LMFDB - Embedded newform 29.7.c.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	29.17
Dual form			29.7.c.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.26981 + 9.26981i) q^{2} +(-17.8548 + 17.8548i) q^{3} -107.859i q^{4} -107.938i q^{5} -331.022i q^{6} -104.064 q^{7} +(406.562 + 406.562i) q^{8} +91.4089i q^{9} +O(q^{10})$	\(q+(-9.26981 + 9.26981i) q^{2} +(-17.8548 + 17.8548i) q^{3} -107.859i q^{4} -107.938i q^{5} -331.022i q^{6} -104.064 q^{7} +(406.562 + 406.562i) q^{8} +91.4089i q^{9} +(1000.56 + 1000.56i) q^{10} +(264.363 - 264.363i) q^{11} +(1925.80 + 1925.80i) q^{12} +392.501i q^{13} +(964.655 - 964.655i) q^{14} +(1927.21 + 1927.21i) q^{15} -634.541 q^{16} +(504.205 - 504.205i) q^{17} +(-847.343 - 847.343i) q^{18} +(7167.80 - 7167.80i) q^{19} -11642.0 q^{20} +(1858.05 - 1858.05i) q^{21} +4901.19i q^{22} -11910.1 q^{23} -14518.2 q^{24} +3974.47 q^{25} +(-3638.41 - 3638.41i) q^{26} +(-14648.3 - 14648.3i) q^{27} +11224.2i q^{28} +(21943.8 - 10643.9i) q^{29} -35729.7 q^{30} +(35799.0 - 35799.0i) q^{31} +(-20137.9 + 20137.9i) q^{32} +9440.33i q^{33} +9347.77i q^{34} +11232.4i q^{35} +9859.25 q^{36} +(37031.8 + 37031.8i) q^{37} +132888. i q^{38} +(-7008.05 - 7008.05i) q^{39} +(43883.3 - 43883.3i) q^{40} +(-23493.4 - 23493.4i) q^{41} +34447.5i q^{42} +(79372.0 - 79372.0i) q^{43} +(-28513.9 - 28513.9i) q^{44} +9866.46 q^{45} +(110404. - 110404. i) q^{46} +(-95180.1 - 95180.1i) q^{47} +(11329.6 - 11329.6i) q^{48} -106820. q^{49} +(-36842.5 + 36842.5i) q^{50} +18005.0i q^{51} +42334.7 q^{52} +41716.8 q^{53} +271573. q^{54} +(-28534.7 - 28534.7i) q^{55} +(-42308.5 - 42308.5i) q^{56} +255960. i q^{57} +(-104748. + 302082. i) q^{58} -327530. q^{59} +(207866. - 207866. i) q^{60} +(-32964.1 + 32964.1i) q^{61} +663700. i q^{62} -9512.39i q^{63} -413959. i q^{64} +42365.7 q^{65} +(-87510.0 - 87510.0i) q^{66} -146406. i q^{67} +(-54382.9 - 54382.9i) q^{68} +(212652. - 212652. i) q^{69} +(-104123. - 104123. i) q^{70} +23182.2i q^{71} +(-37163.4 + 37163.4i) q^{72} +(-114018. - 114018. i) q^{73} -686555. q^{74} +(-70963.5 + 70963.5i) q^{75} +(-773110. - 773110. i) q^{76} +(-27510.7 + 27510.7i) q^{77} +129927. q^{78} +(118729. - 118729. i) q^{79} +68490.9i q^{80} +456448. q^{81} +435558. q^{82} +613491. q^{83} +(-200407. - 200407. i) q^{84} +(-54422.7 - 54422.7i) q^{85} +1.47153e6i q^{86} +(-201758. + 581849. i) q^{87} +214960. q^{88} +(957764. - 957764. i) q^{89} +(-91460.2 + 91460.2i) q^{90} -40845.3i q^{91} +1.28460e6i q^{92} +1.27837e6i q^{93} +1.76460e6 q^{94} +(-773676. - 773676. i) q^{95} -719117. i q^{96} +(701549. + 701549. i) q^{97} +(990198. - 990198. i) q^{98} +(24165.1 + 24165.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−9.26981	+	9.26981i	−1.15873	+	1.15873i	−0.173976	+	0.984750i	$0.555662\pi$
$2$	−9.26981	+	9.26981i	−1.15873	+	1.15873i	−0.984750	+	0.173976i	$0.944338\pi$
$3$	−17.8548	+	17.8548i	−0.661291	+	0.661291i	−0.955684	−	0.294394i	$-0.904882\pi$
$3$	−17.8548	+	17.8548i	−0.661291	+	0.661291i	0.294394	+	0.955684i	$0.404882\pi$
$4$		−	107.859i		−	1.68529i
$5$		−	107.938i		−	0.863501i	−0.901993	−	0.431751i	$-0.857896\pi$
$5$		−	107.938i		−	0.863501i	0.901993	−	0.431751i	$-0.142104\pi$
$6$		−	331.022i		−	1.53251i
$7$	−104.064			−0.303394			−0.151697	−	0.988427i	$-0.548474\pi$
$7$	−104.064			−0.303394			−0.151697	+	0.988427i	$0.548474\pi$
$8$	406.562	+	406.562i	0.794066	+	0.794066i
$9$			91.4089i			0.125389i
$10$	1000.56	+	1000.56i	1.00056	+	1.00056i
$11$	264.363	−	264.363i	0.198620	−	0.198620i	−0.600788	−	0.799408i	$-0.705147\pi$
$11$	264.363	−	264.363i	0.198620	−	0.198620i	0.799408	+	0.600788i	$0.205147\pi$
$12$	1925.80	+	1925.80i	1.11447	+	1.11447i
$13$			392.501i			0.178653i	0.996002	+	0.0893266i	$0.0284715\pi$
$13$			392.501i			0.178653i	−0.996002	+	0.0893266i	$0.971528\pi$
$14$	964.655	−	964.655i	0.351550	−	0.351550i
$15$	1927.21	+	1927.21i	0.571025	+	0.571025i
$16$	−634.541			−0.154917
$17$	504.205	−	504.205i	0.102627	−	0.102627i	−0.653929	−	0.756556i	$-0.726881\pi$
$17$	504.205	−	504.205i	0.102627	−	0.102627i	0.756556	+	0.653929i	$0.226881\pi$
$18$	−847.343	−	847.343i	−0.145292	−	0.145292i
$19$	7167.80	−	7167.80i	1.04502	−	1.04502i	0.0460842	−	0.998938i	$-0.485326\pi$
$19$	7167.80	−	7167.80i	1.04502	−	1.04502i	0.998938	−	0.0460842i	$-0.0146743\pi$
$20$	−11642.0			−1.45525
$21$	1858.05	−	1858.05i	0.200632	−	0.200632i
$22$			4901.19i			0.460292i
$23$	−11910.1			−0.978882			−0.489441	−	0.872036i	$-0.662799\pi$
$23$	−11910.1			−0.978882			−0.489441	+	0.872036i	$0.662799\pi$
$24$	−14518.2			−1.05022
$25$	3974.47			0.254366
$26$	−3638.41	−	3638.41i	−0.207010	−	0.207010i
$27$	−14648.3	−	14648.3i	−0.744209	−	0.744209i
$28$			11224.2i			0.511307i
$29$	21943.8	−	10643.9i	0.899742	−	0.436422i
$29$	21943.8	−	10643.9i	0.899742	−	0.436422i
$30$	−35729.7			−1.32332
$31$	35799.0	−	35799.0i	1.20167	−	1.20167i	0.228015	−	0.973658i	$-0.426777\pi$
$31$	35799.0	−	35799.0i	1.20167	−	1.20167i	0.973658	−	0.228015i	$-0.0732234\pi$
$32$	−20137.9	+	20137.9i	−0.614559	+	0.614559i
$33$			9440.33i			0.262691i
$34$			9347.77i			0.237833i
$35$			11232.4i			0.261981i
$36$	9859.25			0.211318
$37$	37031.8	+	37031.8i	0.731088	+	0.731088i	0.970835	−	0.239748i	$-0.0770647\pi$
$37$	37031.8	+	37031.8i	0.731088	+	0.731088i	−0.239748	+	0.970835i	$0.577065\pi$
$38$			132888.i			2.42179i
$39$	−7008.05	−	7008.05i	−0.118142	−	0.118142i
$40$	43883.3	−	43883.3i	0.685677	−	0.685677i
$41$	−23493.4	−	23493.4i	−0.340874	−	0.340874i	0.515822	−	0.856696i	$-0.327487\pi$
$41$	−23493.4	−	23493.4i	−0.340874	−	0.340874i	−0.856696	+	0.515822i	$0.827487\pi$
$42$			34447.5i			0.464954i
$43$	79372.0	−	79372.0i	0.998303	−	0.998303i	−0.00169593	−	0.999999i	$-0.500540\pi$
$43$	79372.0	−	79372.0i	0.998303	−	0.998303i	0.999999	+	0.00169593i	$0.000539833\pi$
$44$	−28513.9	−	28513.9i	−0.334733	−	0.334733i
$45$	9866.46			0.108274
$46$	110404.	−	110404.i	1.13426	−	1.13426i
$47$	−95180.1	−	95180.1i	−0.916754	−	0.916754i	0.0800381	−	0.996792i	$-0.474496\pi$
$47$	−95180.1	−	95180.1i	−0.916754	−	0.916754i	−0.996792	+	0.0800381i	$0.974496\pi$
$48$	11329.6	−	11329.6i	0.102445	−	0.102445i
$49$	−106820.			−0.907952
$50$	−36842.5	+	36842.5i	−0.294740	+	0.294740i
$51$			18005.0i			0.135732i
$52$	42334.7			0.301083
$53$	41716.8			0.280210			0.140105	−	0.990137i	$-0.455256\pi$
$53$	41716.8			0.280210			0.140105	+	0.990137i	$0.455256\pi$
$54$	271573.			1.72467
$55$	−28534.7	−	28534.7i	−0.171509	−	0.171509i
$56$	−42308.5	−	42308.5i	−0.240915	−	0.240915i
$57$			255960.i			1.38213i
$58$	−104748.	+	302082.i	−0.536861	+	1.54825i
$59$	−327530.			−1.59476			−0.797379	−	0.603479i	$-0.793781\pi$
$59$	−327530.			−1.59476			−0.797379	+	0.603479i	$0.793781\pi$
$60$	207866.	−	207866.i	0.962344	−	0.962344i
$61$	−32964.1	+	32964.1i	−0.145228	+	0.145228i	−0.775983	−	0.630754i	$-0.782746\pi$
$61$	−32964.1	+	32964.1i	−0.145228	+	0.145228i	0.630754	+	0.775983i	$0.282746\pi$
$62$			663700.i			2.78482i
$63$		−	9512.39i		−	0.0380424i
$64$		−	413959.i		−	1.57913i
$65$	42365.7			0.154267
$66$	−87510.0	−	87510.0i	−0.304387	−	0.304387i
$67$		−	146406.i		−	0.486783i	−0.969928	−	0.243392i	$-0.921740\pi$
$67$		−	146406.i		−	0.486783i	0.969928	−	0.243392i	$-0.0782600\pi$
$68$	−54382.9	−	54382.9i	−0.172956	−	0.172956i
$69$	212652.	−	212652.i	0.647326	−	0.647326i
$70$	−104123.	−	104123.i	−0.303564	−	0.303564i
$71$			23182.2i			0.0647709i	0.999475	+	0.0323854i	$0.0103104\pi$
$71$			23182.2i			0.0647709i	−0.999475	+	0.0323854i	$0.989690\pi$
$72$	−37163.4	+	37163.4i	−0.0995675	+	0.0995675i
$73$	−114018.	−	114018.i	−0.293092	−	0.293092i	0.545209	−	0.838300i	$-0.316450\pi$
$73$	−114018.	−	114018.i	−0.293092	−	0.293092i	−0.838300	+	0.545209i	$0.816450\pi$
$74$	−686555.			−1.69426
$75$	−70963.5	+	70963.5i	−0.168210	+	0.168210i
$76$	−773110.	−	773110.i	−1.76117	−	1.76117i
$77$	−27510.7	+	27510.7i	−0.0602601	+	0.0602601i
$78$	129927.			0.273788
$79$	118729.	−	118729.i	0.240810	−	0.240810i	−0.576375	−	0.817185i	$-0.695533\pi$
$79$	118729.	−	118729.i	0.240810	−	0.240810i	0.817185	+	0.576375i	$0.195533\pi$
$80$			68490.9i			0.133771i
$81$	456448.			0.858888
$82$	435558.			0.789959
$83$	613491.			1.07294			0.536468	−	0.843921i	$-0.319758\pi$
$83$	613491.			1.07294			0.536468	+	0.843921i	$0.319758\pi$
$84$	−200407.	−	200407.i	−0.338123	−	0.338123i
$85$	−54422.7	−	54422.7i	−0.0886183	−	0.0886183i
$86$			1.47153e6i			2.31352i
$87$	−201758.	+	581849.i	−0.306389	+	0.883593i
$88$	214960.			0.315435
$89$	957764.	−	957764.i	1.35859	−	1.35859i	0.482934	−	0.875657i	$-0.339571\pi$
$89$	957764.	−	957764.i	1.35859	−	1.35859i	0.875657	−	0.482934i	$-0.160429\pi$
$90$	−91460.2	+	91460.2i	−0.125460	+	0.125460i
$91$		−	40845.3i		−	0.0542023i
$92$			1.28460e6i			1.64970i
$93$			1.27837e6i			1.58931i
$94$	1.76460e6			2.12453
$95$	−773676.	−	773676.i	−0.902377	−	0.902377i
$96$		−	719117.i		−	0.812804i
$97$	701549.	+	701549.i	0.768675	+	0.768675i	0.977873	−	0.209198i	$-0.0670853\pi$
$97$	701549.	+	701549.i	0.768675	+	0.768675i	−0.209198	+	0.977873i	$0.567085\pi$
$98$	990198.	−	990198.i	1.05207	−	1.05207i
$99$	24165.1	+	24165.1i	0.0249048	+	0.0249048i
$100$		−	428681.i		−	0.428681i
$101$	−364022.	+	364022.i	−0.353316	+	0.353316i	−0.861342	−	0.508026i	$-0.830375\pi$
$101$	−364022.	+	364022.i	−0.353316	+	0.353316i	0.508026	+	0.861342i	$0.330375\pi$
$102$	−166903.	−	166903.i	−0.157276	−	0.157276i
$103$	−54441.2			−0.0498214			−0.0249107	−	0.999690i	$-0.507930\pi$
$103$	−54441.2			−0.0498214			−0.0249107	+	0.999690i	$0.507930\pi$
$104$	−159576.	+	159576.i	−0.141862	+	0.141862i
$105$	−200553.	−	200553.i	−0.173246	−	0.173246i
$106$	−386707.	+	386707.i	−0.324686	+	0.324686i
$107$	−443644.			−0.362145			−0.181073	−	0.983470i	$-0.557957\pi$
$107$	−443644.			−0.362145			−0.181073	+	0.983470i	$0.557957\pi$
$108$	−1.57994e6	+	1.57994e6i	−1.25421	+	1.25421i
$109$		−	709009.i		−	0.547485i	−0.961803	−	0.273743i	$-0.911738\pi$
$109$		−	709009.i		−	0.547485i	0.961803	−	0.273743i	$-0.0882616\pi$
$110$	529023.			0.397463
$111$	−1.32239e6			−0.966923
$112$	66033.0			0.0470010
$113$	−244555.	−	244555.i	−0.169489	−	0.169489i	0.617266	−	0.786755i	$-0.288240\pi$
$113$	−244555.	−	244555.i	−0.169489	−	0.169489i	−0.786755	+	0.617266i	$0.788240\pi$
$114$	−2.37270e6	−	2.37270e6i	−1.60151	−	1.60151i
$115$			1.28554e6i			0.845266i
$116$	−1.14804e6	−	2.36683e6i	−0.735499	−	1.51633i
$117$	−35878.1			−0.0224012
$118$	3.03614e6	−	3.03614e6i	1.84789	−	1.84789i
$119$	−52469.7	+	52469.7i	−0.0311363	+	0.0311363i
$120$			1.56706e6i			0.906863i
$121$			1.63179e6i			0.921100i
$122$		−	611141.i		−	0.336560i
$123$	838941.			0.450833
$124$	−3.86124e6	−	3.86124e6i	−2.02517	−	2.02517i
$125$		−	2.11552e6i		−	1.08315i
$126$	88178.0	+	88178.0i	0.0440807	+	0.0440807i
$127$	−973626.	+	973626.i	−0.475314	+	0.475314i	−0.903629	−	0.428315i	$-0.859107\pi$
$127$	−973626.	+	973626.i	−0.475314	+	0.475314i	0.428315	+	0.903629i	$0.359107\pi$
$128$	2.54850e6	+	2.54850e6i	1.21522	+	1.21522i
$129$			2.83435e6i			1.32034i
$130$	−392722.	+	392722.i	−0.178754	+	0.178754i
$131$	1.55891e6	+	1.55891e6i	0.693436	+	0.693436i	0.962986	−	0.269550i	$-0.0868751\pi$
$131$	1.55891e6	+	1.55891e6i	0.693436	+	0.693436i	−0.269550	+	0.962986i	$0.586875\pi$
$132$	1.01822e6			0.442711
$133$	−745911.	+	745911.i	−0.317053	+	0.317053i
$134$	1.35716e6	+	1.35716e6i	0.564049	+	0.564049i
$135$	−1.58110e6	+	1.58110e6i	−0.642626	+	0.642626i
$136$	409981.			0.162985
$137$	−806951.	+	806951.i	−0.313824	+	0.313824i	−0.846389	−	0.532565i	$-0.821228\pi$
$137$	−806951.	+	806951.i	−0.313824	+	0.313824i	0.532565	+	0.846389i	$0.321228\pi$
$138$			3.94249e6i			1.50015i
$139$	−4.28994e6			−1.59738			−0.798688	−	0.601746i	$-0.794472\pi$
$139$	−4.28994e6			−1.59738			−0.798688	+	0.601746i	$0.794472\pi$
$140$	1.21152e6			0.441515
$141$	3.39885e6			1.21248
$142$	−214895.	−	214895.i	−0.0750517	−	0.0750517i
$143$	103763.	+	103763.i	0.0354841	+	0.0354841i
$144$		−	58002.7i		−	0.0194250i
$145$	−1.14888e6	−	2.36856e6i	−0.376851	−	0.776928i
$146$	2.11385e6			0.679226
$147$	1.90725e6	−	1.90725e6i	0.600420	−	0.600420i
$148$	3.99420e6	−	3.99420e6i	1.23210	−	1.23210i
$149$			2564.59i			0.000775282i	1.00000		0.000387641i	$0.000123390\pi$
$149$			2564.59i			0.000775282i	−1.00000		0.000387641i	$0.999877\pi$
$150$		−	1.31564e6i		−	0.389818i
$151$		−	4.33794e6i		−	1.25995i	−0.776616	−	0.629975i	$-0.783065\pi$
$151$		−	4.33794e6i		−	1.25995i	0.776616	−	0.629975i	$-0.216935\pi$
$152$	5.82831e6			1.65963
$153$	46088.8	+	46088.8i	0.0128683	+	0.0128683i
$154$		−	510038.i		−	0.139650i
$155$	−3.86406e6	−	3.86406e6i	−1.03765	−	1.03765i
$156$	−755879.	+	755879.i	−0.199103	+	0.199103i
$157$	−2.56047e6	−	2.56047e6i	−0.661638	−	0.661638i	0.294128	−	0.955766i	$-0.404971\pi$
$157$	−2.56047e6	−	2.56047e6i	−0.661638	−	0.661638i	−0.955766	+	0.294128i	$0.904971\pi$
$158$			2.20119e6i			0.558066i
$159$	−744847.	+	744847.i	−0.185300	+	0.185300i
$160$	2.17363e6	+	2.17363e6i	0.530672	+	0.530672i
$161$	1.23941e6			0.296987
$162$	−4.23119e6	+	4.23119e6i	−0.995216	+	0.995216i
$163$	5.92509e6	+	5.92509e6i	1.36815	+	1.36815i	0.863083	+	0.505063i	$0.168531\pi$
$163$	5.92509e6	+	5.92509e6i	1.36815	+	1.36815i	0.505063	+	0.863083i	$0.331469\pi$
$164$	−2.53396e6	+	2.53396e6i	−0.574472	+	0.574472i
$165$	1.01897e6			0.226834
$166$	−5.68694e6	+	5.68694e6i	−1.24324	+	1.24324i
$167$		−	5.43058e6i		−	1.16600i	−0.812473	−	0.582998i	$-0.801879\pi$
$167$		−	5.43058e6i		−	1.16600i	0.812473	−	0.582998i	$-0.198121\pi$
$168$	1.51082e6			0.318629
$169$	4.67275e6			0.968083
$170$	1.00898e6			0.205369
$171$	655201.	+	655201.i	0.131035	+	0.131035i
$172$	−8.56097e6	−	8.56097e6i	−1.68243	−	1.68243i
$173$			6.71273e6i			1.29647i	0.761442	+	0.648233i	$0.224492\pi$
$173$			6.71273e6i			1.29647i	−0.761442	+	0.648233i	$0.775508\pi$
$174$	−3.52336e6	−	7.26388e6i	−0.668821	−	1.37886i
$175$	−413599.			−0.0771730
$176$	−167749.	+	167749.i	−0.0307697	+	0.0307697i
$177$	5.84800e6	−	5.84800e6i	1.05460	−	1.05460i
$178$			1.77566e7i			3.14847i
$179$		−	5.96478e6i		−	1.04000i	−0.854165	−	0.520002i	$-0.825931\pi$
$179$		−	5.96478e6i		−	1.04000i	0.854165	−	0.520002i	$-0.174069\pi$
$180$		−	1.06418e6i		−	0.182473i
$181$	4.11106e6			0.693295			0.346648	−	0.937995i	$-0.387320\pi$
$181$	4.11106e6			0.693295			0.346648	+	0.937995i	$0.387320\pi$
$182$	378628.	+	378628.i	0.0628057	+	0.0628057i
$183$		−	1.17714e6i		−	0.192076i
$184$	−4.84217e6	−	4.84217e6i	−0.777297	−	0.777297i
$185$	3.99712e6	−	3.99712e6i	0.631295	−	0.631295i
$186$	−1.18503e7	−	1.18503e7i	−1.84157	−	1.84157i
$187$		−	266586.i		−	0.0407674i
$188$	−1.02660e7	+	1.02660e7i	−1.54500	+	1.54500i
$189$	1.52436e6	+	1.52436e6i	0.225789	+	0.225789i
$190$	1.43437e7			2.09122
$191$	−6.15358e6	+	6.15358e6i	−0.883137	+	0.883137i	−0.993852	−	0.110715i	$-0.964686\pi$
$191$	−6.15358e6	+	6.15358e6i	−0.883137	+	0.883137i	0.110715	+	0.993852i	$0.464686\pi$
$192$	7.39118e6	+	7.39118e6i	1.04426	+	1.04426i
$193$	8.51227e6	−	8.51227e6i	1.18406	−	1.18406i	0.205376	−	0.978683i	$-0.434158\pi$
$193$	8.51227e6	−	8.51227e6i	1.18406	−	1.18406i	0.978683	−	0.205376i	$-0.0658418\pi$
$194$	−1.30065e7			−1.78137
$195$	−756432.	+	756432.i	−0.102016	+	0.102016i
$196$			1.15214e7i			1.53016i
$197$	−6.89035e6			−0.901244			−0.450622	−	0.892715i	$-0.648798\pi$
$197$	−6.89035e6			−0.901244			−0.450622	+	0.892715i	$0.648798\pi$
$198$	−448013.			−0.0577158
$199$	−3.17466e6			−0.402845			−0.201423	−	0.979504i	$-0.564556\pi$
$199$	−3.17466e6			−0.402845			−0.201423	+	0.979504i	$0.564556\pi$
$200$	1.61587e6	+	1.61587e6i	0.201983	+	0.201983i
$201$	2.61406e6	+	2.61406e6i	0.321905	+	0.321905i
$202$		−	6.74882e6i		−	0.818793i
$203$	−2.28356e6	+	1.10765e6i	−0.272976	+	0.132408i
$204$	1.94200e6			0.228748
$205$	−2.53582e6	+	2.53582e6i	−0.294345	+	0.294345i
$206$	504660.	−	504660.i	0.0577294	−	0.0577294i
$207$		−	1.08869e6i		−	0.122742i
$208$		−	249058.i		−	0.0276765i
$209$		−	3.78981e6i		−	0.415124i
$210$	3.71818e6			0.401488
$211$	−2.93663e6	−	2.93663e6i	−0.312609	−	0.312609i	0.533311	−	0.845920i	$-0.320948\pi$
$211$	−2.93663e6	−	2.93663e6i	−0.312609	−	0.312609i	−0.845920	+	0.533311i	$0.820948\pi$
$212$		−	4.49952e6i		−	0.472235i
$213$	−413915.	−	413915.i	−0.0428324	−	0.0428324i
$214$	4.11249e6	−	4.11249e6i	0.419627	−	0.419627i
$215$	−8.56723e6	−	8.56723e6i	−0.862035	−	0.862035i
$216$		−	1.19109e7i		−	1.18190i
$217$	−3.72539e6	+	3.72539e6i	−0.364580	+	0.364580i
$218$	6.57238e6	+	6.57238e6i	0.634385	+	0.634385i
$219$	4.07154e6			0.387638
$220$	−3.07772e6	+	3.07772e6i	−0.289042	+	0.289042i
$221$	197901.	+	197901.i	0.0183346	+	0.0183346i
$222$	1.22583e7	−	1.22583e7i	1.12040	−	1.12040i
$223$	−4.73789e6			−0.427238			−0.213619	−	0.976917i	$-0.568525\pi$
$223$	−4.73789e6			−0.427238			−0.213619	+	0.976917i	$0.568525\pi$
$224$	2.09563e6	−	2.09563e6i	0.186454	−	0.186454i
$225$			363302.i			0.0318948i
$226$	4.53395e6			0.392782
$227$	−2.10790e7			−1.80207			−0.901035	−	0.433746i	$-0.857191\pi$
$227$	−2.10790e7			−1.80207			−0.901035	+	0.433746i	$0.857191\pi$
$228$	2.76075e7			2.32929
$229$	1.31785e7	+	1.31785e7i	1.09739	+	1.09739i	0.994715	+	0.102673i	$0.0327396\pi$
$229$	1.31785e7	+	1.31785e7i	1.09739	+	1.09739i	0.102673	+	0.994715i	$0.467260\pi$
$230$	−1.19167e7	−	1.19167e7i	−0.979432	−	0.979432i
$231$		−	982399.i		−	0.0796989i
$232$	1.32489e7	+	4.59411e6i	1.06100	+	0.367907i
$233$	1.68759e7			1.33414			0.667068	−	0.744997i	$-0.267549\pi$
$233$	1.68759e7			1.33414			0.667068	+	0.744997i	$0.267549\pi$
$234$	332583.	−	332583.i	0.0259569	−	0.0259569i
$235$	−1.02735e7	+	1.02735e7i	−0.791618	+	0.791618i
$236$			3.53269e7i			2.68763i
$237$			4.23977e6i			0.318491i
$238$		−	972767.i		−	0.0721569i
$239$	3.19688e6			0.234171			0.117086	−	0.993122i	$-0.462645\pi$
$239$	3.19688e6			0.234171			0.117086	+	0.993122i	$0.462645\pi$
$240$	−1.22289e6	−	1.22289e6i	−0.0884617	−	0.0884617i
$241$			5.19058e6i			0.370821i	0.982661	+	0.185411i	$0.0593616\pi$
$241$			5.19058e6i			0.370821i	−0.982661	+	0.185411i	$0.940638\pi$
$242$	−1.51263e7	−	1.51263e7i	−1.06730	−	1.06730i
$243$	2.52878e6	−	2.52878e6i	0.176235	−	0.176235i
$244$	3.55546e6	+	3.55546e6i	0.244752	+	0.244752i
$245$			1.15299e7i			0.784018i
$246$	−7.77682e6	+	7.77682e6i	−0.522392	+	0.522392i
$247$	2.81337e6	+	2.81337e6i	0.186697	+	0.186697i
$248$	2.91090e7			1.90841
$249$	−1.09538e7	+	1.09538e7i	−0.709522	+	0.709522i
$250$	1.96105e7	+	1.96105e7i	1.25507	+	1.25507i
$251$	9.47157e6	−	9.47157e6i	0.598964	−	0.598964i	−0.341073	−	0.940037i	$-0.610790\pi$
$251$	9.47157e6	−	9.47157e6i	0.598964	−	0.598964i	0.940037	+	0.341073i	$0.110790\pi$
$252$	−1.02599e6			−0.0641126
$253$	−3.14858e6	+	3.14858e6i	−0.194426	+	0.194426i
$254$		−	1.80506e7i		−	1.10152i
$255$	1.94342e6			0.117205
$256$	−2.07548e7			−1.23708
$257$	1.27002e7			0.748189			0.374094	−	0.927391i	$-0.377954\pi$
$257$	1.27002e7			0.748189			0.374094	+	0.927391i	$0.377954\pi$
$258$	−2.62739e7	−	2.62739e7i	−1.52991	−	1.52991i
$259$	−3.85368e6	−	3.85368e6i	−0.221808	−	0.221808i
$260$		−	4.56950e6i		−	0.259985i
$261$	972947.	+	2.00586e6i	0.0547227	+	0.112818i
$262$	−2.89015e7			−1.60700
$263$	1.39476e6	−	1.39476e6i	0.0766711	−	0.0766711i	−0.667731	−	0.744402i	$-0.732734\pi$
$263$	1.39476e6	−	1.39476e6i	0.0766711	−	0.0766711i	0.744402	+	0.667731i	$0.232734\pi$
$264$	−3.83808e6	+	3.83808e6i	−0.208594	+	0.208594i
$265$		−	4.50281e6i		−	0.241961i
$266$		−	1.38289e7i		−	0.734756i
$267$			3.42015e7i			1.79685i
$268$	−1.57912e7			−0.820372
$269$	−1.76761e7	−	1.76761e7i	−0.908093	−	0.908093i	0.0880253	−	0.996118i	$-0.471944\pi$
$269$	−1.76761e7	−	1.76761e7i	−0.908093	−	0.908093i	−0.996118	+	0.0880253i	$0.971944\pi$
$270$		−	2.93130e7i		−	1.48925i
$271$	−1.61108e7	−	1.61108e7i	−0.809487	−	0.809487i	0.175069	−	0.984556i	$-0.443985\pi$
$271$	−1.61108e7	−	1.61108e7i	−0.809487	−	0.809487i	−0.984556	+	0.175069i	$0.943985\pi$
$272$	−319939.	+	319939.i	−0.0158987	+	0.0158987i
$273$	729287.	+	729287.i	0.0358435	+	0.0358435i
$274$		−	1.49606e7i		−	0.727271i
$275$	1.05070e6	−	1.05070e6i	0.0505221	−	0.0505221i
$276$	−2.29364e7	−	2.29364e7i	−1.09093	−	1.09093i
$277$	−2.81445e7			−1.32420			−0.662102	−	0.749414i	$-0.730335\pi$
$277$	−2.81445e7			−1.32420			−0.662102	+	0.749414i	$0.730335\pi$
$278$	3.97669e7	−	3.97669e7i	1.85092	−	1.85092i
$279$	3.27235e6	+	3.27235e6i	0.150677	+	0.150677i
$280$	−4.56668e6	+	4.56668e6i	−0.208030	+	0.208030i
$281$	2.16250e7			0.974622			0.487311	−	0.873228i	$-0.337978\pi$
$281$	2.16250e7			0.974622			0.487311	+	0.873228i	$0.337978\pi$
$282$	−3.15067e7	+	3.15067e7i	−1.40493	+	1.40493i
$283$		−	2.66532e7i		−	1.17595i	−0.808877	−	0.587977i	$-0.799924\pi$
$283$		−	2.66532e7i		−	1.17595i	0.808877	−	0.587977i	$-0.200076\pi$
$284$	2.50040e6			0.109158
$285$	2.76277e7			1.19347
$286$	−1.92372e6			−0.0822327
$287$	2.44482e6	+	2.44482e6i	0.103419	+	0.103419i
$288$	−1.84078e6	−	1.84078e6i	−0.0770592	−	0.0770592i
$289$			2.36291e7i			0.978936i
$290$	3.26060e7	+	1.13063e7i	1.33691	+	0.463580i
$291$	−2.50521e7			−1.01664
$292$	−1.22978e7	+	1.22978e7i	−0.493945	+	0.493945i
$293$	−3.53447e6	+	3.53447e6i	−0.140515	+	0.140515i	−0.773865	−	0.633350i	$-0.781679\pi$
$293$	−3.53447e6	+	3.53447e6i	−0.140515	+	0.140515i	0.633350	+	0.773865i	$0.281679\pi$
$294$			3.53597e7i			1.39145i
$295$			3.53528e7i			1.37708i
$296$			3.01114e7i			1.16106i
$297$	−7.74493e6			−0.295630
$298$	−23773.3	−	23773.3i	−0.000898339	−	0.000898339i
$299$		−	4.67471e6i		−	0.174881i
$300$	7.65403e6	+	7.65403e6i	0.283483	+	0.283483i
$301$	−8.25978e6	+	8.25978e6i	−0.302879	+	0.302879i
$302$	4.02119e7	+	4.02119e7i	1.45994	+	1.45994i
$303$		−	1.29991e7i		−	0.467289i
$304$	−4.54827e6	+	4.54827e6i	−0.161892	+	0.161892i
$305$	3.55806e6	+	3.55806e6i	0.125405	+	0.125405i
$306$	−854469.			−0.0298217
$307$	4.01511e6	−	4.01511e6i	0.138766	−	0.138766i	−0.634312	−	0.773077i	$-0.718716\pi$
$307$	4.01511e6	−	4.01511e6i	0.138766	−	0.138766i	0.773077	+	0.634312i	$0.218716\pi$
$308$	2.96727e6	+	2.96727e6i	0.101556	+	0.101556i
$309$	972040.	−	972040.i	0.0329465	−	0.0329465i
$310$	7.16382e7			2.40469
$311$	3.78813e7	−	3.78813e7i	1.25934	−	1.25934i	0.307935	−	0.951408i	$-0.400362\pi$
$311$	3.78813e7	−	3.78813e7i	1.25934	−	1.25934i	0.951408	−	0.307935i	$-0.0996378\pi$
$312$		−	5.69841e6i		−	0.187625i
$313$	2.45104e7			0.799315			0.399658	−	0.916665i	$-0.369129\pi$
$313$	2.45104e7			0.799315			0.399658	+	0.916665i	$0.369129\pi$
$314$	4.74701e7			1.53332
$315$	−1.02674e6			−0.0328497
$316$	−1.28059e7	−	1.28059e7i	−0.405835	−	0.405835i
$317$	−1.53489e6	−	1.53489e6i	−0.0481835	−	0.0481835i	0.682605	−	0.730788i	$-0.260847\pi$
$317$	−1.53489e6	−	1.53489e6i	−0.0481835	−	0.0481835i	−0.730788	+	0.682605i	$0.760847\pi$
$318$		−	1.38092e7i		−	0.429424i
$319$	2.98728e6	−	8.61499e6i	0.0920246	−	0.265389i
$320$	−4.46818e7			−1.36358
$321$	7.92119e6	−	7.92119e6i	0.239483	−	0.239483i
$322$	−1.14891e7	+	1.14891e7i	−0.344127	+	0.344127i
$323$		−	7.22809e6i		−	0.214494i
$324$		−	4.92319e7i		−	1.44748i
$325$			1.55998e6i			0.0454433i
$326$	−1.09849e8			−3.17061
$327$	1.26592e7	+	1.26592e7i	0.362047	+	0.362047i
$328$		−	1.91030e7i		−	0.541353i
$329$	9.90484e6	+	9.90484e6i	0.278138	+	0.278138i
$330$	−9.44563e6	+	9.44563e6i	−0.262838	+	0.262838i
$331$	4.65970e7	+	4.65970e7i	1.28491	+	1.28491i	0.937836	+	0.347077i	$0.112826\pi$
$331$	4.65970e7	+	4.65970e7i	1.28491	+	1.28491i	0.347077	+	0.937836i	$0.387174\pi$
$332$		−	6.61703e7i		−	1.80821i
$333$	−3.38503e6	+	3.38503e6i	−0.0916707	+	0.0916707i
$334$	5.03405e7	+	5.03405e7i	1.35107	+	1.35107i
$335$	−1.58028e7			−0.420338
$336$	−1.17901e6	+	1.17901e6i	−0.0310813	+	0.0310813i
$337$	−5.15962e7	−	5.15962e7i	−1.34812	−	1.34812i	−0.887704	−	0.460414i	$-0.847701\pi$
$337$	−5.15962e7	−	5.15962e7i	−1.34812	−	1.34812i	−0.460414	−	0.887704i	$-0.652299\pi$
$338$	−4.33155e7	+	4.33155e7i	−1.12174	+	1.12174i
$339$	8.73298e6			0.224163
$340$	−5.86996e6	+	5.86996e6i	−0.149348	+	0.149348i
$341$		−	1.89279e7i		−	0.477352i
$342$	−1.21472e7			−0.303667
$343$	2.33591e7			0.578861
$344$	6.45393e7			1.58544
$345$	−2.29532e7	−	2.29532e7i	−0.558966	−	0.558966i
$346$	−6.22257e7	−	6.22257e7i	−1.50225	−	1.50225i
$347$			2.37373e7i			0.568123i	0.958806	+	0.284061i	$0.0916819\pi$
$347$			2.37373e7i			0.568123i	−0.958806	+	0.284061i	$0.908318\pi$
$348$	6.27574e7	+	2.17614e7i	1.48911	+	0.516355i
$349$	−2.08811e7			−0.491220			−0.245610	−	0.969369i	$-0.578988\pi$
$349$	−2.08811e7			−0.491220			−0.245610	+	0.969369i	$0.578988\pi$
$350$	3.83399e6	−	3.83399e6i	0.0894224	−	0.0894224i
$351$	5.74947e6	−	5.74947e6i	0.132955	−	0.132955i
$352$			1.06474e7i			0.244127i
$353$		−	2.71250e7i		−	0.616660i	−0.951279	−	0.308330i	$-0.900230\pi$
$353$		−	2.71250e7i		−	0.616660i	0.951279	−	0.308330i	$-0.0997702\pi$
$354$			1.08420e8i			2.44398i
$355$	2.50223e6			0.0559297
$356$	−1.03303e8	−	1.03303e8i	−2.28962	−	2.28962i
$357$		−	1.87368e6i		−	0.0411803i
$358$	5.52924e7	+	5.52924e7i	1.20508	+	1.20508i
$359$	−1.50277e7	+	1.50277e7i	−0.324795	+	0.324795i	−0.850603	−	0.525808i	$-0.823763\pi$
$359$	−1.50277e7	+	1.50277e7i	−0.324795	+	0.324795i	0.525808	+	0.850603i	$0.323763\pi$
$360$	4.01133e6	+	4.01133e6i	0.0859766	+	0.0859766i
$361$		−	5.57090e7i		−	1.18414i
$362$	−3.81088e7	+	3.81088e7i	−0.803339	+	0.803339i
$363$	−2.91353e7	−	2.91353e7i	−0.609115	−	0.609115i
$364$	−4.40552e6			−0.0913468
$365$	−1.23068e7	+	1.23068e7i	−0.253085	+	0.253085i
$366$	1.09118e7	+	1.09118e7i	0.222564	+	0.222564i
$367$	4.69244e7	−	4.69244e7i	0.949294	−	0.949294i	−0.0494813	−	0.998775i	$-0.515757\pi$
$367$	4.69244e7	−	4.69244e7i	0.949294	−	0.949294i	0.998775	+	0.0494813i	$0.0157568\pi$
$368$	7.55742e6			0.151646
$369$	2.14750e6	−	2.14750e6i	0.0427420	−	0.0427420i
$370$			7.41051e7i			1.46300i
$371$	−4.34122e6			−0.0850139
$372$	1.37884e8			2.67845
$373$	−5.76631e7			−1.11115			−0.555574	−	0.831467i	$-0.687501\pi$
$373$	−5.76631e7			−1.11115			−0.555574	+	0.831467i	$0.687501\pi$
$374$	2.47121e6	+	2.47121e6i	0.0472383	+	0.0472383i
$375$	3.77723e7	+	3.77723e7i	0.716274	+	0.716274i
$376$		−	7.73932e7i		−	1.45593i
$377$	4.17774e6	+	8.61297e6i	0.0779682	+	0.160742i
$378$	−2.82610e7			−0.523254
$379$	−5.73880e7	+	5.73880e7i	−1.05415	+	1.05415i	−0.0557048	+	0.998447i	$0.517741\pi$
$379$	−5.73880e7	+	5.73880e7i	−1.05415	+	1.05415i	−0.998447	+	0.0557048i	$0.982259\pi$
$380$	−8.34477e7	+	8.34477e7i	−1.52077	+	1.52077i
$381$		−	3.47679e7i		−	0.628642i
$382$		−	1.14085e8i		−	2.04663i
$383$			5.15806e7i			0.918101i	0.888410	+	0.459050i	$0.151810\pi$
$383$			5.15806e7i			0.918101i	−0.888410	+	0.459050i	$0.848190\pi$
$384$	−9.10061e7			−1.60722
$385$	2.96944e6	+	2.96944e6i	0.0520347	+	0.0520347i
$386$			1.57814e8i			2.74400i
$387$	7.25531e6	+	7.25531e6i	0.125177	+	0.125177i
$388$	7.56682e7	−	7.56682e7i	1.29544	−	1.29544i
$389$	3.81267e7	+	3.81267e7i	0.647709	+	0.647709i	0.952439	−	0.304730i	$-0.0985661\pi$
$389$	3.81267e7	+	3.81267e7i	0.647709	+	0.647709i	−0.304730	+	0.952439i	$0.598566\pi$
$390$		−	1.40240e7i		−	0.236416i
$391$	−6.00511e6	+	6.00511e6i	−0.100459	+	0.100459i
$392$	−4.34288e7	−	4.34288e7i	−0.720974	−	0.720974i
$393$	−5.56681e7			−0.917125
$394$	6.38722e7	−	6.38722e7i	1.04429	−	1.04429i
$395$	−1.28153e7	−	1.28153e7i	−0.207940	−	0.207940i
$396$	2.60642e6	−	2.60642e6i	0.0419719	−	0.0419719i
$397$	6.99317e6			0.111764			0.0558821	−	0.998437i	$-0.482203\pi$
$397$	6.99317e6			0.111764			0.0558821	+	0.998437i	$0.482203\pi$
$398$	2.94285e7	−	2.94285e7i	0.466788	−	0.466788i
$399$		−	2.66363e7i		−	0.419329i
$400$	−2.52196e6			−0.0394057
$401$	7.59929e6			0.117853			0.0589264	−	0.998262i	$-0.481232\pi$
$401$	7.59929e6			0.117853			0.0589264	+	0.998262i	$0.481232\pi$
$402$	−4.84637e7			−0.746000
$403$	1.40512e7	+	1.40512e7i	0.214683	+	0.214683i
$404$	3.92629e7	+	3.92629e7i	0.595441	+	0.595441i
$405$		−	4.92680e7i		−	0.741651i
$406$	1.09005e7	−	3.14359e7i	0.162880	−	0.469729i
$407$	1.95797e7			0.290417
$408$	−7.32015e6	+	7.32015e6i	−0.107780	+	0.107780i
$409$	−6.79838e7	+	6.79838e7i	−0.993655	+	0.993655i	−0.999980	−	0.00632495i	$-0.997987\pi$
$409$	−6.79838e7	+	6.79838e7i	−0.993655	+	0.993655i	0.00632495	+	0.999980i	$0.497987\pi$
$410$		−	4.70131e7i		−	0.682130i
$411$		−	2.88160e7i		−	0.415057i
$412$			5.87196e6i			0.0839637i
$413$	3.40841e7			0.483840
$414$	1.00919e7	+	1.00919e7i	0.142224	+	0.142224i
$415$		−	6.62187e7i		−	0.926481i
$416$	−7.90414e6	−	7.90414e6i	−0.109793	−	0.109793i
$417$	7.65963e7	−	7.65963e7i	1.05633	−	1.05633i
$418$	3.51308e7	+	3.51308e7i	0.481015	+	0.481015i
$419$			8.99145e7i			1.22233i	0.791504	+	0.611164i	$0.209298\pi$
$419$			8.99145e7i			1.22233i	−0.791504	+	0.611164i	$0.790702\pi$
$420$	−2.16314e7	+	2.16314e7i	−0.291969	+	0.291969i
$421$	−8.09549e7	−	8.09549e7i	−1.08492	−	1.08492i	−0.996043	−	0.0888753i	$-0.971673\pi$
$421$	−8.09549e7	−	8.09549e7i	−1.08492	−	1.08492i	−0.0888753	−	0.996043i	$-0.528327\pi$
$422$	5.44439e7			0.724456
$423$	8.70031e6	−	8.70031e6i	0.114951	−	0.114951i
$424$	1.69604e7	+	1.69604e7i	0.222505	+	0.222505i
$425$	2.00395e6	−	2.00395e6i	0.0261047	−	0.0261047i
$426$	7.67382e6			0.0992620
$427$	3.43038e6	−	3.43038e6i	0.0440614	−	0.0440614i
$428$			4.78508e7i			0.610321i
$429$	−3.70534e6			−0.0469306
$430$	1.58833e8			1.99773
$431$	1.25478e8			1.56724			0.783620	−	0.621240i	$-0.213371\pi$
$431$	1.25478e8			1.56724			0.783620	+	0.621240i	$0.213371\pi$
$432$	9.29493e6	+	9.29493e6i	0.115291	+	0.115291i
$433$	2.29528e6	+	2.29528e6i	0.0282729	+	0.0282729i	0.721102	−	0.692829i	$-0.243636\pi$
$433$	2.29528e6	+	2.29528e6i	0.0282729	+	0.0282729i	−0.692829	+	0.721102i	$0.743636\pi$
$434$		−	6.90674e7i		−	0.844897i
$435$	6.28034e7	+	2.17773e7i	0.762983	+	0.264567i
$436$	−7.64728e7			−0.922672
$437$	−8.53690e7	+	8.53690e7i	−1.02295	+	1.02295i
$438$	−3.77424e7	+	3.77424e7i	−0.449166	+	0.449166i
$439$			1.37413e7i			0.162418i	0.996697	+	0.0812088i	$0.0258781\pi$
$439$			1.37413e7i			0.162418i	−0.996697	+	0.0812088i	$0.974122\pi$
$440$		−	2.32023e7i		−	0.272378i
$441$		−	9.76427e6i		−	0.113848i
$442$	−3.66901e6			−0.0424896
$443$	5.24045e7	+	5.24045e7i	0.602778	+	0.602778i	0.941049	−	0.338271i	$-0.109842\pi$
$443$	5.24045e7	+	5.24045e7i	0.602778	+	0.602778i	−0.338271	+	0.941049i	$0.609842\pi$
$444$			1.42632e8i			1.62955i
$445$	−1.03379e8	−	1.03379e8i	−1.17314	−	1.17314i
$446$	4.39193e7	−	4.39193e7i	0.495052	−	0.495052i
$447$	−45790.4	−	45790.4i	−0.000512687	−	0.000512687i
$448$			4.30783e7i			0.479098i
$449$	−1.01827e8	+	1.01827e8i	−1.12493	+	1.12493i	−0.133941	+	0.990989i	$0.542763\pi$
$449$	−1.01827e8	+	1.01827e8i	−1.12493	+	1.12493i	−0.990989	+	0.133941i	$0.957237\pi$
$450$	−3.36774e6	−	3.36774e6i	−0.0369573	−	0.0369573i
$451$	−1.24216e7			−0.135409
$452$	−2.63774e7	+	2.63774e7i	−0.285638	+	0.285638i
$453$	7.74533e7	+	7.74533e7i	0.833193	+	0.833193i
$454$	1.95398e8	−	1.95398e8i	2.08811	−	2.08811i
$455$	−4.40875e6			−0.0468038
$456$	−1.04064e8	+	1.04064e8i	−1.09750	+	1.09750i
$457$			1.04185e8i			1.09158i	0.837921	+	0.545792i	$0.183771\pi$
$457$			1.04185e8i			1.09158i	−0.837921	+	0.545792i	$0.816229\pi$
$458$	−2.44325e8			−2.54314
$459$	−1.47715e7			−0.152752
$460$	1.38657e8			1.42452
$461$	2.84289e7	+	2.84289e7i	0.290173	+	0.290173i	0.837149	−	0.546975i	$-0.184221\pi$
$461$	2.84289e7	+	2.84289e7i	0.290173	+	0.290173i	−0.546975	+	0.837149i	$0.684221\pi$
$462$	9.10665e6	+	9.10665e6i	0.0923492	+	0.0923492i
$463$		−	1.06418e8i		−	1.07219i	−0.844158	−	0.536095i	$-0.819899\pi$
$463$		−	1.06418e8i		−	1.07219i	0.844158	−	0.536095i	$-0.180101\pi$
$464$	−1.39243e7	+	6.75399e6i	−0.139386	+	0.0676093i
$465$	1.37984e8			1.37237
$466$	−1.56437e8	+	1.56437e8i	−1.54590	+	1.54590i
$467$	2.82306e7	−	2.82306e7i	0.277185	−	0.277185i	−0.554799	−	0.831984i	$-0.687205\pi$
$467$	2.82306e7	−	2.82306e7i	0.277185	−	0.277185i	0.831984	+	0.554799i	$0.187205\pi$
$468$			3.86977e6i			0.0377526i
$469$			1.52357e7i			0.147687i
$470$		−	1.90467e8i		−	1.83454i
$471$	9.14336e7			0.875070
$472$	−1.33161e8	−	1.33161e8i	−1.26634	−	1.26634i
$473$		−	4.19661e7i		−	0.396566i
$474$	−3.93018e7	−	3.93018e7i	−0.369044	−	0.369044i
$475$	2.84882e7	−	2.84882e7i	0.265818	−	0.265818i
$476$	5.65931e6	+	5.65931e6i	0.0524738	+	0.0524738i
$477$			3.81329e6i			0.0351353i
$478$	−2.96345e7	+	2.96345e7i	−0.271340	+	0.271340i
$479$	−9.14240e7	−	9.14240e7i	−0.831867	−	0.831867i	0.155905	−	0.987772i	$-0.450170\pi$
$479$	−9.14240e7	−	9.14240e7i	−0.831867	−	0.831867i	−0.987772	+	0.155905i	$0.950170\pi$
$480$	−7.76198e7			−0.701857
$481$	−1.45350e7	+	1.45350e7i	−0.130611	+	0.130611i
$482$	−4.81157e7	−	4.81157e7i	−0.429681	−	0.429681i
$483$	−2.21295e7	+	2.21295e7i	−0.196395	+	0.196395i
$484$	1.76002e8			1.55232
$485$	7.57236e7	−	7.57236e7i	0.663752	−	0.663752i
$486$			4.68826e7i			0.408416i
$487$	−5.58116e7			−0.483212			−0.241606	−	0.970374i	$-0.577674\pi$
$487$	−5.58116e7			−0.483212			−0.241606	+	0.970374i	$0.577674\pi$
$488$	−2.68039e7			−0.230642
$489$	−2.11583e8			−1.80948
$490$	−1.06880e8	−	1.06880e8i	−0.908462	−	0.908462i
$491$	6.97579e7	+	6.97579e7i	0.589317	+	0.589317i	0.937446	−	0.348130i	$-0.113183\pi$
$491$	6.97579e7	+	6.97579e7i	0.589317	+	0.589317i	−0.348130	+	0.937446i	$0.613183\pi$
$492$		−	9.04871e7i		−	0.759786i
$493$	5.69747e6	−	1.64309e7i	0.0475490	−	0.137126i
$494$	−5.21588e7			−0.432660
$495$	2.60833e6	−	2.60833e6i	0.0215054	−	0.0215054i
$496$	−2.27160e7	+	2.27160e7i	−0.186160	+	0.186160i
$497$		−	2.41244e6i		−	0.0196511i
$498$		−	2.03079e8i		−	1.64428i
$499$		−	6.57759e7i		−	0.529377i	−0.964334	−	0.264688i	$-0.914731\pi$
$499$		−	6.57759e7i		−	0.529377i	0.964334	−	0.264688i	$-0.0852691\pi$
$500$	−2.28177e8			−1.82542
$501$	9.69623e7	+	9.69623e7i	0.771062	+	0.771062i
$502$			1.75599e8i			1.38807i
$503$	5.37582e7	+	5.37582e7i	0.422416	+	0.422416i	0.886035	−	0.463619i	$-0.153449\pi$
$503$	5.37582e7	+	5.37582e7i	0.422416	+	0.422416i	−0.463619	+	0.886035i	$0.653449\pi$
$504$	3.86737e6	−	3.86737e6i	0.0302082	−	0.0302082i
$505$	3.92917e7	+	3.92917e7i	0.305089	+	0.305089i
$506$		−	5.83735e7i		−	0.450572i
$507$	−8.34313e7	+	8.34313e7i	−0.640184	+	0.640184i
$508$	1.05014e8	+	1.05014e8i	0.801043	+	0.801043i
$509$	9.14038e7			0.693124			0.346562	−	0.938027i	$-0.387349\pi$
$509$	9.14038e7			0.693124			0.346562	+	0.938027i	$0.387349\pi$
$510$	−1.80151e7	+	1.80151e7i	−0.135808	+	0.135808i
$511$	1.18652e7	+	1.18652e7i	0.0889223	+	0.0889223i
$512$	2.92890e7	−	2.92890e7i	0.218220	−	0.218220i
$513$	−2.09992e8			−1.55543
$514$	−1.17728e8	+	1.17728e8i	−0.866946	+	0.866946i
$515$			5.87626e6i			0.0430209i
$516$	3.05709e8			2.22515
$517$	−5.03242e7			−0.364171
$518$	7.14457e7			0.514028
$519$	−1.19855e8	−	1.19855e8i	−0.857340	−	0.857340i
$520$	1.72243e7	+	1.72243e7i	0.122498	+	0.122498i
$521$			1.75661e8i			1.24211i	0.783765	+	0.621057i	$0.213297\pi$
$521$			1.75661e8i			1.24211i	−0.783765	+	0.621057i	$0.786703\pi$
$522$	−2.76130e7	−	9.57490e6i	−0.194134	−	0.0673167i
$523$	1.59042e8			1.11175			0.555873	−	0.831267i	$-0.312384\pi$
$523$	1.59042e8			1.11175			0.555873	+	0.831267i	$0.312384\pi$
$524$	1.68142e8	−	1.68142e8i	1.16864	−	1.16864i
$525$	7.38475e6	−	7.38475e6i	0.0510338	−	0.0510338i
$526$			2.58583e7i			0.177682i
$527$		−	3.61001e7i		−	0.246647i
$528$		−	5.99028e6i		−	0.0406954i
$529$	−6.18635e6			−0.0417895
$530$	4.17402e7	+	4.17402e7i	0.280367	+	0.280367i
$531$		−	2.99391e7i		−	0.199966i
$532$	8.04530e7	+	8.04530e7i	0.534327	+	0.534327i
$533$	9.22118e6	−	9.22118e6i	0.0608982	−	0.0608982i
$534$	−3.17041e8	−	3.17041e8i	−2.08205	−	2.08205i
$535$			4.78858e7i			0.312713i
$536$	5.95232e7	−	5.95232e7i	0.386538	−	0.386538i
$537$	1.06500e8	+	1.06500e8i	0.687745	+	0.687745i
$538$	3.27709e8			2.10446
$539$	−2.82392e7	+	2.82392e7i	−0.180337	+	0.180337i
$540$	1.70535e8	+	1.70535e8i	1.08301	+	1.08301i
$541$	3.52986e7	−	3.52986e7i	0.222929	−	0.222929i	−0.586802	−	0.809731i	$-0.699613\pi$
$541$	3.52986e7	−	3.52986e7i	0.222929	−	0.222929i	0.809731	+	0.586802i	$0.199613\pi$
$542$	2.98688e8			1.87595
$543$	−7.34024e7	+	7.34024e7i	−0.458470	+	0.458470i
$544$			2.03072e7i			0.126140i
$545$	−7.65288e7			−0.472754
$546$	−1.35207e7			−0.0830656
$547$	−2.51560e8			−1.53702			−0.768512	−	0.639836i	$-0.779002\pi$
$547$	−2.51560e8			−1.53702			−0.768512	+	0.639836i	$0.779002\pi$
$548$	8.70367e7	+	8.70367e7i	0.528884	+	0.528884i
$549$	−3.01321e6	−	3.01321e6i	−0.0182101	−	0.0182101i
$550$			1.94796e7i			0.117083i
$551$	8.09955e7	−	2.33582e8i	0.484179	−	1.39632i
$552$	1.72913e8			1.02804
$553$	−1.23554e7	+	1.23554e7i	−0.0730603	+	0.0730603i
$554$	2.60894e8	−	2.60894e8i	1.53439	−	1.53439i
$555$			1.42736e8i			0.834939i
$556$			4.62708e8i			2.69204i
$557$			2.35384e8i			1.36211i	0.732234	+	0.681053i	$0.238478\pi$
$557$			2.35384e8i			1.36211i	−0.732234	+	0.681053i	$0.761522\pi$
$558$	−6.06681e7			−0.349187
$559$	3.11536e7	+	3.11536e7i	0.178350	+	0.178350i
$560$		−	7.12744e6i		−	0.0405854i
$561$	4.75986e6	+	4.75986e6i	0.0269591	+	0.0269591i
$562$	−2.00459e8	+	2.00459e8i	−1.12932	+	1.12932i
$563$	8.24030e7	+	8.24030e7i	0.461762	+	0.461762i	0.899233	−	0.437471i	$-0.144126\pi$
$563$	8.24030e7	+	8.24030e7i	0.461762	+	0.461762i	−0.437471	+	0.899233i	$0.644126\pi$
$564$		−	3.66596e8i		−	2.04338i
$565$	−2.63967e7	+	2.63967e7i	−0.146354	+	0.146354i
$566$	2.47070e8	+	2.47070e8i	1.36261	+	1.36261i
$567$	−4.74999e7			−0.260581
$568$	−9.42500e6	+	9.42500e6i	−0.0514323	+	0.0514323i
$569$	−1.55645e8	−	1.55645e8i	−0.844887	−	0.844887i	0.144603	−	0.989490i	$-0.453810\pi$
$569$	−1.55645e8	−	1.55645e8i	−0.844887	−	0.844887i	−0.989490	+	0.144603i	$0.953810\pi$
$570$	−2.56104e8	+	2.56104e8i	−1.38290	+	1.38290i
$571$	−2.24915e8			−1.20812			−0.604060	−	0.796939i	$-0.706451\pi$
$571$	−2.24915e8			−1.20812			−0.604060	+	0.796939i	$0.706451\pi$
$572$	1.11917e7	−	1.11917e7i	0.0598011	−	0.0598011i
$573$		−	2.19743e8i		−	1.16802i
$574$	−4.53260e7			−0.239669
$575$	−4.73361e7			−0.248994
$576$	3.78395e7			0.198006
$577$	−9.55531e7	−	9.55531e7i	−0.497413	−	0.497413i	0.413219	−	0.910632i	$-0.364405\pi$
$577$	−9.55531e7	−	9.55531e7i	−0.497413	−	0.497413i	−0.910632	+	0.413219i	$0.864405\pi$
$578$	−2.19037e8	−	2.19037e8i	−1.13432	−	1.13432i
$579$			3.03971e8i			1.56601i
$580$	−2.55470e8	+	1.23916e8i	−1.30935	+	0.635104i
$581$	−6.38424e7			−0.325522
$582$	2.32228e8	−	2.32228e8i	1.17800	−	1.17800i
$583$	1.10284e7	−	1.10284e7i	0.0556552	−	0.0556552i
$584$		−	9.27105e7i		−	0.465469i
$585$			3.87260e6i			0.0193435i
$586$		−	6.55278e7i		−	0.325636i
$587$	2.08316e8			1.02993			0.514966	−	0.857211i	$-0.327805\pi$
$587$	2.08316e8			1.02993			0.514966	+	0.857211i	$0.327805\pi$
$588$	−2.05713e8	−	2.05713e8i	−1.01188	−	1.01188i
$589$		−	5.13201e8i		−	2.51155i
$590$	−3.27714e8	−	3.27714e8i	−1.59565	−	1.59565i
$591$	1.23026e8	−	1.23026e8i	0.595984	−	0.595984i
$592$	−2.34982e7	−	2.34982e7i	−0.113258	−	0.113258i
$593$		−	9.61157e7i		−	0.460925i	−0.973081	−	0.230462i	$-0.925976\pi$
$593$		−	9.61157e7i		−	0.460925i	0.973081	−	0.230462i	$-0.0740239\pi$
$594$	7.17940e7	−	7.17940e7i	0.342554	−	0.342554i
$595$	5.66345e6	+	5.66345e6i	0.0268863	+	0.0268863i
$596$	276614.			0.00130658
$597$	5.66831e7	−	5.66831e7i	0.266398	−	0.266398i
$598$	4.33337e7	+	4.33337e7i	0.202639	+	0.202639i
$599$	8.62345e7	−	8.62345e7i	0.401237	−	0.401237i	−0.477432	−	0.878669i	$-0.658432\pi$
$599$	8.62345e7	−	8.62345e7i	0.401237	−	0.401237i	0.878669	+	0.477432i	$0.158432\pi$
$600$	−5.77021e7			−0.267139
$601$	9.89205e7	−	9.89205e7i	0.455683	−	0.455683i	−0.441552	−	0.897235i	$-0.645572\pi$
$601$	9.89205e7	−	9.89205e7i	0.455683	−	0.455683i	0.897235	+	0.441552i	$0.145572\pi$
$602$		−	1.53133e8i		−	0.701908i
$603$	1.33829e7			0.0610375
$604$	−4.67885e8			−2.12338
$605$	1.76131e8			0.795371
$606$	1.20499e8	+	1.20499e8i	0.541460	+	0.541460i
$607$	−1.97287e8	−	1.97287e8i	−0.882129	−	0.882129i	0.111621	−	0.993751i	$-0.464396\pi$
$607$	−1.97287e8	−	1.97287e8i	−0.882129	−	0.882129i	−0.993751	+	0.111621i	$0.964396\pi$
$608$			2.88689e8i			1.28446i
$609$	2.09958e7	−	6.05496e7i	0.0929566	−	0.268077i
$610$	−6.59652e7			−0.290620
$611$	3.73583e7	−	3.73583e7i	0.163781	−	0.163781i
$612$	4.97108e6	−	4.97108e6i	0.0216869	−	0.0216869i
$613$			2.07435e8i			0.900534i	0.892894	+	0.450267i	$0.148671\pi$
$613$			2.07435e8i			0.900534i	−0.892894	+	0.450267i	$0.851329\pi$
$614$			7.44386e7i			0.321583i
$615$		−	9.05533e7i		−	0.389295i
$616$	−2.23696e7			−0.0957010
$617$	1.34746e8	+	1.34746e8i	0.573669	+	0.573669i	0.933152	−	0.359482i	$-0.117047\pi$
$617$	1.34746e8	+	1.34746e8i	0.573669	+	0.573669i	−0.359482	+	0.933152i	$0.617047\pi$
$618$			1.80212e7i			0.0763518i
$619$	1.47759e8	+	1.47759e8i	0.622993	+	0.622993i	0.946296	−	0.323303i	$-0.104793\pi$
$619$	1.47759e8	+	1.47759e8i	0.622993	+	0.622993i	−0.323303	+	0.946296i	$0.604793\pi$
$620$	−4.16773e8	+	4.16773e8i	−1.74874	+	1.74874i
$621$	1.74462e8	+	1.74462e8i	0.728493	+	0.728493i
$622$			7.02305e8i			2.91846i
$623$	−9.96689e7	+	9.96689e7i	−0.412188	+	0.412188i
$624$	4.44690e6	+	4.44690e6i	0.0183022	+	0.0183022i
$625$	−1.66243e8			−0.680932
$626$	−2.27207e8	+	2.27207e8i	−0.926187	+	0.926187i
$627$	6.76664e7	+	6.76664e7i	0.274518	+	0.274518i
$628$	−2.76169e8	+	2.76169e8i	−1.11505	+	1.11505i
$629$	3.73432e7			0.150058
$630$	9.51773e6	−	9.51773e6i	0.0380638	−	0.0380638i
$631$		−	1.33119e8i		−	0.529849i	−0.964269	−	0.264924i	$-0.914653\pi$
$631$		−	1.33119e8i		−	0.529849i	0.964269	−	0.264924i	$-0.0853470\pi$
$632$	9.65411e7			0.382438
$633$	1.04866e8			0.413451
$634$	2.84562e7			0.111663
$635$	1.05091e8	+	1.05091e8i	0.410434	+	0.410434i
$636$	8.03382e7	+	8.03382e7i	0.312285	+	0.312285i
$637$		−	4.19269e7i		−	0.162209i
$638$	5.21678e7	+	1.07551e8i	0.200882	+	0.414144i
$639$	−2.11906e6			−0.00812159
$640$	2.75079e8	−	2.75079e8i	1.04934	−	1.04934i
$641$	2.73444e8	−	2.73444e8i	1.03823	−	1.03823i	0.0389929	−	0.999239i	$-0.487585\pi$
$641$	2.73444e8	−	2.73444e8i	1.03823	−	1.03823i	0.999239	−	0.0389929i	$-0.0124150\pi$
$642$			1.46856e8i			0.554991i
$643$			2.42272e8i			0.911319i	0.890154	+	0.455659i	$0.150596\pi$
$643$			2.42272e8i			0.911319i	−0.890154	+	0.455659i	$0.849404\pi$
$644$		−	1.33681e8i		−	0.500510i
$645$	3.05933e8			1.14011
$646$	6.70030e7	+	6.70030e7i	0.248540	+	0.248540i
$647$		−	3.27272e8i		−	1.20836i	−0.796849	−	0.604179i	$-0.793501\pi$
$647$		−	3.27272e8i		−	1.20836i	0.796849	−	0.604179i	$-0.206499\pi$
$648$	1.85574e8	+	1.85574e8i	0.682014	+	0.682014i
$649$	−8.65868e7	+	8.65868e7i	−0.316751	+	0.316751i
$650$	−1.44607e7	−	1.44607e7i	−0.0526563	−	0.0526563i
$651$		−	1.33033e8i		−	0.482187i
$652$	6.39073e8	−	6.39073e8i	2.30572	−	2.30572i
$653$	−3.20069e8	−	3.20069e8i	−1.14949	−	1.14949i	−0.986653	−	0.162835i	$-0.947936\pi$
$653$	−3.20069e8	−	3.20069e8i	−1.14949	−	1.14949i	−0.162835	−	0.986653i	$-0.552064\pi$
$654$	−2.34698e8			−0.839026
$655$	1.68265e8	−	1.68265e8i	0.598783	−	0.598783i
$656$	1.49075e7	+	1.49075e7i	0.0528073	+	0.0528073i
$657$	1.04222e7	−	1.04222e7i	0.0367506	−	0.0367506i
$658$	−1.83632e8			−0.644570
$659$	5.64678e7	−	5.64678e7i	0.197308	−	0.197308i	−0.601537	−	0.798845i	$-0.705445\pi$
$659$	5.64678e7	−	5.64678e7i	0.197308	−	0.197308i	0.798845	+	0.601537i	$0.205445\pi$
$660$		−	1.09904e8i		−	0.382282i
$661$	1.98334e8			0.686739			0.343370	−	0.939200i	$-0.388432\pi$
$661$	1.98334e8			0.686739			0.343370	+	0.939200i	$0.388432\pi$
$662$	−8.63891e8			−2.97773
$663$	−7.06699e6			−0.0242490
$664$	2.49422e8	+	2.49422e8i	0.851981	+	0.851981i
$665$	8.05119e7	+	8.05119e7i	0.273776	+	0.273776i
$666$		−	6.27572e7i		−	0.212442i
$667$	−2.61352e8	+	1.26769e8i	−0.880742	+	0.427206i
$668$	−5.85736e8			−1.96504
$669$	8.45943e7	−	8.45943e7i	0.282529	−	0.282529i
$670$	1.46489e8	−	1.46489e8i	0.487057	−	0.487057i
$671$			1.74290e7i			0.0576905i
$672$			7.48343e7i			0.246600i
$673$			2.14732e8i			0.704453i	0.935915	+	0.352227i	$0.114575\pi$
$673$			2.14732e8i			0.704453i	−0.935915	+	0.352227i	$0.885425\pi$
$674$	9.56574e8			3.12420
$675$	−5.82191e7	−	5.82191e7i	−0.189301	−	0.189301i
$676$		−	5.03997e8i		−	1.63150i
$677$	−3.41303e8	−	3.41303e8i	−1.09995	−	1.09995i	−0.994415	−	0.105539i	$-0.966343\pi$
$677$	−3.41303e8	−	3.41303e8i	−1.09995	−	1.09995i	−0.105539	−	0.994415i	$-0.533657\pi$
$678$	−8.09530e7	+	8.09530e7i	−0.259743	+	0.259743i
$679$	−7.30061e7	−	7.30061e7i	−0.233211	−	0.233211i
$680$		−	4.42524e7i		−	0.140737i
$681$	3.76362e8	−	3.76362e8i	1.19169	−	1.19169i
$682$	1.75458e8	+	1.75458e8i	0.553120	+	0.553120i
$683$	−3.36516e8			−1.05619			−0.528097	−	0.849184i	$-0.677094\pi$
$683$	−3.36516e8			−1.05619			−0.528097	+	0.849184i	$0.677094\pi$
$684$	7.06691e7	−	7.06691e7i	0.220832	−	0.220832i
$685$	8.71004e7	+	8.71004e7i	0.270987	+	0.270987i
$686$	−2.16535e8	+	2.16535e8i	−0.670741	+	0.670741i
$687$	−4.70601e8			−1.45139
$688$	−5.03648e7	+	5.03648e7i	−0.154654	+	0.154654i
$689$			1.63739e7i			0.0500604i
$690$	4.25543e8			1.29538
$691$	1.72356e8			0.522386			0.261193	−	0.965287i	$-0.415884\pi$
$691$	1.72356e8			0.522386			0.261193	+	0.965287i	$0.415884\pi$
$692$	7.24026e8			2.18492
$693$	−2.51473e6	−	2.51473e6i	−0.00755598	−	0.00755598i
$694$	−2.20040e8	−	2.20040e8i	−0.658298	−	0.658298i
$695$			4.63046e8i			1.37934i
$696$	−3.18584e8	+	1.54530e8i	−0.944924	+	0.458338i
$697$	−2.36910e7			−0.0699655
$698$	1.93563e8	−	1.93563e8i	0.569190	−	0.569190i
$699$	−3.01317e8	+	3.01317e8i	−0.882251	+	0.882251i
$700$			4.46103e7i			0.130059i
$701$			5.80771e8i			1.68598i	0.537933	+	0.842988i	$0.319205\pi$
$701$			5.80771e8i			1.68598i	−0.537933	+	0.842988i	$0.680795\pi$
$702$			1.06593e8i			0.308118i
$703$	5.30873e8			1.52800
$704$	−1.09436e8	−	1.09436e8i	−0.313646	−	0.313646i
$705$		−	3.66864e8i		−	1.04698i
$706$	2.51444e8	+	2.51444e8i	0.714541	+	0.714541i
$707$	3.78816e7	−	3.78816e7i	0.107194	−	0.107194i
$708$	−6.30757e8	−	6.30757e8i	−1.77731	−	1.77731i
$709$			5.94954e8i			1.66934i	0.550750	+	0.834670i	$0.314342\pi$
$709$			5.94954e8i			1.66934i	−0.550750	+	0.834670i	$0.685658\pi$
$710$	−2.31952e7	+	2.31952e7i	−0.0648072	+	0.0648072i
$711$	1.08529e7	+	1.08529e7i	0.0301950	+	0.0301950i
$712$	7.78781e8			2.15762
$713$	−4.26368e8	+	4.26368e8i	−1.17630	+	1.17630i
$714$	1.73686e7	+	1.73686e7i	0.0477167	+	0.0477167i
$715$	1.11999e7	−	1.11999e7i	0.0306406	−	0.0306406i
$716$	−6.43353e8			−1.75271
$717$	−5.70799e7	+	5.70799e7i	−0.154855	+	0.154855i
$718$		−	2.78608e8i		−	0.752697i
$719$	−5.37536e7			−0.144617			−0.0723087	−	0.997382i	$-0.523037\pi$
$719$	−5.37536e7			−0.144617			−0.0723087	+	0.997382i	$0.523037\pi$
$720$	−6.26068e6			−0.0167735
$721$	5.66538e6			0.0151155
$722$	5.16411e8	+	5.16411e8i	1.37209	+	1.37209i
$723$	−9.26770e7	−	9.26770e7i	−0.245221	−	0.245221i
$724$		−	4.43414e8i		−	1.16841i
$725$	8.72149e7	−	4.23038e7i	0.228864	−	0.111011i
$726$	5.40157e8			1.41159
$727$	3.91242e7	−	3.91242e7i	0.101822	−	0.101822i	−0.654361	−	0.756183i	$-0.727062\pi$
$727$	3.91242e7	−	3.91242e7i	0.101822	−	0.101822i	0.756183	+	0.654361i	$0.227062\pi$
$728$	1.66061e7	−	1.66061e7i	0.0430402	−	0.0430402i
$729$			4.23053e8i			1.09197i
$730$		−	2.28163e8i		−	0.586513i
$731$		−	8.00396e7i		−	0.204905i
$732$	−1.26964e8			−0.323705
$733$	2.82070e8	+	2.82070e8i	0.716218	+	0.716218i	0.967829	−	0.251610i	$-0.0809602\pi$
$733$	2.82070e8	+	2.82070e8i	0.716218	+	0.716218i	−0.251610	+	0.967829i	$0.580960\pi$
$734$			8.69961e8i			2.19994i
$735$	−2.05864e8	−	2.05864e8i	−0.518464	−	0.518464i
$736$	2.39843e8	−	2.39843e8i	0.601581	−	0.601581i
$737$	−3.87045e7	−	3.87045e7i	−0.0966849	−	0.0966849i
$738$			3.98139e7i			0.0990525i
$739$	−2.46780e8	+	2.46780e8i	−0.611471	+	0.611471i	−0.943329	−	0.331858i	$-0.892324\pi$
$739$	−2.46780e8	+	2.46780e8i	−0.611471	+	0.611471i	0.331858	+	0.943329i	$0.392324\pi$
$740$	−4.31124e8	−	4.31124e8i	−1.06392	−	1.06392i
$741$	−1.00465e8			−0.246921
$742$	4.02423e7	−	4.02423e7i	0.0985079	−	0.0985079i
$743$	−3.65369e8	−	3.65369e8i	−0.890769	−	0.890769i	0.103826	−	0.994595i	$-0.466891\pi$
$743$	−3.65369e8	−	3.65369e8i	−0.890769	−	0.890769i	−0.994595	+	0.103826i	$0.966891\pi$
$744$	−5.19737e8	+	5.19737e8i	−1.26202	+	1.26202i
$745$	276816.			0.000669457
$746$	5.34526e8	−	5.34526e8i	1.28752	−	1.28752i
$747$			5.60785e7i			0.134535i
$748$	−2.87537e7			−0.0687050
$749$	4.61674e7			0.109873
$750$	−7.00284e8			−1.65993
$751$	−2.08816e8	−	2.08816e8i	−0.492998	−	0.492998i	0.416252	−	0.909249i	$-0.363344\pi$
$751$	−2.08816e8	−	2.08816e8i	−0.492998	−	0.492998i	−0.909249	+	0.416252i	$0.863344\pi$
$752$	6.03957e7	+	6.03957e7i	0.142021	+	0.142021i
$753$			3.38227e8i			0.792179i
$754$	−1.18567e8	−	4.11137e7i	−0.276600	−	0.0959120i
$755$	−4.68227e8			−1.08797
$756$	1.64415e8	−	1.64415e8i	0.380520	−	0.380520i
$757$	−2.33322e8	+	2.33322e8i	−0.537858	+	0.537858i	−0.922899	−	0.385042i	$-0.874187\pi$
$757$	−2.33322e8	+	2.33322e8i	−0.537858	+	0.537858i	0.385042	+	0.922899i	$0.374187\pi$
$758$		−	1.06395e9i		−	2.44295i
$759$		−	1.12435e8i		−	0.257144i
$760$		−	6.29094e8i		−	1.43309i
$761$	−4.01815e8			−0.911743			−0.455871	−	0.890046i	$-0.650672\pi$
$761$	−4.01815e8			−0.911743			−0.455871	+	0.890046i	$0.650672\pi$
$762$	3.22292e8	+	3.22292e8i	0.728423	+	0.728423i
$763$			7.37824e7i			0.166104i
$764$	6.63718e8	+	6.63718e8i	1.48834	+	1.48834i
$765$	4.97472e6	−	4.97472e6i	0.0111118	−	0.0111118i
$766$	−4.78143e8	−	4.78143e8i	−1.06383	−	1.06383i
$767$		−	1.28556e8i		−	0.284909i
$768$	3.70573e8	−	3.70573e8i	0.818070	−	0.818070i
$769$	5.39076e8	+	5.39076e8i	1.18542	+	1.18542i	0.978321	+	0.207095i	$0.0664011\pi$
$769$	5.39076e8	+	5.39076e8i	1.18542	+	1.18542i	0.207095	+	0.978321i	$0.433599\pi$
$770$	−5.50523e7			−0.120588
$771$	−2.26760e8	+	2.26760e8i	−0.494770	+	0.494770i
$772$	−9.18122e8	−	9.18122e8i	−1.99549	−	1.99549i
$773$	5.82455e8	−	5.82455e8i	1.26102	−	1.26102i	0.310428	−	0.950597i	$-0.399528\pi$
$773$	5.82455e8	−	5.82455e8i	1.26102	−	1.26102i	0.950597	−	0.310428i	$-0.100472\pi$
$774$	−1.34511e8			−0.290091
$775$	1.42282e8	−	1.42282e8i	0.305664	−	0.305664i
$776$			5.70446e8i			1.22076i
$777$	1.37614e8			0.293358
$778$	−7.06854e8			−1.50104
$779$	−3.36792e8			−0.712441
$780$	8.15878e7	+	8.15878e7i	0.171926	+	0.171926i
$781$	6.12852e6	+	6.12852e6i	0.0128648	+	0.0128648i
$782$		−	1.11332e8i		−	0.232810i
$783$	−4.77354e8	−	1.65524e8i	−0.994386	−	0.344807i
$784$	6.77815e7			0.140657
$785$	−2.76371e8	+	2.76371e8i	−0.571325	+	0.571325i
$786$	5.16033e8	−	5.16033e8i	1.06270	−	1.06270i
$787$			1.33290e8i			0.273447i	0.990609	+	0.136723i	$0.0436572\pi$
$787$			1.33290e8i			0.273447i	−0.990609	+	0.136723i	$0.956343\pi$
$788$			7.43184e8i			1.51886i
$789$			4.98064e7i			0.101404i
$790$	2.37591e8			0.481890
$791$	2.54494e7	+	2.54494e7i	0.0514219	+	0.0514219i
$792$			1.96492e7i			0.0395522i
$793$	−1.29384e7	−	1.29384e7i	−0.0259455	−	0.0259455i
$794$	−6.48253e7	+	6.48253e7i	−0.129504	+	0.129504i
$795$	8.03970e7	+	8.03970e7i	0.160007	+	0.160007i
$796$			3.42415e8i			0.678912i
$797$	3.11323e8	−	3.11323e8i	0.614945	−	0.614945i	−0.329286	−	0.944230i	$-0.606808\pi$
$797$	3.11323e8	−	3.11323e8i	0.614945	−	0.614945i	0.944230	+	0.329286i	$0.106808\pi$
$798$	2.46913e8	+	2.46913e8i	0.485887	+	0.485887i
$799$	−9.59806e7			−0.188167
$800$	−8.00373e7	+	8.00373e7i	−0.156323	+	0.156323i
$801$	8.75482e7	+	8.75482e7i	0.170353	+	0.170353i
$802$	−7.04440e7	+	7.04440e7i	−0.136559	+	0.136559i
$803$	−6.02842e7			−0.116428
$804$	2.81950e8	−	2.81950e8i	0.542504	−	0.542504i
$805$		−	1.33779e8i		−	0.256449i
$806$	−2.60503e8			−0.497517
$807$	6.31209e8			1.20103
$808$	−2.95995e8			−0.561112
$809$	3.10583e8	+	3.10583e8i	0.586586	+	0.586586i	0.936705	−	0.350119i	$-0.113859\pi$
$809$	3.10583e8	+	3.10583e8i	0.586586	+	0.586586i	−0.350119	+	0.936705i	$0.613859\pi$
$810$	4.56704e8	+	4.56704e8i	0.859370	+	0.859370i
$811$			4.91317e8i			0.921084i	0.887638	+	0.460542i	$0.152345\pi$
$811$			4.91317e8i			0.921084i	−0.887638	+	0.460542i	$0.847655\pi$
$812$	1.19469e8	+	2.46302e8i	0.223146	+	0.460045i
$813$	5.75312e8			1.07061
$814$	−1.81500e8	+	1.81500e8i	−0.336514	+	0.336514i
$815$	6.39540e8	−	6.39540e8i	1.18140	−	1.18140i
$816$		−	1.14249e7i		−	0.0210273i
$817$		−	1.13785e9i		−	2.08650i
$818$		−	1.26039e9i		−	2.30275i
$819$	3.73362e6			0.00679640
$820$	2.73510e8	+	2.73510e8i	0.496057	+	0.496057i
$821$			8.09091e8i			1.46207i	0.682341	+	0.731034i	$0.260962\pi$
$821$			8.09091e8i			1.46207i	−0.682341	+	0.731034i	$0.739038\pi$
$822$	2.67119e8	+	2.67119e8i	0.480938	+	0.480938i
$823$	−1.94758e7	+	1.94758e7i	−0.0349378	+	0.0349378i	−0.724360	−	0.689422i	$-0.757865\pi$
$823$	−1.94758e7	+	1.94758e7i	−0.0349378	+	0.0349378i	0.689422	+	0.724360i	$0.257865\pi$
$824$	−2.21337e7	−	2.21337e7i	−0.0395615	−	0.0395615i
$825$			3.75203e7i			0.0668196i
$826$	−3.15953e8	+	3.15953e8i	−0.560638	+	0.560638i
$827$	3.09220e8	+	3.09220e8i	0.546702	+	0.546702i	0.925485	−	0.378783i	$-0.123657\pi$
$827$	3.09220e8	+	3.09220e8i	0.546702	+	0.546702i	−0.378783	+	0.925485i	$0.623657\pi$
$828$	−1.17424e8			−0.206855
$829$	4.31383e8	−	4.31383e8i	0.757181	−	0.757181i	−0.218627	−	0.975808i	$-0.570158\pi$
$829$	4.31383e8	−	4.31383e8i	0.757181	−	0.757181i	0.975808	+	0.218627i	$0.0701579\pi$
$830$	6.13835e8	+	6.13835e8i	1.07354	+	1.07354i
$831$	5.02516e8	−	5.02516e8i	0.875683	−	0.875683i
$832$	1.62479e8			0.282117
$833$	−5.38590e7	+	5.38590e7i	−0.0931801	+	0.0931801i
$834$			1.42007e9i			2.44799i
$835$	−5.86165e8			−1.00684
$836$	−4.08764e8			−0.699606
$837$	−1.04879e9			−1.78859
$838$	−8.33490e8	−	8.33490e8i	−1.41634	−	1.41634i
$839$	6.82733e8	+	6.82733e8i	1.15602	+	1.15602i	0.985324	+	0.170695i	$0.0546011\pi$
$839$	6.82733e8	+	6.82733e8i	1.15602	+	1.15602i	0.170695	+	0.985324i	$0.445399\pi$
$840$		−	1.63075e8i		−	0.275137i
$841$	3.68238e8	−	4.67135e8i	0.619071	−	0.785335i
$842$	1.50087e9			2.51425
$843$	−3.86110e8	+	3.86110e8i	−0.644509	+	0.644509i
$844$	−3.16741e8	+	3.16741e8i	−0.526837	+	0.526837i
$845$		−	5.04366e8i		−	0.835941i
$846$			1.61300e8i			0.266394i
$847$		−	1.69810e8i		−	0.279456i
$848$	−2.64710e7			−0.0434093
$849$	4.75889e8	+	4.75889e8i	0.777648	+	0.777648i
$850$			3.71524e7i			0.0604965i
$851$	−4.41051e8	−	4.41051e8i	−0.715649	−	0.715649i
$852$	−4.46443e7	+	4.46443e7i	−0.0721851	+	0.0721851i
$853$	4.69262e8	+	4.69262e8i	0.756081	+	0.756081i	0.975607	−	0.219526i	$-0.0704511\pi$
$853$	4.69262e8	+	4.69262e8i	0.756081	+	0.756081i	−0.219526	+	0.975607i	$0.570451\pi$
$854$			6.35979e7i			0.102110i
$855$	7.07209e7	−	7.07209e7i	0.113149	−	0.113149i
$856$	−1.80368e8	−	1.80368e8i	−0.287567	−	0.287567i
$857$	4.67996e7			0.0743532			0.0371766	−	0.999309i	$-0.488164\pi$
$857$	4.67996e7			0.0743532			0.0371766	+	0.999309i	$0.488164\pi$
$858$	3.43478e7	−	3.43478e7i	0.0543797	−	0.0543797i
$859$	2.90000e8	+	2.90000e8i	0.457529	+	0.457529i	0.897844	−	0.440314i	$-0.145133\pi$
$859$	2.90000e8	+	2.90000e8i	0.457529	+	0.457529i	−0.440314	+	0.897844i	$0.645133\pi$
$860$	−9.24050e8	+	9.24050e8i	−1.45278	+	1.45278i
$861$	−8.73037e7			−0.136780
$862$	−1.16316e9	+	1.16316e9i	−1.81600	+	1.81600i
$863$		−	1.14453e9i		−	1.78071i	−0.455268	−	0.890355i	$-0.650457\pi$
$863$		−	1.14453e9i		−	1.78071i	0.455268	−	0.890355i	$-0.349543\pi$
$864$	5.89970e8			0.914721
$865$	7.24556e8			1.11950
$866$	−4.25535e7			−0.0655212
$867$	−4.21894e8	−	4.21894e8i	−0.647361	−	0.647361i
$868$	4.01816e8	+	4.01816e8i	0.614424	+	0.614424i
$869$		−	6.27750e7i		−	0.0956593i
$870$	−7.84046e8	+	3.80304e8i	−1.19065	+	0.577528i
$871$	5.74647e7			0.0869654
$872$	2.88256e8	−	2.88256e8i	0.434739	−	0.434739i
$873$	−6.41279e7	+	6.41279e7i	−0.0963838	+	0.0963838i
$874$		−	1.58271e9i		−	2.37065i
$875$			2.20150e8i			0.328620i
$876$		−	4.39151e8i		−	0.653283i
$877$	−4.42601e8			−0.656166			−0.328083	−	0.944649i	$-0.606403\pi$
$877$	−4.42601e8			−0.656166			−0.328083	+	0.944649i	$0.606403\pi$
$878$	−1.27379e8	−	1.27379e8i	−0.188198	−	0.188198i
$879$		−	1.26215e8i		−	0.185842i
$880$	1.81065e7	+	1.81065e7i	0.0265696	+	0.0265696i
$881$	−4.09943e7	+	4.09943e7i	−0.0599509	+	0.0599509i	−0.736447	−	0.676496i	$-0.763498\pi$
$881$	−4.09943e7	+	4.09943e7i	−0.0599509	+	0.0599509i	0.676496	+	0.736447i	$0.263498\pi$
$882$	9.05129e7	+	9.05129e7i	0.131918	+	0.131918i
$883$		−	8.70922e6i		−	0.0126502i	−0.999980	−	0.00632510i	$-0.997987\pi$
$883$		−	8.70922e6i		−	0.0126502i	0.999980	−	0.00632510i	$-0.00201335\pi$
$884$	2.13454e7	−	2.13454e7i	0.0308992	−	0.0308992i
$885$	−6.31219e8	−	6.31219e8i	−0.910647	−	0.910647i
$886$	−9.71560e8			−1.39691
$887$	−4.20031e8	+	4.20031e8i	−0.601881	+	0.601881i	−0.940811	−	0.338930i	$-0.889935\pi$
$887$	−4.20031e8	+	4.20031e8i	−0.601881	+	0.601881i	0.338930	+	0.940811i	$0.389935\pi$
$888$	−5.37634e8	−	5.37634e8i	−0.767800	−	0.767800i
$889$	1.01319e8	−	1.01319e8i	0.144207	−	0.144207i
$890$	1.91660e9			2.71871
$891$	1.20668e8	−	1.20668e8i	0.170592	−	0.170592i
$892$			5.11022e8i			0.720021i
$893$	−1.36446e9			−1.91606
$894$	848937.			0.00118813
$895$	−6.43824e8			−0.898045
$896$	−2.65207e8	−	2.65207e8i	−0.368690	−	0.368690i
$897$	8.34663e7	+	8.34663e7i	0.115647	+	0.115647i
$898$		−	1.88784e9i		−	2.60697i
$899$	4.04526e8	−	1.16661e9i	0.556759	−	1.60563i
$900$	3.91852e7			0.0537520
$901$	2.10338e7	−	2.10338e7i	0.0287570	−	0.0287570i
$902$	1.15146e8	−	1.15146e8i	0.156902	−	0.156902i
$903$		−	2.94954e8i		−	0.400582i
$904$		−	1.98853e8i		−	0.269170i
$905$		−	4.43738e8i		−	0.598661i
$906$	−1.43595e9			−1.93088
$907$	7.90511e8	+	7.90511e8i	1.05946	+	1.05946i	0.998117	+	0.0613464i	$0.0195394\pi$
$907$	7.90511e8	+	7.90511e8i	1.05946	+	1.05946i	0.0613464	+	0.998117i	$0.480461\pi$
$908$			2.27355e9i			3.03701i
$909$	−3.32748e7	−	3.32748e7i	−0.0443021	−	0.0443021i
$910$	4.08682e7	−	4.08682e7i	0.0542328	−	0.0542328i
$911$	6.15153e7	+	6.15153e7i	0.0813631	+	0.0813631i	0.746617	−	0.665254i	$-0.231677\pi$
$911$	6.15153e7	+	6.15153e7i	0.0813631	+	0.0813631i	−0.665254	+	0.746617i	$0.731677\pi$
$912$		−	1.62417e8i		−	0.214115i
$913$	1.62184e8	−	1.62184e8i	0.213106	−	0.213106i
$914$	−9.65776e8	−	9.65776e8i	−1.26485	−	1.26485i
$915$	−1.27057e8			−0.165858
$916$	1.42142e9	−	1.42142e9i	1.84942	−	1.84942i
$917$	−1.62226e8	−	1.62226e8i	−0.210384	−	0.210384i
$918$	1.36929e8	−	1.36929e8i	0.176997	−	0.176997i
$919$	3.09322e8			0.398533			0.199267	−	0.979945i	$-0.436144\pi$
$919$	3.09322e8			0.398533			0.199267	+	0.979945i	$0.436144\pi$
$920$	−5.22653e8	+	5.22653e8i	−0.671197	+	0.671197i
$921$			1.43378e8i			0.183529i
$922$	−5.27061e8			−0.672463
$923$	−9.09905e6			−0.0115715
$924$	−1.05960e8			−0.134316
$925$	1.47182e8	+	1.47182e8i	0.185964	+	0.185964i
$926$	9.86473e8	+	9.86473e8i	1.24237	+	1.24237i
$927$		−	4.97641e6i		−	0.00624708i
$928$	−2.27556e8	+	6.56247e8i	−0.284737	+	0.821152i
$929$	−1.10022e8			−0.137225			−0.0686126	−	0.997643i	$-0.521857\pi$
$929$	−1.10022e8			−0.137225			−0.0686126	+	0.997643i	$0.521857\pi$
$930$	−1.27909e9	+	1.27909e9i	−1.59020	+	1.59020i
$931$	−7.65662e8	+	7.65662e8i	−0.948830	+	0.948830i
$932$		−	1.82022e9i		−	2.24841i
$933$			1.35273e9i			1.66558i
$934$			5.23385e8i			0.642364i
$935$	−2.87747e7			−0.0352027
$936$	−1.45867e7	−	1.45867e7i	−0.0177881	−	0.0177881i
$937$		−	4.35308e8i		−	0.529149i	−0.964365	−	0.264574i	$-0.914769\pi$
$937$		−	4.35308e8i		−	0.529149i	0.964365	−	0.264574i	$-0.0852315\pi$
$938$	−1.41232e8	−	1.41232e8i	−0.171129	−	0.171129i
$939$	−4.37630e8	+	4.37630e8i	−0.528580	+	0.528580i
$940$	1.10809e9	+	1.10809e9i	1.33411	+	1.33411i
$941$		−	2.22989e8i		−	0.267617i	−0.991007	−	0.133808i	$-0.957279\pi$
$941$		−	2.22989e8i		−	0.267617i	0.991007	−	0.133808i	$-0.0427207\pi$
$942$	−8.47572e8	+	8.47572e8i	−1.01397	+	1.01397i
$943$	2.79807e8	+	2.79807e8i	0.333675	+	0.333675i
$944$	2.07831e8			0.247056
$945$	1.64536e8	−	1.64536e8i	0.194969	−	0.194969i
$946$	3.89018e8	+	3.89018e8i	0.459511	+	0.459511i
$947$	1.39469e8	−	1.39469e8i	0.164221	−	0.164221i	−0.620213	−	0.784434i	$-0.712954\pi$
$947$	1.39469e8	−	1.39469e8i	0.164221	−	0.164221i	0.784434	+	0.620213i	$0.212954\pi$
$948$	4.57296e8			0.536750
$949$	4.47521e7	−	4.47521e7i	0.0523618	−	0.0523618i
$950$			5.28160e8i			0.616020i
$951$	5.48103e7			0.0637266
$952$	−4.26643e7			−0.0494486
$953$	−7.40672e7			−0.0855751			−0.0427875	−	0.999084i	$-0.513624\pi$
$953$	−7.40672e7			−0.0855751			−0.0427875	+	0.999084i	$0.513624\pi$
$954$	−3.53484e7	−	3.53484e7i	−0.0407122	−	0.0407122i
$955$	6.64203e8	+	6.64203e8i	0.762590	+	0.762590i
$956$		−	3.44812e8i		−	0.394647i
$957$	1.00482e8	+	2.07157e8i	0.114644	+	0.236354i
$958$	1.69497e9			1.92781
$959$	8.39747e7	−	8.39747e7i	0.0952122	−	0.0952122i
$960$	7.97786e8	−	7.97786e8i	0.901722	−	0.901722i
$961$		−	1.67564e9i		−	1.88803i
$962$		−	2.69474e8i		−	0.302685i
$963$		−	4.05530e7i		−	0.0454092i
$964$	5.59849e8			0.624943
$965$	−9.18794e8	−	9.18794e8i	−1.02244	−	1.02244i
$966$		−	4.10272e8i		−	0.455135i
$967$	5.85524e8	+	5.85524e8i	0.647538	+	0.647538i	0.952397	−	0.304859i	$-0.0986094\pi$
$967$	5.85524e8	+	5.85524e8i	0.647538	+	0.647538i	−0.304859	+	0.952397i	$0.598609\pi$
$968$	−6.63421e8	+	6.63421e8i	−0.731414	+	0.731414i
$969$	1.29056e8	+	1.29056e8i	0.141843	+	0.141843i
$970$			1.40389e9i			1.53821i
$971$	−1.38828e8	+	1.38828e8i	−0.151642	+	0.151642i	−0.778851	−	0.627209i	$-0.784197\pi$
$971$	−1.38828e8	+	1.38828e8i	−0.151642	+	0.151642i	0.627209	+	0.778851i	$0.284197\pi$
$972$	−2.72751e8	−	2.72751e8i	−0.297007	−	0.297007i
$973$	4.46429e8			0.484634
$974$	5.17363e8	−	5.17363e8i	0.559911	−	0.559911i
$975$	−2.78533e7	−	2.78533e7i	−0.0300512	−	0.0300512i
$976$	2.09171e7	−	2.09171e7i	0.0224984	−	0.0224984i
$977$	6.03042e6			0.00646642			0.00323321	−	0.999995i	$-0.498971\pi$
$977$	6.03042e6			0.00646642			0.00323321	+	0.999995i	$0.498971\pi$
$978$	1.96134e9	−	1.96134e9i	2.09670	−	2.09670i
$979$		−	5.06395e8i		−	0.539686i
$980$	1.24360e9			1.32130
$981$	6.48098e7			0.0686489
$982$	−1.29328e9			−1.36571
$983$	5.21590e8	+	5.21590e8i	0.549122	+	0.549122i	0.926187	−	0.377065i	$-0.123067\pi$
$983$	5.21590e8	+	5.21590e8i	0.549122	+	0.549122i	−0.377065	+	0.926187i	$0.623067\pi$
$984$	3.41081e8	+	3.41081e8i	0.357991	+	0.357991i
$985$			7.43728e8i			0.778225i
$986$	9.94967e7	+	2.05126e8i	0.103795	+	0.213988i
$987$	−3.53699e8			−0.367859
$988$	3.03447e8	−	3.03447e8i	0.314638	−	0.314638i
$989$	−9.45326e8	+	9.45326e8i	−0.977221	+	0.977221i
$990$			4.83574e7i			0.0498377i
$991$		−	8.93970e8i		−	0.918548i	−0.888295	−	0.459274i	$-0.848110\pi$
$991$		−	8.93970e8i		−	0.918548i	0.888295	−	0.459274i	$-0.151890\pi$
$992$			1.44183e9i			1.47700i
$993$	−1.66396e9			−1.69940
$994$	2.23628e7	+	2.23628e7i	0.0227702	+	0.0227702i
$995$			3.42666e8i			0.347858i
$996$	1.18146e9	+	1.18146e9i	1.19575	+	1.19575i
$997$	5.91681e8	−	5.91681e8i	0.597038	−	0.597038i	−0.342485	−	0.939523i	$-0.611269\pi$
$997$	5.91681e8	−	5.91681e8i	0.597038	−	0.597038i	0.939523	+	0.342485i	$0.111269\pi$
$998$	6.09730e8	+	6.09730e8i	0.613403	+	0.613403i
$999$		−	1.08490e9i		−	1.08816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.17.2	yes	28
29.12	odd	4	inner	29.7.c.a.12.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.2	✓	28	29.12	odd	4	inner
29.7.c.a.17.2	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.26981 + 9.26981i) q^{2} +(-17.8548 + 17.8548i) q^{3} -107.859i q^{4} -107.938i q^{5} -331.022i q^{6} -104.064 q^{7} +(406.562 + 406.562i) q^{8} +91.4089i q^{9} +O(q^{10})\)	\(q+(-9.26981 + 9.26981i) q^{2} +(-17.8548 + 17.8548i) q^{3} -107.859i q^{4} -107.938i q^{5} -331.022i q^{6} -104.064 q^{7} +(406.562 + 406.562i) q^{8} +91.4089i q^{9} +(1000.56 + 1000.56i) q^{10} +(264.363 - 264.363i) q^{11} +(1925.80 + 1925.80i) q^{12} +392.501i q^{13} +(964.655 - 964.655i) q^{14} +(1927.21 + 1927.21i) q^{15} -634.541 q^{16} +(504.205 - 504.205i) q^{17} +(-847.343 - 847.343i) q^{18} +(7167.80 - 7167.80i) q^{19} -11642.0 q^{20} +(1858.05 - 1858.05i) q^{21} +4901.19i q^{22} -11910.1 q^{23} -14518.2 q^{24} +3974.47 q^{25} +(-3638.41 - 3638.41i) q^{26} +(-14648.3 - 14648.3i) q^{27} +11224.2i q^{28} +(21943.8 - 10643.9i) q^{29} -35729.7 q^{30} +(35799.0 - 35799.0i) q^{31} +(-20137.9 + 20137.9i) q^{32} +9440.33i q^{33} +9347.77i q^{34} +11232.4i q^{35} +9859.25 q^{36} +(37031.8 + 37031.8i) q^{37} +132888. i q^{38} +(-7008.05 - 7008.05i) q^{39} +(43883.3 - 43883.3i) q^{40} +(-23493.4 - 23493.4i) q^{41} +34447.5i q^{42} +(79372.0 - 79372.0i) q^{43} +(-28513.9 - 28513.9i) q^{44} +9866.46 q^{45} +(110404. - 110404. i) q^{46} +(-95180.1 - 95180.1i) q^{47} +(11329.6 - 11329.6i) q^{48} -106820. q^{49} +(-36842.5 + 36842.5i) q^{50} +18005.0i q^{51} +42334.7 q^{52} +41716.8 q^{53} +271573. q^{54} +(-28534.7 - 28534.7i) q^{55} +(-42308.5 - 42308.5i) q^{56} +255960. i q^{57} +(-104748. + 302082. i) q^{58} -327530. q^{59} +(207866. - 207866. i) q^{60} +(-32964.1 + 32964.1i) q^{61} +663700. i q^{62} -9512.39i q^{63} -413959. i q^{64} +42365.7 q^{65} +(-87510.0 - 87510.0i) q^{66} -146406. i q^{67} +(-54382.9 - 54382.9i) q^{68} +(212652. - 212652. i) q^{69} +(-104123. - 104123. i) q^{70} +23182.2i q^{71} +(-37163.4 + 37163.4i) q^{72} +(-114018. - 114018. i) q^{73} -686555. q^{74} +(-70963.5 + 70963.5i) q^{75} +(-773110. - 773110. i) q^{76} +(-27510.7 + 27510.7i) q^{77} +129927. q^{78} +(118729. - 118729. i) q^{79} +68490.9i q^{80} +456448. q^{81} +435558. q^{82} +613491. q^{83} +(-200407. - 200407. i) q^{84} +(-54422.7 - 54422.7i) q^{85} +1.47153e6i q^{86} +(-201758. + 581849. i) q^{87} +214960. q^{88} +(957764. - 957764. i) q^{89} +(-91460.2 + 91460.2i) q^{90} -40845.3i q^{91} +1.28460e6i q^{92} +1.27837e6i q^{93} +1.76460e6 q^{94} +(-773676. - 773676. i) q^{95} -719117. i q^{96} +(701549. + 701549. i) q^{97} +(990198. - 990198. i) q^{98} +(24165.1 + 24165.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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