LMFDB - Embedded newform 48.6.k.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(11,48)]

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, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	48.11
Dual form			48.6.k.a.35.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31086 + 5.50288i) q^{2} +(-10.2553 + 11.7400i) q^{3} +(-28.5633 - 14.4270i) q^{4} +(55.5354 - 55.5354i) q^{5} +(-51.1607 - 71.8233i) q^{6} -177.545 q^{7} +(116.833 - 138.268i) q^{8} +(-32.6571 - 240.796i) q^{9} +O(q^{10})$	\(q+(-1.31086 + 5.50288i) q^{2} +(-10.2553 + 11.7400i) q^{3} +(-28.5633 - 14.4270i) q^{4} +(55.5354 - 55.5354i) q^{5} +(-51.1607 - 71.8233i) q^{6} -177.545 q^{7} +(116.833 - 138.268i) q^{8} +(-32.6571 - 240.796i) q^{9} +(232.805 + 378.403i) q^{10} +(186.978 + 186.978i) q^{11} +(462.299 - 187.381i) q^{12} +(594.279 - 594.279i) q^{13} +(232.737 - 977.011i) q^{14} +(82.4550 + 1221.52i) q^{15} +(607.723 + 824.165i) q^{16} +677.041i q^{17} +(1367.88 + 135.941i) q^{18} +(-1358.05 - 1358.05i) q^{19} +(-2387.48 + 785.064i) q^{20} +(1820.78 - 2084.39i) q^{21} +(-1274.02 + 783.814i) q^{22} -3446.42i q^{23} +(425.124 + 2789.60i) q^{24} -3043.35i q^{25} +(2491.23 + 4049.26i) q^{26} +(3161.86 + 2086.04i) q^{27} +(5071.28 + 2561.45i) q^{28} +(-2786.52 - 2786.52i) q^{29} +(-6829.96 - 1147.50i) q^{30} -8376.06i q^{31} +(-5331.92 + 2263.86i) q^{32} +(-4112.65 + 277.612i) q^{33} +(-3725.67 - 887.506i) q^{34} +(-9860.05 + 9860.05i) q^{35} +(-2541.16 + 7349.06i) q^{36} +(-2269.37 - 2269.37i) q^{37} +(9253.40 - 5692.97i) q^{38} +(882.343 + 13071.4i) q^{39} +(-1190.45 - 14167.1i) q^{40} -1966.38 q^{41} +(9083.35 + 12751.9i) q^{42} +(-3787.80 + 3787.80i) q^{43} +(-2643.17 - 8038.24i) q^{44} +(-15186.3 - 11559.0i) q^{45} +(18965.2 + 4517.77i) q^{46} +14716.1 q^{47} +(-15908.1 - 1317.38i) q^{48} +14715.4 q^{49} +(16747.2 + 3989.41i) q^{50} +(-7948.49 - 6943.27i) q^{51} +(-25548.2 + 8400.90i) q^{52} +(4524.62 - 4524.62i) q^{53} +(-15624.0 + 14664.8i) q^{54} +20767.8 q^{55} +(-20743.1 + 24548.9i) q^{56} +(29870.8 - 2016.34i) q^{57} +(18986.6 - 11681.1i) q^{58} +(-6001.11 - 6001.11i) q^{59} +(15267.7 - 36080.2i) q^{60} +(-21018.9 + 21018.9i) q^{61} +(46092.4 + 10979.8i) q^{62} +(5798.13 + 42752.2i) q^{63} +(-5468.33 - 32308.5i) q^{64} -66007.0i q^{65} +(3863.44 - 22995.3i) q^{66} +(-7888.53 - 7888.53i) q^{67} +(9767.67 - 19338.5i) q^{68} +(40461.1 + 35344.1i) q^{69} +(-41333.5 - 67183.8i) q^{70} +57173.9i q^{71} +(-37109.8 - 23617.3i) q^{72} -27272.7i q^{73} +(15462.9 - 9513.23i) q^{74} +(35729.1 + 31210.5i) q^{75} +(19197.8 + 58383.0i) q^{76} +(-33197.1 - 33197.1i) q^{77} +(-73086.8 - 12279.3i) q^{78} -3330.97i q^{79} +(79520.4 + 12020.2i) q^{80} +(-56916.0 + 15727.4i) q^{81} +(2577.65 - 10820.7i) q^{82} +(-13075.3 + 13075.3i) q^{83} +(-82079.1 + 33268.6i) q^{84} +(37599.7 + 37599.7i) q^{85} +(-15878.5 - 25809.0i) q^{86} +(61290.4 - 4137.22i) q^{87} +(47698.3 - 4008.05i) q^{88} -102215. q^{89} +(83515.1 - 68416.0i) q^{90} +(-105512. + 105512. i) q^{91} +(-49721.5 + 98441.1i) q^{92} +(98335.2 + 85899.1i) q^{93} +(-19290.7 + 80980.6i) q^{94} -150840. q^{95} +(28102.7 - 85813.5i) q^{96} +150592. q^{97} +(-19289.8 + 80977.0i) q^{98} +(38917.3 - 51129.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.31086	+	5.50288i	−0.231730	+	0.972780i
$2$	−1.31086	+	5.50288i	−0.231730	+	0.972780i
$3$	−10.2553	+	11.7400i	−0.657879	+	0.753124i
$3$	−10.2553	+	11.7400i	−0.657879	+	0.753124i
$4$	−28.5633	−	14.4270i	−0.892603	−	0.450844i
$5$	55.5354	−	55.5354i	0.993447	−	0.993447i	−0.00653188	−	0.999979i	$-0.502079\pi$
$5$	55.5354	−	55.5354i	0.993447	−	0.993447i	0.999979	+	0.00653188i	$0.00207918\pi$
$6$	−51.1607	−	71.8233i	−0.580174	−	0.814492i
$7$	−177.545			−1.36951			−0.684754	−	0.728774i	$-0.740090\pi$
$7$	−177.545			−1.36951			−0.684754	+	0.728774i	$0.740090\pi$
$8$	116.833	−	138.268i	0.645414	−	0.763833i
$9$	−32.6571	−	240.796i	−0.134392	−	0.990928i
$10$	232.805	+	378.403i	0.736194	+	1.19662i
$11$	186.978	+	186.978i	0.465917	+	0.465917i	0.900589	−	0.434672i	$-0.143136\pi$
$11$	186.978	+	186.978i	0.465917	+	0.465917i	−0.434672	+	0.900589i	$0.643136\pi$
$12$	462.299	−	187.381i	0.926766	−	0.375640i
$13$	594.279	−	594.279i	0.975286	−	0.975286i	−0.0244161	−	0.999702i	$-0.507773\pi$
$13$	594.279	−	594.279i	0.975286	−	0.975286i	0.999702	+	0.0244161i	$0.00777267\pi$
$14$	232.737	−	977.011i	0.317355	−	1.33223i
$15$	82.4550	+	1221.52i	0.0946212	+	1.40176i
$16$	607.723	+	824.165i	0.593480	+	0.804849i
$17$			677.041i			0.568189i	0.958796	+	0.284094i	$0.0916929\pi$
$17$			677.041i			0.568189i	−0.958796	+	0.284094i	$0.908307\pi$
$18$	1367.88	+	135.941i	0.995098	+	0.0988940i
$19$	−1358.05	−	1358.05i	−0.863042	−	0.863042i	0.128648	−	0.991690i	$-0.458936\pi$
$19$	−1358.05	−	1358.05i	−0.863042	−	0.863042i	−0.991690	+	0.128648i	$0.958936\pi$
$20$	−2387.48	+	785.064i	−1.33464	+	0.438864i
$21$	1820.78	−	2084.39i	0.900970	−	1.03141i
$22$	−1274.02	+	783.814i	−0.561202	+	0.345268i
$23$		−	3446.42i		−	1.35846i	−0.733923	−	0.679232i	$-0.762313\pi$
$23$		−	3446.42i		−	1.35846i	0.733923	−	0.679232i	$-0.237687\pi$
$24$	425.124	+	2789.60i	0.150656	+	0.988586i
$25$		−	3043.35i		−	0.973873i
$26$	2491.23	+	4049.26i	0.722736	+	1.17474i
$27$	3161.86	+	2086.04i	0.834705	+	0.550697i
$28$	5071.28	+	2561.45i	1.22243	+	0.617434i
$29$	−2786.52	−	2786.52i	−0.615272	−	0.615272i	0.329043	−	0.944315i	$-0.393274\pi$
$29$	−2786.52	−	2786.52i	−0.615272	−	0.615272i	−0.944315	+	0.329043i	$0.893274\pi$
$30$	−6829.96	−	1147.50i	−1.38553	−	0.232783i
$31$		−	8376.06i		−	1.56544i	−0.622377	−	0.782718i	$-0.713833\pi$
$31$		−	8376.06i		−	1.56544i	0.622377	−	0.782718i	$-0.286167\pi$
$32$	−5331.92	+	2263.86i	−0.920468	+	0.390818i
$33$	−4112.65	+	277.612i	−0.657410	+	0.0443765i
$34$	−3725.67	−	887.506i	−0.552723	−	0.131666i
$35$	−9860.05	+	9860.05i	−1.36053	+	1.36053i
$36$	−2541.16	+	7349.06i	−0.326796	+	0.945095i
$37$	−2269.37	−	2269.37i	−0.272522	−	0.272522i	0.557593	−	0.830115i	$-0.311725\pi$
$37$	−2269.37	−	2269.37i	−0.272522	−	0.272522i	−0.830115	+	0.557593i	$0.811725\pi$
$38$	9253.40	−	5692.97i	1.03954	−	0.639558i
$39$	882.343	+	13071.4i	0.0928915	+	1.37613i
$40$	−1190.45	−	14167.1i	−0.117642	−	1.40001i
$41$	−1966.38			−0.182687			−0.0913434	−	0.995819i	$-0.529116\pi$
$41$	−1966.38			−0.182687			−0.0913434	+	0.995819i	$0.529116\pi$
$42$	9083.35	+	12751.9i	0.794553	+	1.11545i
$43$	−3787.80	+	3787.80i	−0.312403	+	0.312403i	−0.845840	−	0.533437i	$-0.820900\pi$
$43$	−3787.80	+	3787.80i	−0.312403	+	0.312403i	0.533437	+	0.845840i	$0.320900\pi$
$44$	−2643.17	−	8038.24i	−0.205823	−	0.625935i
$45$	−15186.3	−	11559.0i	−1.11795	−	0.850924i
$46$	18965.2	+	4517.77i	1.32149	+	0.314796i
$47$	14716.1			0.971732			0.485866	−	0.874033i	$-0.338504\pi$
$47$	14716.1			0.971732			0.485866	+	0.874033i	$0.338504\pi$
$48$	−15908.1	−	1317.38i	−0.996589	−	0.0825292i
$49$	14715.4			0.875551
$50$	16747.2	+	3989.41i	0.947364	+	0.225675i
$51$	−7948.49	−	6943.27i	−0.427917	−	0.373799i
$52$	−25548.2	+	8400.90i	−1.31024	+	0.430841i
$53$	4524.62	−	4524.62i	0.221255	−	0.221255i	−0.587772	−	0.809027i	$-0.699995\pi$
$53$	4524.62	−	4524.62i	0.221255	−	0.221255i	0.809027	+	0.587772i	$0.199995\pi$
$54$	−15624.0	+	14664.8i	−0.729133	+	0.684372i
$55$	20767.8			0.925728
$56$	−20743.1	+	24548.9i	−0.883900	+	1.04607i
$57$	29870.8	−	2016.34i	1.21775	−	0.0822008i
$58$	18986.6	−	11681.1i	0.741101	−	0.455947i
$59$	−6001.11	−	6001.11i	−0.224441	−	0.224441i	0.585925	−	0.810365i	$-0.300731\pi$
$59$	−6001.11	−	6001.11i	−0.224441	−	0.224441i	−0.810365	+	0.585925i	$0.800731\pi$
$60$	15267.7	−	36080.2i	0.547514	−	1.29387i
$61$	−21018.9	+	21018.9i	−0.723245	+	0.723245i	−0.969265	−	0.246020i	$-0.920877\pi$
$61$	−21018.9	+	21018.9i	−0.723245	+	0.723245i	0.246020	+	0.969265i	$0.420877\pi$
$62$	46092.4	+	10979.8i	1.52283	+	0.362758i
$63$	5798.13	+	42752.2i	0.184050	+	1.35708i
$64$	−5468.33	−	32308.5i	−0.166880	−	0.985977i
$65$		−	66007.0i		−	1.93779i
$66$	3863.44	−	22995.3i	0.109173	−	0.649799i
$67$	−7888.53	−	7888.53i	−0.214689	−	0.214689i	0.591567	−	0.806256i	$-0.298509\pi$
$67$	−7888.53	−	7888.53i	−0.214689	−	0.214689i	−0.806256	+	0.591567i	$0.798509\pi$
$68$	9767.67	−	19338.5i	0.256164	−	0.507167i
$69$	40461.1	+	35344.1i	1.02309	+	0.893705i
$70$	−41333.5	−	67183.8i	−1.00822	−	1.63878i
$71$			57173.9i			1.34602i	0.739633	+	0.673011i	$0.234999\pi$
$71$			57173.9i			1.34602i	−0.739633	+	0.673011i	$0.765001\pi$
$72$	−37109.8	−	23617.3i	−0.843642	−	0.536907i
$73$		−	27272.7i		−	0.598991i	−0.954098	−	0.299496i	$-0.903182\pi$
$73$		−	27272.7i		−	0.598991i	0.954098	−	0.299496i	$-0.0968184\pi$
$74$	15462.9	−	9513.23i	0.328255	−	0.201952i
$75$	35729.1	+	31210.5i	0.733447	+	0.640690i
$76$	19197.8	+	58383.0i	0.381257	+	1.15945i
$77$	−33197.1	−	33197.1i	−0.638077	−	0.638077i
$78$	−73086.8	−	12279.3i	−1.36020	−	0.228527i
$79$		−	3330.97i		−	0.0600486i	−0.999549	−	0.0300243i	$-0.990442\pi$
$79$		−	3330.97i		−	0.0600486i	0.999549	−	0.0300243i	$-0.00955846\pi$
$80$	79520.4	+	12020.2i	1.38917	+	0.209984i
$81$	−56916.0	+	15727.4i	−0.963878	+	0.266345i
$82$	2577.65	−	10820.7i	0.0423339	−	0.177714i
$83$	−13075.3	+	13075.3i	−0.208332	+	0.208332i	−0.803558	−	0.595226i	$-0.797062\pi$
$83$	−13075.3	+	13075.3i	−0.208332	+	0.208332i	0.595226	+	0.803558i	$0.297062\pi$
$84$	−82079.1	+	33268.6i	−1.26921	+	0.514442i
$85$	37599.7	+	37599.7i	0.564465	+	0.564465i
$86$	−15878.5	−	25809.0i	−0.231507	−	0.376293i
$87$	61290.4	−	4137.22i	0.868150	−	0.0586018i
$88$	47698.3	−	4008.05i	0.656592	−	0.0551730i
$89$	−102215.			−1.36786			−0.683930	−	0.729548i	$-0.739731\pi$
$89$	−102215.			−1.36786			−0.683930	+	0.729548i	$0.739731\pi$
$90$	83515.1	−	68416.0i	1.08682	−	0.890331i
$91$	−105512.	+	105512.i	−1.33566	+	1.33566i
$92$	−49721.5	+	98441.1i	−0.612456	+	1.21257i
$93$	98335.2	+	85899.1i	1.17897	+	1.02987i
$94$	−19290.7	+	80980.6i	−0.225179	+	0.945282i
$95$	−150840.			−1.71477
$96$	28102.7	−	85813.5i	0.311222	−	0.950337i
$97$	150592.			1.62507			0.812537	−	0.582910i	$-0.198086\pi$
$97$	150592.			1.62507			0.812537	+	0.582910i	$0.198086\pi$
$98$	−19289.8	+	80977.0i	−0.202891	+	0.851719i
$99$	38917.3	−	51129.6i	0.399075	−	0.524306i
$100$	−43906.5	+	86928.2i	−0.439065	+	0.869282i
$101$	26625.3	−	26625.3i	0.259712	−	0.259712i	−0.565225	−	0.824937i	$-0.691211\pi$
$101$	26625.3	−	26625.3i	0.259712	−	0.259712i	0.824937	+	0.565225i	$0.191211\pi$
$102$	48627.3	−	34637.9i	0.462785	−	0.329648i
$103$	79061.9			0.734301			0.367151	−	0.930162i	$-0.380333\pi$
$103$	79061.9			0.734301			0.367151	+	0.930162i	$0.380333\pi$
$104$	−12738.9	−	151601.i	−0.115491	−	1.37442i
$105$	−14639.5	−	216875.i	−0.129585	−	1.91972i
$106$	18967.3	+	30829.6i	0.163961	+	0.266503i
$107$	−166.434	−	166.434i	−0.00140534	−	0.00140534i	0.706404	−	0.707809i	$-0.250316\pi$
$107$	−166.434	−	166.434i	−0.00140534	−	0.00140534i	−0.707809	+	0.706404i	$0.750316\pi$
$108$	−60217.8	−	105200.i	−0.496782	−	0.867875i
$109$	−155525.	+	155525.i	−1.25381	+	1.25381i	−0.299819	+	0.953996i	$0.596926\pi$
$109$	−155525.	+	155525.i	−1.25381	+	1.25381i	−0.953996	+	0.299819i	$0.903074\pi$
$110$	−27223.7	+	114282.i	−0.214518	+	0.900530i
$111$	49915.6	−	3369.40i	0.384529	−	0.0259564i
$112$	−107898.	−	146327.i	−0.812775	−	1.10225i
$113$			98488.6i			0.725588i	0.931869	+	0.362794i	$0.118177\pi$
$113$			98488.6i			0.725588i	−0.931869	+	0.362794i	$0.881823\pi$
$114$	−28060.8	+	167018.i	−0.202226	+	1.20366i
$115$	−191398.	−	191398.i	−1.34956	−	1.34956i
$116$	39391.0	+	119793.i	0.271802	+	0.826585i
$117$	−162507.	−	123692.i	−1.09751	−	0.835368i
$118$	40890.0	−	25156.8i	0.270341	−	0.166322i
$119$		−	120206.i		−	0.778139i
$120$	178531.	+	131312.i	1.13178	+	0.832439i
$121$		−	91129.5i		−	0.565843i
$122$	−88111.5	−	143217.i	−0.535961	−	0.871155i
$123$	20165.8	−	23085.4i	0.120186	−	0.137586i
$124$	−120841.	+	239248.i	−0.705767	+	1.39731i
$125$	4534.28	+	4534.28i	0.0259557	+	0.0259557i
$126$	−242860.	−	24135.7i	−1.36279	−	0.135436i
$127$		−	148936.i		−	0.819391i	−0.912222	−	0.409695i	$-0.865635\pi$
$127$		−	148936.i		−	0.819391i	0.912222	−	0.409695i	$-0.134365\pi$
$128$	184958.	+	12260.4i	0.997810	+	0.0661422i
$129$	−5623.85	−	83313.9i	−0.0297550	−	0.440802i
$130$	363228.	+	86525.9i	1.88504	+	0.449043i
$131$	204918.	−	204918.i	1.04328	−	1.04328i	0.0442630	−	0.999020i	$-0.485906\pi$
$131$	204918.	−	204918.i	1.04328	−	1.04328i	0.999020	−	0.0442630i	$-0.0140939\pi$
$132$	121476.	+	51403.7i	0.606813	+	0.256779i
$133$	241116.	+	241116.i	1.18194	+	1.18194i
$134$	53750.4	−	33068.9i	0.258595	−	0.159095i
$135$	291444.	−	59746.1i	1.37632	−	0.282147i
$136$	93613.4	+	79100.4i	0.434001	+	0.366717i
$137$	217067.			0.988082			0.494041	−	0.869439i	$-0.335519\pi$
$137$	217067.			0.988082			0.494041	+	0.869439i	$0.335519\pi$
$138$	−247533.	+	176321.i	−1.10646	+	0.788146i
$139$	75280.4	−	75280.4i	0.330480	−	0.330480i	−0.522289	−	0.852769i	$-0.674922\pi$
$139$	75280.4	−	75280.4i	0.330480	−	0.330480i	0.852769	+	0.522289i	$0.174922\pi$
$140$	423887.	−	139385.i	1.82780	−	0.601028i
$141$	−150918.	+	172767.i	−0.639282	+	0.731835i
$142$	−314621.	−	74947.0i	−1.30938	−	0.311913i
$143$	222234.			0.908805
$144$	178609.	−	173252.i	0.717789	−	0.696261i
$145$	−309501.			−1.22248
$146$	150078.	+	35750.7i	0.582687	+	0.138804i
$147$	−150911.	+	172759.i	−0.576006	+	0.659399i
$148$	32080.5	+	97560.9i	0.120389	+	0.366118i
$149$	−193532.	+	193532.i	−0.714146	+	0.714146i	−0.967400	−	0.253254i	$-0.918499\pi$
$149$	−193532.	+	193532.i	−0.714146	+	0.714146i	0.253254	+	0.967400i	$0.418499\pi$
$150$	−218584.	+	155700.i	−0.793212	+	0.565016i
$151$	72046.9			0.257142			0.128571	−	0.991700i	$-0.458961\pi$
$151$	72046.9			0.257142			0.128571	+	0.991700i	$0.458961\pi$
$152$	−346440.	+	29111.1i	−1.21624	+	0.102200i
$153$	163028.	−	22110.2i	0.563034	−	0.0763597i
$154$	226196.	−	139163.i	0.768570	−	0.472847i
$155$	−465167.	−	465167.i	−1.55518	−	1.55518i
$156$	163378.	−	386091.i	0.537505	−	1.27022i
$157$	176056.	−	176056.i	0.570034	−	0.570034i	−0.362103	−	0.932138i	$-0.617941\pi$
$157$	176056.	−	176056.i	0.570034	−	0.570034i	0.932138	+	0.362103i	$0.117941\pi$
$158$	18329.9	+	4366.43i	0.0584141	+	0.0139150i
$159$	6717.84	+	99520.6i	0.0210735	+	0.312191i
$160$	−170386.	+	421834.i	−0.526179	+	1.30269i
$161$			611896.i			1.86043i
$162$	−11936.9	−	333818.i	−0.0357359	−	0.999361i
$163$	−306036.	−	306036.i	−0.902203	−	0.902203i	0.0934238	−	0.995626i	$-0.470219\pi$
$163$	−306036.	−	306036.i	−0.902203	−	0.902203i	−0.995626	+	0.0934238i	$0.970219\pi$
$164$	56166.2	+	28368.9i	0.163067	+	0.0823632i
$165$	−212980.	+	243815.i	−0.609016	+	0.697188i
$166$	−54811.8	−	89091.6i	−0.154385	−	0.250938i
$167$			47994.5i			0.133168i	0.997781	+	0.0665841i	$0.0212101\pi$
$167$			47994.5i			0.133168i	−0.997781	+	0.0665841i	$0.978790\pi$
$168$	−75478.8	−	495282.i	−0.206325	−	1.35388i
$169$		−	335042.i		−	0.902365i
$170$	−256195.	+	157619.i	−0.679904	+	0.418297i
$171$	−282663.	+	371363.i	−0.739227	+	0.971198i
$172$	162838.	−	53545.4i	0.419697	−	0.138007i
$173$	111779.	+	111779.i	0.283952	+	0.283952i	0.834683	−	0.550731i	$-0.185651\pi$
$173$	111779.	+	111779.i	0.283952	+	0.283952i	−0.550731	+	0.834683i	$0.685651\pi$
$174$	−57576.6	+	342697.i	−0.144169	+	0.858099i
$175$			540334.i			1.33373i
$176$	−40469.9	+	267732.i	−0.0984806	+	0.651505i
$177$	131997.	−	8910.02i	0.316686	−	0.0213769i
$178$	133990.	−	562479.i	0.316974	−	1.33063i
$179$	−160551.	+	160551.i	−0.374525	+	0.374525i	−0.869122	−	0.494597i	$-0.835316\pi$
$179$	−160551.	+	160551.i	−0.374525	+	0.374525i	0.494597	+	0.869122i	$0.335316\pi$
$180$	267008.	+	549257.i	0.614247	+	1.26356i
$181$	243247.	+	243247.i	0.551889	+	0.551889i	0.926986	−	0.375097i	$-0.122390\pi$
$181$	243247.	+	243247.i	0.551889	+	0.551889i	−0.375097	+	0.926986i	$0.622390\pi$
$182$	−442306.	−	718928.i	−0.989793	−	1.60882i
$183$	−31207.4	−	462318.i	−0.0688857	−	1.02050i
$184$	−476531.	−	402654.i	−1.03764	−	0.876773i
$185$	−252061.			−0.541471
$186$	−601596.	+	428525.i	−1.27504	+	0.908226i
$187$	−126592.	+	126592.i	−0.264729	+	0.264729i
$188$	−420339.	−	212309.i	−0.867371	−	0.438100i
$189$	−561374.	−	370367.i	−1.14314	−	0.754184i
$190$	197730.	−	830052.i	0.397364	−	1.66810i
$191$	317467.			0.629674			0.314837	−	0.949146i	$-0.398050\pi$
$191$	317467.			0.629674			0.314837	+	0.949146i	$0.398050\pi$
$192$	435383.	+	267135.i	0.852350	+	0.522972i
$193$	844913.			1.63275			0.816374	−	0.577524i	$-0.195981\pi$
$193$	844913.			1.63275			0.816374	+	0.577524i	$0.195981\pi$
$194$	−197405.	+	828690.i	−0.376578	+	1.58084i
$195$	774925.	+	676922.i	1.45940	+	1.27483i
$196$	−420320.	−	212299.i	−0.781520	−	0.394737i
$197$	618978.	−	618978.i	1.13634	−	1.13634i	0.147244	−	0.989100i	$-0.452960\pi$
$197$	618978.	−	618978.i	1.13634	−	1.13634i	0.989100	−	0.147244i	$-0.0470403\pi$
$198$	230345.	+	281181.i	0.417557	+	0.509710i
$199$	−184872.			−0.330932			−0.165466	−	0.986215i	$-0.552913\pi$
$199$	−184872.			−0.330932			−0.165466	+	0.986215i	$0.552913\pi$
$200$	−420800.	−	355563.i	−0.743876	−	0.628552i
$201$	173511.	−	11712.3i	0.302926	−	0.0204481i
$202$	111614.	+	181418.i	0.192460	+	0.312825i
$203$	494734.	+	494734.i	0.842619	+	0.842619i
$204$	126864.	+	312995.i	0.213434	+	0.526578i
$205$	−109203.	+	109203.i	−0.181490	+	0.181490i
$206$	−103639.	+	435068.i	−0.170159	+	0.714314i
$207$	−829882.	+	112550.i	−1.34614	+	0.182566i
$208$	850941.	+	128627.i	1.36377	+	0.206146i
$209$		−	507851.i		−	0.804212i
$210$	1.21263e6	+	203734.i	1.89749	+	0.318798i
$211$	−116891.	−	116891.i	−0.180748	−	0.180748i	0.610933	−	0.791682i	$-0.290794\pi$
$211$	−116891.	−	116891.i	−0.180748	−	0.180748i	−0.791682	+	0.610933i	$0.790794\pi$
$212$	−194515.	+	63961.3i	−0.297244	+	0.0977413i
$213$	−671224.	−	586336.i	−1.01372	−	0.885519i
$214$	1134.04	−	697.694i	0.00169275	−	0.00104143i
$215$			420713.i			0.620712i
$216$	657841.	−	193468.i	0.959371	−	0.282147i
$217$			1.48713e6i			2.14388i
$218$	−651962.	−	1.05971e6i	−0.929140	−	1.51023i
$219$	320182.	+	279690.i	0.451115	+	0.394064i
$220$	−593196.	−	299617.i	−0.826307	−	0.417359i
$221$	402351.	+	402351.i	0.554146	+	0.554146i
$222$	−46891.0	+	279096.i	−0.0638568	+	0.380077i
$223$		−	1.13978e6i		−	1.53483i	−0.641152	−	0.767414i	$-0.721543\pi$
$223$		−	1.13978e6i		−	1.53483i	0.641152	−	0.767414i	$-0.278457\pi$
$224$	946658.	−	401938.i	1.26059	−	0.535228i
$225$	−732826.	+	99387.2i	−0.965038	+	0.130880i
$226$	−541971.	−	129105.i	−0.705837	−	0.168140i
$227$	−398760.	+	398760.i	−0.513627	+	0.513627i	−0.915636	−	0.402009i	$-0.868312\pi$
$227$	−398760.	+	398760.i	−0.513627	+	0.513627i	0.402009	+	0.915636i	$0.368312\pi$
$228$	−882298.	−	373353.i	−1.12403	−	0.475645i
$229$	270744.	+	270744.i	0.341169	+	0.341169i	0.856807	−	0.515638i	$-0.172445\pi$
$229$	270744.	+	270744.i	0.341169	+	0.341169i	−0.515638	+	0.856807i	$0.672445\pi$
$230$	1.30414e6	−	802344.i	1.62556	−	1.00009i
$231$	730182.	−	49288.7i	0.900328	−	0.0607739i
$232$	−710843.	+	59731.7i	−0.867070	+	0.0728593i
$233$	−933828.			−1.12688			−0.563439	−	0.826158i	$-0.690522\pi$
$233$	−933828.			−1.12688			−0.563439	+	0.826158i	$0.690522\pi$
$234$	893687.	−	732113.i	1.06695	−	0.874055i
$235$	817261.	−	817261.i	0.965364	−	0.965364i
$236$	84833.4	+	257990.i	0.0991487	+	0.301524i
$237$	39105.7	+	34160.1i	0.0452240	+	0.0395047i
$238$	661476.	+	157573.i	0.756958	+	0.180318i
$239$	687676.			0.778734			0.389367	−	0.921083i	$-0.372694\pi$
$239$	687676.			0.778734			0.389367	+	0.921083i	$0.372694\pi$
$240$	−956625.	+	810302.i	−1.07205	+	0.908069i
$241$	−766745.			−0.850371			−0.425185	−	0.905106i	$-0.639791\pi$
$241$	−766745.			−0.850371			−0.425185	+	0.905106i	$0.639791\pi$
$242$	501474.	+	119458.i	0.550440	+	0.131122i
$243$	399051.	−	829486.i	0.433524	−	0.901142i
$244$	903608.	−	297129.i	0.971641	−	0.319500i
$245$	817225.	−	817225.i	0.869814	−	0.869814i
$246$	100601.	+	141232.i	0.105990	+	0.148797i
$247$	−1.61412e6			−1.68343
$248$	−1.15814e6	−	978595.i	−1.19573	−	1.01036i
$249$	−19413.3	−	287596.i	−0.0198427	−	0.293957i
$250$	−30895.4	+	19007.8i	−0.0312640	+	0.0192345i
$251$	380344.	+	380344.i	0.381059	+	0.381059i	0.871484	−	0.490424i	$-0.163158\pi$
$251$	380344.	+	380344.i	0.381059	+	0.381059i	−0.490424	+	0.871484i	$0.663158\pi$
$252$	451172.	−	1.30479e6i	0.447549	−	1.29431i
$253$	644404.	−	644404.i	0.632932	−	0.632932i
$254$	819578.	+	195235.i	0.797087	+	0.189877i
$255$	−827019.	+	55825.4i	−0.796462	+	0.0537627i
$256$	−309921.	+	1.00173e6i	−0.295564	+	0.955323i
$257$		−	1.15436e6i		−	1.09021i	−0.838369	−	0.545103i	$-0.816490\pi$
$257$		−	1.15436e6i		−	1.09021i	0.838369	−	0.545103i	$-0.183510\pi$
$258$	465838.	+	78265.5i	0.435698	+	0.0732017i
$259$	402916.	+	402916.i	0.373220	+	0.373220i
$260$	−952283.	+	1.88538e6i	−0.873640	+	1.72968i
$261$	−579982.	+	761981.i	−0.527003	+	0.692377i
$262$	859020.	+	1.39626e6i	0.773126	+	1.25664i
$263$			2.15796e6i			1.92377i	0.273451	+	0.961886i	$0.411835\pi$
$263$			2.15796e6i			1.92377i	−0.273451	+	0.961886i	$0.588165\pi$
$264$	−442106.	+	601083.i	−0.390406	+	0.530793i
$265$		−	502553.i		−	0.439610i
$266$	−1.64290e6	+	1.01076e6i	−1.42366	+	0.875879i
$267$	1.04825e6	−	1.20001e6i	0.899886	−	1.03017i
$268$	111515.	+	339130.i	0.0948407	+	0.288423i
$269$	−364986.	−	364986.i	−0.307536	−	0.307536i	0.536417	−	0.843953i	$-0.319777\pi$
$269$	−364986.	−	364986.i	−0.307536	−	0.307536i	−0.843953	+	0.536417i	$0.819777\pi$
$270$	−53266.6	+	1.68210e6i	−0.0444678	+	1.40424i
$271$			2062.18i			0.00170570i	1.00000		0.000852852i	$0.000271471\pi$
$271$			2062.18i			0.00170570i	−1.00000		0.000852852i	$0.999729\pi$
$272$	−557994.	+	411453.i	−0.457306	+	0.337208i
$273$	−156656.	−	2.32076e6i	−0.127216	−	1.88462i
$274$	−284545.	+	1.19449e6i	−0.228968	+	0.961187i
$275$	569040.	−	569040.i	0.453744	−	0.453744i
$276$	−645793.	−	1.59328e6i	−0.510294	−	1.25898i
$277$	−1.25193e6	−	1.25193e6i	−0.980345	−	0.980345i	0.0194651	−	0.999811i	$-0.493804\pi$
$277$	−1.25193e6	−	1.25193e6i	−0.980345	−	0.980345i	−0.999811	+	0.0194651i	$0.993804\pi$
$278$	315576.	+	512941.i	0.244902	+	0.398066i
$279$	−2.01692e6	+	273538.i	−1.55123	+	0.210381i
$280$	211360.	+	2.51531e6i	0.161112	+	1.91733i
$281$	884058.			0.667905			0.333953	−	0.942590i	$-0.391617\pi$
$281$	884058.			0.667905			0.333953	+	0.942590i	$0.391617\pi$
$282$	−752884.	−	1.05696e6i	−0.563774	−	0.791469i
$283$	−941398.	+	941398.i	−0.698727	+	0.698727i	−0.964136	−	0.265409i	$-0.914493\pi$
$283$	−941398.	+	941398.i	−0.698727	+	0.698727i	0.265409	+	0.964136i	$0.414493\pi$
$284$	824848.	−	1.63308e6i	0.606846	−	1.20146i
$285$	1.54691e6	−	1.77086e6i	1.12811	−	1.29144i
$286$	−291318.	+	1.22293e6i	−0.210597	+	0.884067i
$287$	349121.			0.250191
$288$	719253.	+	1.20997e6i	0.510976	+	0.859595i
$289$	961473.			0.677162
$290$	405712.	−	1.70314e6i	0.283285	−	1.18920i
$291$	−1.54437e6	+	1.76796e6i	−1.06910	+	1.22388i
$292$	−393463.	+	778997.i	−0.270052	+	0.534661i
$293$	−248509.	+	248509.i	−0.169112	+	0.169112i	−0.786589	−	0.617477i	$-0.788155\pi$
$293$	−248509.	+	248509.i	−0.169112	+	0.169112i	0.617477	+	0.786589i	$0.288155\pi$
$294$	−752850.	−	1.05691e6i	−0.507972	−	0.713130i
$295$	−666548.			−0.445940
$296$	−578918.	+	48646.1i	−0.384050	+	0.0322715i
$297$	201155.	+	981241.i	0.132324	+	0.645483i
$298$	−811289.	−	1.31868e6i	−0.529218	−	0.860196i
$299$	−2.04813e6	−	2.04813e6i	−1.32489	−	1.32489i
$300$	−570266.	−	1.40694e6i	−0.365826	−	0.902552i
$301$	672506.	−	672506.i	0.427838	−	0.427838i
$302$	−94443.4	+	396465.i	−0.0595874	+	0.250143i
$303$	39531.4	+	585634.i	0.0247364	+	0.366454i
$304$	293940.	−	1.94458e6i	0.182421	−	1.20682i
$305$			2.33458e6i			1.43701i
$306$	−92037.7	+	926109.i	−0.0561904	+	0.565403i
$307$	1.40766e6	+	1.40766e6i	0.852417	+	0.852417i	0.990430	−	0.138013i	$-0.0440716\pi$
$307$	1.40766e6	+	1.40766e6i	0.852417	+	0.852417i	−0.138013	+	0.990430i	$0.544072\pi$
$308$	469283.	+	1.42715e6i	0.281876	+	0.857223i
$309$	−810805.	+	928190.i	−0.483081	+	0.553020i
$310$	3.16953e6	−	1.94999e6i	1.87323	−	1.15247i
$311$			817984.i			0.479561i	0.970827	+	0.239780i	$0.0770755\pi$
$311$			817984.i			0.479561i	−0.970827	+	0.239780i	$0.922925\pi$
$312$	1.91044e6	+	1.40516e6i	1.11109	+	0.817221i
$313$			2.60425e6i			1.50252i	0.660005	+	0.751261i	$0.270554\pi$
$313$			2.60425e6i			1.50252i	−0.660005	+	0.751261i	$0.729446\pi$
$314$	738028.	+	1.19960e6i	0.422424	+	0.686612i
$315$	2.69626e6	+	2.05226e6i	1.53103	+	1.16535i
$316$	−48055.9	+	95143.4i	−0.0270725	+	0.0535995i
$317$	361558.	+	361558.i	0.202083	+	0.202083i	0.800892	−	0.598809i	$-0.204359\pi$
$317$	361558.	+	361558.i	0.202083	+	0.202083i	−0.598809	+	0.800892i	$0.704359\pi$
$318$	−556456.	−	93490.2i	−0.308577	−	0.0518440i
$319$		−	1.04203e6i		−	0.573331i
$320$	−2.09795e6	−	1.49058e6i	−1.14530	−	0.813729i
$321$	3660.77	−	247.109i	0.00198294	−	0.000133852i
$322$	−3.36719e6	−	802110.i	−1.80979	−	0.431116i
$323$	919456.	−	919456.i	0.490371	−	0.490371i
$324$	1.85261e6	+	371902.i	0.980440	+	0.196818i
$325$	−1.80860e6	−	1.80860e6i	−0.949805	−	0.949805i
$326$	2.08525e6	−	1.28291e6i	1.08671	−	0.668578i
$327$	−230912.	−	3.42082e6i	−0.119420	−	1.76914i
$328$	−229737.	+	271888.i	−0.117909	+	0.139542i
$329$	−2.61277e6			−1.33080
$330$	−1.06249e6	−	1.49161e6i	−0.537083	−	0.753998i
$331$	289282.	−	289282.i	0.145128	−	0.145128i	−0.630809	−	0.775938i	$-0.717277\pi$
$331$	289282.	−	289282.i	0.145128	−	0.145128i	0.775938	+	0.630809i	$0.217277\pi$
$332$	562110.	−	184836.i	0.279883	−	0.0920325i
$333$	−472343.	+	620565.i	−0.233425	+	0.306674i
$334$	−264108.	−	62914.1i	−0.129543	−	0.0308590i
$335$	−876185.			−0.426564
$336$	2.82442e6	+	233895.i	1.36484	+	0.113024i
$337$	550304.			0.263954			0.131977	−	0.991253i	$-0.457867\pi$
$337$	550304.			0.263954			0.131977	+	0.991253i	$0.457867\pi$
$338$	1.84369e6	+	439193.i	0.877802	+	0.209105i
$339$	−1.15626e6	−	1.01003e6i	−0.546457	−	0.477349i
$340$	−531520.	−	1.61642e6i	−0.249358	−	0.758329i
$341$	1.56614e6	−	1.56614e6i	0.729363	−	0.729363i
$342$	−1.67303e6	−	2.04226e6i	−0.773462	−	0.944161i
$343$	371356.			0.170433
$344$	81195.0	+	966270.i	0.0369942	+	0.440253i
$345$	4.20987e6	−	284174.i	1.90424	−	0.128540i
$346$	−761634.	+	468580.i	−0.342023	+	0.210423i
$347$	−2.10264e6	−	2.10264e6i	−0.937435	−	0.937435i	0.0607198	−	0.998155i	$-0.480660\pi$
$347$	−2.10264e6	−	2.10264e6i	−0.937435	−	0.937435i	−0.998155	+	0.0607198i	$0.980660\pi$
$348$	−1.81034e6	−	766065.i	−0.801333	−	0.339092i
$349$	−1.98789e6	+	1.98789e6i	−0.873634	+	0.873634i	−0.992866	−	0.119232i	$-0.961957\pi$
$349$	−1.98789e6	+	1.98789e6i	−0.873634	+	0.873634i	0.119232	+	0.992866i	$0.461957\pi$
$350$	−2.97339e6	−	708302.i	−1.29742	−	0.309064i
$351$	3.11871e6	−	639338.i	1.35116	−	0.276989i
$352$	−1.42024e6	−	573660.i	−0.610951	−	0.246773i
$353$			3.92043e6i			1.67454i	0.546787	+	0.837272i	$0.315851\pi$
$353$			3.92043e6i			1.67454i	−0.546787	+	0.837272i	$0.684149\pi$
$354$	−123998.	+	738041.i	−0.0525905	+	0.313020i
$355$	3.17517e6	+	3.17517e6i	1.33720	+	1.33720i
$356$	2.91961e6	+	1.47466e6i	1.22096	+	0.616691i
$357$	1.41122e6	+	1.23275e6i	0.586035	+	0.511921i
$358$	−673033.	−	1.09395e6i	−0.277542	−	0.451119i
$359$		−	3.56347e6i		−	1.45927i	−0.683834	−	0.729637i	$-0.739689\pi$
$359$		−	3.56347e6i		−	1.45927i	0.683834	−	0.729637i	$-0.260311\pi$
$360$	−3.37250e6	+	749314.i	−1.37150	+	0.304725i
$361$			1.21250e6i			0.489683i
$362$	−1.65742e6	+	1.01970e6i	−0.664756	+	0.408978i
$363$	1.06986e6	+	934561.i	0.426150	+	0.372256i
$364$	4.53597e6	−	1.49154e6i	1.79439	−	0.590040i
$365$	−1.51460e6	−	1.51460e6i	−0.595066	−	0.595066i
$366$	2.58499e6	+	434304.i	1.00869	+	0.169469i
$367$			2.09877e6i			0.813392i	0.913563	+	0.406696i	$0.133319\pi$
$367$			2.09877e6i			0.813392i	−0.913563	+	0.406696i	$0.866681\pi$
$368$	2.84042e6	−	2.09447e6i	1.09336	−	0.806221i
$369$	64216.3	+	473495.i	0.0245516	+	0.181030i
$370$	330416.	−	1.38706e6i	0.125475	−	0.526733i
$371$	−803326.	+	803326.i	−0.303010	+	0.303010i
$372$	−1.56951e6	−	3.87224e6i	−0.588040	−	1.45079i
$373$	2.59186e6	+	2.59186e6i	0.964581	+	0.964581i	0.999394	−	0.0348128i	$-0.0110835\pi$
$373$	2.59186e6	+	2.59186e6i	0.964581	+	0.964581i	−0.0348128	+	0.999394i	$0.511084\pi$
$374$	−530674.	−	862563.i	−0.196177	−	0.318868i
$375$	−99733.1	+	6732.18i	−0.0366236	+	0.00247217i
$376$	1.71931e6	−	2.03477e6i	0.627170	−	0.742241i
$377$	−3.31194e6			−1.20013
$378$	2.77396e6	−	2.60367e6i	0.998553	−	0.937253i
$379$	324348.	−	324348.i	0.115988	−	0.115988i	−0.646730	−	0.762719i	$-0.723864\pi$
$379$	324348.	−	324348.i	0.115988	−	0.115988i	0.762719	+	0.646730i	$0.223864\pi$
$380$	4.30848e6	+	2.17616e6i	1.53061	+	0.773095i
$381$	1.74852e6	+	1.52739e6i	0.617103	+	0.539060i
$382$	−416155.	+	1.74698e6i	−0.145914	+	0.612534i
$383$	931018.			0.324311			0.162155	−	0.986765i	$-0.448155\pi$
$383$	931018.			0.324311			0.162155	+	0.986765i	$0.448155\pi$
$384$	−2.04074e6	+	2.04568e6i	−0.706251	+	0.707961i
$385$	−3.68722e6			−1.26779
$386$	−1.10756e6	+	4.64945e6i	−0.378356	+	1.58830i
$387$	1.03578e6	+	788386.i	0.351553	+	0.267585i
$388$	−4.30141e6	−	2.17259e6i	−1.45055	−	0.732654i
$389$	1.73316e6	−	1.73316e6i	0.580718	−	0.580718i	−0.354383	−	0.935100i	$-0.615309\pi$
$389$	1.73316e6	−	1.73316e6i	0.580718	−	0.580718i	0.935100	+	0.354383i	$0.115309\pi$
$390$	−4.74084e6	+	3.37696e6i	−1.57831	+	1.12426i
$391$	2.33337e6			0.771864
$392$	1.71924e6	−	2.03467e6i	0.565093	−	0.668775i
$393$	304248.	+	4.50725e6i	0.0993679	+	1.47207i
$394$	2.59477e6	+	4.21756e6i	0.842089	+	1.36874i
$395$	−184987.	−	184987.i	−0.0596551	−	0.0596551i
$396$	−1.84925e6	+	898970.i	−0.592596	+	0.288076i
$397$	4.28688e6	−	4.28688e6i	1.36510	−	1.36510i	0.497822	−	0.867279i	$-0.334133\pi$
$397$	4.28688e6	−	4.28688e6i	1.36510	−	1.36510i	0.867279	−	0.497822i	$-0.165867\pi$
$398$	242342.	−	1.01733e6i	0.0766867	−	0.321924i
$399$	−5.30343e6	+	357991.i	−1.66772	+	0.112575i
$400$	2.50823e6	−	1.84952e6i	0.783821	−	0.577974i
$401$			1.01426e6i			0.314984i	0.987520	+	0.157492i	$0.0503408\pi$
$401$			1.01426e6i			0.314984i	−0.987520	+	0.157492i	$0.949659\pi$
$402$	−162997.	+	970163.i	−0.0503055	+	0.299419i
$403$	−4.97771e6	−	4.97771e6i	−1.52675	−	1.52675i
$404$	−1.14463e6	+	376383.i	−0.348909	+	0.114730i
$405$	−2.28743e6	+	4.03428e6i	−0.692962	+	1.22216i
$406$	−3.37098e6	+	2.07393e6i	−1.01494	+	0.624424i
$407$		−	848644.i		−	0.253945i
$408$	−1.88868e6	+	287826.i	−0.561703	+	0.0856012i
$409$		−	6.23884e6i		−	1.84415i	−0.387015	−	0.922074i	$-0.626494\pi$
$409$		−	6.23884e6i		−	1.84415i	0.387015	−	0.922074i	$-0.373506\pi$
$410$	−457783.	−	744084.i	−0.134493	−	0.218606i
$411$	−2.22609e6	+	2.54838e6i	−0.650038	+	0.744148i
$412$	−2.25827e6	−	1.14063e6i	−0.655439	−	0.331055i
$413$	1.06547e6	+	1.06547e6i	0.307373	+	0.307373i
$414$	468510.	−	4.71428e6i	0.134344	−	1.35181i
$415$			1.45228e6i			0.413934i
$416$	−1.82328e6	+	4.51401e6i	−0.516560	+	1.27888i
$417$	111771.	+	1.65582e6i	0.0314767	+	0.466308i
$418$	2.79464e6	+	665722.i	0.782322	+	0.186360i
$419$	−242560.	+	242560.i	−0.0674970	+	0.0674970i	−0.740049	−	0.672552i	$-0.765198\pi$
$419$	−242560.	+	242560.i	−0.0674970	+	0.0674970i	0.672552	+	0.740049i	$0.265198\pi$
$420$	−2.71071e6	+	6.40588e6i	−0.749825	+	1.77197i
$421$	−3.63407e6	−	3.63407e6i	−0.999282	−	0.999282i	0.000718192	−	1.00000i	$-0.499771\pi$
$421$	−3.63407e6	−	3.63407e6i	−0.999282	−	0.999282i	−1.00000		0.000718192i	$0.999771\pi$
$422$	796464.	−	490009.i	0.217713	−	0.133944i
$423$	−480584.	−	3.54356e6i	−0.130593	−	0.962917i
$424$	−96989.6	−	1.15424e6i	−0.0262006	−	0.311803i
$425$	2.06047e6			0.553344
$426$	4.10642e6	−	2.92506e6i	1.09632	−	0.780927i
$427$	3.73181e6	−	3.73181e6i	0.990489	−	0.990489i
$428$	2352.76	+	7155.04i	0.000620823	+	0.00188800i
$429$	−2.27908e6	+	2.60904e6i	−0.597883	+	0.684443i
$430$	−2.31513e6	−	551496.i	−0.603816	−	0.143837i
$431$	2.73765e6			0.709880			0.354940	−	0.934889i	$-0.384501\pi$
$431$	2.73765e6			0.709880			0.354940	+	0.934889i	$0.384501\pi$
$432$	202295.	+	3.87363e6i	0.0521525	+	0.998639i
$433$	165058.			0.0423075			0.0211537	−	0.999776i	$-0.493266\pi$
$433$	165058.			0.0423075			0.0211537	+	0.999776i	$0.493266\pi$
$434$	−8.18350e6	−	1.94942e6i	−2.08552	−	0.496800i
$435$	3.17403e6	−	3.63355e6i	0.804243	−	0.920678i
$436$	6.68606e6	−	2.19854e6i	1.68443	−	0.553884i
$437$	−4.68041e6	+	4.68041e6i	−1.17241	+	1.17241i
$438$	−1.95881e6	+	1.39529e6i	−0.487874	+	0.347519i
$439$	135759.			0.0336206			0.0168103	−	0.999859i	$-0.494649\pi$
$439$	135759.			0.0336206			0.0168103	+	0.999859i	$0.494649\pi$
$440$	2.42635e6	−	2.87153e6i	0.597478	−	0.707101i
$441$	−480563.	−	3.54340e6i	−0.117667	−	0.867609i
$442$	−2.74151e6	+	1.68666e6i	−0.667475	+	0.410651i
$443$	−4.42380e6	−	4.42380e6i	−1.07099	−	1.07099i	−0.997279	−	0.0737132i	$-0.976515\pi$
$443$	−4.42380e6	−	4.42380e6i	−1.07099	−	1.07099i	−0.0737132	−	0.997279i	$-0.523485\pi$
$444$	−1.47436e6	−	623891.i	−0.354934	−	0.150194i
$445$	−5.67657e6	+	5.67657e6i	−1.35890	+	1.35890i
$446$	6.27208e6	+	1.49409e6i	1.49305	+	0.355665i
$447$	−287342.	−	4.25680e6i	−0.0680191	−	1.00766i
$448$	970878.	+	5.73623e6i	0.228544	+	1.35030i
$449$		−	3.84711e6i		−	0.900572i	−0.892884	−	0.450286i	$-0.851322\pi$
$449$		−	3.84711e6i		−	0.900572i	0.892884	−	0.450286i	$-0.148678\pi$
$450$	413717.	−	4.16293e6i	0.0963102	−	0.969099i
$451$	−367669.	−	367669.i	−0.0851169	−	0.0851169i
$452$	1.42090e6	−	2.81316e6i	0.327127	−	0.647662i
$453$	−738863.	+	845833.i	−0.169168	+	0.193660i
$454$	−1.67161e6	−	2.71705e6i	−0.380623	−	0.618668i
$455$			1.17192e7i			2.65382i
$456$	3.21108e6	−	4.36576e6i	0.723169	−	0.983214i
$457$		−	6.25336e6i		−	1.40063i	−0.713835	−	0.700314i	$-0.753043\pi$
$457$		−	6.25336e6i		−	1.40063i	0.713835	−	0.700314i	$-0.246957\pi$
$458$	−1.84478e6	+	1.13496e6i	−0.410941	+	0.252823i
$459$	−1.41233e6	+	2.14071e6i	−0.312900	+	0.474270i
$460$	2.70566e6	+	8.22826e6i	0.596181	+	1.81307i
$461$	1.13796e6	+	1.13796e6i	0.249388	+	0.249388i	0.820719	−	0.571332i	$-0.193573\pi$
$461$	1.13796e6	+	1.13796e6i	0.249388	+	0.249388i	−0.571332	+	0.820719i	$0.693573\pi$
$462$	−685937.	+	4.08271e6i	−0.149513	+	0.889905i
$463$			666400.i			0.144472i	0.997388	+	0.0722359i	$0.0230134\pi$
$463$			666400.i			0.144472i	−0.997388	+	0.0722359i	$0.976987\pi$
$464$	603120.	−	3.98998e6i	0.130050	−	0.860352i
$465$	1.02315e7	−	690647.i	2.19436	−	0.148123i
$466$	1.22412e6	−	5.13874e6i	0.261131	−	1.09620i
$467$	12036.9	−	12036.9i	0.00255402	−	0.00255402i	−0.705829	−	0.708383i	$-0.749425\pi$
$467$	12036.9	−	12036.9i	0.00255402	−	0.00255402i	0.708383	+	0.705829i	$0.249425\pi$
$468$	2.85723e6	+	5.87755e6i	0.603018	+	1.24046i
$469$	1.40057e6	+	1.40057e6i	0.294018	+	0.294018i
$470$	3.42597e6	+	5.56860e6i	0.715384	+	1.16279i
$471$	261395.	+	3.87241e6i	0.0542932	+	0.804320i
$472$	−1.53089e6	+	128640.i	−0.316292	+	0.0265778i
$473$	−1.41647e6			−0.291108
$474$	−239241.	+	170415.i	−0.0489091	+	0.0348386i
$475$	−4.13303e6	+	4.13303e6i	−0.840493	+	0.840493i
$476$	−1.73421e6	+	3.43347e6i	−0.350819	+	0.694569i
$477$	−1.23727e6	−	941748.i	−0.248982	−	0.189513i
$478$	−901447.	+	3.78419e6i	−0.180456	+	0.757537i
$479$	−1.05089e6			−0.209276			−0.104638	−	0.994510i	$-0.533368\pi$
$479$	−1.05089e6			−0.209276			−0.104638	+	0.994510i	$0.533368\pi$
$480$	−3.20499e6	−	6.32638e6i	−0.634927	−	1.25329i
$481$	−2.69728e6			−0.531573
$482$	1.00510e6	−	4.21930e6i	0.197056	−	0.827224i
$483$	−7.18368e6	−	6.27518e6i	−1.40113	−	1.22394i
$484$	−1.31473e6	+	2.60296e6i	−0.255107	+	0.505073i
$485$	8.36319e6	−	8.36319e6i	1.61442	−	1.61442i
$486$	4.04146e6	+	3.28327e6i	0.776153	+	0.630545i
$487$	1.03155e7			1.97092			0.985460	−	0.169907i	$-0.0543468\pi$
$487$	1.03155e7			1.97092			0.985460	+	0.169907i	$0.0543468\pi$
$488$	450560.	+	5.36194e6i	0.0856452	+	1.01923i
$489$	6.73138e6	−	454381.i	1.27301	−	0.0859307i
$490$	3.42582e6	+	5.56835e6i	0.644576	+	1.04770i
$491$	1.94353e6	+	1.94353e6i	0.363820	+	0.363820i	0.865217	−	0.501397i	$-0.167180\pi$
$491$	1.94353e6	+	1.94353e6i	0.363820	+	0.363820i	−0.501397	+	0.865217i	$0.667180\pi$
$492$	−909055.	+	368461.i	−0.169308	+	0.0686245i
$493$	1.88659e6	−	1.88659e6i	0.349590	−	0.349590i
$494$	2.11589e6	−	8.88231e6i	0.390099	−	1.63760i
$495$	−678216.	−	5.00079e6i	−0.124410	−	0.917330i
$496$	6.90326e6	−	5.09032e6i	1.25994	−	0.929054i
$497$		−	1.01510e7i		−	1.84339i
$498$	1.60805e6	+	270169.i	0.290554	+	0.0488160i
$499$	3.31585e6	+	3.31585e6i	0.596133	+	0.596133i	0.939281	−	0.343148i	$-0.111493\pi$
$499$	3.31585e6	+	3.31585e6i	0.596133	+	0.596133i	−0.343148	+	0.939281i	$0.611493\pi$
$500$	−64097.9	−	194930.i	−0.0114662	−	0.0348702i
$501$	−563458.	−	492199.i	−0.100292	−	0.0876085i
$502$	−2.59157e6	+	1.59441e6i	−0.458990	+	0.282384i
$503$		−	5.03011e6i		−	0.886457i	−0.896409	−	0.443229i	$-0.853833\pi$
$503$		−	5.03011e6i		−	0.886457i	0.896409	−	0.443229i	$-0.146167\pi$
$504$	6.58869e6	+	4.19314e6i	1.15537	+	0.735298i
$505$		−	2.95730e6i		−	0.516020i
$506$	2.70135e6	+	4.39080e6i	0.469035	+	0.762373i
$507$	3.93340e6	+	3.43596e6i	0.679592	+	0.593646i
$508$	−2.14870e6	+	4.25411e6i	−0.369417	+	0.731391i
$509$	3.79536e6	+	3.79536e6i	0.649320	+	0.649320i	0.952829	−	0.303509i	$-0.0981582\pi$
$509$	3.79536e6	+	3.79536e6i	0.649320	+	0.649320i	−0.303509	+	0.952829i	$0.598158\pi$
$510$	776906.	−	4.62416e6i	0.132264	−	0.787241i
$511$			4.84214e6i			0.820323i
$512$	−5.10613e6	−	3.01858e6i	−0.860828	−	0.508895i
$513$	−1.46102e6	−	7.12691e6i	−0.245111	−	1.19566i
$514$	6.35231e6	+	1.51321e6i	1.06053	+	0.252633i
$515$	4.39073e6	−	4.39073e6i	0.729489	−	0.729489i
$516$	−1.04133e6	+	2.46085e6i	−0.172173	+	0.406876i
$517$	2.75158e6	+	2.75158e6i	0.452747	+	0.452747i
$518$	−2.74536e6	+	1.68903e6i	−0.449548	+	0.276575i
$519$	−2.45862e6	+	165962.i	−0.400658	+	0.0270452i
$520$	−9.12668e6	−	7.71176e6i	−1.48015	−	1.25068i
$521$	−1.06174e7			−1.71366			−0.856830	−	0.515599i	$-0.827569\pi$
$521$	−1.06174e7			−1.71366			−0.856830	+	0.515599i	$0.827569\pi$
$522$	−3.43281e6	−	4.19042e6i	−0.551409	−	0.673102i
$523$	−7.91225e6	+	7.91225e6i	−1.26487	+	1.26487i	−0.316165	+	0.948704i	$0.602395\pi$
$523$	−7.91225e6	+	7.91225e6i	−1.26487	+	1.26487i	−0.948704	+	0.316165i	$0.897605\pi$
$524$	−8.80949e6	+	2.89678e6i	−1.40159	+	0.460880i
$525$	−6.34354e6	−	5.54129e6i	−1.00446	−	0.877430i
$526$	−1.18750e7	−	2.82878e6i	−1.87141	−	0.445795i
$527$	5.67093e6			0.889463
$528$	−2.72815e6	−	3.22079e6i	−0.425876	−	0.502779i
$529$	−5.44146e6			−0.845427
$530$	2.76549e6	+	658777.i	0.427644	+	0.101871i
$531$	−1.24906e6	+	1.64102e6i	−0.192242	+	0.252568i
$532$	−3.40848e6	−	1.03656e7i	−0.522134	−	1.58788i
$533$	−1.16858e6	+	1.16858e6i	−0.178172	+	0.178172i
$534$	5.22942e6	+	7.34145e6i	0.793597	+	1.11411i
$535$	−18485.9			−0.00279227
$536$	−2.01237e6	+	169098.i	−0.302549	+	0.0254230i
$537$	−238375.	−	3.53138e6i	−0.0356718	−	0.528455i
$538$	2.48692e6	−	1.53003e6i	0.370430	−	0.227900i
$539$	2.75145e6	+	2.75145e6i	0.407934	+	0.407934i
$540$	−9.18655e6	−	2.49812e6i	−1.35571	−	0.368662i
$541$	−2.60354e6	+	2.60354e6i	−0.382447	+	0.382447i	−0.871983	−	0.489536i	$-0.837166\pi$
$541$	−2.60354e6	+	2.60354e6i	−0.382447	+	0.382447i	0.489536	+	0.871983i	$0.337166\pi$
$542$	−11347.9	−	2703.23i	−0.00165927	−	0.000395262i
$543$	−5.35031e6	+	361157.i	−0.778717	+	0.0525649i
$544$	−1.53273e6	−	3.60993e6i	−0.222058	−	0.523000i
$545$			1.72743e7i			2.49120i
$546$	1.29762e7	+	2.18014e6i	1.86280	+	0.312970i
$547$	−2.57339e6	−	2.57339e6i	−0.367737	−	0.367737i	0.498914	−	0.866651i	$-0.333732\pi$
$547$	−2.57339e6	−	2.57339e6i	−0.367737	−	0.367737i	−0.866651	+	0.498914i	$0.833732\pi$
$548$	−6.20016e6	−	3.13163e6i	−0.881965	−	0.445471i
$549$	5.74767e6	+	4.37484e6i	0.813882	+	0.619486i
$550$	2.38542e6	+	3.87729e6i	0.336247	+	0.546539i
$551$			7.56846e6i			1.06201i
$552$	9.61415e6	−	1.46515e6i	1.34296	−	0.204661i
$553$			591398.i			0.0822370i
$554$	8.53029e6	−	5.24809e6i	1.18084	−	0.726486i
$555$	2.58496e6	−	2.95920e6i	0.356222	−	0.407795i
$556$	−3.23632e6	+	1.06418e6i	−0.443982	+	0.145992i
$557$	−3.40257e6	−	3.40257e6i	−0.464696	−	0.464696i	0.435495	−	0.900191i	$-0.356573\pi$
$557$	−3.40257e6	−	3.40257e6i	−0.464696	−	0.464696i	−0.900191	+	0.435495i	$0.856573\pi$
$558$	1.13865e6	−	1.14574e7i	0.154812	−	1.55776i
$559$			4.50201e6i			0.609365i
$560$	−1.41185e7	−	2.13413e6i	−1.90247	−	0.287575i
$561$	−187954.	−	2.78443e6i	−0.0252142	−	0.373533i
$562$	−1.15888e6	+	4.86486e6i	−0.154773	+	0.649725i
$563$	−9.61677e6	+	9.61677e6i	−1.27867	+	1.27867i	−0.337256	+	0.941413i	$0.609499\pi$
$563$	−9.61677e6	+	9.61677e6i	−1.27867	+	1.27867i	−0.941413	+	0.337256i	$0.890501\pi$
$564$	6.80322e6	−	2.75751e6i	0.900568	−	0.365022i
$565$	5.46960e6	+	5.46960e6i	0.720833	+	0.720833i
$566$	−3.94636e6	−	6.41444e6i	−0.517792	−	0.841623i
$567$	1.01052e7	−	2.79233e6i	1.32004	−	0.364761i
$568$	7.90535e6	+	6.67977e6i	1.02814	+	0.868742i
$569$	1.12841e7			1.46112			0.730560	−	0.682849i	$-0.239259\pi$
$569$	1.12841e7			1.46112			0.730560	+	0.682849i	$0.239259\pi$
$570$	7.71706e6	+	1.08338e7i	0.994867	+	1.39667i
$571$	1.00616e7	−	1.00616e7i	1.29144	−	1.29144i	0.357549	−	0.933894i	$-0.383612\pi$
$571$	1.00616e7	−	1.00616e7i	1.29144	−	1.29144i	0.933894	−	0.357549i	$-0.116388\pi$
$572$	−6.34774e6	−	3.20617e6i	−0.811202	−	0.409729i
$573$	−3.25573e6	+	3.72708e6i	−0.414249	+	0.474222i
$574$	−457649.	+	1.92117e6i	−0.0579767	+	0.243381i
$575$	−1.04887e7			−1.32297
$576$	−7.60116e6	+	2.37185e6i	−0.954605	+	0.297873i
$577$	7.61662e6			0.952407			0.476203	−	0.879335i	$-0.342013\pi$
$577$	7.61662e6			0.952407			0.476203	+	0.879335i	$0.342013\pi$
$578$	−1.26036e6	+	5.29086e6i	−0.156918	+	0.658729i
$579$	−8.66485e6	+	9.91932e6i	−1.07415	+	1.22966i
$580$	8.84036e6	+	4.46517e6i	1.09119	+	0.551147i
$581$	2.32146e6	−	2.32146e6i	0.285312	−	0.285312i
$582$	−7.70440e6	−	1.08160e7i	−0.942826	−	1.32361i
$583$	1.69201e6			0.206173
$584$	−3.77095e6	−	3.18633e6i	−0.457529	−	0.386598i
$585$	−1.58942e7	+	2.15560e6i	−1.92021	+	0.260422i
$586$	−1.04176e6	−	1.69328e6i	−0.125320	−	0.203697i
$587$	7.46807e6	+	7.46807e6i	0.894567	+	0.894567i	0.994949	−	0.100382i	$-0.0320064\pi$
$587$	7.46807e6	+	7.46807e6i	0.894567	+	0.894567i	−0.100382	+	0.994949i	$0.532006\pi$
$588$	6.80291e6	−	2.75738e6i	0.811431	−	0.328892i
$589$	−1.13751e7	+	1.13751e7i	−1.35104	+	1.35104i
$590$	873751.	−	3.66793e6i	0.103337	−	0.433801i
$591$	919015.	+	1.36147e7i	0.108232	+	1.60338i
$592$	491188.	−	3.24948e6i	0.0576027	−	0.381075i
$593$		−	2.06893e6i		−	0.241607i	−0.992676	−	0.120804i	$-0.961453\pi$
$593$		−	2.06893e6i		−	0.241607i	0.992676	−	0.120804i	$-0.0385471\pi$
$594$	−5.66333e6	−	179340.i	−0.658576	−	0.0208550i
$595$	−6.67566e6	−	6.67566e6i	−0.773039	−	0.773039i
$596$	8.31999e6	−	2.73582e6i	0.959417	−	0.315480i
$597$	1.89592e6	−	2.17041e6i	0.217713	−	0.249233i
$598$	1.39554e7	−	8.58581e6i	1.59584	−	0.981812i
$599$		−	795351.i		−	0.0905716i	−0.998974	−	0.0452858i	$-0.985580\pi$
$599$		−	795351.i		−	0.0905716i	0.998974	−	0.0452858i	$-0.0144198\pi$
$600$	8.48975e6	−	1.29380e6i	0.962757	−	0.146720i
$601$			7.90865e6i			0.893133i	0.894751	+	0.446566i	$0.147353\pi$
$601$			7.90865e6i			0.893133i	−0.894751	+	0.446566i	$0.852647\pi$
$602$	2.81916e6	+	4.58228e6i	0.317050	+	0.515336i
$603$	−1.64191e6	+	2.15714e6i	−0.183889	+	0.241593i
$604$	−2.05790e6	−	1.03942e6i	−0.229526	−	0.115931i
$605$	−5.06091e6	−	5.06091e6i	−0.562134	−	0.562134i
$606$	−3.27449e6	−	550148.i	−0.362211	−	0.0608552i
$607$		−	4.12561e6i		−	0.454482i	−0.973839	−	0.227241i	$-0.927029\pi$
$607$		−	4.12561e6i		−	0.454482i	0.973839	−	0.227241i	$-0.0729705\pi$
$608$	1.03155e7	+	4.16658e6i	1.13169	+	0.457110i
$609$	−1.08818e7	+	734545.i	−1.18894	+	0.0802556i
$610$	−1.28469e7	−	3.06031e6i	−1.39790	−	0.332998i
$611$	8.74544e6	−	8.74544e6i	0.947717	−	0.947717i
$612$	−4.97561e6	−	1.72047e6i	−0.536992	−	0.185682i
$613$	−3.51412e6	−	3.51412e6i	−0.377716	−	0.377716i	0.492561	−	0.870278i	$-0.336061\pi$
$613$	−3.51412e6	−	3.51412e6i	−0.377716	−	0.377716i	−0.870278	+	0.492561i	$0.836061\pi$
$614$	−9.59143e6	+	5.90094e6i	−1.02674	+	0.631684i
$615$	−162138.	−	2.40197e6i	−0.0172861	−	0.256082i
$616$	−8.46861e6	+	711611.i	−0.899208	+	0.0755598i
$617$	6.44943e6			0.682038			0.341019	−	0.940056i	$-0.389228\pi$
$617$	6.44943e6			0.682038			0.341019	+	0.940056i	$0.389228\pi$
$618$	−4.04486e6	−	5.67849e6i	−0.426023	−	0.598083i
$619$	−6.08799e6	+	6.08799e6i	−0.638627	+	0.638627i	−0.950217	−	0.311590i	$-0.899139\pi$
$619$	−6.08799e6	+	6.08799e6i	−0.638627	+	0.638627i	0.311590	+	0.950217i	$0.399139\pi$
$620$	6.57574e6	+	1.99977e7i	0.687013	+	2.08930i
$621$	7.18936e6	−	1.08971e7i	0.748103	−	1.13392i
$622$	−4.50126e6	−	1.07226e6i	−0.466507	−	0.111128i
$623$	1.81479e7			1.87330
$624$	−1.02368e7	+	8.67097e6i	−1.05245	+	0.891469i
$625$	1.00141e7			1.02544
$626$	−1.43308e7	−	3.41380e6i	−1.46162	−	0.348179i
$627$	5.96219e6	+	5.20817e6i	0.605671	+	0.529074i
$628$	−7.56869e6	+	2.48877e6i	−0.765811	+	0.251818i
$629$	1.53646e6	−	1.53646e6i	0.154844	−	0.154844i
$630$	−1.48277e7	+	1.21470e7i	−1.48841	+	1.21932i
$631$	718238.			0.0718117			0.0359058	−	0.999355i	$-0.488568\pi$
$631$	718238.			0.0718117			0.0359058	+	0.999355i	$0.488568\pi$
$632$	−460568.	−	389165.i	−0.0458671	−	0.0387562i
$633$	2.57106e6	−	173551.i	0.255037	−	0.0172155i
$634$	−2.46356e6	+	1.51566e6i	−0.243411	+	0.149754i
$635$	−8.27123e6	−	8.27123e6i	−0.814021	−	0.814021i
$636$	1.24390e6	−	2.93956e6i	0.121939	−	0.288163i
$637$	8.74505e6	−	8.74505e6i	0.853913	−	0.853913i
$638$	5.73419e6	+	1.36596e6i	0.557725	+	0.132858i
$639$	1.37672e7	−	1.86714e6i	1.33381	−	0.180894i
$640$	1.09526e7	−	9.59082e6i	1.05698	−	0.925563i
$641$			3.12187e6i			0.300102i	0.988678	+	0.150051i	$0.0479438\pi$
$641$			3.12187e6i			0.300102i	−0.988678	+	0.150051i	$0.952056\pi$
$642$	−3438.95	+	20468.7i	−0.000329297	+	0.00195999i
$643$	5.80673e6	+	5.80673e6i	0.553865	+	0.553865i	0.927554	−	0.373689i	$-0.121907\pi$
$643$	5.80673e6	+	5.80673e6i	0.553865	+	0.553865i	−0.373689	+	0.927554i	$0.621907\pi$
$644$	8.82783e6	−	1.74778e7i	0.838763	−	1.66062i
$645$	−4.93919e6	−	4.31455e6i	−0.467473	−	0.408353i
$646$	3.85437e6	+	6.26493e6i	0.363390	+	0.590656i
$647$		−	5.44279e6i		−	0.511165i	−0.966787	−	0.255582i	$-0.917733\pi$
$647$		−	5.44279e6i		−	0.511165i	0.966787	−	0.255582i	$-0.0822672\pi$
$648$	−4.47504e6	+	9.70716e6i	−0.418658	+	0.908144i
$649$		−	2.24415e6i		−	0.209142i
$650$	1.23233e7	−	7.58168e6i	1.14405	−	0.703853i
$651$	−1.74590e7	−	1.52510e7i	−1.61460	−	1.41041i
$652$	4.32622e6	+	1.31566e7i	0.398556	+	1.21206i
$653$	−4.26230e6	−	4.26230e6i	−0.391166	−	0.391166i	0.483937	−	0.875103i	$-0.339206\pi$
$653$	−4.26230e6	−	4.26230e6i	−0.391166	−	0.391166i	−0.875103	+	0.483937i	$0.839206\pi$
$654$	1.91271e7	+	3.21354e6i	1.74865	+	0.293792i
$655$		−	2.27604e7i		−	2.07289i
$656$	−1.19501e6	−	1.62062e6i	−0.108421	−	0.147035i
$657$	−6.56714e6	+	890647.i	−0.593557	+	0.0804993i
$658$	3.42497e6	−	1.43777e7i	0.308385	−	1.29457i
$659$	−375589.	+	375589.i	−0.0336899	+	0.0336899i	−0.723751	−	0.690061i	$-0.757584\pi$
$659$	−375589.	+	375589.i	−0.0336899	+	0.0336899i	0.690061	+	0.723751i	$0.257584\pi$
$660$	9.60092e6	−	3.89148e6i	0.857933	−	0.347740i
$661$	−7.15927e6	−	7.15927e6i	−0.637331	−	0.637331i	0.312566	−	0.949896i	$-0.398812\pi$
$661$	−7.15927e6	−	7.15927e6i	−0.637331	−	0.637331i	−0.949896	+	0.312566i	$0.898812\pi$
$662$	1.21268e6	+	1.97109e6i	0.107547	+	0.174808i
$663$	−8.84985e6	+	597382.i	−0.781902	+	0.0527799i
$664$	280281.	+	3.33552e6i	0.0246703	+	0.293591i
$665$	2.67809e7			2.34839
$666$	−2.79572e6	−	3.41272e6i	−0.244235	−	0.298136i
$667$	−9.60351e6	+	9.60351e6i	−0.835825	+	0.835825i
$668$	692417.	−	1.37088e6i	0.0600381	−	0.118866i
$669$	1.33811e7	+	1.16888e7i	1.15592	+	1.00973i
$670$	1.14856e6	−	4.82154e6i	0.0988474	−	0.414953i
$671$	−7.86014e6			−0.673944
$672$	−4.98951e6	+	1.52358e7i	−0.426221	+	1.30149i
$673$	1.12893e7			0.960796			0.480398	−	0.877051i	$-0.340492\pi$
$673$	1.12893e7			0.960796			0.480398	+	0.877051i	$0.340492\pi$
$674$	−721372.	+	3.02826e6i	−0.0611659	+	0.256769i
$675$	6.34855e6	−	9.62265e6i	0.536309	−	0.812897i
$676$	−4.83365e6	+	9.56989e6i	−0.406826	+	0.805453i
$677$	−1.33626e7	+	1.33626e7i	−1.12052	+	1.12052i	−0.128853	+	0.991664i	$0.541130\pi$
$677$	−1.33626e7	+	1.33626e7i	−1.12052	+	1.12052i	−0.991664	+	0.128853i	$0.958870\pi$
$678$	7.07377e6	−	5.03875e6i	0.590986	−	0.420967i
$679$	−2.67370e7			−2.22555
$680$	9.59172e6	−	805986.i	0.795471	−	0.0668429i
$681$	−592051.	−	8.77088e6i	−0.0489206	−	0.724728i
$682$	6.56527e6	+	1.06712e7i	0.540495	+	0.878525i
$683$	5.86430e6	+	5.86430e6i	0.481022	+	0.481022i	0.905458	−	0.424436i	$-0.139528\pi$
$683$	5.86430e6	+	5.86430e6i	0.481022	+	0.481022i	−0.424436	+	0.905458i	$0.639528\pi$
$684$	1.34314e7	−	6.52936e6i	1.09770	−	0.533618i
$685$	1.20549e7	−	1.20549e7i	0.981607	−	0.981607i
$686$	−486796.	+	2.04352e6i	−0.0394945	+	0.165794i
$687$	−5.95510e6	+	401981.i	−0.481390	+	0.0324948i
$688$	−5.42370e6	−	819839.i	−0.436842	−	0.0660325i
$689$		−	5.37777e6i		−	0.431573i
$690$	−3.95477e6	+	2.35389e7i	−0.316227	+	1.88219i
$691$	8.93053e6	+	8.93053e6i	0.711512	+	0.711512i	0.966851	−	0.255340i	$-0.0821872\pi$
$691$	8.93053e6	+	8.93053e6i	0.711512	+	0.711512i	−0.255340	+	0.966851i	$0.582187\pi$
$692$	−1.58014e6	−	4.80542e6i	−0.125438	−	0.381475i
$693$	−6.90959e6	+	9.07783e6i	−0.546536	+	0.718041i
$694$	1.43268e7	−	8.81430e6i	1.12915	−	0.694687i
$695$		−	8.36144e6i		−	0.656628i
$696$	6.58867e6	−	8.95790e6i	0.515555	−	0.700944i
$697$		−	1.33132e6i		−	0.103801i
$698$	−8.33328e6	−	1.35450e7i	−0.647407	−	1.05230i
$699$	9.57670e6	−	1.09632e7i	0.741349	−	0.848679i
$700$	7.79539e6	−	1.54337e7i	0.601302	−	1.19049i
$701$	1.12490e7	+	1.12490e7i	0.864610	+	0.864610i	0.991869	−	0.127260i	$-0.0406181\pi$
$701$	1.12490e7	+	1.12490e7i	0.864610	+	0.864610i	−0.127260	+	0.991869i	$0.540618\pi$
$702$	−570001.	+	1.80000e7i	−0.0436549	+	1.37857i
$703$			6.16384e6i			0.470395i
$704$	5.01852e6	−	7.06343e6i	0.381631	−	0.537136i
$705$	1.21341e6	+	1.79760e7i	0.0919465	+	1.36213i
$706$	−2.15736e7	−	5.13913e6i	−1.62896	−	0.388041i
$707$	−4.72721e6	+	4.72721e6i	−0.355677	+	0.355677i
$708$	−3.89880e6	−	1.64982e6i	−0.292313	−	0.123695i
$709$	−5.97950e6	−	5.97950e6i	−0.446734	−	0.446734i	0.447533	−	0.894267i	$-0.352303\pi$
$709$	−5.97950e6	−	5.97950e6i	−0.446734	−	0.446734i	−0.894267	+	0.447533i	$0.852303\pi$
$710$	−2.16348e7	+	1.33104e7i	−1.61067	+	0.990934i
$711$	−802082.	+	108780.i	−0.0595038	+	0.00807002i
$712$	−1.19421e7	+	1.41332e7i	−0.882837	+	1.04482i
$713$	−2.88674e7			−2.12659
$714$	−8.63355e6	+	6.14980e6i	−0.633788	+	0.451456i
$715$	1.23418e7	−	1.23418e7i	0.902849	−	0.902849i
$716$	6.90214e6	−	2.26960e6i	0.503154	−	0.165450i
$717$	−7.05233e6	+	8.07334e6i	−0.512312	+	0.586483i
$718$	1.96093e7	+	4.67121e6i	1.41955	+	0.338157i
$719$	−1.15861e7			−0.835827			−0.417914	−	0.908487i	$-0.637239\pi$
$719$	−1.15861e7			−0.835827			−0.417914	+	0.908487i	$0.637239\pi$
$720$	297502.	−	1.95407e7i	0.0213874	−	1.40478i
$721$	−1.40371e7			−1.00563
$722$	−6.67226e6	−	1.58942e6i	−0.476354	−	0.113474i
$723$	7.86321e6	−	9.00162e6i	0.559441	−	0.640435i
$724$	−3.43862e6	−	1.04573e7i	−0.243802	−	0.741434i
$725$	−8.48036e6	+	8.48036e6i	−0.599196	+	0.599196i
$726$	−6.54522e6	+	4.66225e6i	−0.460874	+	0.328287i
$727$	1.23350e7			0.865575			0.432788	−	0.901496i	$-0.357530\pi$
$727$	1.23350e7			0.865575			0.432788	+	0.901496i	$0.357530\pi$
$728$	2.26174e6	+	2.69161e7i	0.158166	+	1.88228i
$729$	5.64580e6	+	1.31915e7i	0.393466	+	0.919339i
$730$	1.03201e7	−	6.34922e6i	0.716763	−	0.440974i
$731$	−2.56449e6	−	2.56449e6i	−0.177504	−	0.177504i
$732$	−5.77848e6	+	1.36556e7i	−0.398599	+	0.941958i
$733$	3.70205e6	−	3.70205e6i	0.254497	−	0.254497i	−0.568315	−	0.822811i	$-0.692404\pi$
$733$	3.70205e6	−	3.70205e6i	0.254497	−	0.254497i	0.822811	+	0.568315i	$0.192404\pi$
$734$	−1.15493e7	−	2.75120e6i	−0.791252	−	0.188487i
$735$	1.21336e6	+	1.79751e7i	0.0828457	+	1.22731i
$736$	7.80221e6	+	1.83760e7i	0.530912	+	1.25042i
$737$		−	2.94996e6i		−	0.200054i
$738$	−2.68976e6	−	267312.i	−0.181791	−	0.0180666i
$739$	−1.45938e7	−	1.45938e7i	−0.983010	−	0.983010i	0.0168480	−	0.999858i	$-0.494637\pi$
$739$	−1.45938e7	−	1.45938e7i	−0.983010	−	0.983010i	−0.999858	+	0.0168480i	$0.994637\pi$
$740$	7.19968e6	+	3.63648e6i	0.483319	+	0.244119i
$741$	1.65533e7	−	1.89499e7i	1.10749	−	1.26783i
$742$	−3.36756e6	−	5.47365e6i	−0.224546	−	0.364979i
$743$		−	5.88626e6i		−	0.391172i	−0.980687	−	0.195586i	$-0.937339\pi$
$743$		−	5.88626e6i		−	0.391172i	0.980687	−	0.195586i	$-0.0626609\pi$
$744$	2.33659e7	−	3.56086e6i	1.54757	−	0.235843i
$745$			2.14957e7i			1.41893i
$746$	−1.76602e7	+	1.08651e7i	−1.16185	+	0.714803i
$747$	3.57547e6	+	2.72147e6i	0.234440	+	0.178444i
$748$	5.44221e6	−	1.78954e6i	0.355649	−	0.116946i
$749$	29549.6	+	29549.6i	0.00192463	+	0.00192463i
$750$	93689.9	−	557644.i	0.00608190	−	0.0361996i
$751$		−	1.85295e7i		−	1.19885i	−0.800431	−	0.599425i	$-0.795396\pi$
$751$		−	1.85295e7i		−	1.19885i	0.800431	−	0.599425i	$-0.204604\pi$
$752$	8.94329e6	+	1.21285e7i	0.576703	+	0.782098i
$753$	−8.36581e6	+	564708.i	−0.537676	+	0.0362942i
$754$	4.34149e6	−	1.82252e7i	0.278106	−	1.16746i
$755$	4.00115e6	−	4.00115e6i	0.255457	−	0.255457i
$756$	1.06914e7	+	1.86778e7i	0.680347	+	1.18856i
$757$	−2.09952e6	−	2.09952e6i	−0.133162	−	0.133162i	0.637384	−	0.770546i	$-0.280016\pi$
$757$	−2.09952e6	−	2.09952e6i	−0.133162	−	0.133162i	−0.770546	+	0.637384i	$0.780016\pi$
$758$	1.35967e6	+	2.21002e6i	0.0859531	+	0.139709i
$759$	956766.	+	1.41739e7i	0.0602839	+	0.893069i
$760$	−1.76230e7	+	2.08564e7i	−1.10674	+	1.30980i
$761$	−1.61669e7			−1.01196			−0.505981	−	0.862545i	$-0.668869\pi$
$761$	−1.61669e7			−1.01196			−0.505981	+	0.862545i	$0.668869\pi$
$762$	−1.06971e7	+	7.61968e6i	−0.667388	+	0.475389i
$763$	2.76127e7	−	2.76127e7i	1.71711	−	1.71711i
$764$	−9.06791e6	−	4.58010e6i	−0.562049	−	0.283885i
$765$	7.82595e6	−	1.02817e7i	0.483485	−	0.635204i
$766$	−1.22043e6	+	5.12328e6i	−0.0751523	+	0.315483i
$767$	−7.13267e6			−0.437788
$768$	−8.58200e6	−	1.39115e7i	−0.525031	−	0.851083i
$769$	−9.92642e6			−0.605309			−0.302654	−	0.953100i	$-0.597873\pi$
$769$	−9.92642e6			−0.605309			−0.302654	+	0.953100i	$0.597873\pi$
$770$	4.83344e6	−	2.02903e7i	0.293785	−	1.23328i
$771$	1.35522e7	+	1.18383e7i	0.821061	+	0.717224i
$772$	−2.41335e7	−	1.21896e7i	−1.45739	−	0.736114i
$773$	4.95500e6	−	4.95500e6i	0.298260	−	0.298260i	−0.542072	−	0.840332i	$-0.682360\pi$
$773$	4.95500e6	−	4.95500e6i	0.298260	−	0.298260i	0.840332	+	0.542072i	$0.182360\pi$
$774$	−5.69616e6	+	4.66632e6i	−0.341766	+	0.279977i
$775$	−2.54913e7			−1.52454
$776$	1.75941e7	−	2.08221e7i	1.04885	−	1.24128i
$777$	−8.86228e6	+	598221.i	−0.526615	+	0.0355475i
$778$	7.26544e6	+	1.18093e7i	0.430341	+	0.699480i
$779$	2.67044e6	+	2.67044e6i	0.157666	+	0.157666i
$780$	−1.23684e7	−	3.05150e7i	−0.727911	−	1.79588i
$781$	−1.06903e7	+	1.06903e7i	−0.627135	+	0.627135i
$782$	−3.05872e6	+	1.28402e7i	−0.178864	+	0.750854i
$783$	−2.99780e6	−	1.46234e7i	−0.174742	−	0.852399i
$784$	8.94288e6	+	1.21279e7i	0.519622	+	0.704687i
$785$		−	1.95546e7i		−	1.13260i
$786$	−2.52016e7	−	4.23413e6i	−1.45503	−	0.244460i
$787$	7.74895e6	+	7.74895e6i	0.445970	+	0.445970i	0.894012	−	0.448042i	$-0.147879\pi$
$787$	7.74895e6	+	7.74895e6i	0.445970	+	0.445970i	−0.448042	+	0.894012i	$0.647879\pi$
$788$	−2.66101e7	+	8.75006e6i	−1.52662	+	0.501990i
$789$	−2.53345e7	−	2.21305e7i	−1.44884	−	1.26561i
$790$	1.26045e6	−	775466.i	0.0718551	−	0.0442074i
$791$		−	1.74862e7i		−	0.993698i
$792$	−2.52281e6	−	1.13546e7i	−0.142913	−	0.643221i
$793$			2.49822e7i			1.41074i
$794$	1.79707e7	+	2.92097e7i	1.01161	+	1.64428i
$795$	5.89999e6	+	5.15384e6i	0.331081	+	0.289210i
$796$	5.28056e6	+	2.66715e6i	0.295391	+	0.149199i
$797$	2.08464e7	+	2.08464e7i	1.16248	+	1.16248i	0.983931	+	0.178546i	$0.0571395\pi$
$797$	2.08464e7	+	2.08464e7i	1.16248	+	1.16248i	0.178546	+	0.983931i	$0.442861\pi$
$798$	4.98207e6	−	2.96534e7i	0.276951	−	1.64842i
$799$			9.96337e6i			0.552127i
$800$	6.88972e6	+	1.62269e7i	0.380607	+	0.896419i
$801$	3.33807e6	+	2.46130e7i	0.183829	+	1.35545i
$802$	−5.58134e6	−	1.32955e6i	−0.306410	−	0.0729910i
$803$	5.09939e6	−	5.09939e6i	0.279080	−	0.279080i
$804$	−5.12502e6	−	2.16870e6i	−0.279612	−	0.118320i
$805$	3.39819e7	+	3.39819e7i	1.84824	+	1.84824i
$806$	3.39168e7	−	2.08666e7i	1.83898	−	1.13140i
$807$	8.02801e6	−	541906.i	0.433934	−	0.0292914i
$808$	−570740.	−	6.79215e6i	−0.0307546	−	0.365998i
$809$	−4.76277e6			−0.255852			−0.127926	−	0.991784i	$-0.540832\pi$
$809$	−4.76277e6			−0.255852			−0.127926	+	0.991784i	$0.540832\pi$
$810$	−1.92016e7	−	1.78758e7i	−1.02831	−	0.957311i
$811$	−1.38769e7	+	1.38769e7i	−0.740868	+	0.740868i	−0.972745	−	0.231877i	$-0.925513\pi$
$811$	−1.38769e7	+	1.38769e7i	−0.740868	+	0.740868i	0.231877	+	0.972745i	$0.425513\pi$
$812$	−6.99370e6	−	2.12687e7i	−0.372235	−	1.13201i
$813$	−24210.1	−	21148.3i	−0.00128461	−	0.00112215i
$814$	4.66998e6	+	1.11245e6i	0.247033	+	0.0588465i
$815$	−3.39917e7			−1.79258
$816$	891920.	−	1.07705e7i	0.0468922	−	0.566250i
$817$	1.02880e7			0.539234
$818$	3.43316e7	+	8.17825e6i	1.79395	+	0.427343i
$819$	2.88524e7	+	2.19610e7i	1.50305	+	1.14404i
$820$	4.69469e6	−	1.54373e6i	0.243822	−	0.0801747i
$821$	−1.14689e7	+	1.14689e7i	−0.593830	+	0.593830i	−0.938664	−	0.344834i	$-0.887935\pi$
$821$	−1.14689e7	+	1.14689e7i	−0.593830	+	0.593830i	0.344834	+	0.938664i	$0.387935\pi$
$822$	−1.11053e7	−	1.55905e7i	−0.573260	−	0.804786i
$823$	−1.98054e7			−1.01926			−0.509630	−	0.860394i	$-0.670218\pi$
$823$	−1.98054e7			−1.01926			−0.509630	+	0.860394i	$0.670218\pi$
$824$	9.23700e6	−	1.09318e7i	0.473929	−	0.560883i
$825$	844870.	+	1.25162e7i	0.0432170	+	0.640234i
$826$	−7.25983e6	+	4.46647e6i	−0.370234	+	0.227779i
$827$	5.58177e6	+	5.58177e6i	0.283797	+	0.283797i	0.834621	−	0.550824i	$-0.185686\pi$
$827$	5.58177e6	+	5.58177e6i	0.283797	+	0.283797i	−0.550824	+	0.834621i	$0.685686\pi$
$828$	2.53279e7	+	8.75791e6i	1.28388	+	0.443941i
$829$	2.03722e7	−	2.03722e7i	1.02956	−	1.02956i	0.0300079	−	0.999550i	$-0.490447\pi$
$829$	2.03722e7	−	2.03722e7i	1.02956	−	1.02956i	0.999550	−	0.0300079i	$-0.00955323\pi$
$830$	−7.99173e6	−	1.90374e6i	−0.402666	−	0.0959206i
$831$	2.75365e7	−	1.85877e6i	1.38327	−	0.0933734i
$832$	−2.24500e7	−	1.59505e7i	−1.12437	−	0.798854i
$833$			9.96292e6i			0.497478i
$834$	−9.25828e6	−	1.55548e6i	−0.460909	−	0.0774374i
$835$	2.66539e6	+	2.66539e6i	0.132295	+	0.132295i
$836$	−7.32677e6	+	1.45059e7i	−0.362574	+	0.717842i
$837$	1.74728e7	−	2.64839e7i	0.862081	−	1.30668i
$838$	−1.01682e6	−	1.65274e6i	−0.0500187	−	0.0813008i
$839$		−	3.07100e7i		−	1.50617i	−0.657921	−	0.753087i	$-0.728564\pi$
$839$		−	3.07100e7i		−	1.50617i	0.657921	−	0.753087i	$-0.271436\pi$
$840$	−3.16974e7	−	2.33139e7i	−1.54998	−	1.14003i
$841$		−	4.98178e6i		−	0.242882i
$842$	2.47616e7	−	1.52341e7i	1.20364	−	0.740518i
$843$	−9.06629e6	+	1.03789e7i	−0.439401	+	0.503016i
$844$	1.65240e6	+	5.02517e6i	0.0798472	+	0.242826i
$845$	−1.86067e7	−	1.86067e7i	−0.896451	−	0.896451i
$846$	2.01298e7	+	2.00052e6i	0.966969	+	0.0960985i
$847$			1.61796e7i			0.774926i
$848$	6.47875e6	+	979320.i	0.309387	+	0.0467665i
$849$	−1.39772e6	−	2.07064e7i	−0.0665505	−	0.985905i
$850$	−2.70099e6	+	1.13385e7i	−0.128226	+	0.538282i
$851$	−7.82120e6	+	7.82120e6i	−0.370211	+	0.370211i
$852$	1.07133e7	+	2.64314e7i	0.505620	+	1.24745i
$853$	−6.30634e6	−	6.30634e6i	−0.296759	−	0.296759i	0.542984	−	0.839743i	$-0.317295\pi$
$853$	−6.30634e6	−	6.30634e6i	−0.296759	−	0.296759i	−0.839743	+	0.542984i	$0.817295\pi$
$854$	1.56438e7	+	2.54276e7i	0.734003	+	1.19305i
$855$	4.92599e6	+	3.63215e7i	0.230451	+	1.69922i
$856$	−42457.4	+	3567.67i	−0.00198048	+	0.000166418i
$857$	3.46024e7			1.60936			0.804682	−	0.593706i	$-0.202336\pi$
$857$	3.46024e7			1.60936			0.804682	+	0.593706i	$0.202336\pi$
$858$	−1.13697e7	−	1.59616e7i	−0.527265	−	0.740214i
$859$	−2.42718e7	+	2.42718e7i	−1.12233	+	1.12233i	−0.130936	+	0.991391i	$0.541798\pi$
$859$	−2.42718e7	+	2.42718e7i	−1.12233	+	1.12233i	−0.991391	+	0.130936i	$0.958202\pi$
$860$	6.06963e6	−	1.20170e7i	0.279844	−	0.554049i
$861$	−3.58035e6	+	4.09870e6i	−0.164595	+	0.188425i
$862$	−3.58868e6	+	1.50650e7i	−0.164500	+	0.690557i
$863$	2.38284e7			1.08910			0.544549	−	0.838729i	$-0.316701\pi$
$863$	2.38284e7			1.08910			0.544549	+	0.838729i	$0.316701\pi$
$864$	−2.15813e7	−	3.96458e6i	−0.983542	−	0.180681i
$865$	1.24154e7			0.564183
$866$	−216368.	+	908294.i	−0.00980389	+	0.0411559i
$867$	−9.86020e6	+	1.12877e7i	−0.445490	+	0.509987i
$868$	2.14548e7	−	4.24773e7i	0.966554	−	1.91363i
$869$	622818.	−	622818.i	0.0279777	−	0.0279777i
$870$	1.58343e7	+	2.22293e7i	0.709251	+	0.995700i
$871$	−9.37598e6			−0.418766
$872$	3.33382e6	+	3.96745e7i	0.148474	+	1.76693i
$873$	−4.91791e6	−	3.62619e7i	−0.218396	−	1.61033i
$874$	−1.96204e7	−	3.18911e7i	−0.868817	−	1.41218i
$875$	−805041.	−	805041.i	−0.0355466	−	0.0355466i
$876$	−5.11037e6	−	1.26081e7i	−0.225005	−	0.555125i
$877$	3.95429e6	−	3.95429e6i	0.173608	−	0.173608i	−0.614955	−	0.788563i	$-0.710826\pi$
$877$	3.95429e6	−	3.95429e6i	0.173608	−	0.173608i	0.788563	+	0.614955i	$0.210826\pi$
$878$	−177960.	+	747062.i	−0.00779089	+	0.0327055i
$879$	−368969.	−	5.46605e6i	−0.0161071	−	0.238617i
$880$	1.26211e7	+	1.71161e7i	0.549400	+	0.745071i
$881$		−	3.52531e7i		−	1.53023i	−0.643891	−	0.765117i	$-0.722681\pi$
$881$		−	3.52531e7i		−	1.53023i	0.643891	−	0.765117i	$-0.277319\pi$
$882$	2.01288e7	+	2.00043e6i	0.871259	+	0.0865867i
$883$	6.95354e6	+	6.95354e6i	0.300126	+	0.300126i	0.841063	−	0.540937i	$-0.181930\pi$
$883$	6.95354e6	+	6.95354e6i	0.300126	+	0.300126i	−0.540937	+	0.841063i	$0.681930\pi$
$884$	−5.68775e6	−	1.72972e7i	−0.244799	−	0.744466i
$885$	6.83566e6	−	7.82530e6i	0.293374	−	0.335848i
$886$	3.01426e7	−	1.85447e7i	1.29002	−	0.793660i
$887$			2.70971e7i			1.15641i	0.815890	+	0.578207i	$0.196247\pi$
$887$			2.70971e7i			1.15641i	−0.815890	+	0.578207i	$0.803753\pi$
$888$	5.36588e6	−	7.29541e6i	0.228354	−	0.310468i
$889$			2.64430e7i			1.12216i
$890$	−2.37963e7	−	3.86787e7i	−1.00701	−	1.63680i
$891$	−1.35827e7	−	7.70137e6i	−0.573182	−	0.324993i
$892$	−1.64436e7	+	3.25559e7i	−0.691968	+	1.36999i
$893$	−1.99851e7	−	1.99851e7i	−0.838646	−	0.838646i
$894$	2.38013e7	+	3.99886e6i	0.995995	+	0.167337i
$895$			1.78325e7i			0.744141i
$896$	−3.28384e7	−	2.17677e6i	−1.36651	−	0.0905823i
$897$	4.50494e7	−	3.04092e6i	1.86943	−	0.126190i
$898$	2.11702e7	+	5.04302e6i	0.876059	+	0.208689i
$899$	−2.33400e7	+	2.33400e7i	−0.963168	+	0.963168i
$900$	2.23658e7	+	7.73366e6i	0.920403	+	0.318258i
$901$	3.06335e6	+	3.06335e6i	0.125714	+	0.125714i
$902$	2.50520e6	−	1.54128e6i	0.102524	−	0.0630760i
$903$	998489.	+	1.47920e7i	0.0407496	+	0.603681i
$904$	1.36179e7	+	1.15067e7i	0.554227	+	0.468305i
$905$	2.70177e7			1.09655
$906$	−3.68597e6	−	5.17464e6i	−0.149187	−	0.209440i
$907$	1.87444e7	−	1.87444e7i	0.756578	−	0.756578i	−0.219120	−	0.975698i	$-0.570318\pi$
$907$	1.87444e7	−	1.87444e7i	0.756578	−	0.756578i	0.975698	+	0.219120i	$0.0703185\pi$
$908$	1.71428e7	−	5.63699e6i	0.690030	−	0.226899i
$909$	−7.28077e6	−	5.54176e6i	−0.292259	−	0.222453i
$910$	−6.44895e7	−	1.53623e7i	−2.58158	−	0.614968i
$911$	2.98788e7			1.19280			0.596400	−	0.802688i	$-0.296597\pi$
$911$	2.98788e7			1.19280			0.596400	+	0.802688i	$0.296597\pi$
$912$	1.98150e7	+	2.33931e7i	0.788872	+	0.931324i
$913$	−4.88958e6			−0.194131
$914$	3.44115e7	+	8.19728e6i	1.36250	+	0.324567i
$915$	−2.74081e7	−	2.39419e7i	−1.08225	−	0.945378i
$916$	−3.82731e6	−	1.16393e7i	−0.150714	−	0.458342i
$917$	−3.63823e7	+	3.63823e7i	−1.42878	+	1.42878i
$918$	−9.92868e6	−	1.05781e7i	−0.388852	−	0.414285i
$919$	2.02137e7			0.789508			0.394754	−	0.918787i	$-0.370830\pi$
$919$	2.02137e7			0.789508			0.394754	+	0.918787i	$0.370830\pi$
$920$	−4.88258e7	+	4.10280e6i	−1.90187	+	0.159813i
$921$	−3.09620e7	+	2.09000e6i	−1.20276	+	0.0811888i
$922$	−7.75376e6	+	4.77035e6i	−0.300390	+	0.184809i
$923$	3.39772e7	+	3.39772e7i	1.31276	+	1.31276i
$924$	−2.15675e7	−	9.12649e6i	−0.831035	−	0.351661i
$925$	−6.90649e6	+	6.90649e6i	−0.265401	+	0.265401i
$926$	−3.66712e6	−	873558.i	−0.140539	−	0.0334784i
$927$	−2.58194e6	−	1.90378e7i	−0.0986839	−	0.727640i
$928$	2.11658e7	+	8.54921e6i	0.806797	+	0.325879i
$929$			1.30654e7i			0.496688i	0.968672	+	0.248344i	$0.0798863\pi$
$929$			1.30654e7i			0.496688i	−0.968672	+	0.248344i	$0.920114\pi$
$930$	−9.61155e6	+	5.72081e7i	−0.364406	+	2.16895i
$931$	−1.99842e7	−	1.99842e7i	−0.755638	−	0.755638i
$932$	2.66732e7	+	1.34723e7i	1.00585	+	0.508046i
$933$	−9.60316e6	−	8.38868e6i	−0.361169	−	0.315493i
$934$	50459.0	+	82016.5i	0.00189266	+	0.00307634i
$935$			1.40606e7i			0.525988i
$936$	−3.60889e7	+	8.01834e6i	−1.34643	+	0.299154i
$937$		−	1.35442e7i		−	0.503971i	−0.967731	−	0.251986i	$-0.918916\pi$
$937$		−	1.35442e7i		−	0.503971i	0.967731	−	0.251986i	$-0.0810836\pi$
$938$	−9.54314e6	+	5.87122e6i	−0.354147	+	0.217882i
$939$	−3.05739e7	−	2.67073e7i	−1.13159	−	0.988477i
$940$	−3.51343e7	+	1.15530e7i	−1.29692	+	0.426458i
$941$	−3.48532e7	−	3.48532e7i	−1.28312	−	1.28312i	−0.938880	−	0.344245i	$-0.888135\pi$
$941$	−3.48532e7	−	3.48532e7i	−1.28312	−	1.28312i	−0.344245	−	0.938880i	$-0.611865\pi$
$942$	−2.16520e7	−	3.63776e6i	−0.795008	−	0.133569i
$943$			6.77696e6i			0.248174i
$944$	1.29889e6	−	8.59292e6i	0.0474399	−	0.313842i
$945$	−5.17445e7	+	1.06077e7i	−1.88489	+	0.386402i
$946$	1.85679e6	−	7.79465e6i	0.0674583	−	0.283184i
$947$	−1.61194e6	+	1.61194e6i	−0.0584081	+	0.0584081i	−0.735708	−	0.677299i	$-0.763150\pi$
$947$	−1.61194e6	+	1.61194e6i	−0.0584081	+	0.0584081i	0.677299	+	0.735708i	$0.263150\pi$
$948$	−624159.	−	1.53990e6i	−0.0225567	−	0.0556510i
$949$	−1.62076e7	−	1.62076e7i	−0.584188	−	0.584188i
$950$	−1.73257e7	−	2.81614e7i	−0.622848	−	1.01238i
$951$	−7.95259e6	+	536815.i	−0.285140	+	0.0192475i
$952$	−1.66206e7	−	1.40439e7i	−0.594368	−	0.502222i
$953$	3.00542e7			1.07195			0.535974	−	0.844235i	$-0.319945\pi$
$953$	3.00542e7			1.07195			0.535974	+	0.844235i	$0.319945\pi$
$954$	6.80421e6	−	5.57404e6i	0.242051	−	0.198289i
$955$	1.76307e7	−	1.76307e7i	0.625547	−	0.625547i
$956$	−1.96423e7	−	9.92110e6i	−0.695100	−	0.351087i
$957$	1.22335e7	+	1.06864e7i	0.431789	+	0.377182i
$958$	1.37757e6	−	5.78292e6i	0.0484953	−	0.203579i
$959$	−3.85393e7			−1.35319
$960$	3.90146e7	−	9.34367e6i	1.36631	−	0.327220i
$961$	−4.15291e7			−1.45059
$962$	3.53575e6	−	1.48428e7i	0.123181	−	0.517104i
$963$	−34641.3	+	45511.8i	−0.00120373	+	0.00158146i
$964$	2.19008e7	+	1.10618e7i	0.759043	+	0.383385i
$965$	4.69226e7	−	4.69226e7i	1.62205	−	1.62205i
$966$	4.39484e7	−	3.13050e7i	1.51530	−	1.07937i
$967$	1.06233e7			0.365338			0.182669	−	0.983174i	$-0.441526\pi$
$967$	1.06233e7			0.365338			0.182669	+	0.983174i	$0.441526\pi$
$968$	−1.26003e7	−	1.06469e7i	−0.432209	−	0.365203i
$969$	1.36514e6	+	2.02238e7i	0.0467056	+	0.691914i
$970$	3.50586e7	+	5.69846e7i	1.19637	+	1.94459i
$971$	−1.59763e7	−	1.59763e7i	−0.543787	−	0.543787i	0.380850	−	0.924637i	$-0.375631\pi$
$971$	−1.59763e7	−	1.59763e7i	−0.543787	−	0.543787i	−0.924637	+	0.380850i	$0.875631\pi$
$972$	−2.33652e7	+	1.79357e7i	−0.793239	+	0.608910i
$973$	−1.33657e7	+	1.33657e7i	−0.452594	+	0.452594i
$974$	−1.35222e7	+	5.67651e7i	−0.456720	+	1.91727i
$975$	3.97808e7	−	2.68528e6i	1.34018	−	0.0904645i
$976$	−3.00967e7	−	4.54938e6i	−1.01133	−	0.152872i
$977$		−	1.54947e7i		−	0.519333i	−0.965698	−	0.259666i	$-0.916387\pi$
$977$		−	1.54947e7i		−	0.519333i	0.965698	−	0.259666i	$-0.0836126\pi$
$978$	−6.32350e6	+	3.76376e7i	−0.211402	+	1.25827i
$979$	−1.91120e7	−	1.91120e7i	−0.637309	−	0.637309i
$980$	−3.51327e7	+	1.15525e7i	−1.16855	+	0.384248i
$981$	4.25287e7	+	3.23707e7i	1.41094	+	1.07394i
$982$	−1.32427e7	+	8.14730e6i	−0.438225	+	0.269609i
$983$		−	1.91127e7i		−	0.630869i	−0.948947	−	0.315435i	$-0.897850\pi$
$983$		−	1.91127e7i		−	0.630869i	0.948947	−	0.315435i	$-0.102150\pi$
$984$	−835954.	−	5.48542e6i	−0.0275229	−	0.180602i
$985$		−	6.87504e7i		−	2.25780i
$986$	7.90860e6	+	1.28547e7i	0.259064	+	0.421085i
$987$	2.67948e7	−	3.06740e7i	0.875502	−	1.00225i
$988$	4.61046e7	+	2.32869e7i	1.50263	+	0.758962i
$989$	1.30543e7	+	1.30543e7i	0.424389	+	0.424389i
$990$	2.84078e7	+	2.82320e6i	0.921190	+	0.0915489i
$991$		−	2.57628e7i		−	0.833313i	−0.909064	−	0.416657i	$-0.863202\pi$
$991$		−	2.57628e7i		−	0.833313i	0.909064	−	0.416657i	$-0.136798\pi$
$992$	1.89622e7	+	4.46605e7i	0.611800	+	1.44093i
$993$	429506.	+	6.36287e6i	0.0138228	+	0.204776i
$994$	5.58595e7	+	1.33065e7i	1.79321	+	0.427167i
$995$	−1.02669e7	+	1.02669e7i	−0.328763	+	0.328763i
$996$	−3.59464e6	+	8.49475e6i	−0.114817	+	0.271333i
$997$	1.78731e7	+	1.78731e7i	0.569458	+	0.569458i	0.931977	−	0.362518i	$-0.118083\pi$
$997$	1.78731e7	+	1.78731e7i	0.569458	+	0.569458i	−0.362518	+	0.931977i	$0.618083\pi$
$998$	−2.25933e7	+	1.39001e7i	−0.718049	+	0.441765i
$999$	−2.44144e6	−	1.19094e7i	−0.0773983	−	0.377552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.k.a.11.16	✓	76
3.2	odd	2	inner	48.6.k.a.11.23	yes	76
4.3	odd	2		192.6.k.a.143.29		76
12.11	even	2		192.6.k.a.143.10		76
16.3	odd	4	inner	48.6.k.a.35.23	yes	76
16.13	even	4		192.6.k.a.47.10		76
48.29	odd	4		192.6.k.a.47.29		76
48.35	even	4	inner	48.6.k.a.35.16	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.k.a.11.16	✓	76	1.1	even	1	trivial
48.6.k.a.11.23	yes	76	3.2	odd	2	inner
48.6.k.a.35.16	yes	76	48.35	even	4	inner
48.6.k.a.35.23	yes	76	16.3	odd	4	inner
192.6.k.a.47.10		76	16.13	even	4
192.6.k.a.47.29		76	48.29	odd	4
192.6.k.a.143.10		76	12.11	even	2
192.6.k.a.143.29		76	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31086 + 5.50288i) q^{2} +(-10.2553 + 11.7400i) q^{3} +(-28.5633 - 14.4270i) q^{4} +(55.5354 - 55.5354i) q^{5} +(-51.1607 - 71.8233i) q^{6} -177.545 q^{7} +(116.833 - 138.268i) q^{8} +(-32.6571 - 240.796i) q^{9} +O(q^{10})\)	\(q+(-1.31086 + 5.50288i) q^{2} +(-10.2553 + 11.7400i) q^{3} +(-28.5633 - 14.4270i) q^{4} +(55.5354 - 55.5354i) q^{5} +(-51.1607 - 71.8233i) q^{6} -177.545 q^{7} +(116.833 - 138.268i) q^{8} +(-32.6571 - 240.796i) q^{9} +(232.805 + 378.403i) q^{10} +(186.978 + 186.978i) q^{11} +(462.299 - 187.381i) q^{12} +(594.279 - 594.279i) q^{13} +(232.737 - 977.011i) q^{14} +(82.4550 + 1221.52i) q^{15} +(607.723 + 824.165i) q^{16} +677.041i q^{17} +(1367.88 + 135.941i) q^{18} +(-1358.05 - 1358.05i) q^{19} +(-2387.48 + 785.064i) q^{20} +(1820.78 - 2084.39i) q^{21} +(-1274.02 + 783.814i) q^{22} -3446.42i q^{23} +(425.124 + 2789.60i) q^{24} -3043.35i q^{25} +(2491.23 + 4049.26i) q^{26} +(3161.86 + 2086.04i) q^{27} +(5071.28 + 2561.45i) q^{28} +(-2786.52 - 2786.52i) q^{29} +(-6829.96 - 1147.50i) q^{30} -8376.06i q^{31} +(-5331.92 + 2263.86i) q^{32} +(-4112.65 + 277.612i) q^{33} +(-3725.67 - 887.506i) q^{34} +(-9860.05 + 9860.05i) q^{35} +(-2541.16 + 7349.06i) q^{36} +(-2269.37 - 2269.37i) q^{37} +(9253.40 - 5692.97i) q^{38} +(882.343 + 13071.4i) q^{39} +(-1190.45 - 14167.1i) q^{40} -1966.38 q^{41} +(9083.35 + 12751.9i) q^{42} +(-3787.80 + 3787.80i) q^{43} +(-2643.17 - 8038.24i) q^{44} +(-15186.3 - 11559.0i) q^{45} +(18965.2 + 4517.77i) q^{46} +14716.1 q^{47} +(-15908.1 - 1317.38i) q^{48} +14715.4 q^{49} +(16747.2 + 3989.41i) q^{50} +(-7948.49 - 6943.27i) q^{51} +(-25548.2 + 8400.90i) q^{52} +(4524.62 - 4524.62i) q^{53} +(-15624.0 + 14664.8i) q^{54} +20767.8 q^{55} +(-20743.1 + 24548.9i) q^{56} +(29870.8 - 2016.34i) q^{57} +(18986.6 - 11681.1i) q^{58} +(-6001.11 - 6001.11i) q^{59} +(15267.7 - 36080.2i) q^{60} +(-21018.9 + 21018.9i) q^{61} +(46092.4 + 10979.8i) q^{62} +(5798.13 + 42752.2i) q^{63} +(-5468.33 - 32308.5i) q^{64} -66007.0i q^{65} +(3863.44 - 22995.3i) q^{66} +(-7888.53 - 7888.53i) q^{67} +(9767.67 - 19338.5i) q^{68} +(40461.1 + 35344.1i) q^{69} +(-41333.5 - 67183.8i) q^{70} +57173.9i q^{71} +(-37109.8 - 23617.3i) q^{72} -27272.7i q^{73} +(15462.9 - 9513.23i) q^{74} +(35729.1 + 31210.5i) q^{75} +(19197.8 + 58383.0i) q^{76} +(-33197.1 - 33197.1i) q^{77} +(-73086.8 - 12279.3i) q^{78} -3330.97i q^{79} +(79520.4 + 12020.2i) q^{80} +(-56916.0 + 15727.4i) q^{81} +(2577.65 - 10820.7i) q^{82} +(-13075.3 + 13075.3i) q^{83} +(-82079.1 + 33268.6i) q^{84} +(37599.7 + 37599.7i) q^{85} +(-15878.5 - 25809.0i) q^{86} +(61290.4 - 4137.22i) q^{87} +(47698.3 - 4008.05i) q^{88} -102215. q^{89} +(83515.1 - 68416.0i) q^{90} +(-105512. + 105512. i) q^{91} +(-49721.5 + 98441.1i) q^{92} +(98335.2 + 85899.1i) q^{93} +(-19290.7 + 80980.6i) q^{94} -150840. q^{95} +(28102.7 - 85813.5i) q^{96} +150592. q^{97} +(-19289.8 + 80977.0i) q^{98} +(38917.3 - 51129.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Introduction

L-functions

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