LMFDB - Embedded newform 43.7.f.a.2.3

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			2.3
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.10721 - 10.6052i) q^{2} +(-7.80492 + 16.2071i) q^{3} +(-46.4840 + 58.2891i) q^{4} +(-223.373 - 50.9834i) q^{5} +211.741 q^{6} -193.213i q^{7} +(121.123 + 27.6454i) q^{8} +(252.771 + 316.965i) q^{9} +O(q^{10})$	\(q+(-5.10721 - 10.6052i) q^{2} +(-7.80492 + 16.2071i) q^{3} +(-46.4840 + 58.2891i) q^{4} +(-223.373 - 50.9834i) q^{5} +211.741 q^{6} -193.213i q^{7} +(121.123 + 27.6454i) q^{8} +(252.771 + 316.965i) q^{9} +(600.121 + 2629.30i) q^{10} +(1251.38 + 1569.18i) q^{11} +(-581.893 - 1208.31i) q^{12} +(771.627 - 3380.72i) q^{13} +(-2049.07 + 986.780i) q^{14} +(2569.70 - 3222.30i) q^{15} +(736.345 + 3226.14i) q^{16} +(314.866 + 1379.52i) q^{17} +(2070.53 - 4299.50i) q^{18} +(223.512 + 178.245i) q^{19} +(13355.0 - 10650.3i) q^{20} +(3131.42 + 1508.01i) q^{21} +(10250.5 - 21285.3i) q^{22} +(-5139.50 - 6444.73i) q^{23} +(-1393.41 + 1747.27i) q^{24} +(33218.4 + 15997.1i) q^{25} +(-39794.2 + 9082.76i) q^{26} +(-19894.8 + 4540.85i) q^{27} +(11262.2 + 8981.32i) q^{28} +(19249.8 + 39972.7i) q^{29} +(-47297.2 - 10795.3i) q^{30} +(-10822.8 + 5211.99i) q^{31} +(36669.8 - 29243.2i) q^{32} +(-35198.8 + 8033.90i) q^{33} +(13022.0 - 10384.7i) q^{34} +(-9850.65 + 43158.5i) q^{35} -30225.4 q^{36} +11119.1i q^{37} +(748.806 - 3280.73i) q^{38} +(48769.1 + 38892.1i) q^{39} +(-25646.0 - 12350.5i) q^{40} +(-60151.0 + 28967.2i) q^{41} -40911.2i q^{42} +(74151.0 - 28687.8i) q^{43} -149636. q^{44} +(-40302.2 - 83688.4i) q^{45} +(-42099.3 + 87420.2i) q^{46} +(-22922.5 + 28743.9i) q^{47} +(-58033.4 - 13245.8i) q^{48} +80317.7 q^{49} -433990. i q^{50} +(-24815.5 - 5663.97i) q^{51} +(161191. + 202127. i) q^{52} +(51702.9 + 226525. i) q^{53} +(149764. + 187798. i) q^{54} +(-199522. - 414312. i) q^{55} +(5341.46 - 23402.5i) q^{56} +(-4633.33 + 2231.29i) q^{57} +(325607. - 408298. i) q^{58} +(22342.0 + 97886.6i) q^{59} +(68375.1 + 299571. i) q^{60} +(95119.6 - 197518. i) q^{61} +(110549. + 88159.7i) q^{62} +(61241.8 - 48838.7i) q^{63} +(-306602. - 147652. i) q^{64} +(-344721. + 715820. i) q^{65} +(264969. + 332261. i) q^{66} +(-255441. + 320313. i) q^{67} +(-95047.2 - 45772.3i) q^{68} +(144564. - 32995.7i) q^{69} +(508015. - 115951. i) q^{70} +(-94739.7 - 75552.4i) q^{71} +(21853.7 + 45379.6i) q^{72} +(56840.9 + 12973.6i) q^{73} +(117921. - 56787.8i) q^{74} +(-518534. + 413517. i) q^{75} +(-20779.5 + 4742.78i) q^{76} +(303187. - 241783. i) q^{77} +(163385. - 715838. i) q^{78} +749591. q^{79} -758173. i q^{80} +(15917.9 - 69741.1i) q^{81} +(614408. + 489974. i) q^{82} +(-404629. - 194859. i) q^{83} +(-233462. + 112429. i) q^{84} -324200. i q^{85} +(-682946. - 639874. i) q^{86} -798085. q^{87} +(108190. + 224659. i) q^{88} +(164919. - 342458. i) q^{89} +(-681703. + 854829. i) q^{90} +(-653199. - 149088. i) q^{91} +614562. q^{92} -216085. i q^{93} +(421906. + 96297.4i) q^{94} +(-40839.0 - 51210.4i) q^{95} +(187742. + 822551. i) q^{96} +(54368.0 + 68175.4i) q^{97} +(-410200. - 851788. i) q^{98} +(-181063. + 793288. 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 $

$2$	−5.10721	−	10.6052i	−0.638401	−	1.32565i	−0.929451	−	0.368946i	$-0.879719\pi$
$2$	−5.10721	−	10.6052i	−0.638401	−	1.32565i	0.291049	−	0.956708i	$-0.405996\pi$
$3$	−7.80492	+	16.2071i	−0.289071	+	0.600263i	−0.994045	−	0.108971i	$-0.965244\pi$
$3$	−7.80492	+	16.2071i	−0.289071	+	0.600263i	0.704974	+	0.709233i	$0.250959\pi$
$4$	−46.4840	+	58.2891i	−0.726313	+	0.910768i
$5$	−223.373	−	50.9834i	−1.78698	−	0.407867i	−0.804458	−	0.594009i	$-0.797544\pi$
$5$	−223.373	−	50.9834i	−1.78698	−	0.407867i	−0.982523	+	0.186142i	$0.940402\pi$
$6$	211.741			0.980284
$7$		−	193.213i		−	0.563303i	−0.959517	−	0.281652i	$-0.909118\pi$
$7$		−	193.213i		−	0.563303i	0.959517	−	0.281652i	$-0.0908822\pi$
$8$	121.123	+	27.6454i	0.236568	+	0.0539950i
$9$	252.771	+	316.965i	0.346737	+	0.434794i
$10$	600.121	+	2629.30i	0.600121	+	2.62930i
$11$	1251.38	+	1569.18i	0.940181	+	1.17895i	0.983685	+	0.179897i	$0.0575765\pi$
$11$	1251.38	+	1569.18i	0.940181	+	1.17895i	−0.0435040	+	0.999053i	$0.513852\pi$
$12$	−581.893	−	1208.31i	−0.336744	−	0.699255i
$13$	771.627	−	3380.72i	0.351219	−	1.53879i	−0.423153	−	0.906058i	$-0.639077\pi$
$13$	771.627	−	3380.72i	0.351219	−	1.53879i	0.774372	−	0.632731i	$-0.218066\pi$
$14$	−2049.07	+	986.780i	−0.746745	+	0.359614i
$15$	2569.70	−	3222.30i	0.761392	−	0.954756i
$16$	736.345	+	3226.14i	0.179772	+	0.787632i
$17$	314.866	+	1379.52i	0.0640884	+	0.280789i	0.996810	−	0.0798069i	$-0.0254304\pi$
$17$	314.866	+	1379.52i	0.0640884	+	0.280789i	−0.932722	+	0.360596i	$0.882573\pi$
$18$	2070.53	−	4299.50i	0.355030	−	0.737226i
$19$	223.512	+	178.245i	0.0325867	+	0.0259870i	0.639648	−	0.768668i	$-0.279080\pi$
$19$	223.512	+	178.245i	0.0325867	+	0.0259870i	−0.607061	+	0.794655i	$0.707652\pi$
$20$	13355.0	−	10650.3i	1.66938	−	1.33129i
$21$	3131.42	+	1508.01i	0.338130	+	0.162835i
$22$	10250.5	−	21285.3i	0.962667	−	1.99900i
$23$	−5139.50	−	6444.73i	−0.422413	−	0.529689i	0.524401	−	0.851472i	$-0.324289\pi$
$23$	−5139.50	−	6444.73i	−0.422413	−	0.529689i	−0.946814	+	0.321782i	$0.895718\pi$
$24$	−1393.41	+	1747.27i	−0.100796	+	0.126394i
$25$	33218.4	+	15997.1i	2.12598	+	1.02382i
$26$	−39794.2	+	9082.76i	−2.26412	+	0.516771i
$27$	−19894.8	+	4540.85i	−1.01076	+	0.230699i
$28$	11262.2	+	8981.32i	0.513039	+	0.409135i
$29$	19249.8	+	39972.7i	0.789284	+	1.63896i	0.769066	+	0.639169i	$0.220722\pi$
$29$	19249.8	+	39972.7i	0.789284	+	1.63896i	0.0202177	+	0.999796i	$0.493564\pi$
$30$	−47297.2	−	10795.3i	−1.75175	−	0.399825i
$31$	−10822.8	+	5211.99i	−0.363291	+	0.174952i	−0.606620	−	0.794992i	$-0.707475\pi$
$31$	−10822.8	+	5211.99i	−0.363291	+	0.174952i	0.243329	+	0.969944i	$0.421761\pi$
$32$	36669.8	−	29243.2i	1.11907	−	0.892431i
$33$	−35198.8	+	8033.90i	−0.979459	+	0.223555i
$34$	13022.0	−	10384.7i	0.331316	−	0.264215i
$35$	−9850.65	+	43158.5i	−0.229753	+	1.00661i
$36$	−30225.4			−0.647836
$37$			11119.1i			0.219516i	0.993958	+	0.109758i	$0.0350076\pi$
$37$			11119.1i			0.219516i	−0.993958	+	0.109758i	$0.964992\pi$
$38$	748.806	−	3280.73i	0.0136464	−	0.0597888i
$39$	48769.1	+	38892.1i	0.822150	+	0.655643i
$40$	−25646.0	−	12350.5i	−0.400719	−	0.192976i
$41$	−60151.0	+	28967.2i	−0.872753	+	0.420296i	−0.815972	−	0.578091i	$-0.803798\pi$
$41$	−60151.0	+	28967.2i	−0.872753	+	0.420296i	−0.0567808	+	0.998387i	$0.518084\pi$
$42$		−	40911.2i		−	0.552197i
$43$	74151.0	−	28687.8i	0.932635	−	0.360821i
$43$	74151.0	−	28687.8i	0.932635	−	0.360821i
$44$	−149636.			−1.75662
$45$	−40302.2	−	83688.4i	−0.442274	−	0.918392i
$46$	−42099.3	+	87420.2i	−0.432516	+	0.898128i
$47$	−22922.5	+	28743.9i	−0.220785	+	0.276855i	−0.879872	−	0.475212i	$-0.842371\pi$
$47$	−22922.5	+	28743.9i	−0.220785	+	0.276855i	0.659087	+	0.752067i	$0.270943\pi$
$48$	−58033.4	−	13245.8i	−0.524753	−	0.119771i
$49$	80317.7			0.682689
$50$		−	433990.i		−	3.47192i
$51$	−24815.5	−	5663.97i	−0.187074	−	0.0426983i
$52$	161191.	+	202127.i	1.14638	+	1.43752i
$53$	51702.9	+	226525.i	0.347286	+	1.52156i	0.783314	+	0.621627i	$0.213528\pi$
$53$	51702.9	+	226525.i	0.347286	+	1.52156i	−0.436028	+	0.899933i	$0.643615\pi$
$54$	149764.	+	187798.i	0.951098	+	1.19264i
$55$	−199522.	−	414312.i	−1.19923	−	2.49023i
$56$	5341.46	−	23402.5i	0.0304156	−	0.133259i
$57$	−4633.33	+	2231.29i	−0.0250189	+	0.0120485i
$58$	325607.	−	408298.i	1.66882	−	2.09264i
$59$	22342.0	+	97886.6i	0.108784	+	0.476615i	0.999746	+	0.0225365i	$0.00717418\pi$
$59$	22342.0	+	97886.6i	0.108784	+	0.476615i	−0.890962	+	0.454078i	$0.849969\pi$
$60$	68375.1	+	299571.i	0.316552	+	1.38690i
$61$	95119.6	−	197518.i	0.419064	−	0.870196i	−0.579413	−	0.815034i	$-0.696718\pi$
$61$	95119.6	−	197518.i	0.419064	−	0.870196i	0.998477	−	0.0551619i	$-0.0175675\pi$
$62$	110549.	+	88159.7i	0.463851	+	0.369909i
$63$	61241.8	−	48838.7i	0.244921	−	0.195318i
$64$	−306602.	−	147652.i	−1.16959	−	0.563246i
$65$	−344721.	+	715820.i	−1.25524	+	2.60654i
$66$	264969.	+	332261.i	0.921645	+	1.15571i
$67$	−255441.	+	320313.i	−0.849311	+	1.06500i	0.147799	+	0.989017i	$0.452781\pi$
$67$	−255441.	+	320313.i	−0.849311	+	1.06500i	−0.997109	+	0.0759842i	$0.975790\pi$
$68$	−95047.2	−	45772.3i	−0.302282	−	0.145571i
$69$	144564.	−	32995.7i	0.440060	−	0.100441i
$70$	508015.	−	115951.i	1.48109	−	0.338050i
$71$	−94739.7	−	75552.4i	−0.264702	−	0.211093i	0.482140	−	0.876094i	$-0.339860\pi$
$71$	−94739.7	−	75552.4i	−0.264702	−	0.211093i	−0.746842	+	0.665001i	$0.768431\pi$
$72$	21853.7	+	45379.6i	0.0585500	+	0.121580i
$73$	56840.9	+	12973.6i	0.146114	+	0.0333496i	0.294952	−	0.955512i	$-0.404696\pi$
$73$	56840.9	+	12973.6i	0.146114	+	0.0333496i	−0.148838	+	0.988862i	$0.547553\pi$
$74$	117921.	−	56787.8i	0.291002	−	0.140139i
$75$	−518534.	+	413517.i	−1.22912	+	0.980189i
$76$	−20779.5	+	4742.78i	−0.0473363	+	0.0108042i
$77$	303187.	−	241783.i	0.664107	−	0.529607i
$78$	163385.	−	715838.i	0.344294	−	1.50845i
$79$	749591.			1.52035			0.760175	−	0.649719i	$-0.225113\pi$
$79$	749591.			1.52035			0.760175	+	0.649719i	$0.225113\pi$
$80$		−	758173.i		−	1.48081i
$81$	15917.9	−	69741.1i	0.0299524	−	0.131230i
$82$	614408.	+	489974.i	1.11433	+	0.888652i
$83$	−404629.	−	194859.i	−0.707656	−	0.340789i	0.0451966	−	0.998978i	$-0.485609\pi$
$83$	−404629.	−	194859.i	−0.707656	−	0.340789i	−0.752853	+	0.658189i	$0.771323\pi$
$84$	−233462.	+	112429.i	−0.393893	+	0.189689i
$85$		−	324200.i		−	0.527905i
$86$	−682946.	−	639874.i	−1.07372	−	1.00600i
$87$	−798085.			−1.21197
$88$	108190.	+	224659.i	0.158759	+	0.329667i
$89$	164919.	−	342458.i	0.233938	−	0.485777i	−0.750643	−	0.660708i	$-0.770256\pi$
$89$	164919.	−	342458.i	0.233938	−	0.485777i	0.984581	+	0.174931i	$0.0559703\pi$
$90$	−681703.	+	854829.i	−0.935121	+	1.17260i
$91$	−653199.	−	149088.i	−0.866805	−	0.197843i
$92$	614562.			0.789228
$93$		−	216085.i		−	0.268644i
$94$	421906.	+	96297.4i	0.507963	+	0.115939i
$95$	−40839.0	−	51210.4i	−0.0476326	−	0.0597293i
$96$	187742.	+	822551.i	0.212201	+	0.929714i
$97$	54368.0	+	68175.4i	0.0595701	+	0.0746986i	0.810724	−	0.585429i	$-0.199074\pi$
$97$	54368.0	+	68175.4i	0.0595701	+	0.0746986i	−0.751154	+	0.660127i	$0.770502\pi$
$98$	−410200.	−	851788.i	−0.435830	−	0.905010i
$99$	−181063.	+	793288.i	−0.186605	+	0.817571i
$100$	−2.47659e6	+	1.19266e6i	−2.47659	+	1.19266i
$101$	773222.	−	969590.i	0.750482	−	0.941075i	−0.249143	−	0.968467i	$-0.580149\pi$
$101$	773222.	−	969590.i	0.750482	−	0.941075i	0.999625	+	0.0273920i	$0.00872022\pi$
$102$	66670.2	+	292101.i	0.0628248	+	0.275253i
$103$	167594.	+	734275.i	0.153372	+	0.671966i	0.991891	+	0.127093i	$0.0405648\pi$
$103$	167594.	+	734275.i	0.153372	+	0.671966i	−0.838519	+	0.544872i	$0.816578\pi$
$104$	186923.	−	388150.i	0.166174	−	0.345064i
$105$	−622590.	−	496499.i	−0.537817	−	0.428895i
$106$	2.13830e6	−	1.70523e6i	1.79535	−	1.43175i
$107$	582936.	+	280727.i	0.475849	+	0.229157i	0.656406	−	0.754408i	$-0.272076\pi$
$107$	582936.	+	280727.i	0.475849	+	0.229157i	−0.180557	+	0.983565i	$0.557790\pi$
$108$	660107.	−	1.37073e6i	0.524014	−	1.08813i
$109$	368112.	+	461597.i	0.284250	+	0.356438i	0.903373	−	0.428856i	$-0.141083\pi$
$109$	368112.	+	461597.i	0.284250	+	0.356438i	−0.619123	+	0.785294i	$0.712512\pi$
$110$	−3.37488e6	+	4.23196e6i	−2.53559	+	3.17953i
$111$	−180209.	−	86784.0i	−0.131767	−	0.0634557i
$112$	623332.	−	142271.i	0.443675	−	0.101266i
$113$	−21124.0	+	4821.41i	−0.0146400	+	0.00334148i	−0.229835	−	0.973230i	$-0.573819\pi$
$113$	−21124.0	+	4821.41i	−0.0146400	+	0.00334148i	0.215195	+	0.976571i	$0.430961\pi$
$114$	47326.8	+	37741.8i	0.0319442	+	0.0254747i
$115$	819450.	+	1.70161e6i	0.538802	+	1.11883i
$116$	−3.22479e6	−	736036.i	−2.06598	−	0.471547i
$117$	1.26661e6	−	609969.i	0.790837	−	0.380847i
$118$	924005.	−	736870.i	0.562378	−	0.448482i
$119$	266541.	−	60836.2i	0.158170	−	0.0361012i
$120$	400331.	−	319253.i	0.231673	−	0.184753i
$121$	−502170.	+	2.20015e6i	−0.283462	+	1.24193i
$122$	−2.58052e6			−1.42111
$123$		−	1.20096e6i		−	0.645377i
$124$	199286.	−	873127.i	0.104523	−	0.457944i
$125$	−3.80557e6	−	3.03484e6i	−1.94845	−	1.55384i
$126$	−830720.	−	400054.i	−0.415282	−	0.199989i
$127$	−1.05771e6	+	509368.i	−0.516365	+	0.248668i	−0.673870	−	0.738850i	$-0.735369\pi$
$127$	−1.05771e6	+	509368.i	−0.516365	+	0.248668i	0.157505	+	0.987518i	$0.449655\pi$
$128$			1.00391e6i			0.478703i
$129$	−113798.	+	1.42568e6i	−0.0530107	+	0.664129i
$130$	9.35200e6			4.25672
$131$	1.36148e6	+	2.82714e6i	0.605617	+	1.25758i	0.948076	+	0.318043i	$0.103026\pi$
$131$	1.36148e6	+	2.82714e6i	0.605617	+	1.25758i	−0.342460	+	0.939533i	$0.611260\pi$
$132$	1.16789e6	−	2.42516e6i	0.507787	−	1.05443i
$133$	34439.2	−	43185.4i	0.0146386	−	0.0183562i
$134$	4.70159e6	+	1.07311e6i	1.95403	+	0.445993i
$135$	4.67546e6			1.90030
$136$			175796.i			0.0698861i
$137$	−1.10748e6	−	252775.i	−0.430700	−	0.0983044i	0.00167463	−	0.999999i	$-0.499467\pi$
$137$	−1.10748e6	−	252775.i	−0.430700	−	0.0983044i	−0.432374	+	0.901694i	$0.642324\pi$
$138$	−1.08824e6	−	1.36462e6i	−0.414085	−	0.519246i
$139$	404884.	+	1.77391e6i	0.150760	+	0.660523i	0.992665	+	0.120897i	$0.0385771\pi$
$139$	404884.	+	1.77391e6i	0.150760	+	0.660523i	−0.841905	+	0.539626i	$0.818566\pi$
$140$	−2.05777e6	−	2.58037e6i	−0.749918	−	0.940367i
$141$	−286947.	−	595852.i	−0.102363	−	0.212560i
$142$	−317395.	+	1.39060e6i	−0.110850	+	0.485665i
$143$	6.27057e6	−	3.01975e6i	2.14436	−	1.03267i
$144$	−836446.	+	1.04887e6i	−0.280124	+	0.351265i
$145$	−2.26195e6	−	9.91023e6i	−0.741956	−	3.25072i
$146$	−152711.	−	669069.i	−0.0490694	−	0.214987i
$147$	−626874.	+	1.30172e6i	−0.197346	+	0.409793i
$148$	−648125.	−	516862.i	−0.199928	−	0.159437i
$149$	−1.80641e6	+	1.44056e6i	−0.546081	+	0.435485i	−0.857273	−	0.514862i	$-0.827843\pi$
$149$	−1.80641e6	+	1.44056e6i	−0.546081	+	0.435485i	0.311192	+	0.950347i	$0.399272\pi$
$150$	7.03371e6	+	3.38726e6i	2.08406	+	1.00363i
$151$	−1.04963e6	+	2.17958e6i	−0.304864	+	0.633056i	−0.995969	−	0.0896982i	$-0.971410\pi$
$151$	−1.04963e6	+	2.17958e6i	−0.304864	+	0.633056i	0.691105	+	0.722754i	$0.257124\pi$
$152$	22144.7	+	27768.6i	0.00630578	+	0.00790720i
$153$	−357670.	+	448504.i	−0.0998638	+	0.125225i
$154$	−4.11261e6	−	1.98053e6i	−1.12604	−	0.542274i
$155$	2.68325e6	−	612433.i	0.720552	−	0.164461i
$156$	−4.53397e6	+	1.03485e6i	−1.19428	+	0.272586i
$157$	4.61084e6	+	3.67702e6i	1.19146	+	0.950161i	0.999512	−	0.0312427i	$-0.00994647\pi$
$157$	4.61084e6	+	3.67702e6i	1.19146	+	0.950161i	0.191953	+	0.981404i	$0.438518\pi$
$158$	−3.82832e6	−	7.94959e6i	−0.970593	−	2.01546i
$159$	−4.07485e6	−	930059.i	−1.01373	−	0.231376i
$160$	−9.68194e6	+	4.66258e6i	−2.36376	+	1.13832i
$161$	−1.24521e6	+	993018.i	−0.298376	+	0.237947i
$162$	−820917.	+	187369.i	−0.193088	+	0.0440710i
$163$	−3.21405e6	+	2.56312e6i	−0.742147	+	0.591842i	−0.919863	−	0.392239i	$-0.871701\pi$
$163$	−3.21405e6	+	2.56312e6i	−0.742147	+	0.591842i	0.177716	+	0.984082i	$0.443129\pi$
$164$	1.10759e6	−	4.85266e6i	0.251100	−	1.10014i
$165$	8.27205e6			1.84146
$166$			5.28637e6i			1.15567i
$167$	−1.00033e6	+	4.38275e6i	−0.214781	+	0.941016i	0.746487	+	0.665400i	$0.231739\pi$
$167$	−1.00033e6	+	4.38275e6i	−0.214781	+	0.941016i	−0.961268	+	0.275616i	$0.911118\pi$
$168$	337596.	+	269224.i	0.0711983	+	0.0567788i
$169$	−6.48505e6	−	3.12304e6i	−1.34355	−	0.647019i
$170$	−3.43821e6	+	1.65576e6i	−0.699820	+	0.337015i
$171$			115901.i			0.0231792i
$172$	−1.77465e6	+	5.65572e6i	−0.348761	+	1.11148i
$173$	8.45341e6			1.63265			0.816326	−	0.577591i	$-0.196007\pi$
$173$	8.45341e6			1.63265			0.816326	+	0.577591i	$0.196007\pi$
$174$	4.07599e6	+	8.46388e6i	0.773722	+	1.60665i
$175$	3.09086e6	−	6.41823e6i	0.576720	−	1.19757i
$176$	−4.14095e6	+	5.19259e6i	−0.759560	+	0.952459i
$177$	−1.76084e6	−	401899.i	−0.317540	−	0.0724765i
$178$	−4.47412e6			−0.793319
$179$		−	6.98497e6i		−	1.21788i	−0.793215	−	0.608941i	$-0.791595\pi$
$179$		−	6.98497e6i		−	1.21788i	0.793215	−	0.608941i	$-0.208405\pi$
$180$	6.75154e6	+	1.54099e6i	1.15767	+	0.264231i
$181$	−1.59692e6	−	2.00248e6i	−0.269307	−	0.337700i	0.628727	−	0.777626i	$-0.283576\pi$
$181$	−1.59692e6	−	2.00248e6i	−0.269307	−	0.337700i	−0.898034	+	0.439926i	$0.855005\pi$
$182$	1.75491e6	+	7.68875e6i	0.291099	+	1.27539i
$183$	2.45879e6	+	3.08322e6i	0.401207	+	0.503097i
$184$	−444342.	−	922686.i	−0.0713287	−	0.148116i
$185$	566891.	−	2.48371e6i	0.0895332	−	0.392271i
$186$	−2.29164e6	+	1.10359e6i	−0.356129	+	0.171503i
$187$	−1.77070e6	+	2.22039e6i	−0.270782	+	0.339550i
$188$	−609928.	−	2.67227e6i	−0.0917920	−	0.402167i
$189$	877352.	+	3.84393e6i	0.129954	+	0.569364i
$190$	−334525.	+	694649.i	−0.0487718	+	0.101276i
$191$	−3.99722e6	−	3.18768e6i	−0.573665	−	0.457482i	0.293182	−	0.956057i	$-0.405286\pi$
$191$	−3.99722e6	−	3.18768e6i	−0.573665	−	0.457482i	−0.866847	+	0.498574i	$0.833857\pi$
$192$	4.78600e6	−	3.81671e6i	0.676191	−	0.539244i
$193$	−7.92562e6	−	3.81678e6i	−1.10246	−	0.530915i	−0.208026	−	0.978123i	$-0.566704\pi$
$193$	−7.92562e6	−	3.81678e6i	−1.10246	−	0.530915i	−0.894430	+	0.447208i	$0.852418\pi$
$194$	445347.	−	924772.i	0.0609948	−	0.126657i
$195$	−8.91084e6	−	1.11738e7i	−1.20175	−	1.50695i
$196$	−3.73349e6	+	4.68165e6i	−0.495846	+	0.621772i
$197$	−5.59167e6	−	2.69281e6i	−0.731380	−	0.352214i	0.0308467	−	0.999524i	$-0.490180\pi$
$197$	−5.59167e6	−	2.69281e6i	−0.731380	−	0.352214i	−0.762227	+	0.647310i	$0.775894\pi$
$198$	9.33773e6	−	2.13128e6i	1.20295	−	0.274564i
$199$	−5.34283e6	+	1.21947e6i	−0.677972	+	0.154743i	−0.547623	−	0.836725i	$-0.684467\pi$
$199$	−5.34283e6	+	1.21947e6i	−0.677972	+	0.154743i	−0.130350	+	0.991468i	$0.541610\pi$
$200$	3.58125e6	+	2.85595e6i	0.447657	+	0.356994i
$201$	−3.19764e6	−	6.63998e6i	−0.393769	−	0.817671i
$202$	−1.42317e7	−	3.24830e6i	−1.72665	−	0.394096i
$203$	7.72325e6	−	3.71932e6i	0.923234	−	0.444606i
$204$	1.48367e6	−	1.18319e6i	0.174762	−	0.139368i
$205$	1.49129e7	−	3.40378e6i	1.73102	−	0.395094i
$206$	6.93123e6	−	5.52747e6i	0.792882	−	0.632302i
$207$	743636.	−	3.25808e6i	0.0838396	−	0.367325i
$208$	1.14749e7			1.27514
$209$			573784.i			0.0628506i
$210$	−2.08579e6	+	9.13844e6i	−0.225223	+	0.986766i
$211$	7.92902e6	+	6.32319e6i	0.844058	+	0.673114i	0.946880	−	0.321586i	$-0.104216\pi$
$211$	7.92902e6	+	6.32319e6i	0.844058	+	0.673114i	−0.102822	+	0.994700i	$0.532787\pi$
$212$	−1.56073e7	−	7.51609e6i	−1.63803	−	0.788832i
$213$	1.96392e6	−	945774.i	0.203229	−	0.0978698i
$214$		−	7.61590e6i		−	0.777105i
$215$	−1.80259e7	+	2.62760e6i	−1.81377	+	0.264389i
$216$	−2.53524e6			−0.251570
$217$	1.00702e6	+	2.09111e6i	0.0985510	+	0.204643i
$218$	3.01532e6	−	6.26139e6i	0.291048	−	0.604367i
$219$	−653902.	+	819968.i	−0.0622559	+	0.0780664i
$220$	3.34245e7	+	7.62892e6i	3.13904	+	0.716465i
$221$	4.90672e6			0.454585
$222$			2.35438e6i			0.215188i
$223$	1.25035e7	+	2.85385e6i	1.12750	+	0.257345i	0.745298	−	0.666732i	$-0.232307\pi$
$223$	1.25035e7	+	2.85385e6i	1.12750	+	0.257345i	0.382206	+	0.924077i	$0.375165\pi$
$224$	−5.65016e6	−	7.08508e6i	−0.502709	−	0.630378i
$225$	3.32612e6	+	1.45727e7i	0.292005	+	1.27936i
$226$	159017.	+	199401.i	0.0137758	+	0.0172743i
$227$	9.22704e6	+	1.91601e7i	0.788832	+	1.63803i	0.769865	+	0.638207i	$0.220323\pi$
$227$	9.22704e6	+	1.91601e7i	0.788832	+	1.63803i	0.0189671	+	0.999820i	$0.493962\pi$
$228$	85315.6	−	373792.i	0.00719820	−	0.0315374i
$229$	−3.42151e6	+	1.64771e6i	−0.284912	+	0.137207i	−0.570882	−	0.821032i	$-0.693399\pi$
$229$	−3.42151e6	+	1.64771e6i	−0.284912	+	0.137207i	0.285970	+	0.958239i	$0.407684\pi$
$230$	1.38608e7	−	1.73809e7i	1.13921	−	1.42853i
$231$	1.55225e6	+	6.80087e6i	0.125929	+	0.551733i
$232$	1.22653e6	+	5.37377e6i	0.0982231	+	0.430343i
$233$	−7.19241e6	+	1.49352e7i	−0.568600	+	1.18071i	0.396307	+	0.918118i	$0.370292\pi$
$233$	−7.19241e6	+	1.49352e7i	−0.568600	+	1.18071i	−0.964907	+	0.262592i	$0.915423\pi$
$234$	−1.29377e7	−	1.03175e7i	−1.00974	−	0.805243i
$235$	6.58573e6	−	5.25194e6i	0.507458	−	0.404684i
$236$	−6.74427e6	−	3.24787e6i	−0.513097	−	0.247094i
$237$	−5.85050e6	+	1.21487e7i	−0.439489	+	0.912609i
$238$	−2.00646e6	−	2.51603e6i	−0.148833	−	0.186631i
$239$	9.04094e6	−	1.13370e7i	0.662247	−	0.830431i	−0.331339	−	0.943512i	$-0.607500\pi$
$239$	9.04094e6	−	1.13370e7i	0.662247	−	0.830431i	0.993586	+	0.113081i	$0.0360719\pi$
$240$	1.22878e7	+	5.91748e6i	0.888872	+	0.428058i
$241$	−2.65115e7	+	6.05107e6i	−1.89401	+	0.432296i	−0.999880	−	0.0155062i	$-0.995064\pi$
$241$	−2.65115e7	+	6.05107e6i	−1.89401	+	0.432296i	−0.894133	+	0.447802i	$0.852207\pi$
$242$	2.58978e7	−	5.91100e6i	1.82733	−	0.417076i
$243$	−1.06247e7	−	8.47290e6i	−0.740452	−	0.590491i
$244$	7.09161e6	+	1.47259e7i	0.488175	+	1.01370i
$245$	−1.79408e7	−	4.09487e6i	−1.21995	−	0.278446i
$246$	−1.27365e7	+	6.13356e6i	−0.855546	+	0.412009i
$247$	775064.	−	618093.i	0.0514336	−	0.0410169i
$248$	−1.45498e6	+	332089.i	−0.0953895	+	0.0217720i
$249$	6.31619e6	−	5.03699e6i	0.409126	−	0.326267i
$250$	−1.27494e7	+	5.58586e7i	−0.815959	+	3.57495i
$251$	−3.99842e6			−0.252853			−0.126426	−	0.991976i	$-0.540351\pi$
$251$	−3.99842e6			−0.252853			−0.126426	+	0.991976i	$0.540351\pi$
$252$			5.83995e6i			0.364928i
$253$	3.68148e6	−	1.61296e7i	0.227332	−	0.996008i
$254$	1.08039e7	+	8.61585e6i	0.659296	+	0.525771i
$255$	5.25433e6	+	2.53035e6i	0.316882	+	0.152602i
$256$	−8.97576e6	+	4.32250e6i	−0.534997	+	0.257641i
$257$		−	4.12374e6i		−	0.242936i	−0.992595	−	0.121468i	$-0.961240\pi$
$257$		−	4.12374e6i		−	0.242936i	0.992595	−	0.121468i	$-0.0387602\pi$
$258$	1.57008e7	−	6.07439e6i	0.914248	−	0.353707i
$259$	2.14836e6			0.123654
$260$	−2.57005e7	−	5.33677e7i	−1.46225	−	3.03640i
$261$	−7.80414e6	+	1.62055e7i	−0.438939	+	0.911465i
$262$	2.30292e7	−	2.88777e7i	1.28048	−	1.60568i
$263$	−1.42719e7	−	3.25747e6i	−0.784539	−	0.179066i	−0.188556	−	0.982063i	$-0.560381\pi$
$263$	−1.42719e7	−	3.25747e6i	−0.784539	−	0.179066i	−0.595984	+	0.802997i	$0.703238\pi$
$264$	−4.48547e6			−0.243779
$265$		−	5.32355e7i		−	2.86065i
$266$	−633880.	−	144679.i	−0.0336792	−	0.00768707i
$267$	4.26307e6	+	5.34572e6i	0.223969	+	0.280848i
$268$	−6.79684e6	−	2.97789e7i	−0.353104	−	1.54705i
$269$	5.17499e6	+	6.48923e6i	0.265860	+	0.333378i	0.896785	−	0.442466i	$-0.145896\pi$
$269$	5.17499e6	+	6.48923e6i	0.265860	+	0.333378i	−0.630926	+	0.775843i	$0.717325\pi$
$270$	−2.38786e7	−	4.95843e7i	−1.21316	−	2.51914i
$271$	−5.82341e6	+	2.55140e7i	−0.292597	+	1.28195i	0.588300	+	0.808643i	$0.299797\pi$
$271$	−5.82341e6	+	2.55140e7i	−0.292597	+	1.28195i	−0.880897	+	0.473308i	$0.843060\pi$
$272$	−4.21867e6	+	2.03160e6i	−0.209637	+	0.100956i
$273$	7.51446e6	−	9.42283e6i	0.369326	−	0.463120i
$274$	2.97540e6	+	1.30361e7i	0.144642	+	0.633717i
$275$	1.64665e7	+	7.21443e7i	0.791776	+	3.46900i
$276$	−4.79661e6	+	9.96027e6i	−0.228143	+	0.473744i
$277$	1.19693e7	+	9.54520e6i	0.563157	+	0.449103i	0.863228	−	0.504814i	$-0.168439\pi$
$277$	1.19693e7	+	9.54520e6i	0.563157	+	0.449103i	−0.300071	+	0.953917i	$0.597010\pi$
$278$	1.67449e7	−	1.33536e7i	0.779379	−	0.621534i
$279$	−4.38771e6	−	2.11301e6i	−0.202035	−	0.0972947i
$280$	−2.38627e6	+	4.95515e6i	−0.108704	+	0.225726i
$281$	2.47365e6	+	3.10185e6i	0.111486	+	0.139798i	0.834443	−	0.551094i	$-0.185789\pi$
$281$	2.47365e6	+	3.10185e6i	0.111486	+	0.139798i	−0.722958	+	0.690892i	$0.757218\pi$
$282$	−4.85365e6	+	6.08628e6i	−0.216432	+	0.271397i
$283$	2.65081e7	+	1.27656e7i	1.16955	+	0.563227i	0.914851	−	0.403792i	$-0.132308\pi$
$283$	2.65081e7	+	1.27656e7i	1.16955	+	0.563227i	0.254702	+	0.967019i	$0.418022\pi$
$284$	8.80776e6	−	2.01031e6i	0.384513	−	0.0877625i
$285$	1.14872e6	−	262187.i	0.0496225	−	0.0113260i
$286$	−6.40502e7	−	5.10783e7i	−2.73793	−	2.18343i
$287$	5.59684e6	+	1.16220e7i	0.236754	+	0.491625i
$288$	1.85381e7	+	4.23121e6i	0.776048	+	0.177128i
$289$	1.99433e7	−	9.60417e6i	0.826233	−	0.397893i
$290$	−9.35481e7	+	7.46021e7i	−3.83567	+	3.05884i
$291$	−1.52926e6	+	349044.i	−0.0620588	+	0.0141645i
$292$	−3.39841e6	+	2.71014e6i	−0.136498	+	0.108854i
$293$	1.52240e6	−	6.67008e6i	0.0605238	−	0.265172i	−0.935608	−	0.353040i	$-0.885148\pi$
$293$	1.52240e6	−	6.67008e6i	0.0605238	−	0.265172i	0.996132	+	0.0878674i	$0.0280052\pi$
$294$	1.70066e7			0.669230
$295$		−	2.30043e7i		−	0.896071i
$296$	−307394.	+	1.34678e6i	−0.0118528	+	0.0519303i
$297$	−3.20214e7	−	2.55362e7i	−1.22228	−	0.974736i
$298$	2.45032e7	+	1.18001e7i	0.925922	+	0.445901i
$299$	−2.57536e7	+	1.24023e7i	−0.963439	+	0.463968i
$300$		−	4.94469e7i		−	1.83137i
$301$	−5.54285e6	−	1.43269e7i	−0.203252	−	0.525356i
$302$	2.84756e7			1.03384
$303$	9.67930e6	+	2.00993e7i	0.347949	+	0.722524i
$304$	−410461.	+	852331.i	−0.0146100	+	0.0303380i
$305$	−3.13172e7	+	3.92706e7i	−1.10378	+	1.38410i
$306$	6.58319e6	+	1.50257e6i	0.229759	+	0.0524409i
$307$	4.18713e7			1.44711			0.723555	−	0.690267i	$-0.242507\pi$
$307$	4.18713e7			1.44711			0.723555	+	0.690267i	$0.242507\pi$
$308$			2.89115e7i			0.989508i
$309$	−1.32085e7	−	3.01476e6i	−0.447691	−	0.102183i
$310$	−2.01989e7	−	2.53286e7i	−0.678020	−	0.850210i
$311$	−1.46226e6	−	6.40660e6i	−0.0486121	−	0.212984i	0.944788	−	0.327681i	$-0.106267\pi$
$311$	−1.46226e6	−	6.40660e6i	−0.0486121	−	0.212984i	−0.993400	+	0.114698i	$0.963410\pi$
$312$	4.83186e6	+	6.05896e6i	0.159093	+	0.199496i
$313$	2.55161e6	+	5.29847e6i	0.0832111	+	0.172790i	0.938423	−	0.345490i	$-0.112287\pi$
$313$	2.55161e6	+	5.29847e6i	0.0832111	+	0.172790i	−0.855212	+	0.518279i	$0.826573\pi$
$314$	1.54472e7	−	6.76784e7i	0.498953	−	2.18605i
$315$	−1.61697e7	+	7.78691e6i	−0.517333	+	0.249134i
$316$	−3.48440e7	+	4.36930e7i	−1.10425	+	1.38469i
$317$	−1.13411e6	−	4.96888e6i	−0.0356024	−	0.155984i	0.954002	−	0.299800i	$-0.0969199\pi$
$317$	−1.13411e6	−	4.96888e6i	−0.0356024	−	0.155984i	−0.989605	+	0.143816i	$0.954063\pi$
$318$	1.09476e7	+	4.79648e7i	0.340439	+	1.49156i
$319$	−3.86356e7	+	8.02276e7i	−1.19019	+	2.47145i
$320$	6.09586e7	+	4.86129e7i	1.86031	+	1.48355i
$321$	−9.09953e6	+	7.25664e6i	−0.275109	+	0.219392i
$322$	1.68907e7	+	8.13414e6i	0.505918	+	0.243637i
$323$	−175516.	+	364462.i	−0.00520845	+	0.0108155i
$324$	3.32522e6	+	4.16969e6i	0.0977654	+	0.122594i
$325$	7.97141e7	−	9.99583e7i	2.32212	−	2.91185i
$326$	4.35973e7	+	2.09954e7i	1.25837	+	0.605997i
$327$	−1.03542e7	+	2.36329e6i	−0.296125	+	0.0675885i
$328$	−8.08646e6	+	1.84568e6i	−0.229159	+	0.0523041i
$329$	5.55370e6	+	4.42893e6i	0.155953	+	0.124369i
$330$	−4.22471e7	−	8.77270e7i	−1.17559	−	2.44113i
$331$	−9.76974e6	−	2.22988e6i	−0.269401	−	0.0614890i	0.0856864	−	0.996322i	$-0.472692\pi$
$331$	−9.76974e6	−	2.22988e6i	−0.269401	−	0.0614890i	−0.355087	+	0.934833i	$0.615549\pi$
$332$	3.01669e7	−	1.45276e7i	0.824360	−	0.396991i
$333$	−3.52438e6	+	2.81060e6i	−0.0954442	+	0.0761142i
$334$	5.15890e7	−	1.17748e7i	1.38458	−	0.316021i
$335$	7.33892e7	−	5.85259e7i	1.95208	−	1.55673i
$336$	−2.55925e6	+	1.12128e7i	−0.0674676	+	0.295595i
$337$	−5.08614e7			−1.32892			−0.664459	−	0.747325i	$-0.731338\pi$
$337$	−5.08614e7			−1.32892			−0.664459	+	0.747325i	$0.731338\pi$
$338$			8.47255e7i			2.19414i
$339$	86729.9	−	379989.i	0.00222623	−	0.00975375i
$340$	1.88973e7	+	1.50701e7i	0.480799	+	0.383424i
$341$	−2.17220e7	−	1.04608e7i	−0.547819	−	0.263816i
$342$	1.22915e6	−	591929.i	0.0307275	−	0.0147976i
$343$		−	3.82497e7i		−	0.947864i
$344$	9.77445e6	−	1.42480e6i	0.240114	−	0.0350009i
$345$	−3.39738e7			−0.827346
$346$	−4.31734e7	−	8.96504e7i	−1.04229	−	2.16433i
$347$	7.35240e6	−	1.52674e7i	0.175971	−	0.365407i	−0.794264	−	0.607573i	$-0.792143\pi$
$347$	7.35240e6	−	1.52674e7i	0.175971	−	0.365407i	0.970235	+	0.242165i	$0.0778577\pi$
$348$	3.70982e7	−	4.65197e7i	0.880269	−	1.10382i
$349$	2.85357e7	+	6.51309e6i	0.671294	+	0.153218i	0.544565	−	0.838719i	$-0.316695\pi$
$349$	2.85357e7	+	6.51309e6i	0.671294	+	0.153218i	0.126729	+	0.991937i	$0.459552\pi$
$350$	−8.38525e7			−1.95574
$351$			7.07625e7i			1.63637i
$352$	9.17758e7	+	2.09472e7i	2.10426	+	0.480284i
$353$	6.30440e6	+	7.90546e6i	0.143324	+	0.179723i	0.848312	−	0.529496i	$-0.177619\pi$
$353$	6.30440e6	+	7.90546e6i	0.143324	+	0.179723i	−0.704988	+	0.709219i	$0.749048\pi$
$354$	4.73072e6	+	2.07267e7i	0.106639	+	0.467218i
$355$	1.73103e7	+	2.17065e7i	0.386919	+	0.485182i
$356$	1.22955e7	+	2.55318e7i	0.272518	+	0.565890i
$357$	−1.09435e6	+	4.79468e6i	−0.0240521	+	0.105379i
$358$	−7.40772e7	+	3.56737e7i	−1.61449	+	0.777498i
$359$	−359904.	+	451305.i	−0.00777864	+	0.00975410i	−0.785706	−	0.618601i	$-0.787700\pi$
$359$	−359904.	+	451305.i	−0.00777864	+	0.00975410i	0.777927	+	0.628355i	$0.216271\pi$
$360$	−2.56791e6	−	1.12507e7i	−0.0550392	−	0.241142i
$361$	−1.04505e7	−	4.57867e7i	−0.222134	−	0.973234i
$362$	−1.30809e7	+	2.71628e7i	−0.275748	+	0.572597i
$363$	−3.17386e7	−	2.53107e7i	−0.663541	−	0.529157i
$364$	3.90536e7	−	3.11442e7i	0.809760	−	0.645762i
$365$	−1.20353e7	−	5.79588e6i	−0.247501	−	0.119190i
$366$	2.01408e7	−	4.18227e7i	0.410802	−	0.853039i
$367$	−3.98378e7	−	4.99551e7i	−0.805931	−	1.01061i	−0.999564	−	0.0295311i	$-0.990599\pi$
$367$	−3.98378e7	−	4.99551e7i	−0.805931	−	1.01061i	0.193633	−	0.981074i	$-0.437973\pi$
$368$	1.70071e7	−	2.13263e7i	0.341262	−	0.427929i
$369$	−2.43860e7	−	1.17437e7i	−0.485358	−	0.233736i
$370$	−2.92356e7	+	6.67283e6i	−0.577174	+	0.131736i
$371$	4.37676e7	−	9.98968e6i	0.857100	−	0.195627i
$372$	1.25954e7	+	1.00445e7i	0.244672	+	0.195120i
$373$	−3.14596e7	−	6.53266e7i	−0.606215	−	1.25882i	−0.947769	−	0.318957i	$-0.896667\pi$
$373$	−3.14596e7	−	6.53266e7i	−0.606215	−	1.25882i	0.341554	−	0.939862i	$-0.389047\pi$
$374$	3.25911e7	+	7.43870e6i	0.622994	+	0.142194i
$375$	7.88882e7	−	3.79906e7i	1.49595	−	0.720414i
$376$	−3.57107e6	+	2.84784e6i	−0.0671793	+	0.0535737i
$377$	1.49990e8	−	3.42343e7i	2.79923	−	0.638906i
$378$	3.62850e7	−	2.89363e7i	0.671817	−	0.535757i
$379$	−1.90499e7	+	8.34633e7i	−0.349926	+	1.53313i	0.427421	+	0.904053i	$0.359422\pi$
$379$	−1.90499e7	+	8.34633e7i	−0.349926	+	1.53313i	−0.777346	+	0.629073i	$0.783435\pi$
$380$	4.88337e6			0.0889957
$381$		−	2.11180e7i		−	0.381838i
$382$	−1.33914e7	+	5.86716e7i	−0.240235	+	1.05254i
$383$	−5.77325e7	−	4.60402e7i	−1.02760	−	0.819484i	−0.0438526	−	0.999038i	$-0.513963\pi$
$383$	−5.77325e7	−	4.60402e7i	−1.02760	−	0.819484i	−0.983748	+	0.179554i	$0.942535\pi$
$384$	−1.62705e7	−	7.83547e6i	−0.287348	−	0.138379i
$385$	−8.00505e7	+	3.85503e7i	−1.40276	+	0.675531i
$386$			1.03546e8i			1.80041i
$387$	2.78363e7	+	1.62518e7i	0.480262	+	0.280394i
$388$	−6.50113e6			−0.111300
$389$	3.50636e6	+	7.28103e6i	0.0595672	+	0.123693i	0.928627	−	0.371014i	$-0.120990\pi$
$389$	3.50636e6	+	7.28103e6i	0.0595672	+	0.123693i	−0.869060	+	0.494707i	$0.835276\pi$
$390$	−7.29917e7	+	1.51569e8i	−1.23049	+	2.55515i
$391$	7.27237e6	−	9.11926e6i	0.121659	−	0.152556i
$392$	9.72829e6	+	2.22042e6i	0.161502	+	0.0368618i
$393$	−5.64461e7			−0.929942
$394$			7.30537e7i			1.19441i
$395$	−1.67438e8	−	3.82167e7i	−2.71684	−	0.620100i
$396$	−3.78236e7	−	4.74292e7i	−0.609083	−	0.763766i
$397$	377269.	+	1.65292e6i	0.00602948	+	0.0264169i	0.977853	−	0.209292i	$-0.0671159\pi$
$397$	377269.	+	1.65292e6i	0.00602948	+	0.0264169i	−0.971824	+	0.235709i	$0.924259\pi$
$398$	4.02197e7	+	5.04339e7i	0.637954	+	0.799969i
$399$	431115.	+	895219.i	0.00678694	+	0.0140932i
$400$	−2.71488e7	+	1.18947e8i	−0.424200	+	1.85854i
$401$	8.28259e7	−	3.98868e7i	1.28450	−	0.618581i	0.337955	−	0.941162i	$-0.390265\pi$
$401$	8.28259e7	−	3.98868e7i	1.28450	−	0.618581i	0.946542	+	0.322582i	$0.104551\pi$
$402$	−5.40875e7	+	6.78235e7i	−0.832566	+	1.04400i
$403$	9.26911e6	+	4.06106e7i	0.141619	+	0.620475i
$404$	2.05741e7	+	9.01410e7i	0.312016	+	1.36703i
$405$	−7.11127e6	+	1.47667e7i	−0.107049	+	0.222289i
$406$	−7.88885e7	−	6.29115e7i	−1.17879	−	0.940052i
$407$	−1.74480e7	+	1.39143e7i	−0.258798	+	0.206385i
$408$	−2.84913e6	−	1.37207e6i	−0.0419500	−	0.0202021i
$409$	3.00331e7	−	6.23644e7i	0.438965	−	0.911521i	−0.557709	−	0.830036i	$-0.688320\pi$
$409$	3.00331e7	−	6.23644e7i	0.438965	−	0.911521i	0.996675	−	0.0814844i	$-0.0259661\pi$
$410$	−1.12261e8	−	1.40771e8i	−1.62884	−	2.04250i
$411$	1.27406e7	−	1.59762e7i	0.183511	−	0.230116i
$412$	−5.05907e7	−	2.43632e7i	−0.723401	−	0.348372i
$413$	1.89130e7	−	4.31676e6i	0.268479	−	0.0612785i
$414$	−3.83506e7	+	8.75328e6i	−0.540470	+	0.123359i
$415$	8.04484e7	+	6.41555e7i	1.12557	+	0.897614i
$416$	−7.05676e7	−	1.46535e8i	−0.980224	−	2.03546i
$417$	−3.19100e7	−	7.28326e6i	−0.440067	−	0.100442i
$418$	6.08511e6	−	2.93043e6i	0.0833181	−	0.0401239i
$419$	−3.55968e7	+	2.83875e7i	−0.483914	+	0.385909i	−0.834838	−	0.550495i	$-0.814439\pi$
$419$	−3.55968e7	+	2.83875e7i	−0.483914	+	0.385909i	0.350924	+	0.936404i	$0.385868\pi$
$420$	5.78810e7	−	1.32110e7i	0.781247	−	0.178315i
$421$	3.17210e7	−	2.52966e7i	0.425109	−	0.339013i	−0.387452	−	0.921890i	$-0.626645\pi$
$421$	3.17210e7	−	2.52966e7i	0.425109	−	0.339013i	0.812560	+	0.582877i	$0.198073\pi$
$422$	2.65637e7	−	1.16383e8i	0.353468	−	1.54865i
$423$	−1.49050e7			−0.196929
$424$			2.88667e7i			0.378704i
$425$	−1.16090e7	+	5.08624e7i	−0.151227	+	0.662567i
$426$	−2.00603e7	−	1.59976e7i	−0.259483	−	0.206931i
$427$	−3.81630e7	−	1.83783e7i	−0.490184	−	0.236060i
$428$	−4.34605e7	+	2.09295e7i	−0.554324	+	0.266948i
$429$			1.25197e8i			1.58570i
$430$	1.19928e8	+	1.77749e8i	1.50840	+	2.23564i
$431$	1.19118e8			1.48781			0.743904	−	0.668286i	$-0.232972\pi$
$431$	1.19118e8			1.48781			0.743904	+	0.668286i	$0.232972\pi$
$432$	−2.92988e7	−	6.08397e7i	−0.363412	−	0.754633i
$433$	4.26839e7	−	8.86340e7i	0.525776	−	1.09178i	−0.453873	−	0.891066i	$-0.649958\pi$
$433$	4.26839e7	−	8.86340e7i	0.525776	−	1.09178i	0.979649	−	0.200718i	$-0.0643275\pi$
$434$	1.70336e7	−	2.13595e7i	0.208371	−	0.261289i
$435$	1.78270e8	+	4.06890e7i	2.16577	+	0.494322i
$436$	−4.40174e7			−0.531087
$437$		−	2.35656e6i		−	0.0282381i
$438$	1.20356e7	+	2.74704e6i	0.143233	+	0.0326921i
$439$	−7.29304e7	−	9.14519e7i	−0.862016	−	1.08093i	−0.995947	−	0.0899429i	$-0.971332\pi$
$439$	−7.29304e7	−	9.14519e7i	−0.862016	−	1.08093i	0.133931	−	0.990991i	$-0.457240\pi$
$440$	−1.27128e7	−	5.56985e7i	−0.149239	−	0.653861i
$441$	2.03020e7	+	2.54579e7i	0.236714	+	0.296829i
$442$	−2.50597e7	−	5.20370e7i	−0.290208	−	0.602622i
$443$	−1.36171e7	+	5.96605e7i	−0.156630	+	0.686239i	0.834238	+	0.551404i	$0.185908\pi$
$443$	−1.36171e7	+	5.96605e7i	−0.156630	+	0.686239i	−0.990868	+	0.134835i	$0.956950\pi$
$444$	1.34354e7	−	6.47015e6i	0.153498	−	0.0739206i
$445$	−5.42981e7	+	6.80876e7i	−0.616175	+	0.772659i
$446$	−3.35924e7	−	1.47178e8i	−0.378649	−	1.65897i
$447$	−9.24845e6	−	4.05201e7i	−0.103549	−	0.453678i
$448$	−2.85282e7	+	5.92394e7i	−0.317278	+	0.658835i
$449$	1.31659e8	+	1.04994e8i	1.45449	+	1.15992i	0.956129	+	0.292947i	$0.0946358\pi$
$449$	1.31659e8	+	1.04994e8i	1.45449	+	1.15992i	0.498360	+	0.866970i	$0.333936\pi$
$450$	1.37560e8	−	1.09700e8i	1.50957	−	1.20384i
$451$	−1.20727e8	−	5.81389e7i	−1.31605	−	0.633778i
$452$	700891.	−	1.45542e6i	0.00758989	−	0.0157606i
$453$	−2.71324e7	−	3.40229e7i	−0.291872	−	0.365996i
$454$	1.56073e8	−	1.95710e8i	1.66787	−	2.09144i
$455$	1.38306e8	+	6.66046e7i	1.46827	+	0.707082i
$456$	−622886.	+	142170.i	−0.00656922	+	0.00149938i
$457$	1.01686e8	−	2.32091e7i	1.06540	−	0.243170i	0.346331	−	0.938112i	$-0.387427\pi$
$457$	1.01686e8	−	2.32091e7i	1.06540	−	0.243170i	0.719065	+	0.694942i	$0.244570\pi$
$458$	3.49487e7	+	2.78707e7i	0.363777	+	0.290102i
$459$	−1.25284e7	−	2.60155e7i	−0.129556	−	0.269025i
$460$	−1.37276e8	−	3.13325e7i	−1.41034	−	0.321900i
$461$	−4.31744e7	+	2.07917e7i	−0.440680	+	0.212221i	−0.641049	−	0.767500i	$-0.721500\pi$
$461$	−4.31744e7	+	2.07917e7i	−0.440680	+	0.212221i	0.200368	+	0.979721i	$0.435786\pi$
$462$	6.41971e7	−	5.11955e7i	0.651013	−	0.519166i
$463$	−1.25633e8	+	2.86749e7i	−1.26579	+	0.288908i	−0.802153	−	0.597119i	$-0.796312\pi$
$463$	−1.25633e8	+	2.86749e7i	−1.26579	+	0.288908i	−0.463634	+	0.886027i	$0.653455\pi$
$464$	−1.14783e8	+	9.15364e7i	−1.14901	+	0.916304i
$465$	−1.10168e7	+	4.82676e7i	−0.109571	+	0.480061i
$466$	1.95124e8			1.92821
$467$		−	1.14155e8i		−	1.12085i	−0.828207	−	0.560423i	$-0.810639\pi$
$467$		−	1.14155e8i		−	1.12085i	0.828207	−	0.560423i	$-0.189361\pi$
$468$	−2.33228e7	+	1.02184e8i	−0.227532	+	0.996883i
$469$	6.18887e7	+	4.93546e7i	0.599919	+	0.478419i
$470$	−8.93328e7	−	4.30204e7i	−0.860433	−	0.414363i
$471$	−9.55811e7	+	4.60294e7i	−0.914765	+	0.440527i
$472$			1.24739e7i			0.118625i
$473$	1.37808e8	+	8.04571e7i	1.30224	+	0.760293i
$474$	1.58720e8			1.49037
$475$	4.57331e6	+	9.49657e6i	0.0426726	+	0.0886106i
$476$	−8.84381e6	+	1.83644e7i	−0.0820009	+	0.170277i
$477$	−5.87316e7	+	7.36471e7i	−0.541149	+	0.678579i
$478$	−1.66405e8	−	3.79809e7i	−1.52364	−	0.347762i
$479$	4.37961e7			0.398501			0.199250	−	0.979949i	$-0.436149\pi$
$479$	4.37961e7			0.398501			0.199250	+	0.979949i	$0.436149\pi$
$480$		−	1.93307e8i		−	1.74793i
$481$	3.75907e7	+	8.57983e6i	0.337789	+	0.0770980i
$482$	1.99573e8	+	2.50256e8i	1.78222	+	2.23483i
$483$	−6.37520e6	−	2.79316e7i	−0.0565787	−	0.247887i
$484$	−1.04902e8	−	1.31543e8i	−0.925225	−	1.16020i
$485$	−8.66853e6	−	1.80004e7i	−0.0759836	−	0.157782i
$486$	−3.55946e7	+	1.55950e8i	−0.310081	+	1.35855i
$487$	−1.66148e7	+	8.00125e6i	−0.143849	+	0.0692741i	−0.504424	−	0.863456i	$-0.668295\pi$
$487$	−1.66148e7	+	8.00125e6i	−0.143849	+	0.0692741i	0.360574	+	0.932730i	$0.382581\pi$
$488$	1.69816e7	−	2.12943e7i	0.146123	−	0.183233i
$489$	−1.64553e7	−	7.20954e7i	−0.140728	−	0.616568i
$490$	4.82004e7	+	2.11180e8i	0.409696	+	1.79500i
$491$	4.26932e7	−	8.86534e7i	0.360674	−	0.748947i	−0.639123	−	0.769105i	$-0.720703\pi$
$491$	4.26932e7	−	8.86534e7i	0.360674	−	0.748947i	0.999797	+	0.0201577i	$0.00641683\pi$
$492$	7.00029e7	+	5.58255e7i	0.587788	+	0.468745i
$493$	−4.90820e7	+	3.91416e7i	−0.409620	+	0.326661i
$494$	−1.05134e7	−	5.06300e6i	−0.0872095	−	0.0419979i
$495$	8.08890e7	−	1.67968e8i	0.666920	−	1.38487i
$496$	−2.47839e7	−	3.10781e7i	−0.203107	−	0.254688i
$497$	−1.45977e7	+	1.83049e7i	−0.118909	+	0.149107i
$498$	−8.56766e7	−	4.12597e7i	−0.693704	−	0.334070i
$499$	3.99138e6	−	911005.i	0.0321234	−	0.00733195i	−0.206429	−	0.978462i	$-0.566184\pi$
$499$	3.99138e6	−	911005.i	0.0321234	−	0.00733195i	0.238552	+	0.971130i	$0.423327\pi$
$500$	3.53797e8	−	8.07519e7i	2.83038	−	0.646015i
$501$	−6.32240e7	−	5.04195e7i	−0.502770	−	0.400945i
$502$	2.04208e7	+	4.24042e7i	0.161421	+	0.335195i
$503$	−8.22654e7	−	1.87765e7i	−0.646418	−	0.147541i	−0.113272	−	0.993564i	$-0.536133\pi$
$503$	−8.22654e7	−	1.87765e7i	−0.646418	−	0.147541i	−0.533146	+	0.846023i	$0.678990\pi$
$504$	8.76793e6	−	4.22241e6i	0.0684866	−	0.0329814i
$505$	−2.22150e8	+	1.77159e8i	−1.72493	+	1.37559i
$506$	−1.89861e8	+	4.33344e7i	−1.46549	+	0.334489i
$507$	1.01231e8	−	8.07287e7i	0.776762	−	0.619447i
$508$	1.94762e7	−	8.53307e7i	0.148564	−	0.650900i
$509$	2.96715e7			0.225002			0.112501	−	0.993652i	$-0.464114\pi$
$509$	2.96715e7			0.225002			0.112501	+	0.993652i	$0.464114\pi$
$510$		−	6.86465e7i		−	0.517497i
$511$	2.50666e6	−	1.09824e7i	0.0187859	−	0.0823066i
$512$	1.41915e8	+	1.13174e8i	1.05735	+	0.843209i
$513$	−5.25611e6	−	2.53121e6i	−0.0389325	−	0.0187489i
$514$	−4.37332e7	+	2.10608e7i	−0.322049	+	0.155091i
$515$		−	1.72562e8i		−	1.26335i
$516$	−7.78118e7	−	7.29044e7i	−0.566365	−	0.530646i
$517$	−7.37893e7			−0.533976
$518$	−1.09721e7	−	2.27839e7i	−0.0789409	−	0.163922i
$519$	−6.59782e7	+	1.37005e8i	−0.471953	+	0.980020i
$520$	−6.15427e7	+	7.71721e7i	−0.437690	+	0.548845i
$521$	−4.41496e7	−	1.00769e7i	−0.312186	−	0.0712545i	0.0635572	−	0.997978i	$-0.479755\pi$
$521$	−4.41496e7	−	1.00769e7i	−0.312186	−	0.0712545i	−0.375743	+	0.926724i	$0.622613\pi$
$522$	2.11720e8			1.48851
$523$			2.62682e8i			1.83622i	0.396323	+	0.918111i	$0.370286\pi$
$523$			2.62682e8i			1.83622i	−0.396323	+	0.918111i	$0.629714\pi$
$524$	−2.28079e8	−	5.20575e7i	−1.58523	−	0.361818i
$525$	7.98969e7	+	1.00188e8i	0.552144	+	0.692366i
$526$	3.83434e7	+	1.67993e8i	0.263471	+	1.15434i
$527$	−1.05978e7	−	1.32892e7i	−0.0724074	−	0.0907960i
$528$	−5.18370e7	−	1.07641e8i	−0.352158	−	0.731264i
$529$	1.78210e7	−	7.80790e7i	0.120383	−	0.527433i
$530$	−5.64575e8	+	2.71885e8i	−3.79223	+	1.82624i
$531$	−2.53792e7	+	3.18245e7i	−0.169510	+	0.212559i
$532$	916367.	+	4.01487e6i	0.00608604	+	0.0266647i
$533$	5.15158e7	+	2.25706e8i	0.340219	+	1.49060i
$534$	3.49202e7	−	7.25125e7i	0.229326	−	0.476200i
$535$	−1.15899e8	−	9.24267e7i	−0.756868	−	0.603582i
$536$	−3.97949e7	+	3.17354e7i	−0.258424	+	0.206086i
$537$	1.13206e8	+	5.45171e7i	0.731049	+	0.352055i
$538$	4.23901e7	−	8.80239e7i	0.272218	−	0.565267i
$539$	1.00508e8	+	1.26033e8i	0.641852	+	0.804857i
$540$	−2.17334e8	+	2.72528e8i	−1.38021	+	1.73073i
$541$	−2.16633e8	−	1.04325e8i	−1.36815	−	0.658866i	−0.401711	−	0.915766i	$-0.631584\pi$
$541$	−2.16633e8	−	1.04325e8i	−1.36815	−	0.658866i	−0.966438	+	0.256901i	$0.917299\pi$
$542$	3.00324e8	−	6.85469e7i	1.88622	−	0.430517i
$543$	4.49182e7	−	1.02523e7i	0.280558	−	0.0640355i
$544$	5.18876e7	+	4.13790e7i	0.322305	+	0.257029i
$545$	−5.86923e7	−	1.21876e8i	−0.362570	−	0.752884i
$546$	−1.38309e8	−	3.15682e7i	−0.849715	−	0.193942i
$547$	1.05611e8	−	5.08594e7i	0.645276	−	0.310749i	−0.0824716	−	0.996593i	$-0.526281\pi$
$547$	1.05611e8	−	5.08594e7i	0.645276	−	0.310749i	0.727748	+	0.685845i	$0.240567\pi$
$548$	6.62142e7	−	5.28041e7i	0.402355	−	0.320868i
$549$	8.66497e7	−	1.97772e7i	0.523661	−	0.119522i
$550$	6.81009e8	−	5.43087e8i	4.09322	−	3.26423i
$551$	−2.82236e6	+	1.23656e7i	−0.0168717	+	0.0739196i
$552$	1.84221e7			0.109527
$553$		−	1.44831e8i		−	0.856418i
$554$	4.00993e7	−	1.75687e8i	0.235835	−	1.03326i
$555$	3.58292e7	+	2.85728e7i	0.209584	+	0.167138i
$556$	−1.22220e8	−	5.88583e7i	−0.711082	−	0.342439i
$557$	−2.75080e8	+	1.32472e8i	−1.59182	+	0.766579i	−0.999242	−	0.0389357i	$-0.987603\pi$
$557$	−2.75080e8	+	1.32472e8i	−1.59182	+	0.766579i	−0.592576	+	0.805515i	$0.701889\pi$
$558$			5.73243e7i			0.329941i
$559$	−3.97684e7	−	2.72820e8i	−0.227668	−	1.56186i
$560$	−1.46489e8			−0.834143
$561$	−2.21658e7	−	4.60278e7i	−0.125544	−	0.260695i
$562$	2.02624e7	−	4.20754e7i	0.114152	−	0.237039i
$563$	−1.15129e8	+	1.44367e8i	−0.645148	+	0.808990i	−0.991636	−	0.129064i	$-0.958803\pi$
$563$	−1.15129e8	+	1.44367e8i	−0.645148	+	0.808990i	0.346488	+	0.938054i	$0.387374\pi$
$564$	4.80701e7	+	1.09717e7i	0.267940	+	0.0611556i
$565$	4.96433e6			0.0275242
$566$		−	3.46322e8i		−	1.90999i
$567$	−1.34749e7	−	3.07555e6i	−0.0739224	−	0.0168723i
$568$	−9.38644e6	−	1.17702e7i	−0.0512219	−	0.0642303i
$569$	−4.89281e7	−	2.14368e8i	−0.265596	−	1.16365i	−0.915078	−	0.403276i	$-0.867871\pi$
$569$	−4.89281e7	−	2.14368e8i	−0.265596	−	1.16365i	0.649482	−	0.760377i	$-0.274986\pi$
$570$	−8.64730e6	−	1.08434e7i	−0.0466934	−	0.0585517i
$571$	9.19833e7	+	1.91005e8i	0.494084	+	1.02598i	0.987709	+	0.156301i	$0.0499570\pi$
$571$	9.19833e7	+	1.91005e8i	0.494084	+	1.02598i	−0.493626	+	0.869674i	$0.664329\pi$
$572$	−1.15463e8	+	5.05876e8i	−0.616956	+	2.70306i
$573$	8.28610e7	−	3.99038e7i	0.440440	−	0.212105i
$574$	9.46694e7	−	1.18712e8i	0.500580	−	0.627708i
$575$	−6.76288e7	−	2.96301e8i	−0.355736	−	1.55858i
$576$	−3.06997e7	−	1.34504e8i	−0.160645	−	0.703830i
$577$	−4.14121e7	+	8.59930e7i	−0.215576	+	0.447647i	−0.980512	−	0.196458i	$-0.937056\pi$
$577$	−4.14121e7	+	8.59930e7i	−0.215576	+	0.447647i	0.764937	+	0.644106i	$0.222770\pi$
$578$	−2.03709e8	−	1.62452e8i	−1.05494	−	0.841284i
$579$	1.23718e8	−	9.86616e7i	0.637377	−	0.508291i
$580$	6.82803e8	+	3.28821e8i	3.49955	+	1.68529i
$581$	−3.76493e7	+	7.81795e7i	−0.191968	+	0.398625i
$582$	1.15120e7	+	1.44355e7i	0.0583957	+	0.0732258i
$583$	−2.90759e8	+	3.64601e8i	−1.46733	+	1.83998i
$584$	6.52606e6	+	3.14278e6i	0.0327652	+	0.0157789i
$585$	−3.14025e8	+	7.16742e7i	−1.56855	+	0.358010i
$586$	−7.85130e7	+	1.79201e7i	−0.390165	+	0.0890527i
$587$	−1.30417e8	−	1.04004e8i	−0.644792	−	0.514204i	0.245616	−	0.969367i	$-0.421010\pi$
$587$	−1.30417e8	−	1.04004e8i	−0.644792	−	0.514204i	−0.890408	+	0.455163i	$0.849581\pi$
$588$	−4.67363e7	−	9.70490e7i	−0.229891	−	0.477374i
$589$	−3.34804e6	−	764168.i	−0.0163849	−	0.00373975i
$590$	−2.43966e8	+	1.17488e8i	−1.18788	+	0.572053i
$591$	8.72852e7	−	6.96076e7i	0.422842	−	0.337205i
$592$	−3.58719e7	+	8.18752e6i	−0.172898	+	0.0394628i
$593$	−2.13464e8	+	1.70232e8i	−1.02367	+	0.816349i	−0.983145	−	0.182830i	$-0.941474\pi$
$593$	−2.13464e8	+	1.70232e8i	−1.02367	+	0.816349i	−0.0405246	+	0.999179i	$0.512903\pi$
$594$	−1.07277e8	+	4.70013e8i	−0.511857	+	2.24259i
$595$	−6.26396e7			−0.297371
$596$		−	1.72257e8i		−	0.813652i
$597$	2.19364e7	−	9.61095e7i	0.103096	−	0.451693i
$598$	2.63058e8	+	2.09782e8i	1.23012	+	0.980990i
$599$	−3.31960e7	−	1.59864e7i	−0.154456	−	0.0743822i	0.355059	−	0.934844i	$-0.384461\pi$
$599$	−3.31960e7	−	1.59864e7i	−0.154456	−	0.0743822i	−0.509515	+	0.860462i	$0.670175\pi$
$600$	−7.42381e7	+	3.57512e7i	−0.343695	+	0.165515i
$601$		−	8.92970e6i		−	0.0411352i	−0.999788	−	0.0205676i	$-0.993453\pi$
$601$		−	8.92970e6i		−	0.0411352i	0.999788	−	0.0205676i	$-0.00654733\pi$
$602$	−1.23632e8	+	1.31954e8i	−0.566685	+	0.604830i
$603$	−1.66096e8			−0.757544
$604$	−7.82548e7	−	1.62498e8i	−0.355140	−	0.737457i
$605$	2.24342e8	−	4.65851e8i	1.01308	−	2.10368i
$606$	1.63723e8	−	2.05302e8i	0.735686	−	0.922521i
$607$	2.90669e8	+	6.63433e7i	1.29967	+	0.296641i	0.815716	−	0.578453i	$-0.196343\pi$
$607$	2.90669e8	+	6.63433e7i	1.29967	+	0.296641i	0.483953	+	0.875094i	$0.339200\pi$
$608$	1.34086e7			0.0596585
$609$			1.54200e8i			0.682706i
$610$	5.76418e8	+	1.31564e8i	2.53950	+	0.579624i
$611$	7.94875e7	+	9.96742e7i	0.348478	+	0.436978i
$612$	−9.51697e6	−	4.16966e7i	−0.0415187	−	0.181906i
$613$	2.69162e8	+	3.37518e8i	1.16851	+	1.46526i	0.857223	+	0.514946i	$0.172188\pi$
$613$	2.69162e8	+	3.37518e8i	1.16851	+	1.46526i	0.311285	+	0.950317i	$0.399241\pi$
$614$	−2.13846e8	−	4.44055e8i	−0.923837	−	1.91837i
$615$	−6.12290e7	+	2.68262e8i	−0.263228	+	1.15328i
$616$	4.34070e7	−	2.09037e7i	0.185702	−	0.0894295i
$617$	1.75105e8	−	2.19575e8i	0.745494	−	0.934820i	−0.253981	−	0.967209i	$-0.581740\pi$
$617$	1.75105e8	−	2.19575e8i	0.745494	−	0.934820i	0.999475	+	0.0323892i	$0.0103116\pi$
$618$	3.54865e7	+	1.55476e8i	0.150348	+	0.658718i
$619$	2.35932e7	+	1.03368e8i	0.0994751	+	0.435829i	0.999999	+	0.00102345i	$0.000325774\pi$
$619$	2.35932e7	+	1.03368e8i	0.0994751	+	0.435829i	−0.900524	+	0.434806i	$0.856817\pi$
$620$	−8.90299e7	+	1.84872e8i	−0.373560	+	0.775706i
$621$	1.31514e8	+	1.04879e8i	0.549157	+	0.437938i
$622$	−6.04754e7	+	4.82275e7i	−0.251309	+	0.200412i
$623$	−6.61673e7	−	3.18645e7i	−0.273640	−	0.131778i
$624$	−8.95604e7	+	1.85974e8i	−0.368606	+	0.765418i
$625$	3.36150e8	+	4.21518e8i	1.37687	+	1.72654i
$626$	4.31599e7	−	5.41208e7i	0.175937	−	0.220618i
$627$	−9.29936e6	−	4.47834e6i	−0.0377269	−	0.0181683i
$628$	−4.28661e8	+	9.78391e7i	−1.73075	+	0.395033i
$629$	−1.53391e7	+	3.50104e6i	−0.0616377	+	0.0140684i
$630$	1.65164e8	+	1.31714e8i	0.660532	+	0.526757i
$631$	5.40413e7	+	1.12218e8i	0.215099	+	0.446657i	0.980401	−	0.197014i	$-0.0631246\pi$
$631$	5.40413e7	+	1.12218e8i	0.215099	+	0.446657i	−0.765302	+	0.643672i	$0.777410\pi$
$632$	9.07925e7	+	2.07228e7i	0.359665	+	0.0820913i
$633$	−1.64366e8	+	7.91544e7i	−0.648038	+	0.312079i
$634$	−4.69040e7	+	3.74047e7i	−0.184053	+	0.146777i
$635$	2.62234e8	−	5.98531e7i	1.02416	−	0.233757i
$636$	2.43628e8	−	1.94287e8i	0.947013	−	0.755217i
$637$	6.19753e7	−	2.71532e8i	0.239773	−	1.05051i
$638$	1.04815e9			4.03611
$639$		−	4.91266e7i		−	0.188284i
$640$	5.11829e7	−	2.24247e8i	0.195247	−	0.855434i
$641$	1.02026e8	+	8.13626e7i	0.387378	+	0.308923i	0.797743	−	0.602998i	$-0.206027\pi$
$641$	1.02026e8	+	8.13626e7i	0.387378	+	0.308923i	−0.410365	+	0.911921i	$0.634599\pi$
$642$	1.23432e8	+	5.94415e7i	0.466467	+	0.224639i
$643$	1.90262e8	−	9.16251e7i	0.715679	−	0.344653i	−0.0403550	−	0.999185i	$-0.512849\pi$
$643$	1.90262e8	−	9.16251e7i	0.715679	−	0.344653i	0.756034	+	0.654533i	$0.227135\pi$
$644$		−	1.18741e8i		−	0.444575i
$645$	9.81051e7	−	3.12656e8i	0.365605	−	1.16516i
$646$	4.76160e6			0.0176626
$647$	−1.04711e7	−	2.17435e7i	−0.0386616	−	0.0802817i	0.880743	−	0.473594i	$-0.157043\pi$
$647$	−1.04711e7	−	2.17435e7i	−0.0386616	−	0.0802817i	−0.919405	+	0.393312i	$0.871329\pi$
$648$	3.85605e6	−	8.00717e6i	0.0141716	−	0.0294275i
$649$	−1.25644e8	+	1.57552e8i	−0.459628	+	0.576355i
$650$	−1.46720e9	−	3.34878e8i	−5.34255	−	1.21940i
$651$	−4.17505e7			−0.151328
$652$		−	3.06488e8i		−	1.10579i
$653$	3.31986e7	+	7.57736e6i	0.119228	+	0.0272131i	0.281719	−	0.959497i	$-0.409095\pi$
$653$	3.31986e7	+	7.57736e6i	0.119228	+	0.0272131i	−0.162490	+	0.986710i	$0.551953\pi$
$654$	7.79445e7	+	9.77393e7i	0.278646	+	0.349410i
$655$	−1.59980e8	−	7.00920e8i	−0.569302	−	2.49428i
$656$	−1.37744e8	−	1.72726e8i	−0.487935	−	0.611851i
$657$	1.02556e7	+	2.12959e7i	0.0361629	+	0.0750931i
$658$	1.86059e7	−	8.15178e7i	0.0653090	−	0.286137i
$659$	3.02108e8	−	1.45488e8i	1.05562	−	0.508358i	0.176172	−	0.984359i	$-0.443629\pi$
$659$	3.02108e8	−	1.45488e8i	1.05562	−	0.508358i	0.879444	+	0.476002i	$0.157914\pi$
$660$	−3.84518e8	+	4.82171e8i	−1.33747	+	1.67714i
$661$	7.08590e6	+	3.10454e7i	0.0245353	+	0.107496i	0.985713	−	0.168435i	$-0.0538712\pi$
$661$	7.08590e6	+	3.10454e7i	0.0245353	+	0.107496i	−0.961178	+	0.275931i	$0.911014\pi$
$662$	2.62477e7	+	1.14999e8i	0.0904727	+	0.396387i
$663$	−3.82966e7	+	7.95237e7i	−0.131407	+	0.272870i
$664$	−4.36227e7	−	3.47880e7i	−0.149008	−	0.118830i
$665$	−9.89452e6	+	7.89062e6i	−0.0336457	+	0.0268316i
$666$	4.78068e7	+	2.30225e7i	0.161833	+	0.0779346i
$667$	1.58679e8	−	3.29500e8i	0.534738	−	1.11040i
$668$	−2.08967e8	−	2.62036e8i	−0.701049	−	0.879087i
$669$	−1.43842e8	+	1.80372e8i	−0.480404	+	0.602407i
$670$	−9.95496e8	−	4.79405e8i	−3.30990	−	1.59396i
$671$	4.28973e8	−	9.79102e7i	1.41991	−	0.324086i
$672$	1.58928e8	−	3.62742e7i	0.523711	−	0.119534i
$673$	2.18979e8	+	1.74630e8i	0.718385	+	0.572893i	0.912987	−	0.407989i	$-0.133770\pi$
$673$	2.18979e8	+	1.74630e8i	0.718385	+	0.572893i	−0.194601	+	0.980882i	$0.562341\pi$
$674$	2.59760e8	+	5.39397e8i	0.848383	+	1.76169i
$675$	−7.33514e8	−	1.67420e8i	−2.38505	−	0.544371i
$676$	4.83490e8	−	2.32837e8i	1.56512	−	0.753722i
$677$	−1.70120e8	+	1.35666e8i	−0.548263	+	0.437225i	−0.858039	−	0.513584i	$-0.828317\pi$
$677$	−1.70120e8	+	1.35666e8i	−0.548263	+	0.437225i	0.309776	+	0.950810i	$0.399746\pi$
$678$	−4.47282e6	+	1.02089e6i	−0.0143513	+	0.00327560i
$679$	1.31724e7	−	1.05046e7i	0.0420780	−	0.0335560i
$680$	8.96265e6	−	3.92679e7i	0.0285042	−	0.124885i
$681$	−3.82546e8			−1.21127
$682$			2.83793e8i			0.894640i
$683$	6.98332e7	−	3.05959e8i	0.219179	−	0.960287i	−0.738907	−	0.673808i	$-0.764658\pi$
$683$	6.98332e7	−	3.05959e8i	0.219179	−	0.960287i	0.958086	−	0.286480i	$-0.0924852\pi$
$684$	−6.75575e6	−	5.38753e6i	−0.0211108	−	0.0168353i
$685$	2.34494e8	+	1.12926e8i	0.729557	+	0.351336i
$686$	−4.05648e8	+	1.95350e8i	−1.25654	+	0.605118i
$687$		−	6.83130e7i		−	0.210685i
$688$	1.47152e8	+	2.18097e8i	0.451855	+	0.669707i
$689$	8.05714e8			2.46333
$690$	1.73511e8	+	3.60300e8i	0.528179	+	1.09677i
$691$	−1.66497e8	+	3.45735e8i	−0.504630	+	1.04787i	0.480648	+	0.876913i	$0.340401\pi$
$691$	−1.66497e8	+	3.45735e8i	−0.504630	+	1.04787i	−0.985278	+	0.170961i	$0.945313\pi$
$692$	−3.92949e8	+	4.92742e8i	−1.18582	+	1.48697i
$693$	1.53274e8	+	3.49837e7i	0.460540	+	0.105115i
$694$	−1.99465e8			−0.596744
$695$		−	4.16886e8i		−	1.24183i
$696$	−9.66661e7	−	2.20634e7i	−0.286713	−	0.0654403i
$697$	−5.89003e7	−	7.38587e7i	−0.173948	−	0.218124i
$698$	−7.66651e7	−	3.35892e8i	−0.225440	−	0.987718i
$699$	−1.85920e8	−	2.33136e8i	−0.544370	−	0.682619i
$700$	2.30438e8	+	4.78509e8i	0.671830	+	1.39507i
$701$	4.97616e7	−	2.18020e8i	0.144458	−	0.632910i	−0.849910	−	0.526927i	$-0.823344\pi$
$701$	4.97616e7	−	2.18020e8i	0.144458	−	0.632910i	0.994368	−	0.105983i	$-0.0337989\pi$
$702$	7.50453e8	−	3.61399e8i	2.16926	−	1.04466i
$703$	−1.98193e6	+	2.48526e6i	−0.00570456	+	0.00715329i
$704$	−1.51983e8	−	6.65882e8i	−0.435590	−	1.90844i
$705$	3.37176e7	+	1.47726e8i	0.0962253	+	0.421591i
$706$	5.16414e7	−	1.07234e8i	0.146752	−	0.304734i
$707$	−1.87337e8	−	1.49397e8i	−0.530111	−	0.422749i
$708$	1.05277e8	−	8.39557e7i	0.296643	−	0.236565i
$709$	2.53011e8	+	1.21844e8i	0.709905	+	0.341872i	0.753746	−	0.657166i	$-0.228245\pi$
$709$	2.53011e8	+	1.21844e8i	0.709905	+	0.341872i	−0.0438406	+	0.999039i	$0.513959\pi$
$710$	1.41795e8	−	2.94440e8i	0.396173	−	0.822662i
$711$	1.89475e8	+	2.37594e8i	0.527161	+	0.661039i
$712$	2.94428e7	−	3.69201e7i	0.0815717	−	0.102288i
$713$	8.92137e7	+	4.29631e7i	0.246129	+	0.118530i
$714$	5.64378e7	−	1.28815e7i	0.155051	−	0.0353894i
$715$	−1.55463e9	+	3.54834e8i	−4.25313	+	0.970750i
$716$	4.07148e8	+	3.24689e8i	1.10921	+	0.884564i
$717$	1.13176e8	+	2.35011e8i	0.307040	+	0.637576i
$718$	6.62431e6	+	1.51195e6i	0.0178965	+	0.00408475i
$719$	−6.57487e8	+	3.16629e8i	−1.76889	+	0.851852i	−0.801729	+	0.597688i	$0.796086\pi$
$719$	−6.57487e8	+	3.16629e8i	−1.76889	+	0.851852i	−0.967161	+	0.254164i	$0.918200\pi$
$720$	2.40314e8	−	1.91644e8i	0.643846	−	0.513450i
$721$	1.41872e8	−	3.23813e7i	0.378521	−	0.0863949i
$722$	−4.32205e8	+	3.44672e8i	−1.14836	+	0.915788i
$723$	1.08850e8	−	4.76902e8i	0.288013	−	1.26187i
$724$	1.90954e8			0.503168
$725$			1.63577e9i			4.29249i
$726$	−1.06330e8	+	4.65863e8i	−0.277873	+	1.21744i
$727$	1.66185e8	+	1.32528e8i	0.432501	+	0.344908i	0.815416	−	0.578875i	$-0.196508\pi$
$727$	1.66185e8	+	1.32528e8i	0.432501	+	0.344908i	−0.382915	+	0.923784i	$0.625080\pi$
$728$	−7.49956e7	−	3.61160e7i	−0.194375	−	0.0936063i
$729$	2.67230e8	−	1.28691e8i	0.689768	−	0.332175i
$730$			1.57238e8i			0.404192i
$731$	6.29230e7	+	9.32599e7i	0.161086	+	0.238750i
$732$	−2.94013e8			−0.749606
$733$	−1.39179e8	−	2.89008e8i	−0.353396	−	0.733835i	0.646173	−	0.763191i	$-0.276369\pi$
$733$	−1.39179e8	−	2.89008e8i	−0.353396	−	0.733835i	−0.999569	+	0.0293564i	$0.990654\pi$
$734$	−3.26325e8	+	6.77621e8i	−0.825206	+	1.71356i
$735$	2.06392e8	−	2.58808e8i	0.519794	−	0.651801i
$736$	−3.76929e8	−	8.60315e7i	−0.945422	−	0.215786i
$737$	−8.22284e8			−2.05409
$738$			3.18597e8i			0.792634i
$739$	1.28440e8	+	2.93155e7i	0.318248	+	0.0726380i	0.378661	−	0.925535i	$-0.376385\pi$
$739$	1.28440e8	+	2.93155e7i	0.318248	+	0.0726380i	−0.0604131	+	0.998173i	$0.519242\pi$
$740$	1.18422e8	+	1.48497e8i	0.292238	+	0.366455i
$741$	3.96817e6	+	1.73857e7i	0.00975295	+	0.0427305i
$742$	−3.29473e8	−	4.13147e8i	−0.806508	−	1.01133i
$743$	2.32627e8	+	4.83054e8i	0.567143	+	1.17769i	0.965487	+	0.260449i	$0.0838707\pi$
$743$	2.32627e8	+	4.83054e8i	0.567143	+	1.17769i	−0.398344	+	0.917236i	$0.630415\pi$
$744$	5.97378e6	−	2.61728e7i	0.0145054	−	0.0635524i
$745$	4.76947e8	−	2.29686e8i	1.15346	−	0.555476i
$746$	−5.32133e8	+	6.67273e8i	−1.28175	+	1.60726i
$747$	−4.05150e7	−	1.77508e8i	−0.0971973	−	0.425849i
$748$	−4.71152e7	−	2.06425e8i	−0.112579	−	0.493239i
$749$	5.42401e7	−	1.12631e8i	0.129085	−	0.268047i
$750$	−8.05798e8	−	6.42602e8i	−1.91004	−	1.52321i
$751$	−2.62638e8	+	2.09447e8i	−0.620066	+	0.494486i	−0.882406	−	0.470489i	$-0.844077\pi$
$751$	−2.62638e8	+	2.09447e8i	−0.620066	+	0.494486i	0.262340	+	0.964976i	$0.415506\pi$
$752$	−1.09611e8	−	5.27858e7i	−0.257751	−	0.124126i
$753$	3.12074e7	−	6.48028e7i	0.0730924	−	0.151778i
$754$	−1.12909e9	−	1.41584e9i	−2.63400	−	3.30294i
$755$	3.45581e8	−	4.33345e8i	0.802988	−	1.00692i
$756$	−2.64842e8	−	1.27541e8i	−0.612946	−	0.295179i
$757$	3.49121e8	−	7.96845e7i	0.804800	−	0.183690i	0.199718	−	0.979853i	$-0.435997\pi$
$757$	3.49121e8	−	7.96845e7i	0.804800	−	0.183690i	0.605082	+	0.796163i	$0.293140\pi$
$758$	9.82440e8	−	2.24235e8i	2.25579	−	0.514869i
$759$	2.32681e8	+	1.85557e8i	0.532151	+	0.424376i
$760$	−3.53079e6	−	7.33175e6i	−0.00804323	−	0.0167019i
$761$	1.11709e8	+	2.54968e7i	0.253474	+	0.0578537i	0.347370	−	0.937728i	$-0.387075\pi$
$761$	1.11709e8	+	2.54968e7i	0.253474	+	0.0578537i	−0.0938960	+	0.995582i	$0.529932\pi$
$762$	−2.23962e8	+	1.07854e8i	−0.506185	+	0.243766i
$763$	8.91866e7	−	7.11240e7i	0.200783	−	0.160119i
$764$	3.71614e8	−	8.48185e7i	0.833321	−	0.190200i
$765$	1.02760e8	−	8.19483e7i	0.229530	−	0.183044i
$766$	−1.93414e8	+	8.47404e8i	−0.430331	+	1.88540i
$767$	3.48167e8			0.771616
$768$		−	1.79208e8i		−	0.395615i
$769$	2.99407e6	−	1.31179e7i	0.00658389	−	0.0288459i	−0.971529	−	0.236920i	$-0.923862\pi$
$769$	2.99407e6	−	1.31179e7i	0.00658389	−	0.0288459i	0.978113	+	0.208074i	$0.0667194\pi$
$770$	8.17670e8	+	6.52070e8i	1.79104	+	1.42831i
$771$	6.68338e7	+	3.21855e7i	0.145825	+	0.0702258i
$772$	5.90891e8	−	2.84558e8i	1.28427	−	0.618471i
$773$		−	3.40744e8i		−	0.737717i	−0.929486	−	0.368858i	$-0.879749\pi$
$773$		−	3.40744e8i		−	0.737717i	0.929486	−	0.368858i	$-0.120251\pi$
$774$	3.01888e7	−	3.78212e8i	0.0651063	−	0.815665i
$775$	−4.42894e8			−0.951468
$776$	4.70046e6	+	9.76061e6i	0.0100590	+	0.0208878i
$777$	−1.67678e7	+	3.48187e7i	−0.0357448	+	0.0742249i
$778$	5.93093e7	−	7.43715e7i	0.125946	−	0.157931i
$779$	−1.86077e7	−	4.24709e6i	−0.0393624	−	0.00898420i
$780$	1.06553e9			2.24533
$781$		−	2.43209e8i		−	0.510536i
$782$	−1.33853e8	−	3.05512e7i	−0.279904	−	0.0638863i
$783$	−5.64482e8	−	7.07838e8i	−1.17588	−	1.47451i
$784$	5.91416e7	+	2.59116e8i	0.122728	+	0.537708i
$785$	−8.42469e8	−	1.05642e9i	−1.74159	−	2.18388i
$786$	2.88282e8	+	5.98624e8i	0.593676	+	1.23278i
$787$	−4.54152e6	+	1.98977e7i	−0.00931701	+	0.0408205i	−0.979373	−	0.202062i	$-0.935236\pi$
$787$	−4.54152e6	+	1.98977e7i	−0.00931701	+	0.0408205i	0.970056	+	0.242882i	$0.0780929\pi$
$788$	4.16885e8	−	2.00761e8i	0.851996	−	0.410300i
$789$	1.64185e8	−	2.05882e8i	0.334274	−	0.419167i
$790$	4.49846e8	+	1.97090e9i	0.912394	+	3.99746i
$791$	931558.	+	4.08142e6i	0.00188226	+	0.00824674i
$792$	−4.38616e7	+	9.10796e7i	−0.0882895	+	0.183335i
$793$	−5.94356e8	−	4.73983e8i	−1.19186	−	0.950480i
$794$	1.56028e7	−	1.24429e7i	0.0311704	−	0.0248576i
$795$	8.62793e8	+	4.15499e8i	1.71714	+	0.826930i
$796$	1.77275e8	−	3.68115e8i	0.351485	−	0.729867i
$797$	1.39854e8	+	1.75371e8i	0.276249	+	0.346405i	0.900529	−	0.434795i	$-0.143179\pi$
$797$	1.39854e8	+	1.75371e8i	0.276249	+	0.346405i	−0.624281	+	0.781200i	$0.714608\pi$
$798$	7.29221e6	−	9.14414e6i	0.0143500	−	0.0179943i
$799$	−4.68703e7	−	2.25716e7i	−0.0918877	−	0.0442508i
$800$	1.68592e9	−	3.84800e8i	3.29281	−	0.751563i
$801$	1.50234e8	−	3.42899e7i	0.292328	−	0.0667220i
$802$	−8.46018e8	−	6.74677e8i	−1.64005	−	1.30790i
$803$	5.07717e7	+	1.05429e8i	0.0980563	+	0.203616i
$804$	5.35678e8	+	1.22265e8i	1.03071	+	0.235252i
$805$	3.28772e8	−	1.58328e8i	0.630242	−	0.303509i
$806$	3.83346e8	−	3.05708e8i	0.732125	−	0.583851i
$807$	−1.45562e8	+	3.32236e7i	−0.276967	+	0.0632158i
$808$	1.20460e8	−	9.60632e7i	0.228353	−	0.182106i
$809$	−1.64296e7	+	7.19828e7i	−0.0310300	+	0.135951i	−0.988070	−	0.154004i	$-0.950783\pi$
$809$	−1.64296e7	+	7.19828e7i	−0.0310300	+	0.135951i	0.957040	+	0.289955i	$0.0936404\pi$
$810$	1.92923e8			0.363019
$811$		−	3.82691e8i		−	0.717441i	−0.933445	−	0.358720i	$-0.883213\pi$
$811$		−	3.82691e8i		−	0.717441i	0.933445	−	0.358720i	$-0.116787\pi$
$812$	−1.42212e8	+	6.23071e8i	−0.265624	+	1.16378i
$813$	−3.68057e8	−	2.93516e8i	−0.684926	−	0.546210i
$814$	2.36675e8	+	1.13976e8i	0.438812	+	0.211321i
$815$	8.48608e8	−	4.08668e8i	1.56760	−	0.754914i
$816$		−	8.42288e7i		−	0.155021i
$817$	2.16871e7	+	6.80498e6i	0.0397681	+	0.0124784i
$818$	−8.14774e8			−1.48860
$819$	−1.17854e8	−	2.44726e8i	−0.214532	−	0.445481i
$820$	−4.94810e8	+	1.02748e9i	−0.897423	+	1.86352i
$821$	4.84090e8	−	6.07030e8i	0.874776	−	1.09693i	−0.119787	−	0.992800i	$-0.538221\pi$
$821$	4.84090e8	−	6.07030e8i	0.874776	−	1.09693i	0.994563	−	0.104135i	$-0.0332073\pi$
$822$	−2.34500e8	−	5.35230e7i	−0.422208	−	0.0963662i
$823$	−3.65395e8			−0.655486			−0.327743	−	0.944767i	$-0.606288\pi$
$823$	−3.65395e8			−0.655486			−0.327743	+	0.944767i	$0.606288\pi$
$824$			9.35705e7i			0.167247i
$825$	−1.29777e9	−	2.96207e8i	−2.31119	−	0.527514i
$826$	−1.42373e8	−	1.78530e8i	−0.252631	−	0.316790i
$827$	−9.06960e7	−	3.97365e8i	−0.160351	−	0.702544i	−0.989622	−	0.143697i	$-0.954101\pi$
$827$	−9.06960e7	−	3.97365e8i	−0.160351	−	0.702544i	0.829271	−	0.558847i	$-0.188756\pi$
$828$	1.55344e8	+	1.94795e8i	0.273654	+	0.343152i
$829$	3.45192e8	+	7.16799e8i	0.605895	+	1.25815i	0.947934	+	0.318468i	$0.103168\pi$
$829$	3.45192e8	+	7.16799e8i	0.605895	+	1.25815i	−0.342038	+	0.939686i	$0.611117\pi$
$830$	2.69517e8	−	1.18083e9i	0.471359	−	2.06516i
$831$	−2.48120e8	+	1.19488e8i	−0.432372	+	0.208220i
$832$	−7.35750e8	+	9.22602e8i	−1.27750	+	1.60193i
$833$	2.52893e7	+	1.10800e8i	0.0437524	+	0.191692i
$834$	8.57307e7	+	3.75611e8i	0.147788	+	0.647500i
$835$	4.46894e8	−	9.27985e8i	0.767618	−	1.59398i
$836$	−3.34454e7	−	2.66718e7i	−0.0572423	−	0.0456492i
$837$	1.91651e8	−	1.52836e8i	0.326839	−	0.260645i
$838$	4.82856e8	+	2.32531e8i	0.820513	+	0.395138i
$839$	−1.84007e8	+	3.82095e8i	−0.311565	+	0.646972i	−0.996676	−	0.0814670i	$-0.974039\pi$
$839$	−1.84007e8	+	3.82095e8i	−0.311565	+	0.646972i	0.685111	+	0.728439i	$0.259754\pi$
$840$	−6.16838e7	−	7.73491e7i	−0.104072	−	0.130502i
$841$	−8.56395e8	+	1.07389e9i	−1.43975	+	1.80539i
$842$	−4.30282e8	−	2.07213e8i	−0.720804	−	0.347121i
$843$	−6.95786e7	+	1.58809e7i	−0.116143	+	0.0265089i
$844$	−7.37146e8	+	1.68249e8i	−1.22610	+	0.279850i
$845$	1.28936e9	+	1.02823e9i	2.13700	+	1.70420i
$846$	7.61228e7	+	1.58071e8i	0.125720	+	0.261060i
$847$	4.25097e8	+	9.70257e7i	0.699581	+	0.159675i
$848$	−6.92731e8	+	3.33602e8i	−1.13600	+	0.547067i
$849$	−4.13788e8	+	3.29985e8i	−0.676168	+	0.539226i
$850$	5.98697e8	−	1.36649e8i	0.974878	−	0.222510i
$851$	7.16598e7	−	5.71468e7i	0.116275	−	0.0927264i
$852$	−3.61626e7	+	1.58439e8i	−0.0584710	+	0.256178i
$853$	4.72868e8			0.761891			0.380946	−	0.924597i	$-0.375599\pi$
$853$	4.72868e8			0.761891			0.380946	+	0.924597i	$0.375599\pi$
$854$			4.98590e8i			0.800516i
$855$	5.90900e6	−	2.58890e7i	0.00945401	−	0.0414207i
$856$	6.28459e7	+	5.01179e7i	0.100197	+	0.0799046i
$857$	−1.46121e8	−	7.03683e7i	−0.232151	−	0.111798i	0.314192	−	0.949359i	$-0.398266\pi$
$857$	−1.46121e8	−	7.03683e7i	−0.232151	−	0.111798i	−0.546343	+	0.837561i	$0.683981\pi$
$858$	1.32774e9	−	6.39405e8i	2.10209	−	1.01231i
$859$			1.22622e9i			1.93459i	0.253645	+	0.967297i	$0.418371\pi$
$859$			1.22622e9i			1.93459i	−0.253645	+	0.967297i	$0.581629\pi$
$860$	6.84757e8	−	1.17286e9i	1.07657	−	1.84395i
$861$	−2.32041e8			−0.363543
$862$	−6.08363e8	−	1.26328e9i	−0.949819	−	1.97232i
$863$	1.37856e8	−	2.86261e8i	0.214483	−	0.445379i	−0.765773	−	0.643111i	$-0.777643\pi$
$863$	1.37856e8	−	2.86261e8i	0.214483	−	0.445379i	0.980256	+	0.197732i	$0.0633576\pi$
$864$	−5.96748e8	+	7.48299e8i	−0.925231	+	1.16020i
$865$	−1.88826e9	−	4.30983e8i	−2.91752	−	0.665905i
$866$	−1.15798e9			−1.78298
$867$			3.98182e8i			0.610976i
$868$	−1.68699e8	−	3.85046e7i	−0.257961	−	0.0588780i
$869$	9.38025e8	+	1.17625e9i	1.42940	+	1.79242i
$870$	−4.78948e8	−	2.09841e9i	−0.727328	−	3.18663i
$871$	8.85783e8	+	1.11074e9i	1.34052	+	1.68096i
$872$	3.18256e7	+	6.60865e7i	0.0479984	+	0.0996697i
$873$	−7.86653e6	+	3.44655e7i	−0.0118234	+	0.0518015i
$874$	−2.49919e7	+	1.20355e7i	−0.0374339	+	0.0180272i
$875$	−5.86372e8	+	7.35287e8i	−0.875283	+	1.09757i
$876$	−1.73992e7	−	7.62308e7i	−0.0258831	−	0.113401i
$877$	−1.73781e8	−	7.61383e8i	−0.257634	−	1.12877i	−0.923773	−	0.382940i	$-0.874911\pi$
$877$	−1.73781e8	−	7.61383e8i	−0.257634	−	1.12877i	0.666139	−	0.745827i	$-0.267946\pi$
$878$	−5.97397e8	+	1.24051e9i	−0.882632	+	1.83280i
$879$	9.62204e7	+	7.67332e7i	0.141677	+	0.112984i
$880$	1.18971e9	−	9.48763e8i	1.74580	−	1.39223i
$881$	−1.05133e9	−	5.06296e8i	−1.53749	−	0.740417i	−0.542470	−	0.840075i	$-0.682511\pi$
$881$	−1.05133e9	−	5.06296e8i	−1.53749	−	0.740417i	−0.995022	+	0.0996576i	$0.968225\pi$
$882$	1.66300e8	−	3.45326e8i	0.242375	−	0.503297i
$883$	2.33969e8	+	2.93388e8i	0.339842	+	0.426148i	0.922157	−	0.386815i	$-0.126425\pi$
$883$	2.33969e8	+	2.93388e8i	0.339842	+	0.426148i	−0.582316	+	0.812963i	$0.697853\pi$
$884$	−2.28084e8	+	2.86009e8i	−0.330171	+	0.414021i
$885$	3.72832e8	+	1.79547e8i	0.537878	+	0.259028i
$886$	7.02259e8	−	1.60286e8i	1.00971	−	0.230459i
$887$	−1.39278e8	+	3.17892e7i	−0.199577	+	0.0455521i	−0.321141	−	0.947031i	$-0.604066\pi$
$887$	−1.39278e8	+	3.17892e7i	−0.199577	+	0.0455521i	0.121564	+	0.992584i	$0.461209\pi$
$888$	−1.94282e7	−	1.54935e7i	−0.0277456	−	0.0221263i
$889$	9.84165e7	+	2.04364e8i	0.140076	+	0.290870i
$890$	9.99397e8	+	2.28106e8i	1.41765	+	0.323569i
$891$	1.29356e8	−	6.22945e7i	0.182875	−	0.0880677i
$892$	−7.47563e8	+	5.96161e8i	−1.05330	+	0.839981i
$893$	−1.02469e7	+	2.33879e6i	−0.0143893	+	0.00328426i
$894$	−3.82492e8	+	3.05027e8i	−0.535315	+	0.426899i
$895$	−3.56117e8	+	1.56025e9i	−0.496734	+	2.17633i
$896$	1.93969e8			0.269655
$897$		−	5.14190e8i		−	0.712436i
$898$	4.41080e8	−	1.93250e9i	0.609100	−	2.66864i
$899$	−4.16675e8	−	3.32287e8i	−0.573480	−	0.457335i
$900$	−1.00404e9	−	4.83521e8i	−1.37729	−	0.663266i
$901$	−2.96216e8	+	1.42650e8i	−0.404981	+	0.195029i
$902$			1.57726e9i			2.14924i
$903$	2.75460e8	+	2.19872e7i	0.374106	+	0.0298611i
$904$	−2.69188e6			−0.00364376
$905$	2.54616e8	+	5.28715e8i	0.343510	+	0.713306i
$906$	−2.22250e8	+	4.61507e8i	−0.298853	+	0.620575i
$907$	−3.64831e8	+	4.57483e8i	−0.488956	+	0.613131i	−0.963698	−	0.266994i	$-0.913970\pi$
$907$	−3.64831e8	+	4.57483e8i	−0.488956	+	0.613131i	0.474743	+	0.880125i	$0.342541\pi$
$908$	−1.54574e9	−	3.52805e8i	−2.06480	−	0.471277i
$909$	5.02774e8			0.669394
$910$		−	1.80693e9i		−	2.39782i
$911$	4.91972e8	+	1.12289e8i	0.650706	+	0.148519i	0.535117	−	0.844778i	$-0.320267\pi$
$911$	4.91972e8	+	1.12289e8i	0.650706	+	0.148519i	0.115589	+	0.993297i	$0.463124\pi$
$912$	−1.06102e7	−	1.33048e7i	−0.0139874	−	0.0175397i
$913$	−2.00576e8	−	8.78779e8i	−0.263552	−	1.15470i
$914$	−7.65468e8	−	9.59867e8i	−1.00251	−	1.25711i
$915$	−3.92033e8	−	8.14065e8i	−0.511752	−	1.06266i
$916$	6.30018e7	−	2.76029e8i	0.0819722	−	0.359144i
$917$	5.46241e8	−	2.63056e8i	0.708397	−	0.341146i
$918$	−2.11915e8	+	2.65733e8i	−0.273926	+	0.343493i
$919$	−1.94821e8	−	8.53565e8i	−0.251009	−	1.09974i	−0.930568	−	0.366120i	$-0.880686\pi$
$919$	−1.94821e8	−	8.53565e8i	−0.251009	−	1.09974i	0.679559	−	0.733621i	$-0.262171\pi$
$920$	5.22123e7	+	2.28757e8i	0.0670516	+	0.293772i
$921$	−3.26802e8	+	6.78612e8i	−0.418318	+	0.868645i
$922$	4.41002e8	+	3.51687e8i	0.562662	+	0.448708i
$923$	−3.28525e8	+	2.61990e8i	−0.417795	+	0.333180i
$924$	−4.68572e8	−	2.25652e8i	−0.593964	−	0.286038i
$925$	−1.77874e8	+	3.69360e8i	−0.224744	+	0.466686i
$926$	9.45738e8	+	1.18592e9i	1.19107	+	1.49356i
$927$	−1.90377e8	+	2.38725e8i	−0.238987	+	0.299680i
$928$	1.87482e9	+	9.02864e8i	2.34593	+	1.12974i
$929$	−8.56882e8	+	1.95578e8i	−1.06874	+	0.243934i	−0.720489	−	0.693466i	$-0.756083\pi$
$929$	−8.56882e8	+	1.95578e8i	−1.06874	+	0.243934i	−0.348255	+	0.937400i	$0.613226\pi$
$930$	5.68154e8	−	1.29677e8i	0.706346	−	0.161219i
$931$	1.79520e7	+	1.43162e7i	0.0222466	+	0.0177411i
$932$	−5.36228e8	−	1.11349e9i	−0.662371	−	1.37543i
$933$	1.15245e8	+	2.63040e7i	0.141898	+	0.0323874i
$934$	−1.21064e9	+	5.83016e8i	−1.48585	+	0.715549i
$935$	5.08729e8	−	4.05697e8i	0.622374	−	0.496327i
$936$	1.70279e8	−	3.88650e7i	0.207650	−	0.0473948i
$937$	−4.83585e8	+	3.85646e8i	−0.587833	+	0.468781i	−0.871671	−	0.490091i	$-0.836964\pi$
$937$	−4.83585e8	+	3.85646e8i	−0.587833	+	0.468781i	0.283838	+	0.958872i	$0.408392\pi$
$938$	2.07338e8	−	9.08408e8i	0.251230	−	1.10071i
$939$	−1.05788e8			−0.127773
$940$			6.28008e8i			0.756104i
$941$	2.67538e8	−	1.17216e9i	0.321082	−	1.40675i	−0.514549	−	0.857461i	$-0.672041\pi$
$941$	2.67538e8	−	1.17216e9i	0.321082	−	1.40675i	0.835631	−	0.549292i	$-0.185102\pi$
$942$	9.76306e8	+	7.78578e8i	1.16797	+	0.931428i
$943$	4.95832e8	+	2.38780e8i	0.591288	+	0.284750i
$944$	−2.99344e8	+	1.44157e8i	−0.355840	+	0.171364i
$945$		−	9.03359e8i		−	1.07045i
$946$	1.49454e8	−	1.87239e9i	0.176537	−	2.21169i
$947$	−6.75981e8			−0.795948			−0.397974	−	0.917397i	$-0.630287\pi$
$947$	−6.75981e8			−0.795948			−0.397974	+	0.917397i	$0.630287\pi$
$948$	−4.36182e8	−	9.05741e8i	−0.511968	−	1.06311i
$949$	8.77199e7	−	1.82152e8i	0.102636	−	0.213126i
$950$	7.73565e7	−	9.70019e7i	0.0902248	−	0.113138i
$951$	8.93828e7	+	2.04010e7i	0.103923	+	0.0237198i
$952$	3.39660e7			0.0393671
$953$		−	6.40356e8i		−	0.739848i	−0.929062	−	0.369924i	$-0.879384\pi$
$953$		−	6.40356e8i		−	0.739848i	0.929062	−	0.369924i	$-0.120616\pi$
$954$	1.08100e9	+	2.46731e8i	1.24503	+	0.284170i
$955$	7.30352e8	+	9.15832e8i	0.838536	+	1.05149i
$956$	2.40563e8	+	1.05398e9i	0.275331	+	1.20631i
$957$	−9.98709e8	−	1.25234e9i	−1.13947	−	1.42885i
$958$	−2.23676e8	−	4.64468e8i	−0.254403	−	0.528274i
$959$	−4.88395e7	+	2.13980e8i	−0.0553752	+	0.242615i
$960$	−1.26365e9	+	6.08542e8i	−1.42828	+	0.687823i
$961$	−4.63381e8	+	5.81061e8i	−0.522117	+	0.654714i
$962$	−1.00992e8	−	4.42477e8i	−0.113439	−	0.497010i
$963$	5.83687e7	+	2.55730e8i	0.0653583	+	0.286354i
$964$	8.79649e8	−	1.82661e9i	0.981925	−	2.03899i
$965$	1.57577e9	+	1.25664e9i	1.75353	+	1.39839i
$966$	−2.63662e8	+	2.10263e8i	−0.292493	+	0.233255i
$967$	−1.16601e9	−	5.61520e8i	−1.28950	−	0.620991i	−0.341688	−	0.939814i	$-0.610998\pi$
$967$	−1.16601e9	−	5.61520e8i	−1.28950	−	0.620991i	−0.947815	+	0.318822i	$0.896713\pi$
$968$	−1.21648e8	+	2.52605e8i	−0.134116	+	0.278494i
$969$	−4.53699e6	−	5.68920e6i	−0.00498650	−	0.00625288i
$970$	−1.46626e8	+	1.83864e8i	−0.160656	+	0.201456i
$971$	4.12485e8	+	1.98642e8i	0.450558	+	0.216977i	0.645381	−	0.763861i	$-0.276699\pi$
$971$	4.12485e8	+	1.98642e8i	0.450558	+	0.216977i	−0.194822	+	0.980839i	$0.562413\pi$
$972$	9.87756e8	−	2.25449e8i	1.07560	−	0.245499i
$973$	3.42743e8	−	7.82288e7i	0.372074	−	0.0849236i
$974$	1.69710e8	+	1.35339e8i	0.183667	+	0.146470i
$975$	9.97871e8	+	2.07210e9i	1.07662	+	2.23561i
$976$	7.07261e8	+	1.61428e8i	0.760730	+	0.173632i
$977$	1.54239e9	−	7.42774e8i	1.65390	−	0.796476i	0.654725	−	0.755867i	$-0.272785\pi$
$977$	1.54239e9	−	7.42774e8i	1.65390	−	0.796476i	0.999175	−	0.0406089i	$-0.0129298\pi$
$978$	−6.80548e8	+	5.42719e8i	−0.727515	+	0.580174i
$979$	7.43756e8	−	1.69757e8i	0.792651	−	0.180918i
$980$	1.07265e9	−	8.55407e8i	1.13967	−	0.908855i
$981$	−5.32622e7	+	2.33357e8i	−0.0564173	+	0.247180i
$982$	−1.15823e9			−1.22310
$983$			8.06438e8i			0.849006i	0.905427	+	0.424503i	$0.139551\pi$
$983$			8.06438e8i			0.849006i	−0.905427	+	0.424503i	$0.860449\pi$
$984$	3.32011e7	−	1.45463e8i	0.0348471	−	0.152675i
$985$	1.11174e9	+	8.86582e8i	1.16331	+	0.927706i
$986$	6.65778e8	+	3.20622e8i	0.694542	+	0.334474i
$987$	−1.15126e8	+	5.54419e7i	−0.119736	+	0.0576616i
$988$			7.39093e7i			0.0766352i
$989$	−5.65984e8	−	3.30442e8i	−0.585080	−	0.341591i
$990$	−2.19445e9			−2.26163
$991$	−4.08083e8	−	8.47393e8i	−0.419303	−	0.870691i	−0.998460	−	0.0554752i	$-0.982333\pi$
$991$	−4.08083e8	−	8.47393e8i	−0.419303	−	0.870691i	0.579157	−	0.815216i	$-0.303382\pi$
$992$	−2.44455e8	+	5.07616e8i	−0.250417	+	0.519996i
$993$	1.12392e8	−	1.40935e8i	0.114786	−	0.143937i
$994$	2.68682e8	+	6.13248e7i	0.273577	+	0.0624421i
$995$	1.25561e9			1.27464
$996$			6.02305e8i			0.609591i
$997$	−1.10216e9	−	2.51562e8i	−1.11214	−	0.253839i	−0.373296	−	0.927712i	$-0.621772\pi$
$997$	−1.10216e9	−	2.51562e8i	−1.11214	−	0.253839i	−0.738847	+	0.673873i	$0.764629\pi$
$998$	−3.00462e7	−	3.76768e7i	−0.0302272	−	0.0379037i
$999$	−5.04904e7	−	2.21213e8i	−0.0506421	−	0.221878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.3	✓	126
43.22	odd	14	inner	43.7.f.a.22.3	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.3	✓	126	1.1	even	1	trivial
43.7.f.a.22.3	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)

\(f(q)\)	\(=\)	\(q+(-5.10721 - 10.6052i) q^{2} +(-7.80492 + 16.2071i) q^{3} +(-46.4840 + 58.2891i) q^{4} +(-223.373 - 50.9834i) q^{5} +211.741 q^{6} -193.213i q^{7} +(121.123 + 27.6454i) q^{8} +(252.771 + 316.965i) q^{9} +O(q^{10})\)	\(q+(-5.10721 - 10.6052i) q^{2} +(-7.80492 + 16.2071i) q^{3} +(-46.4840 + 58.2891i) q^{4} +(-223.373 - 50.9834i) q^{5} +211.741 q^{6} -193.213i q^{7} +(121.123 + 27.6454i) q^{8} +(252.771 + 316.965i) q^{9} +(600.121 + 2629.30i) q^{10} +(1251.38 + 1569.18i) q^{11} +(-581.893 - 1208.31i) q^{12} +(771.627 - 3380.72i) q^{13} +(-2049.07 + 986.780i) q^{14} +(2569.70 - 3222.30i) q^{15} +(736.345 + 3226.14i) q^{16} +(314.866 + 1379.52i) q^{17} +(2070.53 - 4299.50i) q^{18} +(223.512 + 178.245i) q^{19} +(13355.0 - 10650.3i) q^{20} +(3131.42 + 1508.01i) q^{21} +(10250.5 - 21285.3i) q^{22} +(-5139.50 - 6444.73i) q^{23} +(-1393.41 + 1747.27i) q^{24} +(33218.4 + 15997.1i) q^{25} +(-39794.2 + 9082.76i) q^{26} +(-19894.8 + 4540.85i) q^{27} +(11262.2 + 8981.32i) q^{28} +(19249.8 + 39972.7i) q^{29} +(-47297.2 - 10795.3i) q^{30} +(-10822.8 + 5211.99i) q^{31} +(36669.8 - 29243.2i) q^{32} +(-35198.8 + 8033.90i) q^{33} +(13022.0 - 10384.7i) q^{34} +(-9850.65 + 43158.5i) q^{35} -30225.4 q^{36} +11119.1i q^{37} +(748.806 - 3280.73i) q^{38} +(48769.1 + 38892.1i) q^{39} +(-25646.0 - 12350.5i) q^{40} +(-60151.0 + 28967.2i) q^{41} -40911.2i q^{42} +(74151.0 - 28687.8i) q^{43} -149636. q^{44} +(-40302.2 - 83688.4i) q^{45} +(-42099.3 + 87420.2i) q^{46} +(-22922.5 + 28743.9i) q^{47} +(-58033.4 - 13245.8i) q^{48} +80317.7 q^{49} -433990. i q^{50} +(-24815.5 - 5663.97i) q^{51} +(161191. + 202127. i) q^{52} +(51702.9 + 226525. i) q^{53} +(149764. + 187798. i) q^{54} +(-199522. - 414312. i) q^{55} +(5341.46 - 23402.5i) q^{56} +(-4633.33 + 2231.29i) q^{57} +(325607. - 408298. i) q^{58} +(22342.0 + 97886.6i) q^{59} +(68375.1 + 299571. i) q^{60} +(95119.6 - 197518. i) q^{61} +(110549. + 88159.7i) q^{62} +(61241.8 - 48838.7i) q^{63} +(-306602. - 147652. i) q^{64} +(-344721. + 715820. i) q^{65} +(264969. + 332261. i) q^{66} +(-255441. + 320313. i) q^{67} +(-95047.2 - 45772.3i) q^{68} +(144564. - 32995.7i) q^{69} +(508015. - 115951. i) q^{70} +(-94739.7 - 75552.4i) q^{71} +(21853.7 + 45379.6i) q^{72} +(56840.9 + 12973.6i) q^{73} +(117921. - 56787.8i) q^{74} +(-518534. + 413517. i) q^{75} +(-20779.5 + 4742.78i) q^{76} +(303187. - 241783. i) q^{77} +(163385. - 715838. i) q^{78} +749591. q^{79} -758173. i q^{80} +(15917.9 - 69741.1i) q^{81} +(614408. + 489974. i) q^{82} +(-404629. - 194859. i) q^{83} +(-233462. + 112429. i) q^{84} -324200. i q^{85} +(-682946. - 639874. i) q^{86} -798085. q^{87} +(108190. + 224659. i) q^{88} +(164919. - 342458. i) q^{89} +(-681703. + 854829. i) q^{90} +(-653199. - 149088. i) q^{91} +614562. q^{92} -216085. i q^{93} +(421906. + 96297.4i) q^{94} +(-40839.0 - 51210.4i) q^{95} +(187742. + 822551. i) q^{96} +(54368.0 + 68175.4i) q^{97} +(-410200. - 851788. i) q^{98} +(-181063. + 793288. 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

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