544i	−0.273155	+	0.961970i	$0.588067\pi$
$228$	2.30614e6	−	2.89516e6i	0.194573	−	0.244269i
$229$	−5.03247e6	+	8.71650e6i	−0.419059	+	0.725831i	−0.995845	−	0.0910639i	$-0.970973\pi$
$229$	−5.03247e6	+	8.71650e6i	−0.419059	+	0.725831i	0.576786	+	0.816895i	$0.304307\pi$
$230$			4.79804e6i			0.394349i
$231$	7.60428e6	−	2.57661e6i	0.616911	−	0.209032i
$232$	−9.55651e6			−0.765306
$233$	−8.58655e6	−	4.95745e6i	−0.678814	−	0.391913i	0.120594	−	0.992702i	$-0.461520\pi$
$233$	−8.58655e6	−	4.95745e6i	−0.678814	−	0.391913i	−0.799408	+	0.600788i	$0.794853\pi$
$234$	2.43367e6	−	7.92150e6i	0.189939	−	0.618244i
$235$	−1.17498e7	−	2.03513e7i	−0.905373	−	1.56815i
$236$	7.35703e6	+	4.24758e6i	0.559714	+	0.323151i
$237$	2.30885e6	+	5.87310e6i	0.173440	+	0.441187i
$238$	1.24804e6	+	2.42246e6i	0.0925762	+	0.179691i
$239$		−	2.52204e7i		−	1.84739i	−0.383134	−	0.923693i	$-0.625155\pi$
$239$		−	2.52204e7i		−	1.84739i	0.383134	−	0.923693i	$-0.374845\pi$
$240$	1.60817e6	−	1.07105e7i	0.116332	−	0.774778i
$241$	−9.30509e6	−	1.61169e7i	−0.664767	−	1.15141i	−0.979348	−	0.202180i	$-0.935197\pi$
$241$	−9.30509e6	−	1.61169e7i	−0.664767	−	1.15141i	0.314581	−	0.949231i	$-0.398136\pi$
$242$	−2.94268e6	+	1.69895e6i	−0.207633	+	0.119877i
$243$	−3.15346e6	+	1.39981e7i	−0.219770	+	0.975552i
$244$	−2.10900e6			−0.145180
$245$	2.05625e7	−	9.37728e6i	1.39823	−	0.637644i
$246$	2.88451e6	+	7.33744e6i	0.193761	+	0.492878i
$247$	−4.42111e6	+	7.65759e6i	−0.293387	+	0.508161i
$248$	6.89286e6	−	3.97960e6i	0.451902	−	0.260906i
$249$	1.84212e7	+	1.46735e7i	1.19322	+	0.950461i
$250$	1.80803e6	−	3.13160e6i	0.115714	−	0.200422i
$251$			1.81135e7i			1.14546i	0.819743	+	0.572731i	$0.194116\pi$
$251$			1.81135e7i			1.14546i	−0.819743	+	0.572731i	$0.805884\pi$
$252$	−1.24441e7	−	4.48527e6i	−0.777612	−	0.280277i
$253$	−6.49995e6			−0.401373
$254$	−4.57822e6	−	2.64323e6i	−0.279380	−	0.161300i
$255$	−7.70626e6	+	9.67453e6i	−0.464754	+	0.583458i
$256$	2.67333e6	+	4.63034e6i	0.159343	+	0.275990i
$257$	3.47119e6	+	2.00409e6i	0.204493	+	0.118064i	0.598750	−	0.800936i	$-0.295664\pi$
$257$	3.47119e6	+	2.00409e6i	0.204493	+	0.118064i	−0.394256	+	0.919001i	$0.628998\pi$
$258$	940119.	−	369582.i	0.0547424	−	0.0215204i
$259$	2.32900e7	+	1.11568e6i	1.34051	+	0.0642158i
$260$			3.46742e7i			1.97282i
$261$	−1.74353e7	+	4.00019e6i	−0.980635	+	0.224988i
$262$	2.15441e6	+	3.73155e6i	0.119791	+	0.207484i
$263$	−1.27194e7	+	7.34356e6i	−0.699197	+	0.403682i	−0.807048	−	0.590485i	$-0.798936\pi$
$263$	−1.27194e7	+	7.34356e6i	−0.699197	+	0.403682i	0.107851	+	0.994167i	$0.465603\pi$
$264$	−9.01533e6	−	1.35364e6i	−0.489970	−	0.0735685i
$265$	−3.21648e7			−1.72840
$266$	−2.49070e6	−	1.60162e6i	−0.132335	−	0.0850969i
$267$	−5.28638e6	+	2.07820e6i	−0.277731	+	0.109182i
$268$	1.95248e6	−	3.38179e6i	0.101433	−	0.175688i
$269$	2.34241e7	−	1.35239e7i	1.20339	−	0.694776i	0.242081	−	0.970256i	$-0.422170\pi$
$269$	2.34241e7	−	1.35239e7i	1.20339	−	0.694776i	0.961307	+	0.275480i	$0.0888367\pi$
$270$	962586.	+	1.25596e7i	0.0489044	+	0.638092i
$271$	1.00753e7	−	1.74509e7i	0.506231	−	0.876817i	−0.493743	−	0.869608i	$-0.664372\pi$
$271$	1.00753e7	−	1.74509e7i	0.506231	−	0.876817i	0.999974	−	0.00720969i	$-0.00229493\pi$
$272$			4.97983e6i			0.247462i
$273$	3.09892e7	+	6.18196e6i	1.52308	+	0.303835i
$274$	−1.53113e7			−0.744321
$275$	1.59739e7	+	9.22251e6i	0.768089	+	0.443456i
$276$	8.37618e6	+	6.67205e6i	0.398399	+	0.317345i
$277$	2.93423e6	+	5.08223e6i	0.138056	+	0.239119i	0.926761	−	0.375653i	$-0.122581\pi$
$277$	2.93423e6	+	5.08223e6i	0.138056	+	0.239119i	−0.788705	+	0.614772i	$0.789248\pi$
$278$	1.02461e7	+	5.91557e6i	0.476895	+	0.275335i
$279$	1.09098e7	−	1.01458e7i	0.502349	−	0.467167i
$280$	−2.56313e7	−	1.22784e6i	−1.16761	−	0.0559330i
$281$		−	2.32651e7i		−	1.04854i	−0.851552	−	0.524270i	$-0.824338\pi$
$281$		−	2.32651e7i		−	1.04854i	0.851552	−	0.524270i	$-0.175662\pi$
$282$	1.08820e7	+	1.63392e6i	0.485244	+	0.0728588i
$283$	−6.93362e6	−	1.20094e7i	−0.305915	−	0.529860i	0.671550	−	0.740959i	$-0.265629\pi$
$283$	−6.93362e6	−	1.20094e7i	−0.305915	−	0.529860i	−0.977465	+	0.211099i	$0.932296\pi$
$284$	−425743.	+	245803.i	−0.0185863	+	0.0107308i
$285$	1.99570e6	−	1.32915e7i	0.0862107	−	0.574168i
$286$	9.85521e6			0.421277
$287$	−2.67253e7	+	1.37688e7i	−1.13052	+	0.582439i
$288$	1.58278e7	+	1.70197e7i	0.662586	+	0.712484i
$289$	−9.22528e6	+	1.59787e7i	−0.382196	+	0.661983i
$290$	−1.35996e7	+	7.85174e6i	−0.557613	+	0.321938i
$291$	1.99740e7	−	2.50756e7i	0.810560	−	1.01759i
$292$	−4.13130e6	+	7.15562e6i	−0.165935	+	0.287408i
$293$		−	1.57688e7i		−	0.626898i	−0.949605	−	0.313449i	$-0.898516\pi$
$293$		−	1.57688e7i		−	0.626898i	0.949605	−	0.313449i	$-0.101484\pi$
$294$	−2.56451e6	+	1.02671e7i	−0.100917	+	0.404024i
$295$	3.08477e7			1.20159
$296$	−2.29277e7	−	1.32373e7i	−0.884069	−	0.510417i
$297$	−1.70145e7	+	1.30402e6i	−0.649458	+	0.0497756i
$298$	3.90915e6	+	6.77085e6i	0.147718	+	0.255855i
$299$	−2.21547e7	−	1.27910e7i	−0.828804	−	0.478510i
$300$	−1.11181e7	−	2.82814e7i	−0.411780	−	1.04746i
$301$	1.76414e6	+	3.42421e6i	0.0646896	+	0.125563i
$302$		−	1.57842e7i		−	0.573062i
$303$	−916763.	+	6.10569e6i	−0.0329556	+	0.219486i
$304$	−2.70569e6	−	4.68639e6i	−0.0963069	−	0.166808i
$305$	−6.63221e6	+	3.82911e6i	−0.233754	+	0.134958i
$306$	−1.29515e6	−	5.64507e6i	−0.0452019	−	0.197018i
$307$	7.65032e6			0.264402			0.132201	−	0.991223i	$-0.457796\pi$
$307$	7.65032e6			0.264402			0.132201	+	0.991223i	$0.457796\pi$
$308$	752722.	−	1.57131e7i	0.0257622	−	0.537787i
$309$	−531648.	−	1.35237e6i	−0.0180198	−	0.0458376i
$310$	6.53937e6	−	1.13265e7i	0.219508	−	0.380199i
$311$	−7.77782e6	+	4.49053e6i	−0.258569	+	0.149285i	−0.623682	−	0.781678i	$-0.714364\pi$
$311$	−7.77782e6	+	4.49053e6i	−0.258569	+	0.149285i	0.365112	+	0.930963i	$0.381031\pi$
$312$	−2.80644e7	−	2.23547e7i	−0.924043	−	0.736047i
$313$	2.64219e6	−	4.57641e6i	0.0861652	−	0.149242i	−0.819722	−	0.572762i	$-0.805872\pi$
$313$	2.64219e6	−	4.57641e6i	0.0861652	−	0.149242i	0.905887	+	0.423519i	$0.139205\pi$
$314$		−	1.87361e7i		−	0.605189i
$315$	−4.72767e7	+	8.48869e6i	−1.51257	+	0.271587i
$316$	1.23644e7			0.391844
$317$	4.77548e7	+	2.75713e7i	1.49913	+	0.865524i	0.999999	−	0.00100269i	$-0.000319167\pi$
$317$	4.77548e7	+	2.75713e7i	1.49913	+	0.865524i	0.499131	+	0.866526i	$0.333653\pi$
$318$	9.38405e6	−	1.17808e7i	0.291816	−	0.366349i
$319$	−1.06368e7	−	1.84235e7i	−0.327672	−	0.567545i
$320$	−4.56326e6	−	2.63460e6i	−0.139260	−	0.0804015i
$321$	9.88515e6	−	3.88607e6i	0.298860	−	0.117489i
$322$	4.63374e6	−	7.20600e6i	0.138792	−	0.215837i
$323$			6.17984e6i			0.183388i
$324$	2.32644e7	+	1.57846e7i	0.684002	+	0.464087i
$325$	3.62973e7	+	6.28687e7i	1.05736	+	1.83141i
$326$	5.02304e6	−	2.90005e6i	0.144982	−	0.0837053i
$327$	−5.36564e6	−	805645.i	−0.153454	−	0.0230410i
$328$	3.41354e7			0.967350
$329$	−2.00777e6	+	4.19123e7i	−0.0563802	+	1.17694i
$330$	−1.39417e7	+	5.48077e6i	−0.387947	+	0.152511i
$331$	3.04619e6	−	5.27616e6i	0.0839989	−	0.145490i	−0.820965	−	0.570978i	$-0.806564\pi$
$331$	3.04619e6	−	5.27616e6i	0.0839989	−	0.145490i	0.904964	+	0.425488i	$0.139897\pi$
$332$	3.99615e7	−	2.30718e7i	1.09201	−	0.630474i
$333$	−4.73712e7	−	1.45536e7i	−1.28287	−	0.394128i
$334$	−4.26216e6	+	7.38227e6i	−0.114391	+	0.198130i
$335$		−	1.41797e7i		−	0.377166i
$336$	−1.27590e7	+	1.45327e7i	−0.336356	+	0.383113i
$337$	1.69875e7			0.443854			0.221927	−	0.975063i	$-0.428765\pi$
$337$	1.69875e7			0.443854			0.221927	+	0.975063i	$0.428765\pi$
$338$	1.96648e7	+	1.13535e7i	0.509259	+	0.294021i
$339$	−2.47619e7	−	1.97241e7i	−0.635601	−	0.506289i
$340$	1.21169e7	+	2.09871e7i	0.308287	+	0.533970i
$341$	1.53441e7	+	8.85894e6i	0.386972	+	0.223418i
$342$	4.28597e6	+	4.60874e6i	0.107145	+	0.115214i
$343$	−3.99382e7	−	5.77498e6i	−0.989707	−	0.143109i
$344$		−	4.37364e6i		−	0.107440i
$345$	3.84545e7	+	5.77390e6i	0.936461	+	0.140609i
$346$	−1.00721e7	−	1.74454e7i	−0.243160	−	0.421165i
$347$	−3.98815e7	+	2.30256e7i	−0.954515	+	0.551090i	−0.894481	−	0.447107i	$-0.852454\pi$
$347$	−3.98815e7	+	2.30256e7i	−0.954515	+	0.551090i	−0.0600345	+	0.998196i	$0.519121\pi$
$348$	−5.20416e6	+	3.46600e7i	−0.123485	+	0.822415i
$349$	−3.52247e7			−0.828649			−0.414325	−	0.910129i	$-0.635982\pi$
$349$	−3.52247e7			−0.828649			−0.414325	+	0.910129i	$0.635982\pi$
$350$	−2.16119e7	+	1.11344e7i	−0.504068	+	0.259694i
$351$	−6.05592e7	−	2.90376e7i	−1.40042	−	0.671490i
$352$	−1.38203e7	+	2.39374e7i	−0.316875	+	0.548844i
$353$	−1.87324e6	+	1.08152e6i	−0.0425864	+	0.0245872i	−0.521142	−	0.853470i	$-0.674494\pi$
$353$	−1.87324e6	+	1.08152e6i	−0.0425864	+	0.0245872i	0.478556	+	0.878057i	$0.341160\pi$
$354$	−8.99978e6	+	1.12984e7i	−0.202872	+	0.254688i
$355$	−892559.	+	1.54596e6i	−0.0199504	+	0.0345551i
$356$			1.11292e7i			0.246669i
$357$	2.09170e7	−	7.08746e6i	0.459721	−	0.155771i
$358$	1.97803e7			0.431105
$359$	482359.	+	278490.i	0.0104253	+	0.00601903i	0.505204	−	0.863000i	$-0.331417\pi$
$359$	482359.	+	278490.i	0.0104253	+	0.00601903i	−0.494778	+	0.869019i	$0.664751\pi$
$360$	5.21334e7	+	1.60166e7i	1.11740	+	0.343292i
$361$	2.01652e7	+	3.49272e7i	0.428629	+	0.742408i
$362$	−4.58622e6	−	2.64785e6i	−0.0966783	−	0.0558172i
$363$	1.00753e7	+	2.56290e7i	0.210639	+	0.535810i
$364$	3.34869e7	−	5.20759e7i	0.694337	−	1.07977i
$365$			3.00032e7i			0.617005i
$366$	532471.	−	3.54629e6i	0.0108606	−	0.0723320i
$367$	−1.48072e6	−	2.56469e6i	−0.0299554	−	0.0518843i	0.850659	−	0.525718i	$-0.176203\pi$
$367$	−1.48072e6	−	2.56469e6i	−0.0299554	−	0.0518843i	−0.880614	+	0.473833i	$0.842870\pi$
$368$	1.35585e7	−	7.82801e6i	0.272062	−	0.157075i
$369$	6.22780e7	−	1.42885e7i	1.23953	−	0.284386i
$370$	−4.35038e7			−0.858860
$371$	4.83072e7	+	3.10634e7i	0.945997	+	0.608313i
$372$	−1.06798e7	−	2.71665e7i	−0.207459	−	0.527722i
$373$	−3.33008e7	+	5.76788e7i	−0.641695	+	1.11145i	0.343359	+	0.939204i	$0.388435\pi$
$373$	−3.33008e7	+	5.76788e7i	−0.641695	+	1.11145i	−0.985054	+	0.172244i	$0.944898\pi$
$374$	5.96503e6	−	3.44391e6i	0.114024	−	0.0658321i
$375$	−2.29228e7	−	1.82592e7i	−0.434685	−	0.346249i
$376$	2.38217e7	−	4.12605e7i	0.448136	−	0.776195i
$377$		−	8.37273e7i		−	1.56258i
$378$	1.06838e7	−	1.97924e7i	0.197811	−	0.366457i
$379$	3.70366e7			0.680321			0.340160	−	0.940367i	$-0.389519\pi$
$379$	3.70366e7			0.680321			0.340160	+	0.940367i	$0.389519\pi$
$380$	−2.28059e7	−	1.31670e7i	−0.415620	−	0.239958i
$381$	−2.66939e7	+	3.35119e7i	−0.482655	+	0.605931i
$382$	3.93511e6	+	6.81581e6i	0.0705939	+	0.122272i
$383$	−9.19421e7	−	5.30828e7i	−1.63651	−	0.944839i	−0.982022	−	0.188764i	$-0.939552\pi$
$383$	−9.19421e7	−	5.30828e7i	−1.63651	−	0.944839i	−0.654486	−	0.756074i	$-0.727115\pi$
$384$	5.35687e7	−	2.10591e7i	0.946058	−	0.371916i
$385$	−2.61617e7	−	5.07799e7i	−0.458441	−	0.889835i
$386$			1.11127e7i			0.193222i
$387$	−1.83073e6	−	7.97945e6i	−0.0315858	−	0.137670i
$388$	−3.14061e7	−	5.43969e7i	−0.537673	−	0.931277i
$389$	−7.78909e6	+	4.49703e6i	−0.132324	+	0.0763972i	−0.564701	−	0.825296i	$-0.691008\pi$
$389$	−7.78909e6	+	4.49703e6i	−0.132324	+	0.0763972i	0.432377	+	0.901693i	$0.357675\pi$
$390$	−5.83047e7	−	8.75438e6i	−0.982901	−	0.147581i
$391$	−1.78793e7			−0.299103
$392$	3.73089e7	+	2.65976e7i	0.619376	+	0.441555i
$393$	3.24996e7	−	1.27763e7i	0.535427	−	0.210488i
$394$	−2.38244e7	+	4.12651e7i	−0.389524	+	0.674675i
$395$	3.88826e7	−	2.24489e7i	0.630906	−	0.364254i
$396$	−9.81891e6	+	3.19601e7i	−0.158117	+	0.514662i
$397$	1.43475e7	−	2.48506e7i	0.229301	−	0.397160i	−0.728300	−	0.685258i	$-0.759689\pi$
$397$	1.43475e7	−	2.48506e7i	0.229301	−	0.397160i	0.957601	+	0.288098i	$0.0930228\pi$
$398$			1.63508e7i			0.259351i
$399$	−1.58336e7	+	1.80347e7i	−0.249265	+	0.283916i
$400$	−4.44274e7			−0.694178
$401$	−3.92358e7	−	2.26528e7i	−0.608484	−	0.351309i	0.163888	−	0.986479i	$-0.447597\pi$
$401$	−3.92358e7	−	2.26528e7i	−0.608484	−	0.351309i	−0.772372	+	0.635170i	$0.780930\pi$
$402$	5.19353e6	+	4.13691e6i	0.0799437	+	0.0636792i
$403$	3.48664e7	+	6.03903e7i	0.532711	+	0.922683i
$404$	1.04763e7	+	6.04849e6i	0.158878	+	0.0917283i
$405$	1.01819e8	+	7.39925e6i	1.53272	+	0.111384i
$406$	2.80077e7	+	1.34168e6i	0.418503	+	0.0200480i
$407$		−	5.89350e7i		−	0.874159i
$408$	−2.47983e7	−	3.72344e6i	−0.365126	−	0.0548232i
$409$	1.47144e7	+	2.54861e7i	0.215067	+	0.372506i	0.953293	−	0.302046i	$-0.0976698\pi$
$409$	1.47144e7	+	2.54861e7i	0.215067	+	0.372506i	−0.738226	+	0.674553i	$0.764336\pi$
$410$	4.85772e7	−	2.80461e7i	0.704825	−	0.406931i
$411$	−1.84254e7	+	1.22714e8i	−0.265394	+	1.76754i
$412$	−2.84711e6			−0.0407110
$413$	−4.63290e7	−	2.97914e7i	−0.657662	−	0.422902i
$414$	−1.33338e7	+	1.24000e7i	−0.187912	+	0.174752i
$415$	8.37784e7	−	1.45109e8i	1.17216	−	2.03025i
$416$	−9.42111e7	+	5.43928e7i	−1.30865	+	0.755547i
$417$	5.97410e7	−	7.49996e7i	0.823881	−	1.03431i
$418$	−3.74236e6	+	6.48196e6i	−0.0512409	+	0.0887519i
$419$			1.20639e8i			1.64001i	0.572359	+	0.820003i	$0.306028\pi$
$419$			1.20639e8i			1.64001i	−0.572359	+	0.820003i	$0.693972\pi$
$420$	−1.84111e7	+	9.22921e7i	−0.248504	+	1.24571i
$421$	−1.36254e8			−1.82601			−0.913003	−	0.407952i	$-0.866243\pi$
$421$	−1.36254e8			−1.82601			−0.913003	+	0.407952i	$0.866243\pi$
$422$	−2.11307e7	−	1.21998e7i	−0.281175	−	0.162336i
$423$	2.61904e7	−	8.52487e7i	0.346036	−	1.12633i
$424$	−3.26057e7	−	5.64747e7i	−0.427755	−	0.740894i
$425$	4.39391e7	+	2.53682e7i	0.572379	+	0.330463i
$426$	−305828.	−	777945.i	−0.00395592	−	0.0100628i
$427$	1.36587e7	+	654306.i	0.175438	+	0.00840421i
$428$		−	2.08109e7i		−	0.265435i
$429$	1.18596e7	−	7.89858e7i	0.150210	−	1.00041i
$430$	−3.59344e6	−	6.22402e6i	−0.0451965	−	0.0782826i
$431$	5.72383e7	−	3.30466e7i	0.714916	−	0.412757i	−0.0979624	−	0.995190i	$-0.531232\pi$
$431$	5.72383e7	−	3.30466e7i	0.714916	−	0.412757i	0.812879	+	0.582433i	$0.197899\pi$
$432$	3.39209e7	−	2.32111e7i	0.420742	−	0.287901i
$433$	−1.11473e8			−1.37311			−0.686554	−	0.727079i	$-0.740877\pi$
$433$	−1.11473e8			−1.37311			−0.686554	+	0.727079i	$0.740877\pi$
$434$	−2.07599e7	+	1.06955e7i	−0.253955	+	0.130837i
$435$	4.65632e7	+	1.18445e8i	0.565685	+	1.43896i
$436$	−5.31538e6	+	9.20650e6i	−0.0641320	+	0.111080i
$437$	1.68258e7	−	9.71436e6i	0.201619	−	0.116405i
$438$	−1.09891e7	−	8.75339e6i	−0.130780	−	0.104173i
$439$	−2.59074e7	+	4.48730e7i	−0.306218	+	0.530385i	−0.977532	−	0.210788i	$-0.932397\pi$
$439$	−2.59074e7	+	4.48730e7i	−0.306218	+	0.530385i	0.671314	+	0.741173i	$0.265730\pi$
$440$			6.48596e7i			0.761406i
$441$	7.92012e7	+	3.29090e7i	0.923455	+	0.383706i
$442$	2.71086e7			0.313935
$443$	3.80317e7	+	2.19576e7i	0.437456	+	0.252565i	0.702518	−	0.711666i	$-0.252059\pi$
$443$	3.80317e7	+	2.19576e7i	0.437456	+	0.252565i	−0.265062	+	0.964231i	$0.585392\pi$
$444$	−6.04955e7	+	7.59468e7i	−0.691153	+	0.867683i
$445$	2.02063e7	+	3.49983e7i	0.229301	+	0.397161i
$446$	6.30061e7	+	3.63766e7i	0.710196	+	0.410032i
$447$	5.89700e7	−	2.31824e7i	0.660251	−	0.259559i
$448$	4.30901e6	+	8.36381e6i	0.0479229	+	0.0930186i
$449$			1.19872e8i			1.32428i	0.749382	+	0.662138i	$0.230351\pi$
$449$			1.19872e8i			1.32428i	−0.749382	+	0.662138i	$0.769649\pi$
$450$	5.03623e7	−	1.15547e7i	0.552672	−	0.126800i
$451$	3.79943e7	+	6.58080e7i	0.414179	+	0.717379i
$452$	−5.37164e7	+	3.10132e7i	−0.581690	+	0.335839i
$453$	−1.26504e8	−	1.89945e7i	−1.36085	−	0.204330i
$454$	−5.59236e7			−0.597624
$455$	1.07575e7	−	2.24563e8i	0.114203	−	2.38399i
$456$	2.53602e7	−	9.96964e6i	0.267459	−	0.105144i
$457$	−7.33515e7	+	1.27049e8i	−0.768529	+	1.33113i	0.169831	+	0.985473i	$0.445678\pi$
$457$	−7.33515e7	+	1.27049e8i	−0.768529	+	1.33113i	−0.938360	+	0.345659i	$0.887655\pi$
$458$	−2.90390e7	+	1.67657e7i	−0.302263	+	0.174512i
$459$	−4.68017e7	+	3.58696e6i	−0.483976	+	0.0370927i
$460$	3.80943e7	−	6.59812e7i	0.391369	−	0.677870i
$461$			1.01847e7i			0.103955i	0.998648	+	0.0519777i	$0.0165525\pi$
$461$			1.01847e7i			0.103955i	−0.998648	+	0.0519777i	$0.983448\pi$
$462$	2.62316e7	+	5.23288e6i	0.266010	+	0.0530658i
$463$	1.62758e8			1.63983			0.819916	−	0.572484i	$-0.194020\pi$
$463$	1.62758e8			1.63983			0.819916	+	0.572484i	$0.194020\pi$
$464$	4.43756e7	+	2.56203e7i	0.444212	+	0.256466i
$465$	−8.29085e7	−	6.60408e7i	−0.824594	−	0.656831i
$466$	−1.65157e7	−	2.86061e7i	−0.163207	−	0.282683i
$467$	1.29582e8	+	7.48142e7i	1.27231	+	0.734570i	0.975423	−	0.220342i	$-0.0707173\pi$
$467$	1.29582e8	+	7.48142e7i	1.27231	+	0.734570i	0.296890	+	0.954912i	$0.404051\pi$
$468$	−9.63602e7	+	8.96118e7i	−0.940070	+	0.874233i
$469$	−1.36941e7	+	2.12960e7i	−0.132744	+	0.206433i
$470$		−	7.82889e7i		−	0.754062i
$471$	−1.50163e8	−	2.25468e7i	−1.43715	−	0.215786i
$472$	3.12705e7	+	5.41621e7i	0.297378	+	0.515074i
$473$	8.43173e6	−	4.86806e6i	0.0796771	−	0.0460016i
$474$	−3.12172e6	+	2.07908e7i	−0.0293129	+	0.195225i
$475$	−5.51333e7			−0.514438
$476$	2.07050e6	−	4.32218e7i	0.0191979	−	0.400758i
$477$	−8.31265e7	−	8.93866e7i	−0.765921	−	0.823601i
$478$	4.20108e7	−	7.27648e7i	0.384660	−	0.666250i
$479$	3.95971e6	−	2.28614e6i	0.0360294	−	0.0208016i	−0.481877	−	0.876239i	$-0.660045\pi$
$479$	3.95971e6	−	2.28614e6i	0.0360294	−	0.0208016i	0.517907	+	0.855437i	$0.326712\pi$
$480$	1.03026e8	−	1.29340e8i	0.931587	−	1.16953i
$481$	1.15976e8	−	2.00876e8i	1.04216	−	1.80507i
$482$		−	6.19998e7i		−	0.553667i
$483$	−5.21772e7	−	4.58093e7i	−0.463063	−	0.406549i
$484$	5.39557e7			0.475884
$485$	−1.97526e8	−	1.14042e8i	−1.73141	−	0.999629i
$486$	−3.24156e7	+	3.51339e7i	−0.282387	+	0.306068i
$487$	7.98594e7	+	1.38321e8i	0.691416	+	1.19757i	0.971374	+	0.237555i	$0.0763460\pi$
$487$	7.98594e7	+	1.38321e8i	0.691416	+	1.19757i	−0.279958	+	0.960012i	$0.590321\pi$
$488$	−1.34462e7	−	7.76319e6i	−0.115702	−	0.0668006i
$489$	−1.71982e7	−	4.37477e7i	−0.147081	−	0.374135i
$490$	7.49463e7	+	7.19697e6i	0.637033	+	0.0611733i
$491$			1.57450e7i			0.133014i	0.997786	+	0.0665070i	$0.0211855\pi$
$491$			1.57450e7i			0.133014i	−0.997786	+	0.0665070i	$0.978815\pi$
$492$	1.85890e7	−	1.23804e8i	0.156085	−	1.03954i
$493$	−2.92586e7	−	5.06773e7i	−0.244181	−	0.422934i
$494$	−2.55112e7	+	1.47289e7i	−0.211617	+	0.122177i
$495$	2.71491e7	+	1.18333e8i	0.223841	+	0.975638i
$496$	−4.26760e7			−0.349735
$497$	2.83352e6	−	1.45982e6i	0.0230812	−	0.0118913i
$498$	2.87059e7	+	7.30204e7i	0.232426	+	0.591230i
$499$	1.32441e7	−	2.29395e7i	0.106591	−	0.184622i	−0.807796	−	0.589462i	$-0.799340\pi$
$499$	1.32441e7	−	2.29395e7i	0.106591	−	0.184622i	0.914387	+	0.404841i	$0.132673\pi$
$500$	−4.97270e7	+	2.87099e7i	−0.397816	+	0.229679i
$501$	5.40371e7	+	4.30433e7i	0.429714	+	0.342289i
$502$	−3.01725e7	+	5.22603e7i	−0.238507	+	0.413105i
$503$			6.85008e7i			0.538259i	0.963104	+	0.269130i	$0.0867360\pi$
$503$			6.85008e7i			0.538259i	−0.963104	+	0.269130i	$0.913264\pi$
$504$	−6.28291e7	−	7.44030e7i	−0.490760	−	0.581164i
$505$	4.39266e7			0.341078
$506$	−1.87534e7	−	1.08273e7i	−0.144753	−	0.0835733i
$507$	1.14658e8	−	1.43943e8i	0.879794	−	1.10450i
$508$	4.19722e7	+	7.26979e7i	0.320162	+	0.554537i
$509$	−4.51737e7	−	2.60810e7i	−0.342556	−	0.197775i	0.318846	−	0.947807i	$-0.396705\pi$
$509$	−4.51737e7	−	2.60810e7i	−0.342556	−	0.197775i	−0.661402	+	0.750032i	$0.730038\pi$
$510$	−3.83491e7	+	1.50759e7i	−0.289098	+	0.113651i
$511$	2.89758e7	−	4.50607e7i	0.217156	−	0.337703i
$512$		−	1.18625e8i		−	0.883824i
$513$	4.20950e7	−	2.88043e7i	0.311802	−	0.213357i
$514$	6.67663e6	+	1.15643e7i	0.0491664	+	0.0851587i
$515$	−8.95334e6	+	5.16921e6i	−0.0655486	+	0.0378445i
$516$	−1.58625e7	−	2.38174e6i	−0.115458	−	0.0173359i
$517$	1.06059e8			0.767493
$518$	6.53369e7	+	4.20142e7i	0.470077	+	0.302278i
$519$	−1.51939e8	+	5.97305e7i	−1.08684	+	0.427262i
$520$	−1.27635e8	+	2.21070e8i	−0.907736	+	1.57224i
$521$	−3.19939e7	+	1.84717e7i	−0.226232	+	0.130615i	−0.608833	−	0.793299i	$-0.708362\pi$
$521$	−3.19939e7	+	1.84717e7i	−0.226232	+	0.130615i	0.382601	+	0.923914i	$0.375029\pi$
$522$	−5.69669e7	−	1.75016e7i	−0.400508	−	0.123046i
$523$	−5.98462e7	+	1.03657e8i	−0.418342	+	0.724589i	−0.995773	−	0.0918501i	$-0.970722\pi$
$523$	−5.98462e7	+	1.03657e8i	−0.418342	+	0.724589i	0.577431	+	0.816440i	$0.304055\pi$
$524$		−	6.84202e7i		−	0.475544i
$525$	6.32305e7	+	1.86610e8i	0.436967	+	1.28961i
$526$	−4.89301e7			−0.336216
$527$	4.22069e7	+	2.43682e7i	0.288371	+	0.166491i
$528$	3.82336e7	+	3.04550e7i	0.259743	+	0.206899i
$529$	−4.59127e7	−	7.95231e7i	−0.310146	−	0.537188i
$530$	−9.28006e7	−	5.35784e7i	−0.623337	−	0.359884i
$531$	7.97225e7	+	8.57262e7i	0.532473	+	0.572572i
$532$	2.15352e7	+	4.18000e7i	0.143026	+	0.277614i
$533$			2.99070e8i			1.97511i
$534$	−1.87138e7	−	2.80986e6i	−0.122896	−	0.0184527i
$535$	−3.77842e7	−	6.54442e7i	−0.246746	−	0.427376i
$536$	2.48966e7	−	1.43740e7i	0.161676	−	0.0933436i
$537$	2.38033e7	−	1.58532e8i	0.153715	−	1.02375i
$538$	9.01096e7			0.578661
$539$	−9.74980e6	+	1.01530e8i	−0.0622629	+	0.648380i
$540$	8.64800e7	−	1.80358e8i	0.549205	−	1.14539i
$541$	1.04374e8	−	1.80780e8i	0.659172	−	1.14172i	−0.321659	−	0.946856i	$-0.604240\pi$
$541$	1.04374e8	−	1.80780e8i	0.659172	−	1.14172i	0.980830	−	0.194863i	$-0.0624263\pi$
$542$	5.81375e7	−	3.35657e7i	0.365139	−	0.210813i
$543$	−2.67405e7	+	3.35704e7i	−0.167021	+	0.209680i
$544$	−3.80152e7	+	6.58443e7i	−0.236135	+	0.408998i
$545$			3.86024e7i			0.238465i
$546$	7.91111e7	+	6.94561e7i	0.486026	+	0.426709i
$547$	−1.93791e8			−1.18405			−0.592026	−	0.805919i	$-0.701672\pi$
$547$	−1.93791e8			−1.18405			−0.592026	+	0.805919i	$0.701672\pi$
$548$	2.10556e8	+	1.21565e8i	1.27946	+	0.738696i
$549$	−2.77814e7	−	8.53511e6i	−0.167895	−	0.0515813i
$550$	3.07247e7	+	5.32168e7i	0.184672	+	0.319861i
$551$	5.50690e7	+	3.17941e7i	0.329194	+	0.190060i
$552$	2.88438e7	+	7.33711e7i	0.171489	+	0.436222i
$553$	−8.00766e7	−	3.83599e6i	−0.473511	−	0.0226831i
$554$			1.95507e7i			0.114983i
$555$	−5.23520e7	+	3.48667e8i	−0.306234	+	2.03954i
$556$	−9.39338e7	−	1.62698e8i	−0.546509	−	0.946582i
$557$	2.06041e8	−	1.18958e8i	1.19230	−	0.688377i	0.233476	−	0.972363i	$-0.424990\pi$
$557$	2.06041e8	−	1.18958e8i	1.19230	−	0.688377i	0.958829	+	0.283985i	$0.0916567\pi$
$558$	4.83769e7	−	1.10992e7i	0.278443	−	0.0638833i
$559$	3.83187e7			0.219369
$560$	1.15727e8	+	7.44170e7i	0.658977	+	0.423748i
$561$	−2.04234e7	−	5.19519e7i	−0.115675	−	0.294247i
$562$	3.87537e7	−	6.71235e7i	0.218326	−	0.378151i
$563$	−4.78391e6	+	2.76199e6i	−0.0268076	+	0.0154774i	−0.513344	−	0.858183i	$-0.671593\pi$
$563$	−4.78391e6	+	2.76199e6i	−0.0268076	+	0.0154774i	0.486536	+	0.873660i	$0.338260\pi$
$564$	−1.36673e8	−	1.08867e8i	−0.761808	−	0.606819i
$565$	−1.12615e8	+	1.95055e8i	−0.624384	+	1.08146i
$566$		−	4.61986e7i		−	0.254789i
$567$	−1.45772e8	−	1.09445e8i	−0.799695	−	0.600407i
$568$	−3.61917e6			−0.0197499
$569$	−1.75153e8	−	1.01125e8i	−0.950783	−	0.548935i	−0.0574589	−	0.998348i	$-0.518300\pi$
$569$	−1.75153e8	−	1.01125e8i	−0.950783	−	0.548935i	−0.893324	+	0.449413i	$0.851633\pi$
$570$	2.78982e7	−	3.50238e7i	0.150644	−	0.189120i
$571$	−1.57754e8	−	2.73237e8i	−0.847366	−	1.46768i	−0.883550	−	0.468336i	$-0.844854\pi$
$571$	−1.57754e8	−	2.73237e8i	−0.847366	−	1.46768i	0.0361839	−	0.999345i	$-0.488480\pi$
$572$	−1.35526e8	−	7.82459e7i	−0.724159	−	0.418094i
$573$	5.93617e7	−	2.33364e7i	0.315531	−	0.124042i
$574$	−1.00042e8	−	4.79242e6i	−0.528990	−	0.0253407i
$575$		−	1.59510e8i		−	0.839041i
$576$	−4.47165e6	−	1.94902e7i	−0.0233992	−	0.101988i
$577$	1.12493e8	+	1.94844e8i	0.585598	+	1.01428i	0.994801	+	0.101841i	$0.0324735\pi$
$577$	1.12493e8	+	1.94844e8i	0.585598	+	1.01428i	−0.409203	+	0.912443i	$0.634193\pi$
$578$	−5.32328e7	+	3.07340e7i	−0.275674	+	0.159161i
$579$	8.90638e7	+	1.33728e7i	0.458845	+	0.0688950i
$580$	2.49357e8			1.27802
$581$	−2.65963e8	+	1.37024e8i	−1.35611	+	0.698662i
$582$	9.93977e7	−	3.90754e7i	0.504205	−	0.198214i
$583$	7.25832e7	−	1.25718e8i	0.366294	−	0.634441i
$584$	−5.26793e7	+	3.04144e7i	−0.264485	+	0.152701i
$585$	−1.40326e8	+	4.56755e8i	−0.700924	+	2.28148i
$586$	2.62669e7	−	4.54956e7i	0.130532	−	0.226088i
$587$		−	2.64378e8i		−	1.30711i	−0.756880	−	0.653554i	$-0.773277\pi$
$587$		−	2.64378e8i		−	1.30711i	0.756880	−	0.653554i	$-0.226723\pi$
$588$	1.16783e8	−	1.20830e8i	0.574443	−	0.594348i
$589$	−5.29598e7			−0.259180
$590$	8.90005e7	+	5.13844e7i	0.433347	+	0.250193i
$591$	3.02055e8	+	2.40602e8i	1.46326	+	1.16556i
$592$	7.09766e7	+	1.22935e8i	0.342098	+	0.592530i
$593$	−1.65881e8	−	9.57713e7i	−0.795485	−	0.459274i	0.0464049	−	0.998923i	$-0.485224\pi$
$593$	−1.65881e8	−	9.57713e7i	−0.795485	−	0.459274i	−0.841890	+	0.539649i	$0.818557\pi$
$594$	−5.12619e7	−	2.45796e7i	−0.244588	−	0.117278i
$595$	−7.19625e7	−	1.39680e8i	−0.341630	−	0.663105i
$596$		−	1.24148e8i		−	0.586407i
$597$	1.31045e8	+	1.96763e7i	0.615883	+	0.0924741i
$598$	−4.26132e7	−	7.38082e7i	−0.199269	−	0.345145i
$599$	−1.32058e8	+	7.62439e7i	−0.614448	+	0.354752i	−0.774704	−	0.632324i	$-0.782101\pi$
$599$	−1.32058e8	+	7.62439e7i	−0.614448	+	0.354752i	0.160256	+	0.987075i	$0.448768\pi$
$600$	3.32186e7	−	2.21238e8i	0.153790	−	1.02425i
$601$	−2.39325e8			−1.10246			−0.551232	−	0.834352i	$-0.685842\pi$
$601$	−2.39325e8			−1.10246			−0.551232	+	0.834352i	$0.685842\pi$
$602$	−614035.	+	1.28180e7i	−0.00281452	+	0.0587532i
$603$	3.94056e7	−	3.66459e7i	0.179724	−	0.167137i
$604$	−1.25319e8	+	2.17059e8i	−0.568731	+	0.985071i
$605$	1.69675e8	−	9.79621e7i	0.766219	−	0.442376i
$606$	−1.28156e7	+	1.60888e7i	−0.0575863	+	0.0722946i
$607$	1.39151e8	−	2.41016e8i	0.622184	−	1.07765i	−0.366894	−	0.930263i	$-0.619579\pi$
$607$	1.39151e8	−	2.41016e8i	0.622184	−	1.07765i	0.989078	−	0.147392i	$-0.0470877\pi$
$608$		−	8.26192e7i		−	0.367596i
$609$	4.44571e7	−	2.22856e8i	0.196829	−	0.986673i
$610$	−2.55133e7			−0.112403
$611$	3.61495e8	+	2.08709e8i	1.58481	+	0.914993i
$612$	−2.70087e7	+	8.79122e7i	−0.117828	+	0.383526i
$613$	−1.70106e8	−	2.94633e8i	−0.738480	−	1.27908i	−0.953180	−	0.302405i	$-0.902211\pi$
$613$	−1.70106e8	−	2.94633e8i	−0.738480	−	1.27908i	0.214700	−	0.976680i	$-0.431123\pi$
$614$	2.20724e7	+	1.27435e7i	0.0953552	+	0.0550533i
$615$	−1.66322e8	−	4.23079e8i	−0.715028	−	1.81884i
$616$	6.26387e7	−	9.74104e7i	0.267979	−	0.416738i
$617$			6.87296e7i			0.292609i	0.989240	+	0.146305i	$0.0467380\pi$
$617$			6.87296e7i			0.292609i	−0.989240	+	0.146305i	$0.953262\pi$
$618$	718824.	−	4.78741e6i	0.00304549	−	0.0202831i
$619$	1.30911e8	+	2.26744e8i	0.551955	+	0.956015i	0.998133	+	0.0610707i	$0.0194515\pi$
$619$	1.30911e8	+	2.26744e8i	0.551955	+	0.956015i	−0.446178	+	0.894944i	$0.647215\pi$
$620$	−1.79855e8	+	1.03839e8i	−0.754653	+	0.435699i
$621$	8.33358e7	+	1.21788e8i	0.347982	+	0.508544i
$622$	−2.99204e7			−0.124336
$623$	3.45278e6	−	7.20770e7i	0.0142792	−	0.298080i
$624$	7.03857e7	+	1.79043e8i	0.289688	+	0.736890i
$625$	6.19628e7	−	1.07323e8i	0.253800	−	0.439594i
$626$	1.52463e7	−	8.80246e6i	0.0621501	−	0.0358824i
$627$	4.74470e7	+	3.77939e7i	0.192489	+	0.153327i
$628$	−1.48756e8	+	2.57654e8i	−0.600616	+	1.04030i
$629$		−	1.62112e8i		−	0.651422i
$630$	−1.50541e8	−	5.42598e7i	−0.602050	−	0.216999i
$631$	3.56304e8			1.41818			0.709092	−	0.705115i	$-0.249105\pi$
$631$	3.56304e8			1.41818			0.709092	+	0.705115i	$0.249105\pi$
$632$	7.88312e7	+	4.55132e7i	0.312282	+	0.180296i
$633$	−1.23205e8	+	1.54674e8i	−0.485757	+	0.609825i
$634$	9.18536e7	+	1.59095e8i	0.360436	+	0.624294i
$635$	2.63981e8	+	1.52409e8i	1.03098	+	0.595238i
$636$	−2.22581e8	+	8.75016e7i	−0.865201	+	0.340130i
$637$	−2.33029e8	+	3.26874e8i	−0.901556	+	1.26462i
$638$		−	7.08731e7i		−	0.272910i
$639$	−6.60297e6	+	1.51492e6i	−0.0253068	+	0.00580615i
$640$	−2.04757e8	−	3.54649e8i	−0.781086	−	1.35288i
$641$	5.99385e7	−	3.46055e7i	0.227579	−	0.131393i	−0.381876	−	0.924214i	$-0.624722\pi$
$641$	5.99385e7	−	3.46055e7i	0.227579	−	0.131393i	0.609455	+	0.792821i	$0.291388\pi$
$642$	3.49935e7	+	5.25423e6i	0.132246	+	0.0198566i
$643$	4.25439e7			0.160031			0.0800155	−	0.996794i	$-0.474503\pi$
$643$	4.25439e7			0.160031			0.0800155	+	0.996794i	$0.474503\pi$
$644$	−1.20934e8	+	6.23050e7i	−0.452785	+	0.233273i
$645$	−5.42075e7	+	2.13102e7i	−0.202013	+	0.0794159i
$646$	−1.02941e7	+	1.78298e7i	−0.0381847	+	0.0661378i
$647$	−2.13302e8	+	1.23150e8i	−0.787558	+	0.454697i	−0.839102	−	0.543974i	$-0.816919\pi$
$647$	−2.13302e8	+	1.23150e8i	−0.787558	+	0.454697i	0.0515443	+	0.998671i	$0.483586\pi$
$648$	9.02226e7	+	1.86273e8i	0.331582	+	0.684581i
$649$	−6.96109e7	+	1.20570e8i	−0.254650	+	0.441066i
$650$			2.41848e8i			0.880650i
$651$	6.07378e7	+	1.79254e8i	0.220149	+	0.649719i
$652$	−9.21004e7			−0.332291
$653$	3.33007e7	+	1.92262e7i	0.119595	+	0.0690483i	0.558604	−	0.829434i	$-0.311337\pi$
$653$	3.33007e7	+	1.92262e7i	0.119595	+	0.0690483i	−0.439009	+	0.898483i	$0.644670\pi$
$654$	−1.41387e7	−	1.12622e7i	−0.0505449	−	0.0402616i
$655$	−1.24224e8	−	2.15162e8i	−0.442060	−	0.765670i
$656$	−1.58508e8	−	9.15144e7i	−0.561486	−	0.324174i
$657$	−8.33793e7	+	7.75400e7i	−0.294010	+	0.273420i
$658$	−7.56081e7	+	1.17579e8i	−0.265394	+	0.412718i
$659$			3.24441e7i			0.113365i	0.998392	+	0.0566825i	$0.0180523\pi$
$659$			3.24441e7i			0.113365i	−0.998392	+	0.0566825i	$0.981948\pi$
$660$	2.35236e8	+	3.53204e7i	0.818224	+	0.122855i
$661$	5.36845e7	+	9.29842e7i	0.185885	+	0.321962i	0.943874	−	0.330305i	$-0.107151\pi$
$661$	5.36845e7	+	9.29842e7i	0.185885	+	0.321962i	−0.757989	+	0.652267i	$0.773818\pi$
$662$	1.75775e7	−	1.01484e7i	0.0605876	−	0.0349803i
$663$	3.26221e7	−	2.17265e8i	0.111937	−	0.745504i
$664$	3.39707e8			1.16038
$665$	1.43614e8	+	9.23496e7i	0.488352	+	0.314029i
$666$	−1.12431e8	−	1.20898e8i	−0.380595	−	0.409257i
$667$	−9.19856e7	+	1.59324e8i	−0.309986	+	0.536912i
$668$	1.17224e8	−	6.76792e7i	0.393266	−	0.227052i
$669$	3.67366e8	−	4.61196e8i	1.22693	−	1.54031i
$670$	2.36198e7	−	4.09107e7i	0.0785328	−	0.136023i
$671$		−	3.45631e7i		−	0.114405i
$672$	−2.79642e8	+	9.47532e7i	−0.921500	+	0.312238i
$673$	3.77762e6			0.0123929			0.00619646	−	0.999981i	$-0.498028\pi$
$673$	3.77762e6			0.0123929			0.00619646	+	0.999981i	$0.498028\pi$
$674$	4.90117e7	+	2.82969e7i	0.160074	+	0.0924186i
$675$	−3.20009e7	−	4.17540e8i	−0.104052	−	1.35765i
$676$	−1.80283e8	−	3.12259e8i	−0.583598	−	1.01082i
$677$	1.32057e7	+	7.62433e6i	0.0425595	+	0.0245717i	0.521129	−	0.853478i	$-0.325511\pi$
$677$	1.32057e7	+	7.62433e6i	0.0425595	+	0.0245717i	−0.478569	+	0.878050i	$0.658844\pi$
$678$	−3.85866e7	−	9.81543e7i	−0.123808	−	0.314934i
$679$	1.86521e8	+	3.62038e8i	0.595824	+	1.15650i
$680$			1.78409e8i			0.567400i
$681$	−6.72978e7	+	4.48207e8i	−0.213088	+	1.41918i
$682$	2.95135e7	+	5.11189e7i	0.0930397	+	0.161149i
$683$	−3.99492e8	+	2.30647e8i	−1.25385	+	0.723912i	−0.971872	−	0.235509i	$-0.924324\pi$
$683$	−3.99492e8	+	2.30647e8i	−1.25385	+	0.723912i	−0.281980	+	0.959420i	$0.590991\pi$
$684$	−2.23481e7	−	9.74066e7i	−0.0698348	−	0.304383i
$685$	8.82853e8			2.74673
$686$	−1.05609e8	−	8.31888e7i	−0.327135	−	0.257687i
$687$	9.94254e7	+	2.52912e8i	0.306639	+	0.780009i
$688$	−1.17254e7	+	2.03090e7i	−0.0360050	+	0.0623624i
$689$	4.94791e8	−	2.85668e8i	1.51274	−	0.873380i
$690$	1.01330e8	+	8.07141e7i	0.308453	+	0.245698i
$691$	6.74637e7	−	1.16851e8i	0.204473	−	0.354158i	−0.745492	−	0.666515i	$-0.767785\pi$
$691$	6.74637e7	−	1.16851e8i	0.204473	−	0.354158i	0.949965	+	0.312357i	$0.101119\pi$
$692$			3.19872e8i			0.965289i
$693$	7.35063e7	−	2.03939e8i	0.220864	−	0.612774i
$694$	−1.53419e8			−0.458988
$695$	−5.90790e8	−	3.41093e8i	−1.75986	−	1.01606i
$696$	−1.60763e8	+	2.01823e8i	−0.476823	+	0.598610i
$697$	1.04510e8	+	1.81017e8i	0.308646	+	0.534591i
$698$	−1.01629e8	−	5.86754e7i	−0.298848	−	0.172540i
$699$	−2.49142e8	+	9.79431e7i	−0.729482	+	0.286776i
$700$	3.85602e8	+	1.84719e7i	1.12420	+	0.0538539i
$701$		−	2.55902e8i		−	0.742883i	−0.928456	−	0.371441i	$-0.878864\pi$
$701$		−	2.55902e8i		−	0.742883i	0.928456	−	0.371441i	$-0.121136\pi$
$702$	−1.26354e8	−	1.84655e8i	−0.365238	−	0.533763i
$703$	8.80802e7	+	1.52559e8i	0.253520	+	0.439109i
$704$	2.05949e7	−	1.18905e7i	0.0590258	−	0.0340786i
$705$	−6.27457e8	−	9.42119e7i	−1.79067	−	0.268868i
$706$	−7.20615e6			−0.0204781
$707$	−6.59718e7	−	4.24225e7i	−0.186681	−	0.120043i
$708$	2.13467e8	−	8.39185e7i	0.601492	−	0.236460i
$709$	3.12030e8	−	5.40452e8i	0.875503	−	1.51641i	0.0192761	−	0.999814i	$-0.493864\pi$
$709$	3.12030e8	−	5.40452e8i	0.875503	−	1.51641i	0.856226	−	0.516601i	$-0.172803\pi$
$710$	−5.15035e6	+	2.97356e6i	−0.0143900	+	0.00830809i
$711$	1.62874e8	+	5.00388e7i	0.453151	+	0.139219i
$712$	−4.09665e7	+	7.09560e7i	−0.113498	+	0.196584i
$713$		−	1.53222e8i		−	0.422718i
$714$	7.21548e7	+	1.43940e7i	0.198231	+	0.0395446i
$715$	−5.68254e8			−1.55462
$716$	−2.72012e8	−	1.57046e8i	−0.741054	−	0.427847i
$717$	−5.32627e8	−	4.24265e8i	−1.44499	−	1.15101i
$718$	927789.	+	1.60698e6i	0.00250655	+	0.00434147i
$719$	7.85417e7	+	4.53461e7i	0.211307	+	0.121998i	0.601919	−	0.798557i	$-0.294403\pi$
$719$	7.85417e7	+	4.53461e7i	0.211307	+	0.121998i	−0.390612	+	0.920556i	$0.627737\pi$
$720$	−1.99142e8	−	2.14139e8i	−0.533538	−	0.573717i
$721$	1.84389e7	+	883298.i	0.0491959	+	0.00235668i
$722$			1.34361e8i			0.356994i
$723$	−4.96905e8	−	7.46097e7i	−1.31480	−	0.197415i
$724$	4.20455e7	+	7.28249e7i	0.110791	+	0.191895i
$725$	4.52116e8	−	2.61029e8i	1.18641	−	0.684976i
$726$	−1.36225e7	+	9.07266e7i	−0.0355997	+	0.237096i
$727$	−3.70448e8			−0.964104			−0.482052	−	0.876143i	$-0.660108\pi$
$727$	−3.70448e8			−0.964104			−0.482052	+	0.876143i	$0.660108\pi$
$728$	4.05190e8	−	2.08753e8i	1.05018	−	0.541051i
$729$	2.42577e8	+	3.02078e8i	0.626132	+	0.779717i
$730$	−4.99777e7	+	8.65639e7i	−0.128472	+	0.222520i
$731$	2.31930e7	−	1.33905e7i	0.0593753	−	0.0342803i
$732$	−3.54783e7	+	4.45399e7i	−0.0904544	+	0.113558i
$733$	−1.44734e8	+	2.50687e8i	−0.367502	+	0.636533i	−0.989174	−	0.146745i	$-0.953120\pi$
$733$	−1.44734e8	+	2.50687e8i	−0.367502	+	0.636533i	0.621672	+	0.783278i	$0.286454\pi$
$734$		−	9.86604e6i		−	0.0249491i
$735$	1.47870e8	−	5.92006e8i	0.372408	−	1.49095i
$736$	2.39031e8			0.599544
$737$	5.54220e7	+	3.19979e7i	0.138446	+	0.0799317i
$738$	2.03483e8	+	6.25149e7i	0.506243	+	0.155530i
$739$	1.21927e8	+	2.11184e8i	0.302112	+	0.523273i	0.976614	−	0.215000i	$-0.0689751\pi$
$739$	1.21927e8	+	2.11184e8i	0.302112	+	0.523273i	−0.674502	+	0.738273i	$0.735642\pi$
$740$	5.98252e8	+	3.45401e8i	1.47635	+	0.852370i
$741$	8.73468e7	+	2.22188e8i	0.214681	+	0.546091i
$742$	8.76301e7	+	1.70090e8i	0.214507	+	0.416359i
$743$		−	6.40566e8i		−	1.56170i	−0.624719	−	0.780850i	$-0.714786\pi$
$743$		−	6.40566e8i		−	1.56170i	0.624719	−	0.780850i	$-0.285214\pi$
$744$	3.19090e7	−	2.12516e8i	0.0774810	−	0.516028i
$745$	−2.25403e8	−	3.90409e8i	−0.545117	−	0.944171i
$746$	−1.92157e8	+	1.10942e8i	−0.462848	+	0.267226i
$747$	6.19776e8	−	1.42196e8i	1.48687	−	0.341133i
$748$	−1.09372e8			−0.261338
$749$	−6.45645e6	+	1.34779e8i	−0.0153656	+	0.320757i
$750$	−3.57208e7	−	9.08644e7i	−0.0846716	−	0.215382i
$751$	−1.12848e8	+	1.95459e8i	−0.266425	+	0.461461i	−0.967936	−	0.251197i	$-0.919176\pi$
$751$	−1.12848e8	+	1.95459e8i	−0.266425	+	0.461461i	0.701511	+	0.712658i	$0.252509\pi$
$752$	−2.21232e8	+	1.27729e8i	−0.520230	+	0.300355i
$753$	3.82538e8	+	3.04711e8i	0.895962	+	0.713679i
$754$	1.39469e8	−	2.41567e8i	0.325359	−	0.563538i
$755$			9.10119e8i			2.11474i
$756$	−3.04063e8	+	1.87354e8i	−0.703718	+	0.433609i
$757$	2.61790e7			0.0603484			0.0301742	−	0.999545i	$-0.490394\pi$
$757$	2.61790e7			0.0603484			0.0301742	+	0.999545i	$0.490394\pi$
$758$	1.06857e8	+	6.16937e7i	0.245354	+	0.141655i
$759$	−1.09344e8	+	1.37272e8i	−0.250075	+	0.313947i
$760$	−9.69347e7	−	1.67896e8i	−0.220820	−	0.382472i
$761$	−4.74442e6	−	2.73919e6i	−0.0107654	−	0.00621539i	0.494608	−	0.869116i	$-0.335312\pi$
$761$	−4.74442e6	−	2.73919e6i	−0.0107654	−	0.00621539i	−0.505373	+	0.862901i	$0.668645\pi$
$762$	−1.32838e8	+	5.22218e7i	−0.300233	+	0.118028i
$763$	3.72806e7	−	5.79756e7i	0.0839284	−	0.130518i
$764$		−	1.24972e8i		−	0.280242i
$765$	7.46788e7	+	3.25496e8i	0.166806	+	0.727045i
$766$	−1.76845e8	−	3.06305e8i	−0.393466	−	0.681503i
$767$	−4.74529e8	+	2.73970e8i	−1.05166	+	0.607178i
$768$	1.42759e8	+	2.14352e7i	0.315153	+	0.0473199i
$769$	−4.52550e8			−0.995148			−0.497574	−	0.867422i	$-0.665776\pi$
$769$	−4.52550e8			−0.995148			−0.497574	+	0.867422i	$0.665776\pi$
$770$	9.10593e6	−	1.90087e8i	0.0199458	−	0.416371i
$771$	1.00718e8	−	3.95944e7i	0.219757	−	0.0863915i
$772$	8.82295e7	−	1.52818e8i	0.191762	−	0.332141i
$773$	−5.00744e8	+	2.89105e8i	−1.08412	+	0.625917i	−0.932005	−	0.362446i	$-0.881942\pi$
$773$	−5.00744e8	+	2.89105e8i	−1.08412	+	0.625917i	−0.152115	+	0.988363i	$0.548608\pi$
$774$	8.00980e6	−	2.60715e7i	0.0172742	−	0.0562269i
$775$	−2.17400e8	+	3.76548e8i	−0.467040	+	0.808937i
$776$		−	4.62420e8i		−	0.989581i
$777$	4.15353e8	−	4.73091e8i	0.885431	−	1.00851i
$778$	−2.99637e7			−0.0636292
$779$	−1.96704e8	−	1.13567e8i	−0.416103	−	0.240237i
$780$	7.32282e8	+	5.83300e8i	1.54310	+	1.22916i
$781$	−4.02830e6	−	6.97723e6i	−0.00845608	−	0.0146464i
$782$	−5.15847e7	−	2.97824e7i	−0.107870	−	0.0622787i
$783$	−2.08822e8	+	4.35507e8i	−0.435002	+	0.907215i
$784$	−1.01937e8	−	2.23528e8i	−0.211537	−	0.463857i
$785$			1.08033e9i			2.23330i
$786$	1.15049e8	+	1.72744e7i	0.236927	+	0.0355742i
$787$	1.72758e8	+	2.99225e8i	0.354416	+	0.613867i	0.987018	−	0.160610i	$-0.0513462\pi$
$787$	1.72758e8	+	2.99225e8i	0.354416	+	0.613867i	−0.632602	+	0.774477i	$0.718013\pi$
$788$	6.55253e8	−	3.78310e8i	1.33915	−	0.773160i
$789$	−5.88818e7	+	3.92156e8i	−0.119881	+	0.798414i
$790$	1.49577e8			0.303377
$791$	3.57509e8	−	1.84188e8i	0.722366	−	0.372161i
$792$	−1.80246e8	+	1.67623e8i	−0.362819	+	0.337410i
$793$	6.80155e7	−	1.17806e8i	0.136392	−	0.236238i
$794$	8.27898e7	−	4.77987e7i	0.165392	−	0.0954893i
$795$	−5.41086e8	+	6.79286e8i	−1.07687	+	1.35192i
$796$	1.29818e8	−	2.24851e8i	0.257392	−	0.445815i
$797$			5.95426e8i			1.17612i	0.808816	+	0.588062i	$0.200109\pi$
$797$			5.95426e8i			1.17612i	−0.808816	+	0.588062i	$0.799891\pi$
$798$	−7.57238e7	+	2.56580e7i	−0.149013	+	0.0504911i
$799$	2.91734e8			0.571936
$800$	−5.87428e8	−	3.39151e8i	−1.14732	−	0.662405i
$801$	−4.50399e7	+	1.46603e8i	−0.0876396	+	0.285263i
$802$	−7.54677e7	−	1.30714e8i	−0.146298	−	0.253395i
$803$	−1.17269e8	−	6.77052e7i	−0.226483	−	0.130760i
$804$	−3.85746e7	−	9.81237e7i	−0.0742221	−	0.188802i
$805$	−2.67183e8	+	4.15500e8i	−0.512178	+	0.796495i
$806$			2.32314e8i			0.443681i
$807$	1.08437e8	−	7.22195e8i	0.206327	−	1.37415i
$808$	4.45287e7	+	7.71260e7i	0.0844124	+	0.146207i
$809$	8.89342e8	−	5.13462e8i	1.67967	−	0.969757i	0.717797	−	0.696252i	$-0.245151\pi$
$809$	8.89342e8	−	5.13462e8i	1.67967	−	0.969757i	0.961871	−	0.273504i	$-0.0881828\pi$
$810$	2.81438e8	+	1.90952e8i	0.529574	+	0.359310i
$811$	−1.50752e8			−0.282618			−0.141309	−	0.989966i	$-0.545131\pi$
$811$	−1.50752e8			−0.282618			−0.141309	+	0.989966i	$0.545131\pi$
$812$	−3.74501e8	−	2.40818e8i	−0.699495	−	0.449802i
$813$	−1.99055e8	−	5.06343e8i	−0.370425	−	0.942265i
$814$	9.81709e7	−	1.70037e8i	0.182016	−	0.315261i
$815$	−2.89630e8	+	1.67218e8i	−0.535020	+	0.308894i
$816$	1.05169e8	+	8.37723e7i	0.193560	+	0.154181i
$817$	−1.45509e7	+	2.52030e7i	−0.0266824	+	0.0462152i
$818$			9.80421e7i			0.179123i
$819$	6.51866e8	−	5.50463e8i	1.18661	−	1.00202i
$820$	−8.90692e8			−1.61542
$821$	4.03042e8	+	2.32697e8i	0.728318	+	0.420495i	0.817807	−	0.575493i	$-0.195190\pi$
$821$	4.03042e8	+	2.32697e8i	0.728318	+	0.420495i	−0.0894884	+	0.995988i	$0.528523\pi$
$822$	−2.57571e8	+	3.23358e8i	−0.463748	+	0.582195i
$823$	−5.46802e8	−	9.47089e8i	−0.980913	−	1.69899i	−0.658851	−	0.752273i	$-0.728957\pi$
$823$	−5.46802e8	−	9.47089e8i	−0.980913	−	1.69899i	−0.322062	−	0.946718i	$-0.604376\pi$
$824$	−1.81521e7	−	1.04801e7i	−0.0324448	−	0.0187320i
$825$	4.63487e8	−	1.82207e8i	0.825421	−	0.324491i
$826$	−8.40417e7	−	1.63125e8i	−0.149126	−	0.289455i
$827$		−	5.14940e8i		−	0.910416i	−0.890385	−	0.455208i	$-0.849565\pi$
$827$		−	5.14940e8i		−	0.910416i	0.890385	−	0.455208i	$-0.150435\pi$
$828$	2.81813e8	−	6.46567e7i	0.496444	−	0.113900i
$829$	−5.06809e7	−	8.77819e7i	−0.0889571	−	0.154078i	0.818113	−	0.575057i	$-0.195020\pi$
$829$	−5.06809e7	−	8.77819e7i	−0.0889571	−	0.154078i	−0.907071	+	0.420979i	$0.861687\pi$
$830$	4.83428e8	−	2.79108e8i	0.845469	−	0.488132i
$831$	1.56692e8	+	2.35271e7i	0.273051	+	0.0409982i
$832$	9.35954e7			0.162512
$833$	−2.68187e7	+	2.79278e8i	−0.0463983	+	0.483172i
$834$	2.97293e8	−	1.16872e8i	0.512491	−	0.201472i
$835$	2.45757e8	−	4.25664e8i	0.422130	−	0.731151i
$836$	1.02928e8	−	5.94253e7i	0.176162	−	0.101707i
$837$	−3.07394e7	−	4.01080e8i	−0.0524227	−	0.683997i
$838$	−2.00954e8	+	3.48063e8i	−0.341480	+	0.591460i
$839$		−	7.74824e8i		−	1.31195i	−0.754783	−	0.655975i	$-0.772258\pi$
$839$		−	7.74824e8i		−	1.31195i	0.754783	−	0.655975i	$-0.227742\pi$
$840$	−4.57108e8	+	5.20650e8i	−0.771225	+	0.878432i
$841$	−7.29555e6			−0.0122651
$842$	−3.93114e8	−	2.26965e8i	−0.658540	−	0.380208i
$843$	−4.91334e8	−	3.91372e8i	−0.820151	−	0.653292i
$844$	1.93722e8	+	3.35536e8i	0.322219	+	0.558100i
$845$	−1.13388e9	−	6.54643e8i	−1.87930	−	1.08501i
$846$	2.17566e8	−	2.02329e8i	0.359319	−	0.334155i
$847$	−3.49437e8	−	1.67394e7i	−0.575067	−	0.0275480i
$848$			3.49653e8i			0.573390i
$849$	−3.70265e8	−	5.55948e7i	−0.605047	−	0.0908472i
$850$	8.45142e7	+	1.46383e8i	0.137617	+	0.238360i
$851$	−4.41379e8	+	2.54831e8i	−0.716182	+	0.413488i
$852$	−1.97088e6	+	1.31262e7i	−0.00318671	+	0.0212237i
$853$	6.26279e8			1.00907			0.504534	−	0.863392i	$-0.331664\pi$
$853$	6.26279e8			1.00907			0.504534	+	0.863392i	$0.331664\pi$
$854$	3.83175e7	+	2.46397e7i	0.0615211	+	0.0395605i
$855$	−2.47130e8	−	2.65741e8i	−0.395391	−	0.425167i
$856$	7.66043e7	−	1.32683e8i	0.122133	−	0.211540i
$857$	−3.06647e8	+	1.77043e8i	−0.487188	+	0.281278i	−0.723407	−	0.690422i	$-0.757425\pi$
$857$	−3.06647e8	+	1.77043e8i	−0.487188	+	0.281278i	0.236219	+	0.971700i	$0.424092\pi$
$858$	1.65787e8	−	2.08132e8i	0.262476	−	0.329516i
$859$	−1.66085e8	+	2.87667e8i	−0.262030	+	0.453849i	−0.966781	−	0.255606i	$-0.917725\pi$
$859$	−1.66085e8	+	2.87667e8i	−0.262030	+	0.453849i	0.704752	+	0.709454i	$0.251058\pi$
$860$			1.14121e8i			0.179420i
$861$	−1.58799e8	+	7.96033e8i	−0.248793	+	1.24716i
$862$	2.20189e8			0.343775
$863$	9.38497e8	+	5.41842e8i	1.46016	+	0.843024i	0.999018	−	0.0443023i	$-0.0141065\pi$
$863$	9.38497e8	+	5.41842e8i	1.46016	+	0.843024i	0.461142	+	0.887326i	$0.347440\pi$
$864$	6.25698e8	−	4.79546e7i	0.970116	−	0.0743514i
$865$	5.80759e8	+	1.00590e9i	0.897321	+	1.55421i
$866$	−3.21616e8	−	1.85685e8i	−0.495204	−	0.285906i
$867$	1.82262e8	+	4.63626e8i	0.279665	+	0.711395i
$868$	3.70401e8	+	1.77437e7i	0.566387	+	0.0271322i
$869$			2.02633e8i			0.308781i
$870$	−6.29565e7	+	4.19294e8i	−0.0956055	+	0.636738i
$871$	1.25935e8	+	2.18126e8i	0.190586	+	0.330105i
$872$	−6.77778e7	+	3.91315e7i	−0.102221	+	0.0590171i
$873$	−1.93561e8	−	8.43658e8i	−0.290921	−	1.26801i
$874$	6.47267e7			0.0969503
$875$	3.30957e8	−	1.70508e8i	0.494023	−	0.254519i
$876$	8.16211e7	+	2.07623e8i	0.121420	+	0.308860i
$877$	−1.23485e8	+	2.13882e8i	−0.183069	+	0.317085i	−0.942924	−	0.333008i	$-0.891936\pi$
$877$	−1.23485e8	+	2.13882e8i	−0.183069	+	0.317085i	0.759855	+	0.650092i	$0.225270\pi$
$878$	−1.49494e8	+	8.63104e7i	−0.220872	+	0.127520i
$879$	−3.33021e8	−	2.65268e8i	−0.490349	−	0.390588i
$880$	1.73884e8	−	3.01176e8i	0.255159	−	0.441949i
$881$		−	8.00824e8i		−	1.17114i	−0.810621	−	0.585570i	$-0.800871\pi$
$881$		−	8.00824e8i		−	1.17114i	0.810621	−	0.585570i	$-0.199129\pi$
$882$	1.73690e8	+	2.26877e8i	0.253145	+	0.330662i
$883$	9.22086e8			1.33934			0.669668	−	0.742661i	$-0.266436\pi$
$883$	9.22086e8			1.33934			0.669668	+	0.742661i	$0.266436\pi$
$884$	−3.72789e8	−	2.15230e8i	−0.539643	−	0.311563i
$885$	5.18929e8	−	6.51470e8i	0.748649	−	0.939863i
$886$	7.31516e7	+	1.26702e8i	0.105178	+	0.182173i
$887$	7.00140e8	+	4.04226e8i	1.00326	+	0.579233i	0.909212	−	0.416334i	$-0.136685\pi$
$887$	7.00140e8	+	4.04226e8i	1.00326	+	0.579233i	0.0940499	+	0.995567i	$0.470019\pi$
$888$	−6.65256e8	+	2.61527e8i	−0.950058	+	0.373489i
$889$	−2.49273e8	−	4.83840e8i	−0.354789	−	0.688647i
$890$			1.34634e8i			0.190979i
$891$	−2.58684e8	+	3.81266e8i	−0.365710	+	0.539008i
$892$	−5.77628e8	−	1.00048e9i	−0.813867	−	1.40966i
$893$	−2.74544e8	+	1.58508e8i	−0.385529	+	0.222585i
$894$	2.08754e8	+	3.13442e7i	0.292161	+	0.0438677i
$895$	−1.14054e9			−1.59089
$896$	−3.49882e7	+	7.30381e8i	−0.0486404	+	1.01537i
$897$	−6.42825e8	+	2.52709e8i	−0.890667	+	0.350141i
$898$	−1.99676e8	+	3.45850e8i	−0.275739	+	0.477593i
$899$	4.34293e8	−	2.50739e8i	0.597728	−	0.345098i
$900$	−7.84305e8	−	2.40957e8i	−1.07586	−	0.330532i
$901$	1.99654e8	−	3.45810e8i	0.272962	−	0.472785i
$902$			2.53155e8i			0.344959i
$903$	1.01993e8	+	2.03463e7i	0.138518	+	0.0276326i
$904$	−4.56635e8			−0.618108
$905$	2.64442e8	+	1.52676e8i	0.356767	+	0.205980i
$906$	−3.33345e8	−	2.65526e8i	−0.448239	−	0.357045i
$907$	2.77209e8	+	4.80140e8i	0.371523	+	0.643497i	0.989800	−	0.142464i	$-0.0455024\pi$
$907$	2.77209e8	+	4.80140e8i	0.371523	+	0.643497i	−0.618277	+	0.785960i	$0.712169\pi$
$908$	7.69045e8	+	4.44008e8i	1.02729	+	0.593108i
$909$	1.13524e8	+	1.22073e8i	0.151145	+	0.162528i
$910$	4.05102e8	−	6.29980e8i	0.537577	−	0.835994i
$911$		−	7.28942e8i		−	0.964135i	−0.876134	−	0.482068i	$-0.839886\pi$
$911$		−	7.28942e8i		−	0.964135i	0.876134	−	0.482068i	$-0.160114\pi$
$912$	−1.44488e8	−	2.16947e7i	−0.190479	−	0.0286001i
$913$	3.78109e8	+	6.54905e8i	0.496827	+	0.860529i
$914$	−4.23262e8	+	2.44370e8i	−0.554333	+	0.320044i
$915$	−3.07024e7	+	2.04480e8i	−0.0400783	+	0.266924i
$916$	5.32447e8			0.692772
$917$	−2.12270e7	+	4.43114e8i	−0.0275283	+	0.574656i
$918$	−1.41005e8	−	6.76109e7i	−0.182267	−	0.0873954i
$919$	−4.65306e8	+	8.05933e8i	−0.599504	+	1.03837i	0.393391	+	0.919371i	$0.371302\pi$
$919$	−4.65306e8	+	8.05933e8i	−0.599504	+	1.03837i	−0.992894	+	0.118999i	$0.962031\pi$
$920$	4.85750e8	−	2.80448e8i	0.623806	−	0.360155i
$921$	1.28696e8	−	1.61567e8i	0.164735	−	0.206811i
$922$	−1.69652e7	+	2.93846e7i	−0.0216454	+	0.0374910i
$923$		−	3.17086e7i		−	0.0403248i
$924$	−3.19182e8	−	2.80228e8i	−0.404597	−	0.355218i
$925$	1.44627e9			1.82737
$926$	4.69583e8	+	2.71114e8i	0.591397	+	0.341443i
$927$	−3.75043e7	−	1.15222e7i	−0.0470806	−	0.0144643i
$928$	3.91162e8	+	6.77513e8i	0.489455	+	0.847761i
$929$	5.88364e8	+	3.39692e8i	0.733835	+	0.423680i	0.819824	−	0.572616i	$-0.194071\pi$
$929$	5.88364e8	+	3.39692e8i	0.733835	+	0.423680i	−0.0859883	+	0.996296i	$0.527405\pi$
$930$	−1.29197e8	−	3.28643e8i	−0.160621	−	0.408578i
$931$	−1.26502e8	−	2.77393e8i	−0.156764	−	0.343753i
$932$			5.24509e8i			0.647896i
$933$	−3.60058e7	+	2.39800e8i	−0.0443330	+	0.295260i
$934$	2.49243e8	+	4.31702e8i	0.305902	+	0.529838i
$935$	−3.43945e8	+	1.98577e8i	−0.420779	+	0.242937i
$936$	−9.44217e8	+	2.16632e8i	−1.15145	+	0.264178i
$937$	−3.23272e8			−0.392961			−0.196480	−	0.980508i	$-0.562951\pi$
$937$	−3.23272e8			−0.392961			−0.196480	+	0.980508i	$0.562951\pi$
$938$	−7.49835e7	+	3.86313e7i	−0.0908567	+	0.0468091i
$939$	−5.22012e7	−	1.32786e8i	−0.0630498	−	0.160382i
$940$	−6.21579e8	+	1.07661e9i	−0.748363	+	1.29620i
$941$	8.31102e7	−	4.79837e7i	0.0997437	−	0.0575870i	−0.449298	−	0.893382i	$-0.648326\pi$
$941$	8.31102e7	−	4.79837e7i	0.0997437	−	0.0575870i	0.549042	+	0.835795i	$0.314993\pi$
$942$	−3.95687e8	−	3.15185e8i	−0.473369	−	0.377062i
$943$	3.28568e8	−	5.69097e8i	0.391824	−	0.678659i
$944$		−	3.35335e8i		−	0.398624i
$945$	−6.16031e8	+	1.14123e9i	−0.729974	+	1.35232i
$946$	3.24359e7			0.0383135
$947$	3.28793e8	+	1.89829e8i	0.387144	+	0.223518i	0.680922	−	0.732356i	$-0.261579\pi$
$947$	3.28793e8	+	1.89829e8i	0.387144	+	0.223518i	−0.293778	+	0.955874i	$0.594913\pi$
$948$	2.07998e8	−	2.61124e8i	0.244138	−	0.306494i
$949$	−2.66469e8	−	4.61538e8i	−0.311780	−	0.540019i
$950$	−1.59068e8	−	9.18381e7i	−0.185529	−	0.107115i
$951$	1.38562e9	−	5.44719e8i	1.61103	−	0.633331i
$952$	1.72299e8	−	2.67945e8i	0.199698	−	0.310553i
$953$		−	1.29416e9i		−	1.49523i	−0.664131	−	0.747616i	$-0.731198\pi$
$953$		−	1.29416e9i		−	1.49523i	0.664131	−	0.747616i	$-0.268802\pi$
$954$	−9.09377e7	−	3.96362e8i	−0.104737	−	0.456507i
$955$	−2.26899e8	−	3.93001e8i	−0.260509	−	0.451215i
$956$	−1.15544e9	+	6.67093e8i	−1.32243	+	0.763506i
$957$	−5.68021e8	−	8.52878e7i	−0.648080	−	0.0973085i
$958$	1.52325e7			0.0173251
$959$	−1.32592e9	−	8.52622e8i	−1.50336	−	0.966720i
$960$	−1.32404e8	+	5.20511e7i	−0.149654	+	0.0588324i
$961$	2.34922e8	−	4.06897e8i	0.264700	−	0.458474i
$962$	6.69219e8	−	3.86374e8i	0.751698	−	0.433993i
$963$	8.42214e7	−	2.74137e8i	0.0943069	−	0.306965i
$964$	−4.92250e8	+	8.52602e8i	−0.549483	+	0.951733i
$965$		−	6.40759e8i		−	0.713038i
$966$	−7.42329e7	−	2.19081e8i	−0.0823503	−	0.243038i
$967$	−2.10612e8			−0.232919			−0.116459	−	0.993195i	$-0.537154\pi$
$967$	−2.10612e8			−0.232919			−0.116459	+	0.993195i	$0.537154\pi$
$968$	3.44002e8	+	1.98610e8i	0.379258	+	0.218965i
$969$	1.30512e8	+	1.03959e8i	0.143443	+	0.114259i
$970$	−3.79930e8	−	6.58058e8i	−0.416283	−	0.721023i
$971$	−2.13862e8	−	1.23473e8i	−0.233601	−	0.134870i	0.378631	−	0.925548i	$-0.376395\pi$
$971$	−2.13862e8	−	1.23473e8i	−0.233601	−	0.134870i	−0.612232	+	0.790678i	$0.709728\pi$
$972$	7.24716e8	−	2.25786e8i	0.789167	−	0.245866i
$973$	5.57874e8	+	1.08284e9i	0.605616	+	1.17550i
$974$			5.32103e8i			0.575862i
$975$	1.93832e9	+	2.91037e8i	2.09128	+	0.314004i
$976$	4.16250e7	+	7.20967e7i	0.0447719	+	0.0775471i
$977$	−5.19265e8	+	2.99798e8i	−0.556808	+	0.321473i	−0.751863	−	0.659319i	$-0.770845\pi$
$977$	−5.19265e8	+	2.99798e8i	−0.556808	+	0.321473i	0.195056	+	0.980792i	$0.437511\pi$
$978$	2.32531e7	−	1.54867e8i	0.0248579	−	0.165555i
$979$	−1.82390e8			−0.194381
$980$	−9.73498e8	−	6.94010e8i	−1.03432	−	0.737373i
$981$	−1.07277e8	+	9.97638e7i	−0.113632	+	0.105674i
$982$	−2.62271e7	+	4.54267e7i	−0.0276960	+	0.0479708i
$983$	−4.66487e8	+	2.69326e8i	−0.491110	+	0.283543i	−0.725035	−	0.688712i	$-0.758176\pi$
$983$	−4.66487e8	+	2.69326e8i	−0.491110	+	0.283543i	0.233925	+	0.972255i	$0.424843\pi$
$984$	5.74237e8	−	7.20904e8i	0.602706	−	0.756645i
$985$	1.37372e9	−	2.37936e9i	1.43744	−	2.48972i
$986$		−	1.94950e8i		−	0.203372i
$987$	8.51369e8	+	7.47464e8i	0.885455	+	0.777390i
$988$	4.67763e8			0.485015
$989$	−7.29163e7	−	4.20982e7i	−0.0753765	−	0.0435186i
$990$	−1.18783e8	+	3.86632e8i	−0.122419	+	0.398467i
$991$	1.95240e8	+	3.38166e8i	0.200608	+	0.347463i	0.948724	−	0.316104i	$-0.102375\pi$
$991$	1.95240e8	+	3.38166e8i	0.200608	+	0.347463i	−0.748117	+	0.663567i	$0.769042\pi$
$992$	−5.64270e8	−	3.25782e8i	−0.578032	−	0.333727i
$993$	−6.01830e7	−	1.53090e8i	−0.0614647	−	0.156350i
$994$	1.06069e7	+	508112.i	0.0108001	+	0.000517369i
$995$		−	9.42788e8i		−	0.957073i
$996$	1.84993e8	−	1.23207e9i	0.187231	−	1.24697i
$997$	6.93594e7	+	1.20134e8i	0.0699874	+	0.121222i	0.898895	−	0.438163i	$-0.144371\pi$
$997$	6.93594e7	+	1.20134e8i	0.0699874	+	0.121222i	−0.828908	+	0.559385i	$0.811037\pi$
$998$	7.64230e7	−	4.41228e7i	0.0768834	−	0.0443886i
$999$	−1.10425e9	+	7.55606e8i	−1.10757	+	0.757877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.2.9	yes	28
3.2	odd	2	inner	21.7.h.a.2.6	✓	28
7.2	even	3		147.7.b.e.50.6		14
7.4	even	3	inner	21.7.h.a.11.6	yes	28
7.5	odd	6		147.7.b.d.50.6		14
21.2	odd	6		147.7.b.e.50.9		14
21.5	even	6		147.7.b.d.50.9		14
21.11	odd	6	inner	21.7.h.a.11.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.6	✓	28	3.2	odd	2	inner
21.7.h.a.2.9	yes	28	1.1	even	1	trivial
21.7.h.a.11.6	yes	28	7.4	even	3	inner
21.7.h.a.11.9	yes	28	21.11	odd	6	inner
147.7.b.d.50.6		14	7.5	odd	6
147.7.b.d.50.9		14	21.5	even	6
147.7.b.e.50.6		14	7.2	even	3
147.7.b.e.50.9		14	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88516 + 1.66575i) q^{2} +(16.8223 - 21.1189i) q^{3} +(-26.4506 - 45.8137i) q^{4} +(-166.359 - 96.0474i) q^{5} +(83.7139 - 32.9098i) q^{6} +(157.090 + 304.913i) q^{7} -389.456i q^{8} +(-163.020 - 710.539i) q^{9} +O(q^{10})\)	\(q+(2.88516 + 1.66575i) q^{2} +(16.8223 - 21.1189i) q^{3} +(-26.4506 - 45.8137i) q^{4} +(-166.359 - 96.0474i) q^{5} +(83.7139 - 32.9098i) q^{6} +(157.090 + 304.913i) q^{7} -389.456i q^{8} +(-163.020 - 710.539i) q^{9} +(-319.982 - 554.224i) q^{10} +(750.813 - 433.482i) q^{11} +(-1412.50 - 212.085i) q^{12} +3412.13 q^{13} +(-54.6774 + 1141.39i) q^{14} +(-4826.96 + 1897.59i) q^{15} +(-1044.10 + 1808.44i) q^{16} +(2065.25 - 1192.37i) q^{17} +(713.242 - 2321.57i) q^{18} +(-1295.70 + 2244.22i) q^{19} +10162.0i q^{20} +(9082.05 + 1811.76i) q^{21} +2888.29 q^{22} +(-6492.91 - 3748.68i) q^{23} +(-8224.89 - 6551.55i) q^{24} +(10637.7 + 18425.1i) q^{25} +(9844.55 + 5683.75i) q^{26} +(-17748.2 - 8510.11i) q^{27} +(9814.06 - 15262.0i) q^{28} -24538.1i q^{29} +(-17087.5 - 2565.66i) q^{30} +(10218.4 + 17698.7i) q^{31} +(-27610.6 + 15941.0i) q^{32} +(3475.73 - 23148.5i) q^{33} +7944.77 q^{34} +(3152.71 - 65813.1i) q^{35} +(-28240.5 + 26262.7i) q^{36} +(33989.3 - 58871.2i) q^{37} +(-7476.62 + 4316.63i) q^{38} +(57400.0 - 72060.6i) q^{39} +(-37406.2 + 64789.5i) q^{40} +87649.0i q^{41} +(23185.2 + 20355.6i) q^{42} +11230.1 q^{43} +(-39718.8 - 22931.7i) q^{44} +(-41125.7 + 133862. i) q^{45} +(-12488.7 - 21631.1i) q^{46} +(105944. + 61166.8i) q^{47} +(20628.1 + 52472.4i) q^{48} +(-68294.4 + 95797.5i) q^{49} +70879.0i q^{50} +(9560.63 - 63674.4i) q^{51} +(-90252.8 - 156322. i) q^{52} +(145009. - 83721.1i) q^{53} +(-37030.7 - 54117.1i) q^{54} -166539. q^{55} +(118750. - 61179.6i) q^{56} +(25598.9 + 65116.9i) q^{57} +(40874.3 - 70796.4i) q^{58} +(-139071. + 80292.8i) q^{59} +(214611. + 170949. i) q^{60} +(19933.4 - 34525.7i) q^{61} +68084.8i q^{62} +(191044. - 161325. i) q^{63} +27430.2 q^{64} +(-567639. - 327726. i) q^{65} +(48587.7 - 60997.6i) q^{66} +(36908.0 + 63926.6i) q^{67} +(-109254. - 63077.9i) q^{68} +(-188394. + 74061.9i) q^{69} +(118724. - 184630. i) q^{70} -9292.90i q^{71} +(-276723. + 63488.9i) q^{72} +(-78094.7 - 135264. i) q^{73} +(196129. - 113235. i) q^{74} +(568069. + 85294.9i) q^{75} +137088. q^{76} +(250119. + 160836. i) q^{77} +(285643. - 112293. i) q^{78} +(-116864. + 202414. i) q^{79} +(347391. - 200566. i) q^{80} +(-478290. + 231663. i) q^{81} +(-146001. + 252881. i) q^{82} +872261. i q^{83} +(-157222. - 464005. i) q^{84} -458097. q^{85} +(32400.8 + 18706.6i) q^{86} +(-518219. - 412788. i) q^{87} +(-168822. - 292408. i) q^{88} +(-182193. - 105189. i) q^{89} +(-341635. + 317709. i) q^{90} +(536012. + 1.04040e6i) q^{91} +396619. i q^{92} +(545674. + 81932.4i) q^{93} +(203777. + 352952. i) q^{94} +(431104. - 248898. i) q^{95} +(-127817. + 851272. i) q^{96} +1.18735e6 q^{97} +(-356615. + 162630. i) q^{98} +(-430403. - 462816. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

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