LMFDB - Embedded newform 198.6.e.b.67.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.7
Character	$\chi$	$=$	198.67
Dual form			198.6.e.b.133.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(3.31846 + 15.2311i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(25.8529 - 44.7785i) q^{5} +(-46.1253 + 41.9578i) q^{6} +(-53.8618 - 93.2913i) q^{7} -64.0000 q^{8} +(-220.976 + 101.088i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(3.31846 + 15.2311i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(25.8529 - 44.7785i) q^{5} +(-46.1253 + 41.9578i) q^{6} +(-53.8618 - 93.2913i) q^{7} -64.0000 q^{8} +(-220.976 + 101.088i) q^{9} +206.823 q^{10} +(-60.5000 - 104.789i) q^{11} +(-237.597 - 75.8672i) q^{12} +(315.102 - 545.773i) q^{13} +(215.447 - 373.165i) q^{14} +(767.820 + 245.173i) q^{15} +(-128.000 - 221.703i) q^{16} +1069.30 q^{17} +(-792.130 - 563.306i) q^{18} +570.408 q^{19} +(413.646 + 716.456i) q^{20} +(1242.20 - 1129.96i) q^{21} +(242.000 - 419.156i) q^{22} +(1164.30 - 2016.63i) q^{23} +(-212.382 - 974.793i) q^{24} +(225.757 + 391.022i) q^{25} +2520.82 q^{26} +(-2272.99 - 3030.25i) q^{27} +1723.58 q^{28} +(-2526.31 - 4375.69i) q^{29} +(686.335 + 3150.15i) q^{30} +(2557.35 - 4429.46i) q^{31} +(512.000 - 886.810i) q^{32} +(1395.29 - 1269.22i) q^{33} +(2138.60 + 3704.17i) q^{34} -5569.93 q^{35} +(367.088 - 3870.63i) q^{36} +5422.30 q^{37} +(1140.82 + 1975.95i) q^{38} +(9358.40 + 2988.24i) q^{39} +(-1654.58 + 2865.82i) q^{40} +(-4129.24 + 7152.06i) q^{41} +(6398.69 + 2043.17i) q^{42} +(3047.43 + 5278.30i) q^{43} +1936.00 q^{44} +(-1186.28 + 12508.4i) q^{45} +9314.39 q^{46} +(-2977.63 - 5157.41i) q^{47} +(2952.02 - 2685.30i) q^{48} +(2601.32 - 4505.61i) q^{49} +(-903.027 + 1564.09i) q^{50} +(3548.44 + 16286.7i) q^{51} +(5041.63 + 8732.36i) q^{52} +9344.52 q^{53} +(5951.14 - 13934.4i) q^{54} -6256.40 q^{55} +(3447.15 + 5970.65i) q^{56} +(1892.88 + 8687.97i) q^{57} +(10105.2 - 17502.8i) q^{58} +(4776.51 - 8273.15i) q^{59} +(-9539.78 + 8677.84i) q^{60} +(8741.51 + 15140.7i) q^{61} +20458.8 q^{62} +(21332.8 + 15170.3i) q^{63} +4096.00 q^{64} +(-16292.6 - 28219.6i) q^{65} +(7187.30 + 2294.98i) q^{66} +(-5429.23 + 9403.70i) q^{67} +(-8554.41 + 14816.7i) q^{68} +(34579.2 + 11041.5i) q^{69} +(-11139.9 - 19294.8i) q^{70} +14111.6 q^{71} +(14142.4 - 6469.63i) q^{72} -51306.5 q^{73} +(10844.6 + 18783.4i) q^{74} +(-5206.55 + 4736.13i) q^{75} +(-4563.27 + 7903.81i) q^{76} +(-6517.28 + 11288.3i) q^{77} +(8365.24 + 38394.9i) q^{78} +(-26375.3 - 45683.4i) q^{79} -13236.7 q^{80} +(38611.4 - 44676.0i) q^{81} -33033.9 q^{82} +(-5450.46 - 9440.47i) q^{83} +(5719.63 + 26252.1i) q^{84} +(27644.5 - 47881.7i) q^{85} +(-12189.7 + 21113.2i) q^{86} +(58263.3 - 52999.1i) q^{87} +(3872.00 + 6706.50i) q^{88} +74711.4 q^{89} +(-45702.9 + 20907.3i) q^{90} -67887.8 q^{91} +(18628.8 + 32266.0i) q^{92} +(75952.3 + 24252.4i) q^{93} +(11910.5 - 20629.6i) q^{94} +(14746.7 - 25542.0i) q^{95} +(15206.2 + 4855.50i) q^{96} +(-34110.2 - 59080.6i) q^{97} +20810.5 q^{98} +(23961.9 + 17040.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) $ 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	3.31846	+	15.2311i	0.212880	+	0.977078i
$3$	3.31846	+	15.2311i	0.212880	+	0.977078i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	25.8529	−	44.7785i	0.462470	−	0.801022i	−0.536613	−	0.843829i	$-0.680296\pi$
$5$	25.8529	−	44.7785i	0.462470	−	0.801022i	0.999083	+	0.0428062i	$0.0136298\pi$
$6$	−46.1253	+	41.9578i	−0.523072	+	0.475811i
$7$	−53.8618	−	93.2913i	−0.415466	−	0.719608i	0.580011	−	0.814609i	$-0.303048\pi$
$7$	−53.8618	−	93.2913i	−0.415466	−	0.719608i	−0.995477	+	0.0950001i	$0.969715\pi$
$8$	−64.0000			−0.353553
$9$	−220.976	+	101.088i	−0.909365	+	0.416000i
$10$	206.823			0.654032
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$12$	−237.597	−	75.8672i	−0.476307	−	0.152090i
$13$	315.102	−	545.773i	0.517122	−	0.895681i	−0.482681	−	0.875796i	$-0.660337\pi$
$13$	315.102	−	545.773i	0.517122	−	0.895681i	0.999802	−	0.0198846i	$-0.00632988\pi$
$14$	215.447	−	373.165i	0.293779	−	0.508840i
$15$	767.820	+	245.173i	0.881112	+	0.281349i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1069.30			0.897383			0.448691	−	0.893687i	$-0.351890\pi$
$17$	1069.30			0.897383			0.448691	+	0.893687i	$0.351890\pi$
$18$	−792.130	−	563.306i	−0.576256	−	0.409792i
$19$	570.408			0.362495			0.181247	−	0.983438i	$-0.441987\pi$
$19$	570.408			0.362495			0.181247	+	0.983438i	$0.441987\pi$
$20$	413.646	+	716.456i	0.231235	+	0.400511i
$21$	1242.20	−	1129.96i	0.614670	−	0.559133i
$22$	242.000	−	419.156i	0.106600	−	0.184637i
$23$	1164.30	−	2016.63i	0.458928	−	0.794887i	−0.539976	−	0.841680i	$-0.681567\pi$
$23$	1164.30	−	2016.63i	0.458928	−	0.794887i	0.998905	+	0.0467929i	$0.0149001\pi$
$24$	−212.382	−	974.793i	−0.0752643	−	0.345449i
$25$	225.757	+	391.022i	0.0722421	+	0.125127i
$26$	2520.82			0.731321
$27$	−2272.99	−	3030.25i	−0.600050	−	0.799963i
$28$	1723.58			0.415466
$29$	−2526.31	−	4375.69i	−0.557816	−	0.966166i	−0.997678	−	0.0681008i	$-0.978306\pi$
$29$	−2526.31	−	4375.69i	−0.557816	−	0.966166i	0.439862	−	0.898065i	$-0.355027\pi$
$30$	686.335	+	3150.15i	0.139230	+	0.639041i
$31$	2557.35	−	4429.46i	0.477954	−	0.827841i	−0.521726	−	0.853113i	$-0.674712\pi$
$31$	2557.35	−	4429.46i	0.477954	−	0.827841i	0.999681	+	0.0252718i	$0.00804512\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	1395.29	−	1269.22i	0.223038	−	0.202886i
$34$	2138.60	+	3704.17i	0.317273	+	0.549532i
$35$	−5569.93			−0.768563
$36$	367.088	−	3870.63i	0.0472078	−	0.497766i
$37$	5422.30			0.651147			0.325574	−	0.945517i	$-0.394443\pi$
$37$	5422.30			0.651147			0.325574	+	0.945517i	$0.394443\pi$
$38$	1140.82	+	1975.95i	0.128161	+	0.221982i
$39$	9358.40	+	2988.24i	0.985235	+	0.314596i
$40$	−1654.58	+	2865.82i	−0.163508	+	0.283204i
$41$	−4129.24	+	7152.06i	−0.383628	+	0.664464i	−0.991578	−	0.129512i	$-0.958659\pi$
$41$	−4129.24	+	7152.06i	−0.383628	+	0.664464i	0.607950	+	0.793976i	$0.291992\pi$
$42$	6398.69	+	2043.17i	0.559716	+	0.178723i
$43$	3047.43	+	5278.30i	0.251340	+	0.435334i	0.963895	−	0.266282i	$-0.0857953\pi$
$43$	3047.43	+	5278.30i	0.251340	+	0.435334i	−0.712555	+	0.701617i	$0.752462\pi$
$44$	1936.00			0.150756
$45$	−1186.28	+	12508.4i	−0.0873288	+	0.920809i
$46$	9314.39			0.649023
$47$	−2977.63	−	5157.41i	−0.196619	−	0.340555i	0.750811	−	0.660517i	$-0.229663\pi$
$47$	−2977.63	−	5157.41i	−0.196619	−	0.340555i	−0.947430	+	0.319963i	$0.896330\pi$
$48$	2952.02	−	2685.30i	0.184934	−	0.168225i
$49$	2601.32	−	4505.61i	0.154776	−	0.268080i
$50$	−903.027	+	1564.09i	−0.0510829	+	0.0884782i
$51$	3548.44	+	16286.7i	0.191034	+	0.876813i
$52$	5041.63	+	8732.36i	0.258561	+	0.447841i
$53$	9344.52			0.456948			0.228474	−	0.973550i	$-0.426626\pi$
$53$	9344.52			0.456948			0.228474	+	0.973550i	$0.426626\pi$
$54$	5951.14	−	13934.4i	0.277725	−	0.650284i
$55$	−6256.40			−0.278880
$56$	3447.15	+	5970.65i	0.146889	+	0.254420i
$57$	1892.88	+	8687.97i	0.0771678	+	0.354186i
$58$	10105.2	−	17502.8i	0.394436	−	0.683183i
$59$	4776.51	−	8273.15i	0.178641	−	0.309415i	−0.762775	−	0.646665i	$-0.776163\pi$
$59$	4776.51	−	8273.15i	0.178641	−	0.309415i	0.941415	+	0.337250i	$0.109497\pi$
$60$	−9539.78	+	8677.84i	−0.342106	+	0.311196i
$61$	8741.51	+	15140.7i	0.300789	+	0.520982i	0.976315	−	0.216355i	$-0.0694167\pi$
$61$	8741.51	+	15140.7i	0.300789	+	0.520982i	−0.675526	+	0.737336i	$0.736083\pi$
$62$	20458.8			0.675929
$63$	21332.8	+	15170.3i	0.677167	+	0.481552i
$64$	4096.00			0.125000
$65$	−16292.6	−	28219.6i	−0.478307	−	0.828452i
$66$	7187.30	+	2294.98i	0.203098	+	0.0648514i
$67$	−5429.23	+	9403.70i	−0.147758	+	0.255924i	−0.930399	−	0.366550i	$-0.880539\pi$
$67$	−5429.23	+	9403.70i	−0.147758	+	0.255924i	0.782640	+	0.622474i	$0.213872\pi$
$68$	−8554.41	+	14816.7i	−0.224346	+	0.388578i
$69$	34579.2	+	11041.5i	0.874364	+	0.279194i
$70$	−11139.9	−	19294.8i	−0.271728	−	0.470647i
$71$	14111.6			0.332224			0.166112	−	0.986107i	$-0.446879\pi$
$71$	14111.6			0.332224			0.166112	+	0.986107i	$0.446879\pi$
$72$	14142.4	−	6469.63i	0.321509	−	0.147078i
$73$	−51306.5			−1.12685			−0.563424	−	0.826168i	$-0.690516\pi$
$73$	−51306.5			−1.12685			−0.563424	+	0.826168i	$0.690516\pi$
$74$	10844.6	+	18783.4i	0.230215	+	0.398745i
$75$	−5206.55	+	4736.13i	−0.106880	+	0.0972232i
$76$	−4563.27	+	7903.81i	−0.0906237	+	0.156965i
$77$	−6517.28	+	11288.3i	−0.125268	+	0.216970i
$78$	8365.24	+	38394.9i	0.155683	+	0.714558i
$79$	−26375.3	−	45683.4i	−0.475478	−	0.823552i	0.524128	−	0.851640i	$-0.324391\pi$
$79$	−26375.3	−	45683.4i	−0.475478	−	0.823552i	−0.999605	+	0.0280880i	$0.991058\pi$
$80$	−13236.7			−0.231235
$81$	38611.4	−	44676.0i	0.653888	−	0.756592i
$82$	−33033.9			−0.542532
$83$	−5450.46	−	9440.47i	−0.0868436	−	0.150417i	0.819332	−	0.573320i	$-0.194345\pi$
$83$	−5450.46	−	9440.47i	−0.0868436	−	0.150417i	−0.906175	+	0.422902i	$0.861011\pi$
$84$	5719.63	+	26252.1i	0.0884443	+	0.405943i
$85$	27644.5	−	47881.7i	0.415013	−	0.718824i
$86$	−12189.7	+	21113.2i	−0.177725	+	0.307828i
$87$	58263.3	−	52999.1i	0.825272	−	0.750707i
$88$	3872.00	+	6706.50i	0.0533002	+	0.0923186i
$89$	74711.4			0.999798			0.499899	−	0.866084i	$-0.333371\pi$
$89$	74711.4			0.999798			0.499899	+	0.866084i	$0.333371\pi$
$90$	−45702.9	+	20907.3i	−0.594754	+	0.272077i
$91$	−67887.8			−0.859386
$92$	18628.8	+	32266.0i	0.229464	+	0.397444i
$93$	75952.3	+	24252.4i	0.910612	+	0.290768i
$94$	11910.5	−	20629.6i	0.139031	−	0.240809i
$95$	14746.7	−	25542.0i	0.167643	−	0.290366i
$96$	15206.2	+	4855.50i	0.168400	+	0.0537719i
$97$	−34110.2	−	59080.6i	−0.368091	−	0.637552i	0.621176	−	0.783671i	$-0.286655\pi$
$97$	−34110.2	−	59080.6i	−0.368091	−	0.637552i	−0.989267	+	0.146119i	$0.953322\pi$
$98$	20810.5			0.218886
$99$	23961.9	+	17040.0i	0.245716	+	0.174736i
$100$	−7224.21			−0.0722421
$101$	3493.79	+	6051.42i	0.0340795	+	0.0590275i	0.882562	−	0.470196i	$-0.155817\pi$
$101$	3493.79	+	6051.42i	0.0340795	+	0.0590275i	−0.848483	+	0.529223i	$0.822483\pi$
$102$	−49321.8	+	44865.5i	−0.469395	+	0.426985i
$103$	83582.1	−	144769.i	0.776284	−	1.34456i	−0.157787	−	0.987473i	$-0.550436\pi$
$103$	83582.1	−	144769.i	0.776284	−	1.34456i	0.934070	−	0.357089i	$-0.116231\pi$
$104$	−20166.5	+	34929.4i	−0.182830	+	0.316671i
$105$	−18483.6	−	84836.4i	−0.163611	−	0.750947i
$106$	18689.0	+	32370.4i	0.161556	+	0.279823i
$107$	708.340			0.00598112			0.00299056	−	0.999996i	$-0.499048\pi$
$107$	708.340			0.00598112			0.00299056	+	0.999996i	$0.499048\pi$
$108$	60172.3	−	7253.39i	0.496406	−	0.0598386i
$109$	−39465.4			−0.318164			−0.159082	−	0.987265i	$-0.550853\pi$
$109$	−39465.4			−0.318164			−0.159082	+	0.987265i	$0.550853\pi$
$110$	−12512.8	−	21672.8i	−0.0985990	−	0.170779i
$111$	17993.7	+	82587.8i	0.138616	+	0.636222i
$112$	−13788.6	+	23882.6i	−0.103867	+	0.179902i
$113$	−121819.	+	210997.i	−0.897469	+	1.55446i	−0.0667500	+	0.997770i	$0.521263\pi$
$113$	−121819.	+	210997.i	−0.897469	+	1.55446i	−0.830719	+	0.556692i	$0.812070\pi$
$114$	−26310.3	+	23933.1i	−0.189611	+	0.172479i
$115$	−60201.0	−	104271.i	−0.424482	−	0.735224i
$116$	80841.8			0.557816
$117$	−14458.8	+	152455.i	−0.0976487	+	1.02962i
$118$	38212.1			0.252636
$119$	−57594.5	−	99756.5i	−0.372832	−	0.645764i
$120$	−49140.5	−	15691.1i	−0.311520	−	0.0994717i
$121$	−7320.50	+	12679.5i	−0.0454545	+	0.0787296i
$122$	−34966.0	+	60562.9i	−0.212690	+	0.368390i
$123$	−122637.	−	39159.2i	−0.730900	−	0.233384i
$124$	40917.6	+	70871.4i	0.238977	+	0.413921i
$125$	184926.			1.05858
$126$	−9886.00	+	104240.i	−0.0554746	+	0.584933i
$127$	−289493.			−1.59268			−0.796340	−	0.604849i	$-0.793234\pi$
$127$	−289493.			−1.59268			−0.796340	+	0.604849i	$0.793234\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−70281.8	+	63931.7i	−0.371851	+	0.338253i
$130$	65170.4	−	112878.i	0.338214	−	0.585804i
$131$	156591.	−	271224.i	0.797241	−	1.38086i	−0.124165	−	0.992262i	$-0.539625\pi$
$131$	156591.	−	271224.i	0.797241	−	1.38086i	0.921406	−	0.388601i	$-0.127041\pi$
$132$	6424.55	+	29487.5i	0.0320928	+	0.147300i
$133$	−30723.2	−	53214.2i	−0.150604	−	0.260854i
$134$	−43433.8			−0.208961
$135$	−194454.	+	23440.1i	−0.918293	+	0.110694i
$136$	−68435.3			−0.317273
$137$	70778.2	+	122591.i	0.322180	+	0.558032i	0.980938	−	0.194323i	$-0.0622511\pi$
$137$	70778.2	+	122591.i	0.322180	+	0.558032i	−0.658758	+	0.752355i	$0.728918\pi$
$138$	30909.5	+	141869.i	0.138164	+	0.634146i
$139$	103846.	−	179867.i	0.455883	−	0.789613i	−0.542855	−	0.839826i	$-0.682657\pi$
$139$	103846.	−	179867.i	0.455883	−	0.789613i	0.998739	+	0.0502132i	$0.0159901\pi$
$140$	44559.4	−	77179.2i	0.192141	−	0.332798i
$141$	68672.1	−	62467.4i	0.290893	−	0.264610i
$142$	28223.3	+	48884.1i	0.117459	+	0.203445i
$143$	−76254.7			−0.311836
$144$	50696.3	+	36051.6i	0.203737	+	0.144883i
$145$	−261249.			−1.03189
$146$	−102613.	−	177731.i	−0.398401	−	0.690051i
$147$	77258.1	+	24669.3i	0.294883	+	0.0941595i
$148$	−43378.4	+	75133.6i	−0.162787	+	0.281955i
$149$	24972.2	−	43253.1i	0.0921491	−	0.159607i	−0.816266	−	0.577676i	$-0.803960\pi$
$149$	24972.2	−	43253.1i	0.0921491	−	0.159607i	0.908415	+	0.418069i	$0.137293\pi$
$150$	−26819.5	−	8563.76i	−0.0973246	−	0.0310768i
$151$	−188000.	−	325625.i	−0.670988	−	1.16219i	−0.977624	−	0.210358i	$-0.932537\pi$
$151$	−188000.	−	325625.i	−0.670988	−	1.16219i	0.306636	−	0.951827i	$-0.400796\pi$
$152$	−36506.1			−0.128161
$153$	−236289.	+	108094.i	−0.816048	+	0.373311i
$154$	−52138.2			−0.177155
$155$	−132230.	−	229029.i	−0.442079	−	0.765704i
$156$	−116273.	+	105768.i	−0.382533	+	0.347970i
$157$	−182351.	+	315842.i	−0.590418	+	1.02263i	0.403758	+	0.914866i	$0.367704\pi$
$157$	−182351.	+	315842.i	−0.590418	+	1.02263i	−0.994176	+	0.107768i	$0.965630\pi$
$158$	105501.	−	182734.i	0.336214	−	0.582339i
$159$	31009.4	+	142328.i	0.0972750	+	0.446474i
$160$	−26473.4	−	45853.2i	−0.0817540	−	0.141602i
$161$	−250845.			−0.762677
$162$	231985.	+	44401.9i	0.694500	+	0.132927i
$163$	−299816.			−0.883865			−0.441932	−	0.897048i	$-0.645707\pi$
$163$	−299816.			−0.883865			−0.441932	+	0.897048i	$0.645707\pi$
$164$	−66067.9	−	114433.i	−0.191814	−	0.332232i
$165$	−20761.6	−	95292.1i	−0.0593679	−	0.272488i
$166$	21801.8	−	37761.9i	0.0614077	−	0.106361i
$167$	297840.	−	515874.i	0.826404	−	1.43137i	−0.0744383	−	0.997226i	$-0.523716\pi$
$167$	297840.	−	515874.i	0.826404	−	1.43137i	0.900842	−	0.434147i	$-0.142950\pi$
$168$	−79500.5	+	72317.5i	−0.217319	+	0.197683i
$169$	−12932.0	−	22398.9i	−0.0348297	−	0.0603268i
$170$	221156.			0.586917
$171$	−126046.	+	57661.5i	−0.329640	+	0.150798i
$172$	−97517.7			−0.251340
$173$	−190879.	−	330612.i	−0.484890	−	0.839854i	0.514959	−	0.857215i	$-0.327807\pi$
$173$	−190879.	−	330612.i	−0.484890	−	0.839854i	−0.999849	+	0.0173607i	$0.994474\pi$
$174$	300121.	+	95831.9i	0.751490	+	0.239959i
$175$	24319.3	−	42122.3i	0.0600283	−	0.103972i
$176$	−15488.0	+	26826.0i	−0.0376889	+	0.0652791i
$177$	141860.	+	45297.5i	0.340351	+	0.108678i
$178$	149423.	+	258808.i	0.353482	+	0.612248i
$179$	−306441.			−0.714849			−0.357424	−	0.933942i	$-0.616345\pi$
$179$	−306441.			−0.714849			−0.357424	+	0.933942i	$0.616345\pi$
$180$	−163831.	−	116505.i	−0.376890	−	0.268017i
$181$	−150935.			−0.342446			−0.171223	−	0.985232i	$-0.554772\pi$
$181$	−150935.			−0.342446			−0.171223	+	0.985232i	$0.554772\pi$
$182$	−135776.	−	235170.i	−0.303839	−	0.526264i
$183$	−201602.	+	183387.i	−0.445008	+	0.404801i
$184$	−74515.1	+	129064.i	−0.162256	+	0.281035i
$185$	140182.	−	242802.i	0.301136	−	0.521583i
$186$	67891.9	+	311611.i	0.143892	+	0.660436i
$187$	−64692.7	−	112051.i	−0.135286	−	0.234321i
$188$	95284.2			0.196619
$189$	−160269.	+	375265.i	−0.326359	+	0.764158i
$190$	117974.			0.237083
$191$	455628.	+	789170.i	0.903705	+	1.56526i	0.822646	+	0.568554i	$0.192497\pi$
$191$	455628.	+	789170.i	0.903705	+	1.56526i	0.0810592	+	0.996709i	$0.474170\pi$
$192$	13592.4	+	62386.8i	0.0266100	+	0.122135i
$193$	−379127.	+	656668.i	−0.732642	+	1.26897i	0.223108	+	0.974794i	$0.428380\pi$
$193$	−379127.	+	656668.i	−0.732642	+	1.26897i	−0.955750	+	0.294179i	$0.904954\pi$
$194$	136441.	−	236323.i	0.260280	−	0.450818i
$195$	375750.	−	341801.i	0.707641	−	0.643704i
$196$	41621.1	+	72089.8i	0.0773879	+	0.134040i
$197$	741959.			1.36212			0.681058	−	0.732229i	$-0.261520\pi$
$197$	741959.			1.36212			0.681058	+	0.732229i	$0.261520\pi$
$198$	−11104.4	+	117087.i	−0.0201295	+	0.212248i
$199$	147504.			0.264040			0.132020	−	0.991247i	$-0.457854\pi$
$199$	147504.			0.264040			0.132020	+	0.991247i	$0.457854\pi$
$200$	−14448.4	−	25025.4i	−0.0255415	−	0.0442391i
$201$	−161246.	−	51487.5i	−0.281513	−	0.0898901i
$202$	−13975.2	+	24205.7i	−0.0240979	+	0.0417387i
$203$	−272143.	+	471365.i	−0.463507	+	0.802818i
$204$	−254062.	−	81124.8i	−0.427430	−	0.136483i
$205$	213506.	+	369803.i	0.354834	+	0.614590i
$206$	668657.			1.09783
$207$	−53425.0	+	563322.i	−0.0866600	+	0.913757i
$208$	−161332.			−0.258561
$209$	−34509.7	−	59772.6i	−0.0546482	−	0.0946534i
$210$	256915.	−	233702.i	0.402014	−	0.365691i
$211$	−25221.4	+	43684.7i	−0.0389998	+	0.0675497i	−0.884866	−	0.465845i	$-0.845751\pi$
$211$	−25221.4	+	43684.7i	−0.0389998	+	0.0675497i	0.845867	+	0.533394i	$0.179084\pi$
$212$	−74756.1	+	129481.i	−0.114237	+	0.197864i
$213$	46829.0	+	214936.i	0.0707238	+	0.324609i
$214$	1416.68	+	2453.76i	0.00211465	+	0.00366267i
$215$	315139.			0.464950
$216$	145471.	+	193936.i	0.212150	+	0.282829i
$217$	−550974.			−0.794295
$218$	−78930.9	−	136712.i	−0.112488	−	0.194835i
$219$	−170259.	−	781457.i	−0.239883	−	1.10102i
$220$	50051.2	−	86691.2i	0.0697200	−	0.120759i
$221$	336939.	−	583595.i	0.464056	−	0.803769i
$222$	−250105.	+	227508.i	−0.340597	+	0.309823i
$223$	−528581.	−	915529.i	−0.711786	−	1.23285i	−0.964186	−	0.265227i	$-0.914553\pi$
$223$	−528581.	−	915529.i	−0.711786	−	1.23285i	0.252400	−	0.967623i	$-0.418780\pi$
$224$	−110309.			−0.146889
$225$	−89414.4	−	63585.0i	−0.117747	−	0.0837334i
$226$	−974553.			−1.26921
$227$	295085.	+	511103.i	0.380087	+	0.658330i	0.991074	−	0.133311i	$-0.0425608\pi$
$227$	295085.	+	511103.i	0.380087	+	0.658330i	−0.610987	+	0.791640i	$0.709227\pi$
$228$	−135527.	−	43275.3i	−0.172659	−	0.0551319i
$229$	336538.	−	582901.i	0.424078	−	0.734524i	−0.572256	−	0.820075i	$-0.693932\pi$
$229$	336538.	−	582901.i	0.424078	−	0.734524i	0.996334	+	0.0855509i	$0.0272650\pi$
$230$	240804.	−	417085.i	0.300154	−	0.519882i
$231$	−193560.	−	61805.9i	−0.238664	−	0.0762079i
$232$	161684.	+	280044.i	0.197218	+	0.341591i
$233$	86208.7			0.104031			0.0520153	−	0.998646i	$-0.483436\pi$
$233$	86208.7			0.104031			0.0520153	+	0.998646i	$0.483436\pi$
$234$	−557039.	+	254824.i	−0.665037	+	0.304229i
$235$	−307922.			−0.363723
$236$	76424.1	+	132370.i	0.0893203	+	0.154707i
$237$	608285.	−	553325.i	0.703455	−	0.639896i
$238$	230378.	−	399026.i	0.263632	−	0.456624i
$239$	−194598.	+	337054.i	−0.220366	+	0.381685i	−0.954919	−	0.296866i	$-0.904058\pi$
$239$	−194598.	+	337054.i	−0.220366	+	0.381685i	0.734553	+	0.678551i	$0.237392\pi$
$240$	−43925.4	−	201610.i	−0.0492253	−	0.225935i
$241$	323137.	+	559689.i	0.358380	+	0.620732i	0.987690	−	0.156422i	$-0.0499960\pi$
$241$	323137.	+	559689.i	0.358380	+	0.620732i	−0.629311	+	0.777154i	$0.716663\pi$
$242$	−58564.0			−0.0642824
$243$	808597.	+	439840.i	0.878449	+	0.477837i
$244$	−279728.			−0.300789
$245$	−134503.	−	232966.i	−0.143159	−	0.247958i
$246$	−109622.	−	503145.i	−0.115494	−	0.530097i
$247$	179737.	−	311313.i	0.187454	−	0.324680i
$248$	−163671.	+	283486.i	−0.168982	+	0.292686i
$249$	125702.	−	114345.i	0.128482	−	0.116874i
$250$	369853.	+	640604.i	0.374265	+	0.648245i
$251$	1.06803e6			1.07004			0.535020	−	0.844839i	$-0.320304\pi$
$251$	1.06803e6			1.07004			0.535020	+	0.844839i	$0.320304\pi$
$252$	−380868.	+	174233.i	−0.377810	+	0.172834i
$253$	−281760.			−0.276744
$254$	−578986.	−	1.00283e6i	−0.563098	−	0.975314i
$255$	821031.	+	262164.i	0.790695	+	0.252477i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	15056.9	−	26079.4i	0.0142201	−	0.0246300i	−0.858828	−	0.512264i	$-0.828807\pi$
$257$	15056.9	−	26079.4i	0.0142201	−	0.0246300i	0.873048	+	0.487634i	$0.162140\pi$
$258$	−362029.	−	115600.i	−0.338606	−	0.108121i
$259$	−292055.	−	505853.i	−0.270530	−	0.468571i
$260$	521363.			0.478307
$261$	1.00058e6	+	711542.i	0.909184	+	0.646546i
$262$	1.25273e6			1.12747
$263$	512010.	+	886828.i	0.456446	+	0.790588i	0.998770	−	0.0495817i	$-0.0157888\pi$
$263$	512010.	+	886828.i	0.456446	+	0.790588i	−0.542324	+	0.840169i	$0.682455\pi$
$264$	−89298.6	+	81230.3i	−0.0788560	+	0.0717312i
$265$	241583.	−	418433.i	0.211325	−	0.366026i
$266$	122893.	−	212857.i	0.106493	−	0.184452i
$267$	247927.	+	1.13794e6i	0.212837	+	0.976881i
$268$	−86867.7	−	150459.i	−0.0738790	−	0.127962i
$269$	1.63678e6			1.37915			0.689573	−	0.724216i	$-0.257798\pi$
$269$	1.63678e6			1.37915			0.689573	+	0.724216i	$0.257798\pi$
$270$	−470106.	−	626726.i	−0.392452	−	0.523201i
$271$	1.92090e6			1.58884			0.794421	−	0.607368i	$-0.207774\pi$
$271$	1.92090e6			1.58884			0.794421	+	0.607368i	$0.207774\pi$
$272$	−136871.	−	237067.i	−0.112173	−	0.194289i
$273$	−225283.	−	1.03401e6i	−0.182946	−	0.839688i
$274$	−283113.	+	490366.i	−0.227815	+	0.394588i
$275$	27316.6	−	47313.7i	0.0217818	−	0.0377272i
$276$	−429629.	+	390811.i	−0.339485	+	0.308812i
$277$	58414.7	+	101177.i	0.0457428	+	0.0792289i	0.887990	−	0.459862i	$-0.152101\pi$
$277$	58414.7	+	101177.i	0.0457428	+	0.0792289i	−0.842247	+	0.539091i	$0.818768\pi$
$278$	830770.			0.644716
$279$	−117347.	+	1.23732e6i	−0.0902526	+	0.951638i
$280$	356475.			0.271728
$281$	625401.	+	1.08323e6i	0.472490	+	0.818377i	0.999504	−	0.0314795i	$-0.0100219\pi$
$281$	625401.	+	1.08323e6i	0.472490	+	0.818377i	−0.527014	+	0.849856i	$0.676689\pi$
$282$	353738.	+	112952.i	0.264886	+	0.0845809i
$283$	−1.27645e6	+	2.21088e6i	−0.947411	+	1.64096i	−0.196559	+	0.980492i	$0.562977\pi$
$283$	−1.27645e6	+	2.21088e6i	−0.947411	+	1.64096i	−0.750851	+	0.660471i	$0.770357\pi$
$284$	−112893.	+	195537.i	−0.0830561	+	0.143857i
$285$	437971.	+	139849.i	0.319399	+	0.101987i
$286$	−152509.	−	264154.i	−0.110251	−	0.190960i
$287$	889633.			0.637538
$288$	−23493.6	+	247720.i	−0.0166905	+	0.175987i
$289$	−276452.			−0.194704
$290$	−522499.	−	904994.i	−0.364830	−	0.631904i
$291$	786672.	−	715595.i	0.544580	−	0.495376i
$292$	410452.	−	710924.i	0.281712	−	0.487940i
$293$	429056.	−	743147.i	0.291975	−	0.505715i	−0.682302	−	0.731071i	$-0.739021\pi$
$293$	429056.	−	743147.i	0.291975	−	0.505715i	0.974277	+	0.225355i	$0.0723543\pi$
$294$	69059.1	+	316968.i	0.0465964	+	0.213869i
$295$	−246973.	−	427770.i	−0.165232	−	0.286190i
$296$	−347027.			−0.230215
$297$	−180022.	+	421515.i	−0.118422	+	0.277282i
$298$	199778.			0.130319
$299$	−733746.	−	1.27089e6i	−0.474644	−	0.822107i
$300$	−23973.3	−	110033.i	−0.0153789	−	0.0705862i
$301$	328280.	−	568597.i	0.208847	−	0.361733i
$302$	751999.	−	1.30250e6i	0.474460	−	0.821789i
$303$	−80576.1	+	73295.9i	−0.0504196	+	0.0458641i
$304$	−73012.3	−	126461.i	−0.0453119	−	0.0784824i
$305$	903973.			0.556424
$306$	−847026.	−	602343.i	−0.517122	−	0.367740i
$307$	−1.92198e6			−1.16386			−0.581932	−	0.813238i	$-0.697703\pi$
$307$	−1.92198e6			−1.16386			−0.581932	+	0.813238i	$0.697703\pi$
$308$	−104276.	−	180612.i	−0.0626339	−	0.108485i
$309$	2.48235e6	+	792643.i	1.47900	+	0.472260i
$310$	528920.	−	916115.i	0.312597	−	0.541435i
$311$	−1.23869e6	+	2.14547e6i	−0.726209	+	1.25783i	0.232265	+	0.972653i	$0.425386\pi$
$311$	−1.23869e6	+	2.14547e6i	−0.726209	+	1.25783i	−0.958474	+	0.285179i	$0.907947\pi$
$312$	−598937.	−	191247.i	−0.348333	−	0.111227i
$313$	613186.	+	1.06207e6i	0.353778	+	0.612762i	0.986908	−	0.161284i	$-0.0515634\pi$
$313$	613186.	+	1.06207e6i	0.353778	+	0.612762i	−0.633130	+	0.774046i	$0.718230\pi$
$314$	−1.45881e6			−0.834977
$315$	1.23082e6	−	563053.i	0.698904	−	0.319722i
$316$	844011.			0.475478
$317$	−587731.	−	1.01798e6i	−0.328496	−	0.568972i	0.653717	−	0.756739i	$-0.273209\pi$
$317$	−587731.	−	1.01798e6i	−0.328496	−	0.568972i	−0.982214	+	0.187766i	$0.939875\pi$
$318$	−431019.	+	392075.i	−0.239017	+	0.217421i
$319$	−305683.	+	529459.i	−0.168188	+	0.291310i
$320$	105893.	−	183413.i	0.0578088	−	0.100128i
$321$	2350.60	+	10788.8i	0.00127326	+	0.00584402i
$322$	−501690.	−	868952.i	−0.269647	−	0.467042i
$323$	609938.			0.325297
$324$	310157.	+	892423.i	0.164142	+	0.472290i
$325$	284546.			0.149432
$326$	−599632.	−	1.03859e6i	−0.312493	−	0.541254i
$327$	−130965.	−	601104.i	−0.0677306	−	0.310871i
$328$	264271.	−	457732.i	0.135633	−	0.234923i
$329$	−320761.	+	555575.i	−0.163377	+	0.282978i
$330$	288578.	−	262505.i	0.145874	−	0.132694i
$331$	−1.44441e6	−	2.50179e6i	−0.724637	−	1.25511i	−0.959123	−	0.282989i	$-0.908674\pi$
$331$	−1.44441e6	−	2.50179e6i	−0.724637	−	1.25511i	0.234486	−	0.972120i	$-0.424659\pi$
$332$	174415.			0.0868436
$333$	−1.19820e6	+	548130.i	−0.592130	+	0.270877i
$334$	2.38272e6			1.16871
$335$	280722.	+	486226.i	0.136667	+	0.236715i
$336$	−409516.	−	130763.i	−0.197890	−	0.0631883i
$337$	842177.	−	1.45869e6i	0.403951	−	0.699663i	−0.590248	−	0.807222i	$-0.700970\pi$
$337$	842177.	−	1.45869e6i	0.403951	−	0.699663i	0.994199	+	0.107559i	$0.0343033\pi$
$338$	51728.1	−	89595.7i	0.0246283	−	0.0426575i
$339$	−3.61798e6	−	1.15526e6i	−1.70988	−	0.545984i
$340$	442312.	+	766107.i	0.207507	+	0.359412i
$341$	−618879.			−0.288217
$342$	−451838.	−	321314.i	−0.208890	−	0.148547i
$343$	−2.37096e6			−1.08815
$344$	−195035.	−	337811.i	−0.0888623	−	0.153914i
$345$	1.38839e6	−	1.26295e6i	0.628008	−	0.571266i
$346$	763516.	−	1.32245e6i	0.342869	−	0.593866i
$347$	156201.	−	270549.i	0.0696404	−	0.120621i	−0.829103	−	0.559096i	$-0.811148\pi$
$347$	156201.	−	270549.i	0.0696404	−	0.120621i	0.898743	+	0.438476i	$0.144481\pi$
$348$	268271.	+	1.23131e6i	0.118748	+	0.545030i
$349$	1.89791e6	+	3.28728e6i	0.834090	+	1.44469i	0.894769	+	0.446529i	$0.147340\pi$
$349$	1.89791e6	+	3.28728e6i	0.834090	+	1.44469i	−0.0606788	+	0.998157i	$0.519327\pi$
$350$	194555.			0.0848929
$351$	−2.37005e6	+	285695.i	−1.02681	+	0.123775i
$352$	−123904.			−0.0533002
$353$	−399850.	−	692561.i	−0.170789	−	0.295816i	0.767907	−	0.640562i	$-0.221298\pi$
$353$	−399850.	−	692561.i	−0.170789	−	0.295816i	−0.938696	+	0.344746i	$0.887965\pi$
$354$	126805.	+	582013.i	0.0537811	+	0.246845i
$355$	364826.	−	631898.i	0.153644	−	0.266119i
$356$	−597691.	+	1.03523e6i	−0.249949	+	0.432925i
$357$	1.32828e6	−	1.20827e6i	0.551594	−	0.501756i
$358$	−612882.	−	1.06154e6i	−0.252737	−	0.437754i
$359$	−2.69706e6			−1.10447			−0.552236	−	0.833688i	$-0.686225\pi$
$359$	−2.69706e6			−1.10447			−0.552236	+	0.833688i	$0.686225\pi$
$360$	75922.2	−	800536.i	0.0308754	−	0.325555i
$361$	−2.15073e6			−0.868597
$362$	−301869.	−	522853.i	−0.121073	−	0.209705i
$363$	−217416.	−	69423.2i	−0.0866013	−	0.0276527i
$364$	543103.	−	940681.i	0.214847	−	0.372125i
$365$	−1.32642e6	+	2.29743e6i	−0.521134	+	0.902631i
$366$	−1.03848e6	−	331597.i	−0.405223	−	0.129392i
$367$	1.94115e6	+	3.36217e6i	0.752306	+	1.30303i	0.946703	+	0.322109i	$0.104392\pi$
$367$	1.94115e6	+	3.36217e6i	0.752306	+	1.30303i	−0.194397	+	0.980923i	$0.562275\pi$
$368$	−596121.			−0.229464
$369$	189474.	−	1.99785e6i	0.0724410	−	0.763829i
$370$	1.12146e6			0.425871
$371$	−503312.	−	871762.i	−0.189847	−	0.328824i
$372$	−943669.	+	858407.i	−0.353559	+	0.321615i
$373$	−503544.	+	872164.i	−0.187398	+	0.324583i	−0.944382	−	0.328850i	$-0.893339\pi$
$373$	−503544.	+	872164.i	−0.187398	+	0.324583i	0.756984	+	0.653434i	$0.226672\pi$
$374$	258771.	−	448204.i	0.0956613	−	0.165690i
$375$	613672.	+	2.81664e6i	0.225350	+	1.03432i
$376$	190568.	+	330074.i	0.0695155	+	0.120404i
$377$	−3.18418e6			−1.15384
$378$	−1.62049e6	+	195340.i	−0.583335	+	0.0703173i
$379$	−3.54244e6			−1.26679			−0.633396	−	0.773828i	$-0.718339\pi$
$379$	−3.54244e6			−1.26679			−0.633396	+	0.773828i	$0.718339\pi$
$380$	235947.	+	408673.i	0.0838216	+	0.145183i
$381$	−960672.	−	4.40931e6i	−0.339049	−	1.55617i
$382$	−1.82251e6	+	3.15668e6i	−0.639016	+	1.10681i
$383$	−2.64492e6	+	4.58113e6i	−0.921330	+	1.59579i	−0.123969	+	0.992286i	$0.539562\pi$
$383$	−2.64492e6	+	4.58113e6i	−0.921330	+	1.59579i	−0.797360	+	0.603504i	$0.793771\pi$
$384$	−188929.	+	171859.i	−0.0653839	+	0.0594764i
$385$	336981.	+	583668.i	0.115865	+	0.200685i
$386$	−3.03302e6			−1.03611
$387$	−1.20698e6	−	858317.i	−0.409659	−	0.291320i
$388$	1.09153e6			0.368091
$389$	2.67810e6	+	4.63861e6i	0.897332	+	1.55423i	0.830891	+	0.556435i	$0.187831\pi$
$389$	2.67810e6	+	4.63861e6i	0.897332	+	1.55423i	0.0664414	+	0.997790i	$0.478835\pi$
$390$	1.93553e6	+	618036.i	0.644375	+	0.205756i
$391$	1.24499e6	−	2.15638e6i	0.411834	−	0.713318i
$392$	−166484.	+	288359.i	−0.0547215	+	0.0947805i
$393$	4.65070e6	+	1.48502e6i	1.51893	+	0.485010i
$394$	1.48392e6	+	2.57022e6i	0.481581	+	0.834123i
$395$	−2.72751e6			−0.879578
$396$	−427809.	+	195706.i	−0.137092	+	0.0627144i
$397$	117620.			0.0374545			0.0187272	−	0.999825i	$-0.494039\pi$
$397$	117620.			0.0374545			0.0187272	+	0.999825i	$0.494039\pi$
$398$	295007.	+	510967.i	0.0933523	+	0.161691i
$399$	708559.	−	644539.i	0.222815	−	0.202683i
$400$	57793.7	−	100102.i	0.0180605	−	0.0312818i
$401$	−2.68026e6	+	4.64235e6i	−0.832370	+	1.44171i	0.0637836	+	0.997964i	$0.479683\pi$
$401$	−2.68026e6	+	4.64235e6i	−0.832370	+	1.44171i	−0.896154	+	0.443744i	$0.853650\pi$
$402$	−144134.	−	661547.i	−0.0444836	−	0.204172i
$403$	−1.61165e6	−	2.79147e6i	−0.494321	−	0.856189i
$404$	−111801.			−0.0340795
$405$	−1.00231e6	−	2.88396e6i	−0.303643	−	0.873680i
$406$	−2.17714e6			−0.655499
$407$	−328049.	−	568198.i	−0.0981641	−	0.170025i
$408$	−227100.	−	1.04235e6i	−0.0675409	−	0.310000i
$409$	−66786.1	+	115677.i	−0.0197414	+	0.0341931i	−0.875727	−	0.482806i	$-0.839618\pi$
$409$	−66786.1	+	115677.i	−0.0197414	+	0.0341931i	0.855986	+	0.516999i	$0.172951\pi$
$410$	−854022.	+	1.47921e6i	−0.250905	+	0.434581i
$411$	−1.63233e6	+	1.48485e6i	−0.476655	+	0.433588i
$412$	1.33731e6	+	2.31630e6i	0.388142	+	0.672281i
$413$	−1.02908e6			−0.296877
$414$	−2.05825e6	+	941574.i	−0.590198	+	0.269994i
$415$	−563640.			−0.160650
$416$	−322664.	−	558871.i	−0.0914151	−	0.158336i
$417$	3.08419e6	+	984815.i	0.868562	+	0.277341i
$418$	138039.	−	239090.i	0.0386421	−	0.0669300i
$419$	−2.14227e6	+	3.71052e6i	−0.596128	+	1.03252i	0.397259	+	0.917707i	$0.369961\pi$
$419$	−2.14227e6	+	3.71052e6i	−0.596128	+	1.03252i	−0.993387	+	0.114817i	$0.963372\pi$
$420$	1.32340e6	+	422575.i	0.366072	+	0.116891i
$421$	1.56175e6	+	2.70503e6i	0.429444	+	0.743818i	0.996824	−	0.0796375i	$-0.0253763\pi$
$421$	1.56175e6	+	2.70503e6i	0.429444	+	0.743818i	−0.567380	+	0.823456i	$0.692043\pi$
$422$	−201771.			−0.0551541
$423$	1.17934e6	+	838659.i	0.320470	+	0.227895i
$424$	−598049.			−0.161556
$425$	241402.	+	418120.i	0.0648289	+	0.112287i
$426$	−650903.	+	592093.i	−0.173777	+	0.158076i
$427$	941666.	−	1.63101e6i	0.249935	−	0.432900i
$428$	−5666.72	+	9815.05i	−0.00149528	+	0.00258990i
$429$	−253048.	−	1.16145e6i	−0.0663836	−	0.304688i
$430$	630279.	+	1.09167e6i	0.164385	+	0.284723i
$431$	1.02210e6			0.265034			0.132517	−	0.991181i	$-0.457694\pi$
$431$	1.02210e6			0.265034			0.132517	+	0.991181i	$0.457694\pi$
$432$	−380873.	+	891799.i	−0.0981907	+	0.229910i
$433$	3.19786e6			0.819671			0.409836	−	0.912159i	$-0.365586\pi$
$433$	3.19786e6			0.819671			0.409836	+	0.912159i	$0.365586\pi$
$434$	−1.10195e6	−	1.90863e6i	−0.280826	−	0.486404i
$435$	−866947.	−	3.97913e6i	−0.219669	−	1.00824i
$436$	315723.	−	546849.i	0.0795409	−	0.137769i
$437$	664126.	−	1.15030e6i	0.166359	−	0.288143i
$438$	2.36653e6	−	2.15271e6i	0.589423	−	0.536167i
$439$	−2.75542e6	−	4.77254e6i	−0.682381	−	1.18192i	−0.974252	−	0.225462i	$-0.927611\pi$
$439$	−2.75542e6	−	4.77254e6i	−0.682381	−	1.18192i	0.291871	−	0.956458i	$-0.405722\pi$
$440$	400409.			0.0985990
$441$	−119364.	+	1.25859e6i	−0.0292265	+	0.308169i
$442$	2.69551e6			0.656274
$443$	723275.	+	1.25275e6i	0.175103	+	0.303288i	0.940197	−	0.340631i	$-0.110641\pi$
$443$	723275.	+	1.25275e6i	0.175103	+	0.303288i	−0.765094	+	0.643919i	$0.777307\pi$
$444$	−1.28832e6	−	411374.i	−0.310146	−	0.0990330i
$445$	1.93151e6	−	3.34547e6i	0.462377	−	0.800860i
$446$	2.11432e6	−	3.66212e6i	0.503309	−	0.871756i
$447$	741664.	+	236821.i	0.175565	+	0.0560598i
$448$	−220618.	−	382121.i	−0.0519333	−	0.0899510i
$449$	−1.21428e6			−0.284252			−0.142126	−	0.989849i	$-0.545394\pi$
$449$	−1.21428e6			−0.284252			−0.142126	+	0.989849i	$0.545394\pi$
$450$	41436.3	−	436911.i	0.00964604	−	0.101709i
$451$	999276.			0.231337
$452$	−1.94911e6	−	3.37595e6i	−0.448734	−	0.777231i
$453$	4.33577e6	−	3.94403e6i	0.992706	−	0.903013i
$454$	−1.18034e6	+	2.04441e6i	−0.268762	+	0.465509i
$455$	−1.75510e6	+	3.03992e6i	−0.397441	+	0.688387i
$456$	−121144.	−	556030.i	−0.0272829	−	0.125224i
$457$	−3.11174e6	−	5.38969e6i	−0.696968	−	1.20718i	−0.969513	−	0.245041i	$-0.921199\pi$
$457$	−3.11174e6	−	5.38969e6i	−0.696968	−	1.20718i	0.272545	−	0.962143i	$-0.412135\pi$
$458$	2.69230e6			0.599736
$459$	−2.43051e6	−	3.24025e6i	−0.538474	−	0.717873i
$460$	1.92643e6			0.424482
$461$	−617847.	−	1.07014e6i	−0.135403	−	0.234525i	0.790348	−	0.612658i	$-0.209900\pi$
$461$	−617847.	−	1.07014e6i	−0.135403	−	0.234525i	−0.925751	+	0.378133i	$0.876566\pi$
$462$	−173019.	−	794125.i	−0.0377128	−	0.173095i
$463$	−2.48153e6	+	4.29813e6i	−0.537980	+	0.931809i	0.461033	+	0.887383i	$0.347479\pi$
$463$	−2.48153e6	+	4.29813e6i	−0.537980	+	0.931809i	−0.999013	+	0.0444257i	$0.985854\pi$
$464$	−646735.	+	1.12018e6i	−0.139454	+	0.241542i
$465$	3.04957e6	−	2.77404e6i	0.654043	−	0.594949i
$466$	172417.	+	298636.i	0.0367804	+	0.0637055i
$467$	2.87465e6			0.609948			0.304974	−	0.952361i	$-0.401352\pi$
$467$	2.87465e6			0.609948			0.304974	+	0.952361i	$0.401352\pi$
$468$	−1.99681e6	−	1.41999e6i	−0.421428	−	0.299689i
$469$	1.16971e6			0.245554
$470$	−615843.	−	1.06667e6i	−0.128595	−	0.222734i
$471$	−5.41576e6	−	1.72931e6i	−1.12488	−	0.359187i
$472$	−305696.	+	529482.i	−0.0631590	+	0.109395i
$473$	368739.	−	638674.i	0.0757820	−	0.131258i
$474$	3.13335e6	+	1.00051e6i	0.640564	+	0.204539i
$475$	128773.	+	223042.i	0.0261874	+	0.0453579i
$476$	1.84302e6			0.372832
$477$	−2.06491e6	+	944619.i	−0.415533	+	0.190091i
$478$	−1.55679e6			−0.311644
$479$	−3.50635e6	−	6.07318e6i	−0.698259	−	1.20942i	−0.969070	−	0.246788i	$-0.920625\pi$
$479$	−3.50635e6	−	6.07318e6i	−0.698259	−	1.20942i	0.270810	−	0.962633i	$-0.412708\pi$
$480$	610546.	−	555382.i	0.120953	−	0.110024i
$481$	1.70858e6	−	2.95934e6i	0.336722	−	0.583220i
$482$	−1.29255e6	+	2.23876e6i	−0.253413	+	0.438924i
$483$	−832420.	−	3.82066e6i	−0.162358	−	0.745195i
$484$	−117128.	−	202872.i	−0.0227273	−	0.0393648i
$485$	−3.52739e6			−0.680925
$486$	93541.8	+	3.68074e6i	0.0179645	+	0.706879i
$487$	8.60786e6			1.64465			0.822324	−	0.569020i	$-0.192677\pi$
$487$	8.60786e6			1.64465			0.822324	+	0.569020i	$0.192677\pi$
$488$	−559456.	−	969007.i	−0.106345	−	0.184195i
$489$	−994929.	−	4.56654e6i	−0.188157	−	0.863605i
$490$	538013.	−	931865.i	0.101228	−	0.175333i
$491$	−4.89361e6	+	8.47597e6i	−0.916063	+	1.58667i	−0.110725	+	0.993851i	$0.535317\pi$
$491$	−4.89361e6	+	8.47597e6i	−0.916063	+	1.58667i	−0.805338	+	0.592816i	$0.798016\pi$
$492$	1.52370e6	−	1.38603e6i	0.283783	−	0.258143i
$493$	−2.70138e6	−	4.67893e6i	−0.500575	−	0.867021i
$494$	1.43789e6			0.265100
$495$	1.38251e6	−	632447.i	0.253604	−	0.116014i
$496$	−1.30936e6			−0.238977
$497$	−760078.	−	1.31649e6i	−0.138028	−	0.239071i
$498$	647505.	+	206755.i	0.116996	+	0.0373580i
$499$	653761.	−	1.13235e6i	0.117535	−	0.203577i	−0.801255	−	0.598323i	$-0.795834\pi$
$499$	653761.	−	1.13235e6i	0.117535	−	0.203577i	0.918790	+	0.394746i	$0.129167\pi$
$500$	−1.47941e6	+	2.56242e6i	−0.264645	+	0.458379i
$501$	8.84573e6	+	2.82454e6i	1.57449	+	0.502751i
$502$	2.13607e6	+	3.69978e6i	0.378317	+	0.655264i
$503$	4.22769e6			0.745047			0.372523	−	0.928023i	$-0.378493\pi$
$503$	4.22769e6			0.745047			0.372523	+	0.928023i	$0.378493\pi$
$504$	−1.36530e6	−	970901.i	−0.239415	−	0.170254i
$505$	361298.			0.0630431
$506$	−563521.	−	976047.i	−0.0978439	−	0.169471i
$507$	298247.	−	271300.i	0.0515295	−	0.0468737i
$508$	2.31594e6	−	4.01133e6i	0.398170	−	0.689651i
$509$	−2.66363e6	+	4.61355e6i	−0.455701	+	0.789297i	−0.998728	−	0.0504182i	$-0.983945\pi$
$509$	−2.66363e6	+	4.61355e6i	−0.455701	+	0.789297i	0.543028	+	0.839715i	$0.317278\pi$
$510$	733899.	+	3.36846e6i	0.124943	+	0.573464i
$511$	2.76346e6	+	4.78646e6i	0.468167	+	0.810890i
$512$	−262144.			−0.0441942
$513$	−1.29653e6	−	1.72848e6i	−0.217515	−	0.289982i
$514$	120455.			0.0201103
$515$	−4.32168e6	−	7.48537e6i	−0.718017	−	1.24364i
$516$	−323609.	−	1.48531e6i	−0.0535053	−	0.245579i
$517$	−360294.	+	624047.i	−0.0592830	+	0.102681i
$518$	1.16822e6	−	2.02341e6i	0.191293	−	0.331330i
$519$	4.40218e6	−	4.00443e6i	0.717380	−	0.652563i
$520$	1.04273e6	+	1.80605e6i	0.169107	+	0.292902i
$521$	1.14471e7			1.84757			0.923783	−	0.382916i	$-0.125080\pi$
$521$	1.14471e7			1.84757			0.923783	+	0.382916i	$0.125080\pi$
$522$	−463688.	+	4.88920e6i	−0.0744817	+	0.785347i
$523$	7.05392e6			1.12766			0.563828	−	0.825892i	$-0.309328\pi$
$523$	7.05392e6			1.12766			0.563828	+	0.825892i	$0.309328\pi$
$524$	2.50546e6	+	4.33959e6i	0.398621	+	0.690431i
$525$	722273.	+	230630.i	0.114368	+	0.0365188i
$526$	−2.04804e6	+	3.54731e6i	−0.322756	+	0.559030i
$527$	2.73458e6	−	4.73643e6i	0.428908	−	0.742890i
$528$	−459987.	−	146879.i	−0.0718060	−	0.0229284i
$529$	506986.	+	878126.i	0.0787693	+	0.136432i
$530$	1.93266e6			0.298859
$531$	−219175.	+	2.31101e6i	−0.0337329	+	0.355685i
$532$	983143.			0.150604
$533$	2.60226e6	+	4.50725e6i	0.396765	+	0.687217i
$534$	−3.44609e6	+	3.13473e6i	−0.522966	+	0.475715i
$535$	18312.6	−	31718.4i	0.00276609	−	0.00479101i
$536$	347471.	−	601837.i	0.0522404	−	0.0904829i
$537$	−1.01691e6	−	4.66745e6i	−0.152177	−	0.698463i
$538$	3.27357e6	+	5.66998e6i	0.487602	+	0.844551i
$539$	−629519.			−0.0933334
$540$	1.23083e6	−	2.88195e6i	0.181641	−	0.425306i
$541$	−4.82045e6			−0.708100			−0.354050	−	0.935226i	$-0.615196\pi$
$541$	−4.82045e6			−0.708100			−0.354050	+	0.935226i	$0.615196\pi$
$542$	3.84179e6	+	6.65418e6i	0.561740	+	0.972963i
$543$	−500871.	−	2.29891e6i	−0.0728999	−	0.334597i
$544$	547482.	−	948267.i	0.0793182	−	0.137383i
$545$	−1.02030e6	+	1.76720e6i	−0.147141	+	0.254856i
$546$	3.13135e6	−	2.84842e6i	0.449520	−	0.408905i
$547$	3.38278e6	+	5.85915e6i	0.483399	+	0.837271i	0.999818	−	0.0190646i	$-0.00606881\pi$
$547$	3.38278e6	+	5.85915e6i	0.483399	+	0.837271i	−0.516420	+	0.856336i	$0.672735\pi$
$548$	−2.26490e6			−0.322180
$549$	−3.46221e6	−	2.46207e6i	−0.490255	−	0.348634i
$550$	218532.			0.0308042
$551$	−1.44103e6	−	2.49593e6i	−0.202206	−	0.350230i
$552$	−2.21307e6	−	706657.i	−0.309134	−	0.0987099i
$553$	−2.84124e6	+	4.92118e6i	−0.395090	+	0.684316i
$554$	−233659.	+	404709.i	−0.0323451	+	0.0560233i
$555$	4.16335e6	+	1.32940e6i	0.573734	+	0.183199i
$556$	1.66154e6	+	2.87787e6i	0.227942	+	0.394807i
$557$	1.14325e7			1.56136			0.780682	−	0.624929i	$-0.214872\pi$
$557$	1.14325e7			1.56136			0.780682	+	0.624929i	$0.214872\pi$
$558$	−4.52090e6	+	2.06814e6i	−0.614666	+	0.281187i
$559$	3.84100e6			0.519894
$560$	712951.	+	1.23487e6i	0.0960704	+	0.166399i
$561$	1.49199e6	−	1.35718e6i	0.200151	−	0.182067i
$562$	−2.50160e6	+	4.33291e6i	−0.334101	+	0.578680i
$563$	4.13683e6	−	7.16519e6i	0.550043	−	0.952702i	−0.448228	−	0.893919i	$-0.647945\pi$
$563$	4.13683e6	−	7.16519e6i	0.550043	−	0.952702i	0.998271	−	0.0587826i	$-0.0187219\pi$
$564$	316197.	+	1.45129e6i	0.0418563	+	0.192113i
$565$	6.29875e6	+	1.09098e7i	0.830106	+	1.43779i
$566$	−1.02116e7			−1.33984
$567$	−6.24756e6	−	1.19578e6i	−0.816118	−	0.156205i
$568$	−903145.			−0.117459
$569$	−1.07131e6	−	1.85557e6i	−0.138719	−	0.240268i	0.788293	−	0.615300i	$-0.210965\pi$
$569$	−1.07131e6	−	1.85557e6i	−0.138719	−	0.240268i	−0.927012	+	0.375032i	$0.877632\pi$
$570$	391491.	+	1.79687e6i	0.0504702	+	0.231649i
$571$	−3.70435e6	+	6.41613e6i	−0.475469	+	0.823536i	−0.999605	−	0.0280981i	$-0.991055\pi$
$571$	−3.70435e6	+	6.41613e6i	−0.475469	+	0.823536i	0.524136	+	0.851634i	$0.324388\pi$
$572$	610037.	−	1.05662e6i	0.0779590	−	0.135029i
$573$	−1.05080e7	+	9.55857e6i	−1.33700	+	1.21620i
$574$	1.77927e6	+	3.08178e6i	0.225404	+	0.390411i
$575$	1.05139e6			0.132616
$576$	−905116.	+	414057.i	−0.113671	+	0.0520000i
$577$	2.40915e6			0.301248			0.150624	−	0.988591i	$-0.451872\pi$
$577$	2.40915e6			0.301248			0.150624	+	0.988591i	$0.451872\pi$
$578$	−552904.	−	957659.i	−0.0688383	−	0.119232i
$579$	−1.12599e7	−	3.59541e6i	−1.39585	−	0.445710i
$580$	2.08999e6	−	3.61998e6i	0.257974	−	0.446823i
$581$	−587143.	+	1.01696e6i	−0.0721611	+	0.124987i
$582$	4.05224e6	+	1.29392e6i	0.495892	+	0.158344i
$583$	−565343.	−	979203.i	−0.0688876	−	0.119317i
$584$	3.28362e6			0.398401
$585$	6.45293e6	+	4.58886e6i	0.779592	+	0.554389i
$586$	3.43245e6			0.412915
$587$	−3.75562e6	−	6.50493e6i	−0.449870	−	0.779197i	0.548507	−	0.836146i	$-0.315196\pi$
$587$	−3.75562e6	−	6.50493e6i	−0.449870	−	0.779197i	−0.998377	+	0.0569483i	$0.981863\pi$
$588$	−959893.	+	873164.i	−0.114493	+	0.104148i
$589$	1.45874e6	−	2.52660e6i	0.173256	−	0.300088i
$590$	987892.	−	1.71108e6i	0.116837	−	0.202367i
$591$	2.46216e6	+	1.13009e7i	0.289967	+	1.33089i
$592$	−694054.	−	1.20214e6i	−0.0813934	−	0.140977i
$593$	1.38935e7			1.62247			0.811234	−	0.584722i	$-0.198796\pi$
$593$	1.38935e7			1.62247			0.811234	+	0.584722i	$0.198796\pi$
$594$	−1.82021e6	+	219415.i	−0.211668	+	0.0255153i
$595$	−5.95593e6			−0.689695
$596$	399555.	+	692050.i	0.0460746	+	0.0798035i
$597$	489485.	+	2.24665e6i	0.0562088	+	0.257988i
$598$	2.93498e6	−	5.08354e6i	0.335624	−	0.581318i
$599$	−4.31504e6	+	7.47387e6i	−0.491381	+	0.851096i	−0.999951	−	0.00992421i	$-0.996841\pi$
$599$	−4.31504e6	+	7.47387e6i	−0.491381	+	0.851096i	0.508570	+	0.861021i	$0.330174\pi$
$600$	333219.	−	303112.i	0.0377878	−	0.0343736i
$601$	−7.27201e6	−	1.25955e7i	−0.821236	−	1.42242i	−0.904762	−	0.425917i	$-0.859951\pi$
$601$	−7.27201e6	−	1.25955e7i	−0.821236	−	1.42242i	0.0835260	−	0.996506i	$-0.473382\pi$
$602$	2.62624e6			0.295354
$603$	249125.	−	2.62682e6i	0.0279013	−	0.294196i
$604$	6.01599e6			0.670988
$605$	378512.	+	655602.i	0.0420428	+	0.0728202i
$606$	−415057.	−	132532.i	−0.0459120	−	0.0146602i
$607$	−1.91627e6	+	3.31908e6i	−0.211099	+	0.365634i	−0.952059	−	0.305916i	$-0.901037\pi$
$607$	−1.91627e6	+	3.31908e6i	−0.211099	+	0.365634i	0.740960	+	0.671549i	$0.234371\pi$
$608$	292049.	−	505844.i	0.0320403	−	0.0554955i
$609$	−8.08253e6	−	2.58084e6i	−0.883088	−	0.281979i
$610$	1.80795e6	+	3.13145e6i	0.196726	+	0.340739i
$611$	−3.75303e6			−0.406705
$612$	392527.	−	4.13887e6i	0.0423634	−	0.446687i
$613$	1.33244e7			1.43217			0.716086	−	0.698012i	$-0.245932\pi$
$613$	1.33244e7			1.43217			0.716086	+	0.698012i	$0.245932\pi$
$614$	−3.84395e6	−	6.65792e6i	−0.411488	−	0.712718i
$615$	−4.92401e6	+	4.47911e6i	−0.524966	+	0.477534i
$616$	417106.	−	722448.i	0.0442888	−	0.0767105i
$617$	1.32531e6	−	2.29550e6i	0.140154	−	0.242753i	−0.787401	−	0.616441i	$-0.788574\pi$
$617$	1.32531e6	−	2.29550e6i	0.140154	−	0.242753i	0.927554	+	0.373688i	$0.121907\pi$
$618$	2.21892e6	+	1.01844e7i	0.233706	+	1.07267i
$619$	−351031.	−	608004.i	−0.0368230	−	0.0637793i	0.847027	−	0.531551i	$-0.178390\pi$
$619$	−351031.	−	608004.i	−0.0368230	−	0.0637793i	−0.883850	+	0.467771i	$0.845057\pi$
$620$	4.23136e6			0.442079
$621$	−8.75732e6	+	1.05564e6i	−0.911260	+	0.109847i
$622$	−9.90952e6			−1.02701
$623$	−4.02409e6	−	6.96993e6i	−0.415382	−	0.719463i
$624$	−535375.	−	2.45727e6i	−0.0550423	−	0.252634i
$625$	4.07539e6	−	7.05878e6i	0.417320	−	0.722819i
$626$	−2.45274e6	+	4.24827e6i	−0.250159	+	0.433288i
$627$	795885.	−	723975.i	0.0808503	−	0.0735453i
$628$	−2.91762e6	−	5.05347e6i	−0.295209	−	0.511317i
$629$	5.79807e6			0.584328
$630$	4.41211e6	+	3.13757e6i	0.442889	+	0.314951i
$631$	−1.22215e6			−0.122194			−0.0610970	−	0.998132i	$-0.519460\pi$
$631$	−1.22215e6			−0.122194			−0.0610970	+	0.998132i	$0.519460\pi$
$632$	1.68802e6	+	2.92374e6i	0.168107	+	0.291169i
$633$	−749065.	−	239184.i	−0.0743036	−	0.0237260i
$634$	2.35092e6	−	4.07192e6i	0.232282	−	0.402324i
$635$	−7.48423e6	+	1.29631e7i	−0.736568	+	1.27577i
$636$	−2.22023e6	−	708942.i	−0.217648	−	0.0694973i
$637$	−1.63936e6	−	2.83946e6i	−0.160076	−	0.277260i
$638$	−2.44547e6			−0.237854
$639$	−3.11833e6	+	1.42652e6i	−0.302113	+	0.138205i
$640$	847147.			0.0817540
$641$	9.62222e6	+	1.66662e7i	0.924976	+	1.60211i	0.791600	+	0.611040i	$0.209248\pi$
$641$	9.62222e6	+	1.66662e7i	0.924976	+	1.60211i	0.133376	+	0.991066i	$0.457418\pi$
$642$	−32672.4	+	29720.4i	−0.00312855	+	0.00284588i
$643$	−4.27528e6	+	7.40500e6i	−0.407790	+	0.706313i	−0.994642	−	0.103381i	$-0.967034\pi$
$643$	−4.27528e6	+	7.40500e6i	−0.407790	+	0.706313i	0.586852	+	0.809694i	$0.300367\pi$
$644$	2.00676e6	−	3.47581e6i	0.190669	−	0.330249i
$645$	1.04578e6	+	4.79993e6i	0.0989784	+	0.454293i
$646$	1.21988e6	+	2.11289e6i	0.115010	+	0.199203i
$647$	−1.83816e6			−0.172632			−0.0863161	−	0.996268i	$-0.527509\pi$
$647$	−1.83816e6			−0.172632			−0.0863161	+	0.996268i	$0.527509\pi$
$648$	−2.47113e6	+	2.85926e6i	−0.231184	+	0.267496i
$649$	−1.15591e6			−0.107724
$650$	569091.	+	985695.i	0.0528322	+	0.0915080i
$651$	−1.82839e6	−	8.39197e6i	−0.169089	−	0.776089i
$652$	2.39853e6	−	4.15437e6i	0.220966	−	0.382725i
$653$	1.85122e6	−	3.20640e6i	0.169893	−	0.294263i	−0.768489	−	0.639863i	$-0.778991\pi$
$653$	1.85122e6	−	3.20640e6i	0.169893	−	0.294263i	0.938382	+	0.345600i	$0.112325\pi$
$654$	1.82036e6	−	1.65588e6i	0.166422	−	0.151386i
$655$	−8.09668e6	−	1.40239e7i	−0.737401	−	1.27722i
$656$	2.11417e6			0.191814
$657$	1.13375e7	−	5.18648e6i	1.02472	−	0.468769i
$658$	−2.56609e6			−0.231051
$659$	−5.00363e6	−	8.66655e6i	−0.448820	−	0.777379i	0.549490	−	0.835500i	$-0.314822\pi$
$659$	−5.00363e6	−	8.66655e6i	−0.448820	−	0.777379i	−0.998309	+	0.0581218i	$0.981489\pi$
$660$	1.48650e6	+	474655.i	0.132833	+	0.0424149i
$661$	−6.96346e6	+	1.20611e7i	−0.619899	+	1.07370i	0.369604	+	0.929189i	$0.379493\pi$
$661$	−6.96346e6	+	1.20611e7i	−0.619899	+	1.07370i	−0.989504	+	0.144508i	$0.953840\pi$
$662$	5.77764e6	−	1.00072e7i	0.512396	−	0.887496i
$663$	1.00069e7	+	3.19532e6i	0.884133	+	0.282313i
$664$	348829.	+	604190.i	0.0307038	+	0.0531806i
$665$	−3.17713e6			−0.278600
$666$	−4.29517e6	−	3.05441e6i	−0.375227	−	0.266835i
$667$	−1.17655e7			−1.02399
$668$	4.76544e6	+	8.25399e6i	0.413202	+	0.715687i
$669$	1.21905e7	−	1.10890e7i	1.05307	−	0.957919i
$670$	−1.12289e6	+	1.94490e6i	−0.0966385	+	0.167383i
$671$	1.05772e6	−	1.83203e6i	0.0906913	−	0.157082i
$672$	−366056.	−	1.68013e6i	−0.0312698	−	0.143523i
$673$	−535991.	−	928363.i	−0.0456163	−	0.0790097i	0.842316	−	0.538984i	$-0.181192\pi$
$673$	−535991.	−	928363.i	−0.0456163	−	0.0790097i	−0.887932	+	0.459975i	$0.847858\pi$
$674$	6.73741e6			0.571273
$675$	671754.	−	1.57289e6i	0.0567481	−	0.132874i
$676$	413825.			0.0348297
$677$	−9.53116e6	−	1.65085e7i	−0.799234	−	1.38431i	−0.920115	−	0.391648i	$-0.871905\pi$
$677$	−9.53116e6	−	1.65085e7i	−0.799234	−	1.38431i	0.120881	−	0.992667i	$-0.461428\pi$
$678$	−3.23402e6	−	1.48436e7i	−0.270190	−	1.24012i
$679$	−3.67447e6	+	6.36438e6i	−0.305859	+	0.529763i
$680$	−1.76925e6	+	3.06443e6i	−0.146729	+	0.254143i
$681$	−6.80545e6	+	6.19056e6i	−0.562327	+	0.511520i
$682$	−1.23776e6	−	2.14386e6i	−0.101900	−	0.176496i
$683$	1.75226e7			1.43730			0.718650	−	0.695372i	$-0.244760\pi$
$683$	1.75226e7			1.43730			0.718650	+	0.695372i	$0.244760\pi$
$684$	209390.	−	2.20784e6i	0.0171126	−	0.180438i
$685$	7.31928e6			0.595994
$686$	−4.74191e6	−	8.21323e6i	−0.384719	−	0.666352i
$687$	9.99504e6	+	3.19152e6i	0.807965	+	0.257992i
$688$	780142.	−	1.35125e6i	0.0628351	−	0.108834i
$689$	2.94448e6	−	5.09998e6i	0.236298	−	0.409280i
$690$	7.15178e6	+	2.28364e6i	0.571862	+	0.182602i
$691$	58906.5	+	102029.i	0.00469319	+	0.00812884i	0.868362	−	0.495930i	$-0.165173\pi$
$691$	58906.5	+	102029.i	0.00469319	+	0.00812884i	−0.863669	+	0.504059i	$0.831839\pi$
$692$	6.10813e6			0.484890
$693$	299051.	−	3.15325e6i	0.0236544	−	0.249416i
$694$	1.24961e6			0.0984864
$695$	−5.36945e6	−	9.30016e6i	−0.421665	−	0.730346i
$696$	−3.72885e6	+	3.39194e6i	−0.291778	+	0.265415i
$697$	−4.41540e6	+	7.64770e6i	−0.344261	+	0.596278i
$698$	−7.59166e6	+	1.31491e7i	−0.589791	+	1.02155i
$699$	286081.	+	1.31306e6i	0.0221460	+	0.101646i
$700$	389109.	+	673957.i	0.0300142	+	0.0519861i
$701$	−1.11262e7			−0.855167			−0.427583	−	0.903976i	$-0.640635\pi$
$701$	−1.11262e7			−0.855167			−0.427583	+	0.903976i	$0.640635\pi$
$702$	−5.72978e6	−	7.63871e6i	−0.438829	−	0.585029i
$703$	3.09292e6			0.236037
$704$	−247808.	−	429216.i	−0.0188445	−	0.0326396i
$705$	−1.02183e6	−	4.69000e6i	−0.0774292	−	0.355386i
$706$	1.59940e6	−	2.77025e6i	0.120766	−	0.209173i
$707$	376364.	−	651881.i	0.0283178	−	0.0490478i
$708$	−1.76254e6	+	1.60329e6i	−0.132147	+	0.120207i
$709$	−4.42416e6	−	7.66287e6i	−0.330533	−	0.572501i	0.652083	−	0.758147i	$-0.273895\pi$
$709$	−4.42416e6	−	7.66287e6i	−0.330533	−	0.572501i	−0.982617	+	0.185647i	$0.940562\pi$
$710$	2.91861e6			0.217285
$711$	1.04464e7	+	7.42869e6i	0.774980	+	0.551110i
$712$	−4.78153e6			−0.353482
$713$	−5.95505e6	−	1.03144e7i	−0.438694	−	0.759840i
$714$	6.84213e6	+	2.18476e6i	0.502280	+	0.160383i
$715$	−1.97140e6	+	3.41457e6i	−0.144215	+	0.249788i
$716$	2.45153e6	−	4.24617e6i	0.178712	−	0.309539i
$717$	−5.77948e6	−	1.84545e6i	−0.419847	−	0.134062i
$718$	−5.39412e6	−	9.34290e6i	−0.390490	−	0.676348i
$719$	−4.85421e6			−0.350184			−0.175092	−	0.984552i	$-0.556022\pi$
$719$	−4.85421e6			−0.350184			−0.175092	+	0.984552i	$0.556022\pi$
$720$	2.92498e6	−	1.33807e6i	0.210277	−	0.0961939i
$721$	−1.80075e7			−1.29008
$722$	−4.30147e6	−	7.45036e6i	−0.307096	−	0.531905i
$723$	−7.45239e6	+	6.77905e6i	−0.530212	+	0.482306i
$724$	1.20748e6	−	2.09141e6i	0.0856116	−	0.148284i
$725$	1.14066e6	−	1.97568e6i	0.0805957	−	0.139596i
$726$	−194343.	−	891997.i	−0.0136844	−	0.0628090i
$727$	−1.07805e7	−	1.86723e7i	−0.756487	−	1.31027i	−0.944632	−	0.328133i	$-0.893581\pi$
$727$	−1.07805e7	−	1.86723e7i	−0.756487	−	1.31027i	0.188144	−	0.982141i	$-0.439753\pi$
$728$	4.34482e6			0.303839
$729$	−4.01597e6	+	1.37755e7i	−0.279880	+	0.960035i
$730$	−1.06114e7			−0.736995
$731$	3.25862e6	+	5.64409e6i	0.225549	+	0.390662i
$732$	−928268.	−	4.26058e6i	−0.0640318	−	0.293894i
$733$	−1.06401e7	+	1.84293e7i	−0.731455	+	1.26692i	0.224807	+	0.974403i	$0.427825\pi$
$733$	−1.06401e7	+	1.84293e7i	−0.731455	+	1.26692i	−0.956261	+	0.292513i	$0.905508\pi$
$734$	−7.76461e6	+	1.34487e7i	−0.531960	+	0.921382i
$735$	3.10200e6	−	2.82173e6i	0.211799	−	0.192662i
$736$	−1.19224e6	−	2.06502e6i	−0.0811279	−	0.140518i
$737$	1.31387e6			0.0891014
$738$	7.29969e6	−	3.33934e6i	0.493360	−	0.225694i
$739$	5.71302e6			0.384817			0.192409	−	0.981315i	$-0.438370\pi$
$739$	5.71302e6			0.384817			0.192409	+	0.981315i	$0.438370\pi$
$740$	2.24291e6	+	3.88484e6i	0.150568	+	0.260792i
$741$	5.33811e6	+	1.70452e6i	0.357143	+	0.114040i
$742$	2.01325e6	−	3.48705e6i	0.134242	−	0.232514i
$743$	8.05296e6	−	1.39481e7i	0.535160	−	0.926924i	−0.463996	−	0.885837i	$-0.653585\pi$
$743$	8.05296e6	−	1.39481e7i	0.535160	−	0.926924i	0.999156	−	0.0410865i	$-0.0130819\pi$
$744$	−4.86095e6	−	1.55215e6i	−0.321950	−	0.102802i
$745$	−1.29121e6	−	2.23644e6i	−0.0852325	−	0.147627i
$746$	−4.02835e6			−0.265021
$747$	2.15874e6	+	1.53514e6i	0.141546	+	0.100657i
$748$	2.07017e6			0.135286
$749$	−38152.5	−	66082.0i	−0.00248495	−	0.00430406i
$750$	−8.52979e6	+	7.75910e6i	−0.553713	+	0.503684i
$751$	−8.65308e6	+	1.49876e7i	−0.559849	+	0.969687i	0.437660	+	0.899141i	$0.355807\pi$
$751$	−8.65308e6	+	1.49876e7i	−0.559849	+	0.969687i	−0.997509	+	0.0705460i	$0.977526\pi$
$752$	−762274.	+	1.32030e6i	−0.0491549	+	0.0851387i
$753$	3.54423e6	+	1.62674e7i	0.227790	+	1.04551i
$754$	−6.36836e6	−	1.10303e7i	−0.407942	−	0.706577i
$755$	−1.94413e7			−1.24125
$756$	−3.91767e6	−	5.22288e6i	−0.249300	−	0.332357i
$757$	1.57827e7			1.00102			0.500508	−	0.865732i	$-0.333147\pi$
$757$	1.57827e7			1.00102			0.500508	+	0.865732i	$0.333147\pi$
$758$	−7.08489e6	−	1.22714e7i	−0.447878	−	0.775748i
$759$	−935012.	−	4.29153e6i	−0.0589132	−	0.270401i
$760$	−943789.	+	1.63469e6i	−0.0592708	+	0.102660i
$761$	3.38619e6	−	5.86506e6i	0.211958	−	0.367122i	−0.740369	−	0.672200i	$-0.765349\pi$
$761$	3.38619e6	−	5.86506e6i	0.211958	−	0.367122i	0.952327	+	0.305078i	$0.0986827\pi$
$762$	1.33530e7	−	1.21465e7i	0.833086	−	0.757815i
$763$	2.12568e6	+	3.68178e6i	0.132186	+	0.228953i
$764$	−1.45801e7			−0.903705
$765$	−1.26850e6	+	1.33752e7i	−0.0783674	+	0.826318i
$766$	−2.11593e7			−1.30296
$767$	−3.01017e6	−	5.21377e6i	−0.184758	−	0.320010i
$768$	−973196.	−	310752.i	−0.0595384	−	0.0190113i
$769$	−4.10679e6	+	7.11316e6i	−0.250430	+	0.433757i	−0.963644	−	0.267189i	$-0.913905\pi$
$769$	−4.10679e6	+	7.11316e6i	−0.250430	+	0.433757i	0.713214	+	0.700946i	$0.247239\pi$
$770$	−1.34792e6	+	2.33467e6i	−0.0819291	+	0.141905i
$771$	447184.	+	142791.i	0.0270926	+	0.00865096i
$772$	−6.06604e6	−	1.05067e7i	−0.366321	−	0.634486i
$773$	2.00400e7			1.20628			0.603140	−	0.797635i	$-0.293916\pi$
$773$	2.00400e7			1.20628			0.603140	+	0.797635i	$0.293916\pi$
$774$	559337.	−	5.89774e6i	0.0335599	−	0.353861i
$775$	2.30936e6			0.138114
$776$	2.18305e6	+	3.78116e6i	0.130140	+	0.225409i
$777$	6.73555e6	−	6.12698e6i	0.400240	−	0.364078i
$778$	−1.07124e7	+	1.85544e7i	−0.634510	+	1.09900i
$779$	−2.35535e6	+	4.07959e6i	−0.139063	+	0.240865i
$780$	1.73012e6	+	7.94095e6i	0.101822	+	0.467343i
$781$	−853754.	−	1.47874e6i	−0.0500847	−	0.0867492i
$782$	9.95989e6			0.582422
$783$	−7.51720e6	+	1.76012e7i	−0.438179	+	1.02598i
$784$	−1.33187e6			−0.0773879
$785$	9.42861e6	+	1.63308e7i	0.546102	+	0.945876i
$786$	4.15715e6	+	1.90805e7i	0.240015	+	1.10163i
$787$	1.09265e7	−	1.89252e7i	0.628843	−	1.08919i	−0.358941	−	0.933360i	$-0.616862\pi$
$787$	1.09265e7	−	1.89252e7i	0.628843	−	1.08919i	0.987784	−	0.155828i	$-0.0498047\pi$
$788$	−5.93567e6	+	1.02809e7i	−0.340529	+	0.589814i
$789$	−1.18083e7	+	1.07414e7i	−0.675298	+	0.614284i
$790$	−5.45503e6	−	9.44838e6i	−0.310978	−	0.538629i
$791$	2.62456e7			1.49147
$792$	−1.53356e6	−	1.09056e6i	−0.0868739	−	0.0617784i
$793$	1.10179e7			0.622178
$794$	235239.	+	407446.i	0.0132422	+	0.0229361i
$795$	7.17490e6	+	2.29102e6i	0.402623	+	0.128562i
$796$	−1.18003e6	+	2.04387e6i	−0.0660100	+	0.114333i
$797$	3.99595e6	−	6.92119e6i	0.222830	−	0.385953i	−0.732836	−	0.680405i	$-0.761804\pi$
$797$	3.99595e6	−	6.92119e6i	0.222830	−	0.385953i	0.955666	+	0.294452i	$0.0951371\pi$
$798$	3.64987e6	+	1.16544e6i	0.202894	+	0.0647863i
$799$	−3.18399e6	−	5.51482e6i	−0.176443	−	0.305608i
$800$	462350.			0.0255415
$801$	−1.65094e7	+	7.55243e6i	−0.909180	+	0.415916i
$802$	−2.14421e7			−1.17715
$803$	3.10405e6	+	5.37636e6i	0.169879	+	0.294239i
$804$	2.00340e6	−	1.82239e6i	0.109302	−	0.0994261i
$805$	−6.48506e6	+	1.12325e7i	−0.352716	+	0.610921i
$806$	6.44662e6	−	1.11659e7i	0.349538	−	0.605417i
$807$	5.43161e6	+	2.49301e7i	0.293592	+	1.34753i
$808$	−223603.	−	387291.i	−0.0120489	−	0.0208694i
$809$	1.51555e6			0.0814138			0.0407069	−	0.999171i	$-0.487039\pi$
$809$	1.51555e6			0.0814138			0.0407069	+	0.999171i	$0.487039\pi$
$810$	7.98573e6	−	9.24002e6i	0.427664	−	0.494835i
$811$	1.88387e7			1.00577			0.502886	−	0.864353i	$-0.332271\pi$
$811$	1.88387e7			1.00577			0.502886	+	0.864353i	$0.332271\pi$
$812$	−4.35428e6	−	7.54184e6i	−0.231754	−	0.401409i
$813$	6.37443e6	+	2.92574e7i	0.338232	+	1.55242i
$814$	1.31220e6	−	2.27279e6i	0.0694125	−	0.120226i
$815$	−7.75111e6	+	1.34253e7i	−0.408761	+	0.707995i
$816$	3.15660e6	−	2.87139e6i	0.165956	−	0.150962i
$817$	1.73828e6	+	3.01079e6i	0.0911096	+	0.157806i
$818$	−534289.			−0.0279185
$819$	1.50015e7	−	6.86265e6i	0.781495	−	0.357505i
$820$	−6.83218e6			−0.354834
$821$	−3.72602e6	−	6.45365e6i	−0.192924	−	0.334155i	0.753294	−	0.657684i	$-0.228464\pi$
$821$	−3.72602e6	−	6.45365e6i	−0.192924	−	0.334155i	−0.946218	+	0.323530i	$0.895130\pi$
$822$	−8.40833e6	−	2.68487e6i	−0.434041	−	0.138594i
$823$	1.20864e7	−	2.09342e7i	0.622009	−	1.07735i	−0.367102	−	0.930181i	$-0.619650\pi$
$823$	1.20864e7	−	2.09342e7i	0.622009	−	1.07735i	0.989111	−	0.147171i	$-0.0470167\pi$
$824$	−5.34926e6	+	9.26519e6i	−0.274458	+	0.475375i
$825$	811290.	+	259054.i	0.0414994	+	0.0132512i
$826$	−2.05817e6	−	3.56485e6i	−0.104962	−	0.181799i
$827$	−1.89225e7			−0.962090			−0.481045	−	0.876696i	$-0.659743\pi$
$827$	−1.89225e7			−0.962090			−0.481045	+	0.876696i	$0.659743\pi$
$828$	−7.37821e6	−	5.24685e6i	−0.374003	−	0.265964i
$829$	−9.87454e6			−0.499034			−0.249517	−	0.968370i	$-0.580272\pi$
$829$	−9.87454e6			−0.499034			−0.249517	+	0.968370i	$0.580272\pi$
$830$	−1.12728e6	−	1.95251e6i	−0.0567985	−	0.0983779i
$831$	−1.34720e6	+	1.22548e6i	−0.0676751	+	0.0615605i
$832$	1.29066e6	−	2.23548e6i	0.0646402	−	0.111960i
$833$	2.78159e6	−	4.81786e6i	0.138893	−	0.240570i
$834$	2.75688e6	+	1.26536e7i	0.137247	+	0.629939i
$835$	−1.54001e7	−	2.66737e7i	−0.764375	−	1.32394i
$836$	1.10431e6			0.0546482
$837$	−1.92352e7	+	2.31868e6i	−0.949038	+	0.114401i
$838$	−1.71382e7			−0.843052
$839$	−7.19533e6	−	1.24627e7i	−0.352895	−	0.611233i	0.633860	−	0.773448i	$-0.281469\pi$
$839$	−7.19533e6	−	1.24627e7i	−0.352895	−	0.611233i	−0.986755	+	0.162215i	$0.948136\pi$
$840$	1.18295e6	+	5.42953e6i	0.0578454	+	0.265500i
$841$	−2.50888e6	+	4.34551e6i	−0.122318	+	0.211861i
$842$	−6.24700e6	+	1.08201e7i	−0.303663	+	0.525959i
$843$	−1.44234e7	+	1.31202e7i	−0.699035	+	0.635876i
$844$	−403542.	−	698956.i	−0.0194999	−	0.0337749i
$845$	−1.33732e6			−0.0644308
$846$	−546526.	+	5.76266e6i	−0.0262534	+	0.276820i
$847$	1.57718e6			0.0755393
$848$	−1.19610e6	−	2.07170e6i	−0.0571185	−	0.0989322i
$849$	−3.79101e7	−	1.21051e7i	−1.80503	−	0.576367i
$850$	−965608.	+	1.67248e6i	−0.0458409	+	0.0793988i
$851$	6.31318e6	−	1.09347e7i	0.298830	−	0.517589i
$852$	−3.35288e6	−	1.07061e6i	−0.158241	−	0.0505280i
$853$	−6.95645e6	−	1.20489e7i	−0.327352	−	0.566991i	0.654633	−	0.755947i	$-0.272823\pi$
$853$	−6.95645e6	−	1.20489e7i	−0.327352	−	0.566991i	−0.981986	+	0.188956i	$0.939490\pi$
$854$	7.53333e6			0.353462
$855$	−676667.	+	7.13488e6i	−0.0316562	+	0.333789i
$856$	−45333.8			−0.00211465
$857$	7.51530e6	+	1.30169e7i	0.349538	+	0.605417i	0.986167	−	0.165752i	$-0.0530053\pi$
$857$	7.51530e6	+	1.30169e7i	0.349538	+	0.605417i	−0.636630	+	0.771170i	$0.719672\pi$
$858$	3.51727e6	−	3.19948e6i	0.163113	−	0.148375i
$859$	1.02819e7	−	1.78088e7i	0.475434	−	0.823476i	−0.524170	−	0.851614i	$-0.675624\pi$
$859$	1.02819e7	−	1.78088e7i	0.475434	−	0.823476i	0.999604	+	0.0281380i	$0.00895778\pi$
$860$	−2.52111e6	+	4.36670e6i	−0.116238	+	0.201329i
$861$	2.95222e6	+	1.35501e7i	0.135719	+	0.622925i
$862$	2.04420e6	+	3.54067e6i	0.0937036	+	0.162299i
$863$	3.04830e7			1.39326			0.696628	−	0.717433i	$-0.254683\pi$
$863$	3.04830e7			1.39326			0.696628	+	0.717433i	$0.254683\pi$
$864$	−3.85103e6	+	464217.i	−0.175506	+	0.0211561i
$865$	−1.97391e7			−0.896989
$866$	6.39572e6	+	1.10777e7i	0.289798	+	0.501944i
$867$	−917397.	−	4.21068e6i	−0.0414486	−	0.190241i
$868$	4.40779e6	−	7.63452e6i	0.198574	−	0.343940i
$869$	−3.19142e6	+	5.52769e6i	−0.143362	+	0.248310i
$870$	1.20502e7	−	1.09614e7i	0.539755	−	0.490987i
$871$	3.42152e6	+	5.92625e6i	0.152818	+	0.264688i
$872$	2.52579e6			0.112488
$873$	1.35099e7	+	9.60724e6i	0.599951	+	0.426642i
$874$	5.31301e6			0.235267
$875$	−9.96046e6	−	1.72520e7i	−0.439804	−	0.761763i
$876$	1.21903e7	+	3.89248e6i	0.536726	+	0.171382i
$877$	1.98399e7	−	3.43637e7i	0.871046	−	1.50870i	0.0101293	−	0.999949i	$-0.496776\pi$
$877$	1.98399e7	−	3.43637e7i	0.871046	−	1.50870i	0.860916	−	0.508747i	$-0.169891\pi$
$878$	1.10217e7	−	1.90901e7i	0.482517	−	0.835743i
$879$	1.27428e7	+	4.06891e6i	0.556279	+	0.177626i
$880$	800819.	+	1.38706e6i	0.0348600	+	0.0603793i
$881$	3.20076e7			1.38935			0.694677	−	0.719321i	$-0.255547\pi$
$881$	3.20076e7			1.38935			0.694677	+	0.719321i	$0.255547\pi$
$882$	−4.59862e6	+	2.10370e6i	−0.199047	+	0.0910567i
$883$	3.70822e7			1.60053			0.800266	−	0.599645i	$-0.204692\pi$
$883$	3.70822e7			1.60053			0.800266	+	0.599645i	$0.204692\pi$
$884$	5.39102e6	+	9.33752e6i	0.232028	+	0.401884i
$885$	5.69585e6	−	5.18122e6i	0.244456	−	0.222369i
$886$	−2.89310e6	+	5.01100e6i	−0.123817	+	0.214457i
$887$	−6.14736e6	+	1.06475e7i	−0.262349	+	0.454402i	−0.966866	−	0.255285i	$-0.917831\pi$
$887$	−6.14736e6	+	1.06475e7i	−0.262349	+	0.454402i	0.704517	+	0.709688i	$0.251164\pi$
$888$	−1.15160e6	−	5.28562e6i	−0.0490081	−	0.224938i
$889$	1.55926e7	+	2.70072e7i	0.661705	+	1.14611i
$890$	1.54520e7			0.653900
$891$	−7.01754e6	−	1.34316e6i	−0.296136	−	0.0566804i
$892$	1.69146e7			0.711786
$893$	−1.69847e6	−	2.94183e6i	−0.0712735	−	0.123449i
$894$	662955.	+	3.04284e6i	0.0277422	+	0.127331i
$895$	−7.92238e6	+	1.37220e7i	−0.330596	+	0.572610i
$896$	882471.	−	1.52849e6i	0.0367224	−	0.0636050i
$897$	1.69221e7	−	1.53932e7i	0.702221	−	0.638774i
$898$	−2.42856e6	−	4.20640e6i	−0.100498	−	0.174068i
$899$	−2.58426e7			−1.06644
$900$	1.59638e6	−	730282.i	0.0656944	−	0.0300527i
$901$	9.99210e6			0.410058
$902$	1.99855e6	+	3.46160e6i	0.0817898	+	0.141664i
$903$	9.74977e6	+	3.11321e6i	0.397901	+	0.127054i
$904$	7.79643e6	−	1.35038e7i	0.317303	−	0.549585i
$905$	−3.90210e6	+	6.75863e6i	−0.158371	+	0.274307i
$906$	2.23340e7	+	7.13150e6i	0.903955	+	0.288643i
$907$	3.71655e6	+	6.43726e6i	0.150011	+	0.259826i	0.931231	−	0.364429i	$-0.118736\pi$
$907$	3.71655e6	+	6.43726e6i	0.150011	+	0.259826i	−0.781220	+	0.624255i	$0.785403\pi$
$908$	−9.44273e6			−0.380087
$909$	−1.38377e6	−	984037.i	−0.0555462	−	0.0395004i
$910$	−1.40408e7			−0.562066
$911$	−4.23892e6	−	7.34203e6i	−0.169223	−	0.293103i	0.768924	−	0.639340i	$-0.220793\pi$
$911$	−4.23892e6	−	7.34203e6i	−0.169223	−	0.293103i	−0.938147	+	0.346237i	$0.887459\pi$
$912$	1.68386e6	−	1.53172e6i	0.0670375	−	0.0609805i
$913$	−659505.	+	1.14230e6i	−0.0261843	+	0.0453526i
$914$	1.24470e7	−	2.15588e7i	0.492831	−	0.853608i
$915$	2.99980e6	+	1.37685e7i	0.118451	+	0.543670i
$916$	5.38461e6	+	9.32642e6i	0.212039	+	0.367262i
$917$	−3.37372e7			−1.32491
$918$	6.36356e6	−	1.49000e7i	0.249226	−	0.583553i
$919$	−1.47099e6			−0.0574539			−0.0287270	−	0.999587i	$-0.509145\pi$
$919$	−1.47099e6			−0.0574539			−0.0287270	+	0.999587i	$0.509145\pi$
$920$	3.85286e6	+	6.67335e6i	0.150077	+	0.259941i
$921$	−6.37801e6	−	2.92739e7i	−0.247763	−	1.13719i
$922$	2.47139e6	−	4.28057e6i	0.0957445	−	0.165834i
$923$	4.44660e6	−	7.70174e6i	0.171800	−	0.297567i
$924$	2.40489e6	−	2.18760e6i	0.0926649	−	0.0842925i
$925$	1.22412e6	+	2.12024e6i	0.0470403	+	0.0814761i
$926$	−1.98522e7			−0.760819
$927$	−3.83525e6	+	4.04395e7i	−0.146587	+	1.54563i
$928$	−5.17388e6			−0.197218
$929$	1.39874e7	+	2.42270e7i	0.531740	+	0.921000i	0.999314	+	0.0370462i	$0.0117949\pi$
$929$	1.39874e7	+	2.42270e7i	0.531740	+	0.921000i	−0.467574	+	0.883954i	$0.654872\pi$
$930$	1.57087e7	+	5.01595e6i	0.595570	+	0.190172i
$931$	1.48381e6	−	2.57004e6i	0.0561055	−	0.0971775i
$932$	−689670.	+	1.19454e6i	−0.0260077	+	0.0450466i
$933$	−3.67886e7	−	1.17470e7i	−1.38359	−	0.441797i
$934$	5.74930e6	+	9.95809e6i	0.215649	+	0.373516i
$935$	−6.68997e6			−0.250262
$936$	925361.	−	9.75715e6i	0.0345240	−	0.364027i
$937$	−1.90588e7			−0.709165			−0.354582	−	0.935025i	$-0.615377\pi$
$937$	−1.90588e7			−0.709165			−0.354582	+	0.935025i	$0.615377\pi$
$938$	2.33942e6	+	4.05200e6i	0.0868164	+	0.150370i
$939$	−1.41417e7	+	1.28640e7i	−0.523404	+	0.476114i
$940$	2.46337e6	−	4.26669e6i	0.0909307	−	0.157497i
$941$	1.71339e7	−	2.96768e7i	0.630786	−	1.09255i	−0.356606	−	0.934255i	$-0.616066\pi$
$941$	1.71339e7	−	2.96768e7i	0.630786	−	1.09255i	0.987391	−	0.158298i	$-0.0506006\pi$
$942$	−4.84101e6	−	2.22194e7i	−0.177750	−	0.815838i
$943$	9.61535e6	+	1.66543e7i	0.352116	+	0.609883i
$944$	−2.44557e6			−0.0893203
$945$	1.26604e7	+	1.68783e7i	0.461176	+	0.614822i
$946$	2.94991e6			0.107172
$947$	−1.01979e7	−	1.76633e7i	−0.369518	−	0.640025i	0.619972	−	0.784624i	$-0.287144\pi$
$947$	−1.01979e7	−	1.76633e7i	−0.369518	−	0.640025i	−0.989490	+	0.144599i	$0.953811\pi$
$948$	2.80082e6	+	1.28552e7i	0.101220	+	0.464579i
$949$	−1.61668e7	+	2.80017e7i	−0.582718	+	1.00930i
$950$	−515094.	+	892169.i	−0.0185173	+	0.0320729i
$951$	1.35546e7	−	1.23299e7i	0.486000	−	0.442089i
$952$	3.68605e6	+	6.38442e6i	0.131816	+	0.228312i
$953$	1.00275e7			0.357651			0.178825	−	0.983881i	$-0.442770\pi$
$953$	1.00275e7			0.357651			0.178825	+	0.983881i	$0.442770\pi$
$954$	−7.40207e6	−	5.26382e6i	−0.263319	−	0.187254i
$955$	4.71172e7			1.67175
$956$	−3.11357e6	−	5.39286e6i	−0.110183	−	0.190842i
$957$	−9.07866e6	−	2.89891e6i	−0.320437	−	0.102319i
$958$	1.40254e7	−	2.42927e7i	0.493744	−	0.855189i
$959$	7.62448e6	−	1.32060e7i	0.267709	−	0.463686i
$960$	3.14499e6	+	1.00423e6i	0.110139	+	0.0351686i
$961$	1.23447e6	+	2.13817e6i	0.0431194	+	0.0746850i
$962$	1.36686e7			0.476197
$963$	−156526.	+	71604.7i	−0.00543902	+	0.00248815i
$964$	−1.03404e7			−0.358380
$965$	1.96031e7	+	3.39535e7i	0.677650	+	1.17372i
$966$	1.15703e7	−	1.05249e7i	0.398935	−	0.362890i
$967$	8.60328e6	−	1.49013e7i	0.295868	−	0.512459i	−0.679318	−	0.733844i	$-0.737724\pi$
$967$	8.60328e6	−	1.49013e7i	0.295868	−	0.512459i	0.975186	+	0.221385i	$0.0710578\pi$
$968$	468512.	−	811487.i	0.0160706	−	0.0278351i
$969$	2.02406e6	+	9.29006e6i	0.0692490	+	0.317840i
$970$	−7.05478e6	−	1.22192e7i	−0.240743	−	0.416980i
$971$	−4.20212e7			−1.43028			−0.715139	−	0.698983i	$-0.753636\pi$
$971$	−4.20212e7			−1.43028			−0.715139	+	0.698983i	$0.753636\pi$
$972$	−1.25634e7	+	7.68552e6i	−0.426522	+	0.260920i
$973$	−2.23734e7			−0.757616
$974$	1.72157e7	+	2.98185e7i	0.581471	+	1.00714i
$975$	944254.	+	4.33395e6i	0.0318110	+	0.146007i
$976$	2.23783e6	−	3.87603e6i	0.0751972	−	0.130245i
$977$	1.41188e7	−	2.44544e7i	0.473217	−	0.819635i	−0.526313	−	0.850291i	$-0.676426\pi$
$977$	1.41188e7	−	2.44544e7i	0.473217	−	0.819635i	0.999530	+	0.0306555i	$0.00975946\pi$
$978$	1.38291e7	−	1.25796e7i	0.462324	−	0.420552i
$979$	−4.52004e6	−	7.82894e6i	−0.150725	−	0.261064i
$980$	4.30410e6			0.143159
$981$	8.72090e6	−	3.98948e6i	0.289327	−	0.132356i
$982$	−3.91488e7			−1.29551
$983$	4.01212e6	+	6.94920e6i	0.132431	+	0.229378i	0.924613	−	0.380907i	$-0.124388\pi$
$983$	4.01212e6	+	6.94920e6i	0.132431	+	0.229378i	−0.792182	+	0.610285i	$0.791055\pi$
$984$	7.84875e6	+	2.50619e6i	0.258412	+	0.0825138i
$985$	1.91818e7	−	3.32238e7i	0.629939	−	1.09109i
$986$	1.08055e7	−	1.87157e7i	0.353960	−	0.613076i
$987$	−9.52647e6	−	3.04190e6i	−0.311271	−	0.0993923i
$988$	2.87579e6	+	4.98101e6i	0.0937270	+	0.162340i
$989$	1.41925e7			0.461389
$990$	4.95588e6	+	3.52427e6i	0.160706	+	0.114283i
$991$	5.25291e6			0.169909			0.0849543	−	0.996385i	$-0.472926\pi$
$991$	5.25291e6			0.169909			0.0849543	+	0.996385i	$0.472926\pi$
$992$	−2.61873e6	−	4.53577e6i	−0.0844912	−	0.146343i
$993$	3.33119e7	−	3.03021e7i	1.07208	−	0.975215i
$994$	3.04031e6	−	5.26597e6i	0.0976005	−	0.169049i
$995$	3.81339e6	−	6.60499e6i	0.122111	−	0.211502i
$996$	578789.	+	2.65653e6i	0.0184872	+	0.0848530i
$997$	6.56371e6	+	1.13687e7i	0.209128	+	0.362220i	0.951440	−	0.307834i	$-0.0996042\pi$
$997$	6.56371e6	+	1.13687e7i	0.209128	+	0.362220i	−0.742312	+	0.670054i	$0.766271\pi$
$998$	5.23009e6			0.166220
$999$	−1.23248e7	−	1.64309e7i	−0.390721	−	0.520893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.e.b.67.7	✓	24
3.2	odd	2		594.6.e.a.199.2		24
9.2	odd	6		594.6.e.a.397.2		24
9.7	even	3	inner	198.6.e.b.133.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.e.b.67.7	✓	24	1.1	even	1	trivial
198.6.e.b.133.7	yes	24	9.7	even	3	inner
594.6.e.a.199.2		24	3.2	odd	2
594.6.e.a.397.2		24	9.2	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(3.31846 + 15.2311i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(25.8529 - 44.7785i) q^{5} +(-46.1253 + 41.9578i) q^{6} +(-53.8618 - 93.2913i) q^{7} -64.0000 q^{8} +(-220.976 + 101.088i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(3.31846 + 15.2311i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(25.8529 - 44.7785i) q^{5} +(-46.1253 + 41.9578i) q^{6} +(-53.8618 - 93.2913i) q^{7} -64.0000 q^{8} +(-220.976 + 101.088i) q^{9} +206.823 q^{10} +(-60.5000 - 104.789i) q^{11} +(-237.597 - 75.8672i) q^{12} +(315.102 - 545.773i) q^{13} +(215.447 - 373.165i) q^{14} +(767.820 + 245.173i) q^{15} +(-128.000 - 221.703i) q^{16} +1069.30 q^{17} +(-792.130 - 563.306i) q^{18} +570.408 q^{19} +(413.646 + 716.456i) q^{20} +(1242.20 - 1129.96i) q^{21} +(242.000 - 419.156i) q^{22} +(1164.30 - 2016.63i) q^{23} +(-212.382 - 974.793i) q^{24} +(225.757 + 391.022i) q^{25} +2520.82 q^{26} +(-2272.99 - 3030.25i) q^{27} +1723.58 q^{28} +(-2526.31 - 4375.69i) q^{29} +(686.335 + 3150.15i) q^{30} +(2557.35 - 4429.46i) q^{31} +(512.000 - 886.810i) q^{32} +(1395.29 - 1269.22i) q^{33} +(2138.60 + 3704.17i) q^{34} -5569.93 q^{35} +(367.088 - 3870.63i) q^{36} +5422.30 q^{37} +(1140.82 + 1975.95i) q^{38} +(9358.40 + 2988.24i) q^{39} +(-1654.58 + 2865.82i) q^{40} +(-4129.24 + 7152.06i) q^{41} +(6398.69 + 2043.17i) q^{42} +(3047.43 + 5278.30i) q^{43} +1936.00 q^{44} +(-1186.28 + 12508.4i) q^{45} +9314.39 q^{46} +(-2977.63 - 5157.41i) q^{47} +(2952.02 - 2685.30i) q^{48} +(2601.32 - 4505.61i) q^{49} +(-903.027 + 1564.09i) q^{50} +(3548.44 + 16286.7i) q^{51} +(5041.63 + 8732.36i) q^{52} +9344.52 q^{53} +(5951.14 - 13934.4i) q^{54} -6256.40 q^{55} +(3447.15 + 5970.65i) q^{56} +(1892.88 + 8687.97i) q^{57} +(10105.2 - 17502.8i) q^{58} +(4776.51 - 8273.15i) q^{59} +(-9539.78 + 8677.84i) q^{60} +(8741.51 + 15140.7i) q^{61} +20458.8 q^{62} +(21332.8 + 15170.3i) q^{63} +4096.00 q^{64} +(-16292.6 - 28219.6i) q^{65} +(7187.30 + 2294.98i) q^{66} +(-5429.23 + 9403.70i) q^{67} +(-8554.41 + 14816.7i) q^{68} +(34579.2 + 11041.5i) q^{69} +(-11139.9 - 19294.8i) q^{70} +14111.6 q^{71} +(14142.4 - 6469.63i) q^{72} -51306.5 q^{73} +(10844.6 + 18783.4i) q^{74} +(-5206.55 + 4736.13i) q^{75} +(-4563.27 + 7903.81i) q^{76} +(-6517.28 + 11288.3i) q^{77} +(8365.24 + 38394.9i) q^{78} +(-26375.3 - 45683.4i) q^{79} -13236.7 q^{80} +(38611.4 - 44676.0i) q^{81} -33033.9 q^{82} +(-5450.46 - 9440.47i) q^{83} +(5719.63 + 26252.1i) q^{84} +(27644.5 - 47881.7i) q^{85} +(-12189.7 + 21113.2i) q^{86} +(58263.3 - 52999.1i) q^{87} +(3872.00 + 6706.50i) q^{88} +74711.4 q^{89} +(-45702.9 + 20907.3i) q^{90} -67887.8 q^{91} +(18628.8 + 32266.0i) q^{92} +(75952.3 + 24252.4i) q^{93} +(11910.5 - 20629.6i) q^{94} +(14746.7 - 25542.0i) q^{95} +(15206.2 + 4855.50i) q^{96} +(-34110.2 - 59080.6i) q^{97} +20810.5 q^{98} +(23961.9 + 17040.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Introduction

L-functions

Modular forms

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