LMFDB - Embedded newform 43.7.d.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	43.7
Dual form			43.7.d.a.37.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.28699i q^{2} +(-41.9299 + 24.2082i) q^{3} +45.6217 q^{4} +(-171.014 + 98.7351i) q^{5} +(103.780 + 179.753i) q^{6} +(223.732 + 129.172i) q^{7} -469.947i q^{8} +(807.577 - 1398.76i) q^{9} +O(q^{10})$	\(q-4.28699i q^{2} +(-41.9299 + 24.2082i) q^{3} +45.6217 q^{4} +(-171.014 + 98.7351i) q^{5} +(103.780 + 179.753i) q^{6} +(223.732 + 129.172i) q^{7} -469.947i q^{8} +(807.577 - 1398.76i) q^{9} +(423.276 + 733.136i) q^{10} -1622.51 q^{11} +(-1912.91 + 1104.42i) q^{12} +(1102.52 - 1909.63i) q^{13} +(553.758 - 959.138i) q^{14} +(4780.40 - 8279.90i) q^{15} +905.130 q^{16} +(-209.407 + 362.703i) q^{17} +(-5996.49 - 3462.07i) q^{18} +(4693.50 - 2709.79i) q^{19} +(-7801.96 + 4504.46i) q^{20} -12508.1 q^{21} +6955.67i q^{22} +(-9995.93 - 17313.5i) q^{23} +(11376.6 + 19704.8i) q^{24} +(11684.7 - 20238.5i) q^{25} +(-8186.55 - 4726.51i) q^{26} +42904.4i q^{27} +(10207.0 + 5893.04i) q^{28} +(20365.0 + 11757.8i) q^{29} +(-35495.8 - 20493.5i) q^{30} +(7076.11 + 12256.2i) q^{31} -33956.9i q^{32} +(68031.5 - 39278.0i) q^{33} +(1554.90 + 897.724i) q^{34} -51015.1 q^{35} +(36843.0 - 63814.0i) q^{36} +(-14233.3 + 8217.61i) q^{37} +(-11616.9 - 20121.0i) q^{38} +106761. i q^{39} +(46400.3 + 80367.6i) q^{40} +66456.8 q^{41} +53622.0i q^{42} +(-78190.6 - 14407.9i) q^{43} -74021.5 q^{44} +318944. i q^{45} +(-74222.6 + 42852.5i) q^{46} +30699.7 q^{47} +(-37952.0 + 21911.6i) q^{48} +(-25453.8 - 44087.3i) q^{49} +(-86762.4 - 50092.3i) q^{50} -20277.5i q^{51} +(50299.0 - 87120.4i) q^{52} +(-102057. - 176768. i) q^{53} +183931. q^{54} +(277471. - 160198. i) q^{55} +(60703.9 - 105142. i) q^{56} +(-131199. + 227243. i) q^{57} +(50405.4 - 87304.7i) q^{58} -326010. q^{59} +(218090. - 377743. i) q^{60} +(-277713. - 160338. i) q^{61} +(52542.1 - 30335.2i) q^{62} +(361362. - 208632. i) q^{63} -87644.7 q^{64} +435431. i q^{65} +(-168384. - 291650. i) q^{66} +(-110396. - 191211. i) q^{67} +(-9553.49 + 16547.1i) q^{68} +(838256. + 483967. i) q^{69} +218701. i q^{70} +(153277. + 88494.7i) q^{71} +(-657345. - 379518. i) q^{72} +(-470207. - 271474. i) q^{73} +(35228.8 + 61018.1i) q^{74} +1.13147e6i q^{75} +(214126. - 123625. i) q^{76} +(-363007. - 209582. i) q^{77} +457681. q^{78} +(300121. - 519825. i) q^{79} +(-154790. + 89368.0i) q^{80} +(-449916. - 779278. i) q^{81} -284900. i q^{82} +(387964. + 671973. i) q^{83} -570640. q^{84} -82703.1i q^{85} +(-61766.5 + 335203. i) q^{86} -1.13854e6 q^{87} +762492. i q^{88} +(1.01577e6 - 586458. i) q^{89} +1.36731e6 q^{90} +(493340. - 284830. i) q^{91} +(-456031. - 789870. i) q^{92} +(-593401. - 342600. i) q^{93} -131610. i q^{94} +(-535103. + 926826. i) q^{95} +(822037. + 1.42381e6i) q^{96} +417105. q^{97} +(-189002. + 109120. i) q^{98} +(-1.31030e6 + 2.26950e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	4.28699i		−	0.535874i	−0.963436	−	0.267937i	$-0.913658\pi$
$2$		−	4.28699i		−	0.535874i	0.963436	−	0.267937i	$-0.0863419\pi$
$3$	−41.9299	+	24.2082i	−1.55296	+	0.896601i	−0.555060	+	0.831811i	$0.687305\pi$
$3$	−41.9299	+	24.2082i	−1.55296	+	0.896601i	−0.997899	+	0.0647905i	$0.979362\pi$
$4$	45.6217			0.712839
$5$	−171.014	+	98.7351i	−1.36811	+	0.789880i	−0.990687	−	0.136159i	$-0.956524\pi$
$5$	−171.014	+	98.7351i	−1.36811	+	0.789880i	−0.377426	+	0.926040i	$0.623191\pi$
$6$	103.780	+	179.753i	0.480465	+	0.832190i
$7$	223.732	+	129.172i	0.652280	+	0.376594i	0.789329	−	0.613970i	$-0.210428\pi$
$7$	223.732	+	129.172i	0.652280	+	0.376594i	−0.137049	+	0.990564i	$0.543762\pi$
$8$		−	469.947i		−	0.917866i
$9$	807.577	−	1398.76i	1.10779	−	1.91874i
$10$	423.276	+	733.136i	0.423276	+	0.733136i
$11$	−1622.51			−1.21901			−0.609506	−	0.792781i	$-0.708632\pi$
$11$	−1622.51			−1.21901			−0.609506	+	0.792781i	$0.708632\pi$
$12$	−1912.91	+	1104.42i	−1.10701	+	0.639132i
$13$	1102.52	−	1909.63i	0.501831	−	0.869197i	−0.498167	−	0.867081i	$-0.665993\pi$
$13$	1102.52	−	1909.63i	0.501831	−	0.869197i	0.999998	−	0.00211584i	$-0.000673495\pi$
$14$	553.758	−	959.138i	0.201807	−	0.349540i
$15$	4780.40	−	8279.90i	1.41642	−	2.45330i
$16$	905.130			0.220979
$17$	−209.407	+	362.703i	−0.0426230	+	0.0738251i	−0.886550	−	0.462633i	$-0.846905\pi$
$17$	−209.407	+	362.703i	−0.0426230	+	0.0738251i	0.843927	+	0.536458i	$0.180238\pi$
$18$	−5996.49	−	3462.07i	−1.02820	−	0.593634i
$19$	4693.50	−	2709.79i	0.684284	−	0.395071i	−0.117183	−	0.993110i	$-0.537387\pi$
$19$	4693.50	−	2709.79i	0.684284	−	0.395071i	0.801467	+	0.598039i	$0.204053\pi$
$20$	−7801.96	+	4504.46i	−0.975245	+	0.563058i
$21$	−12508.1			−1.35062
$22$			6955.67i			0.653237i
$23$	−9995.93	−	17313.5i	−0.821561	−	1.42298i	−0.904520	−	0.426432i	$-0.859770\pi$
$23$	−9995.93	−	17313.5i	−0.821561	−	1.42298i	0.0829589	−	0.996553i	$-0.473563\pi$
$24$	11376.6	+	19704.8i	0.822959	+	1.42541i
$25$	11684.7	−	20238.5i	0.747822	−	1.29527i
$26$	−8186.55	−	4726.51i	−0.465780	−	0.268918i
$27$			42904.4i			2.17977i
$28$	10207.0	+	5893.04i	0.464971	+	0.268451i
$29$	20365.0	+	11757.8i	0.835009	+	0.482092i	0.855564	−	0.517696i	$-0.173210\pi$
$29$	20365.0	+	11757.8i	0.835009	+	0.482092i	−0.0205559	+	0.999789i	$0.506544\pi$
$30$	−35495.8	−	20493.5i	−1.31466	−	0.759020i
$31$	7076.11	+	12256.2i	0.237525	+	0.411406i	0.960004	−	0.279988i	$-0.0903305\pi$
$31$	7076.11	+	12256.2i	0.237525	+	0.411406i	−0.722478	+	0.691393i	$0.756997\pi$
$32$		−	33956.9i		−	1.03628i
$33$	68031.5	−	39278.0i	1.89308	−	1.09297i
$34$	1554.90	+	897.724i	0.0395610	+	0.0228405i
$35$	−51015.1			−1.18986
$36$	36843.0	−	63814.0i	0.789674	−	1.36776i
$37$	−14233.3	+	8217.61i	−0.280997	+	0.162233i	−0.633874	−	0.773436i	$-0.718536\pi$
$37$	−14233.3	+	8217.61i	−0.280997	+	0.162233i	0.352878	+	0.935669i	$0.385203\pi$
$38$	−11616.9	−	20121.0i	−0.211708	−	0.366690i
$39$			106761.i			1.79977i
$40$	46400.3	+	80367.6i	0.725004	+	1.25574i
$41$	66456.8			0.964246			0.482123	−	0.876103i	$-0.339866\pi$
$41$	66456.8			0.964246			0.482123	+	0.876103i	$0.339866\pi$
$42$			53622.0i			0.723761i
$43$	−78190.6	−	14407.9i	−0.983443	−	0.181215i
$43$	−78190.6	−	14407.9i	−0.983443	−	0.181215i
$44$	−74021.5			−0.868960
$45$			318944.i			3.50008i
$46$	−74222.6	+	42852.5i	−0.762540	+	0.440253i
$47$	30699.7			0.295693			0.147847	−	0.989010i	$-0.452766\pi$
$47$	30699.7			0.295693			0.147847	+	0.989010i	$0.452766\pi$
$48$	−37952.0	+	21911.6i	−0.343171	+	0.198130i
$49$	−25453.8	−	44087.3i	−0.216354	−	0.374736i
$50$	−86762.4	−	50092.3i	−0.694099	−	0.400738i
$51$		−	20277.5i		−	0.152863i
$52$	50299.0	−	87120.4i	0.357725	−	0.619598i
$53$	−102057.	−	176768.i	−0.685511	−	1.18734i	−0.973276	−	0.229639i	$-0.926246\pi$
$53$	−102057.	−	176768.i	−0.685511	−	1.18734i	0.287765	−	0.957701i	$-0.407088\pi$
$54$	183931.			1.16808
$55$	277471.	−	160198.i	1.66775	−	0.962874i
$56$	60703.9	−	105142.i	0.345663	−	0.598706i
$57$	−131199.	+	227243.i	−0.708443	+	1.22706i
$58$	50405.4	−	87304.7i	0.258341	−	0.447459i
$59$	−326010.			−1.58736			−0.793680	−	0.608336i	$-0.791837\pi$
$59$	−326010.			−1.58736			−0.793680	+	0.608336i	$0.791837\pi$
$60$	218090.	−	377743.i	1.00968	−	1.74881i
$61$	−277713.	−	160338.i	−1.22351	−	0.706392i	−0.257843	−	0.966187i	$-0.583012\pi$
$61$	−277713.	−	160338.i	−1.22351	−	0.706392i	−0.965664	+	0.259795i	$0.916345\pi$
$62$	52542.1	−	30335.2i	0.220461	−	0.127283i
$63$	361362.	−	208632.i	1.44517	−	0.834372i
$64$	−87644.7			−0.334338
$65$			435431.i			1.58555i
$66$	−168384.	−	291650.i	−0.585693	−	1.01445i
$67$	−110396.	−	191211.i	−0.367052	−	0.635752i	0.622051	−	0.782976i	$-0.286299\pi$
$67$	−110396.	−	191211.i	−0.367052	−	0.635752i	−0.989103	+	0.147224i	$0.952966\pi$
$68$	−9553.49	+	16547.1i	−0.0303833	+	0.0526254i
$69$	838256.	+	483967.i	2.55170	+	1.47322i
$70$			218701.i			0.637614i
$71$	153277.	+	88494.7i	0.428256	+	0.247253i	0.698603	−	0.715509i	$-0.253805\pi$
$71$	153277.	+	88494.7i	0.428256	+	0.247253i	−0.270348	+	0.962763i	$0.587139\pi$
$72$	−657345.	−	379518.i	−1.76115	−	1.01680i
$73$	−470207.	−	271474.i	−1.20871	−	0.697846i	−0.246229	−	0.969212i	$-0.579191\pi$
$73$	−470207.	−	271474.i	−1.20871	−	0.697846i	−0.962476	+	0.271366i	$0.912525\pi$
$74$	35228.8	+	61018.1i	0.0869367	+	0.150579i
$75$			1.13147e6i			2.68199i
$76$	214126.	−	123625.i	0.487784	−	0.281622i
$77$	−363007.	−	209582.i	−0.795138	−	0.459073i
$78$	457681.			0.964450
$79$	300121.	−	519825.i	0.608717	−	1.05433i	−0.382735	−	0.923858i	$-0.625018\pi$
$79$	300121.	−	519825.i	0.608717	−	1.05433i	0.991452	−	0.130471i	$-0.0416490\pi$
$80$	−154790.	+	89368.0i	−0.302324	+	0.174547i
$81$	−449916.	−	779278.i	−0.846597	−	1.46635i
$82$		−	284900.i		−	0.516714i
$83$	387964.	+	671973.i	0.678511	+	1.17522i	0.975429	+	0.220313i	$0.0707078\pi$
$83$	387964.	+	671973.i	0.678511	+	1.17522i	−0.296918	+	0.954903i	$0.595959\pi$
$84$	−570640.			−0.962774
$85$		−	82703.1i		−	0.134668i
$86$	−61766.5	+	335203.i	−0.0971085	+	0.527002i
$87$	−1.13854e6			−1.72898
$88$			762492.i			1.11889i
$89$	1.01577e6	−	586458.i	1.44088	−	0.831892i	0.442970	−	0.896536i	$-0.353925\pi$
$89$	1.01577e6	−	586458.i	1.44088	−	0.831892i	0.997908	+	0.0646445i	$0.0205913\pi$
$90$	1.36731e6			1.87560
$91$	493340.	−	284830.i	0.654669	−	0.377973i
$92$	−456031.	−	789870.i	−0.585641	−	1.01436i
$93$	−593401.	−	342600.i	−0.737733	−	0.425930i
$94$		−	131610.i		−	0.158454i
$95$	−535103.	+	926826.i	−0.624118	+	1.08100i
$96$	822037.	+	1.42381e6i	0.929132	+	1.60930i
$97$	417105.			0.457015			0.228507	−	0.973542i	$-0.426616\pi$
$97$	417105.			0.457015			0.228507	+	0.973542i	$0.426616\pi$
$98$	−189002.	+	109120.i	−0.200811	+	0.115938i
$99$	−1.31030e6	+	2.26950e6i	−1.35041	+	2.33897i
$100$	533077.	−	923316.i	0.533077	−	0.923316i
$101$	218273.	−	378060.i	0.211853	−	0.366941i	−0.740441	−	0.672121i	$-0.765383\pi$
$101$	218273.	−	378060.i	0.211853	−	0.366941i	0.952295	+	0.305180i	$0.0987167\pi$
$102$	−86929.2			−0.0819154
$103$	−704980.	+	1.22106e6i	−0.645157	+	1.11744i	0.339108	+	0.940747i	$0.389875\pi$
$103$	−704980.	+	1.22106e6i	−0.645157	+	1.11744i	−0.984265	+	0.176697i	$0.943459\pi$
$104$	−897424.	−	518128.i	−0.797806	−	0.460614i
$105$	2.13906e6	−	1.23499e6i	1.84780	−	1.06683i
$106$	−757801.	+	437517.i	−0.636264	+	0.367347i
$107$	−311727.			−0.254462			−0.127231	−	0.991873i	$-0.540609\pi$
$107$	−311727.			−0.254462			−0.127231	+	0.991873i	$0.540609\pi$
$108$			1.95737e6i			1.55382i
$109$	394763.	+	683749.i	0.304829	+	0.527980i	0.977223	−	0.212213i	$-0.0680672\pi$
$109$	394763.	+	683749.i	0.304829	+	0.527980i	−0.672394	+	0.740193i	$0.734734\pi$
$110$	−686768.	−	1.18952e6i	−0.515979	−	0.893702i
$111$	397868.	−	689127.i	0.290917	−	0.503884i
$112$	202507.	+	116917.i	0.144140	+	0.0832194i
$113$		−	1.34099e6i		−	0.929370i	−0.885476	−	0.464685i	$-0.846168\pi$
$113$		−	1.34099e6i		−	0.929370i	0.885476	−	0.464685i	$-0.153832\pi$
$114$	974188.	+	562447.i	0.657549	+	0.379636i
$115$	3.41889e6	+	1.97390e6i	2.24798	+	1.29787i
$116$	929087.	+	536409.i	0.595227	+	0.343654i
$117$	−1.78074e6	−	3.08434e6i	−1.11184	−	1.92577i
$118$			1.39760e6i			0.850625i
$119$	−93702.0	+	54098.9i	−0.0556042	+	0.0321031i
$120$	−3.89112e6	−	2.24654e6i	−2.25180	−	1.30008i
$121$	860963.			0.485991
$122$	−687366.	+	1.19055e6i	−0.378537	+	0.655645i
$123$	−2.78653e6	+	1.60880e6i	−1.49743	+	0.864544i
$124$	322824.	+	559148.i	0.169317	+	0.293266i
$125$			1.52930e6i			0.783000i
$126$	−894405.	−	1.54915e6i	−0.447118	−	0.774432i
$127$	−356295.			−0.173939			−0.0869697	−	0.996211i	$-0.527718\pi$
$127$	−356295.			−0.173939			−0.0869697	+	0.996211i	$0.527718\pi$
$128$		−	1.79751e6i		−	0.857120i
$129$	3.62731e6	−	1.28874e6i	1.68972	−	0.600337i
$130$	1.86669e6			0.849653
$131$			2.48144e6i			1.10380i	0.833911	+	0.551899i	$0.186097\pi$
$131$			2.48144e6i			1.10380i	−0.833911	+	0.551899i	$0.813903\pi$
$132$	3.10371e6	−	1.79193e6i	1.34946	−	0.779110i
$133$	1.40012e6			0.595126
$134$	−819719.	+	473265.i	−0.340683	+	0.196693i
$135$	−4.23617e6	−	7.33726e6i	−1.72176	−	2.98217i
$136$	170451.	+	98410.1i	0.0677616	+	0.0391222i
$137$		−	3.40926e6i		−	1.32586i	−0.748680	−	0.662932i	$-0.769312\pi$
$137$		−	3.40926e6i		−	1.32586i	0.748680	−	0.662932i	$-0.230688\pi$
$138$	2.07476e6	−	3.59360e6i	0.789462	−	1.36739i
$139$	93126.7	+	161300.i	0.0346760	+	0.0600607i	0.882843	−	0.469669i	$-0.155627\pi$
$139$	93126.7	+	161300.i	0.0346760	+	0.0600607i	−0.848167	+	0.529730i	$0.822293\pi$
$140$	−2.32740e6			−0.848177
$141$	−1.28724e6	+	743186.i	−0.459199	+	0.265119i
$142$	379376.	−	657099.i	0.132497	−	0.229491i
$143$	−1.78885e6	+	3.09838e6i	−0.611738	+	1.05956i
$144$	730961.	−	1.26606e6i	0.244798	−	0.424002i
$145$	−4.64361e6			−1.52318
$146$	−1.16381e6	+	2.01577e6i	−0.373958	+	0.647713i
$147$	2.13455e6	+	1.23238e6i	0.671976	+	0.387966i
$148$	−649348.	+	374901.i	−0.200305	+	0.115646i
$149$	1.31662e6	−	760150.i	0.398016	−	0.229795i	−0.287611	−	0.957747i	$-0.592861\pi$
$149$	1.31662e6	−	760150.i	0.398016	−	0.229795i	0.685628	+	0.727952i	$0.259528\pi$
$150$	4.85058e6			1.43721
$151$			13111.3i			0.00380816i	0.999998	+	0.00190408i	$0.000606088\pi$
$151$			13111.3i			0.00380816i	−0.999998	+	0.00190408i	$0.999394\pi$
$152$	−1.27346e6	−	2.20570e6i	−0.362623	−	0.628081i
$153$	338224.	+	585821.i	0.0944343	+	0.163565i
$154$	−898476.	+	1.55621e6i	−0.246005	+	0.426093i
$155$	−2.42023e6	−	1.39732e6i	−0.649922	−	0.375233i
$156$			4.87060e6i			1.28295i
$157$	−871187.	−	502980.i	−0.225119	−	0.129973i	0.383199	−	0.923666i	$-0.374822\pi$
$157$	−871187.	−	502980.i	−0.225119	−	0.129973i	−0.608318	+	0.793693i	$0.708156\pi$
$158$	−2.22849e6	−	1.28662e6i	−0.564988	−	0.326196i
$159$	8.55846e6	+	4.94123e6i	2.12914	+	1.22926i
$160$	3.35274e6	+	5.80711e6i	0.818539	+	1.41775i
$161$		−	5.16477e6i		−	1.23758i
$162$	−3.34076e6	+	1.92879e6i	−0.785778	+	0.453669i
$163$	−403987.	−	233242.i	−0.0932834	−	0.0538572i	0.452633	−	0.891697i	$-0.350485\pi$
$163$	−403987.	−	233242.i	−0.0932834	−	0.0538572i	−0.545916	+	0.837840i	$0.683818\pi$
$164$	3.03187e6			0.687353
$165$	−7.75623e6	+	1.34342e7i	−1.72663	+	2.99061i
$166$	2.88074e6	−	1.66320e6i	0.629767	−	0.363596i
$167$	−3.46667e6	−	6.00445e6i	−0.744326	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$167$	−3.46667e6	−	6.00445e6i	−0.744326	−	1.28921i	0.206184	−	0.978513i	$-0.433896\pi$
$168$			5.87814e6i			1.23969i
$169$	−17710.6	−	30675.7i	−0.00366922	−	0.00635527i
$170$	−354547.			−0.0721652
$171$		−	8.75347e6i		−	1.75062i
$172$	−3.56719e6	−	657312.i	−0.701037	−	0.129177i
$173$	−7.72842e6			−1.49263			−0.746315	−	0.665593i	$-0.768179\pi$
$173$	−7.72842e6			−1.49263			−0.746315	+	0.665593i	$0.768179\pi$
$174$			4.88090e6i			0.926514i
$175$	5.22850e6	−	3.01867e6i	0.975579	−	0.563251i
$176$	−1.46858e6			−0.269376
$177$	1.36696e7	−	7.89213e6i	2.46510	−	1.42323i
$178$	−2.51414e6	−	4.35462e6i	−0.445789	−	0.772129i
$179$	6.32202e6	+	3.65002e6i	1.10229	+	0.636409i	0.936822	−	0.349806i	$-0.113753\pi$
$179$	6.32202e6	+	3.65002e6i	1.10229	+	0.636409i	0.165470	+	0.986215i	$0.447086\pi$
$180$			1.45508e7i			2.49499i
$181$	5.88505e6	−	1.01932e7i	0.992463	−	1.71900i	0.390106	−	0.920770i	$-0.372438\pi$
$181$	5.88505e6	−	1.01932e7i	0.992463	−	1.71900i	0.602357	−	0.798227i	$-0.294228\pi$
$182$	−1.22106e6	−	2.11494e6i	−0.202546	−	0.350820i
$183$	1.55259e7			2.53341
$184$	−8.13641e6	+	4.69756e6i	−1.30611	+	0.754082i
$185$	1.62273e6	−	2.81065e6i	0.256290	−	0.443907i
$186$	−1.46872e6	+	2.54390e6i	−0.228245	+	0.395332i
$187$	339763.	−	588487.i	0.0519579	−	0.0899937i
$188$	1.40057e6			0.210782
$189$	−5.54204e6	+	9.59909e6i	−0.820888	+	1.42182i
$190$	3.97330e6	+	2.29398e6i	0.579282	+	0.334449i
$191$	−9.69149e6	+	5.59538e6i	−1.39088	+	0.803026i	−0.993413	−	0.114589i	$-0.963445\pi$
$191$	−9.69149e6	+	5.59538e6i	−1.39088	+	0.803026i	−0.397469	+	0.917615i	$0.630111\pi$
$192$	3.67493e6	−	2.12172e6i	0.519213	−	0.299768i
$193$	−434453.			−0.0604326			−0.0302163	−	0.999543i	$-0.509620\pi$
$193$	−434453.			−0.0604326			−0.0302163	+	0.999543i	$0.509620\pi$
$194$		−	1.78813e6i		−	0.244902i
$195$	−1.05410e7	−	1.82576e7i	−1.42160	−	2.46229i
$196$	−1.16125e6	−	2.01134e6i	−0.154225	−	0.267126i
$197$	−1.56637e6	+	2.71303e6i	−0.204878	+	0.354859i	−0.950094	−	0.311964i	$-0.899013\pi$
$197$	−1.56637e6	+	2.71303e6i	−0.204878	+	0.354859i	0.745216	+	0.666823i	$0.232346\pi$
$198$	9.72933e6	+	5.61723e6i	1.25339	+	0.723647i
$199$			2.40666e6i			0.305390i	0.988273	+	0.152695i	$0.0487953\pi$
$199$			2.40666e6i			0.305390i	−0.988273	+	0.152695i	$0.951205\pi$
$200$	−9.51104e6	−	5.49120e6i	−1.18888	−	0.686400i
$201$	9.25775e6	+	5.34496e6i	1.14003	+	0.658198i
$202$	−1.62074e6	−	935734.i	−0.196634	−	0.113527i
$203$	3.03754e6	+	5.26117e6i	0.363106	+	0.628919i
$204$		−	925092.i		−	0.108967i
$205$	−1.13651e7	+	6.56162e6i	−1.31920	+	0.761639i
$206$	5.23468e6	+	3.02224e6i	0.598809	+	0.345723i
$207$	−3.22899e7			−3.64046
$208$	997926.	−	1.72846e6i	0.110894	−	0.192074i
$209$	−7.61523e6	+	4.39666e6i	−0.834150	+	0.481597i
$210$	−5.29437e6	−	9.17013e6i	−0.571685	−	0.990187i
$211$			1.56410e7i			1.66501i	0.554014	+	0.832507i	$0.313095\pi$
$211$			1.56410e7i			1.66501i	−0.554014	+	0.832507i	$0.686905\pi$
$212$	−4.65601e6	−	8.06444e6i	−0.488659	−	0.846382i
$213$	−8.56920e6			−0.886751
$214$			1.33637e6i			0.136359i
$215$	1.47943e7	−	5.25621e6i	1.48860	−	0.528880i
$216$	2.01628e7			2.00074
$217$			3.65614e6i			0.357802i
$218$	2.93123e6	−	1.69235e6i	0.282931	−	0.163350i
$219$	2.62876e7			2.50276
$220$	1.26587e7	−	7.30851e6i	1.18884	−	0.686374i
$221$	461751.	+	799777.i	0.0427791	+	0.0740955i
$222$	−2.95428e6	−	1.70565e6i	−0.270018	−	0.155895i
$223$			4.31505e6i			0.389109i	0.980892	+	0.194555i	$0.0623261\pi$
$223$			4.31505e6i			0.389109i	−0.980892	+	0.194555i	$0.937674\pi$
$224$	4.38628e6	−	7.59725e6i	0.390258	−	0.675947i
$225$	−1.88726e7	−	3.26883e7i	−1.65686	−	2.86976i
$226$	−5.74879e6			−0.498025
$227$	−139404.	+	80485.2i	−0.0119179	+	0.00688079i	−0.505947	−	0.862565i	$-0.668857\pi$
$227$	−139404.	+	80485.2i	−0.0119179	+	0.00688079i	0.494029	+	0.869445i	$0.335524\pi$
$228$	−5.98551e6	+	1.03672e7i	−0.505006	+	0.874696i
$229$	7.22892e6	−	1.25209e7i	0.601959	−	1.04262i	−0.390565	−	0.920575i	$-0.627720\pi$
$229$	7.22892e6	−	1.25209e7i	0.601959	−	1.04262i	0.992524	−	0.122048i	$-0.0389463\pi$
$230$	8.46208e6	−	1.46568e7i	0.695494	−	1.20463i
$231$	2.02944e7			1.64642
$232$	5.52552e6	−	9.57049e6i	0.442496	−	0.766426i
$233$	606452.	+	350135.i	0.0479434	+	0.0276801i	0.523780	−	0.851854i	$-0.324521\pi$
$233$	606452.	+	350135.i	0.0479434	+	0.0276801i	−0.475837	+	0.879534i	$0.657855\pi$
$234$	−1.32225e7	+	7.63403e6i	−1.03197	+	0.595808i
$235$	−5.25009e6	+	3.03114e6i	−0.404542	+	0.233562i
$236$	−1.48732e7			−1.13153
$237$			2.90616e7i			2.18311i
$238$	231921.	+	401699.i	0.0172032	+	0.0297969i
$239$	−7.05387e6	−	1.22177e7i	−0.516694	−	0.894941i	−0.999812	−	0.0193855i	$-0.993829\pi$
$239$	−7.05387e6	−	1.22177e7i	−0.516694	−	0.894941i	0.483118	−	0.875555i	$-0.339504\pi$
$240$	4.32688e6	−	7.49438e6i	0.312998	−	0.542128i
$241$	−1.07852e7	−	6.22685e6i	−0.770510	−	0.444854i	0.0625467	−	0.998042i	$-0.480078\pi$
$241$	−1.07852e7	−	6.22685e6i	−0.770510	−	0.444854i	−0.833056	+	0.553188i	$0.813411\pi$
$242$		−	3.69094e6i		−	0.260430i
$243$	1.06429e7	+	6.14469e6i	0.741723	+	0.428234i
$244$	−1.26697e7	−	7.31487e6i	−0.872163	−	0.503544i
$245$	8.70592e6	+	5.02636e6i	0.591992	+	0.341787i
$246$	6.89692e6	+	1.19458e7i	0.463287	+	0.802436i
$247$		−	1.19504e7i		−	0.793037i
$248$	5.75976e6	−	3.32540e6i	0.377615	−	0.218016i
$249$	−3.25345e7	−	1.87838e7i	−2.10740	−	1.21671i
$250$	6.55608e6			0.419589
$251$	5.32932e6	−	9.23066e6i	0.337016	−	0.583730i	−0.646854	−	0.762614i	$-0.723916\pi$
$251$	5.32932e6	−	9.23066e6i	0.337016	−	0.583730i	0.983870	+	0.178885i	$0.0572489\pi$
$252$	1.64859e7	−	9.51816e6i	1.03018	−	0.594773i
$253$	1.62184e7	+	2.80912e7i	1.00149	+	1.73464i
$254$			1.52743e6i			0.0932096i
$255$	2.00210e6	+	3.46773e6i	0.120744	+	0.209134i
$256$	−1.33152e7			−0.793646
$257$			2.56928e7i			1.51360i	0.653644	+	0.756802i	$0.273239\pi$
$257$			2.56928e7i			1.51360i	−0.653644	+	0.756802i	$0.726761\pi$
$258$	−5.52480e6	−	1.55503e7i	−0.321705	−	0.905479i
$259$	−4.24593e6			−0.244385
$260$			1.98651e7i			1.13024i
$261$	3.28926e7	−	1.89906e7i	1.85002	−	1.06811i
$262$	1.06379e7			0.591497
$263$	−9.22786e6	+	5.32771e6i	−0.507264	+	0.292869i	−0.731708	−	0.681618i	$-0.761277\pi$
$263$	−9.22786e6	+	5.32771e6i	−0.507264	+	0.292869i	0.224444	+	0.974487i	$0.427943\pi$
$264$	−1.84586e7	−	3.19712e7i	−1.00320	−	1.73759i
$265$	3.49063e7	+	2.01532e7i	1.87571	+	1.08294i
$266$		−	6.00229e6i		−	0.318913i
$267$	−2.83942e7	+	4.91802e7i	−1.49175	+	2.58379i
$268$	−5.03644e6	−	8.72336e6i	−0.261649	−	0.453189i
$269$	−9.80000e6			−0.503465			−0.251733	−	0.967797i	$-0.581000\pi$
$269$	−9.80000e6			−0.503465			−0.251733	+	0.967797i	$0.581000\pi$
$270$	−3.14548e7	+	1.81604e7i	−1.59807	+	0.922645i
$271$	187353.	−	324504.i	0.00941352	−	0.0163047i	−0.861280	−	0.508130i	$-0.830337\pi$
$271$	187353.	−	324504.i	0.00941352	−	0.0163047i	0.870694	+	0.491825i	$0.163670\pi$
$272$	−189540.	+	328293.i	−0.00941877	+	0.0163138i
$273$	−1.37905e7	+	2.38858e7i	−0.677783	+	1.17395i
$274$	−1.46155e7			−0.710496
$275$	−1.89585e7	+	3.28371e7i	−0.911604	+	1.57895i
$276$	3.82427e7	+	2.20794e7i	1.81895	+	1.05017i
$277$	−7.09322e6	+	4.09527e6i	−0.333737	+	0.192683i	−0.657499	−	0.753455i	$-0.728386\pi$
$277$	−7.09322e6	+	4.09527e6i	−0.333737	+	0.192683i	0.323762	+	0.946139i	$0.395052\pi$
$278$	691492.	−	399233.i	0.0321849	−	0.0185820i
$279$	2.28580e7			1.05251
$280$			2.39744e7i			1.09213i
$281$	−9.28075e6	−	1.60747e7i	−0.418277	−	0.724477i	0.577489	−	0.816398i	$-0.304033\pi$
$281$	−9.28075e6	−	1.60747e7i	−0.418277	−	0.724477i	−0.995766	+	0.0919212i	$0.970699\pi$
$282$	3.18603e6	+	5.51837e6i	0.142070	+	0.246073i
$283$	−9188.11	+	15914.3i	−0.000405384	+	0.000702146i	−0.866228	−	0.499649i	$-0.833462\pi$
$283$	−9188.11	+	15914.3i	−0.000405384	+	0.000702146i	0.865823	+	0.500351i	$0.166796\pi$
$284$	6.99278e6	+	4.03728e6i	0.305277	+	0.176252i
$285$		−	5.18156e7i		−	2.23834i
$286$	1.32827e7	+	7.66878e6i	0.567792	+	0.327815i
$287$	1.48685e7	+	8.58435e6i	0.628959	+	0.363130i
$288$	−4.74977e7	−	2.74228e7i	−1.98836	−	1.14798i
$289$	1.19811e7	+	2.07518e7i	0.496367	+	0.859732i
$290$			1.99071e7i			0.816233i
$291$	−1.74892e7	+	1.00974e7i	−0.709725	+	0.409760i
$292$	−2.14516e7	−	1.23851e7i	−0.861612	−	0.497452i
$293$	2.74963e7			1.09313			0.546564	−	0.837417i	$-0.315936\pi$
$293$	2.74963e7			1.09313			0.546564	+	0.837417i	$0.315936\pi$
$294$	5.28321e6	−	9.15079e6i	0.207901	−	0.360095i
$295$	5.57524e7	−	3.21887e7i	2.17169	−	1.25382i
$296$	3.86184e6	+	6.68891e6i	0.148909	+	0.257917i
$297$		−	6.96126e7i		−	2.65717i
$298$	−3.25876e6	−	5.64433e6i	−0.123141	−	0.213287i
$299$	−4.40830e7			−1.64914
$300$			5.16194e7i			1.91183i
$301$	−1.56327e7	−	1.33235e7i	−0.573236	−	0.488562i
$302$	56208.1			0.00204069
$303$			2.11360e7i			0.759792i
$304$	4.24823e6	−	2.45272e6i	0.151212	−	0.0873024i
$305$	6.33237e7			2.23186
$306$	2.51141e6	−	1.44996e6i	0.0876502	−	0.0506049i
$307$	1.15520e7	+	2.00087e7i	0.399248	+	0.691519i	0.993633	−	0.112662i	$-0.0359378\pi$
$307$	1.15520e7	+	2.00087e7i	0.399248	+	0.691519i	−0.594385	+	0.804181i	$0.702604\pi$
$308$	−1.65610e7	−	9.56149e6i	−0.566805	−	0.327245i
$309$		−	6.82653e7i		−	2.31379i
$310$	−5.99030e6	+	1.03755e7i	−0.201077	+	0.348276i
$311$	1.12965e7	+	1.95661e7i	0.375546	+	0.650465i	0.990409	−	0.138170i	$-0.0441219\pi$
$311$	1.12965e7	+	1.95661e7i	0.375546	+	0.650465i	−0.614863	+	0.788634i	$0.710789\pi$
$312$	5.01718e7			1.65195
$313$	−1.11591e7	+	6.44270e6i	−0.363911	+	0.210104i	−0.670795	−	0.741643i	$-0.734047\pi$
$313$	−1.11591e7	+	6.44270e6i	−0.363911	+	0.210104i	0.306884	+	0.951747i	$0.400714\pi$
$314$	−2.15627e6	+	3.73477e6i	−0.0696489	+	0.120635i
$315$	−4.11986e7	+	7.13581e7i	−1.31811	+	2.28303i
$316$	1.36921e7	−	2.37153e7i	0.433918	−	0.751567i
$317$	4.07849e6			0.128033			0.0640165	−	0.997949i	$-0.479609\pi$
$317$	4.07849e6			0.128033			0.0640165	+	0.997949i	$0.479609\pi$
$318$	2.11830e7	−	3.66900e7i	0.658728	−	1.14095i
$319$	−3.30424e7	−	1.90770e7i	−1.01789	−	0.587677i
$320$	1.49885e7	−	8.65360e6i	0.457412	−	0.264087i
$321$	1.30707e7	−	7.54635e6i	0.395169	−	0.228151i
$322$	−2.21413e7			−0.663187
$323$			2.26980e6i			0.0673564i
$324$	−2.05259e7	−	3.55520e7i	−0.603487	−	1.04527i
$325$	−2.57654e7	−	4.46269e7i	−0.750561	−	1.30001i
$326$	−999905.	+	1.73189e6i	−0.0288606	+	0.0499881i
$327$	−3.31047e7	−	1.91130e7i	−0.946775	−	0.546621i
$328$		−	3.12312e7i		−	0.885049i
$329$	6.86852e6	+	3.96554e6i	0.192875	+	0.111356i
$330$	5.75922e7	+	3.32509e7i	1.60259	+	0.925255i
$331$	3.72466e6	+	2.15044e6i	0.102708	+	0.0592983i	0.550474	−	0.834852i	$-0.314447\pi$
$331$	3.72466e6	+	2.15044e6i	0.102708	+	0.0592983i	−0.447766	+	0.894151i	$0.647780\pi$
$332$	1.76996e7	+	3.06566e7i	0.483669	+	0.837740i
$333$			2.65454e7i			0.718880i
$334$	−2.57410e7	+	1.48616e7i	−0.690854	+	0.398865i
$335$	3.77584e7	+	2.17998e7i	1.00434	+	0.579854i
$336$	−1.13214e7			−0.298458
$337$	1.92033e7	−	3.32611e7i	0.501749	−	0.869055i	−0.498249	−	0.867034i	$-0.666023\pi$
$337$	1.92033e7	−	3.32611e7i	0.501749	−	0.869055i	0.999998	−	0.00202086i	$-0.000643259\pi$
$338$	−131506.	+	75925.3i	−0.00340563	+	0.00196624i
$339$	3.24629e7	+	5.62274e7i	0.833274	+	1.44327i
$340$		−	3.77306e6i		−	0.0959967i
$341$	−1.14810e7	−	1.98857e7i	−0.289546	−	0.501508i
$342$	−3.75260e7			−0.938111
$343$		−	4.35455e7i		−	1.07910i
$344$	−6.77094e6	+	3.67455e7i	−0.166331	+	0.902669i
$345$	−1.91138e8			−4.65468
$346$			3.31317e7i			0.799862i
$347$	2.71823e7	−	1.56937e7i	0.650575	−	0.375610i	−0.138101	−	0.990418i	$-0.544100\pi$
$347$	2.71823e7	−	1.56937e7i	0.650575	−	0.375610i	0.788677	+	0.614808i	$0.210767\pi$
$348$	−5.19420e7			−1.23248
$349$	−2.72881e7	+	1.57548e7i	−0.641943	+	0.370626i	−0.785363	−	0.619036i	$-0.787524\pi$
$349$	−2.72881e7	+	1.57548e7i	−0.641943	+	0.370626i	0.143420	+	0.989662i	$0.454190\pi$
$350$	−1.29410e7	−	2.24145e7i	−0.301831	−	0.522787i
$351$	8.19314e7	+	4.73031e7i	1.89465	+	1.09388i
$352$			5.50953e7i			1.26324i
$353$	−8.62770e6	+	1.49436e7i	−0.196142	+	0.339728i	−0.947274	−	0.320424i	$-0.896175\pi$
$353$	−8.62770e6	+	1.49436e7i	−0.196142	+	0.339728i	0.751132	+	0.660152i	$0.229508\pi$
$354$	−3.38335e7	−	5.86013e7i	−0.762671	−	1.32098i
$355$	−3.49501e7			−0.781203
$356$	4.63414e7	−	2.67552e7i	1.02711	−	0.593005i
$357$	2.61927e6	−	4.53672e6i	0.0575674	−	0.0997096i
$358$	1.56476e7	−	2.71024e7i	0.341035	−	0.590689i
$359$	1.39417e7	−	2.41478e7i	0.301323	−	0.521908i	−0.675113	−	0.737715i	$-0.735905\pi$
$359$	1.39417e7	−	2.41478e7i	0.301323	−	0.521908i	0.976436	+	0.215807i	$0.0692383\pi$
$360$	1.49887e8			3.21260
$361$	−8.83697e6	+	1.53061e7i	−0.187837	+	0.325344i
$362$	−4.36982e7	−	2.52292e7i	−0.921165	−	0.531835i
$363$	−3.61001e7	+	2.08424e7i	−0.754724	+	0.435740i
$364$	2.25070e7	−	1.29944e7i	0.466674	−	0.269434i
$365$	1.07216e8			2.20486
$366$		−	6.65596e7i		−	1.35759i
$367$	−4.62799e6	−	8.01592e6i	−0.0936256	−	0.162164i	0.815409	−	0.578886i	$-0.196512\pi$
$367$	−4.62799e6	−	8.01592e6i	−0.0936256	−	0.162164i	−0.909034	+	0.416722i	$0.863179\pi$
$368$	−9.04761e6	−	1.56709e7i	−0.181548	−	0.314450i
$369$	5.36690e7	−	9.29574e7i	1.06818	−	1.85014i
$370$	−1.20493e7	−	6.95664e6i	−0.237878	−	0.137339i
$371$		−	5.27314e7i		−	1.03264i
$372$	−2.70720e7	−	1.56300e7i	−0.525885	−	0.303620i
$373$	−3.79597e7	−	2.19161e7i	−0.731470	−	0.422314i	0.0874898	−	0.996165i	$-0.472115\pi$
$373$	−3.79597e7	−	2.19161e7i	−0.731470	−	0.422314i	−0.818960	+	0.573851i	$0.805449\pi$
$374$	−2.52284e6	−	1.45656e6i	−0.0482253	−	0.0278429i
$375$	−3.70215e7	−	6.41232e7i	−0.702038	−	1.21597i
$376$		−	1.44273e7i		−	0.271407i
$377$	4.49058e7	−	2.59264e7i	0.838067	−	0.483858i
$378$	4.11512e7	+	2.37587e7i	0.761916	+	0.439893i
$379$	−6.61347e7			−1.21482			−0.607410	−	0.794388i	$-0.707792\pi$
$379$	−6.61347e7			−1.21482			−0.607410	+	0.794388i	$0.707792\pi$
$380$	−2.44123e7	+	4.22834e7i	−0.444896	+	0.770582i
$381$	1.49394e7	−	8.62526e6i	0.270121	−	0.155954i
$382$	2.39874e7	+	4.15473e7i	0.430321	+	0.745337i
$383$			6.63164e7i			1.18039i	0.807261	+	0.590194i	$0.200949\pi$
$383$			6.63164e7i			1.18039i	−0.807261	+	0.590194i	$0.799051\pi$
$384$	4.35145e7	+	7.53694e7i	0.768494	+	1.33107i
$385$	8.27723e7			1.45045
$386$			1.86250e6i			0.0323842i
$387$	−8.32982e7	+	9.77348e7i	−1.43715	+	1.68623i
$388$	1.90290e7			0.325778
$389$			2.90881e7i			0.494159i	0.968995	+	0.247080i	$0.0794709\pi$
$389$			2.90881e7i			0.494159i	−0.968995	+	0.247080i	$0.920529\pi$
$390$	−7.82700e7	+	4.51892e7i	−1.31948	+	0.761800i
$391$	8.37285e6			0.140069
$392$	−2.07187e7	+	1.19619e7i	−0.343957	+	0.198584i
$393$	−6.00713e7	−	1.04046e8i	−0.989667	−	1.71415i
$394$	1.16307e7	+	6.71501e6i	0.190160	+	0.109789i
$395$			1.18530e8i			1.92326i
$396$	−5.97780e7	+	1.03539e8i	−0.962622	+	1.66731i
$397$	4.14560e6	+	7.18039e6i	0.0662545	+	0.114756i	0.897250	−	0.441523i	$-0.145562\pi$
$397$	4.14560e6	+	7.18039e6i	0.0662545	+	0.114756i	−0.830995	+	0.556279i	$0.812228\pi$
$398$	1.03173e7			0.163651
$399$	−5.87067e7	+	3.38943e7i	−0.924207	+	0.533591i
$400$	1.05762e7	−	1.83185e7i	0.165253	−	0.286226i
$401$	−6.16405e6	+	1.06765e7i	−0.0955946	+	0.165575i	−0.909857	−	0.414923i	$-0.863809\pi$
$401$	−6.16405e6	+	1.06765e7i	−0.0955946	+	0.165575i	0.814262	+	0.580497i	$0.197142\pi$
$402$	2.29138e7	−	3.96879e7i	0.352711	−	0.610914i
$403$	3.12063e7			0.476790
$404$	9.95798e6	−	1.72477e7i	0.151017	−	0.261570i
$405$	1.53884e8	+	8.88450e7i	2.31648	+	1.33742i
$406$	2.25546e7	−	1.30219e7i	0.337021	−	0.194579i
$407$	2.30936e7	−	1.33331e7i	0.342538	−	0.197765i
$408$	−9.52933e6			−0.140308
$409$			4.52417e7i			0.661255i	0.943761	+	0.330628i	$0.107260\pi$
$409$			4.52417e7i			0.661255i	−0.943761	+	0.330628i	$0.892740\pi$
$410$	2.81296e7	+	4.87219e7i	0.408143	+	0.706924i
$411$	8.25322e7	+	1.42950e8i	1.18877	+	2.05901i
$412$	−3.21624e7	+	5.57069e7i	−0.459893	+	0.796558i
$413$	−7.29390e7	−	4.21113e7i	−1.03540	−	0.597790i
$414$			1.38427e8i			1.95083i
$415$	−1.32695e8	−	7.66112e7i	−1.85656	−	1.07189i
$416$	−6.48450e7	−	3.74383e7i	−0.900734	−	0.520039i
$417$	−7.80958e6	−	4.50886e6i	−0.107701	−	0.0621812i
$418$	1.88484e7	+	3.26464e7i	0.258075	+	0.446999i
$419$		−	4.18627e7i		−	0.569095i	−0.958662	−	0.284548i	$-0.908157\pi$
$419$		−	4.18627e7i		−	0.569095i	0.958662	−	0.284548i	$-0.0918434\pi$
$420$	9.75875e7	−	5.63422e7i	1.31718	−	0.760476i
$421$	4.38905e7	+	2.53402e7i	0.588199	+	0.339597i	0.764385	−	0.644760i	$-0.223043\pi$
$421$	4.38905e7	+	2.53402e7i	0.588199	+	0.339597i	−0.176186	+	0.984357i	$0.556376\pi$
$422$	6.70530e7			0.892238
$423$	2.47924e7	−	4.29417e7i	0.327565	−	0.567359i
$424$	−8.30714e7	+	4.79613e7i	−1.08982	+	0.629207i
$425$	4.89372e6	+	8.47616e6i	0.0637488	+	0.110416i
$426$			3.67361e7i			0.475187i
$427$	−4.14222e7	−	7.17453e7i	−0.532046	−	0.921531i
$428$	−1.42215e7			−0.181390
$429$		−	1.73220e8i		−	2.19394i
$430$	−2.25333e7	−	6.34229e7i	−0.283413	−	0.797702i
$431$	1.43600e7			0.179358			0.0896791	−	0.995971i	$-0.471416\pi$
$431$	1.43600e7			0.179358			0.0896791	+	0.995971i	$0.471416\pi$
$432$			3.88340e7i			0.481683i
$433$	1.84296e7	−	1.06403e7i	0.227014	−	0.131066i	−0.382180	−	0.924088i	$-0.624827\pi$
$433$	1.84296e7	−	1.06403e7i	0.227014	−	0.131066i	0.609194	+	0.793022i	$0.291493\pi$
$434$	1.56738e7			0.191737
$435$	1.94706e8	−	1.12414e8i	2.36544	−	1.36569i
$436$	1.80098e7	+	3.11938e7i	0.217294	+	0.376365i
$437$	−9.38318e7	−	5.41738e7i	−1.12436	−	0.649150i
$438$		−	1.12695e8i		−	1.34116i
$439$	1.98888e7	−	3.44484e7i	0.235080	−	0.407170i	−0.724216	−	0.689573i	$-0.757798\pi$
$439$	1.98888e7	−	3.44484e7i	0.235080	−	0.407170i	0.959296	+	0.282403i	$0.0911316\pi$
$440$	−7.52847e7	−	1.30397e8i	−0.883789	−	1.53077i
$441$	−8.22235e7			−0.958695
$442$	3.42864e6	−	1.97952e6i	0.0397059	−	0.0229242i
$443$	6.60404e7	−	1.14385e8i	0.759624	−	1.31571i	−0.183418	−	0.983035i	$-0.558716\pi$
$443$	6.60404e7	−	1.14385e8i	0.759624	−	1.31571i	0.943042	−	0.332673i	$-0.107950\pi$
$444$	1.81514e7	−	3.14391e7i	0.207377	−	0.359188i
$445$	−1.15808e8	+	2.00585e8i	−1.31419	+	2.27624i
$446$	1.84986e7			0.208513
$447$	−3.68038e7	+	6.37460e7i	−0.412069	+	0.713724i
$448$	−1.96089e7	−	1.13212e7i	−0.218082	−	0.125910i
$449$	3.51449e7	−	2.02909e7i	0.388260	−	0.224162i	−0.293146	−	0.956068i	$-0.594702\pi$
$449$	3.51449e7	−	2.02909e7i	0.388260	−	0.224162i	0.681406	+	0.731906i	$0.261369\pi$
$450$	−1.40135e8	+	8.09067e7i	−1.53783	+	0.887865i
$451$	−1.07827e8			−1.17543
$452$		−	6.11780e7i		−	0.662491i
$453$	−317402.	−	549756.i	−0.00341440	−	0.00591392i
$454$	345039.	+	597625.i	0.00368724	+	0.00638648i
$455$	−5.62454e7	+	9.74199e7i	−0.597108	+	1.03422i
$456$	1.06792e8	+	6.16565e7i	1.12628	+	0.650255i
$457$		−	6.55165e7i		−	0.686439i	−0.939255	−	0.343220i	$-0.888482\pi$
$457$		−	6.55165e7i		−	0.686439i	0.939255	−	0.343220i	$-0.111518\pi$
$458$	−5.36768e7	−	3.09903e7i	−0.558715	−	0.322574i
$459$	−1.55615e7	−	8.98446e6i	−0.160922	−	0.0929082i
$460$	1.55976e8	+	9.00526e7i	1.60245	+	0.925172i
$461$	4.15478e7	+	7.19628e7i	0.424077	+	0.734523i	0.996334	−	0.0855515i	$-0.0272652\pi$
$461$	4.15478e7	+	7.19628e7i	0.424077	+	0.734523i	−0.572257	+	0.820075i	$0.693932\pi$
$462$		−	8.70020e7i		−	0.882274i
$463$	5.26538e7	−	3.03997e7i	0.530502	−	0.306285i	−0.210719	−	0.977547i	$-0.567580\pi$
$463$	5.26538e7	−	3.03997e7i	0.530502	−	0.306285i	0.741221	+	0.671261i	$0.234247\pi$
$464$	1.84330e7	+	1.06423e7i	0.184519	+	0.106532i
$465$	1.35307e8			1.34574
$466$	1.50103e6	−	2.59985e6i	0.0148330	−	0.0256916i
$467$	6.25414e7	−	3.61083e7i	0.614069	−	0.354533i	−0.160487	−	0.987038i	$-0.551307\pi$
$467$	6.25414e7	−	3.61083e7i	0.614069	−	0.354533i	0.774556	+	0.632505i	$0.217973\pi$
$468$	−8.12406e7	−	1.40713e8i	−0.792566	−	1.37276i
$469$		−	5.70400e7i		−	0.552918i
$470$	1.29945e7	+	2.25071e7i	0.125160	+	0.216783i
$471$	4.87050e7			0.466134
$472$			1.53208e8i			1.45698i
$473$	1.26865e8	+	2.33769e7i	1.19883	+	0.220904i
$474$	1.24587e8			1.16987
$475$		−	1.26653e8i		−	1.18177i
$476$	−4.27484e6	+	2.46808e6i	−0.0396369	+	0.0228844i
$477$	−3.29675e8			−3.03760
$478$	−5.23770e7	+	3.02399e7i	−0.479575	+	0.276883i
$479$	−1.95238e7	−	3.38162e7i	−0.177647	−	0.307694i	0.763427	−	0.645894i	$-0.223515\pi$
$479$	−1.95238e7	−	3.38162e7i	−0.177647	−	0.307694i	−0.941074	+	0.338200i	$0.890182\pi$
$480$	−2.81160e8	−	1.62328e8i	−2.54232	−	1.46781i
$481$			3.62404e7i			0.325655i
$482$	−2.66945e7	+	4.62362e7i	−0.238386	+	0.412896i
$483$	1.25030e8	+	2.16558e8i	1.10962	+	1.92191i
$484$	3.92786e7			0.346433
$485$	−7.13308e7	+	4.11829e7i	−0.625248	+	0.360987i
$486$	2.63422e7	−	4.56261e7i	0.229479	−	0.397470i
$487$	5.93251e7	−	1.02754e8i	0.513631	−	0.889636i	−0.486244	−	0.873823i	$-0.661633\pi$
$487$	5.93251e7	−	1.02754e8i	0.513631	−	0.889636i	0.999875	−	0.0158124i	$-0.00503344\pi$
$488$	−7.53502e7	+	1.30510e8i	−0.648373	+	1.12301i
$489$	2.25855e7			0.193154
$490$	2.15480e7	−	3.73222e7i	0.183155	−	0.317233i
$491$	4.92435e7	+	2.84307e7i	0.416011	+	0.240184i	0.693369	−	0.720583i	$-0.256126\pi$
$491$	4.92435e7	+	2.84307e7i	0.416011	+	0.240184i	−0.277358	+	0.960767i	$0.589459\pi$
$492$	−1.27126e8	+	7.33963e7i	−1.06743	+	0.616281i
$493$	−8.52914e6	+	4.92430e6i	−0.0711811	+	0.0410964i
$494$	−5.12315e7			−0.424968
$495$		−	5.17489e8i		−	4.26664i
$496$	6.40480e6	+	1.10934e7i	0.0524880	+	0.0909119i
$497$	2.28620e7	+	3.95982e7i	0.186228	+	0.322557i
$498$	−8.05261e7	+	1.39475e8i	−0.652002	+	1.12930i
$499$	−7.73282e7	−	4.46455e7i	−0.622352	−	0.359315i	0.155432	−	0.987847i	$-0.450323\pi$
$499$	−7.73282e7	−	4.46455e7i	−0.622352	−	0.359315i	−0.777784	+	0.628531i	$0.783656\pi$
$500$			6.97691e7i			0.558153i
$501$	2.90714e8	+	1.67844e8i	2.31181	+	1.33473i
$502$	−3.95718e7	−	2.28468e7i	−0.312805	−	0.180598i
$503$	9.16572e7	+	5.29183e7i	0.720216	+	0.415817i	0.814832	−	0.579697i	$-0.196829\pi$
$503$	9.16572e7	+	5.29183e7i	0.720216	+	0.415817i	−0.0946163	+	0.995514i	$0.530162\pi$
$504$	−9.80462e7	−	1.69821e8i	−0.765842	−	1.32648i
$505$			8.62047e7i			0.669356i
$506$	1.20427e8	−	6.95283e7i	0.929546	−	0.536674i
$507$	1.48521e6	+	857485.i	0.0113963	+	0.00657965i
$508$	−1.62548e7			−0.123991
$509$	−4.07676e7	+	7.06116e7i	−0.309145	+	0.535455i	−0.978176	−	0.207780i	$-0.933376\pi$
$509$	−4.07676e7	+	7.06116e7i	−0.309145	+	0.535455i	0.669031	+	0.743235i	$0.266710\pi$
$510$	1.48661e7	−	8.58296e6i	0.112069	−	0.0647034i
$511$	−7.01336e7	−	1.21475e8i	−0.525610	−	0.910383i
$512$		−	5.79586e7i		−	0.431826i
$513$	1.16262e8	+	2.01372e8i	0.861165	+	1.49158i
$514$	1.10145e8			0.811101
$515$		−	2.78425e8i		−	2.03839i
$516$	1.65484e8	−	5.87943e7i	1.20450	−	0.427943i
$517$	−4.98105e7			−0.360453
$518$			1.82023e7i			0.130959i
$519$	3.24052e8	−	1.87091e8i	2.31799	−	1.33829i
$520$	2.04630e8			1.45532
$521$	−2.32675e8	+	1.34335e8i	−1.64527	+	0.949896i	−0.666351	+	0.745638i	$0.732145\pi$
$521$	−2.32675e8	+	1.34335e8i	−1.64527	+	0.949896i	−0.978917	+	0.204257i	$0.934522\pi$
$522$	−8.14124e7	−	1.41010e8i	−0.572373	−	0.991379i
$523$	−1.87003e7	−	1.07966e7i	−0.130721	−	0.0754716i	0.433214	−	0.901291i	$-0.357380\pi$
$523$	−1.87003e7	−	1.07966e7i	−0.130721	−	0.0754716i	−0.563934	+	0.825820i	$0.690713\pi$
$524$			1.13208e8i			0.786831i
$525$	−1.46153e8	+	2.53145e8i	−1.01002	+	1.74941i
$526$	2.28398e7	+	3.95598e7i	0.156941	+	0.271829i
$527$	−5.92714e6			−0.0404961
$528$	6.15773e7	−	3.55517e7i	0.418330	−	0.241523i
$529$	−1.25819e8	+	2.17925e8i	−0.849924	+	1.47211i
$530$	8.63965e7	−	1.49643e8i	0.580321	−	1.00515i
$531$	−2.63278e8	+	4.56011e8i	−1.75846	+	3.04574i
$532$	6.38757e7			0.424229
$533$	7.32702e7	−	1.26908e8i	0.483889	−	0.838120i
$534$	2.10835e8	+	1.21726e8i	1.38458	+	0.799390i
$535$	5.33097e7	−	3.07784e7i	0.348133	−	0.200994i
$536$	−8.98590e7	+	5.18801e7i	−0.583535	+	0.336904i
$537$	−3.53442e8			−2.28242
$538$			4.20125e7i			0.269794i
$539$	4.12989e7	+	7.15318e7i	0.263738	+	0.456807i
$540$	−1.93261e8	−	3.34738e8i	−1.22734	−	2.12581i
$541$	1.43291e8	−	2.48187e8i	0.904953	−	1.56742i	0.0839719	−	0.996468i	$-0.473239\pi$
$541$	1.43291e8	−	2.48187e8i	0.904953	−	1.56742i	0.820981	−	0.570956i	$-0.193427\pi$
$542$	−1.39115e6	−	803180.i	−0.00873726	−	0.00504446i
$543$			5.69867e8i			3.55937i
$544$	1.23163e7	+	7.11080e6i	0.0765037	+	0.0441694i
$545$	−1.35020e8	−	7.79539e7i	−0.834082	−	0.481558i
$546$	1.02398e8	+	5.91195e7i	0.629091	+	0.363206i
$547$	−1.33412e7	−	2.31076e7i	−0.0815140	−	0.141186i	0.822386	−	0.568929i	$-0.192642\pi$
$547$	−1.33412e7	−	2.31076e7i	−0.0815140	−	0.141186i	−0.903900	+	0.427743i	$0.859309\pi$
$548$		−	1.55536e8i		−	0.945128i
$549$	−4.48549e8	+	2.58970e8i	−2.71077	+	1.56506i
$550$	1.40772e8	+	8.12750e7i	0.846115	+	0.488505i
$551$	1.27444e8			0.761844
$552$	2.27439e8	−	3.93936e8i	1.35222	−	2.34212i
$553$	1.34294e8	−	7.75344e7i	0.794109	−	0.458479i
$554$	1.75564e7	+	3.04086e7i	0.103254	+	0.178841i
$555$			1.57134e8i			0.919160i
$556$	4.24860e6	+	7.35879e6i	0.0247184	+	0.0428136i
$557$	1.78573e8			1.03335			0.516677	−	0.856180i	$-0.327169\pi$
$557$	1.78573e8			1.03335			0.516677	+	0.856180i	$0.327169\pi$
$558$		−	9.79921e7i		−	0.564012i
$559$	−1.13721e8	+	1.33430e8i	−0.651034	+	0.763867i
$560$	−4.61753e7			−0.262933
$561$			3.29003e7i			0.186342i
$562$	−6.89122e7	+	3.97865e7i	−0.388228	+	0.224144i
$563$	−2.40345e8			−1.34682			−0.673412	−	0.739267i	$-0.735172\pi$
$563$	−2.40345e8			−1.34682			−0.673412	+	0.739267i	$0.735172\pi$
$564$	−5.87259e7	+	3.39054e7i	−0.327335	+	0.188987i
$565$	1.32402e8	+	2.29327e8i	0.734091	+	1.27148i
$566$	68224.4	+	39389.4i	0.000376262	+	0.000217235i
$567$		−	2.32466e8i		−	1.27529i
$568$	4.15879e7	−	7.20323e7i	0.226945	−	0.393081i
$569$	1.26403e8	+	2.18936e8i	0.686152	+	1.18845i	0.973073	+	0.230496i	$0.0740348\pi$
$569$	1.26403e8	+	2.18936e8i	0.686152	+	1.18845i	−0.286921	+	0.957954i	$0.592632\pi$
$570$	−2.22133e8			−1.19947
$571$	1.07818e8	−	6.22489e7i	0.579141	−	0.334367i	−0.181651	−	0.983363i	$-0.558144\pi$
$571$	1.07818e8	−	6.22489e7i	0.579141	−	0.334367i	0.760792	+	0.648996i	$0.224811\pi$
$572$	−8.16104e7	+	1.41353e8i	−0.436071	+	0.755297i
$573$	2.70909e8	−	4.69227e8i	1.43999	−	2.49413i
$574$	3.68010e7	−	6.37412e7i	0.194592	−	0.337043i
$575$	−4.67199e8			−2.45753
$576$	−7.07798e7	+	1.22594e8i	−0.370375	+	0.641508i
$577$	−1.52174e7	−	8.78578e6i	−0.0792161	−	0.0457354i	0.459869	−	0.887987i	$-0.347896\pi$
$577$	−1.52174e7	−	8.78578e6i	−0.0792161	−	0.0457354i	−0.539085	+	0.842251i	$0.681230\pi$
$578$	8.89630e7	−	5.13628e7i	0.460708	−	0.265990i
$579$	1.82166e7	−	1.05173e7i	0.0938493	−	0.0541839i
$580$	−2.11849e8			−1.08578
$581$			2.00456e8i			1.02209i
$582$	4.32873e7	+	7.49759e7i	0.219580	+	0.380323i
$583$	1.65588e8	+	2.86806e8i	0.835646	+	1.44738i
$584$	−1.27578e8	+	2.20972e8i	−0.640529	+	1.10943i
$585$	6.09065e8	+	3.51644e8i	3.04226	+	1.75645i
$586$		−	1.17876e8i		−	0.585779i
$587$	−2.39183e8	−	1.38093e8i	−1.18254	−	0.682741i	−0.225941	−	0.974141i	$-0.572546\pi$
$587$	−2.39183e8	−	1.38093e8i	−1.18254	−	0.682741i	−0.956601	+	0.291400i	$0.905879\pi$
$588$	9.73818e7	+	5.62234e7i	0.479011	+	0.276557i
$589$	6.64235e7	+	3.83496e7i	0.325069	+	0.187679i
$590$	−1.37992e8	−	2.39010e8i	−0.671892	−	1.16375i
$591$		−	1.51676e8i		−	0.734776i
$592$	−1.28830e7	+	7.43800e6i	−0.0620943	+	0.0358502i
$593$	3.91346e6	+	2.25944e6i	0.0187671	+	0.0108352i	0.509354	−	0.860557i	$-0.329884\pi$
$593$	3.91346e6	+	2.25944e6i	0.0187671	+	0.0108352i	−0.490587	+	0.871392i	$0.663218\pi$
$594$	−2.98429e8			−1.42391
$595$	1.06829e7	−	1.85033e7i	0.0507152	−	0.0878414i
$596$	6.00664e7	−	3.46793e7i	0.283722	−	0.163807i
$597$	−5.82610e7	−	1.00911e8i	−0.273813	−	0.474259i
$598$			1.88983e8i			0.883731i
$599$	2.72993e7	+	4.72838e7i	0.127020	+	0.220005i	0.922521	−	0.385948i	$-0.126125\pi$
$599$	2.72993e7	+	4.72838e7i	0.127020	+	0.220005i	−0.795501	+	0.605952i	$0.792792\pi$
$600$	5.31729e8			2.46171
$601$		−	1.39963e8i		−	0.644746i	−0.946613	−	0.322373i	$-0.895520\pi$
$601$		−	1.39963e8i		−	0.644746i	0.946613	−	0.322373i	$-0.104480\pi$
$602$	−5.71179e7	+	6.70171e7i	−0.261808	+	0.307182i
$603$	−3.56612e8			−1.62646
$604$			598160.i			0.00271461i
$605$	−1.47237e8	+	8.50072e7i	−0.664891	+	0.383875i
$606$	9.06098e7			0.407153
$607$	−2.16886e8	+	1.25219e8i	−0.969764	+	0.559893i	−0.899164	−	0.437611i	$-0.855825\pi$
$607$	−2.16886e8	+	1.25219e8i	−0.969764	+	0.559893i	−0.0705996	+	0.997505i	$0.522491\pi$
$608$	−9.20163e7	−	1.59377e8i	−0.409406	−	0.709111i
$609$	−2.54727e8	−	1.47067e8i	−1.12778	−	0.651123i
$610$		−	2.71468e8i		−	1.19600i
$611$	3.38472e7	−	5.86250e7i	0.148388	−	0.257016i
$612$	1.54303e7	+	2.67261e7i	0.0673165	+	0.116596i
$613$	3.59651e8			1.56135			0.780674	−	0.624939i	$-0.214876\pi$
$613$	3.59651e8			1.56135			0.780674	+	0.624939i	$0.214876\pi$
$614$	8.57771e7	−	4.95235e7i	0.370567	−	0.213947i
$615$	3.17690e8	−	5.50256e8i	1.36577	−	2.36559i
$616$	−9.84925e7	+	1.70594e8i	−0.421367	+	0.729830i
$617$	1.61630e8	−	2.79952e8i	0.688124	−	1.19187i	−0.284320	−	0.958730i	$-0.591768\pi$
$617$	1.61630e8	−	2.79952e8i	0.688124	−	1.19187i	0.972444	−	0.233137i	$-0.0748990\pi$
$618$	−2.92653e8			−1.23990
$619$	−1.43452e8	+	2.48465e8i	−0.604830	+	1.04760i	0.387249	+	0.921975i	$0.373426\pi$
$619$	−1.43452e8	+	2.48465e8i	−0.604830	+	1.04760i	−0.992078	+	0.125621i	$0.959908\pi$
$620$	−1.10415e8	−	6.37481e7i	−0.463290	−	0.267481i
$621$	7.42824e8	−	4.28869e8i	3.10178	−	1.79081i
$622$	8.38798e7	−	4.84280e7i	0.348567	−	0.201245i
$623$	3.03015e8			1.25314
$624$			9.66321e7i			0.397711i
$625$	3.15787e7	+	5.46958e7i	0.129346	+	0.224034i
$626$	2.76198e7	+	4.78389e7i	0.112589	+	0.195010i
$627$	2.12871e8	−	3.68703e8i	0.863601	−	1.49580i
$628$	−3.97450e7	−	2.29468e7i	−0.160474	−	0.0926495i
$629$		−	6.88329e6i		−	0.0276595i
$630$	3.05912e8	+	1.76618e8i	1.22342	+	0.706340i
$631$	−4.08952e8	−	2.36109e8i	−1.62774	−	0.939775i	−0.984766	−	0.173885i	$-0.944368\pi$
$631$	−4.08952e8	−	2.36109e8i	−1.62774	−	0.939775i	−0.642972	−	0.765890i	$-0.722299\pi$
$632$	−2.44291e8	−	1.41041e8i	−0.967733	−	0.558721i
$633$	−3.78642e8	−	6.55827e8i	−1.49285	−	2.58570i
$634$		−	1.74845e7i		−	0.0686096i
$635$	6.09314e7	−	3.51788e7i	0.237969	−	0.137391i
$636$	3.90452e8	+	2.25427e8i	1.51773	+	0.876264i
$637$	−1.12254e8			−0.434292
$638$	−8.17830e7	+	1.41652e8i	−0.314921	+	0.545458i
$639$	2.47566e8	−	1.42933e8i	0.948832	−	0.547808i
$640$	1.77477e8	+	3.07400e8i	0.677022	+	1.17264i
$641$		−	2.26172e8i		−	0.858745i	−0.903127	−	0.429373i	$-0.858735\pi$
$641$		−	2.26172e8i		−	0.858745i	0.903127	−	0.429373i	$-0.141265\pi$
$642$	−3.23511e7	−	5.60338e7i	−0.122260	−	0.211761i
$643$	8.31389e7			0.312731			0.156366	−	0.987699i	$-0.450022\pi$
$643$	8.31389e7			0.312731			0.156366	+	0.987699i	$0.450022\pi$
$644$		−	2.35626e8i		−	0.882196i
$645$	−4.93078e8	+	5.78535e8i	−1.83754	+	2.15601i
$646$	9.73059e6			0.0360946
$647$			8.91000e7i			0.328977i	0.986379	+	0.164488i	$0.0525973\pi$
$647$			8.91000e7i			0.328977i	−0.986379	+	0.164488i	$0.947403\pi$
$648$	−3.66219e8	+	2.11437e8i	−1.34591	+	0.777062i
$649$	5.28954e8			1.93501
$650$	−1.91315e8	+	1.10456e8i	−0.696641	+	0.402206i
$651$	−8.85086e7	−	1.53301e8i	−0.320806	−	0.555652i
$652$	−1.84306e7	−	1.06409e7i	−0.0664960	−	0.0383915i
$653$			7.29592e7i			0.262024i	0.991381	+	0.131012i	$0.0418226\pi$
$653$			7.29592e7i			0.262024i	−0.991381	+	0.131012i	$0.958177\pi$
$654$	−8.19374e7	+	1.41920e8i	−0.292920	+	0.507352i
$655$	−2.45005e8	−	4.24361e8i	−0.871869	−	1.51012i
$656$	6.01520e7			0.213078
$657$	−7.59456e8	+	4.38472e8i	−2.67798	+	1.54613i
$658$	1.70002e7	−	2.94453e7i	0.0596729	−	0.103357i
$659$	3.53221e7	−	6.11797e7i	0.123421	−	0.213772i	−0.797693	−	0.603063i	$-0.793947\pi$
$659$	3.53221e7	−	6.11797e7i	0.123421	−	0.213772i	0.921115	+	0.389291i	$0.127280\pi$
$660$	−3.53852e8	+	6.12890e8i	−1.23081	+	2.13182i
$661$	−8.55699e7			−0.296290			−0.148145	−	0.988966i	$-0.547330\pi$
$661$	−8.55699e7			−0.296290			−0.148145	+	0.988966i	$0.547330\pi$
$662$	9.21890e6	−	1.59676e7i	0.0317764	−	0.0550384i
$663$	−3.87224e7	−	2.23564e7i	−0.132868	−	0.0767115i
$664$	3.15792e8	−	1.82323e8i	1.07869	−	0.622782i
$665$	−2.39440e8	+	1.38241e8i	−0.814200	+	0.470079i
$666$	1.13800e8			0.385229
$667$		−	4.70119e8i		−	1.58427i
$668$	−1.58155e8	−	2.73933e8i	−0.530584	−	0.918999i
$669$	−1.04460e8	−	1.80930e8i	−0.348876	−	0.604270i
$670$	9.34557e7	−	1.61870e8i	0.310729	−	0.538198i
$671$	4.50590e8	+	2.60148e8i	1.49147	+	0.861100i
$672$			4.24736e8i			1.39962i
$673$	2.17027e7	+	1.25301e7i	0.0711981	+	0.0411062i	0.535176	−	0.844740i	$-0.320245\pi$
$673$	2.17027e7	+	1.25301e7i	0.0711981	+	0.0411062i	−0.463978	+	0.885847i	$0.653578\pi$
$674$	−1.42590e8	−	8.23245e7i	−0.465704	−	0.268874i
$675$	8.68322e8	+	5.01326e8i	2.82338	+	1.63008i
$676$	−807989.	−	1.39948e6i	−0.00261556	−	0.00453029i
$677$		−	2.44656e8i		−	0.788478i	−0.919008	−	0.394239i	$-0.871008\pi$
$677$		−	2.44656e8i		−	0.788478i	0.919008	−	0.394239i	$-0.128992\pi$
$678$	2.41046e8	−	1.39168e8i	0.773412	−	0.446530i
$679$	9.33198e7	+	5.38782e7i	0.298102	+	0.172109i
$680$	−3.88661e7			−0.123607
$681$	3.89681e6	−	6.74947e6i	0.0123386	−	0.0213712i
$682$	−8.52499e7	+	4.92191e7i	−0.268745	+	0.155160i
$683$	7.95565e6	+	1.37796e7i	0.0249697	+	0.0432488i	0.878240	−	0.478220i	$-0.158718\pi$
$683$	7.95565e6	+	1.37796e7i	0.0249697	+	0.0432488i	−0.853271	+	0.521469i	$0.825384\pi$
$684$		−	3.99348e8i		−	1.24791i
$685$	3.36614e8	+	5.83032e8i	1.04727	+	1.81393i
$686$	−1.86679e8			−0.578261
$687$			6.99997e8i			2.15887i
$688$	−7.07727e7	−	1.30410e7i	−0.217320	−	0.0400447i
$689$	−4.50080e8			−1.37604
$690$			8.19408e8i			2.49432i
$691$	−4.09123e8	+	2.36207e8i	−1.23999	+	0.715911i	−0.969093	−	0.246696i	$-0.920655\pi$
$691$	−4.09123e8	+	2.36207e8i	−1.23999	+	0.715911i	−0.270902	+	0.962607i	$0.587322\pi$
$692$	−3.52584e8			−1.06401
$693$	−5.86311e8	+	3.38507e8i	−1.76169	+	1.01711i
$694$	−6.72787e7	−	1.16530e8i	−0.201279	−	0.348626i
$695$	−3.18519e7	−	1.83897e7i	−0.0948815	−	0.0547799i
$696$			5.35052e8i			1.58697i
$697$	−1.39165e7	+	2.41041e7i	−0.0410990	+	0.0711856i
$698$	6.75406e7	+	1.16984e8i	0.198609	+	0.344001i
$699$	−3.39046e7			−0.0992720
$700$	2.38533e8	−	1.37717e8i	0.695431	−	0.401507i
$701$	1.46099e8	−	2.53050e8i	0.424123	−	0.734603i	−0.572215	−	0.820104i	$-0.693916\pi$
$701$	1.46099e8	−	2.53050e8i	0.424123	−	0.734603i	0.996338	+	0.0855008i	$0.0272490\pi$
$702$	2.02788e8	−	3.51239e8i	0.586180	−	1.01529i
$703$	−4.45361e7	+	7.71387e7i	−0.128188	+	0.222027i
$704$	1.42204e8			0.407562
$705$	1.46757e8	−	2.54191e8i	0.418824	−	0.725425i
$706$	6.40631e7	+	3.69869e7i	0.182051	+	0.105107i
$707$	9.76693e7	−	5.63894e7i	0.276376	−	0.159566i
$708$	6.23629e8	−	3.60053e8i	1.75722	−	1.01453i
$709$	−2.48444e8			−0.697090			−0.348545	−	0.937292i	$-0.613324\pi$
$709$	−2.48444e8			−0.697090			−0.348545	+	0.937292i	$0.613324\pi$
$710$			1.49831e8i			0.418626i
$711$	−4.84742e8	−	8.39598e8i	−1.34866	−	2.33594i
$712$	−2.75604e8	−	4.77361e8i	−0.763565	−	1.32253i
$713$	1.41465e8	−	2.45024e8i	0.390283	−	0.675989i
$714$	−1.94489e7	−	1.12288e7i	−0.0534318	−	0.0308489i
$715$		−	7.06489e8i		−	1.93280i
$716$	2.88421e8	+	1.66520e8i	0.785757	+	0.453657i
$717$	5.91536e8	+	3.41523e8i	1.60481	+	0.926537i
$718$	−1.03521e8	−	5.97680e7i	−0.279677	−	0.161471i
$719$	2.72842e8	+	4.72575e8i	0.734047	+	1.27141i	0.955140	+	0.296154i	$0.0957042\pi$
$719$	2.72842e8	+	4.72575e8i	0.734047	+	1.27141i	−0.221093	+	0.975253i	$0.570962\pi$
$720$			2.88686e8i			0.773443i
$721$	−3.15454e8	+	1.82127e8i	−0.841646	+	0.485925i
$722$	6.56170e7	+	3.78840e7i	0.174343	+	0.100657i
$723$	6.02964e8			1.59543
$724$	2.68486e8	−	4.65031e8i	0.707467	−	1.22537i
$725$	4.75919e8	−	2.74772e8i	1.24888	−	0.721039i
$726$	8.93511e7	+	1.54761e8i	0.233502	+	0.404437i
$727$			5.40636e8i			1.40702i	0.710683	+	0.703512i	$0.248386\pi$
$727$			5.40636e8i			1.40702i	−0.710683	+	0.703512i	$0.751614\pi$
$728$	−1.33855e8	−	2.31844e8i	−0.346929	−	0.600898i
$729$	6.09694e7			0.157373
$730$		−	4.59634e8i		−	1.18153i
$731$	2.15994e7	−	2.53429e7i	0.0552955	−	0.0648789i
$732$	7.08320e8			1.80591
$733$		−	1.23308e8i		−	0.313096i	−0.987670	−	0.156548i	$-0.949963\pi$
$733$		−	1.23308e8i		−	0.313096i	0.987670	−	0.156548i	$-0.0500367\pi$
$734$	−3.43642e7	+	1.98402e7i	−0.0868996	+	0.0501715i
$735$	−4.86717e8			−1.22579
$736$	−5.87911e8	+	3.39431e8i	−1.47461	+	0.851369i
$737$	1.79117e8	+	3.10241e8i	0.447441	+	0.774990i
$738$	−3.98507e8	−	2.30078e8i	−0.991442	−	0.572409i
$739$		−	3.23751e8i		−	0.802192i	−0.916036	−	0.401096i	$-0.868629\pi$
$739$		−	3.23751e8i		−	0.802192i	0.916036	−	0.401096i	$-0.131371\pi$
$740$	7.40318e7	−	1.28227e8i	0.182694	−	0.316435i
$741$	2.89299e8	+	5.01081e8i	0.711038	+	1.23155i
$742$	−2.26059e8			−0.553364
$743$	−3.22340e8	+	1.86103e8i	−0.785865	+	0.453719i	−0.838505	−	0.544894i	$-0.816570\pi$
$743$	−3.22340e8	+	1.86103e8i	−0.785865	+	0.453719i	0.0526399	+	0.998614i	$0.483236\pi$
$744$	−1.61004e8	+	2.78867e8i	−0.390947	+	0.677140i
$745$	−1.50107e8	+	2.59993e8i	−0.363021	+	0.628771i
$746$	−9.39539e7	+	1.62733e8i	−0.226307	+	0.391976i
$747$	1.25324e9			3.00658
$748$	1.55006e7	−	2.68478e7i	0.0370376	−	0.0641511i
$749$	−6.97433e7	−	4.02663e7i	−0.165980	−	0.0958289i
$750$	−2.74896e8	+	1.58711e8i	−0.651604	+	0.376204i
$751$	−4.22379e8	+	2.43860e8i	−0.997200	+	0.575733i	−0.907419	−	0.420228i	$-0.861950\pi$
$751$	−4.22379e8	+	2.43860e8i	−0.997200	+	0.575733i	−0.0897811	+	0.995962i	$0.528617\pi$
$752$	2.77872e7			0.0653419
$753$			5.16054e8i			1.20868i
$754$	−1.11146e8	−	1.92511e8i	−0.259287	−	0.449098i
$755$	−1.29455e6	−	2.24222e6i	−0.00300799	−	0.00520999i
$756$	−2.52837e8	+	4.37927e8i	−0.585161	+	1.01353i
$757$	5.05455e8	+	2.91824e8i	1.16518	+	0.672720i	0.952541	−	0.304410i	$-0.0984594\pi$
$757$	5.05455e8	+	2.91824e8i	1.16518	+	0.672720i	0.212643	+	0.977130i	$0.431793\pi$
$758$			2.83519e8i			0.650990i
$759$	−1.36008e9	−	7.85240e8i	−3.11055	−	1.79588i
$760$	4.35560e8	+	2.51470e8i	0.992217	+	0.572857i
$761$	−3.53607e7	−	2.04155e7i	−0.0802355	−	0.0463240i	0.459345	−	0.888258i	$-0.348084\pi$
$761$	−3.53607e7	−	2.04155e7i	−0.0802355	−	0.0463240i	−0.539581	+	0.841934i	$0.681417\pi$
$762$	−3.69764e7	−	6.40450e7i	−0.0835718	−	0.144751i
$763$			2.03969e8i			0.459188i
$764$	−4.42142e8	+	2.55271e8i	−0.991475	+	0.572429i
$765$	−1.15682e8	−	6.67891e7i	−0.258394	−	0.149184i
$766$	2.84298e8			0.632539
$767$	−3.59434e8	+	6.22558e8i	−0.796587	+	1.37973i
$768$	5.58303e8	−	3.22337e8i	1.23250	−	0.711584i
$769$	−1.47799e8	−	2.55995e8i	−0.325007	−	0.562929i	0.656507	−	0.754320i	$-0.272033\pi$
$769$	−1.47799e8	−	2.55995e8i	−0.325007	−	0.562929i	−0.981514	+	0.191392i	$0.938700\pi$
$770$		−	3.54844e8i		−	0.777259i
$771$	−6.21977e8	−	1.07730e9i	−1.35710	−	2.35056i
$772$	−1.98205e7			−0.0430787
$773$		−	2.59590e8i		−	0.562018i	−0.959705	−	0.281009i	$-0.909331\pi$
$773$		−	2.59590e8i		−	0.562018i	0.959705	−	0.281009i	$-0.0906690\pi$
$774$	4.18988e8	+	3.57098e8i	0.903605	+	0.770132i
$775$	3.30729e8			0.710506
$776$		−	1.96017e8i		−	0.419478i
$777$	1.78032e8	−	1.02787e8i	0.379519	−	0.219116i
$778$	1.24700e8			0.264807
$779$	3.11915e8	−	1.80084e8i	0.659818	−	0.380946i
$780$	−4.80899e8	−	8.32941e8i	−1.01337	−	1.75522i
$781$	−2.48693e8	−	1.43583e8i	−0.522049	−	0.301405i
$782$		−	3.58944e7i		−	0.0750595i
$783$	−5.04459e8	+	8.73749e8i	−1.05085	+	1.82013i
$784$	−2.30390e7	−	3.99047e7i	−0.0478096	−	0.0828086i
$785$	1.98647e8			0.410651
$786$	−4.46046e8	+	2.57525e8i	−0.918570	+	0.530337i
$787$	1.61611e8	−	2.79919e8i	0.331549	−	0.574259i	−0.651267	−	0.758849i	$-0.725762\pi$
$787$	1.61611e8	−	2.79919e8i	0.331549	−	0.574259i	0.982816	+	0.184589i	$0.0590955\pi$
$788$	−7.14604e7	+	1.23773e8i	−0.146045	+	0.252958i
$789$	2.57949e8	−	4.46780e8i	0.525173	−	0.909626i
$790$	5.08137e8			1.03062
$791$	1.73217e8	−	3.00021e8i	0.349995	−	0.606210i
$792$	1.06655e9	+	6.15771e8i	2.14686	+	1.23949i
$793$	−6.12370e8	+	3.53552e8i	−1.22799	+	0.708979i
$794$	3.07823e7	−	1.77721e7i	0.0614949	−	0.0355041i
$795$	−1.95149e9			−3.88387
$796$			1.09796e8i			0.217694i
$797$	−6.86622e7	−	1.18926e8i	−0.135626	−	0.234911i	0.790210	−	0.612836i	$-0.209971\pi$
$797$	−6.86622e7	−	1.18926e8i	−0.135626	−	0.234911i	−0.925836	+	0.377925i	$0.876638\pi$
$798$	1.45305e8	+	2.51675e8i	0.285937	+	0.495258i
$799$	−6.42873e6	+	1.11349e7i	−0.0126033	+	0.0218296i
$800$	−6.87238e8	−	3.96777e8i	−1.34226	−	0.774955i
$801$		−	1.89444e9i		−	3.68623i
$802$	4.57698e7	+	2.64252e7i	0.0887271	+	0.0512266i
$803$	7.62913e8	+	4.40468e8i	1.47343	+	0.850683i
$804$	4.22354e8	+	2.43846e8i	0.812660	+	0.469189i
$805$	5.09944e8	+	8.83248e8i	0.977540	+	1.69315i
$806$		−	1.33781e8i		−	0.255499i
$807$	4.10913e8	−	2.37241e8i	0.781860	−	0.451407i
$808$	−1.77668e8	−	1.02577e8i	−0.336803	−	0.194453i
$809$	6.32294e8			1.19419			0.597096	−	0.802170i	$-0.296321\pi$
$809$	6.32294e8			1.19419			0.597096	+	0.802170i	$0.296321\pi$
$810$	3.80878e8	−	6.59699e8i	0.716689	−	1.24134i
$811$	−3.05173e8	+	1.76192e8i	−0.572116	+	0.330311i	−0.757994	−	0.652261i	$-0.773820\pi$
$811$	−3.05173e8	+	1.76192e8i	−0.572116	+	0.330311i	0.185878	+	0.982573i	$0.440487\pi$
$812$	1.38578e8	+	2.40024e8i	0.258836	+	0.448318i
$813$			1.81419e7i			0.0337607i
$814$	−5.71589e7	−	9.90022e7i	−0.105977	−	0.183557i
$815$	9.21166e7			0.170163
$816$		−	1.83537e7i		−	0.0337795i
$817$	−4.06030e8	+	1.44257e8i	−0.744547	+	0.264528i
$818$	1.93951e8			0.354349
$819$		−	9.20088e8i		−	1.67486i
$820$	−5.18493e8	+	2.99352e8i	−0.940376	+	0.542926i
$821$	−3.33765e7			−0.0603130			−0.0301565	−	0.999545i	$-0.509601\pi$
$821$	−3.33765e7			−0.0603130			−0.0301565	+	0.999545i	$0.509601\pi$
$822$	6.12825e8	−	3.53815e8i	1.10337	−	0.637031i
$823$	1.32501e8	+	2.29498e8i	0.237694	+	0.411699i	0.960052	−	0.279821i	$-0.0902750\pi$
$823$	1.32501e8	+	2.29498e8i	0.237694	+	0.411699i	−0.722358	+	0.691519i	$0.756942\pi$
$824$	5.73835e8	+	3.31304e8i	1.02566	+	0.592168i
$825$		−	1.83581e9i		−	3.26938i
$826$	−1.80531e8	+	3.12689e8i	−0.320340	+	0.554846i
$827$	−5.20188e8	−	9.00993e8i	−0.919695	−	1.59296i	−0.799877	−	0.600163i	$-0.795102\pi$
$827$	−5.20188e8	−	9.00993e8i	−0.919695	−	1.59296i	−0.119818	−	0.992796i	$-0.538231\pi$
$828$	−1.47312e9			−2.59506
$829$	2.57618e8	−	1.48736e8i	0.452180	−	0.261067i	−0.256570	−	0.966526i	$-0.582592\pi$
$829$	2.57618e8	−	1.48736e8i	0.452180	−	0.261067i	0.708751	+	0.705459i	$0.249259\pi$
$830$	−3.28432e8	+	5.68860e8i	−0.574395	+	0.994882i
$831$	1.98279e8	−	3.43429e8i	0.345520	−	0.598458i
$832$	−9.66303e7	+	1.67369e8i	−0.167781	+	0.290606i
$833$	2.13208e7			0.0368865
$834$	−1.93295e7	+	3.34796e7i	−0.0333213	+	0.0577141i
$835$	1.18570e9	+	6.84563e8i	2.03664	+	1.17586i
$836$	−3.47420e8	+	2.00583e8i	−0.594615	+	0.343301i
$837$	−5.25844e8	+	3.03596e8i	−0.896769	+	0.517750i
$838$	−1.79465e8			−0.304963
$839$		−	4.98295e8i		−	0.843725i	−0.906660	−	0.421862i	$-0.861377\pi$
$839$		−	4.98295e8i		−	0.843725i	0.906660	−	0.421862i	$-0.138623\pi$
$840$	−5.80378e8	−	1.00524e9i	−0.979204	−	1.69603i
$841$	−2.09222e7	−	3.62384e7i	−0.0351739	−	0.0609229i
$842$	1.08633e8	−	1.88158e8i	0.181981	−	0.315201i
$843$	7.78281e8	+	4.49341e8i	1.29913	+	0.750055i
$844$			7.13571e8i			1.18689i
$845$	6.05753e6	+	3.49732e6i	0.0100398	+	0.00579649i
$846$	−1.84091e8	−	1.06285e8i	−0.304033	−	0.175533i
$847$	1.92625e8	+	1.11212e8i	0.317002	+	0.183021i
$848$	−9.23746e7	−	1.59998e8i	−0.151483	−	0.262377i
$849$		−	889712.i		−	0.00145387i
$850$	3.63372e7	−	2.09793e7i	0.0591691	−	0.0341613i
$851$	2.84550e8	+	1.64285e8i	0.461711	+	0.266569i
$852$	−3.90942e8			−0.632111
$853$	−8.52870e7	+	1.47721e8i	−0.137415	+	0.238011i	−0.926518	−	0.376251i	$-0.877213\pi$
$853$	−8.52870e7	+	1.47721e8i	−0.137415	+	0.238011i	0.789102	+	0.614262i	$0.210546\pi$
$854$	−3.07572e8	+	1.77576e8i	−0.493824	+	0.285110i
$855$	8.64274e8	+	1.49697e9i	1.38278	+	2.39505i
$856$			1.46495e8i			0.233562i
$857$	2.65170e8	+	4.59288e8i	0.421291	+	0.729697i	0.996066	−	0.0886142i	$-0.0282438\pi$
$857$	2.65170e8	+	4.59288e8i	0.421291	+	0.729697i	−0.574775	+	0.818311i	$0.694910\pi$
$858$	−7.42591e8			−1.17568
$859$		−	6.93807e8i		−	1.09461i	−0.836933	−	0.547305i	$-0.815654\pi$
$859$		−	6.93807e8i		−	1.09461i	0.836933	−	0.547305i	$-0.184346\pi$
$860$	6.74940e8	−	2.39797e8i	1.06113	−	0.377006i
$861$	−8.31247e8			−1.30233
$862$		−	6.15610e7i		−	0.0961134i
$863$	8.40900e8	−	4.85494e8i	1.30831	−	0.755356i	0.326500	−	0.945197i	$-0.394131\pi$
$863$	8.40900e8	−	4.85494e8i	1.30831	−	0.755356i	0.981815	+	0.189841i	$0.0607974\pi$
$864$	1.45690e9			2.25886
$865$	1.32167e9	−	7.63066e8i	2.04209	−	1.17900i
$866$	−4.56150e7	−	7.90075e7i	−0.0702351	−	0.121651i
$867$	−1.00473e9	−	5.80082e8i	−1.54167	−	0.890086i
$868$			1.66799e8i			0.255055i
$869$	−4.86949e8	+	8.43420e8i	−0.742034	+	1.28524i
$870$	−4.81916e8	−	8.34703e8i	−0.731835	−	1.26758i
$871$	−4.86855e8			−0.736792
$872$	3.21326e8	−	1.85518e8i	0.484615	−	0.279792i
$873$	3.36844e8	−	5.83431e8i	0.506275	−	0.876894i
$874$	−2.32243e8	+	4.02256e8i	−0.347863	+	0.602516i
$875$	−1.97542e8	+	3.42153e8i	−0.294873	+	0.510735i
$876$	1.19929e9			1.78406
$877$	−5.84101e8	+	1.01169e9i	−0.865942	+	1.49986i	0.000166568		1.00000i	$0.499947\pi$
$877$	−5.84101e8	+	1.01169e9i	−0.865942	+	1.49986i	−0.866109	+	0.499856i	$0.833386\pi$
$878$	−1.47680e8	−	8.52631e7i	−0.218192	−	0.125973i
$879$	−1.15292e9	+	6.65636e8i	−1.69758	+	0.980100i
$880$	2.51148e8	−	1.45000e8i	0.368537	−	0.212775i
$881$	9.15828e8			1.33933			0.669663	−	0.742665i	$-0.266439\pi$
$881$	9.15828e8			1.33933			0.669663	+	0.742665i	$0.266439\pi$
$882$			3.52492e8i			0.513740i
$883$	5.19216e7	+	8.99309e7i	0.0754165	+	0.130625i	0.901267	−	0.433263i	$-0.142638\pi$
$883$	5.19216e7	+	8.99309e7i	0.0754165	+	0.130625i	−0.825851	+	0.563889i	$0.809305\pi$
$884$	2.10659e7	+	3.64872e7i	0.0304946	+	0.0528182i
$885$	−1.55846e9	+	2.69933e9i	−2.24836	+	3.89427i
$886$	−4.90369e8	−	2.83115e8i	−0.705053	−	0.407063i
$887$			1.30256e9i			1.86650i	0.359233	+	0.933248i	$0.383038\pi$
$887$			1.30256e9i			1.86650i	−0.359233	+	0.933248i	$0.616962\pi$
$888$	−3.23853e8	−	1.86977e8i	−0.462497	−	0.267023i
$889$	−7.97146e7	−	4.60232e7i	−0.113457	−	0.0655046i
$890$	8.59907e8	+	4.96467e8i	1.21978	+	0.704240i
$891$	7.29991e8	+	1.26438e9i	1.03201	+	1.78750i
$892$			1.96860e8i			0.277372i
$893$	1.44089e8	−	8.31900e7i	0.202338	−	0.116820i
$894$	2.73278e8	+	1.57777e8i	0.382466	+	0.220817i
$895$	−1.44154e9			−2.01075
$896$	2.32188e8	−	4.02161e8i	0.322786	−	0.559082i
$897$	1.84839e9	−	1.06717e9i	2.56105	−	1.47862i
$898$	−8.69869e7	−	1.50666e8i	−0.120123	−	0.208058i
$899$			3.32797e8i			0.458036i
$900$	−8.61001e8	−	1.49130e9i	−1.18107	−	2.04568i
$901$	8.54855e7			0.116874
$902$			4.62251e8i			0.629881i
$903$	9.78015e8	+	1.80215e8i	1.32826	+	0.244753i
$904$	−6.30192e8			−0.853037
$905$			2.32424e9i			3.13571i
$906$	−2.35680e6	+	1.36070e6i	−0.00316911	+	0.00182969i
$907$	4.61854e8			0.618989			0.309494	−	0.950901i	$-0.399840\pi$
$907$	4.61854e8			0.618989			0.309494	+	0.950901i	$0.399840\pi$
$908$	−6.35987e6	+	3.67187e6i	−0.00849553	+	0.00490490i
$909$	−3.52544e8	−	6.10624e8i	−0.469377	−	0.812985i
$910$	4.17638e8	+	2.41123e8i	0.554212	+	0.319974i
$911$		−	6.66793e8i		−	0.881933i	−0.897523	−	0.440967i	$-0.854636\pi$
$911$		−	6.66793e8i		−	0.881933i	0.897523	−	0.440967i	$-0.145364\pi$
$912$	−1.18752e8	+	2.05684e8i	−0.156551	+	0.271154i
$913$	−6.29473e8	−	1.09028e9i	−0.827113	−	1.43260i
$914$	−2.80869e8			−0.367845
$915$	−2.65516e9	+	1.53296e9i	−3.46599	+	2.00109i
$916$	3.29796e8	−	5.71223e8i	0.429100	−	0.743223i
$917$	−3.20532e8	+	5.55178e8i	−0.415684	+	0.719986i
$918$	−3.85163e7	+	6.67122e7i	−0.0497871	+	0.0862338i
$919$	1.30086e9			1.67603			0.838017	−	0.545644i	$-0.183715\pi$
$919$	1.30086e9			1.67603			0.838017	+	0.545644i	$0.183715\pi$
$920$	9.27628e8	−	1.60670e9i	1.19127	−	2.06334i
$921$	−9.68751e8	−	5.59308e8i	−1.24003	−	0.715933i
$922$	3.08504e8	−	1.78115e8i	0.393612	−	0.227252i
$923$	3.37984e8	−	1.95135e8i	0.429824	−	0.248159i
$924$	9.25867e8			1.17363
$925$			3.84082e8i			0.485287i
$926$	−1.30323e8	−	2.25727e8i	−0.164130	−	0.284282i
$927$	1.13865e9	+	1.97220e9i	1.42939	+	2.47578i
$928$	3.99257e8	−	6.91533e8i	0.499584	−	0.865305i
$929$	5.56364e8	+	3.21217e8i	0.693925	+	0.400638i	0.805081	−	0.593165i	$-0.202122\pi$
$929$	5.56364e8	+	3.21217e8i	0.693925	+	0.400638i	−0.111156	+	0.993803i	$0.535455\pi$
$930$		−	5.80058e8i		−	0.721145i
$931$	−2.38935e8	−	1.37949e8i	−0.296095	−	0.170950i
$932$	2.76674e7	+	1.59738e7i	0.0341759	+	0.0197315i
$933$	−9.47323e8	−	5.46937e8i	−1.16641	−	0.673430i
$934$	−1.54796e8	−	2.68114e8i	−0.189985	−	0.329063i
$935$			1.34186e8i			0.164162i
$936$	−1.44948e9	+	8.36856e8i	−1.76760	+	1.02052i
$937$	−9.61983e8	−	5.55401e8i	−1.16936	−	0.675131i	−0.215831	−	0.976431i	$-0.569246\pi$
$937$	−9.61983e8	−	5.55401e8i	−1.16936	−	0.675131i	−0.953529	+	0.301300i	$0.902579\pi$
$938$	−2.44530e8			−0.296294
$939$	3.11932e8	−	5.40283e8i	0.376759	−	0.652566i
$940$	−2.39518e8	+	1.38286e8i	−0.288373	+	0.166492i
$941$	1.25986e7	+	2.18215e7i	0.0151201	+	0.0261888i	0.873486	−	0.486848i	$-0.161854\pi$
$941$	1.25986e7	+	2.18215e7i	0.0151201	+	0.0261888i	−0.858366	+	0.513037i	$0.828520\pi$
$942$		−	2.08798e8i		−	0.249789i
$943$	−6.64298e8	−	1.15060e9i	−0.792187	−	1.37211i
$944$	−2.95082e8			−0.350773
$945$		−	2.18877e9i		−	2.59361i
$946$	1.00216e8	−	5.43868e8i	0.118376	−	0.642422i
$947$	6.61251e8			0.778604			0.389302	−	0.921110i	$-0.372716\pi$
$947$	6.61251e8			0.778604			0.389302	+	0.921110i	$0.372716\pi$
$948$			1.32584e9i			1.55620i
$949$	−1.03683e9	+	5.98613e8i	−1.21313	+	0.700402i
$950$	−5.42959e8			−0.633281
$951$	−1.71011e8	+	9.87331e7i	−0.198830	+	0.114795i
$952$	2.54236e7	+	4.40350e7i	0.0294664	+	0.0510372i
$953$	7.07244e8	+	4.08327e8i	0.817128	+	0.471769i	0.849425	−	0.527709i	$-0.176949\pi$
$953$	7.07244e8	+	4.08327e8i	0.817128	+	0.471769i	−0.0322969	+	0.999478i	$0.510282\pi$
$954$			1.41331e9i			1.62777i
$955$	1.10492e9	−	1.91378e9i	1.26859	−	2.19726i
$956$	−3.21810e8	−	5.57391e8i	−0.368320	−	0.637949i
$957$	1.84728e9			2.10765
$958$	−1.44970e8	+	8.36984e7i	−0.164885	+	0.0951964i
$959$	4.40381e8	−	7.62762e8i	0.499313	−	0.864835i
$960$	−4.18977e8	+	7.25689e8i	−0.473561	+	0.820232i
$961$	3.43609e8	−	5.95149e8i	0.387164	−	0.670587i
$962$	1.55362e8			0.174510
$963$	−2.51743e8	+	4.36032e8i	−0.281890	+	0.488247i
$964$	−4.92040e8	−	2.84080e8i	−0.549250	−	0.317109i
$965$	7.42976e7	−	4.28958e7i	0.0826786	−	0.0477345i
$966$	9.28383e8	−	5.36002e8i	1.02990	−	0.594614i
$967$	−1.91786e8			−0.212098			−0.106049	−	0.994361i	$-0.533820\pi$
$967$	−1.91786e8			−0.212098			−0.106049	+	0.994361i	$0.533820\pi$
$968$		−	4.04607e8i		−	0.446075i
$969$	−5.49477e7	−	9.51723e7i	−0.0603919	−	0.104602i
$970$	1.76551e8	+	3.05795e8i	0.193443	+	0.335054i
$971$	7.55924e8	−	1.30930e9i	0.825697	−	1.43015i	−0.0756889	−	0.997131i	$-0.524116\pi$
$971$	7.55924e8	−	1.30930e9i	0.825697	−	1.43015i	0.901386	−	0.433017i	$-0.142551\pi$
$972$	4.85548e8	+	2.80331e8i	0.528729	+	0.305262i
$973$			4.81174e7i			0.0522352i
$974$	−4.40506e8	−	2.54326e8i	−0.476733	−	0.275242i
$975$	2.16068e9	+	1.24747e9i	2.33118	+	1.34591i
$976$	−2.51366e8	−	1.45126e8i	−0.270369	−	0.156098i
$977$	−2.03751e8	−	3.52907e8i	−0.218482	−	0.378422i	0.735862	−	0.677132i	$-0.236777\pi$
$977$	−2.03751e8	−	3.52907e8i	−0.218482	−	0.378422i	−0.954344	+	0.298709i	$0.903444\pi$
$978$		−	9.68237e7i		−	0.103506i
$979$	−1.64810e9	+	9.51531e8i	−1.75645	+	1.01409i
$980$	3.97179e8	+	2.29311e8i	0.421995	+	0.243639i
$981$	1.27521e9			1.35074
$982$	1.21882e8	−	2.11106e8i	0.128708	−	0.222929i
$983$	−7.78026e8	+	4.49193e8i	−0.819094	+	0.472904i	−0.850104	−	0.526615i	$-0.823461\pi$
$983$	−7.78026e8	+	4.49193e8i	−0.819094	+	0.472904i	0.0310102	+	0.999519i	$0.490128\pi$
$984$	7.56052e8	+	1.30952e9i	0.793536	+	1.37444i
$985$		−	6.18622e8i		−	0.647317i
$986$	2.11104e7	+	3.65643e7i	0.0220225	+	0.0381441i
$987$	−3.83995e8			−0.399369
$988$		−	5.45200e8i		−	0.565308i
$989$	5.32138e8	+	1.49777e9i	0.550092	+	1.54830i
$990$	−2.21847e9			−2.28638
$991$			9.70138e8i			0.996811i	0.866944	+	0.498405i	$0.166081\pi$
$991$			9.70138e8i			0.996811i	−0.866944	+	0.498405i	$0.833919\pi$
$992$	4.16182e8	−	2.40283e8i	0.426332	−	0.246143i
$993$	−2.08233e8			−0.212668
$994$	1.69757e8	−	9.80094e7i	0.172850	−	0.0997950i
$995$	−2.37622e8	−	4.11573e8i	−0.241222	−	0.417809i
$996$	−1.48428e9	−	8.56950e8i	−1.50224	−	0.867317i
$997$			7.47089e8i			0.753853i	0.926243	+	0.376927i	$0.123019\pi$
$997$			7.47089e8i			0.753853i	−0.926243	+	0.376927i	$0.876981\pi$
$998$	−1.91395e8	+	3.31505e8i	−0.192548	+	0.333502i
$999$	−3.52572e8	−	6.10672e8i	−0.353631	−	0.612508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.7.8	✓	42
43.37	odd	6	inner	43.7.d.a.37.14	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.8	✓	42	1.1	even	1	trivial
43.7.d.a.37.14	yes	42	43.37	odd	6	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-4.28699i q^{2} +(-41.9299 + 24.2082i) q^{3} +45.6217 q^{4} +(-171.014 + 98.7351i) q^{5} +(103.780 + 179.753i) q^{6} +(223.732 + 129.172i) q^{7} -469.947i q^{8} +(807.577 - 1398.76i) q^{9} +O(q^{10})\)	\(q-4.28699i q^{2} +(-41.9299 + 24.2082i) q^{3} +45.6217 q^{4} +(-171.014 + 98.7351i) q^{5} +(103.780 + 179.753i) q^{6} +(223.732 + 129.172i) q^{7} -469.947i q^{8} +(807.577 - 1398.76i) q^{9} +(423.276 + 733.136i) q^{10} -1622.51 q^{11} +(-1912.91 + 1104.42i) q^{12} +(1102.52 - 1909.63i) q^{13} +(553.758 - 959.138i) q^{14} +(4780.40 - 8279.90i) q^{15} +905.130 q^{16} +(-209.407 + 362.703i) q^{17} +(-5996.49 - 3462.07i) q^{18} +(4693.50 - 2709.79i) q^{19} +(-7801.96 + 4504.46i) q^{20} -12508.1 q^{21} +6955.67i q^{22} +(-9995.93 - 17313.5i) q^{23} +(11376.6 + 19704.8i) q^{24} +(11684.7 - 20238.5i) q^{25} +(-8186.55 - 4726.51i) q^{26} +42904.4i q^{27} +(10207.0 + 5893.04i) q^{28} +(20365.0 + 11757.8i) q^{29} +(-35495.8 - 20493.5i) q^{30} +(7076.11 + 12256.2i) q^{31} -33956.9i q^{32} +(68031.5 - 39278.0i) q^{33} +(1554.90 + 897.724i) q^{34} -51015.1 q^{35} +(36843.0 - 63814.0i) q^{36} +(-14233.3 + 8217.61i) q^{37} +(-11616.9 - 20121.0i) q^{38} +106761. i q^{39} +(46400.3 + 80367.6i) q^{40} +66456.8 q^{41} +53622.0i q^{42} +(-78190.6 - 14407.9i) q^{43} -74021.5 q^{44} +318944. i q^{45} +(-74222.6 + 42852.5i) q^{46} +30699.7 q^{47} +(-37952.0 + 21911.6i) q^{48} +(-25453.8 - 44087.3i) q^{49} +(-86762.4 - 50092.3i) q^{50} -20277.5i q^{51} +(50299.0 - 87120.4i) q^{52} +(-102057. - 176768. i) q^{53} +183931. q^{54} +(277471. - 160198. i) q^{55} +(60703.9 - 105142. i) q^{56} +(-131199. + 227243. i) q^{57} +(50405.4 - 87304.7i) q^{58} -326010. q^{59} +(218090. - 377743. i) q^{60} +(-277713. - 160338. i) q^{61} +(52542.1 - 30335.2i) q^{62} +(361362. - 208632. i) q^{63} -87644.7 q^{64} +435431. i q^{65} +(-168384. - 291650. i) q^{66} +(-110396. - 191211. i) q^{67} +(-9553.49 + 16547.1i) q^{68} +(838256. + 483967. i) q^{69} +218701. i q^{70} +(153277. + 88494.7i) q^{71} +(-657345. - 379518. i) q^{72} +(-470207. - 271474. i) q^{73} +(35228.8 + 61018.1i) q^{74} +1.13147e6i q^{75} +(214126. - 123625. i) q^{76} +(-363007. - 209582. i) q^{77} +457681. q^{78} +(300121. - 519825. i) q^{79} +(-154790. + 89368.0i) q^{80} +(-449916. - 779278. i) q^{81} -284900. i q^{82} +(387964. + 671973. i) q^{83} -570640. q^{84} -82703.1i q^{85} +(-61766.5 + 335203. i) q^{86} -1.13854e6 q^{87} +762492. i q^{88} +(1.01577e6 - 586458. i) q^{89} +1.36731e6 q^{90} +(493340. - 284830. i) q^{91} +(-456031. - 789870. i) q^{92} +(-593401. - 342600. i) q^{93} -131610. i q^{94} +(-535103. + 926826. i) q^{95} +(822037. + 1.42381e6i) q^{96} +417105. q^{97} +(-189002. + 109120. i) q^{98} +(-1.31030e6 + 2.26950e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

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