LMFDB - Embedded newform 43.7.f.a.22.7

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			22.7
Character	$\chi$	$=$	43.22
Dual form			43.7.f.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.64714 + 7.57336i) q^{2} +(2.80632 + 5.82738i) q^{3} +(-4.15080 - 5.20494i) q^{4} +(190.781 - 43.5445i) q^{5} -54.3678 q^{6} -593.422i q^{7} +(-469.925 + 107.257i) q^{8} +(428.441 - 537.248i) q^{9} +O(q^{10})$	\(q+(-3.64714 + 7.57336i) q^{2} +(2.80632 + 5.82738i) q^{3} +(-4.15080 - 5.20494i) q^{4} +(190.781 - 43.5445i) q^{5} -54.3678 q^{6} -593.422i q^{7} +(-469.925 + 107.257i) q^{8} +(428.441 - 537.248i) q^{9} +(-366.026 + 1603.66i) q^{10} +(1309.13 - 1641.60i) q^{11} +(18.6827 - 38.7950i) q^{12} +(203.429 + 891.283i) q^{13} +(4494.20 + 2164.29i) q^{14} +(789.141 + 989.552i) q^{15} +(996.393 - 4365.48i) q^{16} +(-837.881 + 3671.00i) q^{17} +(2506.19 + 5204.16i) q^{18} +(-6305.71 + 5028.64i) q^{19} +(-1018.54 - 812.258i) q^{20} +(3458.09 - 1665.33i) q^{21} +(7657.84 + 15901.7i) q^{22} +(5379.15 - 6745.25i) q^{23} +(-1943.79 - 2437.43i) q^{24} +(20423.5 - 9835.45i) q^{25} +(-7491.94 - 1709.99i) q^{26} +(8929.97 + 2038.21i) q^{27} +(-3088.73 + 2463.18i) q^{28} +(-6988.90 + 14512.6i) q^{29} +(-10372.3 + 2367.42i) q^{30} +(-24316.2 - 11710.1i) q^{31} +(5308.94 + 4233.74i) q^{32} +(13240.1 + 3021.96i) q^{33} +(-24745.9 - 19734.2i) q^{34} +(-25840.2 - 113214. i) q^{35} -4574.72 q^{36} +56433.9i q^{37} +(-15085.9 - 66095.6i) q^{38} +(-4622.95 + 3686.68i) q^{39} +(-84982.2 + 40925.3i) q^{40} +(-35014.3 - 16862.0i) q^{41} +32263.1i q^{42} +(79227.2 + 6663.89i) q^{43} -13978.4 q^{44} +(58344.1 - 121153. i) q^{45} +(31465.7 + 65339.1i) q^{46} +(62864.2 + 78829.2i) q^{47} +(28235.5 - 6444.57i) q^{48} -234501. q^{49} +190546. i q^{50} +(-23743.6 + 5419.33i) q^{51} +(3794.68 - 4758.38i) q^{52} +(-16522.9 + 72391.6i) q^{53} +(-48004.9 + 60196.2i) q^{54} +(178275. - 370191. i) q^{55} +(63648.9 + 278864. i) q^{56} +(-46999.6 - 22633.8i) q^{57} +(-84419.7 - 105859. i) q^{58} +(28352.8 - 124222. i) q^{59} +(1874.99 - 8214.87i) q^{60} +(76364.2 + 158572. i) q^{61} +(177369. - 141447. i) q^{62} +(-318815. - 254246. i) q^{63} +(206770. - 99575.2i) q^{64} +(77620.8 + 161181. i) q^{65} +(-71174.7 + 89250.3i) q^{66} +(247136. + 309899. i) q^{67} +(22585.2 - 10876.5i) q^{68} +(54402.7 + 12417.1i) q^{69} +(951649. + 217208. i) q^{70} +(-94719.4 + 75536.2i) q^{71} +(-143712. + 298420. i) q^{72} +(212584. - 48520.9i) q^{73} +(-427394. - 205822. i) q^{74} +(114630. + 91414.2i) q^{75} +(52347.5 + 11948.0i) q^{76} +(-974162. - 776869. i) q^{77} +(-11060.0 - 48457.1i) q^{78} +729548. q^{79} -876238. i q^{80} +(-98287.7 - 430626. i) q^{81} +(255404. - 203678. i) q^{82} +(-697139. + 335725. i) q^{83} +(-23021.8 - 11086.7i) q^{84} +736840. i q^{85} +(-339421. + 575712. i) q^{86} -104184. q^{87} +(-439121. + 911844. i) q^{88} +(205458. + 426638. i) q^{89} +(704745. + 883722. i) q^{90} +(528907. - 120720. i) q^{91} -57436.4 q^{92} -174562. i q^{93} +(-826276. + 188592. i) q^{94} +(-984039. + 1.23395e6i) q^{95} +(-9773.02 + 42818.4i) q^{96} +(64522.4 - 80908.5i) q^{97} +(855257. - 1.77596e6i) q^{98} +(-321061. - 1.40666e6i) 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 $

$2$	−3.64714	+	7.57336i	−0.455892	+	0.946670i	0.538669	+	0.842517i	$0.318927\pi$
$2$	−3.64714	+	7.57336i	−0.455892	+	0.946670i	−0.994561	+	0.104152i	$0.966787\pi$
$3$	2.80632	+	5.82738i	0.103938	+	0.215829i	0.946452	−	0.322846i	$-0.104640\pi$
$3$	2.80632	+	5.82738i	0.103938	+	0.215829i	−0.842514	+	0.538675i	$0.818925\pi$
$4$	−4.15080	−	5.20494i	−0.0648563	−	0.0813272i
$5$	190.781	−	43.5445i	1.52625	−	0.348356i	0.624640	−	0.780913i	$-0.285246\pi$
$5$	190.781	−	43.5445i	1.52625	−	0.348356i	0.901606	+	0.432558i	$0.142389\pi$
$6$	−54.3678			−0.251703
$7$		−	593.422i		−	1.73009i	−0.501691	−	0.865047i	$-0.667289\pi$
$7$		−	593.422i		−	1.73009i	0.501691	−	0.865047i	$-0.332711\pi$
$8$	−469.925	+	107.257i	−0.917823	+	0.209487i
$9$	428.441	−	537.248i	0.587711	−	0.736966i
$10$	−366.026	+	1603.66i	−0.366026	+	1.60366i
$11$	1309.13	−	1641.60i	0.983571	−	1.23336i	0.0111955	−	0.999937i	$-0.496436\pi$
$11$	1309.13	−	1641.60i	0.983571	−	1.23336i	0.972376	−	0.233422i	$-0.0749923\pi$
$12$	18.6827	−	38.7950i	0.0108117	−	0.0224508i
$13$	203.429	+	891.283i	0.0925942	+	0.405682i	0.999890	−	0.0148106i	$-0.00471454\pi$
$13$	203.429	+	891.283i	0.0925942	+	0.405682i	−0.907296	+	0.420492i	$0.861857\pi$
$14$	4494.20	+	2164.29i	1.63783	+	0.788736i
$15$	789.141	+	989.552i	0.233820	+	0.293200i
$16$	996.393	−	4365.48i	0.243260	−	1.06579i
$17$	−837.881	+	3671.00i	−0.170544	+	0.747200i	0.815232	+	0.579134i	$0.196609\pi$
$17$	−837.881	+	3671.00i	−0.170544	+	0.747200i	−0.985776	+	0.168066i	$0.946248\pi$
$18$	2506.19	+	5204.16i	0.429731	+	0.892345i
$19$	−6305.71	+	5028.64i	−0.919334	+	0.733145i	−0.964013	−	0.265857i	$-0.914345\pi$
$19$	−6305.71	+	5028.64i	−0.919334	+	0.733145i	0.0446782	+	0.999001i	$0.485774\pi$
$20$	−1018.54	−	812.258i	−0.127317	−	0.101532i
$21$	3458.09	−	1665.33i	0.373404	−	0.179822i
$22$	7657.84	+	15901.7i	0.719182	+	1.49340i
$23$	5379.15	−	6745.25i	0.442110	−	0.554389i	−0.509988	−	0.860182i	$-0.670350\pi$
$23$	5379.15	−	6745.25i	0.442110	−	0.554389i	0.952098	+	0.305793i	$0.0989215\pi$
$24$	−1943.79	−	2437.43i	−0.140610	−	0.176319i
$25$	20423.5	−	9835.45i	1.30711	−	0.629469i
$26$	−7491.94	−	1709.99i	−0.426260	−	0.0972910i
$27$	8929.97	+	2038.21i	0.453690	+	0.103552i
$28$	−3088.73	+	2463.18i	−0.140704	+	0.112207i
$29$	−6988.90	+	14512.6i	−0.286560	+	0.595047i	−0.993706	−	0.112020i	$-0.964268\pi$
$29$	−6988.90	+	14512.6i	−0.286560	+	0.595047i	0.707146	+	0.707067i	$0.249982\pi$
$30$	−10372.3	+	2367.42i	−0.384161	+	0.0876821i
$31$	−24316.2	−	11710.1i	−0.816226	−	0.393074i	−0.0212946	−	0.999773i	$-0.506779\pi$
$31$	−24316.2	−	11710.1i	−0.816226	−	0.393074i	−0.794931	+	0.606700i	$0.792493\pi$
$32$	5308.94	+	4233.74i	0.162016	+	0.129203i
$33$	13240.1	+	3021.96i	0.368424	+	0.0840905i
$34$	−24745.9	−	19734.2i	−0.629603	−	0.502091i
$35$	−25840.2	−	113214.i	−0.602688	−	2.64055i
$36$	−4574.72			−0.0980521
$37$			56433.9i			1.11413i	0.830470	+	0.557064i	$0.188072\pi$
$37$			56433.9i			1.11413i	−0.830470	+	0.557064i	$0.811928\pi$
$38$	−15085.9	−	66095.6i	−0.274929	−	1.20454i
$39$	−4622.95	+	3686.68i	−0.0779337	+	0.0621501i
$40$	−84982.2	+	40925.3i	−1.32785	+	0.639458i
$41$	−35014.3	−	16862.0i	−0.508035	−	0.244657i	0.162265	−	0.986747i	$-0.448120\pi$
$41$	−35014.3	−	16862.0i	−0.508035	−	0.244657i	−0.670300	+	0.742090i	$0.733834\pi$
$42$			32263.1i			0.435470i
$43$	79227.2	+	6663.89i	0.996481	+	0.0838152i
$43$	79227.2	+	6663.89i	0.996481	+	0.0838152i
$44$	−13978.4			−0.164096
$45$	58344.1	−	121153.i	0.640265	−	1.32952i
$46$	31465.7	+	65339.1i	0.323268	+	0.671274i
$47$	62864.2	+	78829.2i	0.605494	+	0.759265i	0.986223	−	0.165421i	$-0.0528984\pi$
$47$	62864.2	+	78829.2i	0.605494	+	0.759265i	−0.380729	+	0.924687i	$0.624327\pi$
$48$	28235.5	−	6444.57i	0.255312	−	0.0582734i
$49$	−234501.			−1.99322
$50$			190546.i			1.52437i
$51$	−23743.6	+	5419.33i	−0.178993	+	0.0408540i
$52$	3794.68	−	4758.38i	0.0269876	−	0.0338414i
$53$	−16522.9	+	72391.6i	−0.110984	+	0.486251i	0.888634	+	0.458616i	$0.151655\pi$
$53$	−16522.9	+	72391.6i	−0.110984	+	0.486251i	−0.999618	+	0.0276349i	$0.991202\pi$
$54$	−48004.9	+	60196.2i	−0.304863	+	0.382286i
$55$	178275.	−	370191.i	1.07152	−	2.22504i
$56$	63648.9	+	278864.i	0.362432	+	1.58792i
$57$	−46999.6	−	22633.8i	−0.253787	−	0.122217i
$58$	−84419.7	−	105859.i	−0.432673	−	0.542555i
$59$	28352.8	−	124222.i	0.138051	−	0.604842i	−0.857811	−	0.513965i	$-0.828176\pi$
$59$	28352.8	−	124222.i	0.138051	−	0.604842i	0.995862	−	0.0908767i	$-0.0289669\pi$
$60$	1874.99	−	8214.87i	0.00868051	−	0.0380318i
$61$	76364.2	+	158572.i	0.336434	+	0.698613i	0.998717	−	0.0506413i	$-0.0161265\pi$
$61$	76364.2	+	158572.i	0.336434	+	0.698613i	−0.662283	+	0.749254i	$0.730412\pi$
$62$	177369.	−	141447.i	0.744222	−	0.593497i
$63$	−318815.	−	254246.i	−1.27502	−	1.01679i
$64$	206770.	−	99575.2i	0.788765	−	0.379849i
$65$	77620.8	+	161181.i	0.282643	+	0.586914i
$66$	−71174.7	+	89250.3i	−0.247568	+	0.310440i
$67$	247136.	+	309899.i	0.821696	+	1.03037i	0.998932	+	0.0462062i	$0.0147131\pi$
$67$	247136.	+	309899.i	0.821696	+	1.03037i	−0.177236	+	0.984168i	$0.556715\pi$
$68$	22585.2	−	10876.5i	0.0718285	−	0.0345908i
$69$	54402.7	+	12417.1i	0.165605	+	0.0377982i
$70$	951649.	+	217208.i	2.77449	+	0.633259i
$71$	−94719.4	+	75536.2i	−0.264645	+	0.211047i	−0.746818	−	0.665029i	$-0.768419\pi$
$71$	−94719.4	+	75536.2i	−0.264645	+	0.211047i	0.482173	+	0.876076i	$0.339848\pi$
$72$	−143712.	+	298420.i	−0.385030	+	0.799522i
$73$	212584.	−	48520.9i	0.546464	−	0.124727i	0.0596287	−	0.998221i	$-0.481008\pi$
$73$	212584.	−	48520.9i	0.546464	−	0.124727i	0.486835	+	0.873494i	$0.338151\pi$
$74$	−427394.	−	205822.i	−1.05471	−	0.507922i
$75$	114630.	+	91414.2i	0.271715	+	0.216686i
$76$	52347.5	+	11948.0i	0.119249	+	0.0272179i
$77$	−974162.	−	776869.i	−2.13383	−	1.70167i
$78$	−11060.0	−	48457.1i	−0.0233062	−	0.102111i
$79$	729548.			1.47970			0.739848	−	0.672774i	$-0.234897\pi$
$79$	729548.			1.47970			0.739848	+	0.672774i	$0.234897\pi$
$80$		−	876238.i		−	1.71140i
$81$	−98287.7	−	430626.i	−0.184946	−	0.810299i
$82$	255404.	−	203678.i	0.463219	−	0.369405i
$83$	−697139.	+	335725.i	−1.21923	+	0.587150i	−0.929097	−	0.369837i	$-0.879414\pi$
$83$	−697139.	+	335725.i	−1.21923	+	0.587150i	−0.290132	+	0.956987i	$0.593699\pi$
$84$	−23021.8	−	11086.7i	−0.0388420	−	0.0187053i
$85$			736840.i			1.19982i
$86$	−339421.	+	575712.i	−0.533633	+	0.905128i
$87$	−104184.			−0.158213
$88$	−439121.	+	911844.i	−0.644371	+	1.33805i
$89$	205458.	+	426638.i	0.291443	+	0.605187i	0.994357	−	0.106088i	$-0.0338324\pi$
$89$	205458.	+	426638.i	0.291443	+	0.605187i	−0.702914	+	0.711275i	$0.748118\pi$
$90$	704745.	+	883722.i	0.966728	+	1.21224i
$91$	528907.	−	120720.i	0.701867	−	0.160197i
$92$	−57436.4			−0.0737605
$93$		−	174562.i		−	0.217020i
$94$	−826276.	+	188592.i	−0.994814	+	0.227060i
$95$	−984039.	+	1.23395e6i	−1.14774	+	1.43921i
$96$	−9773.02	+	42818.4i	−0.0110463	+	0.0483968i
$97$	64522.4	−	80908.5i	0.0706961	−	0.0886501i	−0.745226	−	0.666812i	$-0.767658\pi$
$97$	64522.4	−	80908.5i	0.0706961	−	0.0886501i	0.815922	+	0.578162i	$0.196230\pi$
$98$	855257.	−	1.77596e6i	0.908695	−	1.88693i
$99$	−321061.	−	1.40666e6i	−0.330888	−	1.44972i
$100$	−135967.	−	65478.2i	−0.135967	−	0.0654782i
$101$	−999564.	−	1.25341e6i	−0.970167	−	1.21655i	−0.976267	−	0.216570i	$-0.930513\pi$
$101$	−999564.	−	1.25341e6i	−0.970167	−	1.21655i	0.00610005	−	0.999981i	$-0.498058\pi$
$102$	45553.8	−	199584.i	0.0429263	−	0.188073i
$103$	169888.	−	744329.i	0.155472	−	0.681167i	−0.835767	−	0.549084i	$-0.814977\pi$
$103$	169888.	−	744329.i	0.155472	−	0.681167i	0.991239	−	0.132082i	$-0.0421663\pi$
$104$	−191193.	−	397017.i	−0.169970	−	0.352947i
$105$	587222.	−	468294.i	0.507264	−	0.404530i
$106$	−487986.	−	389156.i	−0.409723	−	0.326743i
$107$	−983394.	+	473577.i	−0.802742	+	0.386580i	−0.789822	−	0.613336i	$-0.789827\pi$
$107$	−983394.	+	473577.i	−0.802742	+	0.386580i	−0.0129202	+	0.999917i	$0.504113\pi$
$108$	−26457.8	−	54940.2i	−0.0210030	−	0.0436133i
$109$	−522019.	+	654592.i	−0.403095	+	0.505465i	−0.941403	−	0.337283i	$-0.890492\pi$
$109$	−522019.	+	654592.i	−0.403095	+	0.505465i	0.538309	+	0.842748i	$0.319063\pi$
$110$	2.15340e6	+	2.70028e6i	1.61788	+	2.02876i
$111$	−328862.	+	158371.i	−0.240461	+	0.115800i
$112$	−2.59058e6	−	591282.i	−1.84392	−	0.420863i
$113$	−975072.	−	222554.i	−0.675774	−	0.154241i	−0.129157	−	0.991624i	$-0.541227\pi$
$113$	−975072.	−	222554.i	−0.675774	−	0.154241i	−0.546616	+	0.837383i	$0.684084\pi$
$114$	342828.	−	273396.i	0.231399	−	0.184535i
$115$	732521.	−	1.52110e6i	0.481644	−	1.00014i
$116$	104547.	−	23862.1i	0.0669787	−	0.0152875i
$117$	565998.	+	272570.i	0.353392	+	0.170185i
$118$	837370.	+	667780.i	0.509649	+	0.406432i
$119$	2.17845e6	+	497217.i	1.29273	+	0.295056i
$120$	−476974.	−	380374.i	−0.276027	−	0.220124i
$121$	−586815.	−	2.57100e6i	−0.331242	−	1.45126i
$122$	−1.47943e6			−0.814733
$123$		−	251362.i		−	0.135078i
$124$	39981.5	+	175170.i	0.0209698	+	0.0918747i
$125$	1.07760e6	−	859358.i	0.551732	−	0.439991i
$126$	3.08826e6	−	1.48723e6i	1.54384	−	0.743474i
$127$	2.27509e6	+	1.09563e6i	1.11068	+	0.534874i	0.897000	−	0.442030i	$-0.145742\pi$
$127$	2.27509e6	+	1.09563e6i	1.11068	+	0.534874i	0.213677	+	0.976904i	$0.431456\pi$
$128$			2.36369e6i			1.12710i
$129$	183504.	+	480388.i	0.0854822	+	0.223781i
$130$	−1.50378e6			−0.684469
$131$	−1.27870e6	+	2.65525e6i	−0.568794	+	1.18111i	0.396036	+	0.918235i	$0.370386\pi$
$131$	−1.27870e6	+	2.65525e6i	−0.568794	+	1.18111i	−0.964829	+	0.262877i	$0.915329\pi$
$132$	−39227.8	−	81457.3i	−0.0170558	−	0.0354167i
$133$	2.98411e6	+	3.74195e6i	1.26841	+	1.59053i
$134$	−3.24831e6	+	741406.i	−1.35003	+	0.308135i
$135$	1.79242e6			0.728515
$136$		−	1.81496e6i		−	0.721524i
$137$	2.83761e6	−	647665.i	1.10355	−	0.251877i	0.368320	−	0.929699i	$-0.379933\pi$
$137$	2.83761e6	−	647665.i	1.10355	−	0.251877i	0.735226	+	0.677822i	$0.237076\pi$
$138$	−292453.	+	366724.i	−0.111280	+	0.139541i
$139$	−645471.	+	2.82799e6i	−0.240343	+	1.05301i	0.700362	+	0.713788i	$0.253022\pi$
$139$	−645471.	+	2.82799e6i	−0.240343	+	1.05301i	−0.940705	+	0.339225i	$0.889835\pi$
$140$	−482012.	+	604424.i	−0.175660	+	0.220271i
$141$	−282951.	+	587553.i	−0.100938	+	0.209599i
$142$	−226608.	−	992835.i	−0.0791426	−	0.346746i
$143$	1.72945e6	+	832858.i	0.591424	+	0.284815i
$144$	−1.91845e6	−	2.40566e6i	−0.642486	−	0.805652i
$145$	−701405.	+	3.07305e6i	−0.230072	+	1.00801i
$146$	−407856.	+	1.78694e6i	−0.131054	+	0.574183i
$147$	−658084.	−	1.36652e6i	−0.207171	−	0.430195i
$148$	293735.	−	234246.i	0.0906089	−	0.0722582i
$149$	1.68975e6	+	1.34753e6i	0.510814	+	0.407360i	0.844689	−	0.535257i	$-0.179785\pi$
$149$	1.68975e6	+	1.34753e6i	0.510814	+	0.407360i	−0.333876	+	0.942617i	$0.608357\pi$
$150$	−1.11038e6	+	534732.i	−0.329002	+	0.158439i
$151$	−2.50544e6	−	5.20260e6i	−0.727701	−	1.51109i	−0.854665	−	0.519179i	$-0.826238\pi$
$151$	−2.50544e6	−	5.20260e6i	−0.727701	−	1.51109i	0.126964	−	0.991907i	$-0.459477\pi$
$152$	2.42386e6	−	3.03942e6i	0.690202	−	0.865486i
$153$	1.61325e6	+	2.02296e6i	0.450431	+	0.564823i
$154$	9.43641e6	−	4.54433e6i	2.58371	−	1.24425i
$155$	−5.14897e6	−	1.17522e6i	−1.38269	−	0.315590i
$156$	38377.9	+	8759.51i	0.0101090	+	0.00230731i
$157$	−3.60458e6	+	2.87456e6i	−0.931442	+	0.742800i	−0.966522	−	0.256585i	$-0.917403\pi$
$157$	−3.60458e6	+	2.87456e6i	−0.931442	+	0.742800i	0.0350802	+	0.999385i	$0.488831\pi$
$158$	−2.66076e6	+	5.52513e6i	−0.674582	+	1.40078i
$159$	−468222.	+	106869.i	−0.116482	+	0.0265863i
$160$	1.19720e6	+	576541.i	0.292285	+	0.140757i
$161$	−4.00278e6	−	3.19211e6i	−0.959144	−	0.764892i
$162$	3.61976e6	+	826186.i	0.851401	+	0.194327i
$163$	5.43871e6	+	4.33723e6i	1.25584	+	1.00150i	0.999389	+	0.0349389i	$0.0111237\pi$
$163$	5.43871e6	+	4.33723e6i	1.25584	+	1.00150i	0.256448	+	0.966558i	$0.417448\pi$
$164$	57571.7	+	252238.i	0.0130520	+	0.0571846i
$165$	2.65754e6			0.591600
$166$		−	6.50412e6i		−	1.42188i
$167$	−882855.	−	3.86804e6i	−0.189557	−	0.830504i	−0.976850	−	0.213925i	$-0.931375\pi$
$167$	−882855.	−	3.86804e6i	−0.189557	−	0.830504i	0.787293	−	0.616579i	$-0.211482\pi$
$168$	−1.44643e6	+	1.15349e6i	−0.305048	+	0.243268i
$169$	3.59580e6	−	1.73165e6i	0.744965	−	0.358756i
$170$	−5.58036e6	−	2.68736e6i	−1.13583	−	0.546989i
$171$			5.54221e6i			1.10840i
$172$	−294171.	−	440034.i	−0.0578116	−	0.0864770i
$173$	−6.52581e6			−1.26037			−0.630183	−	0.776447i	$-0.717020\pi$
$173$	−6.52581e6			−1.26037			−0.630183	+	0.776447i	$0.717020\pi$
$174$	379972.	−	789019.i	0.0721279	−	0.149775i
$175$	−5.83658e6	−	1.21198e7i	−1.08904	−	2.26142i
$176$	−5.86197e6	−	7.35068e6i	−1.07524	−	1.34831i
$177$	803455.	−	183383.i	0.144891	−	0.0330704i
$178$	−3.98042e6			−0.705779
$179$		−	4.52514e6i		−	0.788993i	−0.918897	−	0.394497i	$-0.870919\pi$
$179$		−	4.52514e6i		−	0.788993i	0.918897	−	0.394497i	$-0.129081\pi$
$180$	−872768.	+	199204.i	−0.149652	+	0.0341570i
$181$	−3.06282e6	+	3.84066e6i	−0.516519	+	0.647694i	−0.969866	−	0.243640i	$-0.921658\pi$
$181$	−3.06282e6	+	3.84066e6i	−0.516519	+	0.647694i	0.453347	+	0.891334i	$0.350230\pi$
$182$	−1.01474e6	+	4.44588e6i	−0.168322	+	0.737469i
$183$	−709756.	+	890005.i	−0.115813	+	0.145224i
$184$	−1.80432e6	+	3.74672e6i	−0.289642	+	0.601447i
$185$	2.45738e6	+	1.07665e7i	0.388113	+	1.70043i
$186$	1.32202e6	+	636650.i	0.205446	+	0.0989378i
$187$	4.92941e6	+	6.18129e6i	0.753825	+	0.945266i
$188$	149365.	−	654409.i	0.0224788	−	0.0984863i
$189$	1.20952e6	−	5.29924e6i	0.179154	−	0.784925i
$190$	−5.75619e6	−	1.19529e7i	−0.839217	−	1.74265i
$191$	3.33521e6	−	2.65974e6i	0.478655	−	0.381715i	−0.354232	−	0.935158i	$-0.615258\pi$
$191$	3.33521e6	−	2.65974e6i	0.478655	−	0.381715i	0.832887	+	0.553443i	$0.186686\pi$
$192$	1.16052e6	+	925487.i	0.163965	+	0.130758i
$193$	2.15299e6	−	1.03682e6i	0.299481	−	0.144222i	−0.278109	−	0.960550i	$-0.589708\pi$
$193$	2.15299e6	−	1.03682e6i	0.299481	−	0.144222i	0.577590	+	0.816327i	$0.303993\pi$
$194$	377427.	+	783736.i	0.0516926	+	0.107341i
$195$	−721436.	+	904652.i	−0.0972957	+	0.122005i
$196$	973367.	+	1.22056e6i	0.129273	+	0.162103i
$197$	−5.54184e6	+	2.66881e6i	−0.724862	+	0.349075i	−0.759661	−	0.650319i	$-0.774635\pi$
$197$	−5.54184e6	+	2.66881e6i	−0.724862	+	0.349075i	0.0347990	+	0.999394i	$0.488921\pi$
$198$	1.18241e7	+	2.69877e6i	1.52325	+	0.347672i
$199$	−6.65940e6	−	1.51996e6i	−0.845037	−	0.192874i	−0.221981	−	0.975051i	$-0.571252\pi$
$199$	−6.65940e6	−	1.51996e6i	−0.845037	−	0.192874i	−0.623056	+	0.782177i	$0.714109\pi$
$200$	−8.54261e6	+	6.81250e6i	−1.06783	+	0.851563i
$201$	−1.11235e6	+	2.30983e6i	−0.136979	+	0.284440i
$202$	1.31381e7	−	2.99869e6i	1.59396	−	0.363812i
$203$	8.61210e6	+	4.14737e6i	1.02949	+	0.495775i
$204$	126762.	+	101090.i	0.0149314	+	0.0119074i
$205$	−7.41430e6	−	1.69227e6i	−0.860614	−	0.196430i
$206$	5.01747e6	+	4.00130e6i	0.573962	+	0.457719i
$207$	−1.31922e6	−	5.77988e6i	−0.148733	−	0.651640i
$208$	4.09358e6			0.454897
$209$			1.69346e7i			1.85497i
$210$	1.40488e6	+	6.15517e6i	0.151698	+	0.664634i
$211$	−7.39213e6	+	5.89502e6i	−0.786904	+	0.627535i	−0.932237	−	0.361847i	$-0.882146\pi$
$211$	−7.39213e6	+	5.89502e6i	−0.786904	+	0.627535i	0.145333	+	0.989383i	$0.453575\pi$
$212$	445377.	−	214482.i	0.0467434	−	0.0225105i
$213$	−705990.	−	339987.i	−0.0730567	−	0.0351822i
$214$		−	9.17479e6i		−	0.936171i
$215$	1.54052e7	−	2.17856e6i	1.55007	−	0.219207i
$216$	−4.41503e6			−0.438099
$217$	−6.94901e6	+	1.44298e7i	−0.680054	+	1.41215i
$218$	−3.05358e6	−	6.34082e6i	−0.294741	−	0.612035i
$219$	879327.	+	1.10264e6i	0.0837178	+	0.104979i
$220$	−2.66681e6	+	608681.i	−0.250451	+	0.0571639i
$221$	−3.44234e6			−0.318917
$222$		−	3.06819e6i		−	0.280429i
$223$	8.51734e6	−	1.94403e6i	0.768050	−	0.175302i	0.179494	−	0.983759i	$-0.442554\pi$
$223$	8.51734e6	−	1.94403e6i	0.768050	−	0.175302i	0.588556	+	0.808457i	$0.299697\pi$
$224$	2.51239e6	−	3.15044e6i	0.223534	−	0.280303i
$225$	3.46620e6	−	1.51864e7i	0.304303	−	1.33324i
$226$	5.24170e6	−	6.57289e6i	0.454095	−	0.569417i
$227$	8.27225e6	−	1.71775e7i	0.707206	−	1.46853i	−0.168508	−	0.985700i	$-0.553895\pi$
$227$	8.27225e6	−	1.71775e7i	0.707206	−	1.46853i	0.875715	−	0.482829i	$-0.160391\pi$
$228$	77278.4	+	338579.i	0.00652009	+	0.0285664i
$229$	−1.20038e7	−	5.78074e6i	−0.999570	−	0.481367i	−0.138777	−	0.990324i	$-0.544317\pi$
$229$	−1.20038e7	−	5.78074e6i	−0.999570	−	0.481367i	−0.860792	+	0.508956i	$0.830032\pi$
$230$	8.84820e6	+	1.10953e7i	0.727229	+	0.911916i
$231$	1.79330e6	−	7.85695e6i	0.145484	−	0.637409i
$232$	1.72768e6	−	7.56945e6i	0.138356	−	0.606179i
$233$	1.34518e6	+	2.79330e6i	0.106344	+	0.220826i	0.947350	−	0.320200i	$-0.103750\pi$
$233$	1.34518e6	+	2.79330e6i	0.106344	+	0.220826i	−0.841006	+	0.541026i	$0.818036\pi$
$234$	−4.12854e6	+	3.29240e6i	−0.322217	+	0.256960i
$235$	1.54259e7	+	1.23017e7i	1.18863	+	0.947898i
$236$	−764255.	+	368046.i	−0.0581436	+	0.0280005i
$237$	2.04734e6	+	4.25135e6i	0.153796	+	0.319361i
$238$	−1.17107e7	+	1.46848e7i	−0.868665	+	1.08927i
$239$	−1.14008e6	−	1.42962e6i	−0.0835109	−	0.104719i	0.738321	−	0.674450i	$-0.235619\pi$
$239$	−1.14008e6	−	1.42962e6i	−0.0835109	−	0.104719i	−0.821832	+	0.569730i	$0.807048\pi$
$240$	5.10617e6	−	2.45900e6i	0.369370	−	0.177879i
$241$	1.43495e7	+	3.27517e6i	1.02514	+	0.233982i	0.701857	−	0.712318i	$-0.252355\pi$
$241$	1.43495e7	+	3.27517e6i	1.02514	+	0.233982i	0.323288	+	0.946301i	$0.395212\pi$
$242$	2.16113e7	+	4.93265e6i	1.52488	+	0.348044i
$243$	7.45417e6	−	5.94450e6i	0.519494	−	0.414283i
$244$	508384.	−	1.05567e6i	0.0349963	−	0.0726707i
$245$	−4.47382e7	+	1.02112e7i	−3.04215	+	0.694351i
$246$	1.90365e6	+	916750.i	0.127874	+	0.0615809i
$247$	−5.76471e6	−	4.59720e6i	−0.382548	−	0.305072i
$248$	1.26828e7	+	2.89476e6i	0.831495	+	0.189783i
$249$	−3.91279e6	−	3.12034e6i	−0.253448	−	0.202118i
$250$	2.57807e6	+	1.12953e7i	0.164996	+	0.722896i
$251$	−7.20623e6			−0.455708			−0.227854	−	0.973695i	$-0.573171\pi$
$251$	−7.20623e6			−0.455708			−0.227854	+	0.973695i	$0.573171\pi$
$252$			2.71474e6i			0.169639i
$253$	−4.03097e6	−	1.76609e7i	−0.248913	−	1.09056i
$254$	−1.65952e7	+	1.32342e7i	−1.01270	+	0.807600i
$255$	−4.29385e6	+	2.06781e6i	−0.258956	+	0.124707i
$256$	−4.66781e6	−	2.24790e6i	−0.278223	−	0.133985i
$257$		−	2.03575e7i		−	1.19930i	−0.800264	−	0.599648i	$-0.795307\pi$
$257$		−	2.03575e7i		−	1.19930i	0.800264	−	0.599648i	$-0.204693\pi$
$258$	−4.30741e6	−	362301.i	−0.250817	−	0.0210965i
$259$	3.34891e7			1.92754
$260$	516751.	−	1.07304e6i	0.0294009	−	0.0610516i
$261$	4.80254e6	+	9.97257e6i	0.270115	+	0.560900i
$262$	−1.54455e7	−	1.93681e7i	−0.858815	−	1.07692i
$263$	1.66693e7	−	3.80466e6i	0.916328	−	0.209146i	0.261746	−	0.965137i	$-0.415702\pi$
$263$	1.66693e7	−	3.80466e6i	0.916328	−	0.209146i	0.654582	+	0.755991i	$0.272845\pi$
$264$	−6.54597e6			−0.355764
$265$			1.45304e7i			0.780801i
$266$	−3.92226e7	+	8.95230e6i	−2.08397	+	0.475652i
$267$	−1.90960e6	+	2.39456e6i	−0.100325	+	0.125803i
$268$	587192.	−	2.57266e6i	0.0305053	−	0.133653i
$269$	2.18216e7	−	2.73634e7i	1.12106	−	1.40577i	0.218162	−	0.975913i	$-0.429994\pi$
$269$	2.18216e7	−	2.73634e7i	1.12106	−	1.40577i	0.902899	−	0.429853i	$-0.141435\pi$
$270$	−6.53720e6	+	1.35746e7i	−0.332124	+	0.689663i
$271$	−7.07984e6	−	3.10188e7i	−0.355726	−	1.55854i	−0.763717	−	0.645551i	$-0.776628\pi$
$271$	−7.07984e6	−	3.10188e7i	−0.355726	−	1.55854i	0.407991	−	0.912986i	$-0.366229\pi$
$272$	1.51908e7	+	7.31551e6i	0.754874	+	0.363528i
$273$	2.18776e6	+	2.74336e6i	0.107525	+	0.134833i
$274$	−5.44414e6	+	2.38523e7i	−0.264653	+	1.15952i
$275$	1.05912e7	−	4.64032e7i	0.509270	−	2.23126i
$276$	−161185.	−	334704.i	−0.00766649	−	0.0159196i
$277$	−2.22370e7	+	1.77334e7i	−1.04625	+	0.834357i	−0.986484	−	0.163855i	$-0.947607\pi$
$277$	−2.22370e7	+	1.77334e7i	−1.04625	+	0.834357i	−0.0597667	+	0.998212i	$0.519036\pi$
$278$	−1.90633e7	−	1.52025e7i	−0.887285	−	0.707586i
$279$	−1.67093e7	+	8.04676e6i	−0.769387	+	0.370517i
$280$	2.42860e7	+	5.04303e7i	1.10632	+	2.29730i
$281$	−1.29964e7	+	1.62969e7i	−0.585737	+	0.734491i	−0.983080	−	0.183179i	$-0.941361\pi$
$281$	−1.29964e7	+	1.62969e7i	−0.585737	+	0.734491i	0.397342	+	0.917670i	$0.369933\pi$
$282$	−3.41779e6	−	4.28577e6i	−0.152405	−	0.191109i
$283$	−4.83720e6	+	2.32947e6i	−0.213420	+	0.102777i	−0.537540	−	0.843239i	$-0.680646\pi$
$283$	−4.83720e6	+	2.32947e6i	−0.213420	+	0.102777i	0.324120	+	0.946016i	$0.394932\pi$
$284$	786323.	+	179473.i	0.0343278	+	0.00783509i
$285$	−9.95220e6	−	2.27152e6i	−0.429917	−	0.0981257i
$286$	−1.26151e7	+	1.00602e7i	−0.539251	+	0.430039i
$287$	−1.00063e7	+	2.07783e7i	−0.423279	+	0.878949i
$288$	4.54914e6	−	1.03831e6i	0.190437	−	0.0434660i
$289$	8.97303e6	+	4.32119e6i	0.371746	+	0.179023i
$290$	−2.07152e7	−	1.65198e7i	−0.849367	−	0.677348i
$291$	652555.	+	148941.i	0.0264812	+	0.00604417i
$292$	−1.13494e6	−	905086.i	−0.0455853	−	0.0363531i
$293$	2.07816e6	+	9.10500e6i	0.0826182	+	0.361974i	0.999290	−	0.0376661i	$-0.0119923\pi$
$293$	2.07816e6	+	9.10500e6i	0.0826182	+	0.361974i	−0.916672	+	0.399640i	$0.869135\pi$
$294$	1.27493e7			0.501700
$295$		−	2.49338e7i		−	0.971229i
$296$	−6.05295e6	−	2.65197e7i	−0.233395	−	1.02257i
$297$	1.50364e7	−	1.19912e7i	0.573952	−	0.457712i
$298$	−1.63680e7	+	7.88243e6i	−0.618512	+	0.297860i
$299$	7.10620e6	+	3.42217e6i	0.265842	+	0.128023i
$300$		−	976084.i		−	0.0361512i
$301$	3.95450e6	−	4.70152e7i	0.145008	−	1.72401i
$302$	4.85388e7			1.76225
$303$	4.49902e6	−	9.34231e6i	0.161730	−	0.335835i
$304$	1.56695e7	+	3.25380e7i	0.557742	+	1.15816i
$305$	2.14737e7	+	2.69272e7i	0.756847	+	0.949056i
$306$	−2.12043e7	+	4.83975e6i	−0.740048	+	0.168911i
$307$	−3.68390e7			−1.27319			−0.636594	−	0.771199i	$-0.719657\pi$
$307$	−3.68390e7			−1.27319			−0.636594	+	0.771199i	$0.719657\pi$
$308$			8.29509e6i			0.283902i
$309$	4.81425e6	−	1.09882e6i	0.163175	−	0.0372436i
$310$	2.76793e7	−	3.47088e7i	0.929118	−	1.16508i
$311$	3.44523e6	−	1.50946e7i	0.114535	−	0.501810i	−0.884821	−	0.465931i	$-0.845720\pi$
$311$	3.44523e6	−	1.50946e7i	0.114535	−	0.501810i	0.999356	−	0.0358793i	$-0.0114232\pi$
$312$	1.77702e6	−	2.22831e6i	0.0585097	−	0.0733689i
$313$	−1.85985e7	+	3.86201e7i	−0.606519	+	1.25945i	0.341095	+	0.940029i	$0.389202\pi$
$313$	−1.85985e7	+	3.86201e7i	−0.606519	+	1.25945i	−0.947613	+	0.319420i	$0.896512\pi$
$314$	−8.62365e6	−	3.77827e7i	−0.278549	−	1.22040i
$315$	−7.18948e7	−	3.46227e7i	−2.30020	−	1.10772i
$316$	−3.02821e6	−	3.79725e6i	−0.0959676	−	0.120340i
$317$	−2.70517e6	+	1.18521e7i	−0.0849213	+	0.372065i	−0.999475	−	0.0324000i	$-0.989685\pi$
$317$	−2.70517e6	+	1.18521e7i	−0.0849213	+	0.372065i	0.914554	+	0.404465i	$0.132542\pi$
$318$	898315.	−	3.93578e6i	0.0279349	−	0.122391i
$319$	1.46745e7	+	3.04719e7i	0.452055	+	0.938702i
$320$	3.51118e7	−	2.80007e7i	1.07153	−	0.854514i
$321$	−5.51943e6	−	4.40160e6i	−0.166870	−	0.133075i
$322$	3.87737e7	−	1.86724e7i	1.16137	−	0.559285i
$323$	−1.31767e7	−	2.73617e7i	−0.391019	−	0.811960i
$324$	−1.83341e6	+	2.29903e6i	−0.0539045	+	0.0675941i
$325$	1.29209e7	+	1.62023e7i	0.376394	+	0.471984i
$326$	−5.26831e7	+	2.53709e7i	−1.52061	+	0.732289i
$327$	−5.27950e6	−	1.20501e6i	−0.150991	−	0.0344626i
$328$	1.82627e7	+	4.16834e6i	0.517539	+	0.118125i
$329$	4.67790e7	−	3.73050e7i	1.31360	−	1.04756i
$330$	−9.69241e6	+	2.01265e7i	−0.269706	+	0.560050i
$331$	−3.38127e7	+	7.71753e6i	−0.932387	+	0.212811i	−0.661625	−	0.749835i	$-0.730133\pi$
$331$	−3.38127e7	+	7.71753e6i	−0.932387	+	0.212811i	−0.270762	+	0.962646i	$0.587276\pi$
$332$	4.64111e6	+	2.23504e6i	0.126826	+	0.0610761i
$333$	3.03190e7	+	2.41786e7i	0.821074	+	0.654785i
$334$	3.25139e7	+	7.42110e6i	0.872630	+	0.199172i
$335$	6.06431e7	+	4.83613e7i	1.61305	+	1.28636i
$336$	−3.82435e6	−	1.67556e7i	−0.100818	−	0.441715i
$337$	4.36719e7			1.14107			0.570536	−	0.821273i	$-0.306736\pi$
$337$	4.36719e7			1.14107			0.570536	+	0.821273i	$0.306736\pi$
$338$			3.35479e7i			0.868790i
$339$	−1.43946e6	−	6.30667e6i	−0.0369487	−	0.161883i
$340$	3.83521e6	−	3.05848e6i	0.0975781	−	0.0778160i
$341$	−5.10564e7	+	2.45874e7i	−1.28762	+	0.620084i
$342$	−4.19731e7	−	2.02132e7i	−1.04928	−	0.505309i
$343$			6.93425e7i			1.71837i
$344$	−3.79456e7	+	5.36617e6i	−0.932152	+	0.131822i
$345$	1.09197e7			0.265921
$346$	2.38005e7	−	4.94223e7i	0.574591	−	1.19315i
$347$	9.69209e6	+	2.01258e7i	0.231968	+	0.481687i	0.984166	−	0.177251i	$-0.0567203\pi$
$347$	9.69209e6	+	2.01258e7i	0.231968	+	0.481687i	−0.752197	+	0.658938i	$0.771006\pi$
$348$	432445.	+	542269.i	0.0102611	+	0.0128670i
$349$	4.98057e7	−	1.13678e7i	1.17166	−	0.267425i	0.407965	−	0.912998i	$-0.366239\pi$
$349$	4.98057e7	−	1.13678e7i	1.17166	−	0.267425i	0.763698	+	0.645573i	$0.223381\pi$
$350$	1.13074e8			2.63730
$351$			8.37376e6i			0.193642i
$352$	1.39002e7	−	3.17264e6i	0.318709	−	0.0727432i
$353$	−2.81633e7	+	3.53156e7i	−0.640264	+	0.802866i	−0.991036	−	0.133595i	$-0.957348\pi$
$353$	−2.81633e7	+	3.53156e7i	−0.640264	+	0.802866i	0.350772	+	0.936461i	$0.385919\pi$
$354$	−1.54148e6	+	6.75367e6i	−0.0347479	+	0.152241i
$355$	−1.47814e7	+	1.85354e7i	−0.330394	+	0.414301i
$356$	1.36781e6	−	2.84029e6i	0.0303163	−	0.0629524i
$357$	3.21595e6	+	1.40900e7i	0.0706813	+	0.309675i
$358$	3.42705e7	+	1.65038e7i	0.746916	+	0.359696i
$359$	−3.52207e7	−	4.41654e7i	−0.761228	−	0.954550i	0.238635	−	0.971109i	$-0.423300\pi$
$359$	−3.52207e7	−	4.41654e7i	−0.761228	−	0.954550i	−0.999863	+	0.0165594i	$0.994729\pi$
$360$	−1.44228e7	+	6.31906e7i	−0.309132	+	1.35439i
$361$	4.00613e6	−	1.75520e7i	0.0851536	−	0.373082i
$362$	−1.79161e7	−	3.72032e7i	−0.377675	−	0.784251i
$363$	1.33354e7	−	1.06346e7i	0.278796	−	0.222333i
$364$	−2.82373e6	−	2.25185e6i	−0.0585488	−	0.0466911i
$365$	3.84441e7	−	1.85137e7i	0.790589	−	0.380728i
$366$	−4.15175e6	−	8.62120e6i	−0.0846815	−	0.175843i
$367$	−5.50204e6	+	6.89934e6i	−0.111308	+	0.139576i	−0.834364	−	0.551213i	$-0.814165\pi$
$367$	−5.50204e6	+	6.89934e6i	−0.111308	+	0.139576i	0.723057	+	0.690789i	$0.242737\pi$
$368$	−2.40865e7	−	3.02035e7i	−0.483315	−	0.606058i
$369$	−2.40606e7	+	1.15870e7i	−0.478882	+	0.230617i
$370$	−9.05010e7	−	2.06563e7i	−1.78669	−	0.407799i
$371$	4.29588e7	+	9.80506e6i	0.841260	+	0.192012i
$372$	−908583.	+	724571.i	−0.0176496	+	0.0140751i
$373$	−3.64787e7	+	7.57489e7i	−0.702932	+	1.45965i	0.176831	+	0.984241i	$0.443415\pi$
$373$	−3.64787e7	+	7.57489e7i	−0.702932	+	1.45965i	−0.879763	+	0.475412i	$0.842299\pi$
$374$	−6.47914e7	+	1.47882e7i	−1.23852	+	0.282684i
$375$	8.03189e6	+	3.86796e6i	0.152308	+	0.0733479i
$376$	−3.79965e7	−	3.03012e7i	−0.714792	−	0.570028i
$377$	−1.43566e7	−	3.27680e6i	−0.267934	−	0.0611541i
$378$	3.57218e7	+	2.84872e7i	0.661390	+	0.527441i
$379$	−3.38696e6	−	1.48392e7i	−0.0622146	−	0.272580i	0.934247	−	0.356626i	$-0.116073\pi$
$379$	−3.38696e6	−	1.48392e7i	−0.0622146	−	0.272580i	−0.996462	+	0.0840458i	$0.973216\pi$
$380$	1.05072e7			0.191485
$381$			1.63325e7i			0.295310i
$382$	7.97920e6	+	3.49592e7i	0.143143	+	0.627149i
$383$	5.34629e7	−	4.26352e7i	0.951604	−	0.758879i	−0.0189359	−	0.999821i	$-0.506028\pi$
$383$	5.34629e7	−	4.26352e7i	0.951604	−	0.758879i	0.970539	+	0.240942i	$0.0774564\pi$
$384$	−1.37741e7	+	6.63327e6i	−0.243260	+	0.117148i
$385$	−2.19680e8	−	1.05792e8i	−3.84953	−	1.85384i
$386$			2.00868e7i			0.349259i
$387$	3.75244e7	−	3.97096e7i	0.647412	−	0.685114i
$388$	−688944.			−0.0117947
$389$	−3.49048e7	+	7.24805e7i	−0.592974	+	1.23132i	0.361317	+	0.932443i	$0.382327\pi$
$389$	−3.49048e7	+	7.24805e7i	−0.592974	+	1.23132i	−0.954291	+	0.298880i	$0.903387\pi$
$390$	−4.22008e6	−	8.76308e6i	−0.0711421	−	0.147728i
$391$	2.02547e7	+	2.53986e7i	0.338840	+	0.424892i
$392$	1.10198e8	−	2.51519e7i	1.82943	−	0.417555i
$393$	−1.90616e7			−0.314037
$394$		−	5.17039e7i		−	0.845346i
$395$	1.39184e8	−	3.17678e7i	2.25838	−	0.515461i
$396$	−5.98892e6	+	7.50986e6i	−0.0964412	+	0.120933i
$397$	8.68489e6	−	3.80510e7i	0.138801	−	0.608127i	−0.856898	−	0.515485i	$-0.827612\pi$
$397$	8.68489e6	−	3.80510e7i	0.138801	−	0.608127i	0.995699	−	0.0926419i	$-0.0295312\pi$
$398$	3.57990e7	−	4.48905e7i	0.567834	−	0.712041i
$399$	−1.34314e7	+	2.78906e7i	−0.211448	+	0.439076i
$400$	−2.25867e7	−	9.89586e7i	−0.352916	−	1.54623i
$401$	−6.39971e7	−	3.08194e7i	−0.992492	−	0.477959i	−0.134108	−	0.990967i	$-0.542817\pi$
$401$	−6.39971e7	−	3.08194e7i	−0.992492	−	0.477959i	−0.858384	+	0.513008i	$0.828531\pi$
$402$	−1.34362e7	−	1.68485e7i	−0.206823	−	0.259348i
$403$	5.49034e6	−	2.40548e7i	0.0838850	−	0.367524i
$404$	−2.37495e6	+	1.04053e7i	−0.0360173	+	0.157802i
$405$	−3.75028e7	−	7.78753e7i	−0.564545	−	1.17229i
$406$	−6.28190e7	+	5.00965e7i	−0.938671	+	0.748565i
$407$	9.26419e7	+	7.38795e7i	1.37412	+	1.09582i
$408$	1.05765e7	−	5.09336e6i	0.155726	−	0.0749935i
$409$	2.63135e7	+	5.46405e7i	0.384599	+	0.798628i	0.999946	+	0.0103720i	$0.00330158\pi$
$409$	2.63135e7	+	5.46405e7i	0.384599	+	0.798628i	−0.615347	+	0.788256i	$0.710984\pi$
$410$	3.98571e7	−	4.99792e7i	0.578301	−	0.725167i
$411$	1.17374e7	+	1.47182e7i	0.169062	+	0.211997i
$412$	−4.57936e6	+	2.20531e6i	−0.0654807	+	0.0315339i
$413$	−7.37160e7	−	1.68252e7i	−1.04643	−	0.238842i
$414$	4.85845e7	+	1.10891e7i	0.684694	+	0.156277i
$415$	−1.18382e8	+	9.44063e7i	−1.65631	+	1.32086i
$416$	−2.69346e6	+	5.59303e6i	−0.0374137	+	0.0776904i
$417$	−1.82912e7	+	4.17484e6i	−0.252251	+	0.0575747i
$418$	−1.28252e8	−	6.17629e7i	−1.75604	−	0.845666i
$419$	−6.31198e7	−	5.03364e7i	−0.858072	−	0.684289i	0.0921901	−	0.995741i	$-0.470613\pi$
$419$	−6.31198e7	−	5.03364e7i	−0.858072	−	0.684289i	−0.950262	+	0.311452i	$0.899185\pi$
$420$	−4.87488e6	−	1.11266e6i	−0.0657986	−	0.0150181i
$421$	2.95213e7	+	2.35424e7i	0.395630	+	0.315504i	0.801018	−	0.598640i	$-0.204292\pi$
$421$	2.95213e7	+	2.35424e7i	0.395630	+	0.315504i	−0.405388	+	0.914145i	$0.632864\pi$
$422$	−1.76850e7	−	7.74832e7i	−0.235325	−	1.03103i
$423$	6.92845e7			0.915408
$424$		−	3.57909e7i		−	0.469542i
$425$	1.89934e7	+	8.32156e7i	0.247421	+	1.08402i
$426$	5.14969e6	−	4.10674e6i	0.0666119	−	0.0531212i
$427$	9.41000e7	−	4.53162e7i	1.20867	−	0.582063i
$428$	6.54681e6	+	3.15278e6i	0.0835024	+	0.0402126i
$429$			1.24154e7i			0.157249i
$430$	−3.96859e7	+	1.24615e8i	−0.499149	+	1.56734i
$431$	7.61272e6			0.0950842			0.0475421	−	0.998869i	$-0.484861\pi$
$431$	7.61272e6			0.0950842			0.0475421	+	0.998869i	$0.484861\pi$
$432$	1.77955e7	−	3.69528e7i	0.220729	−	0.458349i
$433$	−4.36209e6	−	9.05796e6i	−0.0537317	−	0.111575i	0.872374	−	0.488839i	$-0.162579\pi$
$433$	−4.36209e6	−	9.05796e6i	−0.0537317	−	0.111575i	−0.926106	+	0.377264i	$0.876865\pi$
$434$	−8.39378e7	−	1.05255e8i	−1.02681	−	1.28757i
$435$	−1.98762e7	+	4.53661e6i	−0.241471	+	0.0551143i
$436$	5.57391e6			0.0672513
$437$			6.95834e7i			0.833799i
$438$	−1.15577e7	+	2.63797e6i	−0.137547	+	0.0313941i
$439$	3.79944e7	−	4.76435e7i	0.449083	−	0.563132i	−0.504829	−	0.863219i	$-0.668444\pi$
$439$	3.79944e7	−	4.76435e7i	0.449083	−	0.563132i	0.953912	+	0.300087i	$0.0970158\pi$
$440$	−4.40701e7	+	1.93084e8i	−0.517351	+	2.26666i
$441$	−1.00470e8	+	1.25985e8i	−1.17144	+	1.46894i
$442$	1.25547e7	−	2.60701e7i	0.145392	−	0.301909i
$443$	−3.25386e7	−	1.42561e8i	−0.374272	−	1.63979i	−0.714633	−	0.699500i	$-0.753406\pi$
$443$	−3.25386e7	−	1.42561e8i	−0.374272	−	1.63979i	0.340360	−	0.940295i	$-0.389451\pi$
$444$	2.18935e6	+	1.05434e6i	0.0250131	+	0.0120457i
$445$	5.77752e7	+	7.24478e7i	0.655634	+	0.822139i
$446$	−1.63411e7	+	7.15950e7i	−0.184194	+	0.807009i
$447$	−3.11059e6	+	1.36284e7i	−0.0348273	+	0.152588i
$448$	−5.90901e7	−	1.22702e8i	−0.657175	−	1.36464i
$449$	7.24780e7	−	5.77993e7i	0.800695	−	0.638533i	−0.135197	−	0.990819i	$-0.543167\pi$
$449$	7.24780e7	−	5.77993e7i	0.800695	−	0.638533i	0.935893	+	0.352286i	$0.114595\pi$
$450$	1.02370e8	+	8.16377e7i	1.12341	+	0.895887i
$451$	−7.35191e7	+	3.54049e7i	−0.801439	+	0.385952i
$452$	2.88895e6	+	5.99897e6i	0.0312842	+	0.0649623i
$453$	2.32864e7	−	2.92003e7i	0.250500	−	0.314118i
$454$	9.99214e7	+	1.25297e8i	1.06780	+	1.33898i
$455$	9.56486e7	−	4.60619e7i	1.01542	−	0.488999i
$456$	2.45139e7	+	5.59515e6i	0.258535	+	0.0590088i
$457$	9.74104e7	+	2.22333e7i	1.02060	+	0.232946i	0.699905	−	0.714236i	$-0.253226\pi$
$457$	9.74104e7	+	2.22333e7i	1.02060	+	0.232946i	0.320697	+	0.947182i	$0.396083\pi$
$458$	8.75592e7	−	6.98261e7i	0.911392	−	0.726811i
$459$	−1.49645e7	+	3.10741e7i	−0.154748	+	0.321337i
$460$	−1.09578e7	+	2.50104e6i	−0.112577	+	0.0256949i
$461$	6.00153e7	+	2.89018e7i	0.612575	+	0.295000i	0.714330	−	0.699809i	$-0.246732\pi$
$461$	6.00153e7	+	2.89018e7i	0.612575	+	0.295000i	−0.101755	+	0.994809i	$0.532446\pi$
$462$	5.29631e7	+	4.22367e7i	0.537090	+	0.428315i
$463$	−2.38766e7	−	5.44967e6i	−0.240563	−	0.0549069i	0.100539	−	0.994933i	$-0.467943\pi$
$463$	−2.38766e7	−	5.44967e6i	−0.240563	−	0.0549069i	−0.341102	+	0.940026i	$0.610800\pi$
$464$	5.63909e7	+	4.49702e7i	0.564488	+	0.450164i
$465$	−7.60119e6	−	3.33030e7i	−0.0756002	−	0.331226i
$466$	−2.60607e7			−0.257531
$467$			1.36788e8i			1.34307i	0.740972	+	0.671535i	$0.234365\pi$
$467$			1.36788e8i			1.34307i	−0.740972	+	0.671535i	$0.765635\pi$
$468$	−930633.	−	4.07737e6i	−0.00907906	−	0.0397779i
$469$	1.83901e8	−	1.46656e8i	1.78264	−	1.42161i
$470$	−1.49425e8	+	7.19595e7i	−1.43923	+	0.693098i
$471$	−2.68667e7	−	1.29383e7i	−0.257129	−	0.123827i
$472$			6.14161e7i			0.584058i
$473$	1.14658e8	−	1.21336e8i	1.08348	−	1.14658i
$474$	−3.96639e7			−0.372444
$475$	−7.93260e7	+	1.64722e8i	−0.740175	+	1.53699i
$476$	−6.45433e6	−	1.34026e7i	−0.0598453	−	0.124270i
$477$	3.18132e7	+	3.98925e7i	0.293124	+	0.367566i
$478$	1.49851e7	−	3.42025e6i	0.137207	−	0.0313165i
$479$	−1.43188e7			−0.130287			−0.0651434	−	0.997876i	$-0.520750\pi$
$479$	−1.43188e7			−0.130287			−0.0651434	+	0.997876i	$0.520750\pi$
$480$			8.59449e6i			0.0777135i
$481$	−5.02985e7	+	1.14803e7i	−0.451981	+	0.103162i
$482$	−7.71386e7	+	9.67287e7i	−0.688859	+	0.863802i
$483$	7.36856e6	−	3.22838e7i	0.0653945	−	0.286512i
$484$	−1.09462e7	+	1.37261e7i	−0.0965442	+	0.121063i
$485$	8.78651e6	−	1.82454e7i	0.0770178	−	0.159929i
$486$	1.78335e7	+	7.81335e7i	0.155356	+	0.680657i
$487$	5.91680e7	+	2.84938e7i	0.512271	+	0.246697i	0.672117	−	0.740445i	$-0.265385\pi$
$487$	5.91680e7	+	2.84938e7i	0.512271	+	0.246697i	−0.159846	+	0.987142i	$0.551100\pi$
$488$	−5.28934e7	−	6.63263e7i	−0.455137	−	0.570724i
$489$	−1.00119e7	+	4.38651e7i	−0.0856230	+	0.375139i
$490$	8.58333e7	−	3.76060e8i	0.729571	−	3.19646i
$491$	−1.54312e7	−	3.20433e7i	−0.130363	−	0.270703i	0.825562	−	0.564311i	$-0.190858\pi$
$491$	−1.54312e7	−	3.20433e7i	−0.130363	−	0.270703i	−0.955926	+	0.293608i	$0.905144\pi$
$492$	−1.30832e6	+	1.04335e6i	−0.0109855	+	0.00876064i
$493$	−4.74199e7	−	3.78161e7i	−0.395749	−	0.315599i
$494$	5.58409e7	−	2.68916e7i	0.463203	−	0.223067i
$495$	−1.22504e8	−	2.54383e8i	−1.01003	−	2.09736i
$496$	−7.53486e7	+	9.44841e7i	−0.617490	+	0.774308i
$497$	4.48248e7	+	5.62086e7i	0.365132	+	0.457861i
$498$	3.79020e7	−	1.82526e7i	0.306884	−	0.147787i
$499$	9.41371e7	+	2.14862e7i	0.757634	+	0.172925i	0.583853	−	0.811859i	$-0.301544\pi$
$499$	9.41371e7	+	2.14862e7i	0.757634	+	0.172925i	0.173781	+	0.984784i	$0.444402\pi$
$500$	−8.94582e6	−	2.04182e6i	−0.0715665	−	0.0163346i
$501$	2.00630e7	−	1.59997e7i	0.159544	−	0.127232i
$502$	2.62821e7	−	5.45753e7i	0.207754	−	0.431405i
$503$	−9.03110e7	+	2.06129e7i	−0.709638	+	0.161970i	−0.562080	−	0.827083i	$-0.689999\pi$
$503$	−9.03110e7	+	2.06129e7i	−0.709638	+	0.161970i	−0.147558	+	0.989053i	$0.547141\pi$
$504$	1.77089e8	+	8.52816e7i	1.38325	+	0.666137i
$505$	−2.45277e8	−	1.95602e8i	−1.90451	−	1.51879i
$506$	1.48453e8	+	3.38835e7i	1.14588	+	0.261539i
$507$	2.01819e7	+	1.60945e7i	0.154860	+	0.123497i
$508$	−3.74079e6	−	1.63895e7i	−0.0285346	−	0.125018i
$509$	6.33147e7			0.480122			0.240061	−	0.970758i	$-0.422833\pi$
$509$	6.33147e7			0.480122			0.240061	+	0.970758i	$0.422833\pi$
$510$		−	4.00604e7i		−	0.301999i
$511$	−2.87934e7	−	1.26152e8i	−0.215789	−	0.945434i
$512$	−8.42243e7	+	6.71667e7i	−0.627520	+	0.500431i
$513$	−6.65593e7	+	3.20532e7i	−0.493011	+	0.237421i
$514$	1.54175e8	+	7.42468e7i	1.13534	+	0.546749i
$515$		−	1.49401e8i		−	1.09379i
$516$	1.73870e6	−	2.94912e6i	0.0126554	−	0.0214656i
$517$	2.11704e8			1.53199
$518$	−1.22139e8	+	2.53625e8i	−0.878753	+	1.82475i
$519$	−1.83135e7	−	3.80284e7i	−0.130999	−	0.272023i
$520$	−5.37639e7	−	6.74178e7i	−0.382367	−	0.479473i
$521$	−2.15711e8	+	4.92346e7i	−1.52531	+	0.348143i	−0.901273	−	0.433251i	$-0.857366\pi$
$521$	−2.15711e8	+	4.92346e7i	−1.52531	+	0.348143i	−0.624039	+	0.781393i	$0.714509\pi$
$522$	−9.30414e7			−0.654131
$523$			8.00246e6i			0.0559395i	0.999609	+	0.0279697i	$0.00890420\pi$
$523$			8.00246e6i			0.0559395i	−0.999609	+	0.0279697i	$0.991096\pi$
$524$	1.91280e7	−	4.36585e6i	0.132946	−	0.0303441i
$525$	5.42472e7	−	6.80239e7i	0.374886	−	0.470092i
$526$	−3.19812e7	+	1.40119e8i	−0.219755	+	0.962808i
$527$	6.33616e7	−	7.94530e7i	0.432907	−	0.542848i
$528$	2.63846e7	−	5.47883e7i	0.179246	−	0.372208i
$529$	1.63780e7	+	7.17569e7i	0.110636	+	0.484726i
$530$	−1.10044e8	−	5.29944e7i	−0.739160	−	0.355961i
$531$	−5.45905e7	−	6.84543e7i	−0.364614	−	0.457211i
$532$	7.09020e6	−	3.10642e7i	0.0470894	−	0.206312i
$533$	7.90587e6	−	3.46379e7i	0.0522117	−	0.228754i
$534$	−1.11703e7	−	2.31954e7i	−0.0733570	−	0.152327i
$535$	−1.66991e8	+	1.33171e8i	−1.09051	+	0.869656i
$536$	−1.49374e8	−	1.19122e8i	−0.970022	−	0.773567i
$537$	2.63697e7	−	1.26990e7i	0.170287	−	0.0820061i
$538$	1.27646e8	+	2.65061e8i	0.819713	+	1.70215i
$539$	−3.06993e8	+	3.84957e8i	−1.96048	+	2.45836i
$540$	−7.43998e6	−	9.32944e6i	−0.0472487	−	0.0592481i
$541$	1.17600e8	−	5.66331e7i	0.742702	−	0.357667i	−0.0239635	−	0.999713i	$-0.507629\pi$
$541$	1.17600e8	−	5.66331e7i	0.742702	−	0.357667i	0.766666	+	0.642046i	$0.221914\pi$
$542$	2.60738e8	+	5.95117e7i	1.63759	+	0.373770i
$543$	−3.09762e7	−	7.07011e6i	−0.193477	−	0.0441598i
$544$	−1.99903e7	+	1.59417e7i	−0.124172	+	0.0990236i
$545$	−7.10874e7	+	1.47614e8i	−0.439140	+	0.911884i
$546$	−2.87555e7	+	6.56326e6i	−0.176662	+	0.0403220i
$547$	−1.08232e8	−	5.21219e7i	−0.661294	−	0.318462i	0.0729625	−	0.997335i	$-0.476755\pi$
$547$	−1.08232e8	−	5.21219e7i	−0.661294	−	0.318462i	−0.734256	+	0.678872i	$0.762469\pi$
$548$	−1.51494e7	−	1.20812e7i	−0.0920563	−	0.0734125i
$549$	1.17910e8	+	2.69122e7i	0.712580	+	0.162642i
$550$	3.12800e8	+	2.49450e8i	1.88009	+	1.49932i
$551$	−2.89086e7	−	1.26657e8i	−0.172812	−	0.757137i
$552$	−2.68970e7			−0.159914
$553$		−	4.32930e8i		−	2.56001i
$554$	−5.32000e7	−	2.33084e8i	−0.312883	−	1.37083i
$555$	−5.58443e7	+	4.45343e7i	−0.326663	+	0.260505i
$556$	1.73988e7	−	8.37880e6i	0.101226	−	0.0487481i
$557$	2.39300e8	+	1.15241e8i	1.38477	+	0.666870i	0.970011	−	0.243062i	$-0.0781519\pi$
$557$	2.39300e8	+	1.15241e8i	1.38477	+	0.666870i	0.414758	+	0.909932i	$0.363866\pi$
$558$		−	1.55893e8i		−	0.897271i
$559$	1.01777e7	+	7.19695e7i	0.0582661	+	0.412015i
$560$	−5.19979e8			−2.96089
$561$	−2.21872e7	+	4.60722e7i	−0.125665	+	0.260946i
$562$	−7.60229e7	−	1.57863e8i	−0.428288	−	0.889348i
$563$	8.39775e7	+	1.05304e8i	0.470585	+	0.590095i	0.959314	−	0.282341i	$-0.0911109\pi$
$563$	8.39775e7	+	1.05304e8i	0.470585	+	0.590095i	−0.488729	+	0.872435i	$0.662539\pi$
$564$	4.23265e6	−	966075.i	0.0235926	−	0.00538485i
$565$	−1.95716e8			−1.08513
$566$		−	4.51297e7i		−	0.248893i
$567$	−2.55543e8	+	5.83261e7i	−1.40189	+	0.319973i
$568$	3.64092e7	−	4.56557e7i	0.198686	−	0.249144i
$569$	3.81772e7	−	1.67265e8i	0.207237	−	0.907965i	−0.759158	−	0.650906i	$-0.774389\pi$
$569$	3.81772e7	−	1.67265e8i	0.207237	−	0.907965i	0.966396	−	0.257060i	$-0.0827536\pi$
$570$	5.35001e7	−	6.70870e7i	0.288888	−	0.362254i
$571$	−1.04989e8	+	2.18012e8i	−0.563944	+	1.17104i	0.402798	+	0.915289i	$0.368038\pi$
$571$	−1.04989e8	+	2.18012e8i	−0.563944	+	1.17104i	−0.966742	+	0.255753i	$0.917676\pi$
$572$	−2.84362e6	−	1.24587e7i	−0.0151944	−	0.0665709i
$573$	2.48590e7	+	1.19714e7i	0.132135	+	0.0636330i
$574$	−1.20867e8	−	1.51562e8i	−0.639104	−	0.801412i
$575$	4.35188e7	−	1.90668e8i	0.228914	−	1.00294i
$576$	3.50922e7	−	1.53749e8i	0.183630	−	0.804535i
$577$	−2.87504e7	−	5.97009e7i	−0.149664	−	0.310780i	0.812636	−	0.582772i	$-0.198032\pi$
$577$	−2.87504e7	−	5.97009e7i	−0.149664	−	0.310780i	−0.962300	+	0.271992i	$0.912318\pi$
$578$	−6.54518e7	+	5.21960e7i	−0.338952	+	0.270305i
$579$	1.20839e7	+	9.63660e6i	0.0622547	+	0.0496465i
$580$	1.89065e7	−	9.10487e6i	0.0969005	−	0.0466648i
$581$	1.99226e8	+	4.13698e8i	1.01582	+	2.10938i
$582$	−3.50794e6	+	4.39882e6i	−0.0177944	+	0.0223135i
$583$	9.72075e7	+	1.21894e8i	0.490562	+	0.615145i
$584$	−9.46943e7	+	4.56024e7i	−0.475428	+	0.228954i
$585$	1.19850e8	+	2.73551e7i	0.598648	+	0.136638i
$586$	−7.65348e7	−	1.74686e7i	−0.380335	−	0.0868089i
$587$	−1.10519e8	+	8.81356e7i	−0.546413	+	0.435750i	−0.857390	−	0.514668i	$-0.827915\pi$
$587$	−1.10519e8	+	8.81356e7i	−0.546413	+	0.435750i	0.310977	+	0.950417i	$0.399344\pi$
$588$	−4.38111e6	+	9.09746e6i	−0.0215502	+	0.0447495i
$589$	2.12217e8	−	4.84370e7i	1.03856	−	0.237046i
$590$	1.88832e8	+	9.09368e7i	0.919433	+	0.442776i
$591$	−3.11043e7	−	2.48049e7i	−0.150681	−	0.120164i
$592$	2.46361e8	+	5.62304e7i	1.18743	+	0.271023i
$593$	−1.52164e8	−	1.21346e8i	−0.729704	−	0.581919i	0.186584	−	0.982439i	$-0.440258\pi$
$593$	−1.52164e8	−	1.21346e8i	−0.729704	−	0.581919i	−0.916288	+	0.400520i	$0.868830\pi$
$594$	3.59734e7	+	1.57610e8i	0.171641	+	0.752010i
$595$	4.37257e8			2.07580
$596$		−	1.43883e7i		−	0.0679629i
$597$	−9.83097e6	−	4.30723e7i	−0.0462034	−	0.202430i
$598$	−5.18346e7	+	4.13367e7i	−0.242391	+	0.193300i
$599$	−8.66757e7	+	4.17408e7i	−0.403290	+	0.194214i	−0.624522	−	0.781007i	$-0.714706\pi$
$599$	−8.66757e7	+	4.17408e7i	−0.403290	+	0.194214i	0.221233	+	0.975221i	$0.428992\pi$
$600$	−6.36723e7	−	3.06630e7i	−0.294779	−	0.141958i
$601$		−	9.50294e7i		−	0.437759i	−0.975752	−	0.218879i	$-0.929760\pi$
$601$		−	9.50294e7i		−	0.437759i	0.975752	−	0.218879i	$-0.0702401\pi$
$602$	3.41640e8	+	2.01420e8i	1.56596	+	0.923236i
$603$	2.72376e8			1.24227
$604$	−1.66796e7	+	3.46356e7i	−0.0756965	+	0.157185i
$605$	−2.23906e8	−	4.64946e8i	−1.01111	−	2.09960i
$606$	5.43441e7	+	6.81454e7i	0.244194	+	0.306209i
$607$	−2.42123e8	+	5.52630e7i	−1.08260	+	0.247097i	−0.726373	−	0.687300i	$-0.758796\pi$
$607$	−2.42123e8	+	5.52630e7i	−1.08260	+	0.247097i	−0.356231	+	0.934398i	$0.615939\pi$
$608$	−5.47666e7			−0.243672
$609$			6.18248e7i			0.273723i
$610$	−2.82247e8	+	6.44210e7i	−1.24348	+	0.283817i
$611$	−5.74707e7	+	7.20659e7i	−0.251955	+	0.315941i
$612$	3.83307e6	−	1.67938e7i	0.0167222	−	0.0732646i
$613$	−6.64195e6	+	8.32875e6i	−0.0288346	+	0.0361575i	−0.796040	−	0.605244i	$-0.793075\pi$
$613$	−6.64195e6	+	8.32875e6i	−0.0288346	+	0.0361575i	0.767205	+	0.641402i	$0.221647\pi$
$614$	1.34357e8	−	2.78995e8i	0.580436	−	1.20529i
$615$	−1.09454e7	−	4.79550e7i	−0.0470551	−	0.206162i
$616$	5.41108e8	+	2.60584e8i	2.31495	+	1.11482i
$617$	−1.88301e8	−	2.36121e8i	−0.801671	−	1.00526i	−0.999686	−	0.0250646i	$-0.992021\pi$
$617$	−1.88301e8	−	2.36121e8i	−0.801671	−	1.00526i	0.198015	−	0.980199i	$-0.436551\pi$
$618$	−9.23646e6	+	4.04676e7i	−0.0391327	+	0.171452i
$619$	−7.61331e6	+	3.33561e7i	−0.0320997	+	0.140638i	−0.988439	−	0.151622i	$-0.951550\pi$
$619$	−7.61331e6	+	3.33561e7i	−0.0320997	+	0.140638i	0.956339	+	0.292260i	$0.0944074\pi$
$620$	1.52554e7	+	3.16782e7i	0.0640101	+	0.132918i
$621$	6.17839e7	−	4.92710e7i	0.257989	−	0.205739i
$622$	1.01751e8	+	8.11439e7i	0.422833	+	0.337198i
$623$	2.53177e8	−	1.21923e8i	1.04703	−	0.504223i
$624$	1.14879e7	+	2.38548e7i	0.0472809	+	0.0981798i
$625$	−5.26710e7	+	6.60474e7i	−0.215741	+	0.270530i
$626$	−2.24653e8	−	2.81706e8i	−0.915775	−	1.14835i
$627$	−9.86844e7	+	4.75239e7i	−0.400356	+	0.192801i
$628$	2.99238e7	+	6.82991e6i	0.120820	+	0.0275763i
$629$	−2.07169e8	−	4.72849e7i	−0.832477	−	0.190007i
$630$	5.24420e8	−	4.18211e8i	2.09729	−	1.67253i
$631$	1.18109e7	−	2.45255e7i	0.0470104	−	0.0976180i	−0.876141	−	0.482056i	$-0.839890\pi$
$631$	1.18109e7	−	2.45255e7i	0.0470104	−	0.0976180i	0.923151	+	0.384438i	$0.125605\pi$
$632$	−3.42833e8	+	7.82494e7i	−1.35810	+	0.309977i
$633$	−5.50972e7	−	2.65334e7i	−0.217229	−	0.104612i
$634$	−7.98942e7	−	6.37135e7i	−0.313507	−	0.250014i
$635$	4.81752e8	+	1.09957e8i	1.88149	+	0.429439i
$636$	2.49974e6	+	1.99348e6i	0.00971681	+	0.00774889i
$637$	−4.77044e7	−	2.09007e8i	−0.184561	−	0.808614i
$638$	−2.84295e8			−1.09473
$639$			8.32506e7i			0.319069i
$640$	1.02926e8	+	4.50947e8i	0.392631	+	1.72023i
$641$	−1.73764e8	+	1.38572e8i	−0.659759	+	0.526140i	−0.895153	−	0.445760i	$-0.852934\pi$
$641$	−1.73764e8	+	1.38572e8i	−0.659759	+	0.526140i	0.235394	+	0.971900i	$0.424362\pi$
$642$	5.34650e7	−	2.57474e7i	0.202053	−	0.0973034i
$643$	−9.42643e7	−	4.53953e7i	−0.354580	−	0.170757i	0.248110	−	0.968732i	$-0.420190\pi$
$643$	−9.42643e7	−	4.53953e7i	−0.354580	−	0.170757i	−0.602691	+	0.797975i	$0.705905\pi$
$644$			3.40840e7i			0.127613i
$645$	5.59272e7	+	8.36582e7i	0.208422	+	0.311766i
$646$	2.55277e8			0.946921
$647$	1.76705e7	−	3.66933e7i	0.0652435	−	0.135479i	−0.865797	−	0.500395i	$-0.833188\pi$
$647$	1.76705e7	−	3.66933e7i	0.0652435	−	0.135479i	0.931040	+	0.364916i	$0.118902\pi$
$648$	9.23757e7	+	1.91820e8i	0.339495	+	0.704968i
$649$	−1.66805e8	−	2.09167e8i	−0.610204	−	0.765172i
$650$	−1.69830e8	+	3.87627e7i	−0.618408	+	0.141148i
$651$	−1.03589e8			−0.375465
$652$		−	4.63112e7i		−	0.167087i
$653$	3.21669e8	−	7.34188e7i	1.15523	−	0.263674i	0.398355	−	0.917231i	$-0.369581\pi$
$653$	3.21669e8	−	7.34188e7i	1.15523	−	0.263674i	0.756877	+	0.653557i	$0.226724\pi$
$654$	2.83811e7	−	3.55887e7i	0.101460	−	0.127227i
$655$	−1.28330e8	+	5.62250e8i	−0.456672	+	2.00081i
$656$	−1.08499e8	+	1.36053e8i	−0.384338	+	0.481945i
$657$	6.50119e7	−	1.34999e8i	0.229243	−	0.476029i
$658$	1.11915e8	+	4.90331e8i	0.392835	+	1.72112i
$659$	−3.36278e8	−	1.61943e8i	−1.17501	−	0.565857i	−0.258559	−	0.965995i	$-0.583248\pi$
$659$	−3.36278e8	−	1.61943e8i	−1.17501	−	0.565857i	−0.916455	+	0.400139i	$0.868962\pi$
$660$	−1.10309e7	−	1.38323e7i	−0.0383690	−	0.0481131i
$661$	1.65143e7	−	7.23539e7i	0.0571815	−	0.250529i	−0.938256	−	0.345941i	$-0.887560\pi$
$661$	1.65143e7	−	7.23539e7i	0.0571815	−	0.250529i	0.995438	+	0.0954122i	$0.0304169\pi$
$662$	6.48720e7	−	2.84223e8i	0.223606	−	0.979682i
$663$	−9.66031e6	−	2.00598e7i	−0.0331475	−	0.0688314i
$664$	2.91594e8	−	2.32539e8i	0.996036	−	0.794312i
$665$	7.32251e8	+	5.83951e8i	2.48998	+	1.98569i
$666$	−2.93691e8	+	1.41434e8i	−0.994186	+	0.478775i
$667$	6.02967e7	+	1.25207e8i	0.203197	+	0.421942i
$668$	−1.64684e7	+	2.06507e7i	−0.0552486	+	0.0692795i
$669$	3.52309e7	+	4.41782e7i	0.117665	+	0.147547i
$670$	−5.87431e8	+	2.82892e8i	−1.95314	+	0.940581i
$671$	3.60282e8	+	8.22321e7i	1.19255	+	0.272191i
$672$	2.54094e7	+	5.79953e6i	0.0837310	+	0.0191111i
$673$	−4.18308e7	+	3.33590e7i	−0.137231	+	0.109438i	−0.689699	−	0.724096i	$-0.742257\pi$
$673$	−4.18308e7	+	3.33590e7i	−0.137231	+	0.109438i	0.552469	+	0.833534i	$0.313686\pi$
$674$	−1.59278e8	+	3.30743e8i	−0.520205	+	1.08022i
$675$	2.02428e8	−	4.62029e7i	0.658203	−	0.150230i
$676$	−2.39386e7	−	1.15282e7i	−0.0774923	−	0.0373183i
$677$	1.43511e8	+	1.14447e8i	0.462509	+	0.368839i	0.826846	−	0.562428i	$-0.190133\pi$
$677$	1.43511e8	+	1.14447e8i	0.462509	+	0.368839i	−0.364337	+	0.931267i	$0.618704\pi$
$678$	5.30126e7	+	1.20998e7i	0.170094	+	0.0388229i
$679$	−4.80129e7	−	3.82890e7i	−0.153373	−	0.122311i
$680$	−7.90316e7	−	3.46260e8i	−0.251347	−	1.10122i
$681$	1.23314e8			0.390456
$682$		−	4.76342e8i		−	1.50164i
$683$	7.10034e7	+	3.11086e8i	0.222852	+	0.976380i	0.955319	+	0.295577i	$0.0955118\pi$
$683$	7.10034e7	+	3.11086e8i	0.222852	+	0.976380i	−0.732467	+	0.680803i	$0.761631\pi$
$684$	2.88469e7	−	2.30046e7i	0.0901427	−	0.0718864i
$685$	5.13158e8	−	2.47124e8i	1.59654	−	0.768853i
$686$	−5.25155e8	−	2.52901e8i	−1.62673	−	0.783392i
$687$		−	8.61734e7i		−	0.265768i
$688$	1.08033e8	−	3.39225e8i	0.331734	−	1.04165i
$689$	−6.78826e7			−0.207540
$690$	−3.98256e7	+	8.26987e7i	−0.121231	+	0.251739i
$691$	−1.58158e8	−	3.28419e8i	−0.479356	−	0.995393i	−0.990706	−	0.136021i	$-0.956569\pi$
$691$	−1.58158e8	−	3.28419e8i	−0.479356	−	0.995393i	0.511350	−	0.859373i	$-0.329146\pi$
$692$	2.70874e7	+	3.39665e7i	0.0817426	+	0.102502i
$693$	−8.34743e8	+	1.90525e8i	−2.50815	+	0.572468i
$694$	−1.87768e8			−0.561751
$695$			5.67633e8i			1.69088i
$696$	4.89585e7	−	1.11745e7i	0.145211	−	0.0331435i
$697$	9.12381e7	−	1.14409e8i	0.269450	−	0.337879i
$698$	−9.55556e7	+	4.18657e8i	−0.280989	+	1.23110i
$699$	−1.25026e7	+	1.56778e7i	−0.0366074	+	0.0459043i
$700$	−3.88562e7	+	8.06858e7i	−0.113284	+	0.235236i
$701$	−1.33926e8	−	5.86768e8i	−0.388786	−	1.70338i	−0.668847	−	0.743400i	$-0.733212\pi$
$701$	−1.33926e8	−	5.86768e8i	−0.388786	−	1.70338i	0.280061	−	0.959982i	$-0.409645\pi$
$702$	−6.34175e7	−	3.05402e7i	−0.183315	−	0.0882798i
$703$	−2.83786e8	−	3.55856e8i	−0.816817	−	1.02426i
$704$	1.07227e8	−	4.69791e8i	0.307316	−	1.34644i
$705$	−2.83969e7	+	1.24415e8i	−0.0810406	+	0.355062i
$706$	−1.64743e8	−	3.42092e8i	−0.468157	−	0.972139i
$707$	−7.43803e8	+	5.93163e8i	−2.10475	+	1.67848i
$708$	−4.28948e6	−	3.42075e6i	−0.0120866	−	0.00963876i
$709$	4.13394e8	−	1.99080e8i	1.15991	−	0.558584i	0.247916	−	0.968782i	$-0.420254\pi$
$709$	4.13394e8	−	1.99080e8i	1.15991	−	0.558584i	0.911997	+	0.410197i	$0.134540\pi$
$710$	−8.64649e7	−	1.79546e8i	−0.241582	−	0.501650i
$711$	3.12568e8	−	3.91948e8i	0.869633	−	1.09049i
$712$	−1.42310e8	−	1.78451e8i	−0.394272	−	0.494401i
$713$	−2.09788e8	+	1.01028e8i	−0.578777	+	0.278724i
$714$	−1.18438e8	−	2.70326e7i	−0.325383	−	0.0742666i
$715$	3.66211e8	+	8.35854e7i	1.00188	+	0.228672i
$716$	−2.35531e7	+	1.87830e7i	−0.0641666	+	0.0511712i
$717$	5.13150e6	−	1.06557e7i	0.0139215	−	0.0289084i
$718$	4.62935e8	−	1.05662e8i	1.25068	−	0.285460i
$719$	−1.32529e8	−	6.38228e7i	−0.356554	−	0.171707i	0.247028	−	0.969008i	$-0.420546\pi$
$719$	−1.32529e8	−	6.38228e7i	−0.356554	−	0.171707i	−0.603582	+	0.797301i	$0.706260\pi$
$720$	−4.70757e8	−	3.75416e8i	−1.26124	−	1.00581i
$721$	−4.41702e8	−	1.00815e8i	−1.17848	−	0.268981i
$722$	1.18317e8	+	9.43543e7i	0.314365	+	0.250698i
$723$	2.11835e7	+	9.28110e7i	0.0560509	+	0.245575i
$724$	3.27036e7			0.0861746
$725$			3.65138e8i			0.958170i
$726$	3.19039e7	+	1.39780e8i	0.0833745	+	0.365288i
$727$	4.44181e8	−	3.54223e8i	1.15600	−	0.921877i	0.158147	−	0.987416i	$-0.449448\pi$
$727$	4.44181e8	−	3.54223e8i	1.15600	−	0.921877i	0.997850	+	0.0655385i	$0.0208765\pi$
$728$	−2.35599e8	+	1.13458e8i	−0.610631	+	0.294064i
$729$	−2.34552e8	−	1.12954e8i	−0.605420	−	0.291555i
$730$			3.58673e8i			0.921998i
$731$	−9.08461e7	+	2.85259e8i	−0.232570	+	0.730277i
$732$	7.57848e6			0.0193219
$733$	−5.91735e7	+	1.22875e8i	−0.150250	+	0.311998i	−0.962486	−	0.271332i	$-0.912536\pi$
$733$	−5.91735e7	+	1.22875e8i	−0.150250	+	0.311998i	0.812236	+	0.583329i	$0.198250\pi$
$734$	−3.21845e7	−	6.68318e7i	−0.0813877	−	0.169003i
$735$	−1.85054e8	−	2.32051e8i	−0.466055	−	0.584414i
$736$	5.71152e7	−	1.30362e7i	0.143258	−	0.0326977i
$737$	8.32264e8			2.07902
$738$		−	2.24479e8i		−	0.558479i
$739$	−3.76116e7	+	8.58459e6i	−0.0931940	+	0.0212709i	−0.268864	−	0.963178i	$-0.586648\pi$
$739$	−3.76116e7	+	8.58459e6i	−0.0931940	+	0.0212709i	0.175670	+	0.984449i	$0.443791\pi$
$740$	4.58389e7	−	5.74801e7i	0.113120	−	0.141848i
$741$	1.06120e7	−	4.64943e7i	0.0260822	−	0.114273i
$742$	−2.30934e8	+	2.89582e8i	−0.565296	+	0.708859i
$743$	−6.77621e7	+	1.40710e8i	−0.165204	+	0.343050i	−0.967093	−	0.254423i	$-0.918114\pi$
$743$	−6.77621e7	+	1.40710e8i	−0.165204	+	0.343050i	0.801889	+	0.597473i	$0.203829\pi$
$744$	1.87230e7	+	8.20310e7i	0.0454629	+	0.199186i
$745$	3.81048e8	+	1.83503e8i	0.921534	+	0.443787i
$746$	−4.40630e8	−	5.52533e8i	−1.06135	−	1.33089i
$747$	−1.18316e8	+	5.18375e8i	−0.283845	+	1.24360i
$748$	1.17122e7	−	5.13146e7i	0.0279856	−	0.122613i
$749$	2.81031e8	+	5.83567e8i	0.668820	+	1.38882i
$750$	−5.85868e7	+	4.67214e7i	−0.138872	+	0.110747i
$751$	−1.49971e8	−	1.19598e8i	−0.354070	−	0.282361i	0.430260	−	0.902705i	$-0.358422\pi$
$751$	−1.49971e8	−	1.19598e8i	−0.354070	−	0.282361i	−0.784330	+	0.620344i	$0.786993\pi$
$752$	4.06765e8	−	1.95888e8i	0.956512	−	0.460632i
$753$	−2.02230e7	−	4.19934e7i	−0.0473652	−	0.0983549i
$754$	7.71768e7	−	9.67766e7i	0.180042	−	0.225765i
$755$	−7.04534e8	−	8.83457e8i	−1.63705	−	2.05279i
$756$	−3.26027e7	+	1.57006e7i	−0.0754551	+	0.0363372i
$757$	−6.17672e8	−	1.40980e8i	−1.42387	−	0.324989i	−0.559911	−	0.828552i	$-0.689165\pi$
$757$	−6.17672e8	−	1.40980e8i	−1.42387	−	0.324989i	−0.863958	+	0.503564i	$0.832022\pi$
$758$	1.24736e8	+	2.84701e7i	0.286406	+	0.0653704i
$759$	9.16042e7	−	7.30519e7i	0.209503	−	0.167073i
$760$	3.30075e8	−	6.85408e8i	0.751921	−	1.56138i
$761$	1.25779e8	−	2.87083e7i	0.285401	−	0.0651409i	−0.0774238	−	0.996998i	$-0.524669\pi$
$761$	1.25779e8	−	2.87083e7i	0.285401	−	0.0651409i	0.362825	+	0.931857i	$0.381812\pi$
$762$	−1.23692e8	−	5.95669e7i	−0.279561	−	0.134629i
$763$	3.88449e8	+	3.09778e8i	0.874501	+	0.697392i
$764$	−2.76876e7	−	6.31951e6i	−0.0620876	−	0.0141711i
$765$	3.95866e8	+	3.15693e8i	0.884228	+	0.705148i
$766$	1.27905e8	+	5.60390e8i	0.284579	+	1.24682i
$767$	1.16485e8			0.258156
$768$		−	3.35094e7i		−	0.0739747i
$769$	−1.29023e7	−	5.65286e7i	−0.0283719	−	0.124305i	0.958759	−	0.284221i	$-0.0917349\pi$
$769$	−1.29023e7	−	5.65286e7i	−0.0283719	−	0.124305i	−0.987131	+	0.159916i	$0.948878\pi$
$770$	1.60240e9	−	1.27787e9i	3.50994	−	2.79909i
$771$	1.18631e8	−	5.71297e7i	0.258842	−	0.124652i
$772$	−1.43332e7	−	6.90252e6i	−0.0311524	−	0.0150022i
$773$			7.63081e7i			0.165208i	0.996582	+	0.0826042i	$0.0263237\pi$
$773$			7.63081e7i			0.165208i	−0.996582	+	0.0826042i	$0.973676\pi$
$774$	1.63879e8	+	4.29012e8i	0.353427	+	0.925223i
$775$	−6.11796e8			−1.31432
$776$	−2.16427e7	+	4.49415e7i	−0.0463154	+	0.0961750i
$777$	9.39811e7	+	1.95154e8i	0.200344	+	0.416020i
$778$	−4.21618e8	−	5.28692e8i	−0.895324	−	1.12270i
$779$	3.05583e8	−	6.97473e7i	0.646423	−	0.147542i
$780$	7.70319e6			0.0162326
$781$			2.54378e8i			0.533982i
$782$	−2.66224e8	+	6.07639e7i	−0.556707	+	0.127065i
$783$	−9.19904e7	+	1.15352e8i	−0.191627	+	0.240293i
$784$	−2.33655e8	+	1.02371e9i	−0.484872	+	2.12436i
$785$	−5.62513e8	+	7.05369e8i	−1.16285	+	1.45817i
$786$	6.95201e7	−	1.44360e8i	0.143167	−	0.297289i
$787$	−6.00927e7	−	2.63283e8i	−0.123281	−	0.540131i	−0.998417	−	0.0562526i	$-0.982085\pi$
$787$	−6.00927e7	−	2.63283e8i	−0.123281	−	0.540131i	0.875135	−	0.483879i	$-0.160772\pi$
$788$	3.68941e7	+	1.77673e7i	0.0754012	+	0.0363113i
$789$	6.89506e7	+	8.64613e7i	0.140381	+	0.176032i
$790$	−2.67033e8	+	1.16995e9i	−0.541607	+	2.37293i
$791$	−1.32068e8	+	5.78629e8i	−0.266851	+	1.16915i
$792$	3.01749e8	+	6.26588e8i	0.607394	+	1.26127i
$793$	−1.25798e8	+	1.00320e8i	−0.252262	+	0.201173i
$794$	2.56499e8	+	2.04551e8i	0.512417	+	0.408639i
$795$	−8.46742e7	+	4.07769e7i	−0.168519	+	0.0811546i
$796$	1.97305e7	+	4.09708e7i	0.0391200	+	0.0812336i
$797$	1.66024e8	−	2.08187e8i	0.327940	−	0.411224i	−0.590340	−	0.807155i	$-0.701006\pi$
$797$	1.66024e8	−	2.08187e8i	0.327940	−	0.411224i	0.918281	+	0.395930i	$0.129578\pi$
$798$	−1.62239e8	−	2.03442e8i	−0.319262	−	0.400342i
$799$	−3.42054e8	+	1.64725e8i	−0.670587	+	0.322937i
$800$	1.50068e8	+	3.42521e7i	0.293102	+	0.0668986i
$801$	3.17237e8	+	7.24074e7i	0.617286	+	0.140892i
$802$	4.66812e8	−	3.72270e8i	0.904939	−	0.721665i
$803$	1.98649e8	−	4.12498e8i	0.383653	−	0.796664i
$804$	1.66397e7	−	3.79790e6i	0.0320167	−	0.00730761i
$805$	−9.02652e8	−	4.34694e8i	−1.73034	−	0.833290i
$806$	1.62151e8	+	1.29311e8i	0.309682	+	0.246963i
$807$	2.20695e8	+	5.03722e7i	0.419925	+	0.0958452i
$808$	6.04158e8	+	4.81800e8i	1.14529	+	0.913341i
$809$	−1.37977e8	−	6.04516e8i	−0.260592	−	1.14173i	−0.920612	−	0.390479i	$-0.872309\pi$
$809$	−1.37977e8	−	6.04516e8i	−0.260592	−	1.14173i	0.660020	−	0.751248i	$-0.270548\pi$
$810$	7.26556e8			1.36714
$811$		−	4.08292e8i		−	0.765435i	−0.923865	−	0.382717i	$-0.874988\pi$
$811$		−	4.08292e8i		−	0.765435i	0.923865	−	0.382717i	$-0.125012\pi$
$812$	−1.41603e7	−	6.20404e7i	−0.0264487	−	0.115879i
$813$	1.60890e8	−	1.28305e8i	0.299404	−	0.238767i
$814$	−8.97394e8	+	4.32162e8i	−1.66383	+	0.801260i
$815$	1.22646e9	+	5.90634e8i	2.26559	+	1.09105i
$816$			1.09052e8i			0.200708i
$817$	−5.33095e8	+	3.56385e8i	−0.977548	+	0.653511i
$818$	−5.09781e8			−0.931373
$819$	1.61749e8	−	3.35875e8i	0.294435	−	0.611402i
$820$	2.19671e7	+	4.56153e7i	0.0398412	+	0.0827311i
$821$	1.48122e8	+	1.85739e8i	0.267664	+	0.335640i	0.897440	−	0.441137i	$-0.145425\pi$
$821$	1.48122e8	+	1.85739e8i	0.267664	+	0.335640i	−0.629776	+	0.776777i	$0.716853\pi$
$822$	−1.54274e8	+	3.52121e7i	−0.277766	+	0.0633982i
$823$	9.03415e8			1.62064			0.810322	−	0.585985i	$-0.199292\pi$
$823$	9.03415e8			1.62064			0.810322	+	0.585985i	$0.199292\pi$
$824$			3.68001e8i			0.657760i
$825$	3.00131e8	−	6.85030e7i	0.534502	−	0.121997i
$826$	3.96276e8	−	4.96914e8i	0.703165	−	0.881741i
$827$	6.74935e7	−	2.95708e8i	0.119329	−	0.522814i	−0.879564	−	0.475780i	$-0.842166\pi$
$827$	6.74935e7	−	2.95708e8i	0.119329	−	0.522814i	0.998893	−	0.0470342i	$-0.0149770\pi$
$828$	−2.46081e7	+	3.08576e7i	−0.0433498	+	0.0543590i
$829$	−1.90934e8	+	3.96479e8i	−0.335135	+	0.695915i	−0.998633	−	0.0522628i	$-0.983357\pi$
$829$	−1.90934e8	+	3.96479e8i	−0.335135	+	0.695915i	0.663498	+	0.748178i	$0.269071\pi$
$830$	−2.83218e8	−	1.24086e9i	−0.495321	−	2.17015i
$831$	−1.65743e8	−	7.98176e7i	−0.288823	−	0.139090i
$832$	1.30813e8	+	1.64034e8i	0.227133	+	0.284816i
$833$	1.96484e8	−	8.60852e8i	0.339932	−	1.48934i
$834$	3.50929e7	−	1.53752e8i	0.0604951	−	0.265047i
$835$	−3.36863e8	−	6.99504e8i	−0.578621	−	1.20152i
$836$	8.81437e7	−	7.02923e7i	0.150859	−	0.120306i
$837$	−1.93275e8	−	1.54132e8i	−0.329610	−	0.262855i
$838$	6.11422e8	−	2.94445e8i	1.03898	−	0.500348i
$839$	3.56079e8	+	7.39406e8i	0.602921	+	1.25198i	0.949444	+	0.313937i	$0.101648\pi$
$839$	3.56079e8	+	7.39406e8i	0.602921	+	1.25198i	−0.346522	+	0.938042i	$0.612638\pi$
$840$	−2.25722e8	+	2.83047e8i	−0.380835	+	0.477552i
$841$	2.09095e8	+	2.62197e8i	0.351525	+	0.440798i
$842$	−2.85964e8	+	1.37713e8i	−0.479043	+	0.230695i
$843$	−1.31440e8	−	3.00004e7i	−0.219404	−	0.0500776i
$844$	6.13665e7	+	1.40065e7i	0.102071	+	0.0232971i
$845$	6.10606e8	−	4.86942e8i	1.01202	−	0.807063i
$846$	−2.52690e8	+	5.24716e8i	−0.417327	+	0.866589i
$847$	−1.52569e9	+	3.48229e8i	−2.51082	+	0.573079i
$848$	2.99561e8	+	1.44261e8i	0.491245	+	0.236571i
$849$	−2.71494e7	−	2.16509e7i	−0.0443647	−	0.0353796i
$850$	−6.99493e8	−	1.59655e8i	−1.13901	−	0.259971i
$851$	3.80661e8	+	3.03567e8i	0.617660	+	0.492567i
$852$	1.16081e6	+	5.08586e6i	0.00187691	+	0.00822328i
$853$	1.66839e8			0.268812			0.134406	−	0.990926i	$-0.457087\pi$
$853$	1.66839e8			0.268812			0.134406	+	0.990926i	$0.457087\pi$
$854$			8.77927e8i			1.40956i
$855$	2.41333e8	+	1.05735e9i	0.386116	+	1.69168i
$856$	4.11327e8	−	3.28022e8i	0.655791	−	0.522976i
$857$	−5.38708e8	+	2.59428e8i	−0.855877	+	0.412169i	−0.809756	−	0.586767i	$-0.800400\pi$
$857$	−5.38708e8	+	2.59428e8i	−0.855877	+	0.412169i	−0.0461213	+	0.998936i	$0.514686\pi$
$858$	−9.40263e7	−	4.52807e7i	−0.148863	−	0.0716887i
$859$		−	8.23857e8i		−	1.29979i	−0.760025	−	0.649894i	$-0.774813\pi$
$859$		−	8.23857e8i		−	1.29979i	0.760025	−	0.649894i	$-0.225187\pi$
$860$	−7.52833e7	−	7.11404e7i	−0.118359	−	0.111846i
$861$	−1.49164e8			−0.233697
$862$	−2.77647e7	+	5.76539e7i	−0.0433481	+	0.0900133i
$863$	2.66437e8	+	5.53262e8i	0.414536	+	0.860792i	0.998788	+	0.0492200i	$0.0156736\pi$
$863$	2.66437e8	+	5.53262e8i	0.414536	+	0.860792i	−0.584252	+	0.811572i	$0.698612\pi$
$864$	3.87795e7	+	4.86279e7i	0.0601257	+	0.0753953i
$865$	−1.24500e9	+	2.84163e8i	−1.92363	+	0.439055i
$866$	8.45083e7			0.130121
$867$			6.44159e7i			0.0988406i
$868$	1.03950e8	−	2.37259e7i	0.158952	−	0.0362797i
$869$	9.55075e8	−	1.19763e9i	1.45539	−	1.82500i
$870$	3.81338e7	−	1.67075e8i	0.0579099	−	0.253720i
$871$	−2.25932e8	+	2.83310e8i	−0.341920	+	0.428754i
$872$	1.75100e8	−	3.63600e8i	0.264081	−	0.548370i
$873$	−1.58239e7	−	6.93291e7i	−0.0237832	−	0.104201i
$874$	−5.26980e8	−	2.53780e8i	−0.789333	−	0.380123i
$875$	−5.09962e8	−	6.39472e8i	−0.761226	−	0.954548i
$876$	2.08927e6	−	9.15369e6i	0.00310801	−	0.0136171i
$877$	1.78168e8	−	7.80607e8i	0.264139	−	1.15727i	−0.652576	−	0.757724i	$-0.726312\pi$
$877$	1.78168e8	−	7.80607e8i	0.264139	−	1.15727i	0.916714	−	0.399543i	$-0.130831\pi$
$878$	2.22251e8	+	4.61508e8i	0.328367	+	0.681861i
$879$	−4.72263e7	+	3.76617e7i	−0.0695372	+	0.0554541i
$880$	−1.43843e9	−	1.14711e9i	−2.11077	−	1.68329i
$881$	3.22527e8	−	1.55321e8i	0.471670	−	0.227144i	−0.182921	−	0.983128i	$-0.558555\pi$
$881$	3.22527e8	−	1.55321e8i	0.471670	−	0.227144i	0.654591	+	0.755983i	$0.272841\pi$
$882$	−5.87704e8	−	1.22038e9i	−0.856550	−	1.77864i
$883$	−1.77687e8	+	2.22812e8i	−0.258091	+	0.323636i	−0.893948	−	0.448171i	$-0.852075\pi$
$883$	−1.77687e8	+	2.22812e8i	−0.258091	+	0.323636i	0.635857	+	0.771807i	$0.280647\pi$
$884$	1.42885e7	+	1.79172e7i	0.0206838	+	0.0259366i
$885$	1.45298e8	−	6.99720e7i	0.209619	−	0.100947i
$886$	1.19834e9	+	2.73513e8i	1.72297	+	0.393257i
$887$	−1.10295e9	−	2.51740e8i	−1.58046	−	0.360729i	−0.659906	−	0.751348i	$-0.729404\pi$
$887$	−1.10295e9	−	2.51740e8i	−1.58046	−	0.360729i	−0.920553	+	0.390618i	$0.872261\pi$
$888$	1.37554e8	−	1.09696e8i	0.196442	−	0.156657i
$889$	6.50169e8	−	1.35009e9i	0.925382	−	1.92158i
$890$	−7.59387e8	+	1.73325e8i	−1.07719	+	0.245862i
$891$	−8.35588e8	−	4.02398e8i	−1.18130	−	0.568883i
$892$	−4.54723e7	−	3.62630e7i	−0.0640697	−	0.0510939i
$893$	−7.92807e8	−	1.80953e8i	−1.11330	−	0.254104i
$894$	−9.18678e7	−	7.32621e7i	−0.128573	−	0.102534i
$895$	−1.97045e8	−	8.63310e8i	−0.274850	−	1.20420i
$896$	1.40267e9			1.94998
$897$			5.10142e7i			0.0706828i
$898$	1.73397e8	+	7.59704e8i	0.239449	+	1.04910i
$899$	3.39887e8	−	2.71051e8i	0.467795	−	0.373054i
$900$	−9.34319e7	+	4.49944e7i	−0.128165	+	0.0617208i
$901$	−2.51905e8	−	1.21311e8i	−0.344400	−	0.165854i
$902$		−	6.85913e8i		−	0.934650i
$903$	2.85073e8	−	1.08895e8i	0.387162	−	0.147892i
$904$	4.82082e8			0.652552
$905$	−4.17088e8	+	8.66092e8i	−0.562707	+	1.16847i
$906$	1.36215e8	+	2.82854e8i	0.183164	+	0.380345i
$907$	6.01576e8	+	7.54352e8i	0.806247	+	1.01100i	0.999554	+	0.0298640i	$0.00950741\pi$
$907$	6.01576e8	+	7.54352e8i	0.806247	+	1.01100i	−0.193306	+	0.981138i	$0.561921\pi$
$908$	−1.23744e8	+	2.82439e7i	−0.165298	+	0.0377282i
$909$	−1.10165e9			−1.46673
$910$			8.92375e8i			1.18419i
$911$	1.23588e8	−	2.82081e7i	0.163464	−	0.0373095i	−0.140006	−	0.990151i	$-0.544712\pi$
$911$	1.23588e8	−	2.82081e7i	0.163464	−	0.0373095i	0.303469	+	0.952841i	$0.401855\pi$
$912$	−1.45638e8	+	1.82624e8i	−0.191995	+	0.240754i
$913$	−3.61522e8	+	1.58393e9i	−0.475032	+	2.08125i
$914$	−5.23650e8	+	6.56636e8i	−0.685808	+	0.859975i
$915$	−9.66529e7	+	2.00702e8i	−0.126169	+	0.261992i
$916$	1.97371e7	+	8.64739e7i	0.0256801	+	0.112512i
$917$	1.57568e9	+	7.58809e8i	2.04343	+	0.984066i
$918$	−1.80758e8	−	2.26663e8i	−0.233652	−	0.292990i
$919$	−1.07507e8	+	4.71021e8i	−0.138513	+	0.606867i	0.857249	+	0.514902i	$0.172172\pi$
$919$	−1.07507e8	+	4.71021e8i	−0.138513	+	0.606867i	−0.995762	+	0.0919646i	$0.970685\pi$
$920$	−1.81081e8	+	7.93370e8i	−0.232547	+	1.01885i
$921$	−1.03382e8	−	2.14675e8i	−0.132332	−	0.274791i
$922$	−4.37768e8	+	3.49108e8i	−0.558536	+	0.445418i
$923$	−8.65928e7	−	6.90554e7i	−0.110123	−	0.0878199i
$924$	−4.83386e7	+	2.32786e7i	−0.0612743	+	0.0295081i
$925$	5.55053e8	+	1.15258e9i	0.701309	+	1.45628i
$926$	1.28353e8	−	1.60950e8i	0.161650	−	0.202702i
$927$	−3.27102e8	−	4.10174e8i	−0.410624	−	0.514907i
$928$	−9.85463e7	+	4.74574e7i	−0.123309	+	0.0593827i
$929$	3.67430e8	+	8.38634e7i	0.458276	+	0.104598i	0.445426	−	0.895319i	$-0.353052\pi$
$929$	3.67430e8	+	8.38634e7i	0.458276	+	0.104598i	0.0128503	+	0.999917i	$0.495910\pi$
$930$	2.79938e8	+	6.38941e7i	0.348027	+	0.0794350i
$931$	1.47870e9	−	1.17922e9i	1.83244	−	1.46132i
$932$	8.95538e6	−	1.85960e7i	0.0110621	−	0.0229706i
$933$	9.76301e7	−	2.22834e7i	0.120209	−	0.0274370i
$934$	−1.03595e9	−	4.98886e8i	−1.27144	−	0.612295i
$935$	1.20960e9	+	9.64622e8i	1.47981	+	1.18011i
$936$	−2.95212e8	−	6.73801e7i	−0.360003	−	0.0821683i
$937$	−8.38546e8	−	6.68718e8i	−1.01931	−	0.812876i	−0.0368493	−	0.999321i	$-0.511732\pi$
$937$	−8.38546e8	−	6.68718e8i	−1.01931	−	0.812876i	−0.982466	+	0.186444i	$0.940304\pi$
$938$	4.39967e8	+	1.92762e9i	0.533103	+	2.33568i
$939$	−2.77247e8			−0.334865
$940$		−	1.31353e8i		−	0.158145i
$941$	−2.15971e8	−	9.46232e8i	−0.259195	−	1.13561i	−0.922114	−	0.386918i	$-0.873540\pi$
$941$	−2.15971e8	−	9.46232e8i	−0.259195	−	1.13561i	0.662919	−	0.748691i	$-0.269317\pi$
$942$	1.95973e8	−	1.56283e8i	0.234447	−	0.186965i
$943$	−3.02086e8	+	1.45477e8i	−0.360243	+	0.173484i
$944$	−5.14038e8	−	2.47548e8i	−0.611054	−	0.294268i
$945$		−	1.06366e9i		−	1.26040i
$946$	5.00743e8	+	1.31088e9i	0.591482	+	1.54842i
$947$	−1.07800e9			−1.26931			−0.634655	−	0.772796i	$-0.718858\pi$
$947$	−1.07800e9			−1.26931			−0.634655	+	0.772796i	$0.718858\pi$
$948$	1.36299e7	−	2.83028e7i	0.0159981	−	0.0332204i
$949$	8.64916e7	+	1.79602e8i	0.101199	+	0.210141i
$950$	−9.58187e8	−	1.20153e9i	−1.11758	−	1.40140i
$951$	−7.66583e7	+	1.74968e7i	−0.0891287	+	0.0203431i
$952$	−1.07704e9			−1.24830
$953$		−	3.18144e8i		−	0.367574i	−0.982966	−	0.183787i	$-0.941164\pi$
$953$		−	3.18144e8i		−	0.367574i	0.982966	−	0.183787i	$-0.0588357\pi$
$954$	−4.18147e8	+	9.54393e7i	−0.481597	+	0.109921i
$955$	5.20476e8	−	6.52657e8i	0.597573	−	0.749333i
$956$	−2.70883e6	+	1.18681e7i	−0.00310033	+	0.0135834i
$957$	−1.36390e8	+	1.71028e8i	−0.155613	+	0.195133i
$958$	5.22227e7	−	1.08441e8i	0.0593967	−	0.123339i
$959$	−3.84339e8	−	1.68390e9i	−0.435771	−	1.90924i
$960$	2.61706e8	+	1.26031e8i	0.295801	+	0.142450i
$961$	−9.91981e7	−	1.24391e8i	−0.111772	−	0.140158i
$962$	9.65012e7	−	4.22799e8i	0.108395	−	0.474907i
$963$	−1.66898e8	+	7.31226e8i	−0.186884	+	0.818791i
$964$	−4.25148e7	−	8.82828e7i	−0.0474579	−	0.0985474i
$965$	3.65600e8	−	2.91556e8i	0.406841	−	0.324445i
$966$	2.17622e8	+	1.73548e8i	0.241419	+	0.192526i
$967$	2.49766e8	−	1.20281e8i	0.276219	−	0.133020i	−0.290646	−	0.956831i	$-0.593870\pi$
$967$	2.49766e8	−	1.20281e8i	0.276219	−	0.133020i	0.566865	+	0.823810i	$0.308156\pi$
$968$	5.51518e8	+	1.14524e9i	0.608042	+	1.26261i
$969$	1.22469e8	−	1.53571e8i	0.134603	−	0.168786i
$970$	1.06133e8	+	1.33087e8i	0.116288	+	0.145821i
$971$	−3.76647e8	+	1.81384e8i	−0.411412	+	0.198126i	−0.628130	−	0.778109i	$-0.716179\pi$
$971$	−3.76647e8	+	1.81384e8i	−0.411412	+	0.198126i	0.216717	+	0.976234i	$0.430465\pi$
$972$	−6.18816e7	−	1.41241e7i	−0.0673849	−	0.0153802i
$973$	1.67819e9	+	3.83037e8i	1.82181	+	0.415817i
$974$	−4.31587e8	+	3.44180e8i	−0.467081	+	0.372484i
$975$	−5.81568e7	+	1.20764e8i	−0.0627461	+	0.130294i
$976$	7.68331e8	−	1.75367e8i	0.826417	−	0.188624i
$977$	5.15255e8	+	2.48134e8i	0.552508	+	0.266074i	0.689239	−	0.724534i	$-0.257945\pi$
$977$	5.15255e8	+	2.48134e8i	0.552508	+	0.266074i	−0.136730	+	0.990608i	$0.543659\pi$
$978$	−2.95691e8	−	2.35806e8i	−0.316098	−	0.252080i
$979$	9.69342e8	+	2.21246e8i	1.03307	+	0.235791i
$980$	2.38848e8	+	1.90475e8i	0.253772	+	0.202377i
$981$	1.28024e8	+	5.60908e8i	0.135607	+	0.594134i
$982$	2.98955e8			0.315698
$983$		−	1.03429e9i		−	1.08889i	−0.838797	−	0.544444i	$-0.816741\pi$
$983$		−	1.03429e9i		−	1.08889i	0.838797	−	0.544444i	$-0.183259\pi$
$984$	2.69604e7	+	1.18121e8i	0.0282970	+	0.123977i
$985$	−9.41065e8	+	7.50474e8i	−0.984716	+	0.785284i
$986$	4.59341e8	−	2.21207e8i	0.479187	−	0.230764i
$987$	3.48667e8	+	1.67909e8i	0.362626	+	0.174632i
$988$			4.90870e7i			0.0508974i
$989$	4.71125e8	−	4.98561e8i	0.487021	−	0.515382i
$990$	2.37332e9			2.44597
$991$	6.94678e8	−	1.44251e9i	0.713777	−	1.48217i	−0.155494	−	0.987837i	$-0.549697\pi$
$991$	6.94678e8	−	1.44251e9i	0.713777	−	1.48217i	0.869271	−	0.494336i	$-0.164589\pi$
$992$	−7.95159e7	−	1.65116e8i	−0.0814552	−	0.169143i
$993$	−1.39862e8	−	1.75382e8i	−0.142841	−	0.179117i
$994$	−5.89170e8	+	1.34474e8i	−0.599904	+	0.136924i
$995$	−1.33667e9			−1.35692
$996$			3.33178e7i			0.0337208i
$997$	−2.75072e8	+	6.27834e7i	−0.277563	+	0.0633519i	−0.359036	−	0.933324i	$-0.616895\pi$
$997$	−2.75072e8	+	6.27834e7i	−0.277563	+	0.0633519i	0.0814735	+	0.996676i	$0.474037\pi$
$998$	−5.06054e8	+	6.34571e8i	−0.509102	+	0.638394i
$999$	−1.15024e8	+	5.03953e8i	−0.115370	+	0.505468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.22.7	yes	126
43.2	odd	14	inner	43.7.f.a.2.7	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.7	✓	126	43.2	odd	14	inner
43.7.f.a.22.7	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)

\(f(q)\)	\(=\)	\(q+(-3.64714 + 7.57336i) q^{2} +(2.80632 + 5.82738i) q^{3} +(-4.15080 - 5.20494i) q^{4} +(190.781 - 43.5445i) q^{5} -54.3678 q^{6} -593.422i q^{7} +(-469.925 + 107.257i) q^{8} +(428.441 - 537.248i) q^{9} +O(q^{10})\)	\(q+(-3.64714 + 7.57336i) q^{2} +(2.80632 + 5.82738i) q^{3} +(-4.15080 - 5.20494i) q^{4} +(190.781 - 43.5445i) q^{5} -54.3678 q^{6} -593.422i q^{7} +(-469.925 + 107.257i) q^{8} +(428.441 - 537.248i) q^{9} +(-366.026 + 1603.66i) q^{10} +(1309.13 - 1641.60i) q^{11} +(18.6827 - 38.7950i) q^{12} +(203.429 + 891.283i) q^{13} +(4494.20 + 2164.29i) q^{14} +(789.141 + 989.552i) q^{15} +(996.393 - 4365.48i) q^{16} +(-837.881 + 3671.00i) q^{17} +(2506.19 + 5204.16i) q^{18} +(-6305.71 + 5028.64i) q^{19} +(-1018.54 - 812.258i) q^{20} +(3458.09 - 1665.33i) q^{21} +(7657.84 + 15901.7i) q^{22} +(5379.15 - 6745.25i) q^{23} +(-1943.79 - 2437.43i) q^{24} +(20423.5 - 9835.45i) q^{25} +(-7491.94 - 1709.99i) q^{26} +(8929.97 + 2038.21i) q^{27} +(-3088.73 + 2463.18i) q^{28} +(-6988.90 + 14512.6i) q^{29} +(-10372.3 + 2367.42i) q^{30} +(-24316.2 - 11710.1i) q^{31} +(5308.94 + 4233.74i) q^{32} +(13240.1 + 3021.96i) q^{33} +(-24745.9 - 19734.2i) q^{34} +(-25840.2 - 113214. i) q^{35} -4574.72 q^{36} +56433.9i q^{37} +(-15085.9 - 66095.6i) q^{38} +(-4622.95 + 3686.68i) q^{39} +(-84982.2 + 40925.3i) q^{40} +(-35014.3 - 16862.0i) q^{41} +32263.1i q^{42} +(79227.2 + 6663.89i) q^{43} -13978.4 q^{44} +(58344.1 - 121153. i) q^{45} +(31465.7 + 65339.1i) q^{46} +(62864.2 + 78829.2i) q^{47} +(28235.5 - 6444.57i) q^{48} -234501. q^{49} +190546. i q^{50} +(-23743.6 + 5419.33i) q^{51} +(3794.68 - 4758.38i) q^{52} +(-16522.9 + 72391.6i) q^{53} +(-48004.9 + 60196.2i) q^{54} +(178275. - 370191. i) q^{55} +(63648.9 + 278864. i) q^{56} +(-46999.6 - 22633.8i) q^{57} +(-84419.7 - 105859. i) q^{58} +(28352.8 - 124222. i) q^{59} +(1874.99 - 8214.87i) q^{60} +(76364.2 + 158572. i) q^{61} +(177369. - 141447. i) q^{62} +(-318815. - 254246. i) q^{63} +(206770. - 99575.2i) q^{64} +(77620.8 + 161181. i) q^{65} +(-71174.7 + 89250.3i) q^{66} +(247136. + 309899. i) q^{67} +(22585.2 - 10876.5i) q^{68} +(54402.7 + 12417.1i) q^{69} +(951649. + 217208. i) q^{70} +(-94719.4 + 75536.2i) q^{71} +(-143712. + 298420. i) q^{72} +(212584. - 48520.9i) q^{73} +(-427394. - 205822. i) q^{74} +(114630. + 91414.2i) q^{75} +(52347.5 + 11948.0i) q^{76} +(-974162. - 776869. i) q^{77} +(-11060.0 - 48457.1i) q^{78} +729548. q^{79} -876238. i q^{80} +(-98287.7 - 430626. i) q^{81} +(255404. - 203678. i) q^{82} +(-697139. + 335725. i) q^{83} +(-23021.8 - 11086.7i) q^{84} +736840. i q^{85} +(-339421. + 575712. i) q^{86} -104184. q^{87} +(-439121. + 911844. i) q^{88} +(205458. + 426638. i) q^{89} +(704745. + 883722. i) q^{90} +(528907. - 120720. i) q^{91} -57436.4 q^{92} -174562. i q^{93} +(-826276. + 188592. i) q^{94} +(-984039. + 1.23395e6i) q^{95} +(-9773.02 + 42818.4i) q^{96} +(64522.4 - 80908.5i) q^{97} +(855257. - 1.77596e6i) q^{98} +(-321061. - 1.40666e6i) 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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