LMFDB - Embedded newform 48.6.k.a.11.9

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			11.9
Character	$\chi$	$=$	48.11
Dual form			48.6.k.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.35628 + 3.60872i) q^{2} +(4.78598 + 14.8356i) q^{3} +(5.95430 - 31.4412i) q^{4} +(-31.7606 + 31.7606i) q^{5} +(-74.3865 - 47.3566i) q^{6} -71.3548 q^{7} +(87.5237 + 158.454i) q^{8} +(-197.189 + 142.006i) q^{9} +O(q^{10})$	\(q+(-4.35628 + 3.60872i) q^{2} +(4.78598 + 14.8356i) q^{3} +(5.95430 - 31.4412i) q^{4} +(-31.7606 + 31.7606i) q^{5} +(-74.3865 - 47.3566i) q^{6} -71.3548 q^{7} +(87.5237 + 158.454i) q^{8} +(-197.189 + 142.006i) q^{9} +(23.7429 - 252.973i) q^{10} +(-154.070 - 154.070i) q^{11} +(494.945 - 62.1414i) q^{12} +(230.393 - 230.393i) q^{13} +(310.841 - 257.499i) q^{14} +(-623.193 - 319.181i) q^{15} +(-953.093 - 374.420i) q^{16} -1397.75i q^{17} +(346.550 - 1330.21i) q^{18} +(-1208.54 - 1208.54i) q^{19} +(809.478 + 1187.70i) q^{20} +(-341.503 - 1058.59i) q^{21} +(1227.17 + 115.177i) q^{22} +885.382i q^{23} +(-1931.87 + 2056.82i) q^{24} +1107.53i q^{25} +(-172.232 + 1835.08i) q^{26} +(-3050.48 - 2245.77i) q^{27} +(-424.868 + 2243.48i) q^{28} +(-801.108 - 801.108i) q^{29} +(3866.63 - 858.485i) q^{30} +9955.11i q^{31} +(5503.11 - 1808.37i) q^{32} +(1548.34 - 3023.10i) q^{33} +(5044.09 + 6088.99i) q^{34} +(2266.27 - 2266.27i) q^{35} +(3290.70 + 7045.39i) q^{36} +(-3424.22 - 3424.22i) q^{37} +(9626.01 + 903.453i) q^{38} +(4520.67 + 2315.36i) q^{39} +(-7812.39 - 2252.78i) q^{40} -13334.9 q^{41} +(5307.83 + 3379.12i) q^{42} +(-16355.3 + 16355.3i) q^{43} +(-5761.53 + 3926.77i) q^{44} +(1752.65 - 10773.0i) q^{45} +(-3195.10 - 3856.97i) q^{46} +11368.9 q^{47} +(993.252 - 15931.6i) q^{48} -11715.5 q^{49} +(-3996.76 - 4824.70i) q^{50} +(20736.5 - 6689.61i) q^{51} +(-5871.99 - 8615.65i) q^{52} +(-15048.0 + 15048.0i) q^{53} +(21393.1 - 1225.11i) q^{54} +9786.73 q^{55} +(-6245.23 - 11306.4i) q^{56} +(12145.3 - 23713.4i) q^{57} +(6380.82 + 598.875i) q^{58} +(4253.09 + 4253.09i) q^{59} +(-13746.1 + 17693.4i) q^{60} +(30704.5 - 30704.5i) q^{61} +(-35925.2 - 43367.2i) q^{62} +(14070.4 - 10132.8i) q^{63} +(-17447.2 + 27736.9i) q^{64} +14634.8i q^{65} +(4164.50 + 18757.0i) q^{66} +(-983.712 - 983.712i) q^{67} +(-43946.9 - 8322.63i) q^{68} +(-13135.2 + 4237.42i) q^{69} +(-1694.17 + 18050.8i) q^{70} +77935.2i q^{71} +(-39760.0 - 18816.4i) q^{72} -62095.1i q^{73} +(27273.9 + 2559.81i) q^{74} +(-16430.8 + 5300.61i) q^{75} +(-45193.9 + 30801.9i) q^{76} +(10993.7 + 10993.7i) q^{77} +(-28048.7 + 6227.49i) q^{78} +33253.3i q^{79} +(42162.6 - 18379.0i) q^{80} +(18717.8 - 56003.8i) q^{81} +(58090.6 - 48121.9i) q^{82} +(-26282.9 + 26282.9i) q^{83} +(-35316.7 + 4434.08i) q^{84} +(44393.4 + 44393.4i) q^{85} +(12226.5 - 130270. i) q^{86} +(8050.81 - 15719.0i) q^{87} +(10928.2 - 37897.8i) q^{88} +142750. q^{89} +(31241.8 + 53255.1i) q^{90} +(-16439.6 + 16439.6i) q^{91} +(27837.4 + 5271.83i) q^{92} +(-147690. + 47645.0i) q^{93} +(-49526.0 + 41027.1i) q^{94} +76767.8 q^{95} +(53166.0 + 72987.0i) q^{96} +45553.1 q^{97} +(51036.0 - 42277.9i) q^{98} +(52259.8 + 8502.08i) 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 $

$2$	−4.35628	+	3.60872i	−0.770088	+	0.637937i
$2$	−4.35628	+	3.60872i	−0.770088	+	0.637937i
$3$	4.78598	+	14.8356i	0.307021	+	0.951703i
$3$	4.78598	+	14.8356i	0.307021	+	0.951703i
$4$	5.95430	−	31.4412i	0.186072	−	0.982536i
$5$	−31.7606	+	31.7606i	−0.568151	+	0.568151i	−0.931610	−	0.363459i	$-0.881596\pi$
$5$	−31.7606	+	31.7606i	−0.568151	+	0.568151i	0.363459	+	0.931610i	$0.381596\pi$
$6$	−74.3865	−	47.3566i	−0.843560	−	0.537035i
$7$	−71.3548			−0.550399			−0.275200	−	0.961387i	$-0.588744\pi$
$7$	−71.3548			−0.550399			−0.275200	+	0.961387i	$0.588744\pi$
$8$	87.5237	+	158.454i	0.483505	+	0.875342i
$9$	−197.189	+	142.006i	−0.811476	+	0.584385i
$10$	23.7429	−	252.973i	0.0750816	−	0.799971i
$11$	−154.070	−	154.070i	−0.383917	−	0.383917i	0.488594	−	0.872511i	$-0.337510\pi$
$11$	−154.070	−	154.070i	−0.383917	−	0.383917i	−0.872511	+	0.488594i	$0.837510\pi$
$12$	494.945	−	62.1414i	0.992210	−	0.124574i
$13$	230.393	−	230.393i	0.378104	−	0.378104i	−0.492314	−	0.870418i	$-0.663849\pi$
$13$	230.393	−	230.393i	0.378104	−	0.378104i	0.870418	+	0.492314i	$0.163849\pi$
$14$	310.841	−	257.499i	0.423856	−	0.351120i
$15$	−623.193	−	319.181i	−0.715145	−	0.366277i
$16$	−953.093	−	374.420i	−0.930755	−	0.365645i
$17$		−	1397.75i		−	1.17303i	−0.809940	−	0.586513i	$-0.800500\pi$
$17$		−	1397.75i		−	1.17303i	0.809940	−	0.586513i	$-0.199500\pi$
$18$	346.550	−	1330.21i	0.252107	−	0.967699i
$19$	−1208.54	−	1208.54i	−0.768027	−	0.768027i	0.209732	−	0.977759i	$-0.432741\pi$
$19$	−1208.54	−	1208.54i	−0.768027	−	0.768027i	−0.977759	+	0.209732i	$0.932741\pi$
$20$	809.478	+	1187.70i	0.452512	+	0.663946i
$21$	−341.503	−	1058.59i	−0.168984	−	0.523817i
$22$	1227.17	+	115.177i	0.540565	+	0.0507350i
$23$			885.382i			0.348989i	0.984658	+	0.174494i	$0.0558291\pi$
$23$			885.382i			0.348989i	−0.984658	+	0.174494i	$0.944171\pi$
$24$	−1931.87	+	2056.82i	−0.684619	+	0.728901i
$25$			1107.53i			0.354409i
$26$	−172.232	+	1835.08i	−0.0499667	+	0.532379i
$27$	−3050.48	−	2245.77i	−0.805301	−	0.592866i
$28$	−424.868	+	2243.48i	−0.102414	+	0.540787i
$29$	−801.108	−	801.108i	−0.176887	−	0.176887i	0.613110	−	0.789997i	$-0.289918\pi$
$29$	−801.108	−	801.108i	−0.176887	−	0.176887i	−0.789997	+	0.613110i	$0.789918\pi$
$30$	3866.63	−	858.485i	0.784386	−	0.174152i
$31$			9955.11i			1.86055i	0.366860	+	0.930276i	$0.380433\pi$
$31$			9955.11i			1.86055i	−0.366860	+	0.930276i	$0.619567\pi$
$32$	5503.11	−	1808.37i	0.950021	−	0.312185i
$33$	1548.34	−	3023.10i	0.247504	−	0.483245i
$34$	5044.09	+	6088.99i	0.748317	+	0.903334i
$35$	2266.27	−	2266.27i	0.312710	−	0.312710i
$36$	3290.70	+	7045.39i	0.423187	+	0.906042i
$37$	−3424.22	−	3424.22i	−0.411204	−	0.411204i	0.470954	−	0.882158i	$-0.343910\pi$
$37$	−3424.22	−	3424.22i	−0.411204	−	0.411204i	−0.882158	+	0.470954i	$0.843910\pi$
$38$	9626.01	+	903.453i	1.08140	+	0.101495i
$39$	4520.67	+	2315.36i	0.475928	+	0.243756i
$40$	−7812.39	−	2252.78i	−0.772030	−	0.222622i
$41$	−13334.9			−1.23888			−0.619442	−	0.785043i	$-0.712641\pi$
$41$	−13334.9			−1.23888			−0.619442	+	0.785043i	$0.712641\pi$
$42$	5307.83	+	3379.12i	0.464295	+	0.295584i
$43$	−16355.3	+	16355.3i	−1.34892	+	1.34892i	−0.462090	+	0.886833i	$0.652900\pi$
$43$	−16355.3	+	16355.3i	−1.34892	+	1.34892i	−0.886833	+	0.462090i	$0.847100\pi$
$44$	−5761.53	+	3926.77i	−0.448648	+	0.305776i
$45$	1752.65	−	10773.0i	0.129022	−	0.793060i
$46$	−3195.10	−	3856.97i	−0.222633	−	0.268752i
$47$	11368.9			0.750711			0.375356	−	0.926881i	$-0.377521\pi$
$47$	11368.9			0.750711			0.375356	+	0.926881i	$0.377521\pi$
$48$	993.252	−	15931.6i	0.0622238	−	0.998062i
$49$	−11715.5			−0.697061
$50$	−3996.76	−	4824.70i	−0.226091	−	0.272926i
$51$	20736.5	−	6689.61i	1.11637	−	0.360144i
$52$	−5871.99	−	8615.65i	−0.301146	−	0.441855i
$53$	−15048.0	+	15048.0i	−0.735849	+	0.735849i	−0.971772	−	0.235922i	$-0.924189\pi$
$53$	−15048.0	+	15048.0i	−0.735849	+	0.735849i	0.235922	+	0.971772i	$0.424189\pi$
$54$	21393.1	−	1225.11i	0.998364	−	0.0571730i
$55$	9786.73			0.436246
$56$	−6245.23	−	11306.4i	−0.266121	−	0.481787i
$57$	12145.3	−	23713.4i	0.495133	−	0.966734i
$58$	6380.82	+	598.875i	0.249061	+	0.0233758i
$59$	4253.09	+	4253.09i	0.159065	+	0.159065i	0.782152	−	0.623087i	$-0.214122\pi$
$59$	4253.09	+	4253.09i	0.159065	+	0.159065i	−0.623087	+	0.782152i	$0.714122\pi$
$60$	−13746.1	+	17693.4i	−0.492948	+	0.634502i
$61$	30704.5	−	30704.5i	1.05652	−	1.05652i	0.0582139	−	0.998304i	$-0.481459\pi$
$61$	30704.5	−	30704.5i	1.05652	−	1.05652i	0.998304	−	0.0582139i	$-0.0185406\pi$
$62$	−35925.2	−	43367.2i	−1.18692	−	1.43279i
$63$	14070.4	−	10132.8i	0.446636	−	0.321645i
$64$	−17447.2	+	27736.9i	−0.532446	+	0.846464i
$65$			14634.8i			0.429640i
$66$	4164.50	+	18757.0i	0.117680	+	0.530034i
$67$	−983.712	−	983.712i	−0.0267720	−	0.0267720i	0.693594	−	0.720366i	$-0.256026\pi$
$67$	−983.712	−	983.712i	−0.0267720	−	0.0267720i	−0.720366	+	0.693594i	$0.756026\pi$
$68$	−43946.9	−	8322.63i	−1.15254	−	0.218267i
$69$	−13135.2	+	4237.42i	−0.332133	+	0.107147i
$70$	−1694.17	+	18050.8i	−0.0413249	+	0.440303i
$71$			77935.2i			1.83480i	0.397972	+	0.917398i	$0.369714\pi$
$71$			77935.2i			1.83480i	−0.397972	+	0.917398i	$0.630286\pi$
$72$	−39760.0	−	18816.4i	−0.903890	−	0.427766i
$73$		−	62095.1i		−	1.36380i	−0.731447	−	0.681899i	$-0.761154\pi$
$73$		−	62095.1i		−	1.36380i	0.731447	−	0.681899i	$-0.238846\pi$
$74$	27273.9	+	2559.81i	0.578986	+	0.0543410i
$75$	−16430.8	+	5300.61i	−0.337292	+	0.108811i
$76$	−45193.9	+	30801.9i	−0.897523	+	0.611706i
$77$	10993.7	+	10993.7i	0.211308	+	0.211308i
$78$	−28048.7	+	6227.49i	−0.522008	+	0.115898i
$79$			33253.3i			0.599469i	0.954023	+	0.299734i	$0.0968981\pi$
$79$			33253.3i			0.599469i	−0.954023	+	0.299734i	$0.903102\pi$
$80$	42162.6	−	18379.0i	0.736550	−	0.321068i
$81$	18717.8	−	56003.8i	0.316988	−	0.948430i
$82$	58090.6	−	48121.9i	0.954050	−	0.790330i
$83$	−26282.9	+	26282.9i	−0.418772	+	0.418772i	−0.884780	−	0.466008i	$-0.845692\pi$
$83$	−26282.9	+	26282.9i	−0.418772	+	0.418772i	0.466008	+	0.884780i	$0.345692\pi$
$84$	−35316.7	+	4434.08i	−0.546112	+	0.0685655i
$85$	44393.4	+	44393.4i	0.666456	+	0.666456i
$86$	12226.5	−	130270.i	0.178261	−	1.89932i
$87$	8050.81	−	15719.0i	0.114036	−	0.222652i
$88$	10928.2	−	37897.8i	0.150433	−	0.521684i
$89$	142750.			1.91030			0.955149	−	0.296126i	$-0.0956947\pi$
$89$	142750.			1.91030			0.955149	+	0.296126i	$0.0956947\pi$
$90$	31241.8	+	53255.1i	0.406564	+	0.693034i
$91$	−16439.6	+	16439.6i	−0.208108	+	0.208108i
$92$	27837.4	+	5271.83i	0.342894	+	0.0649369i
$93$	−147690.	+	47645.0i	−1.77069	+	0.571229i
$94$	−49526.0	+	41027.1i	−0.578114	+	0.478907i
$95$	76767.8			0.872711
$96$	53166.0	+	72987.0i	0.588783	+	0.808291i
$97$	45553.1			0.491573			0.245787	−	0.969324i	$-0.420954\pi$
$97$	45553.1			0.491573			0.245787	+	0.969324i	$0.420954\pi$
$98$	51036.0	−	42277.9i	0.536798	−	0.444681i
$99$	52259.8	+	8502.08i	0.535895	+	0.0871841i
$100$	34822.0	+	6594.56i	0.348220	+	0.0659456i
$101$	−116392.	+	116392.i	−1.13532	+	1.13532i	−0.146043	+	0.989278i	$0.546654\pi$
$101$	−116392.	+	116392.i	−1.13532	+	1.13532i	−0.989278	+	0.146043i	$0.953346\pi$
$102$	−66192.8	+	103974.i	−0.629956	+	0.989518i
$103$	−43191.6			−0.401149			−0.200575	−	0.979678i	$-0.564281\pi$
$103$	−43191.6			−0.401149			−0.200575	+	0.979678i	$0.564281\pi$
$104$	56671.5	+	16341.8i	0.513785	+	0.148155i
$105$	44467.8	+	22775.1i	0.393615	+	0.201598i
$106$	11249.3	−	119857.i	0.0972431	−	1.03609i
$107$	−112415.	−	112415.i	−0.949215	−	0.949215i	0.0495568	−	0.998771i	$-0.484219\pi$
$107$	−112415.	−	112415.i	−0.949215	−	0.949215i	−0.998771	+	0.0495568i	$0.984219\pi$
$108$	−88773.1	+	82538.5i	−0.732356	+	0.680922i
$109$	−5292.82	+	5292.82i	−0.0426698	+	0.0426698i	−0.728120	−	0.685450i	$-0.759606\pi$
$109$	−5292.82	+	5292.82i	−0.0426698	+	0.0426698i	0.685450	+	0.728120i	$0.259606\pi$
$110$	−42633.7	+	35317.6i	−0.335948	+	0.278297i
$111$	34412.1	−	67188.6i	0.265096	−	0.517593i
$112$	68007.7	+	26716.7i	0.512287	+	0.201251i
$113$			5278.74i			0.0388897i	0.999811	+	0.0194448i	$0.00618988\pi$
$113$			5278.74i			0.0388897i	−0.999811	+	0.0194448i	$0.993810\pi$
$114$	32666.6	+	147131.i	0.235420	+	1.06033i
$115$	−28120.3	−	28120.3i	−0.198278	−	0.198278i
$116$	−29957.8	+	20417.7i	−0.206712	+	0.140884i
$117$	−12713.8	+	78148.0i	−0.0858639	+	0.527780i
$118$	−33875.8	−	3179.43i	−0.223968	−	0.0210206i
$119$			99736.2i			0.645633i
$120$	−3968.67	−	126683.i	−0.0251589	−	0.803093i
$121$		−	113576.i		−	0.705215i
$122$	−22953.4	+	244561.i	−0.139620	+	1.48760i
$123$	−63820.6	−	197831.i	−0.380363	−	1.17905i
$124$	313000.	+	59275.7i	1.82806	+	0.346196i
$125$	−134428.	−	134428.i	−0.769509	−	0.769509i
$126$	−24728.0	+	94917.1i	−0.138760	+	0.532621i
$127$		−	148501.i		−	0.816997i	−0.912759	−	0.408499i	$-0.866052\pi$
$127$		−	148501.i		−	0.816997i	0.912759	−	0.408499i	$-0.133948\pi$
$128$	−24089.9	−	183792.i	−0.129960	−	0.991519i
$129$	−320916.	−	164364.i	−1.69792	−	0.869626i
$130$	−52813.0	−	63753.4i	−0.274083	−	0.330860i
$131$	28264.8	−	28264.8i	0.143902	−	0.143902i	−0.631485	−	0.775388i	$-0.717554\pi$
$131$	28264.8	−	28264.8i	0.143902	−	0.143902i	0.775388	+	0.631485i	$0.217554\pi$
$132$	−85830.5	−	66682.2i	−0.428753	−	0.333100i
$133$	86235.0	+	86235.0i	0.422722	+	0.422722i
$134$	7835.26	+	735.382i	0.0376957	+	0.00353794i
$135$	168212.	−	25557.9i	0.794370	−	0.120696i
$136$	221479.	−	122336.i	1.02680	−	0.567164i
$137$	38668.6			0.176018			0.0880089	−	0.996120i	$-0.471950\pi$
$137$	38668.6			0.176018			0.0880089	+	0.996120i	$0.471950\pi$
$138$	41928.7	−	65860.5i	0.187419	−	0.294393i
$139$	−160964.	+	160964.i	−0.706630	+	0.706630i	−0.965825	−	0.259195i	$-0.916543\pi$
$139$	−160964.	+	160964.i	−0.706630	+	0.706630i	0.259195	+	0.965825i	$0.416543\pi$
$140$	−57760.1	−	84748.2i	−0.249062	−	0.365435i
$141$	54411.3	+	168664.i	0.230484	+	0.714454i
$142$	−281246.	−	339507.i	−1.17048	−	1.41295i
$143$	−70993.4			−0.290321
$144$	241109.	−	61513.1i	0.968963	−	0.247207i
$145$	50887.3			0.200997
$146$	224084.	+	270503.i	0.870017	+	1.05024i
$147$	−56070.2	−	173806.i	−0.214012	−	0.663395i
$148$	−128050.	+	87272.7i	−0.480537	+	0.327510i
$149$	−30765.3	+	30765.3i	−0.113526	+	0.113526i	−0.761588	−	0.648062i	$-0.775580\pi$
$149$	−30765.3	+	30765.3i	−0.113526	+	0.113526i	0.648062	+	0.761588i	$0.275580\pi$
$150$	52448.8	−	82385.2i	0.190330	−	0.298965i
$151$	186824.			0.666792			0.333396	−	0.942787i	$-0.391805\pi$
$151$	186824.			0.666792			0.333396	+	0.942787i	$0.391805\pi$
$152$	85721.7	−	297273.i	0.300941	−	1.04363i
$153$	198489.	+	275621.i	0.685499	+	0.951883i
$154$	−87564.4	−	8218.40i	−0.297527	−	0.0279245i
$155$	−316180.	−	316180.i	−1.05707	−	1.05707i
$156$	99714.9	−	128349.i	0.328056	−	0.422260i
$157$	−40152.2	+	40152.2i	−0.130005	+	0.130005i	−0.769115	−	0.639110i	$-0.779303\pi$
$157$	−40152.2	+	40152.2i	−0.130005	+	0.130005i	0.639110	+	0.769115i	$0.279303\pi$
$158$	−120002.	−	144860.i	−0.382424	−	0.461644i
$159$	−295265.	−	151226.i	−0.926231	−	0.474389i
$160$	−117347.	+	232217.i	−0.362388	+	0.717123i
$161$		−	63176.2i		−	0.192083i
$162$	120562.	+	311515.i	0.360930	+	0.932593i
$163$	−205355.	−	205355.i	−0.605391	−	0.605391i	0.336347	−	0.941738i	$-0.390809\pi$
$163$	−205355.	−	205355.i	−0.605391	−	0.605391i	−0.941738	+	0.336347i	$0.890809\pi$
$164$	−79400.0	+	419265.i	−0.230521	+	1.21725i
$165$	46839.1	+	145192.i	0.133937	+	0.415176i
$166$	19648.0	−	209343.i	0.0553411	−	0.589642i
$167$			483299.i			1.34099i	0.741915	+	0.670494i	$0.233918\pi$
$167$			483299.i			1.34099i	−0.741915	+	0.670494i	$0.766082\pi$
$168$	137848.	−	146764.i	0.376814	−	0.401187i
$169$			265131.i			0.714075i
$170$	−353593.	−	33186.7i	−0.938387	−	0.0880727i
$171$	409930.	+	66690.9i	1.07206	+	0.174412i
$172$	416845.	+	611614.i	1.07437	+	1.57636i
$173$	194515.	+	194515.i	0.494127	+	0.494127i	0.909604	−	0.415477i	$-0.136385\pi$
$173$	194515.	+	194515.i	0.494127	+	0.494127i	−0.415477	+	0.909604i	$0.636385\pi$
$174$	21653.8	+	97529.3i	0.0542203	+	0.244209i
$175$		−	79027.4i		−	0.195067i
$176$	89156.3	+	204530.i	0.216955	+	0.497710i
$177$	−42741.8	+	83452.2i	−0.102546	+	0.200219i
$178$	−621859.	+	515145.i	−1.47110	+	1.21865i
$179$	120785.	−	120785.i	0.281762	−	0.281762i	−0.552050	−	0.833811i	$-0.686154\pi$
$179$	120785.	−	120785.i	0.281762	−	0.281762i	0.833811	+	0.552050i	$0.186154\pi$
$180$	−328280.	−	119251.i	−0.755203	−	0.274335i
$181$	172365.	+	172365.i	0.391068	+	0.391068i	0.875068	−	0.484000i	$-0.160816\pi$
$181$	172365.	+	172365.i	0.391068	+	0.391068i	−0.484000	+	0.875068i	$0.660816\pi$
$182$	12289.6	−	130942.i	0.0275016	−	0.293021i
$183$	602469.	+	308567.i	1.32986	+	0.681118i
$184$	−140292.	+	77492.0i	−0.305484	+	0.168738i
$185$	217511.			0.467252
$186$	471441.	−	740526.i	0.999182	−	1.56949i
$187$	−215352.	+	215352.i	−0.450345	+	0.450345i
$188$	67693.7	−	357451.i	0.139686	−	0.737601i
$189$	217666.	+	160247.i	0.443237	+	0.326313i
$190$	−334422.	+	277033.i	−0.672064	+	0.556735i
$191$	761321.			1.51003			0.755013	−	0.655710i	$-0.227630\pi$
$191$	761321.			1.51003			0.755013	+	0.655710i	$0.227630\pi$
$192$	−494995.	−	126091.i	−0.969054	−	0.246848i
$193$	243010.			0.469604			0.234802	−	0.972043i	$-0.424556\pi$
$193$	243010.			0.469604			0.234802	+	0.972043i	$0.424556\pi$
$194$	−198442.	+	164388.i	−0.378555	+	0.313593i
$195$	−217116.	+	70042.1i	−0.408889	+	0.131908i
$196$	−69757.6	+	368349.i	−0.129703	+	0.684887i
$197$	589825.	−	589825.i	1.08282	−	1.08282i	0.0865775	−	0.996245i	$-0.472407\pi$
$197$	589825.	−	589825.i	1.08282	−	1.08282i	0.996245	−	0.0865775i	$-0.0275930\pi$
$198$	−258340.	+	151554.i	−0.468304	+	0.274728i
$199$	−789095.			−1.41253			−0.706263	−	0.707950i	$-0.749620\pi$
$199$	−789095.			−1.41253			−0.706263	+	0.707950i	$0.749620\pi$
$200$	−175492.	+	96935.0i	−0.310229	+	0.171359i
$201$	9885.90	−	19302.0i	0.0172594	−	0.0336985i
$202$	87009.6	−	927059.i	0.150034	−	1.59856i
$203$	57162.8	+	57162.8i	0.0973585	+	0.0973585i
$204$	−86858.2	−	691810.i	−0.146129	−	1.16389i
$205$	423525.	−	423525.i	0.703873	−	0.703873i
$206$	188154.	−	155866.i	0.308920	−	0.255908i
$207$	−125729.	−	174587.i	−0.203944	−	0.283196i
$208$	−305850.	+	133322.i	−0.490173	+	0.213670i
$209$			372400.i			0.589717i
$210$	−275903.	+	61257.0i	−0.431726	+	0.0958534i
$211$	370683.	+	370683.i	0.573187	+	0.573187i	0.933018	−	0.359831i	$-0.117166\pi$
$211$	370683.	+	370683.i	0.573187	+	0.573187i	−0.359831	+	0.933018i	$0.617166\pi$
$212$	383526.	+	562727.i	0.586078	+	0.859919i
$213$	−1.15621e6	+	372996.i	−1.74618	+	0.563321i
$214$	895384.	+	84036.7i	1.33652	+	0.125440i
$215$		−	1.03891e6i		−	1.53278i
$216$	88861.9	−	679918.i	0.129593	−	0.991567i
$217$		−	710345.i		−	1.02405i
$218$	3956.69	−	42157.3i	0.00563885	−	0.0600802i
$219$	921216.	−	297186.i	1.29793	−	0.418714i
$220$	58273.1	−	307706.i	0.0811730	−	0.428627i
$221$	−322032.	−	322032.i	−0.443525	−	0.443525i
$222$	92556.3	+	416876.i	0.126044	+	0.567707i
$223$			993614.i			1.33800i	0.743263	+	0.668999i	$0.233277\pi$
$223$			993614.i			1.33800i	−0.743263	+	0.668999i	$0.766723\pi$
$224$	−392673.	+	129036.i	−0.522891	+	0.171826i
$225$	−157275.	−	218392.i	−0.207112	−	0.287595i
$226$	−19049.5	−	22995.7i	−0.0248092	−	0.0299485i
$227$	−480562.	+	480562.i	−0.618992	+	0.618992i	−0.945273	−	0.326281i	$-0.894204\pi$
$227$	−480562.	+	480562.i	−0.618992	+	0.618992i	0.326281	+	0.945273i	$0.394204\pi$
$228$	−673260.	−	523060.i	−0.857721	−	0.666368i
$229$	−663145.	−	663145.i	−0.835641	−	0.835641i	0.152641	−	0.988282i	$-0.451222\pi$
$229$	−663145.	−	663145.i	−0.835641	−	0.835641i	−0.988282	+	0.152641i	$0.951222\pi$
$230$	223978.	+	21021.5i	0.279181	+	0.0262026i
$231$	−110482.	+	215713.i	−0.136226	+	0.265978i
$232$	56822.6	−	197054.i	0.0693108	−	0.240362i
$233$	−1.07930e6			−1.30242			−0.651210	−	0.758898i	$-0.725738\pi$
$233$	−1.07930e6			−1.30242			−0.651210	+	0.758898i	$0.725738\pi$
$234$	−226629.	−	386315.i	−0.270568	−	0.461213i
$235$	−361082.	+	361082.i	−0.426517	+	0.426517i
$236$	159046.	−	108398.i	0.185885	−	0.126690i
$237$	−493331.	+	159150.i	−0.570516	+	0.184049i
$238$	−359920.	−	434479.i	−0.411873	−	0.497194i
$239$	−197683.			−0.223860			−0.111930	−	0.993716i	$-0.535703\pi$
$239$	−197683.			−0.223860			−0.111930	+	0.993716i	$0.535703\pi$
$240$	474452.	+	537545.i	0.531697	+	0.602402i
$241$	894359.			0.991903			0.495952	−	0.868350i	$-0.334819\pi$
$241$	894359.			0.991903			0.495952	+	0.868350i	$0.334819\pi$
$242$	409863.	+	494767.i	0.449883	+	0.543078i
$243$	920432.	+	9655.95i	0.999945	+	0.0104901i
$244$	−782560.	−	1.14821e6i	−0.841479	−	1.23466i
$245$	372091.	−	372091.i	0.396036	−	0.396036i
$246$	991937.	+	631496.i	1.04507	+	0.665324i
$247$	−556877.			−0.580788
$248$	−1.57743e6	+	871309.i	−1.62862	+	0.899586i
$249$	−515711.	−	264132.i	−0.527118	−	0.269975i
$250$	1.07072e6	+	100492.i	1.08349	+	0.101691i
$251$	−39565.3	−	39565.3i	−0.0396397	−	0.0396397i	0.687009	−	0.726649i	$-0.258923\pi$
$251$	−39565.3	−	39565.3i	−0.0396397	−	0.0396397i	−0.726649	+	0.687009i	$0.758923\pi$
$252$	−234807.	−	502722.i	−0.232922	−	0.498685i
$253$	136411.	−	136411.i	0.133983	−	0.133983i
$254$	535899.	+	646912.i	0.521193	+	0.629160i
$255$	−446136.	+	871068.i	−0.429652	+	0.838884i
$256$	768195.	+	713714.i	0.732608	+	0.680651i
$257$			317668.i			0.300014i	0.988685	+	0.150007i	$0.0479296\pi$
$257$			317668.i			0.300014i	−0.988685	+	0.150007i	$0.952070\pi$
$258$	1.99114e6	−	442082.i	1.86232	−	0.413479i
$259$	244335.	+	244335.i	0.226327	+	0.226327i
$260$	460136.	+	87140.2i	0.422137	+	0.0799438i
$261$	271731.	+	44207.6i	0.246910	+	0.0401694i
$262$	−21129.6	+	225129.i	−0.0190168	+	0.202618i
$263$		−	1.15142e6i		−	1.02647i	−0.858248	−	0.513235i	$-0.828447\pi$
$263$		−	1.15142e6i		−	1.02647i	0.858248	−	0.513235i	$-0.171553\pi$
$264$	614539.	−	19252.0i	0.542674	−	0.0170006i
$265$		−	955867.i		−	0.836147i
$266$	−686861.	−	64465.7i	−0.595203	−	0.0558630i
$267$	683199.	+	2.11778e6i	0.586501	+	1.81804i
$268$	−36786.3	+	25071.7i	−0.0312860	+	0.0213229i
$269$	−1.01591e6	−	1.01591e6i	−0.856000	−	0.856000i	0.134864	−	0.990864i	$-0.456940\pi$
$269$	−1.01591e6	−	1.01591e6i	−0.856000	−	0.856000i	−0.990864	+	0.134864i	$0.956940\pi$
$270$	−640547.	+	718367.i	−0.534739	+	0.599704i
$271$			316944.i			0.262156i	0.991372	+	0.131078i	$0.0418439\pi$
$271$			316944.i			0.262156i	−0.991372	+	0.131078i	$0.958156\pi$
$272$	−523346.	+	1.33219e6i	−0.428911	+	1.09180i
$273$	−322571.	−	165212.i	−0.261950	−	0.134163i
$274$	−168451.	+	139544.i	−0.135549	+	0.112288i
$275$	170637.	−	170637.i	0.136064	−	0.136064i
$276$	55018.9	+	438215.i	0.0434750	+	0.346270i
$277$	116789.	+	116789.i	0.0914541	+	0.0914541i	0.751354	−	0.659900i	$-0.229401\pi$
$277$	116789.	+	116789.i	0.0914541	+	0.0914541i	−0.659900	+	0.751354i	$0.729401\pi$
$278$	120330.	−	1.28208e6i	0.0933818	−	0.994954i
$279$	−1.41368e6	−	1.96304e6i	−1.08728	−	1.50979i
$280$	557451.	+	160747.i	0.424925	+	0.122531i
$281$	−1.22385e6			−0.924615			−0.462307	−	0.886720i	$-0.652978\pi$
$281$	−1.22385e6			−0.924615			−0.462307	+	0.886720i	$0.652978\pi$
$282$	−845691.	−	538392.i	−0.633270	−	0.403158i
$283$	511559.	−	511559.i	0.379691	−	0.379691i	−0.491300	−	0.870991i	$-0.663478\pi$
$283$	511559.	−	511559.i	0.379691	−	0.379691i	0.870991	+	0.491300i	$0.163478\pi$
$284$	2.45037e6	+	464049.i	1.80275	+	0.341404i
$285$	367409.	+	1.13890e6i	0.267940	+	0.830561i
$286$	309267.	−	256195.i	0.223573	−	0.185206i
$287$	951509.			0.681881
$288$	−828354.	+	1.13806e6i	−0.588484	+	0.808509i
$289$	−533852.			−0.375990
$290$	−221679.	+	183638.i	−0.154785	+	0.128223i
$291$	218016.	+	675806.i	0.150923	+	0.467832i
$292$	−1.95234e6	−	369733.i	−1.33998	−	0.253764i
$293$	1.61698e6	−	1.61698e6i	1.10036	−	1.10036i	0.105993	−	0.994367i	$-0.466198\pi$
$293$	1.61698e6	−	1.61698e6i	1.10036	−	1.10036i	0.994367	−	0.105993i	$-0.0338021\pi$
$294$	871475.	+	554806.i	0.588012	+	0.374346i
$295$	−270161.			−0.180746
$296$	242880.	−	842282.i	0.161125	−	0.558764i
$297$	123981.	+	815995.i	0.0815577	+	0.536780i
$298$	22998.9	−	245046.i	0.0150026	−	0.159848i
$299$	203986.	+	203986.i	0.131954	+	0.131954i
$300$	68823.4	+	548166.i	0.0441502	+	0.351648i
$301$	1.16703e6	−	1.16703e6i	0.742446	−	0.742446i
$302$	−813858.	+	674196.i	−0.513489	+	0.425372i
$303$	−2.28379e6	−	1.16969e6i	−1.42906	−	0.731921i
$304$	699348.	+	1.60435e6i	0.434020	+	0.995670i
$305$			1.95038e6i			1.20052i
$306$	−1.85931e6	−	484391.i	−1.13514	−	0.295728i
$307$	−11119.0	−	11119.0i	−0.00673315	−	0.00673315i	0.703732	−	0.710465i	$-0.251515\pi$
$307$	−11119.0	−	11119.0i	−0.00673315	−	0.00673315i	−0.710465	+	0.703732i	$0.751515\pi$
$308$	411113.	−	280194.i	0.246936	−	0.168299i
$309$	−206714.	−	640772.i	−0.123161	−	0.381775i
$310$	2.51838e6	+	236363.i	1.48839	+	0.139693i
$311$			752435.i			0.441132i	0.975372	+	0.220566i	$0.0707904\pi$
$311$			752435.i			0.441132i	−0.975372	+	0.220566i	$0.929210\pi$
$312$	28788.9	+	918965.i	0.0167432	+	0.534457i
$313$			2.82769e6i			1.63144i	0.578448	+	0.815719i	$0.303658\pi$
$313$			2.82769e6i			1.63144i	−0.578448	+	0.815719i	$0.696342\pi$
$314$	30016.1	−	319812.i	0.0171803	−	0.183051i
$315$	−125060.	+	768706.i	−0.0710136	+	0.436500i
$316$	1.04552e6	+	198000.i	0.589000	+	0.111544i
$317$	355748.	+	355748.i	0.198836	+	0.198836i	0.799501	−	0.600665i	$-0.205097\pi$
$317$	355748.	+	355748.i	0.198836	+	0.198836i	−0.600665	+	0.799501i	$0.705097\pi$
$318$	1.83199e6	−	406745.i	1.01591	−	0.225556i
$319$			246854.i			0.135820i
$320$	−326808.	−	1.43507e6i	−0.178409	−	0.783429i
$321$	1.12972e6	−	2.20576e6i	0.611941	−	1.19480i
$322$	227985.	+	275213.i	0.122537	+	0.147921i
$323$	−1.68924e6	+	1.68924e6i	−0.900916	+	0.900916i
$324$	−1.64937e6	−	921973.i	−0.872884	−	0.487928i
$325$	255167.	+	255167.i	0.134003	+	0.134003i
$326$	1.63565e6	+	153515.i	0.852406	+	0.0800030i
$327$	−103853.	−	53190.7i	−0.0537095	−	0.0275084i
$328$	−1.16712e6	−	2.11297e6i	−0.599006	−	1.08445i
$329$	−811224.			−0.413191
$330$	−728001.	−	463467.i	−0.367999	−	0.234279i
$331$	1.54309e6	−	1.54309e6i	0.774145	−	0.774145i	−0.204683	−	0.978828i	$-0.565616\pi$
$331$	1.54309e6	−	1.54309e6i	0.774145	−	0.774145i	0.978828	+	0.204683i	$0.0656165\pi$
$332$	669868.	+	982860.i	0.333537	+	0.489380i
$333$	1.16148e6	+	188959.i	0.573984	+	0.0933808i
$334$	−1.74409e6	−	2.10539e6i	−0.855466	−	1.03268i
$335$	62486.5			0.0304211
$336$	−70873.3	+	1.13680e6i	−0.0342479	+	0.549333i
$337$	−764015.			−0.366460			−0.183230	−	0.983070i	$-0.558655\pi$
$337$	−764015.			−0.366460			−0.183230	+	0.983070i	$0.558655\pi$
$338$	−956784.	−	1.15499e6i	−0.455535	−	0.549901i
$339$	−78313.2	+	25264.0i	−0.0370114	+	0.0119399i
$340$	1.66011e6	−	1.13145e6i	0.778825	−	0.530808i
$341$	1.53379e6	−	1.53379e6i	0.714298	−	0.714298i
$342$	−2.02644e6	+	1.18880e6i	−0.936844	+	0.549594i
$343$	2.03522e6			0.934061
$344$	−4.02303e6	−	1.16008e6i	−1.83298	−	0.528558i
$345$	282597.	−	551764.i	0.127826	−	0.249577i
$346$	−1.54931e6	−	145411.i	−0.695743	−	0.0652993i
$347$	−129263.	−	129263.i	−0.0576300	−	0.0576300i	0.677704	−	0.735334i	$-0.262975\pi$
$347$	−129263.	−	129263.i	−0.0576300	−	0.0576300i	−0.735334	+	0.677704i	$0.762975\pi$
$348$	−446286.	−	346722.i	−0.197545	−	0.153474i
$349$	−1.33247e6	+	1.33247e6i	−0.585589	+	0.585589i	−0.936434	−	0.350844i	$-0.885895\pi$
$349$	−1.33247e6	+	1.33247e6i	−0.585589	+	0.585589i	0.350844	+	0.936434i	$0.385895\pi$
$350$	285188.	+	344265.i	0.124440	+	0.150218i
$351$	−1.22022e6	+	185398.i	−0.528652	+	0.0803227i
$352$	−1.12648e6	−	569251.i	−0.484582	−	0.244876i
$353$			4.45462e6i			1.90272i	0.308087	+	0.951358i	$0.400311\pi$
$353$			4.45462e6i			1.90272i	−0.308087	+	0.951358i	$0.599689\pi$
$354$	−114960.	−	517784.i	−0.0487574	−	0.219604i
$355$	−2.47527e6	−	2.47527e6i	−1.04244	−	1.04244i
$356$	849976.	−	4.48823e6i	0.355453	−	1.87694i
$357$	−1.47964e6	+	477336.i	−0.614450	+	0.198223i
$358$	−90294.1	+	962055.i	−0.0372350	+	0.396728i
$359$			2.68062e6i			1.09774i	0.835908	+	0.548870i	$0.184942\pi$
$359$			2.68062e6i			1.09774i	−0.835908	+	0.548870i	$0.815058\pi$
$360$	1.86042e6	−	665181.i	0.756581	−	0.270510i
$361$			445032.i			0.179731i
$362$	−1.37289e6	−	128853.i	−0.550634	−	0.0516800i
$363$	1.68496e6	−	543571.i	0.671155	−	0.216516i
$364$	418995.	+	614767.i	0.165751	+	0.243197i
$365$	1.97218e6	+	1.97218e6i	0.774843	+	0.774843i
$366$	−3.73806e6	+	829938.i	−1.45862	+	0.323849i
$367$		−	1.59177e6i		−	0.616900i	−0.951241	−	0.308450i	$-0.900190\pi$
$367$		−	1.59177e6i		−	0.616900i	0.951241	−	0.308450i	$-0.0998102\pi$
$368$	331505.	−	843851.i	0.127606	−	0.324823i
$369$	2.62949e6	−	1.89363e6i	1.00532	−	0.723985i
$370$	−947537.	+	784935.i	−0.359826	+	0.298078i
$371$	1.07375e6	−	1.07375e6i	0.405011	−	0.405011i
$372$	618625.	+	4.92723e6i	0.231777	+	1.84606i
$373$	−2.48953e6	−	2.48953e6i	−0.926501	−	0.926501i	0.0709766	−	0.997478i	$-0.477388\pi$
$373$	−2.48953e6	−	2.48953e6i	−0.926501	−	0.926501i	−0.997478	+	0.0709766i	$0.977388\pi$
$374$	160988.	−	1.71528e6i	0.0595134	−	0.634097i
$375$	1.35094e6	−	2.63768e6i	0.496088	−	0.968599i
$376$	995047.	+	1.80144e6i	0.362973	+	0.657129i
$377$	−369139.			−0.133763
$378$	−1.52650e6	+	87417.4i	−0.549499	+	0.0314680i
$379$	1.45336e6	−	1.45336e6i	0.519728	−	0.519728i	−0.397761	−	0.917489i	$-0.630213\pi$
$379$	1.45336e6	−	1.45336e6i	0.519728	−	0.519728i	0.917489	+	0.397761i	$0.130213\pi$
$380$	457099.	−	2.41367e6i	0.162387	−	0.857470i
$381$	2.20310e6	−	710724.i	0.777539	−	0.250835i
$382$	−3.31653e6	+	2.74739e6i	−1.16285	+	0.963302i
$383$	3.67151e6			1.27893			0.639466	−	0.768820i	$-0.279156\pi$
$383$	3.67151e6			1.27893			0.639466	+	0.768820i	$0.279156\pi$
$384$	2.61136e6	−	1.23701e6i	0.903731	−	0.428101i
$385$	−698330.			−0.240109
$386$	−1.05862e6	+	876956.i	−0.361636	+	0.299578i
$387$	902536.	−	5.54762e6i	0.306328	−	1.88291i
$388$	271237.	−	1.43224e6i	0.0914680	−	0.482989i
$389$	−1.07313e6	+	1.07313e6i	−0.359565	+	0.359565i	−0.863653	−	0.504087i	$-0.831829\pi$
$389$	−1.07313e6	+	1.07313e6i	−0.359565	+	0.359565i	0.504087	+	0.863653i	$0.331829\pi$
$390$	693056.	−	1.08863e6i	0.230732	−	0.362427i
$391$	1.23754e6			0.409373
$392$	−1.02538e6	−	1.85636e6i	−0.337032	−	0.610166i
$393$	554600.	+	284050.i	0.181133	+	0.0927713i
$394$	−440928.	+	4.69795e6i	−0.143096	+	1.52464i
$395$	−1.05614e6	−	1.05614e6i	−0.340589	−	0.340589i
$396$	578486.	−	1.59248e6i	0.185376	−	0.510314i
$397$	−1.66681e6	+	1.66681e6i	−0.530776	+	0.530776i	−0.920803	−	0.390028i	$-0.872465\pi$
$397$	−1.66681e6	+	1.66681e6i	−0.530776	+	0.530776i	0.390028	+	0.920803i	$0.372465\pi$
$398$	3.43751e6	−	2.84762e6i	1.08777	−	0.901103i
$399$	−866627.	+	1.69207e6i	−0.272521	+	0.532090i
$400$	414681.	−	1.05558e6i	0.129588	−	0.329868i
$401$		−	832014.i		−	0.258386i	−0.991619	−	0.129193i	$-0.958761\pi$
$401$		−	832014.i		−	0.258386i	0.991619	−	0.129193i	$-0.0412387\pi$
$402$	26589.6	+	119760.i	0.00820629	+	0.0369613i
$403$	2.29359e6	+	2.29359e6i	0.703482	+	0.703482i
$404$	2.96646e6	+	4.35252e6i	0.904243	+	1.32674i
$405$	1.18423e6	+	2.37320e6i	0.358754	+	0.718948i
$406$	−455302.	−	42732.5i	−0.137083	−	0.0128660i
$407$			1.05514e6i			0.315737i
$408$	2.87493e6	+	2.70027e6i	0.855020	+	0.803076i
$409$			5.79131e6i			1.71186i	0.517090	+	0.855931i	$0.327015\pi$
$409$			5.79131e6i			1.71186i	−0.517090	+	0.855931i	$0.672985\pi$
$410$	−316609.	+	3.37337e6i	−0.0930174	+	0.991071i
$411$	185067.	+	573671.i	0.0540412	+	0.167517i
$412$	−257176.	+	1.35799e6i	−0.0746426	+	0.394144i
$413$	−303478.	−	303478.i	−0.0875492	−	0.0875492i
$414$	1.17775e6	+	306830.i	0.337716	+	0.0879825i
$415$		−	1.66952e6i		−	0.475851i
$416$	851243.	−	1.68451e6i	0.241168	−	0.477245i
$417$	−3.15837e6	−	1.61763e6i	−0.889453	−	0.455552i
$418$	−1.34389e6	−	1.62228e6i	−0.376203	−	0.454134i
$419$	−3.70460e6	+	3.70460e6i	−1.03088	+	1.03088i	−0.0313672	+	0.999508i	$0.509986\pi$
$419$	−3.70460e6	+	3.70460e6i	−1.03088	+	1.03088i	−0.999508	+	0.0313672i	$0.990014\pi$
$420$	980850.	−	1.26251e6i	0.271318	−	0.349229i
$421$	4.07096e6	+	4.07096e6i	1.11942	+	1.11942i	0.991827	+	0.127590i	$0.0407241\pi$
$421$	4.07096e6	+	4.07096e6i	1.11942	+	1.11942i	0.127590	+	0.991827i	$0.459276\pi$
$422$	−2.95249e6	−	277107.i	−0.807062	−	0.0757472i
$423$	−2.24181e6	+	1.61444e6i	−0.609184	+	0.438705i
$424$	−3.70147e6	−	1.06735e6i	−0.999906	−	0.288333i
$425$	1.54805e6			0.415731
$426$	3.69075e6	−	5.79732e6i	0.985349	−	1.54776i
$427$	−2.19091e6	+	2.19091e6i	−0.581507	+	0.581507i
$428$	−4.20381e6	+	2.86510e6i	−1.10926	+	0.756016i
$429$	−339773.	−	1.05323e6i	−0.0891346	−	0.276299i
$430$	3.74913e6	+	4.52577e6i	0.977820	+	1.18038i
$431$	−3.41242e6			−0.884848			−0.442424	−	0.896806i	$-0.645881\pi$
$431$	−3.41242e6			−0.884848			−0.442424	+	0.896806i	$0.645881\pi$
$432$	2.06653e6	+	3.28259e6i	0.532760	+	0.846266i
$433$	−3.06425e6			−0.785424			−0.392712	−	0.919661i	$-0.628463\pi$
$433$	−3.06425e6			−0.785424			−0.392712	+	0.919661i	$0.628463\pi$
$434$	2.56343e6	+	3.09446e6i	0.653278	+	0.788606i
$435$	243546.	+	754943.i	0.0617103	+	0.191289i
$436$	134897.	+	197927.i	0.0339850	+	0.0498643i
$437$	1.07002e6	−	1.07002e6i	0.268033	−	0.268033i
$438$	−2.94061e6	+	4.61903e6i	−0.732407	+	1.15045i
$439$	−152889.			−0.0378631			−0.0189315	−	0.999821i	$-0.506026\pi$
$439$	−152889.			−0.0378631			−0.0189315	+	0.999821i	$0.506026\pi$
$440$	856571.	+	1.55074e6i	0.210927	+	0.381864i
$441$	2.31016e6	−	1.66367e6i	0.565648	−	0.407352i
$442$	2.56498e6	+	240738.i	0.624495	+	0.0586123i
$443$	−5.54337e6	−	5.54337e6i	−1.34204	−	1.34204i	−0.894029	−	0.448008i	$-0.852133\pi$
$443$	−5.54337e6	−	5.54337e6i	−1.34204	−	1.34204i	−0.448008	−	0.894029i	$-0.647867\pi$
$444$	−1.90759e6	−	1.48202e6i	−0.459227	−	0.356776i
$445$	−4.53383e6	+	4.53383e6i	−1.08534	+	1.08534i
$446$	−3.58567e6	−	4.32846e6i	−0.853559	−	1.03038i
$447$	−603664.	−	309179.i	−0.142898	−	0.0731882i
$448$	1.24494e6	−	1.97916e6i	0.293058	−	0.465893i
$449$			2.96539e6i			0.694171i	0.937833	+	0.347086i	$0.112829\pi$
$449$			2.96539e6i			0.694171i	−0.937833	+	0.347086i	$0.887171\pi$
$450$	1.47325e6	+	383814.i	0.342962	+	0.0893491i
$451$	2.05451e6	+	2.05451e6i	0.475628	+	0.475628i
$452$	165970.	+	31431.2i	0.0382105	+	0.00723627i
$453$	894137.	+	2.77164e6i	0.204719	+	0.634588i
$454$	359248.	−	3.82768e6i	0.0818003	−	0.871557i
$455$		−	1.04427e6i		−	0.236473i
$456$	4.82048e6	−	151014.i	1.08562	−	0.0340098i
$457$		−	6.72657e6i		−	1.50662i	−0.657667	−	0.753309i	$-0.728456\pi$
$457$		−	6.72657e6i		−	1.50662i	0.657667	−	0.753309i	$-0.271544\pi$
$458$	5.28195e6	+	495740.i	1.17660	+	0.110431i
$459$	−3.13903e6	+	4.26381e6i	−0.695447	+	0.944639i
$460$	−1.05157e6	+	716697.i	−0.231709	+	0.157922i
$461$	−5.57882e6	−	5.57882e6i	−1.22262	−	1.22262i	−0.966699	−	0.255918i	$-0.917622\pi$
$461$	−5.57882e6	−	5.57882e6i	−1.22262	−	1.22262i	−0.255918	−	0.966699i	$-0.582378\pi$
$462$	−297157.	−	1.33840e6i	−0.0647711	−	0.291730i
$463$		−	6.41134e6i		−	1.38994i	−0.719038	−	0.694971i	$-0.755417\pi$
$463$		−	6.41134e6i		−	1.38994i	0.719038	−	0.694971i	$-0.244583\pi$
$464$	463579.	+	1.06348e6i	0.0999606	+	0.229316i
$465$	3.17748e6	−	6.20395e6i	0.681477	−	1.33056i
$466$	4.70171e6	−	3.89488e6i	1.00298	−	0.830862i
$467$	−102897.	+	102897.i	−0.0218328	+	0.0218328i	−0.717939	−	0.696106i	$-0.754914\pi$
$467$	−102897.	+	102897.i	−0.0218328	+	0.0218328i	0.696106	+	0.717939i	$0.254914\pi$
$468$	2.38136e6	+	865053.i	0.502586	+	0.182569i
$469$	70192.5	+	70192.5i	0.0147353	+	0.0147353i
$470$	269930.	−	2.87602e6i	0.0563646	−	0.600547i
$471$	−787850.	−	403514.i	−0.163641	−	0.0838120i
$472$	−301672.	+	1.04616e6i	−0.0623275	+	0.216145i
$473$	5.03973e6			1.03575
$474$	1.57476e6	−	2.47359e6i	0.321936	−	0.505688i
$475$	1.33849e6	−	1.33849e6i	0.272196	−	0.272196i
$476$	3.13582e6	+	593859.i	0.634357	+	0.120134i
$477$	830395.	−	5.10419e6i	0.167105	−	1.02714i
$478$	861164.	−	713384.i	0.172392	−	0.142808i
$479$	4.32363e6			0.861013			0.430507	−	0.902587i	$-0.358335\pi$
$479$	4.32363e6			0.861013			0.430507	+	0.902587i	$0.358335\pi$
$480$	−4.00669e6	−	629530.i	−0.793749	−	0.124713i
$481$	−1.57783e6			−0.310956
$482$	−3.89608e6	+	3.22749e6i	−0.763853	+	0.632772i
$483$	937256.	−	302360.i	0.182806	−	0.0589735i
$484$	−3.57095e6	−	676263.i	−0.692900	−	0.131221i
$485$	−1.44679e6	+	1.44679e6i	−0.279288	+	0.279288i
$486$	−4.04450e6	+	3.27952e6i	−0.776738	+	0.629824i
$487$	−621385.			−0.118724			−0.0593620	−	0.998237i	$-0.518907\pi$
$487$	−621385.			−0.118724			−0.0593620	+	0.998237i	$0.518907\pi$
$488$	7.55261e6	+	2.17787e6i	1.43565	+	0.413983i
$489$	2.06373e6	−	4.02938e6i	0.390285	−	0.762020i
$490$	−278160.	+	2.96371e6i	−0.0523365	+	0.557628i
$491$	−1.53108e6	−	1.53108e6i	−0.286611	−	0.286611i	0.549128	−	0.835739i	$-0.314960\pi$
$491$	−1.53108e6	−	1.53108e6i	−0.286611	−	0.286611i	−0.835739	+	0.549128i	$0.814960\pi$
$492$	−6.60005e6	+	828650.i	−1.22923	+	0.154333i
$493$	−1.11975e6	+	1.11975e6i	−0.207493	+	0.207493i
$494$	2.42591e6	−	2.00961e6i	0.447258	−	0.370506i
$495$	−1.92983e6	+	1.38977e6i	−0.354003	+	0.254936i
$496$	3.72739e6	−	9.48815e6i	0.680301	−	1.73172i
$497$		−	5.56105e6i		−	1.00987i
$498$	3.19976e6	−	710423.i	0.578155	−	0.128364i
$499$	−1.91690e6	−	1.91690e6i	−0.344627	−	0.344627i	0.513477	−	0.858103i	$-0.328357\pi$
$499$	−1.91690e6	−	1.91690e6i	−0.344627	−	0.344627i	−0.858103	+	0.513477i	$0.828357\pi$
$500$	−5.02698e6	+	3.42614e6i	−0.899254	+	0.612886i
$501$	−7.17002e6	+	2.31306e6i	−1.27622	+	0.411711i
$502$	315137.	+	29577.4i	0.0558137	+	0.00523842i
$503$			3.37792e6i			0.595291i	0.954677	+	0.297645i	$0.0962013\pi$
$503$			3.37792e6i			0.595291i	−0.954677	+	0.297645i	$0.903799\pi$
$504$	2.83707e6	+	1.34264e6i	0.497500	+	0.235442i
$505$		−	7.39334e6i		−	1.29007i
$506$	−101975.	+	1.08651e6i	−0.0177059	+	0.188651i
$507$	−3.93337e6	+	1.26891e6i	−0.679588	+	0.219236i
$508$	−4.66905e6	−	884220.i	−0.802729	−	0.152020i
$509$	266728.	+	266728.i	0.0456325	+	0.0456325i	0.729555	−	0.683922i	$-0.239727\pi$
$509$	266728.	+	266728.i	0.0456325	+	0.0456325i	−0.683922	+	0.729555i	$0.739727\pi$
$510$	−1.19995e6	−	5.40459e6i	−0.204285	−	0.920105i
$511$			4.43078e6i			0.750633i
$512$	−5.92206e6	−	336935.i	−0.998385	−	0.0568030i
$513$	972518.	+	6.40072e6i	0.163156	+	1.07383i
$514$	−1.14638e6	−	1.38385e6i	−0.191390	−	0.231037i
$515$	1.37179e6	−	1.37179e6i	0.227913	−	0.227913i
$516$	−7.07863e6	+	9.11131e6i	−1.17037	+	1.50646i
$517$	−1.75161e6	−	1.75161e6i	−0.288211	−	0.288211i
$518$	−1.94612e6	−	182654.i	−0.318674	−	0.0299093i
$519$	−1.95480e6	+	3.81669e6i	−0.318554	+	0.621969i
$520$	−2.31894e6	+	1.28090e6i	−0.376082	+	0.207733i
$521$	−3.10786e6			−0.501612			−0.250806	−	0.968037i	$-0.580696\pi$
$521$	−3.10786e6			−0.501612			−0.250806	+	0.968037i	$0.580696\pi$
$522$	−1.34327e6	+	788021.i	−0.215768	+	0.126579i
$523$	799621.	−	799621.i	0.127829	−	0.127829i	−0.640298	−	0.768127i	$-0.721189\pi$
$523$	799621.	−	799621.i	0.127829	−	0.127829i	0.768127	+	0.640298i	$0.221189\pi$
$524$	−720382.	−	1.05698e6i	−0.114613	−	0.168166i
$525$	1.17242e6	−	378224.i	0.185645	−	0.0598895i
$526$	4.15517e6	+	5.01592e6i	0.654823	+	0.790472i
$527$	1.39148e7			2.18248
$528$	−2.60763e6	+	2.30156e6i	−0.407062	+	0.359284i
$529$	5.65244e6			0.878207
$530$	3.44945e6	+	4.16402e6i	0.533409	+	0.643907i
$531$	−1.44262e6	−	234699.i	−0.222033	−	0.0361222i
$532$	3.22480e6	−	2.19786e6i	0.493996	−	0.336683i
$533$	−3.07227e6	+	3.07227e6i	−0.468426	+	0.468426i
$534$	−1.06187e7	−	6.76016e6i	−1.61145	−	1.02590i
$535$	7.14073e6			1.07859
$536$	69774.7	−	241971.i	0.0104903	−	0.0363790i
$537$	2.37000e6	+	1.21384e6i	0.354660	+	0.181647i
$538$	8.09171e6	+	759451.i	1.20527	+	0.113121i
$539$	1.80501e6	+	1.80501e6i	0.267613	+	0.267613i
$540$	198014.	−	5.44096e6i	0.0292221	−	0.802955i
$541$	2.20972e6	−	2.20972e6i	0.324597	−	0.324597i	−0.525931	−	0.850527i	$-0.676283\pi$
$541$	2.20972e6	−	2.20972e6i	0.324597	−	0.324597i	0.850527	+	0.525931i	$0.176283\pi$
$542$	−1.14376e6	−	1.38070e6i	−0.167239	−	0.201883i
$543$	−1.73220e6	+	3.38207e6i	−0.252115	+	0.492247i
$544$	−2.52765e6	−	7.69198e6i	−0.366201	−	1.11440i
$545$		−	336206.i		−	0.0484858i
$546$	2.00141e6	−	444361.i	0.287313	−	0.0637903i
$547$	4.18236e6	+	4.18236e6i	0.597658	+	0.597658i	0.939689	−	0.342031i	$-0.111115\pi$
$547$	4.18236e6	+	4.18236e6i	0.597658	+	0.597658i	−0.342031	+	0.939689i	$0.611115\pi$
$548$	230244.	−	1.21578e6i	0.0327520	−	0.172944i
$549$	−1.69437e6	+	1.04148e7i	−0.239926	+	1.47475i
$550$	−127561.	+	1.35913e6i	−0.0179809	+	0.191581i
$551$			1.93634e6i			0.271708i
$552$	−1.82107e6	−	1.71044e6i	−0.254378	−	0.238924i
$553$		−	2.37278e6i		−	0.329947i
$554$	−930225.	−	87306.7i	−0.128770	−	0.0120857i
$555$	1.04100e6	+	3.22690e6i	0.143456	+	0.444685i
$556$	4.10247e6	+	6.01933e6i	0.562806	+	0.825774i
$557$	−2.92739e6	−	2.92739e6i	−0.399800	−	0.399800i	0.478362	−	0.878163i	$-0.341231\pi$
$557$	−2.92739e6	−	2.92739e6i	−0.399800	−	0.399800i	−0.878163	+	0.478362i	$0.841231\pi$
$558$	1.32424e7	+	3.44995e6i	1.80046	+	0.469059i
$559$			7.53629e6i			1.02007i
$560$	−3.00850e6	+	1.31143e6i	−0.405397	+	0.176715i
$561$	−4.22554e6	−	2.16420e6i	−0.566859	−	0.290329i
$562$	5.33141e6	−	4.41651e6i	0.712035	−	0.589846i
$563$	8.56066e6	−	8.56066e6i	1.13825	−	1.13825i	0.149482	−	0.988764i	$-0.452239\pi$
$563$	8.56066e6	−	8.56066e6i	1.13825	−	1.13825i	0.988764	−	0.149482i	$-0.0477606\pi$
$564$	5.62697e6	−	706478.i	0.744864	−	0.0935192i
$565$	−167656.	−	167656.i	−0.0220952	−	0.0220952i
$566$	−382421.	+	4.07457e6i	−0.0501765	+	0.534614i
$567$	−1.33560e6	+	3.99614e6i	−0.174470	+	0.522015i
$568$	−1.23491e7	+	6.82118e6i	−1.60607	+	0.887132i
$569$	−844745.			−0.109382			−0.0546909	−	0.998503i	$-0.517417\pi$
$569$	−844745.			−0.109382			−0.0546909	+	0.998503i	$0.517417\pi$
$570$	−5.71049e6	−	3.63546e6i	−0.736184	−	0.468676i
$571$	−4.36625e6	+	4.36625e6i	−0.560426	+	0.560426i	−0.929428	−	0.369002i	$-0.879699\pi$
$571$	−4.36625e6	+	4.36625e6i	−0.560426	+	0.560426i	0.369002	+	0.929428i	$0.379699\pi$
$572$	−422716.	+	2.23212e6i	−0.0540205	+	0.285251i
$573$	3.64367e6	+	1.12946e7i	0.463610	+	1.43710i
$574$	−4.14504e6	+	3.43373e6i	−0.525108	+	0.434997i
$575$	−980586.			−0.123685
$576$	−498410.	−	7.94701e6i	−0.0625936	−	0.998039i
$577$	−4.11444e6			−0.514483			−0.257242	−	0.966347i	$-0.582814\pi$
$577$	−4.11444e6			−0.514483			−0.257242	+	0.966347i	$0.582814\pi$
$578$	2.32561e6	−	1.92652e6i	0.289545	−	0.239858i
$579$	1.16304e6	+	3.60520e6i	0.144178	+	0.446923i
$580$	302998.	−	1.59996e6i	0.0373999	−	0.197487i
$581$	1.87541e6	−	1.87541e6i	0.230492	−	0.230492i
$582$	−3.38853e6	−	2.15724e6i	−0.414672	−	0.263992i
$583$	4.63690e6			0.565010
$584$	9.83920e6	−	5.43479e6i	1.19379	−	0.659403i
$585$	−2.07823e6	−	2.88582e6i	−0.251075	−	0.348642i
$586$	−1.20878e6	+	1.28792e7i	−0.145414	+	1.54933i
$587$	−5.31943e6	−	5.31943e6i	−0.637191	−	0.637191i	0.312671	−	0.949862i	$-0.398776\pi$
$587$	−5.31943e6	−	5.31943e6i	−0.637191	−	0.637191i	−0.949862	+	0.312671i	$0.898776\pi$
$588$	−5.79853e6	+	728017.i	−0.691631	+	0.0868357i
$589$	1.20311e7	−	1.20311e7i	1.42895	−	1.42895i
$590$	1.17690e6	−	974936.i	0.139190	−	0.115304i
$591$	1.15733e7	+	5.92750e6i	1.36297	+	0.698076i
$592$	1.98150e6	+	4.54570e6i	0.232376	+	0.533085i
$593$		−	1.13011e6i		−	0.131972i	−0.997821	−	0.0659861i	$-0.978981\pi$
$593$		−	1.13011e6i		−	0.131972i	0.997821	−	0.0659861i	$-0.0210193\pi$
$594$	−3.48479e6	−	3.10729e6i	−0.405239	−	0.361339i
$595$	−3.16768e6	−	3.16768e6i	−0.366817	−	0.366817i
$596$	784111.	+	1.15048e6i	0.0904195	+	0.132668i
$597$	−3.77659e6	−	1.17067e7i	−0.433675	−	1.34430i
$598$	−1.62475e6	−	152491.i	−0.185794	−	0.0174378i
$599$			7.94636e6i			0.904901i	0.891790	+	0.452450i	$0.149450\pi$
$599$			7.94636e6i			0.904901i	−0.891790	+	0.452450i	$0.850550\pi$
$600$	−2.27799e6	−	2.13960e6i	−0.258329	−	0.242635i
$601$			8.06671e6i			0.910984i	0.890240	+	0.455492i	$0.150537\pi$
$601$			8.06671e6i			0.910984i	−0.890240	+	0.455492i	$0.849463\pi$
$602$	−872421.	+	9.29537e6i	−0.0981149	+	1.04538i
$603$	333669.	+	54284.2i	0.0373700	+	0.00607968i
$604$	1.11241e6	−	5.87397e6i	0.124071	−	0.655148i
$605$	3.60723e6	+	3.60723e6i	0.400669	+	0.400669i
$606$	1.41699e7	−	3.14605e6i	1.56742	−	0.348004i
$607$		−	6.79820e6i		−	0.748898i	−0.927248	−	0.374449i	$-0.877832\pi$
$607$		−	6.79820e6i		−	0.748898i	0.927248	−	0.374449i	$-0.122168\pi$
$608$	−8.83620e6	−	4.46524e6i	−0.969408	−	0.489876i
$609$	−574463.	+	1.12162e6i	−0.0627652	+	0.122547i
$610$	−7.03839e6	−	8.49641e6i	−0.765859	−	0.924509i
$611$	2.61931e6	−	2.61931e6i	0.283847	−	0.283847i
$612$	9.84770e6	−	4.59958e6i	1.06281	−	0.496409i
$613$	−1.30052e6	−	1.30052e6i	−0.139787	−	0.139787i	0.633750	−	0.773538i	$-0.281515\pi$
$613$	−1.30052e6	−	1.30052e6i	−0.139787	−	0.139787i	−0.773538	+	0.633750i	$0.781515\pi$
$614$	88562.4	+	8312.07i	0.00948044	+	0.000889791i
$615$	8.31022e6	+	4.25625e6i	0.885981	+	0.453774i
$616$	−779780.	+	2.70419e6i	−0.0827981	+	0.287135i
$617$	8.48143e6			0.896925			0.448462	−	0.893802i	$-0.351972\pi$
$617$	8.48143e6			0.896925			0.448462	+	0.893802i	$0.351972\pi$
$618$	3.21287e6	+	2.04541e6i	0.338393	+	0.215431i
$619$	−2.22240e6	+	2.22240e6i	−0.233129	+	0.233129i	−0.813997	−	0.580869i	$-0.802713\pi$
$619$	−2.22240e6	+	2.22240e6i	−0.233129	+	0.233129i	0.580869	+	0.813997i	$0.302713\pi$
$620$	−1.18237e7	+	8.05844e6i	−1.23531	+	0.841922i
$621$	1.98837e6	−	2.70084e6i	0.206903	−	0.281041i
$622$	−2.71533e6	−	3.27782e6i	−0.281414	−	0.339710i
$623$	−1.01859e7			−1.05143
$624$	−3.44170e6	−	3.89938e6i	−0.353844	−	0.400898i
$625$	5.07798e6			0.519985
$626$	−1.02043e7	−	1.23182e7i	−1.04076	−	1.25635i
$627$	−5.52477e6	+	1.78230e6i	−0.561236	+	0.181056i
$628$	1.02335e6	+	1.50151e6i	0.103545	+	0.151925i
$629$	−4.78621e6	+	4.78621e6i	−0.482353	+	0.482353i
$630$	−2.22925e6	−	3.80000e6i	−0.223773	−	0.381445i
$631$	−7.29091e6			−0.728968			−0.364484	−	0.931210i	$-0.618755\pi$
$631$	−7.29091e6			−0.728968			−0.364484	+	0.931210i	$0.618755\pi$
$632$	−5.26911e6	+	2.91045e6i	−0.524740	+	0.289846i
$633$	−3.72521e6	+	7.27338e6i	−0.369523	+	0.721484i
$634$	−2.83353e6	−	265942.i	−0.279966	−	0.0262763i
$635$	4.71649e6	+	4.71649e6i	0.464178	+	0.464178i
$636$	−6.51282e6	+	8.38303e6i	−0.638450	+	0.821785i
$637$	−2.69917e6	+	2.69917e6i	−0.263561	+	0.263561i
$638$	−890826.	−	1.07536e6i	−0.0866446	−	0.104593i
$639$	−1.10672e7	−	1.53679e7i	−1.07223	−	1.48889i
$640$	6.60245e6	+	5.07223e6i	0.637170	+	0.489495i
$641$		−	9.12358e6i		−	0.877041i	−0.898721	−	0.438521i	$-0.855503\pi$
$641$		−	9.12358e6i		−	0.877041i	0.898721	−	0.438521i	$-0.144497\pi$
$642$	3.03856e6	+	1.36857e7i	0.290958	+	1.31048i
$643$	−5.52179e6	−	5.52179e6i	−0.526687	−	0.526687i	0.392896	−	0.919583i	$-0.371473\pi$
$643$	−5.52179e6	−	5.52179e6i	−0.526687	−	0.526687i	−0.919583	+	0.392896i	$0.871473\pi$
$644$	−1.98633e6	−	376170.i	−0.188729	−	0.0357412i
$645$	1.54128e7	−	4.97220e6i	1.45875	−	0.470597i
$646$	1.26280e6	−	1.34548e7i	0.119057	−	1.26851i
$647$		−	1.14581e7i		−	1.07610i	−0.842914	−	0.538048i	$-0.819162\pi$
$647$		−	1.14581e7i		−	1.07610i	0.842914	−	0.538048i	$-0.180838\pi$
$648$	1.05123e7	−	1.93576e6i	0.983465	−	0.181098i
$649$		−	1.31055e6i		−	0.122135i
$650$	−2.03240e6	−	190752.i	−0.188680	−	0.0177087i
$651$	1.05384e7	−	3.39970e6i	0.974588	−	0.314404i
$652$	−7.67934e6	+	5.23385e6i	−0.707465	+	0.482173i
$653$	−2.22360e6	−	2.22360e6i	−0.204068	−	0.204068i	0.597673	−	0.801740i	$-0.296092\pi$
$653$	−2.22360e6	−	2.22360e6i	−0.204068	−	0.204068i	−0.801740	+	0.597673i	$0.796092\pi$
$654$	644364.	−	143064.i	0.0589097	−	0.0130794i
$655$			1.79542e6i			0.163517i
$656$	1.27094e7	+	4.99286e6i	1.15310	+	0.452991i
$657$	8.81785e6	+	1.22444e7i	0.796983	+	1.10669i
$658$	3.53391e6	−	2.92748e6i	0.318194	−	0.263590i
$659$	−1.27437e7	+	1.27437e7i	−1.14310	+	1.14310i	−0.155216	+	0.987880i	$0.549607\pi$
$659$	−1.27437e7	+	1.27437e7i	−1.14310	+	1.14310i	−0.987880	+	0.155216i	$0.950393\pi$
$660$	4.84389e6	−	608161.i	0.432847	−	0.0543449i
$661$	1.85177e6	+	1.85177e6i	0.164848	+	0.164848i	0.784710	−	0.619863i	$-0.212812\pi$
$661$	1.85177e6	+	1.85177e6i	0.164848	+	0.164848i	−0.619863	+	0.784710i	$0.712812\pi$
$662$	−1.15355e6	+	1.22907e7i	−0.102304	+	1.09002i
$663$	3.23629e6	−	6.31877e6i	0.285933	−	0.558276i
$664$	−6.46500e6	−	1.86425e6i	−0.569047	−	0.164090i
$665$	−5.47775e6			−0.480339
$666$	−5.74162e6	+	3.36829e6i	−0.501590	+	0.294255i
$667$	709287.	−	709287.i	0.0617315	−	0.0617315i
$668$	1.51955e7	+	2.87771e6i	1.31757	+	0.249520i
$669$	−1.47408e7	+	4.75542e6i	−1.27338	+	0.410794i
$670$	−272209.	+	225496.i	−0.0234269	+	0.0194067i
$671$	−9.46130e6			−0.811231
$672$	−3.79364e6	−	5.20797e6i	−0.324066	−	0.444883i
$673$	−1.38338e7			−1.17734			−0.588672	−	0.808372i	$-0.700349\pi$
$673$	−1.38338e7			−1.17734			−0.588672	+	0.808372i	$0.700349\pi$
$674$	3.32826e6	−	2.75711e6i	0.282207	−	0.233779i
$675$	2.48726e6	−	3.37849e6i	0.210117	−	0.285406i
$676$	8.33603e6	+	1.57867e6i	0.701605	+	0.132869i
$677$	1.15725e7	−	1.15725e7i	0.970414	−	0.970414i	−0.0291609	−	0.999575i	$-0.509284\pi$
$677$	1.15725e7	−	1.15725e7i	0.970414	−	0.970414i	0.999575	+	0.0291609i	$0.00928352\pi$
$678$	249983.	−	392667.i	0.0208851	−	0.0328058i
$679$	−3.25043e6			−0.270562
$680$	−3.14883e6	+	1.09198e7i	−0.261142	+	0.905611i
$681$	−9.42938e6	−	4.82946e6i	−0.779140	−	0.399053i
$682$	−1.14660e6	+	1.22166e7i	−0.0943951	+	1.00575i
$683$	−7.04621e6	−	7.04621e6i	−0.577968	−	0.577968i	0.356375	−	0.934343i	$-0.384013\pi$
$683$	−7.04621e6	−	7.04621e6i	−0.577968	−	0.577968i	−0.934343	+	0.356375i	$0.884013\pi$
$684$	4.53768e6	−	1.24916e7i	0.370846	−	1.02088i
$685$	−1.22814e6	+	1.22814e6i	−0.100005	+	0.100005i
$686$	−8.86596e6	+	7.34452e6i	−0.719309	+	0.595872i
$687$	6.66434e6	−	1.30119e7i	0.538723	−	1.05184i
$688$	2.17119e7	−	9.46436e6i	1.74874	−	0.762290i
$689$			6.93390e6i			0.556454i
$690$	760088.	+	3.42345e6i	0.0607772	+	0.273742i
$691$	−9.74829e6	−	9.74829e6i	−0.776664	−	0.776664i	0.202598	−	0.979262i	$-0.435062\pi$
$691$	−9.74829e6	−	9.74829e6i	−0.776664	−	0.776664i	−0.979262	+	0.202598i	$0.935062\pi$
$692$	7.27398e6	−	4.95758e6i	0.577440	−	0.393554i
$693$	−3.72899e6	−	606664.i	−0.294956	−	0.0479860i
$694$	1.02958e6	+	96631.3i	0.0811446	+	0.00761586i
$695$		−	1.02246e7i		−	0.802945i
$696$	3.19537e6	−	100103.i	0.250033	−	0.00783293i
$697$			1.86389e7i			1.45324i
$698$	996097.	−	1.06131e7i	0.0773862	−	0.824525i
$699$	−5.16549e6	−	1.60120e7i	−0.399870	−	1.23952i
$700$	−2.48471e6	−	470553.i	−0.191660	−	0.0362964i
$701$	4.07922e6	+	4.07922e6i	0.313532	+	0.313532i	0.846276	−	0.532744i	$-0.178839\pi$
$701$	4.07922e6	+	4.07922e6i	0.313532	+	0.313532i	−0.532744	+	0.846276i	$0.678839\pi$
$702$	4.64656e6	−	5.21107e6i	0.355868	−	0.399102i
$703$			8.27661e6i			0.631632i
$704$	6.96153e6	−	1.58534e6i	0.529387	−	0.120557i
$705$	−7.08500e6	−	3.62873e6i	−0.536867	−	0.274968i
$706$	−1.60755e7	−	1.94056e7i	−1.21381	−	1.46526i
$707$	8.30510e6	−	8.30510e6i	0.624880	−	0.624880i
$708$	2.36934e6	+	1.84075e6i	0.177641	+	0.138010i
$709$	1.29085e7	+	1.29085e7i	0.964408	+	0.964408i	0.999388	−	0.0349803i	$-0.0111369\pi$
$709$	1.29085e7	+	1.29085e7i	0.964408	+	0.964408i	−0.0349803	+	0.999388i	$0.511137\pi$
$710$	1.97155e7	+	1.85041e6i	1.46778	+	0.137759i
$711$	−4.72215e6	−	6.55717e6i	−0.350321	−	0.486455i
$712$	1.24940e7	+	2.26193e7i	0.923638	+	1.67216i
$713$	−8.81408e6			−0.649312
$714$	4.72317e6	−	7.41903e6i	0.346727	−	0.544630i
$715$	2.25479e6	−	2.25479e6i	0.164946	−	0.164946i
$716$	−3.07844e6	−	4.51682e6i	−0.224413	−	0.329269i
$717$	−946110.	−	2.93275e6i	−0.0687296	−	0.213048i
$718$	−9.67361e6	−	1.16775e7i	−0.700289	−	0.845356i
$719$	−2.28789e7			−1.65049			−0.825244	−	0.564776i	$-0.808962\pi$
$719$	−2.28789e7			−1.65049			−0.825244	+	0.564776i	$0.808962\pi$
$720$	−5.70407e6	+	9.61146e6i	−0.410066	+	0.690968i
$721$	3.08192e6			0.220792
$722$	−1.60600e6	−	1.93868e6i	−0.114657	−	0.138409i
$723$	4.28039e6	+	1.32683e7i	0.304535	+	0.943997i
$724$	6.44567e6	−	4.39304e6i	0.457006	−	0.311472i
$725$	887250.	−	887250.i	0.0626904	−	0.0626904i
$726$	−5.37856e6	+	8.44849e6i	−0.378725	+	0.594892i
$727$	−1.68671e7			−1.18360			−0.591798	−	0.806086i	$-0.701582\pi$
$727$	−1.68671e7			−1.18360			−0.591798	+	0.806086i	$0.701582\pi$
$728$	−4.04378e6	−	1.16606e6i	−0.282787	−	0.0815444i
$729$	4.26192e6	+	1.37014e7i	0.297021	+	0.954871i
$730$	−1.57084e7	−	1.47432e6i	−1.09100	−	0.102396i
$731$	2.28606e7	+	2.28606e7i	1.58232	+	1.58232i
$732$	1.32890e7	−	1.71050e7i	0.916673	−	1.17990i
$733$	−1.23293e7	+	1.23293e7i	−0.847573	+	0.847573i	−0.989830	−	0.142257i	$-0.954564\pi$
$733$	−1.23293e7	+	1.23293e7i	−0.847573	+	0.847573i	0.142257	+	0.989830i	$0.454564\pi$
$734$	5.74424e6	+	6.93418e6i	0.393543	+	0.475067i
$735$	7.30101e6	+	3.73937e6i	0.498499	+	0.255317i
$736$	1.60110e6	+	4.87236e6i	0.108949	+	0.331547i
$737$			303122.i			0.0205565i
$738$	−4.62122e6	+	1.77383e7i	−0.312331	+	1.19887i
$739$	1.50087e7	+	1.50087e7i	1.01095	+	1.01095i	0.999939	+	0.0110154i	$0.00350638\pi$
$739$	1.50087e7	+	1.50087e7i	1.01095	+	1.01095i	0.0110154	+	0.999939i	$0.496494\pi$
$740$	1.29512e6	−	6.83879e6i	0.0869425	−	0.459092i
$741$	−2.66521e6	−	8.26160e6i	−0.178314	−	0.552737i
$742$	−802688.	+	8.55238e6i	−0.0535226	+	0.570266i
$743$		−	1.76030e7i		−	1.16981i	−0.811103	−	0.584903i	$-0.801132\pi$
$743$		−	1.76030e7i		−	1.16981i	0.811103	−	0.584903i	$-0.198868\pi$
$744$	−2.04759e7	−	1.92319e7i	−1.35616	−	1.27377i
$745$		−	1.95425e6i		−	0.129000i
$746$	1.98291e7	+	1.86107e6i	1.30454	+	0.122438i
$747$	1.45037e6	−	8.91501e6i	0.0950993	−	0.584548i
$748$	5.48865e6	+	8.05319e6i	0.358683	+	0.526276i
$749$	8.02134e6	+	8.02134e6i	0.522447	+	0.522447i
$750$	3.63356e6	+	1.63656e7i	0.235874	+	1.06238i
$751$			6.41305e6i			0.414920i	0.978243	+	0.207460i	$0.0665197\pi$
$751$			6.41305e6i			0.414920i	−0.978243	+	0.207460i	$0.933480\pi$
$752$	−1.08356e7	−	4.25674e6i	−0.698728	−	0.274494i
$753$	397615.	−	776333.i	0.0255550	−	0.0498954i
$754$	1.60807e6	−	1.33212e6i	0.103009	−	0.0853325i
$755$	−5.93365e6	+	5.93365e6i	−0.378839	+	0.378839i
$756$	6.33439e6	−	5.88952e6i	0.403088	−	0.374779i
$757$	−1.73899e7	−	1.73899e7i	−1.10295	−	1.10295i	−0.994052	−	0.108902i	$-0.965266\pi$
$757$	−1.73899e7	−	1.73899e7i	−1.10295	−	1.10295i	−0.108902	−	0.994052i	$-0.534734\pi$
$758$	−1.08647e6	+	1.15760e7i	−0.0686825	+	0.731790i
$759$	2.67660e6	+	1.37088e6i	0.168647	+	0.0863762i
$760$	6.71901e6	+	1.21642e7i	0.421960	+	0.763920i
$761$	1.19968e7			0.750935			0.375468	−	0.926835i	$-0.377482\pi$
$761$	1.19968e7			0.750935			0.375468	+	0.926835i	$0.377482\pi$
$762$	−7.03251e6	+	1.10465e7i	−0.438756	+	0.689186i
$763$	377668.	−	377668.i	0.0234854	−	0.0234854i
$764$	4.53313e6	−	2.39368e7i	0.280973	−	1.48366i
$765$	−1.50580e7	−	2.44977e6i	−0.930280	−	0.151346i
$766$	−1.59941e7	+	1.32494e7i	−0.984890	+	0.815878i
$767$	1.95976e6			0.120286
$768$	−6.91179e6	+	1.48124e7i	−0.422851	+	0.906199i
$769$	1.91939e7			1.17043			0.585217	−	0.810877i	$-0.301010\pi$
$769$	1.91939e7			1.17043			0.585217	+	0.810877i	$0.301010\pi$
$770$	3.04212e6	−	2.52008e6i	0.184905	−	0.153175i
$771$	−4.71280e6	+	1.52036e6i	−0.285524	+	0.0921105i
$772$	1.44696e6	−	7.64053e6i	0.0873800	−	0.461403i
$773$	788060.	−	788060.i	0.0474363	−	0.0474363i	−0.682991	−	0.730427i	$-0.739321\pi$
$773$	788060.	−	788060.i	0.0474363	−	0.0474363i	0.730427	+	0.682991i	$0.239321\pi$
$774$	1.60881e7	+	2.74240e7i	0.965279	+	1.64543i
$775$	−1.10256e7			−0.659397
$776$	3.98698e6	+	7.21806e6i	0.237678	+	0.430295i
$777$	−2.45546e6	+	4.79423e6i	−0.145909	+	0.284883i
$778$	802226.	−	8.54747e6i	0.0475169	−	0.506277i
$779$	1.61158e7	+	1.61158e7i	0.951496	+	0.951496i
$780$	909429.	+	7.24344e6i	0.0535220	+	0.426293i
$781$	1.20075e7	−	1.20075e7i	0.704409	−	0.704409i
$782$	−5.39109e6	+	4.46595e6i	−0.315253	+	0.261154i
$783$	644656.	+	4.24287e6i	0.0375771	+	0.247318i
$784$	1.11660e7	+	4.38652e6i	0.648792	+	0.254876i
$785$		−	2.55052e6i		−	0.147725i
$786$	−3.44105e6	+	763995.i	−0.198671	+	0.0441097i
$787$	6.26901e6	+	6.26901e6i	0.360796	+	0.360796i	0.864106	−	0.503310i	$-0.167885\pi$
$787$	6.26901e6	+	6.26901e6i	0.360796	+	0.360796i	−0.503310	+	0.864106i	$0.667885\pi$
$788$	−1.50328e7	−	2.20568e7i	−0.862430	−	1.26540i
$789$	1.70820e7	−	5.51070e6i	0.976894	−	0.315148i
$790$	8.41218e6	+	789529.i	0.479558	+	0.0450091i
$791$		−	376663.i		−	0.0214049i
$792$	3.22679e6	+	9.02490e6i	0.182792	+	0.511245i
$793$		−	1.41482e7i		−	0.798946i
$794$	1.24604e6	−	1.32762e7i	0.0701425	−	0.747346i
$795$	1.41808e7	−	4.57476e6i	0.795763	−	0.256715i
$796$	−4.69850e6	+	2.48100e7i	−0.262831	+	1.38786i
$797$	2.03563e7	+	2.03563e7i	1.13515	+	1.13515i	0.989308	+	0.145844i	$0.0465897\pi$
$797$	2.03563e7	+	2.03563e7i	1.13515	+	1.13515i	0.145844	+	0.989308i	$0.453410\pi$
$798$	−2.33092e6	−	1.04985e7i	−0.129575	−	0.583607i
$799$		−	1.58909e7i		−	0.880604i
$800$	2.00282e6	+	6.09485e6i	0.110641	+	0.336696i
$801$	−2.81487e7	+	2.02713e7i	−1.55016	+	1.11635i
$802$	3.00250e6	+	3.62448e6i	0.164834	+	0.198980i
$803$	−9.56701e6	+	9.56701e6i	−0.523585	+	0.523585i
$804$	−548012.	−	425754.i	−0.0298986	−	0.0232284i
$805$	2.00652e6	+	2.00652e6i	0.109132	+	0.109132i
$806$	−1.82684e7	−	1.71459e6i	−0.990520	−	0.0929657i
$807$	1.02095e7	−	1.99337e7i	0.551848	−	1.07747i
$808$	−2.86297e7	−	8.25567e6i	−1.54273	−	0.444861i
$809$	−2.55481e7			−1.37242			−0.686211	−	0.727403i	$-0.740727\pi$
$809$	−2.55481e7			−1.37242			−0.686211	+	0.727403i	$0.740727\pi$
$810$	−1.37230e7	−	6.06479e6i	−0.734916	−	0.324790i
$811$	1.57540e7	−	1.57540e7i	0.841083	−	0.841083i	−0.147917	−	0.989000i	$-0.547257\pi$
$811$	1.57540e7	−	1.57540e7i	0.841083	−	0.841083i	0.989000	+	0.147917i	$0.0472569\pi$
$812$	2.13763e6	−	1.45690e6i	0.113774	−	0.0775425i
$813$	−4.70205e6	+	1.51689e6i	−0.249495	+	0.0804874i
$814$	−3.80771e6	−	4.59649e6i	−0.201420	−	0.243145i
$815$	1.30444e7			0.687907
$816$	−2.22685e7	−	1.38832e6i	−1.17075	−	0.0729901i
$817$	3.95320e7			2.07202
$818$	−2.08992e7	−	2.52286e7i	−1.09206	−	1.31828i
$819$	907190.	−	5.57623e6i	0.0472594	−	0.290490i
$820$	−1.07943e7	−	1.58379e7i	−0.560609	−	0.822551i
$821$	−2.66221e7	+	2.66221e7i	−1.37843	+	1.37843i	−0.531147	+	0.847279i	$0.678239\pi$
$821$	−2.66221e7	+	2.66221e7i	−1.37843	+	1.37843i	−0.847279	+	0.531147i	$0.821761\pi$
$822$	−2.87642e6	−	1.83121e6i	−0.148482	−	0.0945278i
$823$	−2.94320e6			−0.151468			−0.0757338	−	0.997128i	$-0.524130\pi$
$823$	−2.94320e6			−0.151468			−0.0757338	+	0.997128i	$0.524130\pi$
$824$	−3.78029e6	−	6.84387e6i	−0.193958	−	0.351143i
$825$	3.34817e6	+	1.71484e6i	0.171267	+	0.0877178i
$826$	2.41720e6	+	226868.i	0.123272	+	0.0115697i
$827$	9.90611e6	+	9.90611e6i	0.503662	+	0.503662i	0.912574	−	0.408912i	$-0.134092\pi$
$827$	9.90611e6	+	9.90611e6i	0.503662	+	0.503662i	−0.408912	+	0.912574i	$0.634092\pi$
$828$	−6.23786e6	+	2.91353e6i	−0.316199	+	0.147687i
$829$	4.51290e6	−	4.51290e6i	0.228071	−	0.228071i	−0.583816	−	0.811886i	$-0.698441\pi$
$829$	4.51290e6	−	4.51290e6i	0.228071	−	0.228071i	0.811886	+	0.583816i	$0.198441\pi$
$830$	6.02483e6	+	7.27289e6i	0.303563	+	0.366448i
$831$	−1.17368e6	+	2.29158e6i	−0.0589588	+	0.115115i
$832$	2.37068e6	+	1.04101e7i	0.118731	+	0.521371i
$833$			1.63754e7i			0.817670i
$834$	1.95963e7	−	4.35084e6i	0.975570	−	0.216600i
$835$	−1.53499e7	−	1.53499e7i	−0.761884	−	0.761884i
$836$	1.17087e7	+	2.21738e6i	0.579419	+	0.109730i
$837$	2.23569e7	−	3.03679e7i	1.10306	−	1.49831i
$838$	2.76940e6	−	2.95071e7i	0.136231	−	1.45150i
$839$			9.43115e6i			0.462551i	0.972888	+	0.231275i	$0.0742899\pi$
$839$			9.43115e6i			0.462551i	−0.972888	+	0.231275i	$0.925710\pi$
$840$	283183.	+	9.03944e6i	0.0138474	+	0.442022i
$841$		−	1.92276e7i		−	0.937422i
$842$	−3.24252e7	−	3.04328e6i	−1.57617	−	0.147932i
$843$	−5.85730e6	−	1.81565e7i	−0.283876	−	0.879958i
$844$	1.38619e7	−	9.44754e6i	0.669831	−	0.456523i
$845$	−8.42073e6	−	8.42073e6i	−0.405703	−	0.405703i
$846$	3.93989e6	−	1.51230e7i	0.189260	−	0.726463i
$847$			8.10416e6i			0.388150i
$848$	1.99764e7	−	8.70786e6i	0.953954	−	0.415836i
$849$	1.00376e7	+	5.14097e6i	0.477926	+	0.244780i
$850$	−6.74373e6	+	5.58648e6i	−0.320150	+	0.265210i
$851$	3.03175e6	−	3.03175e6i	0.143506	−	0.143506i
$852$	4.84300e6	+	3.85736e7i	0.228568	+	1.82050i
$853$	−1.43763e7	−	1.43763e7i	−0.676512	−	0.676512i	0.282697	−	0.959209i	$-0.408771\pi$
$853$	−1.43763e7	−	1.43763e7i	−0.676512	−	0.676512i	−0.959209	+	0.282697i	$0.908771\pi$
$854$	1.63783e6	−	1.74506e7i	0.0768466	−	0.818776i
$855$	−1.51378e7	+	1.09015e7i	−0.708184	+	0.509999i
$856$	7.97359e6	−	2.76515e7i	0.371937	−	1.28984i
$857$	8.37430e6			0.389490			0.194745	−	0.980854i	$-0.437612\pi$
$857$	8.37430e6			0.389490			0.194745	+	0.980854i	$0.437612\pi$
$858$	5.28095e6	+	3.36201e6i	0.244903	+	0.155912i
$859$	−2.05279e7	+	2.05279e7i	−0.949206	+	0.949206i	−0.998771	−	0.0495645i	$-0.984217\pi$
$859$	−2.05279e7	+	2.05279e7i	−0.949206	+	0.949206i	0.0495645	+	0.998771i	$0.484217\pi$
$860$	−3.26645e7	−	6.18597e6i	−1.50602	−	0.285208i
$861$	4.55391e6	+	1.41162e7i	0.209352	+	0.648948i
$862$	1.48654e7	−	1.23144e7i	0.681411	−	0.564478i
$863$	−2.47102e7			−1.12940			−0.564701	−	0.825296i	$-0.691008\pi$
$863$	−2.47102e7			−1.12940			−0.564701	+	0.825296i	$0.691008\pi$
$864$	−2.08483e7	−	6.84236e6i	−0.950137	−	0.311832i
$865$	−1.23558e7			−0.561477
$866$	1.33487e7	−	1.10580e7i	0.604846	−	0.501052i
$867$	−2.55501e6	−	7.92000e6i	−0.115437	−	0.357831i
$868$	−2.23341e7	−	4.22960e6i	−1.00616	−	0.190546i
$869$	5.12334e6	−	5.12334e6i	0.230146	−	0.230146i
$870$	−3.78533e6	−	2.40985e6i	−0.169553	−	0.107942i
$871$	−453280.			−0.0202452
$872$	−1.30191e6	−	375420.i	−0.0579817	−	0.0167196i
$873$	−8.98255e6	+	6.46879e6i	−0.398900	+	0.287268i
$874$	−799901.	+	8.52270e6i	−0.0354208	+	0.377397i
$875$	9.59205e6	+	9.59205e6i	0.423537	+	0.423537i
$876$	−3.85867e6	−	3.07336e7i	−0.169894	−	1.35317i
$877$	1.73778e7	−	1.73778e7i	0.762950	−	0.762950i	−0.213905	−	0.976854i	$-0.568618\pi$
$877$	1.73778e7	−	1.73778e7i	0.762950	−	0.762950i	0.976854	+	0.213905i	$0.0686183\pi$
$878$	666028.	−	551734.i	0.0291579	−	0.0241543i
$879$	3.17276e7	+	1.62500e7i	1.38505	+	0.709382i
$880$	−9.32766e6	−	3.66435e6i	−0.406038	−	0.159511i
$881$		−	2.51288e7i		−	1.09077i	−0.838187	−	0.545383i	$-0.816384\pi$
$881$		−	2.51288e7i		−	1.09077i	0.838187	−	0.545383i	$-0.183616\pi$
$882$	−4.06001e6	+	1.55841e7i	−0.175734	+	0.674545i
$883$	1.39231e7	+	1.39231e7i	0.600942	+	0.600942i	0.940563	−	0.339620i	$-0.110299\pi$
$883$	1.39231e7	+	1.39231e7i	0.600942	+	0.600942i	−0.339620	+	0.940563i	$0.610299\pi$
$884$	−1.20425e7	+	8.20758e6i	−0.518307	+	0.353252i
$885$	−1.29299e6	−	4.00800e6i	−0.0554927	−	0.172016i
$886$	4.41529e7	+	4.14399e6i	1.88962	+	0.177351i
$887$			1.14986e7i			0.490722i	0.969432	+	0.245361i	$0.0789065\pi$
$887$			1.14986e7i			0.490722i	−0.969432	+	0.245361i	$0.921093\pi$
$888$	1.36582e7	−	427876.i	0.581246	−	0.0182090i
$889$			1.05963e7i			0.449675i
$890$	3.38930e6	−	3.61119e7i	0.143428	−	1.52818i
$891$	−1.15124e7	+	5.74467e6i	−0.485815	+	0.242421i
$892$	3.12404e7	+	5.91628e6i	1.31463	+	0.248964i
$893$	−1.37397e7	−	1.37397e7i	−0.576567	−	0.576567i
$894$	3.74547e6	−	831583.i	0.156734	−	0.0347986i
$895$			7.67243e6i			0.320166i
$896$	1.71893e6	+	1.31144e7i	0.0715301	+	0.545731i
$897$	−2.04997e6	+	4.00252e6i	−0.0850682	+	0.166093i
$898$	−1.07013e7	−	1.29181e7i	−0.442838	−	0.534573i
$899$	7.97512e6	−	7.97512e6i	0.329108	−	0.329108i
$900$	−7.80297e6	+	3.64455e6i	−0.321110	+	0.149981i
$901$	2.10334e7	+	2.10334e7i	0.863170	+	0.863170i
$902$	−1.63642e7	−	1.53587e6i	−0.669697	−	0.0628547i
$903$	2.28989e7	+	1.17282e7i	0.934535	+	0.478642i
$904$	−836437.	+	462015.i	−0.0340418	+	0.0188034i
$905$	−1.09488e7			−0.444372
$906$	−1.38972e7	−	8.84736e6i	−0.562479	−	0.358091i
$907$	−6.00973e6	+	6.00973e6i	−0.242570	+	0.242570i	−0.817913	−	0.575343i	$-0.804869\pi$
$907$	−6.00973e6	+	6.00973e6i	−0.242570	+	0.242570i	0.575343	+	0.817913i	$0.304869\pi$
$908$	1.22480e7	+	1.79708e7i	0.493005	+	0.723359i
$909$	6.42285e6	−	3.94794e7i	0.257821	−	1.58475i
$910$	3.76846e6	+	4.54911e6i	0.150855	+	0.182105i
$911$	−2.46546e7			−0.984241			−0.492120	−	0.870527i	$-0.663778\pi$
$911$	−2.46546e7			−0.984241			−0.492120	+	0.870527i	$0.663778\pi$
$912$	−2.04544e7	+	1.80536e7i	−0.814328	+	0.718749i
$913$	8.09883e6			0.321547
$914$	2.42743e7	+	2.93028e7i	0.961128	+	1.16023i
$915$	−2.89351e7	+	9.33451e6i	−1.14254	+	0.368586i
$916$	−2.47986e7	+	1.69015e7i	−0.976537	+	0.665558i
$917$	−2.01683e6	+	2.01683e6i	−0.0792038	+	0.0792038i
$918$	−1.71240e6	−	2.99022e7i	−0.0670654	−	1.17111i
$919$	1.08466e7			0.423648			0.211824	−	0.977308i	$-0.432060\pi$
$919$	1.08466e7			0.423648			0.211824	+	0.977308i	$0.432060\pi$
$920$	1.99457e6	−	6.91695e6i	0.0776927	−	0.269430i
$921$	111741.	−	218171.i	0.00434074	−	0.00847517i
$922$	4.44353e7	+	4.17049e6i	1.72147	+	0.161570i
$923$	1.79557e7	+	1.79557e7i	0.693743	+	0.693743i
$924$	6.12441e6	+	4.75809e6i	0.235985	+	0.183338i
$925$	3.79243e6	−	3.79243e6i	0.145735	−	0.145735i
$926$	2.31367e7	+	2.79296e7i	0.886696	+	1.07038i
$927$	8.51689e6	−	6.13345e6i	0.325523	−	0.234426i
$928$	−5.85728e6	−	2.95989e6i	−0.223268	−	0.112825i
$929$		−	6.54583e6i		−	0.248843i	−0.992229	−	0.124422i	$-0.960292\pi$
$929$		−	6.54583e6i		−	0.248843i	0.992229	−	0.124422i	$-0.0397075\pi$
$930$	8.54632e6	+	3.84928e7i	0.324020	+	1.45939i
$931$	1.41586e7	+	1.41586e7i	0.535361	+	0.535361i
$932$	−6.42645e6	+	3.39343e7i	−0.242344	+	1.27967i
$933$	−1.11628e7	+	3.60114e6i	−0.419826	+	0.135437i
$934$	76921.2	−	819571.i	0.00288522	−	0.0307411i
$935$		−	1.36794e7i		−	0.511727i
$936$	−1.34956e7	+	4.82525e6i	−0.503504	+	0.180024i
$937$		−	2.03173e7i		−	0.755990i	−0.925808	−	0.377995i	$-0.876614\pi$
$937$		−	2.03173e7i		−	0.755990i	0.925808	−	0.377995i	$-0.123386\pi$
$938$	−559083.	−	52473.0i	−0.0207477	−	0.00194728i
$939$	−4.19504e7	+	1.35333e7i	−1.55264	+	0.500886i
$940$	9.20286e6	+	1.35028e7i	0.339706	+	0.498432i
$941$	3.13525e7	+	3.13525e7i	1.15424	+	1.15424i	0.985693	+	0.168552i	$0.0539091\pi$
$941$	3.13525e7	+	3.13525e7i	1.15424	+	1.15424i	0.168552	+	0.985693i	$0.446091\pi$
$942$	4.88826e6	−	1.08531e6i	0.179485	−	0.0398498i
$943$		−	1.18065e7i		−	0.432356i
$944$	−2.46115e6	−	5.64603e6i	−0.0898892	−	0.206212i
$945$	−1.20027e7	+	1.82368e6i	−0.437221	+	0.0664307i
$946$	−2.19545e7	+	1.81870e7i	−0.797618	+	0.660743i
$947$	2.00411e7	−	2.00411e7i	0.726186	−	0.726186i	−0.243672	−	0.969858i	$-0.578352\pi$
$947$	2.00411e7	−	2.00411e7i	0.726186	−	0.726186i	0.969858	+	0.243672i	$0.0783521\pi$
$948$	2.06640e6	+	1.64585e7i	0.0746783	+	0.594799i
$949$	−1.43063e7	−	1.43063e7i	−0.515657	−	0.515657i
$950$	−1.00060e6	+	1.06611e7i	−0.0359709	+	0.383259i
$951$	−3.57512e6	+	6.98033e6i	−0.128186	+	0.250279i
$952$	−1.58036e7	+	8.72928e6i	−0.565149	+	0.312166i
$953$	1.61675e7			0.576646			0.288323	−	0.957533i	$-0.406902\pi$
$953$	1.61675e7			0.576646			0.288323	+	0.957533i	$0.406902\pi$
$954$	1.48022e7	+	2.52319e7i	0.526568	+	0.897594i
$955$	−2.41800e7	+	2.41800e7i	−0.857923	+	0.857923i
$956$	−1.17707e6	+	6.21540e6i	−0.0416540	+	0.219950i
$957$	−3.66222e6	+	1.18144e6i	−0.129260	+	0.0416995i
$958$	−1.88349e7	+	1.56028e7i	−0.663056	+	0.549272i
$959$	−2.75919e6			−0.0968801
$960$	1.97261e7	−	1.17166e7i	0.690816	−	0.410322i
$961$	−7.04751e7			−2.46166
$962$	6.87348e6	−	5.69396e6i	0.239463	−	0.198370i
$963$	3.81305e7	+	6.20340e6i	1.32497	+	0.215558i
$964$	5.32528e6	−	2.81197e7i	0.184565	−	0.974581i
$965$	−7.71816e6	+	7.71816e6i	−0.266806	+	0.266806i
$966$	−2.99181e6	+	4.69946e6i	−0.103155	+	0.162034i
$967$	1.11349e7			0.382930			0.191465	−	0.981499i	$-0.438676\pi$
$967$	1.11349e7			0.382930			0.191465	+	0.981499i	$0.438676\pi$
$968$	1.79965e7	−	9.94056e6i	0.617304	−	0.340975i
$969$	−3.31455e7	−	1.69761e7i	−1.13400	−	0.580804i
$970$	1.08156e6	−	1.15237e7i	0.0369081	−	0.393244i
$971$	−2.38041e7	−	2.38041e7i	−0.810220	−	0.810220i	0.174447	−	0.984667i	$-0.444186\pi$
$971$	−2.38041e7	−	2.38041e7i	−0.810220	−	0.810220i	−0.984667	+	0.174447i	$0.944186\pi$
$972$	5.78412e6	−	2.88820e7i	0.196368	−	0.980530i
$973$	1.14856e7	−	1.14856e7i	0.388929	−	0.388929i
$974$	2.70693e6	−	2.24241e6i	0.0914280	−	0.0757385i
$975$	−2.56432e6	+	5.00677e6i	−0.0863895	+	0.168673i
$976$	−4.07606e7	+	1.77678e7i	−1.36967	+	0.597049i
$977$		−	5.03489e7i		−	1.68754i	−0.536706	−	0.843769i	$-0.680332\pi$
$977$		−	5.03489e7i		−	1.68754i	0.536706	−	0.843769i	$-0.319668\pi$
$978$	5.55072e6	+	2.50006e7i	0.185568	+	0.835800i
$979$	−2.19935e7	−	2.19935e7i	−0.733396	−	0.733396i
$980$	−9.48344e6	−	1.39145e7i	−0.315428	−	0.462810i
$981$	292074.	−	1.79529e6i	0.00968992	−	0.0595611i
$982$	1.21950e7	+	1.14457e6i	0.403556	+	0.0378759i
$983$			7.69440e6i			0.253975i	0.991904	+	0.126988i	$0.0405308\pi$
$983$			7.69440e6i			0.253975i	−0.991904	+	0.126988i	$0.959469\pi$
$984$	2.57613e7	−	2.74275e7i	0.848163	−	0.903023i
$985$			3.74664e7i			1.23041i
$986$	837078.	−	8.91880e6i	0.0274204	−	0.292155i
$987$	−3.88250e6	−	1.20350e7i	−0.126858	−	0.393235i
$988$	−3.31581e6	+	1.75089e7i	−0.108068	+	0.570645i
$989$	−1.44807e7	−	1.44807e7i	−0.470759	−	0.470759i
$990$	3.39160e6	−	1.30185e7i	0.109981	−	0.422155i
$991$			4.18208e7i			1.35272i	0.736570	+	0.676361i	$0.236444\pi$
$991$			4.18208e7i			1.35272i	−0.736570	+	0.676361i	$0.763556\pi$
$992$	1.80025e7	+	5.47841e7i	0.580836	+	1.76757i
$993$	3.02779e7	+	1.55075e7i	0.974435	+	0.499077i
$994$	2.00682e7	+	2.42255e7i	0.644234	+	0.777689i
$995$	2.50621e7	−	2.50621e7i	0.802528	−	0.802528i
$996$	−1.13753e7	+	1.46418e7i	−0.363342	+	0.467678i
$997$	2.67373e6	+	2.67373e6i	0.0851882	+	0.0851882i	0.748417	−	0.663229i	$-0.230814\pi$
$997$	2.67373e6	+	2.67373e6i	0.0851882	+	0.0851882i	−0.663229	+	0.748417i	$0.730814\pi$
$998$	1.52681e7	+	1.43300e6i	0.485243	+	0.0455427i
$999$	2.75549e6	+	1.81355e7i	0.0873545	+	0.574932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.k.a.11.9	✓	76
3.2	odd	2	inner	48.6.k.a.11.30	yes	76
4.3	odd	2		192.6.k.a.143.15		76
12.11	even	2		192.6.k.a.143.3		76
16.3	odd	4	inner	48.6.k.a.35.30	yes	76
16.13	even	4		192.6.k.a.47.3		76
48.29	odd	4		192.6.k.a.47.15		76
48.35	even	4	inner	48.6.k.a.35.9	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.k.a.11.9	✓	76	1.1	even	1	trivial
48.6.k.a.11.30	yes	76	3.2	odd	2	inner
48.6.k.a.35.9	yes	76	48.35	even	4	inner
48.6.k.a.35.30	yes	76	16.3	odd	4	inner
192.6.k.a.47.3		76	16.13	even	4
192.6.k.a.47.15		76	48.29	odd	4
192.6.k.a.143.3		76	12.11	even	2
192.6.k.a.143.15		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)

\(f(q)\)	\(=\)	\(q+(-4.35628 + 3.60872i) q^{2} +(4.78598 + 14.8356i) q^{3} +(5.95430 - 31.4412i) q^{4} +(-31.7606 + 31.7606i) q^{5} +(-74.3865 - 47.3566i) q^{6} -71.3548 q^{7} +(87.5237 + 158.454i) q^{8} +(-197.189 + 142.006i) q^{9} +O(q^{10})\)	\(q+(-4.35628 + 3.60872i) q^{2} +(4.78598 + 14.8356i) q^{3} +(5.95430 - 31.4412i) q^{4} +(-31.7606 + 31.7606i) q^{5} +(-74.3865 - 47.3566i) q^{6} -71.3548 q^{7} +(87.5237 + 158.454i) q^{8} +(-197.189 + 142.006i) q^{9} +(23.7429 - 252.973i) q^{10} +(-154.070 - 154.070i) q^{11} +(494.945 - 62.1414i) q^{12} +(230.393 - 230.393i) q^{13} +(310.841 - 257.499i) q^{14} +(-623.193 - 319.181i) q^{15} +(-953.093 - 374.420i) q^{16} -1397.75i q^{17} +(346.550 - 1330.21i) q^{18} +(-1208.54 - 1208.54i) q^{19} +(809.478 + 1187.70i) q^{20} +(-341.503 - 1058.59i) q^{21} +(1227.17 + 115.177i) q^{22} +885.382i q^{23} +(-1931.87 + 2056.82i) q^{24} +1107.53i q^{25} +(-172.232 + 1835.08i) q^{26} +(-3050.48 - 2245.77i) q^{27} +(-424.868 + 2243.48i) q^{28} +(-801.108 - 801.108i) q^{29} +(3866.63 - 858.485i) q^{30} +9955.11i q^{31} +(5503.11 - 1808.37i) q^{32} +(1548.34 - 3023.10i) q^{33} +(5044.09 + 6088.99i) q^{34} +(2266.27 - 2266.27i) q^{35} +(3290.70 + 7045.39i) q^{36} +(-3424.22 - 3424.22i) q^{37} +(9626.01 + 903.453i) q^{38} +(4520.67 + 2315.36i) q^{39} +(-7812.39 - 2252.78i) q^{40} -13334.9 q^{41} +(5307.83 + 3379.12i) q^{42} +(-16355.3 + 16355.3i) q^{43} +(-5761.53 + 3926.77i) q^{44} +(1752.65 - 10773.0i) q^{45} +(-3195.10 - 3856.97i) q^{46} +11368.9 q^{47} +(993.252 - 15931.6i) q^{48} -11715.5 q^{49} +(-3996.76 - 4824.70i) q^{50} +(20736.5 - 6689.61i) q^{51} +(-5871.99 - 8615.65i) q^{52} +(-15048.0 + 15048.0i) q^{53} +(21393.1 - 1225.11i) q^{54} +9786.73 q^{55} +(-6245.23 - 11306.4i) q^{56} +(12145.3 - 23713.4i) q^{57} +(6380.82 + 598.875i) q^{58} +(4253.09 + 4253.09i) q^{59} +(-13746.1 + 17693.4i) q^{60} +(30704.5 - 30704.5i) q^{61} +(-35925.2 - 43367.2i) q^{62} +(14070.4 - 10132.8i) q^{63} +(-17447.2 + 27736.9i) q^{64} +14634.8i q^{65} +(4164.50 + 18757.0i) q^{66} +(-983.712 - 983.712i) q^{67} +(-43946.9 - 8322.63i) q^{68} +(-13135.2 + 4237.42i) q^{69} +(-1694.17 + 18050.8i) q^{70} +77935.2i q^{71} +(-39760.0 - 18816.4i) q^{72} -62095.1i q^{73} +(27273.9 + 2559.81i) q^{74} +(-16430.8 + 5300.61i) q^{75} +(-45193.9 + 30801.9i) q^{76} +(10993.7 + 10993.7i) q^{77} +(-28048.7 + 6227.49i) q^{78} +33253.3i q^{79} +(42162.6 - 18379.0i) q^{80} +(18717.8 - 56003.8i) q^{81} +(58090.6 - 48121.9i) q^{82} +(-26282.9 + 26282.9i) q^{83} +(-35316.7 + 4434.08i) q^{84} +(44393.4 + 44393.4i) q^{85} +(12226.5 - 130270. i) q^{86} +(8050.81 - 15719.0i) q^{87} +(10928.2 - 37897.8i) q^{88} +142750. q^{89} +(31241.8 + 53255.1i) q^{90} +(-16439.6 + 16439.6i) q^{91} +(27837.4 + 5271.83i) q^{92} +(-147690. + 47645.0i) q^{93} +(-49526.0 + 41027.1i) q^{94} +76767.8 q^{95} +(53166.0 + 72987.0i) q^{96} +45553.1 q^{97} +(51036.0 - 42277.9i) q^{98} +(52259.8 + 8502.08i) 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

Modular forms

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