LMFDB - Embedded newform 43.7.f.a.2.6

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			2.6
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.35509 - 9.04344i) q^{2} +(15.2129 - 31.5900i) q^{3} +(-22.9137 + 28.7328i) q^{4} +(-93.5256 - 21.3466i) q^{5} -351.936 q^{6} +345.453i q^{7} +(-266.657 - 60.8626i) q^{8} +(-311.968 - 391.196i) q^{9} +O(q^{10})$	\(q+(-4.35509 - 9.04344i) q^{2} +(15.2129 - 31.5900i) q^{3} +(-22.9137 + 28.7328i) q^{4} +(-93.5256 - 21.3466i) q^{5} -351.936 q^{6} +345.453i q^{7} +(-266.657 - 60.8626i) q^{8} +(-311.968 - 391.196i) q^{9} +(214.266 + 938.759i) q^{10} +(-1066.21 - 1336.99i) q^{11} +(559.085 + 1160.95i) q^{12} +(211.655 - 927.319i) q^{13} +(3124.08 - 1504.48i) q^{14} +(-2097.13 + 2629.72i) q^{15} +(1134.29 + 4969.63i) q^{16} +(860.461 + 3769.92i) q^{17} +(-2179.10 + 4524.96i) q^{18} +(3083.67 + 2459.15i) q^{19} +(2756.36 - 2198.13i) q^{20} +(10912.8 + 5255.35i) q^{21} +(-7447.51 + 15464.9i) q^{22} +(-8840.87 - 11086.1i) q^{23} +(-5979.27 + 7497.77i) q^{24} +(-5786.29 - 2786.53i) q^{25} +(-9307.93 + 2124.47i) q^{26} +(7815.70 - 1783.88i) q^{27} +(-9925.84 - 7915.59i) q^{28} +(-6307.91 - 13098.5i) q^{29} +(32915.0 + 7512.63i) q^{30} +(2617.24 - 1260.39i) q^{31} +(26316.7 - 20986.9i) q^{32} +(-58455.5 + 13342.1i) q^{33} +(30345.7 - 24199.9i) q^{34} +(7374.24 - 32308.7i) q^{35} +18388.5 q^{36} -31333.5i q^{37} +(8809.48 - 38596.9i) q^{38} +(-26074.1 - 20793.4i) q^{39} +(23640.0 + 11384.4i) q^{40} +(-103346. + 49768.6i) q^{41} -121577. i q^{42} +(-50100.9 - 61735.4i) q^{43} +62846.2 q^{44} +(20826.3 + 43246.2i) q^{45} +(-61753.7 + 128233. i) q^{46} +(-47379.2 + 59411.7i) q^{47} +(174246. + 39770.5i) q^{48} -1688.64 q^{49} +64463.5i q^{50} +(132182. + 30169.6i) q^{51} +(21794.7 + 27329.7i) q^{52} +(-53480.5 - 234313. i) q^{53} +(-50170.5 - 62911.9i) q^{54} +(71177.9 + 147802. i) q^{55} +(21025.2 - 92117.2i) q^{56} +(124596. - 60002.3i) q^{57} +(-90984.1 + 114090. i) q^{58} +(8375.71 + 36696.4i) q^{59} +(-27506.4 - 120513. i) q^{60} +(-110436. + 229323. i) q^{61} +(-22796.6 - 18179.7i) q^{62} +(135140. - 107770. i) q^{63} +(-10477.6 - 5045.73i) q^{64} +(-39590.2 + 82209.9i) q^{65} +(375238. + 470533. i) q^{66} +(42707.3 - 53553.3i) q^{67} +(-128037. - 61659.3i) q^{68} +(-484705. + 110631. i) q^{69} +(-324297. + 74018.7i) q^{70} +(-256542. - 204585. i) q^{71} +(59379.1 + 123302. i) q^{72} +(-420672. - 96015.5i) q^{73} +(-283363. + 136460. i) q^{74} +(-176053. + 140397. i) q^{75} +(-141317. + 32254.6i) q^{76} +(461866. - 368326. i) q^{77} +(-74488.8 + 326357. i) q^{78} +34711.4 q^{79} -489000. i q^{80} +(143714. - 629651. i) q^{81} +(900159. + 717853. i) q^{82} +(923422. + 444697. i) q^{83} +(-401054. + 193137. i) q^{84} -370952. i q^{85} +(-340107. + 721948. i) q^{86} -509743. q^{87} +(202940. + 421409. i) q^{88} +(525024. - 1.09022e6i) q^{89} +(300394. - 376683. i) q^{90} +(320345. + 73116.7i) q^{91} +521112. q^{92} -101853. i q^{93} +(743627. + 169728. i) q^{94} +(-235908. - 295819. i) q^{95} +(-262621. - 1.15062e6i) q^{96} +(210713. + 264226. i) q^{97} +(7354.20 + 15271.2i) q^{98} +(-190399. + 834194. 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−4.35509	−	9.04344i	−0.544387	−	1.13043i	−0.973818	−	0.227331i	$-0.927000\pi$
$2$	−4.35509	−	9.04344i	−0.544387	−	1.13043i	0.429431	−	0.903100i	$-0.358714\pi$
$3$	15.2129	−	31.5900i	0.563441	−	1.17000i	−0.403495	−	0.914982i	$-0.632205\pi$
$3$	15.2129	−	31.5900i	0.563441	−	1.17000i	0.966937	−	0.255016i	$-0.0820809\pi$
$4$	−22.9137	+	28.7328i	−0.358026	+	0.448951i
$5$	−93.5256	−	21.3466i	−0.748204	−	0.170773i	−0.168616	−	0.985682i	$-0.553930\pi$
$5$	−93.5256	−	21.3466i	−0.748204	−	0.170773i	−0.579589	+	0.814909i	$0.696787\pi$
$6$	−351.936			−1.62933
$7$			345.453i			1.00715i	0.863951	+	0.503576i	$0.167982\pi$
$7$			345.453i			1.00715i	−0.863951	+	0.503576i	$0.832018\pi$
$8$	−266.657	−	60.8626i	−0.520814	−	0.118872i
$9$	−311.968	−	391.196i	−0.427940	−	0.536619i
$10$	214.266	+	938.759i	0.214266	+	0.938759i
$11$	−1066.21	−	1336.99i	−0.801060	−	1.00450i	−0.999702	−	0.0244256i	$-0.992224\pi$
$11$	−1066.21	−	1336.99i	−0.801060	−	1.00450i	0.198641	−	0.980072i	$-0.436347\pi$
$12$	559.085	+	1160.95i	0.323545	+	0.671847i
$13$	211.655	−	927.319i	0.0963380	−	0.422084i	−0.903643	−	0.428287i	$-0.859117\pi$
$13$	211.655	−	927.319i	0.0963380	−	0.422084i	0.999981	+	0.00620268i	$0.00197439\pi$
$14$	3124.08	−	1504.48i	1.13851	−	0.548279i
$15$	−2097.13	+	2629.72i	−0.621373	+	0.779177i
$16$	1134.29	+	4969.63i	0.276925	+	1.21329i
$17$	860.461	+	3769.92i	0.175140	+	0.767336i	0.983830	+	0.179103i	$0.0573194\pi$
$17$	860.461	+	3769.92i	0.175140	+	0.767336i	−0.808691	+	0.588234i	$0.799823\pi$
$18$	−2179.10	+	4524.96i	−0.373646	+	0.775884i
$19$	3083.67	+	2459.15i	0.449581	+	0.358529i	0.821954	−	0.569555i	$-0.192884\pi$
$19$	3083.67	+	2459.15i	0.449581	+	0.358529i	−0.372373	+	0.928083i	$0.621456\pi$
$20$	2756.36	−	2198.13i	0.344545	−	0.274766i
$21$	10912.8	+	5255.35i	1.17836	+	0.567471i
$22$	−7447.51	+	15464.9i	−0.699428	+	1.45238i
$23$	−8840.87	−	11086.1i	−0.726627	−	0.911161i	0.272066	−	0.962279i	$-0.412293\pi$
$23$	−8840.87	−	11086.1i	−0.726627	−	0.911161i	−0.998693	+	0.0511177i	$0.983722\pi$
$24$	−5979.27	+	7497.77i	−0.432528	+	0.542373i
$25$	−5786.29	−	2786.53i	−0.370322	−	0.178338i
$26$	−9307.93	+	2124.47i	−0.529582	+	0.120874i
$27$	7815.70	−	1783.88i	0.397079	−	0.0906306i
$28$	−9925.84	−	7915.59i	−0.452161	−	0.360586i
$29$	−6307.91	−	13098.5i	−0.258638	−	0.537067i	0.730701	−	0.682697i	$-0.239193\pi$
$29$	−6307.91	−	13098.5i	−0.258638	−	0.537067i	−0.989339	+	0.145631i	$0.953479\pi$
$30$	32915.0	+	7512.63i	1.21907	+	0.278245i
$31$	2617.24	−	1260.39i	0.0878532	−	0.0423079i	−0.389441	−	0.921051i	$-0.627332\pi$
$31$	2617.24	−	1260.39i	0.0878532	−	0.0423079i	0.477294	+	0.878743i	$0.341618\pi$
$32$	26316.7	−	20986.9i	0.803123	−	0.640469i
$33$	−58455.5	+	13342.1i	−1.62661	+	0.371263i
$34$	30345.7	−	24199.9i	0.772077	−	0.615711i
$35$	7374.24	−	32308.7i	0.171994	−	0.753555i
$36$	18388.5			0.394129
$37$		−	31333.5i		−	0.618591i	−0.950966	−	0.309296i	$-0.899907\pi$
$37$		−	31333.5i		−	0.618591i	0.950966	−	0.309296i	$-0.100093\pi$
$38$	8809.48	−	38596.9i	0.160546	−	0.703398i
$39$	−26074.1	−	20793.4i	−0.439557	−	0.350535i
$40$	23640.0	+	11384.4i	0.369375	+	0.177882i
$41$	−103346.	+	49768.6i	−1.49948	+	0.722111i	−0.990351	−	0.138580i	$-0.955746\pi$
$41$	−103346.	+	49768.6i	−1.49948	+	0.722111i	−0.509128	+	0.860691i	$0.670032\pi$
$42$		−	121577.i		−	1.64098i
$43$	−50100.9	−	61735.4i	−0.630144	−	0.776478i
$43$	−50100.9	−	61735.4i	−0.630144	−	0.776478i
$44$	62846.2			0.737770
$45$	20826.3	+	43246.2i	0.228546	+	0.474581i
$46$	−61753.7	+	128233.i	−0.634438	+	1.31742i
$47$	−47379.2	+	59411.7i	−0.456346	+	0.572240i	−0.955769	−	0.294118i	$-0.904974\pi$
$47$	−47379.2	+	59411.7i	−0.456346	+	0.572240i	0.499423	+	0.866358i	$0.333545\pi$
$48$	174246.	+	39770.5i	1.57558	+	0.359615i
$49$	−1688.64			−0.0143532
$50$			64463.5i			0.515708i
$51$	132182.	+	30169.6i	0.996463	+	0.227436i
$52$	21794.7	+	27329.7i	0.155003	+	0.194368i
$53$	−53480.5	−	234313.i	−0.359226	−	1.57387i	−0.755127	−	0.655578i	$-0.772425\pi$
$53$	−53480.5	−	234313.i	−0.359226	−	1.57387i	0.395901	−	0.918293i	$-0.370432\pi$
$54$	−50170.5	−	62911.9i	−0.318616	−	0.399532i
$55$	71177.9	+	147802.i	0.427816	+	0.888369i
$56$	21025.2	−	92117.2i	0.119722	−	0.524538i
$57$	124596.	−	60002.3i	0.672790	−	0.323999i
$58$	−90984.1	+	114090.i	−0.466317	+	0.584744i
$59$	8375.71	+	36696.4i	0.0407817	+	0.178677i	0.991217	−	0.132246i	$-0.0422190\pi$
$59$	8375.71	+	36696.4i	0.0407817	+	0.178677i	−0.950435	+	0.310923i	$0.899362\pi$
$60$	−27506.4	−	120513.i	−0.127344	−	0.557932i
$61$	−110436.	+	229323.i	−0.486544	+	1.01032i	0.502757	+	0.864428i	$0.332319\pi$
$61$	−110436.	+	229323.i	−0.486544	+	1.01032i	−0.989301	+	0.145890i	$0.953395\pi$
$62$	−22796.6	−	18179.7i	−0.0956522	−	0.0762801i
$63$	135140.	−	107770.i	0.540457	−	0.431000i
$64$	−10477.6	−	5045.73i	−0.0399688	−	0.0192479i
$65$	−39590.2	+	82209.9i	−0.144161	+	0.299353i
$66$	375238.	+	470533.i	1.30519	+	1.63666i
$67$	42707.3	−	53553.3i	0.141997	−	0.178058i	−0.705748	−	0.708463i	$-0.749389\pi$
$67$	42707.3	−	53553.3i	0.141997	−	0.178058i	0.847744	+	0.530405i	$0.177960\pi$
$68$	−128037.	−	61659.3i	−0.407201	−	0.196097i
$69$	−484705.	+	110631.i	−1.47547	+	0.336766i
$70$	−324297.	+	74018.7i	−0.945472	+	0.215798i
$71$	−256542.	−	204585.i	−0.716776	−	0.571610i	0.195738	−	0.980656i	$-0.437290\pi$
$71$	−256542.	−	204585.i	−0.716776	−	0.571610i	−0.912513	+	0.409047i	$0.865861\pi$
$72$	59379.1	+	123302.i	0.159088	+	0.330349i
$73$	−420672.	−	96015.5i	−1.08137	−	0.246816i	−0.355520	−	0.934669i	$-0.615696\pi$
$73$	−420672.	−	96015.5i	−1.08137	−	0.246816i	−0.725850	+	0.687853i	$0.758553\pi$
$74$	−283363.	+	136460.i	−0.699274	+	0.336753i
$75$	−176053.	+	140397.i	−0.417310	+	0.332794i
$76$	−141317.	+	32254.6i	−0.321923	+	0.0734769i
$77$	461866.	−	368326.i	1.01168	−	0.806789i
$78$	−74488.8	+	326357.i	−0.156966	+	0.687715i
$79$	34711.4			0.0704029			0.0352014	−	0.999380i	$-0.488793\pi$
$79$	34711.4			0.0704029			0.0352014	+	0.999380i	$0.488793\pi$
$80$		−	489000.i		−	0.955079i
$81$	143714.	−	629651.i	0.270423	−	1.18480i
$82$	900159.	+	717853.i	1.63259	+	1.30195i
$83$	923422.	+	444697.i	1.61498	+	0.777731i	0.999942	−	0.0107693i	$-0.00342806\pi$
$83$	923422.	+	444697.i	1.61498	+	0.777731i	0.615034	+	0.788501i	$0.289142\pi$
$84$	−401054.	+	193137.i	−0.676652	+	0.325858i
$85$		−	370952.i		−	0.604034i
$86$	−340107.	+	721948.i	−0.534712	+	1.13504i
$87$	−509743.			−0.774094
$88$	202940.	+	421409.i	0.297796	+	0.618380i
$89$	525024.	−	1.09022e6i	0.744748	−	1.54648i	−0.0900560	−	0.995937i	$-0.528705\pi$
$89$	525024.	−	1.09022e6i	0.744748	−	1.54648i	0.834804	−	0.550548i	$-0.185581\pi$
$90$	300394.	−	376683.i	0.412064	−	0.516711i
$91$	320345.	+	73116.7i	0.425103	+	0.0970269i
$92$	521112.			0.669217
$93$		−	101853.i		−	0.126626i
$94$	743627.	+	169728.i	0.895306	+	0.204348i
$95$	−235908.	−	295819.i	−0.275151	−	0.345029i
$96$	−262621.	−	1.15062e6i	−0.296835	−	1.30052i
$97$	210713.	+	264226.i	0.230875	+	0.289508i	0.883752	−	0.467956i	$-0.155010\pi$
$97$	210713.	+	264226.i	0.230875	+	0.289508i	−0.652877	+	0.757464i	$0.726438\pi$
$98$	7354.20	+	15271.2i	0.00781371	+	0.0162253i
$99$	−190399.	+	834194.i	−0.196228	+	0.859729i
$100$	212650.	−	102407.i	0.212650	−	0.102407i
$101$	826639.	−	1.03657e6i	0.802327	−	1.00609i	−0.197341	−	0.980335i	$-0.563231\pi$
$101$	826639.	−	1.03657e6i	0.802327	−	1.00609i	0.999668	−	0.0257517i	$-0.00819793\pi$
$102$	−302827.	−	1.32677e6i	−0.285360	−	1.25025i
$103$	−64607.6	−	283064.i	−0.0591251	−	0.259044i	0.936723	−	0.350070i	$-0.113842\pi$
$103$	−64607.6	−	283064.i	−0.0591251	−	0.259044i	−0.995848	+	0.0910264i	$0.970985\pi$
$104$	−112878.	+	234394.i	−0.100348	+	0.208375i
$105$	−908445.	−	724461.i	−0.784749	−	0.625817i
$106$	−1.88609e6	+	1.50410e6i	−1.58359	+	1.26287i
$107$	679554.	+	327256.i	0.554719	+	0.267138i	0.690172	−	0.723645i	$-0.257535\pi$
$107$	679554.	+	327256.i	0.554719	+	0.267138i	−0.135453	+	0.990784i	$0.543249\pi$
$108$	−127830.	+	265443.i	−0.101476	+	0.210717i
$109$	−836856.	−	1.04938e6i	−0.646206	−	0.810317i	0.345558	−	0.938398i	$-0.387690\pi$
$109$	−836856.	−	1.04938e6i	−0.646206	−	0.810317i	−0.991764	+	0.128081i	$0.959118\pi$
$110$	1.02666e6	−	1.28739e6i	0.771342	−	0.967232i
$111$	−989823.	−	476674.i	−0.723750	−	0.348540i
$112$	−1.71677e6	+	391842.i	−1.22196	+	0.278905i
$113$	−14550.6	+	3321.07i	−0.0100843	+	0.00230167i	−0.227560	−	0.973764i	$-0.573075\pi$
$113$	−14550.6	+	3321.07i	−0.0100843	+	0.00230167i	0.217476	+	0.976066i	$0.430218\pi$
$114$	−1.08525e6	−	865462.i	−0.732516	−	0.584162i
$115$	590196.	+	1.22556e6i	0.388064	+	0.805823i
$116$	520895.	+	118891.i	0.333715	+	0.0761683i
$117$	−428793.	+	206496.i	−0.267725	+	0.128930i
$118$	295385.	−	235562.i	0.179780	−	0.143370i
$119$	−1.30233e6	+	297249.i	−0.772824	+	0.176392i
$120$	719266.	−	573596.i	0.416242	−	0.331942i
$121$	−256517.	+	1.12388e6i	−0.144797	+	0.634399i
$122$	2.55483e6			1.40696
$123$			4.02181e6i			2.16126i
$124$	−23755.8	+	104081.i	−0.0124596	+	0.0545891i
$125$	1.65358e6	+	1.31869e6i	0.846635	+	0.675169i
$126$	−1.56316e6	−	752778.i	−0.781433	−	0.376318i
$127$	1.29409e6	−	623202.i	0.631763	−	0.304241i	−0.0904615	−	0.995900i	$-0.528834\pi$
$127$	1.29409e6	−	623202.i	0.631763	−	0.304241i	0.722224	+	0.691659i	$0.243120\pi$
$128$		−	2.03754e6i		−	0.971573i
$129$	−2.71240e6	+	643509.i	−1.26353	+	0.299768i
$130$	915880.			0.416877
$131$	−1.16865e6	−	2.42672e6i	−0.519840	−	1.07946i	−0.981333	−	0.192315i	$-0.938401\pi$
$131$	−1.16865e6	−	2.42672e6i	−0.519840	−	1.07946i	0.461493	−	0.887144i	$-0.347314\pi$
$132$	956075.	−	1.98531e6i	0.415690	−	0.863190i
$133$	−849520.	+	1.06526e6i	−0.361093	+	0.452796i
$134$	−670301.	−	152992.i	−0.278583	−	0.0635848i
$135$	−769048.			−0.312573
$136$		−	1.05764e6i		−	0.420458i
$137$	4.52528e6	+	1.03287e6i	1.75988	+	0.401682i	0.975746	−	0.218906i	$-0.0702487\pi$
$137$	4.52528e6	+	1.03287e6i	1.75988	+	0.401682i	0.784137	+	0.620588i	$0.213106\pi$
$138$	3.11141e6	+	3.90159e6i	1.18392	+	1.48458i
$139$	470896.	+	2.06313e6i	0.175340	+	0.768214i	0.983743	+	0.179584i	$0.0574752\pi$
$139$	470896.	+	2.06313e6i	0.175340	+	0.768214i	−0.808403	+	0.588630i	$0.799668\pi$
$140$	759349.	+	952193.i	0.276731	+	0.347009i
$141$	1.15604e6	+	2.40053e6i	0.412395	+	0.856348i
$142$	−732892.	+	3.21101e6i	−0.255962	+	1.12144i
$143$	−1.46548e6	+	705739.i	−0.501155	+	0.241344i
$144$	1.59024e6	−	1.99409e6i	0.532567	−	0.667817i
$145$	310342.	+	1.35970e6i	0.101797	+	0.446004i
$146$	963752.	+	4.22248e6i	0.309676	+	1.35678i
$147$	−25689.2	+	53344.2i	−0.00808721	+	0.0167933i
$148$	900300.	+	717965.i	0.277717	+	0.221472i
$149$	−4.15143e6	+	3.31065e6i	−1.25499	+	1.00082i	−0.255565	+	0.966792i	$0.582262\pi$
$149$	−4.15143e6	+	3.31065e6i	−1.25499	+	1.00082i	−0.999421	+	0.0340262i	$0.989167\pi$
$150$	2.03640e6	+	980679.i	0.603378	+	0.290571i
$151$	2.10654e6	−	4.37427e6i	0.611840	−	1.27050i	−0.332988	−	0.942931i	$-0.608057\pi$
$151$	2.10654e6	−	4.37427e6i	0.611840	−	1.27050i	0.944828	−	0.327568i	$-0.106229\pi$
$152$	−672612.	−	843428.i	−0.191529	−	0.240169i
$153$	1.20634e6	−	1.51270e6i	0.336818	−	0.422357i
$154$	−5.34240e6	−	2.57276e6i	−1.46276	−	0.704430i
$155$	−271684.	+	62010.0i	−0.0729572	+	0.0166520i
$156$	1.19491e6	−	272729.i	0.314746	−	0.0718387i
$157$	−3.18392e6	−	2.53909e6i	−0.822742	−	0.656115i	0.118835	−	0.992914i	$-0.462084\pi$
$157$	−3.18392e6	−	2.53909e6i	−0.822742	−	0.656115i	−0.941576	+	0.336799i	$0.890656\pi$
$158$	−151171.	−	313910.i	−0.0383264	−	0.0795855i
$159$	−8.21554e6	−	1.87514e6i	−2.04383	−	0.466491i
$160$	−2.90929e6	+	1.40104e6i	−0.710275	+	0.342050i
$161$	3.82972e6	−	3.05410e6i	0.917677	−	0.731823i
$162$	−6.32010e6	+	1.44252e6i	−1.48655	+	0.339295i
$163$	−290331.	+	231531.i	−0.0670395	+	0.0534622i	−0.656436	−	0.754381i	$-0.727937\pi$
$163$	−290331.	+	231531.i	−0.0670395	+	0.0534622i	0.589397	+	0.807844i	$0.299365\pi$
$164$	938034.	−	4.10979e6i	0.212661	−	0.931727i
$165$	5.75189e6			1.28044
$166$		−	1.02876e7i		−	2.24900i
$167$	−778084.	+	3.40901e6i	−0.167062	+	0.731945i	0.820100	+	0.572221i	$0.193918\pi$
$167$	−778084.	+	3.40901e6i	−0.167062	+	0.731945i	−0.987162	+	0.159725i	$0.948939\pi$
$168$	−2.59013e6	−	2.06556e6i	−0.546252	−	0.435621i
$169$	3.53368e6	+	1.70173e6i	0.732095	+	0.352558i
$170$	−3.35468e6	+	1.61553e6i	−0.682818	+	0.328828i
$171$		−	1.97350e6i		−	0.394682i
$172$	2.92183e6	−	24955.4i	0.574208	−	0.00490433i
$173$	6.60399e6			1.27546			0.637732	−	0.770258i	$-0.279873\pi$
$173$	6.60399e6			1.27546			0.637732	+	0.770258i	$0.279873\pi$
$174$	2.21998e6	+	4.60983e6i	0.421406	+	0.875059i
$175$	962614.	−	1.99889e6i	0.179613	−	0.372971i
$176$	5.43494e6	−	6.81520e6i	0.996912	−	1.25009i
$177$	1.28666e6	+	293671.i	0.232029	+	0.0529592i
$178$	−1.21459e7			−2.15362
$179$		−	2.69026e6i		−	0.469068i	−0.972108	−	0.234534i	$-0.924644\pi$
$179$		−	2.69026e6i		−	0.469068i	0.972108	−	0.234534i	$-0.0753564\pi$
$180$	−1.71979e6	−	392532.i	−0.294889	−	0.0673065i
$181$	−3.79280e6	−	4.75602e6i	−0.639623	−	0.802061i	0.351333	−	0.936251i	$-0.385728\pi$
$181$	−3.79280e6	−	4.75602e6i	−0.639623	−	0.802061i	−0.990956	+	0.134189i	$0.957157\pi$
$182$	−733906.	−	3.21545e6i	−0.121738	−	0.533369i
$183$	5.56425e6	+	6.97734e6i	0.907932	+	1.13851i
$184$	1.68275e6	+	3.49426e6i	0.270125	+	0.560921i
$185$	−668863.	+	2.93048e6i	−0.105639	+	0.462833i
$186$	−921098.	+	443578.i	−0.143142	+	0.0689336i
$187$	4.12291e6	−	5.16996e6i	0.630490	−	0.790610i
$188$	−621434.	−	2.72268e6i	−0.0935236	−	0.409754i
$189$	616247.	+	2.69996e6i	0.0912787	+	0.399918i
$190$	−1.64782e6	+	3.42174e6i	−0.240242	+	0.498869i
$191$	−7.05504e6	−	5.62621e6i	−1.01251	−	0.807450i	−0.0311280	−	0.999515i	$-0.509910\pi$
$191$	−7.05504e6	−	5.62621e6i	−1.01251	−	0.807450i	−0.981382	+	0.192066i	$0.938481\pi$
$192$	−318789.	+	254226.i	−0.0450401	+	0.0359183i
$193$	1.10362e7	+	5.31477e6i	1.53514	+	0.739286i	0.994770	−	0.102139i	$-0.0325688\pi$
$193$	1.10362e7	+	5.31477e6i	1.53514	+	0.739286i	0.540373	+	0.841425i	$0.318283\pi$
$194$	1.47184e6	−	3.05630e6i	0.201583	−	0.418592i
$195$	1.99473e6	+	2.50131e6i	0.269017	+	0.337336i
$196$	38693.0	−	48519.5i	0.00513883	−	0.00644389i
$197$	1.84830e6	+	890093.i	0.241754	+	0.116422i	0.550838	−	0.834612i	$-0.314308\pi$
$197$	1.84830e6	+	890093.i	0.241754	+	0.116422i	−0.309084	+	0.951035i	$0.600023\pi$
$198$	8.37319e6	−	1.91113e6i	1.07869	−	0.246203i
$199$	2.70975e6	−	618482.i	0.343850	−	0.0784816i	−0.0471084	−	0.998890i	$-0.515001\pi$
$199$	2.70975e6	−	618482.i	0.343850	−	0.0784816i	0.390959	+	0.920408i	$0.372143\pi$
$200$	1.37336e6	+	1.09521e6i	0.171669	+	0.136902i
$201$	−1.04204e6	−	2.16382e6i	−0.128321	−	0.266461i
$202$	−1.29743e7	−	2.96129e6i	−1.57409	−	0.359275i
$203$	4.52492e6	−	2.17909e6i	0.540907	−	0.260487i
$204$	−3.89563e6	+	3.10666e6i	−0.458867	+	0.365935i
$205$	1.07278e7	−	2.44856e6i	1.24523	−	0.284217i
$206$	−2.27850e6	+	1.81705e6i	−0.260644	+	0.207857i
$207$	−1.57876e6	+	6.91701e6i	−0.177994	+	0.779844i
$208$	4.84851e6			0.538788
$209$		−	6.74480e6i		−	0.738806i
$210$	−2.59526e6	+	1.13706e7i	−0.280235	+	1.22779i
$211$	−6.83637e6	−	5.45182e6i	−0.727743	−	0.580356i	0.187977	−	0.982173i	$-0.439807\pi$
$211$	−6.83637e6	−	5.45182e6i	−0.727743	−	0.580356i	−0.915720	+	0.401818i	$0.868378\pi$
$212$	7.95792e6	+	3.83233e6i	0.835203	+	0.402212i
$213$	−1.03656e7	+	4.99181e6i	−1.07264	+	0.516558i
$214$		−	7.57074e6i		−	0.772497i
$215$	3.36787e6	+	6.84332e6i	0.338876	+	0.688576i
$216$	−2.19268e6			−0.217577
$217$	435407.	+	904131.i	0.0426104	+	0.0884815i
$218$	−5.84546e6	+	1.21382e7i	−0.564221	+	1.17162i
$219$	−9.43277e6	+	1.18283e7i	−0.898063	+	1.12614i
$220$	−5.87773e6	−	1.34155e6i	−0.552003	−	0.125991i
$221$	3.67804e6			0.340753
$222$			1.10274e7i			1.00789i
$223$	−1.49952e7	−	3.42255e6i	−1.35219	−	0.308628i	−0.515774	−	0.856725i	$-0.672496\pi$
$223$	−1.49952e7	−	3.42255e6i	−1.35219	−	0.308628i	−0.836415	+	0.548096i	$0.815353\pi$
$224$	7.24998e6	+	9.09119e6i	0.645049	+	0.808866i
$225$	715059.	+	3.13288e6i	0.0627761	+	0.275040i
$226$	93403.0	+	117124.i	0.00809162	+	0.0101466i
$227$	967075.	+	2.00815e6i	0.0826766	+	0.171680i	0.938209	−	0.346070i	$-0.112484\pi$
$227$	967075.	+	2.00815e6i	0.0826766	+	0.171680i	−0.855532	+	0.517750i	$0.826770\pi$
$228$	−1.13092e6	+	4.95487e6i	−0.0954171	+	0.418050i
$229$	−107907.	+	51965.2i	−0.00898550	+	0.00432719i	−0.438371	−	0.898794i	$-0.644444\pi$
$229$	−107907.	+	51965.2i	−0.00898550	+	0.00432719i	0.429386	+	0.903121i	$0.358730\pi$
$230$	8.51288e6	−	1.06748e7i	0.699670	−	0.877358i
$231$	−4.60906e6	−	2.01936e7i	−0.373918	−	1.63824i
$232$	884836.	+	3.87672e6i	0.0708596	+	0.310456i
$233$	496135.	−	1.03024e6i	0.0392222	−	0.0814458i	−0.880437	−	0.474163i	$-0.842751\pi$
$233$	496135.	−	1.03024e6i	0.0392222	−	0.0814458i	0.919659	+	0.392717i	$0.128465\pi$
$234$	3.73486e6	+	2.97845e6i	0.291492	+	0.232457i
$235$	5.69941e6	−	4.54512e6i	0.439163	−	0.350221i
$236$	−1.24631e6	−	600191.i	−0.0948179	−	0.0456619i
$237$	528061.	−	1.09653e6i	0.0396679	−	0.0823712i
$238$	8.35992e6	+	1.04830e7i	0.620114	+	0.777598i
$239$	−1.15883e7	+	1.45313e7i	−0.848841	+	1.06441i	0.148307	+	0.988941i	$0.452617\pi$
$239$	−1.15883e7	+	1.45313e7i	−0.848841	+	1.06441i	−0.997148	+	0.0754711i	$0.975954\pi$
$240$	−1.54475e7	−	7.43912e6i	−1.11744	−	0.538131i
$241$	−1.92345e7	+	4.39016e6i	−1.37414	+	0.313638i	−0.844941	−	0.534860i	$-0.820364\pi$
$241$	−1.92345e7	+	4.39016e6i	−1.37414	+	0.313638i	−0.529199	+	0.848498i	$0.677507\pi$
$242$	1.12809e7	−	2.57478e6i	0.795969	−	0.181675i
$243$	−1.31352e7	−	1.04750e7i	−0.915414	−	0.730018i
$244$	−4.05860e6	−	8.42778e6i	−0.279388	−	0.580154i
$245$	157931.	+	36046.8i	0.0107392	+	0.00245114i
$246$	3.63710e7	−	1.75153e7i	2.44315	−	1.17656i
$247$	2.93309e6	−	2.33906e6i	0.194641	−	0.155221i
$248$	−774614.	+	176801.i	−0.0507844	+	0.0115912i
$249$	2.80959e7	−	2.24057e7i	1.81989	−	1.45131i
$250$	4.72398e6	−	2.06971e7i	0.302335	−	1.32461i
$251$	9.30643e6			0.588521			0.294261	−	0.955725i	$-0.404927\pi$
$251$	9.30643e6			0.588521			0.294261	+	0.955725i	$0.404927\pi$
$252$			6.35236e6i			0.396948i
$253$	−5.39573e6	+	2.36402e7i	−0.333187	+	1.45979i
$254$	−1.12718e7	−	8.98894e6i	−0.687846	−	0.548539i
$255$	−1.17184e7	−	5.64326e6i	−0.706718	−	0.340338i
$256$	−1.90969e7	+	9.19659e6i	−1.13826	+	0.548159i
$257$		−	3.97449e6i		−	0.234143i	−0.993123	−	0.117072i	$-0.962649\pi$
$257$		−	3.97449e6i		−	0.234143i	0.993123	−	0.117072i	$-0.0373507\pi$
$258$	1.76323e7	+	2.17269e7i	1.02671	+	1.26514i
$259$	1.08242e7			0.623015
$260$	−1.45497e6	−	3.02127e6i	−0.0827815	−	0.171898i
$261$	−3.15621e6	+	6.55394e6i	−0.177519	+	0.368622i
$262$	−1.68563e7	+	2.11372e7i	−0.937259	+	1.17529i
$263$	−2.81327e7	−	6.42110e6i	−1.54648	−	0.352974i	−0.637711	−	0.770276i	$-0.720118\pi$
$263$	−2.81327e7	−	6.42110e6i	−1.54648	−	0.352974i	−0.908768	+	0.417302i	$0.862976\pi$
$264$	1.63996e7			0.891294
$265$			2.30559e7i			1.23892i
$266$	1.33334e7	+	3.04326e6i	0.708428	+	0.161694i
$267$	−2.64530e7	−	3.31710e7i	−1.38976	−	1.74271i
$268$	560156.	+	2.45421e6i	0.0291008	+	0.127499i
$269$	1.63159e7	+	2.04595e7i	0.838214	+	1.05109i	0.997955	+	0.0639279i	$0.0203628\pi$
$269$	1.63159e7	+	2.04595e7i	0.838214	+	1.05109i	−0.159741	+	0.987159i	$0.551066\pi$
$270$	3.34927e6	+	6.95484e6i	0.170161	+	0.353342i
$271$	−6.81735e6	+	2.98687e7i	−0.342537	+	1.50075i	0.451162	+	0.892442i	$0.351010\pi$
$271$	−6.81735e6	+	2.98687e7i	−0.342537	+	1.50075i	−0.793699	+	0.608311i	$0.791847\pi$
$272$	−1.77591e7	+	8.55234e6i	−0.882500	+	0.424989i
$273$	7.18313e6	−	9.00737e6i	0.353042	−	0.442700i
$274$	−1.03674e7	−	4.54223e7i	−0.503983	−	2.20810i
$275$	2.44385e6	+	1.07072e7i	0.117511	+	0.514847i
$276$	7.92763e6	−	1.64619e7i	0.377065	−	0.782983i
$277$	2.47775e7	+	1.97594e7i	1.16578	+	0.929681i	0.998419	−	0.0562145i	$-0.0179031\pi$
$277$	2.47775e7	+	1.97594e7i	1.16578	+	0.929681i	0.167364	+	0.985895i	$0.446475\pi$
$278$	1.66070e7	−	1.32436e7i	0.772960	−	0.616415i
$279$	−1.30955e6	−	630648.i	−0.0602991	−	0.0290385i
$280$	−3.93278e6	+	8.16650e6i	−0.179154	+	0.372016i
$281$	−2.55088e7	−	3.19870e7i	−1.14966	−	1.44163i	−0.877626	−	0.479346i	$-0.840874\pi$
$281$	−2.55088e7	−	3.19870e7i	−1.14966	−	1.44163i	−0.272037	−	0.962287i	$-0.587697\pi$
$282$	1.66744e7	−	2.09091e7i	0.743539	−	0.932369i
$283$	2.57536e7	+	1.24023e7i	1.13626	+	0.547196i	0.904880	−	0.425666i	$-0.139960\pi$
$283$	2.57536e7	+	1.24023e7i	1.13626	+	0.547196i	0.231384	+	0.972862i	$0.425675\pi$
$284$	1.17566e7	−	2.68338e6i	0.513249	−	0.117146i
$285$	−1.29338e7	+	2.95205e6i	−0.558715	+	0.127523i
$286$	1.27646e7	+	1.01794e7i	0.545644	+	0.435137i
$287$	−1.71927e7	−	3.57010e7i	−0.727275	−	1.51020i
$288$	−1.64200e7	−	3.74775e6i	−0.687377	−	0.156889i
$289$	8.27526e6	−	3.98516e6i	0.342838	−	0.165102i
$290$	1.09448e7	−	8.72817e6i	0.448759	−	0.357873i
$291$	1.15525e7	−	2.63677e6i	0.468808	−	0.107002i
$292$	1.23979e7	−	9.88702e6i	0.497967	−	0.397115i
$293$	2.88650e6	−	1.26466e7i	0.114754	−	0.502772i	−0.884583	−	0.466382i	$-0.845557\pi$
$293$	2.88650e6	−	1.26466e7i	0.114754	−	0.502772i	0.999338	−	0.0363897i	$-0.0115857\pi$
$294$	594294.			0.0233862
$295$		−	3.61084e6i		−	0.140651i
$296$	−1.90704e6	+	8.35528e6i	−0.0735333	+	0.322171i
$297$	−1.07182e7	−	8.54749e6i	−0.409122	−	0.326264i
$298$	4.80196e7	+	2.31250e7i	1.81455	+	0.873842i
$299$	−1.21516e7	+	5.85188e6i	−0.454588	+	0.218918i
$300$		−	8.27551e6i		−	0.306500i
$301$	2.13267e7	−	1.73075e7i	0.782031	−	0.634651i
$302$	−4.87326e7			−1.76929
$303$	−2.01697e7	−	4.18828e7i	−0.725055	−	1.50559i
$304$	−8.72329e6	+	1.81141e7i	−0.310498	+	0.644757i
$305$	1.52239e7	−	1.90901e7i	0.536569	−	0.672836i
$306$	−1.89338e7	−	4.32151e6i	−0.660805	−	0.150824i
$307$	1.93584e7			0.669044			0.334522	−	0.942388i	$-0.391425\pi$
$307$	1.93584e7			0.669044			0.334522	+	0.942388i	$0.391425\pi$
$308$			2.17104e7i			0.743046i
$309$	−9.92486e6	−	2.26528e6i	−0.336395	−	0.0767799i
$310$	1.74399e6	+	2.18690e6i	0.0585409	+	0.0734079i
$311$	6.31336e6	+	2.76606e7i	0.209884	+	0.919562i	0.964643	+	0.263560i	$0.0848967\pi$
$311$	6.31336e6	+	2.76606e7i	0.209884	+	0.919562i	−0.754759	+	0.656002i	$0.772246\pi$
$312$	5.68728e6	+	7.13163e6i	0.187258	+	0.234815i
$313$	−1.16951e7	−	2.42851e7i	−0.381391	−	0.791967i	−0.999980	−	0.00625261i	$-0.998010\pi$
$313$	−1.16951e7	−	2.42851e7i	−0.381391	−	0.791967i	0.618589	−	0.785715i	$-0.287705\pi$
$314$	−9.09587e6	+	3.98516e7i	−0.293802	+	1.28723i
$315$	−1.49395e7	+	7.19450e6i	−0.477975	+	0.230181i
$316$	−795365.	+	997356.i	−0.0252061	+	0.0316074i
$317$	−7.91522e6	−	3.46789e7i	−0.248476	−	1.08865i	−0.933062	−	0.359714i	$-0.882874\pi$
$317$	−7.91522e6	−	3.46789e7i	−0.248476	−	1.08865i	0.684586	−	0.728932i	$-0.259983\pi$
$318$	1.88217e7	+	8.24632e7i	0.585298	+	2.56436i
$319$	−1.07870e7	+	2.23994e7i	−0.332298	+	0.690024i
$320$	872211.	+	695565.i	0.0266178	+	0.0212270i
$321$	2.06760e7	−	1.64886e7i	0.625103	−	0.498503i
$322$	−4.42984e7	−	2.13330e7i	−1.32685	−	0.638975i
$323$	−6.61742e6	+	1.37412e7i	−0.196373	+	0.407772i
$324$	1.47987e7	+	1.85569e7i	0.435098	+	0.545596i
$325$	−3.80870e6	+	4.77595e6i	−0.110950	+	0.139127i
$326$	3.35826e6	+	1.61725e6i	0.0969307	+	0.0466794i
$327$	−4.58810e7	+	1.04720e7i	−1.31217	+	0.299494i
$328$	3.05868e7	−	6.98124e6i	0.866788	−	0.197839i
$329$	−2.05239e7	−	1.63673e7i	−0.576332	−	0.459610i
$330$	−2.50500e7	−	5.20169e7i	−0.697054	−	1.44745i
$331$	−2.79808e7	−	6.38642e6i	−0.771570	−	0.176106i	−0.181427	−	0.983404i	$-0.558072\pi$
$331$	−2.79808e7	−	6.38642e6i	−0.771570	−	0.176106i	−0.590143	+	0.807299i	$0.700929\pi$
$332$	−3.39364e7	+	1.63429e7i	−0.927366	+	0.446596i
$333$	−1.22575e7	+	9.77505e6i	−0.331948	+	0.264720i
$334$	3.42178e7	−	7.80999e6i	0.918359	−	0.209610i
$335$	−5.13741e6	+	4.09695e6i	−0.136650	+	0.108975i
$336$	−1.37388e7	+	6.01938e7i	−0.362187	+	1.58684i
$337$	6.37186e7			1.66485			0.832427	−	0.554134i	$-0.186951\pi$
$337$	6.37186e7			1.66485			0.832427	+	0.554134i	$0.186951\pi$
$338$		−	3.93678e7i		−	1.01951i
$339$	−116444.	+	510175.i	−0.00298895	+	0.0130954i
$340$	1.06585e7	+	8.49988e6i	0.271181	+	0.216260i
$341$	−4.47566e6	−	2.15536e6i	−0.112874	−	0.0543572i
$342$	−1.78472e7	+	8.59475e6i	−0.446161	+	0.214860i
$343$			4.00588e7i			0.992695i
$344$	9.60235e6	+	1.95114e7i	0.235886	+	0.479307i
$345$	4.76938e7			1.16146
$346$	−2.87610e7	−	5.97228e7i	−0.694345	−	1.44182i
$347$	−2.04961e7	+	4.25606e7i	−0.490549	+	1.01864i	0.497922	+	0.867222i	$0.334097\pi$
$347$	−2.04961e7	+	4.25606e7i	−0.490549	+	1.01864i	−0.988471	+	0.151413i	$0.951618\pi$
$348$	1.16801e7	−	1.46464e7i	0.277146	−	0.347530i
$349$	6.53001e7	+	1.49043e7i	1.53616	+	0.350619i	0.905129	−	0.425136i	$-0.139774\pi$
$349$	6.53001e7	+	1.49043e7i	1.53616	+	0.350619i	0.631034	+	0.775755i	$0.282631\pi$
$350$	−2.22691e7			−0.519396
$351$		−	7.62522e6i		−	0.176332i
$352$	−5.61184e7	−	1.28087e7i	−1.28670	−	0.293681i
$353$	4.56843e7	+	5.72863e7i	1.03859	+	1.30235i	0.951998	+	0.306103i	$0.0990252\pi$
$353$	4.56843e7	+	5.72863e7i	1.03859	+	1.30235i	0.0865890	+	0.996244i	$0.472403\pi$
$354$	−2.94771e6	−	1.29148e7i	−0.0664470	−	0.291123i
$355$	1.96260e7	+	2.46103e7i	0.438679	+	0.550087i
$356$	1.92950e7	+	4.00665e7i	0.427656	+	0.888037i
$357$	−1.04222e7	+	4.56626e7i	−0.229063	+	1.00359i
$358$	−2.43292e7	+	1.17163e7i	−0.530249	+	0.255354i
$359$	−2.64429e7	+	3.31584e7i	−0.571513	+	0.716655i	−0.980639	−	0.195823i	$-0.937262\pi$
$359$	−2.64429e7	+	3.31584e7i	−0.571513	+	0.716655i	0.409126	+	0.912478i	$0.365834\pi$
$360$	−2.92139e6	−	1.27994e7i	−0.0626155	−	0.274336i
$361$	−7.00706e6	−	3.06999e7i	−0.148941	−	0.652553i
$362$	−2.64928e7	+	5.50128e7i	−0.558473	+	1.15968i
$363$	3.16008e7	+	2.52008e7i	0.660661	+	0.526859i
$364$	−9.44113e6	+	7.52905e6i	−0.195758	+	0.156112i
$365$	3.72939e7	+	1.79598e7i	0.766937	+	0.369337i
$366$	3.88664e7	−	8.07069e7i	0.792741	−	1.64614i
$367$	8.76277e6	+	1.09882e7i	0.177273	+	0.222294i	0.862527	−	0.506010i	$-0.168880\pi$
$367$	8.76277e6	+	1.09882e7i	0.177273	+	0.222294i	−0.685254	+	0.728304i	$0.740309\pi$
$368$	4.50657e7	−	5.65106e7i	0.904279	−	1.13393i
$369$	5.17098e7	+	2.49021e7i	1.02919	+	0.495630i
$370$	2.94146e7	−	6.71369e6i	0.580708	−	0.132543i
$371$	8.09442e7	−	1.84750e7i	1.58513	−	0.361795i
$372$	2.92651e6	+	2.33382e6i	0.0568489	+	0.0453355i
$373$	−2.23501e7	−	4.64105e7i	−0.430679	−	0.894314i	−0.997513	−	0.0704823i	$-0.977546\pi$
$373$	−2.23501e7	−	4.64105e7i	−0.430679	−	0.894314i	0.566834	−	0.823832i	$-0.308168\pi$
$374$	−6.47099e7	−	1.47696e7i	−1.23696	−	0.282328i
$375$	6.68132e7	−	3.21755e7i	1.26698	−	0.610143i
$376$	1.62499e7	−	1.29589e7i	0.305695	−	0.243783i
$377$	−1.34816e7	+	3.07709e6i	−0.251604	+	0.0574270i
$378$	2.17331e7	−	1.73316e7i	0.402389	−	0.320894i
$379$	−2.18705e6	+	9.58208e6i	−0.0401736	+	0.176012i	−0.991034	−	0.133607i	$-0.957344\pi$
$379$	−2.18705e6	+	9.58208e6i	−0.0401736	+	0.176012i	0.950861	+	0.309618i	$0.100201\pi$
$380$	1.39052e7			0.253412
$381$		−	5.03610e7i		−	0.910583i
$382$	−2.01549e7	+	8.83045e7i	−0.361569	+	1.58414i
$383$	−1.09290e7	−	8.71556e6i	−0.194528	−	0.155131i	0.521382	−	0.853323i	$-0.325417\pi$
$383$	−1.09290e7	−	8.71556e6i	−0.194528	−	0.155131i	−0.715910	+	0.698192i	$0.753988\pi$
$384$	−6.43657e7	−	3.09969e7i	−1.13674	−	0.547424i
$385$	−5.10588e7	+	2.45886e7i	−0.894722	+	0.430875i
$386$		−	1.22952e8i		−	2.13783i
$387$	−8.52075e6	+	3.88587e7i	−0.147009	+	0.670433i
$388$	−1.24202e7			−0.212634
$389$	−6.77897e6	−	1.40767e7i	−0.115164	−	0.239140i	0.835418	−	0.549616i	$-0.185226\pi$
$389$	−6.77897e6	−	1.40767e7i	−0.115164	−	0.239140i	−0.950581	+	0.310476i	$0.899512\pi$
$390$	1.39332e7	−	2.89326e7i	0.234886	−	0.487746i
$391$	3.41865e7	−	4.28685e7i	0.571906	−	0.717147i
$392$	450288.	+	102775.i	0.00747536	+	0.00170620i
$393$	−9.44385e7			−1.55586
$394$		−	2.05914e7i		−	0.336664i
$395$	−3.24640e6	−	740969.i	−0.0526757	−	0.0120229i
$396$	−1.96060e7	−	2.45852e7i	−0.315721	−	0.395902i
$397$	−1.22522e7	−	5.36805e7i	−0.195814	−	0.857916i	−0.973395	−	0.229134i	$-0.926411\pi$
$397$	−1.22522e7	−	5.36805e7i	−0.195814	−	0.857916i	0.777581	−	0.628783i	$-0.216446\pi$
$398$	−1.73944e7	−	2.18119e7i	−0.275906	−	0.345975i
$399$	2.07280e7	+	4.30421e7i	0.326316	+	0.677602i
$400$	7.28471e6	−	3.19164e7i	0.113824	−	0.498694i
$401$	−9.72466e7	+	4.68315e7i	−1.50814	+	0.726281i	−0.991522	−	0.129936i	$-0.958523\pi$
$401$	−9.72466e7	+	4.68315e7i	−1.50814	+	0.726281i	−0.516616	+	0.856217i	$0.672809\pi$
$402$	−1.50302e7	+	1.88473e7i	−0.231360	+	0.290116i
$403$	−614838.	−	2.69378e6i	−0.00939389	−	0.0411573i
$404$	1.08423e7	+	4.75033e7i	0.164429	+	0.720411i
$405$	−2.68818e7	+	5.58207e7i	−0.404663	+	0.840292i
$406$	−3.94129e7	−	3.14307e7i	−0.588925	−	0.469652i
$407$	−4.18925e7	+	3.34081e7i	−0.621373	+	0.495529i
$408$	−3.34109e7	−	1.60899e7i	−0.491936	−	0.236904i
$409$	3.66065e6	−	7.60142e6i	0.0535043	−	0.111103i	−0.872503	−	0.488610i	$-0.837504\pi$
$409$	3.66065e6	−	7.60142e6i	0.0535043	−	0.111103i	0.926007	+	0.377507i	$0.123219\pi$
$410$	−6.88642e7	−	8.63529e7i	−0.999176	−	1.25293i
$411$	1.01471e8	−	1.27240e8i	1.46156	−	1.83274i
$412$	9.61364e6	+	4.62969e6i	0.137466	+	0.0662003i
$413$	−1.26769e7	+	2.89341e6i	−0.179954	+	0.0410734i
$414$	6.94293e7	−	1.58468e7i	0.978457	−	0.223326i
$415$	−7.68708e7	−	6.13024e7i	−1.07552	−	0.857696i
$416$	−1.38915e7	−	2.88460e7i	−0.192961	−	0.400687i
$417$	7.23379e7	+	1.65106e7i	0.997602	+	0.227696i
$418$	−6.09962e7	+	2.93742e7i	−0.835169	+	0.402196i
$419$	−9.62482e7	+	7.67553e7i	−1.30843	+	1.04344i	−0.312822	+	0.949812i	$0.601274\pi$
$419$	−9.62482e7	+	7.67553e7i	−1.30843	+	1.04344i	−0.995607	+	0.0936260i	$0.970154\pi$
$420$	4.16316e7	−	9.50215e6i	0.561921	−	0.128255i
$421$	7.44755e7	−	5.93922e7i	0.998083	−	0.795945i	0.0190861	−	0.999818i	$-0.493924\pi$
$421$	7.44755e7	−	5.93922e7i	0.998083	−	0.795945i	0.978997	+	0.203873i	$0.0653529\pi$
$422$	−1.95302e7	+	8.55675e7i	−0.259878	+	1.13860i
$423$	3.80224e7			0.502364
$424$			6.57361e7i			0.862395i
$425$	5.52613e6	−	2.42116e7i	0.0719870	−	0.315396i
$426$	9.02862e7	+	7.20009e7i	1.16787	+	0.931341i
$427$	−7.92203e7	−	3.81505e7i	−1.01754	−	0.490023i
$428$	−2.49741e7	+	1.20269e7i	−0.318536	+	0.153399i
$429$			5.70308e7i			0.722334i
$430$	4.72198e7	−	6.02605e7i	0.593908	−	0.757927i
$431$	1.02269e8			1.27735			0.638676	−	0.769476i	$-0.279482\pi$
$431$	1.02269e8			1.27735			0.638676	+	0.769476i	$0.279482\pi$
$432$	1.77305e7	+	3.68177e7i	0.219922	+	0.456673i
$433$	1.23730e7	−	2.56927e7i	0.152409	−	0.316480i	−0.810760	−	0.585379i	$-0.800946\pi$
$433$	1.23730e7	−	2.56927e7i	0.152409	−	0.316480i	0.963168	+	0.268899i	$0.0866599\pi$
$434$	6.28022e6	−	7.87515e6i	0.0768256	−	0.0963362i
$435$	4.76740e7	+	1.08813e7i	0.579181	+	0.132194i
$436$	4.93272e7			0.595151
$437$		−	5.59269e7i		−	0.670157i
$438$	1.48049e8	+	3.37913e7i	1.76191	+	0.402145i
$439$	−9.54585e7	−	1.19701e8i	−1.12829	−	1.41483i	−0.897046	−	0.441937i	$-0.854292\pi$
$439$	−9.54585e7	−	1.19701e8i	−1.12829	−	1.41483i	−0.231245	−	0.972896i	$-0.574280\pi$
$440$	−9.98441e6	−	4.37445e7i	−0.117210	−	0.513530i
$441$	526803.	+	660590.i	0.00614232	+	0.00770223i
$442$	−1.60182e7	−	3.32622e7i	−0.185501	−	0.385198i
$443$	7.86595e6	−	3.44630e7i	0.0904773	−	0.396407i	−0.909329	−	0.416077i	$-0.863405\pi$
$443$	7.86595e6	−	3.44630e7i	0.0904773	−	0.396407i	0.999807	+	0.0196703i	$0.00626166\pi$
$444$	3.63767e7	−	1.75181e7i	0.415599	−	0.200142i
$445$	−7.23757e7	+	9.07563e7i	−0.821321	+	1.02990i
$446$	3.43538e7	+	1.50514e8i	0.387231	+	1.69657i
$447$	4.14281e7	+	1.81508e8i	0.463844	+	2.03223i
$448$	1.74306e6	−	3.61951e6i	0.0193856	−	0.0402546i
$449$	4.10833e7	+	3.27629e7i	0.453865	+	0.361945i	0.823580	−	0.567200i	$-0.191973\pi$
$449$	4.10833e7	+	3.27629e7i	0.453865	+	0.361945i	−0.369715	+	0.929145i	$0.620545\pi$
$450$	2.52178e7	−	2.01106e7i	0.276739	−	0.220692i
$451$	1.76728e8	+	8.51078e7i	1.92653	+	0.927769i
$452$	237983.	−	494177.i	0.00257710	−	0.00535140i
$453$	−1.06136e8	−	1.33091e8i	−1.14175	−	1.43170i
$454$	1.39489e7	−	1.74914e7i	0.149064	−	0.186920i
$455$	−2.83997e7	−	1.36766e7i	−0.301494	−	0.145192i
$456$	−3.68763e7	+	8.41676e6i	−0.388913	+	0.0887668i
$457$	6.70704e7	−	1.53084e7i	0.702720	−	0.160391i	0.143793	−	0.989608i	$-0.454070\pi$
$457$	6.70704e7	−	1.53084e7i	0.702720	−	0.160391i	0.558927	+	0.829217i	$0.311213\pi$
$458$	939888.	+	749536.i	0.00978317	+	0.00780182i
$459$	1.34502e7	+	2.79296e7i	0.139088	+	0.288820i
$460$	−4.87373e7	−	1.11240e7i	−0.500711	−	0.114284i
$461$	5.97382e7	−	2.87684e7i	0.609747	−	0.293639i	−0.103415	−	0.994638i	$-0.532977\pi$
$461$	5.97382e7	−	2.87684e7i	0.609747	−	0.293639i	0.713161	+	0.701000i	$0.247263\pi$
$462$	−1.62547e8	+	1.29627e8i	−1.64836	+	1.31453i
$463$	−4.41252e7	+	1.00713e7i	−0.444573	+	0.101471i	−0.438947	−	0.898513i	$-0.644648\pi$
$463$	−4.41252e7	+	1.00713e7i	−0.444573	+	0.101471i	−0.00562693	+	0.999984i	$0.501791\pi$
$464$	5.79398e7	−	4.62054e7i	0.579993	−	0.462529i
$465$	−2.17421e6	+	9.52582e6i	−0.0216243	+	0.0947422i
$466$	−1.14776e7			−0.113421
$467$			1.26683e8i			1.24385i	0.783078	+	0.621923i	$0.213648\pi$
$467$			1.26683e8i			1.24385i	−0.783078	+	0.621923i	$0.786352\pi$
$468$	3.89201e6	−	1.70520e7i	0.0379696	−	0.166356i
$469$	1.85001e7	+	1.47534e7i	0.179331	+	0.143012i
$470$	−6.59250e7	−	3.17478e7i	−0.634975	−	0.305788i
$471$	−1.28647e8	+	6.19530e7i	−1.23122	+	0.592924i
$472$		−	1.02951e7i		−	0.0979050i
$473$	−2.91213e7	+	1.32807e8i	−0.275187	+	1.25498i
$474$	−1.22162e7			−0.114710
$475$	−1.09905e7	−	2.28221e7i	−0.102551	−	0.212948i
$476$	2.13004e7	−	4.42307e7i	0.197500	−	0.410113i
$477$	−7.49781e7	+	9.40195e7i	−0.690843	+	0.866289i
$478$	1.81881e8	+	4.15131e7i	1.66534	+	0.380103i
$479$	−1.23793e8			−1.12639			−0.563195	−	0.826324i	$-0.690428\pi$
$479$	−1.23793e8			−1.12639			−0.563195	+	0.826324i	$0.690428\pi$
$480$			1.13218e8i			1.02375i
$481$	−2.90561e7	−	6.63188e6i	−0.261098	−	0.0595938i
$482$	1.23470e8	+	1.54827e8i	1.10261	+	1.38263i
$483$	−3.82177e7	−	1.67443e8i	−0.339174	−	1.48602i
$484$	−2.64144e7	−	3.31226e7i	−0.232972	−	0.292138i
$485$	−1.40667e7	−	2.92099e7i	−0.123302	−	0.256038i
$486$	−3.75248e7	+	1.64407e8i	−0.326896	+	1.43222i
$487$	8.71350e7	−	4.19620e7i	0.754407	−	0.363303i	−0.0168243	−	0.999858i	$-0.505356\pi$
$487$	8.71350e7	−	4.19620e7i	0.754407	−	0.363303i	0.771231	+	0.636555i	$0.219641\pi$
$488$	4.34057e7	−	5.44290e7i	0.373497	−	0.468351i
$489$	2.89728e6	+	1.26938e7i	0.0247779	+	0.108559i
$490$	−361819.	−	1.58523e6i	−0.00307541	−	0.0134742i
$491$	−2.49897e7	+	5.18917e7i	−0.211114	+	0.438382i	−0.979456	−	0.201657i	$-0.935368\pi$
$491$	−2.49897e7	+	5.18917e7i	−0.211114	+	0.438382i	0.768342	+	0.640039i	$0.221082\pi$
$492$	−1.15558e8	−	9.21544e7i	−0.970297	−	0.773786i
$493$	4.39527e7	−	3.50511e7i	0.366813	−	0.292524i
$494$	−3.39270e7	−	1.63384e7i	−0.281427	−	0.135528i
$495$	3.56144e7	−	7.39541e7i	0.293637	−	0.609743i
$496$	9.23238e6	+	1.15770e7i	0.0756604	+	0.0948752i
$497$	7.06746e7	−	8.86231e7i	0.575697	−	0.721901i
$498$	−3.24985e8	−	1.56505e8i	−2.63133	−	1.26718i
$499$	−1.52013e8	+	3.46960e7i	−1.22343	+	0.279240i	−0.784983	−	0.619517i	$-0.787329\pi$
$499$	−1.52013e8	+	3.46960e7i	−1.22343	+	0.279240i	−0.438447	+	0.898757i	$0.644471\pi$
$500$	−7.57794e7	+	1.72961e7i	−0.606235	+	0.138369i
$501$	9.58535e7	+	7.64406e7i	0.762245	+	0.607870i
$502$	−4.05304e7	−	8.41622e7i	−0.320383	−	0.665282i
$503$	−7.74365e7	−	1.76744e7i	−0.608473	−	0.138880i	−0.0928279	−	0.995682i	$-0.529591\pi$
$503$	−7.74365e7	−	1.76744e7i	−0.608473	−	0.138880i	−0.515645	+	0.856802i	$0.672448\pi$
$504$	−4.25950e7	+	2.05127e7i	−0.332711	+	0.160225i
$505$	−9.94391e7	+	7.93001e7i	−0.772117	+	0.615743i
$506$	2.37288e8	−	5.41594e7i	1.83157	−	0.418045i
$507$	1.07515e8	−	8.57405e7i	0.824985	−	0.657904i
$508$	−1.17460e7	+	5.14628e7i	−0.0895984	+	0.392556i
$509$	−2.18946e8			−1.66029			−0.830146	−	0.557546i	$-0.811743\pi$
$509$	−2.18946e8			−1.66029			−0.830146	+	0.557546i	$0.811743\pi$
$510$			1.30551e8i			0.984171i
$511$	3.31688e7	−	1.45322e8i	0.248581	−	1.08910i
$512$	6.43849e7	+	5.13453e7i	0.479705	+	0.382552i
$513$	2.84879e7	+	1.37191e7i	0.211013	+	0.101618i
$514$	−3.59430e7	+	1.73093e7i	−0.264683	+	0.127464i
$515$			2.78529e7i			0.203915i
$516$	4.36612e7	−	9.26801e7i	0.317795	−	0.674586i
$517$	1.29949e8			0.940375
$518$	−4.71406e7	−	9.78884e7i	−0.339161	−	0.704275i
$519$	1.00466e8	−	2.08620e8i	0.718649	−	1.49229i
$520$	1.55605e7	−	1.95123e7i	0.110666	−	0.138771i
$521$	5.71618e7	+	1.30468e7i	0.404197	+	0.0922553i	0.419786	−	0.907623i	$-0.362105\pi$
$521$	5.71618e7	+	1.30468e7i	0.404197	+	0.0922553i	−0.0155890	+	0.999878i	$0.504962\pi$
$522$	7.30158e7			0.513340
$523$		−	9.26923e7i		−	0.647946i	−0.946066	−	0.323973i	$-0.894981\pi$
$523$		−	9.26923e7i		−	0.647946i	0.946066	−	0.323973i	$-0.105019\pi$
$524$	9.65046e7	+	2.20265e7i	0.670740	+	0.153092i
$525$	−4.85006e7	−	6.08179e7i	−0.335173	−	0.420294i
$526$	6.44516e7	+	2.82381e8i	0.442870	+	1.94034i
$527$	7.00362e6	+	8.78226e6i	0.0478510	+	0.0600032i
$528$	−1.32610e8	−	2.75368e8i	−0.900899	−	1.87074i
$529$	−1.17995e7	+	5.16970e7i	−0.0797071	+	0.349219i
$530$	2.08505e8	−	1.00411e8i	1.40052	−	0.674453i
$531$	1.17425e7	−	1.47246e7i	0.0784291	−	0.0983470i
$532$	−1.11424e7	−	4.88182e7i	−0.0740023	−	0.324225i
$533$	2.42778e7	+	1.06368e8i	0.160335	+	0.702473i
$534$	−1.84775e8	+	3.83688e8i	−1.21344	+	2.51974i
$535$	−5.65699e7	−	4.51130e7i	−0.369423	−	0.294605i
$536$	−1.46476e7	+	1.16811e7i	−0.0951200	+	0.0758556i
$537$	−8.49853e7	−	4.09268e7i	−0.548809	−	0.264292i
$538$	1.13967e8	−	2.36655e8i	0.731868	−	1.51974i
$539$	1.80045e6	+	2.25769e6i	0.0114978	+	0.0144178i
$540$	1.76217e7	−	2.20969e7i	0.111909	−	0.140330i
$541$	1.43879e8	+	6.92886e7i	0.908670	+	0.437593i	0.829013	−	0.559230i	$-0.188903\pi$
$541$	1.43879e8	+	6.92886e7i	0.908670	+	0.437593i	0.0796577	+	0.996822i	$0.474617\pi$
$542$	2.99806e8	−	6.84289e7i	1.88297	−	0.429775i
$543$	−2.07942e8	+	4.74614e7i	−1.29880	+	0.296443i
$544$	1.01764e8	+	8.11537e7i	0.632114	+	0.504094i
$545$	5.58666e7	+	1.16008e8i	0.345114	+	0.716637i
$546$	−1.12741e8	−	2.57324e7i	−0.692633	−	0.158089i
$547$	7.79784e7	−	3.75524e7i	0.476444	−	0.229443i	−0.180220	−	0.983626i	$-0.557681\pi$
$547$	7.79784e7	−	3.75524e7i	0.476444	−	0.229443i	0.656664	+	0.754183i	$0.271967\pi$
$548$	−1.33368e8	+	1.06357e8i	−0.810419	+	0.646288i
$549$	1.24163e8	−	2.83393e7i	0.750368	−	0.171266i
$550$	8.61869e7	−	6.87318e7i	0.518028	−	0.413113i
$551$	1.27596e7	−	5.59037e7i	0.0762753	−	0.334184i
$552$	1.35983e8			0.808476
$553$			1.19911e7i			0.0709063i
$554$	7.07846e7	−	3.10127e8i	0.416303	−	1.82394i
$555$	8.23984e7	+	6.57106e7i	0.481992	+	0.384376i
$556$	−7.00695e7	−	3.37437e7i	−0.407666	−	0.196322i
$557$	−1.03383e8	+	4.97865e7i	−0.598249	+	0.288102i	−0.708398	−	0.705813i	$-0.750582\pi$
$557$	−1.03383e8	+	4.97865e7i	−0.598249	+	0.288102i	0.110148	+	0.993915i	$0.464867\pi$
$558$			1.45894e7i			0.0839721i
$559$	−6.78525e7	+	3.33929e7i	−0.388446	+	0.191170i
$560$	1.68927e8			0.961909
$561$	−1.00597e8	−	2.08893e8i	−0.569768	−	1.18314i
$562$	−1.78179e8	+	3.69994e8i	−1.00380	+	2.08442i
$563$	6.29302e7	−	7.89120e7i	0.352642	−	0.442199i	−0.573596	−	0.819138i	$-0.694452\pi$
$563$	6.29302e7	−	7.89120e7i	0.352642	−	0.442199i	0.926238	+	0.376939i	$0.123024\pi$
$564$	−9.54631e7	−	2.17888e7i	−0.532106	−	0.121450i
$565$	1.43174e6			0.00793816
$566$		−	2.86915e8i		−	1.58235i
$567$	2.17515e8	+	4.96463e7i	1.19327	+	0.272357i
$568$	5.59570e7	+	7.01678e7i	0.305358	+	0.382907i
$569$	−7.50086e7	−	3.28634e8i	−0.407169	−	1.78392i	−0.597145	−	0.802133i	$-0.703698\pi$
$569$	−7.50086e7	−	3.28634e8i	−0.407169	−	1.78392i	0.189976	−	0.981789i	$-0.439159\pi$
$570$	8.30244e7	+	1.04109e8i	0.448313	+	0.562166i
$571$	−9.86820e7	−	2.04915e8i	−0.530066	−	1.10069i	−0.978380	−	0.206817i	$-0.933690\pi$
$571$	−9.86820e7	−	2.04915e8i	−0.530066	−	1.10069i	0.448314	−	0.893876i	$-0.352025\pi$
$572$	1.33017e7	−	5.82785e7i	0.0710753	−	0.311401i
$573$	−2.85059e8	+	1.37277e8i	−1.51520	+	0.729684i
$574$	−2.47984e8	+	3.10963e8i	−1.31126	+	1.64427i
$575$	2.02641e7	+	8.87826e7i	0.106592	+	0.467008i
$576$	1.29480e6	+	5.67288e6i	0.00677540	+	0.0296850i
$577$	−1.18363e7	+	2.45784e7i	−0.0616156	+	0.127946i	−0.929503	−	0.368816i	$-0.879763\pi$
$577$	−1.18363e7	+	2.45784e7i	−0.0616156	+	0.127946i	0.867887	+	0.496762i	$0.165478\pi$
$578$	−7.20791e7	−	5.74811e7i	−0.373272	−	0.297675i
$579$	3.35787e8	−	2.67781e8i	1.72993	−	1.37957i
$580$	−4.61791e7	−	2.22387e7i	−0.236680	−	0.113979i
$581$	−1.53622e8	+	3.18999e8i	−0.783293	+	1.62652i
$582$	−7.41575e7	−	9.29905e7i	−0.376172	−	0.471704i
$583$	−2.56252e8	+	3.21330e8i	−1.29319	+	1.62161i
$584$	1.06331e8	+	5.12063e7i	0.533853	+	0.257090i
$585$	4.45110e7	−	1.01594e7i	0.222331	−	0.0507456i
$586$	−1.26940e8	+	2.89732e7i	−0.630819	+	0.143980i
$587$	8.67493e7	+	6.91803e7i	0.428896	+	0.342033i	0.814025	−	0.580830i	$-0.197272\pi$
$587$	8.67493e7	+	6.91803e7i	0.428896	+	0.342033i	−0.385129	+	0.922863i	$0.625843\pi$
$588$	−944096.	−	1.96043e6i	−0.00464391	−	0.00964318i
$589$	1.11702e7	+	2.54953e6i	0.0546657	+	0.0124771i
$590$	−3.26545e7	+	1.57256e7i	−0.158996	+	0.0765685i
$591$	5.62360e7	−	4.48467e7i	0.272428	−	0.217254i
$592$	1.55716e8	−	3.55411e7i	0.750529	−	0.171303i
$593$	2.01265e8	−	1.60504e8i	0.965173	−	0.769699i	−0.00795448	−	0.999968i	$-0.502532\pi$
$593$	2.01265e8	−	1.60504e8i	0.965173	−	0.769699i	0.973127	+	0.230269i	$0.0739606\pi$
$594$	−3.06199e7	+	1.34155e8i	−0.146098	+	0.640098i
$595$	1.28146e8			0.608353
$596$		−	1.95142e8i		−	0.921746i
$597$	2.16853e7	−	9.50097e7i	0.101916	−	0.446524i
$598$	1.05842e8	+	8.44064e7i	0.494944	+	0.394704i
$599$	−6.79874e7	−	3.27410e7i	−0.316335	−	0.152339i	0.268978	−	0.963146i	$-0.413314\pi$
$599$	−6.79874e7	−	3.27410e7i	−0.316335	−	0.152339i	−0.585313	+	0.810807i	$0.699028\pi$
$600$	5.54905e7	−	2.67228e7i	0.256901	−	0.123717i
$601$			2.98650e8i			1.37575i	0.725831	+	0.687873i	$0.241456\pi$
$601$			2.98650e8i			1.37575i	−0.725831	+	0.687873i	$0.758544\pi$
$602$	−2.49399e8	−	1.17491e8i	−1.14316	−	0.538536i
$603$	−3.42731e7			−0.156315
$604$	7.74166e7	+	1.60757e8i	0.351336	+	0.729558i
$605$	4.79819e7	−	9.96354e7i	0.216676	−	0.449933i
$606$	−2.90924e8	+	3.64807e8i	−1.30726	+	1.63925i
$607$	−1.88308e8	−	4.29800e7i	−0.841980	−	0.192176i	−0.220285	−	0.975436i	$-0.570699\pi$
$607$	−1.88308e8	−	4.29800e7i	−0.841980	−	0.192176i	−0.621695	+	0.783259i	$0.713556\pi$
$608$	1.32762e8			0.590695
$609$		−	1.76092e8i		−	0.779630i
$610$	−2.38942e8	−	5.45369e7i	−1.05270	−	0.240271i
$611$	4.50656e7	+	5.65104e7i	0.197570	+	0.247745i
$612$	1.58226e7	+	6.93232e7i	0.0690276	+	0.302430i
$613$	−1.23278e8	−	1.54586e8i	−0.535187	−	0.671104i	0.438569	−	0.898698i	$-0.355486\pi$
$613$	−1.23278e8	−	1.54586e8i	−0.535187	−	0.671104i	−0.973756	+	0.227594i	$0.926914\pi$
$614$	−8.43077e7	−	1.75067e8i	−0.364219	−	0.756308i
$615$	8.58519e7	−	3.76142e8i	0.369084	−	1.61706i
$616$	−1.45577e8	+	7.01061e7i	−0.622802	+	0.299926i
$617$	−1.16800e8	+	1.46463e8i	−0.497265	+	0.623551i	−0.965610	−	0.259995i	$-0.916279\pi$
$617$	−1.16800e8	+	1.46463e8i	−0.497265	+	0.623551i	0.468345	+	0.883546i	$0.344851\pi$
$618$	2.27377e7	+	9.96204e7i	0.0963344	+	0.422069i
$619$	5.90669e7	+	2.58789e8i	0.249042	+	1.09112i	0.932510	+	0.361143i	$0.117613\pi$
$619$	5.90669e7	+	2.58789e8i	0.249042	+	1.09112i	−0.683469	+	0.729980i	$0.739529\pi$
$620$	4.44354e6	−	9.22712e6i	0.0186447	−	0.0387160i
$621$	−8.88739e7	−	7.08745e7i	−0.371107	−	0.295948i
$622$	2.22652e8	−	1.77559e8i	0.925243	−	0.737857i
$623$	3.76621e8	+	1.81371e8i	1.55754	+	0.750073i
$624$	7.37600e7	−	1.53164e8i	0.303576	−	0.630381i
$625$	−6.39367e7	−	8.01740e7i	−0.261885	−	0.328393i
$626$	−1.68688e8	+	2.11528e8i	−0.687639	+	0.862273i
$627$	−2.13068e8	−	1.02608e8i	−0.864402	−	0.416274i
$628$	1.45911e8	−	3.33032e7i	0.589126	−	0.134464i
$629$	1.18125e8	−	2.69612e7i	0.474667	−	0.108340i
$630$	1.30126e8	+	1.03772e8i	0.520407	+	0.415010i
$631$	−4.93297e7	−	1.02434e8i	−0.196345	−	0.407716i	0.779430	−	0.626489i	$-0.215509\pi$
$631$	−4.93297e7	−	1.02434e8i	−0.196345	−	0.407716i	−0.975776	+	0.218774i	$0.929794\pi$
$632$	−9.25601e6	−	2.11262e6i	−0.0366668	−	0.00836895i
$633$	−2.76224e8	+	1.33022e8i	−1.08906	+	0.524462i
$634$	−2.79145e8	+	2.22610e8i	−1.09537	+	0.873530i
$635$	−1.34334e8	+	3.06608e7i	−0.524644	+	0.119746i
$636$	2.42126e8	−	1.93089e8i	0.941175	−	0.750562i
$637$	−357409.	+	1.56591e6i	−0.00138276	+	0.00605828i
$638$	2.49546e8			0.960922
$639$			1.64182e8i			0.629250i
$640$	−4.34945e7	+	1.90562e8i	−0.165918	+	0.726935i
$641$	5.22181e7	+	4.16426e7i	0.198266	+	0.158111i	0.717590	−	0.696465i	$-0.245245\pi$
$641$	5.22181e7	+	4.16426e7i	0.198266	+	0.158111i	−0.519325	+	0.854577i	$0.673816\pi$
$642$	−2.39159e8	−	1.15173e8i	−0.903820	−	0.435257i
$643$	1.31732e8	−	6.34387e7i	0.495516	−	0.238628i	−0.169398	−	0.985548i	$-0.554182\pi$
$643$	1.31732e8	−	6.34387e7i	0.495516	−	0.238628i	0.664914	+	0.746920i	$0.268468\pi$
$644$			1.80019e8i			0.674003i
$645$	2.67415e8	−	2.28400e6i	0.996569	−	0.00851172i
$646$	1.53087e8			0.567861
$647$	1.10830e8	+	2.30141e8i	0.409208	+	0.849729i	0.999107	+	0.0422518i	$0.0134532\pi$
$647$	1.10830e8	+	2.30141e8i	0.409208	+	0.849729i	−0.589899	+	0.807477i	$0.700833\pi$
$648$	−7.66444e7	+	1.59154e8i	−0.281680	+	0.584914i
$649$	4.01323e7	−	5.03243e7i	0.146812	−	0.184096i
$650$	5.97783e7	+	1.36440e7i	0.217672	+	0.0496823i
$651$	3.51853e7			0.127532
$652$		−	1.36473e7i		−	0.0492383i
$653$	−2.64151e8	−	6.02908e7i	−0.948666	−	0.216527i	−0.279925	−	0.960022i	$-0.590309\pi$
$653$	−2.64151e8	−	6.02908e7i	−0.948666	−	0.216527i	−0.668741	+	0.743495i	$0.733167\pi$
$654$	2.94519e8	+	3.69316e8i	1.05288	+	1.32027i
$655$	5.74961e7	+	2.51907e8i	0.204604	+	0.896430i
$656$	−3.64555e8	−	4.57137e8i	−1.29137	−	1.61933i
$657$	9.36752e7	+	1.94519e8i	0.330315	+	0.685907i
$658$	−5.86330e7	+	2.56888e8i	−0.205809	+	0.901709i
$659$	3.04948e8	−	1.46855e8i	1.06554	−	0.513136i	0.182872	−	0.983137i	$-0.441461\pi$
$659$	3.04948e8	−	1.46855e8i	1.06554	−	0.513136i	0.882666	+	0.470001i	$0.155746\pi$
$660$	−1.31797e8	+	1.65268e8i	−0.458431	+	0.574854i
$661$	−4.08103e7	−	1.78801e8i	−0.141307	−	0.619108i	−0.995132	−	0.0985479i	$-0.968580\pi$
$661$	−4.08103e7	−	1.78801e8i	−0.141307	−	0.619108i	0.853825	−	0.520560i	$-0.174277\pi$
$662$	6.41035e7	+	2.80856e8i	0.220957	+	0.968076i
$663$	5.59538e7	−	1.16189e8i	0.191994	−	0.398681i
$664$	−2.19171e8	−	1.74783e8i	−0.748651	−	0.597029i
$665$	1.02192e8	−	8.14951e7i	0.347496	−	0.277119i
$666$	1.41783e8	+	6.82790e7i	0.479955	+	0.231134i
$667$	−8.94440e7	+	1.85732e8i	−0.301421	+	0.625907i
$668$	−8.01217e7	−	1.00469e8i	−0.268795	−	0.337058i
$669$	−3.36239e8	+	4.21630e8i	−1.12297	+	1.40816i
$670$	5.94244e7	+	2.86173e7i	0.197579	+	0.0951489i
$671$	4.24350e8	−	9.68551e7i	1.40461	−	0.320594i
$672$	3.97484e8	−	9.07231e7i	1.30982	−	0.298958i
$673$	−1.29728e6	−	1.03454e6i	−0.00425586	−	0.00339394i	0.621360	−	0.783526i	$-0.286581\pi$
$673$	−1.29728e6	−	1.03454e6i	−0.00425586	−	0.00339394i	−0.625615	+	0.780132i	$0.715152\pi$
$674$	−2.77500e8	−	5.76235e8i	−0.906325	−	1.88200i
$675$	−5.01947e7	−	1.14566e7i	−0.163210	−	0.0372516i
$676$	−1.29865e8	+	6.25398e7i	−0.420390	+	0.202449i
$677$	1.86734e8	−	1.48915e8i	0.601807	−	0.479925i	−0.274560	−	0.961570i	$-0.588532\pi$
$677$	1.86734e8	−	1.48915e8i	0.601807	−	0.479925i	0.876366	+	0.481645i	$0.159961\pi$
$678$	5.12086e6	−	1.16880e6i	0.0164306	−	0.00375018i
$679$	−9.12776e7	+	7.27915e7i	−0.291578	+	0.232526i
$680$	−2.25771e7	+	9.89168e7i	−0.0718029	+	0.314589i
$681$	7.81495e7			0.247448
$682$			4.98621e7i			0.157187i
$683$	−6.53993e7	+	2.86533e8i	−0.205263	+	0.899317i	0.762407	+	0.647098i	$0.224017\pi$
$683$	−6.53993e7	+	2.86533e8i	−0.205263	+	0.899317i	−0.967670	+	0.252219i	$0.918840\pi$
$684$	5.67041e7	+	4.52200e7i	0.177193	+	0.141307i
$685$	−4.01181e8	−	1.93199e8i	−1.24816	−	0.601080i
$686$	3.62270e8	−	1.74460e8i	1.12217	−	0.540410i
$687$			4.19931e6i			0.0129511i
$688$	2.49973e8	−	3.19008e8i	0.767589	−	0.979573i
$689$	−2.28603e8			−0.698913
$690$	−2.07711e8	−	4.31317e8i	−0.632284	−	1.31295i
$691$	−2.03608e8	+	4.22797e8i	−0.617109	+	1.28144i	0.324867	+	0.945760i	$0.394680\pi$
$691$	−2.03608e8	+	4.22797e8i	−0.617109	+	1.28144i	−0.941976	+	0.335680i	$0.891034\pi$
$692$	−1.51322e8	+	1.89751e8i	−0.456649	+	0.572620i
$693$	−2.88175e8	−	6.57740e7i	−0.865877	−	0.197631i
$694$	4.74156e8			1.41854
$695$		−	2.03007e8i		−	0.604724i
$696$	1.35926e8	+	3.10243e7i	0.403159	+	0.0920183i
$697$	−2.76549e8	−	3.46781e8i	−0.816720	−	1.02413i
$698$	−1.49602e8	−	6.55447e8i	−0.439916	−	1.92740i
$699$	−2.49974e7	−	3.13458e7i	−0.0731920	−	0.0917798i
$700$	3.53767e7	+	7.34605e7i	0.103139	+	0.214171i
$701$	−1.60840e7	+	7.04688e7i	−0.0466919	+	0.204570i	−0.992893	−	0.119008i	$-0.962029\pi$
$701$	−1.60840e7	+	7.04688e7i	−0.0466919	+	0.204570i	0.946201	+	0.323578i	$0.104886\pi$
$702$	−6.89582e7	+	3.32085e7i	−0.199331	+	0.0959927i
$703$	7.70537e7	−	9.66223e7i	0.221783	−	0.278107i
$704$	4.42523e6	+	1.93882e7i	0.0126829	+	0.0555673i
$705$	−5.68757e7	−	2.49189e8i	−0.162315	−	0.711149i
$706$	3.19106e8	−	6.62631e8i	0.906820	−	1.88303i
$707$	3.58087e8	+	2.85565e8i	1.01328	+	0.808065i
$708$	−3.79200e7	+	3.02402e7i	−0.106849	+	0.0852089i
$709$	−2.89816e8	−	1.39568e8i	−0.813174	−	0.391604i	−0.0193963	−	0.999812i	$-0.506174\pi$
$709$	−2.89816e8	−	1.39568e8i	−0.813174	−	0.391604i	−0.793778	+	0.608208i	$0.791889\pi$
$710$	1.37088e8	−	2.84667e8i	0.383023	−	0.795356i
$711$	−1.08288e7	−	1.35789e7i	−0.0301282	−	0.0377795i
$712$	−2.06355e8	+	2.58761e8i	−0.571709	+	0.716900i
$713$	−3.71115e7	−	1.78719e7i	−0.102386	−	0.0493064i
$714$	4.58337e8	−	1.04612e8i	1.25919	−	0.287401i
$715$	1.52125e8	−	3.47216e7i	0.416182	−	0.0949907i
$716$	7.72989e7	+	6.16438e7i	0.210588	+	0.167939i
$717$	2.82750e8	+	5.87137e8i	0.767089	+	1.59288i
$718$	4.15028e8	+	9.47273e7i	1.12125	+	0.255919i
$719$	4.51348e7	−	2.17358e7i	0.121430	−	0.0584775i	−0.372183	−	0.928160i	$-0.621390\pi$
$719$	4.51348e7	−	2.17358e7i	0.121430	−	0.0584775i	0.493612	+	0.869682i	$0.335676\pi$
$720$	−1.91295e8	+	1.52552e8i	−0.512514	+	0.408716i
$721$	9.77854e7	−	2.23189e7i	0.260896	−	0.0595479i
$722$	−2.47117e8	+	1.97069e8i	−0.656584	+	0.523608i
$723$	−1.53929e8	+	6.74405e8i	−0.407291	+	1.78446i
$724$	2.23561e8			0.589088
$725$			9.33689e7i			0.245013i
$726$	9.02776e7	−	3.95532e8i	0.235923	−	1.03365i
$727$	4.26592e7	+	3.40196e7i	0.111022	+	0.0885371i	0.677427	−	0.735590i	$-0.263095\pi$
$727$	4.26592e7	+	3.40196e7i	0.111022	+	0.0885371i	−0.566405	+	0.824127i	$0.691666\pi$
$728$	−8.09720e7	−	3.89941e7i	−0.209865	−	0.101066i
$729$	−1.06534e8	+	5.13040e7i	−0.274982	+	0.132424i
$730$		−	4.15482e8i		−	1.06803i
$731$	1.89628e8	−	2.41997e8i	0.485457	−	0.619525i
$732$	−3.27976e8			−0.836198
$733$	−2.97110e7	−	6.16956e7i	−0.0754407	−	0.156654i	0.859837	−	0.510568i	$-0.170565\pi$
$733$	−2.97110e7	−	6.16956e7i	−0.0754407	−	0.156654i	−0.935278	+	0.353914i	$0.884851\pi$
$734$	6.12082e7	−	1.27100e8i	0.154782	−	0.321409i
$735$	3.54131e6	−	4.44067e6i	0.00891872	−	0.0111837i
$736$	−4.65326e8	−	1.06208e8i	−1.16714	−	0.266392i
$737$	−1.17135e8			−0.292607
$738$		−	5.76086e8i		−	1.43324i
$739$	−3.85450e8	−	8.79764e7i	−0.955068	−	0.217988i	−0.283535	−	0.958962i	$-0.591507\pi$
$739$	−3.85450e8	−	8.79764e7i	−0.955068	−	0.217988i	−0.671534	+	0.740974i	$0.734364\pi$
$740$	−6.88749e7	−	8.63665e7i	−0.169968	−	0.213133i
$741$	−2.92700e7	−	1.28240e8i	−0.0719395	−	0.315188i
$742$	−5.19597e8	−	6.51554e8i	−1.27190	−	1.59492i
$743$	3.06728e8	+	6.36927e8i	0.747802	+	1.55283i	0.830987	+	0.556292i	$0.187777\pi$
$743$	3.06728e8	+	6.36927e8i	0.747802	+	1.55283i	−0.0831847	+	0.996534i	$0.526509\pi$
$744$	−6.19902e6	+	2.71597e7i	−0.0150523	+	0.0659486i
$745$	4.58936e8	−	2.21012e8i	1.10990	−	0.534499i
$746$	−3.22374e8	+	4.04244e8i	−0.776504	+	0.973705i
$747$	−1.14115e8	−	4.99970e8i	−0.273767	−	1.19945i
$748$	5.40767e7	+	2.36926e8i	0.129213	+	0.566118i
$749$	−1.13052e8	+	2.34754e8i	−0.269049	+	0.558685i
$750$	−5.81955e8	−	4.64094e8i	−1.37945	−	1.10007i
$751$	5.64777e8	−	4.50395e8i	1.33339	−	1.06334i	0.341019	−	0.940056i	$-0.389228\pi$
$751$	5.64777e8	−	4.50395e8i	1.33339	−	1.06334i	0.992371	−	0.123287i	$-0.0393435\pi$
$752$	−3.48996e8	−	1.68067e8i	−0.820666	−	0.395212i
$753$	1.41578e8	−	2.93990e8i	0.331597	−	0.688569i
$754$	8.65411e7	+	1.08519e8i	0.201887	+	0.253158i
$755$	−2.90391e8	+	3.64138e8i	−0.674748	+	0.846107i
$756$	−9.16979e7	−	4.41594e7i	−0.212224	−	0.102202i
$757$	4.50438e8	−	1.02810e8i	1.03836	−	0.236999i	0.330835	−	0.943689i	$-0.392670\pi$
$757$	4.50438e8	−	1.02810e8i	1.03836	−	0.236999i	0.707523	+	0.706690i	$0.249812\pi$
$758$	9.61798e7	−	2.19524e7i	0.220839	−	0.0504051i
$759$	6.64709e8	+	5.30088e8i	1.52022	+	1.21233i
$760$	4.49021e7	+	9.32401e7i	0.102288	+	0.212404i
$761$	−5.99466e8	−	1.36824e8i	−1.36022	−	0.310462i	−0.520679	−	0.853752i	$-0.674321\pi$
$761$	−5.99466e8	−	1.36824e8i	−1.36022	−	0.310462i	−0.839545	+	0.543290i	$0.817178\pi$
$762$	−4.55437e8	+	2.19327e8i	−1.02935	+	0.495709i
$763$	3.62513e8	−	2.89094e8i	0.816112	−	0.650827i
$764$	3.23314e8	−	7.37942e7i	0.725010	−	0.165479i
$765$	−1.45115e8	+	1.15725e8i	−0.324136	+	0.258490i
$766$	−3.12220e7	+	1.36793e8i	−0.0694664	+	0.304352i
$767$	3.58020e7			0.0793454
$768$			7.43177e8i			1.64062i
$769$	8.89844e7	−	3.89866e8i	0.195675	−	0.857307i	−0.777800	−	0.628512i	$-0.783664\pi$
$769$	8.89844e7	−	3.89866e8i	0.195675	−	0.857307i	0.973475	−	0.228795i	$-0.0734786\pi$
$770$	4.44731e8	+	3.54661e8i	0.974149	+	0.776858i
$771$	−1.25554e8	−	6.04635e7i	−0.273947	−	0.131926i
$772$	−4.05589e8	+	1.95321e8i	−0.881524	+	0.424520i
$773$			4.68240e8i			1.01375i	0.862020	+	0.506874i	$0.169199\pi$
$773$			4.68240e8i			1.01375i	−0.862020	+	0.506874i	$0.830801\pi$
$774$	3.88525e8	−	9.21765e7i	0.837908	−	0.198791i
$775$	−1.86562e7			−0.0400791
$776$	−4.01066e7	−	8.32821e7i	−0.0858283	−	0.178224i
$777$	1.64668e8	−	3.41937e8i	0.351032	−	0.728926i
$778$	−9.77786e7	+	1.22611e8i	−0.207637	+	0.260369i
$779$	−4.41073e8	−	1.00672e8i	−0.933035	−	0.212959i
$780$	−1.17576e8			−0.247762
$781$			5.61124e8i			1.17789i
$782$	−5.36565e8	−	1.22467e8i	−1.12202	−	0.256094i
$783$	−7.26670e7	−	9.11215e7i	−0.151374	−	0.189817i
$784$	−1.91540e6	−	8.39193e6i	−0.00397477	−	0.0174146i
$785$	2.43577e8	+	3.05436e8i	0.503533	+	0.631410i
$786$	4.11288e8	+	8.54049e8i	0.846991	+	1.75880i
$787$	−2.56481e6	+	1.12372e7i	−0.00526176	+	0.0230533i	−0.977491	−	0.210979i	$-0.932335\pi$
$787$	−2.56481e6	+	1.12372e7i	−0.00526176	+	0.0230533i	0.972229	+	0.234032i	$0.0751921\pi$
$788$	−6.79261e7	+	3.27115e7i	−0.138822	+	0.0668532i
$789$	−6.30822e8	+	7.91026e8i	−1.28433	+	1.61050i
$790$	7.43745e6	+	3.25856e7i	0.0150849	+	0.0660913i
$791$	−1.14727e6	−	5.02653e6i	−0.00231813	−	0.0101564i
$792$	1.01542e8	−	2.10855e8i	0.204396	−	0.424432i
$793$	1.89281e8	+	1.50947e8i	0.379567	+	0.302694i
$794$	−4.32097e8	+	3.44586e8i	−0.863216	+	0.688392i
$795$	7.28335e8	+	3.50748e8i	1.44954	+	0.698061i
$796$	−4.43195e7	+	9.20304e7i	−0.0878731	+	0.182470i
$797$	2.60217e7	+	3.26302e7i	0.0513997	+	0.0644532i	0.806867	−	0.590733i	$-0.201161\pi$
$797$	2.60217e7	+	3.26302e7i	0.0513997	+	0.0644532i	−0.755467	+	0.655187i	$0.772590\pi$
$798$	2.98976e8	−	3.74904e8i	0.588339	−	0.737754i
$799$	−2.64745e8	−	1.27495e8i	−0.519025	−	0.249949i
$800$	−2.10757e8	+	4.81039e7i	−0.411634	+	0.0939529i
$801$	−5.90281e8	+	1.34728e8i	−1.14858	+	0.262156i
$802$	8.47036e8	+	6.75489e8i	1.64202	+	1.30947i
$803$	3.20153e8	+	6.64805e8i	0.618317	+	1.28395i
$804$	8.60499e7	+	1.96403e7i	0.165570	+	0.0377903i
$805$	−4.23372e8	+	2.03885e8i	−0.811585	+	0.390839i
$806$	−2.16834e7	+	1.72919e7i	−0.0414116	+	0.0330246i
$807$	8.94528e8	−	2.04170e8i	1.70205	−	0.388483i
$808$	−2.83517e8	+	2.26097e8i	−0.537459	+	0.428609i
$809$	1.86079e8	−	8.15264e8i	0.351440	−	1.53976i	−0.422419	−	0.906401i	$-0.638819\pi$
$809$	1.86079e8	−	8.15264e8i	0.351440	−	1.53976i	0.773859	−	0.633358i	$-0.218324\pi$
$810$	6.21884e8			1.17018
$811$		−	7.97953e8i		−	1.49594i	−0.663731	−	0.747971i	$-0.731028\pi$
$811$		−	7.97953e8i		−	1.49594i	0.663731	−	0.747971i	$-0.268972\pi$
$812$	−4.10712e7	+	1.79945e8i	−0.0767130	+	0.336102i
$813$	8.39841e8	+	6.69750e8i	1.56288	+	1.24635i
$814$	4.84570e8	+	2.33357e8i	0.898428	+	0.432660i
$815$	3.20958e7	−	1.54565e7i	0.0592891	−	0.0285521i
$816$			6.91115e8i			1.27198i
$817$	−2.67827e6	−	3.13578e8i	−0.00491121	−	0.575014i
$818$	−8.46855e7			−0.154721
$819$	−7.13345e7	−	1.48128e8i	−0.129852	−	0.269640i
$820$	−1.75460e8	+	3.64347e8i	−0.318227	+	0.660805i
$821$	−7.82389e7	+	9.81085e7i	−0.141382	+	0.177287i	−0.847481	−	0.530826i	$-0.821882\pi$
$821$	−7.82389e7	+	9.81085e7i	−0.141382	+	0.177287i	0.706099	+	0.708113i	$0.250453\pi$
$822$	−1.59261e9	−	3.63502e8i	−2.86743	−	0.654473i
$823$	−3.35436e8			−0.601742			−0.300871	−	0.953665i	$-0.597277\pi$
$823$	−3.35436e8			−0.601742			−0.300871	+	0.953665i	$0.597277\pi$
$824$			7.94132e7i			0.141942i
$825$	3.75419e8	+	8.56868e7i	0.668581	+	0.152599i
$826$	8.13754e7	+	1.02042e8i	0.144395	+	0.181066i
$827$	−2.21252e8	−	9.69366e8i	−0.391174	−	1.71384i	−0.660526	−	0.750803i	$-0.729667\pi$
$827$	−2.21252e8	−	9.69366e8i	−0.391174	−	1.71384i	0.269353	−	0.963042i	$-0.413190\pi$
$828$	−1.62570e8	−	2.03857e8i	−0.286385	−	0.359115i
$829$	−1.93507e8	−	4.01822e8i	−0.339652	−	0.705294i	0.659261	−	0.751914i	$-0.270869\pi$
$829$	−1.93507e8	−	4.01822e8i	−0.339652	−	0.705294i	−0.998913	+	0.0466204i	$0.985155\pi$
$830$	−2.19605e8	+	9.62154e8i	−0.384069	+	1.68271i
$831$	1.00114e9	−	4.82121e8i	1.74457	−	0.840143i
$832$	−6.89663e6	+	8.64810e6i	−0.0119748	+	0.0150159i
$833$	−1.45301e6	−	6.36606e6i	−0.00251382	−	0.0110138i
$834$	−1.65725e8	−	7.26089e8i	−0.285687	−	1.25167i
$835$	1.45541e8	−	3.02220e8i	0.249993	−	0.519115i
$836$	1.93797e8	+	1.54548e8i	0.331687	+	0.264512i
$837$	1.82071e7	−	1.45197e7i	0.0310503	−	0.0247618i
$838$	1.11330e9	+	5.36138e8i	1.89183	+	0.911055i
$839$	1.91443e8	−	3.97536e8i	0.324156	−	0.673117i	−0.673669	−	0.739033i	$-0.735283\pi$
$839$	1.91443e8	−	3.97536e8i	0.324156	−	0.673117i	0.997825	+	0.0659161i	$0.0209970\pi$
$840$	1.98150e8	+	2.48473e8i	0.334316	+	0.419219i
$841$	2.39085e8	−	2.99803e8i	0.401943	−	0.504020i
$842$	−8.61457e8	−	4.14856e8i	−1.44310	−	0.694962i
$843$	−1.39853e9	+	3.19206e8i	−2.33448	+	0.532829i
$844$	3.13293e8	−	7.15070e7i	0.521102	−	0.118938i
$845$	−2.94163e8	−	2.34587e8i	−0.487549	−	0.388807i
$846$	−1.65591e8	−	3.43853e8i	−0.273480	−	0.567887i
$847$	−3.88246e8	−	8.86147e7i	−0.638936	−	0.145833i
$848$	1.10379e9	−	5.31556e8i	1.81008	−	0.871689i
$849$	7.83576e8	−	6.24881e8i	1.28044	−	1.02111i
$850$	−2.43023e8	+	5.54683e7i	−0.395722	+	0.0903209i
$851$	−3.47366e8	+	2.77015e8i	−0.563636	+	0.449485i
$852$	9.40850e7	−	4.12213e8i	0.152125	−	0.666505i
$853$	2.45309e8			0.395245			0.197622	−	0.980278i	$-0.436678\pi$
$853$	2.45309e8			0.395245			0.197622	+	0.980278i	$0.436678\pi$
$854$			8.82573e8i			1.41702i
$855$	−4.21274e7	+	1.84572e8i	−0.0674010	+	0.295303i
$856$	−1.61290e8	−	1.28624e8i	−0.257150	−	0.205070i
$857$	6.96273e8	+	3.35307e8i	1.10621	+	0.532722i	0.895605	−	0.444850i	$-0.146743\pi$
$857$	6.96273e8	+	3.35307e8i	1.10621	+	0.532722i	0.210603	+	0.977572i	$0.432457\pi$
$858$	5.15755e8	−	2.48375e8i	0.816548	−	0.393229i
$859$			1.13579e7i			0.0179192i	0.999960	+	0.00895961i	$0.00285197\pi$
$859$			1.13579e7i			0.0179192i	−0.999960	+	0.00895961i	$0.997148\pi$
$860$	−2.73798e8	−	6.00371e7i	−0.430463	−	0.0943897i
$861$	−1.38935e9			−2.17671
$862$	−4.45389e8	−	9.24860e8i	−0.695373	−	1.44396i
$863$	−8.43018e7	+	1.75054e8i	−0.131161	+	0.272358i	−0.956198	−	0.292720i	$-0.905440\pi$
$863$	−8.43018e7	+	1.75054e8i	−0.131161	+	0.272358i	0.825037	+	0.565078i	$0.191154\pi$
$864$	1.68246e8	−	2.10973e8i	0.260857	−	0.327104i
$865$	−6.17642e8	−	1.40973e8i	−0.954308	−	0.217815i
$866$	−2.86236e8			−0.440728
$867$		−	3.22041e8i		−	0.494144i
$868$	−3.59550e7	−	8.20650e6i	−0.0549795	−	0.0125487i
$869$	−3.70096e7	−	4.64086e7i	−0.0563969	−	0.0707195i
$870$	−1.09220e8	−	4.78526e8i	−0.165862	−	0.726688i
$871$	−4.06218e7	−	5.09381e7i	−0.0614759	−	0.0770883i
$872$	1.59285e8	+	3.30758e8i	0.240229	+	0.498840i
$873$	3.76283e7	−	1.64860e8i	0.0565550	−	0.247784i
$874$	−5.05772e8	+	2.43567e8i	−0.757566	+	0.364824i
$875$	−4.55545e8	+	5.71235e8i	−0.679997	+	0.852689i
$876$	−1.23722e8	−	5.42060e8i	−0.184049	−	0.806372i
$877$	3.89686e7	+	1.70733e8i	0.0577719	+	0.253115i	0.995565	−	0.0940806i	$-0.0299911\pi$
$877$	3.89686e7	+	1.70733e8i	0.0577719	+	0.253115i	−0.937793	+	0.347196i	$0.887134\pi$
$878$	−6.66780e8	+	1.38458e9i	−0.985143	+	2.04567i
$879$	−3.55593e8	−	2.83576e8i	−0.523585	−	0.417545i
$880$	−6.53787e8	+	5.21378e8i	−0.959375	+	0.765076i
$881$	2.19090e8	+	1.05508e8i	0.320401	+	0.154297i	0.587170	−	0.809463i	$-0.300242\pi$
$881$	2.19090e8	+	1.05508e8i	0.320401	+	0.154297i	−0.266769	+	0.963760i	$0.585956\pi$
$882$	3.67973e6	−	7.64104e6i	0.00536303	−	0.0111365i
$883$	−5.69366e7	−	7.13963e7i	−0.0827008	−	0.103704i	0.738760	−	0.673969i	$-0.235412\pi$
$883$	−5.69366e7	−	7.13963e7i	−0.0827008	−	0.103704i	−0.821461	+	0.570265i	$0.806840\pi$
$884$	−8.42775e7	+	1.05681e8i	−0.121999	+	0.152981i
$885$	−1.14066e8	−	5.49315e7i	−0.164561	−	0.0792486i
$886$	−3.45921e8	+	7.89542e7i	−0.497365	+	0.113520i
$887$	−3.25177e8	+	7.42196e7i	−0.465961	+	0.106353i	−0.449054	−	0.893505i	$-0.648239\pi$
$887$	−3.25177e8	+	7.42196e7i	−0.465961	+	0.106353i	−0.0169067	+	0.999857i	$0.505382\pi$
$888$	2.34931e8	+	1.87351e8i	0.335507	+	0.267558i
$889$	2.15287e8	+	4.47048e8i	0.306416	+	0.636280i
$890$	1.13595e9	+	2.59274e8i	1.61135	+	0.367780i
$891$	−9.95065e8	+	4.79198e8i	−1.40675	+	0.677457i
$892$	4.41935e8	−	3.52431e8i	0.622678	−	0.496569i
$893$	−2.92204e8	+	6.66937e7i	−0.410329	+	0.0936549i
$894$	1.46104e9	−	1.16514e9i	2.04479	−	1.63066i
$895$	−5.74280e7	+	2.51608e8i	−0.0801040	+	0.350959i
$896$	7.03873e8			0.978521
$897$			4.72891e8i			0.655215i
$898$	1.17367e8	−	5.14220e8i	0.162076	−	0.710101i
$899$	−3.30186e7	−	2.63314e7i	−0.0454443	−	0.0362406i
$900$	−1.06401e8	−	5.12401e7i	−0.145955	−	0.0702881i
$901$	8.37325e8	−	4.03235e8i	1.14477	−	0.551294i
$902$		−	1.96888e9i		−	2.68288i
$903$	−2.22302e8	−	9.37006e8i	−0.301912	−	1.27256i
$904$	4.08213e6			0.00552563
$905$	2.53199e8	+	5.25772e8i	0.341598	+	0.709336i
$906$	−7.41365e8	+	1.53946e9i	−0.996890	+	2.07006i
$907$	4.67042e8	−	5.85652e8i	0.625942	−	0.784907i	−0.363225	−	0.931702i	$-0.618324\pi$
$907$	4.67042e8	−	5.85652e8i	0.625942	−	0.784907i	0.989167	+	0.146795i	$0.0468957\pi$
$908$	−7.98592e7	−	1.82273e7i	−0.106676	−	0.0243481i
$909$	−6.63387e8			−0.883233
$910$			3.16393e8i			0.419859i
$911$	−2.08795e8	−	4.76560e7i	−0.276162	−	0.0630322i	0.0821967	−	0.996616i	$-0.473806\pi$
$911$	−2.08795e8	−	4.76560e7i	−0.276162	−	0.0630322i	−0.358359	+	0.933584i	$0.616664\pi$
$912$	4.39517e8	+	5.51136e8i	0.579416	+	0.726565i
$913$	−3.90010e8	−	1.70874e9i	−0.512464	−	2.24525i
$914$	−4.30538e8	−	5.39878e8i	−0.563863	−	0.707061i
$915$	−3.71457e8	−	7.71338e8i	−0.484892	−	1.00689i
$916$	979434.	−	4.29118e6i	0.00127435	−	0.00558329i
$917$	8.38318e8	−	4.03712e8i	1.08718	−	0.523557i
$918$	1.94003e8	−	2.43272e8i	0.250773	−	0.314459i
$919$	2.41489e8	+	1.05803e9i	0.311136	+	1.36318i	0.852649	+	0.522484i	$0.174994\pi$
$919$	2.41489e8	+	1.05803e9i	0.311136	+	1.36318i	−0.541513	+	0.840692i	$0.682148\pi$
$920$	−8.27892e7	−	3.62723e8i	−0.106319	−	0.465813i
$921$	2.94498e8	−	6.11531e8i	0.376967	−	0.782780i
$922$	−5.20331e8	−	4.14950e8i	−0.663876	−	0.529423i
$923$	−2.44014e8	+	1.94595e8i	−0.310320	+	0.247472i
$924$	6.85831e8	+	3.30279e8i	0.869363	+	0.418663i
$925$	−8.73117e7	+	1.81305e8i	−0.110318	+	0.229078i
$926$	2.83248e8	+	3.55182e8i	0.356726	+	0.447320i
$927$	−9.05780e7	+	1.13581e8i	−0.113706	+	0.142583i
$928$	−4.40901e8	−	2.12327e8i	−0.551693	−	0.265681i
$929$	1.18820e9	−	2.71198e8i	1.48197	−	0.338251i	0.596377	−	0.802704i	$-0.296606\pi$
$929$	1.18820e9	−	2.71198e8i	1.48197	−	0.338251i	0.885598	+	0.464453i	$0.153749\pi$
$930$	9.56151e7	−	2.18235e7i	0.118871	−	0.0271316i
$931$	−5.20723e6	−	4.15263e6i	−0.00645294	−	0.00514605i
$932$	1.82333e7	+	3.78618e7i	0.0225225	+	0.0467685i
$933$	9.69843e8	+	2.21360e8i	1.19414	+	0.272555i
$934$	1.14565e9	−	5.51715e8i	1.40608	−	0.677133i
$935$	−4.95958e8	+	3.95513e8i	−0.606750	+	0.483867i
$936$	1.26908e8	−	2.89660e7i	0.154761	−	0.0353232i
$937$	1.06421e9	−	8.48683e8i	1.29363	−	1.03164i	0.296571	−	0.955011i	$-0.404157\pi$
$937$	1.06421e9	−	8.48683e8i	1.29363	−	1.03164i	0.997060	−	0.0766254i	$-0.0244145\pi$
$938$	5.28514e7	−	2.31557e8i	0.0640395	−	0.280576i
$939$	−9.45082e8			−1.14149
$940$			2.67906e8i			0.322551i
$941$	−8.15451e7	+	3.57272e8i	−0.0978653	+	0.428776i	−0.999996	−	0.00268611i	$-0.999145\pi$
$941$	−8.15451e7	+	3.57272e8i	−0.0978653	+	0.428776i	0.902131	+	0.431462i	$0.142002\pi$
$942$	1.12054e9	+	8.93598e8i	1.34052	+	1.06903i
$943$	1.46540e9	+	7.05701e8i	1.74752	+	0.841562i
$944$	−1.72867e8	+	8.32484e7i	−0.205493	+	0.0989600i
$945$		−	2.65670e8i		−	0.314809i
$946$	1.32786e9	−	3.15031e8i	1.56848	−	0.372117i
$947$	−2.62753e8			−0.309383			−0.154692	−	0.987963i	$-0.549438\pi$
$947$	−2.62753e8			−0.309383			−0.154692	+	0.987963i	$0.549438\pi$
$948$	1.94066e7	+	4.02982e7i	0.0227785	+	0.0473000i
$949$	−1.78074e8	+	3.69775e8i	−0.208354	+	0.432652i
$950$	−1.58525e8	+	1.98785e8i	−0.184896	+	0.231853i
$951$	−1.21592e9	−	2.77525e8i	−1.41372	−	0.322672i
$952$	3.65366e8			0.423465
$953$		−	6.41175e7i		−	0.0740795i	−0.999314	−	0.0370398i	$-0.988207\pi$
$953$		−	6.41175e7i		−	0.0740795i	0.999314	−	0.0370398i	$-0.0117928\pi$
$954$	1.17680e9	+	2.68596e8i	1.35537	+	0.309353i
$955$	5.39726e8	+	6.76795e8i	0.619674	+	0.777047i
$956$	−1.51994e8	−	6.65930e8i	−0.173961	−	0.762175i
$957$	5.43494e8	+	6.81520e8i	0.620096	+	0.777576i
$958$	5.39129e8	+	1.11951e9i	0.613191	+	1.27330i
$959$	−3.56806e8	+	1.56327e9i	−0.404554	+	1.77247i
$960$	3.52417e7	−	1.69715e7i	0.0398331	−	0.0191826i
$961$	−5.48088e8	+	6.87281e8i	−0.617562	+	0.774398i
$962$	6.65672e7	+	2.91650e8i	0.0747713	+	0.327595i
$963$	−8.39781e7	−	3.67932e8i	−0.0940345	−	0.411992i
$964$	3.14592e8	−	6.53258e8i	0.351170	−	0.729211i
$965$	−9.18718e8	−	7.32653e8i	−1.02235	−	0.815298i
$966$	−1.34782e9	+	1.07485e9i	−1.49520	+	1.19238i
$967$	1.77791e8	+	8.56194e7i	0.196621	+	0.0946875i	0.529603	−	0.848245i	$-0.322341\pi$
$967$	1.77791e8	+	8.56194e7i	0.196621	+	0.0946875i	−0.332983	+	0.942933i	$0.608055\pi$
$968$	1.36804e8	−	2.84077e8i	0.150825	−	0.313191i
$969$	3.33414e8	+	4.18088e8i	0.366448	+	0.459512i
$970$	−2.02896e8	+	2.54424e8i	−0.222310	+	0.278768i
$971$	−8.24607e8	−	3.97110e8i	−0.900719	−	0.433763i	−0.0745701	−	0.997216i	$-0.523758\pi$
$971$	−8.24607e8	−	3.97110e8i	−0.900719	−	0.433763i	−0.826148	+	0.563453i	$0.809473\pi$
$972$	6.01951e8	−	1.37391e8i	0.655484	−	0.149610i
$973$	−7.12714e8	+	1.62672e8i	−0.773707	+	0.176594i
$974$	−7.58962e8	−	6.05252e8i	−0.821378	−	0.655027i
$975$	9.29307e7	+	1.92973e8i	0.100264	+	0.208201i
$976$	−1.26492e9	−	2.88709e8i	−1.36054	−	0.310535i
$977$	−1.13755e9	+	5.47816e8i	−1.21980	+	0.587423i	−0.929255	−	0.369439i	$-0.879550\pi$
$977$	−1.13755e9	+	5.47816e8i	−1.21980	+	0.587423i	−0.290542	+	0.956862i	$0.593836\pi$
$978$	1.02178e8	−	8.14841e7i	0.109230	−	0.0871076i
$979$	−2.01740e9	+	4.60459e8i	−2.15003	+	0.490730i
$980$	−4.65451e6	+	3.71185e6i	−0.00494534	+	0.00394378i
$981$	−1.49442e8	+	6.54749e8i	−0.158295	+	0.693534i
$982$	5.78112e8			0.610488
$983$		−	1.36669e9i		−	1.43883i	−0.694578	−	0.719417i	$-0.744409\pi$
$983$		−	1.36669e9i		−	1.43883i	0.694578	−	0.719417i	$-0.255591\pi$
$984$	2.44778e8	−	1.07244e9i	0.256913	−	1.12561i
$985$	−1.53863e8	−	1.22701e8i	−0.160999	−	0.128393i
$986$	−5.08401e8	−	2.44833e8i	−0.530366	−	0.255411i
$987$	−8.29271e8	+	3.99356e8i	−0.862472	+	0.415345i
$988$			1.37872e8i			0.142957i
$989$	−2.41470e8	+	1.10122e9i	−0.249617	+	1.13837i
$990$	−8.23904e8			−0.849123
$991$	−1.21484e8	−	2.52264e8i	−0.124824	−	0.259199i	0.829187	−	0.558971i	$-0.188804\pi$
$991$	−1.21484e8	−	2.52264e8i	−0.124824	−	0.259199i	−0.954011	+	0.299772i	$0.903089\pi$
$992$	4.24253e7	−	8.80971e7i	0.0434601	−	0.0902458i
$993$	−6.27416e8	+	7.86754e8i	−0.640778	+	0.803510i
$994$	−1.10925e9	−	2.53180e8i	−1.12946	−	0.257792i
$995$	−2.66633e8			−0.270673
$996$			1.32067e9i			1.33665i
$997$	2.71159e8	+	6.18902e7i	0.273614	+	0.0624505i	0.357126	−	0.934056i	$-0.383757\pi$
$997$	2.71159e8	+	6.18902e7i	0.273614	+	0.0624505i	−0.0835124	+	0.996507i	$0.526614\pi$
$998$	9.75802e8	+	1.22362e9i	0.981681	+	1.23099i
$999$	−5.58953e7	−	2.44893e8i	−0.0560633	−	0.245629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.6	✓	126
43.22	odd	14	inner	43.7.f.a.22.6	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.6	✓	126	1.1	even	1	trivial
43.7.f.a.22.6	yes	126	43.22	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.35509 - 9.04344i) q^{2} +(15.2129 - 31.5900i) q^{3} +(-22.9137 + 28.7328i) q^{4} +(-93.5256 - 21.3466i) q^{5} -351.936 q^{6} +345.453i q^{7} +(-266.657 - 60.8626i) q^{8} +(-311.968 - 391.196i) q^{9} +O(q^{10})\)	\(q+(-4.35509 - 9.04344i) q^{2} +(15.2129 - 31.5900i) q^{3} +(-22.9137 + 28.7328i) q^{4} +(-93.5256 - 21.3466i) q^{5} -351.936 q^{6} +345.453i q^{7} +(-266.657 - 60.8626i) q^{8} +(-311.968 - 391.196i) q^{9} +(214.266 + 938.759i) q^{10} +(-1066.21 - 1336.99i) q^{11} +(559.085 + 1160.95i) q^{12} +(211.655 - 927.319i) q^{13} +(3124.08 - 1504.48i) q^{14} +(-2097.13 + 2629.72i) q^{15} +(1134.29 + 4969.63i) q^{16} +(860.461 + 3769.92i) q^{17} +(-2179.10 + 4524.96i) q^{18} +(3083.67 + 2459.15i) q^{19} +(2756.36 - 2198.13i) q^{20} +(10912.8 + 5255.35i) q^{21} +(-7447.51 + 15464.9i) q^{22} +(-8840.87 - 11086.1i) q^{23} +(-5979.27 + 7497.77i) q^{24} +(-5786.29 - 2786.53i) q^{25} +(-9307.93 + 2124.47i) q^{26} +(7815.70 - 1783.88i) q^{27} +(-9925.84 - 7915.59i) q^{28} +(-6307.91 - 13098.5i) q^{29} +(32915.0 + 7512.63i) q^{30} +(2617.24 - 1260.39i) q^{31} +(26316.7 - 20986.9i) q^{32} +(-58455.5 + 13342.1i) q^{33} +(30345.7 - 24199.9i) q^{34} +(7374.24 - 32308.7i) q^{35} +18388.5 q^{36} -31333.5i q^{37} +(8809.48 - 38596.9i) q^{38} +(-26074.1 - 20793.4i) q^{39} +(23640.0 + 11384.4i) q^{40} +(-103346. + 49768.6i) q^{41} -121577. i q^{42} +(-50100.9 - 61735.4i) q^{43} +62846.2 q^{44} +(20826.3 + 43246.2i) q^{45} +(-61753.7 + 128233. i) q^{46} +(-47379.2 + 59411.7i) q^{47} +(174246. + 39770.5i) q^{48} -1688.64 q^{49} +64463.5i q^{50} +(132182. + 30169.6i) q^{51} +(21794.7 + 27329.7i) q^{52} +(-53480.5 - 234313. i) q^{53} +(-50170.5 - 62911.9i) q^{54} +(71177.9 + 147802. i) q^{55} +(21025.2 - 92117.2i) q^{56} +(124596. - 60002.3i) q^{57} +(-90984.1 + 114090. i) q^{58} +(8375.71 + 36696.4i) q^{59} +(-27506.4 - 120513. i) q^{60} +(-110436. + 229323. i) q^{61} +(-22796.6 - 18179.7i) q^{62} +(135140. - 107770. i) q^{63} +(-10477.6 - 5045.73i) q^{64} +(-39590.2 + 82209.9i) q^{65} +(375238. + 470533. i) q^{66} +(42707.3 - 53553.3i) q^{67} +(-128037. - 61659.3i) q^{68} +(-484705. + 110631. i) q^{69} +(-324297. + 74018.7i) q^{70} +(-256542. - 204585. i) q^{71} +(59379.1 + 123302. i) q^{72} +(-420672. - 96015.5i) q^{73} +(-283363. + 136460. i) q^{74} +(-176053. + 140397. i) q^{75} +(-141317. + 32254.6i) q^{76} +(461866. - 368326. i) q^{77} +(-74488.8 + 326357. i) q^{78} +34711.4 q^{79} -489000. i q^{80} +(143714. - 629651. i) q^{81} +(900159. + 717853. i) q^{82} +(923422. + 444697. i) q^{83} +(-401054. + 193137. i) q^{84} -370952. i q^{85} +(-340107. + 721948. i) q^{86} -509743. q^{87} +(202940. + 421409. i) q^{88} +(525024. - 1.09022e6i) q^{89} +(300394. - 376683. i) q^{90} +(320345. + 73116.7i) q^{91} +521112. q^{92} -101853. i q^{93} +(743627. + 169728. i) q^{94} +(-235908. - 295819. i) q^{95} +(-262621. - 1.15062e6i) q^{96} +(210713. + 264226. i) q^{97} +(7354.20 + 15271.2i) q^{98} +(-190399. + 834194. 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

Related objects

Downloads

Learn more