LMFDB - Embedded newform 21.7.h.a.2.3

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			2.3
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.3

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

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 $

$2$	−9.23947	−	5.33441i	−1.15493	−	0.666802i	−0.204850	−	0.978793i	$-0.565671\pi$
$2$	−9.23947	−	5.33441i	−1.15493	−	0.666802i	−0.950085	+	0.311992i	$0.899004\pi$
$3$	−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	−0.257221	−	0.966353i	$-0.582807\pi$
$5$	−152.840	−	88.2420i	−1.22272	−	0.705936i	−0.965496	+	0.260417i	$0.916140\pi$
$6$	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	−0.183611	−	0.982999i	$-0.558779\pi$
$11$	766.504	−	442.541i	0.575886	−	0.332488i	0.759497	+	0.650511i	$0.225445\pi$
$12$	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	−0.457842	−	0.889034i	$-0.651377\pi$
$17$	408.579	−	235.893i	0.0831628	−	0.0480141i	0.541005	+	0.841020i	$0.318044\pi$
$18$	1071.64	−	7703.39i	0.183752	−	1.32088i
$19$	−4203.86	+	7281.30i	−0.612897	+	1.06157i	0.377852	+	0.925866i	$0.376663\pi$
$19$	−4203.86	+	7281.30i	−0.612897	+	1.06157i	−0.990750	+	0.135703i	$0.956671\pi$
$20$		−	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	0.479759	−	0.877400i	$-0.340724\pi$
$23$	−489.271	−	282.481i	−0.0402129	−	0.0232169i	−0.519972	+	0.854183i	$0.674058\pi$
$24$	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	$0.255192\pi$
$29$			35049.2i			1.43709i	−0.695480	+	0.718546i	$0.744808\pi$
$30$	3510.74	−	50716.3i	0.130027	−	1.87838i
$31$	12963.8	+	22453.9i	0.435158	+	0.753715i	0.997308	−	0.0733197i	$-0.0233593\pi$
$31$	12963.8	+	22453.9i	0.435158	+	0.753715i	−0.562151	+	0.827035i	$0.690026\pi$
$32$	−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	−0.848209	−	0.529661i	$-0.822319\pi$
$37$	1752.36	−	3035.18i	0.0345954	−	0.0599210i	0.882805	+	0.469740i	$0.155652\pi$
$38$	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	$0.00268060\pi$
$41$			1160.80i			0.0168425i	−0.999965	+	0.00842126i	$0.997319\pi$
$42$	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	0.252177	−	0.967681i	$-0.418853\pi$
$47$	−47734.7	−	27559.7i	−0.459770	−	0.265449i	−0.711948	+	0.702232i	$0.752187\pi$
$48$	−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	−0.449456	−	0.893303i	$-0.648382\pi$
$53$	14804.2	−	8547.21i	0.0994392	−	0.0574112i	0.548895	+	0.835891i	$0.315049\pi$
$54$	−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	−0.604128	+	0.796888i	$0.706478\pi$
$59$	−327850.	+	189284.i	−1.59632	+	0.921634i	−0.992189	+	0.124746i	$0.960188\pi$
$60$	−132622.	+	196918.i	−0.613992	+	0.911658i
$61$	−39480.6	+	68382.4i	−0.173938	+	0.301269i	−0.939793	−	0.341744i	$-0.888983\pi$
$61$	−39480.6	+	68382.4i	−0.173938	+	0.301269i	0.765855	+	0.643013i	$0.222316\pi$
$62$		−	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	0.911786	−	0.410667i	$-0.134704\pi$
$67$	30150.0	+	52221.3i	0.100245	+	0.173629i	−0.811541	+	0.584296i	$0.801371\pi$
$68$	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	$0.152583\pi$
$71$			330141.i			0.922410i	−0.887294	+	0.461205i	$0.847417\pi$
$72$	−102170.	+	41445.8i	−0.273731	+	0.111041i
$73$	−182079.	−	315369.i	−0.468048	−	0.810683i	0.531285	−	0.847193i	$-0.321709\pi$
$73$	−182079.	−	315369.i	−0.468048	−	0.810683i	−0.999333	+	0.0365102i	$0.988376\pi$
$74$	−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	−0.617125	−	0.786865i	$-0.711703\pi$
$79$	183846.	−	318430.i	0.372883	−	0.645852i	0.990008	+	0.141013i	$0.0450360\pi$
$80$	−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	$-0.850316\pi$
$83$		−	518160.i		−	0.906212i	0.891457	−	0.453106i	$-0.149684\pi$
$84$	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	−0.0392888	−	0.999228i	$-0.512509\pi$
$89$	−651596.	−	376199.i	−0.924290	−	0.533639i	−0.885001	+	0.465589i	$0.845843\pi$
$90$	−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	−0.404982	−	0.914325i	$-0.632722\pi$
$101$	189942.	−	109663.i	0.184356	−	0.106438i	0.589338	+	0.807887i	$0.299389\pi$
$102$	112721.	+	75916.5i	0.106220	+	0.0715378i
$103$	−857597.	+	1.48540e6i	−0.784823	+	1.35935i	0.144282	+	0.989537i	$0.453913\pi$
$103$	−857597.	+	1.48540e6i	−0.784823	+	1.35935i	−0.929105	+	0.369816i	$0.879421\pi$
$104$		−	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	−0.996606	−	0.0823201i	$-0.973767\pi$
$107$	−1.91866e6	−	1.10774e6i	−1.56620	−	0.904246i	−0.569594	−	0.821926i	$-0.692900\pi$
$108$	932046.	−	305007.i	0.739888	−	0.242124i
$109$	25554.5	+	44261.7i	0.0197328	+	0.0341781i	0.875723	−	0.482814i	$-0.160385\pi$
$109$	25554.5	+	44261.7i	0.0197328	+	0.0341781i	−0.855990	+	0.516992i	$0.827052\pi$
$110$	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	$0.306429\pi$
$113$			2.36844e6i			1.64145i	−0.571326	+	0.820723i	$0.693571\pi$
$114$	−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	0.831937	−	0.554870i	$-0.187232\pi$
$131$	1.72512e6	+	996001.i	0.767373	+	0.443043i	−0.0645636	+	0.997914i	$0.520566\pi$
$132$	−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	−0.0260045	−	0.999662i	$-0.508278\pi$
$137$	2.12580e6	−	1.22733e6i	0.826726	−	0.477310i	0.852730	+	0.522351i	$0.174945\pi$
$138$	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	0.490331	−	0.871536i	$-0.336876\pi$
$149$	−63765.1	−	36814.8i	−0.0192763	−	0.0111292i	−0.509607	+	0.860407i	$0.670209\pi$
$150$	−2.49763e6	+	3.70848e6i	−0.740037	+	1.09881i
$151$	424826.	+	735820.i	0.123390	+	0.213718i	0.921102	−	0.389320i	$-0.127290\pi$
$151$	424826.	+	735820.i	0.123390	+	0.213718i	−0.797712	+	0.603038i	$0.793957\pi$
$152$	−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	0.620146	−	0.784486i	$-0.287073\pi$
$157$	−1.42920e6	−	2.47544e6i	−0.369312	−	0.639667i	−0.989458	+	0.144819i	$0.953740\pi$
$158$	−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	0.470861	+	0.882207i	$0.343943\pi$
$163$	−2.28916e6	+	3.96494e6i	−0.528584	+	0.915534i	−0.999445	+	0.0333262i	$0.989390\pi$
$164$	−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	$0.0142893\pi$
$167$			418018.i			0.0897523i	−0.998993	+	0.0448762i	$0.985711\pi$
$168$	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	0.328860	−	0.944379i	$-0.393336\pi$
$173$	−1.68052e6	−	970246.i	−0.324567	−	0.187389i	−0.653426	+	0.756990i	$0.726669\pi$
$174$	−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	−0.332750	−	0.943015i	$-0.607976\pi$
$179$	1.82126e6	−	1.05150e6i	0.317550	−	0.183338i	0.650300	+	0.759677i	$0.274643\pi$
$180$	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	−0.102304	−	0.994753i	$-0.532621\pi$
$191$	−7.07195e6	−	4.08299e6i	−1.01494	−	0.585974i	−0.912633	+	0.408779i	$0.865955\pi$
$192$	−3.04567e6	−	2.05123e6i	−0.430308	−	0.289808i
$193$	−7.09039e6	−	1.22809e7i	−0.986276	−	1.70828i	−0.636125	−	0.771586i	$-0.719464\pi$
$193$	−7.09039e6	−	1.22809e7i	−0.986276	−	1.70828i	−0.350150	−	0.936694i	$-0.613869\pi$
$194$	−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	$0.160601\pi$
$197$			7.39165e6i			0.966814i	−0.875396	+	0.483407i	$0.839399\pi$
$198$	−2.58765e6	−	6.37893e6i	−0.333358	−	0.821774i
$199$	−4.06219e6	−	7.03592e6i	−0.515467	−	0.892815i	−0.999839	−	0.0179528i	$-0.994285\pi$
$199$	−4.06219e6	−	7.03592e6i	−0.515467	−	0.892815i	0.484372	−	0.874862i	$-0.339048\pi$
$200$	−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	−0.166856	−	0.985981i	$-0.553362\pi$
$227$	7.06037e6	−	4.07630e6i	0.603601	−	0.348489i	0.770457	+	0.637492i	$0.220028\pi$
$228$	9.38121e6	+	6.31815e6i	0.791506	+	0.533072i
$229$	−3.29935e6	+	5.71465e6i	−0.274740	+	0.475864i	−0.970070	−	0.242827i	$-0.921925\pi$
$229$	−3.29935e6	+	5.71465e6i	−0.274740	+	0.475864i	0.695329	+	0.718691i	$0.255259\pi$
$230$		−	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	0.0129778	−	0.999916i	$-0.495869\pi$
$233$	−1.07075e7	−	6.18197e6i	−0.846486	−	0.488719i	−0.859464	+	0.511197i	$0.829202\pi$
$234$	−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	$-0.907264\pi$
$239$		−	7.84259e6i		−	0.574468i	0.957860	−	0.287234i	$-0.0927357\pi$
$240$	2.28287e7	+	1.58027e6i	1.65138	+	0.114314i
$241$	3.41141e6	+	5.90873e6i	0.243715	+	0.422127i	0.961770	−	0.273860i	$-0.0883005\pi$
$241$	3.41141e6	+	5.90873e6i	0.243715	+	0.422127i	−0.718055	+	0.695987i	$0.754967\pi$
$242$	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	$-0.847160\pi$
$251$		−	1.46090e7i		−	0.923846i	0.886920	−	0.461923i	$-0.152840\pi$
$252$	−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	0.687539	−	0.726147i	$-0.258691\pi$
$257$	6.83136e6	+	3.94409e6i	0.402446	+	0.232353i	−0.285093	+	0.958500i	$0.592024\pi$
$258$	−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	−0.957345	−	0.288948i	$-0.906695\pi$
$263$	−2.15711e7	+	1.24541e7i	−1.18578	+	0.684611i	−0.228437	+	0.973559i	$0.573361\pi$
$264$	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	0.253709	−	0.967281i	$-0.418349\pi$
$269$	2.37134e7	−	1.36910e7i	1.21825	−	0.703359i	0.964544	+	0.263922i	$0.0850160\pi$
$270$	3.52227e7	−	1.15264e7i	1.78950	−	0.585603i
$271$	−2.58227e6	+	4.47262e6i	−0.129746	+	0.224726i	−0.923578	−	0.383410i	$-0.874749\pi$
$271$	−2.58227e6	+	4.47262e6i	−0.129746	+	0.224726i	0.793832	+	0.608137i	$0.208083\pi$
$272$		−	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	0.569121	−	0.822254i	$-0.307283\pi$
$277$	−9.08673e6	−	1.57387e7i	−0.427532	−	0.740507i	−0.996653	+	0.0817467i	$0.973950\pi$
$278$	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	$-0.711678\pi$
$281$		−	3.49201e7i		−	1.57382i	0.617065	−	0.786912i	$-0.288322\pi$
$282$	1.09647e6	−	1.58397e7i	0.0488933	−	0.706316i
$283$	2.43250e6	+	4.21321e6i	0.107323	+	0.185889i	0.914685	−	0.404167i	$-0.132439\pi$
$283$	2.43250e6	+	4.21321e6i	0.107323	+	0.185889i	−0.807362	+	0.590057i	$0.799105\pi$
$284$	−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	$0.0912806\pi$
$293$			1.42296e7i			0.565705i	−0.959163	+	0.282852i	$0.908719\pi$
$294$	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	−0.802813	−	0.596231i	$-0.796664\pi$
$311$	−2.06912e7	+	1.19461e7i	−0.687868	+	0.397141i	0.114945	+	0.993372i	$0.463331\pi$
$312$	−6.93263e6	+	1.02936e7i	−0.228262	+	0.338925i
$313$	2.62841e6	−	4.55255e6i	0.0857158	−	0.148464i	−0.819980	−	0.572392i	$-0.806016\pi$
$313$	2.62841e6	−	4.55255e6i	0.0857158	−	0.148464i	0.905696	+	0.423928i	$0.139349\pi$
$314$			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	0.925809	−	0.377991i	$-0.123385\pi$
$317$	3.38098e7	+	1.95201e7i	1.06136	+	0.612779i	0.135555	+	0.990770i	$0.456718\pi$
$318$	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	0.498954	+	0.866628i	$0.333718\pi$
$331$	−1.81703e7	+	3.14718e7i	−0.501045	+	0.867836i	−0.999999	+	0.00120735i	$0.999616\pi$
$332$	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	−0.430630	−	0.902528i	$-0.641709\pi$
$347$	5.66844e6	−	3.27267e6i	0.135667	−	0.0783275i	0.566297	+	0.824201i	$0.308375\pi$
$348$	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	−0.899407	−	0.437112i	$-0.856001\pi$
$353$	−4.26921e7	+	2.46483e7i	−0.970561	+	0.560354i	−0.0711539	+	0.997465i	$0.522668\pi$
$354$	−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	0.273959	−	0.961741i	$-0.411667\pi$
$359$	−1.95231e7	−	1.12717e7i	−0.421955	−	0.243616i	−0.695913	+	0.718126i	$0.745000\pi$
$360$	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	0.926389	+	0.376567i	$0.122896\pi$
$367$	3.90163e7	+	6.75783e7i	0.789311	+	1.36713i	−0.137078	+	0.990560i	$0.543771\pi$
$368$	−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	−0.630584	−	0.776121i	$-0.717185\pi$
$373$	1.85187e7	−	3.20753e7i	0.356848	−	0.618079i	0.987432	+	0.158042i	$0.0505181\pi$
$374$	−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	0.875189	−	0.483781i	$-0.160737\pi$
$383$	5.02164e7	+	2.89924e7i	0.893818	+	0.516046i	0.0186284	+	0.999826i	$0.494070\pi$
$384$	−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	0.147750	−	0.989025i	$-0.452797\pi$
$389$	6.34639e7	−	3.66409e7i	1.07815	−	0.622468i	0.930396	+	0.366557i	$0.119463\pi$
$390$	−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	−0.946101	−	0.323872i	$-0.895015\pi$
$397$	−1.20492e7	+	2.08698e7i	−0.192569	+	0.333539i	0.753532	+	0.657411i	$0.228349\pi$
$398$			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	0.459328	−	0.888267i	$-0.348090\pi$
$401$	−5.17591e6	−	2.98831e6i	−0.0802701	−	0.0463439i	−0.539598	+	0.841923i	$0.681424\pi$
$402$	−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	0.844845	−	0.535012i	$-0.179693\pi$
$409$	−2.79908e6	−	4.84814e6i	−0.0409115	−	0.0708607i	−0.885756	+	0.464151i	$0.846359\pi$
$410$	−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	$-0.963140\pi$
$419$		−	1.69985e7i		−	0.231084i	0.993303	−	0.115542i	$-0.0368604\pi$
$420$	−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	−0.692473	−	0.721444i	$-0.743479\pi$
$431$	−3.31397e7	+	1.91332e7i	−0.413921	+	0.238977i	0.278552	+	0.960421i	$0.410146\pi$
$432$	−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	−0.930597	−	0.366045i	$-0.880712\pi$
$439$	−1.25464e7	+	2.17310e7i	−0.148295	+	0.256854i	0.782303	+	0.622899i	$0.214045\pi$
$440$		−	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	0.618437	−	0.785835i	$-0.287766\pi$
$443$	2.14827e7	+	1.24030e7i	0.247103	+	0.142665i	−0.371334	+	0.928499i	$0.621100\pi$
$444$	−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	$-0.709406\pi$
$449$		−	1.43255e8i		−	1.58259i	0.611432	−	0.791297i	$-0.290594\pi$
$450$	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	−0.331765	−	0.943362i	$-0.607644\pi$
$457$	6.21429e7	−	1.07635e8i	0.651093	−	1.12773i	0.982858	−	0.184364i	$-0.0590226\pi$
$458$	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	$0.294933\pi$
$461$			1.56669e8i			1.59912i	−0.600588	+	0.799559i	$0.705067\pi$
$462$	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	−0.235427	−	0.971892i	$-0.575649\pi$
$467$	−1.21690e8	−	7.02577e7i	−1.19482	−	0.689832i	−0.959397	+	0.282060i	$0.908982\pi$
$468$	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	−0.447024	−	0.894522i	$-0.647516\pi$
$479$	1.14456e7	−	6.60811e6i	0.104143	−	0.0601272i	0.551167	+	0.834395i	$0.314183\pi$
$480$	−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	0.884635	+	0.466284i	$0.154407\pi$
$487$	9.77292e7	+	1.69272e8i	0.846131	+	1.46554i	−0.0385041	+	0.999258i	$0.512259\pi$
$488$	−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	$-0.842261\pi$
$491$		−	1.12575e8i		−	0.951034i	0.879707	−	0.475517i	$-0.157739\pi$
$492$	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	−0.338441	−	0.940987i	$-0.609900\pi$
$499$	8.02290e7	−	1.38961e8i	0.645698	−	1.11838i	0.984140	−	0.177395i	$-0.0567670\pi$
$500$	−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	$0.0523897\pi$
$503$			4.17030e7i			0.327690i	−0.986486	+	0.163845i	$0.947610\pi$
$504$	−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	0.940067	−	0.340990i	$-0.110762\pi$
$509$	1.47010e8	+	8.48765e7i	1.11479	+	0.643627i	0.174727	+	0.984617i	$0.444096\pi$
$510$	−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	−0.284994	−	0.958529i	$-0.591991\pi$
$521$	5.69389e7	−	3.28737e7i	0.402620	−	0.232453i	0.687614	+	0.726076i	$0.258658\pi$
$522$	2.69998e8	+	3.75601e7i	1.89823	+	0.264068i
$523$	−1.04627e7	+	1.81220e7i	−0.0731374	+	0.126678i	−0.900275	−	0.435322i	$-0.856634\pi$
$523$	−1.04627e7	+	1.81220e7i	−0.0731374	+	0.126678i	0.827137	+	0.562000i	$0.189968\pi$
$524$			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	−0.625364	−	0.780333i	$-0.715050\pi$
$541$	5.74944e7	−	9.95832e7i	0.363106	−	0.628918i	0.988470	+	0.151415i	$0.0483829\pi$
$542$	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	0.0292895	−	0.999571i	$-0.490676\pi$
$557$	1.57185e8	−	9.07506e7i	0.909588	−	0.525151i	0.880299	+	0.474420i	$0.157342\pi$
$558$	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	−0.611653	−	0.791127i	$-0.709495\pi$
$563$	−4.14625e7	+	2.39384e7i	−0.232343	+	0.134143i	0.379309	+	0.925270i	$0.376162\pi$
$564$	−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	0.190235	−	0.981739i	$-0.439075\pi$
$569$	−1.04058e8	−	6.00781e7i	−0.564859	−	0.326121i	−0.755093	+	0.655617i	$0.772408\pi$
$570$	3.54522e8	+	2.38767e8i	1.91434	+	1.28929i
$571$	−1.45541e8	−	2.52085e8i	−0.781769	−	1.35406i	−0.930910	−	0.365248i	$-0.880984\pi$
$571$	−1.45541e8	−	2.52085e8i	−0.781769	−	1.35406i	0.149141	−	0.988816i	$-0.452349\pi$
$572$	−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	0.856762	−	0.515713i	$-0.172473\pi$
$577$	−3.50380e6	−	6.06877e6i	−0.0182395	−	0.0315917i	−0.875001	+	0.484121i	$0.839139\pi$
$578$	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	$0.0461714\pi$
$587$			5.84714e7i			0.289087i	−0.989498	+	0.144544i	$0.953829\pi$
$588$	−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	0.975137	−	0.221601i	$-0.0711283\pi$
$593$	2.64996e8	+	1.52995e8i	1.27079	+	0.733693i	0.295656	+	0.955294i	$0.404462\pi$
$594$	−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	−0.999986	−	0.00534498i	$-0.998299\pi$
$599$	−3.21383e8	+	1.85551e8i	−1.49535	+	0.863341i	−0.495364	+	0.868686i	$0.664965\pi$
$600$	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	0.141060	+	0.990001i	$0.454949\pi$
$607$	−1.75975e8	+	3.04797e8i	−0.786836	+	1.36284i	−0.927896	+	0.372839i	$0.878384\pi$
$608$		−	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	0.988740	+	0.149643i	$0.0478123\pi$
$613$	1.43728e8	+	2.48944e8i	0.623964	+	1.08074i	−0.364776	+	0.931095i	$0.618854\pi$
$614$	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	$0.389088\pi$
$617$			4.41540e8i			1.87981i	−0.341432	+	0.939907i	$0.610912\pi$
$618$	−4.92896e8	−	3.41198e7i	−2.08829	−	0.144558i
$619$	4.35278e7	+	7.53924e7i	0.183525	+	0.317875i	0.943078	−	0.332570i	$-0.107916\pi$
$619$	4.35278e7	+	7.53924e7i	0.183525	+	0.317875i	−0.759554	+	0.650445i	$0.774583\pi$
$620$	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	−0.924420	−	0.381375i	$-0.875451\pi$
$641$	−2.78216e8	+	1.60628e8i	−1.05635	+	0.609884i	−0.131930	+	0.991259i	$0.542117\pi$
$642$	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	−0.629424	+	0.777062i	$0.716709\pi$
$647$	−4.37973e8	+	2.52864e8i	−1.61709	+	0.933628i	−0.987667	+	0.156566i	$0.949957\pi$
$648$	−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	0.723978	−	0.689823i	$-0.242312\pi$
$653$	1.36038e8	+	7.85415e7i	0.488563	+	0.282072i	−0.235415	+	0.971895i	$0.575645\pi$
$654$	−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	$-0.868062\pi$
$659$		−	2.30514e8i		−	0.805454i	0.915320	−	0.402727i	$-0.131938\pi$
$660$	−1.45112e7	+	2.09630e8i	−0.0504744	+	0.729156i
$661$	8.24137e7	+	1.42745e8i	0.285361	+	0.494260i	0.972697	−	0.232080i	$-0.0745531\pi$
$661$	8.24137e7	+	1.42745e8i	0.285361	+	0.494260i	−0.687335	+	0.726340i	$0.741220\pi$
$662$	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	−0.973426	−	0.229002i	$-0.926454\pi$
$677$	−5.14602e8	−	2.97105e8i	−1.65846	−	0.957513i	−0.685035	−	0.728510i	$-0.740213\pi$
$678$	−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	−0.593347	−	0.804947i	$-0.702194\pi$
$683$	−6.14652e7	+	3.54870e7i	−0.192916	+	0.111380i	0.400431	+	0.916327i	$0.368860\pi$
$684$	−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	−0.999156	−	0.0410845i	$-0.986919\pi$
$691$	−1.53091e8	+	2.65162e8i	−0.463998	+	0.803668i	0.535158	+	0.844752i	$0.320252\pi$
$692$		−	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	$-0.936421\pi$
$701$		−	1.36696e8i		−	0.396829i	0.980118	−	0.198414i	$-0.0635791\pi$
$702$	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	0.467350	+	0.884073i	$0.345209\pi$
$709$	−1.89589e8	+	3.28378e8i	−0.531954	+	0.921372i	−0.999304	+	0.0372996i	$0.988124\pi$
$710$	−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	0.610475	−	0.792036i	$-0.290979\pi$
$719$	8.54115e7	+	4.93123e7i	0.229789	+	0.132669i	−0.380686	+	0.924705i	$0.624312\pi$
$720$	−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	−0.391520	−	0.920170i	$-0.628051\pi$
$733$	2.36745e8	−	4.10054e8i	0.601130	−	1.04119i	0.992650	−	0.121018i	$-0.0386160\pi$
$734$		−	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	−0.983477	−	0.181033i	$-0.942056\pi$
$739$	−2.61731e8	−	4.53331e8i	−0.648518	−	1.12327i	0.334960	−	0.942233i	$-0.391277\pi$
$740$	−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	$-0.933265\pi$
$743$		−	1.70732e8i		−	0.416244i	0.978103	−	0.208122i	$-0.0667352\pi$
$744$	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	−0.258461	−	0.966022i	$-0.583215\pi$
$751$	2.99617e8	−	5.18951e8i	0.707369	−	1.22520i	0.965830	−	0.259177i	$-0.0834515\pi$
$752$	−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	0.929006

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