LMFDB - Embedded newform 69.7.h.a.2.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(2,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 2]))

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

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

chi := DirichletCharacter("69.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.h (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			2.16
Character	$\chi$	$=$	69.2
Dual form			69.7.h.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)

$f(q)$	$=$	$q+(-3.34719 + 5.20832i) q^{2} +(26.9538 - 1.57802i) q^{3} +(10.6636 + 23.3500i) q^{4} +(-60.8684 + 207.299i) q^{5} +(-82.0007 + 145.666i) q^{6} +(-164.718 + 190.095i) q^{7} +(-549.508 - 79.0073i) q^{8} +(724.020 - 85.0674i) q^{9} +O(q^{10})$	\(q+(-3.34719 + 5.20832i) q^{2} +(26.9538 - 1.57802i) q^{3} +(10.6636 + 23.3500i) q^{4} +(-60.8684 + 207.299i) q^{5} +(-82.0007 + 145.666i) q^{6} +(-164.718 + 190.095i) q^{7} +(-549.508 - 79.0073i) q^{8} +(724.020 - 85.0674i) q^{9} +(-875.940 - 1010.89i) q^{10} +(-283.610 - 441.306i) q^{11} +(324.272 + 612.545i) q^{12} +(-1381.32 - 1594.13i) q^{13} +(-438.733 - 1494.19i) q^{14} +(-1313.52 + 5683.55i) q^{15} +(1174.95 - 1355.97i) q^{16} +(8161.28 + 3727.13i) q^{17} +(-1980.37 + 4055.66i) q^{18} +(-3096.85 - 6781.15i) q^{19} +(-5489.50 + 789.271i) q^{20} +(-4139.81 + 5383.71i) q^{21} +3247.76 q^{22} +(6779.47 + 10103.2i) q^{23} +(-14936.0 - 1262.42i) q^{24} +(-26123.2 - 16788.4i) q^{25} +(12926.3 - 1858.52i) q^{26} +(19380.9 - 3435.41i) q^{27} +(-6195.20 - 1819.07i) q^{28} +(-17454.4 - 7971.14i) q^{29} +(-25205.2 - 25865.1i) q^{30} +(-522.312 + 3632.76i) q^{31} +(-6880.46 - 23432.7i) q^{32} +(-8340.78 - 11447.4i) q^{33} +(-46729.4 + 30031.2i) q^{34} +(-29380.3 - 45716.6i) q^{35} +(9706.98 + 15998.7i) q^{36} +(-28459.3 + 8356.39i) q^{37} +(45684.1 + 6568.39i) q^{38} +(-39747.5 - 40788.2i) q^{39} +(49825.7 - 109103. i) q^{40} +(-28238.1 + 96170.0i) q^{41} +(-14183.4 - 39581.7i) q^{42} +(6892.41 + 47937.8i) q^{43} +(7280.20 - 11328.2i) q^{44} +(-26435.5 + 155266. i) q^{45} +(-75312.9 + 1492.35i) q^{46} +67505.3i q^{47} +(29529.7 - 38402.6i) q^{48} +(7739.22 + 53827.5i) q^{49} +(174878. - 79864.3i) q^{50} +(225859. + 87581.9i) q^{51} +(22493.1 - 49253.1i) q^{52} +(98130.9 + 85030.9i) q^{53} +(-46978.7 + 112441. i) q^{54} +(108745. - 31930.4i) q^{55} +(105533. - 91444.6i) q^{56} +(-94172.7 - 177891. i) q^{57} +(99939.2 - 64227.1i) q^{58} +(-272678. + 236277. i) q^{59} +(-146718. + 29936.4i) q^{60} +(9707.52 - 67517.3i) q^{61} +(-17172.3 - 14879.9i) q^{62} +(-103088. + 151644. i) q^{63} +(255253. + 74949.0i) q^{64} +(414540. - 189314. i) q^{65} +(87539.6 - 5125.03i) q^{66} +(-78480.4 - 50436.3i) q^{67} +230311. i q^{68} +(198676. + 261622. i) q^{69} +336448. q^{70} +(-5249.31 + 8168.08i) q^{71} +(-404575. - 10457.6i) q^{72} +(-30700.2 - 67224.0i) q^{73} +(51735.6 - 176195. i) q^{74} +(-730613. - 411288. i) q^{75} +(125316. - 144623. i) q^{76} +(130606. + 18778.3i) q^{77} +(345481. - 70492.2i) q^{78} +(234893. + 271081. i) q^{79} +(209573. + 326102. i) q^{80} +(516968. - 123181. i) q^{81} +(-406366. - 468972. i) q^{82} +(-285817. - 973405. i) q^{83} +(-169855. - 39254.9i) q^{84} +(-1.26939e6 + 1.46496e6i) q^{85} +(-272745. - 124559. i) q^{86} +(-483041. - 187310. i) q^{87} +(120980. + 264908. i) q^{88} +(1.10356e6 - 158668. i) q^{89} +(-720192. - 657390. i) q^{90} +530565. q^{91} +(-163616. + 266037. i) q^{92} +(-8345.75 + 98741.1i) q^{93} +(-351589. - 225953. i) q^{94} +(1.59422e6 - 229215. i) q^{95} +(-222432. - 620744. i) q^{96} +(1.24172e6 + 364601. i) q^{97} +(-306255. - 139862. i) q^{98} +(-242880. - 295388. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) $ 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$

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 $

$2$	−3.34719	+	5.20832i	−0.418398	+	0.651040i	−0.984921	−	0.173006i	$-0.944652\pi$
$2$	−3.34719	+	5.20832i	−0.418398	+	0.651040i	0.566523	+	0.824046i	$0.308288\pi$
$3$	26.9538	−	1.57802i	0.998291	−	0.0584452i
$3$	26.9538	−	1.57802i	0.998291	−	0.0584452i
$4$	10.6636	+	23.3500i	0.166619	+	0.364844i
$5$	−60.8684	+	207.299i	−0.486947	+	1.65839i	0.239292	+	0.970948i	$0.423085\pi$
$5$	−60.8684	+	207.299i	−0.486947	+	1.65839i	−0.726239	+	0.687442i	$0.758734\pi$
$6$	−82.0007	+	145.666i	−0.379633	+	0.674381i
$7$	−164.718	+	190.095i	−0.480227	+	0.554212i	−0.943228	−	0.332146i	$-0.892227\pi$
$7$	−164.718	+	190.095i	−0.480227	+	0.554212i	0.463001	+	0.886358i	$0.346773\pi$
$8$	−549.508	−	79.0073i	−1.07326	−	0.154311i
$9$	724.020	−	85.0674i	0.993168	−	0.116691i
$10$	−875.940	−	1010.89i	−0.875940	−	1.01089i
$11$	−283.610	−	441.306i	−0.213081	−	0.331560i	0.718217	−	0.695819i	$-0.244959\pi$
$11$	−283.610	−	441.306i	−0.213081	−	0.331560i	−0.931298	+	0.364259i	$0.881322\pi$
$12$	324.272	+	612.545i	0.187657	+	0.354482i
$13$	−1381.32	−	1594.13i	−0.628731	−	0.725595i	0.348609	−	0.937268i	$-0.386654\pi$
$13$	−1381.32	−	1594.13i	−0.628731	−	0.725595i	−0.977340	+	0.211673i	$0.932109\pi$
$14$	−438.733	−	1494.19i	−0.159888	−	0.544529i
$15$	−1313.52	+	5683.55i	−0.389190	+	1.68401i
$16$	1174.95	−	1355.97i	0.286854	−	0.331047i
$17$	8161.28	+	3727.13i	1.66116	+	0.758627i	0.999965	+	0.00841318i	$0.00267803\pi$
$17$	8161.28	+	3727.13i	1.66116	+	0.758627i	0.661196	+	0.750213i	$0.270049\pi$
$18$	−1980.37	+	4055.66i	−0.339570	+	0.695416i
$19$	−3096.85	−	6781.15i	−0.451501	−	0.988650i	−0.989343	−	0.145604i	$-0.953487\pi$
$19$	−3096.85	−	6781.15i	−0.451501	−	0.988650i	0.537842	−	0.843046i	$-0.319240\pi$
$20$	−5489.50	+	789.271i	−0.686188	+	0.0986589i
$21$	−4139.81	+	5383.71i	−0.447015	+	0.581332i
$22$	3247.76			0.305011
$23$	6779.47	+	10103.2i	0.557201	+	0.830378i
$23$	6779.47	+	10103.2i	0.557201	+	0.830378i
$24$	−14936.0	−	1262.42i	−1.08044	−	0.0913206i
$25$	−26123.2	−	16788.4i	−1.67188	−	1.07446i
$26$	12926.3	−	1858.52i	0.735451	−	0.105742i
$27$	19380.9	−	3435.41i	0.984651	−	0.174537i
$28$	−6195.20	−	1819.07i	−0.282216	−	0.0828660i
$29$	−17454.4	−	7971.14i	−0.715665	−	0.326833i	0.0240896	−	0.999710i	$-0.492331\pi$
$29$	−17454.4	−	7971.14i	−0.715665	−	0.326833i	−0.739755	+	0.672876i	$0.765059\pi$
$30$	−25205.2	−	25865.1i	−0.933525	−	0.957967i
$31$	−522.312	+	3632.76i	−0.0175325	+	0.121942i	−0.996708	−	0.0810738i	$-0.974165\pi$
$31$	−522.312	+	3632.76i	−0.0175325	+	0.121942i	0.979176	+	0.203015i	$0.0650741\pi$
$32$	−6880.46	−	23432.7i	−0.209975	−	0.715109i
$33$	−8340.78	−	11447.4i	−0.232094	−	0.318540i
$34$	−46729.4	+	30031.2i	−1.18892	+	0.764074i
$35$	−29380.3	−	45716.6i	−0.685254	−	1.06628i
$36$	9706.98	+	15998.7i	0.208054	+	0.342909i
$37$	−28459.3	+	8356.39i	−0.561847	+	0.164973i	−0.550310	−	0.834960i	$-0.685491\pi$
$37$	−28459.3	+	8356.39i	−0.561847	+	0.164973i	−0.0115370	+	0.999933i	$0.503672\pi$
$38$	45684.1	+	6568.39i	0.832558	+	0.119704i
$39$	−39747.5	−	40788.2i	−0.670064	−	0.687608i
$40$	49825.7	−	109103.i	0.778527	−	1.70474i
$41$	−28238.1	+	96170.0i	−0.409716	+	1.39537i	0.453827	+	0.891090i	$0.350059\pi$
$41$	−28238.1	+	96170.0i	−0.409716	+	1.39537i	−0.863543	+	0.504275i	$0.831760\pi$
$42$	−14183.4	−	39581.7i	−0.191440	−	0.534253i
$43$	6892.41	+	47937.8i	0.0866893	+	0.602938i	0.986140	+	0.165915i	$0.0530578\pi$
$43$	6892.41	+	47937.8i	0.0866893	+	0.602938i	−0.899451	+	0.437022i	$0.856033\pi$
$44$	7280.20	−	11328.2i	0.0854644	−	0.132985i
$45$	−26435.5	+	155266.i	−0.290102	+	1.70388i
$46$	−75312.9	+	1492.35i	−0.773741	+	0.0153320i
$47$			67505.3i			0.650196i	0.945680	+	0.325098i	$0.105397\pi$
$47$			67505.3i			0.650196i	−0.945680	+	0.325098i	$0.894603\pi$
$48$	29529.7	−	38402.6i	0.267015	−	0.347246i
$49$	7739.22	+	53827.5i	0.0657823	+	0.457526i
$50$	174878.	−	79864.3i	1.39903	−	0.638914i
$51$	225859.	+	87581.9i	1.70266	+	0.660243i
$52$	22493.1	−	49253.1i	0.159970	−	0.350287i
$53$	98130.9	+	85030.9i	0.659141	+	0.571149i	0.918884	−	0.394529i	$-0.129092\pi$
$53$	98130.9	+	85030.9i	0.659141	+	0.571149i	−0.259742	+	0.965678i	$0.583638\pi$
$54$	−46978.7	+	112441.i	−0.298345	+	0.714073i
$55$	108745.	−	31930.4i	0.653614	−	0.191918i
$56$	105533.	−	91444.6i	0.600928	−	0.520707i
$57$	−94172.7	−	177891.i	−0.508511	−	0.960572i
$58$	99939.2	−	64227.1i	0.512215	−	0.329180i
$59$	−272678.	+	236277.i	−1.32768	+	1.15044i	−0.350851	+	0.936431i	$0.614108\pi$
$59$	−272678.	+	236277.i	−1.32768	+	1.15044i	−0.976831	+	0.214011i	$0.931347\pi$
$60$	−146718.	+	29936.4i	−0.679249	+	0.138595i
$61$	9707.52	−	67517.3i	0.0427680	−	0.297458i	−0.957200	−	0.289428i	$-0.906535\pi$
$61$	9707.52	−	67517.3i	0.0427680	−	0.297458i	0.999968	−	0.00802980i	$-0.00255599\pi$
$62$	−17172.3	−	14879.9i	−0.0720532	−	0.0624345i
$63$	−103088.	+	151644.i	−0.412275	+	0.606464i
$64$	255253.	+	74949.0i	0.973712	+	0.285908i
$65$	414540.	−	189314.i	1.50948	−	0.689355i
$66$	87539.6	−	5125.03i	0.304490	−	0.0178264i
$67$	−78480.4	−	50436.3i	−0.260938	−	0.167694i	0.403631	−	0.914922i	$-0.367748\pi$
$67$	−78480.4	−	50436.3i	−0.260938	−	0.167694i	−0.664568	+	0.747228i	$0.731384\pi$
$68$			230311.i			0.732466i
$69$	198676.	+	261622.i	0.604780	+	0.796392i
$70$	336448.			0.980898
$71$	−5249.31	+	8168.08i	−0.0146665	+	0.0228215i	−0.848509	−	0.529180i	$-0.822500\pi$
$71$	−5249.31	+	8168.08i	−0.0146665	+	0.0228215i	0.833843	+	0.552002i	$0.186136\pi$
$72$	−404575.	−	10457.6i	−1.08393	−	0.0280179i
$73$	−30700.2	−	67224.0i	−0.0789173	−	0.172805i	0.866061	−	0.499939i	$-0.166644\pi$
$73$	−30700.2	−	67224.0i	−0.0789173	−	0.172805i	−0.944978	+	0.327134i	$0.893917\pi$
$74$	51735.6	−	176195.i	0.127672	−	0.434810i
$75$	−730613.	−	411288.i	−1.73182	−	0.974905i
$76$	125316.	−	144623.i	0.285474	−	0.329455i
$77$	130606.	+	18778.3i	0.286082	+	0.0411323i
$78$	345481.	−	70492.2i	0.728014	−	0.148545i
$79$	234893.	+	271081.i	0.476418	+	0.549816i	0.942186	−	0.335091i	$-0.108767\pi$
$79$	234893.	+	271081.i	0.476418	+	0.549816i	−0.465767	+	0.884907i	$0.654222\pi$
$80$	209573.	+	326102.i	0.409322	+	0.636917i
$81$	516968.	−	123181.i	0.972767	−	0.231787i
$82$	−406366.	−	468972.i	−0.737014	−	0.850560i
$83$	−285817.	−	973405.i	−0.499867	−	1.70239i	−0.692758	−	0.721170i	$-0.743604\pi$
$83$	−285817.	−	973405.i	−0.499867	−	1.70239i	0.192891	−	0.981220i	$-0.438214\pi$
$84$	−169855.	−	39254.9i	−0.286576	−	0.0662302i
$85$	−1.26939e6	+	1.46496e6i	−2.06700	+	2.38544i
$86$	−272745.	−	124559.i	−0.428807	−	0.195830i
$87$	−483041.	−	187310.i	−0.733544	−	0.284448i
$88$	120980.	+	264908.i	0.177527	+	0.388730i
$89$	1.10356e6	−	158668.i	1.56540	−	0.225071i	0.695586	−	0.718443i	$-0.255145\pi$
$89$	1.10356e6	−	158668.i	1.56540	−	0.225071i	0.869819	+	0.493372i	$0.164236\pi$
$90$	−720192.	−	657390.i	−0.987918	−	0.901769i
$91$	530565.			0.704067
$92$	−163616.	+	266037.i	−0.210118	+	0.341648i
$93$	−8345.75	+	98741.1i	−0.0103757	+	0.122758i
$94$	−351589.	−	225953.i	−0.423304	−	0.272041i
$95$	1.59422e6	−	229215.i	1.85942	−	0.267345i
$96$	−222432.	−	620744.i	−0.251411	−	0.701615i
$97$	1.24172e6	+	364601.i	1.36053	+	0.399487i	0.878949	−	0.476915i	$-0.158245\pi$
$97$	1.24172e6	+	364601.i	1.36053	+	0.399487i	0.481579	+	0.876402i	$0.340063\pi$
$98$	−306255.	−	139862.i	−0.325391	−	0.148601i
$99$	−242880.	−	295388.i	−0.250315	−	0.304430i
$100$	113441.	−	789001.i	0.113441	−	0.789001i
$101$	348932.	+	1.18835e6i	0.338670	+	1.15340i	0.936174	+	0.351537i	$0.114341\pi$
$101$	348932.	+	1.18835e6i	0.338670	+	1.15340i	−0.597504	+	0.801866i	$0.703841\pi$
$102$	−1.21215e6	+	883196.i	−1.14223	+	0.832255i
$103$	−417006.	+	267994.i	−0.381620	+	0.245252i	−0.717360	−	0.696702i	$-0.754650\pi$
$103$	−417006.	+	267994.i	−0.381620	+	0.245252i	0.335741	+	0.941955i	$0.391013\pi$
$104$	633099.	+	985122.i	0.562823	+	0.875770i
$105$	−864053.	−	1.18588e6i	−0.746401	−	1.02440i
$106$	−771331.	+	226483.i	−0.647624	+	0.190160i
$107$	−339161.	−	48764.0i	−0.276857	−	0.0398060i	0.00248789	−	0.999997i	$-0.499208\pi$
$107$	−339161.	−	48764.0i	−0.276857	−	0.0398060i	−0.279345	+	0.960191i	$0.590117\pi$
$108$	286887.	+	415910.i	0.227740	+	0.330163i
$109$	−241075.	+	527880.i	−0.186154	+	0.407620i	−0.979582	−	0.201043i	$-0.935567\pi$
$109$	−241075.	+	527880.i	−0.186154	+	0.407620i	0.793428	+	0.608664i	$0.208294\pi$
$110$	−197686.	+	673256.i	−0.148524	+	0.505827i
$111$	−753900.	+	270146.i	−0.551245	+	0.197529i
$112$	64226.4	+	446704.i	0.0457151	+	0.317955i
$113$	−794900.	+	1.23689e6i	−0.550906	+	0.857226i	−0.999330	−	0.0365945i	$-0.988349\pi$
$113$	−794900.	+	1.23689e6i	−0.550906	+	0.857226i	0.448424	+	0.893821i	$0.351985\pi$
$114$	1.24173e6	+	104953.i	0.838131	+	0.0708402i
$115$	−2.50704e6	+	790409.i	−1.64842	+	0.519707i
$116$		−	492561.i		−	0.315563i
$117$	−1.13571e6	−	1.03668e6i	−0.709106	−	0.647271i
$118$	−317902.	−	2.21106e6i	−0.193485	−	1.34572i
$119$	−2.05282e6	+	937491.i	−1.21817	+	0.556322i
$120$	1.17083e6	−	3.01938e6i	0.677563	−	1.74732i
$121$	621617.	−	1.36115e6i	0.350886	−	0.768334i
$122$	319159.	+	276553.i	0.175763	+	0.152299i
$123$	−609366.	+	2.63671e6i	−0.327463	+	1.41693i
$124$	−90394.7	+	26542.3i	−0.0474109	+	0.0139211i
$125$	2.51903e6	−	2.18276e6i	1.28975	−	1.11757i
$126$	−444758.	−	1.04450e6i	−0.222337	−	0.522151i
$127$	2.79190e6	−	1.79424e6i	1.36298	−	0.875932i	0.364505	−	0.931201i	$-0.381238\pi$
$127$	2.79190e6	−	1.79424e6i	1.36298	−	0.875932i	0.998471	+	0.0552695i	$0.0176018\pi$
$128$	−63495.6	+	55019.2i	−0.0302771	+	0.0262352i
$129$	261424.	+	1.28123e6i	0.121780	+	0.596840i
$130$	−401534.	+	2.79273e6i	−0.182765	+	1.27116i
$131$	−870591.	−	754372.i	−0.387258	−	0.335561i	0.439374	−	0.898304i	$-0.355200\pi$
$131$	−870591.	−	754372.i	−0.387258	−	0.335561i	−0.826632	+	0.562743i	$0.809746\pi$
$132$	178353.	−	316827.i	0.0775460	−	0.137753i
$133$	1.79917e6	+	528283.i	0.764745	+	0.224549i
$134$	525377.	−	239932.i	0.218352	−	0.0997179i
$135$	−467526.	+	4.22674e6i	−0.190022	+	1.71792i
$136$	−4.19022e6	−	2.69289e6i	−1.66579	−	1.07054i
$137$		−	3.01600e6i		−	1.17292i	−0.809977	−	0.586462i	$-0.800520\pi$
$137$		−	3.01600e6i		−	1.17292i	0.809977	−	0.586462i	$-0.199480\pi$
$138$	−2.02762e6	+	159070.i	−0.771522	+	0.0605272i
$139$	−1.32944e6			−0.495021			−0.247511	−	0.968885i	$-0.579612\pi$
$139$	−1.32944e6			−0.495021			−0.247511	+	0.968885i	$0.579612\pi$
$140$	754184.	−	1.17353e6i	0.274848	−	0.427672i
$141$	106525.	+	1.81953e6i	0.0380008	+	0.649085i
$142$	−24971.6	−	54680.2i	−0.00872130	−	0.0190970i
$143$	−311743.	+	1.06170e6i	−0.106608	+	0.363072i
$144$	735340.	−	1.08170e6i	0.246264	−	0.362258i
$145$	2.71483e6	−	3.13308e6i	0.890508	−	1.02770i
$146$	452884.	+	65114.8i	0.145522	+	0.0209229i
$147$	293543.	+	1.43864e6i	0.0924100	+	0.452899i
$148$	−498600.	−	575415.i	−0.153804	−	0.177499i
$149$	−142953.	−	222440.i	−0.0432151	−	0.0672440i	0.818974	−	0.573831i	$-0.194543\pi$
$149$	−142953.	−	222440.i	−0.0432151	−	0.0672440i	−0.862189	+	0.506587i	$0.830907\pi$
$150$	4.58762e6	−	2.42861e6i	1.35929	−	0.719588i
$151$	1.82736e6	+	2.10889e6i	0.530754	+	0.612523i	0.956291	−	0.292418i	$-0.0944599\pi$
$151$	1.82736e6	+	2.10889e6i	0.530754	+	0.612523i	−0.425536	+	0.904941i	$0.639914\pi$
$152$	1.16598e6	+	3.97097e6i	0.332017	+	1.13075i
$153$	6.22599e6	+	2.00426e6i	1.73834	+	0.559602i
$154$	−534965.	+	617382.i	−0.146475	+	0.169041i
$155$	−721274.	−	329395.i	−0.193689	−	0.0884549i
$156$	528554.	−	1.36305e6i	0.139224	−	0.359037i
$157$	2.31756e6	+	5.07475e6i	0.598870	+	1.31134i	0.929932	+	0.367733i	$0.119866\pi$
$157$	2.31756e6	+	5.07475e6i	0.598870	+	1.31134i	−0.331062	+	0.943609i	$0.607407\pi$
$158$	−2.19811e6	+	316040.i	−0.557285	+	0.0801255i
$159$	2.77919e6	+	2.13706e6i	0.691395	+	0.531649i
$160$	5.27637e6			1.28818
$161$	−3.03727e6	−	375439.i	−0.727788	−	0.0899625i
$162$	−1.08882e6	+	3.10485e6i	−0.256101	+	0.730289i
$163$	−5.69763e6	−	3.66164e6i	−1.31562	−	0.845500i	−0.320802	−	0.947146i	$-0.603953\pi$
$163$	−5.69763e6	−	3.66164e6i	−1.31562	−	0.845500i	−0.994821	+	0.101647i	$0.967589\pi$
$164$	−2.54669e6	+	366159.i	−0.577357	+	0.0830114i
$165$	2.88071e6	−	1.03225e6i	0.641280	−	0.229791i
$166$	6.02649e6	+	1.76954e6i	1.31747	+	0.386844i
$167$	3.86330e6	+	1.76431e6i	0.829486	+	0.378813i	0.784465	−	0.620173i	$-0.212937\pi$
$167$	3.86330e6	+	1.76431e6i	0.829486	+	0.378813i	0.0450203	+	0.998986i	$0.485665\pi$
$168$	2.70021e6	−	2.63132e6i	0.569468	−	0.554939i
$169$	53723.7	−	373657.i	0.0111303	−	0.0774128i
$170$	−3.38108e6	−	1.15149e7i	−0.688190	−	2.34376i
$171$	−2.81903e6	−	4.64625e6i	−0.563783	−	0.929210i
$172$	−1.04585e6	+	672127.i	−0.205534	+	0.132089i
$173$	−107799.	−	167738.i	−0.0208197	−	0.0323961i	0.830688	−	0.556739i	$-0.187948\pi$
$173$	−107799.	−	167738.i	−0.0208197	−	0.0323961i	−0.851507	+	0.524343i	$0.824311\pi$
$174$	2.59240e6	−	1.88887e6i	0.492100	−	0.358554i
$175$	7.49434e6	−	2.20054e6i	1.39836	−	0.410596i
$176$	−931625.	−	133947.i	−0.170885	−	0.0245695i
$177$	−6.97687e6	+	6.79886e6i	−1.25817	+	1.22607i
$178$	−2.86743e6	+	6.27880e6i	−0.508432	+	1.11331i
$179$	−2.01888e6	+	6.87568e6i	−0.352008	+	1.19883i	0.573216	+	0.819405i	$0.305696\pi$
$179$	−2.01888e6	+	6.87568e6i	−0.352008	+	1.19883i	−0.925223	+	0.379423i	$0.876122\pi$
$180$	−3.90737e6	+	1.03843e6i	−0.669987	+	0.178057i
$181$	740562.	+	5.15072e6i	0.124889	+	0.868625i	0.951894	+	0.306429i	$0.0991342\pi$
$181$	740562.	+	5.15072e6i	0.124889	+	0.868625i	−0.827004	+	0.562196i	$0.809957\pi$
$182$	−1.77590e6	+	2.76335e6i	−0.294581	+	0.458376i
$183$	155111.	−	1.83517e6i	0.0253099	−	0.299449i
$184$	−2.92714e6	−	6.08741e6i	−0.469884	−	0.977191i
$185$		−	6.40821e6i		−	1.01209i
$186$	−486340.	−	373972.i	−0.0755791	−	0.0581166i
$187$	−669816.	−	4.65868e6i	−0.102431	−	0.712423i
$188$	−1.57625e6	+	719849.i	−0.237220	+	0.108335i
$189$	−2.53933e6	+	4.25008e6i	−0.376126	+	0.629523i
$190$	−4.14234e6	+	9.07045e6i	−0.603927	+	1.32242i
$191$	−3.84728e6	−	3.33369e6i	−0.552146	−	0.478437i	0.333531	−	0.942739i	$-0.391760\pi$
$191$	−3.84728e6	−	3.33369e6i	−0.552146	−	0.478437i	−0.885677	+	0.464302i	$0.846305\pi$
$192$	6.99832e6	+	1.61737e6i	0.988758	+	0.228510i
$193$	3.91783e6	−	1.15038e6i	0.544971	−	0.160018i	0.00235281	−	0.999997i	$-0.499251\pi$
$193$	3.91783e6	−	1.15038e6i	0.544971	−	0.160018i	0.542619	+	0.839979i	$0.317433\pi$
$194$	−6.05522e6	+	5.24688e6i	−0.829325	+	0.718614i
$195$	1.08747e7	−	5.75690e6i	1.46661	−	0.776399i
$196$	−1.17434e6	+	754705.i	−0.155965	+	0.100233i
$197$	−2.33255e6	+	2.02116e6i	−0.305092	+	0.264364i	−0.793928	−	0.608012i	$-0.791967\pi$
$197$	−2.33255e6	+	2.02116e6i	−0.305092	+	0.264364i	0.488835	+	0.872376i	$0.337422\pi$
$198$	2.35144e6	−	276279.i	0.302928	−	0.0355919i
$199$	1.11093e6	−	7.72672e6i	0.140971	−	0.980473i	−0.789407	−	0.613871i	$-0.789612\pi$
$199$	1.11093e6	−	7.72672e6i	0.140971	−	0.980473i	0.930378	−	0.366603i	$-0.119479\pi$
$200$	1.30285e7	+	1.12893e7i	1.62856	+	1.41116i
$201$	−2.19494e6	−	1.23561e6i	−0.270293	−	0.152157i
$202$	−7.35726e6	−	2.16029e6i	−0.892610	−	0.262094i
$203$	4.39032e6	−	2.00499e6i	0.524817	−	0.239676i
$204$	363435.	+	6.20776e6i	0.0428091	+	0.731214i
$205$	−1.82171e7	−	1.17074e7i	−2.11455	−	1.35894i
$206$		−	3.06893e6i		−	0.351063i
$207$	5.76792e6	+	6.73821e6i	0.650292	+	0.759685i
$208$	−3.78458e6			−0.420560
$209$	−2.11427e6	+	3.28986e6i	−0.231590	+	0.360362i
$210$	9.06856e6	−	530921.i	0.979221	−	0.0573287i
$211$	3.60328e6	+	7.89009e6i	0.383576	+	0.839914i	0.998675	+	0.0514638i	$0.0163887\pi$
$211$	3.60328e6	+	7.89009e6i	0.383576	+	0.839914i	−0.615099	+	0.788450i	$0.710884\pi$
$212$	−939045.	+	3.19809e6i	−0.0985551	+	0.335648i
$213$	−128600.	+	228445.i	−0.0133076	+	0.0236397i
$214$	1.38921e6	−	1.60324e6i	0.141752	−	0.163590i
$215$	−1.03570e7	−	1.48911e6i	−1.04212	−	0.149834i
$216$	−1.09214e7	+	356555.i	−1.08372	+	0.0353806i
$217$	−604534.	−	697670.i	−0.0591618	−	0.0682764i
$218$	−1.94245e6	−	3.02251e6i	−0.187491	−	0.291741i
$219$	−933569.	−	1.76350e6i	−0.0888820	−	0.167897i
$220$	1.90519e6	+	2.19871e6i	0.178925	+	0.206490i
$221$	−5.33183e6	−	1.81585e7i	−0.493968	−	1.68230i
$222$	1.11643e6	−	4.83078e6i	0.102041	−	0.441528i
$223$	−1.86719e6	+	2.15485e6i	−0.168374	+	0.194314i	−0.833665	−	0.552270i	$-0.813762\pi$
$223$	−1.86719e6	+	2.15485e6i	−0.168374	+	0.194314i	0.665292	+	0.746584i	$0.268307\pi$
$224$	5.58777e6	+	2.55185e6i	0.497158	+	0.227044i
$225$	−2.03419e7	−	9.93287e6i	−1.78584	−	0.872022i
$226$	−3.78144e6	−	8.28020e6i	−0.327591	−	0.717324i
$227$	−534688.	+	76876.5i	−0.0457112	+	0.00657228i	−0.165133	−	0.986271i	$-0.552805\pi$
$227$	−534688.	+	76876.5i	−0.0457112	+	0.00657228i	0.119421	+	0.992844i	$0.461896\pi$
$228$	3.14954e6	−	4.09589e6i	0.265731	−	0.345576i
$229$	1.05091e7			0.875102			0.437551	−	0.899194i	$-0.355846\pi$
$229$	1.05091e7			0.875102			0.437551	+	0.899194i	$0.355846\pi$
$230$	4.27481e6	−	1.57031e7i	0.351345	−	1.29063i
$231$	3.54996e6	+	300048.i	0.287997	+	0.0243419i
$232$	8.96153e6	+	5.75922e6i	0.717659	+	0.461211i
$233$	−1.87660e7	+	2.69815e6i	−1.48356	+	0.213304i	−0.836008	−	0.548718i	$-0.815116\pi$
$233$	−1.87660e7	+	2.69815e6i	−1.48356	+	0.213304i	−0.647552	+	0.762021i	$0.724207\pi$
$234$	9.20079e6	−	2.44521e6i	0.718088	−	0.190840i
$235$	−1.39938e7	−	4.10894e6i	−1.07828	−	0.316611i
$236$	−8.42479e6	−	3.84747e6i	−0.640949	−	0.292711i
$237$	6.75904e6	+	6.93600e6i	0.507738	+	0.521032i
$238$	1.98841e6	−	1.38297e7i	0.147494	−	1.02584i
$239$	3.67783e6	+	1.25255e7i	0.269400	+	0.917492i	0.977421	+	0.211301i	$0.0677699\pi$
$239$	3.67783e6	+	1.25255e7i	0.269400	+	0.917492i	−0.708021	+	0.706191i	$0.750412\pi$
$240$	6.16339e6	+	8.45898e6i	0.445847	+	0.611905i
$241$	1.66969e6	−	1.07304e6i	0.119284	−	0.0766595i	−0.479638	−	0.877466i	$-0.659232\pi$
$241$	1.66969e6	−	1.07304e6i	0.119284	−	0.0766595i	0.598923	+	0.800807i	$0.295596\pi$
$242$	5.00864e6	+	7.79360e6i	0.353406	+	0.549911i
$243$	1.37399e7	−	4.13599e6i	0.957557	−	0.288244i
$244$	1.68005e6	−	493306.i	0.115652	−	0.0339584i
$245$	−1.16294e7	−	1.67206e6i	−0.790789	−	0.113698i
$246$	−1.16932e7	−	1.19993e7i	−0.785466	−	0.806031i
$247$	−6.53230e6	+	1.43037e7i	−0.433486	+	0.949202i
$248$	574029.	−	1.95496e6i	0.0376338	−	0.128169i
$249$	−9.23993e6	−	2.57860e7i	−0.598509	−	1.67027i
$250$	2.93682e6	+	2.04260e7i	0.187956	+	1.30727i
$251$	1.24672e7	−	1.93993e7i	0.788400	−	1.22677i	−0.181529	−	0.983386i	$-0.558105\pi$
$251$	1.24672e7	−	1.93993e7i	0.788400	−	1.22677i	0.969929	−	0.243389i	$-0.0782590\pi$
$252$	−4.64019e6	−	790036.i	−0.289957	−	0.0493680i
$253$	2.53588e6	−	5.85719e6i	0.156591	−	0.361683i
$254$			2.05468e7i			1.25384i
$255$	−3.19033e7	+	4.14894e7i	−1.92404	+	2.50217i
$256$	2.34900e6	+	1.63377e7i	0.140012	+	0.973802i
$257$	−305643.	+	139582.i	−0.0180059	+	0.00822302i	−0.424398	−	0.905476i	$-0.639514\pi$
$257$	−305643.	+	139582.i	−0.0180059	+	0.00822302i	0.406392	+	0.913699i	$0.366787\pi$
$258$	−7.54810e6	−	2.92694e6i	−0.439520	−	0.170433i
$259$	3.09925e6	−	6.78640e6i	0.178384	−	0.390607i
$260$	8.84098e6	+	7.66075e6i	0.503014	+	0.435864i
$261$	−1.33154e7	−	4.28647e6i	−0.748915	−	0.241089i
$262$	6.84304e6	−	2.00930e6i	0.380492	−	0.111722i
$263$	7.56346e6	−	6.55378e6i	0.415770	−	0.360267i	−0.421714	−	0.906729i	$-0.638571\pi$
$263$	7.56346e6	−	6.55378e6i	0.415770	−	0.360267i	0.837484	+	0.546462i	$0.184026\pi$
$264$	3.67890e6	+	6.94939e6i	0.199943	+	0.377689i
$265$	−2.35999e7	+	1.51667e7i	−1.26815	+	0.814993i
$266$	−8.77361e6	+	7.60238e6i	−0.466159	+	0.403929i
$267$	2.94949e7	−	6.01816e6i	1.54957	−	0.316177i
$268$	340805.	−	2.37035e6i	0.0177052	−	0.123143i
$269$	1.08378e7	+	9.39098e6i	0.556779	+	0.482452i	0.887202	−	0.461381i	$-0.152646\pi$
$269$	1.08378e7	+	9.39098e6i	0.556779	+	0.482452i	−0.330423	+	0.943833i	$0.607191\pi$
$270$	−2.04493e7	−	1.65827e7i	−1.03893	−	0.842489i
$271$	2.68128e7	+	7.87295e6i	1.34721	+	0.395576i	0.874236	−	0.485502i	$-0.161363\pi$
$271$	2.68128e7	+	7.87295e6i	1.34721	+	0.395576i	0.472972	+	0.881078i	$0.343181\pi$
$272$	1.46430e7	−	6.68723e6i	0.727650	−	0.332307i
$273$	1.43008e7	−	837242.i	0.702864	−	0.0411494i
$274$	1.57083e7	+	1.00951e7i	0.763620	+	0.490749i
$275$			1.62897e7i			0.783275i
$276$	−3.99028e6	+	7.42891e6i	−0.189791	+	0.353344i
$277$	−4.85458e6			−0.228408			−0.114204	−	0.993457i	$-0.536432\pi$
$277$	−4.85458e6			−0.228408			−0.114204	+	0.993457i	$0.536432\pi$
$278$	4.44988e6	−	6.92414e6i	0.207116	−	0.322279i
$279$	−69134.7	+	2.67462e6i	−0.00318334	+	0.123154i
$280$	1.25327e7	+	2.74429e7i	0.570915	+	1.25013i
$281$	4.27543e6	−	1.45608e7i	0.192691	−	0.656244i	−0.805299	−	0.592869i	$-0.797995\pi$
$281$	4.27543e6	−	1.45608e7i	0.192691	−	0.656244i	0.997990	−	0.0633753i	$-0.0201865\pi$
$282$	−9.83324e6	−	5.53548e6i	−0.438480	−	0.246836i
$283$	1.00016e7	−	1.15425e7i	0.441277	−	0.509261i	−0.490924	−	0.871203i	$-0.663341\pi$
$283$	1.00016e7	−	1.15425e7i	0.441277	−	0.509261i	0.932201	+	0.361942i	$0.117886\pi$
$284$	−246701.	−	35470.3i	−0.0107700	−	0.00154849i
$285$	4.26088e7	−	8.69394e6i	1.84062	−	0.375562i
$286$	−4.48621e6	−	5.17736e6i	−0.191770	−	0.221315i
$287$	−1.36301e7	−	2.12088e7i	−0.576571	−	0.897162i
$288$	−6.97495e6	−	1.63804e7i	−0.291987	−	0.685722i
$289$	3.69082e7	+	4.25944e7i	1.52908	+	1.76465i
$290$	7.23104e6	+	2.46267e7i	0.296488	+	1.00975i
$291$	3.40444e7	+	7.86795e6i	1.38155	+	0.319288i
$292$	1.24231e6	−	1.43370e6i	0.0498977	−	0.0575850i
$293$	4.01513e7	+	1.83365e7i	1.59623	+	0.728975i	0.997411	−	0.0719070i	$-0.0229085\pi$
$293$	4.01513e7	+	1.83365e7i	1.59623	+	0.728975i	0.598822	+	0.800882i	$0.295636\pi$
$294$	−8.47546e6	−	3.28655e6i	−0.333520	−	0.129330i
$295$	−3.23824e7	−	7.09076e7i	−1.26137	−	2.76202i
$296$	1.62988e7	−	2.34341e6i	0.628464	−	0.0903594i
$297$	−7.01268e6	−	7.57858e6i	−0.267679	−	0.289280i
$298$	1.63703e6			0.0618597
$299$	6.74120e6	−	2.47632e7i	0.252188	−	0.926387i
$300$	1.81262e6	−	2.14456e7i	0.0671340	−	0.794283i
$301$	−1.02480e7	−	6.58600e6i	−0.375786	−	0.241503i
$302$	−1.71003e7	+	2.45865e6i	−0.620844	+	0.0892639i
$303$	1.12803e7	+	3.14800e7i	0.405502	+	1.13164i
$304$	−1.28337e7	−	3.76830e6i	−0.456804	−	0.134130i
$305$	1.34054e7	+	6.12202e6i	0.472475	+	0.215772i
$306$	−3.12783e7	+	2.57183e7i	−1.09164	+	0.897590i
$307$	6.17649e6	−	4.29584e7i	0.213465	−	1.48468i	−0.548002	−	0.836477i	$-0.684612\pi$
$307$	6.17649e6	−	4.29584e7i	0.213465	−	1.48468i	0.761467	−	0.648204i	$-0.224479\pi$
$308$	954253.	+	3.24989e6i	0.0326596	+	0.111229i
$309$	−1.08170e7	+	7.88150e6i	−0.366634	+	0.267137i
$310$	4.12983e6	−	2.65408e6i	0.138627	−	0.0890901i
$311$	8.60206e6	+	1.33851e7i	0.285971	+	0.444979i	0.954284	−	0.298901i	$-0.0966199\pi$
$311$	8.60206e6	+	1.33851e7i	0.285971	+	0.444979i	−0.668314	+	0.743880i	$0.732984\pi$
$312$	1.86190e7	+	2.55538e7i	0.613046	+	0.841379i
$313$	−3.99269e6	+	1.17236e6i	−0.130207	+	0.0382321i	−0.346187	−	0.938166i	$-0.612524\pi$
$313$	−3.99269e6	+	1.17236e6i	−0.130207	+	0.0382321i	0.215980	+	0.976398i	$0.430705\pi$
$314$	−3.41883e7	−	4.91553e6i	−1.10430	−	0.158775i
$315$	−2.51609e7	−	3.06004e7i	−0.804997	−	0.979029i
$316$	−3.82494e6	+	8.37545e6i	−0.121217	+	0.265428i
$317$	−1.03643e7	+	3.52975e7i	−0.325358	+	1.10807i	0.620694	+	0.784053i	$0.286851\pi$
$317$	−1.03643e7	+	3.52975e7i	−0.325358	+	1.10807i	−0.946052	+	0.324015i	$0.894967\pi$
$318$	−2.04329e7	+	7.32177e6i	−0.635403	+	0.227685i
$319$	1.43252e6	+	9.96341e6i	0.0441295	+	0.306928i
$320$	−3.10736e7	+	4.83515e7i	−0.948293	+	1.47557i
$321$	−9.21865e6	−	779175.i	−0.278710	−	0.0235570i
$322$	1.21217e7	−	1.45624e7i	0.363075	−	0.436179i
$323$		−	6.68852e7i		−	1.98483i
$324$	8.38902e6	+	1.07577e7i	0.246647	+	0.316288i
$325$	9.32172e6	+	6.48340e7i	0.271548	+	1.88865i
$326$	3.81420e7	−	1.74189e7i	1.10091	−	0.502768i
$327$	−5.66489e6	+	1.46088e7i	−0.162012	+	0.417803i
$328$	2.31151e7	−	5.06151e7i	0.655051	−	1.43436i
$329$	−1.28324e7	−	1.11193e7i	−0.360346	−	0.312242i
$330$	−4.26598e6	+	1.84588e7i	−0.118707	+	0.513643i
$331$	1.52913e7	−	4.48992e6i	0.421657	−	0.123810i	−0.0640189	−	0.997949i	$-0.520392\pi$
$331$	1.52913e7	−	4.48992e6i	0.421657	−	0.123810i	0.485676	+	0.874139i	$0.338574\pi$
$332$	1.96812e7	−	1.70538e7i	0.537820	−	0.466024i
$333$	−1.98942e7	+	8.47115e6i	−0.538758	+	0.229409i
$334$	−2.21203e7	+	1.42158e7i	−0.593678	+	0.381534i
$335$	1.52324e7	−	1.31989e7i	0.405166	−	0.351078i
$336$	2.43606e6	+	1.19390e7i	0.0642199	+	0.314740i
$337$	2.16723e6	−	1.50734e7i	0.0566259	−	0.393842i	−0.941722	−	0.336391i	$-0.890794\pi$
$337$	2.16723e6	−	1.50734e7i	0.0566259	−	0.393842i	0.998348	−	0.0574510i	$-0.0182973\pi$
$338$	1.76630e6	+	1.53051e6i	0.0457420	+	0.0396356i
$339$	−1.94738e7	+	3.45933e7i	−0.499863	+	0.887959i
$340$	−4.77431e7	−	1.40186e7i	−1.21471	−	0.356672i
$341$	1.75129e6	−	799788.i	0.0441668	−	0.0201703i
$342$	3.36350e7	+	869410.i	0.840839	+	0.0217343i
$343$	−3.64018e7	−	2.33940e7i	−0.902071	−	0.579726i
$344$		−	2.68867e7i		−	0.660484i
$345$	−6.63270e7	+	2.52607e7i	−1.61522	+	0.615160i
$346$	1.23446e6			0.0298021
$347$	4.17645e7	−	6.49868e7i	0.999583	−	1.55538i	0.179003	−	0.983848i	$-0.442713\pi$
$347$	4.17645e7	−	6.49868e7i	0.999583	−	1.55538i	0.820579	−	0.571533i	$-0.193651\pi$
$348$	−777271.	−	1.32764e7i	−0.0184431	−	0.315023i
$349$	−1.44296e7	−	3.15964e7i	−0.339452	−	0.743296i	0.660520	−	0.750808i	$-0.270336\pi$
$349$	−1.44296e7	−	3.15964e7i	−0.339452	−	0.743296i	−0.999972	+	0.00751278i	$0.997609\pi$
$350$	−1.36238e7	+	4.63985e7i	−0.317757	+	1.08218i
$351$	−3.22478e7	−	2.61503e7i	−0.745724	−	0.604720i
$352$	−8.38963e6	+	9.68215e6i	−0.192360	+	0.221995i
$353$	−1.46639e7	−	2.10835e6i	−0.333368	−	0.0479312i	−0.0264018	−	0.999651i	$-0.508405\pi$
$353$	−1.46639e7	−	2.10835e6i	−0.333368	−	0.0479312i	−0.306967	+	0.951720i	$0.599314\pi$
$354$	−1.20578e7	−	5.90948e7i	−0.271805	−	1.33211i
$355$	−1.37372e6	−	1.58535e6i	−0.0307052	−	0.0354357i
$356$	1.54728e7	+	2.40762e7i	0.342941	+	0.533627i
$357$	−5.38520e7	+	2.85084e7i	−1.18358	+	0.626567i
$358$	−2.90532e7	−	3.35292e7i	−0.633206	−	0.730758i
$359$	1.99826e7	+	6.80546e7i	0.431887	+	1.47087i	0.832191	+	0.554488i	$0.187086\pi$
$359$	1.99826e7	+	6.80546e7i	0.431887	+	1.47087i	−0.400305	+	0.916382i	$0.631096\pi$
$360$	2.67937e7	−	8.32314e7i	0.574282	−	1.78394i
$361$	−5.58503e6	+	6.44547e6i	−0.118715	+	0.137004i
$362$	−2.93054e7	−	1.33833e7i	−0.617763	−	0.282123i
$363$	1.46070e7	−	3.76692e7i	0.305381	−	0.787528i
$364$	5.65773e6	+	1.23887e7i	0.117311	+	0.256875i
$365$	1.58041e7	−	2.27229e6i	0.325006	−	0.0467289i
$366$	9.03896e6	+	6.95052e6i	0.184364	+	0.141767i
$367$	−1.10538e7			−0.223622			−0.111811	−	0.993730i	$-0.535665\pi$
$367$	−1.10538e7			−0.223622			−0.111811	+	0.993730i	$0.535665\pi$
$368$	2.16652e7	+	2.67805e6i	0.434729	+	0.0537371i
$369$	−1.22640e7	+	7.20311e7i	−0.244091	+	1.43364i
$370$	3.33760e7	+	2.14495e7i	0.658915	+	0.423459i
$371$	−3.23279e7	+	4.64805e6i	−0.633075	+	0.0910225i
$372$	−2.39460e6	+	858061.i	−0.0465162	+	0.0166682i
$373$	−7.65268e7	−	2.24703e7i	−1.47464	−	0.432995i	−0.557039	−	0.830487i	$-0.688062\pi$
$373$	−7.65268e7	−	2.24703e7i	−1.47464	−	0.432995i	−0.917606	+	0.397492i	$0.869881\pi$
$374$	2.65059e7	+	1.21048e7i	0.506673	+	0.231390i
$375$	6.44532e7	−	6.28087e7i	1.22222	−	1.19104i
$376$	5.33341e6	−	3.70947e7i	0.100332	−	0.697827i
$377$	1.14031e7	+	3.88353e7i	0.212813	+	0.724774i
$378$	−1.36362e7	−	2.74514e7i	−0.252474	−	0.508264i
$379$	−3.74820e6	+	2.40882e6i	−0.0688502	+	0.0442473i	−0.574613	−	0.818425i	$-0.694847\pi$
$379$	−3.74820e6	+	2.40882e6i	−0.0688502	+	0.0442473i	0.505763	+	0.862673i	$0.331211\pi$
$380$	2.23523e7	+	3.47809e7i	0.407354	+	0.633855i
$381$	7.24210e7	−	5.27674e7i	1.30945	−	0.954094i
$382$	3.02405e7	−	8.87941e6i	0.542499	−	0.159292i
$383$	1.16614e7	+	1.67666e6i	0.207566	+	0.0298434i	0.245313	−	0.969444i	$-0.421109\pi$
$383$	1.16614e7	+	1.67666e6i	0.207566	+	0.0298434i	−0.0377476	+	0.999287i	$0.512018\pi$
$384$	−1.62463e6	+	1.58318e6i	−0.0286920	+	0.0279599i
$385$	−1.18425e7	+	2.59314e7i	−0.207520	+	0.454405i
$386$	−7.12216e6	+	2.42559e7i	−0.123837	+	0.421750i
$387$	9.06818e6	+	3.41216e7i	0.156454	+	0.588703i
$388$	4.72773e6	+	3.28821e7i	0.0809389	+	0.562943i
$389$	−4.98645e7	+	7.75907e7i	−0.847116	+	1.31814i	0.0992568	+	0.995062i	$0.468353\pi$
$389$	−4.98645e7	+	7.75907e7i	−0.847116	+	1.31814i	−0.946373	+	0.323076i	$0.895283\pi$
$390$	−6.41590e6	+	7.59084e7i	−0.108159	+	1.27966i
$391$	1.76732e7	+	1.07723e8i	0.295654	+	1.80210i
$392$		−	3.01901e7i		−	0.501194i
$393$	−2.46562e7	−	1.89594e7i	−0.406208	−	0.312354i
$394$	−2.71940e6	−	1.89139e7i	−0.0444616	−	0.309237i
$395$	−7.04922e7	+	3.21927e7i	−1.14380	+	0.522356i
$396$	4.30735e6	−	8.82116e6i	0.0693624	−	0.142050i
$397$	−4.10470e7	+	8.98805e7i	−0.656010	+	1.43646i	0.230185	+	0.973147i	$0.426067\pi$
$397$	−4.10470e7	+	8.98805e7i	−0.656010	+	1.43646i	−0.886194	+	0.463314i	$0.846660\pi$
$398$	3.65247e7	+	3.16489e7i	0.579346	+	0.502006i
$399$	4.93281e7	+	1.14001e7i	0.776562	+	0.179470i
$400$	−5.34580e7	+	1.56967e7i	−0.835281	+	0.245261i
$401$	5.76907e7	−	4.99893e7i	0.894691	−	0.775254i	−0.0804688	−	0.996757i	$-0.525642\pi$
$401$	5.76907e7	−	4.99893e7i	0.894691	−	0.775254i	0.975160	+	0.221503i	$0.0710963\pi$
$402$	1.37823e7	−	7.29613e6i	0.212150	−	0.112309i
$403$	6.51258e6	−	4.18538e6i	0.0995034	−	0.0639470i
$404$	−2.40272e7	+	2.08197e7i	−0.364383	+	0.315740i
$405$	−5.93176e6	+	1.14665e8i	−0.0892932	+	1.72609i
$406$	−4.25257e6	+	2.95773e7i	−0.0635438	+	0.441957i
$407$	1.17591e7	+	1.01893e7i	0.174417	+	0.151133i
$408$	−1.17192e8	−	6.59714e7i	−1.72551	−	0.971349i
$409$	−5.47102e6	−	1.60644e6i	−0.0799647	−	0.0234798i	0.241505	−	0.970399i	$-0.422359\pi$
$409$	−5.47102e6	−	1.60644e6i	−0.0799647	−	0.0234798i	−0.321470	+	0.946920i	$0.604177\pi$
$410$	1.21952e8	−	5.56936e7i	1.76945	−	0.808079i
$411$	−4.75931e6	−	8.12928e7i	−0.0685517	−	1.17092i
$412$	−1.07044e7	−	6.87933e6i	−0.153064	−	0.0983681i
$413$		−	9.07537e7i		−	1.28829i
$414$	−5.44010e7	+	7.48716e6i	−0.766666	+	0.105516i
$415$	2.19183e8			3.06664
$416$	−2.78507e7	+	4.33365e7i	−0.386862	+	0.601969i
$417$	−3.58335e7	+	2.09788e6i	−0.494175	+	0.0289316i
$418$	−1.00578e7	−	2.20235e7i	−0.137713	−	0.301549i
$419$	1.05849e7	−	3.60489e7i	0.143895	−	0.490060i	−0.855731	−	0.517421i	$-0.826892\pi$
$419$	1.05849e7	−	3.60489e7i	0.143895	−	0.490060i	0.999626	+	0.0273609i	$0.00871032\pi$
$420$	1.84763e7	−	3.28213e7i	0.249383	−	0.443005i
$421$	7.82553e7	−	9.03114e7i	1.04874	−	1.21031i	0.0716604	−	0.997429i	$-0.477170\pi$
$421$	7.82553e7	−	9.03114e7i	1.04874	−	1.21031i	0.977078	−	0.212880i	$-0.0682843\pi$
$422$	−5.31550e7	−	7.64253e6i	−0.707305	−	0.101695i
$423$	5.74250e6	+	4.88752e7i	0.0758717	+	0.645754i
$424$	−4.72056e7	−	5.44782e7i	−0.619293	−	0.714702i
$425$	−1.50626e8	−	2.34379e8i	−1.96216	−	3.05318i
$426$	−759367.	−	1.43443e6i	−0.00982252	−	0.0185546i
$427$	1.12357e7	+	1.29667e7i	0.144316	+	0.166550i
$428$	−2.47804e6	−	8.43942e6i	−0.0316065	−	0.107642i
$429$	−6.72729e6	+	2.91088e7i	−0.0852056	+	0.368682i
$430$	4.24224e7	−	4.89581e7i	0.533568	−	0.615771i
$431$	−1.08651e8	−	4.96193e7i	−1.35707	−	0.619754i	−0.401866	−	0.915698i	$-0.631638\pi$
$431$	−1.08651e8	−	4.96193e7i	−1.35707	−	0.619754i	−0.955205	+	0.295945i	$0.904366\pi$
$432$	1.81133e7	−	3.03163e7i	0.224671	−	0.376032i
$433$	2.54026e7	+	5.56240e7i	0.312907	+	0.685170i	0.999107	−	0.0422420i	$-0.0134500\pi$
$433$	2.54026e7	+	5.56240e7i	0.312907	+	0.685170i	−0.686201	+	0.727412i	$0.740723\pi$
$434$	5.65718e6	−	813379.i	0.0692039	−	0.00995002i
$435$	6.82309e7	−	8.87325e7i	0.828922	−	1.07799i
$436$	−1.48967e7			−0.179735
$437$	4.75164e7	−	7.72607e7i	0.569376	−	0.925793i
$438$	1.23097e7	+	1.04044e6i	0.146496	+	0.0123821i
$439$	−2.93887e7	−	1.88870e7i	−0.347366	−	0.223238i	0.355310	−	0.934748i	$-0.384375\pi$
$439$	−2.93887e7	−	1.88870e7i	−0.347366	−	0.223238i	−0.702676	+	0.711510i	$0.748012\pi$
$440$	−6.22790e7	+	8.95436e6i	−0.731111	+	0.105118i
$441$	1.01823e7	+	3.83138e7i	0.118722	+	0.446724i
$442$	1.12422e8	+	3.30101e7i	1.30192	+	0.382279i
$443$	−4.39298e7	−	2.00621e7i	−0.505298	−	0.230762i	0.146421	−	0.989222i	$-0.453225\pi$
$443$	−4.39298e7	−	2.00621e7i	−0.505298	−	0.230762i	−0.651719	+	0.758460i	$0.725952\pi$
$444$	−1.43472e7	−	1.47228e7i	−0.163915	−	0.168206i
$445$	−3.42803e7	+	2.38425e8i	−0.389013	+	2.70565i
$446$	−4.97334e6	−	1.69376e7i	−0.0560587	−	0.190919i
$447$	−4.20416e6	−	5.77002e6i	−0.0470713	−	0.0646033i
$448$	−5.62921e7	+	3.61768e7i	−0.626057	+	0.402342i
$449$	9.42114e7	+	1.46596e8i	1.04079	+	1.61951i	0.748448	+	0.663193i	$0.230799\pi$
$449$	9.42114e7	+	1.46596e8i	1.04079	+	1.61951i	0.292345	+	0.956313i	$0.405564\pi$
$450$	1.19822e8	−	7.26998e7i	1.31491	−	0.797803i
$451$	5.04490e7	−	1.48132e7i	0.549950	−	0.161480i
$452$	−3.73579e7	−	5.37125e6i	−0.404545	−	0.0581648i
$453$	5.25823e7	+	5.39590e7i	0.565646	+	0.580456i
$454$	1.38930e6	−	3.04215e6i	0.0148467	−	0.0325097i
$455$	−3.22946e7	+	1.09985e8i	−0.342844	+	1.16762i
$456$	3.76939e7	+	1.05193e8i	0.397536	+	1.10941i
$457$	−6.75336e6	−	4.69707e7i	−0.0707573	−	0.492128i	−0.994127	−	0.108217i	$-0.965486\pi$
$457$	−6.75336e6	−	4.69707e7i	−0.0707573	−	0.492128i	0.923370	−	0.383911i	$-0.125423\pi$
$458$	−3.51759e7	+	5.47347e7i	−0.366141	+	0.569726i
$459$	1.70977e8	+	4.41977e7i	1.76807	+	0.457048i
$460$	−4.51901e7	−	5.01107e7i	−0.464269	−	0.514822i
$461$		−	3.35166e7i		−	0.342103i	−0.985262	−	0.171051i	$-0.945284\pi$
$461$		−	3.35166e7i		−	0.342103i	0.985262	−	0.171051i	$-0.0547164\pi$
$462$	−1.34451e7	+	1.74850e7i	−0.136345	+	0.177313i
$463$	−8.68574e6	−	6.04107e7i	−0.0875112	−	0.608654i	−0.985632	−	0.168906i	$-0.945977\pi$
$463$	−8.68574e6	−	6.04107e7i	−0.0875112	−	0.608654i	0.898121	−	0.439748i	$-0.144932\pi$
$464$	−3.13166e7	+	1.43018e7i	−0.313488	+	0.143165i
$465$	−1.99609e7	−	7.74027e6i	−0.198528	−	0.0769835i
$466$	4.87606e7	−	1.06771e8i	0.481849	−	1.05510i
$467$	3.62470e7	+	3.14082e7i	0.355895	+	0.308384i	0.814396	−	0.580309i	$-0.197068\pi$
$467$	3.62470e7	+	3.14082e7i	0.355895	+	0.308384i	−0.458502	+	0.888694i	$0.651614\pi$
$468$	1.20956e7	−	3.75736e7i	0.118002	−	0.366561i
$469$	2.25148e7	−	6.61094e6i	0.218248	−	0.0640833i
$470$	6.82404e7	−	5.91306e7i	0.657276	−	0.569533i
$471$	7.04753e7	+	1.33127e8i	0.674488	+	1.27410i
$472$	1.68506e8	−	1.08292e8i	1.60247	−	1.02984i
$473$	1.92005e7	−	1.66373e7i	0.181438	−	0.157217i
$474$	−5.87487e7	+	1.19871e7i	−0.551649	+	0.112559i
$475$	−3.29448e7	+	2.29136e8i	−0.307402	+	2.13803i
$476$	−4.37808e7	−	3.79363e7i	−0.405941	−	0.351750i
$477$	7.82821e7	+	5.32163e7i	0.721286	+	0.490332i
$478$	−7.75473e7	−	2.27700e7i	−0.710041	−	0.208487i
$479$	−1.66861e7	+	7.62028e6i	−0.151827	+	0.0693369i	−0.489879	−	0.871790i	$-0.662959\pi$
$479$	−1.66861e7	+	7.62028e6i	−0.151827	+	0.0693369i	0.338053	+	0.941127i	$0.390232\pi$
$480$	1.42219e8	−	8.32622e6i	1.28597	−	0.0752877i
$481$	5.26326e7	+	3.38249e7i	0.472955	+	0.303950i
$482$			1.22879e7i			0.109733i
$483$	−8.24584e7	−	5.32665e6i	−0.731802	−	0.0472730i
$484$	3.84116e7			0.338786
$485$	−1.51163e8	+	2.35214e8i	−1.32501	+	2.06176i
$486$	−2.44484e7	+	8.54057e7i	−0.212982	+	0.744009i
$487$	−3.91781e7	−	8.57880e7i	−0.339200	−	0.742745i	0.660769	−	0.750589i	$-0.270230\pi$
$487$	−3.91781e7	−	8.57880e7i	−0.339200	−	0.742745i	−0.999969	+	0.00784435i	$0.997503\pi$
$488$	−1.06687e7	+	3.63343e7i	−0.0918021	+	0.312649i
$489$	−1.59351e8	−	8.97044e7i	−1.36279	−	0.767162i
$490$	4.76345e7	−	5.49731e7i	0.404887	−	0.467264i
$491$	1.63041e8	+	2.34418e7i	1.37738	+	0.198037i	0.790909	−	0.611934i	$-0.209608\pi$
$491$	1.63041e8	+	2.34418e7i	1.37738	+	0.198037i	0.586469	+	0.809971i	$0.300517\pi$
$492$	−6.80653e7	+	1.38881e7i	−0.571518	+	0.116613i
$493$	−1.12740e8	−	1.30109e8i	−0.940891	−	1.08585i
$494$	−5.26337e7	−	8.18996e7i	−0.436599	−	0.679361i
$495$	7.60173e7	−	3.23689e7i	0.626754	−	0.266878i
$496$	4.31221e6	+	4.97656e6i	0.0353391	+	0.0407834i
$497$	−688054.	−	2.34330e6i	−0.00560471	−	0.0190879i
$498$	1.65229e8	+	3.81859e7i	1.33783	+	0.309183i
$499$	−4.79129e7	+	5.52945e7i	−0.385612	+	0.445020i	−0.915057	−	0.403324i	$-0.867855\pi$
$499$	−4.79129e7	+	5.52945e7i	−0.385612	+	0.445020i	0.529445	+	0.848344i	$0.322400\pi$
$500$	7.78293e7	+	3.55435e7i	0.622635	+	0.284348i
$501$	1.06915e8	+	4.14586e7i	0.850208	+	0.329686i
$502$	5.93078e7	+	1.29866e8i	0.468814	+	1.02656i
$503$	−1.09425e7	+	1.57329e6i	−0.0859827	+	0.0123624i	−0.185172	−	0.982706i	$-0.559284\pi$
$503$	−1.09425e7	+	1.57329e6i	−0.0859827	+	0.0123624i	0.0991892	+	0.995069i	$0.468375\pi$
$504$	6.86288e7	−	7.51851e7i	0.536061	−	0.587273i
$505$	−2.67583e8			−2.07771
$506$	2.20181e7	+	3.28128e7i	0.169953	+	0.253275i
$507$	858424.	−	1.01563e7i	0.00658685	−	0.0779310i
$508$	7.16673e7	+	4.60578e7i	0.546676	+	0.351327i
$509$	−1.65552e8	+	2.38028e7i	−1.25540	+	0.180499i	−0.737737	−	0.675088i	$-0.764106\pi$
$509$	−1.65552e8	+	2.38028e7i	−1.25540	+	0.180499i	−0.517660	+	0.855587i	$0.673197\pi$
$510$	−1.09304e8	−	3.05035e8i	−0.823995	−	2.29953i
$511$	1.78358e7	+	5.23706e6i	0.133669	+	0.0392487i
$512$	−9.78456e7	−	4.46846e7i	−0.729007	−	0.332926i
$513$	−8.33157e7	−	1.20786e8i	−0.617127	−	0.894671i
$514$	296053.	−	2.05910e6i	0.00218012	−	0.0151631i
$515$	−3.01722e7	−	1.02757e8i	−0.220895	−	0.752299i
$516$	−2.71290e7	+	1.97668e7i	−0.197463	+	0.143875i
$517$	2.97905e7	−	1.91452e7i	0.215579	−	0.138544i
$518$	2.49720e7	+	3.88572e7i	0.179665	+	0.279565i
$519$	−3.17028e6	−	4.35108e6i	−0.0226776	−	0.0311240i
$520$	−2.42750e8	+	7.12779e7i	−1.72643	+	0.506926i
$521$	−5.87576e7	−	8.44807e6i	−0.415481	−	0.0597371i	−0.0685953	−	0.997645i	$-0.521852\pi$
$521$	−5.87576e7	−	8.44807e6i	−0.415481	−	0.0597371i	−0.346886	+	0.937907i	$0.612761\pi$
$522$	6.68944e7	−	5.50032e7i	0.470303	−	0.386702i
$523$	7.30626e7	−	1.59985e8i	0.510729	−	1.11834i	−0.462103	−	0.886826i	$-0.652905\pi$
$523$	7.30626e7	−	1.59985e8i	0.510729	−	1.11834i	0.972832	−	0.231513i	$-0.0743677\pi$
$524$	8.33096e6	−	2.83726e7i	0.0579030	−	0.197199i
$525$	1.98529e8	−	7.11391e7i	1.37197	−	0.491621i
$526$	8.81787e6	+	6.13297e7i	0.0605908	+	0.421418i
$527$	−1.78025e7	+	2.77012e7i	−0.121632	+	0.189264i
$528$	−2.53222e7	−	2.14028e6i	−0.172029	−	0.0145401i
$529$	−5.61135e7	+	1.36989e8i	−0.379054	+	0.925375i
$530$		−	1.73682e8i		−	1.16661i
$531$	−1.77325e8	+	1.94265e8i	−1.18437	+	1.29751i
$532$	6.85017e6	+	4.76440e7i	0.0454953	+	0.316427i
$533$	1.92314e8	−	8.78266e7i	1.27007	−	0.580022i
$534$	−6.73802e7	+	1.73763e8i	−0.442495	+	1.14112i
$535$	3.07529e7	−	6.73395e7i	0.200828	−	0.439753i
$536$	3.91407e7	+	3.39156e7i	0.254176	+	0.220245i
$537$	−4.35667e7	+	1.88512e8i	−0.281340	+	1.21735i
$538$	−8.51873e7	+	2.50132e7i	−0.547051	+	0.160629i
$539$	2.15595e7	−	1.86814e7i	0.137680	−	0.119301i
$540$	−1.03680e8	+	3.41555e7i	−0.658436	+	0.216910i
$541$	−6.30444e7	+	4.05162e7i	−0.398157	+	0.255880i	−0.724363	−	0.689419i	$-0.757866\pi$
$541$	−6.30444e7	+	4.05162e7i	−0.398157	+	0.255880i	0.326206	+	0.945299i	$0.394230\pi$
$542$	−1.30752e8	+	1.13298e8i	−0.821205	+	0.711578i
$543$	2.80889e7	+	1.37663e8i	0.175443	+	0.859841i
$544$	3.11834e7	−	2.16885e8i	0.193699	−	1.34720i
$545$	−9.47550e7	−	8.21057e7i	−0.585346	−	0.507205i
$546$	−4.35067e7	+	7.72854e7i	−0.267287	+	0.474809i
$547$	1.55688e8	+	4.57141e7i	0.951246	+	0.279311i	0.720305	−	0.693657i	$-0.244002\pi$
$547$	1.55688e8	+	4.57141e7i	0.951246	+	0.279311i	0.230940	+	0.972968i	$0.425820\pi$
$548$	7.04236e7	−	3.21614e7i	0.427934	−	0.195431i
$549$	1.28491e6	−	4.97096e7i	0.00776528	−	0.300416i
$550$	−8.48419e7	−	5.45246e7i	−0.509944	−	0.327721i
$551$			1.43046e8i			0.855108i
$552$	−8.85038e7	−	1.59460e8i	−0.526192	−	0.948058i
$553$	−9.02221e7			−0.533504
$554$	1.62492e7	−	2.52842e7i	0.0955657	−	0.148703i
$555$	−1.01123e7	−	1.72726e8i	−0.0591521	−	1.01036i
$556$	−1.41766e7	−	3.10424e7i	−0.0824797	−	0.180605i
$557$	−9.62561e6	+	3.27818e7i	−0.0557010	+	0.189700i	−0.982644	−	0.185503i	$-0.940609\pi$
$557$	−9.62561e6	+	3.27818e7i	−0.0557010	+	0.189700i	0.926943	+	0.375203i	$0.122427\pi$
$558$	−1.36989e7	−	9.31253e6i	−0.0788465	−	0.0536000i
$559$	6.68985e7	−	7.72049e7i	0.382984	−	0.441987i
$560$	−9.65106e7	−	1.38761e7i	−0.549555	−	0.0790140i
$561$	−2.54056e7	−	1.24512e8i	−0.143893	−	0.705218i
$562$	6.15265e7	+	7.10054e7i	0.346620	+	0.400021i
$563$	−5.24916e7	−	8.16786e7i	−0.294147	−	0.457702i	0.662454	−	0.749103i	$-0.269515\pi$
$563$	−5.24916e7	−	8.16786e7i	−0.294147	−	0.457702i	−0.956601	+	0.291401i	$0.905879\pi$
$564$	−4.13501e7	+	2.18901e7i	−0.230483	+	0.122014i
$565$	−2.08021e8	−	2.40069e8i	−1.15335	−	1.33104i
$566$	2.66397e7	+	9.07265e7i	0.146920	+	0.500363i
$567$	−6.17379e7	+	1.18563e8i	−0.338690	+	0.650429i
$568$	3.52987e6	−	4.07369e6i	0.0192626	−	0.0222302i
$569$	2.83801e7	+	1.29607e7i	0.154055	+	0.0703547i	0.490951	−	0.871187i	$-0.336650\pi$
$569$	2.83801e7	+	1.29607e7i	0.154055	+	0.0703547i	−0.336895	+	0.941542i	$0.609377\pi$
$570$	−9.73386e7	+	2.51020e8i	−0.525606	+	1.35545i
$571$	4.66679e7	+	1.02188e8i	0.250674	+	0.548900i	0.992579	−	0.121606i	$-0.0388043\pi$
$571$	4.66679e7	+	1.02188e8i	0.250674	+	0.548900i	−0.741904	+	0.670506i	$0.766077\pi$
$572$	−2.81150e7	+	4.04232e6i	−0.150228	+	0.0215995i
$573$	−1.08960e8	−	8.37847e7i	−0.579165	−	0.445349i
$574$	1.56085e8			0.825325
$575$	−7.48515e6	−	3.77744e8i	−0.0393728	−	1.98698i
$576$	1.91184e8	+	3.25508e7i	1.00042	+	0.170331i
$577$	−2.85850e8	−	1.83705e8i	−1.48803	−	0.956298i	−0.996336	−	0.0855297i	$-0.972742\pi$
$577$	−2.85850e8	−	1.83705e8i	−1.48803	−	0.956298i	−0.491693	−	0.870768i	$-0.663622\pi$
$578$	−3.45384e8	+	4.96587e7i	−1.78862	+	0.257165i
$579$	1.03785e8	−	3.71896e7i	0.534688	−	0.191595i
$580$	1.02107e8	+	2.99814e7i	0.523326	+	0.153662i
$581$	2.32118e8	+	1.06005e8i	1.18354	+	0.540502i
$582$	−1.54932e8	+	1.50979e8i	−0.785908	+	0.765856i
$583$	9.69374e6	−	6.74214e7i	0.0489199	−	0.340245i
$584$	1.15588e7	+	3.93656e7i	0.0580329	+	0.197642i
$585$	2.84031e8	−	1.72331e8i	1.41872	−	0.860788i
$586$	−2.29896e8	+	1.47745e8i	−1.14245	+	0.734210i
$587$	2.57546e6	+	4.00749e6i	0.0127333	+	0.0198134i	0.847562	−	0.530697i	$-0.178070\pi$
$587$	2.57546e6	+	4.00749e6i	0.0127333	+	0.0198134i	−0.834829	+	0.550510i	$0.814433\pi$
$588$	−3.04622e7	+	2.21953e7i	−0.149840	+	0.109177i
$589$	2.62518e7	−	7.70823e6i	0.128473	−	0.0377232i
$590$	4.77699e8	+	6.86828e7i	2.32594	+	0.334420i
$591$	−5.96816e7	+	5.81589e7i	−0.289120	+	0.281743i
$592$	−2.21073e7	+	4.84082e7i	−0.106554	+	0.233321i
$593$	1.33464e7	−	4.54536e7i	0.0640029	−	0.217974i	−0.921282	−	0.388896i	$-0.872857\pi$
$593$	1.33464e7	−	4.54536e7i	0.0640029	−	0.217974i	0.985285	+	0.170922i	$0.0546747\pi$
$594$	6.29444e7	−	1.11574e7i	0.300330	−	0.0532358i
$595$	−6.93888e7	−	4.82610e8i	−0.329412	−	2.29111i
$596$	3.66957e6	−	5.70997e6i	0.0173331	−	0.0269709i
$597$	1.77510e7	−	2.10018e8i	0.0834259	−	0.987037i
$598$	1.06410e8	+	1.17997e8i	0.497600	+	0.551783i
$599$		−	2.88687e8i		−	1.34322i	−0.740905	−	0.671610i	$-0.765603\pi$
$599$		−	2.88687e8i		−	1.34322i	0.740905	−	0.671610i	$-0.234397\pi$
$600$	3.68983e8	+	2.83730e8i	1.70825	+	1.31356i
$601$	1.85400e7	+	1.28948e8i	0.0854055	+	0.594008i	0.986914	+	0.161247i	$0.0515516\pi$
$601$	1.85400e7	+	1.28948e8i	0.0854055	+	0.594008i	−0.901509	+	0.432761i	$0.857539\pi$
$602$	6.86040e7	−	3.13304e7i	0.314456	−	0.143607i
$603$	−6.11118e7	−	2.98407e7i	−0.278723	−	0.136100i
$604$	−2.97563e7	+	6.51572e7i	−0.135042	+	0.295700i
$605$	2.44328e8	+	2.11711e8i	1.10333	+	0.956044i
$606$	−2.01715e8	−	4.66181e7i	−0.906403	−	0.209477i
$607$	1.15342e8	−	3.38675e7i	0.515729	−	0.151432i	−0.0135030	−	0.999909i	$-0.504298\pi$
$607$	1.15342e8	−	3.38675e7i	0.515729	−	0.151432i	0.529232	+	0.848477i	$0.322480\pi$
$608$	−1.37593e8	+	1.19225e8i	−0.612189	+	0.530465i
$609$	1.15172e8	−	6.09703e7i	0.509912	−	0.269939i
$610$	−7.67557e7	+	4.93279e7i	−0.338159	+	0.217322i
$611$	1.07612e8	−	9.32466e7i	0.471779	−	0.408799i
$612$	1.95919e7	+	1.66749e8i	0.0854718	+	0.727462i
$613$	4.65966e7	−	3.24087e8i	0.202289	−	1.40695i	−0.595179	−	0.803593i	$-0.702919\pi$
$613$	4.65966e7	−	3.24087e8i	0.202289	−	1.40695i	0.797468	−	0.603361i	$-0.206172\pi$
$614$	2.03067e8	+	1.75959e8i	0.877273	+	0.760162i
$615$	−5.09496e8	−	2.86813e8i	−2.19036	−	1.23303i
$616$	−7.02852e7	−	2.06376e7i	−0.300692	−	0.0882911i
$617$	2.14594e8	−	9.80016e7i	0.913611	−	0.417232i	0.0975717	−	0.995229i	$-0.468892\pi$
$617$	2.14594e8	−	9.80016e7i	0.913611	−	0.417232i	0.816039	+	0.577996i	$0.196165\pi$
$618$	−4.84283e6	−	8.27194e7i	−0.0205179	−	0.350463i
$619$	3.20760e8	+	2.06140e8i	1.35241	+	0.869140i	0.997827	−	0.0658855i	$-0.0209872\pi$
$619$	3.20760e8	+	2.06140e8i	1.35241	+	0.869140i	0.354581	+	0.935025i	$0.384624\pi$
$620$		−	2.03543e7i		−	0.0854045i
$621$	1.66101e8	+	1.72519e8i	0.693580	+	0.720380i
$622$	−9.85064e7			−0.409349
$623$	−1.51614e8	+	2.35917e8i	−0.627013	+	0.975651i
$624$	−1.02009e8	+	5.97214e6i	−0.419841	+	0.0245797i
$625$	9.75940e7	+	2.13701e8i	0.399745	+	0.875320i
$626$	7.25825e6	−	2.47193e7i	0.0295876	−	0.100766i
$627$	−5.17961e7	+	9.20108e7i	−0.210133	+	0.373281i
$628$	−9.37820e7	+	1.08230e8i	−0.378652	+	0.436988i
$629$	−2.63409e8	−	3.78725e7i	−1.05847	−	0.152185i
$630$	2.43595e8	−	2.86208e7i	0.974196	−	0.114461i
$631$	2.71493e8	+	3.13319e8i	1.08061	+	1.24709i	0.967327	+	0.253531i	$0.0815920\pi$
$631$	2.71493e8	+	3.13319e8i	1.08061	+	1.24709i	0.113285	+	0.993562i	$0.463863\pi$
$632$	−1.07658e8	−	1.67519e8i	−0.426477	−	0.663611i
$633$	1.09573e8	+	2.06982e8i	0.432009	+	0.816060i
$634$	−1.49150e8	−	1.72128e8i	−0.585267	−	0.675435i
$635$	2.02006e8	+	6.87970e8i	0.788939	+	2.68688i
$636$	−2.02642e7	+	8.76828e7i	−0.0787696	+	0.340834i
$637$	7.51177e7	−	8.66905e7i	0.290619	−	0.335392i
$638$	−5.66876e7	−	2.58884e7i	−0.218286	−	0.0996879i
$639$	−3.10576e6	+	6.36040e6i	−0.0119033	+	0.0243771i
$640$	−7.54054e6	−	1.65115e7i	−0.0287649	−	0.0629863i
$641$	2.73087e8	−	3.92641e7i	1.03688	−	0.149081i	0.397207	−	0.917729i	$-0.369980\pi$
$641$	2.73087e8	−	3.92641e7i	1.03688	−	0.149081i	0.639671	+	0.768649i	$0.279070\pi$
$642$	3.49147e7	−	4.54057e7i	0.131948	−	0.171595i
$643$	1.66756e7			0.0627260			0.0313630	−	0.999508i	$-0.490015\pi$
$643$	1.66756e7			0.0627260			0.0313630	+	0.999508i	$0.490015\pi$
$644$	−2.36217e7	−	7.49237e7i	−0.0884409	−	0.280519i
$645$	−2.81510e8	−	2.37937e7i	−1.04909	−	0.0886711i
$646$	3.48360e8	+	2.23877e8i	1.29220	+	0.830448i
$647$	−7.42336e7	+	1.06732e7i	−0.274087	+	0.0394077i	−0.277988	−	0.960585i	$-0.589667\pi$
$647$	−7.42336e7	+	1.06732e7i	−0.274087	+	0.0394077i	0.00390086	+	0.999992i	$0.498758\pi$
$648$	−2.93810e8	+	2.68446e7i	−1.07980	+	0.0986581i
$649$	1.81605e8	+	5.33239e7i	0.664344	+	0.195069i
$650$	−3.68878e8	−	1.68461e8i	−1.34321	−	0.613421i
$651$	−1.73955e7	−	1.78509e7i	−0.0630511	−	0.0647020i
$652$	2.47422e7	−	1.72086e8i	0.0892681	−	0.620873i
$653$	−3.36848e7	−	1.14720e8i	−0.120975	−	0.412002i	0.876631	−	0.481164i	$-0.159786\pi$
$653$	−3.36848e7	−	1.14720e8i	−0.120975	−	0.412002i	−0.997605	+	0.0691619i	$0.977968\pi$
$654$	−5.71260e7	−	7.84030e7i	−0.204221	−	0.280285i
$655$	2.09372e8	−	1.34555e8i	0.745065	−	0.478824i
$656$	9.72250e7	+	1.51285e8i	0.344402	+	0.535901i
$657$	−2.79461e7	−	4.60599e7i	−0.0985429	−	0.162415i
$658$	1.00866e8	−	2.96168e7i	0.354050	−	0.103959i
$659$	3.60734e8	+	5.18657e7i	1.26046	+	0.181227i	0.739971	−	0.672638i	$-0.234839\pi$
$659$	3.60734e8	+	5.18657e7i	1.26046	+	0.181227i	0.520493	+	0.853866i	$0.325748\pi$
$660$	5.48218e7	+	5.62572e7i	0.190687	+	0.195680i
$661$	3.60736e7	−	7.89902e7i	0.124907	−	0.273507i	−0.836840	−	0.547447i	$-0.815600\pi$
$661$	3.60736e7	−	7.89902e7i	0.124907	−	0.273507i	0.961747	+	0.273940i	$0.0883269\pi$
$662$	−2.77977e7	+	9.46703e7i	−0.0958154	+	0.326317i
$663$	−1.72368e8	−	4.81029e8i	−0.591446	−	1.65056i
$664$	8.01528e7	+	5.57475e8i	0.273788	+	1.90424i
$665$	−2.19025e8	+	3.40809e8i	−0.744781	+	1.15890i
$666$	2.24691e7	−	1.31970e8i	0.0760612	−	0.446737i
$667$	−3.77972e7	−	2.30385e8i	−0.127374	−	0.776384i
$668$			1.09022e8i			0.365750i
$669$	−4.69276e7	+	6.10281e7i	−0.156729	+	0.203822i
$670$	1.77587e7	+	1.23514e8i	0.0590454	+	0.410669i
$671$	−3.25489e7	+	1.48646e7i	−0.107738	+	0.0492023i
$672$	1.54639e8	+	5.99645e7i	0.509578	+	0.197600i
$673$	3.84176e6	−	8.41229e6i	0.0126033	−	0.0275974i	−0.903226	−	0.429166i	$-0.858808\pi$
$673$	3.84176e6	−	8.41229e6i	0.0126033	−	0.0275974i	0.915829	+	0.401568i	$0.131535\pi$
$674$	7.12531e7	+	6.17412e7i	0.232715	+	0.201649i
$675$	−5.63965e8	−	2.35629e8i	−1.83375	−	0.766157i
$676$	9.29778e6	−	2.73008e6i	0.0300981	−	0.00883760i
$677$	−2.63916e8	+	2.28684e8i	−0.850549	+	0.737005i	−0.966614	−	0.256237i	$-0.917517\pi$
$677$	−2.63916e8	+	2.28684e8i	−0.850549	+	0.737005i	0.116065	+	0.993242i	$0.462972\pi$
$678$	−1.14991e8	−	2.17216e8i	−0.368955	−	0.696952i
$679$	−2.73842e8	+	1.75988e8i	−0.874764	+	0.562177i
$680$	8.13284e8	−	7.04714e8i	2.58652	−	2.24123i
$681$	−1.42906e7	+	2.91587e6i	−0.0452490	+	0.00923265i
$682$	−1.69634e6	+	1.17983e7i	−0.00534762	+	0.0371935i
$683$	−1.89642e8	−	1.64326e8i	−0.595214	−	0.515756i	0.304341	−	0.952563i	$-0.401564\pi$
$683$	−1.89642e8	−	1.64326e8i	−0.595214	−	0.515756i	−0.899555	+	0.436807i	$0.856109\pi$
$684$	7.84289e7	−	1.15370e8i	0.245080	−	0.360516i
$685$	6.25213e8	+	1.83579e8i	1.94516	+	0.571152i
$686$	2.43687e8	−	1.11288e8i	0.754850	−	0.344728i
$687$	2.83260e8	−	1.65836e7i	0.873606	−	0.0511455i
$688$	7.31003e7	+	4.69787e7i	0.224468	+	0.144257i
$689$		−	2.73889e8i		−	0.837369i
$690$	9.04428e7	−	4.30005e8i	0.275313	−	1.30896i
$691$	−1.90272e8			−0.576687			−0.288344	−	0.957527i	$-0.593105\pi$
$691$	−1.90272e8			−0.576687			−0.288344	+	0.957527i	$0.593105\pi$
$692$	2.76716e6	−	4.30579e6i	0.00835058	−	0.0129938i
$693$	9.61585e7	+	2.48554e6i	0.288927	+	0.00746830i
$694$	1.98679e8	+	4.35046e8i	0.594392	+	1.30154i
$695$	8.09207e7	−	2.75591e8i	0.241049	−	0.820938i
$696$	2.50636e8	+	1.41092e8i	0.743388	+	0.418479i
$697$	−5.88897e8	+	6.79623e8i	−1.73917	+	2.00710i
$698$	2.12863e8	+	3.06051e7i	0.625941	+	0.0899968i
$699$	−5.01559e8	+	1.02339e8i	−1.46856	+	0.299646i
$700$	1.31299e8	+	1.51527e8i	0.382796	+	0.441771i
$701$	1.61898e8	+	2.51918e8i	0.469989	+	0.731317i	0.992623	−	0.121240i	$-0.0386870\pi$
$701$	1.61898e8	+	2.51918e8i	0.469989	+	0.731317i	−0.522634	+	0.852557i	$0.675051\pi$
$702$	2.44138e8	−	8.04269e7i	0.705707	−	0.232482i
$703$	1.44800e8	+	1.67108e8i	0.416776	+	0.480985i
$704$	−3.93169e7	−	1.33901e8i	−0.112684	−	0.383765i
$705$	−3.83670e8	−	8.86693e7i	−1.09494	−	0.253050i
$706$	6.00636e7	−	6.93171e7i	0.170686	−	0.196982i
$707$	−2.83375e8	−	1.29413e8i	−0.801868	−	0.366201i
$708$	−2.33152e8	−	9.04097e7i	−0.656961	−	0.254751i
$709$	−1.93319e8	−	4.23310e8i	−0.542420	−	1.18774i	−0.960232	−	0.279202i	$-0.909930\pi$
$709$	−1.93319e8	−	4.23310e8i	−0.542420	−	1.18774i	0.417812	−	0.908534i	$-0.362797\pi$
$710$	1.28551e7	−	1.84829e6i	0.0359170	−	0.00516409i
$711$	1.93127e8	+	1.76286e8i	0.537322	+	0.490466i
$712$	−6.18951e8			−1.71481
$713$	−4.02435e7	+	1.93512e7i	−0.111027	+	0.0533873i
$714$	3.17718e7	−	3.75901e8i	0.0872864	−	1.03271i
$715$	−2.01113e8	−	1.29248e8i	−0.550203	−	0.353594i
$716$	−1.82076e8	+	2.61786e7i	−0.496036	+	0.0713192i
$717$	1.18897e8	+	3.31807e8i	0.322562	+	0.900178i
$718$	−4.21336e8	−	1.23715e8i	−1.13830	−	0.334234i
$719$	−2.87731e8	−	1.31402e8i	−0.774106	−	0.353522i	−0.0111204	−	0.999938i	$-0.503540\pi$
$719$	−2.87731e8	−	1.31402e8i	−0.774106	−	0.353522i	−0.762985	+	0.646416i	$0.776267\pi$
$720$	1.79475e8	+	2.18276e8i	0.480848	+	0.584802i
$721$	1.77443e7	−	1.23414e8i	0.0473426	−	0.329275i
$722$	−1.48759e7	−	5.06628e7i	−0.0395251	−	0.134610i
$723$	4.33112e7	−	3.15574e7i	0.114600	−	0.0835000i
$724$	−1.12372e8	+	7.22173e7i	−0.296104	+	0.190294i
$725$	3.22141e8	+	5.01262e8i	0.845342	+	1.31538i
$726$	1.47301e8	+	2.02164e8i	0.384942	+	0.528316i
$727$	5.14708e8	−	1.51132e8i	1.33955	−	0.393326i	0.468039	−	0.883708i	$-0.344961\pi$
$727$	5.14708e8	−	1.51132e8i	1.33955	−	0.393326i	0.871508	+	0.490382i	$0.163143\pi$
$728$	−2.91549e8	−	4.19185e7i	−0.755645	−	0.108645i
$729$	3.63816e8	−	1.33163e8i	0.939074	−	0.343716i
$730$	−4.10645e7	+	8.99187e7i	−0.105560	+	0.231143i
$731$	−1.22419e8	+	4.16922e8i	−0.313400	+	1.06734i
$732$	4.45053e7	−	1.59476e7i	0.113469	−	0.0406596i
$733$	−1.03751e8	−	7.21603e8i	−0.263439	−	1.83226i	−0.506493	−	0.862244i	$-0.669058\pi$
$733$	−1.03751e8	−	7.21603e8i	−0.263439	−	1.83226i	0.243054	−	0.970013i	$-0.421851\pi$
$734$	3.69992e7	−	5.75718e7i	0.0935629	−	0.145587i
$735$	−3.16097e8	−	2.67170e7i	−0.796082	−	0.0672861i
$736$	1.90100e8	−	2.28376e8i	0.476812	−	0.572818i
$737$			4.89381e7i			0.122249i
$738$	−3.34111e8	−	3.04976e8i	−0.831232	−	0.758747i
$739$	−6.73428e7	−	4.68380e8i	−0.166862	−	1.16055i	−0.885320	−	0.464982i	$-0.846061\pi$
$739$	−6.73428e7	−	4.68380e8i	−0.166862	−	1.16055i	0.718458	−	0.695570i	$-0.244848\pi$
$740$	1.49632e8	−	6.83345e7i	0.369257	−	0.168634i
$741$	−1.53499e8	+	3.95849e8i	−0.377269	+	0.972915i
$742$	8.39988e7	−	1.83932e8i	0.205618	−	0.450241i
$743$	3.00135e8	+	2.60068e8i	0.731728	+	0.634046i	0.938873	−	0.344264i	$-0.111872\pi$
$743$	3.00135e8	+	2.60068e8i	0.731728	+	0.634046i	−0.207144	+	0.978310i	$0.566417\pi$
$744$	1.23873e7	−	5.35996e7i	0.0300786	−	0.130150i
$745$	5.48128e7	−	1.60945e7i	0.132560	−	0.0389232i
$746$	3.73182e8	−	3.23364e8i	0.898885	−	0.778889i
$747$	−2.89743e8	−	6.80451e8i	−0.695105	−	1.63243i
$748$	1.01637e8	−	6.53185e7i	0.242856	−	0.156074i
$749$	6.51358e7	−	5.64405e7i	0.155015	−	0.134321i
$750$	1.11391e8	+	5.45926e8i	0.264039	+	1.29405i
$751$	−7.02086e7	+	4.88312e8i	−0.165757	+	1.15286i	0.721779	+	0.692123i	$0.243325\pi$
$751$	−7.02086e7	+	4.88312e8i	−0.165757	+	1.15286i	−0.887536	+	0.460739i	$0.847585\pi$
$752$	9.15350e7	+	7.93155e7i	0.215245	+	0.186511i
$753$	3.05426e8	−	5.42559e8i	0.715353	−	1.27076i
$754$	−2.40435e8	−	7.05980e7i	−0.560897	−	0.164694i
$755$	−5.48398e8	+	2.50445e8i	−1.27425	+	0.581931i
$756$	−1.26318e8	−	1.39722e7i	−0.292347	−	0.0323370i
$757$	−9.62890e7	−	6.18812e7i	−0.221967	−	0.142650i	0.424932	−	0.905225i	$-0.360298\pi$
$757$	−9.62890e7	−	6.18812e7i	−0.221967	−	0.142650i	−0.646899	+	0.762576i	$0.723934\pi$
$758$		−	2.75846e7i		−	0.0633372i
$759$	5.91089e7	−	1.61876e8i	0.135185	−	0.370217i
$760$	−8.94147e8			−2.03689
$761$	−2.49715e7	+	3.88564e7i	−0.0566618	+	0.0881674i	−0.868429	−	0.495814i	$-0.834870\pi$
$761$	−2.49715e7	+	3.88564e7i	−0.0566618	+	0.0881674i	0.811767	+	0.583982i	$0.198506\pi$
$762$	3.24232e7	+	5.53814e8i	0.0732810	+	1.25170i
$763$	−6.06379e7	−	1.32778e8i	−0.136512	−	0.298919i
$764$	3.68158e7	−	1.25383e8i	0.0825572	−	0.281164i
$765$	−7.94446e8	+	1.16864e9i	−1.77452	+	2.61034i
$766$	−4.77655e7	+	5.51244e7i	−0.106274	+	0.122647i
$767$	7.53313e8	+	1.08310e8i	1.66951	+	0.240039i
$768$	8.90959e7	+	4.36657e8i	0.196686	+	0.963954i
$769$	1.29502e7	+	1.49453e7i	0.0284772	+	0.0328644i	0.769810	−	0.638274i	$-0.220351\pi$
$769$	1.29502e7	+	1.49453e7i	0.0284772	+	0.0328644i	−0.741332	+	0.671138i	$0.765806\pi$
$770$	−9.54200e7	−	1.48476e8i	−0.209010	−	0.325226i
$771$	−8.01799e6	+	4.24459e6i	−0.0174945	+	0.00926132i
$772$	6.86395e7	+	7.92142e7i	0.149184	+	0.172168i
$773$	2.18478e7	+	7.44066e7i	0.0473008	+	0.161092i	0.979757	−	0.200192i	$-0.0641567\pi$
$773$	2.18478e7	+	7.44066e7i	0.0473008	+	0.161092i	−0.932456	+	0.361284i	$0.882339\pi$
$774$	−2.08069e8	−	6.69812e7i	−0.448729	−	0.144454i
$775$	7.46325e7	−	8.61305e7i	0.160333	−	0.185034i
$776$	−6.53527e8	−	2.98456e8i	−1.39855	−	0.638697i
$777$	7.28275e7	−	1.87810e8i	0.155250	−	0.400365i
$778$	−2.37212e8	−	5.19421e8i	−0.503729	−	1.10301i
$779$	7.39592e8	−	1.06337e8i	1.56452	−	0.224943i
$780$	2.50387e8	+	1.92536e8i	0.527629	+	0.405721i
$781$	5.09338e6			0.0106919
$782$	−6.20212e8	−	2.68521e8i	−1.29694	−	0.561512i
$783$	−3.65665e8	−	9.45248e7i	−0.761725	−	0.196907i
$784$	8.20815e7	+	5.27506e7i	0.170332	+	0.109466i
$785$	−1.19306e9	+	1.71536e8i	−2.46633	+	0.354605i
$786$	1.81276e8	−	6.49568e7i	0.373312	−	0.133769i
$787$	−3.73799e6	−	1.09757e6i	−0.00766856	−	0.00225169i	0.277896	−	0.960611i	$-0.410363\pi$
$787$	−3.73799e6	−	1.09757e6i	−0.00766856	−	0.00225169i	−0.285565	+	0.958359i	$0.592181\pi$
$788$	−7.20675e7	−	3.29121e7i	−0.147286	−	0.0672631i
$789$	1.93522e8	−	1.88585e8i	0.394004	−	0.383951i
$790$	6.82805e7	−	4.74901e8i	0.138489	−	0.963212i
$791$	−1.04192e8	−	3.54844e8i	−0.210525	−	0.716982i
$792$	1.10127e8	+	1.81507e8i	0.221675	+	0.365358i
$793$	−1.21041e8	+	7.77881e7i	−0.242723	+	0.155989i
$794$	−3.30734e8	−	5.14633e8i	−0.660720	−	1.02810i
$795$	−6.12174e8	+	4.46042e8i	−1.21835	+	0.887718i
$796$	1.92266e8	−	5.64543e7i	0.381208	−	0.111933i
$797$	8.06407e8	+	1.15944e8i	1.59287	+	0.229020i	0.880938	−	0.473232i	$-0.156913\pi$
$797$	8.06407e8	+	1.15944e8i	1.59287	+	0.229020i	0.711929	+	0.702252i	$0.247822\pi$
$798$	−2.24486e8	+	2.18758e8i	−0.441754	+	0.430483i
$799$	−2.51601e8	+	5.50930e8i	−0.493256	+	1.08008i
$800$	−2.13657e8	+	7.27649e8i	−0.417299	+	1.42119i
$801$	7.85503e8	−	2.08756e8i	1.52845	−	0.406202i
$802$	6.72588e7	+	4.67795e8i	0.130385	+	0.906845i
$803$	−2.09595e7	+	3.26136e7i	−0.0404794	+	0.0629872i
$804$	5.44554e6	−	6.44279e7i	0.0104779	−	0.123967i
$805$	2.62701e8	−	6.06769e8i	0.503587	−	1.16315i
$806$			4.79289e7i			0.0915360i
$807$	3.06939e8	+	2.36021e8i	0.584025	+	0.449086i
$808$	−9.78521e7	−	6.80577e8i	−0.185497	−	1.29016i
$809$	−3.92411e8	+	1.79208e8i	−0.741131	+	0.338463i	−0.749947	−	0.661498i	$-0.769921\pi$
$809$	−3.92411e8	+	1.79208e8i	−0.741131	+	0.338463i	0.00881579	+	0.999961i	$0.497194\pi$
$810$	−5.77356e8	−	4.14698e8i	−1.08640	−	0.780328i
$811$	−2.67786e8	+	5.86369e8i	−0.502024	+	1.09928i	0.473782	+	0.880642i	$0.342889\pi$
$811$	−2.67786e8	+	5.86369e8i	−0.502024	+	1.09928i	−0.975806	+	0.218638i	$0.929839\pi$
$812$	9.36332e7	+	8.11336e7i	0.174889	+	0.151542i
$813$	7.35132e8	+	1.69895e8i	1.36802	+	0.316162i
$814$	−9.24288e7	+	2.71396e7i	−0.171370	+	0.0503187i
$815$	1.10586e9	−	9.58233e8i	2.04281	−	1.77010i
$816$	3.84132e8	−	2.03353e8i	0.706985	−	0.374266i
$817$	3.03728e8	−	1.95194e8i	0.556954	−	0.357933i
$818$	2.66794e7	−	2.31178e7i	0.0487434	−	0.0422364i
$819$	3.84139e8	−	4.51338e7i	0.699257	−	0.0821580i
$820$	7.91087e7	−	5.50213e8i	0.143477	−	0.997905i
$821$	−7.96175e8	−	6.89890e8i	−1.43873	−	1.24667i	−0.920109	−	0.391661i	$-0.871901\pi$
$821$	−7.96175e8	−	6.89890e8i	−1.43873	−	1.24667i	−0.518620	−	0.855005i	$-0.673554\pi$
$822$	4.39329e8	+	2.47314e8i	0.790997	+	0.445280i
$823$	−1.11079e8	−	3.26159e7i	−0.199267	−	0.0585099i	0.180576	−	0.983561i	$-0.442204\pi$
$823$	−1.11079e8	−	3.26159e7i	−0.199267	−	0.0585099i	−0.379843	+	0.925051i	$0.624022\pi$
$824$	2.50322e8	−	1.14318e8i	0.447421	−	0.204330i
$825$	2.57054e7	+	4.39069e8i	0.0457787	+	0.781936i
$826$	4.72674e8	+	3.03769e8i	0.838730	+	0.539019i
$827$			8.23610e8i			1.45615i	0.685499	+	0.728074i	$0.259584\pi$
$827$			8.23610e8i			1.45615i	−0.685499	+	0.728074i	$0.740416\pi$
$828$	−9.58304e7	+	2.06535e8i	−0.168816	+	0.363833i
$829$	−6.47183e7			−0.113596			−0.0567981	−	0.998386i	$-0.518089\pi$
$829$	−6.47183e7			−0.113596			−0.0567981	+	0.998386i	$0.518089\pi$
$830$	−7.33645e8	+	1.14157e9i	−1.28307	+	1.99650i
$831$	−1.30850e8	+	7.66062e6i	−0.228018	+	0.0133494i
$832$	−2.33108e8	−	5.10435e8i	−0.404750	−	0.886280i
$833$	−1.37460e8	+	4.68146e8i	−0.237816	+	0.809928i
$834$	1.09015e8	−	1.93654e8i	0.187926	−	0.333833i
$835$	−6.00892e8	+	6.93466e8i	−1.03214	+	1.19115i
$836$	−9.93640e7	−	1.42864e7i	−0.170063	−	0.0244514i
$837$	2.35716e6	+	7.22004e7i	0.00401988	+	0.123130i
$838$	1.52324e8	+	1.75792e8i	0.258844	+	0.298721i
$839$	1.12392e8	+	1.74885e8i	0.190304	+	0.296119i	0.923274	−	0.384142i	$-0.125503\pi$
$839$	1.12392e8	+	1.74885e8i	0.190304	+	0.296119i	−0.732970	+	0.680261i	$0.761866\pi$
$840$	3.81111e8	+	7.19914e8i	0.643004	+	1.21463i
$841$	−1.48411e8	−	1.71275e8i	−0.249504	−	0.287943i
$842$	2.08436e8	+	7.09868e8i	0.349170	+	1.18916i
$843$	9.22620e7	−	3.99215e8i	0.154007	−	0.666384i
$844$	−1.45810e8	+	1.68273e8i	−0.242527	+	0.279891i
$845$	7.41885e7	+	3.38808e7i	0.122961	+	0.0561543i
$846$	−2.73779e8	−	1.33685e8i	−0.452156	−	0.220787i
$847$	1.56356e8	+	3.42372e8i	0.257315	+	0.563441i
$848$	2.30598e8	−	3.31550e7i	0.378154	−	0.0543703i
$849$	2.51368e8	−	3.26897e8i	0.410759	−	0.534181i
$850$	1.72490e9			2.80871
$851$	−2.77365e8	−	2.30878e8i	−0.450052	−	0.374622i
$852$	−6.70552e6	−	566761.i	−0.0108421	−	0.000916392i
$853$	3.48933e8	+	2.24245e8i	0.562205	+	0.361307i	0.790668	−	0.612246i	$-0.209734\pi$
$853$	3.48933e8	+	2.24245e8i	0.562205	+	0.361307i	−0.228463	+	0.973553i	$0.573370\pi$
$854$	−1.05142e8	+	1.51172e7i	−0.168812	+	0.0242716i
$855$	1.13475e9	−	3.01572e8i	1.81552	−	0.482496i
$856$	1.82519e8	+	5.35924e7i	0.290996	+	0.0854441i
$857$	−7.79412e8	−	3.55945e8i	−1.23830	−	0.565511i	−0.314814	−	0.949153i	$-0.601942\pi$
$857$	−7.79412e8	−	3.55945e8i	−1.23830	−	0.565511i	−0.923482	+	0.383643i	$0.874669\pi$
$858$	−1.29090e8	−	1.32470e8i	−0.204377	−	0.209728i
$859$	1.44592e7	−	1.00566e8i	0.0228121	−	0.158661i	−0.975231	−	0.221188i	$-0.929007\pi$
$859$	1.44592e7	−	1.00566e8i	0.0228121	−	0.158661i	0.998043	+	0.0625264i	$0.0199158\pi$
$860$	−7.56718e7	−	2.57715e8i	−0.118970	−	0.405176i
$861$	−4.00851e8	−	5.50151e8i	−0.628020	−	0.861931i
$862$	6.22109e8	−	3.99805e8i	0.971281	−	0.624204i
$863$	−1.33833e8	−	2.08248e8i	−0.208224	−	0.324003i	0.721396	−	0.692523i	$-0.243501\pi$
$863$	−1.33833e8	−	2.08248e8i	−0.208224	−	0.324003i	−0.929620	+	0.368520i	$0.879865\pi$
$864$	−2.13850e8	−	4.30509e8i	−0.331565	−	0.667485i
$865$	4.13334e7	−	1.21366e7i	0.0638635	−	0.0187520i
$866$	−3.74735e8	−	5.38788e7i	−0.576993	−	0.0829591i
$867$	1.06203e9	+	1.08984e9i	1.62960	+	1.67227i
$868$	9.84409e6	−	2.15555e7i	0.0150528	−	0.0329610i
$869$	5.30116e7	−	1.80541e8i	0.0807814	−	0.275116i
$870$	2.33766e8	+	6.52373e8i	0.354996	+	0.990691i
$871$	2.80047e7	+	1.94777e8i	0.0423815	+	0.294770i
$872$	1.74179e8	−	2.71027e8i	0.262691	−	0.408756i
$873$	9.30044e8	+	1.58349e8i	1.39785	+	0.237997i
$874$	2.43352e8	+	5.06086e8i	0.364503	+	0.758037i
$875$			8.38394e8i			1.25148i
$876$	3.12226e7	−	4.06041e7i	0.0464468	−	0.0604029i
$877$	1.05797e8	+	7.35836e8i	0.156847	+	1.09089i	0.904398	+	0.426689i	$0.140320\pi$
$877$	1.05797e8	+	7.35836e8i	0.156847	+	1.09089i	−0.747552	+	0.664204i	$0.768771\pi$
$878$	1.96739e8	−	8.98476e7i	0.290674	−	0.132747i
$879$	1.11117e9	+	4.30879e8i	1.63611	+	0.634437i
$880$	8.44736e7	−	1.84971e8i	0.123958	−	0.271429i
$881$	−4.54271e8	−	3.93628e8i	−0.664336	−	0.575650i	0.256049	−	0.966664i	$-0.417579\pi$
$881$	−4.54271e8	−	3.93628e8i	−0.664336	−	0.575650i	−0.920385	+	0.391014i	$0.872125\pi$
$882$	−2.33633e8	−	7.52106e7i	−0.340508	−	0.109616i
$883$	−3.88782e8	+	1.14157e8i	−0.564709	+	0.165813i	−0.551612	−	0.834101i	$-0.685987\pi$
$883$	−3.88782e8	+	1.14157e8i	−0.564709	+	0.165813i	−0.0130967	+	0.999914i	$0.504169\pi$
$884$	3.67146e8	−	3.18133e8i	0.531473	−	0.460524i
$885$	−9.84724e8	−	1.86013e9i	−1.42064	−	2.68358i
$886$	2.51531e8	−	1.61649e8i	0.361651	−	0.232419i
$887$	4.78616e8	−	4.14724e8i	0.685830	−	0.594275i	−0.240653	−	0.970611i	$-0.577362\pi$
$887$	4.78616e8	−	4.14724e8i	0.685830	−	0.594275i	0.926483	+	0.376336i	$0.122816\pi$
$888$	4.35617e8	−	8.88838e7i	0.622108	−	0.126936i
$889$	−1.18800e8	+	8.26269e8i	−0.169087	+	1.17602i
$890$	−1.12705e9	−	9.76595e8i	−1.59872	−	1.38530i
$891$	−2.00978e8	−	1.93206e8i	−0.284129	−	0.273141i
$892$	−7.02268e7	−	2.06205e7i	−0.0989483	−	0.0290539i
$893$	4.57764e8	−	2.09054e8i	0.642816	−	0.293564i
$894$	4.41242e7	−	2.58326e6i	0.0617539	−	0.00361540i
$895$	−1.30243e9	−	8.37024e8i	−1.81671	−	1.16753i
$896$		−	2.11328e7i		−	0.0293788i
$897$	1.42625e8	−	6.78100e8i	0.197614	−	0.939542i
$898$	−1.07886e9			−1.48983
$899$	3.80739e7	−	5.92441e7i	0.0524020	−	0.0815391i
$900$	1.50154e7	−	5.80903e8i	0.0205973	−	0.796849i
$901$	4.83953e8	+	1.05971e9i	0.661650	+	1.44881i
$902$	−9.17104e7	+	3.12337e8i	−0.124968	+	0.425602i
$903$	−2.86616e8	−	1.61346e8i	−0.389258	−	0.219127i
$904$	5.34527e8	−	6.16877e8i	0.723543	−	0.835013i
$905$	−1.11281e9	−	1.59999e8i	−1.50133	−	0.215859i
$906$	−4.57039e8	+	9.32547e7i	−0.614566	+	0.125397i
$907$	3.39895e8	+	3.92260e8i	0.455536	+	0.525717i	0.936332	−	0.351116i	$-0.114198\pi$
$907$	3.39895e8	+	3.92260e8i	0.455536	+	0.525717i	−0.480796	+	0.876833i	$0.659652\pi$
$908$	−7.49676e6	−	1.16652e7i	−0.0100142	−	0.0155824i
$909$	3.53723e8	+	8.30708e8i	0.470947	+	1.10600i
$910$	−4.64743e8	−	5.36342e8i	−0.616721	−	0.711734i
$911$	−3.02816e8	−	1.03130e9i	−0.400519	−	1.36404i	−0.875147	−	0.483857i	$-0.839236\pi$
$911$	−3.02816e8	−	1.03130e9i	−0.400519	−	1.36404i	0.474628	−	0.880187i	$-0.342583\pi$
$912$	−3.51863e8	−	8.13185e7i	−0.463862	−	0.107202i
$913$	−3.48509e8	+	4.02201e8i	−0.457932	+	0.528482i
$914$	2.67243e8	+	1.22046e8i	0.350000	+	0.159840i
$915$	3.70987e8	+	1.43858e8i	0.484278	+	0.187789i
$916$	1.12065e8	+	2.45387e8i	0.145808	+	0.319276i
$917$	2.86804e8	−	4.12362e7i	0.371944	−	0.0534774i
$918$	−8.02488e8	+	7.42565e8i	−1.03731	+	0.959857i
$919$	−1.10364e8			−0.142194			−0.0710968	−	0.997469i	$-0.522650\pi$
$919$	−1.10364e8			−0.142194			−0.0710968	+	0.997469i	$0.522650\pi$
$920$	1.44008e9	−	2.36262e8i	1.84937	−	0.303410i
$921$	9.86908e7	−	1.16764e9i	0.126327	−	1.49462i
$922$	1.74565e8	+	1.12186e8i	0.222723	+	0.143135i
$923$	2.02720e7	−	2.91467e6i	0.0257805	−	0.00370668i
$924$	3.08492e7	+	8.60911e7i	0.0391046	+	0.109130i
$925$	8.83737e8	+	2.59489e8i	1.11660	+	0.327863i
$926$	3.43711e8	+	1.56968e8i	0.432873	+	0.197686i
$927$	−2.79123e8	+	2.29506e8i	−0.350394	+	0.288108i
$928$	−6.66913e7	+	4.63848e8i	−0.0834498	+	0.580406i
$929$	−9.91715e7	−	3.37747e8i	−0.123691	−	0.421254i	0.874243	−	0.485488i	$-0.161358\pi$
$929$	−9.91715e7	−	3.37747e8i	−0.123691	−	0.421254i	−0.997935	+	0.0642335i	$0.979540\pi$
$930$	1.07127e8	−	7.80547e7i	0.133183	−	0.0970398i
$931$	3.41045e8	−	2.19176e8i	0.422632	−	0.271609i
$932$	−2.63115e8	−	4.09415e8i	−0.325011	−	0.505727i
$933$	2.52981e8	+	3.47205e8i	0.311489	+	0.427505i
$934$	−2.84909e8	+	8.36570e7i	−0.349676	+	0.102674i
$935$	1.00651e9	+	1.44714e8i	1.23135	+	0.177042i
$936$	5.42178e8	+	6.59392e8i	0.661172	+	0.804111i
$937$	3.60086e8	−	7.88478e8i	0.437711	−	0.958453i	−0.554302	−	0.832316i	$-0.687015\pi$
$937$	3.60086e8	−	7.88478e8i	0.437711	−	0.958453i	0.992013	−	0.126137i	$-0.0402580\pi$
$938$	−4.09293e7	+	1.39392e8i	−0.0495936	+	0.168900i
$939$	−1.05768e8	+	3.79002e7i	−0.127750	+	0.0457767i
$940$	−5.32800e7	−	3.70571e8i	−0.0641476	−	0.446157i
$941$	−6.50175e8	+	1.01169e9i	−0.780299	+	1.21417i	0.192221	+	0.981352i	$0.438431\pi$
$941$	−6.50175e8	+	1.01169e9i	−0.780299	+	1.21417i	−0.972520	+	0.232818i	$0.925206\pi$
$942$	−9.29262e8	−	7.85427e7i	−1.11169	−	0.0939621i
$943$	−1.16306e9	+	3.66686e8i	−1.38697	+	0.437280i
$944$			6.47356e8i			0.769533i
$945$	−7.26471e8	−	7.85094e8i	−0.860840	−	0.930307i
$946$	2.23849e7	+	1.55690e8i	0.0264412	+	0.183903i
$947$	−6.97701e8	+	3.18629e8i	−0.821522	+	0.375177i	−0.781409	−	0.624019i	$-0.785499\pi$
$947$	−6.97701e8	+	3.18629e8i	−0.821522	+	0.375177i	−0.0401126	+	0.999195i	$0.512772\pi$
$948$	−8.98802e7	+	2.31786e8i	−0.105497	+	0.272059i
$949$	−6.47571e7	+	1.41798e8i	−0.0757685	+	0.165910i
$950$	−1.08314e9	−	9.38549e8i	−1.26332	−	1.09468i
$951$	−2.23657e8	+	9.67759e8i	−0.260041	+	1.12519i
$952$	1.20211e9	−	3.52971e8i	1.39326	−	0.409098i
$953$	−9.04575e8	+	7.83819e8i	−1.04512	+	0.905601i	−0.995650	−	0.0931748i	$-0.970298\pi$
$953$	−9.04575e8	+	7.83819e8i	−1.04512	+	0.905601i	−0.0494693	+	0.998776i	$0.515753\pi$
$954$	−5.39192e8	+	2.29593e8i	−0.621010	+	0.264432i
$955$	9.25248e8	−	5.94621e8i	1.06230	−	0.682700i
$956$	−2.53252e8	+	2.19444e8i	−0.289854	+	0.251160i
$957$	5.43345e7	+	2.66292e8i	0.0619926	+	0.303824i
$958$	1.61626e7	−	1.12413e8i	0.0183829	−	0.127856i
$959$	5.73326e8	+	4.96789e8i	0.650048	+	0.563270i
$960$	−7.61255e8	+	1.35229e9i	−0.860431	+	1.52847i
$961$	8.38629e8	+	2.46244e8i	0.944931	+	0.277457i
$962$	−3.52342e8	+	1.60909e8i	−0.395767	+	0.180741i
$963$	−2.49708e8	−	6.45454e6i	−0.279610	−	0.00722748i
$964$	4.28604e7	+	2.75447e7i	0.0478438	+	0.0307473i
$965$			8.82183e8i			0.981695i
$966$	3.03747e8	−	4.11641e8i	0.336961	−	0.456654i
$967$	1.24413e9			1.37590			0.687950	−	0.725759i	$-0.258511\pi$
$967$	1.24413e9			1.37590			0.687950	+	0.725759i	$0.258511\pi$
$968$	−4.49124e8	+	6.98850e8i	−0.495154	+	0.770474i
$969$	−1.05546e8	−	1.80281e9i	−0.116004	−	1.98143i
$970$	−7.19099e8	−	1.57461e9i	−0.787905	−	1.72527i
$971$	1.49012e8	−	5.07488e8i	0.162766	−	0.554330i	−0.837206	−	0.546887i	$-0.815813\pi$
$971$	1.49012e8	−	5.07488e8i	0.162766	−	0.554330i	0.999972	−	0.00744261i	$-0.00236908\pi$
$972$	2.43092e8	+	2.76722e8i	0.264711	+	0.301332i
$973$	2.18982e8	−	2.52719e8i	0.237723	−	0.274347i
$974$	5.77948e8	+	8.30964e7i	0.625478	+	0.0899301i
$975$	3.53565e8	+	1.73282e9i	0.381466	+	1.86956i
$976$	−8.01453e7	−	9.24926e7i	−0.0862043	−	0.0994850i
$977$	8.92305e8	+	1.38845e9i	0.956819	+	1.48884i	0.870260	+	0.492593i	$0.163951\pi$
$977$	8.92305e8	+	1.38845e9i	0.956819	+	1.48884i	0.0865589	+	0.996247i	$0.472413\pi$
$978$	1.00059e9	−	5.29695e8i	1.06964	−	0.566251i
$979$	−3.83003e8	−	4.42009e8i	−0.408182	−	0.471067i
$980$	−8.49690e7	−	2.89378e8i	−0.0902780	−	0.307459i
$981$	−1.29637e8	+	4.02703e8i	−0.137317	+	0.426558i
$982$	−6.67822e8	+	7.70707e8i	−0.705222	+	0.813870i
$983$	−7.44572e8	−	3.40035e8i	−0.783874	−	0.357983i	−0.0170617	−	0.999854i	$-0.505431\pi$
$983$	−7.44572e8	−	3.40035e8i	−0.783874	−	0.357983i	−0.766813	+	0.641871i	$0.778158\pi$
$984$	5.43171e8	−	1.40075e9i	0.570100	−	1.47019i
$985$	−2.77006e8	−	6.06559e8i	−0.289855	−	0.634693i
$986$	1.05502e9	−	1.51688e8i	1.10060	−	0.158242i
$987$	−3.63429e8	−	2.79459e8i	−0.377979	−	0.290648i
$988$	−4.03650e8			−0.418538
$989$	−4.37598e8	+	3.94628e8i	−0.452362	+	0.407942i
$990$	−8.58563e7	+	5.04268e8i	−0.0884844	+	0.519703i
$991$	−1.25983e9	−	8.09645e8i	−1.29447	−	0.831905i	−0.301872	−	0.953349i	$-0.597611\pi$
$991$	−1.25983e9	−	8.09645e8i	−1.29447	−	0.831905i	−0.992598	+	0.121443i	$0.961248\pi$
$992$	8.87191e7	−	1.27559e7i	0.0908829	−	0.0130670i
$993$	4.05073e8	−	1.45150e8i	0.413700	−	0.148242i
$994$	1.45077e7	+	4.25984e6i	0.0147720	+	0.00433745i
$995$	1.53412e9	+	7.00608e8i	1.55736	+	0.711223i
$996$	5.03572e8	−	4.90724e8i	0.509664	−	0.496660i
$997$	2.49610e7	−	1.73607e8i	0.0251870	−	0.175179i	−0.973345	−	0.229346i	$-0.926341\pi$
$997$	2.49610e7	−	1.73607e8i	0.0251870	−	0.175179i	0.998532	+	0.0541669i	$0.0172503\pi$
$998$	−1.27618e8	−	4.34627e8i	−0.128387	−	0.437245i
$999$	−5.22858e8	+	2.59723e8i	−0.524429	+	0.260504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.16	✓	460
3.2	odd	2	inner	69.7.h.a.2.31	yes	460
23.12	even	11	inner	69.7.h.a.35.31	yes	460
69.35	odd	22	inner	69.7.h.a.35.16	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.16	✓	460	1.1	even	1	trivial
69.7.h.a.2.31	yes	460	3.2	odd	2	inner
69.7.h.a.35.16	yes	460	69.35	odd	22	inner
69.7.h.a.35.31	yes	460	23.12	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.34719 + 5.20832i) q^{2} +(26.9538 - 1.57802i) q^{3} +(10.6636 + 23.3500i) q^{4} +(-60.8684 + 207.299i) q^{5} +(-82.0007 + 145.666i) q^{6} +(-164.718 + 190.095i) q^{7} +(-549.508 - 79.0073i) q^{8} +(724.020 - 85.0674i) q^{9} +O(q^{10})\)	\(q+(-3.34719 + 5.20832i) q^{2} +(26.9538 - 1.57802i) q^{3} +(10.6636 + 23.3500i) q^{4} +(-60.8684 + 207.299i) q^{5} +(-82.0007 + 145.666i) q^{6} +(-164.718 + 190.095i) q^{7} +(-549.508 - 79.0073i) q^{8} +(724.020 - 85.0674i) q^{9} +(-875.940 - 1010.89i) q^{10} +(-283.610 - 441.306i) q^{11} +(324.272 + 612.545i) q^{12} +(-1381.32 - 1594.13i) q^{13} +(-438.733 - 1494.19i) q^{14} +(-1313.52 + 5683.55i) q^{15} +(1174.95 - 1355.97i) q^{16} +(8161.28 + 3727.13i) q^{17} +(-1980.37 + 4055.66i) q^{18} +(-3096.85 - 6781.15i) q^{19} +(-5489.50 + 789.271i) q^{20} +(-4139.81 + 5383.71i) q^{21} +3247.76 q^{22} +(6779.47 + 10103.2i) q^{23} +(-14936.0 - 1262.42i) q^{24} +(-26123.2 - 16788.4i) q^{25} +(12926.3 - 1858.52i) q^{26} +(19380.9 - 3435.41i) q^{27} +(-6195.20 - 1819.07i) q^{28} +(-17454.4 - 7971.14i) q^{29} +(-25205.2 - 25865.1i) q^{30} +(-522.312 + 3632.76i) q^{31} +(-6880.46 - 23432.7i) q^{32} +(-8340.78 - 11447.4i) q^{33} +(-46729.4 + 30031.2i) q^{34} +(-29380.3 - 45716.6i) q^{35} +(9706.98 + 15998.7i) q^{36} +(-28459.3 + 8356.39i) q^{37} +(45684.1 + 6568.39i) q^{38} +(-39747.5 - 40788.2i) q^{39} +(49825.7 - 109103. i) q^{40} +(-28238.1 + 96170.0i) q^{41} +(-14183.4 - 39581.7i) q^{42} +(6892.41 + 47937.8i) q^{43} +(7280.20 - 11328.2i) q^{44} +(-26435.5 + 155266. i) q^{45} +(-75312.9 + 1492.35i) q^{46} +67505.3i q^{47} +(29529.7 - 38402.6i) q^{48} +(7739.22 + 53827.5i) q^{49} +(174878. - 79864.3i) q^{50} +(225859. + 87581.9i) q^{51} +(22493.1 - 49253.1i) q^{52} +(98130.9 + 85030.9i) q^{53} +(-46978.7 + 112441. i) q^{54} +(108745. - 31930.4i) q^{55} +(105533. - 91444.6i) q^{56} +(-94172.7 - 177891. i) q^{57} +(99939.2 - 64227.1i) q^{58} +(-272678. + 236277. i) q^{59} +(-146718. + 29936.4i) q^{60} +(9707.52 - 67517.3i) q^{61} +(-17172.3 - 14879.9i) q^{62} +(-103088. + 151644. i) q^{63} +(255253. + 74949.0i) q^{64} +(414540. - 189314. i) q^{65} +(87539.6 - 5125.03i) q^{66} +(-78480.4 - 50436.3i) q^{67} +230311. i q^{68} +(198676. + 261622. i) q^{69} +336448. q^{70} +(-5249.31 + 8168.08i) q^{71} +(-404575. - 10457.6i) q^{72} +(-30700.2 - 67224.0i) q^{73} +(51735.6 - 176195. i) q^{74} +(-730613. - 411288. i) q^{75} +(125316. - 144623. i) q^{76} +(130606. + 18778.3i) q^{77} +(345481. - 70492.2i) q^{78} +(234893. + 271081. i) q^{79} +(209573. + 326102. i) q^{80} +(516968. - 123181. i) q^{81} +(-406366. - 468972. i) q^{82} +(-285817. - 973405. i) q^{83} +(-169855. - 39254.9i) q^{84} +(-1.26939e6 + 1.46496e6i) q^{85} +(-272745. - 124559. i) q^{86} +(-483041. - 187310. i) q^{87} +(120980. + 264908. i) q^{88} +(1.10356e6 - 158668. i) q^{89} +(-720192. - 657390. i) q^{90} +530565. q^{91} +(-163616. + 266037. i) q^{92} +(-8345.75 + 98741.1i) q^{93} +(-351589. - 225953. i) q^{94} +(1.59422e6 - 229215. i) q^{95} +(-222432. - 620744. i) q^{96} +(1.24172e6 + 364601. i) q^{97} +(-306255. - 139862. i) q^{98} +(-242880. - 295388. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Introduction

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