LMFDB - Embedded newform 43.7.f.a.22.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(2,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([9]))

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

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

chi := DirichletCharacter("43.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.f (of order $14$, degree $6$, 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:	$126$
Relative dimension:	$21$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			22.10
Character	$\chi$	$=$	43.22
Dual form			43.7.f.a.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.716329 + 1.48747i) q^{2} +(3.40007 + 7.06031i) q^{3} +(38.2039 + 47.9062i) q^{4} +(69.5466 - 15.8736i) q^{5} -12.9376 q^{6} +168.130i q^{7} +(-201.638 + 46.0227i) q^{8} +(416.237 - 521.944i) q^{9} +O(q^{10})$	\(q+(-0.716329 + 1.48747i) q^{2} +(3.40007 + 7.06031i) q^{3} +(38.2039 + 47.9062i) q^{4} +(69.5466 - 15.8736i) q^{5} -12.9376 q^{6} +168.130i q^{7} +(-201.638 + 46.0227i) q^{8} +(416.237 - 521.944i) q^{9} +(-26.2068 + 114.819i) q^{10} +(-494.032 + 619.497i) q^{11} +(-208.337 + 432.616i) q^{12} +(419.543 + 1838.14i) q^{13} +(-250.089 - 120.436i) q^{14} +(348.535 + 437.049i) q^{15} +(-796.646 + 3490.33i) q^{16} +(-1487.47 + 6517.04i) q^{17} +(478.215 + 993.023i) q^{18} +(7489.56 - 5972.73i) q^{19} +(3417.39 + 2725.28i) q^{20} +(-1187.05 + 571.653i) q^{21} +(-567.595 - 1178.62i) q^{22} +(-10784.3 + 13523.1i) q^{23} +(-1010.52 - 1267.15i) q^{24} +(-9492.88 + 4571.53i) q^{25} +(-3034.71 - 692.652i) q^{26} +(10669.8 + 2435.31i) q^{27} +(-8054.46 + 6423.22i) q^{28} +(16175.3 - 33588.4i) q^{29} +(-899.764 + 205.365i) q^{30} +(22421.8 + 10797.8i) q^{31} +(-14970.0 - 11938.2i) q^{32} +(-6053.58 - 1381.69i) q^{33} +(-8628.40 - 6880.92i) q^{34} +(2668.82 + 11692.9i) q^{35} +40906.2 q^{36} -93504.2i q^{37} +(3519.27 + 15418.9i) q^{38} +(-11551.3 + 9211.89i) q^{39} +(-13292.7 + 6401.44i) q^{40} +(-68207.6 - 32847.0i) q^{41} -2175.19i q^{42} +(44101.9 - 66154.2i) q^{43} -48551.7 q^{44} +(20662.7 - 42906.6i) q^{45} +(-12390.1 - 25728.4i) q^{46} +(41930.8 + 52579.6i) q^{47} +(-27351.5 + 6242.80i) q^{48} +89381.3 q^{49} -17395.1i q^{50} +(-51069.8 + 11656.4i) q^{51} +(-72030.0 + 90322.7i) q^{52} +(-295.187 + 1293.30i) q^{53} +(-11265.5 + 14126.5i) q^{54} +(-24524.7 + 50926.0i) q^{55} +(-7737.79 - 33901.5i) q^{56} +(67634.3 + 32571.0i) q^{57} +(38375.0 + 48120.7i) q^{58} +(60509.5 - 265109. i) q^{59} +(-7621.96 + 33394.0i) q^{60} +(115247. + 239313. i) q^{61} +(-32122.7 + 25617.0i) q^{62} +(87754.5 + 69981.8i) q^{63} +(-177954. + 85698.3i) q^{64} +(58355.6 + 121177. i) q^{65} +(6391.58 - 8014.79i) q^{66} +(113411. + 142213. i) q^{67} +(-369034. + 177717. i) q^{68} +(-132145. - 30161.2i) q^{69} +(-19304.6 - 4406.14i) q^{70} +(120336. - 95964.5i) q^{71} +(-59908.0 + 124400. i) q^{72} +(127177. - 29027.2i) q^{73} +(139085. + 66979.7i) q^{74} +(-64552.8 - 51479.2i) q^{75} +(572261. + 130615. i) q^{76} +(-104156. - 83061.7i) q^{77} +(-5427.87 - 23781.0i) q^{78} -574914. q^{79} +255387. i q^{80} +(-89211.3 - 390860. i) q^{81} +(97718.0 - 77927.5i) q^{82} +(536050. - 258148. i) q^{83} +(-72735.6 - 35027.6i) q^{84} +476850. i q^{85} +(66811.1 + 112989. i) q^{86} +292142. q^{87} +(71105.0 - 147651. i) q^{88} +(-200851. - 417071. i) q^{89} +(49021.0 + 61470.4i) q^{90} +(-309046. + 70537.8i) q^{91} -1.05984e6 q^{92} +195018. i q^{93} +(-108247. + 24706.6i) q^{94} +(426065. - 534269. i) q^{95} +(33388.3 - 146283. i) q^{96} +(847827. - 1.06314e6i) q^{97} +(-64026.4 + 132952. i) q^{98} +(117709. + 515715. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) $ 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

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 $

$2$	−0.716329	+	1.48747i	−0.0895411	+	0.185934i	−0.940930	−	0.338601i	$-0.890046\pi$
$2$	−0.716329	+	1.48747i	−0.0895411	+	0.185934i	0.851389	+	0.524535i	$0.175761\pi$
$3$	3.40007	+	7.06031i	0.125928	+	0.261493i	0.954396	−	0.298544i	$-0.0965011\pi$
$3$	3.40007	+	7.06031i	0.125928	+	0.261493i	−0.828467	+	0.560037i	$0.810787\pi$
$4$	38.2039	+	47.9062i	0.596936	+	0.748534i
$5$	69.5466	−	15.8736i	0.556373	−	0.126988i	0.0649165	−	0.997891i	$-0.479322\pi$
$5$	69.5466	−	15.8736i	0.556373	−	0.126988i	0.491456	+	0.870902i	$0.336465\pi$
$6$	−12.9376			−0.0598962
$7$			168.130i			0.490175i	0.969501	+	0.245087i	$0.0788167\pi$
$7$			168.130i			0.490175i	−0.969501	+	0.245087i	$0.921183\pi$
$8$	−201.638	+	46.0227i	−0.393825	+	0.0898880i
$9$	416.237	−	521.944i	0.570969	−	0.715973i
$10$	−26.2068	+	114.819i	−0.0262068	+	0.114819i
$11$	−494.032	+	619.497i	−0.371174	+	0.465437i	−0.931980	−	0.362510i	$-0.881920\pi$
$11$	−494.032	+	619.497i	−0.371174	+	0.465437i	0.560806	+	0.827947i	$0.310491\pi$
$12$	−208.337	+	432.616i	−0.120565	+	0.250356i
$13$	419.543	+	1838.14i	0.190962	+	0.836658i	0.976097	+	0.217334i	$0.0697361\pi$
$13$	419.543	+	1838.14i	0.190962	+	0.836658i	−0.785136	+	0.619324i	$0.787407\pi$
$14$	−250.089	−	120.436i	−0.0911401	−	0.0438908i
$15$	348.535	+	437.049i	0.103270	+	0.129496i
$16$	−796.646	+	3490.33i	−0.194494	+	0.852133i
$17$	−1487.47	+	6517.04i	−0.302763	+	1.32649i	0.563175	+	0.826338i	$0.309580\pi$
$17$	−1487.47	+	6517.04i	−0.302763	+	1.32649i	−0.865938	+	0.500152i	$0.833277\pi$
$18$	478.215	+	993.023i	0.0819984	+	0.170272i
$19$	7489.56	−	5972.73i	1.09193	−	0.870787i	0.0996791	−	0.995020i	$-0.468218\pi$
$19$	7489.56	−	5972.73i	1.09193	−	0.870787i	0.992253	+	0.124233i	$0.0396470\pi$
$20$	3417.39	+	2725.28i	0.427174	+	0.340660i
$21$	−1187.05	+	571.653i	−0.128177	+	0.0617269i
$22$	−567.595	−	1178.62i	−0.0533053	−	0.110690i
$23$	−10784.3	+	13523.1i	−0.886359	+	1.11146i	0.106753	+	0.994286i	$0.465955\pi$
$23$	−10784.3	+	13523.1i	−0.886359	+	1.11146i	−0.993112	+	0.117173i	$0.962617\pi$
$24$	−1010.52	−	1267.15i	−0.0730988	−	0.0916630i
$25$	−9492.88	+	4571.53i	−0.607544	+	0.292578i
$26$	−3034.71	−	692.652i	−0.172662	−	0.0394090i
$27$	10669.8	+	2435.31i	0.542081	+	0.123727i
$28$	−8054.46	+	6423.22i	−0.366913	+	0.292603i
$29$	16175.3	−	33588.4i	0.663222	−	1.37720i	−0.249403	−	0.968400i	$-0.580234\pi$
$29$	16175.3	−	33588.4i	0.663222	−	1.37720i	0.912626	−	0.408796i	$-0.134051\pi$
$30$	−899.764	+	205.365i	−0.0333246	+	0.00760612i
$31$	22421.8	+	10797.8i	0.752635	+	0.362450i	0.770542	−	0.637390i	$-0.219986\pi$
$31$	22421.8	+	10797.8i	0.752635	+	0.362450i	−0.0179063	+	0.999840i	$0.505700\pi$
$32$	−14970.0	−	11938.2i	−0.456848	−	0.364324i
$33$	−6053.58	−	1381.69i	−0.168450	−	0.0384476i
$34$	−8628.40	−	6880.92i	−0.219530	−	0.175069i
$35$	2668.82	+	11692.9i	0.0622466	+	0.272720i
$36$	40906.2			0.876762
$37$		−	93504.2i		−	1.84597i	−0.384830	−	0.922987i	$-0.625740\pi$
$37$		−	93504.2i		−	1.84597i	0.384830	−	0.922987i	$-0.374260\pi$
$38$	3519.27	+	15418.9i	0.0641361	+	0.280998i
$39$	−11551.3	+	9211.89i	−0.194733	+	0.155294i
$40$	−13292.7	+	6401.44i	−0.207699	+	0.100022i
$41$	−68207.6	−	32847.0i	−0.989648	−	0.476590i	−0.132235	−	0.991218i	$-0.542215\pi$
$41$	−68207.6	−	32847.0i	−0.989648	−	0.476590i	−0.857413	+	0.514629i	$0.827930\pi$
$42$		−	2175.19i		−	0.0293596i
$43$	44101.9	−	66154.2i	0.554692	−	0.832055i
$43$	44101.9	−	66154.2i	0.554692	−	0.832055i
$44$	−48551.7			−0.569963
$45$	20662.7	−	42906.6i	0.226751	−	0.470854i
$46$	−12390.1	−	25728.4i	−0.127292	−	0.264325i
$47$	41930.8	+	52579.6i	0.403868	+	0.506435i	0.941624	−	0.336666i	$-0.109299\pi$
$47$	41930.8	+	52579.6i	0.403868	+	0.506435i	−0.537756	+	0.843101i	$0.680728\pi$
$48$	−27351.5	+	6242.80i	−0.247319	+	0.0564489i
$49$	89381.3			0.759729
$50$		−	17395.1i		−	0.139161i
$51$	−51069.8	+	11656.4i	−0.384994	+	0.0878724i
$52$	−72030.0	+	90322.7i	−0.512275	+	0.642373i
$53$	−295.187	+	1293.30i	−0.00198276	+	0.00868703i	−0.975910	−	0.218175i	$-0.929990\pi$
$53$	−295.187	+	1293.30i	−0.00198276	+	0.00868703i	0.973927	+	0.226862i	$0.0728467\pi$
$54$	−11265.5	+	14126.5i	−0.0715435	+	0.0897127i
$55$	−24524.7	+	50926.0i	−0.147406	+	0.306092i
$56$	−7737.79	−	33901.5i	−0.0440608	−	0.193043i
$57$	67634.3	+	32571.0i	0.365210	+	0.175876i
$58$	38375.0	+	48120.7i	0.196682	+	0.246631i
$59$	60509.5	−	265109.i	0.294623	−	1.29083i	−0.583389	−	0.812193i	$-0.698274\pi$
$59$	60509.5	−	265109.i	0.294623	−	1.29083i	0.878013	−	0.478637i	$-0.158869\pi$
$60$	−7621.96	+	33394.0i	−0.0352868	+	0.154602i
$61$	115247.	+	239313.i	0.507739	+	1.05433i	0.984514	+	0.175306i	$0.0560914\pi$
$61$	115247.	+	239313.i	0.507739	+	1.05433i	−0.476775	+	0.879025i	$0.658194\pi$
$62$	−32122.7	+	25617.0i	−0.134784	+	0.107486i
$63$	87754.5	+	69981.8i	0.350952	+	0.279875i
$64$	−177954.	+	85698.3i	−0.678842	+	0.326913i
$65$	58355.6	+	121177.i	0.212492	+	0.441244i
$66$	6391.58	−	8014.79i	0.0222319	−	0.0278779i
$67$	113411.	+	142213.i	0.377078	+	0.472840i	0.933768	−	0.357880i	$-0.116500\pi$
$67$	113411.	+	142213.i	0.377078	+	0.472840i	−0.556690	+	0.830720i	$0.687929\pi$
$68$	−369034.	+	177717.i	−1.17365	+	0.565201i
$69$	−132145.	−	30161.2i	−0.402256	−	0.0918124i
$70$	−19304.6	−	4406.14i	−0.0562815	−	0.0128459i
$71$	120336.	−	95964.5i	0.336217	−	0.268124i	−0.440798	−	0.897606i	$-0.645304\pi$
$71$	120336.	−	95964.5i	0.336217	−	0.268124i	0.777015	+	0.629482i	$0.216733\pi$
$72$	−59908.0	+	124400.i	−0.160505	+	0.333291i
$73$	127177.	−	29027.2i	0.326918	−	0.0746169i	−0.0559121	−	0.998436i	$-0.517807\pi$
$73$	127177.	−	29027.2i	0.326918	−	0.0746169i	0.382830	+	0.923819i	$0.374950\pi$
$74$	139085.	+	66979.7i	0.343229	+	0.165291i
$75$	−64552.8	−	51479.2i	−0.153014	−	0.122025i
$76$	572261.	+	130615.i	1.30363	+	0.297544i
$77$	−104156.	−	83061.7i	−0.228146	−	0.181940i
$78$	−5427.87	−	23781.0i	−0.0114379	−	0.0501126i
$79$	−574914.			−1.16606			−0.583031	−	0.812450i	$-0.698133\pi$
$79$	−574914.			−1.16606			−0.583031	+	0.812450i	$0.698133\pi$
$80$			255387.i			0.498802i
$81$	−89211.3	−	390860.i	−0.167867	−	0.735472i
$82$	97718.0	−	77927.5i	0.177228	−	0.141335i
$83$	536050.	−	258148.i	0.937499	−	0.451476i	0.0982125	−	0.995165i	$-0.468688\pi$
$83$	536050.	−	258148.i	0.937499	−	0.451476i	0.839286	+	0.543690i	$0.182973\pi$
$84$	−72735.6	−	35027.6i	−0.122718	−	0.0590980i
$85$			476850.i			0.776470i
$86$	66811.1	+	112989.i	0.105040	+	0.177639i
$87$	292142.			0.443645
$88$	71105.0	−	147651.i	0.104340	−	0.216665i
$89$	−200851.	−	417071.i	−0.284908	−	0.591617i	0.708570	−	0.705640i	$-0.249340\pi$
$89$	−200851.	−	417071.i	−0.284908	−	0.591617i	−0.993478	+	0.114023i	$0.963626\pi$
$90$	49021.0	+	61470.4i	0.0672442	+	0.0843216i
$91$	−309046.	+	70537.8i	−0.410109	+	0.0936047i
$92$	−1.05984e6			−1.36106
$93$			195018.i			0.242452i
$94$	−108247.	+	24706.6i	−0.130326	+	0.0297461i
$95$	426065.	−	534269.i	0.496942	−	0.623145i
$96$	33388.3	−	146283.i	0.0377381	−	0.165341i
$97$	847827.	−	1.06314e6i	0.928949	−	1.16487i	−0.0570930	−	0.998369i	$-0.518183\pi$
$97$	847827.	−	1.06314e6i	0.928949	−	1.16487i	0.986042	−	0.166496i	$-0.0532454\pi$
$98$	−64026.4	+	132952.i	−0.0680269	+	0.141259i
$99$	117709.	+	515715.i	0.121312	+	0.531501i
$100$	−581669.	−	280117.i	−0.581669	−	0.280117i
$101$	−1.16452e6	−	1.46027e6i	−1.13027	−	1.41732i	−0.895383	−	0.445297i	$-0.853098\pi$
$101$	−1.16452e6	−	1.46027e6i	−1.13027	−	1.41732i	−0.234892	−	0.972022i	$-0.575473\pi$
$102$	19244.3	−	84314.7i	0.0181343	−	0.0794517i
$103$	79315.4	−	347503.i	0.0725848	−	0.318015i	−0.925581	−	0.378549i	$-0.876423\pi$
$103$	79315.4	−	347503.i	0.0725848	−	0.318015i	0.998166	+	0.0605340i	$0.0192804\pi$
$104$	−169192.	−	351331.i	−0.150411	−	0.312332i
$105$	−73481.1	+	58599.2i	−0.0634757	+	0.0506202i
$106$	−1712.29	−	1365.51i	−0.00143768	−	0.00114651i
$107$	337892.	−	162720.i	0.275820	−	0.132828i	−0.290860	−	0.956765i	$-0.593942\pi$
$107$	337892.	−	162720.i	0.275820	−	0.132828i	0.566681	+	0.823937i	$0.308227\pi$
$108$	290961.	+	604187.i	0.230974	+	0.479623i
$109$	101435.	−	127195.i	0.0783261	−	0.0982178i	−0.741125	−	0.671368i	$-0.765707\pi$
$109$	101435.	−	127195.i	0.0783261	−	0.0982178i	0.819451	+	0.573150i	$0.194279\pi$
$110$	−58183.2	−	72959.5i	−0.0437139	−	0.0548155i
$111$	660168.	−	317920.i	0.482709	−	0.232461i
$112$	−586830.	−	133940.i	−0.417694	−	0.0953359i
$113$	594690.	+	135734.i	0.412150	+	0.0940706i	0.423568	−	0.905864i	$-0.360777\pi$
$113$	594690.	+	135734.i	0.412150	+	0.0940706i	−0.0114180	+	0.999935i	$0.503635\pi$
$114$	−96896.8	+	77272.6i	−0.0654026	+	0.0521568i
$115$	−535353.	+	1.11167e6i	−0.352003	+	0.730943i
$116$	2.22705e6	−	508311.i	1.42678	−	0.325653i
$117$	1.13403e6	+	546122.i	0.708058	+	0.340983i
$118$	350998.	+	279911.i	0.213628	+	0.170363i
$119$	−1.09571e6	−	250089.i	−0.650212	−	0.148407i
$120$	−90392.3	−	72085.4i	−0.0523104	−	0.0417161i
$121$	254501.	+	1.11504e6i	0.143659	+	0.629412i
$122$	−438526.			−0.241499
$123$		−	593249.i		−	0.318802i
$124$	339320.	+	1.48666e6i	0.177969	+	0.779733i
$125$	−1.45907e6	+	1.16357e6i	−0.747043	+	0.595747i
$126$	−166957.	+	80402.3i	−0.0834628	+	0.0401936i
$127$	86453.2	+	41633.7i	0.0422056	+	0.0203251i	0.454868	−	0.890559i	$-0.349687\pi$
$127$	86453.2	+	41633.7i	0.0422056	+	0.0203251i	−0.412662	+	0.910884i	$0.635401\pi$
$128$		−	1.55152e6i		−	0.739823i
$129$	617019.	+	86444.6i	0.287428	+	0.0402688i
$130$	−222049.			−0.101069
$131$	−1.09070e6	+	2.26487e6i	−0.485168	+	1.00746i	0.504410	+	0.863464i	$0.331710\pi$
$131$	−1.09070e6	+	2.26487e6i	−0.485168	+	1.00746i	−0.989578	+	0.143997i	$0.954004\pi$
$132$	−165079.	−	342790.i	−0.0717745	−	0.149041i
$133$	1.00419e6	+	1.25922e6i	0.426838	+	0.535238i
$134$	−292777.	+	66824.5i	−0.121681	+	0.0277729i
$135$	780705.			0.317311
$136$		−	1.38254e6i		−	0.549620i
$137$	−3.64184e6	+	831227.i	−1.41631	+	0.323264i	−0.861097	−	0.508441i	$-0.830222\pi$
$137$	−3.64184e6	+	831227.i	−1.41631	+	0.323264i	−0.555217	+	0.831705i	$0.687365\pi$
$138$	139523.	−	174956.i	0.0530895	−	0.0665721i
$139$	−586352.	+	2.56898e6i	−0.218330	+	0.956568i	0.740381	+	0.672188i	$0.234645\pi$
$139$	−586352.	+	2.56898e6i	−0.218330	+	0.956568i	−0.958711	+	0.284381i	$0.908212\pi$
$140$	−458201.	+	574566.i	−0.166983	+	0.209390i
$141$	−228661.	+	474819.i	−0.0815707	+	0.169383i
$142$	56544.6	+	247738.i	0.0197481	+	0.0865223i
$143$	−1.34599e6	−	648194.i	−0.460292	−	0.221665i
$144$	1.49017e6	+	1.86861e6i	0.499054	+	0.625794i
$145$	591772.	−	2.59272e6i	0.194111	−	0.850456i
$146$	−47923.1	+	209965.i	−0.0153988	+	0.0674664i
$147$	303902.	+	631060.i	0.0956714	+	0.198664i
$148$	4.47943e6	−	3.57222e6i	1.38177	−	1.10193i
$149$	−1.71496e6	−	1.36763e6i	−0.518436	−	0.413439i	0.329005	−	0.944328i	$-0.393287\pi$
$149$	−1.71496e6	−	1.36763e6i	−0.518436	−	0.413439i	−0.847441	+	0.530889i	$0.821858\pi$
$150$	122815.	−	59144.5i	0.0363896	−	0.0175243i
$151$	998705.	+	2.07383e6i	0.290072	+	0.602342i	0.994178	−	0.107754i	$-0.0343659\pi$
$151$	998705.	+	2.07383e6i	0.290072	+	0.602342i	−0.704105	+	0.710096i	$0.748652\pi$
$152$	−1.23530e6	+	1.54902e6i	−0.351757	+	0.441089i
$153$	2.78239e6	+	3.48901e6i	0.776862	+	0.974155i
$154$	198162.	−	95429.7i	0.0542572	−	0.0261289i
$155$	1.73076e6	+	395034.i	0.464773	+	0.106081i
$156$	−882613.	−	201451.i	−0.232486	−	0.0530634i
$157$	−1.77670e6	+	1.41687e6i	−0.459108	+	0.366126i	−0.825563	−	0.564309i	$-0.809143\pi$
$157$	−1.77670e6	+	1.41687e6i	−0.459108	+	0.366126i	0.366456	+	0.930435i	$0.380571\pi$
$158$	411827.	−	855168.i	0.104410	−	0.216811i
$159$	−10134.7	+	2313.19i	−0.00252128	+	0.000575466i
$160$	−1.23061e6	−	592633.i	−0.300443	−	0.144686i
$161$	−2.27364e6	−	1.81317e6i	−0.544809	−	0.434471i
$162$	645298.	+	147285.i	0.151780	+	0.0346428i
$163$	3.47035e6	+	2.76751e6i	0.801328	+	0.639038i	0.936059	−	0.351844i	$-0.114445\pi$
$163$	3.47035e6	+	2.76751e6i	0.801328	+	0.639038i	−0.134730	+	0.990882i	$0.543017\pi$
$164$	−1.03222e6	−	4.52245e6i	−0.234013	−	1.02528i
$165$	−442939.			−0.0986034
$166$			982277.i			0.214738i
$167$	44133.1	+	193360.i	0.00947578	+	0.0415161i	0.979445	−	0.201712i	$-0.0646506\pi$
$167$	44133.1	+	193360.i	0.00947578	+	0.0415161i	−0.969969	+	0.243229i	$0.921793\pi$
$168$	213046.	−	169898.i	0.0449309	−	0.0358312i
$169$	1.14607e6	−	551918.i	0.237438	−	0.114344i
$170$	−709300.	−	341581.i	−0.144372	−	0.0695260i
$171$		−	6.39520e6i		−	1.27899i
$172$	4.85406e6	−	414595.i	0.953938	−	0.0814776i
$173$	−8.32663e6			−1.60817			−0.804083	−	0.594517i	$-0.797343\pi$
$173$	−8.32663e6			−1.60817			−0.804083	+	0.594517i	$0.797343\pi$
$174$	−209270.	+	434553.i	−0.0397245	+	0.0824887i
$175$	−768611.	−	1.59604e6i	−0.143414	−	0.297803i
$176$	−1.76868e6	−	2.21786e6i	−0.324423	−	0.406814i
$177$	2.07749e6	−	474173.i	0.374644	−	0.0855101i
$178$	764257.			0.135513
$179$		−	7.64018e6i		−	1.33212i	−0.745896	−	0.666062i	$-0.767979\pi$
$179$		−	7.64018e6i		−	1.33212i	0.745896	−	0.666062i	$-0.232021\pi$
$180$	2.84489e6	−	649327.i	0.487807	−	0.111339i
$181$	1.60887e6	−	2.01746e6i	0.271322	−	0.340227i	−0.627439	−	0.778666i	$-0.715897\pi$
$181$	1.60887e6	−	2.01746e6i	0.271322	−	0.340227i	0.898761	+	0.438439i	$0.144468\pi$
$182$	116456.	−	510225.i	0.0193173	−	0.0846346i
$183$	−1.29778e6	+	1.62736e6i	−0.211761	+	0.265540i
$184$	1.55216e6	−	3.22310e6i	0.249163	−	0.517393i
$185$	−1.48424e6	−	6.50290e6i	−0.234418	−	1.02705i
$186$	−290083.	−	139697.i	−0.0450800	−	0.0217094i
$187$	−3.30243e6	−	4.14112e6i	−0.505020	−	0.633275i
$188$	−916966.	+	4.01749e6i	−0.138000	+	0.604618i
$189$	−409449.	+	1.79391e6i	−0.0606476	+	0.265715i
$190$	489507.	+	1.01647e6i	0.0713671	+	0.148195i
$191$	−3.93125e6	+	3.13507e6i	−0.564197	+	0.449932i	−0.863588	−	0.504198i	$-0.831788\pi$
$191$	−3.93125e6	+	3.13507e6i	−0.564197	+	0.449932i	0.299391	+	0.954131i	$0.403217\pi$
$192$	−1.21011e6	−	965033.i	−0.170971	−	0.136345i
$193$	−1.23255e7	+	5.93566e6i	−1.71449	+	0.825653i	−0.723715	+	0.690099i	$0.757567\pi$
$193$	−1.23255e7	+	5.93566e6i	−1.71449	+	0.825653i	−0.990770	+	0.135554i	$0.956719\pi$
$194$	974070.	+	2.02268e6i	0.133409	+	0.277026i
$195$	−657132.	+	824017.i	−0.0886234	+	0.111130i
$196$	3.41471e6	+	4.28192e6i	0.453509	+	0.568683i
$197$	7.93316e6	−	3.82041e6i	1.03764	−	0.499702i	0.164097	−	0.986444i	$-0.447529\pi$
$197$	7.93316e6	−	3.82041e6i	1.03764	−	0.499702i	0.873546	+	0.486742i	$0.161815\pi$
$198$	−851429.	−	194333.i	−0.109686	−	0.0250352i
$199$	1.00887e7	+	2.30269e6i	1.28020	+	0.292197i	0.807942	−	0.589262i	$-0.200582\pi$
$199$	1.00887e7	+	2.30269e6i	1.28020	+	0.292197i	0.472259	+	0.881460i	$0.343439\pi$
$200$	1.70374e6	−	1.35868e6i	0.212967	−	0.169835i
$201$	−618462.	+	1.28425e6i	−0.0761596	+	0.158147i
$202$	3.00628e6	−	686165.i	0.364734	−	0.0832481i
$203$	5.64722e6	+	2.71956e6i	0.675067	+	0.325095i
$204$	−2.50948e6	−	2.00124e6i	−0.295592	−	0.235727i
$205$	−5.26500e6	−	1.20170e6i	−0.611135	−	0.139488i
$206$	460085.	+	366906.i	0.0526304	+	0.0419714i
$207$	2.56948e6	+	1.12576e7i	0.289691	+	1.26922i
$208$	−6.74994e6			−0.750085
$209$			7.59048e6i			0.831439i
$210$	−34528.1	−	151277.i	−0.00372833	−	0.0163349i
$211$	1.05705e7	−	8.42973e6i	1.12525	−	0.897359i	0.129698	−	0.991553i	$-0.458599\pi$
$211$	1.05705e7	−	8.42973e6i	1.12525	−	0.897359i	0.995554	+	0.0941949i	$0.0300277\pi$
$212$	−73234.3	+	35267.8i	−0.00768612	+	0.00370144i
$213$	1.08669e6	+	523322.i	0.112452	+	0.0541539i
$214$			619166.i			0.0631779i
$215$	2.01704e6	−	5.30086e6i	0.202954	−	0.533373i
$216$	−2.26352e6			−0.224607
$217$	−1.81543e6	+	3.76977e6i	−0.177664	+	0.368923i
$218$	116538.	+	241994.i	0.0112486	+	0.0233580i
$219$	637350.	+	799212.i	0.0606800	+	0.0760903i
$220$	−3.37661e6	+	770688.i	−0.317112	+	0.0723787i
$221$	−1.26033e7			−1.16763
$222$			1.20972e6i			0.110567i
$223$	−1.88336e6	+	429866.i	−0.169832	+	0.0387631i	−0.306591	−	0.951841i	$-0.599188\pi$
$223$	−1.88336e6	+	429866.i	−0.169832	+	0.0387631i	0.136759	+	0.990604i	$0.456331\pi$
$224$	2.00717e6	−	2.51691e6i	0.178583	−	0.223936i
$225$	−1.56520e6	+	6.85759e6i	−0.137411	+	0.602038i
$226$	−627894.	+	787355.i	−0.0543953	+	0.0682095i
$227$	−4.57599e6	+	9.50214e6i	−0.391208	+	0.812351i	0.608614	+	0.793466i	$0.291726\pi$
$227$	−4.57599e6	+	9.50214e6i	−0.391208	+	0.812351i	−0.999822	+	0.0188847i	$0.993988\pi$
$228$	1.02354e6	+	4.48444e6i	0.0863579	+	0.378359i
$229$	4.59930e6	+	2.21491e6i	0.382988	+	0.184437i	0.615464	−	0.788165i	$-0.288969\pi$
$229$	4.59930e6	+	2.21491e6i	0.382988	+	0.184437i	−0.232476	+	0.972602i	$0.574683\pi$
$230$	−1.27009e6	−	1.59265e6i	−0.104388	−	0.130899i
$231$	232304.	−	1.01779e6i	0.0188460	−	0.0825699i
$232$	−1.71574e6	+	7.51715e6i	−0.137400	+	0.601990i
$233$	−3.79858e6	−	7.88783e6i	−0.300299	−	0.623577i	0.695151	−	0.718864i	$-0.255337\pi$
$233$	−3.79858e6	−	7.88783e6i	−0.300299	−	0.623577i	−0.995450	+	0.0952869i	$0.969623\pi$
$234$	−1.62468e6	+	1.29564e6i	−0.126800	+	0.101120i
$235$	3.75077e6	+	2.99114e6i	0.289013	+	0.230480i
$236$	1.50121e7	−	7.22943e6i	1.14210	−	0.550007i
$237$	−1.95475e6	−	4.05907e6i	−0.146840	−	0.304917i
$238$	1.15689e6	−	1.45069e6i	0.0858145	−	0.107608i
$239$	8.14108e6	+	1.02086e7i	0.596332	+	0.747777i	0.984801	−	0.173685i	$-0.0555674\pi$
$239$	8.14108e6	+	1.02086e7i	0.596332	+	0.747777i	−0.388469	+	0.921462i	$0.626996\pi$
$240$	−1.80311e6	+	868331.i	−0.130433	+	0.0628133i
$241$	−1.57620e7	−	3.59756e6i	−1.12605	−	0.257014i	−0.381364	−	0.924425i	$-0.624545\pi$
$241$	−1.57620e7	−	3.59756e6i	−1.12605	−	0.257014i	−0.744690	+	0.667411i	$0.767403\pi$
$242$	−1.84090e6	−	420173.i	−0.129892	−	0.0296471i
$243$	8.69396e6	−	6.93320e6i	0.605897	−	0.483187i
$244$	−7.06169e6	+	1.46637e7i	−0.486115	+	1.00943i
$245$	6.21617e6	−	1.41880e6i	0.422692	−	0.0964768i
$246$	882440.	+	424961.i	0.0592762	+	0.0285459i
$247$	1.41209e7	+	1.12610e7i	0.937068	+	0.747287i
$248$	−5.01803e6	−	1.14533e6i	−0.328987	−	0.0750891i
$249$	3.64521e6	+	2.90696e6i	0.236115	+	0.188296i
$250$	−685603.	−	3.00382e6i	−0.0438786	−	0.192245i
$251$	7.39212e6			0.467463			0.233732	−	0.972301i	$-0.424906\pi$
$251$	7.39212e6			0.467463			0.233732	+	0.972301i	$0.424906\pi$
$252$			6.87756e6i			0.429767i
$253$	−3.04972e6	−	1.33617e7i	−0.188321	−	0.825089i
$254$	−123858.	+	98773.3i	−0.00755827	+	0.00602752i
$255$	−3.36671e6	+	1.62132e6i	−0.203041	+	0.0977796i
$256$	−9.08123e6	−	4.37329e6i	−0.541284	−	0.260669i
$257$			5.63840e6i			0.332167i	0.986112	+	0.166083i	$0.0531121\pi$
$257$			5.63840e6i			0.332167i	−0.986112	+	0.166083i	$0.946888\pi$
$258$	−570572.	+	855875.i	−0.0332240	+	0.0498369i
$259$	1.57209e7			0.904850
$260$	−3.57570e6	+	7.42501e6i	−0.203442	+	0.422452i
$261$	−1.07985e7	−	2.24234e7i	−0.607355	−	1.26119i
$262$	−2.58762e6	−	3.24478e6i	−0.143879	−	0.180418i
$263$	8.41235e6	−	1.92006e6i	0.462434	−	0.105548i	0.0150448	−	0.999887i	$-0.495211\pi$
$263$	8.41235e6	−	1.92006e6i	0.462434	−	0.105548i	0.447390	+	0.894339i	$0.352354\pi$
$264$	1.28422e6			0.0697958
$265$			94630.2i			0.00508502i
$266$	−2.59239e6	+	591695.i	−0.137738	+	0.0314379i
$267$	2.26175e6	−	2.83614e6i	0.118826	−	0.149003i
$268$	−2.48013e6	+	1.08662e7i	−0.128846	+	0.564511i
$269$	583469.	−	731648.i	0.0299751	−	0.0375876i	−0.766618	−	0.642103i	$-0.778062\pi$
$269$	583469.	−	731648.i	0.0299751	−	0.0375876i	0.796593	+	0.604516i	$0.206633\pi$
$270$	−559241.	+	1.16128e6i	−0.0284124	+	0.0589989i
$271$	−6.23936e6	−	2.73364e7i	−0.313496	−	1.37352i	−0.848736	−	0.528817i	$-0.822636\pi$
$271$	−6.23936e6	−	2.73364e7i	−0.313496	−	1.37352i	0.535240	−	0.844700i	$-0.320221\pi$
$272$	−2.15617e7	−	1.03836e7i	−1.07146	−	0.515988i
$273$	−1.54880e6	−	1.94213e6i	−0.0761213	−	0.0954531i
$274$	1.37233e6	−	6.01257e6i	0.0667124	−	0.292286i
$275$	1.85774e6	−	8.13929e6i	0.0893279	−	0.391371i
$276$	−3.60354e6	−	7.48283e6i	−0.171397	−	0.355909i
$277$	1.38371e7	−	1.10347e7i	0.651035	−	0.519183i	−0.241361	−	0.970435i	$-0.577594\pi$
$277$	1.38371e7	−	1.10347e7i	0.651035	−	0.519183i	0.892397	+	0.451252i	$0.149022\pi$
$278$	−3.40126e6	−	2.71241e6i	−0.158309	−	0.126247i
$279$	1.49686e7	−	7.20849e6i	0.689236	−	0.331919i
$280$	−1.07627e6	−	2.23491e6i	−0.0490285	−	0.101809i
$281$	−2.07693e6	+	2.60438e6i	−0.0936056	+	0.117378i	−0.826428	−	0.563042i	$-0.809631\pi$
$281$	−2.07693e6	+	2.60438e6i	−0.0936056	+	0.117378i	0.732823	+	0.680420i	$0.238202\pi$
$282$	−542483.	−	680252.i	−0.0241902	−	0.0303335i
$283$	−2.26763e7	+	1.09203e7i	−1.00049	+	0.481810i	−0.861104	−	0.508428i	$-0.830227\pi$
$283$	−2.26763e7	+	1.09203e7i	−1.00049	+	0.481810i	−0.139384	+	0.990238i	$0.544512\pi$
$284$	9.19459e6	+	2.09861e6i	0.401400	+	0.0916169i
$285$	5.22075e6	+	1.19160e6i	0.225527	+	0.0514751i
$286$	1.92834e6	−	1.53780e6i	0.0824301	−	0.0657358i
$287$	5.52257e6	−	1.14677e7i	0.233612	−	0.485101i
$288$	−1.24621e7	+	2.84440e6i	−0.521693	+	0.119073i
$289$	−1.85121e7	−	8.91495e6i	−0.766941	−	0.369339i
$290$	3.43270e6	+	2.73748e6i	0.140748	+	0.112243i
$291$	1.03888e7	+	2.37117e6i	0.421585	+	0.0962240i
$292$	6.24923e6	+	4.98359e6i	0.251002	+	0.200168i
$293$	1.08178e6	+	4.73958e6i	0.0430066	+	0.188424i	0.991868	−	0.127267i	$-0.0406206\pi$
$293$	1.08178e6	+	4.73958e6i	0.0430066	+	0.188424i	−0.948862	+	0.315692i	$0.897763\pi$
$294$	−1.15638e6			−0.0455048
$295$		−	1.93980e7i		−	0.755596i
$296$	4.30331e6	+	1.88540e7i	0.165931	+	0.726991i
$297$	−6.77989e6	+	5.40678e6i	−0.258793	+	0.206381i
$298$	3.26279e6	−	1.57128e6i	0.123294	−	0.0593751i
$299$	−2.93818e7	−	1.41495e7i	−1.09917	−	0.529333i
$300$		−	5.05918e6i		−	0.187377i
$301$	1.11225e7	+	7.41486e6i	0.407853	+	0.271896i
$302$	−3.80017e6			−0.137969
$303$	6.35047e6	−	1.31869e7i	0.228285	−	0.474039i
$304$	1.48803e7	+	3.08992e7i	0.529652	+	1.09983i
$305$	1.18138e7	+	1.48140e7i	0.416380	+	0.522124i
$306$	−7.18291e6	+	1.63945e6i	−0.250689	+	0.0572182i
$307$	1.79454e7			0.620208			0.310104	−	0.950703i	$-0.399636\pi$
$307$	1.79454e7			0.620208			0.310104	+	0.950703i	$0.399636\pi$
$308$		−	8.16300e6i		−	0.279381i
$309$	2.72316e6	−	621543.i	0.0922991	−	0.0210667i
$310$	−1.82739e6	+	2.29148e6i	−0.0613404	+	0.0769184i
$311$	5.79941e6	−	2.54089e7i	0.192798	−	0.844704i	−0.782295	−	0.622908i	$-0.785951\pi$
$311$	5.79941e6	−	2.54089e7i	0.192798	−	0.844704i	0.975093	−	0.221796i	$-0.0711918\pi$
$312$	1.90524e6	−	2.38910e6i	0.0627315	−	0.0786629i
$313$	−1.47834e6	+	3.06980e6i	−0.0482104	+	0.100110i	−0.923683	−	0.383159i	$-0.874836\pi$
$313$	−1.47834e6	+	3.06980e6i	−0.0482104	+	0.100110i	0.875472	+	0.483269i	$0.160551\pi$
$314$	−834853.	−	3.65773e6i	−0.0269663	−	0.118147i
$315$	7.21389e6	+	3.47402e6i	0.230801	+	0.111148i
$316$	−2.19640e7	−	2.75419e7i	−0.696064	−	0.872837i
$317$	−4.75973e6	+	2.08537e7i	−0.149419	+	0.654645i	0.843629	+	0.536927i	$0.180415\pi$
$317$	−4.75973e6	+	2.08537e7i	−0.149419	+	0.654645i	−0.993047	+	0.117718i	$0.962442\pi$
$318$	3819.00	−	16732.2i	0.000118760	−	0.000520320i
$319$	1.28168e7	+	2.66143e7i	0.394827	+	0.819868i
$320$	−1.10158e7	+	8.78479e6i	−0.336175	+	0.268091i
$321$	2.29771e6	+	1.83236e6i	0.0694672	+	0.0553983i
$322$	4.32571e6	−	2.08315e6i	0.129566	−	0.0623955i
$323$	2.77840e7	+	5.76941e7i	0.824494	+	1.71208i
$324$	1.53164e7	−	1.92062e7i	0.450320	−	0.564684i
$325$	−1.23858e7	−	1.55313e7i	−0.360805	−	0.452436i
$326$	−6.60251e6	+	3.17960e6i	−0.190571	+	0.0917740i
$327$	1.24292e6	+	283688.i	0.0355467	+	0.00811331i
$328$	1.52650e7	+	3.48413e6i	0.432588	+	0.0987354i
$329$	−8.84020e6	+	7.04983e6i	−0.248242	+	0.197966i
$330$	317290.	−	658859.i	0.00882905	−	0.0183337i
$331$	−4.69928e7	+	1.07258e7i	−1.29583	+	0.295764i	−0.814187	−	0.580603i	$-0.802817\pi$
$331$	−4.69928e7	+	1.07258e7i	−1.29583	+	0.295764i	−0.481642	+	0.876368i	$0.659960\pi$
$332$	3.28461e7	+	1.58178e7i	0.897572	+	0.432248i
$333$	−4.88039e7	−	3.89198e7i	−1.32167	−	1.05399i
$334$	−319231.	−	72862.4i	−0.00856772	−	0.00195553i
$335$	1.01448e7	+	8.09019e6i	0.269841	+	0.215191i
$336$	−1.04960e6	−	4.59861e6i	−0.0276698	−	0.121230i
$337$	3.09580e7			0.808879			0.404440	−	0.914565i	$-0.367467\pi$
$337$	3.09580e7			0.808879			0.404440	+	0.914565i	$0.367467\pi$
$338$			2.10010e6i			0.0543864i
$339$	1.06366e6	+	4.66020e6i	0.0273026	+	0.119621i
$340$	−2.28440e7	+	1.82175e7i	−0.581214	+	0.463503i
$341$	−1.77663e7	+	8.55578e6i	−0.448056	+	0.215773i
$342$	9.51268e6	+	4.58106e6i	0.237807	+	0.114522i
$343$			3.48080e7i			0.862575i
$344$	−5.84805e6	+	1.53689e7i	−0.143660	+	0.377545i
$345$	−9.66899e6			−0.235464
$346$	5.96460e6	−	1.23856e7i	0.143997	−	0.299013i
$347$	1.39995e7	+	2.90704e7i	0.335062	+	0.695764i	0.998629	−	0.0523534i	$-0.0166722\pi$
$347$	1.39995e7	+	2.90704e7i	0.335062	+	0.695764i	−0.663566	+	0.748118i	$0.730958\pi$
$348$	1.11610e7	+	1.39954e7i	0.264828	+	0.332084i
$349$	−4.05277e7	+	9.25019e6i	−0.953402	+	0.217608i	−0.670807	−	0.741632i	$-0.734052\pi$
$349$	−4.05277e7	+	9.25019e6i	−0.953402	+	0.217608i	−0.282594	+	0.959239i	$0.591195\pi$
$350$	2.92464e6			0.0682131
$351$			2.06343e7i			0.477164i
$352$	1.47913e7	−	3.37603e6i	0.339140	−	0.0774066i
$353$	1.09577e7	−	1.37405e7i	0.249113	−	0.312378i	−0.641515	−	0.767110i	$-0.721694\pi$
$353$	1.09577e7	−	1.37405e7i	0.249113	−	0.312378i	0.890628	+	0.454733i	$0.150265\pi$
$354$	−782846.	+	3.42987e6i	−0.0176468	+	0.0773157i
$355$	6.84564e6	−	8.58417e6i	0.153013	−	0.191873i
$356$	1.23070e7	−	2.55558e7i	0.272774	−	0.566420i
$357$	−1.95978e6	−	8.58637e6i	−0.0430728	−	0.188714i
$358$	1.13646e7	+	5.47288e6i	0.247687	+	0.119280i
$359$	4.07281e7	+	5.10714e7i	0.880259	+	1.10381i	0.993900	+	0.110288i	$0.0351773\pi$
$359$	4.07281e7	+	5.10714e7i	0.880259	+	1.10381i	−0.113641	+	0.993522i	$0.536251\pi$
$360$	−2.19172e6	+	9.60257e6i	−0.0469763	+	0.205816i
$361$	9.95139e6	−	4.35999e7i	0.211525	−	0.926753i
$362$	1.84843e6	+	3.83831e6i	0.0389653	+	0.0809123i
$363$	−7.00721e6	+	5.58807e6i	−0.146496	+	0.116827i
$364$	−1.51860e7	−	1.21104e7i	−0.314875	−	0.251104i
$365$	8.38394e6	−	4.03749e6i	0.172413	−	0.0830296i
$366$	−1.49102e6	−	3.09613e6i	−0.0304116	−	0.0631504i
$367$	−3.52767e7	+	4.42356e7i	−0.713658	+	0.894898i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−3.52767e7	+	4.42356e7i	−0.713658	+	0.894898i	0.284303	+	0.958735i	$0.408238\pi$
$368$	−3.86089e7	−	4.84140e7i	−0.774719	−	0.971467i
$369$	−4.55348e7	+	2.19284e7i	−0.906284	+	0.436443i
$370$	1.07361e7	+	2.45044e6i	0.211953	+	0.0483770i
$371$	−217442.	−	49629.8i	−0.00425816	−	0.000971898i
$372$	−9.34255e6	+	7.45043e6i	−0.181483	+	0.144728i
$373$	−1.00497e7	+	2.08685e7i	−0.193655	+	0.402128i	−0.975075	−	0.221877i	$-0.928782\pi$
$373$	−1.00497e7	+	2.08685e7i	−0.193655	+	0.402128i	0.781420	+	0.624006i	$0.214496\pi$
$374$	8.52542e6	−	1.94587e6i	0.162967	−	0.0371963i
$375$	−1.31761e7	−	6.34527e6i	−0.249858	−	0.120325i
$376$	−1.08747e7	−	8.67230e6i	−0.204576	−	0.163144i
$377$	6.85264e7	+	1.56407e7i	1.27889	+	0.291899i
$378$	−2.37509e6	−	1.89407e6i	−0.0439749	−	0.0350688i
$379$	−1.60603e7	−	7.03648e7i	−0.295009	−	1.29252i	−0.877458	−	0.479653i	$-0.840762\pi$
$379$	−1.60603e7	−	7.03648e7i	−0.295009	−	1.29252i	0.582449	−	0.812868i	$-0.302095\pi$
$380$	4.18721e7			0.763088
$381$			751944.i			0.0135960i
$382$	−1.84726e6	−	8.09337e6i	−0.0331389	−	0.145191i
$383$	8.18908e7	−	6.53057e7i	1.45760	−	1.16240i	0.503086	−	0.864236i	$-0.332198\pi$
$383$	8.18908e7	−	6.53057e7i	1.45760	−	1.16240i	0.954515	−	0.298162i	$-0.0963736\pi$
$384$	1.09542e7	−	5.27527e6i	0.193458	−	0.0931647i
$385$	−8.56218e6	−	4.12333e6i	−0.150038	−	0.0722547i
$386$		−	2.25858e7i		−	0.392711i
$387$	−1.61720e7	−	5.05546e7i	−0.279017	−	0.872223i
$388$	8.33213e7			1.42646
$389$	−1.17574e7	+	2.44145e7i	−0.199739	+	0.414762i	−0.976646	−	0.214853i	$-0.931073\pi$
$389$	−1.17574e7	+	2.44145e7i	−0.199739	+	0.414762i	0.776908	+	0.629615i	$0.216787\pi$
$390$	−754980.	−	1.56773e6i	−0.0127274	−	0.0264288i
$391$	−7.20893e7	−	9.03972e7i	−1.20598	−	1.51225i
$392$	−1.80227e7	+	4.11357e6i	−0.299200	+	0.0682905i
$393$	−1.96991e7			−0.324541
$394$			1.45370e7i			0.237677i
$395$	−3.99833e7	+	9.12593e6i	−0.648765	+	0.148076i
$396$	−2.02090e7	+	2.53413e7i	−0.325431	+	0.408078i
$397$	−1.72440e7	+	7.55508e7i	−0.275591	+	1.20744i	0.627713	+	0.778445i	$0.283991\pi$
$397$	−1.72440e7	+	7.55508e7i	−0.275591	+	1.20744i	−0.903304	+	0.429000i	$0.858866\pi$
$398$	−1.06520e7	+	1.33572e7i	−0.168960	+	0.211869i
$399$	−5.47616e6	+	1.13714e7i	−0.0862099	+	0.179017i
$400$	−8.39370e6	−	3.67752e7i	−0.131152	−	0.574613i
$401$	−3.32097e7	−	1.59930e7i	−0.515030	−	0.248025i	0.158269	−	0.987396i	$-0.449409\pi$
$401$	−3.32097e7	−	1.59930e7i	−0.515030	−	0.248025i	−0.673298	+	0.739371i	$0.735123\pi$
$402$	−1.46726e6	−	1.83989e6i	−0.0225855	−	0.0283213i
$403$	−1.04409e7	+	4.57444e7i	−0.159522	+	0.698913i
$404$	2.54664e7	−	1.11576e8i	0.386210	−	1.69210i
$405$	−1.24087e7	−	2.57669e7i	−0.186793	−	0.387880i
$406$	−8.09053e6	+	6.45198e6i	−0.120892	+	0.0964085i
$407$	5.79256e7	+	4.61941e7i	0.859186	+	0.685178i
$408$	9.76119e6	−	4.70074e6i	0.143722	−	0.0692127i
$409$	−3.31037e7	−	6.87404e7i	−0.483845	−	1.00471i	−0.989841	−	0.142178i	$-0.954589\pi$
$409$	−3.31037e7	−	6.87404e7i	−0.483845	−	1.00471i	0.505996	−	0.862536i	$-0.331125\pi$
$410$	5.55897e6	−	6.97073e6i	0.0806571	−	0.101141i
$411$	−1.82512e7	−	2.28863e7i	−0.262886	−	0.329648i
$412$	1.96777e7	−	9.47629e6i	0.281373	−	0.135502i
$413$	4.45728e7	+	1.01735e7i	0.632732	+	0.144417i
$414$	−1.85860e7	−	4.24213e6i	−0.261930	−	0.0597838i
$415$	3.31827e7	−	2.64623e7i	0.464267	−	0.370240i
$416$	1.56635e7	−	3.25255e7i	0.217574	−	0.451798i
$417$	−2.01314e7	+	4.59486e6i	−0.277630	+	0.0633672i
$418$	−1.12906e7	−	5.43728e6i	−0.154593	−	0.0744480i
$419$	6.17343e7	+	4.92315e7i	0.839237	+	0.669269i	0.945698	−	0.325048i	$-0.105380\pi$
$419$	6.17343e7	+	4.92315e7i	0.839237	+	0.669269i	−0.106461	+	0.994317i	$0.533952\pi$
$420$	−5.61453e6	−	1.28148e6i	−0.0757819	−	0.0172967i
$421$	3.56171e7	+	2.84037e7i	0.477323	+	0.380652i	0.832391	−	0.554188i	$-0.186971\pi$
$421$	3.56171e7	+	2.84037e7i	0.477323	+	0.380652i	−0.355069	+	0.934840i	$0.615543\pi$
$422$	4.96700e6	+	2.17618e7i	0.0660931	+	0.289573i
$423$	4.48967e7			0.593190
$424$		−	274364.i		−	0.00359940i
$425$	−1.56725e7	−	6.86655e7i	−0.204160	−	0.894483i
$426$	−1.55685e6	+	1.24155e6i	−0.0201381	+	0.0160596i
$427$	−4.02357e7	+	1.93765e7i	−0.516807	+	0.248881i
$428$	2.07041e7	+	9.97056e6i	0.264073	+	0.127171i
$429$		−	1.17070e7i		−	0.148277i
$430$	6.44001e6	+	6.79744e6i	0.0809993	+	0.0854949i
$431$	−2.34929e7			−0.293431			−0.146715	−	0.989179i	$-0.546870\pi$
$431$	−2.34929e7			−0.293431			−0.146715	+	0.989179i	$0.546870\pi$
$432$	−1.70001e7	+	3.53011e7i	−0.210863	+	0.437861i
$433$	−4.65963e7	−	9.67582e7i	−0.573968	−	1.19186i	−0.962716	−	0.270513i	$-0.912807\pi$
$433$	−4.65963e7	−	9.67582e7i	−0.573968	−	1.19186i	0.388749	−	0.921344i	$-0.372907\pi$
$434$	−4.30698e6	−	5.40079e6i	−0.0526871	−	0.0660675i
$435$	2.03175e7	−	4.63733e6i	0.246832	−	0.0563379i
$436$	9.96862e6			0.120275
$437$			1.65694e8i			1.98547i
$438$	−1.64536e6	+	375542.i	−0.0195811	+	0.00446926i
$439$	3.63501e6	−	4.55816e6i	0.0429647	−	0.0538761i	−0.759885	−	0.650058i	$-0.774745\pi$
$439$	3.63501e6	−	4.55816e6i	0.0429647	−	0.0538761i	0.802850	+	0.596182i	$0.203316\pi$
$440$	2.60137e6	−	1.13973e7i	0.0305382	−	0.133797i
$441$	3.72038e7	−	4.66520e7i	0.433782	−	0.543945i
$442$	9.02809e6	−	1.87470e7i	0.104551	−	0.217103i
$443$	1.78535e7	+	7.82215e7i	0.205359	+	0.899735i	0.967609	+	0.252453i	$0.0812373\pi$
$443$	1.78535e7	+	7.82215e7i	0.205359	+	0.899735i	−0.762250	+	0.647282i	$0.775906\pi$
$444$	4.04514e7	+	1.94803e7i	0.462151	+	0.222560i
$445$	−2.05889e7	−	2.58177e7i	−0.233643	−	0.292980i
$446$	709695.	−	3.10938e6i	0.00799958	−	0.0350484i
$447$	3.82495e6	−	1.67582e7i	0.0428256	−	0.187631i
$448$	−1.44085e7	−	2.99195e7i	−0.160245	−	0.332751i
$449$	−1.40388e8	+	1.11955e8i	−1.55092	+	1.23682i	−0.696032	+	0.718011i	$0.745053\pi$
$449$	−1.40388e8	+	1.11955e8i	−1.55092	+	1.23682i	−0.854890	+	0.518809i	$0.826376\pi$
$450$	−9.07927e6	−	7.24048e6i	−0.0996353	−	0.0794565i
$451$	5.40454e7	−	2.60269e7i	0.589154	−	0.283722i
$452$	1.62170e7	+	3.36749e7i	0.175612	+	0.364663i
$453$	−1.12462e7	+	1.41023e7i	−0.120980	+	0.151704i
$454$	−1.08563e7	−	1.36133e7i	−0.116015	−	0.145478i
$455$	−2.03734e7	+	9.81132e6i	−0.216287	+	0.104158i
$456$	−1.51367e7	−	3.45485e6i	−0.159638	−	0.0364363i
$457$	1.08403e7	+	2.47423e6i	0.113578	+	0.0259234i	0.278932	−	0.960311i	$-0.410020\pi$
$457$	1.08403e7	+	2.47423e6i	0.113578	+	0.0259234i	−0.165354	+	0.986234i	$0.552877\pi$
$458$	−6.58922e6	+	5.25473e6i	−0.0685863	+	0.0546958i
$459$	−3.17420e7	+	6.59130e7i	−0.328244	+	0.681606i
$460$	−7.37086e7	+	1.68235e7i	−0.757259	+	0.172839i
$461$	−5.52967e7	−	2.66295e7i	−0.564412	−	0.271806i	0.129844	−	0.991534i	$-0.458552\pi$
$461$	−5.52967e7	−	2.66295e7i	−0.564412	−	0.271806i	−0.694256	+	0.719728i	$0.744267\pi$
$462$	1.34753e6	+	1.07462e6i	0.0136651	+	0.0108975i
$463$	−2.03455e7	−	4.64372e6i	−0.204986	−	0.0467868i	0.118795	−	0.992919i	$-0.462097\pi$
$463$	−2.03455e7	−	4.64372e6i	−0.204986	−	0.0467868i	−0.323781	+	0.946132i	$0.604954\pi$
$464$	1.04349e8	+	8.32154e7i	1.04456	+	0.833009i
$465$	3.09562e6	+	1.35628e7i	0.0307886	+	0.134893i
$466$	1.44540e7			0.142833
$467$		−	6.28255e7i		−	0.616859i	−0.951247	−	0.308429i	$-0.900197\pi$
$467$		−	6.28255e7i		−	0.616859i	0.951247	−	0.308429i	$-0.0998033\pi$
$468$	1.71619e7	+	7.51913e7i	0.167428	+	0.733550i
$469$	−2.39102e7	+	1.90678e7i	−0.231774	+	0.184834i
$470$	−7.13602e6	+	3.43653e6i	−0.0687326	+	0.0330999i
$471$	−1.60444e7	−	7.72659e6i	−0.153554	−	0.0739477i
$472$			5.62410e7i			0.534844i
$473$	1.91946e7	+	6.00034e7i	0.181382	+	0.567012i
$474$	7.43799e6			0.0698427
$475$	−4.37930e7	+	9.09371e7i	−0.408624	+	0.848517i
$476$	−2.98796e7	−	6.20457e7i	−0.277047	−	0.575295i
$477$	552162.	+	692390.i	0.00508758	+	0.00637963i
$478$	−2.10167e7	+	4.79692e6i	−0.192433	+	0.0439217i
$479$	−1.86436e7			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$479$	−1.86436e7			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$480$		−	1.07035e7i		−	0.0967838i
$481$	1.71874e8	−	3.92290e7i	1.54445	−	0.352511i
$482$	1.66420e7	−	2.08684e7i	0.148616	−	0.186358i
$483$	5.07100e6	−	2.22175e7i	0.0450041	−	0.197176i
$484$	−4.36944e7	+	5.47911e7i	−0.385381	+	0.483252i
$485$	4.20876e7	−	8.73959e7i	0.368918	−	0.766065i
$486$	4.08521e6	+	1.78985e7i	0.0355882	+	0.155922i
$487$	1.27716e8	+	6.15048e7i	1.10575	+	0.532503i	0.895463	−	0.445135i	$-0.146844\pi$
$487$	1.27716e8	+	6.15048e7i	1.10575	+	0.532503i	0.210291	+	0.977639i	$0.432559\pi$
$488$	−3.42521e7	−	4.29507e7i	−0.294732	−	0.369582i
$489$	−7.74007e6	+	3.39115e7i	−0.0661940	+	0.290015i
$490$	−2.34239e6	+	1.02627e7i	−0.0199100	+	0.0872315i
$491$	−7.50590e7	−	1.55862e8i	−0.634101	−	1.31672i	−0.932115	−	0.362163i	$-0.882038\pi$
$491$	−7.50590e7	−	1.55862e8i	−0.634101	−	1.31672i	0.298014	−	0.954562i	$-0.403676\pi$
$492$	2.84203e7	−	2.26644e7i	0.238634	−	0.190305i
$493$	1.94837e8	+	1.55377e8i	1.62604	+	1.29672i
$494$	−2.68657e7	+	1.29378e7i	−0.222852	+	0.107320i
$495$	1.63725e7	+	3.39978e7i	0.134989	+	0.280307i
$496$	−5.55500e7	+	6.96575e7i	−0.455238	+	0.570851i
$497$	1.61345e7	+	2.02320e7i	0.131428	+	0.164805i
$498$	−6.93518e6	+	3.33981e6i	−0.0561526	+	0.0270417i
$499$	1.29131e8	+	2.94733e7i	1.03927	+	0.237206i	0.707913	−	0.706299i	$-0.249637\pi$
$499$	1.29131e8	+	2.94733e7i	1.03927	+	0.237206i	0.331356	+	0.943506i	$0.392494\pi$
$500$	−1.11484e8	−	2.54456e7i	−0.891874	−	0.203564i
$501$	−1.21512e6	+	969029.i	−0.00966290	+	0.00770590i
$502$	−5.29518e6	+	1.09956e7i	−0.0418572	+	0.0869173i
$503$	−1.67139e8	+	3.81484e7i	−1.31333	+	0.299759i	−0.821139	−	0.570729i	$-0.806661\pi$
$503$	−1.67139e8	+	3.81484e7i	−1.31333	+	0.299759i	−0.492190	+	0.870488i	$0.663804\pi$
$504$	−2.09154e7	−	1.00723e7i	−0.163371	−	0.0786753i
$505$	−1.04168e8	−	8.30714e7i	−0.808837	−	0.645026i
$506$	2.20598e7	+	5.03500e6i	0.170274	+	0.0388640i
$507$	7.79343e6	+	6.21505e6i	0.0598005	+	0.0476893i
$508$	1.30834e6	+	5.73221e6i	0.00997998	+	0.0437251i
$509$	2.28970e8			1.73630			0.868152	−	0.496298i	$-0.165308\pi$
$509$	2.28970e8			1.73630			0.868152	+	0.496298i	$0.165308\pi$
$510$		−	6.16928e6i		−	0.0465076i
$511$	4.88035e6	+	2.13822e7i	0.0365753	+	0.160247i
$512$	9.06441e7	−	7.22862e7i	0.675351	−	0.538575i
$513$	9.44575e7	−	4.54883e7i	0.699656	−	0.336936i
$514$	−8.38695e6	−	4.03894e6i	−0.0617611	−	0.0297426i
$515$		−	2.54267e7i		−	0.186152i
$516$	1.94313e7	+	3.28615e7i	0.141434	+	0.239188i
$517$	−5.32881e7			−0.385619
$518$	−1.12613e7	+	2.33843e7i	−0.0810213	+	0.168242i
$519$	−2.83111e7	−	5.87886e7i	−0.202514	−	0.420524i
$520$	−1.73436e7	−	2.17482e7i	−0.123347	−	0.154672i
$521$	−8.73534e7	+	1.99378e7i	−0.617684	+	0.140982i	−0.519903	−	0.854225i	$-0.674032\pi$
$521$	−8.73534e7	+	1.99378e7i	−0.617684	+	0.140982i	−0.0977816	+	0.995208i	$0.531175\pi$
$522$	4.10894e7			0.288880
$523$		−	1.33546e8i		−	0.933526i	−0.884383	−	0.466763i	$-0.845420\pi$
$523$		−	1.33546e8i		−	0.933526i	0.884383	−	0.466763i	$-0.154580\pi$
$524$	−1.50170e8	+	3.42754e7i	−1.04373	+	0.238225i
$525$	8.65519e6	−	1.08533e7i	0.0598134	−	0.0750037i
$526$	−3.16997e6	+	1.38885e7i	−0.0217820	+	0.0954331i
$527$	−1.03721e8	+	1.30062e8i	−0.708656	+	0.888627i
$528$	9.64513e6	−	2.00283e7i	0.0655249	−	0.136064i
$529$	−3.36319e7	−	1.47351e8i	−0.227187	−	0.995373i
$530$	−140760.	−	67786.3i	−0.000945477	−	0.000455318i
$531$	−1.13186e8	−	1.41931e8i	−0.755978	−	0.947966i
$532$	−2.19603e7	+	9.62142e7i	−0.145849	+	0.639005i
$533$	3.17614e7	−	1.39156e8i	0.209758	−	0.919008i
$534$	2.59852e6	+	5.39589e6i	0.0170649	+	0.0354356i
$535$	2.09163e7	−	1.66802e7i	0.136591	−	0.108928i
$536$	−2.94130e7	−	2.34561e7i	−0.191005	−	0.152322i
$537$	5.39421e7	−	2.59771e7i	0.348341	−	0.167752i
$538$	670349.	+	1.39199e6i	0.00430481	+	0.00893903i
$539$	−4.41573e7	+	5.53715e7i	−0.281991	+	0.353606i
$540$	2.98260e7	+	3.74006e7i	0.189415	+	0.237518i
$541$	−1.70175e7	+	8.19521e6i	−0.107474	+	0.0517569i	−0.486848	−	0.873486i	$-0.661854\pi$
$541$	−1.70175e7	+	8.19521e6i	−0.107474	+	0.0517569i	0.379374	+	0.925243i	$0.376139\pi$
$542$	4.51316e7	+	1.03010e7i	0.283454	+	0.0646966i
$543$	1.97141e7	+	4.49962e6i	0.123134	+	0.0281046i
$544$	1.00069e8	−	7.98025e7i	0.621589	−	0.495701i
$545$	5.03539e6	−	1.04561e7i	0.0311060	−	0.0645922i
$546$	3.99831e6	−	912587.i	0.0245639	−	0.00560656i
$547$	4.38578e6	+	2.11208e6i	0.0267969	+	0.0129047i	0.447234	−	0.894417i	$-0.352409\pi$
$547$	4.38578e6	+	2.11208e6i	0.0267969	+	0.0129047i	−0.420437	+	0.907322i	$0.638123\pi$
$548$	−1.78954e8	−	1.42711e8i	−1.08742	−	0.867191i
$549$	1.72878e8	+	3.94583e7i	1.04478	+	0.238463i
$550$	1.07762e7	+	8.59375e6i	0.0647706	+	0.0516529i
$551$	−7.94683e7	−	3.48173e8i	−0.475050	−	2.08133i
$552$	2.80336e7			0.166671
$553$		−	9.66603e7i		−	0.571574i
$554$	6.50190e6	+	2.84867e7i	0.0382394	+	0.167538i
$555$	4.08659e7	−	3.25895e7i	0.239047	−	0.190633i
$556$	−1.45471e8	+	7.00551e7i	−0.846353	+	0.407582i
$557$	−9.83206e7	−	4.73487e7i	−0.568956	−	0.273995i	0.127210	−	0.991876i	$-0.459398\pi$
$557$	−9.83206e7	−	4.73487e7i	−0.568956	−	0.273995i	−0.696166	+	0.717881i	$0.745112\pi$
$558$			2.74290e7i			0.157873i
$559$	1.40103e8	+	5.33109e7i	0.802071	+	0.305197i
$560$	−4.29381e7			−0.244500
$561$	1.80091e7	−	3.73962e7i	0.102001	−	0.211807i
$562$	−2.38618e6	−	4.95496e6i	−0.0134430	−	0.0279146i
$563$	6.69233e6	+	8.39191e6i	0.0375018	+	0.0470258i	0.800229	−	0.599695i	$-0.204711\pi$
$563$	6.69233e6	+	8.39191e6i	0.0375018	+	0.0470258i	−0.762727	+	0.646721i	$0.776140\pi$
$564$	−3.14825e7	+	7.18567e6i	−0.175482	+	0.0400525i
$565$	4.35133e7			0.241255
$566$		−	4.15528e7i		−	0.229167i
$567$	6.57153e7	−	1.49991e7i	0.360510	−	0.0822841i
$568$	−1.98478e7	+	2.48883e7i	−0.108310	+	0.135816i
$569$	−6.66881e7	+	2.92180e8i	−0.362003	+	1.58604i	0.386101	+	0.922456i	$0.373821\pi$
$569$	−6.66881e7	+	2.92180e8i	−0.362003	+	1.58604i	−0.748104	+	0.663581i	$0.769036\pi$
$570$	−5.51225e6	+	6.91214e6i	−0.0297649	+	0.0373240i
$571$	−8.67711e7	+	1.80182e8i	−0.466087	+	0.967839i	0.526935	+	0.849906i	$0.323341\pi$
$571$	−8.67711e7	+	1.80182e8i	−0.466087	+	0.967839i	−0.993021	+	0.117934i	$0.962373\pi$
$572$	−2.03695e7	−	8.92447e7i	−0.108841	−	0.476864i
$573$	−3.55011e7	−	1.70964e7i	−0.188703	−	0.0908744i
$574$	1.31020e7	+	1.64293e7i	0.0692788	+	0.0868729i
$575$	4.05530e7	−	1.77674e8i	0.213314	−	0.934589i
$576$	−2.93414e7	+	1.28553e8i	−0.153537	+	0.672690i
$577$	−5.00401e7	−	1.03909e8i	−0.260490	−	0.540912i	0.729173	−	0.684330i	$-0.239905\pi$
$577$	−5.00401e7	−	1.03909e8i	−0.260490	−	0.540912i	−0.989662	+	0.143417i	$0.954191\pi$
$578$	2.65215e7	−	2.11502e7i	0.137345	−	0.109529i
$579$	−8.38152e7	−	6.68404e7i	−0.431805	−	0.344353i
$580$	1.46815e8	−	7.07025e7i	0.752467	−	0.362369i
$581$	4.34024e7	+	9.01260e7i	0.221302	+	0.459538i
$582$	−1.09688e7	+	1.37545e7i	−0.0556405	+	0.0697710i
$583$	−655363.	−	821799.i	−0.00330732	−	0.00414725i
$584$	−2.43078e7	+	1.17060e7i	−0.122041	+	0.0587720i
$585$	8.75371e7	+	1.99798e7i	0.437245	+	0.0997983i
$586$	−7.82489e6	−	1.78598e6i	−0.0388853	−	0.00887532i
$587$	2.89032e7	−	2.30495e7i	0.142900	−	0.113959i	−0.549431	−	0.835539i	$-0.685155\pi$
$587$	2.89032e7	−	2.30495e7i	0.142900	−	0.113959i	0.692331	+	0.721580i	$0.256584\pi$
$588$	−1.86214e7	+	3.86677e7i	−0.0915968	+	0.190203i
$589$	2.32421e8	−	5.30486e7i	1.13744	−	0.259614i
$590$	2.88539e7	+	1.38953e7i	0.140491	+	0.0676569i
$591$	5.39465e7	+	4.30209e7i	0.261337	+	0.208409i
$592$	3.26361e8	+	7.44897e7i	1.57302	+	0.359030i
$593$	1.84927e8	+	1.47474e8i	0.886820	+	0.707215i	0.956928	−	0.290324i	$-0.0937631\pi$
$593$	1.84927e8	+	1.47474e8i	0.886820	+	0.707215i	−0.0701085	+	0.997539i	$0.522335\pi$
$594$	−3.18581e6	−	1.39579e7i	−0.0152006	−	0.0665981i
$595$	−8.01727e7			−0.380606
$596$		−	1.34406e8i		−	0.634864i
$597$	1.80447e7	+	7.90590e7i	0.0848060	+	0.371559i
$598$	4.20941e7	−	3.35689e7i	0.196842	−	0.156976i
$599$	−1.36257e8	+	6.56180e7i	−0.633985	+	0.305311i	−0.723134	−	0.690707i	$-0.757299\pi$
$599$	−1.36257e8	+	6.56180e7i	−0.633985	+	0.305311i	0.0891497	+	0.996018i	$0.471585\pi$
$600$	1.53855e7	+	7.40928e6i	0.0712293	+	0.0343022i
$601$		−	1.11081e8i		−	0.511700i	−0.966716	−	0.255850i	$-0.917645\pi$
$601$		−	1.11081e8i		−	0.511700i	0.966716	−	0.255850i	$-0.0823553\pi$
$602$	−1.89968e7	+	1.12329e7i	−0.0870743	+	0.0514878i
$603$	1.21433e8			0.553840
$604$	−6.11950e7	+	1.27073e8i	−0.277718	+	0.576688i
$605$	3.53993e7	+	7.35075e7i	0.159856	+	0.331944i
$606$	1.50661e7	+	1.88923e7i	0.0676991	+	0.0848920i
$607$	−3.85778e8	+	8.80512e7i	−1.72493	+	0.393704i	−0.966218	−	0.257725i	$-0.917027\pi$
$607$	−3.85778e8	+	8.80512e7i	−1.72493	+	0.393704i	−0.758710	+	0.651429i	$0.774170\pi$
$608$	−1.83422e8			−0.816096
$609$			4.91178e7i			0.217464i
$610$	−3.04980e7	+	6.96097e6i	−0.134364	+	0.0306676i
$611$	−7.90567e7	+	9.91340e7i	−0.346589	+	0.434609i
$612$	−6.08469e7	+	2.66588e8i	−0.265451	+	1.16302i
$613$	−2.53666e8	+	3.18087e8i	−1.10124	+	1.38091i	−0.183829	+	0.982958i	$0.558849\pi$
$613$	−2.53666e8	+	3.18087e8i	−1.10124	+	1.38091i	−0.917408	+	0.397948i	$0.869722\pi$
$614$	−1.28548e7	+	2.66932e7i	−0.0555341	+	0.115318i
$615$	−9.41697e6	−	4.12584e7i	−0.0404842	−	0.177373i
$616$	2.48246e7	+	1.19549e7i	0.106204	+	0.0511450i
$617$	−2.83689e8	−	3.55735e8i	−1.20778	−	1.51451i	−0.798385	−	0.602148i	$-0.794312\pi$
$617$	−2.83689e8	−	3.55735e8i	−1.20778	−	1.51451i	−0.409394	−	0.912358i	$-0.634260\pi$
$618$	−1.02615e6	+	4.49585e6i	−0.00434755	+	0.0190479i
$619$	8.18262e7	−	3.58504e8i	0.345001	−	1.51155i	−0.443365	−	0.896341i	$-0.646215\pi$
$619$	8.18262e7	−	3.58504e8i	0.345001	−	1.51155i	0.788366	−	0.615207i	$-0.210927\pi$
$620$	4.71971e7	+	9.80057e7i	0.198034	+	0.411222i
$621$	−1.47999e8	+	1.18026e8i	−0.617995	+	0.492835i
$622$	3.36407e7	+	2.68276e7i	0.139796	+	0.111483i
$623$	7.01222e7	−	3.37691e7i	0.289996	−	0.139655i
$624$	−2.29503e7	−	4.76567e7i	−0.0944569	−	0.196142i
$625$	1.96416e7	−	2.46298e7i	0.0804520	−	0.100884i
$626$	−3.50726e6	−	4.39797e6i	−0.0142970	−	0.0179279i
$627$	−5.35912e7	+	2.58081e7i	−0.217416	+	0.104702i
$628$	−1.35754e8	−	3.09849e7i	−0.548116	−	0.125104i
$629$	6.09371e8	+	1.39085e8i	2.44867	+	0.558892i
$630$	−1.03350e7	+	8.24191e6i	−0.0413323	+	0.0329614i
$631$	3.61648e6	−	7.50969e6i	0.0143945	−	0.0298906i	−0.893648	−	0.448769i	$-0.851862\pi$
$631$	3.61648e6	−	7.50969e6i	0.0143945	−	0.0298906i	0.908042	+	0.418879i	$0.137577\pi$
$632$	1.15925e8	−	2.64591e7i	0.459225	−	0.104815i
$633$	9.54570e7	+	4.59697e7i	0.376354	+	0.181243i
$634$	−2.76098e7	−	2.20181e7i	−0.108342	−	0.0863996i
$635$	6.67340e6	+	1.52316e6i	0.0260631	+	0.00594873i
$636$	−498003.	−	397144.i	−0.00193580	−	0.00154375i
$637$	3.74993e7	+	1.64295e8i	0.145079	+	0.635633i
$638$	−4.87691e7			−0.187794
$639$		−	1.02752e8i		−	0.393813i
$640$	−2.46282e7	−	1.07903e8i	−0.0939490	−	0.411617i
$641$	1.64515e8	−	1.31197e8i	0.624644	−	0.498137i	−0.259259	−	0.965808i	$-0.583478\pi$
$641$	1.64515e8	−	1.31197e8i	0.624644	−	0.498137i	0.883903	+	0.467671i	$0.154907\pi$
$642$	−4.37150e6	+	2.10520e6i	−0.0165206	+	0.00795589i
$643$	1.99168e7	+	9.59141e6i	0.0749180	+	0.0360786i	0.470968	−	0.882151i	$-0.343905\pi$
$643$	1.99168e7	+	9.59141e6i	0.0749180	+	0.0360786i	−0.396050	+	0.918229i	$0.629619\pi$
$644$		−	1.78192e8i		−	0.667159i
$645$	4.42837e7	−	3.78236e6i	0.165031	−	0.0140956i
$646$	−1.05721e8			−0.392160
$647$	−2.17767e8	+	4.52197e8i	−0.804041	+	1.66961i	−0.0631303	+	0.998005i	$0.520108\pi$
$647$	−2.17767e8	+	4.52197e8i	−0.804041	+	1.66961i	−0.740911	+	0.671603i	$0.765606\pi$
$648$	3.59768e7	+	7.47067e7i	0.132220	+	0.274558i
$649$	1.34341e8	+	1.68458e8i	0.491444	+	0.616251i
$650$	3.19746e7	−	7.29799e6i	0.116430	−	0.0265744i
$651$	−3.27883e7			−0.118844
$652$			2.71981e8i			0.981286i
$653$	−4.13301e7	+	9.43332e6i	−0.148432	+	0.0338786i	−0.296091	−	0.955160i	$-0.595683\pi$
$653$	−4.13301e7	+	9.43332e6i	−0.148432	+	0.0338786i	0.147659	+	0.989038i	$0.452826\pi$
$654$	−1.31232e6	+	1.64559e6i	−0.00469143	+	0.00588287i
$655$	−3.99031e7	+	1.74827e8i	−0.141998	+	0.622135i
$656$	1.68984e8	−	2.11900e8i	0.598598	−	0.750618i
$657$	3.77850e7	−	7.84613e7i	0.133236	−	0.276668i
$658$	−4.15393e6	−	1.81995e7i	−0.0145808	−	0.0638826i
$659$	−1.48666e8	−	7.15937e7i	−0.519463	−	0.250160i	0.155732	−	0.987799i	$-0.450226\pi$
$659$	−1.48666e8	−	7.15937e7i	−0.519463	−	0.250160i	−0.675195	+	0.737639i	$0.735941\pi$
$660$	−1.69220e7	−	2.12195e7i	−0.0588599	−	0.0738080i
$661$	−2.20555e7	+	9.66315e7i	−0.0763682	+	0.334591i	−0.998651	−	0.0519247i	$-0.983464\pi$
$661$	−2.20555e7	+	9.66315e7i	−0.0763682	+	0.334591i	0.922283	+	0.386516i	$0.126322\pi$
$662$	1.77080e7	−	7.75837e7i	0.0610372	−	0.267422i
$663$	−4.28520e7	−	8.89831e7i	−0.147038	−	0.305328i
$664$	−9.62076e7	+	7.67230e7i	−0.328628	+	0.262072i
$665$	8.98266e7	+	7.16343e7i	0.305450	+	0.243588i
$666$	9.28518e7	−	4.47151e7i	0.314317	−	0.151367i
$667$	2.79780e8	+	5.80969e8i	0.942843	+	1.95783i
$668$	−7.57707e6	+	9.50134e6i	−0.0254198	+	0.0318754i
$669$	−9.43855e6	−	1.18356e7i	−0.0315230	−	0.0395285i
$670$	−1.93009e7	+	9.29483e6i	−0.0641732	+	0.0309042i
$671$	−2.05190e8	−	4.68332e7i	−0.679184	−	0.155019i
$672$	2.45946e7	+	5.61357e6i	0.0810462	+	0.0184983i
$673$	3.09813e8	−	2.47068e8i	1.01638	−	0.810534i	0.0343764	−	0.999409i	$-0.489056\pi$
$673$	3.09813e8	−	2.47068e8i	1.01638	−	0.810534i	0.982001	+	0.188875i	$0.0604841\pi$
$674$	−2.21761e7	+	4.60492e7i	−0.0724279	+	0.150398i
$675$	−1.12420e8	+	2.56592e7i	−0.365538	+	0.0834317i
$676$	7.02246e7	+	3.38184e7i	0.227326	+	0.109474i
$677$	−3.49873e8	−	2.79014e8i	−1.12757	−	0.899209i	−0.131820	−	0.991274i	$-0.542082\pi$
$677$	−3.49873e8	−	2.79014e8i	−1.12757	−	0.899209i	−0.995753	+	0.0920645i	$0.970653\pi$
$678$	−7.69385e6	−	1.75607e6i	−0.0246862	−	0.00563447i
$679$	1.78746e8	+	1.42545e8i	0.570988	+	0.455347i
$680$	−2.19459e7	−	9.61512e7i	−0.0697954	−	0.305793i
$681$	−8.26467e7			−0.261688
$682$		−	3.25555e7i		−	0.102629i
$683$	5.38608e7	+	2.35980e8i	0.169048	+	0.740649i	0.986380	+	0.164482i	$0.0525951\pi$
$683$	5.38608e7	+	2.35980e8i	0.169048	+	0.740649i	−0.817332	+	0.576167i	$0.804548\pi$
$684$	3.06370e8	−	2.44322e8i	0.957365	−	0.763473i
$685$	−2.40083e8	+	1.15618e8i	−0.746948	+	0.359711i
$686$	−5.17759e7	−	2.49340e7i	−0.160382	−	0.0772359i
$687$			4.00033e7i			0.123375i
$688$	1.95767e8	+	2.06632e8i	0.601137	+	0.634501i
$689$	−2.50111e6			−0.00764671
$690$	6.92617e6	−	1.43823e7i	0.0210837	−	0.0437807i
$691$	−2.39466e8	−	4.97257e8i	−0.725789	−	1.50712i	−0.856751	−	0.515730i	$-0.827521\pi$
$691$	−2.39466e8	−	4.97257e8i	−0.725789	−	1.50712i	0.130962	−	0.991387i	$-0.458193\pi$
$692$	−3.18110e8	−	3.98897e8i	−0.959972	−	1.20377i
$693$	−8.67071e7	+	1.97903e7i	−0.260528	+	0.0594639i
$694$	−5.32696e7			−0.159368
$695$			1.87971e8i			0.559934i
$696$	−5.89070e7	+	1.34451e7i	−0.174719	+	0.0398784i
$697$	3.15522e8	−	3.95653e8i	0.931820	−	1.16846i
$698$	1.52718e7	−	6.69100e7i	0.0449079	−	0.196755i
$699$	4.27751e7	−	5.36383e7i	0.125245	−	0.157052i
$700$	4.70961e7	−	9.77961e7i	0.137306	−	0.285120i
$701$	−7.03310e7	−	3.08140e8i	−0.204170	−	0.894529i	−0.968364	−	0.249542i	$-0.919720\pi$
$701$	−7.03310e7	−	3.08140e8i	−0.204170	−	0.894529i	0.764194	−	0.644987i	$-0.223137\pi$
$702$	−3.06929e7	−	1.47809e7i	−0.0887210	−	0.0427258i
$703$	−5.58475e8	−	7.00305e8i	−1.60745	−	2.01568i
$704$	3.48254e7	−	1.52580e8i	0.0998109	−	0.437300i
$705$	−8.36551e6	+	3.66517e7i	−0.0238740	+	0.104599i
$706$	1.25893e7	+	2.61420e7i	0.0357758	+	0.0742891i
$707$	2.45514e8	−	1.95791e8i	0.694734	−	0.554032i
$708$	1.02084e8	+	8.14093e7i	0.287646	+	0.229390i
$709$	2.64861e8	−	1.27550e8i	0.743154	−	0.357884i	−0.0236885	−	0.999719i	$-0.507541\pi$
$709$	2.64861e8	−	1.27550e8i	0.743154	−	0.357884i	0.766843	+	0.641835i	$0.221827\pi$
$710$	7.86497e6	+	1.63318e7i	0.0219747	+	0.0456308i
$711$	−2.39300e8	+	3.00073e8i	−0.665786	+	0.834869i
$712$	5.96940e7	+	7.48539e7i	0.165383	+	0.207384i
$713$	−3.87823e8	+	1.86766e8i	−1.06995	+	0.515262i
$714$	1.41758e7	+	3.23554e6i	0.0389452	+	0.00888899i
$715$	−1.03898e8	−	2.37141e7i	−0.284243	−	0.0648766i
$716$	3.66012e8	−	2.91885e8i	0.997140	−	0.795193i
$717$	−4.43956e7	+	9.21884e7i	−0.120443	+	0.250103i
$718$	−1.05142e8	+	2.39980e7i	−0.284055	+	0.0648337i
$719$	−3.82905e8	−	1.84397e8i	−1.03016	−	0.496098i	−0.159092	−	0.987264i	$-0.550857\pi$
$719$	−3.82905e8	−	1.84397e8i	−1.03016	−	0.496098i	−0.871066	+	0.491166i	$0.836571\pi$
$720$	1.33298e8	+	1.06301e8i	0.357129	+	0.284801i
$721$	5.84257e7	+	1.33353e7i	0.155883	+	0.0355792i
$722$	5.77251e7	+	4.60343e7i	0.153375	+	0.122312i
$723$	−2.81918e7	−	1.23516e8i	−0.0745946	−	0.326820i
$724$	1.58114e8			0.416633
$725$			3.92797e8i			1.03075i
$726$	−3.29262e6	−	1.44259e7i	−0.00860463	−	0.0376993i
$727$	4.10357e8	−	3.27249e8i	1.06797	−	0.851678i	0.0785720	−	0.996908i	$-0.474964\pi$
$727$	4.10357e8	−	3.27249e8i	1.06797	−	0.851678i	0.989398	+	0.145231i	$0.0463925\pi$
$728$	5.90692e7	−	2.84462e7i	0.153097	−	0.0737277i
$729$	−1.84811e8	−	8.90002e7i	−0.477029	−	0.229725i
$730$			1.53630e7i			0.0394919i
$731$	3.65530e8	+	3.85817e8i	0.935773	+	0.987709i
$732$	−1.27541e8			−0.325174
$733$	5.56585e7	−	1.15576e8i	0.141325	−	0.293465i	−0.818278	−	0.574823i	$-0.805071\pi$
$733$	5.56585e7	−	1.15576e8i	0.141325	−	0.293465i	0.959603	+	0.281359i	$0.0907851\pi$
$734$	−4.05295e7	−	8.41603e7i	−0.102490	−	0.212823i
$735$	3.11525e7	+	3.90640e7i	0.0784570	+	0.0983819i
$736$	3.22883e8	−	7.36959e7i	0.809863	−	0.184846i
$737$	−1.44129e8			−0.360039
$738$		−	8.34396e7i		−	0.207589i
$739$	−6.85959e8	+	1.56566e8i	−1.69967	+	0.387939i	−0.958883	−	0.283801i	$-0.908405\pi$
$739$	−6.85959e8	+	1.56566e8i	−1.69967	+	0.387939i	−0.740787	+	0.671740i	$0.765547\pi$
$740$	2.54825e8	−	3.19540e8i	0.628850	−	0.788553i
$741$	−3.14944e7	+	1.37986e8i	−0.0774068	+	0.339141i
$742$	229583.	−	287888.i	0.000561989	−	0.000704712i
$743$	−2.01109e8	+	4.17607e8i	−0.490304	+	1.01813i	0.498219	+	0.867051i	$0.333988\pi$
$743$	−2.01109e8	+	4.17607e8i	−0.490304	+	1.01813i	−0.988522	+	0.151075i	$0.951727\pi$
$744$	−8.97523e6	−	3.93231e7i	−0.0217935	−	0.0954835i
$745$	−1.40979e8	−	6.78919e7i	−0.340946	−	0.164191i
$746$	−2.38424e7	−	2.98974e7i	−0.0574293	−	0.0720140i
$747$	8.83847e7	−	3.87238e8i	0.212039	−	0.929002i
$748$	7.22193e7	−	3.16414e8i	0.172563	−	0.756050i
$749$	2.73581e7	+	5.68098e7i	0.0651090	+	0.135200i
$750$	1.88768e7	−	1.50538e7i	0.0447450	−	0.0356830i
$751$	2.57020e8	+	2.04966e8i	0.606801	+	0.483908i	0.878029	−	0.478607i	$-0.158858\pi$
$751$	2.57020e8	+	2.04966e8i	0.606801	+	0.483908i	−0.271228	+	0.962515i	$0.587430\pi$
$752$	−2.16924e8	+	1.04465e8i	−0.510099	+	0.245651i
$753$	2.51337e7	+	5.21906e7i	0.0588669	+	0.122238i
$754$	−7.23525e7	+	9.07272e7i	−0.168787	+	0.211653i
$755$	1.02376e8	+	1.28375e8i	0.237879	+	0.298291i
$756$	−1.01582e8	+	4.89193e7i	−0.235099	+	0.113218i
$757$	7.38865e8	+	1.68641e8i	1.70325	+	0.388755i	0.959942	−	0.280199i	$-0.0904004\pi$
$757$	7.38865e8	+	1.68641e8i	1.70325	+	0.388755i	0.743304	+	0.668954i	$0.233258\pi$
$758$	1.16170e8	+	2.65150e7i	0.266739	+	0.0608814i
$759$	8.39686e7	−	6.69627e7i	0.192040	−	0.153147i
$760$	−6.13227e7	+	1.27338e8i	−0.139695	+	0.290079i
$761$	7.27559e7	−	1.66061e7i	0.165087	−	0.0376801i	−0.139178	−	0.990267i	$-0.544446\pi$
$761$	7.27559e7	−	1.66061e7i	0.165087	−	0.0376801i	0.304266	+	0.952587i	$0.401589\pi$
$762$	−1.11849e6	−	538639.i	−0.00252795	−	0.00121740i
$763$	2.13853e7	+	1.70542e7i	0.0481439	+	0.0383935i
$764$	−3.00379e8	−	6.85594e7i	−0.673579	−	0.153740i
$765$	2.48889e8	+	1.98482e8i	0.555931	+	0.443341i
$766$	3.84797e7	+	1.68591e8i	0.0856141	+	0.375100i
$767$	5.12694e8			1.13624
$768$		−	7.89858e7i		−	0.174367i
$769$	1.25044e8	+	5.47852e8i	0.274968	+	1.20471i	0.904068	+	0.427389i	$0.140567\pi$
$769$	1.25044e8	+	5.47852e8i	0.274968	+	1.20471i	−0.629100	+	0.777325i	$0.716576\pi$
$770$	1.22667e7	−	9.78234e6i	0.0268692	−	0.0214275i
$771$	−3.98088e7	+	1.91709e7i	−0.0868593	+	0.0418292i
$772$	−7.55238e8	−	3.63704e8i	−1.64147	−	0.790489i
$773$		−	2.91037e8i		−	0.630100i	−0.949075	−	0.315050i	$-0.897979\pi$
$773$		−	2.91037e8i		−	0.630100i	0.949075	−	0.315050i	$-0.102021\pi$
$774$	8.67829e7	+	1.21583e7i	0.187159	+	0.0262211i
$775$	−2.62209e8			−0.563304
$776$	−1.22026e8	+	2.53389e8i	−0.261136	+	0.542255i
$777$	5.34519e7	+	1.10994e8i	0.113946	+	0.236612i
$778$	−2.78937e7	−	3.49776e7i	−0.0592335	−	0.0742764i
$779$	−7.07031e8	+	1.61375e8i	−1.49564	+	0.341369i
$780$	−6.45805e7			−0.136087
$781$			1.21957e8i			0.256009i
$782$	1.86103e8	−	4.24768e7i	0.389164	−	0.0888242i
$783$	2.54386e8	−	3.18989e8i	0.529916	−	0.664494i
$784$	−7.12053e7	+	3.11971e8i	−0.147762	+	0.647389i
$785$	−1.01073e8	+	1.26741e8i	−0.208941	+	0.262004i
$786$	1.41110e7	−	2.93019e7i	0.0290597	−	0.0603431i
$787$	−5.96721e7	−	2.61440e8i	−0.122418	−	0.536350i	−0.998528	−	0.0542382i	$-0.982727\pi$
$787$	−5.96721e7	−	2.61440e8i	−0.122418	−	0.536350i	0.876110	−	0.482112i	$-0.160130\pi$
$788$	4.86099e8	+	2.34093e8i	0.993450	+	0.478420i
$789$	4.21588e7	+	5.28655e7i	0.0858336	+	0.107632i
$790$	1.50666e7	−	6.60112e7i	0.0305587	−	0.133886i
$791$	−2.28210e7	+	9.99853e7i	−0.0461110	+	0.202026i
$792$	−4.74691e7	−	9.85707e7i	−0.0955511	−	0.198414i
$793$	−3.91539e8	+	3.12242e8i	−0.785156	+	0.626141i
$794$	−1.00027e8	−	7.97691e7i	−0.199828	−	0.159358i
$795$	−668119.	+	321749.i	−0.00132970	+	0.000640348i
$796$	2.75116e8	+	5.71285e8i	0.545478	+	1.13270i
$797$	4.43007e7	−	5.55513e7i	0.0875055	−	0.109728i	−0.736151	−	0.676817i	$-0.763359\pi$
$797$	4.43007e7	−	5.55513e7i	0.0875055	−	0.109728i	0.823657	+	0.567089i	$0.191930\pi$
$798$	−1.29918e7	−	1.62913e7i	−0.0255660	−	0.0320587i
$799$	−4.05034e8	+	1.95054e8i	−0.794057	+	0.382398i
$800$	1.96684e8	+	4.48919e7i	0.384149	+	0.0876795i
$801$	−3.01290e8	−	6.87674e7i	−0.586255	−	0.133809i
$802$	4.75782e7	−	3.79423e7i	0.0922326	−	0.0735531i
$803$	−4.48471e7	+	9.31259e7i	−0.0866139	+	0.179856i
$804$	−8.51512e7	+	1.94352e7i	−0.163841	+	0.0373956i
$805$	−1.86905e8	−	9.00089e7i	−0.358290	−	0.172543i
$806$	−6.05644e7	−	4.82985e7i	−0.115668	−	0.0922420i
$807$	7.14949e6	+	1.63183e6i	0.0136036	+	0.00310494i
$808$	3.02018e8	+	2.40851e8i	0.572530	+	0.456578i
$809$	−4.92183e6	−	2.15640e7i	−0.00929569	−	0.0407271i	0.970067	−	0.242836i	$-0.0780777\pi$
$809$	−4.92183e6	−	2.15640e7i	−0.00929569	−	0.0407271i	−0.979363	+	0.202109i	$0.935221\pi$
$810$	4.72162e7			0.0888456
$811$		−	1.58909e8i		−	0.297911i	−0.988844	−	0.148955i	$-0.952409\pi$
$811$		−	1.58909e8i		−	0.297911i	0.988844	−	0.148955i	$-0.0475910\pi$
$812$	8.54622e7	+	3.74435e8i	0.159627	+	0.699371i
$813$	1.71789e8	−	1.36997e8i	0.319687	−	0.254942i
$814$	−1.10206e8	+	5.30725e7i	−0.204330	+	0.0984002i
$815$	2.85281e8	+	1.37384e8i	0.526988	+	0.253784i
$816$		−	1.87537e8i		−	0.345157i
$817$	−6.48170e7	−	7.58875e8i	−0.118856	−	1.39157i
$818$	1.25963e8			0.230134
$819$	−9.18195e7	+	1.90665e8i	−0.167141	+	0.347072i
$820$	−1.43575e8	−	2.98136e8i	−0.260397	−	0.540720i
$821$	5.86423e7	+	7.35351e7i	0.105970	+	0.132882i	0.831988	−	0.554794i	$-0.187203\pi$
$821$	5.86423e7	+	7.35351e7i	0.105970	+	0.132882i	−0.726018	+	0.687675i	$0.758631\pi$
$822$	4.71166e7	−	1.07541e7i	0.0848318	−	0.0193623i
$823$	6.26422e8			1.12374			0.561872	−	0.827224i	$-0.310081\pi$
$823$	6.26422e8			1.12374			0.561872	+	0.827224i	$0.310081\pi$
$824$			7.37203e7i			0.131767i
$825$	6.37824e7	−	1.45579e7i	0.113590	−	0.0259261i
$826$	−4.70615e7	+	5.90133e7i	−0.0835075	+	0.104715i
$827$	−2.06700e8	+	9.05612e8i	−0.365447	+	1.60113i	0.373678	+	0.927558i	$0.378096\pi$
$827$	−2.06700e8	+	9.05612e8i	−0.365447	+	1.60113i	−0.739125	+	0.673568i	$0.764761\pi$
$828$	−4.41146e8	+	5.53179e8i	−0.777125	+	0.974485i
$829$	6.00023e7	−	1.24596e8i	0.105318	−	0.218696i	−0.841649	−	0.540024i	$-0.818415\pi$
$829$	6.00023e7	−	1.24596e8i	0.105318	−	0.218696i	0.946968	+	0.321328i	$0.104129\pi$
$830$	1.55922e7	+	6.83140e7i	0.0272693	+	0.119475i
$831$	1.24955e8	+	6.01752e7i	0.217747	+	0.104861i
$832$	−2.32185e8	−	2.91151e8i	−0.403147	−	0.505531i
$833$	−1.32952e8	+	5.82502e8i	−0.230017	+	1.00777i
$834$	7.58598e6	−	3.32363e7i	0.0130772	−	0.0572948i
$835$	6.13861e6	+	1.27470e7i	0.0105441	+	0.0218951i
$836$	−3.63631e8	+	2.89986e8i	−0.622361	+	0.496316i
$837$	2.12940e8	+	1.69814e8i	0.363145	+	0.289598i
$838$	−1.17452e8	+	5.65621e7i	−0.199586	+	0.0961156i
$839$	−8.36026e7	−	1.73603e8i	−0.141558	−	0.293948i	0.818121	−	0.575046i	$-0.195016\pi$
$839$	−8.36026e7	−	1.73603e8i	−0.141558	−	0.293948i	−0.959679	+	0.281098i	$0.909301\pi$
$840$	1.21197e7	−	1.51977e7i	0.0204482	−	0.0256412i
$841$	−4.95675e8	−	6.21556e8i	−0.833314	−	1.04494i
$842$	−6.77632e7	+	3.26330e7i	−0.113516	+	0.0546665i
$843$	−2.54494e7	−	5.80866e6i	−0.0424810	−	0.00969602i
$844$	8.07672e8	+	1.84346e8i	1.34341	+	0.306624i
$845$	7.09444e7	−	5.65762e7i	0.117584	−	0.0937700i
$846$	−3.21608e7	+	6.67826e7i	−0.0531149	+	0.110294i
$847$	−1.87472e8	+	4.27892e7i	−0.308522	+	0.0704181i
$848$	−4.27889e6	−	2.06060e6i	−0.00701687	−	0.00337915i
$849$	−1.54202e8	−	1.22972e8i	−0.251980	−	0.200947i
$850$	1.13365e8	+	2.58747e7i	0.184595	+	0.0421327i
$851$	1.26447e9	+	1.00838e9i	2.05172	+	1.63620i
$852$	1.64454e7	+	7.20520e7i	0.0265905	+	0.116500i
$853$	4.84629e8			0.780841			0.390420	−	0.920637i	$-0.372330\pi$
$853$	4.84629e8			0.780841			0.390420	+	0.920637i	$0.372330\pi$
$854$		−	7.37294e7i		−	0.118377i
$855$	−1.01515e8	−	4.44765e8i	−0.162416	−	0.711593i
$856$	−6.06432e7	+	4.83613e7i	−0.0966853	+	0.0771040i
$857$	−6.67730e7	+	3.21562e7i	−0.106086	+	0.0510884i	−0.486174	−	0.873862i	$-0.661608\pi$
$857$	−6.67730e7	+	3.21562e7i	−0.106086	+	0.0510884i	0.380088	+	0.924950i	$0.375894\pi$
$858$	1.74138e7	+	8.38606e6i	0.0275697	+	0.0132769i
$859$		−	1.10206e9i		−	1.73871i	−0.494187	−	0.869355i	$-0.664534\pi$
$859$		−	1.10206e9i		−	1.73871i	0.494187	−	0.869355i	$-0.335466\pi$
$860$	3.31002e8	−	1.05885e8i	0.520398	−	0.166471i
$861$	9.97429e7			0.156269
$862$	1.68287e7	−	3.49451e7i	0.0262741	−	0.0545587i
$863$	−1.39520e8	−	2.89717e8i	−0.217073	−	0.450756i	0.763788	−	0.645467i	$-0.223337\pi$
$863$	−1.39520e8	−	2.89717e8i	−0.217073	−	0.450756i	−0.980861	+	0.194711i	$0.937623\pi$
$864$	−1.30654e8	−	1.63835e8i	−0.202572	−	0.254018i
$865$	−5.79089e8	+	1.32173e8i	−0.894740	+	0.204219i
$866$	1.77303e8			0.273000
$867$		−	1.61012e8i		−	0.247060i
$868$	−2.49952e8	+	5.70498e7i	−0.382205	+	0.0872359i
$869$	2.84026e8	−	3.56158e8i	0.432812	−	0.542729i
$870$	−7.65609e6	+	3.35435e7i	−0.0116265	+	0.0509391i
$871$	−2.13826e8	+	2.68129e8i	−0.323598	+	0.405779i
$872$	−1.45993e7	+	3.03157e7i	−0.0220182	+	0.0457212i
$873$	−2.02004e8	−	8.85036e8i	−0.303610	−	1.33020i
$874$	−2.46465e8	−	1.18691e8i	−0.369166	−	0.177781i
$875$	−1.95631e8	−	2.45313e8i	−0.292020	−	0.366182i
$876$	−1.39379e7	+	6.10660e7i	−0.0207341	+	0.0908421i
$877$	2.15102e7	−	9.42423e7i	0.0318893	−	0.139716i	−0.956477	−	0.291807i	$-0.905743\pi$
$877$	2.15102e7	−	9.42423e7i	0.0318893	−	0.139716i	0.988367	+	0.152091i	$0.0486006\pi$
$878$	4.17627e6	+	8.67211e6i	0.00617028	+	0.0128127i
$879$	−2.97848e7	+	2.37526e7i	−0.0438558	+	0.0349739i
$880$	−1.58211e8	−	1.26169e8i	−0.232161	−	0.185142i
$881$	1.16985e9	−	5.63368e8i	1.71081	−	0.823881i	0.719167	−	0.694837i	$-0.244523\pi$
$881$	1.16985e9	−	5.63368e8i	1.71081	−	0.823881i	0.991639	−	0.129044i	$-0.0411909\pi$
$882$	4.27435e7	+	8.87577e7i	0.0622966	+	0.129360i
$883$	−3.21125e8	+	4.02678e8i	−0.466435	+	0.584892i	−0.958294	−	0.285783i	$-0.907746\pi$
$883$	−3.21125e8	+	4.02678e8i	−0.466435	+	0.584892i	0.491859	+	0.870675i	$0.336318\pi$
$884$	−4.81495e8	−	6.03775e8i	−0.697003	−	0.874014i
$885$	1.36956e8	−	6.59543e7i	0.197583	−	0.0951510i
$886$	−1.29141e8	−	2.94756e7i	−0.185679	−	0.0423801i
$887$	−4.26318e8	−	9.73043e7i	−0.610889	−	0.139432i	−0.0941268	−	0.995560i	$-0.530006\pi$
$887$	−4.26318e8	−	9.73043e7i	−0.610889	−	0.139432i	−0.516763	+	0.856129i	$0.672863\pi$
$888$	−1.18484e8	+	9.44877e7i	−0.169208	+	0.134939i
$889$	−6.99987e6	+	1.45354e7i	−0.00996287	+	0.0206881i
$890$	5.31515e7	−	1.21315e7i	0.0753955	−	0.0172085i
$891$	2.86210e8	+	1.37831e8i	0.404624	+	0.194857i
$892$	−9.25451e7	−	7.38023e7i	−0.130394	−	0.103986i
$893$	6.28087e8	+	1.43357e8i	0.881994	+	0.201309i
$894$	2.21874e7	+	1.76939e7i	0.0310523	+	0.0247634i
$895$	−1.21277e8	−	5.31349e8i	−0.169164	−	0.741158i
$896$	2.60857e8			0.362643
$897$		−	2.55554e8i		−	0.354084i
$898$	−6.59668e7	−	2.89020e8i	−0.0910954	−	0.399115i
$899$	7.25359e8	−	5.78454e8i	0.998329	−	0.796141i
$900$	−3.88318e8	+	1.87004e8i	−0.532672	+	0.256521i
$901$	−7.98940e6	−	3.84749e6i	−0.0109230	−	0.00526022i
$902$			9.90348e7i			0.134949i
$903$	−1.45339e7	+	1.03739e8i	−0.0197387	+	0.140890i
$904$	−1.26159e8			−0.170771
$905$	7.98671e7	−	1.65846e8i	0.107751	−	0.223748i
$906$	−1.29208e7	−	2.68304e7i	−0.0173742	−	0.0360780i
$907$	−7.63540e8	−	9.57449e8i	−1.02332	−	1.28320i	−0.958437	−	0.285306i	$-0.907905\pi$
$907$	−7.63540e8	−	9.57449e8i	−1.02332	−	1.28320i	−0.0648801	−	0.997893i	$-0.520666\pi$
$908$	−6.30032e8	+	1.43801e8i	−0.841599	+	0.192089i
$909$	−1.24689e9			−1.66011
$910$		−	3.73330e7i		−	0.0495415i
$911$	1.30573e9	−	2.98024e8i	1.72702	−	0.394181i	0.760210	−	0.649678i	$-0.225096\pi$
$911$	1.30573e9	−	2.98024e8i	1.72702	−	0.394181i	0.966810	+	0.255497i	$0.0822390\pi$
$912$	−1.67564e8	+	2.10119e8i	−0.220901	+	0.277000i
$913$	−1.04904e8	+	4.59615e8i	−0.137841	+	0.603923i
$914$	−1.14456e7	+	1.43523e7i	−0.0149899	+	0.0187967i
$915$	−6.44240e7	+	1.33778e8i	−0.0840977	+	0.174631i
$916$	6.96035e7	+	3.04953e8i	0.0905617	+	0.396777i
$917$	−3.80792e8	−	1.83380e8i	−0.493832	−	0.237817i
$918$	−7.53060e7	−	9.44308e7i	−0.0973423	−	0.122063i
$919$	−2.24761e8	+	9.84741e8i	−0.289584	+	1.26875i	0.595515	+	0.803344i	$0.296948\pi$
$919$	−2.24761e8	+	9.84741e8i	−0.289584	+	1.26875i	−0.885098	+	0.465404i	$0.845909\pi$
$920$	5.67857e7	−	2.48794e8i	0.0729248	−	0.319504i
$921$	6.10155e7	+	1.26700e8i	0.0781018	+	0.162180i
$922$	7.92212e7	−	6.31768e7i	0.101076	−	0.0806055i
$923$	2.26882e8	+	1.80932e8i	0.288533	+	0.230097i
$924$	5.76333e7	−	2.77547e7i	0.0730563	−	0.0351820i
$925$	4.27457e8	+	8.87624e8i	0.540091	+	1.12151i
$926$	2.14814e7	−	2.69369e7i	0.0270539	−	0.0339246i
$927$	−1.48363e8	−	1.86042e8i	−0.186246	−	0.233545i
$928$	−6.43130e8	+	3.09715e8i	−0.804738	+	0.387541i
$929$	2.67277e7	+	6.10042e6i	0.0333361	+	0.00760874i	0.239156	−	0.970981i	$-0.423129\pi$
$929$	2.67277e7	+	6.10042e6i	0.0333361	+	0.00760874i	−0.205820	+	0.978590i	$0.565986\pi$
$930$	−2.23918e7	−	5.11078e6i	−0.0278381	−	0.00635387i
$931$	6.69427e8	−	5.33850e8i	0.829572	−	0.661562i
$932$	2.32755e8	−	4.83321e8i	0.287509	−	0.597019i
$933$	1.99113e8	−	4.54462e7i	0.245163	−	0.0559568i
$934$	9.34512e7	+	4.50037e7i	0.114695	+	0.0552342i
$935$	−2.95407e8	−	2.35579e8i	−0.361398	−	0.288205i
$936$	−2.53799e8	−	5.79280e7i	−0.309501	−	0.0706416i
$937$	−6.54064e8	−	5.21599e8i	−0.795063	−	0.634042i	0.139346	−	0.990244i	$-0.455500\pi$
$937$	−6.54064e8	−	5.21599e8i	−0.795063	−	0.634042i	−0.934409	+	0.356202i	$0.884071\pi$
$938$	−1.12352e7	−	4.92246e7i	−0.0136136	−	0.0596450i
$939$	−2.67002e7			−0.0322491
$940$			2.93958e8i			0.353918i
$941$	2.00021e8	+	8.76349e8i	0.240053	+	1.05174i	0.940968	+	0.338496i	$0.109918\pi$
$941$	2.00021e8	+	8.76349e8i	0.240053	+	1.05174i	−0.700915	+	0.713245i	$0.747225\pi$
$942$	2.29862e7	−	1.83308e7i	0.0274988	−	0.0219296i
$943$	1.17977e9	−	5.68146e8i	1.40689	−	0.677524i
$944$	8.77116e8	+	4.22397e8i	1.04266	+	0.502116i
$945$			1.31260e8i			0.155538i
$946$	−1.03003e8	−	1.44307e7i	−0.121668	−	0.0170457i
$947$	7.31114e8			0.860866			0.430433	−	0.902623i	$-0.358361\pi$
$947$	7.31114e8			0.860866			0.430433	+	0.902623i	$0.358361\pi$
$948$	1.19776e8	−	2.48717e8i	0.140586	−	0.291931i
$949$	1.06712e8	+	2.21590e8i	0.124858	+	0.259270i
$950$	−1.03896e8	−	1.30282e8i	−0.121179	−	0.151954i
$951$	−1.63417e8	+	3.72989e7i	−0.190001	+	0.0433665i
$952$	2.32447e8			0.269410
$953$		−	3.12830e8i		−	0.361435i	−0.983535	−	0.180717i	$-0.942158\pi$
$953$		−	3.12830e8i		−	0.361435i	0.983535	−	0.180717i	$-0.0578419\pi$
$954$	−1.42544e6	+	325347.i	−0.00164174	+	0.000374716i
$955$	−2.23641e8	+	2.80437e8i	−0.256768	+	0.321977i
$956$	−1.78034e8	+	7.80016e8i	−0.203764	+	0.892750i
$957$	−1.44328e8	+	1.80981e8i	−0.164670	+	0.206489i
$958$	1.33549e7	−	2.77318e7i	0.0151895	−	0.0315414i
$959$	−1.39754e8	−	6.12303e8i	−0.158456	−	0.694242i
$960$	−9.94778e7	−	4.79060e7i	−0.112438	−	0.0541472i
$961$	−1.67206e8	−	2.09669e8i	−0.188400	−	0.236246i
$962$	−6.47659e7	+	2.83758e8i	−0.0727480	+	0.318730i
$963$	5.57121e7	−	2.44091e8i	0.0623837	−	0.273321i
$964$	−4.29823e8	−	8.92536e8i	−0.479798	−	0.996311i
$965$	−7.62979e8	+	6.08455e8i	−0.849045	+	0.677091i
$966$	2.94154e7	+	2.34580e7i	0.0326320	+	0.0260231i
$967$	6.51860e8	−	3.13919e8i	0.720900	−	0.347167i	−0.0371979	−	0.999308i	$-0.511843\pi$
$967$	6.51860e8	−	3.13919e8i	0.720900	−	0.347167i	0.758098	+	0.652141i	$0.226129\pi$
$968$	−1.02634e8	−	2.13122e8i	−0.113153	−	0.234965i
$969$	−3.12871e8	+	3.92327e8i	−0.343869	+	0.431198i
$970$	9.98503e7	+	1.25208e8i	0.109404	+	0.137189i
$971$	−6.14306e8	+	2.95834e8i	−0.671007	+	0.323140i	−0.738182	−	0.674601i	$-0.764316\pi$
$971$	−6.14306e8	+	2.95834e8i	−0.671007	+	0.323140i	0.0671756	+	0.997741i	$0.478601\pi$
$972$	6.64287e8	+	1.51619e8i	0.723364	+	0.165103i
$973$	−4.31922e8	−	9.85834e7i	−0.468886	−	0.107020i
$974$	−1.82973e8	+	1.45916e8i	−0.198021	+	0.157916i
$975$	6.75431e7	−	1.40255e8i	0.0728731	−	0.151323i
$976$	−9.27094e8	+	2.11603e8i	−0.997182	+	0.227600i
$977$	−2.53361e8	−	1.22012e8i	−0.271680	−	0.130834i	0.293084	−	0.956087i	$-0.405318\pi$
$977$	−2.53361e8	−	1.22012e8i	−0.271680	−	0.130834i	−0.564764	+	0.825253i	$0.691033\pi$
$978$	−4.48979e7	−	3.58049e7i	−0.0479965	−	0.0382759i
$979$	3.57602e8	+	8.16202e7i	0.381111	+	0.0869861i
$980$	3.05451e8	+	2.43589e8i	0.324536	+	0.258809i
$981$	−2.41679e7	−	1.05886e8i	−0.0255995	−	0.112159i
$982$	2.85607e8			0.301602
$983$			3.86768e7i			0.0407183i	0.999793	+	0.0203591i	$0.00648096\pi$
$983$			3.86768e7i			0.0407183i	−0.999793	+	0.0203591i	$0.993519\pi$
$984$	2.73029e7	+	1.19622e8i	0.0286565	+	0.125552i
$985$	4.91081e8	−	3.91624e8i	0.513860	−	0.409789i
$986$	−3.70686e8	+	1.78513e8i	−0.386702	+	0.186226i
$987$	−7.98312e7	−	3.84447e7i	−0.0830274	−	0.0399839i
$988$			1.10669e9i			1.14751i
$989$	4.19002e8	+	1.30982e9i	0.433139	+	1.35402i
$990$	−6.22987e7			−0.0642057
$991$	−7.67854e8	+	1.59447e9i	−0.788965	+	1.63830i	−0.0193344	+	0.999813i	$0.506155\pi$
$991$	−7.67854e8	+	1.59447e9i	−0.788965	+	1.63830i	−0.769631	+	0.638489i	$0.779560\pi$
$992$	−2.06748e8	−	4.29318e8i	−0.211791	−	0.439788i
$993$	−2.35506e8	−	2.95315e8i	−0.240522	−	0.301605i
$994$	−4.16522e7	+	9.50684e6i	−0.0424110	+	0.00968004i
$995$	7.38190e8			0.749375
$996$			2.85685e8i			0.289141i
$997$	−8.47205e8	+	1.93369e8i	−0.854876	+	0.195120i	−0.627432	−	0.778671i	$-0.715894\pi$
$997$	−8.47205e8	+	1.93369e8i	−0.854876	+	0.195120i	−0.227444	+	0.973791i	$0.573037\pi$
$998$	−1.36341e8	+	1.70966e8i	−0.137162	+	0.171996i
$999$	2.27712e8	−	9.97670e8i	0.228396	−	1.00067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.22.10	yes	126
43.2	odd	14	inner	43.7.f.a.2.10	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.10	✓	126	43.2	odd	14	inner
43.7.f.a.22.10	yes	126	1.1	even	1	trivial

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.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.716329 + 1.48747i) q^{2} +(3.40007 + 7.06031i) q^{3} +(38.2039 + 47.9062i) q^{4} +(69.5466 - 15.8736i) q^{5} -12.9376 q^{6} +168.130i q^{7} +(-201.638 + 46.0227i) q^{8} +(416.237 - 521.944i) q^{9} +O(q^{10})\)	\(q+(-0.716329 + 1.48747i) q^{2} +(3.40007 + 7.06031i) q^{3} +(38.2039 + 47.9062i) q^{4} +(69.5466 - 15.8736i) q^{5} -12.9376 q^{6} +168.130i q^{7} +(-201.638 + 46.0227i) q^{8} +(416.237 - 521.944i) q^{9} +(-26.2068 + 114.819i) q^{10} +(-494.032 + 619.497i) q^{11} +(-208.337 + 432.616i) q^{12} +(419.543 + 1838.14i) q^{13} +(-250.089 - 120.436i) q^{14} +(348.535 + 437.049i) q^{15} +(-796.646 + 3490.33i) q^{16} +(-1487.47 + 6517.04i) q^{17} +(478.215 + 993.023i) q^{18} +(7489.56 - 5972.73i) q^{19} +(3417.39 + 2725.28i) q^{20} +(-1187.05 + 571.653i) q^{21} +(-567.595 - 1178.62i) q^{22} +(-10784.3 + 13523.1i) q^{23} +(-1010.52 - 1267.15i) q^{24} +(-9492.88 + 4571.53i) q^{25} +(-3034.71 - 692.652i) q^{26} +(10669.8 + 2435.31i) q^{27} +(-8054.46 + 6423.22i) q^{28} +(16175.3 - 33588.4i) q^{29} +(-899.764 + 205.365i) q^{30} +(22421.8 + 10797.8i) q^{31} +(-14970.0 - 11938.2i) q^{32} +(-6053.58 - 1381.69i) q^{33} +(-8628.40 - 6880.92i) q^{34} +(2668.82 + 11692.9i) q^{35} +40906.2 q^{36} -93504.2i q^{37} +(3519.27 + 15418.9i) q^{38} +(-11551.3 + 9211.89i) q^{39} +(-13292.7 + 6401.44i) q^{40} +(-68207.6 - 32847.0i) q^{41} -2175.19i q^{42} +(44101.9 - 66154.2i) q^{43} -48551.7 q^{44} +(20662.7 - 42906.6i) q^{45} +(-12390.1 - 25728.4i) q^{46} +(41930.8 + 52579.6i) q^{47} +(-27351.5 + 6242.80i) q^{48} +89381.3 q^{49} -17395.1i q^{50} +(-51069.8 + 11656.4i) q^{51} +(-72030.0 + 90322.7i) q^{52} +(-295.187 + 1293.30i) q^{53} +(-11265.5 + 14126.5i) q^{54} +(-24524.7 + 50926.0i) q^{55} +(-7737.79 - 33901.5i) q^{56} +(67634.3 + 32571.0i) q^{57} +(38375.0 + 48120.7i) q^{58} +(60509.5 - 265109. i) q^{59} +(-7621.96 + 33394.0i) q^{60} +(115247. + 239313. i) q^{61} +(-32122.7 + 25617.0i) q^{62} +(87754.5 + 69981.8i) q^{63} +(-177954. + 85698.3i) q^{64} +(58355.6 + 121177. i) q^{65} +(6391.58 - 8014.79i) q^{66} +(113411. + 142213. i) q^{67} +(-369034. + 177717. i) q^{68} +(-132145. - 30161.2i) q^{69} +(-19304.6 - 4406.14i) q^{70} +(120336. - 95964.5i) q^{71} +(-59908.0 + 124400. i) q^{72} +(127177. - 29027.2i) q^{73} +(139085. + 66979.7i) q^{74} +(-64552.8 - 51479.2i) q^{75} +(572261. + 130615. i) q^{76} +(-104156. - 83061.7i) q^{77} +(-5427.87 - 23781.0i) q^{78} -574914. q^{79} +255387. i q^{80} +(-89211.3 - 390860. i) q^{81} +(97718.0 - 77927.5i) q^{82} +(536050. - 258148. i) q^{83} +(-72735.6 - 35027.6i) q^{84} +476850. i q^{85} +(66811.1 + 112989. i) q^{86} +292142. q^{87} +(71105.0 - 147651. i) q^{88} +(-200851. - 417071. i) q^{89} +(49021.0 + 61470.4i) q^{90} +(-309046. + 70537.8i) q^{91} -1.05984e6 q^{92} +195018. i q^{93} +(-108247. + 24706.6i) q^{94} +(426065. - 534269. i) q^{95} +(33388.3 - 146283. i) q^{96} +(847827. - 1.06314e6i) q^{97} +(-64026.4 + 132952. i) q^{98} +(117709. + 515715. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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