LMFDB - Embedded newform 21.7.f.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

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([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$-2.30325 + 3.98935i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.7.f.b.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +(259.420 - 149.776i) q^{10} +(221.304 + 383.310i) q^{11} +(688.408 + 397.452i) q^{12} -696.494i q^{13} +(-904.880 - 843.466i) q^{14} +1294.76 q^{15} +(-883.932 + 1531.01i) q^{16} +(-5447.24 + 3144.96i) q^{17} +(-438.190 - 758.967i) q^{18} +(-2327.56 - 1343.82i) q^{19} +4235.44i q^{20} +(-1564.32 - 5112.89i) q^{21} +1596.27 q^{22} +(-7885.31 + 13657.8i) q^{23} +(5598.76 - 3232.44i) q^{24} +(-4363.11 - 7557.12i) q^{25} +(-2175.37 - 1255.95i) q^{26} -3788.00i q^{27} +(16725.3 - 5117.22i) q^{28} -23274.5 q^{29} +(2334.78 - 4043.95i) q^{30} +(41177.0 - 23773.6i) q^{31} +(16459.0 + 28507.9i) q^{32} +(5975.21 + 3449.79i) q^{33} +22684.6i q^{34} +(19425.3 - 20839.7i) q^{35} +12391.3 q^{36} +(5079.89 - 8798.64i) q^{37} +(-8394.35 + 4846.48i) q^{38} +(-5428.63 - 9402.67i) q^{39} +(29831.5 + 17223.2i) q^{40} -38165.4i q^{41} +(-18790.0 - 4333.95i) q^{42} -151197. q^{43} +(-11285.0 + 19546.2i) q^{44} +(17479.3 - 10091.7i) q^{45} +(28438.4 + 49256.7i) q^{46} +(-43543.1 - 25139.6i) q^{47} +27558.3i q^{48} +(-105763. - 51530.4i) q^{49} -31471.1 q^{50} +(-49025.1 + 84914.0i) q^{51} +(30758.1 - 17758.2i) q^{52} +(99778.2 + 172821. i) q^{53} +(-11831.1 - 6830.70i) q^{54} +36762.6i q^{55} +(31970.7 - 138611. i) q^{56} -41896.1 q^{57} +(-41969.8 + 72693.8i) q^{58} +(335347. - 193612. i) q^{59} +(33012.0 + 57178.4i) q^{60} +(-10203.5 - 5890.98i) q^{61} -171479. i q^{62} +(-60969.3 - 56831.3i) q^{63} +5575.73 q^{64} +(28925.0 - 50099.6i) q^{65} +(21549.6 - 12441.7i) q^{66} +(192138. + 332792. i) q^{67} +(-277772. - 160372. i) q^{68} +245840. i q^{69} +(-30060.4 - 98250.6i) q^{70} +156126. q^{71} +(50388.8 - 87276.0i) q^{72} +(325227. - 187770. i) q^{73} +(-18320.6 - 31732.3i) q^{74} +(-117804. - 68014.1i) q^{75} -137051. i q^{76} +(145172. - 44416.2i) q^{77} -39156.7 q^{78} +(-16591.8 + 28737.9i) q^{79} +(-127164. + 73418.4i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-119203. - 68821.8i) q^{82} +984986. i q^{83} +(185907. - 199444. i) q^{84} -522434. q^{85} +(-272646. + 472237. i) q^{86} +(-314206. + 181407. i) q^{87} +(91779.9 + 158967. i) q^{88} +(-227430. - 131307. i) q^{89} -72791.1i q^{90} +(-232786. - 53692.3i) q^{91} -804193. q^{92} +(370593. - 641886. i) q^{93} +(-157038. + 90666.0i) q^{94} +(-111616. - 193325. i) q^{95} +(444394. + 256571. i) q^{96} -575147. i q^{97} +(-351664. + 237411. i) q^{98} +107554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.80325	−	3.12332i	0.225406	−	0.390415i	−0.731035	−	0.682340i	$-0.760962\pi$
$2$	1.80325	−	3.12332i	0.225406	−	0.390415i	0.956441	+	0.291925i	$0.0942957\pi$
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$4$	25.4966	+	44.1614i	0.398384	+	0.690021i
$5$	71.9311	+	41.5295i	0.575449	+	0.332236i	0.759323	−	0.650714i	$-0.225530\pi$
$5$	71.9311	+	41.5295i	0.575449	+	0.332236i	−0.183874	+	0.982950i	$0.558864\pi$
$6$		−	56.2198i		−	0.260277i
$7$	77.0894	−	334.225i	0.224750	−	0.974416i
$7$	77.0894	−	334.225i	0.224750	−	0.974416i
$8$	414.723			0.810006
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$	259.420	−	149.776i	0.259420	−	0.149776i
$11$	221.304	+	383.310i	0.166269	+	0.287986i	0.937105	−	0.349047i	$-0.113495\pi$
$11$	221.304	+	383.310i	0.166269	+	0.287986i	−0.770836	+	0.637033i	$0.780161\pi$
$12$	688.408	+	397.452i	0.398384	+	0.230007i
$13$		−	696.494i		−	0.317020i	−0.987357	−	0.158510i	$-0.949331\pi$
$13$		−	696.494i		−	0.317020i	0.987357	−	0.158510i	$-0.0506691\pi$
$14$	−904.880	−	843.466i	−0.329767	−	0.307386i
$15$	1294.76			0.383633
$16$	−883.932	+	1531.01i	−0.215804	+	0.373783i
$17$	−5447.24	+	3144.96i	−1.10874	+	0.640131i	−0.938503	−	0.345272i	$-0.887787\pi$
$17$	−5447.24	+	3144.96i	−1.10874	+	0.640131i	−0.170237	+	0.985403i	$0.554453\pi$
$18$	−438.190	−	758.967i	−0.0751354	−	0.130138i
$19$	−2327.56	−	1343.82i	−0.339344	−	0.195920i	0.320638	−	0.947202i	$-0.396103\pi$
$19$	−2327.56	−	1343.82i	−0.339344	−	0.195920i	−0.659982	+	0.751281i	$0.729436\pi$
$20$			4235.44i			0.529430i
$21$	−1564.32	−	5112.89i	−0.168915	−	0.552088i
$22$	1596.27			0.149912
$23$	−7885.31	+	13657.8i	−0.648090	+	1.12252i	0.335489	+	0.942044i	$0.391098\pi$
$23$	−7885.31	+	13657.8i	−0.648090	+	1.12252i	−0.983579	+	0.180480i	$0.942235\pi$
$24$	5598.76	−	3232.44i	0.405003	−	0.233828i
$25$	−4363.11	−	7557.12i	−0.279239	−	0.483656i
$26$	−2175.37	−	1255.95i	−0.123770	−	0.0714584i
$27$		−	3788.00i		−	0.192450i
$28$	16725.3	−	5117.22i	0.761905	−	0.233109i
$29$	−23274.5			−0.954304			−0.477152	−	0.878821i	$-0.658331\pi$
$29$	−23274.5			−0.954304			−0.477152	+	0.878821i	$0.658331\pi$
$30$	2334.78	−	4043.95i	0.0864732	−	0.149776i
$31$	41177.0	−	23773.6i	1.38220	−	0.798012i	0.389778	−	0.920909i	$-0.372552\pi$
$31$	41177.0	−	23773.6i	1.38220	−	0.798012i	0.992419	+	0.122897i	$0.0392185\pi$
$32$	16459.0	+	28507.9i	0.502290	+	0.869991i
$33$	5975.21	+	3449.79i	0.166269	+	0.0959955i
$34$			22684.6i			0.577158i
$35$	19425.3	−	20839.7i	0.453068	−	0.486057i
$36$	12391.3			0.265589
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	−0.811515	−	0.584331i	$-0.801357\pi$
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	0.911803	+	0.410627i	$0.134690\pi$
$38$	−8394.35	+	4846.48i	−0.152981	+	0.0883234i
$39$	−5428.63	−	9402.67i	−0.0915159	−	0.158510i
$40$	29831.5	+	17223.2i	0.466117	+	0.269113i
$41$		−	38165.4i		−	0.553756i	−0.960905	−	0.276878i	$-0.910700\pi$
$41$		−	38165.4i		−	0.553756i	0.960905	−	0.276878i	$-0.0892998\pi$
$42$	−18790.0	−	4333.95i	−0.253618	−	0.0584973i
$43$	−151197.			−1.90168			−0.950841	−	0.309679i	$-0.899779\pi$
$43$	−151197.			−1.90168			−0.950841	+	0.309679i	$0.899779\pi$
$44$	−11285.0	+	19546.2i	−0.132478	+	0.229458i
$45$	17479.3	−	10091.7i	0.191816	−	0.110745i
$46$	28438.4	+	49256.7i	0.292167	+	0.506048i
$47$	−43543.1	−	25139.6i	−0.419397	−	0.242139i	0.275422	−	0.961323i	$-0.411182\pi$
$47$	−43543.1	−	25139.6i	−0.419397	−	0.242139i	−0.694819	+	0.719184i	$0.744516\pi$
$48$			27558.3i			0.249189i
$49$	−105763.	−	51530.4i	−0.898975	−	0.438001i
$50$	−31471.1			−0.251769
$51$	−49025.1	+	84914.0i	−0.369580	+	0.640131i
$52$	30758.1	−	17758.2i	0.218751	−	0.126296i
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	0.977846	+	0.209328i	$0.0671275\pi$
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	−0.307640	+	0.951503i	$0.599539\pi$
$54$	−11831.1	−	6830.70i	−0.0751354	−	0.0433795i
$55$			36762.6i			0.220962i
$56$	31970.7	−	138611.i	0.182049	−	0.789283i
$57$	−41896.1			−0.226229
$58$	−41969.8	+	72693.8i	−0.215106	+	0.372575i
$59$	335347.	−	193612.i	1.63282	−	0.942708i	0.649600	−	0.760277i	$-0.274937\pi$
$59$	335347.	−	193612.i	1.63282	−	0.942708i	0.983219	−	0.182431i	$-0.0583968\pi$
$60$	33012.0	+	57178.4i	0.152833	+	0.264715i
$61$	−10203.5	−	5890.98i	−0.0449530	−	0.0259536i	0.477355	−	0.878711i	$-0.341596\pi$
$61$	−10203.5	−	5890.98i	−0.0449530	−	0.0259536i	−0.522308	+	0.852757i	$0.674929\pi$
$62$		−	171479.i		−	0.719508i
$63$	−60969.3	−	56831.3i	−0.243831	−	0.227283i
$64$	5575.73			0.0212697
$65$	28925.0	−	50099.6i	0.105325	−	0.182429i
$66$	21549.6	−	12441.7i	0.0749562	−	0.0432760i
$67$	192138.	+	332792.i	0.638834	+	1.10649i	0.985689	+	0.168575i	$0.0539165\pi$
$67$	192138.	+	332792.i	0.638834	+	1.10649i	−0.346854	+	0.937919i	$0.612750\pi$
$68$	−277772.	−	160372.i	−0.883408	−	0.510036i
$69$			245840.i			0.748350i
$70$	−30060.4	−	98250.6i	−0.0876395	−	0.286445i
$71$	156126.			0.436213			0.218107	−	0.975925i	$-0.430012\pi$
$71$	156126.			0.436213			0.218107	+	0.975925i	$0.430012\pi$
$72$	50388.8	−	87276.0i	0.135001	−	0.233828i
$73$	325227.	−	187770.i	0.836022	−	0.482677i	−0.0198883	−	0.999802i	$-0.506331\pi$
$73$	325227.	−	187770.i	0.836022	−	0.482677i	0.855910	+	0.517125i	$0.172998\pi$
$74$	−18320.6	−	31732.3i	−0.0452111	−	0.0783080i
$75$	−117804.	−	68014.1i	−0.279239	−	0.161219i
$76$		−	137051.i		−	0.312206i
$77$	145172.	−	44416.2i	0.317988	−	0.0972902i
$78$	−39156.7			−0.0825130
$79$	−16591.8	+	28737.9i	−0.0336521	+	0.0582872i	−0.882361	−	0.470573i	$-0.844047\pi$
$79$	−16591.8	+	28737.9i	−0.0336521	+	0.0582872i	0.848709	+	0.528860i	$0.177380\pi$
$80$	−127164.	+	73418.4i	−0.248368	+	0.143395i
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$	−119203.	−	68821.8i	−0.216195	−	0.124820i
$83$			984986.i			1.72264i	0.508059	+	0.861322i	$0.330363\pi$
$83$			984986.i			1.72264i	−0.508059	+	0.861322i	$0.669637\pi$
$84$	185907.	−	199444.i	0.313660	−	0.336498i
$85$	−522434.			−0.850697
$86$	−272646.	+	472237.i	−0.428651	+	0.742446i
$87$	−314206.	+	181407.i	−0.477152	+	0.275484i
$88$	91779.9	+	158967.i	0.134679	+	0.233271i
$89$	−227430.	−	131307.i	−0.322609	−	0.186259i	0.329946	−	0.944000i	$-0.392970\pi$
$89$	−227430.	−	131307.i	−0.322609	−	0.186259i	−0.652555	+	0.757741i	$0.726303\pi$
$90$		−	72791.1i		−	0.0998507i
$91$	−232786.	−	53692.3i	−0.308910	−	0.0712505i
$92$	−804193.			−1.03275
$93$	370593.	−	641886.i	0.460732	−	0.798012i
$94$	−157038.	+	90666.0i	−0.189070	+	0.109159i
$95$	−111616.	−	193325.i	−0.130184	−	0.225484i
$96$	444394.	+	256571.i	0.502290	+	0.289997i
$97$		−	575147.i		−	0.630179i	−0.949062	−	0.315089i	$-0.897966\pi$
$97$		−	575147.i		−	0.630179i	0.949062	−	0.315089i	$-0.102034\pi$
$98$	−351664.	+	237411.i	−0.373637	+	0.252245i
$99$	107554.			0.110846
$100$	222489.	−	385362.i	0.222489	−	0.385362i
$101$	634688.	−	366437.i	0.616022	−	0.355661i	−0.159297	−	0.987231i	$-0.550923\pi$
$101$	634688.	−	366437.i	0.616022	−	0.355661i	0.775319	+	0.631570i	$0.217589\pi$
$102$	176809.	+	306242.i	0.166611	+	0.288579i
$103$	908207.	+	524353.i	0.831138	+	0.479858i	0.854242	−	0.519875i	$-0.174022\pi$
$103$	908207.	+	524353.i	0.831138	+	0.479858i	−0.0231042	+	0.999733i	$0.507355\pi$
$104$		−	288852.i		−	0.256788i
$105$	99812.3	−	432741.i	0.0862216	−	0.373818i
$106$	719700.			0.604274
$107$	−587412.	+	1.01743e6i	−0.479503	+	0.830524i	−0.999724	−	0.0235083i	$-0.992516\pi$
$107$	−587412.	+	1.01743e6i	−0.479503	+	0.830524i	0.520221	+	0.854032i	$0.325850\pi$
$108$	167283.	−	96580.9i	0.132795	−	0.0766690i
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	0.688800	−	0.724951i	$-0.258138\pi$
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	−0.972226	+	0.234043i	$0.924804\pi$
$110$	114821.	+	66292.1i	0.0862669	+	0.0498062i
$111$		−	158375.i		−	0.115803i
$112$	443561.	+	413457.i	0.315718	+	0.294291i
$113$	2.04925e6			1.42023			0.710116	−	0.704085i	$-0.248643\pi$
$113$	2.04925e6			1.42023			0.710116	+	0.704085i	$0.248643\pi$
$114$	−75549.2	+	130855.i	−0.0509935	+	0.0883234i
$115$	−1.13440e6	+	654945.i	−0.745885	+	0.430637i
$116$	−593421.	−	1.02783e6i	−0.380180	−	0.658490i
$117$	−146573.	−	84624.0i	−0.0915159	−	0.0528367i
$118$		−	1.39653e6i		−	0.849969i
$119$	631201.	+	2.06304e6i	0.374564	+	1.22424i
$120$	536967.			0.310745
$121$	787829.	−	1.36456e6i	0.444709	−	0.770259i
$122$	−36798.9	+	21245.8i	−0.0202654	+	0.0117002i
$123$	−297470.	−	515233.i	−0.159856	−	0.276878i
$124$	2.09975e6	+	1.21229e6i	1.10129	+	0.635830i
$125$		−	2.02259e6i		−	1.03556i
$126$	−287445.	+	87945.6i	−0.143696	+	0.0439645i
$127$	−1.64688e6			−0.803991			−0.401995	−	0.915642i	$-0.631683\pi$
$127$	−1.64688e6			−0.803991			−0.401995	+	0.915642i	$0.631683\pi$
$128$	−1.04332e6	+	1.80709e6i	−0.497495	+	0.861687i
$129$	−2.04116e6	+	1.17846e6i	−0.950841	+	0.548968i
$130$	−104318.	−	180684.i	−0.0474821	−	0.0822413i
$131$	−1.78472e6	−	1.03041e6i	−0.793882	−	0.458348i	0.0474457	−	0.998874i	$-0.484892\pi$
$131$	−1.78472e6	−	1.03041e6i	−0.793882	−	0.458348i	−0.841327	+	0.540526i	$0.818225\pi$
$132$			351831.i			0.152972i
$133$	−628568.	+	674335.i	−0.267176	+	0.286629i
$134$	1.38589e6			0.575989
$135$	157313.	−	272475.i	0.0639388	−	0.110745i
$136$	−2.25909e6	+	1.30429e6i	−0.898085	+	0.518510i
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	−0.987969	−	0.154654i	$-0.950574\pi$
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	0.360050	−	0.932933i	$-0.382760\pi$
$138$	767836.	+	443310.i	0.292167	+	0.168683i
$139$			4.06719e6i			1.51443i	0.653163	+	0.757217i	$0.273442\pi$
$139$			4.06719e6i			1.51443i	−0.653163	+	0.757217i	$0.726558\pi$
$140$	1.41559e6	+	326507.i	0.515885	+	0.118990i
$141$	−783776.			−0.279598
$142$	281533.	−	487630.i	0.0983252	−	0.170304i
$143$	266973.	−	154137.i	0.0912976	−	0.0527107i
$144$	214795.	+	372037.i	0.0719346	+	0.124594i
$145$	−1.67416e6	−	966578.i	−0.549153	−	0.317054i
$146$		−	1.35438e6i		−	0.435194i
$147$	−1.82945e6	+	128684.i	−0.575927	+	0.0405111i
$148$	518080.			0.159813
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	−0.573749	−	0.819031i	$-0.694511\pi$
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	0.996176	+	0.0873655i	$0.0278448\pi$
$150$	−424860.	+	245293.i	−0.125884	+	0.0726794i
$151$	−301549.	−	522299.i	−0.0875846	−	0.151701i	0.818905	−	0.573929i	$-0.194581\pi$
$151$	−301549.	−	522299.i	−0.0875846	−	0.151701i	−0.906490	+	0.422228i	$0.861248\pi$
$152$	−965293.	−	557312.i	−0.274871	−	0.158697i
$153$			1.52845e6i			0.426754i
$154$	123055.	−	533512.i	0.0336929	−	0.146077i
$155$	3.94921e6			1.06051
$156$	276823.	−	479472.i	0.0729170	−	0.126296i
$157$	−1.23763e6	+	714546.i	−0.319810	+	0.184642i	−0.651308	−	0.758814i	$-0.725779\pi$
$157$	−1.23763e6	+	714546.i	−0.319810	+	0.184642i	0.331498	+	0.943456i	$0.392446\pi$
$158$	59838.4	+	103643.i	0.0151708	+	0.0262766i
$159$	2.69401e6	+	1.55539e6i	0.670206	+	0.386943i
$160$			2.73414e6i			0.667514i
$161$	3.95689e6	+	3.68833e6i	0.948148	+	0.883797i
$162$	−212960.			−0.0500903
$163$	2.78644e6	−	4.82625e6i	0.643408	−	1.11442i	−0.341259	−	0.939969i	$-0.610853\pi$
$163$	2.78644e6	−	4.82625e6i	0.643408	−	1.11442i	0.984667	−	0.174446i	$-0.0558135\pi$
$164$	1.68544e6	−	973087.i	0.382103	−	0.220607i
$165$	286536.	+	496295.i	0.0637862	+	0.110481i
$166$	3.07643e6	+	1.77618e6i	0.672546	+	0.388295i
$167$		−	2.24388e6i		−	0.481781i	−0.970552	−	0.240890i	$-0.922561\pi$
$167$		−	2.24388e6i		−	0.481781i	0.970552	−	0.240890i	$-0.0774394\pi$
$168$	−648758.	−	2.12043e6i	−0.136822	−	0.447194i
$169$	4.34171e6			0.899498
$170$	−942080.	+	1.63173e6i	−0.191752	+	0.332125i
$171$	−565597.	+	326548.i	−0.113115	+	0.0653068i
$172$	−3.85501e6	−	6.67707e6i	−0.757600	−	1.31220i
$173$	−5.95864e6	−	3.44022e6i	−1.15082	−	0.664428i	−0.201736	−	0.979440i	$-0.564658\pi$
$173$	−5.95864e6	−	3.44022e6i	−1.15082	−	0.664428i	−0.949088	+	0.315012i	$0.897992\pi$
$174$			1.30849e6i			0.248383i
$175$	−2.86213e6	+	875685.i	−0.534041	+	0.163393i
$176$	−782471.			−0.143526
$177$	3.01812e6	−	5.22754e6i	0.544273	−	0.942708i
$178$	−820225.	+	473557.i	−0.145436	+	0.0839677i
$179$	3.94643e6	+	6.83543e6i	0.688091	+	1.19181i	0.972455	+	0.233092i	$0.0748843\pi$
$179$	3.94643e6	+	6.83543e6i	0.688091	+	1.19181i	−0.284364	+	0.958716i	$0.591782\pi$
$180$	891323.	+	514606.i	0.152833	+	0.0882383i
$181$		−	2.63639e6i		−	0.444604i	−0.974978	−	0.222302i	$-0.928643\pi$
$181$		−	2.63639e6i		−	0.444604i	0.974978	−	0.222302i	$-0.0713571\pi$
$182$	−587469.	+	630243.i	−0.0974475	+	0.104543i
$183$	−183663.			−0.0299687
$184$	−3.27022e6	+	5.66418e6i	−0.524956	+	0.909251i
$185$	730805.	−	421931.i	0.115421	−	0.0666386i
$186$	−1.33654e6	−	2.31496e6i	−0.207704	−	0.359754i
$187$	−2.41099e6	−	1.39199e6i	−0.368698	−	0.212868i
$188$		−	2.56390e6i		−	0.385858i
$189$	−1.26604e6	−	292014.i	−0.187527	−	0.0432532i
$190$	−805087.			−0.117377
$191$	−6.17120e6	+	1.06888e7i	−0.885665	+	1.53402i	−0.0407156	+	0.999171i	$0.512964\pi$
$191$	−6.17120e6	+	1.06888e7i	−0.885665	+	1.53402i	−0.844949	+	0.534846i	$0.820370\pi$
$192$	75272.3	−	43458.5i	0.0106349	−	0.00614004i
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.780871	+	0.624692i	$0.214776\pi$
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.150564	+	0.988600i	$0.451891\pi$
$194$	−1.79637e6	−	1.03713e6i	−0.246031	−	0.142046i
$195$		−	901793.i		−	0.121619i
$196$	−420954.	−	5.98451e6i	−0.0559071	−	0.794804i
$197$	−9.42468e6			−1.23273			−0.616365	−	0.787460i	$-0.711396\pi$
$197$	−9.42468e6			−1.23273			−0.616365	+	0.787460i	$0.711396\pi$
$198$	193946.	−	335925.i	0.0249854	−	0.0432760i
$199$	4.91639e6	−	2.83848e6i	0.623860	−	0.360186i	−0.154510	−	0.987991i	$-0.549380\pi$
$199$	4.91639e6	−	2.83848e6i	0.623860	−	0.360186i	0.778370	+	0.627805i	$0.216047\pi$
$200$	−1.80948e6	−	3.13411e6i	−0.226185	−	0.391764i
$201$	5.18772e6	+	2.99513e6i	0.638834	+	0.368831i
$202$		−	2.64311e6i		−	0.320672i
$203$	−1.79422e6	+	7.77892e6i	−0.214480	+	0.929890i
$204$	−4.99989e6			−0.588939
$205$	1.58499e6	−	2.74528e6i	0.183977	−	0.318658i
$206$	3.27545e6	−	1.89108e6i	0.374687	−	0.216326i
$207$	1.91613e6	+	3.31883e6i	0.216030	+	0.374175i
$208$	1.06634e6	+	615653.i	0.118497	+	0.0684142i
$209$		−	1.18957e6i		−	0.130302i
$210$	−1.17160e6	−	1.09209e6i	−0.126509	−	0.117923i
$211$	1.05196e6			0.111983			0.0559914	−	0.998431i	$-0.482168\pi$
$211$	1.05196e6			0.111983			0.0559914	+	0.998431i	$0.482168\pi$
$212$	−5.08801e6	+	8.81269e6i	−0.533999	+	0.924913i
$213$	2.10770e6	−	1.21688e6i	0.218107	−	0.125924i
$214$	2.11850e6	+	3.66935e6i	0.216166	+	0.374410i
$215$	−1.08758e7	−	6.27913e6i	−1.09432	−	0.631807i
$216$		−	1.57097e6i		−	0.155886i
$217$	−4.77141e6	−	1.55951e7i	−0.466946	−	1.52619i
$218$	−2.64750e6			−0.255544
$219$	2.92704e6	−	5.06978e6i	0.278674	−	0.482677i
$220$	−1.62348e6	+	937319.i	−0.152469	+	0.0880277i
$221$	2.19045e6	+	3.79397e6i	0.202935	+	0.351493i
$222$	−494657.	−	285591.i	−0.0452111	−	0.0261027i
$223$			9.96615e6i			0.898696i	0.893357	+	0.449348i	$0.148344\pi$
$223$			9.96615e6i			0.898696i	−0.893357	+	0.449348i	$0.851656\pi$
$224$	1.07969e7	−	3.30336e6i	0.960624	−	0.293908i
$225$	−2.12047e6			−0.186159
$226$	3.69531e6	−	6.40046e6i	0.320129	−	0.554480i
$227$	1.59963e7	−	9.23545e6i	1.36754	−	0.789552i	0.376930	−	0.926242i	$-0.376980\pi$
$227$	1.59963e7	−	9.23545e6i	1.36754	−	0.789552i	0.990614	+	0.136690i	$0.0436464\pi$
$228$	−1.06821e6	−	1.85019e6i	−0.0901262	−	0.156103i
$229$	1.17915e7	+	6.80784e6i	0.981892	+	0.566896i	0.902841	−	0.429975i	$-0.141478\pi$
$229$	1.17915e7	+	6.80784e6i	0.981892	+	0.566896i	0.0790512	+	0.996871i	$0.474811\pi$
$230$			4.72412e6i			0.388273i
$231$	1.61363e6	−	1.73112e6i	0.130909	−	0.140440i
$232$	−9.65248e6			−0.772992
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	−0.866227	−	0.499651i	$-0.833462\pi$
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	0.865824	+	0.500349i	$0.166795\pi$
$234$	−528616.	+	305196.i	−0.0412565	+	0.0238195i
$235$	−2.08807e6	−	3.61664e6i	−0.160895	−	0.278678i
$236$	1.71004e7	+	9.87291e6i	1.30098	+	0.751120i
$237$			517281.i			0.0388581i
$238$	7.58176e6	+	1.74874e6i	0.562392	+	0.129717i
$239$	2.49567e6			0.182807			0.0914037	−	0.995814i	$-0.470865\pi$
$239$	2.49567e6			0.182807			0.0914037	+	0.995814i	$0.470865\pi$
$240$	−1.14448e6	+	1.98230e6i	−0.0827894	+	0.143395i
$241$	−4.73752e6	+	2.73521e6i	−0.338454	+	0.195407i	−0.659588	−	0.751627i	$-0.729269\pi$
$241$	−4.73752e6	+	2.73521e6i	−0.338454	+	0.195407i	0.321134	+	0.947034i	$0.395936\pi$
$242$	−2.84131e6	−	4.92129e6i	−0.200480	−	0.347242i
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		−	600800.i		−	0.0413581i
$245$	−5.46766e6	−	8.09894e6i	−0.371795	−	0.550719i
$246$	−2.14565e6			−0.144130
$247$	−935961.	+	1.62113e6i	−0.0621108	+	0.107579i
$248$	1.70771e7	−	9.85944e6i	1.11959	−	0.646394i
$249$	7.67720e6	+	1.32973e7i	0.497285	+	0.861322i
$250$	−6.31718e6	−	3.64723e6i	−0.404300	−	0.233423i
$251$		−	2.18424e6i		−	0.138127i	−0.997612	−	0.0690637i	$-0.977999\pi$
$251$		−	2.18424e6i		−	0.138127i	0.997612	−	0.0690637i	$-0.0220012\pi$
$252$	955241.	−	4.14149e6i	0.0596913	−	0.258795i
$253$	−6.98020e6			−0.431029
$254$	−2.96974e6	+	5.14374e6i	−0.181225	+	0.313890i
$255$	−7.05286e6	+	4.07197e6i	−0.425349	+	0.245575i
$256$	3.94117e6	+	6.82631e6i	0.234912	+	0.406880i
$257$	−2.72638e7	−	1.57408e7i	−1.60615	−	0.927313i	−0.990220	−	0.139514i	$-0.955446\pi$
$257$	−2.72638e7	−	1.57408e7i	−1.60615	−	0.927313i	−0.615933	−	0.787799i	$-0.711221\pi$
$258$			8.50027e6i			0.494964i
$259$	−2.54912e6	−	2.37611e6i	−0.146720	−	0.136762i
$260$	2.94996e6			0.167840
$261$	−2.82785e6	+	4.89799e6i	−0.159051	+	0.275484i
$262$	−6.43659e6	+	3.71616e6i	−0.357892	+	0.206629i
$263$	−3.28881e6	−	5.69639e6i	−0.180789	−	0.313136i	0.761360	−	0.648329i	$-0.224532\pi$
$263$	−3.28881e6	−	5.69639e6i	−0.180789	−	0.313136i	−0.942149	+	0.335193i	$0.891198\pi$
$264$	2.47806e6	+	1.43071e6i	0.134679	+	0.0777569i
$265$			1.65749e7i			0.890665i
$266$	972699.	+	3.17921e6i	0.0516813	+	0.168918i
$267$	−4.09373e6			−0.215073
$268$	−9.79771e6	+	1.69701e7i	−0.509003	+	0.881619i
$269$	190420.	−	109939.i	0.00978263	−	0.00564801i	−0.495101	−	0.868836i	$-0.664869\pi$
$269$	190420.	−	109939.i	0.00978263	−	0.00564801i	0.504883	+	0.863188i	$0.331536\pi$
$270$	−567351.	−	982680.i	−0.0288244	−	0.0499253i
$271$	−2.41082e7	−	1.39189e7i	−1.21132	−	0.699354i	−0.248270	−	0.968691i	$-0.579862\pi$
$271$	−2.41082e7	−	1.39189e7i	−1.21132	−	0.699354i	−0.963046	+	0.269337i	$0.913196\pi$
$272$		−	1.11197e7i		−	0.552570i
$273$	−3.56109e6	+	1.08954e6i	−0.175023	+	0.0535494i
$274$	−1.16461e7			−0.566147
$275$	1.93115e6	−	3.34485e6i	0.0928576	−	0.160834i
$276$	−1.08566e7	+	6.26807e6i	−0.516377	+	0.298130i
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	0.925741	−	0.378159i	$-0.123443\pi$
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	−0.790366	+	0.612635i	$0.790109\pi$
$278$	1.27032e7	+	7.33417e6i	0.591258	+	0.341363i
$279$		−	1.15540e7i		−	0.532008i
$280$	8.05612e6	−	8.64270e6i	0.366988	−	0.393709i
$281$	1.75833e7			0.792467			0.396233	−	0.918150i	$-0.370317\pi$
$281$	1.75833e7			0.792467			0.396233	+	0.918150i	$0.370317\pi$
$282$	−1.41334e6	+	2.44798e6i	−0.0630232	+	0.109159i
$283$	1.27466e7	−	7.35922e6i	0.562385	−	0.324693i	−0.191717	−	0.981450i	$-0.561406\pi$
$283$	1.27466e7	−	7.35922e6i	0.562385	−	0.324693i	0.754102	+	0.656757i	$0.228072\pi$
$284$	3.98067e6	+	6.89472e6i	0.173780	+	0.300997i
$285$	−3.01363e6	−	1.73992e6i	−0.130184	−	0.0751615i
$286$		−	1.11179e6i		−	0.0475253i
$287$	−1.27558e7	−	2.94215e6i	−0.539589	−	0.124457i
$288$	7.99909e6			0.334860
$289$	7.71280e6	−	1.33590e7i	0.319535	−	0.553451i
$290$	−6.03787e6	+	3.48597e6i	−0.247565	+	0.142932i
$291$	−4.48283e6	−	7.76448e6i	−0.181917	−	0.315089i
$292$	1.65843e7	+	9.57497e6i	0.666115	+	0.384582i
$293$			3.49743e6i			0.139042i	0.997580	+	0.0695210i	$0.0221471\pi$
$293$			3.49743e6i			0.139042i	−0.997580	+	0.0695210i	$0.977853\pi$
$294$	−2.89703e6	+	5.94600e6i	−0.114001	+	0.233982i
$295$	3.21625e7			1.25280
$296$	2.10675e6	−	3.64900e6i	0.0812339	−	0.140701i
$297$	1.45198e6	−	838299.i	0.0554230	−	0.0319985i
$298$	−5.03961e6	−	8.72886e6i	−0.190436	−	0.329844i
$299$	9.51254e6	+	5.49207e6i	0.355863	+	0.205458i
$300$		−	6.93651e6i		−	0.256908i
$301$	−1.16557e7	+	5.05338e7i	−0.427404	+	1.85303i
$302$	−2.17508e6			−0.0789685
$303$	5.71219e6	−	9.89381e6i	0.205341	−	0.355661i
$304$	4.11481e6	−	2.37569e6i	0.146463	−	0.0845607i
$305$	−489299.	−	847490.i	−0.0172455	−	0.0298700i
$306$	4.77385e6	+	2.75618e6i	0.166611	+	0.0961930i
$307$		−	3.99694e7i		−	1.38138i	−0.723152	−	0.690689i	$-0.757308\pi$
$307$		−	3.99694e7i		−	1.38138i	0.723152	−	0.690689i	$-0.242692\pi$
$308$	5.66287e6	+	5.27853e6i	0.193814	+	0.180659i
$309$	1.63477e7			0.554092
$310$	7.12142e6	−	1.23347e7i	0.239046	−	0.414040i
$311$	−2.88815e7	+	1.66747e7i	−0.960148	+	0.554342i	−0.896219	−	0.443613i	$-0.853697\pi$
$311$	−2.88815e7	+	1.66747e7i	−0.960148	+	0.554342i	−0.0639296	+	0.997954i	$0.520363\pi$
$312$	−2.25138e6	−	3.89950e6i	−0.0741284	−	0.128394i
$313$	1.62725e7	+	9.39495e6i	0.530667	+	0.306381i	0.741288	−	0.671187i	$-0.234215\pi$
$313$	1.62725e7	+	9.39495e6i	0.530667	+	0.306381i	−0.210621	+	0.977568i	$0.567549\pi$
$314$			5.15402e6i			0.166478i
$315$	−2.02542e6	−	6.61996e6i	−0.0648012	−	0.211799i
$316$	−1.69214e6			−0.0536259
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	−0.660364	−	0.750946i	$-0.729598\pi$
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	0.980520	+	0.196419i	$0.0629312\pi$
$318$	9.71596e6	−	5.60951e6i	0.302137	−	0.174439i
$319$	−5.15075e6	−	8.92136e6i	−0.158671	−	0.274827i
$320$	401068.	+	231557.i	0.0122396	+	0.00706656i
$321$			1.83137e7i			0.553682i
$322$	1.86551e7	−	5.70764e6i	0.558766	−	0.170958i
$323$	1.69050e7			0.501659
$324$	1.50555e6	−	2.60768e6i	0.0442649	−	0.0766690i
$325$	−5.26349e6	+	3.03888e6i	−0.153329	+	0.0885244i
$326$	−1.00493e7	−	1.74059e7i	−0.290056	−	0.502393i
$327$	−9.91021e6	−	5.72167e6i	−0.283426	−	0.163636i
$328$		−	1.58281e7i		−	0.448545i
$329$	−1.17590e7	+	1.26152e7i	−0.330204	+	0.354247i
$330$	2.06678e6			0.0575113
$331$	1.06774e7	−	1.84939e7i	0.294431	−	0.509969i	−0.680422	−	0.732821i	$-0.738203\pi$
$331$	1.06774e7	−	1.84939e7i	0.294431	−	0.509969i	0.974852	+	0.222852i	$0.0715366\pi$
$332$	−4.34983e7	+	2.51138e7i	−1.18866	+	0.686274i
$333$	−1.23441e6	−	2.13807e6i	−0.0334294	−	0.0579014i
$334$	−7.00834e6	−	4.04627e6i	−0.188094	−	0.108596i
$335$			3.19175e7i			0.848974i
$336$	9.21066e6	+	2.12445e6i	0.242813	+	0.0560052i
$337$	−1.98824e7			−0.519493			−0.259746	−	0.965677i	$-0.583639\pi$
$337$	−1.98824e7			−0.519493			−0.259746	+	0.965677i	$0.583639\pi$
$338$	7.82918e6	−	1.35605e7i	0.202753	−	0.351178i
$339$	2.76649e7	−	1.59723e7i	0.710116	−	0.409986i
$340$	−1.33203e7	−	2.30714e7i	−0.338904	−	0.586999i
$341$	1.82253e7	+	1.05224e7i	0.459633	+	0.265369i
$342$			2.35539e6i			0.0588823i
$343$	−2.53760e7	+	3.13763e7i	−0.628840	+	0.777535i
$344$	−6.27049e7			−1.54037
$345$	−1.02096e7	+	1.76835e7i	−0.248628	+	0.430637i
$346$	−2.14898e7	+	1.24072e7i	−0.518806	+	0.299533i
$347$	1.66198e7	+	2.87863e7i	0.397774	+	0.688965i	0.993451	−	0.114259i	$-0.0364495\pi$
$347$	1.66198e7	+	2.87863e7i	0.397774	+	0.688965i	−0.595677	+	0.803224i	$0.703116\pi$
$348$	−1.60224e7	−	9.25051e6i	−0.380180	−	0.219497i
$349$			2.57850e7i			0.606584i	0.952898	+	0.303292i	$0.0980858\pi$
$349$			2.57850e7i			0.606584i	−0.952898	+	0.303292i	$0.901914\pi$
$350$	−2.42609e6	+	1.05184e7i	−0.0565851	+	0.245328i
$351$	−2.63832e6			−0.0610106
$352$	−7.28490e6	+	1.26178e7i	−0.167030	+	0.289305i
$353$	−4.82036e7	+	2.78303e7i	−1.09586	+	0.632695i	−0.935130	−	0.354304i	$-0.884718\pi$
$353$	−4.82036e7	+	2.78303e7i	−1.09586	+	0.632695i	−0.160729	+	0.986999i	$0.551385\pi$
$354$	−1.08848e7	−	1.88531e7i	−0.245365	−	0.424985i
$355$	1.12303e7	+	6.48381e6i	0.251019	+	0.144926i
$356$		−	1.33915e7i		−	0.296810i
$357$	2.46010e7	+	2.29314e7i	0.540691	+	0.503994i
$358$	2.84656e7			0.620400
$359$	8.08714e6	−	1.40073e7i	0.174788	−	0.302742i	−0.765300	−	0.643674i	$-0.777409\pi$
$359$	8.08714e6	−	1.40073e7i	0.174788	−	0.302742i	0.940088	+	0.340932i	$0.110743\pi$
$360$	7.24905e6	−	4.18524e6i	0.155372	−	0.0897043i
$361$	−1.99112e7	−	3.44873e7i	−0.423230	−	0.733056i
$362$	−8.23428e6	−	4.75406e6i	−0.173580	−	0.100217i
$363$		−	2.45621e7i		−	0.513506i
$364$	−3.56411e6	−	1.16491e7i	−0.0739004	−	0.241539i
$365$	3.11919e7			0.641451
$366$	−331190.	+	573637.i	−0.00675513	+	0.0117002i
$367$	9.72318e6	−	5.61368e6i	0.196703	−	0.113566i	−0.398414	−	0.917206i	$-0.630439\pi$
$367$	9.72318e6	−	5.61368e6i	0.196703	−	0.113566i	0.595117	+	0.803639i	$0.297106\pi$
$368$	−1.39401e7	−	2.41450e7i	−0.279720	−	0.484490i
$369$	−8.03169e6	−	4.63710e6i	−0.159856	−	0.0922926i
$370$		−	3.04339e6i		−	0.0600830i
$371$	6.54529e7	−	2.00257e7i	1.28176	−	0.392162i
$372$	3.77954e7			0.734194
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	−0.991820	−	0.127642i	$-0.959259\pi$
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	0.606451	+	0.795121i	$0.292593\pi$
$374$	−8.69524e6	+	5.02020e6i	−0.166214	+	0.0959635i
$375$	−1.57645e7	−	2.73049e7i	−0.298942	−	0.517782i
$376$	−1.80583e7	−	1.04260e7i	−0.339714	−	0.196134i
$377$			1.62106e7i			0.302534i
$378$	−3.19504e6	+	3.42768e6i	−0.0591564	+	0.0634636i
$379$	2.92098e7			0.536551			0.268276	−	0.963342i	$-0.413546\pi$
$379$	2.92098e7			0.536551			0.268276	+	0.963342i	$0.413546\pi$
$380$	5.69166e6	−	9.85824e6i	0.103726	−	0.179659i
$381$	−2.22329e7	+	1.28362e7i	−0.401995	+	0.232092i
$382$	2.22564e7	+	3.85493e7i	0.399269	+	0.691554i
$383$	3.97181e7	+	2.29312e7i	0.706955	+	0.408161i	0.809933	−	0.586523i	$-0.199504\pi$
$383$	3.97181e7	+	2.29312e7i	0.706955	+	0.408161i	−0.102978	+	0.994684i	$0.532837\pi$
$384$			3.25276e7i			0.574458i
$385$	1.22870e7	+	2.83400e6i	0.215309	+	0.0496613i
$386$	4.82993e7			0.839805
$387$	−1.83704e7	+	3.18185e7i	−0.316947	+	0.548968i
$388$	2.53993e7	−	1.46643e7i	0.434837	−	0.251053i
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	0.792925	−	0.609319i	$-0.208557\pi$
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	−0.924148	+	0.382034i	$0.875224\pi$
$390$	−2.81659e6	−	1.62616e6i	−0.0474821	−	0.0274138i
$391$		−	9.91960e7i		−	1.65945i
$392$	−4.38625e7	−	2.13708e7i	−0.728174	−	0.354783i
$393$	−3.21249e7			−0.529254
$394$	−1.69951e7	+	2.94363e7i	−0.277865	+	0.481277i
$395$	−2.38693e6	+	1.37810e6i	−0.0387302	+	0.0223609i
$396$	2.74225e6	+	4.74972e6i	0.0441593	+	0.0764861i
$397$	2.54737e7	+	1.47073e7i	0.407118	+	0.235050i	0.689551	−	0.724237i	$-0.257808\pi$
$397$	2.54737e7	+	1.47073e7i	0.407118	+	0.235050i	−0.282433	+	0.959287i	$0.591141\pi$
$398$		−	2.04740e7i		−	0.324753i
$399$	−3.22975e6	+	1.40027e7i	−0.0508452	+	0.220442i
$400$	1.54268e7			0.241043
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.0372810	−	0.999305i	$-0.488130\pi$
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.846783	−	0.531939i	$-0.178536\pi$
$402$	1.87095e7	−	1.08019e7i	0.287995	−	0.166274i
$403$	−1.65581e7	−	2.86796e7i	−0.252986	−	0.438185i
$404$	3.23648e7	+	1.86858e7i	0.490827	+	0.283379i
$405$		−	4.90455e6i		−	0.0738302i
$406$	2.10607e7	+	1.96313e7i	0.314698	+	0.293339i
$407$	4.49681e6			0.0666992
$408$	−2.03318e7	+	3.52158e7i	−0.299362	+	0.518510i
$409$	2.99288e7	−	1.72794e7i	0.437442	−	0.252557i	−0.265070	−	0.964229i	$-0.585395\pi$
$409$	2.99288e7	−	1.72794e7i	0.437442	−	0.252557i	0.702512	+	0.711672i	$0.252062\pi$
$410$	−5.71626e6	−	9.90086e6i	−0.0829393	−	0.143655i
$411$	−4.35942e7	−	2.51691e7i	−0.627919	−	0.362529i
$412$			5.34769e7i			0.764671i
$413$	−3.88584e7	−	1.27007e8i	−0.551614	−	1.80292i
$414$	1.38210e7			0.194778
$415$	−4.09059e7	+	7.08511e7i	−0.572324	+	0.991294i
$416$	1.98556e7	−	1.14636e7i	0.275805	−	0.159236i
$417$	3.17006e7	+	5.49071e7i	0.437180	+	0.757217i
$418$	−3.71541e6	−	2.14509e6i	−0.0508719	−	0.0293709i
$419$			3.73902e7i			0.508294i	0.967166	+	0.254147i	$0.0817948\pi$
$419$			3.73902e7i			0.508294i	−0.967166	+	0.254147i	$0.918205\pi$
$420$	2.16553e7	−	6.62557e6i	0.292292	−	0.0894284i
$421$	−5.93910e7			−0.795929			−0.397965	−	0.917401i	$-0.630283\pi$
$421$	−5.93910e7			−0.795929			−0.397965	+	0.917401i	$0.630283\pi$
$422$	1.89694e6	−	3.28560e6i	0.0252416	−	0.0437198i
$423$	−1.05810e7	+	6.10893e6i	−0.139799	+	0.0807131i
$424$	4.13803e7	+	7.16728e7i	0.542870	+	0.940279i
$425$	4.75338e7	+	2.74436e7i	0.619206	+	0.357499i
$426$		−	8.77734e6i		−	0.113536i
$427$	−2.75549e6	+	2.95612e6i	−0.0353929	+	0.0379699i
$428$	−5.99080e7			−0.764105
$429$	2.40276e6	−	4.16170e6i	0.0304325	−	0.0527107i
$430$	−3.92235e7	+	2.26457e7i	−0.493334	+	0.284826i
$431$	2.97697e7	+	5.15627e7i	0.371829	+	0.644026i	0.989847	−	0.142137i	$-0.0453975\pi$
$431$	2.97697e7	+	5.15627e7i	0.371829	+	0.644026i	−0.618018	+	0.786164i	$0.712064\pi$
$432$	5.79948e6	+	3.34833e6i	0.0719346	+	0.0415314i
$433$			6.40730e7i			0.789244i	0.918843	+	0.394622i	$0.129124\pi$
$433$			6.40730e7i			0.789244i	−0.918843	+	0.394622i	$0.870876\pi$
$434$	−5.73125e7	−	1.32192e7i	−0.701100	−	0.161710i
$435$	−3.01349e7			−0.366102
$436$	1.87168e7	−	3.24184e7i	0.225825	−	0.391140i
$437$	3.67071e7	−	2.11928e7i	0.439851	−	0.253948i
$438$	−1.05564e7	−	1.82842e7i	−0.125630	−	0.217597i
$439$	−1.31778e8	−	7.60819e7i	−1.55757	−	0.899265i	−0.997488	−	0.0708286i	$-0.977436\pi$
$439$	−1.31778e8	−	7.60819e7i	−1.55757	−	0.899265i	−0.560084	−	0.828436i	$-0.689231\pi$
$440$			1.52463e7i			0.178980i
$441$	−2.36945e7	+	1.59964e7i	−0.276269	+	0.186511i
$442$	1.57997e7			0.182971
$443$	−1.72920e7	+	2.99506e7i	−0.198899	+	0.344504i	−0.948172	−	0.317758i	$-0.897070\pi$
$443$	−1.72920e7	+	2.99506e7i	−0.198899	+	0.344504i	0.749273	+	0.662262i	$0.230403\pi$
$444$	6.99408e6	−	4.03803e6i	0.0799064	−	0.0461340i
$445$	−1.09062e7	−	1.88901e7i	−0.123763	−	0.214365i
$446$	3.11275e7	+	1.79715e7i	0.350864	+	0.202572i
$447$		−	4.35656e7i		−	0.487777i
$448$	429829.	−	1.86355e6i	0.00478037	−	0.0207255i
$449$	−1.33795e8			−1.47809			−0.739047	−	0.673654i	$-0.764724\pi$
$449$	−1.33795e8			−1.47809			−0.739047	+	0.673654i	$0.764724\pi$
$450$	−3.82374e6	+	6.62291e6i	−0.0419615	+	0.0726794i
$451$	1.46292e7	−	8.44616e6i	0.159474	−	0.0920724i
$452$	5.22488e7	+	9.04976e7i	0.565798	+	0.979990i
$453$	−8.14183e6	−	4.70069e6i	−0.0875846	−	0.0505670i
$454$		−	6.66153e7i		−	0.711880i
$455$	−1.45147e7	−	1.35296e7i	−0.154090	−	0.143632i
$456$	−1.73753e7			−0.183247
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	−0.903208	−	0.429202i	$-0.858795\pi$
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	0.823304	+	0.567600i	$0.192128\pi$
$458$	4.25262e7	−	2.45525e7i	0.442649	−	0.255564i
$459$	1.19131e7	+	2.06341e7i	0.123193	+	0.213377i
$460$	−5.78465e7	−	3.33977e7i	−0.594298	−	0.343118i
$461$			3.05013e7i			0.311326i	0.987810	+	0.155663i	$0.0497514\pi$
$461$			3.05013e7i			0.311326i	−0.987810	+	0.155663i	$0.950249\pi$
$462$	−2.49707e6	−	8.16153e6i	−0.0253224	−	0.0827648i
$463$	−1.61661e8			−1.62878			−0.814388	−	0.580320i	$-0.802927\pi$
$463$	−1.61661e8			−1.62878			−0.814388	+	0.580320i	$0.802927\pi$
$464$	2.05731e7	−	3.56336e7i	0.205942	−	0.356703i
$465$	5.33144e7	−	3.07811e7i	0.530256	−	0.306143i
$466$	18404.0	+	31876.7i	0.000181868	+	0.000315004i
$467$	5.70833e7	+	3.29570e7i	0.560478	+	0.323592i	0.753337	−	0.657635i	$-0.228443\pi$
$467$	5.70833e7	+	3.29570e7i	0.560478	+	0.323592i	−0.192860	+	0.981226i	$0.561776\pi$
$468$		−	8.63049e6i		−	0.0841972i
$469$	1.26039e8	−	3.85624e7i	1.22176	−	0.373806i
$470$	−1.50612e7			−0.145067
$471$	−1.11387e7	+	1.92927e7i	−0.106603	+	0.184642i
$472$	1.39076e8	−	8.02955e7i	1.32259	−	0.763599i
$473$	−3.34605e7	−	5.79553e7i	−0.316191	−	0.547659i
$474$	1.61564e6	+	932788.i	0.0151708	+	0.00875886i
$475$			2.34529e7i			0.218834i
$476$	−7.50134e7	+	8.04753e7i	−0.695534	+	0.746176i
$477$	4.84922e7			0.446804
$478$	4.50032e6	−	7.79479e6i	0.0412060	−	0.0713708i
$479$	−7.96535e7	+	4.59880e7i	−0.724767	+	0.418444i	−0.816505	−	0.577339i	$-0.804091\pi$
$479$	−7.96535e7	+	4.59880e7i	−0.724767	+	0.418444i	0.0917379	+	0.995783i	$0.470758\pi$
$480$	2.13105e7	+	3.69109e7i	0.192695	+	0.333757i
$481$	−6.12820e6	−	3.53812e6i	−0.0550678	−	0.0317934i
$482$			1.97291e7i			0.176183i
$483$	8.21657e7	+	1.89516e7i	0.729204	+	0.168192i
$484$	8.03478e7			0.708660
$485$	2.38855e7	−	4.13710e7i	0.209368	−	0.362636i
$486$	−2.87496e6	+	1.65986e6i	−0.0250451	+	0.0144598i
$487$	9.53763e7	+	1.65197e8i	0.825759	+	1.43026i	0.901338	+	0.433117i	$0.142586\pi$
$487$	9.53763e7	+	1.65197e8i	0.825759	+	1.43026i	−0.0755785	+	0.997140i	$0.524080\pi$
$488$	−4.23162e6	−	2.44313e6i	−0.0364122	−	0.0210226i
$489$		−	8.68725e7i		−	0.742944i
$490$	−3.51551e7	+	2.47284e6i	−0.298814	+	0.0210188i
$491$	8.85504e7			0.748077			0.374038	−	0.927413i	$-0.377973\pi$
$491$	8.85504e7			0.748077			0.374038	+	0.927413i	$0.377973\pi$
$492$	1.51689e7	−	2.62734e7i	0.127368	−	0.220607i
$493$	1.26782e8	−	7.31975e7i	1.05807	−	0.610880i
$494$	3.37554e6	+	5.84661e6i	0.0280003	+	0.0484980i
$495$	7.73647e6	+	4.46665e6i	0.0637862	+	0.0368270i
$496$			8.40569e7i			0.688856i
$497$	1.20356e7	−	5.21810e7i	0.0980391	−	0.425053i
$498$	5.53757e7			0.448364
$499$	2.61754e7	−	4.53371e7i	0.210665	−	0.364882i	−0.741258	−	0.671220i	$-0.765770\pi$
$499$	2.61754e7	−	4.53371e7i	0.210665	−	0.364882i	0.951923	+	0.306338i	$0.0991038\pi$
$500$	8.93202e7	−	5.15690e7i	0.714561	−	0.412552i
$501$	−1.74893e7	−	3.02923e7i	−0.139078	−	0.240890i
$502$	−6.82210e6	−	3.93874e6i	−0.0539271	−	0.0311348i
$503$			1.34114e8i			1.05383i	0.849919	+	0.526914i	$0.176651\pi$
$503$			1.34114e8i			1.05383i	−0.849919	+	0.526914i	$0.823349\pi$
$504$	−2.52854e7	−	2.35693e7i	−0.197505	−	0.184100i
$505$	6.08718e7			0.472653
$506$	−1.25871e7	+	2.18014e7i	−0.0971566	+	0.168280i
$507$	5.86130e7	−	3.38402e7i	0.449749	−	0.259663i
$508$	−4.19898e7	−	7.27285e7i	−0.320297	−	0.554771i
$509$	−1.62222e8	−	9.36588e7i	−1.23014	−	0.710224i	−0.263084	−	0.964773i	$-0.584740\pi$
$509$	−1.62222e8	−	9.36588e7i	−1.23014	−	0.710224i	−0.967060	+	0.254549i	$0.918073\pi$
$510$			2.93711e7i			0.221417i
$511$	−3.76858e7	−	1.23174e8i	−0.282432	−	0.923115i
$512$	−1.05118e8			−0.783188
$513$	−5.09038e6	+	8.81679e6i	−0.0377049	+	0.0653068i
$514$	−9.83269e7	+	5.67690e7i	−0.724074	+	0.418044i
$515$	4.35522e7	+	7.54347e7i	0.318852	+	0.552267i
$516$	−1.04085e8	−	6.00936e7i	−0.757600	−	0.437401i
$517$		−	2.22540e7i		−	0.161041i
$518$	−1.20180e7	+	3.67699e6i	−0.0864658	+	0.0264547i
$519$	−1.07255e8			−0.767216
$520$	1.19959e7	−	2.07774e7i	0.0853142	−	0.147769i
$521$	−3.89027e7	+	2.24605e7i	−0.275085	+	0.158820i	−0.631196	−	0.775623i	$-0.717436\pi$
$521$	−3.89027e7	+	2.24605e7i	−0.275085	+	0.158820i	0.356111	+	0.934444i	$0.384102\pi$
$522$	1.01987e7	+	1.76646e7i	0.0717021	+	0.124192i
$523$	1.43752e8	+	8.29951e7i	1.00487	+	0.580160i	0.909684	−	0.415300i	$-0.136324\pi$
$523$	1.43752e8	+	8.29951e7i	1.00487	+	0.580160i	0.0951815	+	0.995460i	$0.469657\pi$
$524$		−	1.05087e8i		−	0.730394i
$525$	−3.18134e7	+	3.41298e7i	−0.219853	+	0.235861i
$526$	−2.37222e7			−0.163004
$527$	−1.49534e8	+	2.59000e8i	−1.02166	+	1.76957i
$528$	−1.05634e7	+	6.09876e6i	−0.0717629	+	0.0414324i
$529$	−5.03382e7	−	8.71883e7i	−0.340041	−	0.588967i
$530$	5.17689e7	+	2.98888e7i	0.347729	+	0.200761i
$531$		−	9.40956e7i		−	0.628472i
$532$	−4.58059e7	−	1.05652e7i	−0.304219	−	0.0701685i
$533$	−2.65820e7			−0.175552
$534$	−7.38202e6	+	1.27860e7i	−0.0484788	+	0.0839677i
$535$	−8.45064e7	+	4.87898e7i	−0.551859	+	0.318616i
$536$	7.96839e7	+	1.38017e8i	0.517459	+	0.896266i
$537$	1.06554e8	+	6.15188e7i	0.688091	+	0.397269i
$538$		−	792991.i		−	0.00509238i
$539$	−3.65378e6	−	5.19441e7i	−0.0233333	−	0.331718i
$540$	1.60438e7			0.101889
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	−0.993582	−	0.113112i	$-0.963918\pi$
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	0.594749	+	0.803911i	$0.297251\pi$
$542$	−8.69464e7	+	5.01985e7i	−0.546077	+	0.315278i
$543$	−2.05486e7	−	3.55912e7i	−0.128346	−	0.222302i
$544$	−1.79312e8	−	1.03526e8i	−1.11382	−	0.643062i
$545$		−	6.09727e7i		−	0.376657i
$546$	−3.01857e6	+	1.30871e7i	−0.0185448	+	0.0804021i
$547$	2.31931e8			1.41709			0.708545	−	0.705666i	$-0.249352\pi$
$547$	2.31931e8			1.41709			0.708545	+	0.705666i	$0.249352\pi$
$548$	8.23336e7	−	1.42606e8i	0.500306	−	0.866555i
$549$	−2.47945e6	+	1.43151e6i	−0.0149843	+	0.00865121i
$550$	−6.96468e6	−	1.20632e7i	−0.0418614	−	0.0725060i
$551$	5.41729e7	+	3.12767e7i	0.323838	+	0.186968i
$552$			1.01955e8i			0.606167i
$553$	8.32585e6	+	7.76078e6i	0.0492327	+	0.0458912i
$554$	2.07536e7			0.122057
$555$	6.57725e6	−	1.13921e7i	0.0384738	−	0.0666386i
$556$	−1.79613e8	+	1.03700e8i	−1.04499	+	0.603326i
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	−0.969322	−	0.245794i	$-0.920951\pi$
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	0.271797	−	0.962355i	$-0.412382\pi$
$558$	−3.60867e7	−	2.08347e7i	−0.207704	−	0.119918i
$559$			1.05308e8i			0.602872i
$560$	1.47352e7	+	4.81613e7i	0.0839060	+	0.274242i
$561$	−4.33978e7			−0.245799
$562$	3.17071e7	−	5.49182e7i	0.178627	−	0.309391i
$563$	−1.01477e8	+	5.85878e7i	−0.568647	+	0.328308i	−0.756609	−	0.653868i	$-0.773145\pi$
$563$	−1.01477e8	+	5.85878e7i	−0.568647	+	0.328308i	0.187962	+	0.982176i	$0.439812\pi$
$564$	−1.99836e7	−	3.46126e7i	−0.111387	−	0.192929i
$565$	1.47405e8	+	8.51042e7i	0.817271	+	0.471852i
$566$		−	5.30821e7i		−	0.292751i
$567$	−1.93676e7	+	5.92563e6i	−0.106249	+	0.0325076i
$568$	6.47488e7			0.353335
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	−0.654088	−	0.756418i	$-0.726948\pi$
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	0.982121	+	0.188248i	$0.0602809\pi$
$570$	−1.08687e7	+	6.27503e6i	−0.0586884	+	0.0338837i
$571$	−5.39062e7	−	9.33683e7i	−0.289555	−	0.501523i	0.684149	−	0.729342i	$-0.260174\pi$
$571$	−5.39062e7	−	9.33683e7i	−0.289555	−	0.501523i	−0.973703	+	0.227819i	$0.926841\pi$
$572$	1.36138e7	+	7.85993e6i	0.0727430	+	0.0419982i
$573$			1.92399e8i			1.02268i
$574$	−3.21912e7	+	3.45351e7i	−0.170217	+	0.182610i
$575$	1.37618e8			0.723887
$576$	677451.	−	1.17338e6i	0.00354495	−	0.00614004i
$577$	−6.79444e7	+	3.92277e7i	−0.353693	+	0.204205i	−0.666310	−	0.745674i	$-0.732127\pi$
$577$	−6.79444e7	+	3.92277e7i	−0.353693	+	0.204205i	0.312618	+	0.949879i	$0.398794\pi$
$578$	−2.78162e7	−	4.81791e7i	−0.144050	−	0.249503i
$579$	1.80796e8	+	1.04382e8i	0.931435	+	0.537764i
$580$		−	9.85778e7i		−	0.505237i
$581$	3.29207e8	+	7.59319e7i	1.67857	+	0.387165i
$582$	−3.23346e7			−0.164021
$583$	−4.41627e7	+	7.64920e7i	−0.222869	+	0.386020i
$584$	1.34879e8	−	7.78724e7i	0.677182	−	0.390971i
$585$	−7.02878e6	−	1.21742e7i	−0.0351085	−	0.0608097i
$586$	1.09236e7	+	6.30674e6i	0.0542841	+	0.0313410i
$587$		−	1.98030e8i		−	0.979075i	−0.871982	−	0.489538i	$-0.837166\pi$
$587$		−	1.98030e8i		−	0.979075i	0.871982	−	0.489538i	$-0.162834\pi$
$588$	−5.23275e7	−	7.75098e7i	−0.257394	−	0.381263i
$589$	−1.27789e8			−0.625387
$590$	5.79970e7	−	1.00454e8i	0.282390	−	0.489114i
$591$	−1.27233e8	+	7.34581e7i	−0.616365	+	0.355859i
$592$	8.98056e6	+	1.55548e7i	0.0432851	+	0.0749720i
$593$	−3.26564e6	−	1.88542e6i	−0.0156605	−	0.00904157i	0.492149	−	0.870511i	$-0.336211\pi$
$593$	−3.26564e6	−	1.88542e6i	−0.0156605	−	0.00904157i	−0.507810	+	0.861469i	$0.669545\pi$
$594$		−	6.04665e6i		−	0.0288506i
$595$	−4.02742e7	+	1.74611e8i	−0.191195	+	0.828933i
$596$	1.42512e8			0.673153
$597$	4.42475e7	−	7.66389e7i	0.207953	−	0.360186i
$598$	3.43070e7	−	1.98071e7i	0.160428	−	0.0926229i
$599$	−1.33653e8	−	2.31493e8i	−0.621867	−	1.07710i	−0.989138	−	0.146991i	$-0.953041\pi$
$599$	−1.33653e8	−	2.31493e8i	−0.621867	−	1.07710i	0.367271	−	0.930114i	$-0.380292\pi$
$600$	−4.88560e7	−	2.82070e7i	−0.226185	−	0.130588i
$601$		−	9.26866e7i		−	0.426966i	−0.976947	−	0.213483i	$-0.931519\pi$
$601$		−	9.26866e7i		−	0.426966i	0.976947	−	0.213483i	$-0.0684809\pi$
$602$	1.36815e8	+	1.27530e8i	0.627112	+	0.584550i
$603$	9.33790e7			0.425890
$604$	1.53770e7	−	2.66337e7i	0.0697846	−	0.120870i
$605$	1.13339e8	−	6.54363e7i	0.511815	−	0.295497i
$606$	−2.06010e7	−	3.56820e7i	−0.0925702	−	0.160336i
$607$	1.38921e8	+	8.02061e7i	0.621158	+	0.358625i	0.777320	−	0.629106i	$-0.216579\pi$
$607$	1.38921e8	+	8.02061e7i	0.621158	+	0.358625i	−0.156162	+	0.987731i	$0.549912\pi$
$608$		−	8.84718e7i		−	0.393635i
$609$	3.64088e7	+	1.19000e8i	0.161196	+	0.526860i
$610$	−3.52931e6			−0.0155489
$611$	−1.75096e7	+	3.03275e7i	−0.0767631	+	0.132958i
$612$	−6.74985e7	+	3.89703e7i	−0.294469	+	0.170012i
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	0.776969	−	0.629539i	$-0.216756\pi$
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	−0.933681	+	0.358106i	$0.883423\pi$
$614$	−1.24837e8	−	7.20748e7i	−0.539311	−	0.311371i
$615$		−	4.94151e7i		−	0.212439i
$616$	6.02061e7	−	1.84204e7i	0.257572	−	0.0788056i
$617$	3.16720e6			0.0134841			0.00674203	−	0.999977i	$-0.497854\pi$
$617$	3.16720e6			0.0134841			0.00674203	+	0.999977i	$0.497854\pi$
$618$	2.94790e7	−	5.10592e7i	0.124896	−	0.216326i
$619$	1.20117e8	−	6.93494e7i	0.506444	−	0.292396i	−0.224927	−	0.974376i	$-0.572214\pi$
$619$	1.20117e8	−	6.93494e7i	0.506444	−	0.292396i	0.731371	+	0.681980i	$0.238881\pi$
$620$	1.00691e8	+	1.74403e8i	0.422491	+	0.731776i
$621$	5.17355e7	+	2.98695e7i	0.216030	+	0.124725i
$622$			1.20275e8i			0.499809i
$623$	−6.14183e7	+	6.58903e7i	−0.254000	+	0.272494i
$624$	1.91942e7			0.0789979
$625$	1.58233e7	−	2.74068e7i	0.0648124	−	0.112258i
$626$	5.86869e7	−	3.38829e7i	0.239231	−	0.138120i
$627$	−9.27178e6	−	1.60592e7i	−0.0376150	−	0.0651510i
$628$	−6.31107e7	−	3.64370e7i	−0.254814	−	0.147117i
$629$			6.39043e7i			0.256790i
$630$	−2.43286e7	−	5.61142e6i	−0.0972961	−	0.0224415i
$631$	−1.98716e8			−0.790944			−0.395472	−	0.918478i	$-0.629419\pi$
$631$	−1.98716e8			−0.790944			−0.395472	+	0.918478i	$0.629419\pi$
$632$	−6.88100e6	+	1.19182e7i	−0.0272584	+	0.0472129i
$633$	1.42014e7	−	8.19920e6i	0.0559914	−	0.0323266i
$634$	−3.67812e7	−	6.37069e7i	−0.144331	−	0.249988i
$635$	−1.18462e8	−	6.83941e7i	−0.462656	−	0.267114i
$636$			1.58628e8i			0.616608i
$637$	−3.58906e7	+	7.36636e7i	−0.138855	+	0.284993i
$638$	−3.71523e7			−0.143062
$639$	1.89693e7	−	3.28557e7i	0.0727022	−	0.125924i
$640$	−1.50095e8	+	8.66573e7i	−0.572567	+	0.330571i
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	0.695857	−	0.718180i	$-0.255025\pi$
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	−0.969891	+	0.243540i	$0.921691\pi$
$642$	5.71995e7	+	3.30242e7i	0.216166	+	0.124803i
$643$		−	2.68271e8i		−	1.00911i	−0.863378	−	0.504557i	$-0.831656\pi$
$643$		−	2.68271e8i		−	1.00911i	0.863378	−	0.504557i	$-0.168344\pi$
$644$	−6.19948e7	+	2.68781e8i	−0.232112	+	1.00633i
$645$	−1.95764e8			−0.729548
$646$	3.04840e7	−	5.27999e7i	0.113077	−	0.195855i
$647$	−3.38971e8	+	1.95705e8i	−1.25155	+	0.722585i	−0.971418	−	0.237375i	$-0.923713\pi$
$647$	−3.38971e8	+	1.95705e8i	−1.25155	+	0.722585i	−0.280136	+	0.959960i	$0.590380\pi$
$648$	−1.22445e7	−	2.12081e7i	−0.0450003	−	0.0779428i
$649$	1.48427e8	+	8.56944e7i	0.542974	+	0.313486i
$650$			2.19194e7i			0.0798158i
$651$	−1.85966e8	−	1.73344e8i	−0.674046	−	0.628299i
$652$	2.84179e8			1.02529
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	0.0713566	+	0.997451i	$0.477267\pi$
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	−0.899496	+	0.436929i	$0.856066\pi$
$654$	−3.57412e7	+	2.06352e7i	−0.127772	+	0.0737692i
$655$	−8.55845e7	−	1.48237e8i	−0.304559	−	0.527512i
$656$	5.84318e7	+	3.37356e7i	0.206984	+	0.119503i
$657$		−	9.12561e7i		−	0.321785i
$658$	1.81969e7	+	5.94754e7i	0.0638732	+	0.208766i
$659$	2.90612e8			1.01545			0.507724	−	0.861520i	$-0.330487\pi$
$659$	2.90612e8			1.01545			0.507724	+	0.861520i	$0.330487\pi$
$660$	−1.46114e7	+	2.53076e7i	−0.0508228	+	0.0880277i
$661$	−2.43164e8	+	1.40391e8i	−0.841965	+	0.486109i	−0.857932	−	0.513764i	$-0.828251\pi$
$661$	−2.43164e8	+	1.40391e8i	−0.841965	+	0.486109i	0.0159666	+	0.999873i	$0.494917\pi$
$662$	−3.85082e7	−	6.66981e7i	−0.132733	−	0.229900i
$663$	5.91421e7	+	3.41457e7i	0.202935	+	0.117164i
$664$			4.08496e8i			1.39535i
$665$	−7.32183e7	+	2.24016e7i	−0.248975	+	0.0761752i
$666$	−8.90383e6			−0.0301408
$667$	1.83527e8	−	3.17878e8i	0.618475	−	1.07123i
$668$	9.90926e7	−	5.72111e7i	0.332439	−	0.191934i
$669$	7.76784e7	+	1.34543e8i	0.259431	+	0.449348i
$670$	9.96886e7	+	5.75553e7i	0.331452	+	0.191364i
$671$		−	5.21480e6i		−	0.0172611i
$672$	1.20010e8	−	1.28749e8i	0.395468	−	0.424262i
$673$	−2.35293e8			−0.771904			−0.385952	−	0.922519i	$-0.626127\pi$
$673$	−2.35293e8			−0.771904			−0.385952	+	0.922519i	$0.626127\pi$
$674$	−3.58530e7	+	6.20992e7i	−0.117097	+	0.202818i
$675$	−2.86264e7	+	1.65274e7i	−0.0930796	+	0.0537396i
$676$	1.10699e8	+	1.91736e8i	0.358346	+	0.620673i
$677$	−5.35332e8	−	3.09074e8i	−1.72527	−	0.996085i	−0.906835	−	0.421486i	$-0.861509\pi$
$677$	−5.35332e8	−	3.09074e8i	−1.72527	−	0.996085i	−0.818435	−	0.574599i	$-0.805158\pi$
$678$		−	1.15208e8i		−	0.369653i
$679$	−1.92228e8	−	4.43377e7i	−0.614056	−	0.141633i
$680$	−2.16665e8			−0.689069
$681$	1.43966e8	−	2.49357e8i	0.455848	−	0.789552i
$682$	6.57295e7	−	3.79490e7i	0.207208	−	0.119632i
$683$	−6.53722e6	−	1.13228e7i	−0.0205178	−	0.0355379i	0.855584	−	0.517664i	$-0.173198\pi$
$683$	−6.53722e6	−	1.13228e7i	−0.0205178	−	0.0355379i	−0.876102	+	0.482126i	$0.839865\pi$
$684$	−2.88416e7	−	1.66517e7i	−0.0901262	−	0.0520344i
$685$		−	2.68214e8i		−	0.834468i
$686$	5.22391e7	+	1.35837e8i	0.161817	+	0.420770i
$687$	2.12248e8			0.654595
$688$	1.33648e8	−	2.31485e8i	0.410390	−	0.710817i
$689$	1.20369e8	−	6.94949e7i	0.368007	−	0.212469i
$690$	3.68209e7	+	6.37756e7i	0.112085	+	0.194137i
$691$	2.37346e8	+	1.37032e8i	0.719362	+	0.415324i	0.814518	−	0.580138i	$-0.197002\pi$
$691$	2.37346e8	+	1.37032e8i	0.719362	+	0.415324i	−0.0951555	+	0.995462i	$0.530335\pi$
$692$		−	3.50855e8i		−	1.05879i
$693$	8.29126e6	−	3.59471e7i	0.0249127	−	0.108010i
$694$	1.19878e8			0.358643
$695$	−1.68908e8	+	2.92558e8i	−0.503149	+	0.871480i
$696$	−1.30308e8	+	7.52336e7i	−0.386496	+	0.223143i
$697$	1.20029e8	+	2.07896e8i	0.354476	+	0.613971i
$698$	8.05349e7	+	4.64968e7i	0.236820	+	0.136728i
$699$			159096.i			0.000465831i
$700$	−1.11646e8	−	1.04069e8i	−0.325498	−	0.303407i
$701$	4.35624e8			1.26461			0.632307	−	0.774718i	$-0.282108\pi$
$701$	4.35624e8			1.26461			0.632307	+	0.774718i	$0.282108\pi$
$702$	−4.75754e6	+	8.24031e6i	−0.0137522	+	0.0238195i
$703$	−2.36475e7	+	1.36529e7i	−0.0680644	+	0.0392970i
$704$	1.23393e6	+	2.13723e6i	0.00353649	+	0.00612539i
$705$	−5.63779e7	−	3.25498e7i	−0.160895	−	0.0928925i
$706$			2.00740e8i			0.570454i
$707$	−7.35448e7	−	2.40377e8i	−0.208110	−	0.680197i
$708$	3.07807e8			0.867318
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	−0.492369	−	0.870387i	$-0.663869\pi$
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	0.999961	−	0.00878924i	$-0.00279774\pi$
$710$	4.05020e7	−	2.33839e7i	0.113162	−	0.0653343i
$711$	4.03181e6	+	6.98330e6i	0.0112174	+	0.0194291i
$712$	−9.43202e7	−	5.44558e7i	−0.261315	−	0.150870i
$713$			7.49848e8i			2.06873i
$714$	1.15984e8	−	3.54860e7i	0.318642	−	0.0974904i
$715$	2.56049e7			0.0700495
$716$	−2.01241e8	+	3.48560e8i	−0.548249	+	0.949595i
$717$	3.36916e7	−	1.94518e7i	0.0914037	−	0.0527720i
$718$	−2.91663e7	−	5.05174e7i	−0.0787966	−	0.136480i
$719$	−2.12503e8	−	1.22689e8i	−0.571713	−	0.330079i	0.186120	−	0.982527i	$-0.440409\pi$
$719$	−2.12503e8	−	1.22689e8i	−0.571713	−	0.330079i	−0.757833	+	0.652448i	$0.773742\pi$
$720$			3.56814e7i			0.0955969i
$721$	2.45265e8	−	2.63123e8i	0.654380	−	0.702026i
$722$	−1.43620e8			−0.381595
$723$	−4.26377e7	+	7.38506e7i	−0.112818	+	0.195407i
$724$	1.16426e8	−	6.72188e7i	0.306786	−	0.177123i
$725$	1.01549e8	+	1.75888e8i	0.266479	+	0.461555i
$726$	−7.67153e7	−	4.42916e7i	−0.200480	−	0.115747i
$727$		−	2.59949e8i		−	0.676526i	−0.941052	−	0.338263i	$-0.890161\pi$
$727$		−	2.59949e8i		−	0.676526i	0.941052	−	0.338263i	$-0.109839\pi$
$728$	−9.65415e7	−	2.22674e7i	−0.250219	−	0.0577133i
$729$	−1.43489e7			−0.0370370
$730$	5.62468e7	−	9.74223e7i	0.144587	−	0.250432i
$731$	8.23606e8	−	4.75509e8i	2.10847	−	1.21733i
$732$	−4.68277e6	−	8.11080e6i	−0.0119390	−	0.0206790i
$733$	−1.08280e8	−	6.25152e7i	−0.274938	−	0.158735i	0.356192	−	0.934413i	$-0.384075\pi$
$733$	−1.08280e8	−	6.25152e7i	−0.274938	−	0.158735i	−0.631129	+	0.775678i	$0.717408\pi$
$734$		−	4.04915e7i		−	0.102394i
$735$	−1.36938e8	−	6.67195e7i	−0.344876	−	0.168031i
$736$	−5.19138e8			−1.30212
$737$	−8.50418e7	+	1.47297e8i	−0.212437	+	0.367951i
$738$	−2.89663e7	+	1.67237e7i	−0.0720649	+	0.0416067i
$739$	2.82361e8	+	4.89063e8i	0.699634	+	1.21180i	0.968593	+	0.248650i	$0.0799869\pi$
$739$	2.82361e8	+	4.89063e8i	0.699634	+	1.21180i	−0.268960	+	0.963151i	$0.586680\pi$
$740$	3.72661e7	+	2.15156e7i	0.0919641	+	0.0530955i
$741$			2.91804e7i			0.0717194i
$742$	5.54813e7	−	2.40542e8i	0.135811	−	0.588815i
$743$	2.68677e8			0.655035			0.327518	−	0.944845i	$-0.393788\pi$
$743$	2.68677e8			0.655035			0.327518	+	0.944845i	$0.393788\pi$
$744$	1.53694e8	−	2.66205e8i	0.373196	−	0.646394i
$745$	2.01029e8	−	1.16064e8i	0.486171	−	0.280691i
$746$	7.21256e7	+	1.24925e8i	0.173729	+	0.300908i
$747$	2.07284e8	+	1.19676e8i	0.497285	+	0.287107i
$748$		−	1.41964e8i		−	0.339213i
$749$	2.94766e8	+	2.74760e8i	0.701507	+	0.653896i
$750$	−1.13709e8			−0.269533
$751$	−1.95480e8	+	3.38581e8i	−0.461512	+	0.799362i	−0.999037	−	0.0438862i	$-0.986026\pi$
$751$	−1.95480e8	+	3.38581e8i	−0.461512	+	0.799362i	0.537525	+	0.843248i	$0.319359\pi$
$752$	7.69783e7	−	4.44434e7i	0.181015	−	0.104509i
$753$	−1.70245e7	−	2.94873e7i	−0.0398740	−	0.0690637i
$754$	5.06308e7	+	2.92317e7i	0.118114	+	0.0681930i
$755$		−	5.00927e7i		−	0.116395i
$756$	−1.93840e7	−	6.33555e7i	−0.0448619	−	0.146629i
$757$	−5.67872e8			−1.30907			−0.654535	−	0.756031i	$-0.727136\pi$
$757$	−5.67872e8			−1.30907			−0.654535	+	0.756031i	$0.727136\pi$
$758$	5.26726e7	−	9.12317e7i	0.120942	−	0.209478i
$759$	−9.42327e7	+	5.44053e7i	−0.215515	+	0.124427i
$760$	−4.62897e7	−	8.01762e7i	−0.105449	−	0.182644i
$761$	−1.66316e8	−	9.60225e7i	−0.377381	−	0.217881i	0.299297	−	0.954160i	$-0.403248\pi$
$761$	−1.66316e8	−	9.60225e7i	−0.377381	−	0.217881i	−0.676678	+	0.736279i	$0.736581\pi$
$762$			9.25873e7i			0.209260i
$763$	−2.40776e8	+	7.36667e7i	−0.542049	+	0.165843i
$764$	−6.29378e8			−1.41134
$765$	−6.34758e7	+	1.09943e8i	−0.141783	+	0.245575i
$766$	1.43243e8	−	8.27015e7i	0.318704	−	0.184004i
$767$	−1.34850e8	−	2.33567e8i	−0.298858	−	0.517637i
$768$	1.06412e8	+	6.14368e7i	0.234912	+	0.135627i
$769$			7.75766e8i			1.70589i	0.521999	+	0.852946i	$0.325187\pi$
$769$			7.75766e8i			1.70589i	−0.521999	+	0.852946i	$0.674813\pi$
$770$	3.10080e7	−	3.32657e7i	0.0679205	−	0.0728659i
$771$	−4.90748e8			−1.07077
$772$	−3.41457e8	+	5.91421e8i	−0.742138	+	1.28542i
$773$	2.34180e7	−	1.35204e7i	0.0507005	−	0.0292719i	−0.474436	−	0.880290i	$-0.657348\pi$
$773$	2.34180e7	−	1.35204e7i	0.0507005	−	0.0292719i	0.525136	+	0.851018i	$0.324014\pi$
$774$	6.62530e7	+	1.14754e8i	0.142884	+	0.247482i
$775$	−3.59320e8	−	2.07453e8i	−0.771926	−	0.445672i
$776$		−	2.38527e8i		−	0.510448i
$777$	−5.29330e7	−	1.22091e7i	−0.112840	−	0.0260267i
$778$	−5.57154e7			−0.118314
$779$	−5.12874e7	+	8.88323e7i	−0.108492	+	0.187914i
$780$	3.98244e7	−	2.29926e7i	0.0839200	−	0.0484512i
$781$	3.45512e7	+	5.98445e7i	0.0725288	+	0.125624i
$782$	−3.09821e8	−	1.78875e8i	−0.647874	−	0.374050i
$783$			8.81638e7i			0.183656i
$784$	1.72381e8	−	1.16376e8i	0.357719	−	0.241499i
$785$	−1.18699e8			−0.245379
$786$	−5.79293e7	+	1.00336e8i	−0.119297	+	0.206629i
$787$	−3.68573e8	+	2.12796e8i	−0.756136	+	0.436555i	−0.827907	−	0.560866i	$-0.810468\pi$
$787$	−3.68573e8	+	2.12796e8i	−0.756136	+	0.436555i	0.0717707	+	0.997421i	$0.477135\pi$
$788$	−2.40297e8	−	4.16207e8i	−0.491100	−	0.850610i
$789$	−8.87979e7	−	5.12675e7i	−0.180789	−	0.104379i
$790$			9.94022e6i			0.0201611i
$791$	1.57975e8	−	6.84910e8i	0.319198	−	1.38390i
$792$	4.46050e7			0.0897859
$793$	−4.10303e6	+	7.10666e6i	−0.00822783	+	0.0142510i
$794$	9.18709e7	−	5.30417e7i	0.183534	−	0.105963i
$795$	1.29189e8	+	2.23762e8i	0.257113	+	0.445333i
$796$	2.50702e8	+	1.44743e8i	0.497072	+	0.286985i
$797$		−	7.51386e7i		−	0.148419i	−0.997243	−	0.0742093i	$-0.976357\pi$
$797$		−	7.51386e7i		−	0.148419i	0.997243	−	0.0742093i	$-0.0236433\pi$
$798$	3.79109e7	+	3.53379e7i	0.0746029	+	0.0695397i
$799$	3.16253e8			0.620003
$800$	1.43625e8	−	2.48766e8i	0.280518	−	0.485871i
$801$	−5.52654e7	+	3.19075e7i	−0.107536	+	0.0620862i
$802$	−2.05590e8	−	3.56093e8i	−0.398547	−	0.690304i
$803$	1.43948e8	+	8.31084e7i	0.278009	+	0.160509i
$804$			3.05462e8i			0.587746i
$805$	1.31449e8	+	4.29633e8i	0.251982	+	0.823589i
$806$	−1.19434e8			−0.228099
$807$	1.71378e6	−	2.96835e6i	0.00326088	−	0.00564801i
$808$	2.63220e8	−	1.51970e8i	0.498981	−	0.288087i
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	0.953051	+	0.302810i	$0.0979246\pi$
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	−0.214285	+	0.976771i	$0.568742\pi$
$810$	−1.53185e7	−	8.84412e6i	−0.0288244	−	0.0166418i
$811$		−	8.00635e8i		−	1.50097i	−0.660888	−	0.750485i	$-0.729820\pi$
$811$		−	8.00635e8i		−	1.50097i	0.660888	−	0.750485i	$-0.270180\pi$
$812$	−3.89274e8	+	1.19101e8i	−0.727089	+	0.222457i
$813$	−4.33948e8			−0.807544
$814$	8.10887e6	−	1.40450e7i	0.0150344	−	0.0260404i
$815$	4.00863e8	−	2.31439e8i	0.740497	−	0.427526i
$816$	−8.66697e7	−	1.50116e8i	−0.159513	−	0.276285i
$817$	3.51921e8	+	2.03181e8i	0.645325	+	0.372579i
$818$		−	1.24637e8i		−	0.227712i
$819$	−3.95827e7	+	4.24647e7i	−0.0720532	+	0.0772995i
$820$	1.61647e8			0.293175
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	−0.714200	−	0.699942i	$-0.753209\pi$
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	0.963267	+	0.268544i	$0.0865426\pi$
$822$	−1.57223e8	+	9.07725e7i	−0.283074	+	0.163433i
$823$	3.78952e8	+	6.56364e8i	0.679806	+	1.17746i	0.975039	+	0.222033i	$0.0712693\pi$
$823$	3.78952e8	+	6.56364e8i	0.679806	+	1.17746i	−0.295233	+	0.955425i	$0.595397\pi$
$824$	3.76654e8	+	2.17461e8i	0.673226	+	0.388687i
$825$		−	6.02072e7i		−	0.107223i
$826$	−4.66754e8	−	1.07657e8i	−0.828224	−	0.191031i
$827$	3.06595e8			0.542061			0.271030	−	0.962571i	$-0.412636\pi$
$827$	3.06595e8			0.542061			0.271030	+	0.962571i	$0.412636\pi$
$828$	−9.77095e7	+	1.69238e8i	−0.172126	+	0.298130i
$829$	1.07092e8	−	6.18296e7i	0.187972	−	0.108526i	−0.403061	−	0.915173i	$-0.632054\pi$
$829$	1.07092e8	−	6.18296e7i	0.187972	−	0.108526i	0.591033	+	0.806647i	$0.298720\pi$
$830$	1.47527e8	+	2.55525e8i	0.258011	+	0.446888i
$831$	7.76858e7	+	4.48519e7i	0.135375	+	0.0781588i
$832$		−	3.88346e6i		−	0.00674293i
$833$	7.38180e8	−	5.19240e7i	1.27711	−	0.0898325i
$834$	2.28657e8			0.394172
$835$	9.31869e7	−	1.61405e8i	0.160065	−	0.277240i
$836$	5.25330e7	−	3.03300e7i	0.0899112	−	0.0519102i
$837$	−9.00542e7	−	1.55978e8i	−0.153577	−	0.266004i
$838$	1.16781e8	+	6.74238e7i	0.198446	+	0.114573i
$839$		−	2.04720e8i		−	0.346637i	−0.984866	−	0.173318i	$-0.944551\pi$
$839$		−	2.04720e8i		−	0.346637i	0.984866	−	0.173318i	$-0.0554489\pi$
$840$	4.13944e7	−	1.79468e8i	0.0698400	−	0.302795i
$841$	−5.31198e7			−0.0893035
$842$	−1.07097e8	+	1.85497e8i	−0.179407	+	0.310743i
$843$	2.37374e8	−	1.37048e8i	0.396233	−	0.228765i
$844$	2.68213e7	+	4.64559e7i	0.0446121	+	0.0772705i
$845$	3.12304e8	+	1.80309e8i	0.517615	+	0.298845i
$846$			4.40637e7i			0.0727729i
$847$	−3.95337e8	−	3.68505e8i	−0.650604	−	0.606448i
$848$	−3.52789e8			−0.578532
$849$	1.14719e8	−	1.98699e8i	0.187462	−	0.324693i
$850$	1.71430e8	−	9.89754e7i	0.279146	−	0.161165i
$851$	8.01131e7	+	1.38760e8i	0.129991	+	0.225152i
$852$	1.07478e8	+	6.20525e7i	0.173780	+	0.100332i
$853$			1.81851e8i			0.293001i	0.989211	+	0.146500i	$0.0468010\pi$
$853$			1.81851e8i			0.293001i	−0.989211	+	0.146500i	$0.953199\pi$
$854$	4.26408e6	+	1.39369e7i	0.00684624	+	0.0223766i
$855$	−5.42454e7			−0.0867890
$856$	−2.43613e8	+	4.21950e8i	−0.388400	+	0.672729i
$857$	−5.32176e8	+	3.07252e8i	−0.845499	+	0.488149i	−0.859130	−	0.511758i	$-0.828994\pi$
$857$	−5.32176e8	+	3.07252e8i	−0.845499	+	0.488149i	0.0136307	+	0.999907i	$0.495661\pi$
$858$	−8.66554e6	−	1.50092e7i	−0.0137194	−	0.0237626i
$859$	−1.89532e8	−	1.09426e8i	−0.299022	−	0.172640i	0.342981	−	0.939342i	$-0.388563\pi$
$859$	−1.89532e8	−	1.09426e8i	−0.299022	−	0.172640i	−0.642003	+	0.766702i	$0.721897\pi$
$860$		−	6.40386e8i		−	1.00681i
$861$	−1.95135e8	+	5.97028e7i	−0.305722	+	0.0935374i
$862$	2.14729e8			0.335250
$863$	3.29715e8	−	5.71084e8i	0.512988	−	0.888521i	−0.486899	−	0.873458i	$-0.661872\pi$
$863$	3.29715e8	−	5.71084e8i	0.512988	−	0.888521i	0.999887	−	0.0150623i	$-0.00479467\pi$
$864$	1.07988e8	−	6.23467e7i	0.167430	−	0.0966657i
$865$	−2.85741e8	−	4.94918e8i	−0.441494	−	0.764689i
$866$	2.00121e8	+	1.15540e8i	0.308133	+	0.177901i
$867$		−	2.40461e8i		−	0.368967i
$868$	5.67045e8	−	6.08333e8i	0.867079	−	0.930212i
$869$	−1.46873e7			−0.0223812
$870$	−5.43408e7	+	9.41211e7i	−0.0825218	+	0.142932i
$871$	2.31788e8	−	1.33823e8i	0.350781	−	0.202524i
$872$	−1.52222e8	−	2.63656e8i	−0.229577	−	0.397639i
$873$	−1.21036e8	−	6.98804e7i	−0.181917	−	0.105030i
$874$		−	1.52864e8i		−	0.228966i
$875$	−6.75998e8	−	1.55920e8i	−1.00907	−	0.232743i
$876$	2.98518e8			0.444077
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	−0.919908	−	0.392135i	$-0.871737\pi$
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	0.799552	+	0.600596i	$0.205070\pi$
$878$	−4.75256e8	+	2.74389e8i	−0.702173	+	0.405400i
$879$	2.72598e7	+	4.72153e7i	0.0401380	+	0.0695210i
$880$	−5.62840e7	−	3.24956e7i	−0.0825918	−	0.0476844i
$881$			8.48365e8i			1.24067i	0.784338	+	0.620333i	$0.213003\pi$
$881$			8.48365e8i			1.24067i	−0.784338	+	0.620333i	$0.786997\pi$
$882$	7.23461e6	+	1.02851e8i	0.0105441	+	0.149900i
$883$	3.14592e8			0.456947			0.228473	−	0.973550i	$-0.426627\pi$
$883$	3.14592e8			0.456947			0.228473	+	0.973550i	$0.426627\pi$
$884$	−1.11698e8	+	1.93466e8i	−0.161692	+	0.280058i
$885$	4.34193e8	−	2.50682e8i	0.626402	−	0.361654i
$886$	6.23635e7	+	1.08017e8i	0.0896663	+	0.155307i
$887$	−7.25058e8	−	4.18612e8i	−1.03897	−	0.599848i	−0.119426	−	0.992843i	$-0.538106\pi$
$887$	−7.25058e8	−	4.18612e8i	−1.03897	−	0.599848i	−0.919540	+	0.392995i	$0.871439\pi$
$888$		−	6.56819e7i		−	0.0938009i
$889$	−1.26957e8	+	5.50429e8i	−0.180697	+	0.783422i
$890$	−7.86663e7			−0.111588
$891$	1.30678e7	−	2.26341e7i	0.0184743	−	0.0319985i
$892$	−4.40119e8	+	2.54103e8i	−0.620119	+	0.358026i
$893$	6.75662e7	+	1.17028e8i	0.0948800	+	0.164337i
$894$	−1.36069e8	−	7.85597e7i	−0.190436	−	0.109948i
$895$			6.55573e8i			0.914433i
$896$	5.23545e8	+	4.88012e8i	0.727830	+	0.678432i
$897$	1.71226e8			0.237242
$898$	−2.41267e8	+	4.17886e8i	−0.333172	+	0.577070i
$899$	−9.58376e8	+	5.53319e8i	−1.31904	+	0.761546i
$900$	−5.40647e7	−	9.36429e7i	−0.0741629	−	0.128454i
$901$	−1.08703e9	−	6.27598e8i	−1.48617	−	0.858039i
$902$		−	6.09222e7i		−	0.0830148i
$903$	2.36520e8	+	7.73054e8i	0.321222	+	1.04990i
$904$	8.49870e8			1.15040
$905$	1.09488e8	−	1.89638e8i	0.147713	−	0.255847i
$906$	−2.93635e7	+	1.69530e7i	−0.0394842	+	0.0227962i
$907$	−3.44024e8	−	5.95867e8i	−0.461070	−	0.798596i	0.537945	−	0.842980i	$-0.319201\pi$
$907$	−3.44024e8	−	5.95867e8i	−0.461070	−	0.798596i	−0.999015	+	0.0443839i	$0.985868\pi$
$908$	8.15700e8	+	4.70945e8i	1.08962	+	0.629090i
$909$		−	1.78089e8i		−	0.237107i
$910$	−6.84310e7	+	2.09369e7i	−0.0908089	+	0.0277835i
$911$	2.31613e8			0.306343			0.153171	−	0.988200i	$-0.451051\pi$
$911$	2.31613e8			0.306343			0.153171	+	0.988200i	$0.451051\pi$
$912$	3.70333e7	−	6.41436e7i	0.0488211	−	0.0845607i
$913$	−3.77555e8	+	2.17981e8i	−0.496098	+	0.286422i
$914$	2.75045e7	+	4.76393e7i	0.0360218	+	0.0623917i
$915$	−1.32111e7	−	7.62741e6i	−0.0172455	−	0.00995667i
$916$			6.94307e8i			0.903369i
$917$	−4.81971e8	+	5.17064e8i	−0.625047	+	0.670557i
$918$	8.59292e7			0.111074
$919$	5.62582e8	−	9.74420e8i	0.724835	−	1.25545i	−0.234207	−	0.972187i	$-0.575249\pi$
$919$	5.62582e8	−	9.74420e8i	0.724835	−	1.25545i	0.959042	−	0.283264i	$-0.0914174\pi$
$920$	−4.70461e8	+	2.71621e8i	−0.604171	+	0.348818i
$921$	−3.11530e8	−	5.39587e8i	−0.398769	−	0.690689i
$922$	9.52653e7	+	5.50014e7i	0.121546	+	0.0701748i
$923$		−	1.08740e8i		−	0.138289i
$924$	1.17591e8	+	2.71225e7i	0.149059	+	0.0343806i
$925$	−8.86565e7			−0.112017
$926$	−2.91515e8	+	5.04918e8i	−0.367136	+	0.635899i
$927$	2.20694e8	−	1.27418e8i	0.277046	−	0.159953i
$928$	−3.83076e8	−	6.63507e8i	−0.479337	−	0.830237i
$929$	−5.93421e8	−	3.42612e8i	−0.740143	−	0.427322i	0.0819782	−	0.996634i	$-0.473876\pi$
$929$	−5.93421e8	−	3.42612e8i	−0.740143	−	0.427322i	−0.822121	+	0.569312i	$0.807210\pi$
$930$		−	2.22024e8i		−	0.276027i
$931$	1.76923e8	+	2.62067e8i	0.219248	+	0.324761i
$932$	−520438.			−0.000642867
$933$	−2.59933e8	+	4.50218e8i	−0.320049	+	0.554342i
$934$	2.05871e8	−	1.18860e8i	0.252670	−	0.145879i
$935$	−1.15617e8	−	2.00254e8i	−0.141445	−	0.244989i
$936$	−6.07872e7	−	3.50955e7i	−0.0741284	−	0.0427980i
$937$		−	7.87984e8i		−	0.957852i	−0.877855	−	0.478926i	$-0.841026\pi$
$937$		−	7.87984e8i		−	0.957852i	0.877855	−	0.478926i	$-0.158974\pi$
$938$	1.06837e8	−	4.63199e8i	0.129454	−	0.561253i
$939$	2.92905e8			0.353778
$940$	1.06477e8	−	1.84424e8i	0.128196	−	0.222041i
$941$	1.79551e8	−	1.03664e8i	0.215486	−	0.124411i	−0.388372	−	0.921503i	$-0.626963\pi$
$941$	1.79551e8	−	1.03664e8i	0.215486	−	0.124411i	0.603859	+	0.797092i	$0.293629\pi$
$942$	4.01716e7	+	6.95793e7i	0.0480581	+	0.0832391i
$943$	5.21254e8	+	3.00946e8i	0.621604	+	0.358883i
$944$			6.84561e8i			0.813759i
$945$	−7.89406e7	−	7.35830e7i	−0.0935417	−	0.0871930i
$946$	−2.41351e8			−0.285086
$947$	1.77030e8	−	3.06624e8i	0.208447	−	0.361041i	−0.742778	−	0.669537i	$-0.766492\pi$
$947$	1.77030e8	−	3.06624e8i	0.208447	−	0.361041i	0.951226	+	0.308496i	$0.0998258\pi$
$948$	−2.28439e7	+	1.31889e7i	−0.0268129	+	0.0154805i
$949$	−1.30780e8	−	2.26518e8i	−0.153019	−	0.265036i
$950$	7.32509e7	+	4.22914e7i	0.0854363	+	0.0493267i
$951$		−	3.17960e8i		−	0.369685i
$952$	2.61773e8	+	8.55592e8i	0.303399	+	0.991644i
$953$	−4.28652e8			−0.495252			−0.247626	−	0.968856i	$-0.579650\pi$
$953$	−4.28652e8			−0.495252			−0.247626	+	0.968856i	$0.579650\pi$
$954$	8.74436e7	−	1.51457e8i	0.100712	−	0.174439i
$955$	−8.87803e8	+	5.12573e8i	−1.01931	+	0.588499i
$956$	6.36311e7	+	1.10212e8i	0.0728276	+	0.126141i
$957$	−1.39070e8	−	8.02922e7i	−0.158671	−	0.0916089i
$958$			3.31711e8i			0.377280i
$959$	−1.05915e9	+	3.24054e8i	−1.20089	+	0.367419i
$960$	7.21923e6			0.00815975
$961$	6.86614e8	−	1.18925e9i	0.773646	−	1.33999i
$962$	−2.21013e7	+	1.27602e7i	−0.0248252	+	0.0143329i
$963$	1.42741e8	+	2.47235e8i	0.159834	+	0.276841i
$964$	−2.41581e8	−	1.39477e8i	−0.269669	−	0.155694i
$965$			1.11235e9i			1.23782i
$966$	2.07357e8	−	2.22455e8i	0.230032	−	0.246781i
$967$	1.16972e9			1.29361			0.646805	−	0.762655i	$-0.276105\pi$
$967$	1.16972e9			1.29361			0.646805	+	0.762655i	$0.276105\pi$
$968$	3.26731e8	−	5.65915e8i	0.360217	−	0.623914i
$969$	2.28218e8	−	1.31762e8i	0.250829	−	0.144816i
$970$	−8.61432e7	−	1.49204e8i	−0.0943856	−	0.163481i
$971$	6.09512e8	+	3.51902e8i	0.665770	+	0.384383i	0.794472	−	0.607301i	$-0.207748\pi$
$971$	6.09512e8	+	3.51902e8i	0.665770	+	0.384383i	−0.128702	+	0.991683i	$0.541081\pi$
$972$		−	4.69383e7i		−	0.0511127i
$973$	1.35936e9	+	3.13537e8i	1.47569	+	0.340370i
$974$	6.87949e8			0.744525
$975$	−4.73714e7	+	8.20497e7i	−0.0511096	+	0.0885244i
$976$	1.80384e7	−	1.04145e7i	0.0194021	−	0.0112018i
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	0.722710	−	0.691151i	$-0.242896\pi$
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	−0.959910	+	0.280310i	$0.909563\pi$
$978$	−2.71331e8	−	1.56653e8i	−0.290056	−	0.167464i
$979$		−	1.16235e8i		−	0.123876i
$980$	2.18254e8	−	4.47954e8i	0.231891	−	0.475944i
$981$	−1.78384e8			−0.188951
$982$	1.59679e8	−	2.76571e8i	0.168621	−	0.292061i
$983$	−1.01182e9	+	5.84175e8i	−1.06523	+	0.615011i	−0.926874	−	0.375372i	$-0.877515\pi$
$983$	−1.01182e9	+	5.84175e8i	−1.06523	+	0.615011i	−0.138355	+	0.990383i	$0.544182\pi$
$984$	−1.23368e8	−	2.13679e8i	−0.129484	−	0.224273i
$985$	−6.77928e8	−	3.91402e8i	−0.709374	−	0.409557i
$986$		−	5.27974e8i		−	0.550784i
$987$	−6.04208e7	+	2.61957e8i	−0.0628398	+	0.272445i
$988$	−9.54552e7			−0.0989758
$989$	1.19224e9	−	2.06501e9i	1.23246	−	2.13468i
$990$	2.79016e7	−	1.61090e7i	0.0287556	−	0.0166021i
$991$	5.01818e8	+	8.69174e8i	0.515615	+	0.893071i	0.999836	+	0.0181249i	$0.00576967\pi$
$991$	5.01818e8	+	8.69174e8i	0.515615	+	0.893071i	−0.484221	+	0.874946i	$0.660897\pi$
$992$	1.35547e9	+	7.82580e8i	1.38853	+	0.801666i
$993$		−	3.32890e8i		−	0.339979i
$994$	−1.41275e8	−	1.31687e8i	−0.143849	−	0.134086i
$995$	4.71522e8			0.478666
$996$	−3.91485e8	+	6.78072e8i	−0.396220	+	0.686274i
$997$	1.60115e9	−	9.24424e8i	1.61565	−	0.932794i	0.627619	−	0.778521i	$-0.284030\pi$
$997$	1.60115e9	−	9.24424e8i	1.61565	−	0.932794i	0.988028	−	0.154274i	$-0.0493037\pi$
$998$	−9.44016e7	−	1.63508e8i	−0.0949703	−	0.164493i
$999$	−3.33292e7	−	1.92426e7i	−0.0334294	−	0.0193005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.b.19.3	yes	8
3.2	odd	2		63.7.m.c.19.2		8
4.3	odd	2		336.7.bh.b.145.3		8
7.2	even	3		147.7.d.a.97.4		8
7.3	odd	6	inner	21.7.f.b.10.3	✓	8
7.4	even	3		147.7.f.a.31.3		8
7.5	odd	6		147.7.d.a.97.3		8
7.6	odd	2		147.7.f.a.19.3		8
21.2	odd	6		441.7.d.d.244.6		8
21.5	even	6		441.7.d.d.244.5		8
21.17	even	6		63.7.m.c.10.2		8
28.3	even	6		336.7.bh.b.241.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.3	✓	8	7.3	odd	6	inner
21.7.f.b.19.3	yes	8	1.1	even	1	trivial
63.7.m.c.10.2		8	21.17	even	6
63.7.m.c.19.2		8	3.2	odd	2
147.7.d.a.97.3		8	7.5	odd	6
147.7.d.a.97.4		8	7.2	even	3
147.7.f.a.19.3		8	7.6	odd	2
147.7.f.a.31.3		8	7.4	even	3
336.7.bh.b.145.3		8	4.3	odd	2
336.7.bh.b.241.3		8	28.3	even	6
441.7.d.d.244.5		8	21.5	even	6
441.7.d.d.244.6		8	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +(259.420 - 149.776i) q^{10} +(221.304 + 383.310i) q^{11} +(688.408 + 397.452i) q^{12} -696.494i q^{13} +(-904.880 - 843.466i) q^{14} +1294.76 q^{15} +(-883.932 + 1531.01i) q^{16} +(-5447.24 + 3144.96i) q^{17} +(-438.190 - 758.967i) q^{18} +(-2327.56 - 1343.82i) q^{19} +4235.44i q^{20} +(-1564.32 - 5112.89i) q^{21} +1596.27 q^{22} +(-7885.31 + 13657.8i) q^{23} +(5598.76 - 3232.44i) q^{24} +(-4363.11 - 7557.12i) q^{25} +(-2175.37 - 1255.95i) q^{26} -3788.00i q^{27} +(16725.3 - 5117.22i) q^{28} -23274.5 q^{29} +(2334.78 - 4043.95i) q^{30} +(41177.0 - 23773.6i) q^{31} +(16459.0 + 28507.9i) q^{32} +(5975.21 + 3449.79i) q^{33} +22684.6i q^{34} +(19425.3 - 20839.7i) q^{35} +12391.3 q^{36} +(5079.89 - 8798.64i) q^{37} +(-8394.35 + 4846.48i) q^{38} +(-5428.63 - 9402.67i) q^{39} +(29831.5 + 17223.2i) q^{40} -38165.4i q^{41} +(-18790.0 - 4333.95i) q^{42} -151197. q^{43} +(-11285.0 + 19546.2i) q^{44} +(17479.3 - 10091.7i) q^{45} +(28438.4 + 49256.7i) q^{46} +(-43543.1 - 25139.6i) q^{47} +27558.3i q^{48} +(-105763. - 51530.4i) q^{49} -31471.1 q^{50} +(-49025.1 + 84914.0i) q^{51} +(30758.1 - 17758.2i) q^{52} +(99778.2 + 172821. i) q^{53} +(-11831.1 - 6830.70i) q^{54} +36762.6i q^{55} +(31970.7 - 138611. i) q^{56} -41896.1 q^{57} +(-41969.8 + 72693.8i) q^{58} +(335347. - 193612. i) q^{59} +(33012.0 + 57178.4i) q^{60} +(-10203.5 - 5890.98i) q^{61} -171479. i q^{62} +(-60969.3 - 56831.3i) q^{63} +5575.73 q^{64} +(28925.0 - 50099.6i) q^{65} +(21549.6 - 12441.7i) q^{66} +(192138. + 332792. i) q^{67} +(-277772. - 160372. i) q^{68} +245840. i q^{69} +(-30060.4 - 98250.6i) q^{70} +156126. q^{71} +(50388.8 - 87276.0i) q^{72} +(325227. - 187770. i) q^{73} +(-18320.6 - 31732.3i) q^{74} +(-117804. - 68014.1i) q^{75} -137051. i q^{76} +(145172. - 44416.2i) q^{77} -39156.7 q^{78} +(-16591.8 + 28737.9i) q^{79} +(-127164. + 73418.4i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-119203. - 68821.8i) q^{82} +984986. i q^{83} +(185907. - 199444. i) q^{84} -522434. q^{85} +(-272646. + 472237. i) q^{86} +(-314206. + 181407. i) q^{87} +(91779.9 + 158967. i) q^{88} +(-227430. - 131307. i) q^{89} -72791.1i q^{90} +(-232786. - 53692.3i) q^{91} -804193. q^{92} +(370593. - 641886. i) q^{93} +(-157038. + 90666.0i) q^{94} +(-111616. - 193325. i) q^{95} +(444394. + 256571. i) q^{96} -575147. i q^{97} +(-351664. + 237411. i) q^{98} +107554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Introduction

L-functions

Modular forms

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