LMFDB - Embedded newform 198.6.e.b.133.8

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			133.8
Character	$\chi$	$=$	198.133
Dual form			198.6.e.b.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(6.46136 + 14.1863i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-15.4896 - 26.8288i) q^{5} +(62.0655 + 5.98979i) q^{6} +(29.1617 - 50.5095i) q^{7} -64.0000 q^{8} +(-159.502 + 183.325i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(6.46136 + 14.1863i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-15.4896 - 26.8288i) q^{5} +(62.0655 + 5.98979i) q^{6} +(29.1617 - 50.5095i) q^{7} -64.0000 q^{8} +(-159.502 + 183.325i) q^{9} -123.917 q^{10} +(-60.5000 + 104.789i) q^{11} +(144.880 - 203.022i) q^{12} +(451.536 + 782.083i) q^{13} +(-116.647 - 202.038i) q^{14} +(280.518 - 393.091i) q^{15} +(-128.000 + 221.703i) q^{16} -1597.66 q^{17} +(316.054 + 919.181i) q^{18} +436.908 q^{19} +(-247.834 + 429.261i) q^{20} +(904.966 + 87.3362i) q^{21} +(242.000 + 419.156i) q^{22} +(2120.83 + 3673.38i) q^{23} +(-413.527 - 907.923i) q^{24} +(1082.64 - 1875.19i) q^{25} +3612.29 q^{26} +(-3631.30 - 1078.21i) q^{27} -933.173 q^{28} +(1650.99 - 2859.60i) q^{29} +(-800.672 - 1757.92i) q^{30} +(3201.81 + 5545.70i) q^{31} +(512.000 + 886.810i) q^{32} +(-1877.48 - 181.191i) q^{33} +(-3195.31 + 5534.44i) q^{34} -1806.81 q^{35} +(3816.24 + 743.518i) q^{36} -2692.62 q^{37} +(873.817 - 1513.49i) q^{38} +(-8177.33 + 11458.9i) q^{39} +(991.337 + 1717.05i) q^{40} +(9505.44 + 16463.9i) q^{41} +(2112.47 - 2960.22i) q^{42} +(-7914.36 + 13708.1i) q^{43} +1936.00 q^{44} +(7389.03 + 1439.60i) q^{45} +16966.6 q^{46} +(-12711.0 + 22016.2i) q^{47} +(-3972.19 - 383.347i) q^{48} +(6702.69 + 11609.4i) q^{49} +(-4330.57 - 7500.77i) q^{50} +(-10323.0 - 22664.8i) q^{51} +(7224.57 - 12513.3i) q^{52} -33889.6 q^{53} +(-10997.6 + 10422.8i) q^{54} +3748.49 q^{55} +(-1866.35 + 3232.61i) q^{56} +(2823.02 + 6198.11i) q^{57} +(-6603.96 - 11438.4i) q^{58} +(5155.43 + 8929.47i) q^{59} +(-7690.97 - 742.238i) q^{60} +(13592.8 - 23543.4i) q^{61} +25614.5 q^{62} +(4608.33 + 13402.4i) q^{63} +4096.00 q^{64} +(13988.3 - 24228.4i) q^{65} +(-4382.63 + 6141.40i) q^{66} +(-10042.2 - 17393.6i) q^{67} +(12781.2 + 22137.8i) q^{68} +(-38408.2 + 53821.6i) q^{69} +(-3613.63 + 6258.99i) q^{70} +54794.2 q^{71} +(10208.1 - 11732.8i) q^{72} +2720.69 q^{73} +(-5385.24 + 9327.50i) q^{74} +(33597.3 + 3242.40i) q^{75} +(-3495.27 - 6053.98i) q^{76} +(3528.56 + 6111.65i) q^{77} +(23340.3 + 51245.0i) q^{78} +(-20508.3 + 35521.5i) q^{79} +7930.69 q^{80} +(-8167.37 - 58481.4i) q^{81} +76043.6 q^{82} +(9786.23 - 16950.3i) q^{83} +(-6029.57 - 13238.3i) q^{84} +(24747.1 + 42863.2i) q^{85} +(31657.4 + 54832.3i) q^{86} +(51234.7 + 4944.54i) q^{87} +(3872.00 - 6706.50i) q^{88} -100314. q^{89} +(19765.0 - 22717.1i) q^{90} +52670.2 q^{91} +(33933.2 - 58774.0i) q^{92} +(-57984.9 + 81254.6i) q^{93} +(50844.2 + 88064.7i) q^{94} +(-6767.55 - 11721.7i) q^{95} +(-9272.33 + 12993.4i) q^{96} +(81904.9 - 141863. i) q^{97} +53621.6 q^{98} +(-9560.64 - 27805.2i) 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	6.46136	+	14.1863i	0.414496	+	0.910051i
$3$	6.46136	+	14.1863i	0.414496	+	0.910051i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−15.4896	−	26.8288i	−0.277087	−	0.479929i	0.693572	−	0.720387i	$-0.256036\pi$
$5$	−15.4896	−	26.8288i	−0.277087	−	0.479929i	−0.970660	+	0.240458i	$0.922702\pi$
$6$	62.0655	+	5.98979i	0.703837	+	0.0679256i
$7$	29.1617	−	50.5095i	0.224940	−	0.389608i	−0.731361	−	0.681990i	$-0.761115\pi$
$7$	29.1617	−	50.5095i	0.224940	−	0.389608i	0.956302	+	0.292382i	$0.0944480\pi$
$8$	−64.0000			−0.353553
$9$	−159.502	+	183.325i	−0.656386	+	0.754425i
$10$	−123.917			−0.391860
$11$	−60.5000	+	104.789i	−0.150756	+	0.261116i
$11$	−60.5000	+	104.789i	−0.150756	+	0.261116i
$12$	144.880	−	203.022i	0.290440	−	0.406995i
$13$	451.536	+	782.083i	0.741027	+	1.28350i	0.952028	+	0.306010i	$0.0989942\pi$
$13$	451.536	+	782.083i	0.741027	+	1.28350i	−0.211001	+	0.977486i	$0.567672\pi$
$14$	−116.647	−	202.038i	−0.159057	−	0.275495i
$15$	280.518	−	393.091i	0.321908	−	0.451092i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−1597.66			−1.34079			−0.670395	−	0.742004i	$-0.733875\pi$
$17$	−1597.66			−1.34079			−0.670395	+	0.742004i	$0.733875\pi$
$18$	316.054	+	919.181i	0.229922	+	0.668682i
$19$	436.908			0.277656			0.138828	−	0.990317i	$-0.455667\pi$
$19$	436.908			0.277656			0.138828	+	0.990317i	$0.455667\pi$
$20$	−247.834	+	429.261i	−0.138544	+	0.239964i
$21$	904.966	+	87.3362i	0.447800	+	0.0432161i
$22$	242.000	+	419.156i	0.106600	+	0.184637i
$23$	2120.83	+	3673.38i	0.835960	+	1.44792i	0.893247	+	0.449567i	$0.148422\pi$
$23$	2120.83	+	3673.38i	0.835960	+	1.44792i	−0.0572871	+	0.998358i	$0.518245\pi$
$24$	−413.527	−	907.923i	−0.146547	−	0.321752i
$25$	1082.64	−	1875.19i	0.346446	−	0.600061i
$26$	3612.29			1.04797
$27$	−3631.30	−	1078.21i	−0.958635	−	0.284638i
$28$	−933.173			−0.224940
$29$	1650.99	−	2859.60i	0.364543	−	0.631408i	−0.624159	−	0.781297i	$-0.714558\pi$
$29$	1650.99	−	2859.60i	0.364543	−	0.631408i	0.988703	+	0.149889i	$0.0478917\pi$
$30$	−800.672	−	1757.92i	−0.162425	−	0.356613i
$31$	3201.81	+	5545.70i	0.598400	+	1.03646i	0.993057	+	0.117631i	$0.0375300\pi$
$31$	3201.81	+	5545.70i	0.598400	+	1.03646i	−0.394657	+	0.918828i	$0.629137\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−1877.48	−	181.191i	−0.300117	−	0.0289636i
$34$	−3195.31	+	5534.44i	−0.474041	+	0.821063i
$35$	−1806.81			−0.249312
$36$	3816.24	+	743.518i	0.490772	+	0.0956171i
$37$	−2692.62			−0.323348			−0.161674	−	0.986844i	$-0.551689\pi$
$37$	−2692.62			−0.323348			−0.161674	+	0.986844i	$0.551689\pi$
$38$	873.817	−	1513.49i	0.0981661	−	0.170029i
$39$	−8177.33	+	11458.9i	−0.860894	+	1.20638i
$40$	991.337	+	1717.05i	0.0979651	+	0.169680i
$41$	9505.44	+	16463.9i	0.883106	+	1.52958i	0.847869	+	0.530205i	$0.177885\pi$
$41$	9505.44	+	16463.9i	0.883106	+	1.52958i	0.0352365	+	0.999379i	$0.488782\pi$
$42$	2112.47	−	2960.22i	0.184786	−	0.258941i
$43$	−7914.36	+	13708.1i	−0.652746	+	1.13059i	0.329707	+	0.944083i	$0.393050\pi$
$43$	−7914.36	+	13708.1i	−0.652746	+	1.13059i	−0.982454	+	0.186507i	$0.940283\pi$
$44$	1936.00			0.150756
$45$	7389.03	+	1439.60i	0.543947	+	0.105977i
$46$	16966.6			1.18223
$47$	−12711.0	+	22016.2i	−0.839337	+	1.45378i	0.0511121	+	0.998693i	$0.483723\pi$
$47$	−12711.0	+	22016.2i	−0.839337	+	1.45378i	−0.890449	+	0.455082i	$0.849610\pi$
$48$	−3972.19	−	383.347i	−0.248844	−	0.0240153i
$49$	6702.69	+	11609.4i	0.398804	+	0.690748i
$50$	−4330.57	−	7500.77i	−0.244974	−	0.424307i
$51$	−10323.0	−	22664.8i	−0.555752	−	1.22019i
$52$	7224.57	−	12513.3i	0.370513	−	0.641748i
$53$	−33889.6			−1.65721			−0.828605	−	0.559834i	$-0.810865\pi$
$53$	−33889.6			−1.65721			−0.828605	+	0.559834i	$0.810865\pi$
$54$	−10997.6	+	10422.8i	−0.513233	+	0.486407i
$55$	3748.49			0.167090
$56$	−1866.35	+	3232.61i	−0.0795284	+	0.137747i
$57$	2823.02	+	6198.11i	0.115087	+	0.252681i
$58$	−6603.96	−	11438.4i	−0.257771	−	0.446473i
$59$	5155.43	+	8929.47i	0.192812	+	0.333961i	0.946181	−	0.323637i	$-0.104906\pi$
$59$	5155.43	+	8929.47i	0.192812	+	0.333961i	−0.753369	+	0.657598i	$0.771572\pi$
$60$	−7690.97	−	742.238i	−0.275806	−	0.0266174i
$61$	13592.8	−	23543.4i	0.467717	−	0.810110i	−0.531602	−	0.846994i	$-0.678410\pi$
$61$	13592.8	−	23543.4i	0.467717	−	0.810110i	0.999320	+	0.0368838i	$0.0117431\pi$
$62$	25614.5			0.846266
$63$	4608.33	+	13402.4i	0.146283	+	0.425434i
$64$	4096.00			0.125000
$65$	13988.3	−	24228.4i	0.410658	−	0.711280i
$66$	−4382.63	+	6141.40i	−0.123844	+	0.173543i
$67$	−10042.2	−	17393.6i	−0.273301	−	0.473371i	0.696404	−	0.717650i	$-0.254782\pi$
$67$	−10042.2	−	17393.6i	−0.273301	−	0.473371i	−0.969705	+	0.244279i	$0.921449\pi$
$68$	12781.2	+	22137.8i	0.335198	+	0.580579i
$69$	−38408.2	+	53821.6i	−0.971183	+	1.36093i
$70$	−3613.63	+	6258.99i	−0.0881452	+	0.152672i
$71$	54794.2			1.29000			0.644999	−	0.764184i	$-0.276858\pi$
$71$	54794.2			1.29000			0.644999	+	0.764184i	$0.276858\pi$
$72$	10208.1	−	11732.8i	0.232067	−	0.266730i
$73$	2720.69			0.0597546			0.0298773	−	0.999554i	$-0.490488\pi$
$73$	2720.69			0.0597546			0.0298773	+	0.999554i	$0.490488\pi$
$74$	−5385.24	+	9327.50i	−0.114321	+	0.198009i
$75$	33597.3	+	3242.40i	0.689687	+	0.0665600i
$76$	−3495.27	−	6053.98i	−0.0694139	−	0.120228i
$77$	3528.56	+	6111.65i	0.0678221	+	0.117471i
$78$	23340.3	+	51245.0i	0.434380	+	0.953706i
$79$	−20508.3	+	35521.5i	−0.369711	+	0.640358i	−0.989520	−	0.144394i	$-0.953877\pi$
$79$	−20508.3	+	35521.5i	−0.369711	+	0.640358i	0.619809	+	0.784753i	$0.287210\pi$
$80$	7930.69			0.138544
$81$	−8167.37	−	58481.4i	−0.138315	−	0.990388i
$82$	76043.6			1.24890
$83$	9786.23	−	16950.3i	0.155927	−	0.270073i	−0.777469	−	0.628921i	$-0.783497\pi$
$83$	9786.23	−	16950.3i	0.155927	−	0.270073i	0.933396	+	0.358848i	$0.116830\pi$
$84$	−6029.57	−	13238.3i	−0.0932369	−	0.204707i
$85$	24747.1	+	42863.2i	0.371516	+	0.643484i
$86$	31657.4	+	54832.3i	0.461561	+	0.799448i
$87$	51234.7	+	4944.54i	0.725715	+	0.0700370i
$88$	3872.00	−	6706.50i	0.0533002	−	0.0923186i
$89$	−100314.			−1.34242			−0.671208	−	0.741269i	$-0.734224\pi$
$89$	−100314.			−1.34242			−0.671208	+	0.741269i	$0.734224\pi$
$90$	19765.0	−	22717.1i	0.257212	−	0.295629i
$91$	52670.2			0.666747
$92$	33933.2	−	58774.0i	0.417980	−	0.723962i
$93$	−57984.9	+	81254.6i	−0.695196	+	0.974183i
$94$	50844.2	+	88064.7i	0.593501	+	1.02797i
$95$	−6767.55	−	11721.7i	−0.0769348	−	0.133255i
$96$	−9272.33	+	12993.4i	−0.102686	+	0.143894i
$97$	81904.9	−	141863.i	0.883854	−	1.53088i	0.0368327	−	0.999321i	$-0.488273\pi$
$97$	81904.9	−	141863.i	0.883854	−	1.53088i	0.847021	−	0.531559i	$-0.178394\pi$
$98$	53621.6			0.563994
$99$	−9560.64	−	27805.2i	−0.0980390	−	0.285127i
$100$	−34644.6			−0.346446
$101$	−59182.3	+	102507.i	−0.577282	+	0.999882i	0.418507	+	0.908213i	$0.362553\pi$
$101$	−59182.3	+	102507.i	−0.577282	+	0.999882i	−0.995790	+	0.0916688i	$0.970780\pi$
$102$	−99159.2	−	9569.62i	−0.943697	−	0.0910740i
$103$	−29853.2	−	51707.2i	−0.277266	−	0.480240i	0.693438	−	0.720516i	$-0.256095\pi$
$103$	−29853.2	−	51707.2i	−0.277266	−	0.480240i	−0.970704	+	0.240277i	$0.922762\pi$
$104$	−28898.3	−	50053.3i	−0.261993	−	0.453784i
$105$	−11674.5	−	25632.0i	−0.103339	−	0.226887i
$106$	−67779.3	+	117397.i	−0.585912	+	1.01483i
$107$	210795.			1.77992			0.889961	−	0.456036i	$-0.150731\pi$
$107$	210795.			1.77992			0.889961	+	0.456036i	$0.150731\pi$
$108$	14110.3	+	58942.5i	0.116407	+	0.486261i
$109$	155274.			1.25179			0.625897	−	0.779905i	$-0.284733\pi$
$109$	155274.			1.25179			0.625897	+	0.779905i	$0.284733\pi$
$110$	7496.98	−	12985.2i	0.0590752	−	0.102321i
$111$	−17398.0	−	38198.3i	−0.134027	−	0.294263i
$112$	7465.39	+	12930.4i	0.0562351	+	0.0974020i
$113$	−101167.	−	175227.i	−0.745321	−	1.29093i	−0.950044	−	0.312115i	$-0.898963\pi$
$113$	−101167.	−	175227.i	−0.745321	−	1.29093i	0.204723	−	0.978820i	$-0.434371\pi$
$114$	27116.9	+	2616.99i	0.195424	+	0.0188599i
$115$	65701.6	−	113799.i	0.463267	−	0.802402i
$116$	−52831.7			−0.364543
$117$	−215396.	−	41965.7i	−1.45470	−	0.283419i
$118$	41243.4			0.272678
$119$	−46590.3	+	80696.8i	−0.301598	+	0.522383i
$120$	−17953.1	+	25157.8i	−0.113812	+	0.159485i
$121$	−7320.50	−	12679.5i	−0.0454545	−	0.0787296i
$122$	−54371.1	−	94173.5i	−0.330726	−	0.572835i
$123$	−172144.	+	241226.i	−1.02596	+	1.43768i
$124$	51229.0	−	88731.2i	0.299200	−	0.518230i
$125$	−163889.			−0.938156
$126$	55644.0	+	10841.1i	0.312243	+	0.0608342i
$127$	−167723.			−0.922747			−0.461374	−	0.887206i	$-0.652643\pi$
$127$	−167723.			−0.922747			−0.461374	+	0.887206i	$0.652643\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	−245604.	−	23702.7i	−1.29946	−	0.125407i
$130$	−55953.0	−	96913.5i	−0.290379	−	0.502951i
$131$	−192729.	−	333817.i	−0.981228	−	1.69954i	−0.657628	−	0.753343i	$-0.728440\pi$
$131$	−192729.	−	333817.i	−0.981228	−	1.69954i	−0.323600	−	0.946194i	$-0.604893\pi$
$132$	12509.2	+	27464.7i	0.0624876	+	0.137195i
$133$	12741.0	−	22068.0i	0.0624559	−	0.108177i
$134$	−80337.4			−0.386506
$135$	27320.5	+	114125.i	0.129019	+	0.538946i
$136$	102250.			0.474041
$137$	−56982.9	+	98697.3i	−0.259384	+	0.449267i	−0.966077	−	0.258254i	$-0.916853\pi$
$137$	−56982.9	+	98697.3i	−0.259384	+	0.449267i	0.706693	+	0.707520i	$0.250186\pi$
$138$	109627.	+	240693.i	0.490028	+	1.07589i
$139$	87437.2	+	151446.i	0.383848	+	0.664844i	0.991609	−	0.129276i	$-0.0412654\pi$
$139$	87437.2	+	151446.i	0.383848	+	0.664844i	−0.607761	+	0.794120i	$0.707932\pi$
$140$	14454.5	+	25036.0i	0.0623281	+	0.107955i
$141$	−394458.	−	38068.3i	−1.67091	−	0.161256i
$142$	109588.	−	189813.i	0.456083	−	0.789959i
$143$	−109272.			−0.446856
$144$	−20227.5	−	58827.6i	−0.0812896	−	0.236415i
$145$	−102293.			−0.404041
$146$	5441.37	−	9424.74i	0.0211264	−	0.0365921i
$147$	−121386.	+	170099.i	−0.463314	+	0.649244i
$148$	21540.9	+	37310.0i	0.0808370	+	0.140014i
$149$	−39487.9	−	68395.0i	−0.145713	−	0.252382i	0.783926	−	0.620855i	$-0.213214\pi$
$149$	−39487.9	−	68395.0i	−0.145713	−	0.252382i	−0.929639	+	0.368472i	$0.879881\pi$
$150$	78426.7	−	109900.i	0.284601	−	0.398813i
$151$	76755.2	−	132944.i	0.273946	−	0.474489i	−0.695922	−	0.718117i	$-0.745004\pi$
$151$	76755.2	−	132944.i	0.273946	−	0.474489i	0.969869	+	0.243628i	$0.0783376\pi$
$152$	−27962.1			−0.0981661
$153$	254829.	−	292891.i	0.880076	−	1.01153i
$154$	28228.5			0.0959149
$155$	99189.8	−	171802.i	0.331618	−	0.574379i
$156$	224198.	+	21636.8i	0.737600	+	0.0711840i
$157$	132056.	+	228727.i	0.427570	+	0.740574i	0.996657	−	0.0817041i	$-0.0260363\pi$
$157$	132056.	+	228727.i	0.427570	+	0.740574i	−0.569086	+	0.822278i	$0.692703\pi$
$158$	82033.3	+	142086.i	0.261425	+	0.452802i
$159$	−218973.	−	480768.i	−0.686907	−	1.50815i
$160$	15861.4	−	27472.7i	0.0489825	−	0.0848402i
$161$	247387.			0.752164
$162$	−218920.	−	88670.3i	−0.655388	−	0.265455i
$163$	434916.			1.28214			0.641071	−	0.767482i	$-0.278490\pi$
$163$	434916.			1.28214			0.641071	+	0.767482i	$0.278490\pi$
$164$	152087.	−	263423.i	0.441553	−	0.764792i
$165$	24220.3	+	53177.2i	0.0692581	+	0.152060i
$166$	−39144.9	−	67801.0i	−0.110257	−	0.190970i
$167$	−250135.	−	433246.i	−0.694037	−	1.20211i	−0.970504	−	0.241084i	$-0.922497\pi$
$167$	−250135.	−	433246.i	−0.694037	−	1.20211i	0.276467	−	0.961023i	$-0.410836\pi$
$168$	−57917.8	−	5589.51i	−0.158321	−	0.0152792i
$169$	−222123.	+	384728.i	−0.598241	+	1.03618i
$170$	197977.			0.525402
$171$	−69687.7	+	80096.4i	−0.182249	+	0.209470i
$172$	253259.			0.652746
$173$	−106107.	+	183783.i	−0.269544	+	0.466864i	−0.968744	−	0.248062i	$-0.920206\pi$
$173$	−106107.	+	183783.i	−0.269544	+	0.466864i	0.699200	+	0.714926i	$0.253540\pi$
$174$	119598.	−	167593.i	0.299468	−	0.419646i
$175$	−63143.3	−	109367.i	−0.155859	−	0.269956i
$176$	−15488.0	−	26826.0i	−0.0376889	−	0.0652791i
$177$	−93365.0	+	130833.i	−0.224001	+	0.313895i
$178$	−200628.	+	347498.i	−0.474616	+	0.822058i
$179$	−408820.			−0.953673			−0.476836	−	0.878992i	$-0.658217\pi$
$179$	−408820.			−0.953673			−0.476836	+	0.878992i	$0.658217\pi$
$180$	−39164.5	−	113902.i	−0.0900972	−	0.262030i
$181$	−26536.5			−0.0602070			−0.0301035	−	0.999547i	$-0.509584\pi$
$181$	−26536.5			−0.0602070			−0.0301035	+	0.999547i	$0.509584\pi$
$182$	105340.	−	182455.i	0.235731	−	0.408298i
$183$	421821.	+	40709.0i	0.931109	+	0.0898591i
$184$	−135733.	−	235096.i	−0.295556	−	0.511919i
$185$	41707.7	+	72239.8i	0.0895956	+	0.155184i
$186$	165504.	+	363375.i	0.350774	+	0.770145i
$187$	96658.2	−	167417.i	0.202132	−	0.350102i
$188$	406753.			0.839337
$189$	−160355.	+	151973.i	−0.326533	+	0.309465i
$190$	−54140.4			−0.108802
$191$	468914.	−	812183.i	0.930057	−	1.61091i	0.146839	−	0.989160i	$-0.453090\pi$
$191$	468914.	−	812183.i	0.930057	−	1.61091i	0.783219	−	0.621746i	$-0.213576\pi$
$192$	26465.7	+	58107.1i	0.0518120	+	0.113756i
$193$	−6201.28	−	10740.9i	−0.0119836	−	0.0207562i	0.859971	−	0.510342i	$-0.170481\pi$
$193$	−6201.28	−	10740.9i	−0.0119836	−	0.0207562i	−0.871955	+	0.489586i	$0.837148\pi$
$194$	−327620.	−	567454.i	−0.624979	−	1.08250i
$195$	434094.	+	41893.4i	0.817518	+	0.0788967i
$196$	107243.	−	185751.i	0.199402	−	0.345374i
$197$	−307623.			−0.564745			−0.282373	−	0.959305i	$-0.591121\pi$
$197$	−307623.			−0.564745			−0.282373	+	0.959305i	$0.591121\pi$
$198$	−115441.	−	22491.4i	−0.209266	−	0.0407713i
$199$	366096.			0.655334			0.327667	−	0.944793i	$-0.393738\pi$
$199$	366096.			0.655334			0.327667	+	0.944793i	$0.393738\pi$
$200$	−69289.1	+	120012.i	−0.122487	+	0.212154i
$201$	181864.	−	254847.i	0.317510	−	0.444928i
$202$	236729.	+	410027.i	0.408200	+	0.707024i
$203$	−96291.2	−	166781.i	−0.164001	−	0.284058i
$204$	−231469.	+	324358.i	−0.389419	+	0.545695i
$205$	294472.	−	510040.i	0.489394	−	0.847656i
$206$	−238825.			−0.392114
$207$	−1.01170e6	−	197109.i	−1.64106	−	0.319728i
$208$	−231186.			−0.370513
$209$	−26433.0	+	45783.2i	−0.0418581	+	0.0725004i
$210$	−112141.	−	10822.4i	−0.175475	−	0.0169347i
$211$	558389.	+	967158.i	0.863437	+	1.49552i	0.868591	+	0.495530i	$0.165026\pi$
$211$	558389.	+	967158.i	0.863437	+	1.49552i	−0.00515430	+	0.999987i	$0.501641\pi$
$212$	271117.	+	469589.i	0.414302	+	0.717593i
$213$	354045.	+	777327.i	0.534699	+	1.17396i
$214$	421590.	−	730216.i	0.629298	−	1.08998i
$215$	490362.			0.723470
$216$	232404.	+	69005.3i	0.338929	+	0.100635i
$217$	373481.			0.538417
$218$	310548.	−	537886.i	0.442576	−	0.766565i
$219$	17579.3	+	38596.5i	0.0247681	+	0.0543797i
$220$	−29987.9	−	51940.6i	−0.0417724	−	0.0723520i
$221$	−721399.	−	1.24950e6i	−0.993561	−	1.72090i
$222$	−167119.	−	16128.2i	−0.227584	−	0.0219636i
$223$	−559886.	+	969750.i	−0.753941	+	1.30586i	0.191959	+	0.981403i	$0.438516\pi$
$223$	−559886.	+	969750.i	−0.753941	+	1.30586i	−0.945899	+	0.324460i	$0.894817\pi$
$224$	59723.1			0.0795284
$225$	171087.	+	497572.i	0.225299	+	0.655239i
$226$	−809338.			−1.05404
$227$	−347039.	+	601088.i	−0.447006	+	0.774237i	−0.998190	−	0.0601473i	$-0.980843\pi$
$227$	−347039.	+	601088.i	−0.447006	+	0.774237i	0.551184	+	0.834384i	$0.314176\pi$
$228$	63299.4	−	88701.8i	0.0806422	−	0.113004i
$229$	371435.	+	643345.i	0.468053	+	0.810691i	0.999333	−	0.0365049i	$-0.0116225\pi$
$229$	371435.	+	643345.i	0.468053	+	0.810691i	−0.531281	+	0.847196i	$0.678289\pi$
$230$	−262807.	−	455194.i	−0.327579	−	0.567384i
$231$	−63902.3	+	89546.8i	−0.0787929	+	0.110413i
$232$	−105663.	+	183014.i	−0.128886	+	0.223236i
$233$	226723.			0.273594			0.136797	−	0.990599i	$-0.456319\pi$
$233$	226723.			0.273594			0.136797	+	0.990599i	$0.456319\pi$
$234$	−576166.	+	662224.i	−0.687873	+	0.790615i
$235$	787558.			0.930278
$236$	82486.9	−	142871.i	0.0964062	−	0.166980i
$237$	−636429.	−	61420.3i	−0.736002	−	0.0710299i
$238$	186361.	+	322787.i	0.213262	+	0.369380i
$239$	183410.	+	317676.i	0.207696	+	0.359740i	0.950988	−	0.309227i	$-0.100070\pi$
$239$	183410.	+	317676.i	0.207696	+	0.359740i	−0.743292	+	0.668967i	$0.766737\pi$
$240$	51243.0	+	112507.i	0.0574258	+	0.126082i
$241$	73010.9	−	126459.i	0.0809740	−	0.140251i	−0.822695	−	0.568484i	$-0.807530\pi$
$241$	73010.9	−	126459.i	0.0809740	−	0.140251i	0.903669	+	0.428233i	$0.140864\pi$
$242$	−58564.0			−0.0642824
$243$	776862.	−	493734.i	0.843973	−	0.536386i
$244$	−434969.			−0.467717
$245$	207645.	−	359651.i	0.221007	−	0.382795i
$246$	491344.	+	1.07878e6i	0.517664	+	1.13656i
$247$	197280.	+	341699.i	0.205750	+	0.356370i
$248$	−204916.	−	354925.i	−0.211566	−	0.366444i
$249$	303694.	+	29308.8i	0.310411	+	0.0299570i
$250$	−327778.	+	567729.i	−0.331688	+	0.574501i
$251$	−431791.			−0.432603			−0.216301	−	0.976327i	$-0.569399\pi$
$251$	−431791.			−0.432603			−0.216301	+	0.976327i	$0.569399\pi$
$252$	148843.	−	171074.i	0.147648	−	0.169701i
$253$	−513240.			−0.504103
$254$	−335446.	+	581009.i	−0.326240	+	0.565065i
$255$	−448171.	+	628024.i	−0.431611	+	0.604820i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−135882.	−	235354.i	−0.128330	−	0.222274i	0.794700	−	0.607003i	$-0.207628\pi$
$257$	−135882.	−	235354.i	−0.128330	−	0.222274i	−0.923030	+	0.384729i	$0.874295\pi$
$258$	−573317.	+	803392.i	−0.536223	+	0.751413i
$259$	−78521.2	+	136003.i	−0.0727340	+	0.125979i
$260$	−447624.			−0.410658
$261$	260901.	+	758779.i	0.237069	+	0.689468i
$262$	−1.54184e6			−1.38767
$263$	582828.	−	1.00949e6i	0.519579	−	0.899936i	−0.480162	−	0.877180i	$-0.659422\pi$
$263$	582828.	−	1.00949e6i	0.519579	−	0.899936i	0.999741	−	0.0227569i	$-0.00724437\pi$
$264$	120159.	+	11596.2i	0.106107	+	0.0102402i
$265$	524938.	+	909220.i	0.459191	+	0.795343i
$266$	−50963.9	−	88272.1i	−0.0441630	−	0.0764926i
$267$	−648165.	−	1.42309e6i	−0.556426	−	1.22167i
$268$	−160675.	+	278297.i	−0.136650	+	0.236685i
$269$	665865.			0.561055			0.280528	−	0.959846i	$-0.409491\pi$
$269$	665865.			0.561055			0.280528	+	0.959846i	$0.409491\pi$
$270$	449981.	+	133608.i	0.375651	+	0.111538i
$271$	−479138.			−0.396312			−0.198156	−	0.980170i	$-0.563495\pi$
$271$	−479138.			−0.396312			−0.198156	+	0.980170i	$0.563495\pi$
$272$	204500.	−	354204.i	0.167599	−	0.290290i
$273$	340321.	+	747194.i	0.276364	+	0.606774i
$274$	227932.	+	394789.i	0.183412	+	0.317679i
$275$	131000.	+	226898.i	0.104457	+	0.180925i
$276$	1.05304e6	+	101626.i	0.832094	+	0.0803034i
$277$	545631.	−	945061.i	0.427268	−	0.740049i	−0.569362	−	0.822087i	$-0.692810\pi$
$277$	545631.	−	945061.i	0.427268	−	0.740049i	0.996629	+	0.0820381i	$0.0261429\pi$
$278$	699497.			0.542843
$279$	−1.52736e6	−	297576.i	−1.17471	−	0.228869i
$280$	115636.			0.0881452
$281$	−1.20017e6	+	2.07876e6i	−0.906728	+	1.57050i	−0.0881469	+	0.996107i	$0.528094\pi$
$281$	−1.20017e6	+	2.07876e6i	−0.906728	+	1.57050i	−0.818581	+	0.574391i	$0.805239\pi$
$282$	−920789.	+	1.29031e6i	−0.689505	+	0.966208i
$283$	143984.	+	249387.i	0.106868	+	0.185100i	0.914500	−	0.404586i	$-0.132585\pi$
$283$	143984.	+	249387.i	0.106868	+	0.185100i	−0.807632	+	0.589687i	$0.799251\pi$
$284$	−438354.	−	759251.i	−0.322499	−	0.558585i
$285$	122561.	−	171745.i	0.0893796	−	0.125248i
$286$	−218543.	+	378528.i	−0.157987	+	0.273642i
$287$	1.10878e6			0.794584
$288$	−244240.	−	47585.2i	−0.173514	−	0.0338057i
$289$	1.13265e6			0.797718
$290$	−204586.	+	354353.i	−0.142850	+	0.247424i
$291$	2.54173e6	+	245297.i	1.75953	+	0.169808i
$292$	−21765.5	−	37698.9i	−0.0149387	−	0.0258745i
$293$	703058.	+	1.21773e6i	0.478434	+	0.828672i	0.999694	−	0.0247257i	$-0.00787124\pi$
$293$	703058.	+	1.21773e6i	0.478434	+	0.828672i	−0.521260	+	0.853398i	$0.674538\pi$
$294$	346468.	+	760691.i	0.233773	+	0.513263i
$295$	159712.	−	276628.i	0.106852	−	0.185072i
$296$	172328.			0.114321
$297$	332678.	−	315289.i	0.218843	−	0.207405i
$298$	−315903.			−0.206069
$299$	−1.91526e6	+	3.31732e6i	−1.23894	+	2.14590i
$300$	−223851.	−	491478.i	−0.143600	−	0.315283i
$301$	461592.	+	799500.i	0.293658	+	0.508631i
$302$	−307021.	−	531776.i	−0.193709	−	0.335514i
$303$	−1.83659e6	−	177245.i	−1.14923	−	0.110909i
$304$	−55924.3	+	96863.7i	−0.0347069	+	0.0601142i
$305$	−842189.			−0.518394
$306$	−504946.	−	1.46853e6i	−0.308277	−	0.896563i
$307$	−949267.			−0.574834			−0.287417	−	0.957806i	$-0.592797\pi$
$307$	−949267.			−0.574834			−0.287417	+	0.957806i	$0.592797\pi$
$308$	56457.0	−	97786.4i	0.0339110	−	0.0587356i
$309$	540642.	−	757604.i	0.322117	−	0.451384i
$310$	−396759.	−	687207.i	−0.234489	−	0.406147i
$311$	60703.4	+	105141.i	0.0355887	+	0.0616414i	0.883271	−	0.468863i	$-0.155336\pi$
$311$	60703.4	+	105141.i	0.0355887	+	0.0616414i	−0.847682	+	0.530504i	$0.822003\pi$
$312$	523349.	−	733372.i	0.304372	−	0.426518i
$313$	1.41547e6	−	2.45166e6i	0.816656	−	1.41449i	−0.0914760	−	0.995807i	$-0.529158\pi$
$313$	1.41547e6	−	2.45166e6i	0.816656	−	1.41449i	0.908132	−	0.418683i	$-0.137508\pi$
$314$	1.05644e6			0.604676
$315$	288190.	−	331235.i	0.163645	−	0.188087i
$316$	656266.			0.369711
$317$	985389.	−	1.70674e6i	0.550756	−	0.953938i	−0.447464	−	0.894302i	$-0.647673\pi$
$317$	985389.	−	1.70674e6i	0.550756	−	0.953938i	0.998220	−	0.0596361i	$-0.0189940\pi$
$318$	−2.10338e6	−	202992.i	−1.16640	−	0.112567i
$319$	199770.	+	346011.i	0.109914	+	0.190377i
$320$	−63445.6	−	109891.i	−0.0346359	−	0.0599911i
$321$	1.36202e6	+	2.99040e6i	0.737771	+	1.61982i
$322$	494774.	−	856975.i	0.265930	−	0.460605i
$323$	−698029.			−0.372278
$324$	−745004.	+	581022.i	−0.394272	+	0.307489i
$325$	1.95541e6			1.02690
$326$	869831.	−	1.50659e6i	0.453305	−	0.785148i
$327$	1.00328e6	+	2.20277e6i	0.518864	+	1.13920i
$328$	−608348.	−	1.05369e6i	−0.312225	−	0.540790i
$329$	741351.	+	1.28406e6i	0.377602	+	0.654025i
$330$	232652.	+	22452.7i	0.117604	+	0.0113497i
$331$	1.83672e6	−	3.18129e6i	0.921450	−	1.59600i	0.124278	−	0.992247i	$-0.460339\pi$
$331$	1.83672e6	−	3.18129e6i	0.921450	−	1.59600i	0.797173	−	0.603752i	$-0.206328\pi$
$332$	−313159.			−0.155927
$333$	429477.	−	493625.i	0.212241	−	0.243942i
$334$	−2.00108e6			−0.981516
$335$	−311099.	+	538840.i	−0.151456	+	0.262330i
$336$	−135198.	+	189454.i	−0.0653316	+	0.0915496i
$337$	1.85548e6	+	3.21378e6i	0.889980	+	1.54149i	0.839897	+	0.542746i	$0.182615\pi$
$337$	1.85548e6	+	3.21378e6i	0.889980	+	1.54149i	0.0500833	+	0.998745i	$0.484051\pi$
$338$	888491.	+	1.53891e6i	0.423021	+	0.732693i
$339$	1.83214e6	−	2.56739e6i	0.865884	−	1.21337i
$340$	395954.	−	685812.i	0.185758	−	0.321742i
$341$	−774839.			−0.360849
$342$	138087.	+	401598.i	0.0638391	+	0.185663i
$343$	1.76209e6			0.808709
$344$	506519.	−	877316.i	0.230781	−	0.399724i
$345$	2.03890e6	+	196770.i	0.922250	+	0.0890041i
$346$	424429.	+	735132.i	0.190596	+	0.330123i
$347$	−1.77827e6	−	3.08005e6i	−0.792818	−	1.37320i	−0.924216	−	0.381871i	$-0.875280\pi$
$347$	−1.77827e6	−	3.08005e6i	−0.792818	−	1.37320i	0.131398	−	0.991330i	$-0.458053\pi$
$348$	−341364.	−	749485.i	−0.151102	−	0.331753i
$349$	−1.21027e6	+	2.09625e6i	−0.531886	+	0.921254i	0.467421	+	0.884035i	$0.345183\pi$
$349$	−1.21027e6	+	2.09625e6i	−0.531886	+	0.921254i	−0.999307	+	0.0372193i	$0.988150\pi$
$350$	−505146.			−0.220418
$351$	−796416.	−	3.32683e6i	−0.345042	−	1.44133i
$352$	−123904.			−0.0533002
$353$	−1.19908e6	+	2.07687e6i	−0.512166	+	0.887098i	0.487734	+	0.872992i	$0.337824\pi$
$353$	−1.19908e6	+	2.07687e6i	−0.512166	+	0.887098i	−0.999901	+	0.0141059i	$0.995510\pi$
$354$	266489.	+	585092.i	0.113024	+	0.248151i
$355$	−848742.	−	1.47006e6i	−0.357442	−	0.619107i
$356$	802513.	+	1.38999e6i	0.335604	+	0.581283i
$357$	−1.44582e6	−	139533.i	−0.600406	−	0.0579438i
$358$	−817640.	+	1.41619e6i	−0.337174	+	0.584003i
$359$	−1.14128e6			−0.467367			−0.233683	−	0.972313i	$-0.575078\pi$
$359$	−1.14128e6			−0.467367			−0.233683	+	0.972313i	$0.575078\pi$
$360$	−472898.	−	92134.7i	−0.192314	−	0.0374685i
$361$	−2.28521e6			−0.922907
$362$	−53073.0	+	91925.2i	−0.0212864	+	0.0368691i
$363$	132574.	−	185777.i	0.0528072	−	0.0739991i
$364$	−421361.	−	729819.i	−0.166687	−	0.288710i
$365$	−42142.5	−	72992.9i	−0.0165572	−	0.0286780i
$366$	984662.	−	1.37981e6i	0.384224	−	0.538415i
$367$	616804.	−	1.06834e6i	0.239046	−	0.414040i	−0.721395	−	0.692524i	$-0.756499\pi$
$367$	616804.	−	1.06834e6i	0.239046	−	0.414040i	0.960441	+	0.278484i	$0.0898319\pi$
$368$	−1.08586e6			−0.417980
$369$	−4.53439e6	−	883434.i	−1.73362	−	0.337760i
$370$	333661.			0.126707
$371$	−988279.	+	1.71175e6i	−0.372773	+	0.645662i
$372$	1.58978e6	+	153426.i	0.595633	+	0.0574831i
$373$	−482885.	−	836382.i	−0.179710	−	0.311266i	0.762071	−	0.647493i	$-0.224183\pi$
$373$	−482885.	−	836382.i	−0.179710	−	0.311266i	−0.941781	+	0.336227i	$0.890849\pi$
$374$	−386633.	−	669667.i	−0.142929	−	0.247560i
$375$	−1.05895e6	−	2.32498e6i	−0.388862	−	0.853770i
$376$	813507.	−	1.40904e6i	0.296751	−	0.513987i
$377$	2.98192e6			1.08055
$378$	205741.	+	859431.i	0.0740612	+	0.309372i
$379$	−1.90126e6			−0.679897			−0.339948	−	0.940444i	$-0.610410\pi$
$379$	−1.90126e6			−0.679897			−0.339948	+	0.940444i	$0.610410\pi$
$380$	−108281.	+	187548.i	−0.0384674	+	0.0666275i
$381$	−1.08372e6	−	2.37936e6i	−0.382475	−	0.839747i
$382$	−1.87566e6	−	3.24873e6i	−0.657650	−	1.13908i
$383$	534162.	+	925195.i	0.186070	+	0.322282i	0.943936	−	0.330127i	$-0.107092\pi$
$383$	534162.	+	925195.i	0.186070	+	0.322282i	−0.757867	+	0.652409i	$0.773758\pi$
$384$	254220.	+	24534.2i	0.0879796	+	0.00849070i
$385$	109312.	−	189334.i	0.0375852	−	0.0650995i
$386$	−49610.2			−0.0169474
$387$	−1.25068e6	−	3.63736e6i	−0.424492	−	1.23455i
$388$	−2.62096e6			−0.883854
$389$	424046.	−	734469.i	0.142082	−	0.246093i	−0.786199	−	0.617974i	$-0.787954\pi$
$389$	424046.	−	734469.i	0.142082	−	0.246093i	0.928280	+	0.371881i	$0.121287\pi$
$390$	1.01331e6	−	1.41996e6i	0.337350	−	0.472731i
$391$	−3.38835e6	−	5.86879e6i	−1.12085	−	1.94136i
$392$	−428972.	−	743002.i	−0.140998	−	0.244216i
$393$	3.49034e6	−	4.89103e6i	1.13995	−	1.59742i
$394$	−615245.	+	1.06564e6i	−0.199668	+	0.345835i
$395$	1.27067e6			0.409769
$396$	−308795.	+	354918.i	−0.0989539	+	0.113734i
$397$	681601.			0.217047			0.108523	−	0.994094i	$-0.465388\pi$
$397$	681601.			0.217047			0.108523	+	0.994094i	$0.465388\pi$
$398$	732192.	−	1.26819e6i	0.231695	−	0.401308i
$399$	395387.	+	38157.9i	0.124334	+	0.0119992i
$400$	277156.	+	480049.i	0.0866114	+	0.150015i
$401$	2.35518e6	+	4.07929e6i	0.731414	+	1.26685i	0.956279	+	0.292456i	$0.0944726\pi$
$401$	2.35518e6	+	4.07929e6i	0.731414	+	1.26685i	−0.224865	+	0.974390i	$0.572194\pi$
$402$	−519089.	−	1.13969e6i	−0.160205	−	0.351740i
$403$	−2.89147e6	+	5.00817e6i	−0.886861	+	1.53609i
$404$	1.89383e6			0.577282
$405$	−1.44248e6	+	1.12498e6i	−0.436991	+	0.340805i
$406$	−770330.			−0.231932
$407$	162903.	−	282157.i	0.0487466	−	0.0844315i
$408$	660673.	+	1.45055e6i	0.196488	+	0.431401i
$409$	79819.8	+	138252.i	0.0235940	+	0.0408661i	0.877581	−	0.479428i	$-0.159156\pi$
$409$	79819.8	+	138252.i	0.0235940	+	0.0408661i	−0.853987	+	0.520294i	$0.825822\pi$
$410$	−1.17789e6	−	2.04016e6i	−0.346054	−	0.599383i
$411$	−1.76834e6	−	170658.i	−0.516369	−	0.0498336i
$412$	−477651.	+	827315.i	−0.138633	+	0.240120i
$413$	601364.			0.173485
$414$	−2.70620e6	+	3.11041e6i	−0.775996	+	0.891901i
$415$	−606341.			−0.172821
$416$	−462373.	+	800853.i	−0.130996	+	0.226892i
$417$	−1.58349e6	+	2.21895e6i	−0.445938	+	0.624896i
$418$	105732.	+	183133.i	0.0295982	+	0.0512655i
$419$	1.03238e6	+	1.78813e6i	0.287279	+	0.497581i	0.973159	−	0.230133i	$-0.0739161\pi$
$419$	1.03238e6	+	1.78813e6i	0.287279	+	0.497581i	−0.685881	+	0.727714i	$0.740583\pi$
$420$	−261772.	+	366822.i	−0.0724101	+	0.101469i
$421$	1.57278e6	−	2.72414e6i	0.432477	−	0.749072i	−0.564609	−	0.825358i	$-0.690973\pi$
$421$	1.57278e6	−	2.72414e6i	0.432477	−	0.749072i	0.997086	+	0.0762865i	$0.0243064\pi$
$422$	4.46711e6			1.22108
$423$	−2.00869e6	−	5.84188e6i	−0.545836	−	1.58745i
$424$	2.16894e6			0.585912
$425$	−1.72969e6	+	2.99591e6i	−0.464511	+	0.804556i
$426$	3.40083e6	+	328206.i	0.907947	+	0.0876238i
$427$	−792776.	−	1.37313e6i	−0.210417	−	0.364453i
$428$	−1.68636e6	−	2.92086e6i	−0.444981	−	0.770729i
$429$	−706043.	−	1.55016e6i	−0.185220	−	0.406662i
$430$	980724.	−	1.69866e6i	0.255785	−	0.443033i
$431$	2.54519e6			0.659975			0.329987	−	0.943985i	$-0.392956\pi$
$431$	2.54519e6			0.659975			0.329987	+	0.943985i	$0.392956\pi$
$432$	703848.	−	667059.i	0.181455	−	0.171971i
$433$	474348.			0.121584			0.0607921	−	0.998150i	$-0.480637\pi$
$433$	474348.			0.121584			0.0607921	+	0.998150i	$0.480637\pi$
$434$	746962.	−	1.29378e6i	0.190359	−	0.329712i
$435$	−660951.	−	1.45116e6i	−0.167473	−	0.367698i
$436$	−1.24219e6	−	2.15154e6i	−0.312949	−	0.542043i
$437$	926606.	+	1.60493e6i	0.232109	+	0.402024i
$438$	168861.	+	16296.3i	0.0420575	+	0.00405887i
$439$	−48607.5	+	84190.6i	−0.0120377	+	0.0208498i	−0.871981	−	0.489539i	$-0.837165\pi$
$439$	−48607.5	+	84190.6i	−0.0120377	+	0.0208498i	0.859944	+	0.510389i	$0.170498\pi$
$440$	−239904.			−0.0590752
$441$	−3.19739e6	−	622947.i	−0.782887	−	0.152530i
$442$	−5.77119e6			−1.40511
$443$	−1.18857e6	+	2.05867e6i	−0.287751	+	0.498400i	−0.973273	−	0.229653i	$-0.926241\pi$
$443$	−1.18857e6	+	2.05867e6i	−0.287751	+	0.498400i	0.685521	+	0.728052i	$0.259574\pi$
$444$	−390107.	+	546659.i	−0.0939131	+	0.131601i
$445$	1.55383e6	+	2.69131e6i	0.371966	+	0.644264i
$446$	2.23954e6	+	3.87900e6i	0.533116	+	0.923385i
$447$	715126.	−	1.00211e6i	0.169283	−	0.237218i
$448$	119446.	−	206887.i	0.0281175	−	0.0487010i
$449$	−3.31640e6			−0.776339			−0.388170	−	0.921588i	$-0.626892\pi$
$449$	−3.31640e6			−0.776339			−0.388170	+	0.921588i	$0.626892\pi$
$450$	2.06581e6	+	402482.i	0.480906	+	0.0936948i
$451$	−2.30032e6			−0.532533
$452$	−1.61868e6	+	2.80363e6i	−0.372661	+	0.645467i
$453$	2.38192e6	+	229874.i	0.545359	+	0.0526313i
$454$	1.38815e6	+	2.40435e6i	0.316081	+	0.547468i
$455$	−815842.	−	1.41308e6i	−0.184747	−	0.319991i
$456$	−180673.	−	396679.i	−0.0406895	−	0.0893361i
$457$	−882780.	+	1.52902e6i	−0.197725	+	0.342470i	−0.947790	−	0.318894i	$-0.896689\pi$
$457$	−882780.	+	1.52902e6i	−0.197725	+	0.342470i	0.750065	+	0.661364i	$0.230022\pi$
$458$	2.97148e6			0.661926
$459$	5.80157e6	+	1.72261e6i	1.28533	+	0.381640i
$460$	−2.10245e6			−0.463267
$461$	−3.75837e6	+	6.50969e6i	−0.823658	+	1.42662i	0.0792821	+	0.996852i	$0.474737\pi$
$461$	−3.75837e6	+	6.50969e6i	−0.823658	+	1.42662i	−0.902940	+	0.429766i	$0.858596\pi$
$462$	182394.	+	400458.i	0.0397563	+	0.0872874i
$463$	−3.73926e6	−	6.47659e6i	−0.810650	−	1.40409i	−0.912410	−	0.409278i	$-0.865781\pi$
$463$	−3.73926e6	−	6.47659e6i	−0.810650	−	1.40409i	0.101760	−	0.994809i	$-0.467553\pi$
$464$	422653.	+	732057.i	0.0911359	+	0.157852i
$465$	3.07813e6	+	297063.i	0.660169	+	0.0637113i
$466$	453447.	−	785393.i	0.0967300	−	0.167541i
$467$	6.38083e6			1.35389			0.676947	−	0.736032i	$-0.263303\pi$
$467$	6.38083e6			1.35389			0.676947	+	0.736032i	$0.263303\pi$
$468$	1.14168e6	+	3.32035e6i	0.240951	+	0.700759i
$469$	−1.17139e6			−0.245906
$470$	1.57512e6	−	2.72818e6i	0.328903	−	0.569677i
$471$	−2.39153e6	+	3.35127e6i	−0.496734	+	0.696076i
$472$	−329948.	−	571486.i	−0.0681695	−	0.118073i
$473$	−957637.	−	1.65868e6i	−0.196810	−	0.340886i
$474$	−1.48562e6	+	2.08181e6i	−0.303713	+	0.425595i
$475$	473015.	−	819287.i	0.0961925	−	0.166610i
$476$	1.49089e6			0.301598
$477$	5.40546e6	−	6.21283e6i	1.08777	−	1.25024i
$478$	1.46728e6			0.293727
$479$	−2.57024e6	+	4.45179e6i	−0.511841	+	0.886535i	0.488065	+	0.872807i	$0.337703\pi$
$479$	−2.57024e6	+	4.45179e6i	−0.511841	+	0.886535i	−0.999906	+	0.0137271i	$0.995630\pi$
$480$	492222.	+	47503.2i	0.0975120	+	0.00941065i
$481$	−1.21581e6	−	2.10585e6i	−0.239610	−	0.415016i
$482$	−292044.	−	505835.i	−0.0572572	−	0.0991724i
$483$	1.59846e6	+	3.50951e6i	0.311769	+	0.684508i
$484$	−117128.	+	202872.i	−0.0227273	+	0.0393648i
$485$	−5.07471e6			−0.979618
$486$	−156620.	−	3.67860e6i	−0.0300786	−	0.706467i
$487$	7.91614e6			1.51249			0.756243	−	0.654291i	$-0.227033\pi$
$487$	7.91614e6			1.51249			0.756243	+	0.654291i	$0.227033\pi$
$488$	−869938.	+	1.50678e6i	−0.165363	+	0.286417i
$489$	2.81014e6	+	6.16984e6i	0.531443	+	1.16681i
$490$	−830578.	−	1.43860e6i	−0.156275	−	0.270677i
$491$	−261174.	−	452367.i	−0.0488907	−	0.0846812i	0.840544	−	0.541743i	$-0.182235\pi$
$491$	−261174.	−	452367.i	−0.0488907	−	0.0846812i	−0.889435	+	0.457061i	$0.848902\pi$
$492$	4.71968e6	+	455485.i	0.879022	+	0.0848323i
$493$	−2.63771e6	+	4.56865e6i	−0.488776	+	0.846585i
$494$	1.57824e6			0.290975
$495$	−597891.	+	687194.i	−0.109675	+	0.126057i
$496$	−1.63933e6			−0.299200
$497$	1.59789e6	−	2.76763e6i	0.290172	−	0.502593i
$498$	708916.	−	993408.i	0.128092	−	0.179496i
$499$	3.52549e6	+	6.10633e6i	0.633824	+	1.09782i	0.986763	+	0.162169i	$0.0518489\pi$
$499$	3.52549e6	+	6.10633e6i	0.633824	+	1.09782i	−0.352939	+	0.935646i	$0.614818\pi$
$500$	1.31111e6	+	2.27092e6i	0.234539	+	0.406234i
$501$	4.52994e6	−	6.34784e6i	0.806303	−	1.12988i
$502$	−863582.	+	1.49577e6i	−0.152948	+	0.264914i
$503$	204743.			0.0360819			0.0180410	−	0.999837i	$-0.494257\pi$
$503$	204743.			0.0360819			0.0180410	+	0.999837i	$0.494257\pi$
$504$	−294933.	−	857755.i	−0.0517187	−	0.150414i
$505$	3.66685e6			0.639830
$506$	−1.02648e6	+	1.77791e6i	−0.178227	+	0.308699i
$507$	−6.89308e6	−	665235.i	−1.19095	−	0.114936i
$508$	1.34178e6	+	2.32404e6i	0.230687	+	0.399561i
$509$	−373834.	−	647500.i	−0.0639565	−	0.110776i	0.832274	−	0.554364i	$-0.187039\pi$
$509$	−373834.	−	647500.i	−0.0639565	−	0.110776i	−0.896231	+	0.443588i	$0.853705\pi$
$510$	1.27920e6	+	2.80856e6i	0.217777	+	0.478143i
$511$	79339.8	−	137421.i	0.0134412	−	0.0232809i
$512$	−262144.			−0.0441942
$513$	−1.58655e6	−	471078.i	−0.266170	−	0.0790314i
$514$	−1.08705e6			−0.181486
$515$	−924829.	+	1.60185e6i	−0.153654	+	0.266136i
$516$	1.63640e6	+	3.59281e6i	0.270561	+	0.594033i
$517$	−1.53804e6	−	2.66396e6i	−0.253070	−	0.438330i
$518$	314085.	+	544011.i	0.0514307	+	0.0890806i
$519$	−3.29280e6	−	317780.i	−0.536595	−	0.0517855i
$520$	−895248.	+	1.55062e6i	−0.145189	+	0.251476i
$521$	5.97560e6			0.964467			0.482233	−	0.876043i	$-0.339826\pi$
$521$	5.97560e6			0.964467			0.482233	+	0.876043i	$0.339826\pi$
$522$	3.15029e6	+	613770.i	0.506028	+	0.0985893i
$523$	−3.42985e6			−0.548304			−0.274152	−	0.961686i	$-0.588397\pi$
$523$	−3.42985e6			−0.548304			−0.274152	+	0.961686i	$0.588397\pi$
$524$	−3.08367e6	+	5.34108e6i	−0.490614	+	0.849768i
$525$	1.14353e6	−	1.60243e6i	0.181071	−	0.253735i
$526$	−2.33131e6	−	4.03795e6i	−0.367398	−	0.636351i
$527$	−5.11539e6	−	8.86012e6i	−0.802329	−	1.38967i
$528$	280488.	−	393050.i	0.0437854	−	0.0613568i
$529$	−5.77763e6	+	1.00071e7i	−0.897657	+	1.55479i
$530$	4.19951e6			0.649395
$531$	−2.45930e6	−	479145.i	−0.378508	−	0.0737446i
$532$	−407711.			−0.0624559
$533$	−8.58410e6	+	1.48681e7i	−1.30881	+	2.26693i
$534$	−6.22604e6	−	600861.i	−0.944841	−	0.0911844i
$535$	−3.26514e6	−	5.65539e6i	−0.493194	−	0.854236i
$536$	642699.	+	1.11319e6i	0.0966264	+	0.167362i
$537$	−2.64153e6	−	5.79964e6i	−0.395294	−	0.867891i
$538$	1.33173e6	−	2.30663e6i	0.198363	−	0.343575i
$539$	−1.62205e6			−0.240488
$540$	1.36279e6	−	1.29156e6i	0.201116	−	0.190604i
$541$	2.84031e6			0.417227			0.208614	−	0.977998i	$-0.433105\pi$
$541$	2.84031e6			0.417227			0.208614	+	0.977998i	$0.433105\pi$
$542$	−958276.	+	1.65978e6i	−0.140118	+	0.242691i
$543$	−171462.	−	376455.i	−0.0249556	−	0.0547915i
$544$	−818000.	−	1.41682e6i	−0.118510	−	0.205266i
$545$	−2.40514e6	−	4.16583e6i	−0.346856	−	0.600773i
$546$	3.26900e6	+	315483.i	0.469281	+	0.0452892i
$547$	−488665.	+	846392.i	−0.0698301	+	0.120949i	−0.898826	−	0.438305i	$-0.855579\pi$
$547$	−488665.	+	846392.i	−0.0698301	+	0.120949i	0.828996	+	0.559254i	$0.188912\pi$
$548$	1.82345e6			0.259384
$549$	2.14803e6	+	6.24711e6i	0.304165	+	0.884603i
$550$	1.04800e6			0.147725
$551$	721331.	−	1.24938e6i	0.101217	−	0.175314i
$552$	2.45812e6	−	3.44459e6i	0.343365	−	0.481160i
$553$	1.19611e6	+	2.07173e6i	0.166326	+	0.288085i
$554$	−2.18253e6	−	3.78024e6i	−0.302124	−	0.523294i
$555$	−755327.	+	1.05844e6i	−0.104088	+	0.145860i
$556$	1.39899e6	−	2.42313e6i	0.191924	−	0.332422i
$557$	4.44794e6			0.607464			0.303732	−	0.952757i	$-0.401767\pi$
$557$	4.44794e6			0.607464			0.303732	+	0.952757i	$0.401767\pi$
$558$	−4.08556e6	+	4.69579e6i	−0.555477	+	0.638444i
$559$	−1.42945e7			−1.93481
$560$	231272.	−	400575.i	0.0311640	−	0.0539777i
$561$	2.99957e6	+	289481.i	0.402394	+	0.0388341i
$562$	4.80068e6	+	8.31502e6i	0.641153	+	1.11051i
$563$	−1.85396e6	−	3.21116e6i	−0.246508	−	0.426964i	0.716047	−	0.698052i	$-0.245950\pi$
$563$	−1.85396e6	−	3.21116e6i	−0.246508	−	0.426964i	−0.962554	+	0.271089i	$0.912616\pi$
$564$	2.62818e6	+	5.77032e6i	0.347902	+	0.763840i
$565$	−3.13409e6	+	5.42840e6i	−0.413038	+	0.715403i
$566$	1.15187e6			0.151134
$567$	−3.19204e6	−	1.29289e6i	−0.416976	−	0.168890i
$568$	−3.50683e6			−0.456083
$569$	−1.38780e6	+	2.40374e6i	−0.179699	+	0.311249i	−0.941778	−	0.336236i	$-0.890846\pi$
$569$	−1.38780e6	+	2.40374e6i	−0.179699	+	0.311249i	0.762078	+	0.647485i	$0.224179\pi$
$570$	−349820.	−	768052.i	−0.0450981	−	0.0990155i
$571$	3.22136e6	+	5.57956e6i	0.413475	+	0.716159i	0.995267	−	0.0971781i	$-0.0309816\pi$
$571$	3.22136e6	+	5.57956e6i	0.413475	+	0.716159i	−0.581792	+	0.813337i	$0.697648\pi$
$572$	874174.	+	1.51411e6i	0.111714	+	0.193494i
$573$	1.45517e7	+	1.40435e6i	1.85151	+	0.178685i
$574$	2.21756e6	−	3.84092e6i	0.280928	−	0.486582i
$575$	9.18438e6			1.15846
$576$	−653319.	+	750901.i	−0.0820482	+	0.0943032i
$577$	632386.			0.0790757			0.0395378	−	0.999218i	$-0.487411\pi$
$577$	632386.			0.0790757			0.0395378	+	0.999218i	$0.487411\pi$
$578$	2.26529e6	−	3.92360e6i	0.282036	−	0.488501i
$579$	112305.	−	157374.i	0.0139221	−	0.0195091i
$580$	818343.	+	1.41741e6i	0.101010	+	0.174955i
$581$	−570766.	−	988595.i	−0.0701484	−	0.121501i
$582$	5.93320e6	−	8.31423e6i	0.726075	−	1.01745i
$583$	2.05032e6	−	3.55126e6i	0.249834	−	0.432725i
$584$	−174124.			−0.0211264
$585$	2.21052e6	+	6.42887e6i	0.267058	+	0.776685i
$586$	5.62446e6			0.676608
$587$	3.16216e6	−	5.47702e6i	0.378781	−	0.656068i	−0.612104	−	0.790777i	$-0.709677\pi$
$587$	3.16216e6	−	5.47702e6i	0.378781	−	0.656068i	0.990885	+	0.134709i	$0.0430100\pi$
$588$	3.32805e6	+	321182.i	0.396959	+	0.0383096i
$589$	1.39890e6	+	2.42296e6i	0.166149	+	0.287779i
$590$	−638846.	−	1.10651e6i	−0.0755555	−	0.130866i
$591$	−1.98766e6	−	4.36402e6i	−0.234085	−	0.513947i
$592$	344655.	−	596960.i	0.0404185	−	0.0700069i
$593$	2.04142e6			0.238394			0.119197	−	0.992871i	$-0.461968\pi$
$593$	2.04142e6			0.238394			0.119197	+	0.992871i	$0.461968\pi$
$594$	−426838.	−	1.78301e6i	−0.0496360	−	0.207342i
$595$	2.88667e6			0.334275
$596$	−631806.	+	1.09432e6i	−0.0728565	+	0.126191i
$597$	2.36548e6	+	5.19355e6i	0.271633	+	0.596387i
$598$	7.66103e6	+	1.32693e7i	0.876061	+	1.51738i
$599$	1.44064e6	+	2.49526e6i	0.164054	+	0.284150i	0.936319	−	0.351150i	$-0.114209\pi$
$599$	1.44064e6	+	2.49526e6i	0.164054	+	0.284150i	−0.772265	+	0.635301i	$0.780876\pi$
$600$	−2.15023e6	−	207514.i	−0.243841	−	0.0235325i
$601$	−1.12947e6	+	1.95629e6i	−0.127552	+	0.220926i	−0.922728	−	0.385453i	$-0.874045\pi$
$601$	−1.12947e6	+	1.95629e6i	−0.127552	+	0.220926i	0.795176	+	0.606379i	$0.207379\pi$
$602$	3.69273e6			0.415295
$603$	4.79043e6	+	933318.i	0.536514	+	0.104529i
$604$	−2.45617e6			−0.273946
$605$	−226784.	+	392801.i	−0.0251897	+	0.0436299i
$606$	−4.28717e6	+	6.00764e6i	−0.474230	+	0.664542i
$607$	−4.70005e6	−	8.14073e6i	−0.517763	−	0.896792i	−0.999787	−	0.0206337i	$-0.993432\pi$
$607$	−4.70005e6	−	8.14073e6i	−0.517763	−	0.896792i	0.482024	−	0.876158i	$-0.339902\pi$
$608$	223697.	+	387455.i	0.0245415	+	0.0425071i
$609$	1.74384e6	−	2.44365e6i	0.190530	−	0.266990i
$610$	−1.68438e6	+	2.91743e6i	−0.183280	+	0.317450i
$611$	−2.29580e7			−2.48789
$612$	−6.09704e6	−	1.18789e6i	−0.658023	−	0.128202i
$613$	1.17191e7			1.25963			0.629813	−	0.776747i	$-0.283131\pi$
$613$	1.17191e7			1.25963			0.629813	+	0.776747i	$0.283131\pi$
$614$	−1.89853e6	+	3.28836e6i	−0.203235	+	0.352013i
$615$	9.13826e6	+	881912.i	0.974262	+	0.0940238i
$616$	−225828.	−	391146.i	−0.0239787	−	0.0415324i
$617$	412995.	+	715329.i	0.0436749	+	0.0756472i	0.887037	−	0.461699i	$-0.152760\pi$
$617$	412995.	+	715329.i	0.0436749	+	0.0756472i	−0.843362	+	0.537347i	$0.819427\pi$
$618$	−1.54314e6	−	3.38805e6i	−0.162530	−	0.356844i
$619$	7.24791e6	−	1.25537e7i	0.760302	−	1.31688i	−0.182393	−	0.983226i	$-0.558384\pi$
$619$	7.24791e6	−	1.25537e7i	0.760302	−	1.31688i	0.942695	−	0.333656i	$-0.108282\pi$
$620$	−3.17407e6			−0.331618
$621$	−3.74070e6	−	1.56258e7i	−0.389245	−	1.62598i
$622$	485627.			0.0503300
$623$	−2.92533e6	+	5.06681e6i	−0.301963	+	0.523016i
$624$	−1.49378e6	−	3.27968e6i	−0.153576	−	0.337186i
$625$	−844673.	−	1.46302e6i	−0.0864945	−	0.149813i
$626$	−5.66187e6	−	9.80665e6i	−0.577463	−	1.00020i
$627$	−820287.	−	79163.9i	−0.0833291	−	0.00804190i
$628$	2.11289e6	−	3.65963e6i	0.213785	−	0.370287i
$629$	4.30188e6			0.433542
$630$	−571051.	−	1.66079e6i	−0.0573223	−	0.166711i
$631$	483206.			0.0483125			0.0241562	−	0.999708i	$-0.492310\pi$
$631$	483206.			0.0483125			0.0241562	+	0.999708i	$0.492310\pi$
$632$	1.31253e6	−	2.27337e6i	0.130713	−	0.226401i
$633$	−1.01124e7	+	1.41706e7i	−1.00310	+	1.40566i
$634$	−3.94156e6	−	6.82698e6i	−0.389444	−	0.674536i
$635$	2.59797e6	+	4.49981e6i	0.255681	+	0.442853i
$636$	−4.90994e6	+	6.88033e6i	−0.481319	+	0.674476i
$637$	−6.05301e6	+	1.04841e7i	−0.591048	+	1.02373i
$638$	1.59816e6			0.155442
$639$	−8.73977e6	+	1.00452e7i	−0.846736	+	0.973206i
$640$	−507564.			−0.0489825
$641$	1.50931e6	−	2.61421e6i	0.145089	−	0.251302i	−0.784317	−	0.620360i	$-0.786986\pi$
$641$	1.50931e6	−	2.61421e6i	0.145089	−	0.251302i	0.929406	+	0.369058i	$0.120320\pi$
$642$	1.30831e7	+	1.26262e6i	1.25277	+	0.120902i
$643$	1.47857e6	+	2.56096e6i	0.141031	+	0.244273i	0.927885	−	0.372866i	$-0.121625\pi$
$643$	1.47857e6	+	2.56096e6i	0.141031	+	0.244273i	−0.786854	+	0.617139i	$0.788292\pi$
$644$	−1.97910e6	−	3.42790e6i	−0.188041	−	0.325697i
$645$	3.16840e6	+	6.95642e6i	0.299876	+	0.658395i
$646$	−1.39606e6	+	2.41804e6i	−0.131620	+	0.227973i
$647$	2.67965e6			0.251662			0.125831	−	0.992052i	$-0.459840\pi$
$647$	2.67965e6			0.251662			0.125831	+	0.992052i	$0.459840\pi$
$648$	522712.	+	3.74281e6i	0.0489018	+	0.350155i
$649$	−1.24761e6			−0.116270
$650$	3.91081e6	−	6.77373e6i	0.363065	−	0.628846i
$651$	2.41319e6	+	5.29831e6i	0.223172	+	0.489987i
$652$	−3.47932e6	−	6.02637e6i	−0.320535	−	0.555184i
$653$	1.38283e6	+	2.39514e6i	0.126907	+	0.219810i	0.922477	−	0.386052i	$-0.126162\pi$
$653$	1.38283e6	+	2.39514e6i	0.126907	+	0.219810i	−0.795569	+	0.605862i	$0.792828\pi$
$654$	9.63717e6	+	930060.i	0.881059	+	0.0850289i
$655$	−5.97062e6	+	1.03414e7i	−0.543771	+	0.941839i
$656$	−4.86679e6			−0.441553
$657$	−433954.	+	498771.i	−0.0392221	+	0.0450804i
$658$	5.93080e6			0.534009
$659$	6.28309e6	−	1.08826e7i	0.563585	−	0.976158i	−0.433594	−	0.901108i	$-0.642755\pi$
$659$	6.28309e6	−	1.08826e7i	0.563585	−	0.976158i	0.997180	−	0.0750503i	$-0.0239117\pi$
$660$	543082.	−	761025.i	0.0485295	−	0.0680047i
$661$	1.18262e6	+	2.04837e6i	0.105279	+	0.182349i	0.913852	−	0.406047i	$-0.133093\pi$
$661$	1.18262e6	+	2.04837e6i	0.105279	+	0.182349i	−0.808573	+	0.588396i	$0.799760\pi$
$662$	−7.34686e6	−	1.27251e7i	−0.651564	−	1.12854i
$663$	1.30645e7	−	1.83074e7i	1.15428	−	1.61750i
$664$	−626319.	+	1.08482e6i	−0.0551284	+	0.0954852i
$665$	−789412.			−0.0692229
$666$	−851013.	−	2.47500e6i	−0.0743448	−	0.216217i
$667$	1.40058e7			1.21897
$668$	−4.00215e6	+	6.93193e6i	−0.347018	+	0.601054i
$669$	−1.73748e7	−	1.67680e6i	−1.50091	−	0.144849i
$670$	1.24440e6	+	2.15536e6i	0.107096	+	0.185495i
$671$	1.64473e6	+	2.84875e6i	0.141022	+	0.244257i
$672$	385892.	+	847249.i	0.0329642	+	0.0723749i
$673$	−5.51581e6	+	9.55366e6i	−0.469431	+	0.813078i	−0.999389	−	0.0349458i	$-0.988874\pi$
$673$	−5.51581e6	+	9.55366e6i	−0.469431	+	0.813078i	0.529959	+	0.848024i	$0.322207\pi$
$674$	1.48438e7			1.25862
$675$	−5.95325e6	+	5.64208e6i	−0.502915	+	0.476628i
$676$	7.10793e6			0.598241
$677$	2.70590e6	−	4.68675e6i	0.226903	−	0.393007i	−0.729986	−	0.683462i	$-0.760473\pi$
$677$	2.70590e6	−	4.68675e6i	0.226903	−	0.393007i	0.956889	+	0.290455i	$0.0938067\pi$
$678$	−5.22942e6	−	1.14815e7i	−0.436897	−	0.959234i
$679$	−4.77697e6	−	8.27395e6i	−0.397629	−	0.688713i
$680$	−1.58381e6	−	2.74325e6i	−0.131351	−	0.227506i
$681$	−1.07696e7	−	1.03934e6i	−0.889877	−	0.0858799i
$682$	−1.54968e6	+	2.68412e6i	−0.127579	+	0.220974i
$683$	6.16738e6			0.505882			0.252941	−	0.967482i	$-0.418602\pi$
$683$	6.16738e6			0.505882			0.252941	+	0.967482i	$0.418602\pi$
$684$	1.66735e6	+	324849.i	0.136266	+	0.0265486i
$685$	3.53058e6			0.287488
$686$	3.52417e6	−	6.10405e6i	0.285922	−	0.495231i
$687$	−6.72670e6	+	9.42617e6i	−0.543764	+	0.761980i
$688$	−2.02608e6	−	3.50927e6i	−0.163187	−	0.282647i
$689$	−1.53024e7	−	2.65045e7i	−1.22804	−	2.12702i
$690$	4.75943e6	−	6.66942e6i	0.380568	−	0.533293i
$691$	−1.24951e6	+	2.16422e6i	−0.0995508	+	0.172427i	−0.911499	−	0.411303i	$-0.865074\pi$
$691$	−1.24951e6	+	2.16422e6i	−0.0995508	+	0.172427i	0.811948	+	0.583730i	$0.198407\pi$
$692$	3.39543e6			0.269544
$693$	−1.68323e6	−	327944.i	−0.133141	−	0.0259398i
$694$	−1.42261e7			−1.12121
$695$	2.70874e6	−	4.69168e6i	0.212719	−	0.368439i
$696$	−3.27902e6	−	316451.i	−0.256579	−	0.0247618i
$697$	−1.51864e7	−	2.63037e7i	−1.18406	−	2.05085i
$698$	4.84108e6	+	8.38500e6i	0.376100	+	0.651425i
$699$	1.46494e6	+	3.21636e6i	0.113404	+	0.248984i
$700$	−1.01029e6	+	1.74988e6i	−0.0779296	+	0.134978i
$701$	1.17108e7			0.900098			0.450049	−	0.893004i	$-0.351407\pi$
$701$	1.17108e7			0.900098			0.450049	+	0.893004i	$0.351407\pi$
$702$	−1.31173e7	−	3.89480e6i	−1.00462	−	0.298292i
$703$	−1.17643e6			−0.0897794
$704$	−247808.	+	429216.i	−0.0188445	+	0.0326396i
$705$	5.08869e6	+	1.11725e7i	0.385597	+	0.846601i
$706$	4.79632e6	+	8.30746e6i	0.362156	+	0.627273i
$707$	3.45171e6	+	5.97853e6i	0.259708	+	0.449828i
$708$	2.55979e6	+	247040.i	0.191921	+	0.0185218i
$709$	7.68734e6	−	1.33149e7i	0.574329	−	0.994767i	−0.421785	−	0.906696i	$-0.638596\pi$
$709$	7.68734e6	−	1.33149e7i	0.574329	−	0.994767i	0.996114	−	0.0880712i	$-0.0280703\pi$
$710$	−6.78994e6			−0.505499
$711$	−3.24087e6	−	9.42543e6i	−0.240429	−	0.699241i
$712$	6.42010e6			0.474616
$713$	−1.35810e7	+	2.35229e7i	−1.00048	+	1.73288i
$714$	−3.37501e6	+	4.72942e6i	−0.247759	+	0.347186i
$715$	1.69258e6	+	2.93163e6i	0.123818	+	0.214459i
$716$	3.27056e6	+	5.66477e6i	0.238418	+	0.412952i
$717$	−3.32156e6	+	4.65452e6i	−0.241293	+	0.338125i
$718$	−2.28257e6	+	3.95353e6i	−0.165239	+	0.286203i
$719$	1.23938e7			0.894093			0.447047	−	0.894511i	$-0.352476\pi$
$719$	1.23938e7			0.894093			0.447047	+	0.894511i	$0.352476\pi$
$720$	−1.26496e6	+	1.45390e6i	−0.0909380	+	0.104521i
$721$	−3.48227e6			−0.249474
$722$	−4.57042e6	+	7.91620e6i	−0.326297	+	0.565163i
$723$	2.26573e6	+	218660.i	0.161199	+	0.0155569i
$724$	212292.	+	367701.i	0.0150518	+	0.0260704i
$725$	−3.57486e6	−	6.19184e6i	−0.252589	−	0.437497i
$726$	−378403.	−	830806.i	−0.0266448	−	0.0585003i
$727$	6.46839e6	−	1.12036e7i	0.453900	−	0.786177i	−0.544725	−	0.838615i	$-0.683366\pi$
$727$	6.46839e6	−	1.12036e7i	0.453900	−	0.786177i	0.998624	+	0.0524378i	$0.0166991\pi$
$728$	−3.37089e6			−0.235731
$729$	1.20238e7	+	7.83061e6i	0.837962	+	0.545728i
$730$	−337140.			−0.0234155
$731$	1.26444e7	−	2.19008e7i	0.875196	−	1.51588i
$732$	−2.81049e6	−	6.17060e6i	−0.193867	−	0.425647i
$733$	1.70532e6	+	2.95370e6i	0.117232	+	0.203051i	0.918670	−	0.395027i	$-0.129265\pi$
$733$	1.70532e6	+	2.95370e6i	0.117232	+	0.203051i	−0.801438	+	0.598078i	$0.795931\pi$
$734$	−2.46722e6	−	4.27334e6i	−0.169031	−	0.292771i
$735$	6.44378e6	+	621874.i	0.439969	+	0.0424604i
$736$	−2.17173e6	+	3.76154e6i	−0.147778	+	0.255959i
$737$	2.43021e6			0.164807
$738$	−1.21291e7	+	1.39407e7i	−0.819761	+	0.942202i
$739$	−2.17054e6			−0.146203			−0.0731016	−	0.997324i	$-0.523290\pi$
$739$	−2.17054e6			−0.146203			−0.0731016	+	0.997324i	$0.523290\pi$
$740$	667323.	−	1.15584e6i	0.0447978	−	0.0775921i
$741$	−3.57274e6	+	5.00651e6i	−0.239032	+	0.334957i
$742$	3.95312e6	+	6.84700e6i	0.263590	+	0.456552i
$743$	−1.22340e7	−	2.11899e7i	−0.813012	−	1.40818i	−0.910747	−	0.412965i	$-0.864493\pi$
$743$	−1.22340e7	−	2.11899e7i	−0.813012	−	1.40818i	0.0977351	−	0.995212i	$-0.468840\pi$
$744$	3.71103e6	−	5.20029e6i	0.245789	−	0.344426i
$745$	−1.22331e6	+	2.11883e6i	−0.0807503	+	0.139864i
$746$	−3.86308e6			−0.254148
$747$	1.54649e6	+	4.49766e6i	0.101402	+	0.294907i
$748$	−3.09306e6			−0.202132
$749$	6.14714e6	−	1.06472e7i	0.400376	−	0.693472i
$750$	−1.01719e7	−	981662.i	−0.660309	−	0.0637249i
$751$	1.25126e7	+	2.16725e7i	0.809560	+	1.40220i	0.913169	+	0.407580i	$0.133627\pi$
$751$	1.25126e7	+	2.16725e7i	0.809560	+	1.40220i	−0.103610	+	0.994618i	$0.533039\pi$
$752$	−3.25403e6	−	5.63614e6i	−0.209834	−	0.363444i
$753$	−2.78996e6	−	6.12552e6i	−0.179312	−	0.393691i
$754$	5.96385e6	−	1.03297e7i	0.382031	−	0.661696i
$755$	−4.75564e6			−0.303628
$756$	3.38864e6	+	1.00616e6i	0.215636	+	0.0640266i
$757$	−2.67793e7			−1.69847			−0.849237	−	0.528011i	$-0.822938\pi$
$757$	−2.67793e7			−1.69847			−0.849237	+	0.528011i	$0.822938\pi$
$758$	−3.80252e6	+	6.58615e6i	−0.240380	+	0.416350i
$759$	−3.31622e6	−	7.28097e6i	−0.208949	−	0.458759i
$760$	433123.	+	750192.i	0.0272005	+	0.0471127i
$761$	−8.42181e6	−	1.45870e7i	−0.527161	−	0.913070i	−0.999499	−	0.0316527i	$-0.989923\pi$
$761$	−8.42181e6	−	1.45870e7i	−0.527161	−	0.913070i	0.472337	−	0.881418i	$-0.343410\pi$
$762$	−1.04098e7	−	1.00462e6i	−0.649463	−	0.0626782i
$763$	4.52806e6	−	7.84282e6i	0.281579	−	0.487709i
$764$	−1.50052e7			−0.930057
$765$	−1.18051e7	−	2.29999e6i	−0.729318	−	0.142093i
$766$	4.27329e6			0.263142
$767$	−4.65572e6	+	8.06395e6i	−0.285758	+	0.494948i
$768$	593429.	−	831576.i	0.0363050	−	0.0508744i
$769$	1.59633e7	+	2.76492e7i	0.973433	+	1.68603i	0.685013	+	0.728531i	$0.259796\pi$
$769$	1.59633e7	+	2.76492e7i	0.973433	+	1.68603i	0.288420	+	0.957504i	$0.406870\pi$
$770$	−437249.	−	757338.i	−0.0265768	−	0.0460323i
$771$	2.46082e6	−	3.44836e6i	0.149088	−	0.208919i
$772$	−99220.4	+	171855.i	−0.00599181	+	0.0103781i
$773$	7.82184e6			0.470825			0.235413	−	0.971895i	$-0.424356\pi$
$773$	7.82184e6			0.470825			0.235413	+	0.971895i	$0.424356\pi$
$774$	−1.51016e7	−	2.94224e6i	−0.906086	−	0.176533i
$775$	1.38657e7			0.829252
$776$	−5.24191e6	+	9.07926e6i	−0.312490	+	0.541248i
$777$	−2.43673e6	−	235163.i	−0.144795	−	0.0139739i
$778$	−1.69618e6	−	2.93787e6i	−0.100467	−	0.174014i
$779$	4.15301e6	+	7.19322e6i	0.245199	+	0.424698i
$780$	−2.89226e6	−	6.35013e6i	−0.170216	−	0.373720i
$781$	−3.31505e6	+	5.74183e6i	−0.194474	+	0.336839i
$782$	−2.71068e7			−1.58512
$783$	−9.07849e6	+	8.60396e6i	−0.529187	+	0.501527i
$784$	−3.43178e6			−0.199402
$785$	4.09099e6	−	7.08580e6i	0.236948	−	0.410407i
$786$	−9.96235e6	−	2.18729e7i	−0.575182	−	1.26285i
$787$	−1.40790e6	−	2.43855e6i	−0.0810278	−	0.140344i	0.822664	−	0.568528i	$-0.192487\pi$
$787$	−1.40790e6	−	2.43855e6i	−0.0810278	−	0.140344i	−0.903692	+	0.428184i	$0.859154\pi$
$788$	2.46098e6	+	4.26254e6i	0.141186	+	0.244542i
$789$	1.80868e7	+	1.74551e6i	1.03435	+	0.0998228i
$790$	2.54133e6	−	4.40172e6i	0.144875	−	0.250931i
$791$	−1.18008e7			−0.670611
$792$	611881.	+	1.77953e6i	0.0346620	+	0.100808i
$793$	2.45505e7			1.38636
$794$	1.36320e6	−	2.36113e6i	0.0767377	−	0.132914i
$795$	−9.50665e6	+	1.33217e7i	−0.533469	+	0.747554i
$796$	−2.92877e6	−	5.07278e6i	−0.163833	−	0.283768i
$797$	4.96955e6	+	8.60751e6i	0.277122	+	0.479990i	0.970668	−	0.240423i	$-0.0772860\pi$
$797$	4.96955e6	+	8.60751e6i	0.277122	+	0.479990i	−0.693546	+	0.720412i	$0.743953\pi$
$798$	922958.	−	1.29335e6i	0.0513067	−	0.0718965i
$799$	2.03079e7	−	3.51743e7i	1.12538	−	1.94921i
$800$	2.21725e6			0.122487
$801$	1.60003e7	−	1.83901e7i	0.881143	−	1.01275i
$802$	1.88414e7			1.03438
$803$	−164602.	+	285098.i	−0.00900835	+	0.0156029i
$804$	−4.98618e6	−	481204.i	−0.272037	−	0.0262536i
$805$	−3.83194e6	−	6.63711e6i	−0.208415	−	0.360985i
$806$	1.15659e7	+	2.00327e7i	0.627105	+	1.08618i
$807$	4.30239e6	+	9.44616e6i	0.232555	+	0.510589i
$808$	3.78767e6	−	6.56043e6i	0.204100	−	0.353512i
$809$	−6.55900e6			−0.352343			−0.176172	−	0.984359i	$-0.556371\pi$
$809$	−6.55900e6			−0.352343			−0.176172	+	0.984359i	$0.556371\pi$
$810$	1.01208e6	+	7.24685e6i	0.0542002	+	0.388094i
$811$	1.18286e7			0.631513			0.315757	−	0.948840i	$-0.397742\pi$
$811$	1.18286e7			0.631513			0.315757	+	0.948840i	$0.397742\pi$
$812$	−1.54066e6	+	2.66850e6i	−0.0820005	+	0.142029i
$813$	−3.09588e6	−	6.79719e6i	−0.164270	−	0.360664i
$814$	−651613.	−	1.12863e6i	−0.0344690	−	0.0597021i
$815$	−6.73669e6	−	1.16683e7i	−0.355265	−	0.615337i
$816$	6.34619e6	+	612456.i	0.333647	+	0.0321995i
$817$	−3.45785e6	+	5.98917e6i	−0.181239	+	0.313915i
$818$	638558.			0.0333670
$819$	−8.40098e6	+	9.65578e6i	−0.437643	+	0.503011i
$820$	−9.42310e6			−0.489394
$821$	1.35830e7	−	2.35265e7i	0.703298	−	1.21815i	−0.264005	−	0.964521i	$-0.585043\pi$
$821$	1.35830e7	−	2.35265e7i	0.703298	−	1.21815i	0.967302	−	0.253626i	$-0.0816233\pi$
$822$	−4.12785e6	+	5.78438e6i	−0.213081	+	0.298591i
$823$	−1.88094e7	−	3.25788e7i	−0.967998	−	1.67662i	−0.701336	−	0.712831i	$-0.747413\pi$
$823$	−1.88094e7	−	3.25788e7i	−0.967998	−	1.67662i	−0.266661	−	0.963790i	$-0.585920\pi$
$824$	1.91060e6	+	3.30926e6i	0.0980285	+	0.169790i
$825$	−2.37241e6	+	3.32447e6i	−0.121354	+	0.170054i
$826$	1.20273e6	−	2.08319e6i	0.0613363	−	0.106238i
$827$	−1.12711e6			−0.0573061			−0.0286530	−	0.999589i	$-0.509122\pi$
$827$	−1.12711e6			−0.0573061			−0.0286530	+	0.999589i	$0.509122\pi$
$828$	5.36236e6	+	1.55954e7i	0.271819	+	0.790533i
$829$	1.59351e7			0.805318			0.402659	−	0.915350i	$-0.368086\pi$
$829$	1.59351e7			0.805318			0.402659	+	0.915350i	$0.368086\pi$
$830$	−1.21268e6	+	2.10043e6i	−0.0611015	+	0.105831i
$831$	1.69324e7	+	1.63411e6i	0.850583	+	0.0820878i
$832$	1.84949e6	+	3.20341e6i	0.0926283	+	0.160437i
$833$	−1.07086e7	−	1.85478e7i	−0.534712	−	0.926149i
$834$	4.51970e6	+	9.92327e6i	0.225006	+	0.494015i
$835$	−7.74899e6	+	1.34216e7i	−0.384617	+	0.666177i
$836$	845855.			0.0418581
$837$	−5.64734e6	−	2.35904e7i	−0.278631	−	1.16391i
$838$	8.25902e6			0.406273
$839$	−5.69303e6	+	9.86061e6i	−0.279215	+	0.483614i	−0.971190	−	0.238307i	$-0.923407\pi$
$839$	−5.69303e6	+	9.86061e6i	−0.279215	+	0.483614i	0.691975	+	0.721921i	$0.256741\pi$
$840$	747166.	+	1.64045e6i	0.0365358	+	0.0802166i
$841$	4.80404e6	+	8.32085e6i	0.234216	+	0.405674i
$842$	−6.29112e6	−	1.08965e7i	−0.305807	−	0.529674i
$843$	−3.72446e7	−	3.59438e6i	−1.80507	−	0.174203i
$844$	8.93422e6	−	1.54745e7i	0.431718	−	0.747758i
$845$	1.37624e7			0.663060
$846$	−2.42542e7	−	4.72545e6i	−1.16510	−	0.226995i
$847$	−853912.			−0.0408982
$848$	4.33787e6	−	7.51342e6i	0.207151	−	0.358796i
$849$	−2.60755e6	+	3.65397e6i	−0.124155	+	0.173979i
$850$	6.91876e6	+	1.19836e7i	0.328459	+	0.568907i
$851$	−5.71057e6	−	9.89100e6i	−0.270306	−	0.468184i
$852$	7.93859e6	−	1.11244e7i	0.374666	−	0.525022i
$853$	−7.03043e6	+	1.21771e7i	−0.330833	+	0.573020i	−0.982675	−	0.185335i	$-0.940663\pi$
$853$	−7.03043e6	+	1.21771e7i	−0.330833	+	0.573020i	0.651842	+	0.758355i	$0.273996\pi$
$854$	−6.34221e6			−0.297575
$855$	3.22833e6	+	628975.i	0.151030	+	0.0294251i
$856$	−1.34909e7			−0.629298
$857$	5.12938e6	−	8.88434e6i	0.238568	−	0.413212i	−0.721736	−	0.692169i	$-0.756655\pi$
$857$	5.12938e6	−	8.88434e6i	0.238568	−	0.413212i	0.960304	+	0.278957i	$0.0899886\pi$
$858$	−6.78200e6	−	654515.i	−0.314514	−	0.0303530i
$859$	−5.75662e6	−	9.97075e6i	−0.266185	−	0.461047i	0.701688	−	0.712484i	$-0.252430\pi$
$859$	−5.75662e6	−	9.97075e6i	−0.266185	−	0.461047i	−0.967874	+	0.251438i	$0.919097\pi$
$860$	−3.92290e6	−	6.79466e6i	−0.180868	−	0.313272i
$861$	7.16421e6	+	1.57295e7i	0.329352	+	0.723112i
$862$	5.09038e6	−	8.81680e6i	0.233336	−	0.404150i
$863$	2.57236e7			1.17572			0.587860	−	0.808962i	$-0.299970\pi$
$863$	2.57236e7			1.17572			0.587860	+	0.808962i	$0.299970\pi$
$864$	−903062.	−	3.77232e6i	−0.0411560	−	0.171919i
$865$	6.57425e6			0.298749
$866$	948696.	−	1.64319e6i	0.0429865	−	0.0744549i
$867$	7.31843e6	+	1.60680e7i	0.330651	+	0.725965i
$868$	−2.98785e6	−	5.17510e6i	−0.134604	−	0.233142i
$869$	−2.48151e6	−	4.29810e6i	−0.111472	−	0.193075i
$870$	−6.34886e6	−	612713.i	−0.284379	−	0.0274447i
$871$	9.06881e6	−	1.57076e7i	0.405047	−	0.701561i
$872$	−9.93755e6			−0.442576
$873$	1.29432e7	+	3.76427e7i	0.574785	+	1.67165i
$874$	7.41285e6			0.328251
$875$	−4.77928e6	+	8.27796e6i	−0.211029	+	0.365513i
$876$	394174.	−	552358.i	0.0173551	−	0.0243198i
$877$	−8.13238e6	−	1.40857e7i	−0.357042	−	0.618414i	0.630424	−	0.776251i	$-0.282881\pi$
$877$	−8.13238e6	−	1.40857e7i	−0.357042	−	0.618414i	−0.987465	+	0.157837i	$0.949548\pi$
$878$	194430.	+	336763.i	0.00851191	+	0.0147431i
$879$	−1.27324e7	+	1.78420e7i	−0.555825	+	0.778881i
$880$	−479807.	+	831050.i	−0.0208862	+	0.0361760i
$881$	3.89182e7			1.68932			0.844661	−	0.535301i	$-0.179802\pi$
$881$	3.89182e7			1.68932			0.844661	+	0.535301i	$0.179802\pi$
$882$	−8.55273e6	+	9.83019e6i	−0.370197	+	0.425491i
$883$	2.17478e7			0.938672			0.469336	−	0.883020i	$-0.344493\pi$
$883$	2.17478e7			0.938672			0.469336	+	0.883020i	$0.344493\pi$
$884$	−1.15424e7	+	1.99920e7i	−0.496781	+	0.860449i
$885$	4.95629e6	+	478319.i	0.212715	+	0.0205286i
$886$	4.75430e6	+	8.23469e6i	0.203471	+	0.352422i
$887$	1.15199e7	+	1.99531e7i	0.491633	+	0.851533i	0.999954	−	0.00963462i	$-0.00306684\pi$
$887$	1.15199e7	+	1.99531e7i	0.491633	+	0.851533i	−0.508321	+	0.861168i	$0.669734\pi$
$888$	1.11347e6	+	2.44469e6i	0.0473855	+	0.104038i
$889$	−4.89108e6	+	8.47159e6i	−0.207563	+	0.359510i
$890$	1.24306e7			0.526039
$891$	6.62234e6	+	2.68228e6i	0.279459	+	0.113190i
$892$	1.79163e7			0.753941
$893$	−5.55356e6	+	9.61905e6i	−0.233047	+	0.403649i
$894$	−2.04116e6	−	4.48149e6i	−0.0854149	−	0.187534i
$895$	6.33247e6	+	1.09682e7i	0.264250	+	0.457695i
$896$	−477785.	−	827548.i	−0.0198821	−	0.0344368i
$897$	−5.94357e7	−	5.73600e6i	−2.46641	−	0.238028i
$898$	−6.63281e6	+	1.14884e7i	−0.274477	+	0.475409i
$899$	2.11446e7			0.872571
$900$	5.52587e6	−	6.35122e6i	0.227402	−	0.261367i
$901$	5.41440e7			2.22197
$902$	−4.60063e6	+	7.96853e6i	−0.188279	+	0.326108i
$903$	−8.35944e6	+	1.17141e7i	−0.341160	+	0.478069i
$904$	6.47470e6	+	1.12145e7i	0.263511	+	0.456414i
$905$	411041.	+	711944.i	0.0166826	+	0.0288951i
$906$	5.56016e6	−	7.79148e6i	0.225043	−	0.315355i
$907$	−7.96941e6	+	1.38034e7i	−0.321668	+	0.557146i	−0.980832	−	0.194853i	$-0.937577\pi$
$907$	−7.96941e6	+	1.38034e7i	−0.321668	+	0.557146i	0.659164	+	0.751999i	$0.270910\pi$
$908$	1.11052e7			0.447006
$909$	−9.35240e6	−	2.71996e7i	−0.375417	−	1.09182i
$910$	−6.52673e6			−0.261272
$911$	3.23738e6	−	5.60730e6i	0.129240	−	0.223850i	−0.794142	−	0.607732i	$-0.792080\pi$
$911$	3.23738e6	−	5.60730e6i	0.129240	−	0.223850i	0.923382	+	0.383881i	$0.125413\pi$
$912$	−1.73548e6	−	167487.i	−0.0690929	−	0.00666799i
$913$	1.18413e6	+	2.05098e6i	0.0470137	+	0.0814300i
$914$	3.53112e6	+	6.11608e6i	0.139813	+	0.242163i
$915$	−5.44168e6	−	1.19475e7i	−0.214872	−	0.471765i
$916$	5.94297e6	−	1.02935e7i	0.234026	−	0.405345i
$917$	−2.24813e7			−0.882871
$918$	1.75704e7	−	1.66520e7i	0.688138	−	0.652170i
$919$	5.51910e6			0.215566			0.107783	−	0.994174i	$-0.465625\pi$
$919$	5.51910e6			0.215566			0.107783	+	0.994174i	$0.465625\pi$
$920$	−4.20490e6	+	7.28311e6i	−0.163790	+	0.283692i
$921$	−6.13355e6	−	1.34666e7i	−0.238267	−	0.523128i
$922$	1.50335e7	+	2.60387e7i	0.582414	+	1.00877i
$923$	2.47415e7	+	4.28536e7i	0.955922	+	1.65571i
$924$	1.75201e6	+	169083.i	0.0675084	+	0.00651508i
$925$	−2.91514e6	+	5.04917e6i	−0.112023	+	0.194029i
$926$	−2.99141e7			−1.14643
$927$	1.42409e7	+	2.77455e6i	0.544299	+	0.106046i
$928$	3.38123e6			0.128886
$929$	−1.16018e7	+	2.00949e7i	−0.441047	+	0.763916i	−0.997767	−	0.0667838i	$-0.978726\pi$
$929$	−1.16018e7	+	2.00949e7i	−0.441047	+	0.763916i	0.556720	+	0.830700i	$0.312060\pi$
$930$	7.18532e6	−	1.00688e7i	0.272420	−	0.381744i
$931$	2.92846e6	+	5.07225e6i	0.110730	+	0.191790i
$932$	−1.81379e6	−	3.14157e6i	−0.0683985	−	0.118470i
$933$	−1.09934e6	+	1.54051e6i	−0.0413455	+	0.0579377i
$934$	1.27617e7	−	2.21038e7i	0.478674	−	0.829087i
$935$	−5.98880e6			−0.224032
$936$	1.37854e7	+	2.68580e6i	0.514315	+	0.100204i
$937$	1.69571e7			0.630960			0.315480	−	0.948932i	$-0.397834\pi$
$937$	1.69571e7			0.630960			0.315480	+	0.948932i	$0.397834\pi$
$938$	−2.34277e6	+	4.05780e6i	−0.0869407	+	0.150586i
$939$	4.39259e7	+	4.23918e6i	1.62576	+	0.156898i
$940$	−6.30046e6	−	1.09127e7i	−0.232570	−	0.402822i
$941$	7.99486e6	+	1.38475e7i	0.294332	+	0.509797i	0.974829	−	0.222953i	$-0.0715696\pi$
$941$	7.99486e6	+	1.38475e7i	0.294332	+	0.509797i	−0.680498	+	0.732750i	$0.738236\pi$
$942$	6.82607e6	+	1.49870e7i	0.250636	+	0.550286i
$943$	−4.03188e7	+	6.98342e7i	−1.47648	+	2.55734i
$944$	−2.63958e6			−0.0964062
$945$	6.56110e6	+	1.94812e6i	0.238999	+	0.0709638i
$946$	−7.66110e6			−0.278332
$947$	2.52795e7	−	4.37853e7i	0.915995	−	1.58655i	0.110556	−	0.993870i	$-0.464737\pi$
$947$	2.52795e7	−	4.37853e7i	0.915995	−	1.58655i	0.805439	−	0.592679i	$-0.201930\pi$
$948$	4.24037e6	+	9.30998e6i	0.153244	+	0.336456i
$949$	1.22849e6	+	2.12780e6i	0.0442798	+	0.0766948i
$950$	−1.89206e6	−	3.27715e6i	−0.0680184	−	0.117811i
$951$	3.05793e7	+	2.95114e6i	1.09642	+	0.105813i
$952$	2.98178e6	−	5.16459e6i	0.106631	−	0.184690i
$953$	−3.81662e7			−1.36128			−0.680639	−	0.732619i	$-0.738298\pi$
$953$	−3.81662e7			−1.36128			−0.680639	+	0.732619i	$0.738298\pi$
$954$	−1.07110e7	−	3.11507e7i	−0.381029	−	1.10815i
$955$	−2.90532e7			−1.03083
$956$	2.93456e6	−	5.08281e6i	0.103848	−	0.179870i
$957$	−3.61783e6	+	5.06969e6i	−0.127693	+	0.178938i
$958$	1.02810e7	+	1.78072e7i	0.361926	+	0.626875i
$959$	3.32344e6	+	5.75636e6i	0.116692	+	0.202116i
$960$	1.14900e6	−	1.61010e6i	0.0402385	−	0.0563865i
$961$	−6.18863e6	+	1.07190e7i	−0.216165	+	0.374409i
$962$	−9.72651e6			−0.338859
$963$	−3.36222e7	+	3.86441e7i	−1.16832	+	1.34282i
$964$	−2.33635e6			−0.0809740
$965$	−192111.	+	332746.i	−0.00664101	+	0.0115026i
$966$	1.53542e7	+	1.48180e6i	0.529401	+	0.0510912i
$967$	−1.63195e7	−	2.82662e7i	−0.561229	−	0.972078i	−0.997390	−	0.0722089i	$-0.976995\pi$
$967$	−1.63195e7	−	2.82662e7i	−0.561229	−	0.972078i	0.436160	−	0.899869i	$-0.356338\pi$
$968$	468512.	+	811487.i	0.0160706	+	0.0278351i
$969$	−4.51021e6	−	9.90244e6i	−0.154308	−	0.338792i
$970$	−1.01494e7	+	1.75793e7i	−0.346347	+	0.599891i
$971$	3.21888e7			1.09561			0.547806	−	0.836605i	$-0.315463\pi$
$971$	3.21888e7			1.09561			0.547806	+	0.836605i	$0.315463\pi$
$972$	−1.30563e7	−	6.81465e6i	−0.443255	−	0.231354i
$973$	1.01993e7			0.345371
$974$	1.58323e7	−	2.74223e7i	0.534744	−	0.926205i
$975$	1.26346e7	+	2.77400e7i	0.425647	+	0.934533i
$976$	3.47975e6	+	6.02711e6i	0.116929	+	0.202528i
$977$	−5.38762e6	−	9.33163e6i	−0.180576	−	0.312767i	0.761501	−	0.648164i	$-0.224463\pi$
$977$	−5.38762e6	−	9.33163e6i	−0.180576	−	0.312767i	−0.942077	+	0.335397i	$0.891130\pi$
$978$	2.69932e7	+	2.60505e6i	0.902418	+	0.0870903i
$979$	6.06900e6	−	1.05118e7i	0.202377	−	0.350527i
$980$	−6.64463e6			−0.221007
$981$	−2.47665e7	+	2.84657e7i	−0.821660	+	0.944386i
$982$	−2.08939e6			−0.0691419
$983$	1.01149e7	−	1.75196e7i	0.333872	−	0.578283i	−0.649396	−	0.760451i	$-0.724978\pi$
$983$	1.01149e7	−	1.75196e7i	0.333872	−	0.578283i	0.983267	+	0.182168i	$0.0583114\pi$
$984$	1.10172e7	−	1.54385e7i	0.362730	−	0.508296i
$985$	4.76496e6	+	8.25316e6i	0.156484	+	0.271038i
$986$	1.05508e7	+	1.82746e7i	0.345617	+	0.598626i
$987$	−1.34259e7	+	1.88138e7i	−0.438682	+	0.614728i
$988$	3.15648e6	−	5.46718e6i	0.102875	−	0.178185i
$989$	−6.71399e7			−2.18268
$990$	1.18473e6	+	3.44554e6i	0.0384176	+	0.111730i
$991$	−2.44727e7			−0.791585			−0.395793	−	0.918340i	$-0.629530\pi$
$991$	−2.44727e7			−0.791585			−0.395793	+	0.918340i	$0.629530\pi$
$992$	−3.27866e6	+	5.67880e6i	−0.105783	+	0.183222i
$993$	5.69983e7	+	5.50077e6i	1.83438	+	0.177032i
$994$	−6.39156e6	−	1.10705e7i	−0.205183	−	0.355387i
$995$	−5.67070e6	−	9.82194e6i	−0.181585	−	0.314514i
$996$	−2.02343e6	−	4.44257e6i	−0.0646310	−	0.141901i
$997$	−2.76936e6	+	4.79667e6i	−0.0882350	+	0.152828i	−0.906765	−	0.421636i	$-0.861456\pi$
$997$	−2.76936e6	+	4.79667e6i	−0.0882350	+	0.152828i	0.818530	+	0.574464i	$0.194789\pi$
$998$	2.82039e7			0.896362
$999$	9.77771e6	+	2.90320e6i	0.309973	+	0.0920372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.e.b.133.8	yes	24
3.2	odd	2		594.6.e.a.397.9		24
9.4	even	3	inner	198.6.e.b.67.8	✓	24
9.5	odd	6		594.6.e.a.199.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.e.b.67.8	✓	24	9.4	even	3	inner
198.6.e.b.133.8	yes	24	1.1	even	1	trivial
594.6.e.a.199.9		24	9.5	odd	6
594.6.e.a.397.9		24	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(6.46136 + 14.1863i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-15.4896 - 26.8288i) q^{5} +(62.0655 + 5.98979i) q^{6} +(29.1617 - 50.5095i) q^{7} -64.0000 q^{8} +(-159.502 + 183.325i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(6.46136 + 14.1863i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-15.4896 - 26.8288i) q^{5} +(62.0655 + 5.98979i) q^{6} +(29.1617 - 50.5095i) q^{7} -64.0000 q^{8} +(-159.502 + 183.325i) q^{9} -123.917 q^{10} +(-60.5000 + 104.789i) q^{11} +(144.880 - 203.022i) q^{12} +(451.536 + 782.083i) q^{13} +(-116.647 - 202.038i) q^{14} +(280.518 - 393.091i) q^{15} +(-128.000 + 221.703i) q^{16} -1597.66 q^{17} +(316.054 + 919.181i) q^{18} +436.908 q^{19} +(-247.834 + 429.261i) q^{20} +(904.966 + 87.3362i) q^{21} +(242.000 + 419.156i) q^{22} +(2120.83 + 3673.38i) q^{23} +(-413.527 - 907.923i) q^{24} +(1082.64 - 1875.19i) q^{25} +3612.29 q^{26} +(-3631.30 - 1078.21i) q^{27} -933.173 q^{28} +(1650.99 - 2859.60i) q^{29} +(-800.672 - 1757.92i) q^{30} +(3201.81 + 5545.70i) q^{31} +(512.000 + 886.810i) q^{32} +(-1877.48 - 181.191i) q^{33} +(-3195.31 + 5534.44i) q^{34} -1806.81 q^{35} +(3816.24 + 743.518i) q^{36} -2692.62 q^{37} +(873.817 - 1513.49i) q^{38} +(-8177.33 + 11458.9i) q^{39} +(991.337 + 1717.05i) q^{40} +(9505.44 + 16463.9i) q^{41} +(2112.47 - 2960.22i) q^{42} +(-7914.36 + 13708.1i) q^{43} +1936.00 q^{44} +(7389.03 + 1439.60i) q^{45} +16966.6 q^{46} +(-12711.0 + 22016.2i) q^{47} +(-3972.19 - 383.347i) q^{48} +(6702.69 + 11609.4i) q^{49} +(-4330.57 - 7500.77i) q^{50} +(-10323.0 - 22664.8i) q^{51} +(7224.57 - 12513.3i) q^{52} -33889.6 q^{53} +(-10997.6 + 10422.8i) q^{54} +3748.49 q^{55} +(-1866.35 + 3232.61i) q^{56} +(2823.02 + 6198.11i) q^{57} +(-6603.96 - 11438.4i) q^{58} +(5155.43 + 8929.47i) q^{59} +(-7690.97 - 742.238i) q^{60} +(13592.8 - 23543.4i) q^{61} +25614.5 q^{62} +(4608.33 + 13402.4i) q^{63} +4096.00 q^{64} +(13988.3 - 24228.4i) q^{65} +(-4382.63 + 6141.40i) q^{66} +(-10042.2 - 17393.6i) q^{67} +(12781.2 + 22137.8i) q^{68} +(-38408.2 + 53821.6i) q^{69} +(-3613.63 + 6258.99i) q^{70} +54794.2 q^{71} +(10208.1 - 11732.8i) q^{72} +2720.69 q^{73} +(-5385.24 + 9327.50i) q^{74} +(33597.3 + 3242.40i) q^{75} +(-3495.27 - 6053.98i) q^{76} +(3528.56 + 6111.65i) q^{77} +(23340.3 + 51245.0i) q^{78} +(-20508.3 + 35521.5i) q^{79} +7930.69 q^{80} +(-8167.37 - 58481.4i) q^{81} +76043.6 q^{82} +(9786.23 - 16950.3i) q^{83} +(-6029.57 - 13238.3i) q^{84} +(24747.1 + 42863.2i) q^{85} +(31657.4 + 54832.3i) q^{86} +(51234.7 + 4944.54i) q^{87} +(3872.00 - 6706.50i) q^{88} -100314. q^{89} +(19765.0 - 22717.1i) q^{90} +52670.2 q^{91} +(33933.2 - 58774.0i) q^{92} +(-57984.9 + 81254.6i) q^{93} +(50844.2 + 88064.7i) q^{94} +(-6767.55 - 11721.7i) q^{95} +(-9272.33 + 12993.4i) q^{96} +(81904.9 - 141863. i) q^{97} +53621.6 q^{98} +(-9560.64 - 27805.2i) 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

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