LMFDB - Embedded newform 21.7.h.a.11.3

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			11.3
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.23947 + 5.33441i) q^{2} +(-22.3946 + 15.0825i) q^{3} +(24.9119 - 43.1487i) q^{4} +(-152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} -151.243i q^{8} +(274.035 - 675.534i) q^{9} +O(q^{10})$	\(q+(-9.23947 + 5.33441i) q^{2} +(-22.3946 + 15.0825i) q^{3} +(24.9119 - 43.1487i) q^{4} +(-152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} -151.243i q^{8} +(274.035 - 675.534i) q^{9} +(941.439 - 1630.62i) q^{10} +(766.504 + 442.541i) q^{11} +(92.8995 + 1342.03i) q^{12} -3039.13 q^{13} +(-3258.03 + 1666.29i) q^{14} +(2091.87 - 4281.35i) q^{15} +(2401.15 + 4158.92i) q^{16} +(408.579 + 235.893i) q^{17} +(1071.64 + 7703.39i) q^{18} +(-4203.86 - 7281.30i) q^{19} +8793.11i q^{20} +(-7934.31 + 4776.28i) q^{21} -9442.80 q^{22} +(-489.271 + 282.481i) q^{23} +(2281.12 + 3387.02i) q^{24} +(7760.80 - 13442.1i) q^{25} +(28080.0 - 16212.0i) q^{26} +(4051.86 + 19261.4i) q^{27} +(9285.85 - 14346.7i) q^{28} -35049.2i q^{29} +(3510.74 + 50716.3i) q^{30} +(12963.8 - 22453.9i) q^{31} +(-35988.1 - 20777.7i) q^{32} +(-23840.2 + 1650.29i) q^{33} -5033.41 q^{34} +(-53894.3 + 27563.9i) q^{35} +(-22321.7 - 28653.1i) q^{36} +(1752.36 + 3035.18i) q^{37} +(77683.0 + 44850.3i) q^{38} +(68060.1 - 45837.8i) q^{39} +(13346.0 + 23115.9i) q^{40} -1160.80i q^{41} +(47830.2 - 86455.2i) q^{42} -91849.8 q^{43} +(38190.2 - 22049.1i) q^{44} +(17727.1 + 127430. i) q^{45} +(3013.74 - 5219.94i) q^{46} +(-47734.7 + 27559.7i) q^{47} +(-116500. - 56921.9i) q^{48} +(117041. + 11941.7i) q^{49} +165597. i q^{50} +(-12707.8 + 879.674i) q^{51} +(-75710.6 + 131135. i) q^{52} +(14804.2 + 8547.21i) q^{53} +(-140186. - 156351. i) q^{54} -156203. q^{55} +(2636.20 - 51809.2i) q^{56} +(203964. + 99656.9i) q^{57} +(186967. + 323836. i) q^{58} +(-327850. - 189284. i) q^{59} +(-132622. - 196918. i) q^{60} +(-39480.6 - 68382.4i) q^{61} +276617. i q^{62} +(105647. - 226632. i) q^{63} +136000. q^{64} +(464500. - 268179. i) q^{65} +(211468. - 142421. i) q^{66} +(30150.0 - 52221.3i) q^{67} +(20357.0 - 11753.1i) q^{68} +(6696.49 - 13705.5i) q^{69} +(350918. - 542170. i) q^{70} -330141. i q^{71} +(-102170. - 41445.8i) q^{72} +(-182079. + 315369. i) q^{73} +(-32381.8 - 18695.6i) q^{74} +(28940.9 + 418083. i) q^{75} -418905. q^{76} +(254858. + 164956. i) q^{77} +(-384322. + 786578. i) q^{78} +(183846. + 318430. i) q^{79} +(-733983. - 423765. i) q^{80} +(-381251. - 370240. i) q^{81} +(6192.20 + 10725.2i) q^{82} +518160. i q^{83} +(8431.38 + 461342. i) q^{84} -83262.7 q^{85} +(848644. - 489965. i) q^{86} +(528631. + 784913. i) q^{87} +(66931.2 - 115928. i) q^{88} +(-651596. + 376199. i) q^{89} +(-843552. - 1.08282e6i) q^{90} +(-1.04108e6 - 52972.9i) q^{91} +28148.5i q^{92} +(48343.5 + 698373. i) q^{93} +(294029. - 509274. i) q^{94} +(1.28503e6 + 741915. i) q^{95} +(1.11932e6 - 77482.6i) q^{96} +1.02408e6 q^{97} +(-1.14510e6 + 514012. i) q^{98} +(509001. - 396528. 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−9.23947	+	5.33441i	−1.15493	+	0.666802i	−0.950085	−	0.311992i	$-0.899004\pi$
$2$	−9.23947	+	5.33441i	−1.15493	+	0.666802i	−0.204850	+	0.978793i	$0.565671\pi$
$3$	−22.3946	+	15.0825i	−0.829429	+	0.558612i
$3$	−22.3946	+	15.0825i	−0.829429	+	0.558612i
$4$	24.9119	−	43.1487i	0.389249	−	0.674199i
$5$	−152.840	+	88.2420i	−1.22272	+	0.705936i	−0.965496	−	0.260417i	$-0.916140\pi$
$5$	−152.840	+	88.2420i	−1.22272	+	0.705936i	−0.257221	+	0.966353i	$0.582807\pi$
$6$	126.458	−	258.817i	0.585453	−	1.19822i
$7$	342.557	+	17.4303i	0.998708	+	0.0508171i
$7$	342.557	+	17.4303i	0.998708	+	0.0508171i
$8$		−	151.243i		−	0.295396i
$9$	274.035	−	675.534i	0.375905	−	0.926658i
$10$	941.439	−	1630.62i	0.941439	−	1.63062i
$11$	766.504	+	442.541i	0.575886	+	0.332488i	0.759497	−	0.650511i	$-0.225445\pi$
$11$	766.504	+	442.541i	0.575886	+	0.332488i	−0.183611	+	0.982999i	$0.558779\pi$
$12$	92.8995	+	1342.03i	0.0537613	+	0.776639i
$13$	−3039.13			−1.38331			−0.691655	−	0.722228i	$-0.743118\pi$
$13$	−3039.13			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$14$	−3258.03	+	1666.29i	−1.18733	+	0.607250i
$15$	2091.87	−	4281.35i	0.619813	−	1.26855i
$16$	2401.15	+	4158.92i	0.586219	+	1.01536i
$17$	408.579	+	235.893i	0.0831628	+	0.0480141i	0.541005	−	0.841020i	$-0.318044\pi$
$17$	408.579	+	235.893i	0.0831628	+	0.0480141i	−0.457842	+	0.889034i	$0.651377\pi$
$18$	1071.64	+	7703.39i	0.183752	+	1.32088i
$19$	−4203.86	−	7281.30i	−0.612897	−	1.06157i	−0.990750	−	0.135703i	$-0.956671\pi$
$19$	−4203.86	−	7281.30i	−0.612897	−	1.06157i	0.377852	−	0.925866i	$-0.376663\pi$
$20$			8793.11i			1.09914i
$21$	−7934.31	+	4776.28i	−0.856744	+	0.515741i
$22$	−9442.80			−0.886814
$23$	−489.271	+	282.481i	−0.0402129	+	0.0232169i	−0.519972	−	0.854183i	$-0.674058\pi$
$23$	−489.271	+	282.481i	−0.0402129	+	0.0232169i	0.479759	+	0.877400i	$0.340724\pi$
$24$	2281.12	+	3387.02i	0.165012	+	0.245010i
$25$	7760.80	−	13442.1i	0.496691	−	0.860294i
$26$	28080.0	−	16212.0i	1.59763	−	0.922393i
$27$	4051.86	+	19261.4i	0.205856	+	0.978582i
$28$	9285.85	−	14346.7i	0.423007	−	0.653547i
$29$		−	35049.2i		−	1.43709i	−0.695480	−	0.718546i	$-0.744808\pi$
$29$		−	35049.2i		−	1.43709i	0.695480	−	0.718546i	$-0.255192\pi$
$30$	3510.74	+	50716.3i	0.130027	+	1.87838i
$31$	12963.8	−	22453.9i	0.435158	−	0.753715i	−0.562151	−	0.827035i	$-0.690026\pi$
$31$	12963.8	−	22453.9i	0.435158	−	0.753715i	0.997308	+	0.0733197i	$0.0233593\pi$
$32$	−35988.1	−	20777.7i	−1.09827	−	0.634086i
$33$	−23840.2	+	1650.29i	−0.663388	+	0.0459217i
$34$	−5033.41			−0.128063
$35$	−53894.3	+	27563.9i	−1.25701	+	0.642889i
$36$	−22321.7	−	28653.1i	−0.478431	−	0.614135i
$37$	1752.36	+	3035.18i	0.0345954	+	0.0599210i	0.882805	−	0.469740i	$-0.155652\pi$
$37$	1752.36	+	3035.18i	0.0345954	+	0.0599210i	−0.848209	+	0.529661i	$0.822319\pi$
$38$	77683.0	+	44850.3i	1.41571	+	0.817362i
$39$	68060.1	−	45837.8i	1.14736	−	0.772733i
$40$	13346.0	+	23115.9i	0.208531	+	0.361186i
$41$		−	1160.80i		−	0.0168425i	−0.999965	−	0.00842126i	$-0.997319\pi$
$41$		−	1160.80i		−	0.0168425i	0.999965	−	0.00842126i	$-0.00268060\pi$
$42$	47830.2	−	86455.2i	0.645587	−	1.16693i
$43$	−91849.8			−1.15524			−0.577621	−	0.816305i	$-0.696019\pi$
$43$	−91849.8			−1.15524			−0.577621	+	0.816305i	$0.696019\pi$
$44$	38190.2	−	22049.1i	0.448326	−	0.258841i
$45$	17727.1	+	127430.i	0.194536	+	1.39841i
$46$	3013.74	−	5219.94i	0.0309622	−	0.0536281i
$47$	−47734.7	+	27559.7i	−0.459770	+	0.265449i	−0.711948	−	0.702232i	$-0.752187\pi$
$47$	−47734.7	+	27559.7i	−0.459770	+	0.265449i	0.252177	+	0.967681i	$0.418853\pi$
$48$	−116500.	−	56921.9i	−1.05342	−	0.514701i
$49$	117041.	+	11941.7i	0.994835	+	0.101503i
$50$			165597.i			1.32478i
$51$	−12707.8	+	879.674i	−0.0957989	+	0.00663149i
$52$	−75710.6	+	131135.i	−0.538452	+	0.932626i
$53$	14804.2	+	8547.21i	0.0994392	+	0.0574112i	0.548895	−	0.835891i	$-0.315049\pi$
$53$	14804.2	+	8547.21i	0.0994392	+	0.0574112i	−0.449456	+	0.893303i	$0.648382\pi$
$54$	−140186.	−	156351.i	−0.890270	−	0.992933i
$55$	−156203.			−0.938861
$56$	2636.20	−	51809.2i	0.0150112	−	0.295014i
$57$	203964.	+	99656.9i	1.10136	+	0.538125i
$58$	186967.	+	323836.i	0.958255	+	1.65975i
$59$	−327850.	−	189284.i	−1.59632	−	0.921634i	−0.992189	−	0.124746i	$-0.960188\pi$
$59$	−327850.	−	189284.i	−1.59632	−	0.921634i	−0.604128	−	0.796888i	$-0.706478\pi$
$60$	−132622.	−	196918.i	−0.613992	−	0.911658i
$61$	−39480.6	−	68382.4i	−0.173938	−	0.301269i	0.765855	−	0.643013i	$-0.222316\pi$
$61$	−39480.6	−	68382.4i	−0.173938	−	0.301269i	−0.939793	+	0.341744i	$0.888983\pi$
$62$			276617.i			1.16066i
$63$	105647.	−	226632.i	0.422509	−	0.906359i
$64$	136000.			0.518800
$65$	464500.	−	268179.i	1.69140	−	0.976528i
$66$	211468.	−	142421.i	0.735549	−	0.495385i
$67$	30150.0	−	52221.3i	0.100245	−	0.173629i	−0.811541	−	0.584296i	$-0.801371\pi$
$67$	30150.0	−	52221.3i	0.100245	−	0.173629i	0.911786	+	0.410667i	$0.134704\pi$
$68$	20357.0	−	11753.1i	0.0647421	−	0.0373789i
$69$	6696.49	−	13705.5i	0.0203845	−	0.0417202i
$70$	350918.	−	542170.i	1.02309	−	1.58067i
$71$		−	330141.i		−	0.922410i	−0.887294	−	0.461205i	$-0.847417\pi$
$71$		−	330141.i		−	0.922410i	0.887294	−	0.461205i	$-0.152583\pi$
$72$	−102170.	−	41445.8i	−0.273731	−	0.111041i
$73$	−182079.	+	315369.i	−0.468048	+	0.810683i	−0.999333	−	0.0365102i	$-0.988376\pi$
$73$	−182079.	+	315369.i	−0.468048	+	0.810683i	0.531285	+	0.847193i	$0.321709\pi$
$74$	−32381.8	−	18695.6i	−0.0799108	−	0.0461365i
$75$	28940.9	+	418083.i	0.0686008	+	0.991011i
$76$	−418905.			−0.954279
$77$	254858.	+	164956.i	0.558246	+	0.361323i
$78$	−384322.	+	786578.i	−0.809862	+	1.65752i
$79$	183846.	+	318430.i	0.372883	+	0.645852i	0.990008	−	0.141013i	$-0.0450360\pi$
$79$	183846.	+	318430.i	0.372883	+	0.645852i	−0.617125	+	0.786865i	$0.711703\pi$
$80$	−733983.	−	423765.i	−1.43356	−	0.827667i
$81$	−381251.	−	370240.i	−0.717391	−	0.696671i
$82$	6192.20	+	10725.2i	0.0112306	+	0.0194520i
$83$			518160.i			0.906212i	0.891457	+	0.453106i	$0.149684\pi$
$83$			518160.i			0.906212i	−0.891457	+	0.453106i	$0.850316\pi$
$84$	8431.38	+	461342.i	0.0142253	+	0.778368i
$85$	−83262.7			−0.135579
$86$	848644.	−	489965.i	1.33423	−	0.770317i
$87$	528631.	+	784913.i	0.802777	+	1.19197i
$88$	66931.2	−	115928.i	0.0982156	−	0.170114i
$89$	−651596.	+	376199.i	−0.924290	+	0.533639i	−0.885001	−	0.465589i	$-0.845843\pi$
$89$	−651596.	+	376199.i	−0.924290	+	0.533639i	−0.0392888	+	0.999228i	$0.512509\pi$
$90$	−843552.	−	1.08282e6i	−1.15714	−	1.48535i
$91$	−1.04108e6	−	52972.9i	−1.38152	−	0.0702958i
$92$			28148.5i			0.0361487i
$93$	48343.5	+	698373.i	0.0601020	+	0.868237i
$94$	294029.	−	509274.i	0.354003	−	0.613151i
$95$	1.28503e6	+	741915.i	1.49880	+	0.865333i
$96$	1.11932e6	−	77482.6i	1.26514	−	0.0875771i
$97$	1.02408e6			1.12207			0.561035	−	0.827792i	$-0.310403\pi$
$97$	1.02408e6			1.12207			0.561035	+	0.827792i	$0.310403\pi$
$98$	−1.14510e6	+	514012.i	−1.21665	+	0.546129i
$99$	509001.	−	396528.i	0.524581	−	0.408666i
$100$	−386673.	−	669737.i	−0.386673	−	0.669737i
$101$	189942.	+	109663.i	0.184356	+	0.106438i	0.589338	−	0.807887i	$-0.299389\pi$
$101$	189942.	+	109663.i	0.184356	+	0.106438i	−0.404982	+	0.914325i	$0.632722\pi$
$102$	112721.	−	75916.5i	0.106220	−	0.0715378i
$103$	−857597.	−	1.48540e6i	−0.784823	−	1.35935i	−0.929105	−	0.369816i	$-0.879421\pi$
$103$	−857597.	−	1.48540e6i	−0.784823	−	1.35935i	0.144282	−	0.989537i	$-0.453913\pi$
$104$			459647.i			0.408624i
$105$	791209.	−	1.43014e6i	0.683476	−	1.23541i
$106$	−182378.			−0.153128
$107$	−1.91866e6	+	1.10774e6i	−1.56620	+	0.904246i	−0.569594	+	0.821926i	$0.692900\pi$
$107$	−1.91866e6	+	1.10774e6i	−1.56620	+	0.904246i	−0.996606	+	0.0823201i	$0.973767\pi$
$108$	932046.	+	305007.i	0.739888	+	0.242124i
$109$	25554.5	−	44261.7i	0.0197328	−	0.0341781i	−0.855990	−	0.516992i	$-0.827052\pi$
$109$	25554.5	−	44261.7i	0.0197328	−	0.0341781i	0.875723	+	0.482814i	$0.160385\pi$
$110$	1.44323e6	−	833251.i	1.08432	−	0.626034i
$111$	−85021.5	−	41541.5i	−0.0621670	−	0.0303748i
$112$	750041.	+	1.46652e6i	0.533864	+	1.04384i
$113$		−	2.36844e6i		−	1.64145i	−0.571326	−	0.820723i	$-0.693571\pi$
$113$		−	2.36844e6i		−	1.64145i	0.571326	−	0.820723i	$-0.306429\pi$
$114$	−2.41613e6	+	167252.i	−1.63082	+	0.112890i
$115$	49853.3	−	86348.4i	0.0327794	−	0.0567755i
$116$	−1.51233e6	−	873144.i	−0.968885	−	0.559386i
$117$	−832828.	+	2.05304e6i	−0.519993	+	1.28186i
$118$	4.03888e6			2.45819
$119$	135850.	+	87928.5i	0.0806154	+	0.0521781i
$120$	−647523.	−	316380.i	−0.374724	−	0.183090i
$121$	−494095.	−	855797.i	−0.278903	−	0.483075i
$122$	729560.	+	421211.i	0.401773	+	0.231964i
$123$	17507.8	+	25995.7i	0.00940843	+	0.0139697i
$124$	−645905.	−	1.11874e6i	−0.338769	−	0.586765i
$125$		−	18248.2i		−	0.00934309i
$126$	232825.	+	2.65753e6i	0.116391	+	1.32851i
$127$	−998266.			−0.487344			−0.243672	−	0.969858i	$-0.578352\pi$
$127$	−998266.			−0.487344			−0.243672	+	0.969858i	$0.578352\pi$
$128$	1.04667e6	−	604293.i	0.499090	−	0.288149i
$129$	2.05694e6	−	1.38533e6i	0.958191	−	0.645332i
$130$	−2.86116e6	+	4.95567e6i	−1.30230	+	2.25565i
$131$	1.72512e6	−	996001.i	0.767373	−	0.443043i	−0.0645636	−	0.997914i	$-0.520566\pi$
$131$	1.72512e6	−	996001.i	0.767373	−	0.443043i	0.831937	+	0.554870i	$0.187232\pi$
$132$	−522697.	+	1.06979e6i	−0.227263	+	0.465131i
$133$	−1.31315e6	−	2.56754e6i	−0.558160	−	1.09134i
$134$			643330.i			0.267374i
$135$	−2.31895e6	−	2.58637e6i	−0.942520	−	1.05121i
$136$	35677.1	−	61794.6i	0.0141832	−	0.0245660i
$137$	2.12580e6	+	1.22733e6i	0.826726	+	0.477310i	0.852730	−	0.522351i	$-0.174945\pi$
$137$	2.12580e6	+	1.22733e6i	0.826726	+	0.477310i	−0.0260045	+	0.999662i	$0.508278\pi$
$138$	11238.6	+	162353.i	0.00427636	+	0.0617766i
$139$	−1.87348e6			−0.697598			−0.348799	−	0.937197i	$-0.613410\pi$
$139$	−1.87348e6			−0.697598			−0.348799	+	0.937197i	$0.613410\pi$
$140$	−153266.	+	3.01214e6i	−0.0558551	+	1.09772i
$141$	653330.	−	1.33715e6i	0.233064	−	0.477004i
$142$	1.76111e6	+	3.05033e6i	0.615065	+	1.06532i
$143$	−2.32951e6	−	1.34494e6i	−0.796629	−	0.459934i
$144$	3.46749e6	−	482372.i	1.16126	−	0.161545i
$145$	3.09281e6	+	5.35691e6i	1.01449	+	1.75716i
$146$		−	3.88513e6i		−	1.24838i
$147$	−2.80120e6	+	1.49785e6i	−0.881846	+	0.471538i
$148$	174619.			0.0538649
$149$	−63765.1	+	36814.8i	−0.0192763	+	0.0111292i	−0.509607	−	0.860407i	$-0.670209\pi$
$149$	−63765.1	+	36814.8i	−0.0192763	+	0.0111292i	0.490331	+	0.871536i	$0.336876\pi$
$150$	−2.49763e6	−	3.70848e6i	−0.740037	−	1.09881i
$151$	424826.	−	735820.i	0.123390	−	0.213718i	−0.797712	−	0.603038i	$-0.793957\pi$
$151$	424826.	−	735820.i	0.123390	−	0.213718i	0.921102	+	0.389320i	$0.127290\pi$
$152$	−1.10124e6	+	635804.i	−0.313583	+	0.181047i
$153$	271319.	−	211366.i	0.0757540	−	0.0590148i
$154$	−3.23469e6	−	164590.i	−0.885668	−	0.0450653i
$155$			4.57580e6i			1.22877i
$156$	−282334.	−	4.07861e6i	−0.0743685	−	1.07433i
$157$	−1.42920e6	+	2.47544e6i	−0.369312	+	0.639667i	−0.989458	−	0.144819i	$-0.953740\pi$
$157$	−1.42920e6	+	2.47544e6i	−0.369312	+	0.639667i	0.620146	+	0.784486i	$0.287073\pi$
$158$	−3.39728e6	−	1.96142e6i	−0.861311	−	0.497278i
$159$	−460448.	+	31873.6i	−0.114548	+	0.00792938i
$160$	7.33388e6			1.79050
$161$	−172527.	+	88237.5i	−0.0413408	+	0.0211434i
$162$	5.49757e6	+	1.38707e6i	1.29308	+	0.326252i
$163$	−2.28916e6	−	3.96494e6i	−0.528584	−	0.915534i	−0.999445	−	0.0333262i	$-0.989390\pi$
$163$	−2.28916e6	−	3.96494e6i	−0.528584	−	0.915534i	0.470861	−	0.882207i	$-0.343943\pi$
$164$	−50087.2	−	28917.8i	−0.0113552	−	0.00655593i
$165$	3.49810e6	−	2.35594e6i	0.778718	−	0.524459i
$166$	−2.76408e6	−	4.78753e6i	−0.604264	−	1.04662i
$167$		−	418018.i		−	0.0897523i	−0.998993	−	0.0448762i	$-0.985711\pi$
$167$		−	418018.i		−	0.0897523i	0.998993	−	0.0448762i	$-0.0142893\pi$
$168$	722378.	+	1.20001e6i	0.152348	+	0.253079i
$169$	4.40951e6			0.913545
$170$	769304.	−	444158.i	0.156585	−	0.0904046i
$171$	−6.07077e6	+	844521.i	−1.21410	+	0.168897i
$172$	−2.28816e6	+	3.96320e6i	−0.449677	+	0.778863i
$173$	−1.68052e6	+	970246.i	−0.324567	+	0.187389i	−0.653426	−	0.756990i	$-0.726669\pi$
$173$	−1.68052e6	+	970246.i	−0.324567	+	0.187389i	0.328860	+	0.944379i	$0.393336\pi$
$174$	−9.07132e6	−	4.43225e6i	−1.72196	−	0.841349i
$175$	2.89281e6	−	4.46941e6i	0.539767	−	0.833943i
$176$			4.25044e6i			0.779644i
$177$	1.01969e7	−	705863.i	1.83887	−	0.127292i
$178$	4.01360e6	−	6.95176e6i	0.711663	−	1.23264i
$179$	1.82126e6	+	1.05150e6i	0.317550	+	0.183338i	0.650300	−	0.759677i	$-0.274643\pi$
$179$	1.82126e6	+	1.05150e6i	0.317550	+	0.183338i	−0.332750	+	0.943015i	$0.607976\pi$
$180$	5.94005e6	+	2.40962e6i	1.01853	+	0.413172i
$181$	4.35975e6			0.735234			0.367617	−	0.929977i	$-0.380174\pi$
$181$	4.35975e6			0.735234			0.367617	+	0.929977i	$0.380174\pi$
$182$	9.90157e6	−	5.06408e6i	1.64244	−	0.840014i
$183$	1.91553e6	+	935928.i	0.312562	+	0.152718i
$184$	42723.1	+	73998.7i	0.00685819	+	0.0118787i
$185$	−535660.	−	309264.i	−0.0846008	−	0.0488443i
$186$	−4.17208e6	−	6.19471e6i	−0.648356	−	0.962681i
$187$	208785.	+	361626.i	0.0319282	+	0.0553013i
$188$			2.74626e6i			0.413302i
$189$	1.05226e6	+	6.66876e6i	0.155861	+	0.987779i
$190$	−1.58307e7			−2.30802
$191$	−7.07195e6	+	4.08299e6i	−1.01494	+	0.585974i	−0.912633	−	0.408779i	$-0.865955\pi$
$191$	−7.07195e6	+	4.08299e6i	−1.01494	+	0.585974i	−0.102304	+	0.994753i	$0.532621\pi$
$192$	−3.04567e6	+	2.05123e6i	−0.430308	+	0.289808i
$193$	−7.09039e6	+	1.22809e7i	−0.986276	+	1.70828i	−0.350150	+	0.936694i	$0.613869\pi$
$193$	−7.09039e6	+	1.22809e7i	−0.986276	+	1.70828i	−0.636125	+	0.771586i	$0.719464\pi$
$194$	−9.46199e6	+	5.46288e6i	−1.29592	+	0.748198i
$195$	−6.35746e6	+	1.30116e7i	−0.857393	+	1.75479i
$196$	3.43100e6	−	4.75270e6i	0.455672	−	0.631207i
$197$		−	7.39165e6i		−	0.966814i	−0.875396	−	0.483407i	$-0.839399\pi$
$197$		−	7.39165e6i		−	0.966814i	0.875396	−	0.483407i	$-0.160601\pi$
$198$	−2.58765e6	+	6.37893e6i	−0.333358	+	0.821774i
$199$	−4.06219e6	+	7.03592e6i	−0.515467	+	0.892815i	0.484372	+	0.874862i	$0.339048\pi$
$199$	−4.06219e6	+	7.03592e6i	−0.515467	+	0.892815i	−0.999839	+	0.0179528i	$0.994285\pi$
$200$	−2.03302e6	−	1.17376e6i	−0.254128	−	0.146721i
$201$	112433.	+	1.62421e6i	0.0138454	+	0.200011i
$202$	−2.33995e6			−0.283892
$203$	610917.	−	1.20064e7i	0.0730288	−	1.43523i
$204$	−278620.	+	570241.i	−0.0328187	+	0.0671688i
$205$	102432.	+	177417.i	0.0118897	+	0.0205936i
$206$	1.58475e7	+	9.14955e6i	1.81284	+	1.04664i
$207$	56748.0	+	407928.i	0.00639793	+	0.0459910i
$208$	−7.29742e6	−	1.26395e7i	−0.810923	−	1.40456i
$209$		−	7.44154e6i		−	0.815124i
$210$	318628.	+	1.74344e7i	0.0344053	+	1.88256i
$211$	7.35737e6			0.783205			0.391602	−	0.920135i	$-0.371921\pi$
$211$	7.35737e6			0.783205			0.391602	+	0.920135i	$0.371921\pi$
$212$	737603.	−	425855.i	0.0774132	−	0.0446945i
$213$	4.97936e6	+	7.39336e6i	0.515269	+	0.765074i
$214$	1.18183e7	−	2.04699e7i	1.20591	−	2.08869i
$215$	1.40383e7	−	8.10501e6i	1.41253	−	0.815527i
$216$	2.91315e6	−	612815.i	0.289069	−	0.0608090i
$217$	4.83221e6	−	7.46578e6i	0.472897	−	0.730628i
$218$			545273.i			0.0526313i
$219$	−678993.	−	9.80877e6i	−0.0646447	−	0.933861i
$220$	−3.89132e6	+	6.73996e6i	−0.365451	+	0.632979i
$221$	−1.24173e6	−	716910.i	−0.115040	−	0.0664183i
$222$	1.00715e6	−	69718.2i	0.0920528	−	0.00637217i
$223$	−473067.			−0.0426588			−0.0213294	−	0.999773i	$-0.506790\pi$
$223$	−473067.			−0.0426588			−0.0213294	+	0.999773i	$0.506790\pi$
$224$	−1.19658e7	−	7.74484e6i	−1.06463	−	0.689078i
$225$	−6.95386e6	−	8.92629e6i	−0.610490	−	0.783652i
$226$	1.26342e7	+	2.18831e7i	1.09452	+	1.89576i
$227$	7.06037e6	+	4.07630e6i	0.603601	+	0.348489i	0.770457	−	0.637492i	$-0.220028\pi$
$227$	7.06037e6	+	4.07630e6i	0.603601	+	0.348489i	−0.166856	+	0.985981i	$0.553362\pi$
$228$	9.38121e6	−	6.31815e6i	0.791506	−	0.533072i
$229$	−3.29935e6	−	5.71465e6i	−0.274740	−	0.475864i	0.695329	−	0.718691i	$-0.255259\pi$
$229$	−3.29935e6	−	5.71465e6i	−0.274740	−	0.475864i	−0.970070	+	0.242827i	$0.921925\pi$
$230$			1.06375e6i			0.0874293i
$231$	−8.19538e6	+	149777.i	−0.664865	+	0.0121509i
$232$	−5.30094e6			−0.424511
$233$	−1.07075e7	+	6.18197e6i	−0.846486	+	0.488719i	−0.859464	−	0.511197i	$-0.829202\pi$
$233$	−1.07075e7	+	6.18197e6i	−0.846486	+	0.488719i	0.0129778	+	0.999916i	$0.495869\pi$
$234$	−3.25685e6	−	2.34116e7i	−0.254185	−	1.82719i
$235$	4.86384e6	−	8.42442e6i	0.374779	−	0.649137i
$236$	−1.63347e7	+	9.43087e6i	−1.24273	+	0.717490i
$237$	−8.91988e6	−	4.35825e6i	−0.670061	−	0.327392i
$238$	−1.72423e6	−	87733.6i	−0.127898	−	0.00650781i
$239$			7.84259e6i			0.574468i	0.957860	+	0.287234i	$0.0927357\pi$
$239$			7.84259e6i			0.574468i	−0.957860	+	0.287234i	$0.907264\pi$
$240$	2.28287e7	−	1.58027e6i	1.65138	−	0.114314i
$241$	3.41141e6	−	5.90873e6i	0.243715	−	0.422127i	−0.718055	−	0.695987i	$-0.754967\pi$
$241$	3.41141e6	−	5.90873e6i	0.243715	−	0.422127i	0.961770	+	0.273860i	$0.0883005\pi$
$242$	9.13035e6	+	5.27141e6i	0.644230	+	0.371947i
$243$	1.41221e7	+	2.54113e6i	0.984194	+	0.177096i
$244$	−3.93415e6			−0.270820
$245$	−1.89423e7	+	8.50280e6i	−1.28806	+	0.578181i
$246$	−300435.	−	146793.i	−0.0201811	−	0.00986050i
$247$	1.27761e7	+	2.21288e7i	0.847827	+	1.46848i
$248$	−3.39599e6	−	1.96068e6i	−0.222644	−	0.128544i
$249$	−7.81517e6	−	1.16040e7i	−0.506221	−	0.751639i
$250$	97343.6	+	168604.i	0.00622999	+	0.0107907i
$251$			1.46090e7i			0.923846i	0.886920	+	0.461923i	$0.152840\pi$
$251$			1.46090e7i			0.923846i	−0.886920	+	0.461923i	$0.847160\pi$
$252$	−7.14702e6	−	1.02044e7i	−0.446605	−	0.637654i
$253$	−500037.			−0.0308774
$254$	9.22346e6	−	5.32516e6i	0.562850	−	0.324961i
$255$	1.86463e6	−	1.25581e6i	0.112454	−	0.0757363i
$256$	−1.07991e7	+	1.87046e7i	−0.643677	+	1.11488i
$257$	6.83136e6	−	3.94409e6i	0.402446	−	0.232353i	−0.285093	−	0.958500i	$-0.592024\pi$
$257$	6.83136e6	−	3.94409e6i	0.402446	−	0.232353i	0.687539	+	0.726147i	$0.258691\pi$
$258$	−1.16151e7	+	2.37723e7i	−0.676339	+	1.38424i
$259$	547379.	+	1.07027e6i	0.0315057	+	0.0616016i
$260$		−	2.67234e7i		−	1.52045i
$261$	−2.36769e7	−	9.60471e6i	−1.33169	−	0.540210i
$262$	−1.06262e7	+	1.84051e7i	−0.590844	+	1.02337i
$263$	−2.15711e7	−	1.24541e7i	−1.18578	−	0.684611i	−0.228437	−	0.973559i	$-0.573361\pi$
$263$	−2.15711e7	−	1.24541e7i	−1.18578	−	0.684611i	−0.957345	+	0.288948i	$0.906695\pi$
$264$	249594.	+	3.60566e6i	0.0135651	+	0.195962i
$265$	−3.01689e6			−0.162115
$266$	2.58291e7	+	1.67178e7i	1.37235	+	0.888248i
$267$	8.91818e6	−	1.82525e7i	0.468536	−	0.958935i
$268$	−1.50219e6	−	2.60187e6i	−0.0780405	−	0.135170i
$269$	2.37134e7	+	1.36910e7i	1.21825	+	0.703359i	0.964544	−	0.263922i	$-0.0850160\pi$
$269$	2.37134e7	+	1.36910e7i	1.21825	+	0.703359i	0.253709	+	0.967281i	$0.418349\pi$
$270$	3.52227e7	+	1.15264e7i	1.78950	+	0.585603i
$271$	−2.58227e6	−	4.47262e6i	−0.129746	−	0.224726i	0.793832	−	0.608137i	$-0.208083\pi$
$271$	−2.58227e6	−	4.47262e6i	−0.129746	−	0.224726i	−0.923578	+	0.383410i	$0.874749\pi$
$272$			2.26566e6i			0.112587i
$273$	2.41134e7	−	1.45157e7i	1.18514	−	0.713430i
$274$	−2.61884e7			−1.27309
$275$	1.18974e7	−	6.86895e6i	0.572075	−	0.330288i
$276$	−424551.	−	630375.i	−0.0201931	−	0.0299828i
$277$	−9.08673e6	+	1.57387e7i	−0.427532	+	0.740507i	−0.996653	−	0.0817467i	$-0.973950\pi$
$277$	−9.08673e6	+	1.57387e7i	−0.427532	+	0.740507i	0.569121	+	0.822254i	$0.307283\pi$
$278$	1.73100e7	−	9.99394e6i	0.805680	−	0.465160i
$279$	−1.16159e7	−	1.49106e7i	−0.534858	−	0.686568i
$280$	4.16884e6	+	8.15113e6i	0.189907	+	0.371316i
$281$			3.49201e7i			1.57382i	0.617065	+	0.786912i	$0.288322\pi$
$281$			3.49201e7i			1.57382i	−0.617065	+	0.786912i	$0.711678\pi$
$282$	1.09647e6	+	1.58397e7i	0.0488933	+	0.706316i
$283$	2.43250e6	−	4.21321e6i	0.107323	−	0.185889i	−0.807362	−	0.590057i	$-0.799105\pi$
$283$	2.43250e6	−	4.21321e6i	0.107323	−	0.185889i	0.914685	+	0.404167i	$0.132439\pi$
$284$	−1.42452e7	−	8.22444e6i	−0.621888	−	0.359047i
$285$	−3.99677e7	+	2.76669e6i	−1.72653	+	0.119516i
$286$	2.86979e7			1.22674
$287$	20233.1	−	397641.i	0.000855888	−	0.0168208i
$288$	−2.38981e7	+	1.86174e7i	−1.00043	+	0.779364i
$289$	−1.19575e7	−	2.07110e7i	−0.495389	−	0.858039i
$290$	−5.71519e7	−	3.29967e7i	−2.34335	−	1.35293i
$291$	−2.29339e7	+	1.54458e7i	−0.930677	+	0.626802i
$292$	9.07186e6	+	1.57129e7i	0.364374	+	0.631115i
$293$		−	1.42296e7i		−	0.565705i	−0.959163	−	0.282852i	$-0.908719\pi$
$293$		−	1.42296e7i		−	0.565705i	0.959163	−	0.282852i	$-0.0912806\pi$
$294$	1.78915e7	−	2.87821e7i	0.704052	−	1.13261i
$295$	6.68113e7			2.60246
$296$	459049.	−	265032.i	0.0177004	−	0.0102193i
$297$	−5.41822e6	+	1.65571e7i	−0.206817	+	0.631997i
$298$	392771.	−	680299.i	0.0148419	−	0.0257070i
$299$	1.48696e6	−	858495.i	0.0556269	−	0.0321162i
$300$	1.87607e7	+	9.16648e6i	0.694841	+	0.339499i
$301$	−3.14638e7	−	1.60097e6i	−1.15375	−	0.0587060i
$302$			9.06479e6i			0.329107i
$303$	−5.90766e6	+	408946.i	−0.212367	+	0.0147007i
$304$	2.01883e7	−	3.49671e7i	0.718585	−	1.24463i
$305$	1.20684e7	+	6.96769e6i	0.425353	+	0.245578i
$306$	−1.37933e6	+	3.40024e6i	−0.0481397	+	0.118671i
$307$	−1.26849e7			−0.438400			−0.219200	−	0.975680i	$-0.570345\pi$
$307$	−1.26849e7			−0.438400			−0.219200	+	0.975680i	$0.570345\pi$
$308$	1.34666e7	−	6.88741e6i	0.460900	−	0.235724i
$309$	4.16091e7	+	2.03302e7i	1.41031	+	0.689075i
$310$	−2.44092e7	−	4.22780e7i	−0.819348	−	1.41915i
$311$	−2.06912e7	−	1.19461e7i	−0.687868	−	0.397141i	0.114945	−	0.993372i	$-0.463331\pi$
$311$	−2.06912e7	−	1.19461e7i	−0.687868	−	0.397141i	−0.802813	+	0.596231i	$0.796664\pi$
$312$	−6.93263e6	−	1.02936e7i	−0.228262	−	0.338925i
$313$	2.62841e6	+	4.55255e6i	0.0857158	+	0.148464i	0.905696	−	0.423928i	$-0.139349\pi$
$313$	2.62841e6	+	4.55255e6i	0.0857158	+	0.148464i	−0.819980	+	0.572392i	$0.806016\pi$
$314$		−	3.04957e7i		−	0.985031i
$315$	3.85140e6	+	4.39609e7i	0.123222	+	1.40648i
$316$	1.83198e7			0.580577
$317$	3.38098e7	−	1.95201e7i	1.06136	−	0.612779i	0.135555	−	0.990770i	$-0.456718\pi$
$317$	3.38098e7	−	1.95201e7i	1.06136	−	0.612779i	0.925809	+	0.377991i	$0.123385\pi$
$318$	4.08427e6	−	2.75071e6i	0.127009	−	0.0855390i
$319$	1.55107e7	−	2.68654e7i	0.477816	−	0.827601i
$320$	−2.07862e7	+	1.20009e7i	−0.634346	+	0.366240i
$321$	2.62601e7	−	5.37457e7i	0.793929	−	1.62491i
$322$	1.12336e6	−	1.73560e6i	0.0336474	−	0.0519854i
$323$		−	3.96665e6i		−	0.117711i
$324$	−2.54731e7	+	7.22711e6i	−0.748938	+	0.212486i
$325$	−2.35861e7	+	4.08523e7i	−0.687078	+	1.19005i
$326$	4.23013e7	+	2.44227e7i	1.22096	+	0.704921i
$327$	95295.7	+	1.37665e6i	0.00272540	+	0.0393713i
$328$	−175563.			−0.00497521
$329$	−1.68322e7	+	8.60872e6i	−0.472666	+	0.241741i
$330$	−1.97531e7	+	4.04279e7i	−0.549659	+	1.12497i
$331$	−1.81703e7	−	3.14718e7i	−0.501045	−	0.867836i	−0.999999	−	0.00120735i	$-0.999616\pi$
$331$	−1.81703e7	−	3.14718e7i	−0.501045	−	0.867836i	0.498954	−	0.866628i	$-0.333718\pi$
$332$	2.23580e7	+	1.29084e7i	0.610967	+	0.352742i
$333$	2.53057e6	−	352035.i	0.0685309	−	0.00953351i
$334$	2.22988e6	+	3.86227e6i	0.0598470	+	0.103658i
$335$			1.06420e7i			0.283066i
$336$	−3.89157e7	−	2.15296e7i	−1.02590	−	0.567568i
$337$	−6.05675e7			−1.58252			−0.791262	−	0.611477i	$-0.790575\pi$
$337$	−6.05675e7			−1.58252			−0.791262	+	0.611477i	$0.790575\pi$
$338$	−4.07415e7	+	2.35221e7i	−1.05508	+	0.609153i
$339$	3.57220e7	+	5.30402e7i	0.916932	+	1.36146i
$340$	−2.07424e6	+	3.59268e6i	−0.0527742	+	0.0914075i
$341$	1.98736e7	−	1.14740e7i	0.501202	−	0.289369i
$342$	5.15857e7	−	4.01869e7i	1.28959	−	1.00463i
$343$	3.98852e7	+	6.13078e6i	0.988392	+	0.151926i
$344$			1.38916e7i			0.341254i
$345$	185909.	+	2.68565e6i	0.00452734	+	0.0654022i
$346$	1.03514e7	−	1.79291e7i	0.249902	−	0.432843i
$347$	5.66844e6	+	3.27267e6i	0.135667	+	0.0783275i	0.566297	−	0.824201i	$-0.308375\pi$
$347$	5.66844e6	+	3.27267e6i	0.135667	+	0.0783275i	−0.430630	+	0.902528i	$0.641709\pi$
$348$	4.70372e7	−	3.25606e6i	1.11610	−	0.0772599i
$349$	−2.22302e7			−0.522959			−0.261480	−	0.965209i	$-0.584210\pi$
$349$	−2.22302e7			−0.522959			−0.261480	+	0.965209i	$0.584210\pi$
$350$	−2.88640e6	+	5.67265e7i	−0.0673214	+	1.32307i
$351$	−1.23141e7	−	5.85380e7i	−0.284762	−	1.35368i
$352$	−1.83900e7	−	3.18525e7i	−0.421652	−	0.730323i
$353$	−4.26921e7	−	2.46483e7i	−0.970561	−	0.560354i	−0.0711539	−	0.997465i	$-0.522668\pi$
$353$	−4.26921e7	−	2.46483e7i	−0.970561	−	0.560354i	−0.899407	+	0.437112i	$0.856001\pi$
$354$	−9.04491e7	+	6.09165e7i	−2.03889	+	1.37317i
$355$	2.91323e7	+	5.04586e7i	0.651162	+	1.12785i
$356$			3.74874e7i			0.830874i
$357$	−4.36848e6	+	79837.5i	−0.0960121	+	0.00175470i
$358$	−2.24366e7			−0.489000
$359$	−1.95231e7	+	1.12717e7i	−0.421955	+	0.243616i	−0.695913	−	0.718126i	$-0.745000\pi$
$359$	−1.95231e7	+	1.12717e7i	−0.421955	+	0.243616i	0.273959	+	0.961741i	$0.411667\pi$
$360$	1.92728e7	−	2.68109e6i	0.413083	−	0.0574651i
$361$	−1.18220e7	+	2.04763e7i	−0.251286	+	0.435241i
$362$	−4.02818e7	+	2.32567e7i	−0.849147	+	0.490255i
$363$	2.39726e7	+	1.17130e7i	0.501182	+	0.244878i
$364$	−2.82209e7	+	4.36014e7i	−0.585149	+	0.904058i
$365$		−	6.42679e7i		−	1.32165i
$366$	−2.26911e7	+	1.57075e6i	−0.462821	+	0.0320378i
$367$	3.90163e7	−	6.75783e7i	0.789311	−	1.36713i	−0.137078	−	0.990560i	$-0.543771\pi$
$367$	3.90163e7	−	6.75783e7i	0.789311	−	1.36713i	0.926389	−	0.376567i	$-0.122896\pi$
$368$	−2.34963e6	−	1.35656e6i	−0.0471472	−	0.0272205i
$369$	−784162.	−	318100.i	−0.0156073	−	0.00633119i
$370$	6.59896e6			0.130278
$371$	4.92230e6	+	3.18595e6i	0.0963933	+	0.0623903i
$372$	3.13382e7	+	1.53119e7i	0.608759	+	0.297440i
$373$	1.85187e7	+	3.20753e7i	0.356848	+	0.618079i	0.987432	−	0.158042i	$-0.0505181\pi$
$373$	1.85187e7	+	3.20753e7i	0.356848	+	0.618079i	−0.630584	+	0.776121i	$0.717185\pi$
$374$	−3.85813e6	−	2.22749e6i	−0.0737500	−	0.0425796i
$375$	275229.	+	408661.i	0.00521916	+	0.00774943i
$376$	4.16820e6	+	7.21954e6i	0.0784125	+	0.135814i
$377$			1.06519e8i			1.98794i
$378$	−4.52963e7	−	5.60027e7i	−0.838662	−	1.03689i
$379$	8.17331e6			0.150134			0.0750672	−	0.997178i	$-0.476083\pi$
$379$	8.17331e6			0.150134			0.0750672	+	0.997178i	$0.476083\pi$
$380$	6.40253e7	−	3.69650e7i	1.16681	−	0.673660i
$381$	2.23558e7	−	1.50564e7i	0.404217	−	0.272236i
$382$	4.35607e7	−	7.54494e7i	0.781457	−	1.35352i
$383$	5.02164e7	−	2.89924e7i	0.893818	−	0.516046i	0.0186284	−	0.999826i	$-0.494070\pi$
$383$	5.02164e7	−	2.89924e7i	0.893818	−	0.516046i	0.875189	+	0.483781i	$0.160737\pi$
$384$	−1.43254e7	+	2.93193e7i	−0.252996	+	0.517797i
$385$	−5.35084e7	−	2.72266e6i	−0.937648	−	0.0477102i
$386$		−	1.51292e8i		−	2.63060i
$387$	−2.51700e7	+	6.20477e7i	−0.434261	+	1.07051i
$388$	2.55119e7	−	4.41879e7i	0.436765	−	0.756498i
$389$	6.34639e7	+	3.66409e7i	1.07815	+	0.622468i	0.930396	−	0.366557i	$-0.119463\pi$
$389$	6.34639e7	+	3.66409e7i	1.07815	+	0.622468i	0.147750	+	0.989025i	$0.452797\pi$
$390$	−1.06696e7	−	1.54134e8i	−0.179868	−	2.59838i
$391$	−266541.			−0.00445896
$392$	1.80610e6	−	1.77017e7i	0.0299836	−	0.293870i
$393$	−2.36112e7	+	4.83243e7i	−0.388992	+	0.796137i
$394$	3.94301e7	+	6.82950e7i	0.644673	+	1.11661i
$395$	−5.61979e7	−	3.24458e7i	−0.911861	−	0.526463i
$396$	−4.42948e6	−	3.18410e7i	−0.0713292	−	0.512745i
$397$	−1.20492e7	−	2.08698e7i	−0.192569	−	0.333539i	0.753532	−	0.657411i	$-0.228349\pi$
$397$	−1.20492e7	−	2.08698e7i	−0.192569	−	0.333539i	−0.946101	+	0.323872i	$0.895015\pi$
$398$		−	8.66776e7i		−	1.37486i
$399$	6.81323e7	+	3.76933e7i	1.07259	+	0.593397i
$400$	7.45395e7			1.16468
$401$	−5.17591e6	+	2.98831e6i	−0.0802701	+	0.0463439i	−0.539598	−	0.841923i	$-0.681424\pi$
$401$	−5.17591e6	+	2.98831e6i	−0.0802701	+	0.0463439i	0.459328	+	0.888267i	$0.348090\pi$
$402$	−9.70304e6	−	1.44071e7i	−0.149358	−	0.221768i
$403$	−3.93986e7	+	6.82404e7i	−0.601958	+	1.04262i
$404$	9.46364e6	−	5.46383e6i	0.143521	−	0.0828616i
$405$	9.09409e7	+	2.29449e7i	1.36897	+	0.345400i
$406$	5.84023e7	+	1.14191e8i	0.872673	+	1.70630i
$407$			3.10197e6i			0.0460102i
$408$	133044.	+	1.92197e6i	0.00195892	+	0.0282986i
$409$	−2.79908e6	+	4.84814e6i	−0.0409115	+	0.0708607i	−0.885756	−	0.464151i	$-0.846359\pi$
$409$	−2.79908e6	+	4.84814e6i	−0.0409115	+	0.0708607i	0.844845	+	0.535012i	$0.179693\pi$
$410$	−1.89283e6	−	1.09282e6i	−0.0274637	−	0.0158562i
$411$	−6.61178e7	+	4.57687e6i	−0.952342	+	0.0659240i
$412$	−8.54576e7			−1.22197
$413$	−1.09008e8	−	7.05551e7i	−1.54742	−	1.00156i
$414$	−2.70038e6	−	3.46633e6i	−0.0380561	−	0.0488504i
$415$	−4.57235e7	−	7.91954e7i	−0.639728	−	1.10804i
$416$	1.09373e8	+	6.31463e7i	1.51925	+	0.877137i
$417$	4.19559e7	−	2.82569e7i	0.578608	−	0.389687i
$418$	3.96962e7	+	6.87559e7i	0.543526	+	0.941415i
$419$			1.69985e7i			0.231084i	0.993303	+	0.115542i	$0.0368604\pi$
$419$			1.69985e7i			0.231084i	−0.993303	+	0.115542i	$0.963140\pi$
$420$	−4.19984e7	−	6.97673e7i	−0.566871	−	0.941681i
$421$	1.01292e7			0.135747			0.0678733	−	0.997694i	$-0.478379\pi$
$421$	1.01292e7			0.135747			0.0678733	+	0.997694i	$0.478379\pi$
$422$	−6.79782e7	+	3.92473e7i	−0.904550	+	0.522242i
$423$	5.53651e6	+	3.97987e7i	0.0731501	+	0.525834i
$424$	1.29270e6	−	2.23903e6i	0.0169591	−	0.0293739i
$425$	6.34180e6	−	3.66144e6i	0.0826125	−	0.0476963i
$426$	−8.54459e7	−	4.17489e7i	−1.10525	−	0.540027i
$427$	−1.23324e7	−	2.41130e7i	−0.158403	−	0.309719i
$428$			1.10384e8i			1.40791i
$429$	7.24535e7	−	5.01545e6i	0.917671	−	0.0635240i
$430$	−8.64710e7	+	1.49772e8i	−1.08759	+	1.88376i
$431$	−3.31397e7	−	1.91332e7i	−0.413921	−	0.238977i	0.278552	−	0.960421i	$-0.410146\pi$
$431$	−3.31397e7	−	1.91332e7i	−0.413921	−	0.238977i	−0.692473	+	0.721444i	$0.743479\pi$
$432$	−7.03777e7	+	6.31011e7i	−0.872938	+	0.782682i
$433$	−4.54714e7			−0.560112			−0.280056	−	0.959984i	$-0.590353\pi$
$433$	−4.54714e7			−0.560112			−0.280056	+	0.959984i	$0.590353\pi$
$434$	−4.82150e6	+	9.47569e7i	−0.0589811	+	1.15916i
$435$	−1.50058e8	−	7.33183e7i	−1.82302	−	0.890727i
$436$	−1.27322e6	−	2.20529e6i	−0.0153619	−	0.0266076i
$437$	4.11365e6	+	2.37502e6i	0.0492928	+	0.0284592i
$438$	5.85976e7	+	8.70059e7i	0.697360	+	1.03544i
$439$	−1.25464e7	−	2.17310e7i	−0.148295	−	0.256854i	0.782303	−	0.622899i	$-0.214045\pi$
$439$	−1.25464e7	−	2.17310e7i	−0.148295	−	0.256854i	−0.930597	+	0.366045i	$0.880712\pi$
$440$			2.36246e7i			0.277336i
$441$	4.01404e7	−	7.57930e7i	0.468022	−	0.883717i
$442$	1.52972e7			0.177151
$443$	2.14827e7	−	1.24030e7i	0.247103	−	0.142665i	−0.371334	−	0.928499i	$-0.621100\pi$
$443$	2.14827e7	−	1.24030e7i	0.247103	−	0.142665i	0.618437	+	0.785835i	$0.287766\pi$
$444$	−3.91051e6	+	2.63369e6i	−0.0446771	+	0.0300896i
$445$	6.63931e7	−	1.14996e8i	0.753430	−	1.30498i
$446$	4.37089e6	−	2.52354e6i	0.0492681	−	0.0284449i
$447$	872733.	−	1.78619e6i	0.00977145	−	0.0199989i
$448$	4.65878e7	+	2.37052e6i	0.518130	+	0.0263639i
$449$			1.43255e8i			1.58259i	0.611432	+	0.791297i	$0.290594\pi$
$449$			1.43255e8i			1.58259i	−0.611432	+	0.791297i	$0.709406\pi$
$450$	1.11867e8	+	4.53794e7i	1.22762	+	0.497991i
$451$	513704.	−	889761.i	0.00559993	−	0.00969937i
$452$	−1.02195e8	−	5.90024e7i	−1.10666	−	0.638931i
$453$	1.58423e6	+	2.28858e7i	0.0170421	+	0.246191i
$454$	−8.69788e7			−0.929492
$455$	1.63792e8	−	8.37702e7i	1.73884	−	0.889314i
$456$	1.50724e7	−	3.08481e7i	0.158960	−	0.325337i
$457$	6.21429e7	+	1.07635e8i	0.651093	+	1.12773i	0.982858	+	0.184364i	$0.0590226\pi$
$457$	6.21429e7	+	1.07635e8i	0.651093	+	1.12773i	−0.331765	+	0.943362i	$0.607644\pi$
$458$	6.09686e7	+	3.52002e7i	0.634614	+	0.366395i
$459$	−2.88814e6	+	8.82562e6i	−0.0298662	+	0.0912657i
$460$	−2.48388e6	−	4.30221e6i	−0.0255187	−	0.0441996i
$461$		−	1.56669e8i		−	1.59912i	−0.600588	−	0.799559i	$-0.705067\pi$
$461$		−	1.56669e8i		−	1.59912i	0.600588	−	0.799559i	$-0.294933\pi$
$462$	7.49221e7	−	4.51014e7i	0.759773	−	0.457367i
$463$	8.08752e6			0.0814840			0.0407420	−	0.999170i	$-0.487028\pi$
$463$	8.08752e6			0.0814840			0.0407420	+	0.999170i	$0.487028\pi$
$464$	1.45767e8	−	8.41586e7i	1.45917	−	0.842451i
$465$	−6.90146e7	−	1.02473e8i	−0.686408	−	1.01918i
$466$	6.59544e7	−	1.14236e8i	0.651757	−	1.12888i
$467$	−1.21690e8	+	7.02577e7i	−1.19482	+	0.689832i	−0.959397	−	0.282060i	$-0.908982\pi$
$467$	−1.21690e8	+	7.02577e7i	−1.19482	+	0.689832i	−0.235427	+	0.971892i	$0.575649\pi$
$468$	6.78385e7	+	8.70805e7i	0.661819	+	0.849539i
$469$	1.12383e7	−	1.73632e7i	0.108939	−	0.168311i
$470$			1.03783e8i			0.999614i
$471$	−5.32965e6	−	7.69924e7i	−0.0510077	−	0.736861i
$472$	−2.86279e7	+	4.95849e7i	−0.272247	+	0.471546i
$473$	−7.04033e7	−	4.06474e7i	−0.665288	−	0.384104i
$474$	1.05664e8	−	7.31436e6i	0.992181	−	0.0686818i
$475$	−1.30501e8			−1.21768
$476$	7.17828e6	−	3.67128e6i	0.0665579	−	0.0340406i
$477$	9.83080e6	−	7.65851e6i	0.0905803	−	0.0705650i
$478$	−4.18356e7	−	7.24614e7i	−0.383056	−	0.663473i
$479$	1.14456e7	+	6.60811e6i	0.104143	+	0.0601272i	0.551167	−	0.834395i	$-0.314183\pi$
$479$	1.14456e7	+	6.60811e6i	0.104143	+	0.0601272i	−0.447024	+	0.894522i	$0.647516\pi$
$480$	−1.64239e8	+	1.10613e8i	−1.48509	+	1.00019i
$481$	−5.32565e6	−	9.22430e6i	−0.0478561	−	0.0828893i
$482$			7.27914e7i			0.650038i
$483$	2.53282e6	−	4.57818e6i	0.0224783	−	0.0406305i
$484$	−4.92354e7			−0.434252
$485$	−1.56520e8	+	9.03671e7i	−1.37197	+	0.792110i
$486$	−1.44036e8	+	5.18544e7i	−1.25477	+	0.451728i
$487$	9.77292e7	−	1.69272e8i	0.846131	−	1.46554i	−0.0385041	−	0.999258i	$-0.512259\pi$
$487$	9.77292e7	−	1.69272e8i	0.846131	−	1.46554i	0.884635	−	0.466284i	$-0.154407\pi$
$488$	−1.03423e7	+	5.97115e6i	−0.0889937	+	0.0513805i
$489$	1.11066e8	+	5.42669e7i	0.949851	+	0.464097i
$490$	1.29660e8	−	1.79608e8i	1.10209	−	1.52664i
$491$			1.12575e8i			0.951034i	0.879707	+	0.475517i	$0.157739\pi$
$491$			1.12575e8i			0.951034i	−0.879707	+	0.475517i	$0.842261\pi$
$492$	1.55784e6	−	107838.i	0.0130806	−	0.000905476i
$493$	8.26787e6	−	1.43204e7i	0.0690006	−	0.119513i
$494$	−2.36089e8	−	1.36306e8i	−1.95837	−	1.13066i
$495$	−4.28051e7	+	1.05520e8i	−0.352923	+	0.870003i
$496$	1.24512e8			1.02039
$497$	5.75444e6	−	1.13092e8i	0.0468742	−	0.921218i
$498$	1.34109e8	+	6.55254e7i	1.08585	+	0.530544i
$499$	8.02290e7	+	1.38961e8i	0.645698	+	1.11838i	0.984140	+	0.177395i	$0.0567670\pi$
$499$	8.02290e7	+	1.38961e8i	0.645698	+	1.11838i	−0.338441	+	0.940987i	$0.609900\pi$
$500$	−787388.	−	454599.i	−0.00629910	−	0.00363679i
$501$	6.30477e6	+	9.36134e6i	0.0501367	+	0.0744432i
$502$	−7.79305e7	−	1.34980e8i	−0.616022	−	1.06698i
$503$		−	4.17030e7i		−	0.327690i	−0.986486	−	0.163845i	$-0.947610\pi$
$503$		−	4.17030e7i		−	0.327690i	0.986486	−	0.163845i	$-0.0523897\pi$
$504$	−3.42765e7	−	1.59784e7i	−0.267735	−	0.124808i
$505$	−3.87075e7			−0.300553
$506$	4.62008e6	−	2.66741e6i	0.0356614	−	0.0205891i
$507$	−9.87491e7	+	6.65065e7i	−0.757721	+	0.510317i
$508$	−2.48687e7	+	4.30739e7i	−0.189698	+	0.328566i
$509$	1.47010e8	−	8.48765e7i	1.11479	−	0.643627i	0.174727	−	0.984617i	$-0.444096\pi$
$509$	1.47010e8	−	8.48765e7i	1.11479	−	0.643627i	0.940067	+	0.340990i	$0.110762\pi$
$510$	−1.05292e7	+	2.15498e7i	−0.0793754	+	0.162455i
$511$	−6.78692e7	+	1.04858e8i	−0.508640	+	0.785850i
$512$		−	1.53078e8i		−	1.14052i
$513$	1.23215e8	−	1.10475e8i	0.912665	−	0.818301i
$514$	−4.20788e7	+	7.28826e7i	−0.309866	+	0.536704i
$515$	2.62150e8	+	1.51352e8i	1.91923	+	1.10807i
$516$	−8.53281e6	−	1.23265e8i	−0.0621073	−	0.897206i
$517$	−4.87852e7			−0.353034
$518$	−1.07667e7	−	6.96874e6i	−0.0774631	−	0.0501378i
$519$	2.30007e7	−	4.70747e7i	0.164528	−	0.336733i
$520$	−4.05601e7	−	7.02522e7i	−0.288462	−	0.499632i
$521$	5.69389e7	+	3.28737e7i	0.402620	+	0.232453i	0.687614	−	0.726076i	$-0.258658\pi$
$521$	5.69389e7	+	3.28737e7i	0.402620	+	0.232453i	−0.284994	+	0.958529i	$0.591991\pi$
$522$	2.69998e8	−	3.75601e7i	1.89823	−	0.264068i
$523$	−1.04627e7	−	1.81220e7i	−0.0731374	−	0.126678i	0.827137	−	0.562000i	$-0.189968\pi$
$523$	−1.04627e7	−	1.81220e7i	−0.0731374	−	0.126678i	−0.900275	+	0.435322i	$0.856634\pi$
$524$		−	9.92493e7i		−	0.689816i
$525$	2.62662e6	+	1.43722e8i	0.0181518	+	0.993217i
$526$	2.65741e8			1.82600
$527$	1.05935e7	−	6.11613e6i	0.0723779	−	0.0417874i
$528$	−6.41074e7	−	9.51869e7i	−0.435518	−	0.646659i
$529$	−7.38584e7	+	1.27926e8i	−0.498922	+	0.864158i
$530$	2.78745e7	−	1.60934e7i	0.187232	−	0.108098i
$531$	−2.17710e8	+	1.69603e8i	−1.45410	+	1.13279i
$532$	−1.43499e8	−	7.30163e6i	−0.953046	−	0.0484937i
$533$			3.52783e6i			0.0232984i
$534$	1.49672e7	+	2.16217e8i	0.0982916	+	1.41993i
$535$	1.95498e8	−	3.38613e8i	1.27668	−	2.21127i
$536$	−7.89809e6	−	4.55997e6i	−0.0512894	−	0.0296120i
$537$	−5.66457e7	+	3.92118e6i	−0.365800	+	0.0253218i
$538$	−2.92133e8			−1.87600
$539$	8.44280e7	+	6.09490e7i	0.539163	+	0.389225i
$540$	−1.69368e8	+	3.56285e7i	−1.07560	+	0.226264i
$541$	5.74944e7	+	9.95832e7i	0.363106	+	0.628918i	0.988470	−	0.151415i	$-0.0483829\pi$
$541$	5.74944e7	+	9.95832e7i	0.363106	+	0.628918i	−0.625364	+	0.780333i	$0.715050\pi$
$542$	4.77176e7	+	2.75498e7i	0.299696	+	0.173029i
$543$	−9.76347e7	+	6.57560e7i	−0.609824	+	0.410711i
$544$	−9.80265e6	−	1.69787e7i	−0.0608901	−	0.105465i
$545$			9.01991e6i			0.0557202i
$546$	−1.45362e8	+	2.62749e8i	−0.893046	+	1.61422i
$547$	−1.40074e8			−0.855849			−0.427924	−	0.903815i	$-0.640755\pi$
$547$	−1.40074e8			−0.855849			−0.427924	+	0.903815i	$0.640755\pi$
$548$	1.05916e8	−	6.11505e7i	0.643604	−	0.371585i
$549$	−5.70136e7	+	7.93132e6i	−0.344558	+	0.0479323i
$550$	−7.32837e7	+	1.26931e8i	−0.440473	+	0.762921i
$551$	−2.55204e8	+	1.47342e8i	−1.52557	+	0.880790i
$552$	−2.07285e6	−	1.01280e6i	−0.0123240	−	0.00602150i
$553$	5.74273e7	+	1.12285e8i	0.339581	+	0.663967i
$554$		−	1.93890e8i		−	1.14032i
$555$	1.66604e7	−	1.15328e6i	0.0974553	−	0.00674615i
$556$	−4.66721e7	+	8.08384e7i	−0.271539	+	0.470320i
$557$	1.57185e8	+	9.07506e7i	0.909588	+	0.525151i	0.880299	−	0.474420i	$-0.157342\pi$
$557$	1.57185e8	+	9.07506e7i	0.909588	+	0.525151i	0.0292895	+	0.999571i	$0.490676\pi$
$558$	1.86864e8	+	7.58026e7i	1.07553	+	0.436296i
$559$	2.79144e8			1.59806
$560$	−2.44045e8	−	1.57957e8i	−1.38965	−	0.899447i
$561$	−1.01299e7	−	4.94946e6i	−0.0573741	−	0.0280330i
$562$	−1.86278e8	−	3.22643e8i	−1.04943	−	1.81766i
$563$	−4.14625e7	−	2.39384e7i	−0.232343	−	0.134143i	0.379309	−	0.925270i	$-0.376162\pi$
$563$	−4.14625e7	−	2.39384e7i	−0.232343	−	0.134143i	−0.611653	+	0.791127i	$0.709495\pi$
$564$	−4.14205e7	−	6.15013e7i	−0.230876	−	0.342805i
$565$	2.08996e8	+	3.61991e8i	1.15876	+	2.00702i
$566$			5.19038e7i			0.286253i
$567$	−1.24147e8	−	1.33473e8i	−0.681061	−	0.732227i
$568$	−4.99314e7			−0.272476
$569$	−1.04058e8	+	6.00781e7i	−0.564859	+	0.326121i	−0.755093	−	0.655617i	$-0.772408\pi$
$569$	−1.04058e8	+	6.00781e7i	−0.564859	+	0.326121i	0.190235	+	0.981739i	$0.439075\pi$
$570$	3.54522e8	−	2.38767e8i	1.91434	−	1.28929i
$571$	−1.45541e8	+	2.52085e8i	−0.781769	+	1.35406i	0.149141	+	0.988816i	$0.452349\pi$
$571$	−1.45541e8	+	2.52085e8i	−0.781769	+	1.35406i	−0.930910	+	0.365248i	$0.880984\pi$
$572$	−1.16065e8	+	6.70102e7i	−0.620174	+	0.358057i
$573$	9.67916e7	−	1.98100e8i	0.514486	−	1.05298i
$574$	1.93424e6	+	3.78193e6i	0.0102276	+	0.0199976i
$575$			8.76910e6i			0.0461266i
$576$	3.72688e7	−	9.18728e7i	0.195020	−	0.480750i
$577$	−3.50380e6	+	6.06877e6i	−0.0182395	+	0.0315917i	−0.875001	−	0.484121i	$-0.839139\pi$
$577$	−3.50380e6	+	6.06877e6i	−0.0182395	+	0.0315917i	0.856762	+	0.515713i	$0.172473\pi$
$578$	2.20962e8	+	1.27572e8i	1.14428	+	0.660653i
$579$	−2.64409e7	−	3.81967e8i	−0.136220	−	1.96784i
$580$	3.08192e8			1.57956
$581$	−9.03167e6	+	1.77499e8i	−0.0460511	+	0.905042i
$582$	1.29503e8	−	2.65050e8i	0.656919	−	1.34449i
$583$	7.56499e6	+	1.31030e7i	0.0381771	+	0.0661247i
$584$	4.76973e7	+	2.75381e7i	0.239472	+	0.138259i
$585$	−5.38749e7	−	3.87276e8i	−0.269103	−	1.93443i
$586$	7.59066e7	+	1.31474e8i	0.377213	+	0.653352i
$587$		−	5.84714e7i		−	0.289087i	−0.989498	−	0.144544i	$-0.953829\pi$
$587$		−	5.84714e7i		−	0.289087i	0.989498	−	0.144544i	$-0.0461714\pi$
$588$	−5.15308e6	+	1.58183e8i	−0.0253475	+	0.778085i
$589$	−2.17992e8			−1.06683
$590$	−6.17301e8	+	3.56399e8i	−3.00567	+	1.73532i
$591$	1.11485e8	+	1.65533e8i	0.540074	+	0.801904i
$592$	−8.41538e6	+	1.45759e7i	−0.0405610	+	0.0702537i
$593$	2.64996e8	−	1.52995e8i	1.27079	−	0.733693i	0.295656	−	0.955294i	$-0.404462\pi$
$593$	2.64996e8	−	1.52995e8i	1.27079	−	0.733693i	0.975137	+	0.221601i	$0.0711283\pi$
$594$	−3.82609e7	−	1.81882e8i	−0.182556	−	0.867821i
$595$	−2.85222e7	−	1.45129e6i	−0.135404	−	0.00688976i
$596$			3.66851e6i			0.0173281i
$597$	−1.51484e7	−	2.18835e8i	−0.0711940	−	1.02847i
$598$	−9.15914e6	+	1.58641e7i	−0.0428303	+	0.0741843i
$599$	−3.21383e8	−	1.85551e8i	−1.49535	−	0.863341i	−0.495364	−	0.868686i	$-0.664965\pi$
$599$	−3.21383e8	−	1.85551e8i	−1.49535	−	0.863341i	−0.999986	+	0.00534498i	$0.998299\pi$
$600$	6.32320e7	−	4.37711e6i	0.292741	−	0.0202644i
$601$	3.43605e8			1.58284			0.791418	−	0.611275i	$-0.209343\pi$
$601$	3.43605e8			1.58284			0.791418	+	0.611275i	$0.209343\pi$
$602$	2.99249e8	−	1.53049e8i	1.37165	−	0.701520i
$603$	−2.70151e7	−	3.46778e7i	−0.123213	−	0.158161i
$604$	−2.11665e7	−	3.66614e7i	−0.0960589	−	0.166379i
$605$	1.51034e8	+	8.71998e7i	0.682040	+	0.393776i
$606$	5.24022e7	−	3.52924e7i	0.235468	−	0.158585i
$607$	−1.75975e8	−	3.04797e8i	−0.786836	−	1.36284i	−0.927896	−	0.372839i	$-0.878384\pi$
$607$	−1.75975e8	−	3.04797e8i	−0.786836	−	1.36284i	0.141060	−	0.990001i	$-0.454949\pi$
$608$			3.49387e8i			1.55452i
$609$	1.67405e8	+	2.78091e8i	0.741167	+	1.23122i
$610$	−1.48674e8			−0.655007
$611$	1.45072e8	−	8.37574e7i	0.636005	−	0.367198i
$612$	−2.36110e6	−	1.69726e7i	−0.0103005	−	0.0740447i
$613$	1.43728e8	−	2.48944e8i	0.623964	−	1.08074i	−0.364776	−	0.931095i	$-0.618854\pi$
$613$	1.43728e8	−	2.48944e8i	0.623964	−	1.08074i	0.988740	−	0.149643i	$-0.0478123\pi$
$614$	1.17201e8	−	6.76663e7i	0.506323	−	0.292326i
$615$	−4.96981e6	−	2.42825e6i	−0.0213655	−	0.0104392i
$616$	2.49484e7	−	3.85454e7i	0.106733	−	0.164904i
$617$		−	4.41540e8i		−	1.87981i	−0.341432	−	0.939907i	$-0.610912\pi$
$617$		−	4.41540e8i		−	1.87981i	0.341432	−	0.939907i	$-0.389088\pi$
$618$	−4.92896e8	+	3.41198e7i	−2.08829	+	0.144558i
$619$	4.35278e7	−	7.53924e7i	0.183525	−	0.317875i	−0.759554	−	0.650445i	$-0.774583\pi$
$619$	4.35278e7	−	7.53924e7i	0.183525	−	0.317875i	0.943078	+	0.332570i	$0.107916\pi$
$620$	1.97440e8	+	1.13992e8i	0.828438	+	0.478299i
$621$	−7.42344e6	−	8.27948e6i	−0.0309978	−	0.0345723i
$622$	2.54901e8			1.05926
$623$	−2.29766e8	+	1.17512e8i	−0.950214	+	0.485980i
$624$	3.54059e8	+	1.72993e8i	1.45721	+	0.711991i
$625$	1.22873e8	+	2.12822e8i	0.503287	+	0.871718i
$626$	−4.85703e7	−	2.80421e7i	−0.197992	−	0.114311i
$627$	1.12237e8	+	1.66650e8i	0.455338	+	0.676088i
$628$	7.12081e7	+	1.23336e8i	0.287509	+	0.497979i
$629$			1.65348e6i			0.00664427i
$630$	−2.70091e8	−	3.85631e8i	−1.08016	−	1.54223i
$631$	2.13712e8			0.850630			0.425315	−	0.905045i	$-0.360163\pi$
$631$	2.13712e8			0.850630			0.425315	+	0.905045i	$0.360163\pi$
$632$	4.81603e7	−	2.78054e7i	0.190782	−	0.110148i
$633$	−1.64765e8	+	1.10968e8i	−0.649613	+	0.437508i
$634$	−2.08256e8	+	3.60710e8i	−0.817204	+	1.41544i
$635$	1.52575e8	−	8.80890e7i	0.595883	−	0.344033i
$636$	−1.00953e7	+	2.06618e7i	−0.0392419	+	0.0803149i
$637$	−3.55704e8	−	3.62924e7i	−1.37617	−	0.140410i
$638$			3.30963e8i			1.27443i
$639$	−2.23021e8	−	9.04700e7i	−0.854759	−	0.346739i
$640$	−1.06648e8	+	1.84720e8i	−0.406830	+	0.704651i
$641$	−2.78216e8	−	1.60628e8i	−1.05635	−	0.609884i	−0.131930	−	0.991259i	$-0.542117\pi$
$641$	−2.78216e8	−	1.60628e8i	−1.05635	−	0.609884i	−0.924420	+	0.381375i	$0.875451\pi$
$642$	4.40718e7	+	6.36664e8i	0.166554	+	2.40605i
$643$	−1.70144e8			−0.640005			−0.320002	−	0.947417i	$-0.603684\pi$
$643$	−1.70144e8			−0.640005			−0.320002	+	0.947417i	$0.603684\pi$
$644$	−490637.	+	9.64248e6i	−0.00183697	+	0.0361020i
$645$	−1.92138e8	+	3.93241e8i	−0.716034	+	1.46548i
$646$	2.11598e7	+	3.66498e7i	0.0784898	+	0.135948i
$647$	−4.37973e8	−	2.52864e8i	−1.61709	−	0.933628i	−0.987667	−	0.156566i	$-0.949957\pi$
$647$	−4.37973e8	−	2.52864e8i	−1.61709	−	0.933628i	−0.629424	−	0.777062i	$-0.716709\pi$
$648$	−5.59961e7	+	5.76614e7i	−0.205794	+	0.211914i
$649$	−1.67532e8	−	2.90174e8i	−0.612864	−	1.06151i
$650$		−	5.03272e8i		−	1.83258i
$651$	4.38756e6	+	2.40075e8i	0.0159030	+	0.870170i
$652$	−2.28110e8			−0.823002
$653$	1.36038e8	−	7.85415e7i	0.488563	−	0.282072i	−0.235415	−	0.971895i	$-0.575645\pi$
$653$	1.36038e8	−	7.85415e7i	0.488563	−	0.282072i	0.723978	+	0.689823i	$0.242312\pi$
$654$	−8.22409e6	−	1.22112e7i	−0.0294005	−	0.0436539i
$655$	−1.75778e8	+	3.04457e8i	−0.625520	+	1.08343i
$656$	4.82769e6	−	2.78727e6i	0.0171013	−	0.00987341i
$657$	1.63147e8	+	2.09422e8i	0.575284	+	0.738460i
$658$	1.09599e8	−	1.69330e8i	0.384704	−	0.594370i
$659$			2.30514e8i			0.805454i	0.915320	+	0.402727i	$0.131938\pi$
$659$			2.30514e8i			0.805454i	−0.915320	+	0.402727i	$0.868062\pi$
$660$	−1.45112e7	−	2.09630e8i	−0.0504744	−	0.729156i
$661$	8.24137e7	−	1.42745e8i	0.285361	−	0.494260i	−0.687335	−	0.726340i	$-0.741220\pi$
$661$	8.24137e7	−	1.42745e8i	0.285361	−	0.494260i	0.972697	+	0.232080i	$0.0745531\pi$
$662$	3.35767e8	+	1.93855e8i	1.15735	+	0.668196i
$663$	3.86207e7	−	2.67344e6i	0.132520	−	0.00917340i
$664$	7.83680e7			0.267692
$665$	4.27265e8	+	2.76546e8i	1.45289	+	0.940379i
$666$	−2.15033e7	+	1.67517e7i	−0.0727917	+	0.0567071i
$667$	9.90072e6	+	1.71486e7i	0.0333649	+	0.0577897i
$668$	−1.80370e7	−	1.04136e7i	−0.0605109	−	0.0349360i
$669$	1.05941e7	−	7.13505e6i	0.0353824	−	0.0238297i
$670$	−5.67687e7	−	9.83263e7i	−0.188749	−	0.326923i
$671$		−	6.98872e7i		−	0.231329i
$672$	3.84781e8	−	7.03218e6i	1.26796	−	0.0231730i
$673$	3.03336e8			0.995129			0.497564	−	0.867427i	$-0.334228\pi$
$673$	3.03336e8			0.995129			0.497564	+	0.867427i	$0.334228\pi$
$674$	5.59612e8	−	3.23092e8i	1.82771	−	1.05523i
$675$	2.90360e8	+	9.50186e7i	0.944116	+	0.308957i
$676$	1.09849e8	−	1.90265e8i	0.355596	−	0.615911i
$677$	−5.14602e8	+	2.97105e8i	−1.65846	+	0.957513i	−0.685035	+	0.728510i	$0.740213\pi$
$677$	−5.14602e8	+	2.97105e8i	−1.65846	+	0.957513i	−0.973426	+	0.229002i	$0.926454\pi$
$678$	−6.12991e8	−	2.99507e8i	−1.96682	−	0.960989i
$679$	3.50807e8	+	1.78500e7i	1.12062	+	0.0570203i
$680$			1.25929e7i			0.0400496i
$681$	−2.19595e8	+	1.52010e7i	−0.695314	+	0.0481317i
$682$	−1.22414e8	+	2.12028e8i	−0.385904	+	0.668405i
$683$	−6.14652e7	−	3.54870e7i	−0.192916	−	0.111380i	0.400431	−	0.916327i	$-0.368860\pi$
$683$	−6.14652e7	−	3.54870e7i	−0.192916	−	0.111380i	−0.593347	+	0.804947i	$0.702194\pi$
$684$	−1.14795e8	+	2.82985e8i	−0.358718	+	0.884290i
$685$	−4.33209e8			−1.34780
$686$	−4.01222e8	+	1.56119e8i	−1.24283	+	0.483596i
$687$	1.60079e8	+	7.82146e7i	0.493701	+	0.241222i
$688$	−2.20546e8	−	3.81996e8i	−0.677225	−	1.17299i
$689$	−4.49919e7	−	2.59761e7i	−0.137555	−	0.0794175i
$690$	−1.60441e7	−	2.38223e7i	−0.0488391	−	0.0725164i
$691$	−1.53091e8	−	2.65162e8i	−0.463998	−	0.803668i	0.535158	−	0.844752i	$-0.320252\pi$
$691$	−1.53091e8	−	2.65162e8i	−0.463998	−	0.803668i	−0.999156	+	0.0410845i	$0.986919\pi$
$692$			9.66828e7i			0.291763i
$693$	1.81273e8	−	1.26961e8i	0.544671	−	0.381480i
$694$	−6.98312e7			−0.208916
$695$	2.86343e8	−	1.65320e8i	0.852965	−	0.492460i
$696$	1.18712e8	−	7.99516e7i	0.352102	−	0.237137i
$697$	273826.	−	474280.i	0.000808678	−	0.00140067i
$698$	2.05396e8	−	1.18585e8i	0.603983	−	0.348710i
$699$	1.46550e8	−	2.99939e8i	0.429096	−	0.878215i
$700$	−1.20784e8	−	2.36163e8i	−0.352139	−	0.688522i
$701$			1.36696e8i			0.396829i	0.980118	+	0.198414i	$0.0635791\pi$
$701$			1.36696e8i			0.396829i	−0.980118	+	0.198414i	$0.936421\pi$
$702$	4.26042e8	+	4.75172e8i	1.23152	+	1.37353i
$703$	1.47334e7	−	2.55189e7i	0.0424069	−	0.0734508i
$704$	1.04245e8	+	6.01858e7i	0.298770	+	0.172495i
$705$	1.81378e7	+	2.62020e8i	0.0517628	+	0.747769i
$706$	5.25936e8			1.49458
$707$	6.31544e7	+	4.08765e7i	0.178709	+	0.115669i
$708$	2.23568e8	−	4.57570e8i	0.629957	−	1.28931i
$709$	−1.89589e8	−	3.28378e8i	−0.531954	−	0.921372i	−0.999304	−	0.0372996i	$-0.988124\pi$
$709$	−1.89589e8	−	3.28378e8i	−0.531954	−	0.921372i	0.467350	−	0.884073i	$-0.345209\pi$
$710$	−5.38334e8	−	3.10807e8i	−1.50410	−	0.868392i
$711$	2.65491e8	−	3.69331e7i	0.738653	−	0.102756i
$712$	5.68974e7	+	9.85491e7i	0.157635	+	0.273032i
$713$			1.46481e7i			0.0404121i
$714$	3.99366e7	−	2.40410e7i	0.109718	−	0.0660476i
$715$	4.74721e8			1.29874
$716$	9.07421e7	−	5.23900e7i	0.247212	−	0.142728i
$717$	−1.18286e8	−	1.75631e8i	−0.320905	−	0.476480i
$718$	1.20256e8	−	2.08289e8i	0.324887	−	0.562720i
$719$	8.54115e7	−	4.93123e7i	0.229789	−	0.132669i	−0.380686	−	0.924705i	$-0.624312\pi$
$719$	8.54115e7	−	4.93123e7i	0.229789	−	0.132669i	0.610475	+	0.792036i	$0.290979\pi$
$720$	−4.87405e8	+	3.79704e8i	−1.30585	+	1.01730i
$721$	−2.67885e8	−	5.23783e8i	−0.714730	−	1.39748i
$722$		−	2.52254e8i		−	0.670233i
$723$	1.27215e7	+	1.83776e8i	0.0336608	+	0.486266i
$724$	1.08610e8	−	1.88118e8i	0.286189	−	0.495694i
$725$	−4.71135e8	−	2.72010e8i	−1.23632	−	0.713791i
$726$	−2.83977e8	+	1.96577e7i	−0.742117	+	0.0513716i
$727$	2.45207e8			0.638159			0.319079	−	0.947728i	$-0.396626\pi$
$727$	2.45207e8			0.638159			0.319079	+	0.947728i	$0.396626\pi$
$728$	−8.01176e6	+	1.57455e8i	−0.0207651	+	0.408096i
$729$	−3.54585e8	+	1.56089e8i	−0.915247	+	0.402894i
$730$	3.42832e8	+	5.93802e8i	0.881277	+	1.52642i
$731$	−3.75279e7	−	2.16667e7i	−0.0960732	−	0.0554679i
$732$	8.81036e7	−	5.93369e7i	0.224626	−	0.151284i
$733$	2.36745e8	+	4.10054e8i	0.601130	+	1.04119i	0.992650	+	0.121018i	$0.0386160\pi$
$733$	2.36745e8	+	4.10054e8i	0.601130	+	1.04119i	−0.391520	+	0.920170i	$0.628051\pi$
$734$			8.32517e8i			2.10526i
$735$	2.95962e8	−	4.76115e8i	0.745373	−	1.19908i
$736$	2.34772e7			0.0588862
$737$	4.62202e7	−	2.66852e7i	0.115459	−	0.0666605i
$738$	8.94212e6	−	1.24396e6i	0.0222470	−	0.00309484i
$739$	−2.61731e8	+	4.53331e8i	−0.648518	+	1.12327i	0.334960	+	0.942233i	$0.391277\pi$
$739$	−2.61731e8	+	4.53331e8i	−0.648518	+	1.12327i	−0.983477	+	0.181033i	$0.942056\pi$
$740$	−2.66887e7	+	1.54087e7i	−0.0658615	+	0.0380252i
$741$	−6.19874e8	−	3.02870e8i	−1.52352	−	0.744393i
$742$	−6.24747e7	−	3.17889e6i	−0.152930	−	0.00778150i
$743$			1.70732e8i			0.416244i	0.978103	+	0.208122i	$0.0667352\pi$
$743$			1.70732e8i			0.416244i	−0.978103	+	0.208122i	$0.933265\pi$
$744$	1.05624e8	−	7.31160e6i	0.256474	−	0.0177539i
$745$	6.49723e6	−	1.12535e7i	0.0157130	−	0.0272157i
$746$	−3.42206e8	−	1.97572e8i	−0.824272	−	0.475894i
$747$	3.50035e8	+	1.41994e8i	0.839749	+	0.340650i
$748$	2.08050e7			0.0497121
$749$	−6.76559e8	+	3.46021e8i	−1.61013	+	0.823488i
$750$	−4.72294e6	−	2.30763e6i	−0.0111951	−	0.00546994i
$751$	2.99617e8	+	5.18951e8i	0.707369	+	1.22520i	0.965830	+	0.259177i	$0.0834515\pi$
$751$	2.99617e8	+	5.18951e8i	0.707369	+	1.22520i	−0.258461	+	0.966022i	$0.583215\pi$
$752$	−2.29237e8	−	1.32350e8i	−0.539053	−	0.311222i
$753$	−2.20341e8	−	3.27163e8i	−0.516071	−	0.766265i
$754$	−5.68217e8	−	9.84181e8i	−1.32556	−	2.29594i
$755$			1.49950e8i			0.348422i
$756$	3.13962e8	+	1.20728e8i	0.726628	+	0.279410i
$757$	−3.23640e8			−0.746061			−0.373030	−	0.927819i	$-0.621681\pi$
$757$	−3.23640e8			−0.746061			−0.373030	+	0.927819i	$0.621681\pi$
$758$	−7.55171e7	+	4.35998e7i	−0.173395	+	0.100110i
$759$	1.11981e7	−	7.54183e6i	0.0256106	−	0.0172485i
$760$	1.12209e8	−	1.94352e8i	0.255616	−	0.442740i
$761$	4.72894e8	−	2.73025e8i	1.07302	−	0.619511i	0.144018	−	0.989575i	$-0.453998\pi$
$761$	4.72894e8	−	2.73025e8i	1.07302	−	0.619511i	0.929006	+	0.370064i	$0.120664\pi$
$762$	−1.26239e8	+	2.58368e8i	−0.285317	+	0.583947i
$763$	9.52536e6	−	1.47167e7i	0.0214441	−	0.0331312i
$764$			4.06861e8i			0.912359i
$765$	−2.28169e7	+	5.62468e7i	−0.0509650	+	0.125636i
$766$	−3.09315e8	+	5.35750e8i	−0.688201	+	1.19200i
$767$	9.96379e8	+	5.75259e8i	2.20820	+	1.27490i
$768$	−4.02712e7	−	5.81760e8i	−0.0889018	−	1.28428i
$769$	−5.03008e8			−1.10610			−0.553051	−	0.833147i	$-0.686537\pi$
$769$	−5.03008e8			−1.10610			−0.553051	+	0.833147i	$0.686537\pi$
$770$	5.08913e8	−	2.60280e8i	1.11473	−	0.570123i
$771$	−9.34987e7	+	1.91360e8i	−0.204006	+	0.417531i
$772$	3.53271e8	+	6.11883e8i	0.767813	+	1.32989i
$773$	6.41756e8	+	3.70518e8i	1.38941	+	0.802178i	0.993249	−	0.116001i	$-0.0370077\pi$
$773$	6.41756e8	+	3.70518e8i	1.38941	+	0.802178i	0.396164	+	0.918180i	$0.370341\pi$
$774$	−9.84299e7	−	7.07555e8i	−0.212277	−	1.52594i
$775$	−2.01219e8	−	3.48521e8i	−0.432278	−	0.748727i
$776$		−	1.54885e8i		−	0.331455i
$777$	−2.84006e7	−	1.57123e7i	−0.0605431	−	0.0334947i
$778$	−7.81830e8			−1.66025
$779$	−8.45216e6	+	4.87986e6i	−0.0178795	+	0.0103227i
$780$	4.03057e8	+	5.98460e8i	0.849342	+	1.26111i
$781$	1.46101e8	−	2.53054e8i	0.306690	−	0.531203i
$782$	2.46270e6	−	1.42184e6i	0.00514981	−	0.00297324i
$783$	6.75098e8	−	1.42015e8i	1.40631	−	0.295834i
$784$	2.31370e8	+	5.15440e8i	0.480130	+	1.06962i
$785$		−	5.04461e8i		−	1.04284i
$786$	−3.96262e7	−	5.72443e8i	−0.0816047	−	1.17887i
$787$	−3.27015e8	+	5.66407e8i	−0.670878	+	1.16200i	0.306777	+	0.951781i	$0.400749\pi$
$787$	−3.27015e8	+	5.66407e8i	−0.670878	+	1.16200i	−0.977655	+	0.210214i	$0.932584\pi$
$788$	−3.18941e8	−	1.84140e8i	−0.651825	−	0.376331i
$789$	6.70914e8	−	4.64427e7i	1.36595	−	0.0945554i
$790$	6.92318e8			1.40419
$791$	4.12825e7	−	8.11325e8i	0.0834135	−	1.63933i
$792$	−5.99720e7	−	7.69827e7i	−0.120718	−	0.154959i
$793$	1.19987e8	+	2.07823e8i	0.240610	+	0.416748i
$794$	2.22656e8	+	1.28551e8i	0.444809	+	0.256811i
$795$	6.75621e7	−	4.55024e7i	0.134463	−	0.0905592i
$796$	2.02394e8	+	3.50557e8i	0.401290	+	0.695055i
$797$			4.96423e8i			0.980567i	0.871563	+	0.490283i	$0.163107\pi$
$797$			4.96423e8i			0.980567i	−0.871563	+	0.490283i	$0.836893\pi$
$798$	−8.30578e8	+	1.51795e7i	−1.63445	+	0.0298709i
$799$	−2.60046e7			−0.0509811
$800$	−5.58593e8	+	3.22504e8i	−1.09100	+	0.629890i
$801$	7.55752e7	+	5.43267e8i	0.147056	+	1.05710i
$802$	3.18818e7	−	5.52209e7i	0.0618044	−	0.107048i
$803$	−2.79128e8	+	1.61155e8i	−0.539085	+	0.311241i
$804$	7.28836e7	+	3.56109e7i	0.140237	+	0.0685196i
$805$	1.85827e7	−	2.87103e7i	0.0356222	−	0.0550364i
$806$		−	8.40674e8i		−	1.60555i
$807$	−7.37547e8	+	5.10552e7i	−1.40336	+	0.0971448i
$808$	1.65857e7	−	2.87273e7i	0.0314413	−	0.0544579i
$809$	−6.30926e8	−	3.64265e8i	−1.19161	−	0.687974i	−0.232935	−	0.972492i	$-0.574833\pi$
$809$	−6.30926e8	−	3.64265e8i	−1.19161	−	0.687974i	−0.958671	+	0.284518i	$0.908166\pi$
$810$	−9.62644e8	+	2.73117e8i	−1.81138	+	0.513918i
$811$	−9.45654e8			−1.77284			−0.886420	−	0.462881i	$-0.846816\pi$
$811$	−9.45654e8			−1.77284			−0.886420	+	0.462881i	$0.846816\pi$
$812$	−5.02840e8	−	3.25462e8i	−0.939207	−	0.607899i
$813$	1.25287e8	+	6.12153e7i	0.233150	+	0.113917i
$814$	−1.65472e7	−	2.86606e7i	−0.0306797	−	0.0531388i
$815$	6.99749e8	+	4.04000e8i	1.29262	+	0.746292i
$816$	−3.41719e7	−	5.07386e7i	−0.0628926	−	0.0933831i
$817$	3.86124e8	+	6.68787e8i	0.708045	+	1.22637i
$818$		−	5.97257e7i		−	0.109119i
$819$	−3.21076e8	+	6.88765e8i	−0.584461	+	1.25377i
$820$	1.02071e7			0.0185123
$821$	2.96408e8	−	1.71131e8i	0.535624	−	0.309243i	−0.207680	−	0.978197i	$-0.566591\pi$
$821$	2.96408e8	−	1.71131e8i	0.535624	−	0.309243i	0.743304	+	0.668954i	$0.233258\pi$
$822$	5.86479e8	−	3.94987e8i	1.05593	−	0.711161i
$823$	−1.08674e8	+	1.88229e8i	−0.194952	+	0.337666i	−0.946885	−	0.321573i	$-0.895788\pi$
$823$	−1.08674e8	+	1.88229e8i	−0.194952	+	0.337666i	0.751933	+	0.659240i	$0.229122\pi$
$824$	−2.24656e8	+	1.29705e8i	−0.401547	+	0.231834i
$825$	−1.62836e8	+	3.33270e8i	−0.289993	+	0.593518i
$826$	1.38355e9	+	7.03988e7i	2.45501	+	0.124918i
$827$		−	5.71015e8i		−	1.00956i	−0.863249	−	0.504779i	$-0.831574\pi$
$827$		−	5.71015e8i		−	1.00956i	0.863249	−	0.504779i	$-0.168426\pi$
$828$	1.90153e7	+	7.71368e6i	0.0334975	+	0.0135885i
$829$	5.31373e8	−	9.20364e8i	0.932686	−	1.61546i	0.153978	−	0.988074i	$-0.450792\pi$
$829$	5.31373e8	−	9.20364e8i	0.932686	−	1.61546i	0.778709	−	0.627386i	$-0.215875\pi$
$830$	8.44923e8	+	4.87816e8i	1.47769	+	0.853143i
$831$	−3.38855e7	−	4.89512e8i	−0.0590488	−	0.853022i
$832$	−4.13323e8			−0.717661
$833$	4.50037e7	+	3.24884e7i	0.0778597	+	0.0562074i
$834$	−2.36917e8	+	4.84889e8i	−0.408411	+	0.835880i
$835$	3.68868e7	+	6.38897e7i	0.0633594	+	0.109742i
$836$	−3.21093e8	−	1.85383e8i	−0.549556	−	0.317286i
$837$	4.85022e8	+	1.58721e8i	0.827152	+	0.270681i
$838$	−9.06771e7	−	1.57057e8i	−0.154087	−	0.266886i
$839$		−	9.55834e8i		−	1.61844i	−0.587505	−	0.809220i	$-0.699890\pi$
$839$		−	9.55834e8i		−	1.61844i	0.587505	−	0.809220i	$-0.300110\pi$
$840$	−2.16299e8	−	1.19665e8i	−0.364936	−	0.201896i
$841$	−6.33625e8			−1.06523
$842$	−9.35885e7	+	5.40333e7i	−0.156778	+	0.0905160i
$843$	−5.26683e8	−	7.82021e8i	−0.879157	−	1.30538i
$844$	1.83286e8	−	3.17461e8i	0.304862	−	0.528036i
$845$	−6.73948e8	+	3.89104e8i	−1.11701	+	0.644904i
$846$	−2.63457e8	−	3.38185e8i	−0.435110	−	0.558527i
$847$	−1.54339e8	−	3.01771e8i	−0.253995	−	0.496624i
$848$			8.20927e7i			0.134622i
$849$	9.07108e6	+	1.31041e8i	0.0148230	+	0.214134i
$850$	−3.90633e7	+	6.76596e7i	−0.0636080	+	0.110172i
$851$	−1.71476e6	−	990016.i	−0.00278236	−	0.00160640i
$852$	4.43060e8	−	3.06699e7i	0.716380	−	0.0495900i
$853$	6.17421e8			0.994797			0.497399	−	0.867522i	$-0.334289\pi$
$853$	6.17421e8			0.994797			0.497399	+	0.867522i	$0.334289\pi$
$854$	2.42574e8	+	1.57005e8i	0.389467	+	0.252081i
$855$	8.53332e8	−	6.64773e8i	1.36527	−	1.06359i
$856$	1.67538e8	+	2.90184e8i	0.267111	+	0.462649i
$857$	4.84339e8	+	2.79633e8i	0.769497	+	0.444270i	0.832695	−	0.553732i	$-0.186797\pi$
$857$	4.84339e8	+	2.79633e8i	0.769497	+	0.444270i	−0.0631979	+	0.998001i	$0.520130\pi$
$858$	−6.42677e8	+	4.32837e8i	−1.01749	+	0.685271i
$859$	1.89844e8	+	3.28819e8i	0.299513	+	0.518772i	0.976025	−	0.217660i	$-0.0698423\pi$
$859$	1.89844e8	+	3.28819e8i	0.299513	+	0.518772i	−0.676511	+	0.736432i	$0.736509\pi$
$860$		−	8.07646e8i		−	1.26977i
$861$	5.54432e6	+	9.21017e6i	0.00868638	+	0.0144297i
$862$	4.08258e8			0.637402
$863$	−3.95752e8	+	2.28487e8i	−0.615730	+	0.355492i	−0.775205	−	0.631710i	$-0.782353\pi$
$863$	−3.95752e8	+	2.28487e8i	−0.615730	+	0.355492i	0.159475	+	0.987202i	$0.449020\pi$
$864$	2.54390e8	−	7.77371e8i	0.394420	−	1.20528i
$865$	1.71233e8	−	2.96584e8i	0.264569	−	0.458247i
$866$	4.20132e8	−	2.42563e8i	0.646892	−	0.373483i
$867$	5.80157e8	+	2.83465e8i	0.890201	+	0.434952i
$868$	−2.01759e8	−	3.94491e8i	−0.308514	−	0.603223i
$869$			3.25438e8i			0.495916i
$870$	1.77757e9	−	1.23049e8i	2.69941	−	0.186861i
$871$	−9.16297e7	+	1.58707e8i	−0.138670	+	0.240183i
$872$	−6.69426e6	−	3.86493e6i	−0.0100961	−	0.00582898i
$873$	2.80634e8	−	6.91803e8i	0.421792	−	1.03978i
$874$	−5.06773e7			−0.0759066
$875$	318071.	−	6.25105e6i	0.000474789	−	0.00933102i
$876$	−4.40151e8	−	2.15058e8i	−0.654771	−	0.319921i
$877$	−4.36322e8	−	7.55731e8i	−0.646857	−	1.12039i	−0.983869	−	0.178889i	$-0.942750\pi$
$877$	−4.36322e8	−	7.55731e8i	−0.646857	−	1.12039i	0.337013	−	0.941500i	$-0.390583\pi$
$878$	2.31844e8	+	1.33855e8i	0.342541	+	0.197766i
$879$	2.14618e8	+	3.18666e8i	0.316009	+	0.469212i
$880$	−3.75068e8	−	6.49636e8i	−0.550379	−	0.953284i
$881$			1.10629e9i			1.61786i	0.587903	+	0.808931i	$0.299953\pi$
$881$			1.10629e9i			1.61786i	−0.587903	+	0.808931i	$0.700047\pi$
$882$	3.34344e7	+	9.14413e8i	0.0487290	+	1.33271i
$883$	1.15898e9			1.68343			0.841714	−	0.539923i	$-0.181547\pi$
$883$	1.15898e9			1.68343			0.841714	+	0.539923i	$0.181547\pi$
$884$	−6.18675e7	+	3.57192e7i	−0.0895583	+	0.0517065i
$885$	−1.49621e9	+	1.00768e9i	−2.15855	+	1.45376i
$886$	−1.32326e8	+	2.29195e8i	−0.190258	+	0.329537i
$887$	−5.49576e8	+	3.17298e8i	−0.787511	+	0.454670i	−0.839085	−	0.544000i	$-0.816909\pi$
$887$	−5.49576e8	+	3.17298e8i	−0.787511	+	0.454670i	0.0515747	+	0.998669i	$0.483576\pi$
$888$	−6.28285e6	+	1.28589e7i	−0.00897260	+	0.0183639i
$889$	−3.41963e8	−	1.74000e7i	−0.486714	−	0.0247654i
$890$			1.41667e9i			2.00955i
$891$	−1.28384e8	−	4.52510e8i	−0.181501	−	0.639727i
$892$	−1.17850e7	+	2.04123e7i	−0.0166049	+	0.0287605i
$893$	4.01341e8	+	2.31714e8i	0.563584	+	0.325386i
$894$	1.46469e6	+	2.11590e7i	0.00204990	+	0.0296130i
$895$	−3.71147e8			−0.517699
$896$	3.69076e8	−	1.88761e8i	0.513088	−	0.262415i
$897$	−2.03515e7	+	4.16527e7i	−0.0281981	+	0.0577120i
$898$	−7.64179e8	−	1.32360e9i	−1.05528	−	1.82779i
$899$	−7.86993e8	−	4.54370e8i	−1.08316	−	0.625361i
$900$	−5.58392e8	+	7.76794e7i	−0.765970	+	0.106556i
$901$	4.03246e6	+	6.98442e6i	0.00551310	+	0.00954896i
$902$			1.09612e7i			0.0149362i
$903$	7.28765e8	−	4.38700e8i	0.989747	−	0.595806i
$904$	−3.58209e8			−0.484877
$905$	−6.66342e8	+	3.84713e8i	−0.898983	+	0.519028i
$906$	−1.36720e8	−	2.03002e8i	−0.183843	−	0.272971i
$907$	−2.44110e8	+	4.22812e8i	−0.327163	+	0.566663i	−0.981948	−	0.189152i	$-0.939426\pi$
$907$	−2.44110e8	+	4.22812e8i	−0.327163	+	0.566663i	0.654785	+	0.755816i	$0.272759\pi$
$908$	3.51775e8	−	2.03097e8i	0.469902	−	0.271298i
$909$	1.26132e8	−	9.82607e7i	0.167932	−	0.130824i
$910$	−1.06649e9	+	1.64773e9i	−1.41524	+	2.18656i
$911$			2.29303e8i			0.303287i	0.988435	+	0.151644i	$0.0484566\pi$
$911$			2.29303e8i			0.303287i	−0.988435	+	0.151644i	$0.951543\pi$
$912$	7.52844e7	+	1.08756e9i	0.0992477	+	1.43374i
$913$	−2.29307e8	+	3.97172e8i	−0.301305	+	0.521875i
$914$	−1.14834e9	−	6.62992e8i	−1.50394	−	0.868300i
$915$	−3.75357e8	+	2.59833e7i	−0.489983	+	0.0339181i
$916$	−3.28773e8			−0.427769
$917$	6.08314e8	−	3.11118e8i	0.788896	−	0.403475i
$918$	−2.03947e7	−	9.69506e7i	−0.0263626	−	0.125321i
$919$	−2.33017e8	−	4.03597e8i	−0.300221	−	0.519998i	0.675965	−	0.736934i	$-0.263727\pi$
$919$	−2.33017e8	−	4.03597e8i	−0.300221	−	0.519998i	−0.976186	+	0.216936i	$0.930394\pi$
$920$	−1.30596e7	−	7.53995e6i	−0.0167713	−	0.00968289i
$921$	2.84072e8	−	1.91320e8i	0.363622	−	0.244896i
$922$	8.35738e8	+	1.44754e9i	1.06629	+	1.84688i
$923$			1.00334e9i			1.27598i
$924$	−1.97700e8	+	3.57352e8i	−0.250606	+	0.452981i
$925$	5.43989e7			0.0687329
$926$	−7.47245e7	+	4.31422e7i	−0.0941087	+	0.0543337i
$927$	−1.23845e9	+	1.72284e8i	−1.55467	+	0.216275i
$928$	−7.28244e8	+	1.26135e9i	−0.911240	+	1.57831i
$929$	2.61830e8	−	1.51167e8i	0.326567	−	0.188543i	−0.327749	−	0.944765i	$-0.606290\pi$
$929$	2.61830e8	−	1.51167e8i	0.326567	−	0.188543i	0.654316	+	0.756221i	$0.272957\pi$
$930$	1.18429e9	+	5.78645e8i	1.47235	+	0.719389i
$931$	−4.05075e8	−	9.02415e8i	−0.501980	−	1.11830i
$932$			6.16019e8i			0.760933i
$933$	6.43548e8	−	4.45484e7i	0.792385	−	0.0548513i
$934$	7.49567e8	−	1.29829e9i	0.919962	−	1.59342i
$935$	−6.38213e7	−	3.68472e7i	−0.0780783	−	0.0450785i
$936$	3.10507e8	+	1.25959e8i	0.378655	+	0.153604i
$937$	9.64898e8			1.17290			0.586452	−	0.809984i	$-0.300524\pi$
$937$	9.64898e8			1.17290			0.586452	+	0.809984i	$0.300524\pi$
$938$	−1.12134e7	+	2.20377e8i	−0.0135872	+	0.267029i
$939$	−1.27526e8	−	6.23093e7i	−0.154029	−	0.0752586i
$940$	−2.42335e8	−	4.19737e8i	−0.291765	−	0.505352i
$941$	−5.16290e8	−	2.98080e8i	−0.619619	−	0.357737i	0.157101	−	0.987582i	$-0.449785\pi$
$941$	−5.16290e8	−	2.98080e8i	−0.619619	−	0.357737i	−0.776721	+	0.629845i	$0.783118\pi$
$942$	4.59953e8	+	6.82939e8i	0.550250	+	0.817014i
$943$	327904.	+	567947.i	0.000391032	+	0.000677287i
$944$		−	1.81800e9i		−	2.16112i
$945$	−7.49292e8	−	9.26397e8i	−0.887883	−	1.09775i
$946$	8.67319e8			1.02448
$947$	6.68437e8	−	3.85922e8i	0.787065	−	0.454412i	−0.0518634	−	0.998654i	$-0.516516\pi$
$947$	6.68437e8	−	3.85922e8i	0.787065	−	0.454412i	0.838928	+	0.544242i	$0.183183\pi$
$948$	−4.10265e8	+	2.76309e8i	−0.481547	+	0.324317i
$949$	5.53361e8	−	9.58449e8i	0.647455	−	1.12143i
$950$	1.20576e9	−	6.96148e8i	1.40634	−	0.811953i
$951$	−4.62743e8	+	9.47081e8i	−0.538020	+	1.10115i
$952$	1.32985e7	−	2.05463e7i	0.0154132	−	0.0238135i
$953$		−	6.83235e8i		−	0.789390i	−0.918812	−	0.394695i	$-0.870850\pi$
$953$		−	6.83235e8i		−	0.789390i	0.918812	−	0.394695i	$-0.129150\pi$
$954$	−4.99778e7	+	1.23202e8i	−0.0575615	+	0.141897i
$955$	7.20583e8	−	1.24809e9i	0.827321	−	1.43296i
$956$	3.38398e8	+	1.95374e8i	0.387306	+	0.223611i
$957$	5.78414e7	+	8.35580e8i	0.0659937	+	0.953350i
$958$	−1.41002e8			−0.160372
$959$	7.06816e8	+	4.57485e8i	0.801402	+	0.518705i
$960$	2.84495e8	−	5.82265e8i	0.321559	−	0.658123i
$961$	1.07633e8	+	1.86425e8i	0.121276	+	0.210056i
$962$	9.84125e7	+	5.68185e7i	0.110541	+	0.0638211i
$963$	2.22536e8	+	1.59968e9i	0.249184	+	1.79124i
$964$	−1.69969e8	−	2.94396e8i	−0.189732	−	0.328625i
$965$		−	2.50268e9i		−	2.78499i
$966$	1.01999e6	+	5.58111e7i	0.00113153	+	0.0619141i
$967$	−8.28328e8			−0.916058			−0.458029	−	0.888937i	$-0.651444\pi$
$967$	−8.28328e8			−0.916058			−0.458029	+	0.888937i	$0.651444\pi$
$968$	−1.29433e8	+	7.47282e7i	−0.142698	+	0.0823870i
$969$	5.98271e7	+	8.88315e7i	0.0657547	+	0.0976328i
$970$	9.64111e8	−	1.66989e9i	1.05636	−	1.82967i
$971$	−6.27812e8	+	3.62467e8i	−0.685759	+	0.395923i	−0.802022	−	0.597295i	$-0.796242\pi$
$971$	−6.27812e8	+	3.62467e8i	−0.685759	+	0.395923i	0.116262	+	0.993219i	$0.462909\pi$
$972$	4.61456e8	−	5.46046e8i	0.502494	−	0.594608i
$973$	−6.41775e8	−	3.26553e7i	−0.696697	−	0.0354499i
$974$			2.08531e9i			2.25681i
$975$	−8.79553e7	−	1.27061e9i	−0.0948961	−	1.37087i
$976$	1.89598e8	−	3.28393e8i	0.203931	−	0.353220i
$977$	−2.59683e8	−	1.49928e8i	−0.278458	−	0.160768i	0.354267	−	0.935144i	$-0.384730\pi$
$977$	−2.59683e8	−	1.49928e8i	−0.278458	−	0.160768i	−0.632725	+	0.774376i	$0.718064\pi$
$978$	−1.31568e9	+	9.10750e7i	−1.40648	+	0.0973605i
$979$	−6.65935e8			−0.709714
$980$	−1.05005e8	+	1.02916e9i	−0.111566	+	1.09346i
$981$	−2.28974e7	−	2.93922e7i	−0.0242538	−	0.0311332i
$982$	−6.00519e8	−	1.04013e9i	−0.634151	−	1.09838i
$983$	8.21185e8	+	4.74111e8i	0.864530	+	0.499137i	0.865527	−	0.500863i	$-0.166984\pi$
$983$	8.21185e8	+	4.74111e8i	0.864530	+	0.499137i	−0.000996388		1.00000i	$0.500317\pi$
$984$	3.93166e6	−	2.64793e6i	0.00412659	−	0.00277921i
$985$	6.52254e8	+	1.12974e9i	0.682509	+	1.18214i
$986$			1.76417e8i			0.184039i
$987$	2.47110e8	−	4.46661e8i	0.257003	−	0.464544i
$988$	1.27311e9			1.32006
$989$	4.49394e7	−	2.59458e7i	0.0464557	−	0.0268212i
$990$	−1.67393e8	−	1.20329e9i	−0.172517	−	1.24013i
$991$	−3.43223e8	+	5.94479e8i	−0.352659	+	0.610823i	−0.986714	−	0.162464i	$-0.948056\pi$
$991$	−3.43223e8	+	5.94479e8i	−0.352659	+	0.610823i	0.634056	+	0.773288i	$0.281389\pi$
$992$	−9.33083e8	+	5.38716e8i	−0.955841	+	0.551855i
$993$	8.81589e8	+	4.30745e8i	0.900365	+	0.439918i
$994$	5.50111e8	+	1.07561e9i	0.560133	+	1.09520i
$995$		−	1.43382e9i		−	1.45555i
$996$	−6.95388e8	+	4.81369e7i	−0.703800	+	0.0487192i
$997$	−5.63042e8	+	9.75217e8i	−0.568140	+	0.984047i	0.428610	+	0.903489i	$0.359003\pi$
$997$	−5.63042e8	+	9.75217e8i	−0.568140	+	0.984047i	−0.996750	+	0.0805572i	$0.974330\pi$
$998$	−1.48255e9	−	8.55949e8i	−1.49148	−	0.861106i
$999$	−5.13616e7	+	4.60511e7i	−0.0515160	+	0.0461895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.11.3	yes	28
3.2	odd	2	inner	21.7.h.a.11.12	yes	28
7.2	even	3	inner	21.7.h.a.2.12	yes	28
7.3	odd	6		147.7.b.d.50.3		14
7.4	even	3		147.7.b.e.50.3		14
21.2	odd	6	inner	21.7.h.a.2.3	✓	28
21.11	odd	6		147.7.b.e.50.12		14
21.17	even	6		147.7.b.d.50.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.3	✓	28	21.2	odd	6	inner
21.7.h.a.2.12	yes	28	7.2	even	3	inner
21.7.h.a.11.3	yes	28	1.1	even	1	trivial
21.7.h.a.11.12	yes	28	3.2	odd	2	inner
147.7.b.d.50.3		14	7.3	odd	6
147.7.b.d.50.12		14	21.17	even	6
147.7.b.e.50.3		14	7.4	even	3
147.7.b.e.50.12		14	21.11	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)

\(f(q)\)	\(=\)	\(q+(-9.23947 + 5.33441i) q^{2} +(-22.3946 + 15.0825i) q^{3} +(24.9119 - 43.1487i) q^{4} +(-152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} -151.243i q^{8} +(274.035 - 675.534i) q^{9} +O(q^{10})\)	\(q+(-9.23947 + 5.33441i) q^{2} +(-22.3946 + 15.0825i) q^{3} +(24.9119 - 43.1487i) q^{4} +(-152.840 + 88.2420i) q^{5} +(126.458 - 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} -151.243i q^{8} +(274.035 - 675.534i) q^{9} +(941.439 - 1630.62i) q^{10} +(766.504 + 442.541i) q^{11} +(92.8995 + 1342.03i) q^{12} -3039.13 q^{13} +(-3258.03 + 1666.29i) q^{14} +(2091.87 - 4281.35i) q^{15} +(2401.15 + 4158.92i) q^{16} +(408.579 + 235.893i) q^{17} +(1071.64 + 7703.39i) q^{18} +(-4203.86 - 7281.30i) q^{19} +8793.11i q^{20} +(-7934.31 + 4776.28i) q^{21} -9442.80 q^{22} +(-489.271 + 282.481i) q^{23} +(2281.12 + 3387.02i) q^{24} +(7760.80 - 13442.1i) q^{25} +(28080.0 - 16212.0i) q^{26} +(4051.86 + 19261.4i) q^{27} +(9285.85 - 14346.7i) q^{28} -35049.2i q^{29} +(3510.74 + 50716.3i) q^{30} +(12963.8 - 22453.9i) q^{31} +(-35988.1 - 20777.7i) q^{32} +(-23840.2 + 1650.29i) q^{33} -5033.41 q^{34} +(-53894.3 + 27563.9i) q^{35} +(-22321.7 - 28653.1i) q^{36} +(1752.36 + 3035.18i) q^{37} +(77683.0 + 44850.3i) q^{38} +(68060.1 - 45837.8i) q^{39} +(13346.0 + 23115.9i) q^{40} -1160.80i q^{41} +(47830.2 - 86455.2i) q^{42} -91849.8 q^{43} +(38190.2 - 22049.1i) q^{44} +(17727.1 + 127430. i) q^{45} +(3013.74 - 5219.94i) q^{46} +(-47734.7 + 27559.7i) q^{47} +(-116500. - 56921.9i) q^{48} +(117041. + 11941.7i) q^{49} +165597. i q^{50} +(-12707.8 + 879.674i) q^{51} +(-75710.6 + 131135. i) q^{52} +(14804.2 + 8547.21i) q^{53} +(-140186. - 156351. i) q^{54} -156203. q^{55} +(2636.20 - 51809.2i) q^{56} +(203964. + 99656.9i) q^{57} +(186967. + 323836. i) q^{58} +(-327850. - 189284. i) q^{59} +(-132622. - 196918. i) q^{60} +(-39480.6 - 68382.4i) q^{61} +276617. i q^{62} +(105647. - 226632. i) q^{63} +136000. q^{64} +(464500. - 268179. i) q^{65} +(211468. - 142421. i) q^{66} +(30150.0 - 52221.3i) q^{67} +(20357.0 - 11753.1i) q^{68} +(6696.49 - 13705.5i) q^{69} +(350918. - 542170. i) q^{70} -330141. i q^{71} +(-102170. - 41445.8i) q^{72} +(-182079. + 315369. i) q^{73} +(-32381.8 - 18695.6i) q^{74} +(28940.9 + 418083. i) q^{75} -418905. q^{76} +(254858. + 164956. i) q^{77} +(-384322. + 786578. i) q^{78} +(183846. + 318430. i) q^{79} +(-733983. - 423765. i) q^{80} +(-381251. - 370240. i) q^{81} +(6192.20 + 10725.2i) q^{82} +518160. i q^{83} +(8431.38 + 461342. i) q^{84} -83262.7 q^{85} +(848644. - 489965. i) q^{86} +(528631. + 784913. i) q^{87} +(66931.2 - 115928. i) q^{88} +(-651596. + 376199. i) q^{89} +(-843552. - 1.08282e6i) q^{90} +(-1.04108e6 - 52972.9i) q^{91} +28148.5i q^{92} +(48343.5 + 698373. i) q^{93} +(294029. - 509274. i) q^{94} +(1.28503e6 + 741915. i) q^{95} +(1.11932e6 - 77482.6i) q^{96} +1.02408e6 q^{97} +(-1.14510e6 + 514012. i) q^{98} +(509001. - 396528. 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more