LMFDB - Embedded newform 21.7.h.a.11.12

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			11.12
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.23947 - 5.33441i) q^{2} +(-1.86456 + 26.9355i) q^{3} +(24.9119 - 43.1487i) q^{4} +(152.840 - 88.2420i) q^{5} +(126.458 + 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} +151.243i q^{8} +(-722.047 - 100.446i) q^{9} +O(q^{10})$	\(q+(9.23947 - 5.33441i) q^{2} +(-1.86456 + 26.9355i) 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} +(-722.047 - 100.446i) q^{9} +(941.439 - 1630.62i) q^{10} +(-766.504 - 442.541i) q^{11} +(1115.78 + 751.470i) 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} +(-7207.15 + 2923.63i) q^{18} +(-4203.86 - 7281.30i) q^{19} -8793.11i q^{20} +(-1108.21 + 9194.45i) q^{21} -9442.80 q^{22} +(489.271 - 282.481i) q^{23} +(-4073.81 - 282.001i) 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} +(42166.3 + 28398.5i) q^{30} +(12963.8 - 22453.9i) q^{31} +(35988.1 + 20777.7i) q^{32} +(13349.3 - 19821.1i) 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} +(5666.64 - 81860.6i) q^{39} +(13346.0 + 23115.9i) q^{40} +1160.80i q^{41} +(38807.7 + 90863.6i) q^{42} -91849.8 q^{43} +(-38190.2 + 22049.1i) q^{44} +(-119221. + 48362.8i) 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} +(7115.73 - 10565.5i) q^{51} +(-75710.6 + 131135. i) q^{52} +(-14804.2 - 8547.21i) q^{53} +(-65311.4 - 199580. 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} +(236847. + 16395.3i) q^{60} +(-39480.6 - 68382.4i) q^{61} -276617. i q^{62} +(-245591. - 46993.9i) q^{63} +136000. q^{64} +(-464500. + 268179. i) q^{65} +(17606.7 - 254347. 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} +(15191.7 - 109204. i) q^{72} +(-182079. + 315369. i) q^{73} +(32381.8 + 18695.6i) q^{74} +(347600. + 234105. 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} +(511262. + 145053. i) q^{81} +(6192.20 + 10725.2i) q^{82} -518160. i q^{83} +(369121. + 276870. i) q^{84} -83262.7 q^{85} +(-848644. + 489965. i) q^{86} +(-944070. - 65351.3i) 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} +(580637. + 391053. i) q^{93} +(294029. - 509274. i) q^{94} +(-1.28503e6 - 741915. i) q^{95} +(-626762. + 930618. i) 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	0.204850	−	0.978793i	$-0.434329\pi$
$2$	9.23947	−	5.33441i	1.15493	−	0.666802i	0.950085	+	0.311992i	$0.100996\pi$
$3$	−1.86456	+	26.9355i	−0.0690577	+	0.997613i
$3$	−1.86456	+	26.9355i	−0.0690577	+	0.997613i
$4$	24.9119	−	43.1487i	0.389249	−	0.674199i
$5$	152.840	−	88.2420i	1.22272	−	0.705936i	0.257221	−	0.966353i	$-0.417193\pi$
$5$	152.840	−	88.2420i	1.22272	−	0.705936i	0.965496	+	0.260417i	$0.0838599\pi$
$6$	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
$9$	−722.047	−	100.446i	−0.990462	−	0.137786i
$10$	941.439	−	1630.62i	0.941439	−	1.63062i
$11$	−766.504	−	442.541i	−0.575886	−	0.332488i	0.183611	−	0.982999i	$-0.441221\pi$
$11$	−766.504	−	442.541i	−0.575886	−	0.332488i	−0.759497	+	0.650511i	$0.774555\pi$
$12$	1115.78	+	751.470i	0.645709	+	0.434878i
$13$	−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	$-0.348623\pi$
$17$	−408.579	−	235.893i	−0.0831628	−	0.0480141i	−0.541005	+	0.841020i	$0.681956\pi$
$18$	−7207.15	+	2923.63i	−1.23579	+	0.501308i
$19$	−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
$21$	−1108.21	+	9194.45i	−0.119664	+	0.992814i
$22$	−9442.80			−0.886814
$23$	489.271	−	282.481i	0.0402129	−	0.0232169i	−0.479759	−	0.877400i	$-0.659276\pi$
$23$	489.271	−	282.481i	0.0402129	−	0.0232169i	0.519972	+	0.854183i	$0.325942\pi$
$24$	−4073.81	−	282.001i	−0.294691	−	0.0203994i
$25$	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	$0.744808\pi$
$30$	42166.3	+	28398.5i	1.56171	+	1.05180i
$31$	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
$33$	13349.3	−	19821.1i	0.371464	−	0.551550i
$34$	−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
$39$	5666.64	−	81860.6i	0.0955282	−	1.38001i
$40$	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	$0.997319\pi$
$42$	38807.7	+	90863.6i	0.523806	+	1.22643i
$43$	−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
$45$	−119221.	+	48362.8i	−1.30832	+	0.530730i
$46$	3013.74	−	5219.94i	0.0309622	−	0.0536281i
$47$	47734.7	−	27559.7i	0.459770	−	0.265449i	−0.252177	−	0.967681i	$-0.581147\pi$
$47$	47734.7	−	27559.7i	0.459770	−	0.265449i	0.711948	+	0.702232i	$0.247813\pi$
$48$	−116500.	+	56921.9i	−1.05342	+	0.514701i
$49$	117041.	+	11941.7i	0.994835	+	0.101503i
$50$		−	165597.i		−	1.32478i
$51$	7115.73	−	10565.5i	0.0536425	−	0.0796485i
$52$	−75710.6	+	131135.i	−0.538452	+	0.932626i
$53$	−14804.2	−	8547.21i	−0.0994392	−	0.0574112i	0.449456	−	0.893303i	$-0.351618\pi$
$53$	−14804.2	−	8547.21i	−0.0994392	−	0.0574112i	−0.548895	+	0.835891i	$0.684951\pi$
$54$	−65311.4	−	199580.i	−0.414770	−	1.26746i
$55$	−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	$0.0398116\pi$
$59$	327850.	+	189284.i	1.59632	+	0.921634i	0.604128	+	0.796888i	$0.293522\pi$
$60$	236847.	+	16395.3i	1.09652	+	0.0759041i
$61$	−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
$63$	−245591.	−	46993.9i	−0.982180	−	0.187940i
$64$	136000.			0.518800
$65$	−464500.	+	268179.i	−1.69140	+	0.976528i
$66$	17606.7	−	254347.i	0.0612414	−	0.884697i
$67$	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	$0.152583\pi$
$71$			330141.i			0.922410i	−0.887294	+	0.461205i	$0.847417\pi$
$72$	15191.7	−	109204.i	0.0407014	−	0.292579i
$73$	−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
$75$	347600.	+	234105.i	0.823940	+	0.554915i
$76$	−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
$81$	511262.	+	145053.i	0.962030	+	0.272943i
$82$	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	$-0.149684\pi$
$84$	369121.	+	276870.i	0.622775	+	0.467129i
$85$	−83262.7			−0.135579
$86$	−848644.	+	489965.i	−1.33423	+	0.770317i
$87$	−944070.	−	65351.3i	−1.43366	−	0.0992423i
$88$	66931.2	−	115928.i	0.0982156	−	0.170114i
$89$	651596.	−	376199.i	0.924290	−	0.533639i	0.0392888	−	0.999228i	$-0.487491\pi$
$89$	651596.	−	376199.i	0.924290	−	0.533639i	0.885001	+	0.465589i	$0.154157\pi$
$90$	−843552.	+	1.08282e6i	−1.15714	+	1.48535i
$91$	−1.04108e6	−	52972.9i	−1.38152	−	0.0702958i
$92$		−	28148.5i		−	0.0361487i
$93$	580637.	+	391053.i	0.721865	+	0.486169i
$94$	294029.	−	509274.i	0.354003	−	0.613151i
$95$	−1.28503e6	−	741915.i	−1.49880	−	0.865333i
$96$	−626762.	+	930618.i	−0.708416	+	1.05186i
$97$	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	$-0.367278\pi$
$101$	−189942.	−	109663.i	−0.184356	−	0.106438i	−0.589338	+	0.807887i	$0.700611\pi$
$102$	9385.08	−	135578.i	0.00884377	−	0.127758i
$103$	−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
$105$	641958.	+	1.50307e6i	0.554548	+	1.29841i
$106$	−182378.			−0.153128
$107$	1.91866e6	−	1.10774e6i	1.56620	−	0.904246i	0.569594	−	0.821926i	$-0.307100\pi$
$107$	1.91866e6	−	1.10774e6i	1.56620	−	0.904246i	0.996606	−	0.0823201i	$-0.0262330\pi$
$108$	−730167.	−	654672.i	−0.579630	−	0.519700i
$109$	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	$0.306429\pi$
$113$			2.36844e6i			1.64145i	−0.571326	+	0.820723i	$0.693571\pi$
$114$	1.35291e6	−	2.00881e6i	0.913177	−	1.35589i
$115$	49853.3	−	86348.4i	0.0327794	−	0.0567755i
$116$	1.51233e6	+	873144.i	0.968885	+	0.559386i
$117$	2.19439e6	+	305268.i	1.37012	+	0.190600i
$118$	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
$123$	−31266.9	−	2164.39i	−0.0168023	−	0.00116311i
$124$	−645905.	−	1.11874e6i	−0.338769	−	0.586765i
$125$			18248.2i			0.00934309i
$126$	−2.51982e6	+	875887.i	−1.25967	+	0.437861i
$127$	−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
$129$	171259.	−	2.47402e6i	0.0797784	−	1.15248i
$130$	−2.86116e6	+	4.95567e6i	−1.30230	+	2.25565i
$131$	−1.72512e6	+	996001.i	−0.767373	+	0.443043i	−0.831937	−	0.554870i	$-0.812768\pi$
$131$	−1.72512e6	+	996001.i	−0.767373	+	0.443043i	0.0645636	+	0.997914i	$0.479434\pi$
$132$	−522697.	−	1.06979e6i	−0.227263	−	0.465131i
$133$	−1.31315e6	−	2.56754e6i	−0.558160	−	1.09134i
$134$		−	643330.i		−	0.267374i
$135$	−1.08038e6	−	3.30145e6i	−0.439113	−	1.34185i
$136$	35677.1	−	61794.6i	0.0141832	−	0.0245660i
$137$	−2.12580e6	−	1.22733e6i	−0.826726	−	0.477310i	0.0260045	−	0.999662i	$-0.491722\pi$
$137$	−2.12580e6	−	1.22733e6i	−0.826726	−	0.477310i	−0.852730	+	0.522351i	$0.825055\pi$
$138$	134983.	+	90909.5i	0.0513619	+	0.0345917i
$139$	−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
$144$	−1.31600e6	−	3.24412e6i	−0.440726	−	1.08645i
$145$	3.09281e6	+	5.35691e6i	1.01449	+	1.75716i
$146$			3.88513e6i			1.24838i
$147$	−539887.	+	3.13031e6i	−0.169962	+	0.985451i
$148$	174619.			0.0538649
$149$	63765.1	−	36814.8i	0.0192763	−	0.0111292i	−0.490331	−	0.871536i	$-0.663124\pi$
$149$	63765.1	−	36814.8i	0.0192763	−	0.0111292i	0.509607	+	0.860407i	$0.329791\pi$
$150$	4.46045e6	+	308766.i	1.32162	+	0.0914862i
$151$	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
$156$	−3.39102e6	−	2.28381e6i	−0.893215	−	0.601571i
$157$	−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
$159$	257827.	−	382823.i	0.0641412	−	0.0952371i
$160$	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
$165$	291250.	−	4.20741e6i	0.0648356	−	0.936620i
$166$	−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	$0.985711\pi$
$168$	−1.39059e6	−	167609.i	−0.293273	−	0.0353484i
$169$	4.40951e6			0.913545
$170$	−769304.	+	444158.i	−0.156585	+	0.0904046i
$171$	2.30401e6	+	5.67970e6i	0.460782	+	1.13589i
$172$	−2.28816e6	+	3.96320e6i	−0.449677	+	0.778863i
$173$	1.68052e6	−	970246.i	0.324567	−	0.187389i	−0.328860	−	0.944379i	$-0.606664\pi$
$173$	1.68052e6	−	970246.i	0.324567	−	0.187389i	0.653426	+	0.756990i	$0.273331\pi$
$174$	−9.07132e6	+	4.43225e6i	−1.72196	+	0.841349i
$175$	2.89281e6	−	4.46941e6i	0.539767	−	0.833943i
$176$		−	4.25044e6i		−	0.779644i
$177$	−5.70977e6	+	8.47788e6i	−1.02967	+	1.52886i
$178$	4.01360e6	−	6.95176e6i	0.711663	−	1.23264i
$179$	−1.82126e6	−	1.05150e6i	−0.317550	−	0.183338i	0.332750	−	0.943015i	$-0.392024\pi$
$179$	−1.82126e6	−	1.05150e6i	−0.317550	−	0.183338i	−0.650300	+	0.759677i	$0.725357\pi$
$180$	−883232.	+	6.34904e6i	−0.151446	+	1.08866i
$181$	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
$186$	7.45082e6	+	515768.i	1.15788	+	0.0801522i
$187$	208785.	+	361626.i	0.0319282	+	0.0553013i
$188$		−	2.74626e6i		−	0.413302i
$189$	1.72372e6	−	6.52751e6i	0.255319	−	0.966857i
$190$	−1.58307e7			−2.30802
$191$	7.07195e6	−	4.08299e6i	1.01494	−	0.585974i	0.102304	−	0.994753i	$-0.467379\pi$
$191$	7.07195e6	−	4.08299e6i	1.01494	−	0.585974i	0.912633	+	0.408779i	$0.134045\pi$
$192$	−253581.	+	3.66324e6i	−0.0358272	+	0.517561i
$193$	−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	$0.160601\pi$
$197$			7.39165e6i			0.966814i	−0.875396	+	0.483407i	$0.839399\pi$
$198$	6.81814e6	+	948489.i	0.878356	+	0.122190i
$199$	−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
$201$	1.35039e6	+	909476.i	0.166292	+	0.111996i
$202$	−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
$207$	−381650.	+	154819.i	−0.0430283	+	0.0174547i
$208$	−7.29742e6	−	1.26395e7i	−0.810923	−	1.40456i
$209$			7.44154e6i			0.815124i
$210$	1.39493e7	+	1.04631e7i	1.50625	+	1.12980i
$211$	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
$213$	−8.89252e6	−	615567.i	−0.920208	−	0.0636996i
$214$	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
$219$	−8.15515e6	−	5.49241e6i	−0.776425	−	0.522914i
$220$	−3.89132e6	+	6.73996e6i	−0.365451	+	0.632979i
$221$	1.24173e6	+	716910.i	0.115040	+	0.0664183i
$222$	−563955.	+	837362.i	−0.0515449	+	0.0765340i
$223$	−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	$-0.446638\pi$
$227$	−7.06037e6	−	4.07630e6i	−0.603601	−	0.348489i	−0.770457	+	0.637492i	$0.779972\pi$
$228$	781074.	−	1.12834e7i	0.0659003	−	0.952000i
$229$	−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
$231$	4.91838e6	−	6.55716e6i	0.399012	−	0.531961i
$232$	−5.30094e6			−0.424511
$233$	1.07075e7	−	6.18197e6i	0.846486	−	0.488719i	−0.0129778	−	0.999916i	$-0.504131\pi$
$233$	1.07075e7	−	6.18197e6i	0.846486	−	0.488719i	0.859464	+	0.511197i	$0.170798\pi$
$234$	2.19035e7	−	8.88529e6i	1.70949	−	0.693464i
$235$	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	$-0.0927357\pi$
$240$	−1.27829e7	+	1.89801e7i	−0.924689	+	1.37298i
$241$	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
$243$	−4.86036e6	+	1.35007e7i	−0.338727	+	0.940885i
$244$	−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
$249$	1.39569e7	+	966141.i	0.904049	+	0.0625810i
$250$	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	$-0.152840\pi$
$252$	−8.14588e6	+	9.42624e6i	−0.509022	+	0.589029i
$253$	−500037.			−0.0308774
$254$	−9.22346e6	+	5.32516e6i	−0.562850	+	0.324961i
$255$	155248.	−	2.24273e6i	0.00936281	−	0.135256i
$256$	−1.07991e7	+	1.87046e7i	−0.643677	+	1.11488i
$257$	−6.83136e6	+	3.94409e6i	−0.402446	+	0.232353i	−0.687539	−	0.726147i	$-0.741309\pi$
$257$	−6.83136e6	+	3.94409e6i	−0.402446	+	0.232353i	0.285093	+	0.958500i	$0.407976\pi$
$258$	−1.16151e7	−	2.37723e7i	−0.676339	−	1.38424i
$259$	547379.	+	1.07027e6i	0.0315057	+	0.0616016i
$260$			2.67234e7i			1.52045i
$261$	3.52055e6	−	2.53072e7i	0.198011	−	1.42338i
$262$	−1.06262e7	+	1.84051e7i	−0.590844	+	1.02337i
$263$	2.15711e7	+	1.24541e7i	1.18578	+	0.684611i	0.957345	−	0.288948i	$-0.0933053\pi$
$263$	2.15711e7	+	1.24541e7i	1.18578	+	0.684611i	0.228437	+	0.973559i	$0.426639\pi$
$264$	2.99779e6	+	2.01898e6i	0.162926	+	0.109729i
$265$	−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	$-0.581651\pi$
$269$	−2.37134e7	−	1.36910e7i	−1.21825	−	0.703359i	−0.964544	+	0.263922i	$0.914984\pi$
$270$	−2.75935e7	−	2.47405e7i	−1.40189	−	1.25695i
$271$	−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
$273$	3.36800e6	−	2.79432e7i	0.165533	−	1.37337i
$274$	−2.61884e7			−1.27309
$275$	−1.18974e7	+	6.86895e6i	−0.572075	+	0.330288i
$276$	758196.	+	52484.6i	0.0360624	+	0.00249635i
$277$	−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	$-0.711678\pi$
$281$		−	3.49201e7i		−	1.57382i	0.617065	−	0.786912i	$-0.288322\pi$
$282$	1.31693e7	+	8.86941e6i	0.587241	+	0.395501i
$283$	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
$285$	2.23799e7	−	3.32297e7i	0.966771	−	1.43546i
$286$	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
$291$	−1.90946e6	+	2.75842e7i	−0.0774876	+	1.11939i
$292$	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	$0.908719\pi$
$294$	1.17101e7	+	3.18024e7i	0.460806	+	1.25146i
$295$	6.68113e7			2.60246
$296$	−459049.	+	265032.i	−0.0177004	+	0.0102193i
$297$	−1.16298e7	+	1.29709e7i	−0.443916	+	0.495107i
$298$	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
$303$	3.30799e6	−	4.91171e6i	0.118915	−	0.176565i
$304$	2.01883e7	−	3.49671e7i	0.718585	−	1.24463i
$305$	−1.20684e7	−	6.96769e6i	−0.425353	−	0.245578i
$306$	3.63436e6	+	505585.i	0.126842	+	0.0176453i
$307$	−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	$-0.203336\pi$
$311$	2.06912e7	+	1.19461e7i	0.687868	+	0.397141i	−0.114945	+	0.993372i	$0.536669\pi$
$312$	1.23808e7	+	857038.i	0.407649	+	0.0282187i
$313$	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
$315$	−4.16829e7	+	1.44889e7i	−1.33360	+	0.463559i
$316$	1.83198e7			0.580577
$317$	−3.38098e7	+	1.95201e7i	−1.06136	+	0.612779i	−0.925809	−	0.377991i	$-0.876615\pi$
$317$	−3.38098e7	+	1.95201e7i	−1.06136	+	0.612779i	−0.135555	+	0.990770i	$0.543282\pi$
$318$	340054.	−	4.91244e6i	0.0105747	−	0.152762i
$319$	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
$324$	1.89954e7	−	1.84468e7i	0.558487	−	0.542357i
$325$	−2.35861e7	+	4.08523e7i	−0.687078	+	1.19005i
$326$	−4.23013e7	−	2.44227e7i	−1.22096	−	0.704921i
$327$	1.14456e6	+	770852.i	0.0327338	+	0.0220459i
$328$	−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
$333$	−960416.	−	2.36756e6i	−0.0260092	−	0.0641162i
$334$	2.22988e6	+	3.86227e6i	0.0598470	+	0.103658i
$335$		−	1.06420e7i		−	0.283066i
$336$	−4.09000e7	+	1.74683e7i	−1.07822	+	0.460505i
$337$	−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
$339$	−6.37952e7	−	4.41609e6i	−1.63753	−	0.113355i
$340$	−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
$345$	2.23289e6	+	1.50383e6i	0.0543763	+	0.0366219i
$346$	1.03514e7	−	1.79291e7i	0.249902	−	0.432843i
$347$	−5.66844e6	−	3.27267e6i	−0.135667	−	0.0783275i	0.430630	−	0.902528i	$-0.358291\pi$
$347$	−5.66844e6	−	3.27267e6i	−0.135667	−	0.0783275i	−0.566297	+	0.824201i	$0.691625\pi$
$348$	−2.63384e7	+	3.91074e7i	−0.624960	+	0.927942i
$349$	−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	$-0.143999\pi$
$353$	4.26921e7	+	2.46483e7i	0.970561	+	0.560354i	0.0711539	+	0.997465i	$0.477332\pi$
$354$	−7.53073e6	+	1.08789e8i	−0.169757	+	2.45232i
$355$	2.91323e7	+	5.04586e7i	0.651162	+	1.12785i
$356$		−	3.74874e7i		−	0.830874i
$357$	2.62170e6	−	3.49524e6i	0.0576207	−	0.0768197i
$358$	−2.24366e7			−0.489000
$359$	1.95231e7	−	1.12717e7i	0.421955	−	0.243616i	−0.273959	−	0.961741i	$-0.588333\pi$
$359$	1.95231e7	−	1.12717e7i	0.421955	−	0.243616i	0.695913	+	0.718126i	$0.255000\pi$
$360$	−7.31452e6	−	1.80313e7i	−0.156775	−	0.386473i
$361$	−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
$366$	1.27059e7	−	1.88657e7i	0.259156	−	0.384795i
$367$	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
$369$	116598.	−	838154.i	0.00232066	−	0.0166819i
$370$	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
$375$	−491526.	−	34024.9i	−0.00932079	−	0.000645213i
$376$	4.16820e6	+	7.21954e6i	0.0784125	+	0.135814i
$377$		−	1.06519e8i		−	1.98794i
$378$	−1.88941e7	−	6.95058e7i	−0.349826	−	1.28690i
$379$	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
$381$	1.86133e6	−	2.68888e7i	0.0336548	−	0.486180i
$382$	4.35607e7	−	7.54494e7i	0.781457	−	1.35352i
$383$	−5.02164e7	+	2.89924e7i	−0.893818	+	0.516046i	−0.875189	−	0.483781i	$-0.839263\pi$
$383$	−5.02164e7	+	2.89924e7i	−0.893818	+	0.516046i	−0.0186284	+	0.999826i	$0.505930\pi$
$384$	−1.43254e7	−	2.93193e7i	−0.252996	−	0.517797i
$385$	−5.35084e7	−	2.72266e6i	−0.937648	−	0.0477102i
$386$			1.51292e8i			2.63060i
$387$	6.63199e7	+	9.22593e6i	1.14422	+	0.159176i
$388$	2.55119e7	−	4.41879e7i	0.436765	−	0.756498i
$389$	−6.34639e7	−	3.66409e7i	−1.07815	−	0.622468i	−0.147750	−	0.989025i	$-0.547203\pi$
$389$	−6.34639e7	−	3.66409e7i	−1.07815	−	0.622468i	−0.930396	+	0.366557i	$0.880537\pi$
$390$	−1.28149e8	−	8.63069e7i	−2.16033	−	1.45496i
$391$	−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
$396$	2.97899e7	−	1.20845e7i	0.479715	−	0.194599i
$397$	−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
$399$	7.16064e7	−	3.05830e7i	1.12728	−	0.481461i
$400$	7.45395e7			1.16468
$401$	5.17591e6	−	2.98831e6i	0.0802701	−	0.0463439i	−0.459328	−	0.888267i	$-0.651910\pi$
$401$	5.17591e6	−	2.98831e6i	0.0802701	−	0.0463439i	0.539598	+	0.841923i	$0.318576\pi$
$402$	1.73284e7	+	1.19953e6i	0.266736	+	0.0184642i
$403$	−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
$408$	1.59795e6	+	1.07620e6i	0.0235279	+	0.0158458i
$409$	−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
$411$	3.70226e7	−	5.49712e7i	0.533263	−	0.791790i
$412$	−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
$417$	3.49322e6	−	5.04633e7i	0.0481746	−	0.695933i
$418$	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	$-0.0368604\pi$
$420$	8.08479e7	+	9.74463e6i	1.09124	+	0.131528i
$421$	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
$423$	−3.72350e7	+	1.51046e7i	−0.491960	+	0.199567i
$424$	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
$429$	−4.05702e7	+	6.02388e7i	−0.513849	+	0.762965i
$430$	−8.64710e7	+	1.49772e8i	−1.08759	+	1.88376i
$431$	3.31397e7	+	1.91332e7i	0.413921	+	0.238977i	0.692473	−	0.721444i	$-0.256521\pi$
$431$	3.31397e7	+	1.91332e7i	0.413921	+	0.238977i	−0.278552	+	0.960421i	$0.589854\pi$
$432$	8.98360e7	−	2.93983e7i	1.11429	−	0.364646i
$433$	−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
$438$	−1.04648e8	−	7.24405e6i	−1.24540	−	0.0862103i
$439$	−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
$441$	−8.33099e7	−	2.03788e7i	−0.971361	−	0.237609i
$442$	1.52972e7			0.177151
$443$	−2.14827e7	+	1.24030e7i	−0.247103	+	0.142665i	−0.618437	−	0.785835i	$-0.712234\pi$
$443$	−2.14827e7	+	1.24030e7i	−0.247103	+	0.142665i	0.371334	+	0.928499i	$0.378900\pi$
$444$	−325587.	+	4.70345e6i	−0.00371979	+	0.0537363i
$445$	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	$-0.290594\pi$
$450$	−1.66336e7	+	1.19569e8i	−0.182536	+	1.31214i
$451$	513704.	−	889761.i	0.00559993	−	0.00969937i
$452$	1.02195e8	+	5.90024e7i	1.10666	+	0.638931i
$453$	1.90276e7	+	1.28149e7i	0.204687	+	0.137854i
$454$	−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
$459$	−6.19915e6	+	6.91401e6i	−0.0641053	+	0.0714977i
$460$	−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	$0.705067\pi$
$462$	1.04646e7	−	8.68214e7i	0.106120	−	0.880442i
$463$	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
$465$	1.23252e8	+	8.53185e6i	1.22584	+	0.0848563i
$466$	6.59544e7	−	1.14236e8i	0.651757	−	1.12888i
$467$	1.21690e8	−	7.02577e7i	1.19482	−	0.689832i	0.235427	−	0.971892i	$-0.424351\pi$
$467$	1.21690e8	−	7.02577e7i	1.19482	−	0.689832i	0.959397	+	0.282060i	$0.0910179\pi$
$468$	6.78385e7	−	8.70805e7i	0.661819	−	0.849539i
$469$	1.12383e7	−	1.73632e7i	0.108939	−	0.168311i
$470$		−	1.03783e8i		−	0.999614i
$471$	−6.40126e7	−	4.31118e7i	−0.612636	−	0.412604i
$472$	−2.86279e7	+	4.95849e7i	−0.272247	+	0.471546i
$473$	7.04033e7	+	4.06474e7i	0.665288	+	0.384104i
$474$	−5.91663e7	+	8.78503e7i	−0.555571	+	0.824913i
$475$	−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	$-0.352484\pi$
$479$	−1.14456e7	−	6.60811e6i	−0.104143	−	0.0601272i	−0.551167	+	0.834395i	$0.685817\pi$
$480$	−1.36744e7	+	1.97542e8i	−0.123648	+	1.78622i
$481$	−5.32565e6	−	9.22430e6i	−0.0478561	−	0.0828893i
$482$		−	7.27914e7i		−	0.650038i
$483$	2.05504e6	+	4.81163e6i	0.0182381	+	0.0427022i
$484$	−4.92354e7			−0.434252
$485$	1.56520e8	−	9.03671e7i	1.37197	−	0.792110i
$486$	2.71109e7	+	1.50666e8i	0.236176	+	1.31252i
$487$	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	$-0.842261\pi$
$491$		−	1.12575e8i		−	0.951034i	0.879707	−	0.475517i	$-0.157739\pi$
$492$	−872308.	+	1.29521e6i	−0.00732445	+	0.0108754i
$493$	8.26787e6	−	1.43204e7i	0.0690006	−	0.119513i
$494$	2.36089e8	+	1.36306e8i	1.95837	+	1.13066i
$495$	1.12786e8	+	1.56899e7i	0.929906	+	0.129362i
$496$	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
$501$	−1.12595e7	−	779420.i	−0.0895381	−	0.00619809i
$502$	−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	$0.947610\pi$
$504$	7.10748e6	−	3.71439e7i	0.0555168	−	0.290132i
$505$	−3.87075e7			−0.300553
$506$	−4.62008e6	+	2.66741e6i	−0.0356614	+	0.0205891i
$507$	−8.22179e6	+	1.18772e8i	−0.0630874	+	0.911364i
$508$	−2.48687e7	+	4.30739e7i	−0.189698	+	0.328566i
$509$	−1.47010e8	+	8.48765e7i	−1.11479	+	0.643627i	−0.940067	−	0.340990i	$-0.889238\pi$
$509$	−1.47010e8	+	8.48765e7i	−1.11479	+	0.643627i	−0.174727	+	0.984617i	$0.555904\pi$
$510$	−1.05292e7	−	2.15498e7i	−0.0793754	−	0.162455i
$511$	−6.78692e7	+	1.04858e8i	−0.508640	+	0.785850i
$512$			1.53078e8i			1.14052i
$513$	−1.57282e8	+	5.14696e7i	−1.16500	+	0.381240i
$514$	−4.20788e7	+	7.28826e7i	−0.309866	+	0.536704i
$515$	−2.62150e8	−	1.51352e8i	−1.91923	−	1.10807i
$516$	−1.02485e8	−	6.90224e7i	−0.745950	−	0.502390i
$517$	−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	$-0.408009\pi$
$521$	−5.69389e7	−	3.28737e7i	−0.402620	−	0.232453i	−0.687614	+	0.726076i	$0.741342\pi$
$522$	−1.02471e8	−	2.52605e8i	−0.720426	−	1.77595i
$523$	−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
$525$	1.14992e8	+	8.62530e7i	0.794677	+	0.596069i
$526$	2.65741e8			1.82600
$527$	−1.05935e7	+	6.11613e6i	−0.0723779	+	0.0417874i
$528$	1.14488e8	+	7.92520e6i	0.777782	+	0.0538404i
$529$	−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
$534$	1.79766e8	+	1.21071e8i	1.18055	+	0.795087i
$535$	1.95498e8	−	3.38613e8i	1.27668	−	2.21127i
$536$	7.89809e6	+	4.55997e6i	0.0512894	+	0.0296120i
$537$	3.17187e7	−	4.70960e7i	0.204829	−	0.304131i
$538$	−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
$543$	−8.12901e6	+	1.17432e8i	−0.0507736	+	0.733479i
$544$	−9.80265e6	−	1.69787e7i	−0.0608901	−	0.105465i
$545$		−	9.01991e6i		−	0.0557202i
$546$	−1.17942e8	−	2.76146e8i	−0.724586	−	1.69653i
$547$	−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
$549$	2.16381e7	+	5.33409e7i	0.130768	+	0.322362i
$550$	−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
$555$	−9.32895e6	+	1.38517e7i	−0.0545700	+	0.0810257i
$556$	−4.66721e7	+	8.08384e7i	−0.271539	+	0.470320i
$557$	−1.57185e8	−	9.07506e7i	−0.909588	−	0.525151i	−0.0292895	−	0.999571i	$-0.509324\pi$
$557$	−1.57185e8	−	9.07506e7i	−0.909588	−	0.525151i	−0.880299	+	0.474420i	$0.842658\pi$
$558$	−2.77850e7	+	1.99730e8i	−0.159922	+	1.14958i
$559$	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	$-0.290505\pi$
$563$	4.14625e7	+	2.39384e7i	0.232343	+	0.134143i	−0.379309	+	0.925270i	$0.623838\pi$
$564$	7.39720e7	+	5.12056e6i	0.412316	+	0.0285417i
$565$	2.08996e8	+	3.61991e8i	1.15876	+	2.00702i
$566$		−	5.19038e7i		−	0.286253i
$567$	1.72608e8	+	5.86004e7i	0.946917	+	0.321478i
$568$	−4.99314e7			−0.272476
$569$	1.04058e8	−	6.00781e7i	0.564859	−	0.326121i	−0.190235	−	0.981739i	$-0.560925\pi$
$569$	1.04058e8	−	6.00781e7i	0.564859	−	0.326121i	0.755093	+	0.655617i	$0.227592\pi$
$570$	2.95173e7	−	4.26409e8i	0.159387	−	2.30251i
$571$	−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
$576$	−9.81986e7	−	1.36607e7i	−0.513852	−	0.0714833i
$577$	−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
$579$	−3.17573e8	−	2.13882e8i	−1.63609	−	1.10189i
$580$	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
$585$	3.62328e8	−	1.46981e8i	1.80982	−	0.734164i
$586$	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	$0.953829\pi$
$588$	1.21619e8	+	1.01277e8i	0.598232	+	0.498174i
$589$	−2.17992e8			−1.06683
$590$	6.17301e8	−	3.56399e8i	3.00567	−	1.73532i
$591$	−1.99098e8	−	1.37822e7i	−0.964506	−	0.0667660i
$592$	−8.41538e6	+	1.45759e7i	−0.0405610	+	0.0702537i
$593$	−2.64996e8	+	1.52995e8i	−1.27079	+	0.733693i	−0.975137	−	0.221601i	$-0.928872\pi$
$593$	−2.64996e8	+	1.52995e8i	−1.27079	+	0.733693i	−0.295656	+	0.955294i	$0.595538\pi$
$594$	−3.82609e7	+	1.81882e8i	−0.182556	+	0.867821i
$595$	−2.85222e7	−	1.45129e6i	−0.135404	−	0.00688976i
$596$		−	3.66851e6i		−	0.0173281i
$597$	−1.81942e8	−	1.22536e8i	−0.855087	−	0.575892i
$598$	−9.15914e6	+	1.58641e7i	−0.0428303	+	0.0741843i
$599$	3.21383e8	+	1.85551e8i	1.49535	+	0.863341i	0.999986	−	0.00534498i	$-0.00170137\pi$
$599$	3.21383e8	+	1.85551e8i	1.49535	+	0.863341i	0.495364	+	0.868686i	$0.335035\pi$
$600$	−3.54067e7	+	5.25720e7i	−0.163920	+	0.243389i
$601$	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
$606$	4.36298e6	−	6.30278e7i	0.0196049	−	0.283214i
$607$	−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
$609$	−3.22258e8	−	3.88419e7i	−1.42677	−	0.171969i
$610$	−1.48674e8			−0.655007
$611$	−1.45072e8	+	8.37574e7i	−0.636005	+	0.367198i
$612$	1.58792e7	−	6.44152e6i	0.0692749	−	0.0281018i
$613$	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	$0.389088\pi$
$617$			4.41540e8i			1.87981i	−0.341432	+	0.939907i	$0.610912\pi$
$618$	2.75997e8	−	4.09801e8i	1.16933	−	1.73623i
$619$	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
$621$	−3.45852e6	−	1.05686e7i	−0.0144416	−	0.0441310i
$622$	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
$627$	−2.00442e8	−	1.38752e7i	−0.813178	−	0.0562906i
$628$	7.12081e7	+	1.23336e8i	0.287509	+	0.497979i
$629$		−	1.65348e6i		−	0.00664427i
$630$	−3.07838e8	+	3.56224e8i	−1.23112	+	1.42463i
$631$	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
$633$	−1.37183e7	+	1.98175e8i	−0.0540863	+	0.781335i
$634$	−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
$639$	3.31612e7	−	2.38377e8i	0.127095	−	0.913612i
$640$	−1.06648e8	+	1.84720e8i	−0.406830	+	0.704651i
$641$	2.78216e8	+	1.60628e8i	1.05635	+	0.609884i	0.924420	−	0.381375i	$-0.124549\pi$
$641$	2.78216e8	+	1.60628e8i	1.05635	+	0.609884i	0.131930	+	0.991259i	$0.457883\pi$
$642$	5.29331e8	+	3.56499e8i	2.00043	+	1.34727i
$643$	−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	$0.0500425\pi$
$647$	4.37973e8	+	2.52864e8i	1.61709	+	0.933628i	0.629424	+	0.777062i	$0.283291\pi$
$648$	−2.19382e7	+	7.73247e7i	−0.0806263	+	0.284180i
$649$	−1.67532e8	−	2.90174e8i	−0.612864	−	1.06151i
$650$			5.03272e8i			1.83258i
$651$	1.92085e8	+	1.44079e8i	0.696226	+	0.522223i
$652$	−2.28110e8			−0.823002
$653$	−1.36038e8	+	7.85415e7i	−0.488563	+	0.282072i	−0.723978	−	0.689823i	$-0.757688\pi$
$653$	−1.36038e8	+	7.85415e7i	−0.488563	+	0.282072i	0.235415	+	0.971895i	$0.424355\pi$
$654$	1.46872e7	+	1.01669e6i	0.0525057	+	0.00363460i
$655$	−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	$-0.131938\pi$
$660$	−1.74289e8	−	1.17382e8i	−0.606231	−	0.408290i
$661$	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
$663$	−2.16256e7	+	3.21098e7i	−0.0742042	+	0.110179i
$664$	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
$669$	882062.	−	1.27423e7i	0.00294592	−	0.0425569i
$670$	−5.67687e7	−	9.83263e7i	−0.188749	−	0.326923i
$671$			6.98872e7i			0.231329i
$672$	−2.30922e8	+	3.07865e8i	−0.760954	+	1.01450i
$673$	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
$675$	−2.27468e8	−	2.03950e8i	−0.739622	−	0.663150i
$676$	1.09849e8	−	1.90265e8i	0.355596	−	0.615911i
$677$	5.14602e8	−	2.97105e8i	1.65846	−	0.957513i	0.685035	−	0.728510i	$-0.259787\pi$
$677$	5.14602e8	−	2.97105e8i	1.65846	−	0.957513i	0.973426	−	0.229002i	$-0.0735463\pi$
$678$	−6.12991e8	+	2.99507e8i	−1.96682	+	0.960989i
$679$	3.50807e8	+	1.78500e7i	1.12062	+	0.0570203i
$680$		−	1.25929e7i		−	0.0400496i
$681$	1.22962e8	−	1.82574e8i	0.389340	−	0.578094i
$682$	−1.22414e8	+	2.12028e8i	−0.385904	+	0.668405i
$683$	6.14652e7	+	3.54870e7i	0.192916	+	0.111380i	0.593347	−	0.804947i	$-0.297806\pi$
$683$	6.14652e7	+	3.54870e7i	0.192916	+	0.111380i	−0.400431	+	0.916327i	$0.631140\pi$
$684$	3.02469e8	+	4.20773e7i	0.945177	+	0.131486i
$685$	−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
$690$	2.86527e7	+	1.98343e6i	0.0872206	+	0.00603767i
$691$	−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
$693$	1.67450e8	+	1.44705e8i	0.503136	+	0.434795i
$694$	−6.98312e7			−0.208916
$695$	−2.86343e8	+	1.65320e8i	−0.852965	+	0.492460i
$696$	9.88392e6	−	1.42784e8i	0.0293158	−	0.423498i
$697$	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	$-0.0635791\pi$
$702$	1.98490e8	+	6.06549e8i	0.573756	+	1.75329i
$703$	1.47334e7	−	2.55189e7i	0.0424069	−	0.0734508i
$704$	−1.04245e8	−	6.01858e7i	−0.298770	−	0.172495i
$705$	2.17847e8	+	1.46718e8i	0.621706	+	0.418713i
$706$	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
$711$	−1.00760e8	−	2.48388e8i	−0.280337	−	0.691070i
$712$	5.68974e7	+	9.85491e7i	0.157635	+	0.273032i
$713$		−	1.46481e7i		−	0.0404121i
$714$	5.57808e6	−	4.62794e7i	0.0153246	−	0.127143i
$715$	4.74721e8			1.29874
$716$	−9.07421e7	+	5.23900e7i	−0.247212	+	0.142728i
$717$	2.11244e8	+	1.46230e7i	0.573096	+	0.0396714i
$718$	1.20256e8	−	2.08289e8i	0.324887	−	0.562720i
$719$	−8.54115e7	+	4.93123e7i	−0.229789	+	0.132669i	−0.610475	−	0.792036i	$-0.709021\pi$
$719$	−8.54115e7	+	4.93123e7i	−0.229789	+	0.132669i	0.380686	+	0.924705i	$0.375688\pi$
$720$	−4.87405e8	−	3.79704e8i	−1.30585	−	1.01730i
$721$	−2.67885e8	−	5.23783e8i	−0.714730	−	1.39748i
$722$			2.52254e8i			0.670233i
$723$	1.52794e8	+	1.02905e8i	0.404289	+	0.272284i
$724$	1.08610e8	−	1.88118e8i	0.286189	−	0.495694i
$725$	4.71135e8	+	2.72010e8i	1.23632	+	0.713791i
$726$	1.59012e8	−	2.36102e8i	0.415548	−	0.617007i
$727$	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
$732$	7.33545e6	−	1.05968e8i	0.0187022	−	0.270174i
$733$	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
$735$	1.93708e8	+	5.26076e8i	0.487850	+	1.32491i
$736$	2.34772e7			0.0588862
$737$	−4.62202e7	+	2.66852e7i	−0.115459	+	0.0666605i
$738$	−3.39376e6	−	8.36609e6i	−0.00844329	−	0.0208139i
$739$	−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	$-0.933265\pi$
$743$		−	1.70732e8i		−	0.416244i	0.978103	−	0.208122i	$-0.0667352\pi$
$744$	−5.91439e7	+	8.78171e7i	−0.143612	+	0.213236i
$745$	6.49723e6	−	1.12535e7i	0.0157130	−	0.0272157i
$746$	3.42206e8	+	1.97572e8i	0.824272	+	0.475894i
$747$	−5.20470e7	+	3.74136e8i	−0.124863	+	0.897569i
$748$	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
$753$	3.93501e8	+	2.72394e7i	0.921640	+	0.0637987i
$754$	−5.68217e8	−	9.84181e8i	−1.32556	−	2.29594i
$755$		−	1.49950e8i		−	0.348422i
$756$	−2.38713e8	−	2.36989e8i	−0.552471	−	0.548484i
$757$	−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
$759$	932349.	−	1.34688e7i	0.00213232	−	0.0308037i
$760$	1.12209e8	−	1.94352e8i	0.255616	−	0.442740i
$761$	−4.72894e8	+	2.73025e8i	−1.07302	+	0.619511i	−0.929006	−	0.370064i	$-0.879336\pi$
$761$	−4.72894e8	+	2.73025e8i	−1.07302	+	0.619511i	−0.144018	+	0.989575i	$0.546002\pi$
$762$	−1.26239e8	−	2.58368e8i	−0.285317	−	0.583947i
$763$	9.52536e6	−	1.47167e7i	0.0214441	−	0.0331312i
$764$		−	4.06861e8i		−	0.912359i
$765$	6.01196e7	+	8.36339e6i	0.134286	+	0.0186809i
$766$	−3.09315e8	+	5.35750e8i	−0.688201	+	1.19200i
$767$	−9.96379e8	−	5.75259e8i	−2.20820	−	1.27490i
$768$	−4.83683e8	−	3.25756e8i	−1.06777	−	0.719132i
$769$	−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	−0.396164	−	0.918180i	$-0.629659\pi$
$773$	−6.41756e8	−	3.70518e8i	−1.38941	−	0.802178i	−0.993249	+	0.116001i	$0.962992\pi$
$774$	6.61976e8	−	2.68535e8i	1.42764	−	0.579132i
$775$	−2.01219e8	−	3.48521e8i	−0.432278	−	0.748727i
$776$			1.54885e8i			0.331455i
$777$	−2.98488e7	+	1.27484e7i	−0.0636303	+	0.0271764i
$778$	−7.81830e8			−1.66025
$779$	8.45216e6	−	4.87986e6i	0.0178795	−	0.0103227i
$780$	−7.19810e8	−	4.98274e7i	−1.51682	−	0.104999i
$781$	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
$786$	−4.75937e8	−	3.20539e8i	−0.980126	−	0.660105i
$787$	−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
$789$	−3.75678e8	+	5.57807e8i	−0.764864	+	1.13567i
$790$	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
$795$	5.62518e6	−	8.12617e7i	0.0111953	−	0.161728i
$796$	2.02394e8	+	3.50557e8i	0.401290	+	0.695055i
$797$		−	4.96423e8i		−	0.980567i	−0.871563	−	0.490283i	$-0.836893\pi$
$797$		−	4.96423e8i		−	0.980567i	0.871563	−	0.490283i	$-0.163107\pi$
$798$	4.98463e8	−	6.64549e8i	0.980899	−	1.30773i
$799$	−2.60046e7			−0.0509811
$800$	5.58593e8	−	3.22504e8i	1.09100	−	0.629890i
$801$	−5.08270e8	+	2.06183e8i	−0.989002	+	0.401195i
$802$	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
$807$	4.12988e8	−	6.13207e8i	0.785810	−	1.16677i
$808$	1.65857e7	−	2.87273e7i	0.0314413	−	0.0544579i
$809$	6.30926e8	+	3.64265e8i	1.19161	+	0.687974i	0.958671	−	0.284518i	$-0.0918337\pi$
$809$	6.30926e8	+	3.64265e8i	1.19161	+	0.687974i	0.232935	+	0.972492i	$0.425167\pi$
$810$	7.17849e8	−	6.97116e8i	1.35076	−	1.31175i
$811$	−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
$816$	6.10269e7	+	4.22447e6i	0.112318	+	0.00777502i
$817$	3.86124e8	+	6.68787e8i	0.708045	+	1.22637i
$818$			5.97257e7i			0.109119i
$819$	7.46384e8	+	1.42821e8i	1.35866	+	0.259979i
$820$	1.02071e7			0.0185123
$821$	−2.96408e8	+	1.71131e8i	−0.535624	+	0.309243i	−0.743304	−	0.668954i	$-0.766742\pi$
$821$	−2.96408e8	+	1.71131e8i	−0.535624	+	0.309243i	0.207680	+	0.978197i	$0.433409\pi$
$822$	4.88298e7	−	7.05399e8i	0.0879164	−	1.27005i
$823$	−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	$0.168426\pi$
$827$			5.71015e8i			1.00956i	−0.863249	+	0.504779i	$0.831574\pi$
$828$	−2.82740e6	+	2.03246e7i	−0.00498077	+	0.0358039i
$829$	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
$831$	−4.06987e8	−	2.74102e8i	−0.709215	−	0.477649i
$832$	−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
$837$	−3.79967e8	−	3.40681e8i	−0.647992	−	0.580994i
$838$	−9.06771e7	−	1.57057e8i	−0.154087	−	0.266886i
$839$			9.55834e8i			1.61844i	0.587505	+	0.809220i	$0.300110\pi$
$839$			9.55834e8i			1.61844i	−0.587505	+	0.809220i	$0.699890\pi$
$840$	−2.27328e8	+	9.70916e7i	−0.383544	+	0.163811i
$841$	−6.33625e8			−1.06523
$842$	9.35885e7	−	5.40333e7i	0.156778	−	0.0905160i
$843$	9.40591e8	+	6.51106e7i	1.57007	+	0.108685i
$844$	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
$849$	1.08950e8	+	7.33765e7i	0.178034	+	0.119904i
$850$	−3.90633e7	+	6.76596e7i	−0.0636080	+	0.110172i
$851$	1.71476e6	+	990016.i	0.00278236	+	0.00160640i
$852$	−2.48091e8	+	3.68366e8i	−0.401136	+	0.595608i
$853$	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	0.0631979	−	0.998001i	$-0.479870\pi$
$857$	−4.84339e8	−	2.79633e8i	−0.769497	−	0.444270i	−0.832695	+	0.553732i	$0.813203\pi$
$858$	−5.35089e7	+	7.72993e8i	−0.0847158	+	1.22381i
$859$	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
$861$	−1.06730e7	−	1.28641e6i	−0.0167215	−	0.00201545i
$862$	4.08258e8			0.637402
$863$	3.95752e8	−	2.28487e8i	0.615730	−	0.355492i	−0.159475	−	0.987202i	$-0.550980\pi$
$863$	3.95752e8	−	2.28487e8i	0.615730	−	0.355492i	0.775205	+	0.631710i	$0.217647\pi$
$864$	5.46028e8	−	6.08994e8i	0.846591	−	0.944217i
$865$	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
$870$	−9.95347e8	+	1.47789e9i	−1.51153	+	2.24432i
$871$	−9.16297e7	+	1.58707e8i	−0.138670	+	0.240183i
$872$	6.69426e6	+	3.86493e6i	0.0100961	+	0.00582898i
$873$	−7.39436e8	−	1.02865e8i	−1.11137	−	0.154605i
$874$	−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
$879$	−3.83282e8	−	2.65319e7i	−0.564354	−	0.0390663i
$880$	−3.75068e8	−	6.49636e8i	−0.550379	−	0.953284i
$881$		−	1.10629e9i		−	1.61786i	−0.587903	−	0.808931i	$-0.700047\pi$
$881$		−	1.10629e9i		−	1.61786i	0.587903	−	0.808931i	$-0.299953\pi$
$882$	−8.78448e8	+	2.56120e8i	−1.28030	+	0.373282i
$883$	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
$885$	−1.24574e8	+	1.79960e9i	−0.179720	+	2.59624i
$886$	−1.32326e8	+	2.29195e8i	−0.190258	+	0.329537i
$887$	5.49576e8	−	3.17298e8i	0.787511	−	0.454670i	−0.0515747	−	0.998669i	$-0.516424\pi$
$887$	5.49576e8	−	3.17298e8i	0.787511	−	0.454670i	0.839085	+	0.544000i	$0.183091\pi$
$888$	−6.28285e6	−	1.28589e7i	−0.00897260	−	0.0183639i
$889$	−3.41963e8	−	1.74000e7i	−0.486714	−	0.0247654i
$890$		−	1.41667e9i		−	2.00955i
$891$	−3.27693e8	−	3.37439e8i	−0.463269	−	0.477048i
$892$	−1.17850e7	+	2.04123e7i	−0.0166049	+	0.0287605i
$893$	−4.01341e8	−	2.31714e8i	−0.563584	−	0.325386i
$894$	1.75919e7	+	1.18480e7i	0.0246207	+	0.0165818i
$895$	−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
$900$	2.11924e8	+	5.22421e8i	0.290705	+	0.716627i
$901$	4.03246e6	+	6.98442e6i	0.00551310	+	0.00954896i
$902$		−	1.09612e7i		−	0.0149362i
$903$	1.01789e8	−	8.44509e8i	0.138241	−	1.14694i
$904$	−3.58209e8			−0.484877
$905$	6.66342e8	−	3.84713e8i	0.898983	−	0.519028i
$906$	2.44165e8	+	1.69018e7i	0.328321	+	0.0227274i
$907$	−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	$-0.951543\pi$
$911$		−	2.29303e8i		−	0.303287i	0.988435	−	0.151644i	$-0.0484566\pi$
$912$	9.04215e8	+	6.08980e8i	1.19203	+	0.802820i
$913$	−2.29307e8	+	3.97172e8i	−0.301305	+	0.521875i
$914$	1.14834e9	+	6.62992e8i	1.50394	+	0.868300i
$915$	2.10181e8	−	3.12077e8i	0.274366	−	0.407379i
$916$	−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
$921$	2.36517e7	−	3.41674e8i	0.0302749	−	0.437353i
$922$	8.35738e8	+	1.44754e9i	1.06629	+	1.84688i
$923$		−	1.00334e9i		−	1.27598i
$924$	−1.60407e8	−	3.75573e8i	−0.203333	−	0.476079i
$925$	5.43989e7			0.0687329
$926$	7.47245e7	−	4.31422e7i	0.0941087	−	0.0543337i
$927$	4.70023e8	+	1.15867e9i	0.590038	+	1.45452i
$928$	−7.28244e8	+	1.26135e9i	−0.911240	+	1.57831i
$929$	−2.61830e8	+	1.51167e8i	−0.326567	+	0.188543i	−0.654316	−	0.756221i	$-0.727043\pi$
$929$	−2.61830e8	+	1.51167e8i	−0.326567	+	0.188543i	0.327749	+	0.944765i	$0.393710\pi$
$930$	1.18429e9	−	5.78645e8i	1.47235	−	0.719389i
$931$	−4.05075e8	−	9.02415e8i	−0.501980	−	1.11830i
$932$		−	6.16019e8i		−	0.760933i
$933$	−3.60354e8	+	5.35055e8i	−0.443695	+	0.658800i
$934$	7.49567e8	−	1.29829e9i	0.919962	−	1.59342i
$935$	6.38213e7	+	3.68472e7i	0.0780783	+	0.0450785i
$936$	−4.61696e7	+	3.31886e8i	−0.0563026	+	0.404727i
$937$	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	0.776721	−	0.629845i	$-0.216882\pi$
$941$	5.16290e8	+	2.98080e8i	0.619619	+	0.357737i	−0.157101	+	0.987582i	$0.550215\pi$
$942$	−8.21419e8	−	5.68611e7i	−0.982680	−	0.0680240i
$943$	327904.	+	567947.i	0.000391032	+	0.000677287i
$944$			1.81800e9i			2.16112i
$945$	−3.12547e8	−	1.14977e9i	−0.370357	−	1.36243i
$946$	8.67319e8			1.02448
$947$	−6.68437e8	+	3.85922e8i	−0.787065	+	0.454412i	−0.838928	−	0.544242i	$-0.816817\pi$
$947$	−6.68437e8	+	3.85922e8i	−0.787065	+	0.454412i	0.0518634	+	0.998654i	$0.483484\pi$
$948$	−3.41584e7	+	4.93454e8i	−0.0400933	+	0.579191i
$949$	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	$0.129150\pi$
$953$			6.83235e8i			0.789390i	−0.918812	+	0.394695i	$0.870850\pi$
$954$	1.31685e8	+	1.83191e7i	0.151667	+	0.0210988i
$955$	7.20583e8	−	1.24809e9i	0.827321	−	1.43296i
$956$	−3.38398e8	−	1.95374e8i	−0.387306	−	0.223611i
$957$	6.94713e8	+	4.67882e8i	0.792628	+	0.533827i
$958$	−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
$963$	−1.49663e9	+	6.07119e8i	−1.67585	+	0.679821i
$964$	−1.69969e8	−	2.94396e8i	−0.189732	−	0.328625i
$965$			2.50268e9i			2.78499i
$966$	4.46547e7	+	3.34945e7i	0.0495377	+	0.0371571i
$967$	−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
$969$	−1.06844e8	−	7.39605e6i	−0.117430	−	0.00812884i
$970$	9.64111e8	−	1.66989e9i	1.05636	−	1.82967i
$971$	6.27812e8	−	3.62467e8i	0.685759	−	0.395923i	−0.116262	−	0.993219i	$-0.537091\pi$
$971$	6.27812e8	−	3.62467e8i	0.685759	−	0.395923i	0.802022	+	0.597295i	$0.203758\pi$
$972$	4.61456e8	+	5.46046e8i	0.502494	+	0.594608i
$973$	−6.41775e8	−	3.26553e7i	−0.696697	−	0.0354499i
$974$		−	2.08531e9i		−	2.25681i
$975$	−1.05640e9	−	7.11476e8i	−1.13976	−	0.767620i
$976$	1.89598e8	−	3.28393e8i	0.203931	−	0.353220i
$977$	2.59683e8	+	1.49928e8i	0.278458	+	0.160768i	0.632725	−	0.774376i	$-0.281936\pi$
$977$	2.59683e8	+	1.49928e8i	0.278458	+	0.160768i	−0.354267	+	0.935144i	$0.615270\pi$
$978$	7.36711e8	−	1.09387e9i	0.787555	−	1.16936i
$979$	−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	0.000996388	−	1.00000i	$-0.499683\pi$
$983$	−8.21185e8	−	4.74111e8i	−0.864530	−	0.499137i	−0.865527	+	0.500863i	$0.833016\pi$
$984$	327348.	−	4.72889e6i	0.000343577	−	0.00496334i
$985$	6.52254e8	+	1.12974e9i	0.682509	+	1.18214i
$986$		−	1.76417e8i		−	0.184039i
$987$	2.00496e8	+	4.69437e8i	0.208523	+	0.488231i
$988$	1.27311e9			1.32006
$989$	−4.49394e7	+	2.59458e7i	−0.0464557	+	0.0268212i
$990$	1.12578e9	−	4.56680e8i	1.16024	−	0.470659i
$991$	−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
$996$	3.89382e8	−	5.78155e8i	0.394092	−	0.585149i
$997$	−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
$999$	6.55622e7	−	2.14549e7i	0.0657593	−	0.0215194i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(9.23947 - 5.33441i) q^{2} +(-1.86456 + 26.9355i) q^{3} +(24.9119 - 43.1487i) q^{4} +(152.840 - 88.2420i) q^{5} +(126.458 + 258.817i) q^{6} +(342.557 + 17.4303i) q^{7} +151.243i q^{8} +(-722.047 - 100.446i) q^{9} +O(q^{10})\)	\(q+(9.23947 - 5.33441i) q^{2} +(-1.86456 + 26.9355i) 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} +(-722.047 - 100.446i) q^{9} +(941.439 - 1630.62i) q^{10} +(-766.504 - 442.541i) q^{11} +(1115.78 + 751.470i) 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} +(-7207.15 + 2923.63i) q^{18} +(-4203.86 - 7281.30i) q^{19} -8793.11i q^{20} +(-1108.21 + 9194.45i) q^{21} -9442.80 q^{22} +(489.271 - 282.481i) q^{23} +(-4073.81 - 282.001i) 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} +(42166.3 + 28398.5i) q^{30} +(12963.8 - 22453.9i) q^{31} +(35988.1 + 20777.7i) q^{32} +(13349.3 - 19821.1i) 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} +(5666.64 - 81860.6i) q^{39} +(13346.0 + 23115.9i) q^{40} +1160.80i q^{41} +(38807.7 + 90863.6i) q^{42} -91849.8 q^{43} +(-38190.2 + 22049.1i) q^{44} +(-119221. + 48362.8i) 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} +(7115.73 - 10565.5i) q^{51} +(-75710.6 + 131135. i) q^{52} +(-14804.2 - 8547.21i) q^{53} +(-65311.4 - 199580. 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} +(236847. + 16395.3i) q^{60} +(-39480.6 - 68382.4i) q^{61} -276617. i q^{62} +(-245591. - 46993.9i) q^{63} +136000. q^{64} +(-464500. + 268179. i) q^{65} +(17606.7 - 254347. 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} +(15191.7 - 109204. i) q^{72} +(-182079. + 315369. i) q^{73} +(32381.8 + 18695.6i) q^{74} +(347600. + 234105. 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} +(511262. + 145053. i) q^{81} +(6192.20 + 10725.2i) q^{82} -518160. i q^{83} +(369121. + 276870. i) q^{84} -83262.7 q^{85} +(-848644. + 489965. i) q^{86} +(-944070. - 65351.3i) 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} +(580637. + 391053. i) q^{93} +(294029. - 509274. i) q^{94} +(-1.28503e6 - 741915. i) q^{95} +(-626762. + 930618. i) 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

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