LMFDB - Embedded newform 48.7.l.a.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85723 - 7.47236i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-47.6725 + 42.7006i) q^{4} +(-99.4317 + 99.4317i) q^{5} +(-113.860 - 50.8712i) q^{6} +407.926 q^{7} +(455.285 + 234.221i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(-2.85723 - 7.47236i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-47.6725 + 42.7006i) q^{4} +(-99.4317 + 99.4317i) q^{5} +(-113.860 - 50.8712i) q^{6} +407.926 q^{7} +(455.285 + 234.221i) q^{8} -243.000i q^{9} +(1027.09 + 458.891i) q^{10} +(1305.36 + 1305.36i) q^{11} +(-54.8038 + 996.155i) q^{12} +(-1343.66 - 1343.66i) q^{13} +(-1165.54 - 3048.17i) q^{14} +2192.01i q^{15} +(449.326 - 4071.28i) q^{16} +4694.90 q^{17} +(-1815.78 + 694.307i) q^{18} +(-2519.26 + 2519.26i) q^{19} +(494.365 - 8985.94i) q^{20} +(4496.45 - 4496.45i) q^{21} +(6024.41 - 13483.8i) q^{22} +21920.1 q^{23} +(7600.22 - 2436.73i) q^{24} -4148.34i q^{25} +(-6201.16 + 13879.4i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(-19446.8 + 17418.7i) q^{28} +(11013.8 + 11013.8i) q^{29} +(16379.5 - 6263.09i) q^{30} -29355.4i q^{31} +(-31705.9 + 8275.06i) q^{32} +28777.2 q^{33} +(-13414.4 - 35082.0i) q^{34} +(-40560.8 + 40560.8i) q^{35} +(10376.2 + 11584.4i) q^{36} +(-836.191 + 836.191i) q^{37} +(26022.9 + 11626.7i) q^{38} -29621.5 q^{39} +(-68558.8 + 21980.9i) q^{40} +134247. i q^{41} +(-46446.5 - 20751.7i) q^{42} +(94240.7 + 94240.7i) q^{43} +(-117969. - 6490.12i) q^{44} +(24161.9 + 24161.9i) q^{45} +(-62630.9 - 163795. i) q^{46} +22148.9i q^{47} +(-39923.7 - 49829.3i) q^{48} +48754.4 q^{49} +(-30997.9 + 11852.8i) q^{50} +(51750.5 - 51750.5i) q^{51} +(121430. + 6680.53i) q^{52} +(53365.3 - 53365.3i) q^{53} +(-12361.7 + 27668.0i) q^{54} -259588. q^{55} +(185723. + 95544.6i) q^{56} +55538.1i q^{57} +(50830.1 - 113768. i) q^{58} +(-142793. - 142793. i) q^{59} +(-93600.2 - 104499. i) q^{60} +(10444.7 + 10444.7i) q^{61} +(-219354. + 83875.2i) q^{62} -99126.0i q^{63} +(152425. + 213274. i) q^{64} +267204. q^{65} +(-82223.1 - 215034. i) q^{66} +(32487.9 - 32487.9i) q^{67} +(-223817. + 200475. i) q^{68} +(241619. - 241619. i) q^{69} +(418976. + 187193. i) q^{70} -231804. q^{71} +(56915.6 - 110634. i) q^{72} -23177.3i q^{73} +(8637.51 + 3859.13i) q^{74} +(-45725.9 - 45725.9i) q^{75} +(12525.5 - 227673. i) q^{76} +(532490. + 532490. i) q^{77} +(84635.4 + 221342. i) q^{78} -659707. i q^{79} +(360137. + 449492. i) q^{80} -59049.0 q^{81} +(1.00315e6 - 383576. i) q^{82} +(-575483. + 575483. i) q^{83} +(-22355.9 + 406357. i) q^{84} +(-466822. + 466822. i) q^{85} +(434933. - 973468. i) q^{86} +242804. q^{87} +(288569. + 900053. i) q^{88} -1.12283e6i q^{89} +(111510. - 249583. i) q^{90} +(-548113. - 548113. i) q^{91} +(-1.04499e6 + 936002. i) q^{92} +(-323576. - 323576. i) q^{93} +(165504. - 63284.4i) q^{94} -500989. i q^{95} +(-258271. + 440699. i) q^{96} +751819. q^{97} +(-139303. - 364311. i) q^{98} +(317202. - 317202. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.85723	−	7.47236i	−0.357154	−	0.934046i
$2$	−2.85723	−	7.47236i	−0.357154	−	0.934046i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$4$	−47.6725	+	42.7006i	−0.744882	+	0.667196i
$5$	−99.4317	+	99.4317i	−0.795454	+	0.795454i	−0.982375	−	0.186921i	$-0.940149\pi$
$5$	−99.4317	+	99.4317i	−0.795454	+	0.795454i	0.186921	+	0.982375i	$0.440149\pi$
$6$	−113.860	−	50.8712i	−0.527130	−	0.235515i
$7$	407.926			1.18929			0.594644	−	0.803989i	$-0.297293\pi$
$7$	407.926			1.18929			0.594644	+	0.803989i	$0.297293\pi$
$8$	455.285	+	234.221i	0.889229	+	0.457462i
$9$		−	243.000i		−	0.333333i
$10$	1027.09	+	458.891i	1.02709	+	0.458891i
$11$	1305.36	+	1305.36i	0.980736	+	0.980736i	0.999818	−	0.0190821i	$-0.00607440\pi$
$11$	1305.36	+	1305.36i	0.980736	+	0.980736i	−0.0190821	+	0.999818i	$0.506074\pi$
$12$	−54.8038	+	996.155i	−0.0317152	+	0.576479i
$13$	−1343.66	−	1343.66i	−0.611587	−	0.611587i	0.331772	−	0.943360i	$-0.392353\pi$
$13$	−1343.66	−	1343.66i	−0.611587	−	0.611587i	−0.943360	+	0.331772i	$0.892353\pi$
$14$	−1165.54	−	3048.17i	−0.424759	−	1.11085i
$15$			2192.01i			0.649485i
$16$	449.326	−	4071.28i	0.109699	−	0.993965i
$17$	4694.90			0.955607			0.477804	−	0.878467i	$-0.341433\pi$
$17$	4694.90			0.955607			0.477804	+	0.878467i	$0.341433\pi$
$18$	−1815.78	+	694.307i	−0.311349	+	0.119051i
$19$	−2519.26	+	2519.26i	−0.367293	+	0.367293i	−0.866489	−	0.499196i	$-0.833629\pi$
$19$	−2519.26	+	2519.26i	−0.367293	+	0.367293i	0.499196	+	0.866489i	$0.333629\pi$
$20$	494.365	−	8985.94i	0.0617956	−	1.12324i
$21$	4496.45	−	4496.45i	0.485525	−	0.485525i
$22$	6024.41	−	13483.8i	0.565778	−	1.26633i
$23$	21920.1			1.80161			0.900803	−	0.434229i	$-0.142979\pi$
$23$	21920.1			1.80161			0.900803	+	0.434229i	$0.142979\pi$
$24$	7600.22	−	2436.73i	0.549784	−	0.176268i
$25$		−	4148.34i		−	0.265494i
$26$	−6201.16	+	13879.4i	−0.352820	+	0.789681i
$27$	−2678.52	−	2678.52i	−0.136083	−	0.136083i
$28$	−19446.8	+	17418.7i	−0.885879	+	0.793488i
$29$	11013.8	+	11013.8i	0.451589	+	0.451589i	0.895882	−	0.444293i	$-0.146545\pi$
$29$	11013.8	+	11013.8i	0.451589	+	0.451589i	−0.444293	+	0.895882i	$0.646545\pi$
$30$	16379.5	−	6263.09i	0.606649	−	0.231966i
$31$		−	29355.4i		−	0.985378i	−0.870205	−	0.492689i	$-0.836014\pi$
$31$		−	29355.4i		−	0.985378i	0.870205	−	0.492689i	$-0.163986\pi$
$32$	−31705.9	+	8275.06i	−0.967588	+	0.252535i
$33$	28777.2			0.800767
$34$	−13414.4	−	35082.0i	−0.341299	−	0.892581i
$35$	−40560.8	+	40560.8i	−0.946024	+	0.946024i
$36$	10376.2	+	11584.4i	0.222399	+	0.248294i
$37$	−836.191	+	836.191i	−0.0165082	+	0.0165082i	−0.715313	−	0.698804i	$-0.753716\pi$
$37$	−836.191	+	836.191i	−0.0165082	+	0.0165082i	0.698804	+	0.715313i	$0.253716\pi$
$38$	26022.9	+	11626.7i	0.474248	+	0.211888i
$39$	−29621.5			−0.499359
$40$	−68558.8	+	21980.9i	−1.07123	+	0.343451i
$41$			134247.i			1.94785i	0.226880	+	0.973923i	$0.427147\pi$
$41$			134247.i			1.94785i	−0.226880	+	0.973923i	$0.572853\pi$
$42$	−46446.5	−	20751.7i	−0.626909	−	0.280095i
$43$	94240.7	+	94240.7i	1.18531	+	1.18531i	0.978349	+	0.206964i	$0.0663584\pi$
$43$	94240.7	+	94240.7i	1.18531	+	1.18531i	0.206964	+	0.978349i	$0.433642\pi$
$44$	−117969.	−	6490.12i	−1.38488	−	0.0761894i
$45$	24161.9	+	24161.9i	0.265151	+	0.265151i
$46$	−62630.9	−	163795.i	−0.643450	−	1.68278i
$47$			22148.9i			0.213333i	0.994295	+	0.106666i	$0.0340177\pi$
$47$			22148.9i			0.213333i	−0.994295	+	0.106666i	$0.965982\pi$
$48$	−39923.7	−	49829.3i	−0.361000	−	0.450569i
$49$	48754.4			0.414406
$50$	−30997.9	+	11852.8i	−0.247983	+	0.0948221i
$51$	51750.5	−	51750.5i	0.390125	−	0.390125i
$52$	121430.	+	6680.53i	0.863609	+	0.0475118i
$53$	53365.3	−	53365.3i	0.358452	−	0.358452i	−0.504790	−	0.863242i	$-0.668430\pi$
$53$	53365.3	−	53365.3i	0.358452	−	0.358452i	0.863242	+	0.504790i	$0.168430\pi$
$54$	−12361.7	+	27668.0i	−0.0785050	+	0.175710i
$55$	−259588.			−1.56026
$56$	185723.	+	95544.6i	1.05755	+	0.544054i
$57$			55538.1i			0.299893i
$58$	50830.1	−	113768.i	0.260518	−	0.583091i
$59$	−142793.	−	142793.i	−0.695264	−	0.695264i	0.268121	−	0.963385i	$-0.413597\pi$
$59$	−142793.	−	142793.i	−0.695264	−	0.695264i	−0.963385	+	0.268121i	$0.913597\pi$
$60$	−93600.2	−	104499.i	−0.433334	−	0.483790i
$61$	10444.7	+	10444.7i	0.0460156	+	0.0460156i	0.729740	−	0.683725i	$-0.239641\pi$
$61$	10444.7	+	10444.7i	0.0460156	+	0.0460156i	−0.683725	+	0.729740i	$0.739641\pi$
$62$	−219354.	+	83875.2i	−0.920388	+	0.351932i
$63$		−	99126.0i		−	0.396429i
$64$	152425.	+	213274.i	0.581457	+	0.813577i
$65$	267204.			0.972979
$66$	−82223.1	−	215034.i	−0.285997	−	0.747953i
$67$	32487.9	−	32487.9i	0.108018	−	0.108018i	−0.651032	−	0.759050i	$-0.725664\pi$
$67$	32487.9	−	32487.9i	0.108018	−	0.108018i	0.759050	+	0.651032i	$0.225664\pi$
$68$	−223817.	+	200475.i	−0.711815	+	0.637578i
$69$	241619.	−	241619.i	0.735502	−	0.735502i
$70$	418976.	+	187193.i	1.22151	+	0.545753i
$71$	−231804.			−0.647659			−0.323830	−	0.946115i	$-0.604970\pi$
$71$	−231804.			−0.647659			−0.323830	+	0.946115i	$0.604970\pi$
$72$	56915.6	−	110634.i	0.152487	−	0.296410i
$73$		−	23177.3i		−	0.0595791i	−0.999556	−	0.0297895i	$-0.990516\pi$
$73$		−	23177.3i		−	0.0595791i	0.999556	−	0.0297895i	$-0.00948370\pi$
$74$	8637.51	+	3859.13i	0.0213154	+	0.00952345i
$75$	−45725.9	−	45725.9i	−0.108387	−	0.108387i
$76$	12525.5	−	227673.i	0.0285335	−	0.518646i
$77$	532490.	+	532490.i	1.16638	+	1.16638i
$78$	84635.4	+	221342.i	0.178348	+	0.466424i
$79$		−	659707.i		−	1.33804i	−0.743244	−	0.669021i	$-0.766714\pi$
$79$		−	659707.i		−	1.33804i	0.743244	−	0.669021i	$-0.233286\pi$
$80$	360137.	+	449492.i	0.703393	+	0.877913i
$81$	−59049.0			−0.111111
$82$	1.00315e6	−	383576.i	1.81938	−	0.695681i
$83$	−575483.	+	575483.i	−1.00646	+	1.00646i	−0.00648579	+	0.999979i	$0.502065\pi$
$83$	−575483.	+	575483.i	−1.00646	+	1.00646i	−0.999979	+	0.00648579i	$0.997935\pi$
$84$	−22355.9	+	406357.i	−0.0377185	+	0.685599i
$85$	−466822.	+	466822.i	−0.760142	+	0.760142i
$86$	434933.	−	973468.i	0.683797	−	1.53048i
$87$	242804.			0.368721
$88$	288569.	+	900053.i	0.423449	+	1.32075i
$89$		−	1.12283e6i		−	1.59274i	−0.604810	−	0.796369i	$-0.706751\pi$
$89$		−	1.12283e6i		−	1.59274i	0.604810	−	0.796369i	$-0.293249\pi$
$90$	111510.	−	249583.i	0.152964	−	0.342363i
$91$	−548113.	−	548113.i	−0.727354	−	0.727354i
$92$	−1.04499e6	+	936002.i	−1.34198	+	1.20202i
$93$	−323576.	−	323576.i	−0.402279	−	0.402279i
$94$	165504.	−	63284.4i	0.199263	−	0.0761927i
$95$		−	500989.i		−	0.584328i
$96$	−258271.	+	440699.i	−0.291919	+	0.498113i
$97$	751819.			0.823755			0.411877	−	0.911239i	$-0.364873\pi$
$97$	751819.			0.823755			0.411877	+	0.911239i	$0.364873\pi$
$98$	−139303.	−	364311.i	−0.148007	−	0.387074i
$99$	317202.	−	317202.i	0.326912	−	0.326912i
$100$	177136.	+	197762.i	0.177136	+	0.197762i
$101$	−426592.	+	426592.i	−0.414046	+	0.414046i	−0.883145	−	0.469100i	$-0.844578\pi$
$101$	−426592.	+	426592.i	−0.414046	+	0.414046i	0.469100	+	0.883145i	$0.344578\pi$
$102$	−534562.	−	238835.i	−0.503729	−	0.225060i
$103$	−2.03872e6			−1.86572			−0.932859	−	0.360241i	$-0.882694\pi$
$103$	−2.03872e6			−1.86572			−0.932859	+	0.360241i	$0.882694\pi$
$104$	−297035.	−	926460.i	−0.264063	−	0.823619i
$105$			894179.i			0.772425i
$106$	−551242.	−	246288.i	−0.462833	−	0.206788i
$107$	−66558.3	−	66558.3i	−0.0543314	−	0.0543314i	0.679419	−	0.733750i	$-0.262232\pi$
$107$	−66558.3	−	66558.3i	−0.0543314	−	0.0543314i	−0.733750	+	0.679419i	$0.762232\pi$
$108$	242066.	+	13317.3i	0.192160	+	0.0105717i
$109$	−1.43278e6	−	1.43278e6i	−1.10637	−	1.10637i	−0.993624	−	0.112742i	$-0.964037\pi$
$109$	−1.43278e6	−	1.43278e6i	−1.10637	−	1.10637i	−0.112742	−	0.993624i	$-0.535963\pi$
$110$	741704.	+	1.93974e6i	0.557253	+	1.45735i
$111$			18434.2i			0.0134789i
$112$	183292.	−	1.66078e6i	0.130463	−	1.18211i
$113$	2.33135e6			1.61574			0.807871	−	0.589360i	$-0.200620\pi$
$113$	2.33135e6			1.61574			0.807871	+	0.589360i	$0.200620\pi$
$114$	415001.	−	158685.i	0.280114	−	0.107108i
$115$	−2.17956e6	+	2.17956e6i	−1.43309	+	1.43309i
$116$	−995350.	−	54759.5i	−0.637679	−	0.0350821i
$117$	−326509.	+	326509.i	−0.203862	+	0.203862i
$118$	−659007.	+	1.47499e6i	−0.401092	+	0.897724i
$119$	1.91517e6			1.13649
$120$	−513415.	+	997991.i	−0.297115	+	0.577541i
$121$			1.63637e6i			0.923685i
$122$	48203.5	−	107889.i	0.0265460	−	0.0594153i
$123$	1.47977e6	+	1.47977e6i	0.795205	+	0.795205i
$124$	1.25349e6	+	1.39944e6i	0.657440	+	0.733991i
$125$	−1.14114e6	−	1.14114e6i	−0.584266	−	0.584266i
$126$	−740705.	+	283226.i	−0.370283	+	0.141586i
$127$		−	913501.i		−	0.445962i	−0.974823	−	0.222981i	$-0.928421\pi$
$127$		−	913501.i		−	0.445962i	0.974823	−	0.222981i	$-0.0715788\pi$
$128$	1.15815e6	−	1.74835e6i	0.552248	−	0.833680i
$129$	2.07757e6			0.967804
$130$	−763465.	−	1.99665e6i	−0.347503	−	0.908807i
$131$	−91277.0	+	91277.0i	−0.0406020	+	0.0406020i	−0.727116	−	0.686514i	$-0.759140\pi$
$131$	−91277.0	+	91277.0i	−0.0406020	+	0.0406020i	0.686514	+	0.727116i	$0.259140\pi$
$132$	−1.37188e6	+	1.22880e6i	−0.596477	+	0.534269i
$133$	−1.02767e6	+	1.02767e6i	−0.436817	+	0.436817i
$134$	−335587.	−	149936.i	−0.139473	−	0.0623148i
$135$	532659.			0.216495
$136$	2.13752e6	+	1.09964e6i	0.849754	+	0.437154i
$137$		−	837703.i		−	0.325783i	−0.986644	−	0.162891i	$-0.947918\pi$
$137$		−	837703.i		−	0.325783i	0.986644	−	0.162891i	$-0.0520820\pi$
$138$	−2.49583e6	−	1.11510e6i	−0.949680	−	0.424305i
$139$	1.30129e6	+	1.30129e6i	0.484540	+	0.484540i	0.906578	−	0.422038i	$-0.138685\pi$
$139$	1.30129e6	+	1.30129e6i	0.484540	+	0.484540i	−0.422038	+	0.906578i	$0.638685\pi$
$140$	201664.	−	3.66560e6i	0.0734928	−	1.33586i
$141$	244140.	+	244140.i	0.0870928	+	0.0870928i
$142$	662319.	+	1.73213e6i	0.231314	+	0.604943i
$143$		−	3.50791e6i		−	1.19961i
$144$	−989321.	−	109186.i	−0.331322	−	0.0365662i
$145$	−2.19024e6			−0.718436
$146$	−173189.	+	66222.8i	−0.0556495	+	0.0212789i
$147$	537406.	−	537406.i	0.169180	−	0.169180i
$148$	4157.46	−	75569.1i	0.00128246	−	0.0233109i
$149$	−276371.	+	276371.i	−0.0835475	+	0.0835475i	−0.747646	−	0.664098i	$-0.768816\pi$
$149$	−276371.	+	276371.i	−0.0835475	+	0.0835475i	0.664098	+	0.747646i	$0.268816\pi$
$150$	−211031.	+	472330.i	−0.0625278	+	0.139950i
$151$	5.73959e6			1.66706			0.833528	−	0.552477i	$-0.186317\pi$
$151$	5.73959e6			1.66706			0.833528	+	0.552477i	$0.186317\pi$
$152$	−1.73704e6	+	556919.i	−0.494630	+	0.158585i
$153$		−	1.14086e6i		−	0.318536i
$154$	2.45751e6	−	5.50040e6i	0.672873	−	1.50603i
$155$	2.91886e6	+	2.91886e6i	0.783823	+	0.783823i
$156$	1.41213e6	−	1.26485e6i	0.371964	−	0.333170i
$157$	1.38023e6	+	1.38023e6i	0.356657	+	0.356657i	0.862579	−	0.505922i	$-0.168848\pi$
$157$	1.38023e6	+	1.38023e6i	0.356657	+	0.356657i	−0.505922	+	0.862579i	$0.668848\pi$
$158$	−4.92957e6	+	1.88494e6i	−1.24979	+	0.477887i
$159$		−	1.17646e6i		−	0.292675i
$160$	2.32977e6	−	3.97538e6i	0.568792	−	0.970551i
$161$	8.94179e6			2.14263
$162$	168717.	+	441236.i	0.0396838	+	0.103783i
$163$	1.62992e6	−	1.62992e6i	0.376360	−	0.376360i	−0.493427	−	0.869787i	$-0.664256\pi$
$163$	1.62992e6	−	1.62992e6i	0.376360	−	0.376360i	0.869787	+	0.493427i	$0.164256\pi$
$164$	−5.73244e6	−	6.39991e6i	−1.29959	−	1.45092i
$165$	−2.86136e6	+	2.86136e6i	−0.636974	+	0.636974i
$166$	5.94451e6	+	2.65593e6i	1.29955	+	0.580621i
$167$	−3.73108e6			−0.801097			−0.400549	−	0.916275i	$-0.631180\pi$
$167$	−3.73108e6			−0.801097			−0.400549	+	0.916275i	$0.631180\pi$
$168$	3.10033e6	−	994005.i	0.653852	−	0.209634i
$169$		−	1.21598e6i		−	0.251922i
$170$	4.82208e6	+	2.15445e6i	0.981494	+	0.438519i
$171$	612180.	+	612180.i	0.122431	+	0.122431i
$172$	−8.51681e6	−	468555.i	−1.67375	−	0.0920822i
$173$	−2.05957e6	−	2.05957e6i	−0.397776	−	0.397776i	0.479672	−	0.877448i	$-0.340756\pi$
$173$	−2.05957e6	−	2.05957e6i	−0.397776	−	0.397776i	−0.877448	+	0.479672i	$0.840756\pi$
$174$	−693746.	−	1.81432e6i	−0.131690	−	0.344402i
$175$		−	1.69221e6i		−	0.315749i
$176$	5.90102e6	−	4.72795e6i	1.08240	−	0.867232i
$177$	−3.14792e6			−0.567681
$178$	−8.39021e6	+	3.20819e6i	−1.48769	+	0.568853i
$179$	−4.47273e6	+	4.47273e6i	−0.779854	+	0.779854i	−0.979806	−	0.199952i	$-0.935922\pi$
$179$	−4.47273e6	+	4.47273e6i	−0.779854	+	0.779854i	0.199952	+	0.979806i	$0.435922\pi$
$180$	−2.18358e6	−	120131.i	−0.374414	−	0.0205985i
$181$	−6.94409e6	+	6.94409e6i	−1.17106	+	1.17106i	−0.189104	+	0.981957i	$0.560558\pi$
$181$	−6.94409e6	+	6.94409e6i	−1.17106	+	1.17106i	−0.981957	+	0.189104i	$0.939442\pi$
$182$	−2.52961e6	+	5.66178e6i	−0.419604	+	0.939159i
$183$	230257.			0.0375716
$184$	9.97991e6	+	5.13415e6i	1.60204	+	0.824166i
$185$		−	166288.i		−	0.0262631i
$186$	−1.49335e6	+	3.34241e6i	−0.232071	+	0.519422i
$187$	6.12853e6	+	6.12853e6i	0.937198	+	0.937198i
$188$	−945768.	−	1.05589e6i	−0.142335	−	0.158908i
$189$	−1.09264e6	−	1.09264e6i	−0.161842	−	0.161842i
$190$	−3.74357e6	+	1.43144e6i	−0.545789	+	0.208695i
$191$			6.78277e6i			0.973435i	0.873560	+	0.486717i	$0.161806\pi$
$191$			6.78277e6i			0.973435i	−0.873560	+	0.486717i	$0.838194\pi$
$192$	4.03100e6	+	670720.i	0.569520	+	0.0947627i
$193$	−8.57451e6			−1.19272			−0.596359	−	0.802718i	$-0.703386\pi$
$193$	−8.57451e6			−1.19272			−0.596359	+	0.802718i	$0.703386\pi$
$194$	−2.14812e6	−	5.61786e6i	−0.294207	−	0.769424i
$195$	2.94531e6	−	2.94531e6i	0.397217	−	0.397217i
$196$	−2.32424e6	+	2.08184e6i	−0.308684	+	0.276490i
$197$	7.04633e6	−	7.04633e6i	0.921646	−	0.921646i	−0.0754994	−	0.997146i	$-0.524055\pi$
$197$	7.04633e6	−	7.04633e6i	0.921646	−	0.921646i	0.997146	+	0.0754994i	$0.0240551\pi$
$198$	−3.27657e6	−	1.46393e6i	−0.422109	−	0.188593i
$199$	7.06231e6			0.896164			0.448082	−	0.893992i	$-0.352107\pi$
$199$	7.06231e6			0.896164			0.448082	+	0.893992i	$0.352107\pi$
$200$	971627.	−	1.88868e6i	0.121453	−	0.236085i
$201$		−	716208.i		−	0.0881965i
$202$	4.40652e6	+	1.96878e6i	0.534615	+	0.238859i
$203$	4.49281e6	+	4.49281e6i	0.537069	+	0.537069i
$204$	−257298.	+	4.67685e6i	−0.0303073	+	0.550887i
$205$	−1.33485e7	−	1.33485e7i	−1.54942	−	1.54942i
$206$	5.82510e6	+	1.52341e7i	0.666349	+	1.74267i
$207$		−	5.32659e6i		−	0.600535i
$208$	−6.07415e6	+	4.86667e6i	−0.674987	+	0.540806i
$209$	−6.57708e6			−0.720434
$210$	6.68163e6	−	2.55488e6i	0.721480	−	0.275875i
$211$	−2.66095e6	+	2.66095e6i	−0.283263	+	0.283263i	−0.834409	−	0.551146i	$-0.814191\pi$
$211$	−2.66095e6	+	2.66095e6i	−0.283263	+	0.283263i	0.551146	+	0.834409i	$0.314191\pi$
$212$	−265327.	+	4.82278e6i	−0.0278467	+	0.506163i
$213$	−2.55511e6	+	2.55511e6i	−0.264406	+	0.264406i
$214$	−307175.	+	687520.i	−0.0313433	+	0.0701527i
$215$	−1.87410e7			−1.88572
$216$	−592126.	−	1.84685e6i	−0.0587561	−	0.183261i
$217$		−	1.19748e7i		−	1.17190i
$218$	−6.61245e6	+	1.48000e7i	−0.638253	+	1.42854i
$219$	−255476.	−	255476.i	−0.0243230	−	0.0243230i
$220$	1.23752e7	−	1.10846e7i	1.16221	−	1.04100i
$221$	−6.30834e6	−	6.30834e6i	−0.584437	−	0.584437i
$222$	137747.	−	52670.7i	0.0125899	−	0.00481404i
$223$		−	1.70720e7i		−	1.53947i	−0.638364	−	0.769734i	$-0.720389\pi$
$223$		−	1.70720e7i		−	1.53947i	0.638364	−	0.769734i	$-0.279611\pi$
$224$	−1.29337e7	+	3.37561e6i	−1.15074	+	0.300337i
$225$	−1.00805e6			−0.0884979
$226$	−6.66120e6	−	1.74207e7i	−0.577069	−	1.50918i
$227$	−4.90006e6	+	4.90006e6i	−0.418913	+	0.418913i	−0.884829	−	0.465916i	$-0.845725\pi$
$227$	−4.90006e6	+	4.90006e6i	−0.418913	+	0.418913i	0.465916	+	0.884829i	$0.345725\pi$
$228$	−2.37151e6	−	2.64764e6i	−0.200087	−	0.223385i
$229$	2.48757e6	−	2.48757e6i	0.207142	−	0.207142i	−0.595909	−	0.803052i	$-0.703208\pi$
$229$	2.48757e6	−	2.48757e6i	0.207142	−	0.207142i	0.803052	+	0.595909i	$0.203208\pi$
$230$	2.25139e7	+	1.00589e7i	1.85041	+	0.826740i
$231$	1.17390e7			0.952343
$232$	2.43476e6	+	7.59408e6i	0.194981	+	0.608151i
$233$			1.30662e7i			1.03295i	0.856301	+	0.516477i	$0.172757\pi$
$233$			1.30662e7i			1.03295i	−0.856301	+	0.516477i	$0.827243\pi$
$234$	3.37270e6	+	1.50688e6i	0.263227	+	0.117607i
$235$	−2.20230e6	−	2.20230e6i	−0.169696	−	0.169696i
$236$	1.29046e7	+	709951.i	0.981767	+	0.0540123i
$237$	−7.27175e6	−	7.27175e6i	−0.546253	−	0.546253i
$238$	−5.47209e6	−	1.43109e7i	−0.405903	−	1.06154i
$239$		−	9.59298e6i		−	0.702684i	−0.936247	−	0.351342i	$-0.885725\pi$
$239$		−	9.59298e6i		−	0.702684i	0.936247	−	0.351342i	$-0.114275\pi$
$240$	8.92430e6	+	984928.i	0.645566	+	0.0712477i
$241$	1.87299e7			1.33809			0.669043	−	0.743224i	$-0.266704\pi$
$241$	1.87299e7			1.33809			0.669043	+	0.743224i	$0.266704\pi$
$242$	1.22275e7	−	4.67547e6i	0.862764	−	0.329898i
$243$	−650880.	+	650880.i	−0.0453609	+	0.0453609i
$244$	−943916.	−	51929.9i	−0.0649776	−	0.00357477i
$245$	−4.84774e6	+	4.84774e6i	−0.329641	+	0.329641i
$246$	6.82933e6	−	1.52854e7i	0.458747	−	1.02677i
$247$	6.77004e6			0.449263
$248$	6.87564e6	−	1.33651e7i	0.450773	−	0.876227i
$249$			1.26868e7i			0.821775i
$250$	−5.26653e6	+	1.17876e7i	−0.337058	+	0.754404i
$251$	−4.66553e6	−	4.66553e6i	−0.295039	−	0.295039i	0.544028	−	0.839067i	$-0.316899\pi$
$251$	−4.66553e6	−	4.66553e6i	−0.295039	−	0.295039i	−0.839067	+	0.544028i	$0.816899\pi$
$252$	4.23273e6	+	4.72558e6i	0.264496	+	0.295293i
$253$	2.86136e7	+	2.86136e7i	1.76690	+	1.76690i
$254$	−6.82601e6	+	2.61008e6i	−0.416549	+	0.159277i
$255$			1.02913e7i			0.620653i
$256$	−1.63734e7	−	3.65866e6i	−0.975932	−	0.218073i
$257$	2.54982e7			1.50214			0.751069	−	0.660224i	$-0.229539\pi$
$257$	2.54982e7			1.50214			0.751069	+	0.660224i	$0.229539\pi$
$258$	−5.93611e6	−	1.55244e7i	−0.345655	−	0.903973i
$259$	−341104.	+	341104.i	−0.0196330	+	0.0196330i
$260$	−1.27383e7	+	1.14098e7i	−0.724755	+	0.649168i
$261$	2.67635e6	−	2.67635e6i	0.150530	−	0.150530i
$262$	942855.	+	421256.i	0.0524253	+	0.0234230i
$263$	−1.95340e7			−1.07380			−0.536901	−	0.843645i	$-0.680405\pi$
$263$	−1.95340e7			−1.07380			−0.536901	+	0.843645i	$0.680405\pi$
$264$	1.31018e7	+	6.74021e6i	0.712066	+	0.366321i
$265$			1.06124e7i			0.570265i
$266$	1.06154e7	+	4.74284e6i	0.564017	+	0.251996i
$267$	−1.23766e7	−	1.23766e7i	−0.650233	−	0.650233i
$268$	−161527.	+	2.93603e6i	−0.00839150	+	0.152530i
$269$	1.47261e6	+	1.47261e6i	0.0756539	+	0.0756539i	0.743921	−	0.668267i	$-0.232964\pi$
$269$	1.47261e6	+	1.47261e6i	0.0756539	+	0.0756539i	−0.668267	+	0.743921i	$0.732964\pi$
$270$	−1.52193e6	−	3.98022e6i	−0.0773221	−	0.202216i
$271$		−	1.71707e7i		−	0.862742i	−0.902175	−	0.431371i	$-0.858030\pi$
$271$		−	1.71707e7i		−	0.862742i	0.902175	−	0.431371i	$-0.141970\pi$
$272$	2.10954e6	−	1.91143e7i	0.104829	−	0.949840i
$273$	−1.20834e7			−0.593882
$274$	−6.25962e6	+	2.39351e6i	−0.304296	+	0.116355i
$275$	5.41507e6	−	5.41507e6i	0.260379	−	0.260379i
$276$	−1.20131e6	+	2.18358e7i	−0.0571382	+	1.03859i
$277$	4.08428e6	−	4.08428e6i	0.192166	−	0.192166i	−0.604465	−	0.796631i	$-0.706613\pi$
$277$	4.08428e6	−	4.08428e6i	0.192166	−	0.192166i	0.796631	+	0.604465i	$0.206613\pi$
$278$	6.00562e6	−	1.34418e7i	0.279527	−	0.625637i
$279$	−7.13336e6			−0.328459
$280$	−2.79669e7	+	8.96656e6i	−1.27400	+	0.408462i
$281$		−	1.63532e7i		−	0.737028i	−0.929622	−	0.368514i	$-0.879867\pi$
$281$		−	1.63532e7i		−	0.737028i	0.929622	−	0.368514i	$-0.120133\pi$
$282$	1.12674e6	−	2.52187e6i	0.0502431	−	0.112454i
$283$	−5.07476e6	−	5.07476e6i	−0.223901	−	0.223901i	0.586238	−	0.810139i	$-0.300608\pi$
$283$	−5.07476e6	−	5.07476e6i	−0.223901	−	0.223901i	−0.810139	+	0.586238i	$0.800608\pi$
$284$	1.10507e7	−	9.89818e6i	0.482430	−	0.432116i
$285$	−5.52225e6	−	5.52225e6i	−0.238551	−	0.238551i
$286$	−2.62124e7	+	1.00229e7i	−1.12049	+	0.428446i
$287$			5.47630e7i			2.31655i
$288$	2.01084e6	+	7.70454e6i	0.0841783	+	0.322529i
$289$	−2.09549e6			−0.0868145
$290$	6.25803e6	+	1.63663e7i	0.256592	+	0.671052i
$291$	8.28707e6	−	8.28707e6i	0.336296	−	0.336296i
$292$	989682.	+	1.10492e6i	0.0397509	+	0.0443794i
$293$	1.82645e7	−	1.82645e7i	0.726114	−	0.726114i	−0.243730	−	0.969843i	$-0.578371\pi$
$293$	1.82645e7	−	1.82645e7i	0.726114	−	0.726114i	0.969843	+	0.243730i	$0.0783709\pi$
$294$	−5.55118e6	−	2.48020e6i	−0.218446	−	0.0975988i
$295$	2.83962e7			1.10610
$296$	−576559.	+	184852.i	−0.0222315	+	0.00712771i
$297$		−	6.99285e6i		−	0.266922i
$298$	2.85480e6	+	1.27549e6i	0.107877	+	0.0481979i
$299$	−2.94531e7	−	2.94531e7i	−1.10184	−	1.10184i
$300$	4.13239e6	+	227345.i	0.153051	+	0.00842018i
$301$	3.84432e7	+	3.84432e7i	1.40968	+	1.40968i
$302$	−1.63993e7	−	4.28883e7i	−0.595396	−	1.55711i
$303$			9.40438e6i			0.338067i
$304$	9.12464e6	+	1.13886e7i	0.324784	+	0.405367i
$305$	−2.07706e6			−0.0732066
$306$	−8.52493e6	+	3.25970e6i	−0.297527	+	0.113766i
$307$	−6.22745e6	+	6.22745e6i	−0.215226	+	0.215226i	−0.806483	−	0.591257i	$-0.798632\pi$
$307$	−6.22745e6	+	6.22745e6i	−0.215226	+	0.215226i	0.591257	+	0.806483i	$0.298632\pi$
$308$	−4.81227e7	−	2.64749e6i	−1.64702	−	0.0906112i
$309$	−2.24722e7	+	2.24722e7i	−0.761676	+	0.761676i
$310$	1.34709e7	−	3.01506e7i	0.452181	−	1.01207i
$311$	7.02088e6			0.233405			0.116703	−	0.993167i	$-0.462768\pi$
$311$	7.02088e6			0.233405			0.116703	+	0.993167i	$0.462768\pi$
$312$	−1.34862e7	−	6.93796e6i	−0.444045	−	0.228438i
$313$		−	3.29834e7i		−	1.07563i	−0.843063	−	0.537815i	$-0.819250\pi$
$313$		−	3.29834e7i		−	1.07563i	0.843063	−	0.537815i	$-0.180750\pi$
$314$	6.36992e6	−	1.42572e7i	0.205753	−	0.460516i
$315$	9.85627e6	+	9.85627e6i	0.315341	+	0.315341i
$316$	2.81698e7	+	3.14498e7i	0.892736	+	0.996683i
$317$	2.71810e7	+	2.71810e7i	0.853274	+	0.853274i	0.990535	−	0.137261i	$-0.0438300\pi$
$317$	2.71810e7	+	2.71810e7i	0.853274	+	0.853274i	−0.137261	+	0.990535i	$0.543830\pi$
$318$	−8.79094e6	+	3.36142e6i	−0.273372	+	0.104530i
$319$			2.87539e7i			0.885778i
$320$	−3.63622e7	−	6.05032e6i	−1.10969	−	0.184641i
$321$	−1.46730e6			−0.0443614
$322$	−2.55488e7	−	6.68163e7i	−0.765248	−	2.00131i
$323$	−1.18277e7	+	1.18277e7i	−0.350987	+	0.350987i
$324$	2.81501e6	−	2.52142e6i	0.0827647	−	0.0741329i
$325$	−5.57395e6	+	5.57395e6i	−0.162373	+	0.162373i
$326$	−1.68364e7	−	7.52229e6i	−0.485955	−	0.217119i
$327$	−3.15861e7			−0.903344
$328$	−3.14435e7	+	6.11209e7i	−0.891065	+	1.73208i
$329$			9.03509e6i			0.253714i
$330$	2.95567e7	+	1.32056e7i	0.822460	+	0.367465i
$331$	2.20689e7	+	2.20689e7i	0.608551	+	0.608551i	0.942567	−	0.334017i	$-0.108404\pi$
$331$	2.20689e7	+	2.20689e7i	0.608551	+	0.608551i	−0.334017	+	0.942567i	$0.608404\pi$
$332$	2.86125e6	−	5.20082e7i	0.0781882	−	1.42121i
$333$	203194.	+	203194.i	0.00550274	+	0.00550274i
$334$	1.06606e7	+	2.78800e7i	0.286115	+	0.748261i
$335$			6.46065e6i			0.171847i
$336$	−1.62859e7	−	2.03267e7i	−0.429333	−	0.535856i
$337$	−6.38849e7			−1.66920			−0.834600	−	0.550857i	$-0.814301\pi$
$337$	−6.38849e7			−1.66920			−0.834600	+	0.550857i	$0.814301\pi$
$338$	−9.08623e6	+	3.47433e6i	−0.235306	+	0.0899748i
$339$	2.56978e7	−	2.56978e7i	0.659624	−	0.659624i
$340$	2.32099e6	−	4.21881e7i	0.0590524	−	1.07338i
$341$	3.83193e7	−	3.83193e7i	0.966396	−	0.966396i
$342$	2.82529e6	−	6.32357e6i	0.0706293	−	0.158083i
$343$	−2.81039e7			−0.696440
$344$	2.08333e7	+	6.49795e7i	0.511779	+	1.59625i
$345$			4.80492e7i			1.17012i
$346$	−9.50520e6	+	2.12745e7i	−0.229474	+	0.513608i
$347$	−4.81137e7	−	4.81137e7i	−1.15154	−	1.15154i	−0.986244	−	0.165299i	$-0.947141\pi$
$347$	−4.81137e7	−	4.81137e7i	−1.15154	−	1.15154i	−0.165299	−	0.986244i	$-0.552859\pi$
$348$	−1.15750e7	+	1.03678e7i	−0.274653	+	0.246009i
$349$	1.14069e7	+	1.14069e7i	0.268344	+	0.268344i	0.828433	−	0.560089i	$-0.189233\pi$
$349$	1.14069e7	+	1.14069e7i	0.268344	+	0.268344i	−0.560089	+	0.828433i	$0.689233\pi$
$350$	−1.26448e7	+	4.83505e6i	−0.294924	+	0.112771i
$351$			7.19802e6i			0.166453i
$352$	−5.21895e7	−	3.05857e7i	−1.19662	−	0.701278i
$353$	1.97230e7			0.448382			0.224191	−	0.974545i	$-0.428026\pi$
$353$	1.97230e7			0.448382			0.224191	+	0.974545i	$0.428026\pi$
$354$	8.99434e6	+	2.35224e7i	0.202749	+	0.530239i
$355$	2.30487e7	−	2.30487e7i	0.515183	−	0.515183i
$356$	4.79455e7	+	5.35281e7i	1.06267	+	1.18640i
$357$	2.11104e7	−	2.11104e7i	0.463971	−	0.463971i
$358$	4.62015e7	+	2.06422e7i	1.00695	+	0.449891i
$359$	−1.50385e7			−0.325029			−0.162514	−	0.986706i	$-0.551960\pi$
$359$	−1.50385e7			−0.325029			−0.162514	+	0.986706i	$0.551960\pi$
$360$	5.34135e6	+	1.66598e7i	0.114484	+	0.357077i
$361$			3.43525e7i			0.730192i
$362$	7.17296e7	+	3.20479e7i	1.51207	+	0.675575i
$363$	1.80372e7	+	1.80372e7i	0.377093	+	0.377093i
$364$	4.95346e7	+	2.72516e6i	1.02708	+	0.0565052i
$365$	2.30456e6	+	2.30456e6i	0.0473924	+	0.0473924i
$366$	−657898.	−	1.72056e6i	−0.0134188	−	0.0350936i
$367$			4.43153e7i			0.896511i	0.893906	+	0.448255i	$0.147954\pi$
$367$			4.43153e7i			0.896511i	−0.893906	+	0.448255i	$0.852046\pi$
$368$	9.84928e6	−	8.92430e7i	0.197634	−	1.79073i
$369$	3.26221e7			0.649282
$370$	−1.24256e6	+	475123.i	−0.0245309	+	0.00937995i
$371$	2.17691e7	−	2.17691e7i	0.426303	−	0.426303i
$372$	2.92425e7	+	1.60879e6i	0.568049	+	0.0312514i
$373$	6.45326e7	−	6.45326e7i	1.24352	−	1.24352i	0.284989	−	0.958531i	$-0.408010\pi$
$373$	6.45326e7	−	6.45326e7i	1.24352	−	1.24352i	0.958531	−	0.284989i	$-0.0919899\pi$
$374$	2.82840e7	−	6.33052e7i	0.540662	−	1.21011i
$375$	−2.51570e7			−0.477051
$376$	−5.18772e6	+	1.00840e7i	−0.0975917	+	0.189702i
$377$		−	2.95975e7i		−	0.552372i
$378$	−5.04266e6	+	1.12865e7i	−0.0933651	+	0.208970i
$379$	−7.13304e7	−	7.13304e7i	−1.31026	−	1.31026i	−0.921222	−	0.389037i	$-0.872808\pi$
$379$	−7.13304e7	−	7.13304e7i	−1.31026	−	1.31026i	−0.389037	−	0.921222i	$-0.627192\pi$
$380$	2.13925e7	+	2.38834e7i	0.389862	+	0.435256i
$381$	−1.00693e7	−	1.00693e7i	−0.182063	−	0.182063i
$382$	5.06833e7	−	1.93799e7i	0.909232	−	0.347666i
$383$		−	3.88466e7i		−	0.691444i	−0.938337	−	0.345722i	$-0.887634\pi$
$383$		−	3.88466e7i		−	0.691444i	0.938337	−	0.345722i	$-0.112366\pi$
$384$	−6.50564e6	−	3.20375e7i	−0.114894	−	0.565803i
$385$	−1.05893e8			−1.85560
$386$	2.44994e7	+	6.40719e7i	0.425984	+	1.11405i
$387$	2.29005e7	−	2.29005e7i	0.395104	−	0.395104i
$388$	−3.58410e7	+	3.21031e7i	−0.613600	+	0.549606i
$389$	−3.00068e7	+	3.00068e7i	−0.509766	+	0.509766i	−0.914455	−	0.404688i	$-0.867380\pi$
$389$	−3.00068e7	+	3.00068e7i	−0.509766	+	0.509766i	0.404688	+	0.914455i	$0.367380\pi$
$390$	−3.04239e7	−	1.35930e7i	−0.512886	−	0.229151i
$391$	1.02913e8			1.72163
$392$	2.21972e7	+	1.14193e7i	0.368502	+	0.189575i
$393$			2.01224e6i			0.0331514i
$394$	−7.27857e7	−	3.25198e7i	−1.19003	−	0.531690i
$395$	6.55958e7	+	6.55958e7i	1.06435	+	1.06435i
$396$	−1.57710e6	+	2.86665e7i	−0.0253965	+	0.461625i
$397$	−4.82007e7	−	4.82007e7i	−0.770339	−	0.770339i	0.207827	−	0.978166i	$-0.433361\pi$
$397$	−4.82007e7	−	4.82007e7i	−0.770339	−	0.770339i	−0.978166	+	0.207827i	$0.933361\pi$
$398$	−2.01787e7	−	5.27721e7i	−0.320068	−	0.837058i
$399$			2.26554e7i			0.356659i
$400$	−1.68891e7	−	1.86396e6i	−0.263891	−	0.0291243i
$401$	−6.22689e7			−0.965691			−0.482845	−	0.875706i	$-0.660397\pi$
$401$	−6.22689e7			−0.965691			−0.482845	+	0.875706i	$0.660397\pi$
$402$	−5.35177e6	+	2.04637e6i	−0.0823795	+	0.0314997i
$403$	−3.94436e7	+	3.94436e7i	−0.602645	+	0.602645i
$404$	2.12097e6	−	3.85524e7i	0.0321655	−	0.584665i
$405$	5.87134e6	−	5.87134e6i	0.0883838	−	0.0883838i
$406$	2.07349e7	−	4.64089e7i	0.309831	−	0.693463i
$407$	−2.18306e6			−0.0323804
$408$	3.56823e7	−	1.14402e7i	0.525378	−	0.168443i
$409$		−	2.73346e7i		−	0.399524i	−0.979844	−	0.199762i	$-0.935983\pi$
$409$		−	2.73346e7i		−	0.399524i	0.979844	−	0.199762i	$-0.0640168\pi$
$410$	−6.16049e7	+	1.37884e8i	−0.893848	+	2.00061i
$411$	−9.23375e6	−	9.23375e6i	−0.133000	−	0.133000i
$412$	9.71908e7	−	8.70545e7i	1.38974	−	1.24480i
$413$	−5.82488e7	−	5.82488e7i	−0.826869	−	0.826869i
$414$	−3.98022e7	+	1.52193e7i	−0.560927	+	0.214483i
$415$		−	1.14443e8i		−	1.60119i
$416$	5.37207e7	+	3.14830e7i	0.746212	+	0.437317i
$417$	2.86874e7			0.395625
$418$	1.87922e7	+	4.91463e7i	0.257306	+	0.672918i
$419$	7.07426e7	−	7.07426e7i	0.961698	−	0.961698i	−0.0375948	−	0.999293i	$-0.511970\pi$
$419$	7.07426e7	−	7.07426e7i	0.961698	−	0.961698i	0.999293	+	0.0375948i	$0.0119696\pi$
$420$	−3.81819e7	−	4.26277e7i	−0.515359	−	0.575366i
$421$	−3.49174e7	+	3.49174e7i	−0.467946	+	0.467946i	−0.901249	−	0.433302i	$-0.857348\pi$
$421$	−3.49174e7	+	3.49174e7i	−0.467946	+	0.467946i	0.433302	+	0.901249i	$0.357348\pi$
$422$	2.74865e7	+	1.22806e7i	0.365748	+	0.163412i
$423$	5.38217e6			0.0711109
$424$	3.67957e7	−	1.17972e7i	0.482725	−	0.154768i
$425$		−	1.94760e7i		−	0.253708i
$426$	2.63933e7	+	1.17922e7i	0.341401	+	0.152533i
$427$	4.26065e6	+	4.26065e6i	0.0547258	+	0.0547258i
$428$	6.01507e6	+	330921.i	0.0767202	+	0.00422079i
$429$	−3.86667e7	−	3.86667e7i	−0.489739	−	0.489739i
$430$	5.35474e7	+	1.40040e8i	0.673494	+	1.76135i
$431$			1.08295e8i			1.35262i	0.736618	+	0.676310i	$0.236422\pi$
$431$			1.08295e8i			1.35262i	−0.736618	+	0.676310i	$0.763578\pi$
$432$	−1.21085e7	+	9.70147e6i	−0.150190	+	0.120333i
$433$	−1.27495e8			−1.57047			−0.785234	−	0.619199i	$-0.787457\pi$
$433$	−1.27495e8			−1.57047			−0.785234	+	0.619199i	$0.787457\pi$
$434$	−8.94803e7	+	3.42148e7i	−1.09461	+	0.418548i
$435$	−2.41424e7	+	2.41424e7i	−0.293300	+	0.293300i
$436$	1.29484e8	+	7.12362e6i	1.56228	+	0.0859491i
$437$	−5.52225e7	+	5.52225e7i	−0.661716	+	0.661716i
$438$	−1.17906e6	+	2.63896e6i	−0.0140318	+	0.0314059i
$439$	−4.08483e7			−0.482815			−0.241407	−	0.970424i	$-0.577609\pi$
$439$	−4.08483e7			−0.482815			−0.241407	+	0.970424i	$0.577609\pi$
$440$	−1.18187e8	−	6.08009e7i	−1.38743	−	0.713760i
$441$		−	1.18473e7i		−	0.138135i
$442$	−2.91138e7	+	6.51626e7i	−0.337157	+	0.754625i
$443$	1.64430e7	+	1.64430e7i	0.189134	+	0.189134i	0.795322	−	0.606188i	$-0.207302\pi$
$443$	1.64430e7	+	1.64430e7i	0.189134	+	0.189134i	−0.606188	+	0.795322i	$0.707302\pi$
$444$	−787149.	−	878802.i	−0.00899307	−	0.0100402i
$445$	1.11645e8	+	1.11645e8i	1.26695	+	1.26695i
$446$	−1.27568e8	+	4.87788e7i	−1.43793	+	0.549827i
$447$			6.09271e6i			0.0682163i
$448$	6.21783e7	+	8.70001e7i	0.691520	+	0.967578i
$449$	−1.73176e7			−0.191315			−0.0956574	−	0.995414i	$-0.530495\pi$
$449$	−1.73176e7			−0.191315			−0.0956574	+	0.995414i	$0.530495\pi$
$450$	2.88022e6	+	7.53249e6i	0.0316074	+	0.0826611i
$451$	−1.75241e8	+	1.75241e8i	−1.91032	+	1.91032i
$452$	−1.11141e8	+	9.95499e7i	−1.20354	+	1.07802i
$453$	6.32658e7	−	6.32658e7i	0.680573	−	0.680573i
$454$	5.06157e7	+	2.26144e7i	0.540900	+	0.241667i
$455$	1.09000e8			1.15715
$456$	−1.30082e7	+	2.52857e7i	−0.137190	+	0.266674i
$457$		−	1.27366e8i		−	1.33445i	−0.744854	−	0.667227i	$-0.767481\pi$
$457$		−	1.27366e8i		−	1.33445i	0.744854	−	0.667227i	$-0.232519\pi$
$458$	−2.56956e7	−	1.14805e7i	−0.267462	−	0.119499i
$459$	−1.25754e7	−	1.25754e7i	−0.130042	−	0.130042i
$460$	1.08365e7	−	1.96973e8i	0.111331	−	2.02364i
$461$	2.64080e7	+	2.64080e7i	0.269546	+	0.269546i	0.828917	−	0.559371i	$-0.188957\pi$
$461$	2.64080e7	+	2.64080e7i	0.269546	+	0.269546i	−0.559371	+	0.828917i	$0.688957\pi$
$462$	−3.35409e7	−	8.77177e7i	−0.340133	−	0.889532i
$463$		−	1.72733e7i		−	0.174034i	−0.996207	−	0.0870169i	$-0.972267\pi$
$463$		−	1.72733e7i		−	0.174034i	0.996207	−	0.0870169i	$-0.0277334\pi$
$464$	4.97890e7	−	3.98915e7i	0.498402	−	0.399325i
$465$	6.43474e7			0.639989
$466$	9.76352e7	−	3.73331e7i	0.964826	−	0.368923i
$467$	6.75616e7	−	6.75616e7i	0.663360	−	0.663360i	−0.292811	−	0.956170i	$-0.594591\pi$
$467$	6.75616e7	−	6.75616e7i	0.663360	−	0.663360i	0.956170	+	0.292811i	$0.0945905\pi$
$468$	1.62337e6	−	2.95076e7i	0.0158373	−	0.287870i
$469$	1.32526e7	−	1.32526e7i	0.128465	−	0.128465i
$470$	−1.01639e7	+	2.27489e7i	−0.0978964	+	0.219112i
$471$	3.04276e7			0.291209
$472$	−3.15664e7	−	9.84563e7i	−0.300192	−	0.936306i
$473$			2.46036e8i			2.32496i
$474$	−3.35601e7	+	7.51143e7i	−0.315129	+	0.705322i
$475$	1.04507e7	+	1.04507e7i	0.0975139	+	0.0975139i
$476$	−9.13009e7	+	8.17788e7i	−0.846553	+	0.758263i
$477$	−1.29678e7	−	1.29678e7i	−0.119484	−	0.119484i
$478$	−7.16823e7	+	2.74094e7i	−0.656339	+	0.250966i
$479$			9.57983e7i			0.871669i	0.900027	+	0.435834i	$0.143547\pi$
$479$			9.57983e7i			0.871669i	−0.900027	+	0.435834i	$0.856453\pi$
$480$	−1.81390e7	−	6.94998e7i	−0.164018	−	0.628434i
$481$	2.24711e6			0.0201924
$482$	−5.35156e7	−	1.39956e8i	−0.477903	−	1.24983i
$483$	9.85627e7	−	9.85627e7i	0.874724	−	0.874724i
$484$	−6.98737e7	−	7.80095e7i	−0.616279	−	0.688037i
$485$	−7.47546e7	+	7.47546e7i	−0.655259	+	0.655259i
$486$	6.72332e6	+	3.00390e6i	0.0585700	+	0.0261683i
$487$	2.47709e6			0.0214464			0.0107232	−	0.999943i	$-0.496587\pi$
$487$	2.47709e6			0.0214464			0.0107232	+	0.999943i	$0.496587\pi$
$488$	2.30895e6	+	7.20166e6i	0.0198680	+	0.0619688i
$489$		−	3.59322e7i		−	0.307296i
$490$	5.00752e7	+	2.23730e7i	0.425632	+	0.190167i
$491$	8.25602e7	+	8.25602e7i	0.697472	+	0.697472i	0.963865	−	0.266393i	$-0.0858319\pi$
$491$	8.25602e7	+	8.25602e7i	0.697472	+	0.697472i	−0.266393	+	0.963865i	$0.585832\pi$
$492$	−1.33731e8	−	7.35727e6i	−1.12289	−	0.0617763i
$493$	5.17087e7	+	5.17087e7i	0.431542	+	0.431542i
$494$	−1.93436e7	−	5.05882e7i	−0.160456	−	0.419632i
$495$			6.30800e7i			0.520087i
$496$	−1.19514e8	−	1.31901e7i	−0.979431	−	0.108095i
$497$	−9.45590e7			−0.770253
$498$	9.48001e7	−	3.62490e7i	0.767575	−	0.293500i
$499$	1.35012e7	−	1.35012e7i	0.108661	−	0.108661i	−0.650686	−	0.759347i	$-0.725519\pi$
$499$	1.35012e7	−	1.35012e7i	0.108661	−	0.108661i	0.759347	+	0.650686i	$0.225519\pi$
$500$	1.03129e8	+	5.67366e6i	0.825029	+	0.0453893i
$501$	−4.11266e7	+	4.11266e7i	−0.327047	+	0.327047i
$502$	−2.15320e7	+	4.81930e7i	−0.170206	+	0.380954i
$503$	−8.70792e6			−0.0684243			−0.0342122	−	0.999415i	$-0.510892\pi$
$503$	−8.70792e6			−0.0684243			−0.0342122	+	0.999415i	$0.510892\pi$
$504$	2.32173e7	−	4.51306e7i	0.181351	−	0.352517i
$505$		−	8.48335e7i		−	0.658708i
$506$	1.32056e8	−	2.95567e8i	1.01931	−	2.28142i
$507$	−1.34034e7	−	1.34034e7i	−0.102847	−	0.102847i
$508$	3.90070e7	+	4.35488e7i	0.297544	+	0.332189i
$509$	−1.73915e8	−	1.73915e8i	−1.31882	−	1.31882i	−0.914714	−	0.404102i	$-0.867584\pi$
$509$	−1.73915e8	−	1.73915e8i	−1.31882	−	1.31882i	−0.404102	−	0.914714i	$-0.632416\pi$
$510$	7.69002e7	−	2.94046e7i	0.579718	−	0.221669i
$511$		−	9.45460e6i		−	0.0708566i
$512$	1.94438e7	+	1.32802e8i	0.144868	+	0.989451i
$513$	1.34958e7			0.0999644
$514$	−7.28542e7	−	1.90532e8i	−0.536494	−	1.40306i
$515$	2.02714e8	−	2.02714e8i	1.48409	−	1.48409i
$516$	−9.90430e7	+	8.87135e7i	−0.720900	+	0.645715i
$517$	−2.89122e7	+	2.89122e7i	−0.209223	+	0.209223i
$518$	3.52346e6	+	1.57424e6i	0.0253502	+	0.0113261i
$519$	−4.54041e7			−0.324783
$520$	1.21654e8	+	6.25848e7i	0.865201	+	0.445101i
$521$			2.29977e7i			0.162619i	0.996689	+	0.0813093i	$0.0259102\pi$
$521$			2.29977e7i			0.162619i	−0.996689	+	0.0813093i	$0.974090\pi$
$522$	−2.76456e7	−	1.23517e7i	−0.194364	−	0.0868392i
$523$	1.12981e8	+	1.12981e8i	0.789768	+	0.789768i	0.981456	−	0.191688i	$-0.0613962\pi$
$523$	1.12981e8	+	1.12981e8i	0.789768	+	0.789768i	−0.191688	+	0.981456i	$0.561396\pi$
$524$	453821.	−	8.24898e6i	0.00315421	−	0.0573332i
$525$	−1.86528e7	−	1.86528e7i	−0.128904	−	0.128904i
$526$	5.58132e7	+	1.45965e8i	0.383512	+	1.00298i
$527$		−	1.37821e8i		−	0.941635i
$528$	1.29303e7	−	1.17160e8i	0.0878431	−	0.795935i
$529$	3.32456e8			2.24578
$530$	7.92998e7	−	3.03221e7i	0.532653	−	0.203672i
$531$	−3.46986e7	+	3.46986e7i	−0.231755	+	0.231755i
$532$	5.10948e6	−	9.28737e7i	0.0339345	−	0.616819i
$533$	1.80383e8	−	1.80383e8i	1.19128	−	1.19128i
$534$	−5.71198e7	+	1.27846e8i	−0.375114	+	0.839580i
$535$	1.32360e7			0.0864362
$536$	2.24006e7	−	7.18192e6i	0.145467	−	0.0466387i
$537$			9.86031e7i			0.636748i
$538$	6.79630e6	−	1.52115e7i	0.0436441	−	0.0976843i
$539$	6.36421e7	+	6.36421e7i	0.406423	+	0.406423i
$540$	−2.53932e7	+	2.27448e7i	−0.161263	+	0.144445i
$541$	7.13958e7	+	7.13958e7i	0.450900	+	0.450900i	0.895653	−	0.444753i	$-0.146709\pi$
$541$	7.13958e7	+	7.13958e7i	0.450900	+	0.450900i	−0.444753	+	0.895653i	$0.646709\pi$
$542$	−1.28306e8	+	4.90607e7i	−0.805840	+	0.308132i
$543$			1.53085e8i			0.956167i
$544$	−1.48856e8	+	3.88506e7i	−0.924634	+	0.241324i
$545$	2.84927e8			1.76013
$546$	3.45250e7	+	9.02913e7i	0.212107	+	0.554713i
$547$	−1.27198e8	+	1.27198e8i	−0.777176	+	0.777176i	−0.979350	−	0.202174i	$-0.935199\pi$
$547$	−1.27198e8	+	1.27198e8i	−0.777176	+	0.777176i	0.202174	+	0.979350i	$0.435199\pi$
$548$	3.57704e7	+	3.99354e7i	0.217361	+	0.242670i
$549$	2.53805e6	−	2.53805e6i	0.0153385	−	0.0153385i
$550$	−5.59355e7	−	2.49913e7i	−0.336202	−	0.150211i
$551$	−5.54932e7			−0.331730
$552$	1.66598e8	−	5.34135e7i	0.990494	−	0.317566i
$553$		−	2.69111e8i		−	1.59132i
$554$	−4.21890e7	−	1.88495e7i	−0.248124	−	0.110859i
$555$	−1.83294e6	−	1.83294e6i	−0.0107218	−	0.0107218i
$556$	−1.17601e8	−	6.46988e6i	−0.684208	−	0.0376419i
$557$	−1.50060e7	−	1.50060e7i	−0.0868360	−	0.0868360i	0.662355	−	0.749191i	$-0.269557\pi$
$557$	−1.50060e7	−	1.50060e7i	−0.0868360	−	0.0868360i	−0.749191	+	0.662355i	$0.769557\pi$
$558$	2.03817e7	+	5.33031e7i	0.117311	+	0.306796i
$559$		−	2.53254e8i		−	1.44984i
$560$	1.46909e8	+	1.83359e8i	0.836537	+	1.04409i
$561$	1.35106e8			0.765219
$562$	−1.22197e8	+	4.67249e7i	−0.688418	+	0.263233i
$563$	−2.42642e8	+	2.42642e8i	−1.35969	+	1.35969i	−0.485398	+	0.874293i	$0.661325\pi$
$563$	−2.42642e8	+	2.42642e8i	−1.35969	+	1.35969i	−0.874293	+	0.485398i	$0.838675\pi$
$564$	−2.20637e7	−	1.21384e6i	−0.122982	−	0.00676589i
$565$	−2.31810e8	+	2.31810e8i	−1.28525	+	1.28525i
$566$	−2.34207e7	+	5.24202e7i	−0.129167	+	0.289101i
$567$	−2.40876e7			−0.132143
$568$	−1.05537e8	−	5.42934e7i	−0.575918	−	0.296280i
$569$		−	3.09405e7i		−	0.167954i	−0.996468	−	0.0839771i	$-0.973238\pi$
$569$		−	3.09405e7i		−	0.167954i	0.996468	−	0.0839771i	$-0.0267623\pi$
$570$	−2.54859e7	+	5.70426e7i	−0.137618	+	0.308017i
$571$	−7.48080e7	−	7.48080e7i	−0.401827	−	0.401827i	0.477049	−	0.878877i	$-0.341706\pi$
$571$	−7.48080e7	−	7.48080e7i	−0.401827	−	0.401827i	−0.878877	+	0.477049i	$0.841706\pi$
$572$	1.49790e8	+	1.67231e8i	0.800376	+	0.893569i
$573$	7.47644e7	+	7.47644e7i	0.397403	+	0.397403i
$574$	4.09209e8	−	1.56471e8i	2.16376	−	0.827365i
$575$		−	9.09322e7i		−	0.478315i
$576$	5.18257e7	−	3.70394e7i	0.271192	−	0.193819i
$577$	−2.47348e8			−1.28760			−0.643800	−	0.765194i	$-0.722643\pi$
$577$	−2.47348e8			−1.28760			−0.643800	+	0.765194i	$0.722643\pi$
$578$	5.98730e6	+	1.56583e7i	0.0310061	+	0.0810887i
$579$	−9.45143e7	+	9.45143e7i	−0.486925	+	0.486925i
$580$	1.04414e8	−	9.35245e7i	0.535150	−	0.479338i
$581$	−2.34755e8	+	2.34755e8i	−1.19698	+	1.19698i
$582$	−8.56021e7	−	3.82459e7i	−0.434226	−	0.194007i
$583$	1.39322e8			0.703094
$584$	5.42859e6	−	1.05523e7i	0.0272552	−	0.0529794i
$585$		−	6.49307e7i		−	0.324326i
$586$	−1.88665e8	−	8.42930e7i	−0.937558	−	0.418889i
$587$	−2.03302e8	−	2.03302e8i	−1.00514	−	1.00514i	−0.999987	−	0.00515608i	$-0.998359\pi$
$587$	−2.03302e8	−	2.03302e8i	−1.00514	−	1.00514i	−0.00515608	−	0.999987i	$-0.501641\pi$
$588$	−2.67193e6	+	4.85670e7i	−0.0131430	+	0.238896i
$589$	7.39539e7	+	7.39539e7i	0.361922	+	0.361922i
$590$	−8.11346e7	−	2.12187e8i	−0.395048	−	1.03315i
$591$		−	1.55339e8i		−	0.752521i
$592$	3.02865e6	+	3.78009e6i	0.0145977	+	0.0182195i
$593$	1.11781e8			0.536050			0.268025	−	0.963412i	$-0.413629\pi$
$593$	1.11781e8			0.536050			0.268025	+	0.963412i	$0.413629\pi$
$594$	−5.22532e7	+	1.99802e7i	−0.249318	+	0.0953324i
$595$	−1.90429e8	+	1.90429e8i	−0.904027	+	0.904027i
$596$	1.37409e6	−	2.49765e7i	0.00649047	−	0.117976i
$597$	7.78457e7	−	7.78457e7i	0.365857	−	0.365857i
$598$	−1.35930e8	+	3.04239e8i	−0.635642	+	1.42269i
$599$	2.83959e7			0.132122			0.0660611	−	0.997816i	$-0.478957\pi$
$599$	2.83959e7			0.132122			0.0660611	+	0.997816i	$0.478957\pi$
$600$	−1.01084e7	−	3.15283e7i	−0.0467981	−	0.145964i
$601$			2.58943e8i			1.19284i	0.802674	+	0.596419i	$0.203410\pi$
$601$			2.58943e8i			1.19284i	−0.802674	+	0.596419i	$0.796590\pi$
$602$	1.77420e8	−	3.97103e8i	0.813231	−	1.82018i
$603$	−7.89455e6	−	7.89455e6i	−0.0360061	−	0.0360061i
$604$	−2.73620e8	+	2.45084e8i	−1.24176	+	1.11225i
$605$	−1.62707e8	−	1.62707e8i	−0.734749	−	0.734749i
$606$	7.02730e7	−	2.68705e7i	0.315770	−	0.120742i
$607$		−	1.96421e8i		−	0.878257i	−0.898424	−	0.439128i	$-0.855287\pi$
$607$		−	1.96421e8i		−	0.878257i	0.898424	−	0.439128i	$-0.144713\pi$
$608$	5.90284e7	−	1.00722e8i	0.262634	−	0.448142i
$609$	9.90459e7			0.438515
$610$	5.93465e6	+	1.55206e7i	0.0261460	+	0.0683783i
$611$	2.97605e7	−	2.97605e7i	0.130472	−	0.130472i
$612$	4.87154e7	+	5.43876e7i	0.212526	+	0.237272i
$613$	1.23504e8	−	1.23504e8i	0.536166	−	0.536166i	−0.386234	−	0.922401i	$-0.626224\pi$
$613$	1.23504e8	−	1.23504e8i	0.536166	−	0.536166i	0.922401	+	0.386234i	$0.126224\pi$
$614$	6.43271e7	+	2.87405e7i	0.277900	+	0.124162i
$615$	−2.94272e8			−1.26510
$616$	1.17715e8	+	3.67155e8i	0.503603	+	1.57075i
$617$			3.88338e8i			1.65331i	0.562708	+	0.826656i	$0.309760\pi$
$617$			3.88338e8i			1.65331i	−0.562708	+	0.826656i	$0.690240\pi$
$618$	2.32129e8	+	1.03712e8i	0.983476	+	0.439405i
$619$	−1.12499e8	−	1.12499e8i	−0.474327	−	0.474327i	0.428985	−	0.903312i	$-0.358871\pi$
$619$	−1.12499e8	−	1.12499e8i	−0.474327	−	0.474327i	−0.903312	+	0.428985i	$0.858871\pi$
$620$	−2.63786e8	−	1.45123e7i	−1.10682	−	0.0608921i
$621$	−5.87134e7	−	5.87134e7i	−0.245167	−	0.245167i
$622$	−2.00603e7	−	5.24626e7i	−0.0833616	−	0.218011i
$623$		−	4.58032e8i		−	1.89423i
$624$	−1.33097e7	+	1.20597e8i	−0.0547790	+	0.496345i
$625$	2.91750e8			1.19501
$626$	−2.46464e8	+	9.42413e7i	−1.00469	+	0.384165i
$627$	−7.24972e7	+	7.24972e7i	−0.294116	+	0.294116i
$628$	−1.24735e8	−	6.86235e6i	−0.503628	−	0.0277073i
$629$	−3.92583e6	+	3.92583e6i	−0.0157754	+	0.0157754i
$630$	4.54880e7	−	1.01811e8i	0.181918	−	0.407168i
$631$	−1.38596e8			−0.551648			−0.275824	−	0.961208i	$-0.588951\pi$
$631$	−1.38596e8			−0.551648			−0.275824	+	0.961208i	$0.588951\pi$
$632$	1.54517e8	−	3.00355e8i	0.612103	−	1.18983i
$633$			5.86617e7i			0.231283i
$634$	1.25444e8	−	2.80769e8i	0.492246	−	1.10175i
$635$	9.08310e7	+	9.08310e7i	0.354742	+	0.354742i
$636$	5.02355e7	+	5.60847e7i	0.195272	+	0.218008i
$637$	−6.55093e7	−	6.55093e7i	−0.253445	−	0.253445i
$638$	2.14860e8	−	8.21566e7i	0.827357	−	0.316359i
$639$			5.63285e7i			0.215886i
$640$	5.86850e7	+	2.88999e8i	0.223865	+	1.10244i
$641$	−3.56878e7			−0.135502			−0.0677510	−	0.997702i	$-0.521582\pi$
$641$	−3.56878e7			−0.135502			−0.0677510	+	0.997702i	$0.521582\pi$
$642$	4.19243e6	+	1.09642e7i	0.0158438	+	0.0414356i
$643$	−2.52804e8	+	2.52804e8i	−0.950935	+	0.950935i	−0.998851	−	0.0479167i	$-0.984742\pi$
$643$	−2.52804e8	+	2.52804e8i	−0.950935	+	0.950935i	0.0479167	+	0.998851i	$0.484742\pi$
$644$	−4.26277e8	+	3.81819e8i	−1.59600	+	1.42955i
$645$	−2.06577e8	+	2.06577e8i	−0.769843	+	0.769843i
$646$	1.22175e8	+	5.45863e7i	0.453195	+	0.202482i
$647$	−2.04039e8			−0.753358			−0.376679	−	0.926344i	$-0.622934\pi$
$647$	−2.04039e8			−0.753358			−0.376679	+	0.926344i	$0.622934\pi$
$648$	−2.68841e7	−	1.38305e7i	−0.0988032	−	0.0508291i
$649$		−	3.72791e8i		−	1.36374i
$650$	5.75766e7	+	2.57245e7i	0.209655	+	0.0936714i
$651$	−1.31995e8	−	1.31995e8i	−0.478426	−	0.478426i
$652$	−8.10380e6	+	1.47301e8i	−0.0292379	+	0.531449i
$653$	−1.26644e8	−	1.26644e8i	−0.454826	−	0.454826i	0.442127	−	0.896953i	$-0.354224\pi$
$653$	−1.26644e8	−	1.26644e8i	−0.454826	−	0.454826i	−0.896953	+	0.442127i	$0.854224\pi$
$654$	9.02489e7	+	2.36023e8i	0.322633	+	0.843764i
$655$		−	1.81517e7i		−	0.0645941i
$656$	5.46559e8	+	6.03208e7i	1.93609	+	0.213676i
$657$	−5.63208e6			−0.0198597
$658$	6.75135e7	−	2.58153e7i	0.236981	−	0.0906150i
$659$	3.22381e8	−	3.22381e8i	1.12645	−	1.12645i	0.135702	−	0.990750i	$-0.456671\pi$
$659$	3.22381e8	−	3.22381e8i	1.12645	−	1.12645i	0.990750	−	0.135702i	$-0.0433291\pi$
$660$	1.42264e7	−	2.58590e8i	0.0494839	−	0.899456i
$661$	3.01517e8	−	3.01517e8i	1.04402	−	1.04402i	0.0450302	−	0.998986i	$-0.485662\pi$
$661$	3.01517e8	−	3.01517e8i	1.04402	−	1.04402i	0.998986	−	0.0450302i	$-0.0143384\pi$
$662$	1.01851e8	−	2.27963e8i	0.351068	−	0.785760i
$663$	−1.39070e8			−0.477191
$664$	−3.96799e8	+	1.27219e8i	−1.35540	+	0.434558i
$665$		−	2.04366e8i		−	0.694935i
$666$	937769.	−	2.09892e6i	0.00317448	−	0.00710514i
$667$	2.41424e8	+	2.41424e8i	0.813585	+	0.813585i
$668$	1.77870e8	−	1.59319e8i	0.596723	−	0.534489i
$669$	−1.88180e8	−	1.88180e8i	−0.628485	−	0.628485i
$670$	4.82763e7	−	1.84596e7i	0.160513	−	0.0613758i
$671$			2.72681e7i			0.0902583i
$672$	−1.05356e8	+	1.79772e8i	−0.347176	+	0.592400i
$673$	4.20736e8			1.38027			0.690135	−	0.723680i	$-0.257551\pi$
$673$	4.20736e8			1.38027			0.690135	+	0.723680i	$0.257551\pi$
$674$	1.82534e8	+	4.77371e8i	0.596161	+	1.55911i
$675$	−1.11114e7	+	1.11114e7i	−0.0361291	+	0.0361291i
$676$	5.19229e7	+	5.79687e7i	0.168081	+	0.187652i
$677$	−2.79557e8	+	2.79557e8i	−0.900957	+	0.900957i	−0.995519	−	0.0945619i	$-0.969855\pi$
$677$	−2.79557e8	+	2.79557e8i	−0.900957	+	0.900957i	0.0945619	+	0.995519i	$0.469855\pi$
$678$	−2.65448e8	−	1.18599e8i	−0.851706	−	0.380531i
$679$	3.06686e8			0.979682
$680$	−3.21877e8	+	1.03198e8i	−1.02368	+	0.328204i
$681$			1.08024e8i			0.342041i
$682$	−3.95823e8	−	1.76849e8i	−1.24781	−	0.557505i
$683$	−1.74053e7	−	1.74053e7i	−0.0546286	−	0.0546286i	0.679265	−	0.733893i	$-0.262299\pi$
$683$	−1.74053e7	−	1.74053e7i	−0.0546286	−	0.0546286i	−0.733893	+	0.679265i	$0.762299\pi$
$684$	−5.53245e7	−	3.04370e6i	−0.172882	−	0.00951116i
$685$	8.32943e7	+	8.32943e7i	0.259145	+	0.259145i
$686$	8.02993e7	+	2.10002e8i	0.248736	+	0.650507i
$687$		−	5.48395e7i		−	0.169131i
$688$	4.26025e8	−	3.41335e8i	1.30819	−	1.04813i
$689$	−1.43409e8			−0.438450
$690$	3.59041e8	−	1.37288e8i	1.09294	−	0.417912i
$691$	2.86023e8	−	2.86023e8i	0.866895	−	0.866895i	−0.125233	−	0.992127i	$-0.539968\pi$
$691$	2.86023e8	−	2.86023e8i	0.866895	−	0.866895i	0.992127	+	0.125233i	$0.0399678\pi$
$692$	1.86130e8	+	1.02400e7i	0.561691	+	0.0309016i
$693$	1.29395e8	−	1.29395e8i	0.388792	−	0.388792i
$694$	−2.22051e8	+	4.96995e8i	−0.664315	+	1.48687i
$695$	−2.58779e8			−0.770858
$696$	1.10545e8	+	5.68696e7i	0.327877	+	0.168676i
$697$			6.30278e8i			1.86138i
$698$	5.26444e7	−	1.17829e8i	0.154805	−	0.346485i
$699$	1.44025e8	+	1.44025e8i	0.421701	+	0.421701i
$700$	7.22585e7	+	8.06720e7i	0.210666	+	0.235195i
$701$	3.30099e8	+	3.30099e8i	0.958275	+	0.958275i	0.999164	−	0.0408890i	$-0.0130190\pi$
$701$	3.30099e8	+	3.30099e8i	0.958275	+	0.958275i	−0.0408890	+	0.999164i	$0.513019\pi$
$702$	5.37862e7	−	2.05664e7i	0.155475	−	0.0594493i
$703$		−	4.21316e6i		−	0.0121267i
$704$	−7.94297e7	+	4.77370e8i	−0.227649	+	1.36816i
$705$	−4.85506e7			−0.138557
$706$	−5.63531e7	−	1.47377e8i	−0.160141	−	0.418809i
$707$	−1.74018e8	+	1.74018e8i	−0.492419	+	0.492419i
$708$	1.50069e8	−	1.34418e8i	0.422855	−	0.378754i
$709$	2.96521e8	−	2.96521e8i	0.831988	−	0.831988i	−0.155800	−	0.987789i	$-0.549796\pi$
$709$	2.96521e8	−	2.96521e8i	0.831988	−	0.831988i	0.987789	+	0.155800i	$0.0497956\pi$
$710$	−2.38084e8	−	1.06373e8i	−0.665204	−	0.297205i
$711$	−1.60309e8			−0.446014
$712$	2.62990e8	−	5.11209e8i	0.728618	−	1.41631i
$713$		−	6.43474e8i		−	1.77526i
$714$	−2.18061e8	−	9.74271e7i	−0.599079	−	0.267661i
$715$	3.48798e8	+	3.48798e8i	0.954235	+	0.954235i
$716$	2.22380e7	−	4.04214e8i	0.0605837	−	1.10122i
$717$	−1.05741e8	−	1.05741e8i	−0.286869	−	0.286869i
$718$	4.29685e7	+	1.12373e8i	0.116085	+	0.303592i
$719$			3.98405e8i			1.07186i	0.844263	+	0.535929i	$0.180039\pi$
$719$			3.98405e8i			1.07186i	−0.844263	+	0.535929i	$0.819961\pi$
$720$	1.09226e8	−	8.75133e7i	0.292638	−	0.234464i
$721$	−8.31647e8			−2.21888
$722$	2.56695e8	−	9.81532e7i	0.682033	−	0.260791i
$723$	2.06454e8	−	2.06454e8i	0.546271	−	0.546271i
$724$	3.45253e7	−	6.27558e8i	0.0909750	−	1.65363i
$725$	4.56890e7	−	4.56890e7i	0.119894	−	0.119894i
$726$	8.32439e7	−	1.86317e8i	0.217542	−	0.486902i
$727$	2.05758e8			0.535492			0.267746	−	0.963490i	$-0.413721\pi$
$727$	2.05758e8			0.535492			0.267746	+	0.963490i	$0.413721\pi$
$728$	−1.21168e8	−	3.77927e8i	−0.314047	−	0.979521i
$729$			1.43489e7i			0.0370370i
$730$	1.06358e7	−	2.38051e7i	0.0273403	−	0.0611930i
$731$	4.42450e8	+	4.42450e8i	1.13269	+	1.13269i
$732$	−1.09769e7	+	9.83210e6i	−0.0279864	+	0.0250676i
$733$	2.65126e8	+	2.65126e8i	0.673194	+	0.673194i	0.958451	−	0.285257i	$-0.0920789\pi$
$733$	2.65126e8	+	2.65126e8i	0.673194	+	0.673194i	−0.285257	+	0.958451i	$0.592079\pi$
$734$	3.31140e8	−	1.26619e8i	0.837382	−	0.320192i
$735$			1.06870e8i			0.269151i
$736$	−6.94998e8	+	1.81390e8i	−1.74321	+	0.454968i
$737$	8.48167e7			0.211875
$738$	−9.32090e7	−	2.43764e8i	−0.231894	−	0.606459i
$739$	2.74561e8	−	2.74561e8i	0.680307	−	0.680307i	−0.279762	−	0.960069i	$-0.590256\pi$
$739$	2.74561e8	−	2.74561e8i	0.680307	−	0.680307i	0.960069	+	0.279762i	$0.0902556\pi$
$740$	7.10058e6	+	7.92735e6i	0.0175226	+	0.0195629i
$741$	7.46242e7	−	7.46242e7i	0.183411	−	0.183411i
$742$	−2.24866e8	−	1.00467e8i	−0.550442	−	0.245931i
$743$	1.16840e8			0.284856			0.142428	−	0.989805i	$-0.454509\pi$
$743$	1.16840e8			0.284856			0.142428	+	0.989805i	$0.454509\pi$
$744$	−7.15312e7	−	2.23107e8i	−0.173691	−	0.541746i
$745$		−	5.49601e7i		−	0.132916i
$746$	−6.66596e8	−	2.97826e8i	−1.60563	−	0.717376i
$747$	1.39842e8	+	1.39842e8i	0.335488	+	0.335488i
$748$	−5.53854e8	−	3.04705e7i	−1.32340	−	0.0728072i
$749$	−2.71508e7	−	2.71508e7i	−0.0646157	−	0.0646157i
$750$	7.18793e7	+	1.87982e8i	0.170381	+	0.445587i
$751$			1.91673e8i			0.452524i	0.974066	+	0.226262i	$0.0726506\pi$
$751$			1.91673e8i			0.452524i	−0.974066	+	0.226262i	$0.927349\pi$
$752$	9.01742e7	+	9.95205e6i	0.212045	+	0.0234023i
$753$	−1.02853e8			−0.240898
$754$	−2.21164e8	+	8.45670e7i	−0.515941	+	0.197282i
$755$	−5.70698e8	+	5.70698e8i	−1.32607	+	1.32607i
$756$	9.87448e7	+	5.43248e6i	0.228533	+	0.0125728i
$757$	4.62970e7	−	4.62970e7i	0.106725	−	0.106725i	−0.651728	−	0.758453i	$-0.725956\pi$
$757$	4.62970e7	−	4.62970e7i	0.106725	−	0.106725i	0.758453	+	0.651728i	$0.225956\pi$
$758$	−3.29199e8	+	7.36814e8i	−0.755877	+	1.69181i
$759$	6.30800e8			1.44267
$760$	1.17342e8	−	2.28093e8i	0.267308	−	0.519602i
$761$		−	2.39507e8i		−	0.543456i	−0.962374	−	0.271728i	$-0.912405\pi$
$761$		−	2.39507e8i		−	0.543456i	0.962374	−	0.271728i	$-0.0875951\pi$
$762$	−4.64709e7	+	1.04011e8i	−0.105031	+	0.235080i
$763$	−5.84466e8	−	5.84466e8i	−1.31579	−	1.31579i
$764$	−2.89628e8	−	3.23351e8i	−0.649472	−	0.725094i
$765$	1.13438e8	+	1.13438e8i	0.253381	+	0.253381i
$766$	−2.90276e8	+	1.10994e8i	−0.645840	+	0.246952i
$767$			3.83729e8i			0.850429i
$768$	−2.20808e8	+	1.40151e8i	−0.487451	+	0.309395i
$769$	2.57776e8			0.566844			0.283422	−	0.958995i	$-0.408530\pi$
$769$	2.57776e8			0.566844			0.283422	+	0.958995i	$0.408530\pi$
$770$	3.02560e8	+	7.91269e8i	0.662734	+	1.73321i
$771$	2.81059e8	−	2.81059e8i	0.613245	−	0.613245i
$772$	4.08768e8	−	3.66136e8i	0.888434	−	0.795777i
$773$	−2.50765e8	+	2.50765e8i	−0.542911	+	0.542911i	−0.924381	−	0.381470i	$-0.875418\pi$
$773$	−2.50765e8	+	2.50765e8i	−0.542911	+	0.542911i	0.381470	+	0.924381i	$0.375418\pi$
$774$	−2.36553e8	−	1.05689e8i	−0.510158	−	0.227932i
$775$	−1.21776e8			−0.261612
$776$	3.42292e8	+	1.76091e8i	0.732507	+	0.376837i
$777$			7.51977e6i			0.0160303i
$778$	3.09958e8	+	1.38485e8i	0.658210	+	0.294080i
$779$	−3.38204e8	−	3.38204e8i	−0.715429	−	0.715429i
$780$	−1.46438e7	+	2.66177e8i	−0.0308582	+	0.560902i
$781$	−3.02588e8	−	3.02588e8i	−0.635183	−	0.635183i
$782$	−2.94046e8	−	7.69002e8i	−0.614886	−	1.60808i
$783$		−	5.90013e7i		−	0.122907i
$784$	2.19066e7	−	1.98493e8i	0.0454598	−	0.411905i
$785$	−2.74476e8			−0.567409
$786$	1.50362e7	−	5.74943e6i	0.0309649	−	0.0118402i
$787$	1.66806e8	−	1.66806e8i	0.342205	−	0.342205i	−0.514991	−	0.857196i	$-0.672205\pi$
$787$	1.66806e8	−	1.66806e8i	0.342205	−	0.342205i	0.857196	+	0.514991i	$0.172205\pi$
$788$	−3.50337e7	+	6.36798e8i	−0.0715990	+	1.30144i
$789$	−2.15318e8	+	2.15318e8i	−0.438378	+	0.438378i
$790$	3.02733e8	−	6.77578e8i	0.614015	−	1.37429i
$791$	9.51017e8			1.92158
$792$	2.18713e8	−	7.01222e7i	0.440249	−	0.141150i
$793$		−	2.80681e7i		−	0.0562851i
$794$	−2.22453e8	+	4.97894e8i	−0.444402	+	0.994661i
$795$	1.16977e8	+	1.16977e8i	0.232810	+	0.232810i
$796$	−3.36678e8	+	3.01564e8i	−0.667536	+	0.597917i
$797$	2.34716e8	+	2.34716e8i	0.463625	+	0.463625i	0.899842	−	0.436216i	$-0.143682\pi$
$797$	2.34716e8	+	2.34716e8i	0.463625	+	0.463625i	−0.436216	+	0.899842i	$0.643682\pi$
$798$	1.69290e8	−	6.47318e7i	0.333136	−	0.127382i
$799$			1.03987e8i			0.203862i
$800$	3.43278e7	+	1.31527e8i	0.0670464	+	0.256889i
$801$	−2.72848e8			−0.530913
$802$	1.77917e8	+	4.65296e8i	0.344900	+	0.901999i
$803$	3.02547e7	−	3.02547e7i	0.0584313	−	0.0584313i
$804$	3.05825e7	+	3.41434e7i	0.0588443	+	0.0656960i
$805$	−8.89097e8	+	8.89097e8i	−1.70436	+	1.70436i
$806$	4.07436e8	+	1.82037e8i	0.778135	+	0.347661i
$807$	3.24643e7			0.0617711
$808$	−2.94137e8	+	9.43043e7i	−0.557591	+	0.178771i
$809$			9.79685e8i			1.85030i	0.379607	+	0.925148i	$0.376059\pi$
$809$			9.79685e8i			1.85030i	−0.379607	+	0.925148i	$0.623941\pi$
$810$	−6.06486e7	−	2.70970e7i	−0.114121	−	0.0509878i
$811$	7.93471e7	+	7.93471e7i	0.148754	+	0.148754i	0.777561	−	0.628807i	$-0.216457\pi$
$811$	7.93471e7	+	7.93471e7i	0.148754	+	0.148754i	−0.628807	+	0.777561i	$0.716457\pi$
$812$	−4.06029e8	−	2.23378e7i	−0.758383	−	0.0417227i
$813$	−1.89268e8	−	1.89268e8i	−0.352213	−	0.352213i
$814$	6.23751e6	+	1.63126e7i	0.0115648	+	0.0302448i
$815$			3.24131e8i			0.598753i
$816$	−1.87438e8	−	2.33944e8i	−0.344974	−	0.430567i
$817$	−4.74833e8			−0.870713
$818$	−2.04254e8	+	7.81012e7i	−0.373173	+	0.142691i
$819$	−1.33191e8	+	1.33191e8i	−0.242451	+	0.242451i
$820$	1.20634e9	+	6.63672e7i	2.18790	+	0.120368i
$821$	6.94135e8	−	6.94135e8i	1.25434	−	1.25434i	0.300581	−	0.953756i	$-0.402819\pi$
$821$	6.94135e8	−	6.94135e8i	1.25434	−	1.25434i	0.953756	−	0.300581i	$-0.0971807\pi$
$822$	−4.26150e7	+	9.53809e7i	−0.0767268	+	0.171730i
$823$	−2.35319e8			−0.422141			−0.211070	−	0.977471i	$-0.567695\pi$
$823$	−2.35319e8			−0.422141			−0.211070	+	0.977471i	$0.567695\pi$
$824$	−9.28200e8	−	4.77510e8i	−1.65905	−	0.853495i
$825$		−	1.19378e8i		−	0.212599i
$826$	−2.68826e8	+	6.01686e8i	−0.477014	+	1.06765i
$827$	−4.16675e8	−	4.16675e8i	−0.736683	−	0.736683i	0.235252	−	0.971934i	$-0.424409\pi$
$827$	−4.16675e8	−	4.16675e8i	−0.736683	−	0.736683i	−0.971934	+	0.235252i	$0.924409\pi$
$828$	2.27448e8	+	2.53932e8i	0.400675	+	0.447328i
$829$	−2.08455e8	−	2.08455e8i	−0.365889	−	0.365889i	0.500087	−	0.865975i	$-0.333301\pi$
$829$	−2.08455e8	−	2.08455e8i	−0.365889	−	0.365889i	−0.865975	+	0.500087i	$0.833301\pi$
$830$	−8.55157e8	+	3.26989e8i	−1.49559	+	0.571872i
$831$		−	9.00396e7i		−	0.156903i
$832$	8.17601e7	−	4.91375e8i	0.141962	−	0.853185i
$833$	2.28897e8			0.396009
$834$	−8.19667e7	−	2.14363e8i	−0.141299	−	0.369532i
$835$	3.70988e8	−	3.70988e8i	0.637236	−	0.637236i
$836$	3.13545e8	−	2.80845e8i	0.536638	−	0.480671i
$837$	−7.86289e7	+	7.86289e7i	−0.134093	+	0.134093i
$838$	−7.30742e8	−	3.26486e8i	−1.24174	−	0.554796i
$839$	5.73096e7			0.0970379			0.0485189	−	0.998822i	$-0.484550\pi$
$839$	5.73096e7			0.0970379			0.0485189	+	0.998822i	$0.484550\pi$
$840$	−2.09435e8	+	4.07106e8i	−0.353355	+	0.686863i
$841$		−	3.52216e8i		−	0.592135i
$842$	3.60683e8	+	1.61149e8i	0.604212	+	0.269954i
$843$	−1.80257e8	−	1.80257e8i	−0.300891	−	0.300891i
$844$	1.32300e7	−	2.40478e8i	0.0220055	−	0.399989i
$845$	1.20907e8	+	1.20907e8i	0.200392	+	0.200392i
$846$	−1.53781e7	−	4.02175e7i	−0.0253976	−	0.0664208i
$847$			6.67515e8i			1.09853i
$848$	−1.93287e8	−	2.41244e8i	−0.316967	−	0.395611i
$849$	−1.11875e8			−0.182814
$850$	−1.45532e8	+	5.56476e7i	−0.236975	+	0.0906127i
$851$	−1.83294e7	+	1.83294e7i	−0.0297413	+	0.0297413i
$852$	1.27038e7	−	2.30913e8i	0.0205406	−	0.373362i
$853$	−2.08222e8	+	2.08222e8i	−0.335490	+	0.335490i	−0.854667	−	0.519177i	$-0.826239\pi$
$853$	−2.08222e8	+	2.08222e8i	−0.335490	+	0.335490i	0.519177	+	0.854667i	$0.326239\pi$
$854$	1.96635e7	−	4.40108e7i	0.0315709	−	0.0706619i
$855$	−1.21740e8			−0.194776
$856$	−1.47137e7	−	4.58923e7i	−0.0234585	−	0.0731676i
$857$			3.23257e7i			0.0513577i	0.999670	+	0.0256788i	$0.00817472\pi$
$857$			3.23257e7i			0.0513577i	−0.999670	+	0.0256788i	$0.991825\pi$
$858$	−1.78452e8	+	3.99411e8i	−0.282526	+	0.632351i
$859$	1.26896e8	+	1.26896e8i	0.200202	+	0.200202i	0.800087	−	0.599884i	$-0.204787\pi$
$859$	1.26896e8	+	1.26896e8i	0.200202	+	0.200202i	−0.599884	+	0.800087i	$0.704787\pi$
$860$	8.93431e8	−	8.00252e8i	1.40464	−	1.25815i
$861$	6.03636e8	+	6.03636e8i	0.945727	+	0.945727i
$862$	8.09218e8	−	3.09423e8i	1.26341	−	0.483093i
$863$			2.95082e8i			0.459103i	0.973296	+	0.229552i	$0.0737260\pi$
$863$			2.95082e8i			0.459103i	−0.973296	+	0.229552i	$0.926274\pi$
$864$	1.07090e8	+	6.27599e7i	0.166038	+	0.0973064i
$865$	4.09574e8			0.632825
$866$	3.64283e8	+	9.52689e8i	0.560899	+	1.46689i
$867$	−2.30980e7	+	2.30980e7i	−0.0354419	+	0.0354419i
$868$	5.11332e8	+	5.70869e8i	0.781886	+	0.872926i
$869$	8.61154e8	−	8.61154e8i	1.31227	−	1.31227i
$870$	2.49381e8	+	1.11420e8i	0.378709	+	0.169202i
$871$	−8.73051e7			−0.132125
$872$	−3.16736e8	−	9.87907e8i	−0.477692	−	1.48993i
$873$		−	1.82692e8i		−	0.274585i
$874$	5.70426e8	+	2.54859e8i	0.854408	+	0.381738i
$875$	−4.65502e8	−	4.65502e8i	−0.694860	−	0.694860i
$876$	2.30881e7	+	1.27020e6i	0.0343460	+	0.00188956i
$877$	−7.00284e8	−	7.00284e8i	−1.03819	−	1.03819i	−0.999241	−	0.0389459i	$-0.987600\pi$
$877$	−7.00284e8	−	7.00284e8i	−1.03819	−	1.03819i	−0.0389459	−	0.999241i	$-0.512400\pi$
$878$	1.16713e8	+	3.05233e8i	0.172439	+	0.450971i
$879$		−	4.02648e8i		−	0.592869i
$880$	−1.16640e8	+	1.05686e9i	−0.171158	+	1.55084i
$881$	−4.48321e8			−0.655635			−0.327817	−	0.944741i	$-0.606313\pi$
$881$	−4.48321e8			−0.655635			−0.327817	+	0.944741i	$0.606313\pi$
$882$	−8.85276e7	+	3.38506e7i	−0.129025	+	0.0493356i
$883$	1.06421e7	−	1.06421e7i	0.0154577	−	0.0154577i	−0.699336	−	0.714793i	$-0.746521\pi$
$883$	1.06421e7	−	1.06421e7i	0.0154577	−	0.0154577i	0.714793	+	0.699336i	$0.246521\pi$
$884$	5.70103e8	+	3.13644e7i	0.825271	+	0.0454026i
$885$	3.13003e8	−	3.13003e8i	0.451564	−	0.451564i
$886$	7.58865e7	−	1.69849e8i	0.109110	−	0.244210i
$887$	−2.84309e8			−0.407399			−0.203700	−	0.979033i	$-0.565297\pi$
$887$	−2.84309e8			−0.407399			−0.203700	+	0.979033i	$0.565297\pi$
$888$	−4.31766e6	+	8.39281e6i	−0.00616609	+	0.0119858i
$889$		−	3.72641e8i		−	0.530377i
$890$	5.15257e8	−	1.15325e9i	0.730893	−	1.63589i
$891$	−7.70802e7	−	7.70802e7i	−0.108971	−	0.108971i
$892$	7.28985e8	+	8.13866e8i	1.02713	+	1.14672i
$893$	−5.57987e7	−	5.57987e7i	−0.0783555	−	0.0783555i
$894$	4.55269e7	−	1.74083e7i	0.0637171	−	0.0243637i
$895$		−	8.89462e8i		−	1.24068i
$896$	4.72439e8	−	7.13198e8i	0.656783	−	0.991485i
$897$	−6.49307e8			−0.899648
$898$	4.94804e7	+	1.29403e8i	0.0683288	+	0.178697i
$899$	3.23314e8	−	3.23314e8i	0.444986	−	0.444986i
$900$	4.80561e7	−	4.30441e7i	0.0659205	−	0.0590455i
$901$	2.50545e8	−	2.50545e8i	0.342540	−	0.342540i
$902$	1.81017e9	+	8.08761e8i	2.46661	+	1.10205i
$903$	8.47496e8			1.15100
$904$	1.06143e9	+	5.46050e8i	1.43676	+	0.739141i
$905$		−	1.38093e9i		−	1.86305i
$906$	−6.53510e8	−	2.91980e8i	−0.878755	−	0.392617i
$907$	1.92149e8	+	1.92149e8i	0.257523	+	0.257523i	0.824046	−	0.566523i	$-0.191712\pi$
$907$	1.92149e8	+	1.92149e8i	0.257523	+	0.257523i	−0.566523	+	0.824046i	$0.691712\pi$
$908$	2.43626e7	−	4.42833e8i	0.0325437	−	0.591538i
$909$	1.03662e8	+	1.03662e8i	0.138015	+	0.138015i
$910$	−3.11437e8	−	8.14484e8i	−0.413282	−	1.08083i
$911$		−	2.51367e8i		−	0.332470i	−0.986086	−	0.166235i	$-0.946839\pi$
$911$		−	2.51367e8i		−	0.332470i	0.986086	−	0.166235i	$-0.0531611\pi$
$912$	2.26111e8	+	2.49547e7i	0.298083	+	0.0328979i
$913$	−1.50243e9			−1.97415
$914$	−9.51722e8	+	3.63913e8i	−1.24644	+	0.476606i
$915$	−2.28949e7	+	2.28949e7i	−0.0298865	+	0.0298865i
$916$	−1.23680e7	+	2.24809e8i	−0.0160921	+	0.292501i
$917$	−3.72343e7	+	3.72343e7i	−0.0482875	+	0.0482875i
$918$	−5.80370e7	+	1.29898e8i	−0.0750200	+	0.167910i
$919$	1.72821e8			0.222664			0.111332	−	0.993783i	$-0.464488\pi$
$919$	1.72821e8			0.222664			0.111332	+	0.993783i	$0.464488\pi$
$920$	−1.50282e9	+	4.81823e8i	−1.92993	+	0.618763i
$921$			1.37287e8i			0.175731i
$922$	1.21877e8	−	2.72784e8i	0.155499	−	0.348038i
$923$	3.11466e8	+	3.11466e8i	0.396100	+	0.396100i
$924$	−5.59625e8	+	5.01260e8i	−0.709383	+	0.635400i
$925$	3.46880e6	+	3.46880e6i	0.00438283	+	0.00438283i
$926$	−1.29073e8	+	4.93540e7i	−0.162555	+	0.0621568i
$927$			4.95409e8i			0.621906i
$928$	−4.40342e8	−	2.58063e8i	−0.550994	−	0.322910i
$929$	9.34033e6			0.0116497			0.00582486	−	0.999983i	$-0.498146\pi$
$929$	9.34033e6			0.0116497			0.00582486	+	0.999983i	$0.498146\pi$
$930$	−1.83855e8	−	4.80827e8i	−0.228574	−	0.597779i
$931$	−1.22825e8	+	1.22825e8i	−0.152208	+	0.152208i
$932$	−5.57933e8	−	6.22897e8i	−0.689183	−	0.769429i
$933$	7.73891e7	−	7.73891e7i	0.0952873	−	0.0952873i
$934$	−6.97884e8	−	3.11806e8i	−0.856530	−	0.382687i
$935$	−1.21874e9			−1.49100
$936$	−2.25130e8	+	7.21796e7i	−0.274540	+	0.0880211i
$937$			9.90524e8i			1.20406i	0.798475	+	0.602028i	$0.205640\pi$
$937$			9.90524e8i			1.20406i	−0.798475	+	0.602028i	$0.794360\pi$
$938$	−1.36894e8	−	6.11627e7i	−0.165874	−	0.0741102i
$939$	−3.63567e8	−	3.63567e8i	−0.439124	−	0.439124i
$940$	1.99028e8	+	1.09496e7i	0.239625	+	0.0131830i
$941$	−4.16273e8	−	4.16273e8i	−0.499585	−	0.499585i	0.411723	−	0.911309i	$-0.364927\pi$
$941$	−4.16273e8	−	4.16273e8i	−0.499585	−	0.499585i	−0.911309	+	0.411723i	$0.864927\pi$
$942$	−8.69388e7	−	2.27366e8i	−0.104007	−	0.272003i
$943$			2.94272e9i			3.50925i
$944$	−6.45509e8	+	5.17188e8i	−0.767337	+	0.614798i
$945$	2.17285e8			0.257475
$946$	1.83847e9	−	7.02981e8i	2.17162	−	0.830368i
$947$	4.75744e8	−	4.75744e8i	0.560174	−	0.560174i	−0.369183	−	0.929357i	$-0.620362\pi$
$947$	4.75744e8	−	4.75744e8i	0.560174	−	0.560174i	0.929357	+	0.369183i	$0.120362\pi$
$948$	6.57170e8	+	3.61544e7i	0.771352	+	0.0424362i
$949$	−3.11423e7	+	3.11423e7i	−0.0364378	+	0.0364378i
$950$	4.82316e7	−	1.07952e8i	0.0562549	−	0.125910i
$951$	5.99217e8			0.696695
$952$	8.71949e8	+	4.48572e8i	1.01060	+	0.519902i
$953$			5.32360e8i			0.615073i	0.951536	+	0.307537i	$0.0995046\pi$
$953$			5.32360e8i			0.615073i	−0.951536	+	0.307537i	$0.900495\pi$
$954$	−5.98480e7	+	1.33952e8i	−0.0689294	+	0.154278i
$955$	−6.74422e8	−	6.74422e8i	−0.774322	−	0.774322i
$956$	4.09626e8	+	4.57321e8i	0.468828	+	0.523417i
$957$	3.16946e8	+	3.16946e8i	0.361618	+	0.361618i
$958$	7.15840e8	−	2.73718e8i	0.814178	−	0.311320i
$959$		−	3.41721e8i		−	0.387450i
$960$	−4.67500e8	+	3.34119e8i	−0.528406	+	0.377648i
$961$	2.57641e7			0.0290299
$962$	−6.42051e6	−	1.67912e7i	−0.00721181	−	0.0188607i
$963$	−1.61737e7	+	1.61737e7i	−0.0181105	+	0.0181105i
$964$	−8.92899e8	+	7.99776e8i	−0.996716	+	0.892765i
$965$	8.52579e8	−	8.52579e8i	0.948752	−	0.948752i
$966$	−1.01811e9	−	4.54880e8i	−1.12944	−	0.504621i
$967$	−1.34706e9			−1.48973			−0.744864	−	0.667216i	$-0.767486\pi$
$967$	−1.34706e9			−1.48973			−0.744864	+	0.667216i	$0.767486\pi$
$968$	−3.83270e8	+	7.45013e8i	−0.422551	+	0.821368i
$969$			2.60746e8i			0.286580i
$970$	7.72185e8	+	3.45003e8i	0.846070	+	0.378013i
$971$	2.98809e8	+	2.98809e8i	0.326390	+	0.326390i	0.851212	−	0.524822i	$-0.175868\pi$
$971$	2.98809e8	+	2.98809e8i	0.326390	+	0.326390i	−0.524822	+	0.851212i	$0.675868\pi$
$972$	3.23611e6	−	5.88219e7i	0.00352391	−	0.0640532i
$973$	5.30829e8	+	5.30829e8i	0.576257	+	0.576257i
$974$	−7.07762e6	−	1.85097e7i	−0.00765968	−	0.0200319i
$975$			1.22880e8i			0.132577i
$976$	4.72162e7	−	3.78301e7i	0.0507858	−	0.0406900i
$977$	4.33270e8			0.464595			0.232298	−	0.972645i	$-0.425376\pi$
$977$	4.33270e8			0.464595			0.232298	+	0.972645i	$0.425376\pi$
$978$	−2.68499e8	+	1.02667e8i	−0.287029	+	0.109752i
$979$	1.46570e9	−	1.46570e9i	1.56206	−	1.56206i
$980$	2.41025e7	−	4.38105e8i	0.0256085	−	0.465479i
$981$	−3.48165e8	+	3.48165e8i	−0.368789	+	0.368789i
$982$	3.81026e8	−	8.52814e8i	0.402365	−	0.900575i
$983$	−1.37975e9			−1.45258			−0.726288	−	0.687391i	$-0.758756\pi$
$983$	−1.37975e9			−1.45258			−0.726288	+	0.687391i	$0.758756\pi$
$984$	3.27125e8	+	1.02031e9i	0.343343	+	1.07090i
$985$			1.40126e9i			1.46625i
$986$	2.38642e8	−	5.34130e8i	0.248953	−	0.557206i
$987$	9.95911e7	+	9.95911e7i	0.103578	+	0.103578i
$988$	−3.22745e8	+	2.89085e8i	−0.334648	+	0.299746i
$989$	2.06577e9	+	2.06577e9i	2.13547	+	2.13547i
$990$	4.71356e8	−	1.80234e8i	0.485785	−	0.185751i
$991$		−	1.16289e9i		−	1.19486i	−0.801922	−	0.597428i	$-0.796189\pi$
$991$		−	1.16289e9i		−	1.19486i	0.801922	−	0.597428i	$-0.203811\pi$
$992$	2.42918e8	+	9.30740e8i	0.248842	+	0.953440i
$993$	4.86518e8			0.496879
$994$	2.70177e8	+	7.06579e8i	0.275099	+	0.719452i
$995$	−7.02218e8	+	7.02218e8i	−0.712857	+	0.712857i
$996$	−5.41732e8	−	6.04809e8i	−0.548285	−	0.612126i
$997$	−3.50811e8	+	3.50811e8i	−0.353987	+	0.353987i	−0.861591	−	0.507604i	$-0.830531\pi$
$997$	−3.50811e8	+	3.50811e8i	−0.353987	+	0.353987i	0.507604	+	0.861591i	$0.330531\pi$
$998$	−1.39462e8	−	6.23100e7i	−0.140302	−	0.0626853i
$999$	4.47950e6			0.00449297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.10	✓	48
4.3	odd	2		192.7.l.a.175.9		48
8.3	odd	2		384.7.l.a.223.16		48
8.5	even	2		384.7.l.b.223.9		48
16.3	odd	4		384.7.l.b.31.9		48
16.5	even	4		192.7.l.a.79.9		48
16.11	odd	4	inner	48.7.l.a.43.10	yes	48
16.13	even	4		384.7.l.a.31.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.10	✓	48	1.1	even	1	trivial
48.7.l.a.43.10	yes	48	16.11	odd	4	inner
192.7.l.a.79.9		48	16.5	even	4
192.7.l.a.175.9		48	4.3	odd	2
384.7.l.a.31.16		48	16.13	even	4
384.7.l.a.223.16		48	8.3	odd	2
384.7.l.b.31.9		48	16.3	odd	4
384.7.l.b.223.9		48	8.5	even	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.85723 - 7.47236i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-47.6725 + 42.7006i) q^{4} +(-99.4317 + 99.4317i) q^{5} +(-113.860 - 50.8712i) q^{6} +407.926 q^{7} +(455.285 + 234.221i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(-2.85723 - 7.47236i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-47.6725 + 42.7006i) q^{4} +(-99.4317 + 99.4317i) q^{5} +(-113.860 - 50.8712i) q^{6} +407.926 q^{7} +(455.285 + 234.221i) q^{8} -243.000i q^{9} +(1027.09 + 458.891i) q^{10} +(1305.36 + 1305.36i) q^{11} +(-54.8038 + 996.155i) q^{12} +(-1343.66 - 1343.66i) q^{13} +(-1165.54 - 3048.17i) q^{14} +2192.01i q^{15} +(449.326 - 4071.28i) q^{16} +4694.90 q^{17} +(-1815.78 + 694.307i) q^{18} +(-2519.26 + 2519.26i) q^{19} +(494.365 - 8985.94i) q^{20} +(4496.45 - 4496.45i) q^{21} +(6024.41 - 13483.8i) q^{22} +21920.1 q^{23} +(7600.22 - 2436.73i) q^{24} -4148.34i q^{25} +(-6201.16 + 13879.4i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(-19446.8 + 17418.7i) q^{28} +(11013.8 + 11013.8i) q^{29} +(16379.5 - 6263.09i) q^{30} -29355.4i q^{31} +(-31705.9 + 8275.06i) q^{32} +28777.2 q^{33} +(-13414.4 - 35082.0i) q^{34} +(-40560.8 + 40560.8i) q^{35} +(10376.2 + 11584.4i) q^{36} +(-836.191 + 836.191i) q^{37} +(26022.9 + 11626.7i) q^{38} -29621.5 q^{39} +(-68558.8 + 21980.9i) q^{40} +134247. i q^{41} +(-46446.5 - 20751.7i) q^{42} +(94240.7 + 94240.7i) q^{43} +(-117969. - 6490.12i) q^{44} +(24161.9 + 24161.9i) q^{45} +(-62630.9 - 163795. i) q^{46} +22148.9i q^{47} +(-39923.7 - 49829.3i) q^{48} +48754.4 q^{49} +(-30997.9 + 11852.8i) q^{50} +(51750.5 - 51750.5i) q^{51} +(121430. + 6680.53i) q^{52} +(53365.3 - 53365.3i) q^{53} +(-12361.7 + 27668.0i) q^{54} -259588. q^{55} +(185723. + 95544.6i) q^{56} +55538.1i q^{57} +(50830.1 - 113768. i) q^{58} +(-142793. - 142793. i) q^{59} +(-93600.2 - 104499. i) q^{60} +(10444.7 + 10444.7i) q^{61} +(-219354. + 83875.2i) q^{62} -99126.0i q^{63} +(152425. + 213274. i) q^{64} +267204. q^{65} +(-82223.1 - 215034. i) q^{66} +(32487.9 - 32487.9i) q^{67} +(-223817. + 200475. i) q^{68} +(241619. - 241619. i) q^{69} +(418976. + 187193. i) q^{70} -231804. q^{71} +(56915.6 - 110634. i) q^{72} -23177.3i q^{73} +(8637.51 + 3859.13i) q^{74} +(-45725.9 - 45725.9i) q^{75} +(12525.5 - 227673. i) q^{76} +(532490. + 532490. i) q^{77} +(84635.4 + 221342. i) q^{78} -659707. i q^{79} +(360137. + 449492. i) q^{80} -59049.0 q^{81} +(1.00315e6 - 383576. i) q^{82} +(-575483. + 575483. i) q^{83} +(-22355.9 + 406357. i) q^{84} +(-466822. + 466822. i) q^{85} +(434933. - 973468. i) q^{86} +242804. q^{87} +(288569. + 900053. i) q^{88} -1.12283e6i q^{89} +(111510. - 249583. i) q^{90} +(-548113. - 548113. i) q^{91} +(-1.04499e6 + 936002. i) q^{92} +(-323576. - 323576. i) q^{93} +(165504. - 63284.4i) q^{94} -500989. i q^{95} +(-258271. + 440699. i) q^{96} +751819. q^{97} +(-139303. - 364311. i) q^{98} +(317202. - 317202. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

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