LMFDB - Embedded newform 37.7.g.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(8,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("37.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.g (of order $12$, degree $4$, 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:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	37.8
Dual form			37.7.g.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.9637 - 3.74156i) q^{2} +(7.40363 + 4.27449i) q^{3} +(125.560 + 72.4919i) q^{4} +(-72.2350 + 19.3553i) q^{5} +(-87.3887 - 87.3887i) q^{6} +(180.588 - 312.787i) q^{7} +(-827.827 - 827.827i) q^{8} +(-327.958 - 568.039i) q^{9} +O(q^{10})$	\(q+(-13.9637 - 3.74156i) q^{2} +(7.40363 + 4.27449i) q^{3} +(125.560 + 72.4919i) q^{4} +(-72.2350 + 19.3553i) q^{5} +(-87.3887 - 87.3887i) q^{6} +(180.588 - 312.787i) q^{7} +(-827.827 - 827.827i) q^{8} +(-327.958 - 568.039i) q^{9} +1081.09 q^{10} +1538.32i q^{11} +(619.732 + 1073.41i) q^{12} +(311.914 - 83.5772i) q^{13} +(-3691.99 + 3691.99i) q^{14} +(-617.535 - 165.468i) q^{15} +(3822.67 + 6621.06i) q^{16} +(-2077.54 + 7753.50i) q^{17} +(2454.14 + 9158.99i) q^{18} +(-640.408 + 171.597i) q^{19} +(-10472.9 - 2806.21i) q^{20} +(2674.01 - 1543.84i) q^{21} +(5755.70 - 21480.6i) q^{22} +(3506.23 + 3506.23i) q^{23} +(-2590.39 - 9667.46i) q^{24} +(-8688.38 + 5016.24i) q^{25} -4668.18 q^{26} -11839.6i q^{27} +(45349.1 - 26182.3i) q^{28} +(-23650.4 + 23650.4i) q^{29} +(8003.96 + 4621.09i) q^{30} +(-17581.8 + 17581.8i) q^{31} +(-9213.13 - 34383.9i) q^{32} +(-6575.51 + 11389.1i) q^{33} +(58020.3 - 100494. i) q^{34} +(-6990.67 + 26089.5i) q^{35} -95097.1i q^{36} +(-42385.3 + 27734.7i) q^{37} +9584.49 q^{38} +(2666.55 + 714.500i) q^{39} +(75820.9 + 43775.2i) q^{40} +(-42052.7 - 24279.1i) q^{41} +(-43115.4 + 11552.7i) q^{42} +(73177.5 + 73177.5i) q^{43} +(-111515. + 193150. i) q^{44} +(34684.6 + 34684.6i) q^{45} +(-35841.1 - 62078.7i) q^{46} +61436.5 q^{47} +65359.8i q^{48} +(-6399.48 - 11084.2i) q^{49} +(140090. - 37537.1i) q^{50} +(-48523.6 + 48523.6i) q^{51} +(45222.5 + 12117.3i) q^{52} +(-64579.6 - 111855. i) q^{53} +(-44298.6 + 165325. i) q^{54} +(-29774.6 - 111120. i) q^{55} +(-408429. + 109438. i) q^{56} +(-5474.83 - 1466.98i) q^{57} +(418735. - 241757. i) q^{58} +(-33327.9 + 124381. i) q^{59} +(-65542.4 - 65542.4i) q^{60} +(-90241.4 - 336786. i) q^{61} +(311290. - 179723. i) q^{62} -236901. q^{63} +25295.0i q^{64} +(-20913.5 + 12074.4i) q^{65} +(134431. - 134431. i) q^{66} +(273613. + 157971. i) q^{67} +(-822921. + 822921. i) q^{68} +(10971.5 + 40946.2i) q^{69} +(195231. - 338150. i) q^{70} +(149045. - 258154. i) q^{71} +(-198746. + 741730. i) q^{72} +665296. i q^{73} +(695626. - 228691. i) q^{74} -85767.4 q^{75} +(-92848.7 - 24878.7i) q^{76} +(481166. + 277801. i) q^{77} +(-34561.5 - 19954.1i) q^{78} +(-139097. + 37270.9i) q^{79} +(-404283. - 404283. i) q^{80} +(-188473. + 326444. i) q^{81} +(496369. + 496369. i) q^{82} +(-551572. - 955350. i) q^{83} +447664. q^{84} -600285. i q^{85} +(-748030. - 1.29563e6i) q^{86} +(-276192. + 74005.3i) q^{87} +(1.27346e6 - 1.27346e6i) q^{88} +(175278. + 46965.6i) q^{89} +(-354550. - 614099. i) q^{90} +(30186.1 - 112656. i) q^{91} +(186068. + 694415. i) q^{92} +(-205322. + 55015.9i) q^{93} +(-857880. - 229868. i) q^{94} +(42938.6 - 24790.6i) q^{95} +(78762.8 - 293947. i) q^{96} +(1.10298e6 + 1.10298e6i) q^{97} +(47888.0 + 178721. i) q^{98} +(873823. - 504502. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) $ 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−13.9637	−	3.74156i	−1.74546	−	0.467695i	−0.761813	−	0.647797i	$-0.775690\pi$
$2$	−13.9637	−	3.74156i	−1.74546	−	0.467695i	−0.983648	+	0.180102i	$0.942357\pi$
$3$	7.40363	+	4.27449i	0.274209	+	0.158314i	0.630799	−	0.775947i	$-0.282727\pi$
$3$	7.40363	+	4.27449i	0.274209	+	0.158314i	−0.356590	+	0.934261i	$0.616061\pi$
$4$	125.560	+	72.4919i	1.96187	+	1.13269i
$5$	−72.2350	+	19.3553i	−0.577880	+	0.154843i	−0.535908	−	0.844276i	$-0.680031\pi$
$5$	−72.2350	+	19.3553i	−0.577880	+	0.154843i	−0.0419719	+	0.999119i	$0.513364\pi$
$6$	−87.3887	−	87.3887i	−0.404577	−	0.404577i
$7$	180.588	−	312.787i	0.526495	−	0.911917i	−0.473028	−	0.881047i	$-0.656839\pi$
$7$	180.588	−	312.787i	0.526495	−	0.911917i	0.999523	−	0.0308693i	$-0.00982757\pi$
$8$	−827.827	−	827.827i	−1.61685	−	1.61685i
$9$	−327.958	−	568.039i	−0.449873	−	0.779203i
$10$	1081.09			1.08109
$11$			1538.32i			1.15576i	0.816122	+	0.577879i	$0.196120\pi$
$11$			1538.32i			1.15576i	−0.816122	+	0.577879i	$0.803880\pi$
$12$	619.732	+	1073.41i	0.358641	+	0.621184i
$13$	311.914	−	83.5772i	0.141973	−	0.0380415i	−0.187133	−	0.982335i	$-0.559919\pi$
$13$	311.914	−	83.5772i	0.141973	−	0.0380415i	0.329106	+	0.944293i	$0.393253\pi$
$14$	−3691.99	+	3691.99i	−1.34548	+	1.34548i
$15$	−617.535	−	165.468i	−0.182973	−	0.0490276i
$16$	3822.67	+	6621.06i	0.933269	+	1.61647i
$17$	−2077.54	+	7753.50i	−0.422866	+	1.57816i	0.345672	+	0.938355i	$0.387651\pi$
$17$	−2077.54	+	7753.50i	−0.422866	+	1.57816i	−0.768538	+	0.639804i	$0.779016\pi$
$18$	2454.14	+	9158.99i	0.420807	+	1.57047i
$19$	−640.408	+	171.597i	−0.0933675	+	0.0250177i	−0.305200	−	0.952288i	$-0.598723\pi$
$19$	−640.408	+	171.597i	−0.0933675	+	0.0250177i	0.211833	+	0.977306i	$0.432057\pi$
$20$	−10472.9	−	2806.21i	−1.30911	−	0.350776i
$21$	2674.01	−	1543.84i	0.288739	−	0.166704i
$22$	5755.70	−	21480.6i	0.540542	−	2.01733i
$23$	3506.23	+	3506.23i	0.288176	+	0.288176i	0.836358	−	0.548183i	$-0.184680\pi$
$23$	3506.23	+	3506.23i	0.288176	+	0.288176i	−0.548183	+	0.836358i	$0.684680\pi$
$24$	−2590.39	−	9667.46i	−0.187383	−	0.699324i
$25$	−8688.38	+	5016.24i	−0.556056	+	0.321039i
$26$	−4668.18			−0.265600
$27$		−	11839.6i		−	0.601514i
$28$	45349.1	−	26182.3i	2.06583	−	1.19271i
$29$	−23650.4	+	23650.4i	−0.969714	+	0.969714i	−0.999555	−	0.0298405i	$-0.990500\pi$
$29$	−23650.4	+	23650.4i	−0.969714	+	0.969714i	0.0298405	+	0.999555i	$0.490500\pi$
$30$	8003.96	+	4621.09i	0.296443	+	0.171151i
$31$	−17581.8	+	17581.8i	−0.590171	+	0.590171i	−0.937678	−	0.347506i	$-0.887029\pi$
$31$	−17581.8	+	17581.8i	−0.590171	+	0.590171i	0.347506	+	0.937678i	$0.387029\pi$
$32$	−9213.13	−	34383.9i	−0.281162	−	1.04931i
$33$	−6575.51	+	11389.1i	−0.182973	+	0.316919i
$34$	58020.3	−	100494.i	1.47619	−	2.55684i
$35$	−6990.67	+	26089.5i	−0.163048	+	0.608502i
$36$		−	95097.1i		−	2.03826i
$37$	−42385.3	+	27734.7i	−0.836778	+	0.547543i
$37$	−42385.3	+	27734.7i	−0.836778	+	0.547543i
$38$	9584.49			0.174670
$39$	2666.55	+	714.500i	0.0449527	+	0.0120450i
$40$	75820.9	+	43775.2i	1.18470	+	0.683988i
$41$	−42052.7	−	24279.1i	−0.610158	−	0.352275i	0.162869	−	0.986648i	$-0.447925\pi$
$41$	−42052.7	−	24279.1i	−0.610158	−	0.352275i	−0.773027	+	0.634373i	$0.781258\pi$
$42$	−43115.4	+	11552.7i	−0.581949	+	0.155933i
$43$	73177.5	+	73177.5i	0.920390	+	0.920390i	0.997057	−	0.0766664i	$-0.0244276\pi$
$43$	73177.5	+	73177.5i	0.920390	+	0.920390i	−0.0766664	+	0.997057i	$0.524428\pi$
$44$	−111515.	+	193150.i	−1.30911	+	2.26745i
$45$	34684.6	+	34684.6i	0.380626	+	0.380626i
$46$	−35841.1	−	62078.7i	−0.368221	−	0.637777i
$47$	61436.5			0.591743			0.295871	−	0.955228i	$-0.404390\pi$
$47$	61436.5			0.591743			0.295871	+	0.955228i	$0.404390\pi$
$48$			65359.8i			0.591000i
$49$	−6399.48	−	11084.2i	−0.0543946	−	0.0942143i
$50$	140090.	−	37537.1i	1.12072	−	0.300297i
$51$	−48523.6	+	48523.6i	−0.365799	+	0.365799i
$52$	45222.5	+	12117.3i	0.321621	+	0.0861782i
$53$	−64579.6	−	111855.i	−0.433778	−	0.751326i	0.563417	−	0.826173i	$-0.309486\pi$
$53$	−64579.6	−	111855.i	−0.433778	−	0.751326i	−0.997195	+	0.0748470i	$0.976153\pi$
$54$	−44298.6	+	165325.i	−0.281325	+	1.04992i
$55$	−29774.6	−	111120.i	−0.178961	−	0.667890i
$56$	−408429.	+	109438.i	−2.32570	+	0.623168i
$57$	−5474.83	−	1466.98i	−0.0295628	−	0.00792134i
$58$	418735.	−	241757.i	2.14613	−	1.23907i
$59$	−33327.9	+	124381.i	−0.162275	+	0.605618i	0.836097	+	0.548581i	$0.184832\pi$
$59$	−33327.9	+	124381.i	−0.162275	+	0.605618i	−0.998372	+	0.0570370i	$0.981835\pi$
$60$	−65542.4	−	65542.4i	−0.303437	−	0.303437i
$61$	−90241.4	−	336786.i	−0.397573	−	1.48376i	−0.817354	−	0.576136i	$-0.804560\pi$
$61$	−90241.4	−	336786.i	−0.397573	−	1.48376i	0.419782	−	0.907625i	$-0.362107\pi$
$62$	311290.	−	179723.i	1.30614	−	0.754101i
$63$	−236901.			−0.947424
$64$			25295.0i			0.0964929i
$65$	−20913.5	+	12074.4i	−0.0761529	+	0.0439669i
$66$	134431.	−	134431.i	0.467594	−	0.467594i
$67$	273613.	+	157971.i	0.909729	+	0.525233i	0.880344	−	0.474336i	$-0.157312\pi$
$67$	273613.	+	157971.i	0.909729	+	0.525233i	0.0293853	+	0.999568i	$0.490645\pi$
$68$	−822921.	+	822921.i	−2.61717	+	2.61717i
$69$	10971.5	+	40946.2i	0.0333979	+	0.124643i
$70$	195231.	−	338150.i	0.569187	−	0.985860i
$71$	149045.	−	258154.i	0.416432	−	0.721281i	−0.579146	−	0.815224i	$-0.696614\pi$
$71$	149045.	−	258154.i	0.416432	−	0.721281i	0.995578	+	0.0939431i	$0.0299472\pi$
$72$	−198746.	+	741730.i	−0.532477	+	1.98723i
$73$			665296.i			1.71020i	0.518465	+	0.855099i	$0.326503\pi$
$73$			665296.i			1.71020i	−0.518465	+	0.855099i	$0.673497\pi$
$74$	695626.	−	228691.i	1.71665	−	0.564357i
$75$	−85767.4			−0.203300
$76$	−92848.7	−	24878.7i	−0.211512	−	0.0566745i
$77$	481166.	+	277801.i	1.05396	+	0.608502i
$78$	−34561.5	−	19954.1i	−0.0728298	−	0.0420483i
$79$	−139097.	+	37270.9i	−0.282121	+	0.0755942i	−0.397105	−	0.917773i	$-0.629985\pi$
$79$	−139097.	+	37270.9i	−0.282121	+	0.0755942i	0.114984	+	0.993367i	$0.463318\pi$
$80$	−404283.	−	404283.i	−0.789616	−	0.789616i
$81$	−188473.	+	326444.i	−0.354645	+	0.614263i
$82$	496369.	+	496369.i	0.900250	+	0.900250i
$83$	−551572.	−	955350.i	−0.964645	−	1.67081i	−0.710566	−	0.703631i	$-0.751561\pi$
$83$	−551572.	−	955350.i	−0.964645	−	1.67081i	−0.254079	−	0.967183i	$-0.581772\pi$
$84$	447664.			0.755291
$85$		−	600285.i		−	0.977464i
$86$	−748030.	−	1.29563e6i	−1.17604	−	2.03697i
$87$	−276192.	+	74005.3i	−0.419424	+	0.112384i
$88$	1.27346e6	−	1.27346e6i	1.86869	−	1.86869i
$89$	175278.	+	46965.6i	0.248632	+	0.0666208i	0.380983	−	0.924582i	$-0.375586\pi$
$89$	175278.	+	46965.6i	0.248632	+	0.0666208i	−0.132350	+	0.991203i	$0.542252\pi$
$90$	−354550.	−	614099.i	−0.486352	−	0.842386i
$91$	30186.1	−	112656.i	0.0400574	−	0.149496i
$92$	186068.	+	694415.i	0.238950	+	0.891775i
$93$	−205322.	+	55015.9i	−0.255263	+	0.0683974i
$94$	−857880.	−	229868.i	−1.03286	−	0.276755i
$95$	42938.6	−	24790.6i	0.0500814	−	0.0289145i
$96$	78762.8	−	293947.i	0.0890241	−	0.332242i
$97$	1.10298e6	+	1.10298e6i	1.20852	+	1.20852i	0.971507	+	0.237010i	$0.0761676\pi$
$97$	1.10298e6	+	1.10298e6i	1.20852	+	1.20852i	0.237010	+	0.971507i	$0.423832\pi$
$98$	47888.0	+	178721.i	0.0508802	+	0.189887i
$99$	873823.	−	504502.i	0.900571	−	0.519945i
$100$	−1.45455e6			−1.45455
$101$			396341.i			0.384685i	0.981328	+	0.192342i	$0.0616084\pi$
$101$			396341.i			0.384685i	−0.981328	+	0.192342i	$0.938392\pi$
$102$	859122.	−	496014.i	0.809570	−	0.467405i
$103$	−937285.	+	937285.i	−0.857748	+	0.857748i	−0.991072	−	0.133324i	$-0.957435\pi$
$103$	−937285.	+	937285.i	−0.857748	+	0.857748i	0.133324	+	0.991072i	$0.457435\pi$
$104$	−327399.	−	189024.i	−0.291056	−	0.168041i
$105$	−163276.	+	163276.i	−0.141044	+	0.141044i
$106$	483257.	+	1.80354e6i	0.405752	+	1.51429i
$107$	−297009.	+	514435.i	−0.242448	+	0.419932i	−0.961411	−	0.275116i	$-0.911284\pi$
$107$	−297009.	+	514435.i	−0.242448	+	0.419932i	0.718963	+	0.695048i	$0.244617\pi$
$108$	858276.	−	1.48658e6i	0.681327	−	1.18009i
$109$	451244.	−	1.68406e6i	0.348443	−	1.30041i	−0.540095	−	0.841604i	$-0.681612\pi$
$109$	451244.	−	1.68406e6i	0.348443	−	1.30041i	0.888538	−	0.458803i	$-0.151722\pi$
$110$			1.66305e6i			1.24947i
$111$	−432357.	+	24161.8i	−0.316135	+	0.0176669i
$112$	2.76131e6			1.96545
$113$	−2.14230e6	−	574027.i	−1.48472	−	0.397830i	−0.576770	−	0.816907i	$-0.695687\pi$
$113$	−2.14230e6	−	574027.i	−1.48472	−	0.397830i	−0.907951	+	0.419077i	$0.862354\pi$
$114$	70960.0	+	40968.8i	0.0478960	+	0.0276528i
$115$	−321137.	−	185408.i	−0.211153	−	0.121909i
$116$	−4.68399e6	+	1.25507e6i	−3.00083	+	0.804071i
$117$	−149770.	−	149770.i	−0.0935118	−	0.0935118i
$118$	930760.	−	1.61212e6i	0.566489	−	0.981188i
$119$	2.05002e6	+	2.05002e6i	1.21651	+	1.21651i
$120$	374233.	+	648191.i	0.216570	+	0.375111i
$121$	−594853.			−0.335779
$122$			5.04041e6i			2.77579i
$123$	−207562.	−	359508.i	−0.111540	−	0.193194i
$124$	−3.48210e6	+	933026.i	−1.82632	+	0.489360i
$125$	1.35676e6	−	1.35676e6i	0.694661	−	0.694661i
$126$	3.30801e6	+	886378.i	1.65369	+	0.443105i
$127$	795619.	+	1.37805e6i	0.388413	+	0.672752i	0.992236	−	0.124367i	$-0.0396900\pi$
$127$	795619.	+	1.37805e6i	0.388413	+	0.672752i	−0.603823	+	0.797118i	$0.706357\pi$
$128$	−494997.	+	1.84735e6i	−0.236033	+	0.880887i
$129$	228983.	+	854575.i	0.106668	+	0.398090i
$130$	337206.	−	90354.2i	0.153485	−	0.0411262i
$131$	−3.46409e6	−	928200.i	−1.54090	−	0.412884i	−0.614346	−	0.789037i	$-0.710580\pi$
$131$	−3.46409e6	−	928200.i	−1.54090	−	0.412884i	−0.926558	+	0.376153i	$0.877247\pi$
$132$	−1.65124e6	+	953342.i	−0.717939	+	0.414502i
$133$	−61976.6	+	231300.i	−0.0263435	+	0.0983151i
$134$	−3.22959e6	−	3.22959e6i	−1.34225	−	1.34225i
$135$	229159.	+	855234.i	0.0931400	+	0.347603i
$136$	8.13840e6	−	4.69871e6i	3.23536	−	1.86793i
$137$	3.73853e6			1.45392			0.726958	−	0.686682i	$-0.240934\pi$
$137$	3.73853e6			1.45392			0.726958	+	0.686682i	$0.240934\pi$
$138$		−	612810.i		−	0.233179i
$139$	1.42393e6	−	822104.i	0.530204	−	0.306114i	−0.210895	−	0.977509i	$-0.567638\pi$
$139$	1.42393e6	−	822104.i	0.530204	−	0.306114i	0.741100	+	0.671395i	$0.234305\pi$
$140$	−2.76903e6	+	2.76903e6i	−1.00912	+	1.00912i
$141$	454853.	+	262610.i	0.162261	+	0.0936814i
$142$	−3.04712e6	+	3.04712e6i	−1.06420	+	1.06420i
$143$	128568.	+	479823.i	0.0439668	+	0.164086i
$144$	2.50735e6	−	4.34285e6i	0.839705	−	1.45441i
$145$	1.25062e6	−	2.16614e6i	0.410226	−	0.710532i
$146$	2.48924e6	−	9.28998e6i	0.799850	−	2.98508i
$147$		−	109418.i		−	0.0344458i
$148$	−7.33242e6	+	409764.i	−2.26184	+	0.126401i
$149$	−1.63595e6			−0.494551			−0.247275	−	0.968945i	$-0.579535\pi$
$149$	−1.63595e6			−0.494551			−0.247275	+	0.968945i	$0.579535\pi$
$150$	1.19763e6	+	320904.i	0.354853	+	0.0950826i
$151$	−4.12518e6	−	2.38167e6i	−1.19815	−	0.691754i	−0.238009	−	0.971263i	$-0.576495\pi$
$151$	−4.12518e6	−	2.38167e6i	−1.19815	−	0.691754i	−0.960143	+	0.279509i	$0.909828\pi$
$152$	672199.	+	388094.i	0.191411	+	0.110511i
$153$	5.08563e6	−	1.36269e6i	1.41994	−	0.380472i
$154$	−5.67944e6	−	5.67944e6i	−1.55505	−	1.55505i
$155$	929720.	−	1.61032e6i	0.249665	−	0.432432i
$156$	283016.	+	283016.i	0.0745481	+	0.0745481i
$157$	−1.27589e6	−	2.20991e6i	−0.329697	−	0.571053i	0.652754	−	0.757570i	$-0.273613\pi$
$157$	−1.27589e6	−	2.20991e6i	−0.329697	−	0.571053i	−0.982452	+	0.186517i	$0.940280\pi$
$158$	2.08176e6			0.527787
$159$		−	1.10418e6i		−	0.274693i
$160$	1.33102e6	+	2.30540e6i	0.324956	+	0.562841i
$161$	1.72989e6	−	463522.i	0.414515	−	0.111069i
$162$	3.85319e6	−	3.85319e6i	0.906306	−	0.906306i
$163$	2.59403e6	+	695069.i	0.598981	+	0.160496i	0.545554	−	0.838075i	$-0.316319\pi$
$163$	2.59403e6	+	695069.i	0.598981	+	0.160496i	0.0534262	+	0.998572i	$0.482986\pi$
$164$	−3.52008e6	−	6.09696e6i	−0.798034	−	1.38224i
$165$	254542.	−	949964.i	0.0566641	−	0.211473i
$166$	4.12747e6	+	1.54039e7i	0.902319	+	3.36750i
$167$	−956243.	+	256225.i	−0.205314	+	0.0550138i	−0.360010	−	0.932948i	$-0.617227\pi$
$167$	−956243.	+	256225.i	−0.205314	+	0.0550138i	0.154696	+	0.987962i	$0.450560\pi$
$168$	−3.49165e6	−	935585.i	−0.736382	−	0.197313i
$169$	−4.08983e6	+	2.36127e6i	−0.847316	+	0.489198i
$170$	−2.24600e6	+	8.38220e6i	−0.457155	+	1.70613i
$171$	307500.	+	307500.i	0.0614974	+	0.0614974i
$172$	3.88336e6	+	1.44929e7i	0.763173	+	2.84820i
$173$	8.59262e6	−	4.96095e6i	1.65954	−	0.958135i	0.686611	−	0.727025i	$-0.259097\pi$
$173$	8.59262e6	−	4.96095e6i	1.65954	−	0.958135i	0.972928	−	0.231110i	$-0.0742359\pi$
$174$	4.13355e6			0.784649
$175$			3.62349e6i			0.676103i
$176$	−1.01853e7	+	5.88047e6i	−1.86825	+	1.07863i
$177$	−778414.	+	778414.i	−0.140375	+	0.140375i
$178$	−2.27180e6	−	1.31163e6i	−0.402820	−	0.232568i
$179$	341694.	−	341694.i	0.0595769	−	0.0595769i	−0.676691	−	0.736267i	$-0.736587\pi$
$179$	341694.	−	341694.i	0.0595769	−	0.0595769i	0.736267	+	0.676691i	$0.236587\pi$
$180$	1.84063e6	+	6.86934e6i	0.315609	+	1.17787i
$181$	−377154.	+	653250.i	−0.0636038	+	0.110165i	−0.896074	−	0.443905i	$-0.853593\pi$
$181$	−377154.	+	653250.i	−0.0636038	+	0.110165i	0.832470	+	0.554070i	$0.186926\pi$
$182$	−843018.	+	1.46015e6i	−0.139837	+	0.242205i
$183$	771472.	−	2.87917e6i	0.125883	−	0.469801i
$184$		−	5.80511e6i		−	0.931873i
$185$	2.52489e6	−	2.82380e6i	0.398774	−	0.445983i
$186$	3.07290e6			0.477540
$187$	−1.19273e7	−	3.19592e6i	−1.82397	−	0.488732i
$188$	7.71395e6	+	4.45365e6i	1.16092	+	0.670259i
$189$	−3.70328e6	−	2.13809e6i	−0.548531	−	0.316694i
$190$	−692336.	+	185511.i	−0.100938	+	0.0270463i
$191$	350003.	+	350003.i	0.0502310	+	0.0502310i	0.731776	−	0.681545i	$-0.238692\pi$
$191$	350003.	+	350003.i	0.0502310	+	0.0502310i	−0.681545	+	0.731776i	$0.738692\pi$
$192$	−108123.	+	187275.i	−0.0152762	+	0.0264592i
$193$	−415947.	−	415947.i	−0.0578584	−	0.0578584i	0.677586	−	0.735444i	$-0.263026\pi$
$193$	−415947.	−	415947.i	−0.0578584	−	0.0578584i	−0.735444	+	0.677586i	$0.763026\pi$
$194$	−1.12748e7	−	1.95286e7i	−1.54420	−	2.67464i
$195$	−206448.			−0.0278424
$196$		−	1.85564e6i		−	0.246448i
$197$	4.53306e6	+	7.85149e6i	0.592915	+	1.02696i	0.993837	+	0.110847i	$0.0353564\pi$
$197$	4.53306e6	+	7.85149e6i	0.592915	+	1.02696i	−0.400922	+	0.916112i	$0.631310\pi$
$198$	−1.40894e7	+	3.77525e6i	−1.81509	+	0.486351i
$199$	3.21520e6	−	3.21520e6i	0.407989	−	0.407989i	−0.473047	−	0.881037i	$-0.656846\pi$
$199$	3.21520e6	−	3.21520e6i	0.407989	−	0.407989i	0.881037	+	0.473047i	$0.156846\pi$
$200$	1.13450e7	+	3.03990e6i	1.41813	+	0.379987i
$201$	1.35049e6	+	2.33911e6i	0.166304	+	0.288046i
$202$	1.48293e6	−	5.53438e6i	0.179915	−	0.671452i
$203$	3.12657e6	+	1.16685e7i	0.373749	+	1.39485i
$204$	−9.61017e6	+	2.57504e6i	−1.13198	+	0.303314i
$205$	3.50761e6	+	939861.i	0.407145	+	0.109094i
$206$	1.65949e7	−	9.58104e6i	1.89833	−	1.09600i
$207$	841782.	−	3.14157e6i	0.0949048	−	0.354190i
$208$	1.74572e6	+	1.74572e6i	0.193992	+	0.193992i
$209$	−263970.	−	985149.i	−0.0289145	−	0.107910i
$210$	2.89084e6	−	1.66903e6i	0.312152	−	0.180221i
$211$	−1.63245e7			−1.73777			−0.868885	−	0.495015i	$-0.835163\pi$
$211$	−1.63245e7			−1.73777			−0.868885	+	0.495015i	$0.835163\pi$
$212$		−	1.87260e7i		−	1.96534i
$213$	2.20696e6	−	1.27419e6i	0.228378	−	0.131854i
$214$	6.07213e6	−	6.07213e6i	0.619583	−	0.619583i
$215$	−6.70235e6	−	3.86960e6i	−0.674391	−	0.389360i
$216$	−9.80114e6	+	9.80114e6i	−0.972558	+	0.972558i
$217$	2.32430e6	+	8.67442e6i	0.227465	+	0.848910i
$218$	−1.26021e7	+	2.18274e7i	−1.21639	+	2.10684i
$219$	−2.84380e6	+	4.92560e6i	−0.270749	+	0.468951i
$220$	4.31683e6	−	1.61106e7i	0.405412	−	1.51302i
$221$			2.59206e6i			0.240142i
$222$	6.12770e6	+	1.28030e6i	0.560065	+	0.117018i
$223$	−644914.			−0.0581550			−0.0290775	−	0.999577i	$-0.509257\pi$
$223$	−644914.			−0.0581550			−0.0290775	+	0.999577i	$0.509257\pi$
$224$	−1.24186e7	−	3.32756e6i	−1.10492	−	0.296061i
$225$	5.69884e6	+	3.29023e6i	0.500309	+	0.288854i
$226$	2.77666e7	+	1.60311e7i	2.40546	+	1.38879i
$227$	−7.75726e6	+	2.07855e6i	−0.663179	+	0.177698i	−0.574680	−	0.818378i	$-0.694874\pi$
$227$	−7.75726e6	+	2.07855e6i	−0.663179	+	0.177698i	−0.0884989	+	0.996076i	$0.528207\pi$
$228$	−581074.	−	581074.i	−0.0490260	−	0.0490260i
$229$	−3.38020e6	+	5.85467e6i	−0.281472	+	0.487524i	−0.971748	−	0.236023i	$-0.924156\pi$
$229$	−3.38020e6	+	5.85467e6i	−0.281472	+	0.487524i	0.690275	+	0.723547i	$0.257489\pi$
$230$	3.79054e6	+	3.79054e6i	0.311543	+	0.311543i
$231$	2.37492e6	+	4.11347e6i	0.192669	+	0.333713i
$232$	3.91568e7			3.13576
$233$		−	1.82822e7i		−	1.44531i	−0.691211	−	0.722653i	$-0.742922\pi$
$233$		−	1.82822e7i		−	1.44531i	0.691211	−	0.722653i	$-0.257078\pi$
$234$	1.53097e6	+	2.65171e6i	0.119486	+	0.206956i
$235$	−4.43787e6	+	1.18912e6i	−0.341956	+	0.0916269i
$236$	−1.32013e7	+	1.32013e7i	−1.00434	+	1.00434i
$237$	−1.18914e6	−	318628.i	−0.0893278	−	0.0239353i
$238$	−2.09555e7	−	3.62960e7i	−1.55442	−	2.69233i
$239$	−5.23081e6	+	1.95217e7i	−0.383156	+	1.42996i	0.457897	+	0.889005i	$0.348603\pi$
$239$	−5.23081e6	+	1.95217e7i	−0.383156	+	1.42996i	−0.841053	+	0.540952i	$0.818064\pi$
$240$	−1.26506e6	−	4.72127e6i	−0.0915119	−	0.341527i
$241$	−7.07252e6	+	1.89508e6i	−0.505269	+	0.135387i	−0.502445	−	0.864609i	$-0.667566\pi$
$241$	−7.07252e6	+	1.89508e6i	−0.505269	+	0.135387i	−0.00282499	+	0.999996i	$0.500899\pi$
$242$	8.30634e6	+	2.22568e6i	0.586089	+	0.157042i
$243$	−1.02655e7	+	5.92679e6i	−0.715420	+	0.413048i
$244$	1.30835e7	−	4.88284e7i	0.900650	−	3.36127i
$245$	676805.	+	676805.i	0.0460220	+	0.0460220i
$246$	1.55321e6	+	5.79666e6i	0.104334	+	0.389379i
$247$	−185411.	+	107047.i	−0.0123039	+	0.00710368i
$248$	2.91094e7			1.90844
$249$		−	9.43074e6i		−	0.610869i
$250$	−2.40218e7	+	1.38690e7i	−1.53739	+	0.887614i
$251$	−7.03122e6	+	7.03122e6i	−0.444641	+	0.444641i	−0.893568	−	0.448927i	$-0.851806\pi$
$251$	−7.03122e6	+	7.03122e6i	−0.444641	+	0.444641i	0.448927	+	0.893568i	$0.351806\pi$
$252$	−2.97452e7	−	1.71734e7i	−1.85872	−	1.07313i
$253$	−5.39369e6	+	5.39369e6i	−0.333061	+	0.333061i
$254$	−5.95371e6	−	2.22196e7i	−0.363318	−	1.35592i
$255$	2.56591e6	−	4.44429e6i	0.154747	−	0.268029i
$256$	1.46334e7	−	2.53458e7i	0.872219	−	1.51073i
$257$	−3.62980e6	+	1.35466e7i	−0.213837	+	0.798052i	0.772735	+	0.634729i	$0.218888\pi$
$257$	−3.62980e6	+	1.35466e7i	−0.213837	+	0.798052i	−0.986573	+	0.163324i	$0.947779\pi$
$258$		−	1.27898e7i		−	0.744738i
$259$	1.02078e6	+	1.82661e7i	0.0587535	+	1.05135i
$260$	−3.50119e6			−0.199203
$261$	2.11906e7	+	5.67802e6i	1.19185	+	0.319356i
$262$	4.48986e7	+	2.59222e7i	2.49648	+	1.44135i
$263$	−1.21949e7	−	7.04073e6i	−0.670365	−	0.387035i	0.125850	−	0.992049i	$-0.459834\pi$
$263$	−1.21949e7	−	7.04073e6i	−0.670365	−	0.387035i	−0.796215	+	0.605014i	$0.793168\pi$
$264$	1.48716e7	−	3.98483e6i	0.808250	−	0.216570i
$265$	6.82990e6	+	6.82990e6i	0.367009	+	0.367009i
$266$	1.73084e6	−	2.99791e6i	0.0919629	−	0.159284i
$267$	1.09694e6	+	1.09694e6i	0.0576301	+	0.0576301i
$268$	2.29032e7	+	3.96694e7i	1.18985	+	2.06088i
$269$	1.92701e7			0.989983			0.494991	−	0.868898i	$-0.335171\pi$
$269$	1.92701e7			0.989983			0.494991	+	0.868898i	$0.335171\pi$
$270$		−	1.27996e7i		−	0.650289i
$271$	8.89579e6	+	1.54080e7i	0.446968	+	0.774172i	0.998187	−	0.0601889i	$-0.0191703\pi$
$271$	8.89579e6	+	1.54080e7i	0.446968	+	0.774172i	−0.551219	+	0.834361i	$0.685837\pi$
$272$	−5.92781e7	+	1.58835e7i	−2.94569	+	0.789296i
$273$	705033.	−	705033.i	0.0346515	−	0.0346515i
$274$	−5.22037e7	−	1.39879e7i	−2.53775	−	0.679989i
$275$	−7.71655e6	−	1.33655e7i	−0.371044	−	0.642667i
$276$	−1.59069e6	+	5.93653e6i	−0.0756586	+	0.282362i
$277$	−4.25558e6	−	1.58820e7i	−0.200225	−	0.747251i	−0.990852	−	0.134953i	$-0.956912\pi$
$277$	−4.25558e6	−	1.58820e7i	−0.200225	−	0.747251i	0.790627	−	0.612299i	$-0.209755\pi$
$278$	−2.29592e7	+	6.15190e6i	−1.06862	+	0.286335i
$279$	1.57532e7	+	4.22106e6i	0.725366	+	0.194361i
$280$	2.73847e7	−	1.58106e7i	1.24748	−	0.720233i
$281$	9.08100e6	−	3.38907e7i	0.409274	−	1.52743i	−0.386759	−	0.922181i	$-0.626406\pi$
$281$	9.08100e6	−	3.38907e7i	0.409274	−	1.52743i	0.796034	−	0.605252i	$-0.206928\pi$
$282$	−5.36886e6	−	5.36886e6i	−0.239406	−	0.239406i
$283$	−1.05811e7	−	3.94891e7i	−0.466843	−	1.74228i	−0.650707	−	0.759329i	$-0.725527\pi$
$283$	−1.05811e7	−	3.94891e7i	−0.466843	−	1.74228i	0.183864	−	0.982952i	$-0.441139\pi$
$284$	3.74282e7	−	2.16092e7i	1.63397	−	0.943373i
$285$	423868.			0.0183103
$286$		−	7.18114e6i		−	0.306969i
$287$	−1.51884e7	+	8.76904e6i	−0.642491	+	0.370942i
$288$	−1.65099e7	+	1.65099e7i	−0.691140	+	0.691140i
$289$	−3.48968e7	−	2.01477e7i	−1.44574	−	0.834701i
$290$	−2.55681e7	+	2.55681e7i	−1.04834	+	1.04834i
$291$	3.45139e6	+	1.28807e7i	0.140060	+	0.522712i
$292$	−4.82286e7	+	8.35343e7i	−1.93712	+	3.35518i
$293$	−4.64522e6	+	8.04576e6i	−0.184673	+	0.319863i	−0.943466	−	0.331468i	$-0.892456\pi$
$293$	−4.64522e6	+	8.04576e6i	−0.184673	+	0.319863i	0.758793	+	0.651332i	$0.225789\pi$
$294$	−409394.	+	1.52788e6i	−0.0161101	+	0.0601238i
$295$		−	9.62976e6i		−	0.375102i
$296$	5.80472e7	+	1.21282e7i	2.23824	+	0.467650i
$297$	1.82130e7			0.695206
$298$	2.28439e7	+	6.12100e6i	0.863219	+	0.231299i
$299$	1.38669e6	+	800603.i	0.0518757	+	0.0299505i
$300$	−1.07689e7	−	6.21744e6i	−0.398849	−	0.230276i
$301$	3.61040e7	−	9.67403e6i	1.32390	−	0.354738i
$302$	4.86915e7	+	4.86915e7i	1.76780	+	1.76780i
$303$	−1.69415e6	+	2.93436e6i	−0.0609011	+	0.105484i
$304$	−3.58422e6	−	3.58422e6i	−0.127577	−	0.127577i
$305$	1.30372e7	+	2.25811e7i	0.459498	+	0.795875i
$306$	−7.61128e7			−2.65640
$307$		−	2.89688e6i		−	0.100119i	−0.998746	−	0.0500594i	$-0.984059\pi$
$307$		−	2.89688e6i		−	0.100119i	0.998746	−	0.0500594i	$-0.0159411\pi$
$308$	4.02767e7	+	6.97612e7i	1.37848	+	2.38760i
$309$	−1.09457e7	+	2.93290e6i	−0.370996	+	0.0994080i
$310$	−1.90074e7	+	1.90074e7i	−0.638026	+	0.638026i
$311$	8.56291e6	+	2.29443e6i	0.284669	+	0.0762769i	0.398328	−	0.917243i	$-0.369590\pi$
$311$	8.56291e6	+	2.29443e6i	0.284669	+	0.0762769i	−0.113659	+	0.993520i	$0.536257\pi$
$312$	−1.61596e6	−	2.79892e6i	−0.0532067	−	0.0921567i
$313$	1.51586e6	−	5.65727e6i	0.0494341	−	0.184491i	−0.936794	−	0.349881i	$-0.886222\pi$
$313$	1.51586e6	−	5.65727e6i	0.0494341	−	0.184491i	0.986228	+	0.165391i	$0.0528886\pi$
$314$	9.54766e6	+	3.56324e7i	0.308396	+	1.15095i
$315$	1.71125e7	−	4.58529e6i	0.547498	−	0.146702i
$316$	−2.01668e7	−	5.40368e6i	−0.639110	−	0.171249i
$317$	3.39898e7	−	1.96240e7i	1.06702	−	0.616042i	0.139652	−	0.990201i	$-0.455402\pi$
$317$	3.39898e7	−	1.96240e7i	1.06702	−	0.616042i	0.927365	+	0.374158i	$0.122068\pi$
$318$	−4.13135e6	+	1.54184e7i	−0.128473	+	0.479466i
$319$	−3.63817e7	−	3.63817e7i	−1.12076	−	1.12076i
$320$	−489593.	−	1.82719e6i	−0.0149412	−	0.0557613i
$321$	−4.39789e6	+	2.53912e6i	−0.132963	+	0.0767660i
$322$	−2.58899e7			−0.775466
$323$		−	5.32190e6i		−	0.157928i
$324$	−4.73292e7	+	2.73255e7i	−1.39153	+	0.803402i
$325$	−2.29079e6	+	2.29079e6i	−0.0667321	+	0.0667321i
$326$	−3.36216e7	−	1.94115e7i	−0.970434	−	0.560280i
$327$	1.05394e7	−	1.05394e7i	0.301419	−	0.301419i
$328$	1.47134e7	+	5.49113e7i	0.416958	+	1.55611i
$329$	1.10947e7	−	1.92166e7i	0.311550	−	0.539620i
$330$	−7.10869e6	+	1.23126e7i	−0.197810	+	0.342617i
$331$	9.71942e6	−	3.62734e7i	0.268013	−	1.00024i	−0.692367	−	0.721546i	$-0.743432\pi$
$331$	9.71942e6	−	3.62734e7i	0.268013	−	1.00024i	0.960380	−	0.278693i	$-0.0899013\pi$
$332$		−	1.59938e8i		−	4.37056i
$333$	2.96550e7	+	1.49807e7i	0.803091	+	0.405695i
$334$	1.43114e7			0.384097
$335$	−2.28220e7	−	6.11514e6i	−0.607043	−	0.162657i
$336$	2.04437e7	+	1.18032e7i	0.538942	+	0.311159i
$337$	2.69121e7	+	1.55377e7i	0.703167	+	0.405974i	0.808526	−	0.588461i	$-0.200266\pi$
$337$	2.69121e7	+	1.55377e7i	0.703167	+	0.405974i	−0.105359	+	0.994434i	$0.533599\pi$
$338$	6.59440e7	−	1.76696e7i	1.70775	−	0.457591i
$339$	−1.34071e7	−	1.34071e7i	−0.344141	−	0.344141i
$340$	4.35158e7	−	7.53716e7i	1.10716	−	1.91766i
$341$	−2.70463e7	−	2.70463e7i	−0.682096	−	0.682096i
$342$	−3.14331e6	−	5.44437e6i	−0.0785793	−	0.136103i
$343$	3.78693e7			0.938437
$344$		−	1.21157e8i		−	2.97627i
$345$	−1.58505e6	−	2.74539e6i	−0.0385999	−	0.0668570i
$346$	−1.38546e8	+	3.71234e7i	−3.34477	+	0.896230i
$347$	5.63698e6	−	5.63698e6i	0.134914	−	0.134914i	−0.636425	−	0.771339i	$-0.719587\pi$
$347$	5.63698e6	−	5.63698e6i	0.134914	−	0.134914i	0.771339	+	0.636425i	$0.219587\pi$
$348$	−4.00433e7	−	1.07296e7i	−0.950150	−	0.254592i
$349$	2.01522e6	+	3.49046e6i	0.0474073	+	0.0821118i	0.888755	−	0.458382i	$-0.151571\pi$
$349$	2.01522e6	+	3.49046e6i	0.0474073	+	0.0821118i	−0.841348	+	0.540494i	$0.818237\pi$
$350$	1.35575e7	−	5.05972e7i	0.316210	−	1.18011i
$351$	−989521.	−	3.69294e6i	−0.0228825	−	0.0853987i
$352$	5.28932e7	−	1.41727e7i	1.21275	−	0.324956i
$353$	2.30367e7	+	6.17266e6i	0.523716	+	0.140329i	0.510985	−	0.859590i	$-0.329281\pi$
$353$	2.30367e7	+	6.17266e6i	0.523716	+	0.140329i	0.0127313	+	0.999919i	$0.495947\pi$
$354$	1.37820e7	−	7.95704e6i	0.310672	−	0.179367i
$355$	−5.76964e6	+	2.15326e7i	−0.128963	+	0.481295i
$356$	1.86032e7	+	1.86032e7i	0.412324	+	0.412324i
$357$	6.41479e6	+	2.39403e7i	0.140987	+	0.526169i
$358$	−6.04977e6	+	3.49284e6i	−0.131853	+	0.0761253i
$359$	5.38742e7			1.16439			0.582194	−	0.813050i	$-0.302195\pi$
$359$	5.38742e7			1.16439			0.582194	+	0.813050i	$0.302195\pi$
$360$		−	5.74257e7i		−	1.23083i
$361$	−4.03623e7	+	2.33032e7i	−0.857934	+	0.495328i
$362$	7.71063e6	−	7.71063e6i	0.162542	−	0.162542i
$363$	−4.40407e6	−	2.54269e6i	−0.0920734	−	0.0531586i
$364$	1.19568e7	−	1.19568e7i	0.247919	−	0.247919i
$365$	−1.28770e7	−	4.80576e7i	−0.264811	−	0.988289i
$366$	−2.15452e7	+	3.73173e7i	−0.439447	+	0.761145i
$367$	−4.00609e7	+	6.93876e7i	−0.810444	+	1.40373i	0.102110	+	0.994773i	$0.467441\pi$
$367$	−4.00609e7	+	6.93876e7i	−0.810444	+	1.40373i	−0.912554	+	0.408957i	$0.865893\pi$
$368$	−9.81180e6	+	3.66181e7i	−0.196882	+	0.734772i
$369$			3.18501e7i			0.633916i
$370$	−4.58222e7	+	2.99836e7i	−0.904629	+	0.591941i
$371$	−4.66492e7			−0.913528
$372$	−2.97684e7	−	7.97642e6i	−0.578265	−	0.154946i
$373$	−5.98636e6	−	3.45622e6i	−0.115355	−	0.0666002i	0.441212	−	0.897403i	$-0.354549\pi$
$373$	−5.98636e6	−	3.45622e6i	−0.115355	−	0.0666002i	−0.556567	+	0.830803i	$0.687882\pi$
$374$	1.54592e8	+	8.92535e7i	2.95509	+	1.70612i
$375$	1.58444e7	−	4.24549e6i	0.300457	−	0.0805071i
$376$	−5.08588e7	−	5.08588e7i	−0.956759	−	0.956759i
$377$	−5.40026e6	+	9.35352e6i	−0.100784	+	0.174563i
$378$	4.37116e7	+	4.37116e7i	0.809323	+	0.809323i
$379$	4.85110e7	+	8.40235e7i	0.891092	+	1.54342i	0.838568	+	0.544798i	$0.183394\pi$
$379$	4.85110e7	+	8.40235e7i	0.891092	+	1.54342i	0.0525247	+	0.998620i	$0.483273\pi$
$380$	7.18847e6			0.131004
$381$			1.36035e7i			0.245966i
$382$	−3.57778e6	−	6.19690e6i	−0.0641835	−	0.111169i
$383$	−1.27289e7	+	3.41069e6i	−0.226565	+	0.0607080i	−0.370316	−	0.928906i	$-0.620750\pi$
$383$	−1.27289e7	+	3.41069e6i	−0.226565	+	0.0607080i	0.143750	+	0.989614i	$0.454084\pi$
$384$	−1.15613e7	+	1.15613e7i	−0.204179	+	0.204179i
$385$	−4.01339e7	−	1.07539e7i	−0.703282	−	0.188444i
$386$	4.25186e6	+	7.36444e6i	0.0739294	+	0.128050i
$387$	1.75686e7	−	6.55668e7i	0.303112	−	1.13123i
$388$	5.85327e7	+	2.18447e8i	1.00208	+	3.73982i
$389$	−2.98113e7	+	7.98793e6i	−0.506446	+	0.135702i	−0.502990	−	0.864292i	$-0.667767\pi$
$389$	−2.98113e7	+	7.98793e6i	−0.506446	+	0.135702i	−0.00345581	+	0.999994i	$0.501100\pi$
$390$	2.88277e6	+	772436.i	0.0485977	+	0.0130217i
$391$	−3.44699e7	+	1.99012e7i	−0.576647	+	0.332927i
$392$	−3.87815e6	+	1.44735e7i	−0.0643824	+	0.240278i
$393$	−2.16793e7	−	2.16793e7i	−0.357163	−	0.357163i
$394$	−3.39214e7	−	1.26596e8i	−0.554607	−	2.06982i
$395$	9.32627e6	−	5.38453e6i	0.151327	−	0.0873688i
$396$	1.46289e8			2.35574
$397$			5.96626e7i			0.953522i	0.879033	+	0.476761i	$0.158189\pi$
$397$			5.96626e7i			0.953522i	−0.879033	+	0.476761i	$0.841811\pi$
$398$	−5.69259e7	+	3.28662e7i	−0.902944	+	0.521315i
$399$	−1.44754e6	+	1.44754e6i	−0.0227883	+	0.0227883i
$400$	−6.64256e7	−	3.83508e7i	−1.03790	−	0.599232i
$401$	−1.62832e7	+	1.62832e7i	−0.252526	+	0.252526i	−0.822005	−	0.569480i	$-0.807145\pi$
$401$	−1.62832e7	+	1.62832e7i	−0.252526	+	0.252526i	0.569480	+	0.822005i	$0.307145\pi$
$402$	−1.01058e7	−	3.77155e7i	−0.155559	−	0.580553i
$403$	−4.01458e6	+	6.95345e6i	−0.0613373	+	0.106239i
$404$	−2.87315e7	+	4.97644e7i	−0.435727	+	0.754701i
$405$	7.29590e6	−	2.72287e7i	0.109828	−	0.409884i
$406$		−	1.74634e8i		−	2.60945i
$407$	−4.26647e7	−	6.52020e7i	−0.632827	−	0.967114i
$408$	8.03382e7			1.18288
$409$	27515.4	+	7372.73i	0.000402167	+	0.000107760i	0.259020	−	0.965872i	$-0.416600\pi$
$409$	27515.4	+	7372.73i	0.000402167	+	0.000107760i	−0.258618	+	0.965980i	$0.583267\pi$
$410$	−4.54626e7	−	2.62478e7i	−0.659634	−	0.380840i
$411$	2.76787e7	+	1.59803e7i	0.398676	+	0.230176i
$412$	−1.85631e8	+	4.97396e7i	−2.65435	+	0.711231i
$413$	3.28863e7	+	3.28863e7i	0.466837	+	0.466837i
$414$	−2.35087e7	+	4.07183e7i	−0.331305	+	0.573838i
$415$	5.83339e7	+	5.83339e7i	0.816162	+	0.816162i
$416$	−5.74741e6	−	9.95481e6i	−0.0798348	−	0.138278i
$417$	1.40563e7			0.193849
$418$			1.47440e7i			0.201876i
$419$	2.85370e7	+	4.94276e7i	0.387942	+	0.671935i	0.992173	−	0.124874i	$-0.0398527\pi$
$419$	2.85370e7	+	4.94276e7i	0.387942	+	0.671935i	−0.604231	+	0.796810i	$0.706519\pi$
$420$	−3.23370e7	+	8.66468e6i	−0.436468	+	0.116951i
$421$	1.51763e7	−	1.51763e7i	0.203385	−	0.203385i	−0.598064	−	0.801449i	$-0.704063\pi$
$421$	1.51763e7	−	1.51763e7i	0.203385	−	0.203385i	0.801449	+	0.598064i	$0.204063\pi$
$422$	2.27950e8	+	6.10790e7i	3.03321	+	0.812746i
$423$	−2.01486e7	−	3.48983e7i	−0.266209	−	0.461088i
$424$	−3.91360e7	+	1.46057e8i	−0.513427	+	1.91613i
$425$	−2.08429e7	−	7.77867e7i	−0.271513	−	1.01330i
$426$	−3.55847e7	+	9.53489e6i	−0.460293	+	0.123335i
$427$	−1.21639e8	−	3.25930e7i	−1.56239	−	0.418640i
$428$	−7.45847e7	+	4.30615e7i	−0.951303	+	0.549235i
$429$	−1.09913e6	+	4.10199e6i	−0.0139212	+	0.0519545i
$430$	7.91112e7	+	7.91112e7i	0.995021	+	0.995021i
$431$	2.27489e7	+	8.48999e7i	0.284137	+	1.06041i	0.949468	+	0.313865i	$0.101624\pi$
$431$	2.27489e7	+	8.48999e7i	0.284137	+	1.06041i	−0.665331	+	0.746549i	$0.731709\pi$
$432$	7.83907e7	−	4.52589e7i	0.972329	−	0.561375i
$433$	−9.11615e6			−0.112292			−0.0561459	−	0.998423i	$-0.517881\pi$
$433$	−9.11615e6			−0.112292			−0.0561459	+	0.998423i	$0.517881\pi$
$434$		−	1.29823e8i		−	1.58812i
$435$	1.85183e7	−	1.06916e7i	0.224975	−	0.129889i
$436$	1.78739e8	−	1.78739e8i	2.15655	−	2.15655i
$437$	−2.84708e6	−	1.64376e6i	−0.0341157	−	0.0196967i
$438$	5.81394e7	−	5.81394e7i	0.691907	−	0.691907i
$439$	−1.54314e7	−	5.75909e7i	−0.182395	−	0.680707i	−0.995173	−	0.0981340i	$-0.968713\pi$
$439$	−1.54314e7	−	5.75909e7i	−0.182395	−	0.680707i	0.812778	−	0.582573i	$-0.197954\pi$
$440$	−6.73401e7	+	1.16636e8i	−0.790525	+	1.36923i
$441$	−4.19751e6	+	7.27030e6i	−0.0489414	+	0.0847689i
$442$	9.69835e6	−	3.61947e7i	0.112313	−	0.419159i
$443$			6.57139e7i			0.755868i	0.925832	+	0.377934i	$0.123365\pi$
$443$			6.57139e7i			0.755868i	−0.925832	+	0.377934i	$0.876635\pi$
$444$	−5.60381e7	−	2.83086e7i	−0.640228	−	0.323422i
$445$	−1.35702e7			−0.153995
$446$	9.00538e6	+	2.41298e6i	0.101507	+	0.0271988i
$447$	−1.21120e7	−	6.99284e6i	−0.135610	−	0.0782945i
$448$	7.91197e6	+	4.56798e6i	0.0879935	+	0.0508030i
$449$	−7.52407e7	+	2.01607e7i	−0.831216	+	0.222724i	−0.649244	−	0.760580i	$-0.724915\pi$
$449$	−7.52407e7	+	2.01607e7i	−0.831216	+	0.222724i	−0.181972	+	0.983304i	$0.558248\pi$
$450$	−6.72662e7	−	6.72662e7i	−0.738175	−	0.738175i
$451$	3.73490e7	−	6.46903e7i	0.407145	−	0.705196i
$452$	−2.27374e8	−	2.27374e8i	−2.46221	−	2.46221i
$453$	−2.03609e7	−	3.52661e7i	−0.219029	−	0.379369i
$454$	1.16097e8			1.24066
$455$			8.72196e6i			0.0925934i
$456$	3.31781e6	+	5.74661e6i	0.0349910	+	0.0606063i
$457$	1.20907e8	−	3.23970e7i	1.26679	−	0.339435i	0.437988	−	0.898981i	$-0.355691\pi$
$457$	1.20907e8	−	3.23970e7i	1.26679	−	0.339435i	0.828799	+	0.559546i	$0.189024\pi$
$458$	6.91056e7	−	6.91056e7i	0.719311	−	0.719311i
$459$	9.17983e7	+	2.45973e7i	0.949285	+	0.254360i
$460$	−2.68812e7	−	4.65596e7i	−0.276169	−	0.478339i
$461$	−2.90689e7	+	1.08487e8i	−0.296706	+	1.10732i	0.643147	+	0.765742i	$0.277628\pi$
$461$	−2.90689e7	+	1.08487e8i	−0.296706	+	1.10732i	−0.939853	+	0.341579i	$0.889038\pi$
$462$	−1.77718e7	−	6.63251e7i	−0.180221	−	0.672593i
$463$	7.90964e7	−	2.11938e7i	0.796919	−	0.213534i	0.162688	−	0.986678i	$-0.447984\pi$
$463$	7.90964e7	−	2.11938e7i	0.796919	−	0.213534i	0.634231	+	0.773144i	$0.281317\pi$
$464$	−2.46998e8	−	6.61829e7i	−2.47252	−	0.662509i
$465$	1.37666e7	−	7.94815e6i	0.136920	−	0.0790510i
$466$	−6.84038e7	+	2.55286e8i	−0.675962	+	2.52273i
$467$	−2.30406e7	−	2.30406e7i	−0.226226	−	0.226226i	0.584888	−	0.811114i	$-0.301138\pi$
$467$	−2.30406e7	−	2.30406e7i	−0.226226	−	0.226226i	−0.811114	+	0.584888i	$0.801138\pi$
$468$	−7.94795e6	−	2.96621e7i	−0.0775385	−	0.289378i
$469$	9.88224e7	−	5.70551e7i	0.957937	−	0.553065i
$470$	6.64182e7			0.639725
$471$		−	2.18152e7i		−	0.208783i
$472$	1.30556e8	−	7.53765e7i	1.24157	−	0.716820i
$473$	−1.12570e8	+	1.12570e8i	−1.06375	+	1.06375i
$474$	1.54126e7	+	8.89844e6i	0.144724	+	0.0835563i
$475$	4.70333e6	−	4.70333e6i	0.0438859	−	0.0438859i
$476$	1.08790e8	+	4.06009e8i	1.00871	+	3.76456i
$477$	−4.23587e7	+	7.33674e7i	−0.390290	+	0.676002i
$478$	1.46083e8	−	2.53023e8i	1.33757	−	2.31673i
$479$	−2.71159e6	+	1.01198e7i	−0.0246728	+	0.0920800i	−0.977164	−	0.212485i	$-0.931844\pi$
$479$	−2.71159e6	+	1.01198e7i	−0.0246728	+	0.0920800i	0.952492	+	0.304565i	$0.0985110\pi$
$480$			2.27577e7i			0.205781i
$481$	−1.09026e7	+	1.21933e7i	−0.0979704	+	0.109568i
$482$	1.05849e8			0.945248
$483$	1.47888e7	+	3.96264e6i	0.131247	+	0.0351676i
$484$	−7.46895e7	−	4.31220e7i	−0.658754	−	0.380332i
$485$	−1.01022e8	−	5.83253e7i	−0.885508	−	0.511248i
$486$	1.65520e8	−	4.43508e7i	1.44192	−	0.386361i
$487$	1.10250e7	+	1.10250e7i	0.0954533	+	0.0954533i	0.753221	−	0.657768i	$-0.228499\pi$
$487$	1.10250e7	+	1.10250e7i	0.0954533	+	0.0954533i	−0.657768	+	0.753221i	$0.728499\pi$
$488$	−2.04096e8	+	3.53504e8i	−1.75620	+	3.04183i
$489$	1.62342e7	+	1.62342e7i	0.138837	+	0.138837i
$490$	−6.91838e6	−	1.19830e7i	−0.0588053	−	0.101854i
$491$	−9.71305e7			−0.820562			−0.410281	−	0.911959i	$-0.634569\pi$
$491$	−9.71305e7			−0.820562			−0.410281	+	0.911959i	$0.634569\pi$
$492$		−	6.01862e7i		−	0.505361i
$493$	−1.34238e8	−	2.32508e8i	−1.12030	−	1.94042i
$494$	2.98954e6	−	801045.i	0.0247984	−	0.00664471i
$495$	−5.33558e7	+	5.33558e7i	−0.439912	+	0.439912i
$496$	−1.83619e8	−	4.92007e7i	−1.50478	−	0.403205i
$497$	−5.38316e7	−	9.32391e7i	−0.438499	−	0.759502i
$498$	−3.52857e7	+	1.31688e8i	−0.285700	+	1.06625i
$499$	2.55247e7	+	9.52595e7i	0.205428	+	0.766667i	0.989319	+	0.145768i	$0.0465654\pi$
$499$	2.55247e7	+	9.52595e7i	0.205428	+	0.766667i	−0.783891	+	0.620898i	$0.786768\pi$
$500$	2.68708e8	−	7.20002e7i	2.14967	−	0.576001i
$501$	−8.17490e6	−	2.19046e6i	−0.0650084	−	0.0174189i
$502$	1.24489e8	−	7.18740e7i	0.984060	−	0.568147i
$503$	2.88213e7	−	1.07563e8i	0.226470	−	0.845196i	−0.755341	−	0.655332i	$-0.772529\pi$
$503$	2.88213e7	−	1.07563e8i	0.226470	−	0.845196i	0.981810	−	0.189864i	$-0.0608048\pi$
$504$	1.96113e8	+	1.96113e8i	1.53184	+	1.53184i
$505$	−7.67130e6	−	2.86297e7i	−0.0595655	−	0.222302i
$506$	9.54966e7	−	5.51350e7i	0.737117	−	0.425575i
$507$	−4.03728e7			−0.309788
$508$			2.30704e8i			1.75980i
$509$	349537.	−	201805.i	0.00265057	−	0.00153031i	−0.498674	−	0.866790i	$-0.666180\pi$
$509$	349537.	−	201805.i	0.00265057	−	0.00153031i	0.501325	+	0.865259i	$0.332846\pi$
$510$	−5.24582e7	+	5.24582e7i	−0.395460	+	0.395460i
$511$	2.08096e8	+	1.20144e8i	1.55956	+	0.900411i
$512$	−2.12618e8	+	2.12618e8i	−1.58413	+	1.58413i
$513$	2.03164e6	+	7.58217e6i	0.0150485	+	0.0561619i
$514$	1.01371e8	−	1.75579e8i	0.746490	−	1.29296i
$515$	4.95633e7	−	8.58462e7i	0.362860	−	0.628492i
$516$	−3.31988e7	+	1.23900e8i	−0.241642	+	0.901822i
$517$			9.45087e7i			0.683912i
$518$	5.40899e7	−	2.58882e8i	0.389159	−	1.86257i
$519$	8.48221e7			0.606746
$520$	2.73083e7	+	7.31722e6i	0.194215	+	0.0520399i
$521$	1.83007e8	+	1.05659e8i	1.29406	+	0.747126i	0.979371	−	0.202069i	$-0.0647665\pi$
$521$	1.83007e8	+	1.05659e8i	1.29406	+	0.747126i	0.314689	+	0.949195i	$0.398100\pi$
$522$	−2.74655e8	−	1.58572e8i	−1.93097	−	1.11485i
$523$	−1.16992e8	+	3.13479e7i	−0.817807	+	0.219131i	−0.643387	−	0.765541i	$-0.722471\pi$
$523$	−1.16992e8	+	3.13479e7i	−0.817807	+	0.219131i	−0.174419	+	0.984671i	$0.555805\pi$
$524$	−3.67663e8	−	3.67663e8i	−2.55538	−	2.55538i
$525$	−1.54886e7	+	2.68270e7i	−0.107037	+	0.185393i
$526$	1.43943e8	+	1.43943e8i	0.989081	+	0.989081i
$527$	−9.97934e7	−	1.72847e8i	−0.681821	−	1.18095i
$528$	−1.00544e8			−0.683053
$529$		−	1.23449e8i		−	0.833910i
$530$	−6.98161e7	−	1.20925e8i	−0.468951	−	0.812248i
$531$	8.15836e7	−	2.18603e7i	0.544903	−	0.146006i
$532$	−2.45491e7	+	2.45491e7i	−0.163043	+	0.163043i
$533$	−1.51460e7	−	4.05837e6i	−0.100027	−	0.0268022i
$534$	−1.12131e7	−	1.94216e7i	−0.0736377	−	0.127544i
$535$	1.14974e7	−	4.29089e7i	0.0750825	−	0.280212i
$536$	−9.57319e7	−	3.57276e8i	−0.621674	−	2.32012i
$537$	3.99034e6	−	1.06921e6i	0.0257684	−	0.00690461i
$538$	−2.69082e8	−	7.21003e7i	−1.72798	−	0.463010i
$539$	1.70510e7	−	9.84441e6i	0.108889	−	0.0628671i
$540$	−3.32244e7	+	1.23995e8i	−0.210997	+	0.787450i
$541$	7.35095e7	+	7.35095e7i	0.464250	+	0.464250i	0.900046	−	0.435796i	$-0.143533\pi$
$541$	7.35095e7	+	7.35095e7i	0.464250	+	0.464250i	−0.435796	+	0.900046i	$0.643533\pi$
$542$	−6.65683e7	−	2.48436e8i	−0.418090	−	1.56033i
$543$	−5.58462e6	+	3.22428e6i	−0.0348814	+	0.0201388i
$544$	2.85736e8			1.77488
$545$			1.30382e8i			0.805433i
$546$	−1.24828e7	+	7.20694e6i	−0.0766891	+	0.0442764i
$547$	4.64269e7	−	4.64269e7i	0.283666	−	0.283666i	−0.550903	−	0.834569i	$-0.685717\pi$
$547$	4.64269e7	−	4.64269e7i	0.283666	−	0.283666i	0.834569	+	0.550903i	$0.185717\pi$
$548$	4.69409e8	+	2.71013e8i	2.85239	+	1.64683i
$549$	−1.61712e8	+	1.61712e8i	−0.977294	+	0.977294i
$550$	5.77439e7	+	2.15503e8i	0.347071	+	1.29529i
$551$	1.10875e7	−	1.92042e7i	0.0662797	−	0.114800i
$552$	2.48139e7	−	4.29789e7i	0.147529	−	0.255527i
$553$	−1.34613e7	+	5.02384e7i	−0.0796000	+	0.297071i
$554$			2.37694e8i			1.39794i
$555$	3.07636e7	−	1.01137e7i	0.179953	−	0.0591605i
$556$	2.38384e8			1.38692
$557$	2.32252e7	+	6.22318e6i	0.134398	+	0.0360119i	0.325391	−	0.945580i	$-0.394504\pi$
$557$	2.32252e7	+	6.22318e6i	0.134398	+	0.0360119i	−0.190993	+	0.981591i	$0.561171\pi$
$558$	−2.04180e8	−	1.17883e8i	−1.17520	−	0.678499i
$559$	2.89411e7	+	1.67091e7i	0.165684	+	0.0956574i
$560$	−1.99463e8	+	5.34461e7i	−1.13579	+	0.304335i
$561$	−7.46446e7	−	7.46446e7i	−0.422775	−	0.422775i
$562$	−2.53608e8	+	4.39263e8i	−1.42875	+	2.47466i
$563$	−1.09645e8	−	1.09645e8i	−0.614420	−	0.614420i	0.329674	−	0.944095i	$-0.393061\pi$
$563$	−1.09645e8	−	1.09645e8i	−0.614420	−	0.614420i	−0.944095	+	0.329674i	$0.893061\pi$
$564$	3.80741e7	+	6.59464e7i	0.212223	+	0.367581i
$565$	1.65859e8			0.919591
$566$			5.91003e8i			3.25942i
$567$	6.80718e7	+	1.17904e8i	0.373438	+	0.646813i
$568$	−3.37091e8	+	9.03232e7i	−1.83951	+	0.492895i
$569$	−1.98583e8	+	1.98583e8i	−1.07797	+	1.07797i	−0.0812767	+	0.996692i	$0.525900\pi$
$569$	−1.98583e8	+	1.98583e8i	−1.07797	+	1.07797i	−0.996692	+	0.0812767i	$0.974100\pi$
$570$	−5.91876e6	−	1.58593e6i	−0.0319600	−	0.00856365i
$571$	7.91931e7	+	1.37167e8i	0.425382	+	0.736783i	0.996456	−	0.0841153i	$-0.0268064\pi$
$571$	7.91931e7	+	1.37167e8i	0.425382	+	0.736783i	−0.571074	+	0.820899i	$0.693473\pi$
$572$	−1.86403e7	+	6.95665e7i	−0.0996012	+	0.371717i
$573$	1.09521e6	+	4.08738e6i	0.00582148	+	0.0217261i
$574$	2.44896e8	−	6.56197e7i	1.29493	−	0.346976i
$575$	−4.80516e7	−	1.28754e7i	−0.252757	−	0.0677261i
$576$	1.43686e7	−	8.29569e6i	0.0751876	−	0.0434096i
$577$	−2.89487e7	+	1.08038e8i	−0.150696	+	0.562405i	0.848740	+	0.528811i	$0.177362\pi$
$577$	−2.89487e7	+	1.08038e8i	−0.150696	+	0.562405i	−0.999436	+	0.0335940i	$0.989305\pi$
$578$	4.11904e8	+	4.11904e8i	2.13311	+	2.13311i
$579$	−1.30156e6	−	4.85748e6i	−0.00670545	−	0.0250251i
$580$	3.14056e8	−	1.81320e8i	1.60962	−	0.929313i
$581$	−3.98429e8			−2.03152
$582$		−	1.92776e8i		−	0.977878i
$583$	1.72068e8	−	9.93437e7i	0.868351	−	0.501343i
$584$	5.50750e8	−	5.50750e8i	2.76513	−	2.76513i
$585$	1.37175e7	+	7.91978e6i	0.0685182	+	0.0395590i
$586$	9.49681e7	−	9.49681e7i	0.471938	−	0.471938i
$587$	−2.73621e7	−	1.02117e8i	−0.135281	−	0.504874i	−0.999997	−	0.00261312i	$-0.999168\pi$
$587$	−2.73621e7	−	1.02117e8i	−0.135281	−	0.504874i	0.864716	−	0.502261i	$-0.167498\pi$
$588$	7.93191e6	−	1.37385e7i	0.0390163	−	0.0675782i
$589$	8.24254e6	−	1.42765e7i	0.0403381	−	0.0698676i
$590$	−3.60303e7	+	1.34467e8i	−0.175433	+	0.654726i
$591$			7.75060e7i			0.375468i
$592$	−3.45658e8	−	1.74615e8i	−1.66602	−	0.841621i
$593$	2.01437e8			0.965994			0.482997	−	0.875622i	$-0.339548\pi$
$593$	2.01437e8			0.965994			0.482997	+	0.875622i	$0.339548\pi$
$594$	−2.54321e8	−	6.81452e7i	−1.21345	−	0.325144i
$595$	−1.87762e8	−	1.08404e8i	−0.891366	−	0.514630i
$596$	−2.05409e8	−	1.18593e8i	−0.970244	−	0.560171i
$597$	3.75475e7	−	1.00608e7i	0.176465	−	0.0472836i
$598$	−1.63677e7	−	1.63677e7i	−0.0765394	−	0.0765394i
$599$	6.03028e7	−	1.04447e8i	0.280580	−	0.485979i	−0.690948	−	0.722905i	$-0.742807\pi$
$599$	6.03028e7	−	1.04447e8i	0.280580	−	0.485979i	0.971528	+	0.236926i	$0.0761399\pi$
$600$	7.10005e7	+	7.10005e7i	0.328706	+	0.328706i
$601$	1.97854e7	+	3.42693e7i	0.0911426	+	0.157864i	0.907992	−	0.418987i	$-0.137615\pi$
$601$	1.97854e7	+	3.42693e7i	0.0911426	+	0.157864i	−0.816850	+	0.576851i	$0.804281\pi$
$602$	−5.40340e8			−2.47673
$603$		−	2.07230e8i		−	0.945152i
$604$	−3.45304e8	−	5.98084e8i	−1.56708	−	2.71426i
$605$	4.29692e7	−	1.15136e7i	0.194040	−	0.0519928i
$606$	3.46357e7	−	3.46357e7i	0.155635	−	0.155635i
$607$	3.17176e8	+	8.49870e7i	1.41819	+	0.380002i	0.884841	−	0.465894i	$-0.154267\pi$
$607$	3.17176e8	+	8.49870e7i	1.41819	+	0.380002i	0.533347	+	0.845896i	$0.320934\pi$
$608$	1.18003e7	+	2.04387e7i	0.0525028	+	0.0909376i
$609$	−2.67289e7	+	9.97538e7i	−0.118340	+	0.441649i
$610$	−9.75587e7	−	3.64094e8i	−0.429810	−	1.60407i
$611$	1.91629e7	−	5.13469e6i	0.0840114	−	0.0225108i
$612$	7.37335e8	+	1.97568e8i	3.21670	+	0.861912i
$613$	6.28008e7	−	3.62580e7i	0.272636	−	0.157407i	−0.357449	−	0.933933i	$-0.616353\pi$
$613$	6.28008e7	−	3.62580e7i	0.272636	−	0.157407i	0.630085	+	0.776526i	$0.283020\pi$
$614$	−1.08389e7	+	4.04511e7i	−0.0468250	+	0.174753i
$615$	2.19516e7	+	2.19516e7i	0.0943716	+	0.0943716i
$616$	−1.68351e8	−	6.28293e8i	−0.720232	−	2.68794i
$617$	−2.33643e8	+	1.34894e8i	−0.994713	+	0.574298i	−0.906680	−	0.421819i	$-0.861392\pi$
$617$	−2.33643e8	+	1.34894e8i	−0.994713	+	0.574298i	−0.0880336	+	0.996118i	$0.528058\pi$
$618$	1.63816e8			0.694051
$619$			3.78472e8i			1.59574i	0.602831	+	0.797869i	$0.294039\pi$
$619$			3.78472e8i			1.59574i	−0.602831	+	0.797869i	$0.705961\pi$
$620$	2.33471e8	−	1.34794e8i	0.979619	−	0.565583i
$621$	4.15124e7	−	4.15124e7i	0.173342	−	0.173342i
$622$	−1.10985e8	−	6.40773e7i	−0.461205	−	0.266277i
$623$	4.63434e7	−	4.63434e7i	0.191656	−	0.191656i
$624$	5.46259e6	+	2.03867e7i	0.0224825	+	0.0839059i
$625$	6.63367e6	−	1.14899e7i	0.0271715	−	0.0470625i
$626$	−4.23340e7	+	7.33247e7i	−0.172571	+	0.298901i
$627$	2.25667e6	−	8.42201e6i	0.00915516	−	0.0341675i
$628$		−	3.69968e8i		−	1.49377i
$629$	−1.26983e8	−	3.86254e8i	−0.510264	−	1.55211i
$630$	−2.56110e8			−1.02425
$631$	2.53117e8	+	6.78224e7i	1.00747	+	0.269951i	0.724573	−	0.689199i	$-0.242037\pi$
$631$	2.53117e8	+	6.78224e7i	1.00747	+	0.269951i	0.282899	+	0.959150i	$0.408704\pi$
$632$	1.46002e8	+	8.42943e7i	0.578372	+	0.333923i
$633$	−1.20860e8	−	6.97788e7i	−0.476511	−	0.275114i
$634$	−5.48048e8	+	1.46849e8i	−2.15056	+	0.576240i
$635$	−8.41442e7	−	8.41442e7i	−0.328627	−	0.328627i
$636$	8.00440e7	−	1.38640e8i	0.311141	−	0.538912i
$637$	−2.92248e6	−	2.92248e6i	−0.0113066	−	0.0113066i
$638$	3.71898e8	+	6.44147e8i	1.43206	+	2.48041i
$639$	−1.95522e8			−0.749366
$640$		−	1.43025e8i		−	0.545595i
$641$	−1.46138e8	−	2.53119e8i	−0.554869	−	0.961061i	−0.997914	−	0.0645616i	$-0.979435\pi$
$641$	−1.46138e8	−	2.53119e8i	−0.554869	−	0.961061i	0.443045	−	0.896499i	$-0.353898\pi$
$642$	7.09111e7	−	1.90006e7i	0.267984	−	0.0718061i
$643$	2.50657e8	−	2.50657e8i	0.942858	−	0.942858i	−0.0555950	−	0.998453i	$-0.517706\pi$
$643$	2.50657e8	−	2.50657e8i	0.942858	−	0.942858i	0.998453	+	0.0555950i	$0.0177056\pi$
$644$	2.50806e8	+	6.72032e7i	0.939031	+	0.251613i
$645$	−3.30811e7	−	5.72982e7i	−0.123282	−	0.213532i
$646$	−1.99122e7	+	7.43133e7i	−0.0738621	+	0.275657i
$647$	7.78185e7	+	2.90423e8i	0.287323	+	1.07230i	0.947125	+	0.320864i	$0.103973\pi$
$647$	7.78185e7	+	2.90423e8i	0.287323	+	1.07230i	−0.659803	+	0.751439i	$0.729360\pi$
$648$	4.26262e8	−	1.14217e8i	1.56658	−	0.419763i
$649$	−1.91338e8	−	5.12688e7i	−0.699949	−	0.187551i
$650$	4.05589e7	−	2.34167e7i	0.147688	−	0.0852680i
$651$	−1.98704e7	+	7.41574e7i	−0.0720218	+	0.268789i
$652$	2.75319e8	+	2.75319e8i	0.993330	+	0.993330i
$653$	3.16334e7	+	1.18057e8i	0.113607	+	0.423988i	0.999179	−	0.0405149i	$-0.0128998\pi$
$653$	3.16334e7	+	1.18057e8i	0.113607	+	0.423988i	−0.885572	+	0.464503i	$0.846233\pi$
$654$	−1.86602e8	+	1.07735e8i	−0.667088	+	0.385143i
$655$	2.68194e8			0.954389
$656$		−	3.71245e8i		−	1.31507i
$657$	3.77914e8	−	2.18189e8i	1.33259	−	0.769372i
$658$	−2.26823e8	+	2.26823e8i	−0.796176	+	0.796176i
$659$	−2.01051e8	−	1.16077e8i	−0.702506	−	0.405592i	0.105774	−	0.994390i	$-0.466268\pi$
$659$	−2.01051e8	−	1.16077e8i	−0.702506	−	0.405592i	−0.808280	+	0.588798i	$0.799601\pi$
$660$	1.00825e8	−	1.00825e8i	0.350700	−	0.350700i
$661$	−2.23759e7	−	8.35080e7i	−0.0774776	−	0.289150i	0.916306	−	0.400479i	$-0.131156\pi$
$661$	−2.23759e7	−	8.35080e7i	−0.0774776	−	0.289150i	−0.993784	+	0.111328i	$0.964489\pi$
$662$	−2.71438e8	+	4.70144e8i	−0.935613	+	1.62053i
$663$	−1.10797e7	+	1.91907e7i	−0.0380180	+	0.0658491i
$664$	−3.34259e8	+	1.24747e9i	−1.14177	+	4.26114i
$665$		−	1.79075e7i		−	0.0608934i
$666$	−3.58041e8	−	3.20142e8i	−1.21202	−	1.08373i
$667$	−1.65847e8			−0.558896
$668$	−1.38640e8	−	3.71484e7i	−0.465113	−	0.124627i
$669$	−4.77471e6	−	2.75668e6i	−0.0159466	−	0.00920678i
$670$	2.95799e8	+	1.70780e8i	0.983496	+	0.567822i
$671$	5.18082e8	−	1.38820e8i	1.71487	−	0.459498i
$672$	−7.77192e7	−	7.77192e7i	−0.256107	−	0.256107i
$673$	2.10155e7	−	3.64000e7i	0.0689439	−	0.119414i	−0.829493	−	0.558517i	$-0.811370\pi$
$673$	2.10155e7	−	3.64000e7i	0.0689439	−	0.119414i	0.898437	+	0.439103i	$0.144704\pi$
$674$	−3.17657e8	−	3.17657e8i	−1.03748	−	1.03748i
$675$	5.93903e7	+	1.02867e8i	0.193110	+	0.334476i
$676$	−6.84691e8			−2.21643
$677$			3.01560e8i			0.971869i	0.873995	+	0.485935i	$0.161521\pi$
$677$			3.01560e8i			0.971869i	−0.873995	+	0.485935i	$0.838479\pi$
$678$	1.37049e8	+	2.37376e8i	0.439731	+	0.761637i
$679$	5.44184e8	−	1.45814e8i	1.73835	−	0.465788i
$680$	−4.96932e8	+	4.96932e8i	−1.58041	+	1.58041i
$681$	−6.63167e7	−	1.77695e7i	−0.209982	−	0.0562644i
$682$	2.76471e8	+	4.78862e8i	0.871559	+	1.50958i
$683$	1.19184e8	−	4.44803e8i	0.374074	−	1.39606i	−0.480619	−	0.876930i	$-0.659588\pi$
$683$	1.19184e8	−	4.44803e8i	0.374074	−	1.39606i	0.854693	−	0.519134i	$-0.173745\pi$
$684$	1.63183e7	+	6.09009e7i	0.0509927	+	0.190307i
$685$	−2.70053e8	+	7.23604e7i	−0.840189	+	0.225128i
$686$	−5.28795e8	−	1.41690e8i	−1.63800	−	0.438902i
$687$	−5.00515e7	+	2.88972e7i	−0.154364	+	0.0891222i
$688$	−2.04779e8	+	7.64246e8i	−0.628811	+	2.34675i
$689$	−2.94918e7	−	2.94918e7i	−0.0901663	−	0.0901663i
$690$	1.18611e7	+	4.42664e7i	0.0361060	+	0.134749i
$691$	−4.45985e8	+	2.57489e8i	−1.35172	+	0.780414i	−0.988490	−	0.151286i	$-0.951658\pi$
$691$	−4.45985e8	+	2.57489e8i	−1.35172	+	0.780414i	−0.363227	+	0.931701i	$0.618325\pi$
$692$	1.43852e9			4.34107
$693$		−	3.64428e8i		−	1.09499i
$694$	−9.98041e7	+	5.76219e7i	−0.298586	+	0.172389i
$695$	−8.69453e7	+	8.69453e7i	−0.258995	+	0.258995i
$696$	2.89903e8	+	1.67375e8i	0.859853	+	0.496436i
$697$	2.75615e8	−	2.75615e8i	0.813961	−	0.813961i
$698$	−1.50801e7	−	5.62797e7i	−0.0443443	−	0.165495i
$699$	7.81469e7	−	1.35354e8i	0.228813	−	0.396315i
$700$	−2.62673e8	+	4.54964e8i	−0.765812	+	1.32643i
$701$	1.05735e7	−	3.94608e7i	0.0306948	−	0.114554i	−0.948879	−	0.315641i	$-0.897781\pi$
$701$	1.05735e7	−	3.94608e7i	0.0306948	−	0.114554i	0.979574	+	0.201086i	$0.0644472\pi$
$702$			5.52695e7i			0.159762i
$703$	2.23847e7	−	2.50347e7i	0.0644296	−	0.0720570i
$704$	−3.89117e7			−0.111523
$705$	−3.79392e7	−	1.01658e7i	−0.108273	−	0.0290117i
$706$	−2.98582e8	−	1.72386e8i	−0.848495	−	0.489879i
$707$	1.23970e8	+	7.15744e7i	0.350800	+	0.202535i
$708$	−1.54166e8	+	4.13087e7i	−0.434399	+	0.116397i
$709$	1.21125e8	+	1.21125e8i	0.339856	+	0.339856i	0.856313	−	0.516457i	$-0.172749\pi$
$709$	1.21125e8	+	1.21125e8i	0.339856	+	0.339856i	−0.516457	+	0.856313i	$0.672749\pi$
$710$	1.61131e8	−	2.79087e8i	0.450199	−	0.779767i
$711$	6.67892e7	+	6.67892e7i	0.185822	+	0.185822i
$712$	−1.06220e8	−	1.83979e8i	−0.294285	−	0.509717i
$713$	−1.23292e8			−0.340146
$714$		−	3.58297e8i		−	0.984347i
$715$	−1.85742e7	−	3.21715e7i	−0.0508151	−	0.0880143i
$716$	6.76729e7	−	1.81329e7i	0.184364	−	0.0494002i
$717$	−1.22172e8	+	1.22172e8i	−0.331447	+	0.331447i
$718$	−7.52282e8	−	2.01573e8i	−2.03239	−	0.544578i
$719$	2.06796e8	+	3.58182e8i	0.556360	+	0.963644i	0.997796	+	0.0663512i	$0.0211358\pi$
$719$	2.06796e8	+	3.58182e8i	0.556360	+	0.963644i	−0.441436	+	0.897293i	$0.645531\pi$
$720$	−9.70610e7	+	3.62236e8i	−0.260044	+	0.970498i
$721$	1.23909e8	+	4.62433e8i	0.330594	+	1.23380i
$722$	6.50796e8	−	1.74380e8i	1.72915	−	0.463325i
$723$	−6.04628e7	−	1.62010e7i	−0.159983	−	0.0428673i
$724$	−9.47107e7	+	5.46812e7i	−0.249565	+	0.144086i
$725$	8.68474e7	−	3.24119e8i	0.227899	−	0.850532i
$726$	5.19834e7	+	5.19834e7i	0.135849	+	0.135849i
$727$	−7.61516e7	−	2.84202e8i	−0.198187	−	0.739645i	−0.991419	−	0.130725i	$-0.958270\pi$
$727$	−7.61516e7	−	2.84202e8i	−0.198187	−	0.739645i	0.793232	−	0.608920i	$-0.208397\pi$
$728$	−1.18248e8	+	6.82708e7i	−0.306479	+	0.176946i
$729$	1.73457e8			0.447724
$730$			7.19242e8i			1.84887i
$731$	−7.19411e8	+	4.15352e8i	−1.84172	+	1.06332i
$732$	3.05582e8	−	3.05582e8i	0.779103	−	0.779103i
$733$	4.05145e7	+	2.33911e7i	0.102872	+	0.0593934i	0.550554	−	0.834800i	$-0.314417\pi$
$733$	4.05145e7	+	2.33911e7i	0.102872	+	0.0593934i	−0.447681	+	0.894193i	$0.647750\pi$
$734$	8.19016e8	−	8.19016e8i	2.07112	−	2.07112i
$735$	2.11782e6	+	7.90380e6i	0.00533368	+	0.0199056i
$736$	8.82544e7	−	1.52861e8i	0.221362	−	0.383410i
$737$	−2.43008e8	+	4.20903e8i	−0.607042	+	1.05143i
$738$	1.19169e8	−	4.44745e8i	0.296479	−	1.10648i
$739$		−	4.75196e8i		−	1.17744i	−0.808336	−	0.588721i	$-0.799631\pi$
$739$		−	4.75196e8i		−	1.17744i	0.808336	−	0.588721i	$-0.200369\pi$
$740$	5.21727e8	−	1.71521e8i	1.28750	−	0.423274i
$741$	−1.83028e6			−0.00449846
$742$	6.51394e8	+	1.74541e8i	1.59453	+	0.427253i
$743$	−5.70413e8	−	3.29328e8i	−1.39067	−	0.802902i	−0.397278	−	0.917698i	$-0.630045\pi$
$743$	−5.70413e8	−	3.29328e8i	−1.39067	−	0.802902i	−0.993389	+	0.114796i	$0.963379\pi$
$744$	2.15515e8	+	1.24428e8i	0.523310	+	0.302133i
$745$	1.18173e8	−	3.16643e7i	0.285791	−	0.0765775i
$746$	7.06599e7	+	7.06599e7i	0.170199	+	0.170199i
$747$	−3.61784e8	+	6.26628e8i	−0.867936	+	1.50331i
$748$	−1.26591e9	−	1.26591e9i	−3.02481	−	3.02481i
$749$	1.07273e8	+	1.85801e8i	0.255295	+	0.442185i
$750$	−2.37131e8			−0.562088
$751$		−	6.09733e8i		−	1.43953i	−0.694220	−	0.719763i	$-0.744250\pi$
$751$		−	6.09733e8i		−	1.43953i	0.694220	−	0.719763i	$-0.255750\pi$
$752$	2.34852e8	+	4.06775e8i	0.552255	+	0.956534i
$753$	−8.21114e7	+	2.20017e7i	−0.192317	+	0.0515313i
$754$	1.10404e8	−	1.10404e8i	0.257556	−	0.257556i
$755$	3.44080e8	+	9.21961e7i	0.799501	+	0.214226i
$756$	−3.09988e8	−	5.36916e8i	−0.717431	−	1.24263i
$757$	−1.04964e8	+	3.91732e8i	−0.241966	+	0.903030i	0.732918	+	0.680317i	$0.238158\pi$
$757$	−1.04964e8	+	3.91732e8i	−0.241966	+	0.903030i	−0.974884	+	0.222713i	$0.928509\pi$
$758$	−3.63014e8	−	1.35479e9i	−0.833519	−	3.11073i
$759$	−6.29881e7	+	1.68776e7i	−0.144057	+	0.0385999i
$760$	−5.60680e7	−	1.50234e7i	−0.127725	−	0.0342237i
$761$	6.87727e8	−	3.97059e8i	1.56049	−	0.900951i	0.563287	−	0.826262i	$-0.309537\pi$
$761$	6.87727e8	−	3.97059e8i	1.56049	−	0.900951i	0.997207	−	0.0746897i	$-0.0237966\pi$
$762$	5.08981e7	−	1.89954e8i	0.115037	−	0.429323i
$763$	−4.45265e8	−	4.45265e8i	−1.00241	−	1.00241i
$764$	1.85739e7	+	6.93187e7i	0.0416508	+	0.155443i
$765$	−3.40986e8	+	1.96868e8i	−0.761643	+	0.439735i
$766$	1.90503e8			0.423854
$767$			4.15818e7i			0.0921546i
$768$	2.16681e8	−	1.25101e8i	0.478340	−	0.276170i
$769$	−2.64169e8	+	2.64169e8i	−0.580902	+	0.580902i	−0.935151	−	0.354249i	$-0.884737\pi$
$769$	−2.64169e8	+	2.64169e8i	−0.580902	+	0.580902i	0.354249	+	0.935151i	$0.384737\pi$
$770$	5.20181e8	+	3.00327e8i	1.13942	+	0.657843i
$771$	−8.47785e7	+	8.47785e7i	−0.184979	+	0.184979i
$772$	−2.20734e7	−	8.23790e7i	−0.0479752	−	0.179046i
$773$	9.04869e7	−	1.56728e8i	0.195906	−	0.339319i	−0.751291	−	0.659971i	$-0.770569\pi$
$773$	9.04869e7	−	1.56728e8i	0.195906	−	0.339319i	0.947197	+	0.320652i	$0.103902\pi$
$774$	−4.90644e8	+	8.49820e8i	−1.05814	+	1.83275i
$775$	6.45628e7	−	2.40952e8i	0.138700	−	0.517637i
$776$		−	1.82615e9i		−	3.90798i
$777$	−7.05209e7	+	1.39599e8i	−0.150333	+	0.297591i
$778$	4.46164e8			0.947448
$779$	3.10971e7	+	8.33244e6i	0.0657821	+	0.0176263i
$780$	−2.59215e7	−	1.49658e7i	−0.0546231	−	0.0315366i
$781$	3.97123e8	+	2.29279e8i	0.833627	+	0.481295i
$782$	5.55788e8	−	1.48923e8i	1.16222	−	0.311417i
$783$	2.80011e8	+	2.80011e8i	0.583297	+	0.583297i
$784$	4.89262e7	−	8.47426e7i	0.101530	−	0.175855i
$785$	1.34938e8	+	1.34938e8i	0.278949	+	0.278949i
$786$	2.21608e8	+	3.83837e8i	0.456371	+	0.790458i
$787$	−2.42932e7			−0.0498380			−0.0249190	−	0.999689i	$-0.507933\pi$
$787$	−2.42932e7			−0.0498380			−0.0249190	+	0.999689i	$0.507933\pi$
$788$			1.31444e9i			2.68635i
$789$	−6.01911e7	−	1.04254e8i	−0.122547	−	0.212257i
$790$	−1.50376e8	+	4.02930e7i	−0.304998	+	0.0817239i
$791$	−5.66422e8	+	5.66422e8i	−1.14449	+	1.14449i
$792$	−1.14101e9	−	3.05734e8i	−2.29676	−	0.615415i
$793$	−5.62952e7	−	9.75061e7i	−0.112889	−	0.195530i
$794$	2.23231e8	−	8.33110e8i	0.445958	−	1.66434i
$795$	2.13717e7	+	7.97604e7i	0.0425342	+	0.158740i
$796$	6.36776e8	−	1.70624e8i	1.26255	−	0.338298i
$797$	8.40406e8	+	2.25186e8i	1.66002	+	0.444802i	0.962394	−	0.271657i	$-0.0875715\pi$
$797$	8.40406e8	+	2.25186e8i	1.66002	+	0.444802i	0.697629	+	0.716459i	$0.254238\pi$
$798$	2.56290e7	−	1.47969e7i	0.0504340	−	0.0291181i
$799$	−1.27637e8	+	4.76348e8i	−0.250228	+	0.933864i
$800$	2.52525e8	+	2.52525e8i	0.493212	+	0.493212i
$801$	−3.08055e7	−	1.14968e8i	−0.0599418	−	0.223706i
$802$	2.88297e8	−	1.66448e8i	0.558878	−	0.322669i
$803$	−1.02343e9			−1.97658
$804$			3.91597e8i			0.753480i
$805$	−1.15987e8	+	6.69651e7i	−0.222342	+	0.128369i
$806$	8.20751e7	−	8.20751e7i	0.156749	−	0.156749i
$807$	1.42669e8	+	8.23699e7i	0.271462	+	0.156728i
$808$	3.28102e8	−	3.28102e8i	0.621977	−	0.621977i
$809$	−6.48769e7	−	2.42124e8i	−0.122531	−	0.457290i	0.877209	−	0.480109i	$-0.159403\pi$
$809$	−6.48769e7	−	2.42124e8i	−0.122531	−	0.457290i	−0.999740	+	0.0228183i	$0.992736\pi$
$810$	−2.03755e8	+	3.52915e8i	−0.383402	+	0.664071i
$811$	−1.91113e8	+	3.31018e8i	−0.358285	+	0.620567i	−0.987674	−	0.156523i	$-0.949972\pi$
$811$	−1.91113e8	+	3.31018e8i	−0.358285	+	0.620567i	0.629390	+	0.777090i	$0.283305\pi$
$812$	−4.53301e8	+	1.69174e9i	−0.846679	+	3.15985i
$813$			1.52100e8i			0.283046i
$814$	3.51799e8	+	1.07009e9i	0.652261	+	1.98403i
$815$	−2.00833e8			−0.370991
$816$	−5.06767e8	−	1.35788e8i	−0.932691	−	0.249914i
$817$	−5.94204e7	−	3.43064e7i	−0.108961	−	0.0629085i
$818$	−356631.	−	205901.i	−0.000651567	−	0.000376182i
$819$	−7.38927e7	+	1.97995e7i	−0.134509	+	0.0360415i
$820$	3.72282e8	+	3.72282e8i	0.675197	+	0.675197i
$821$	−2.87056e8	+	4.97195e8i	−0.518724	+	0.898457i	0.481039	+	0.876699i	$0.340260\pi$
$821$	−2.87056e8	+	4.97195e8i	−0.518724	+	0.898457i	−0.999763	+	0.0217577i	$0.993074\pi$
$822$	−3.26705e8	−	3.26705e8i	−0.588221	−	0.588221i
$823$	5.08169e8	+	8.80175e8i	0.911609	+	1.57895i	0.811791	+	0.583948i	$0.198493\pi$
$823$	5.08169e8	+	8.80175e8i	0.911609	+	1.57895i	0.0998179	+	0.995006i	$0.468174\pi$
$824$	1.55182e9			2.77370
$825$		−	1.31937e8i		−	0.234966i
$826$	−3.36168e8	−	5.82260e8i	−0.596508	−	1.03318i
$827$	−3.20834e8	+	8.59673e7i	−0.567236	+	0.151991i	−0.531029	−	0.847354i	$-0.678194\pi$
$827$	−3.20834e8	+	8.59673e7i	−0.567236	+	0.151991i	−0.0362076	+	0.999344i	$0.511528\pi$
$828$	3.33432e8	−	3.33432e8i	0.587377	−	0.587377i
$829$	−2.39188e8	−	6.40901e7i	−0.419832	−	0.112494i	0.0427176	−	0.999087i	$-0.486398\pi$
$829$	−2.39188e8	−	6.40901e7i	−0.419832	−	0.112494i	−0.462549	+	0.886594i	$0.653065\pi$
$830$	−5.96296e8	−	1.03282e9i	−1.04286	−	1.80629i
$831$	3.63808e7	−	1.35775e8i	0.0633971	−	0.236601i
$832$	2.11409e6	+	7.88988e6i	0.00367074	+	0.0136994i
$833$	9.92366e7	−	2.65904e7i	0.171687	−	0.0460033i
$834$	−1.96278e8	−	5.25925e7i	−0.338355	−	0.0906620i
$835$	6.41149e7	−	3.70168e7i	0.110129	−	0.0635827i
$836$	3.82714e7	−	1.42831e8i	0.0655021	−	0.244457i
$837$	2.08162e8	+	2.08162e8i	0.354997	+	0.354997i
$838$	−2.13546e8	−	7.96964e8i	−0.362877	−	1.35428i
$839$	−2.82459e8	+	1.63078e8i	−0.478267	+	0.276127i	−0.719694	−	0.694292i	$-0.755718\pi$
$839$	−2.82459e8	+	1.63078e8i	−0.478267	+	0.276127i	0.241427	+	0.970419i	$0.422385\pi$
$840$	2.70328e8			0.456093
$841$		−	5.23856e8i		−	0.880691i
$842$	−2.68700e8	+	1.55134e8i	−0.450122	+	0.259878i
$843$	2.12098e8	−	2.12098e8i	0.354041	−	0.354041i
$844$	−2.04970e9	−	1.18339e9i	−3.40928	−	1.96835i
$845$	2.49726e8	−	2.49726e8i	0.413899	−	0.413899i
$846$	1.50774e8	+	5.62697e8i	0.249009	+	0.929315i
$847$	−1.07423e8	+	1.86062e8i	−0.176786	+	0.306202i
$848$	4.93733e8	−	8.55170e8i	0.809663	−	1.40238i
$849$	9.04574e7	−	3.37592e8i	0.147816	−	0.551656i
$850$			1.16417e9i			1.89566i
$851$	−2.45857e8	−	5.13685e7i	−0.398927	−	0.0833505i
$852$	3.69473e8			0.597398
$853$	4.89872e8	+	1.31261e8i	0.789287	+	0.211489i	0.630875	−	0.775884i	$-0.282696\pi$
$853$	4.89872e8	+	1.31261e8i	0.789287	+	0.211489i	0.158412	+	0.987373i	$0.449363\pi$
$854$	1.57658e9	+	9.10237e8i	2.53129	+	1.46144i
$855$	−2.81640e7	−	1.62605e7i	−0.0450606	−	0.0260157i
$856$	6.71735e8	−	1.79991e8i	1.07097	−	0.286965i
$857$	−2.21558e8	−	2.21558e8i	−0.352001	−	0.352001i	0.508853	−	0.860854i	$-0.330070\pi$
$857$	−2.21558e8	−	2.21558e8i	−0.352001	−	0.352001i	−0.860854	+	0.508853i	$0.830070\pi$
$858$	3.06957e7	−	5.31665e7i	0.0485977	−	0.0841737i
$859$	2.89308e8	+	2.89308e8i	0.456436	+	0.456436i	0.897484	−	0.441047i	$-0.145393\pi$
$859$	2.89308e8	+	2.89308e8i	0.456436	+	0.456436i	−0.441047	+	0.897484i	$0.645393\pi$
$860$	−5.61030e8	−	9.71732e8i	−0.882045	−	1.52775i
$861$	−1.49933e8			−0.234902
$862$		−	1.27063e9i		−	1.98380i
$863$	2.03341e8	+	3.52197e8i	0.316368	+	0.547966i	0.979727	−	0.200335i	$-0.0642032\pi$
$863$	2.03341e8	+	3.52197e8i	0.316368	+	0.547966i	−0.663359	+	0.748301i	$0.730870\pi$
$864$	−4.07091e8	+	1.09080e8i	−0.631176	+	0.169123i
$865$	−5.24667e8	+	5.24667e8i	−0.810654	+	0.810654i
$866$	1.27295e8	+	3.41086e7i	0.196001	+	0.0525183i
$867$	−1.72242e8	−	2.98332e8i	−0.264290	−	0.457764i
$868$	−3.36987e8	+	1.25765e9i	−0.515292	+	1.92310i
$869$	−5.73344e7	−	2.13975e8i	−0.0873687	−	0.326064i
$870$	−2.98587e8	+	8.00062e7i	−0.453433	+	0.121497i
$871$	9.85466e7	+	2.64055e7i	0.149138	+	0.0399613i
$872$	−1.76767e9	+	1.02056e9i	−2.66594	+	1.53918i
$873$	2.64805e8	−	9.88267e8i	0.398001	−	1.48536i
$874$	3.36054e7	+	3.36054e7i	0.0503356	+	0.0503356i
$875$	−1.79363e8	−	6.69392e8i	−0.267737	−	0.999209i
$876$	−7.14133e8	+	4.12305e8i	−1.06235	+	0.613347i
$877$	−3.70180e8			−0.548800			−0.274400	−	0.961616i	$-0.588479\pi$
$877$	−3.70180e8			−0.548800			−0.274400	+	0.961616i	$0.588479\pi$
$878$			8.61919e8i			1.27345i
$879$	−6.87830e7	+	3.97119e7i	−0.101278	+	0.0584728i
$880$	6.21915e8	−	6.21915e8i	0.912605	−	0.912605i
$881$	3.79021e8	+	2.18828e8i	0.554288	+	0.320018i	0.750850	−	0.660473i	$-0.229644\pi$
$881$	3.79021e8	+	2.18828e8i	0.554288	+	0.320018i	−0.196562	+	0.980491i	$0.562978\pi$
$882$	8.58150e7	−	8.58150e7i	0.125071	−	0.125071i
$883$	−9.98270e7	−	3.72559e8i	−0.144999	−	0.541145i	−0.999755	−	0.0221148i	$-0.992960\pi$
$883$	−9.98270e7	−	3.72559e8i	−0.144999	−	0.541145i	0.854756	−	0.519030i	$-0.173707\pi$
$884$	−1.87904e8	+	3.25458e8i	−0.272006	+	0.471128i
$885$	4.11623e7	−	7.12952e7i	0.0593840	−	0.102856i
$886$	2.45872e8	−	9.17608e8i	0.353516	−	1.31934i
$887$		−	2.16087e8i		−	0.309640i	−0.987943	−	0.154820i	$-0.950520\pi$
$887$		−	2.16087e8i		−	0.309640i	0.987943	−	0.154820i	$-0.0494798\pi$
$888$	3.77918e8	+	3.37915e8i	0.539708	+	0.482579i
$889$	5.74717e8			0.817991
$890$	1.89491e8	+	5.07739e7i	0.268793	+	0.0720229i
$891$	−5.02174e8	−	2.89931e8i	−0.709940	−	0.409884i
$892$	−8.09752e7	−	4.67510e7i	−0.114093	−	0.0658714i
$893$	−3.93444e7	+	1.05423e7i	−0.0552496	+	0.0148041i
$894$	1.42964e8	+	1.42964e8i	0.200084	+	0.200084i
$895$	−1.80687e7	+	3.12958e7i	−0.0252033	+	0.0436533i
$896$	4.88439e8	+	4.88439e8i	0.679026	+	0.679026i
$897$	6.84434e6	+	1.18547e7i	0.00948318	+	0.0164254i
$898$	1.12607e9			1.55502
$899$		−	8.31632e8i		−	1.14460i
$900$	4.77029e8	+	8.26239e8i	0.654361	+	1.13339i
$901$	1.00143e9	−	2.68334e8i	1.36914	−	0.366860i
$902$	−7.63572e8	+	7.63572e8i	−1.04047	+	1.04047i
$903$	3.08652e8	+	8.27030e7i	0.419185	+	0.112320i
$904$	1.29826e9	+	2.24865e9i	1.75734	+	3.04380i
$905$	1.45999e7	−	5.44875e7i	0.0196971	−	0.0735107i
$906$	1.52363e8	+	5.68626e8i	0.204878	+	0.764613i
$907$	−1.30200e9	+	3.48870e8i	−1.74498	+	0.467565i	−0.983543	−	0.180676i	$-0.942171\pi$
$907$	−1.30200e9	+	3.48870e8i	−1.74498	+	0.467565i	−0.761435	+	0.648242i	$0.775505\pi$
$908$	−1.12468e9	−	3.01356e8i	−1.50235	−	0.402553i
$909$	2.25137e8	−	1.29983e8i	0.299747	−	0.173059i
$910$	3.26337e7	−	1.21791e8i	0.0433055	−	0.161618i
$911$	8.73078e8	+	8.73078e8i	1.15478	+	1.15478i	0.985583	+	0.169193i	$0.0541163\pi$
$911$	8.73078e8	+	8.73078e8i	1.15478	+	1.15478i	0.169193	+	0.985583i	$0.445884\pi$
$912$	−1.12155e7	−	4.18569e7i	−0.0147855	−	0.0551802i
$913$	1.46963e9	−	8.48491e8i	1.93106	−	1.11490i
$914$	−1.80953e9			−2.36988
$915$			2.22909e8i			0.290981i
$916$	−8.48833e8	+	4.90074e8i	−1.10442	+	0.637639i
$917$	−9.15902e8	+	9.15902e8i	−1.18779	+	1.18779i
$918$	−1.18981e9	−	6.86938e8i	−1.53798	−	0.887952i
$919$	−6.01029e8	+	6.01029e8i	−0.774371	+	0.774371i	−0.978867	−	0.204496i	$-0.934444\pi$
$919$	−6.01029e8	+	6.01029e8i	−0.774371	+	0.774371i	0.204496	+	0.978867i	$0.434444\pi$
$920$	1.12360e8	+	4.19332e8i	0.144294	+	0.538511i
$921$	1.23827e7	−	2.14474e7i	0.0158502	−	0.0274534i
$922$	8.11819e8	−	1.40611e9i	1.03578	−	1.79402i
$923$	2.49136e7	−	9.29789e7i	0.0316834	−	0.118244i
$924$			6.88648e8i			0.872934i
$925$	2.29136e8	−	4.53584e8i	0.289513	−	0.573103i
$926$	−1.18378e9			−1.49086
$927$	8.39804e8	+	2.25025e8i	1.05424	+	0.282482i
$928$	1.03108e9	+	5.95297e8i	1.29018	+	0.744886i
$929$	2.63258e8	+	1.51992e8i	0.328348	+	0.189572i	0.655107	−	0.755536i	$-0.272623\pi$
$929$	2.63258e8	+	1.51992e8i	0.328348	+	0.189572i	−0.326760	+	0.945108i	$0.605957\pi$
$930$	−2.21971e8	+	5.94770e7i	−0.275961	+	0.0739435i
$931$	6.00029e6	+	6.00029e6i	0.00743572	+	0.00743572i
$932$	1.32531e9	−	2.29550e9i	1.63708	−	2.83550i
$933$	5.35892e7	+	5.35892e7i	0.0659830	+	0.0659830i
$934$	2.35524e8	+	4.07939e8i	0.289064	+	0.500674i
$935$	9.23428e8			1.12971
$936$			2.47967e8i			0.302389i
$937$	−4.67139e8	−	8.09108e8i	−0.567841	−	0.983530i	−0.996779	−	0.0801959i	$-0.974445\pi$
$937$	−4.67139e8	−	8.09108e8i	−0.567841	−	0.983530i	0.428938	−	0.903334i	$-0.358888\pi$
$938$	−1.59340e9	+	4.26950e8i	−1.93071	+	0.517331i
$939$	3.54048e7	−	3.54048e7i	0.0427627	−	0.0427627i
$940$	−6.43419e8	−	1.72404e8i	−0.774658	−	0.207569i
$941$	−2.89979e8	−	5.02258e8i	−0.348015	−	0.602779i	0.637882	−	0.770134i	$-0.279811\pi$
$941$	−2.89979e8	−	5.02258e8i	−0.348015	−	0.602779i	−0.985897	+	0.167355i	$0.946477\pi$
$942$	−8.16227e7	+	3.04620e8i	−0.0976469	+	0.364423i
$943$	−6.23182e7	−	2.32575e8i	−0.0743156	−	0.277350i
$944$	−9.50937e8	+	2.54803e8i	−1.13041	+	0.302892i
$945$	3.08890e8	+	8.27668e7i	0.366023	+	0.0980755i
$946$	1.99308e9	−	1.15071e9i	2.35424	−	1.35922i
$947$	2.31086e8	−	8.62426e8i	0.272097	−	1.01548i	−0.685664	−	0.727918i	$-0.740488\pi$
$947$	2.31086e8	−	8.62426e8i	0.272097	−	1.01548i	0.957762	−	0.287563i	$-0.0928452\pi$
$948$	−1.26210e8	−	1.26210e8i	−0.148138	−	0.148138i
$949$	5.56036e7	+	2.07515e8i	0.0650585	+	0.242802i
$950$	−8.32737e7	+	4.80781e7i	−0.0971263	+	0.0560759i
$951$	3.35531e8			0.390113
$952$		−	3.39412e9i		−	3.93383i
$953$	−8.72190e8	+	5.03559e8i	−1.00770	+	0.581797i	−0.910518	−	0.413469i	$-0.864317\pi$
$953$	−8.72190e8	+	5.03559e8i	−1.00770	+	0.581797i	−0.0971842	+	0.995266i	$0.530984\pi$
$954$	8.65992e8	−	8.65992e8i	0.997399	−	0.997399i
$955$	−3.20569e7	−	1.85081e7i	−0.0368054	−	0.0212496i
$956$	−2.07194e9	+	2.07194e9i	−2.37139	+	2.37139i
$957$	−1.13844e8	−	4.24870e8i	−0.129889	−	0.484753i
$958$	7.57276e7	−	1.31164e8i	0.0861307	−	0.149183i
$959$	6.75133e8	−	1.16937e9i	0.765480	−	1.32585i
$960$	4.18552e6	−	1.56206e7i	0.00473081	−	0.0176556i
$961$			2.69265e8i			0.303396i
$962$	1.97862e8	−	1.29471e8i	0.222248	−	0.145427i
$963$	3.89626e8			0.436283
$964$	−1.02540e9	−	2.74755e8i	−1.14462	−	0.306701i
$965$	3.80967e7	+	2.19952e7i	0.0423941	+	0.0244763i
$966$	−1.91679e8	−	1.10666e8i	−0.212639	−	0.122767i
$967$	−2.57780e8	+	6.90720e7i	−0.285082	+	0.0763876i	−0.398527	−	0.917157i	$-0.630478\pi$
$967$	−2.57780e8	+	6.90720e7i	−0.285082	+	0.0763876i	0.113444	+	0.993544i	$0.463812\pi$
$968$	4.92435e8	+	4.92435e8i	0.542904	+	0.542904i
$969$	2.27484e7	−	3.94014e7i	0.0250023	−	0.0433052i
$970$	1.19242e9	+	1.19242e9i	1.30651	+	1.30651i
$971$	−8.60953e7	−	1.49122e8i	−0.0940420	−	0.162886i	0.815166	−	0.579227i	$-0.196645\pi$
$971$	−8.60953e7	−	1.49122e8i	−0.0940420	−	0.162886i	−0.909208	+	0.416341i	$0.863312\pi$
$972$	−1.71858e9			−1.87141
$973$		−	5.93848e8i		−	0.644669i
$974$	−1.12699e8	−	1.95200e8i	−0.121967	−	0.211253i
$975$	−2.67521e7	+	7.16820e6i	−0.0288632	+	0.00773386i
$976$	1.88491e9	−	1.88491e9i	2.02741	−	2.02741i
$977$	1.16117e9	+	3.11134e8i	1.24512	+	0.333629i	0.820449	−	0.571719i	$-0.193723\pi$
$977$	1.16117e9	+	3.11134e8i	1.24512	+	0.333629i	0.424670	+	0.905348i	$0.360390\pi$
$978$	−1.65948e8	−	2.87430e8i	−0.177401	−	0.307267i
$979$	−7.22479e7	+	2.69633e8i	−0.0769976	+	0.287359i
$980$	3.59165e7	+	1.34042e8i	0.0381607	+	0.142418i
$981$	−1.10460e9	+	2.95978e8i	−1.17004	+	0.313510i
$982$	1.35630e9	+	3.63420e8i	1.43226	+	0.383773i
$983$	3.21579e8	−	1.85664e8i	0.338553	−	0.195464i	−0.321079	−	0.947052i	$-0.604045\pi$
$983$	3.21579e8	−	1.85664e8i	0.338553	−	0.195464i	0.659632	+	0.751589i	$0.270712\pi$
$984$	−1.25785e8	+	4.69435e8i	−0.132021	+	0.492709i
$985$	−4.79413e8	−	4.79413e8i	−0.501651	−	0.501651i
$986$	1.00452e9	+	3.74892e9i	1.04792	+	3.91089i
$987$	1.64282e8	−	9.48482e7i	0.170859	−	0.0986456i
$988$	−3.10402e7			−0.0321850
$989$			5.13154e8i			0.530468i
$990$	9.44678e8	−	5.45410e8i	0.973595	−	0.562105i
$991$	−3.20818e8	+	3.20818e8i	−0.329639	+	0.329639i	−0.852449	−	0.522810i	$-0.824884\pi$
$991$	−3.20818e8	+	3.20818e8i	−0.329639	+	0.329639i	0.522810	+	0.852449i	$0.324884\pi$
$992$	7.66513e8	+	4.42547e8i	0.785208	+	0.453340i
$993$	2.27009e8	−	2.27009e8i	0.231844	−	0.231844i
$994$	4.02828e8	+	1.50338e9i	0.410167	+	1.53076i
$995$	−1.70019e8	+	2.94481e8i	−0.172595	+	0.298943i
$996$	6.83653e8	−	1.18412e9i	0.691922	−	1.19844i
$997$	3.91565e8	−	1.46134e9i	0.395110	−	1.47457i	−0.426482	−	0.904496i	$-0.640247\pi$
$997$	3.91565e8	−	1.46134e9i	0.395110	−	1.47457i	0.821592	−	0.570076i	$-0.193086\pi$
$998$		−	1.42568e9i		−	1.43426i
$999$	3.28368e8	+	5.01825e8i	0.329355	+	0.503334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.8.1	✓	72
37.14	odd	12	inner	37.7.g.a.14.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.1	✓	72	1.1	even	1	trivial
37.7.g.a.14.1	yes	72	37.14	odd	12	inner

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.9637 - 3.74156i) q^{2} +(7.40363 + 4.27449i) q^{3} +(125.560 + 72.4919i) q^{4} +(-72.2350 + 19.3553i) q^{5} +(-87.3887 - 87.3887i) q^{6} +(180.588 - 312.787i) q^{7} +(-827.827 - 827.827i) q^{8} +(-327.958 - 568.039i) q^{9} +O(q^{10})\)	\(q+(-13.9637 - 3.74156i) q^{2} +(7.40363 + 4.27449i) q^{3} +(125.560 + 72.4919i) q^{4} +(-72.2350 + 19.3553i) q^{5} +(-87.3887 - 87.3887i) q^{6} +(180.588 - 312.787i) q^{7} +(-827.827 - 827.827i) q^{8} +(-327.958 - 568.039i) q^{9} +1081.09 q^{10} +1538.32i q^{11} +(619.732 + 1073.41i) q^{12} +(311.914 - 83.5772i) q^{13} +(-3691.99 + 3691.99i) q^{14} +(-617.535 - 165.468i) q^{15} +(3822.67 + 6621.06i) q^{16} +(-2077.54 + 7753.50i) q^{17} +(2454.14 + 9158.99i) q^{18} +(-640.408 + 171.597i) q^{19} +(-10472.9 - 2806.21i) q^{20} +(2674.01 - 1543.84i) q^{21} +(5755.70 - 21480.6i) q^{22} +(3506.23 + 3506.23i) q^{23} +(-2590.39 - 9667.46i) q^{24} +(-8688.38 + 5016.24i) q^{25} -4668.18 q^{26} -11839.6i q^{27} +(45349.1 - 26182.3i) q^{28} +(-23650.4 + 23650.4i) q^{29} +(8003.96 + 4621.09i) q^{30} +(-17581.8 + 17581.8i) q^{31} +(-9213.13 - 34383.9i) q^{32} +(-6575.51 + 11389.1i) q^{33} +(58020.3 - 100494. i) q^{34} +(-6990.67 + 26089.5i) q^{35} -95097.1i q^{36} +(-42385.3 + 27734.7i) q^{37} +9584.49 q^{38} +(2666.55 + 714.500i) q^{39} +(75820.9 + 43775.2i) q^{40} +(-42052.7 - 24279.1i) q^{41} +(-43115.4 + 11552.7i) q^{42} +(73177.5 + 73177.5i) q^{43} +(-111515. + 193150. i) q^{44} +(34684.6 + 34684.6i) q^{45} +(-35841.1 - 62078.7i) q^{46} +61436.5 q^{47} +65359.8i q^{48} +(-6399.48 - 11084.2i) q^{49} +(140090. - 37537.1i) q^{50} +(-48523.6 + 48523.6i) q^{51} +(45222.5 + 12117.3i) q^{52} +(-64579.6 - 111855. i) q^{53} +(-44298.6 + 165325. i) q^{54} +(-29774.6 - 111120. i) q^{55} +(-408429. + 109438. i) q^{56} +(-5474.83 - 1466.98i) q^{57} +(418735. - 241757. i) q^{58} +(-33327.9 + 124381. i) q^{59} +(-65542.4 - 65542.4i) q^{60} +(-90241.4 - 336786. i) q^{61} +(311290. - 179723. i) q^{62} -236901. q^{63} +25295.0i q^{64} +(-20913.5 + 12074.4i) q^{65} +(134431. - 134431. i) q^{66} +(273613. + 157971. i) q^{67} +(-822921. + 822921. i) q^{68} +(10971.5 + 40946.2i) q^{69} +(195231. - 338150. i) q^{70} +(149045. - 258154. i) q^{71} +(-198746. + 741730. i) q^{72} +665296. i q^{73} +(695626. - 228691. i) q^{74} -85767.4 q^{75} +(-92848.7 - 24878.7i) q^{76} +(481166. + 277801. i) q^{77} +(-34561.5 - 19954.1i) q^{78} +(-139097. + 37270.9i) q^{79} +(-404283. - 404283. i) q^{80} +(-188473. + 326444. i) q^{81} +(496369. + 496369. i) q^{82} +(-551572. - 955350. i) q^{83} +447664. q^{84} -600285. i q^{85} +(-748030. - 1.29563e6i) q^{86} +(-276192. + 74005.3i) q^{87} +(1.27346e6 - 1.27346e6i) q^{88} +(175278. + 46965.6i) q^{89} +(-354550. - 614099. i) q^{90} +(30186.1 - 112656. i) q^{91} +(186068. + 694415. i) q^{92} +(-205322. + 55015.9i) q^{93} +(-857880. - 229868. i) q^{94} +(42938.6 - 24790.6i) q^{95} +(78762.8 - 293947. i) q^{96} +(1.10298e6 + 1.10298e6i) q^{97} +(47888.0 + 178721. i) q^{98} +(873823. - 504502. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more