LMFDB - Embedded newform 29.9.c.a.12.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,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, 9, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.4
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.3962 - 15.3962i) q^{2} +(5.11102 + 5.11102i) q^{3} +218.083i q^{4} -625.365i q^{5} -157.380i q^{6} -974.923 q^{7} +(-583.770 + 583.770i) q^{8} -6508.75i q^{9} +O(q^{10})$	\(q+(-15.3962 - 15.3962i) q^{2} +(5.11102 + 5.11102i) q^{3} +218.083i q^{4} -625.365i q^{5} -157.380i q^{6} -974.923 q^{7} +(-583.770 + 583.770i) q^{8} -6508.75i q^{9} +(-9628.22 + 9628.22i) q^{10} +(-15822.4 - 15822.4i) q^{11} +(-1114.63 + 1114.63i) q^{12} +37005.1i q^{13} +(15010.1 + 15010.1i) q^{14} +(3196.26 - 3196.26i) q^{15} +73805.0 q^{16} +(62375.2 + 62375.2i) q^{17} +(-100210. + 100210. i) q^{18} +(103682. + 103682. i) q^{19} +136382. q^{20} +(-4982.85 - 4982.85i) q^{21} +487207. i q^{22} -482512. q^{23} -5967.33 q^{24} -456.492 q^{25} +(569737. - 569737. i) q^{26} +(66799.8 - 66799.8i) q^{27} -212614. i q^{28} +(-202609. + 677640. i) q^{29} -98420.1 q^{30} +(-422266. - 422266. i) q^{31} +(-986868. - 986868. i) q^{32} -161737. i q^{33} -1.92068e6i q^{34} +609683. i q^{35} +1.41945e6 q^{36} +(-1.77473e6 + 1.77473e6i) q^{37} -3.19261e6i q^{38} +(-189134. + 189134. i) q^{39} +(365070. + 365070. i) q^{40} +(72589.6 - 72589.6i) q^{41} +153434. i q^{42} +(1.58751e6 + 1.58751e6i) q^{43} +(3.45060e6 - 3.45060e6i) q^{44} -4.07035e6 q^{45} +(7.42883e6 + 7.42883e6i) q^{46} +(6.68132e6 - 6.68132e6i) q^{47} +(377219. + 377219. i) q^{48} -4.81433e6 q^{49} +(7028.22 + 7028.22i) q^{50} +637602. i q^{51} -8.07021e6 q^{52} -1.04312e7 q^{53} -2.05692e6 q^{54} +(-9.89476e6 + 9.89476e6i) q^{55} +(569131. - 569131. i) q^{56} +1.05984e6i q^{57} +(1.35525e7 - 7.31366e6i) q^{58} +3.32798e6 q^{59} +(697050. + 697050. i) q^{60} +(-6.53250e6 - 6.53250e6i) q^{61} +1.30026e7i q^{62} +6.34553e6i q^{63} +1.14939e7i q^{64} +2.31417e7 q^{65} +(-2.49013e6 + 2.49013e6i) q^{66} -1.74158e6i q^{67} +(-1.36030e7 + 1.36030e7i) q^{68} +(-2.46613e6 - 2.46613e6i) q^{69} +(9.38677e6 - 9.38677e6i) q^{70} -4.04978e6i q^{71} +(3.79962e6 + 3.79962e6i) q^{72} +(-9.71878e6 + 9.71878e6i) q^{73} +5.46481e7 q^{74} +(-2333.14 - 2333.14i) q^{75} +(-2.26114e7 + 2.26114e7i) q^{76} +(1.54256e7 + 1.54256e7i) q^{77} +5.82388e6 q^{78} +(-3.20149e7 - 3.20149e7i) q^{79} -4.61551e7i q^{80} -4.20211e7 q^{81} -2.23520e6 q^{82} -6.20738e6 q^{83} +(1.08668e6 - 1.08668e6i) q^{84} +(3.90073e7 - 3.90073e7i) q^{85} -4.88832e7i q^{86} +(-4.49897e6 + 2.42790e6i) q^{87} +1.84733e7 q^{88} +(-3.84789e7 - 3.84789e7i) q^{89} +(6.26677e7 + 6.26677e7i) q^{90} -3.60771e7i q^{91} -1.05228e8i q^{92} -4.31643e6i q^{93} -2.05733e8 q^{94} +(6.48392e7 - 6.48392e7i) q^{95} -1.00878e7i q^{96} +(-2.17348e7 + 2.17348e7i) q^{97} +(7.41221e7 + 7.41221e7i) q^{98} +(-1.02984e8 + 1.02984e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−15.3962	−	15.3962i	−0.962260	−	0.962260i	0.0370534	−	0.999313i	$-0.488203\pi$
$2$	−15.3962	−	15.3962i	−0.962260	−	0.962260i	−0.999313	+	0.0370534i	$0.988203\pi$
$3$	5.11102	+	5.11102i	0.0630991	+	0.0630991i	0.737952	−	0.674853i	$-0.235793\pi$
$3$	5.11102	+	5.11102i	0.0630991	+	0.0630991i	−0.674853	+	0.737952i	$0.735793\pi$
$4$			218.083i			0.851888i
$5$		−	625.365i		−	1.00058i	−0.865857	−	0.500292i	$-0.833226\pi$
$5$		−	625.365i		−	1.00058i	0.865857	−	0.500292i	$-0.166774\pi$
$6$		−	157.380i		−	0.121435i
$7$	−974.923			−0.406049			−0.203024	−	0.979174i	$-0.565077\pi$
$7$	−974.923			−0.406049			−0.203024	+	0.979174i	$0.565077\pi$
$8$	−583.770	+	583.770i	−0.142522	+	0.142522i
$9$		−	6508.75i		−	0.992037i
$10$	−9628.22	+	9628.22i	−0.962822	+	0.962822i
$11$	−15822.4	−	15822.4i	−1.08069	−	1.08069i	−0.996445	−	0.0842438i	$-0.973153\pi$
$11$	−15822.4	−	15822.4i	−1.08069	−	1.08069i	−0.0842438	−	0.996445i	$-0.526847\pi$
$12$	−1114.63	+	1114.63i	−0.0537533	+	0.0537533i
$13$			37005.1i			1.29565i	0.761788	+	0.647826i	$0.224322\pi$
$13$			37005.1i			1.29565i	−0.761788	+	0.647826i	$0.775678\pi$
$14$	15010.1	+	15010.1i	0.390724	+	0.390724i
$15$	3196.26	−	3196.26i	0.0631359	−	0.0631359i
$16$	73805.0			1.12617
$17$	62375.2	+	62375.2i	0.746821	+	0.746821i	0.973881	−	0.227060i	$-0.0729114\pi$
$17$	62375.2	+	62375.2i	0.746821	+	0.746821i	−0.227060	+	0.973881i	$0.572911\pi$
$18$	−100210.	+	100210.i	−0.954597	+	0.954597i
$19$	103682.	+	103682.i	0.795591	+	0.795591i	0.982397	−	0.186806i	$-0.0598136\pi$
$19$	103682.	+	103682.i	0.795591	+	0.795591i	−0.186806	+	0.982397i	$0.559814\pi$
$20$	136382.			0.852386
$21$	−4982.85	−	4982.85i	−0.0256213	−	0.0256213i
$22$			487207.i			2.07981i
$23$	−482512.			−1.72424			−0.862118	−	0.506707i	$-0.830862\pi$
$23$	−482512.			−1.72424			−0.862118	+	0.506707i	$0.830862\pi$
$24$	−5967.33			−0.0179860
$25$	−456.492			−0.00116862
$26$	569737.	−	569737.i	1.24675	−	1.24675i
$27$	66799.8	−	66799.8i	0.125696	−	0.125696i
$28$		−	212614.i		−	0.345908i
$29$	−202609.	+	677640.i	−0.286461	+	0.958092i
$29$	−202609.	+	677640.i	−0.286461	+	0.958092i
$30$	−98420.1			−0.121506
$31$	−422266.	−	422266.i	−0.457235	−	0.457235i	0.440512	−	0.897747i	$-0.354797\pi$
$31$	−422266.	−	422266.i	−0.457235	−	0.457235i	−0.897747	+	0.440512i	$0.854797\pi$
$32$	−986868.	−	986868.i	−0.941151	−	0.941151i
$33$		−	161737.i		−	0.136381i
$34$		−	1.92068e6i		−	1.43727i
$35$			609683.i			0.406286i
$36$	1.41945e6			0.845105
$37$	−1.77473e6	+	1.77473e6i	−0.946947	+	0.946947i	−0.998662	−	0.0517150i	$-0.983531\pi$
$37$	−1.77473e6	+	1.77473e6i	−0.946947	+	0.946947i	0.0517150	+	0.998662i	$0.483531\pi$
$38$		−	3.19261e6i		−	1.53113i
$39$	−189134.	+	189134.i	−0.0817545	+	0.0817545i
$40$	365070.	+	365070.i	0.142605	+	0.142605i
$41$	72589.6	−	72589.6i	0.0256885	−	0.0256885i	−0.694146	−	0.719834i	$-0.744218\pi$
$41$	72589.6	−	72589.6i	0.0256885	−	0.0256885i	0.719834	+	0.694146i	$0.244218\pi$
$42$			153434.i			0.0493087i
$43$	1.58751e6	+	1.58751e6i	0.464348	+	0.464348i	0.900078	−	0.435729i	$-0.143510\pi$
$43$	1.58751e6	+	1.58751e6i	0.464348	+	0.464348i	−0.435729	+	0.900078i	$0.643510\pi$
$44$	3.45060e6	−	3.45060e6i	0.920626	−	0.920626i
$45$	−4.07035e6			−0.992617
$46$	7.42883e6	+	7.42883e6i	1.65916	+	1.65916i
$47$	6.68132e6	−	6.68132e6i	1.36921	−	1.36921i	0.507648	−	0.861565i	$-0.330515\pi$
$47$	6.68132e6	−	6.68132e6i	1.36921	−	1.36921i	0.861565	−	0.507648i	$-0.169485\pi$
$48$	377219.	+	377219.i	0.0710606	+	0.0710606i
$49$	−4.81433e6			−0.835125
$50$	7028.22	+	7028.22i	0.00112452	+	0.00112452i
$51$			637602.i			0.0942474i
$52$	−8.07021e6			−1.10375
$53$	−1.04312e7			−1.32200			−0.661002	−	0.750384i	$-0.729869\pi$
$53$	−1.04312e7			−1.32200			−0.661002	+	0.750384i	$0.729869\pi$
$54$	−2.05692e6			−0.241904
$55$	−9.89476e6	+	9.89476e6i	−1.08132	+	1.08132i
$56$	569131.	−	569131.i	0.0578709	−	0.0578709i
$57$			1.05984e6i			0.100402i
$58$	1.35525e7	−	7.31366e6i	1.19758	−	0.646283i
$59$	3.32798e6			0.274645			0.137323	−	0.990526i	$-0.456150\pi$
$59$	3.32798e6			0.274645			0.137323	+	0.990526i	$0.456150\pi$
$60$	697050.	+	697050.i	0.0537847	+	0.0537847i
$61$	−6.53250e6	−	6.53250e6i	−0.471802	−	0.471802i	0.430695	−	0.902497i	$-0.358268\pi$
$61$	−6.53250e6	−	6.53250e6i	−0.471802	−	0.471802i	−0.902497	+	0.430695i	$0.858268\pi$
$62$			1.30026e7i			0.879958i
$63$			6.34553e6i			0.402815i
$64$			1.14939e7i			0.685088i
$65$	2.31417e7			1.29641
$66$	−2.49013e6	+	2.49013e6i	−0.131234	+	0.131234i
$67$		−	1.74158e6i		−	0.0864261i	−0.999066	−	0.0432131i	$-0.986241\pi$
$67$		−	1.74158e6i		−	0.0864261i	0.999066	−	0.0432131i	$-0.0137594\pi$
$68$	−1.36030e7	+	1.36030e7i	−0.636208	+	0.636208i
$69$	−2.46613e6	−	2.46613e6i	−0.108798	−	0.108798i
$70$	9.38677e6	−	9.38677e6i	0.390952	−	0.390952i
$71$		−	4.04978e6i		−	0.159367i	−0.996820	−	0.0796835i	$-0.974609\pi$
$71$		−	4.04978e6i		−	0.159367i	0.996820	−	0.0796835i	$-0.0253910\pi$
$72$	3.79962e6	+	3.79962e6i	0.141387	+	0.141387i
$73$	−9.71878e6	+	9.71878e6i	−0.342232	+	0.342232i	−0.857206	−	0.514974i	$-0.827802\pi$
$73$	−9.71878e6	+	9.71878e6i	−0.342232	+	0.342232i	0.514974	+	0.857206i	$0.327802\pi$
$74$	5.46481e7			1.82242
$75$	−2333.14	−	2333.14i	−7.37388e−5	−	7.37388e-5i
$76$	−2.26114e7	+	2.26114e7i	−0.677754	+	0.677754i
$77$	1.54256e7	+	1.54256e7i	0.438812	+	0.438812i
$78$	5.82388e6			0.157338
$79$	−3.20149e7	−	3.20149e7i	−0.821948	−	0.821948i	0.164439	−	0.986387i	$-0.447419\pi$
$79$	−3.20149e7	−	3.20149e7i	−0.821948	−	0.821948i	−0.986387	+	0.164439i	$0.947419\pi$
$80$		−	4.61551e7i		−	1.12683i
$81$	−4.20211e7			−0.976174
$82$	−2.23520e6			−0.0494381
$83$	−6.20738e6			−0.130796			−0.0653982	−	0.997859i	$-0.520832\pi$
$83$	−6.20738e6			−0.130796			−0.0653982	+	0.997859i	$0.520832\pi$
$84$	1.08668e6	−	1.08668e6i	0.0218265	−	0.0218265i
$85$	3.90073e7	−	3.90073e7i	0.747257	−	0.747257i
$86$		−	4.88832e7i		−	0.893648i
$87$	−4.49897e6	+	2.42790e6i	−0.0785301	+	0.0423792i
$88$	1.84733e7			0.308044
$89$	−3.84789e7	−	3.84789e7i	−0.613286	−	0.613286i	0.330515	−	0.943801i	$-0.392778\pi$
$89$	−3.84789e7	−	3.84789e7i	−0.613286	−	0.613286i	−0.943801	+	0.330515i	$0.892778\pi$
$90$	6.26677e7	+	6.26677e7i	0.955155	+	0.955155i
$91$		−	3.60771e7i		−	0.526098i
$92$		−	1.05228e8i		−	1.46886i
$93$		−	4.31643e6i		−	0.0577022i
$94$	−2.05733e8			−2.63508
$95$	6.48392e7	−	6.48392e7i	0.796056	−	0.796056i
$96$		−	1.00878e7i		−	0.118771i
$97$	−2.17348e7	+	2.17348e7i	−0.245510	+	0.245510i	−0.819125	−	0.573615i	$-0.805541\pi$
$97$	−2.17348e7	+	2.17348e7i	−0.245510	+	0.245510i	0.573615	+	0.819125i	$0.305541\pi$
$98$	7.41221e7	+	7.41221e7i	0.803607	+	0.803607i
$99$	−1.02984e8	+	1.02984e8i	−1.07208	+	1.07208i
$100$		−	99553.3i		−	0.000995533i
$101$	−3.39507e7	−	3.39507e7i	−0.326259	−	0.326259i	0.524903	−	0.851162i	$-0.324102\pi$
$101$	−3.39507e7	−	3.39507e7i	−0.326259	−	0.326259i	−0.851162	+	0.524903i	$0.824102\pi$
$102$	9.81663e6	−	9.81663e6i	0.0906905	−	0.0906905i
$103$	−7.58914e7			−0.674285			−0.337142	−	0.941454i	$-0.609460\pi$
$103$	−7.58914e7			−0.674285			−0.337142	+	0.941454i	$0.609460\pi$
$104$	−2.16025e7	−	2.16025e7i	−0.184659	−	0.184659i
$105$	−3.11610e6	+	3.11610e6i	−0.0256362	+	0.0256362i
$106$	1.60601e8	+	1.60601e8i	1.27211	+	1.27211i
$107$	1.95421e8			1.49086			0.745431	−	0.666583i	$-0.232244\pi$
$107$	1.95421e8			1.49086			0.745431	+	0.666583i	$0.232244\pi$
$108$	1.45679e7	+	1.45679e7i	0.107079	+	0.107079i
$109$			5.72364e7i			0.405477i	0.979233	+	0.202738i	$0.0649841\pi$
$109$			5.72364e7i			0.405477i	−0.979233	+	0.202738i	$0.935016\pi$
$110$	3.04682e8			2.08102
$111$	−1.81414e7			−0.119503
$112$	−7.19541e7			−0.457282
$113$	−1.64446e8	+	1.64446e8i	−1.00858	+	1.00858i	−0.00861582	+	0.999963i	$0.502743\pi$
$113$	−1.64446e8	+	1.64446e8i	−1.00858	+	1.00858i	−0.999963	+	0.00861582i	$0.997257\pi$
$114$	1.63175e7	−	1.63175e7i	0.0966129	−	0.0966129i
$115$			3.01746e8i			1.72524i
$116$	−1.47782e8	−	4.41856e7i	−0.816187	−	0.244033i
$117$	2.40857e8			1.28534
$118$	−5.12381e7	−	5.12381e7i	−0.264280	−	0.264280i
$119$	−6.08110e7	−	6.08110e7i	−0.303245	−	0.303245i
$120$			3.73176e6i			0.0179965i
$121$			2.86336e8i			1.33578i
$122$			2.01151e8i			0.907993i
$123$	742015.			0.00324184
$124$	9.20893e7	−	9.20893e7i	0.389513	−	0.389513i
$125$		−	2.43998e8i		−	0.999415i
$126$	9.76968e7	−	9.76968e7i	0.387613	−	0.387613i
$127$	−8.73909e7	−	8.73909e7i	−0.335932	−	0.335932i	0.518902	−	0.854834i	$-0.326341\pi$
$127$	−8.73909e7	−	8.73909e7i	−0.335932	−	0.335932i	−0.854834	+	0.518902i	$0.826341\pi$
$128$	−7.56767e7	+	7.56767e7i	−0.281918	+	0.281918i
$129$			1.62276e7i			0.0585999i
$130$	−3.56294e8	−	3.56294e8i	−1.24748	−	1.24748i
$131$	8.43780e7	−	8.43780e7i	0.286513	−	0.286513i	−0.549187	−	0.835700i	$-0.685062\pi$
$131$	8.43780e7	−	8.43780e7i	0.286513	−	0.286513i	0.835700	+	0.549187i	$0.185062\pi$
$132$	3.52721e7			0.116181
$133$	−1.01082e8	−	1.01082e8i	−0.323049	−	0.323049i
$134$	−2.68137e7	+	2.68137e7i	−0.0831644	+	0.0831644i
$135$	−4.17743e7	−	4.17743e7i	−0.125769	−	0.125769i
$136$	−7.28256e7			−0.212877
$137$	−1.78140e7	−	1.78140e7i	−0.0505685	−	0.0505685i	0.681370	−	0.731939i	$-0.261384\pi$
$137$	−1.78140e7	−	1.78140e7i	−0.0505685	−	0.0505685i	−0.731939	+	0.681370i	$0.761384\pi$
$138$			7.59379e7i			0.209383i
$139$	−6.04503e8			−1.61934			−0.809672	−	0.586882i	$-0.800355\pi$
$139$	−6.04503e8			−1.61934			−0.809672	+	0.586882i	$0.800355\pi$
$140$	−1.32962e8			−0.346110
$141$	6.82968e7			0.172792
$142$	−6.23511e7	+	6.23511e7i	−0.153352	+	0.153352i
$143$	5.85509e8	−	5.85509e8i	1.40020	−	1.40020i
$144$		−	4.80379e8i		−	1.11721i
$145$	4.23772e8	+	1.26704e8i	0.958651	+	0.286629i
$146$	2.99264e8			0.658632
$147$	−2.46061e7	−	2.46061e7i	−0.0526956	−	0.0526956i
$148$	−3.87039e8	−	3.87039e8i	−0.806693	−	0.806693i
$149$			3.70622e8i			0.751944i	0.926631	+	0.375972i	$0.122691\pi$
$149$			3.70622e8i			0.751944i	−0.926631	+	0.375972i	$0.877309\pi$
$150$			71842.8i			0.000141912i
$151$			5.95173e8i			1.14481i	0.819969	+	0.572407i	$0.193990\pi$
$151$			5.95173e8i			1.14481i	−0.819969	+	0.572407i	$0.806010\pi$
$152$	−1.21053e8			−0.226778
$153$	4.05985e8	−	4.05985e8i	0.740874	−	0.740874i
$154$		−	4.74989e8i		−	0.844503i
$155$	−2.64071e8	+	2.64071e8i	−0.457502	+	0.457502i
$156$	−4.12470e7	−	4.12470e7i	−0.0696457	−	0.0696457i
$157$	7.11088e8	−	7.11088e8i	1.17037	−	1.17037i	0.188254	−	0.982120i	$-0.439717\pi$
$157$	7.11088e8	−	7.11088e8i	1.17037	−	1.17037i	0.982120	−	0.188254i	$-0.0602827\pi$
$158$			9.85814e8i			1.58186i
$159$	−5.33144e7	−	5.33144e7i	−0.0834172	−	0.0834172i
$160$	−6.17153e8	+	6.17153e8i	−0.941700	+	0.941700i
$161$	4.70412e8			0.700124
$162$	6.46964e8	+	6.46964e8i	0.939334	+	0.939334i
$163$	5.60213e8	−	5.60213e8i	0.793602	−	0.793602i	−0.188476	−	0.982078i	$-0.560355\pi$
$163$	5.60213e8	−	5.60213e8i	0.793602	−	0.793602i	0.982078	+	0.188476i	$0.0603546\pi$
$164$	1.58306e7	+	1.58306e7i	0.0218837	+	0.0218837i
$165$	−1.01145e8			−0.136461
$166$	9.55698e7	+	9.55698e7i	0.125860	+	0.125860i
$167$		−	4.47213e8i		−	0.574975i	−0.957784	−	0.287487i	$-0.907180\pi$
$167$		−	4.47213e8i		−	0.574975i	0.957784	−	0.287487i	$-0.0928200\pi$
$168$	5.81768e6			0.00730320
$169$	−5.53650e8			−0.678716
$170$	−1.20112e9			−1.43811
$171$	6.74842e8	−	6.74842e8i	0.789256	−	0.789256i
$172$	−3.46211e8	+	3.46211e8i	−0.395573	+	0.395573i
$173$			1.76058e9i			1.96549i	0.184966	+	0.982745i	$0.440783\pi$
$173$			1.76058e9i			1.96549i	−0.184966	+	0.982745i	$0.559217\pi$
$174$	1.06647e8	+	3.18866e7i	0.116346	+	0.0347866i
$175$	445044.			0.000474516
$176$	−1.16777e9	−	1.16777e9i	−1.21704	−	1.21704i
$177$	1.70094e7	+	1.70094e7i	0.0173299	+	0.0173299i
$178$			1.18486e9i			1.18028i
$179$		−	2.09374e8i		−	0.203944i	−0.994787	−	0.101972i	$-0.967485\pi$
$179$		−	2.09374e8i		−	0.203944i	0.994787	−	0.101972i	$-0.0325151\pi$
$180$		−	8.87675e8i		−	0.845598i
$181$	−9.46921e8			−0.882266			−0.441133	−	0.897442i	$-0.645423\pi$
$181$	−9.46921e8			−0.882266			−0.441133	+	0.897442i	$0.645423\pi$
$182$	−5.55449e8	+	5.55449e8i	−0.506243	+	0.506243i
$183$		−	6.67755e7i		−	0.0595406i
$184$	2.81676e8	−	2.81676e8i	0.245742	−	0.245742i
$185$	1.10985e9	+	1.10985e9i	0.947500	+	0.947500i
$186$	−6.64564e7	+	6.64564e7i	−0.0555245	+	0.0555245i
$187$		−	1.97385e9i		−	1.61416i
$188$	1.45708e9	+	1.45708e9i	1.16642	+	1.16642i
$189$	−6.51247e7	+	6.51247e7i	−0.0510385	+	0.0510385i
$190$	−1.99655e9			−1.53202
$191$	1.01513e9	+	1.01513e9i	0.762759	+	0.762759i	0.976820	−	0.214062i	$-0.0686693\pi$
$191$	1.01513e9	+	1.01513e9i	0.762759	+	0.762759i	−0.214062	+	0.976820i	$0.568669\pi$
$192$	−5.87455e7	+	5.87455e7i	−0.0432284	+	0.0432284i
$193$	2.55546e8	+	2.55546e8i	0.184179	+	0.184179i	0.793174	−	0.608995i	$-0.208427\pi$
$193$	2.55546e8	+	2.55546e8i	0.184179	+	0.184179i	−0.608995	+	0.793174i	$0.708427\pi$
$194$	6.69266e8			0.472489
$195$	1.18278e8	+	1.18278e8i	0.0818022	+	0.0818022i
$196$		−	1.04992e9i		−	0.711433i
$197$	−2.52773e9			−1.67829			−0.839144	−	0.543909i	$-0.816944\pi$
$197$	−2.52773e9			−1.67829			−0.839144	+	0.543909i	$0.816944\pi$
$198$	3.17111e9			2.06325
$199$	−5.21666e8			−0.332645			−0.166322	−	0.986071i	$-0.553189\pi$
$199$	−5.21666e8			−0.332645			−0.166322	+	0.986071i	$0.553189\pi$
$200$	266487.	−	266487.i	0.000166554	−	0.000166554i
$201$	8.90127e6	−	8.90127e6i	0.00545341	−	0.00545341i
$202$			1.04542e9i			0.627892i
$203$	1.97528e8	−	6.60647e8i	0.116317	−	0.389032i
$204$	−1.39050e8			−0.0802882
$205$	−4.53950e7	−	4.53950e7i	−0.0257035	−	0.0257035i
$206$	1.16844e9	+	1.16844e9i	0.648837	+	0.648837i
$207$			3.14055e9i			1.71051i
$208$			2.73116e9i			1.45913i
$209$		−	3.28100e9i		−	1.71957i
$210$	9.59520e7			0.0493375
$211$	4.89698e8	−	4.89698e8i	0.247058	−	0.247058i	−0.572704	−	0.819762i	$-0.694106\pi$
$211$	4.89698e8	−	4.89698e8i	0.247058	−	0.247058i	0.819762	+	0.572704i	$0.194106\pi$
$212$		−	2.27488e9i		−	1.12620i
$213$	2.06985e7	−	2.06985e7i	0.0100559	−	0.0100559i
$214$	−3.00874e9	−	3.00874e9i	−1.43460	−	1.43460i
$215$	9.92776e8	−	9.92776e8i	0.464620	−	0.464620i
$216$			7.79915e7i			0.0358288i
$217$	4.11677e8	+	4.11677e8i	0.185660	+	0.185660i
$218$	8.81220e8	−	8.81220e8i	0.390174	−	0.390174i
$219$	−9.93458e7			−0.0431890
$220$	−2.15788e9	−	2.15788e9i	−0.921164	−	0.921164i
$221$	−2.30820e9	+	2.30820e9i	−0.967620	+	0.967620i
$222$	2.79308e8	+	2.79308e8i	0.114993	+	0.114993i
$223$	7.72341e8			0.312313			0.156156	−	0.987732i	$-0.450090\pi$
$223$	7.72341e8			0.312313			0.156156	+	0.987732i	$0.450090\pi$
$224$	9.62120e8	+	9.62120e8i	0.382153	+	0.382153i
$225$			2.97119e6i			0.00115931i
$226$	5.06368e9			1.94103
$227$	1.74551e9			0.657384			0.328692	−	0.944437i	$-0.393392\pi$
$227$	1.74551e9			0.657384			0.328692	+	0.944437i	$0.393392\pi$
$228$	−2.31134e8			−0.0855313
$229$	−1.13096e9	+	1.13096e9i	−0.411249	+	0.411249i	−0.882173	−	0.470925i	$-0.843920\pi$
$229$	−1.13096e9	+	1.13096e9i	−0.411249	+	0.411249i	0.470925	+	0.882173i	$0.343920\pi$
$230$	4.64573e9	−	4.64573e9i	1.66013	−	1.66013i
$231$			1.57681e8i			0.0553773i
$232$	−2.77309e8	−	5.13863e8i	−0.0957221	−	0.177376i
$233$	−3.63823e9			−1.23443			−0.617215	−	0.786795i	$-0.711739\pi$
$233$	−3.63823e9			−1.23443			−0.617215	+	0.786795i	$0.711739\pi$
$234$	−3.70828e9	−	3.70828e9i	−1.23683	−	1.23683i
$235$	−4.17826e9	−	4.17826e9i	−1.37001	−	1.37001i
$236$			7.25777e8i			0.233967i
$237$		−	3.27258e8i		−	0.103728i
$238$			1.87251e9i			0.583602i
$239$	−5.64884e9			−1.73128			−0.865641	−	0.500665i	$-0.833089\pi$
$239$	−5.64884e9			−1.73128			−0.865641	+	0.500665i	$0.833089\pi$
$240$	2.35900e8	−	2.35900e8i	0.0711021	−	0.0711021i
$241$			2.12849e9i			0.630962i	0.948932	+	0.315481i	$0.102166\pi$
$241$			2.12849e9i			0.630962i	−0.948932	+	0.315481i	$0.897834\pi$
$242$	4.40847e9	−	4.40847e9i	1.28536	−	1.28536i
$243$	−6.53045e8	−	6.53045e8i	−0.187291	−	0.187291i
$244$	1.42463e9	−	1.42463e9i	0.401923	−	0.401923i
$245$			3.01071e9i			0.835612i
$246$	−1.14242e7	−	1.14242e7i	−0.00311950	−	0.00311950i
$247$	−3.83677e9	+	3.83677e9i	−1.03081	+	1.03081i
$248$	4.93013e8			0.130332
$249$	−3.17261e7	−	3.17261e7i	−0.00825314	−	0.00825314i
$250$	−3.75663e9	+	3.75663e9i	−0.961697	+	0.961697i
$251$	−5.06223e9	−	5.06223e9i	−1.27540	−	1.27540i	−0.943213	−	0.332188i	$-0.892213\pi$
$251$	−5.06223e9	−	5.06223e9i	−1.27540	−	1.27540i	−0.332188	−	0.943213i	$-0.607787\pi$
$252$	−1.38386e9			−0.343154
$253$	7.63448e9	+	7.63448e9i	1.86336	+	1.86336i
$254$			2.69097e9i			0.646508i
$255$	3.98734e8			0.0943024
$256$	5.27269e9			1.22764
$257$	1.67332e9			0.383573			0.191786	−	0.981437i	$-0.438572\pi$
$257$	1.67332e9			0.383573			0.191786	+	0.981437i	$0.438572\pi$
$258$	2.49843e8	−	2.49843e8i	0.0563883	−	0.0563883i
$259$	1.73023e9	−	1.73023e9i	0.384506	−	0.384506i
$260$			5.04682e9i			1.10440i
$261$	4.41059e9	+	1.31873e9i	0.950463	+	0.284180i
$262$	−2.59819e9			−0.551400
$263$	−1.44369e9	−	1.44369e9i	−0.301752	−	0.301752i	0.539947	−	0.841699i	$-0.318444\pi$
$263$	−1.44369e9	−	1.44369e9i	−0.301752	−	0.301752i	−0.841699	+	0.539947i	$0.818444\pi$
$264$	9.44173e7	+	9.44173e7i	0.0194373	+	0.0194373i
$265$			6.52334e9i			1.32278i
$266$			3.11255e9i			0.621713i
$267$		−	3.93334e8i		−	0.0773955i
$268$	3.79810e8			0.0736254
$269$	3.20579e9	−	3.20579e9i	0.612245	−	0.612245i	−0.331285	−	0.943531i	$-0.607482\pi$
$269$	3.20579e9	−	3.20579e9i	0.612245	−	0.612245i	0.943531	+	0.331285i	$0.107482\pi$
$270$			1.28633e9i			0.242045i
$271$	6.39663e9	−	6.39663e9i	1.18597	−	1.18597i	0.207800	−	0.978171i	$-0.433370\pi$
$271$	6.39663e9	−	6.39663e9i	1.18597	−	1.18597i	0.978171	−	0.207800i	$-0.0666304\pi$
$272$	4.60360e9	+	4.60360e9i	0.841051	+	0.841051i
$273$	1.84391e8	−	1.84391e8i	0.0331963	−	0.0331963i
$274$			5.48535e8i			0.0973200i
$275$	7.22278e6	+	7.22278e6i	0.00126291	+	0.00126291i
$276$	5.37822e8	−	5.37822e8i	0.0926835	−	0.0926835i
$277$	−7.76872e9			−1.31956			−0.659782	−	0.751457i	$-0.729351\pi$
$277$	−7.76872e9			−1.31956			−0.659782	+	0.751457i	$0.729351\pi$
$278$	9.30703e9	+	9.30703e9i	1.55823	+	1.55823i
$279$	−2.74843e9	+	2.74843e9i	−0.453594	+	0.453594i
$280$	−3.55915e8	−	3.55915e8i	−0.0579047	−	0.0579047i
$281$	6.54485e9			1.04972			0.524861	−	0.851188i	$-0.324117\pi$
$281$	6.54485e9			1.04972			0.524861	+	0.851188i	$0.324117\pi$
$282$	−1.05151e9	−	1.05151e9i	−0.166271	−	0.166271i
$283$			8.00184e8i			0.124751i	0.998053	+	0.0623755i	$0.0198676\pi$
$283$			8.00184e8i			0.124751i	−0.998053	+	0.0623755i	$0.980132\pi$
$284$	8.83190e8			0.135763
$285$	6.62790e8			0.100461
$286$	−1.80292e10			−2.69471
$287$	−7.07693e7	+	7.07693e7i	−0.0104308	+	0.0104308i
$288$	−6.42328e9	+	6.42328e9i	−0.933656	+	0.933656i
$289$			8.05576e8i			0.115482i
$290$	−4.57371e9	−	8.47523e9i	−0.646660	−	1.19828i
$291$	−2.22174e8			−0.0309829
$292$	−2.11950e9	−	2.11950e9i	−0.291543	−	0.291543i
$293$	−6.27226e9	−	6.27226e9i	−0.851047	−	0.851047i	0.139215	−	0.990262i	$-0.455542\pi$
$293$	−6.27226e9	−	6.27226e9i	−0.851047	−	0.851047i	−0.990262	+	0.139215i	$0.955542\pi$
$294$			7.57680e8i			0.101414i
$295$		−	2.08120e9i		−	0.274806i
$296$		−	2.07207e9i		−	0.269922i
$297$	−2.11386e9			−0.271676
$298$	5.70615e9	−	5.70615e9i	0.723566	−	0.723566i
$299$		−	1.78554e10i		−	2.23401i
$300$	508819.	−	508819.i	6.28172e−5	−	6.28172e-5i
$301$	−1.54770e9	−	1.54770e9i	−0.188548	−	0.188548i
$302$	9.16337e9	−	9.16337e9i	1.10161	−	1.10161i
$303$		−	3.47045e8i		−	0.0411733i
$304$	7.65226e9	+	7.65226e9i	0.895974	+	0.895974i
$305$	−4.08520e9	+	4.08520e9i	−0.472078	+	0.472078i
$306$	−1.25012e10			−1.42583
$307$	2.17142e9	+	2.17142e9i	0.244450	+	0.244450i	0.818688	−	0.574238i	$-0.194702\pi$
$307$	2.17142e9	+	2.17142e9i	0.244450	+	0.244450i	−0.574238	+	0.818688i	$0.694702\pi$
$308$	−3.36406e9	+	3.36406e9i	−0.373819	+	0.373819i
$309$	−3.87883e8	−	3.87883e8i	−0.0425467	−	0.0425467i
$310$	8.13135e9			0.880472
$311$	−2.26859e9	−	2.26859e9i	−0.242501	−	0.242501i	0.575383	−	0.817884i	$-0.304853\pi$
$311$	−2.26859e9	−	2.26859e9i	−0.242501	−	0.242501i	−0.817884	+	0.575383i	$0.804853\pi$
$312$		−	2.20822e8i		−	0.0233036i
$313$	8.10812e9			0.844778			0.422389	−	0.906415i	$-0.361192\pi$
$313$	8.10812e9			0.844778			0.422389	+	0.906415i	$0.361192\pi$
$314$	−2.18960e10			−2.25241
$315$	3.96827e9			0.403051
$316$	6.98193e9	−	6.98193e9i	0.700208	−	0.700208i
$317$	9.22023e9	−	9.22023e9i	0.913072	−	0.913072i	−0.0834409	−	0.996513i	$-0.526591\pi$
$317$	9.22023e9	−	9.22023e9i	0.913072	−	0.913072i	0.996513	+	0.0834409i	$0.0265910\pi$
$318$			1.64167e9i			0.160538i
$319$	1.39276e10	−	7.51612e9i	1.34497	−	0.725823i
$320$	7.18787e9			0.685489
$321$	9.98804e8	+	9.98804e8i	0.0940719	+	0.0940719i
$322$	−7.24253e9	−	7.24253e9i	−0.673701	−	0.673701i
$323$			1.29344e10i			1.18833i
$324$		−	9.16411e9i		−	0.831591i
$325$		−	1.68926e7i		−	0.00151413i
$326$	−1.72503e10			−1.52730
$327$	−2.92536e8	+	2.92536e8i	−0.0255852	+	0.0255852i
$328$			8.47513e7i			0.00732236i
$329$	−6.51377e9	+	6.51377e9i	−0.555967	+	0.555967i
$330$	1.55724e9	+	1.55724e9i	0.131311	+	0.131311i
$331$	3.31393e9	−	3.31393e9i	0.276078	−	0.276078i	−0.555463	−	0.831541i	$-0.687459\pi$
$331$	3.31393e9	−	3.31393e9i	0.276078	−	0.276078i	0.831541	+	0.555463i	$0.187459\pi$
$332$		−	1.35373e9i		−	0.111424i
$333$	1.15513e10	+	1.15513e10i	0.939406	+	0.939406i
$334$	−6.88537e9	+	6.88537e9i	−0.553275	+	0.553275i
$335$	−1.08913e9			−0.0864766
$336$	−3.67759e8	−	3.67759e8i	−0.0288540	−	0.0288540i
$337$	−4.29759e9	+	4.29759e9i	−0.333200	+	0.333200i	−0.853800	−	0.520600i	$-0.825708\pi$
$337$	−4.29759e9	+	4.29759e9i	−0.333200	+	0.333200i	0.520600	+	0.853800i	$0.325708\pi$
$338$	8.52408e9	+	8.52408e9i	0.653101	+	0.653101i
$339$	−1.68098e9			−0.127281
$340$	8.50684e9	+	8.50684e9i	0.636579	+	0.636579i
$341$			1.33625e10i			0.988258i
$342$	−2.07799e10			−1.51894
$343$	1.03138e10			0.745150
$344$	−1.85349e9			−0.132360
$345$	−1.54223e9	+	1.54223e9i	−0.108861	+	0.108861i
$346$	2.71061e10	−	2.71061e10i	1.89131	−	1.89131i
$347$		−	9.59620e9i		−	0.661883i	−0.943651	−	0.330942i	$-0.892634\pi$
$347$		−	9.59620e9i		−	0.661883i	0.943651	−	0.330942i	$-0.107366\pi$
$348$	−5.29484e8	−	9.81151e8i	−0.0361024	−	0.0668989i
$349$	−4.29666e9			−0.289620			−0.144810	−	0.989459i	$-0.546257\pi$
$349$	−4.29666e9			−0.289620			−0.144810	+	0.989459i	$0.546257\pi$
$350$	−6.85197e6	−	6.85197e6i	−0.000456608	−	0.000456608i
$351$	2.47194e9	+	2.47194e9i	0.162858	+	0.162858i
$352$			3.12292e10i			2.03418i
$353$			1.28648e10i			0.828524i	0.910158	+	0.414262i	$0.135960\pi$
$353$			1.28648e10i			0.828524i	−0.910158	+	0.414262i	$0.864040\pi$
$354$		−	5.23758e8i		−	0.0333517i
$355$	−2.53259e9			−0.159460
$356$	8.39162e9	−	8.39162e9i	0.522451	−	0.522451i
$357$		−	6.21613e8i		−	0.0382690i
$358$	−3.22355e9	+	3.22355e9i	−0.196247	+	0.196247i
$359$	−1.60765e10	−	1.60765e10i	−0.967865	−	0.967865i	0.0316345	−	0.999500i	$-0.489929\pi$
$359$	−1.60765e10	−	1.60765e10i	−0.967865	−	0.967865i	−0.999500	+	0.0316345i	$0.989929\pi$
$360$	2.37615e9	−	2.37615e9i	0.141470	−	0.141470i
$361$			4.51643e9i			0.265930i
$362$	1.45789e10	+	1.45789e10i	0.848969	+	0.848969i
$363$	−1.46347e9	+	1.46347e9i	−0.0842863	+	0.0842863i
$364$	7.86783e9			0.448177
$365$	6.07779e9	+	6.07779e9i	0.342432	+	0.342432i
$366$	−1.02809e9	+	1.02809e9i	−0.0572935	+	0.0572935i
$367$	8.53482e9	+	8.53482e9i	0.470468	+	0.470468i	0.902066	−	0.431598i	$-0.142050\pi$
$367$	8.53482e9	+	8.53482e9i	0.470468	+	0.470468i	−0.431598	+	0.902066i	$0.642050\pi$
$368$	−3.56118e10			−1.94179
$369$	−4.72468e8	−	4.72468e8i	−0.0254840	−	0.0254840i
$370$		−	3.41750e10i		−	1.82348i
$371$	1.01697e10			0.536798
$372$	9.41341e8			0.0491559
$373$	−7.18241e9			−0.371052			−0.185526	−	0.982639i	$-0.559399\pi$
$373$	−7.18241e9			−0.371052			−0.185526	+	0.982639i	$0.559399\pi$
$374$	−3.03897e10	+	3.03897e10i	−1.55324	+	1.55324i
$375$	1.24708e9	−	1.24708e9i	0.0630621	−	0.0630621i
$376$			7.80071e9i			0.390286i
$377$	−2.50762e10	−	7.49756e9i	−1.24135	−	0.371155i
$378$	2.00534e9			0.0982247
$379$	−3.44008e9	−	3.44008e9i	−0.166729	−	0.166729i	0.618811	−	0.785540i	$-0.287615\pi$
$379$	−3.44008e9	−	3.44008e9i	−0.166729	−	0.166729i	−0.785540	+	0.618811i	$0.787615\pi$
$380$	1.41404e10	+	1.41404e10i	0.678150	+	0.678150i
$381$		−	8.93314e8i		−	0.0423940i
$382$		−	3.12581e10i		−	1.46794i
$383$			2.05015e10i			0.952777i	0.879235	+	0.476389i	$0.158054\pi$
$383$			2.05015e10i			0.952777i	−0.879235	+	0.476389i	$0.841946\pi$
$384$	−7.73571e8			−0.0355775
$385$	9.64662e9	−	9.64662e9i	0.439069	−	0.439069i
$386$		−	7.86885e9i		−	0.354456i
$387$	1.03327e10	−	1.03327e10i	0.460651	−	0.460651i
$388$	−4.74001e9	−	4.74001e9i	−0.209147	−	0.209147i
$389$	−1.01573e10	+	1.01573e10i	−0.443587	+	0.443587i	−0.893215	−	0.449629i	$-0.851556\pi$
$389$	−1.01573e10	+	1.01573e10i	−0.443587	+	0.443587i	0.449629	+	0.893215i	$0.351556\pi$
$390$		−	3.64205e9i		−	0.157430i
$391$	−3.00968e10	−	3.00968e10i	−1.28770	−	1.28770i
$392$	2.81046e9	−	2.81046e9i	0.119024	−	0.119024i
$393$	8.62516e8			0.0361574
$394$	3.89174e10	+	3.89174e10i	1.61495	+	1.61495i
$395$	−2.00210e10	+	2.00210e10i	−0.822428	+	0.822428i
$396$	−2.24591e10	−	2.24591e10i	−0.913295	−	0.913295i
$397$	3.04739e10			1.22678			0.613389	−	0.789781i	$-0.289806\pi$
$397$	3.04739e10			1.22678			0.613389	+	0.789781i	$0.289806\pi$
$398$	8.03166e9	+	8.03166e9i	0.320091	+	0.320091i
$399$		−	1.03327e9i		−	0.0407681i
$400$	−3.36914e7			−0.00131607
$401$	−2.05367e10			−0.794241			−0.397121	−	0.917766i	$-0.629991\pi$
$401$	−2.05367e10			−0.794241			−0.397121	+	0.917766i	$0.629991\pi$
$402$	−2.74091e8			−0.0104952
$403$	1.56260e10	−	1.56260e10i	0.592418	−	0.592418i
$404$	7.40407e9	−	7.40407e9i	0.277936	−	0.277936i
$405$			2.62785e10i			0.976745i
$406$	−1.32126e10	+	7.13025e9i	−0.486277	+	0.262422i
$407$	5.61609e10			2.04671
$408$	−3.72213e8	−	3.72213e8i	−0.0134323	−	0.0134323i
$409$	2.57540e10	+	2.57540e10i	0.920346	+	0.920346i	0.997054	−	0.0767079i	$-0.0244409\pi$
$409$	2.57540e10	+	2.57540e10i	0.920346	+	0.920346i	−0.0767079	+	0.997054i	$0.524441\pi$
$410$			1.39782e9i			0.0494669i
$411$		−	1.82096e8i		−	0.00638164i
$412$		−	1.65506e10i		−	0.574415i
$413$	−3.24452e9			−0.111519
$414$	4.83524e10	−	4.83524e10i	1.64595	−	1.64595i
$415$			3.88188e9i			0.130873i
$416$	3.65192e10	−	3.65192e10i	1.21940	−	1.21940i
$417$	−3.08963e9	−	3.08963e9i	−0.102179	−	0.102179i
$418$	−5.05147e10	+	5.05147e10i	−1.65468	+	1.65468i
$419$		−	2.15134e10i		−	0.697997i	−0.937123	−	0.348998i	$-0.886522\pi$
$419$		−	2.15134e10i		−	0.697997i	0.937123	−	0.348998i	$-0.113478\pi$
$420$	−6.79570e8	−	6.79570e8i	−0.0218392	−	0.0218392i
$421$	1.90506e10	−	1.90506e10i	0.606430	−	0.606430i	−0.335581	−	0.942011i	$-0.608933\pi$
$421$	1.90506e10	−	1.90506e10i	0.606430	−	0.606430i	0.942011	+	0.335581i	$0.108933\pi$
$422$	−1.50789e10			−0.475467
$423$	−4.34871e10	−	4.34871e10i	−1.35831	−	1.35831i
$424$	6.08945e9	−	6.08945e9i	0.188415	−	0.188415i
$425$	−2.84738e7	−	2.84738e7i	−0.000872749	−	0.000872749i
$426$	−6.37356e8			−0.0193528
$427$	6.36868e9	+	6.36868e9i	0.191575	+	0.191575i
$428$			4.26182e10i			1.27005i
$429$	5.98510e9			0.176702
$430$	−3.05699e10			−0.894170
$431$	−4.35541e10			−1.26218			−0.631088	−	0.775711i	$-0.717391\pi$
$431$	−4.35541e10			−1.26218			−0.631088	+	0.775711i	$0.717391\pi$
$432$	4.93016e9	−	4.93016e9i	0.141555	−	0.141555i
$433$	9.45946e9	−	9.45946e9i	0.269101	−	0.269101i	−0.559637	−	0.828738i	$-0.689059\pi$
$433$	9.45946e9	−	9.45946e9i	0.269101	−	0.269101i	0.828738	+	0.559637i	$0.189059\pi$
$434$		−	1.26765e10i		−	0.357306i
$435$	1.51832e9	+	2.81350e9i	0.0424040	+	0.0785760i
$436$	−1.24823e10			−0.345421
$437$	−5.00279e10	−	5.00279e10i	−1.37179	−	1.37179i
$438$	1.52954e9	+	1.52954e9i	0.0415590	+	0.0415590i
$439$			1.17055e10i			0.315162i	0.987506	+	0.157581i	$0.0503695\pi$
$439$			1.17055e10i			0.315162i	−0.987506	+	0.157581i	$0.949630\pi$
$440$		−	1.15525e10i		−	0.308224i
$441$			3.13353e10i			0.828474i
$442$	7.10749e10			1.86220
$443$	−1.84824e10	+	1.84824e10i	−0.479891	+	0.479891i	−0.905097	−	0.425205i	$-0.860202\pi$
$443$	−1.84824e10	+	1.84824e10i	−0.479891	+	0.479891i	0.425205	+	0.905097i	$0.360202\pi$
$444$		−	3.95633e9i		−	0.101803i
$445$	−2.40634e10	+	2.40634e10i	−0.613644	+	0.613644i
$446$	−1.18911e10	−	1.18911e10i	−0.300526	−	0.300526i
$447$	−1.89426e9	+	1.89426e9i	−0.0474470	+	0.0474470i
$448$		−	1.12056e10i		−	0.278179i
$449$	3.25734e10	+	3.25734e10i	0.801451	+	0.801451i	0.983322	−	0.181871i	$-0.0582154\pi$
$449$	3.25734e10	+	3.25734e10i	0.801451	+	0.801451i	−0.181871	+	0.983322i	$0.558215\pi$
$450$	4.57450e7	−	4.57450e7i	0.00111556	−	0.00111556i
$451$	−2.29708e9			−0.0555226
$452$	−3.58630e10	−	3.58630e10i	−0.859196	−	0.859196i
$453$	−3.04194e9	+	3.04194e9i	−0.0722367	+	0.0722367i
$454$	−2.68741e10	−	2.68741e10i	−0.632574	−	0.632574i
$455$	−2.25614e10			−0.526405
$456$	−6.18706e8	−	6.18706e8i	−0.0143095	−	0.0143095i
$457$		−	4.28176e10i		−	0.981652i	−0.871258	−	0.490826i	$-0.836695\pi$
$457$		−	4.28176e10i		−	0.981652i	0.871258	−	0.490826i	$-0.163305\pi$
$458$	3.48248e10			0.791456
$459$	8.33331e9			0.187744
$460$	−6.58058e10			−1.46971
$461$	4.92743e10	−	4.92743e10i	1.09098	−	1.09098i	0.0955557	−	0.995424i	$-0.469537\pi$
$461$	4.92743e10	−	4.92743e10i	1.09098	−	1.09098i	0.995424	−	0.0955557i	$-0.0304628\pi$
$462$	2.42768e9	−	2.42768e9i	0.0532873	−	0.0532873i
$463$		−	2.96324e10i		−	0.644826i	−0.946599	−	0.322413i	$-0.895506\pi$
$463$		−	2.96324e10i		−	0.644826i	0.946599	−	0.322413i	$-0.104494\pi$
$464$	−1.49535e10	+	5.00132e10i	−0.322606	+	1.07898i
$465$	−2.69934e9			−0.0577359
$466$	5.60147e10	+	5.60147e10i	1.18784	+	1.18784i
$467$	2.61019e10	+	2.61019e10i	0.548789	+	0.548789i	0.926090	−	0.377302i	$-0.123148\pi$
$467$	2.61019e10	+	2.61019e10i	0.548789	+	0.548789i	−0.377302	+	0.926090i	$0.623148\pi$
$468$			5.25270e10i			1.09496i
$469$			1.69791e9i			0.0350932i
$470$			1.28658e11i			2.63662i
$471$	7.26877e9			0.147699
$472$	−1.94278e9	+	1.94278e9i	−0.0391430	+	0.0391430i
$473$		−	5.02365e10i		−	1.00363i
$474$	−5.03852e9	+	5.03852e9i	−0.0998136	+	0.0998136i
$475$	−4.73301e7	−	4.73301e7i	−0.000929743	−	0.000929743i
$476$	1.32619e10	−	1.32619e10i	0.258331	−	0.258331i
$477$			6.78944e10i			1.31148i
$478$	8.69705e10	+	8.69705e10i	1.66594	+	1.66594i
$479$	−3.59885e8	+	3.59885e8i	−0.00683632	+	0.00683632i	−0.710517	−	0.703680i	$-0.751539\pi$
$479$	−3.59885e8	+	3.59885e8i	−0.00683632	+	0.00683632i	0.703680	+	0.710517i	$0.251539\pi$
$480$	−6.30857e9			−0.118841
$481$	−6.56742e10	−	6.56742e10i	−1.22691	−	1.22691i
$482$	3.27706e10	−	3.27706e10i	0.607149	−	0.607149i
$483$	2.40429e9	+	2.40429e9i	0.0441771	+	0.0441771i
$484$	−6.24451e10			−1.13793
$485$	1.35922e10	+	1.35922e10i	0.245654	+	0.245654i
$486$			2.01088e10i			0.360446i
$487$	−4.61783e10			−0.820961			−0.410480	−	0.911869i	$-0.634639\pi$
$487$	−4.61783e10			−0.820961			−0.410480	+	0.911869i	$0.634639\pi$
$488$	7.62696e9			0.134484
$489$	5.72653e9			0.100151
$490$	4.63534e10	−	4.63534e10i	0.804076	−	0.804076i
$491$	−1.64278e10	+	1.64278e10i	−0.282653	+	0.282653i	−0.834166	−	0.551513i	$-0.814051\pi$
$491$	−1.64278e10	+	1.64278e10i	−0.282653	+	0.282653i	0.551513	+	0.834166i	$0.314051\pi$
$492$			1.61821e8i			0.00276169i
$493$	−5.49057e10	+	2.96302e10i	−0.929458	+	0.501587i
$494$	1.18143e11			1.98381
$495$	6.44025e10	+	6.44025e10i	1.07271	+	1.07271i
$496$	−3.11654e10	−	3.11654e10i	−0.514927	−	0.514927i
$497$			3.94822e9i			0.0647107i
$498$			9.76919e8i			0.0158833i
$499$			6.49573e10i			1.04767i	0.851819	+	0.523837i	$0.175500\pi$
$499$			6.49573e10i			1.04767i	−0.851819	+	0.523837i	$0.824500\pi$
$500$	5.32119e10			0.851390
$501$	2.28572e9	−	2.28572e9i	0.0362804	−	0.0362804i
$502$			1.55878e11i			2.45453i
$503$	1.73843e9	−	1.73843e9i	0.0271571	−	0.0271571i	−0.693398	−	0.720555i	$-0.743887\pi$
$503$	1.73843e9	−	1.73843e9i	0.0271571	−	0.0271571i	0.720555	+	0.693398i	$0.243887\pi$
$504$	−3.70433e9	−	3.70433e9i	−0.0574101	−	0.0574101i
$505$	−2.12316e10	+	2.12316e10i	−0.326450	+	0.326450i
$506$		−	2.35083e11i		−	3.58608i
$507$	−2.82972e9	−	2.82972e9i	−0.0428264	−	0.0428264i
$508$	1.90585e10	−	1.90585e10i	0.286176	−	0.286176i
$509$	1.04956e11			1.56364			0.781818	−	0.623507i	$-0.214293\pi$
$509$	1.04956e11			1.56364			0.781818	+	0.623507i	$0.214293\pi$
$510$	−6.13898e9	−	6.13898e9i	−0.0907434	−	0.0907434i
$511$	9.47506e9	−	9.47506e9i	0.138963	−	0.138963i
$512$	−6.18060e10	−	6.18060e10i	−0.899395	−	0.899395i
$513$	1.38519e10			0.200005
$514$	−2.57628e10	−	2.57628e10i	−0.369097	−	0.369097i
$515$			4.74598e10i			0.674679i
$516$	−3.53898e9			−0.0499205
$517$	−2.11429e11			−2.95939
$518$	−5.32776e10			−0.739990
$519$	−8.99836e9	+	8.99836e9i	−0.124021	+	0.124021i
$520$	−1.35095e10	+	1.35095e10i	−0.184767	+	0.184767i
$521$		−	4.52368e10i		−	0.613961i	−0.951716	−	0.306980i	$-0.900681\pi$
$521$		−	4.52368e10i		−	0.613961i	0.951716	−	0.306980i	$-0.0993186\pi$
$522$	−4.76028e10	−	8.82096e10i	−0.641137	−	1.18805i
$523$	−6.91992e10			−0.924899			−0.462450	−	0.886646i	$-0.653029\pi$
$523$	−6.91992e10			−0.924899			−0.462450	+	0.886646i	$0.653029\pi$
$524$	1.84014e10	+	1.84014e10i	0.244077	+	0.244077i
$525$	2.27463e6	+	2.27463e6i	2.99415e−5	+	2.99415e-5i
$526$			4.44545e10i			0.580728i
$527$		−	5.26779e10i		−	0.682946i
$528$		−	1.19370e10i		−	0.153589i
$529$	1.54507e11			1.97299
$530$	1.00434e11	−	1.00434e11i	1.27285	−	1.27285i
$531$		−	2.16610e10i		−	0.272458i
$532$	2.20443e10	−	2.20443e10i	0.275201	−	0.275201i
$533$	2.68619e9	+	2.68619e9i	0.0332834	+	0.0332834i
$534$	−6.05583e9	+	6.05583e9i	−0.0744746	+	0.0744746i
$535$		−	1.22210e11i		−	1.49173i
$536$	1.01668e9	+	1.01668e9i	0.0123176	+	0.0123176i
$537$	1.07011e9	−	1.07011e9i	0.0128686	−	0.0128686i
$538$	−9.87136e10			−1.17828
$539$	7.61740e10	+	7.61740e10i	0.902510	+	0.902510i
$540$	9.11028e9	−	9.11028e9i	0.107141	−	0.107141i
$541$	−5.19984e10	−	5.19984e10i	−0.607017	−	0.607017i	0.335148	−	0.942165i	$-0.391214\pi$
$541$	−5.19984e10	−	5.19984e10i	−0.607017	−	0.607017i	−0.942165	+	0.335148i	$0.891214\pi$
$542$	−1.96967e11			−2.28243
$543$	−4.83974e9	−	4.83974e9i	−0.0556702	−	0.0556702i
$544$		−	1.23112e11i		−	1.40574i
$545$	3.57936e10			0.405714
$546$	−5.67783e9			−0.0638869
$547$	4.18664e10			0.467646			0.233823	−	0.972279i	$-0.424876\pi$
$547$	4.18664e10			0.467646			0.233823	+	0.972279i	$0.424876\pi$
$548$	3.88494e9	−	3.88494e9i	0.0430787	−	0.0430787i
$549$	−4.25184e10	+	4.25184e10i	−0.468045	+	0.468045i
$550$		−	2.22406e8i		−	0.00243050i
$551$	−9.12661e10	+	4.92523e10i	−0.990155	+	0.534343i
$552$	2.87931e9			0.0310121
$553$	3.12121e10	+	3.12121e10i	0.333751	+	0.333751i
$554$	1.19608e11	+	1.19608e11i	1.26976	+	1.26976i
$555$			1.13450e10i			0.119573i
$556$		−	1.31832e11i		−	1.37950i
$557$		−	1.47805e11i		−	1.53556i	−0.640711	−	0.767782i	$-0.721360\pi$
$557$		−	1.47805e11i		−	1.53556i	0.640711	−	0.767782i	$-0.278640\pi$
$558$	8.46305e10			0.872951
$559$	−5.87462e10	+	5.87462e10i	−0.601634	+	0.601634i
$560$			4.49976e10i			0.457549i
$561$	1.00884e10	−	1.00884e10i	0.101852	−	0.101852i
$562$	−1.00766e11	−	1.00766e11i	−1.01011	−	1.01011i
$563$	−7.72760e10	+	7.72760e10i	−0.769150	+	0.769150i	−0.977957	−	0.208807i	$-0.933042\pi$
$563$	−7.72760e10	+	7.72760e10i	−0.769150	+	0.769150i	0.208807	+	0.977957i	$0.433042\pi$
$564$			1.48944e10i			0.147200i
$565$	1.02839e11	+	1.02839e11i	1.00917	+	1.00917i
$566$	1.23198e10	−	1.23198e10i	0.120043	−	0.120043i
$567$	4.09673e10			0.396374
$568$	2.36414e9	+	2.36414e9i	0.0227133	+	0.0227133i
$569$	−7.41270e9	+	7.41270e9i	−0.0707175	+	0.0707175i	−0.741581	−	0.670863i	$-0.765924\pi$
$569$	−7.41270e9	+	7.41270e9i	−0.0707175	+	0.0707175i	0.670863	+	0.741581i	$0.265924\pi$
$570$	−1.02044e10	−	1.02044e10i	−0.0966693	−	0.0966693i
$571$	−1.93838e10			−0.182345			−0.0911727	−	0.995835i	$-0.529062\pi$
$571$	−1.93838e10			−0.182345			−0.0911727	+	0.995835i	$0.529062\pi$
$572$	1.27690e11	+	1.27690e11i	1.19281	+	1.19281i
$573$			1.03767e10i			0.0962587i
$574$	2.17915e9			0.0200743
$575$	2.20263e8			0.00201498
$576$	7.48108e10			0.679633
$577$	3.16644e10	−	3.16644e10i	0.285672	−	0.285672i	−0.549694	−	0.835366i	$-0.685256\pi$
$577$	3.16644e10	−	3.16644e10i	0.285672	−	0.285672i	0.835366	+	0.549694i	$0.185256\pi$
$578$	1.24028e10	−	1.24028e10i	0.111124	−	0.111124i
$579$			2.61220e9i			0.0232430i
$580$	−2.76321e10	+	9.24177e10i	−0.244176	+	0.816664i
$581$	6.05172e9			0.0531097
$582$	3.42063e9	+	3.42063e9i	0.0298136	+	0.0298136i
$583$	1.65047e11	+	1.65047e11i	1.42868	+	1.42868i
$584$		−	1.13471e10i		−	0.0975512i
$585$		−	1.50624e11i		−	1.28609i
$586$			1.93137e11i			1.63786i
$587$	1.77159e11			1.49214			0.746071	−	0.665867i	$-0.231938\pi$
$587$	1.77159e11			1.49214			0.746071	+	0.665867i	$0.231938\pi$
$588$	5.36619e9	−	5.36619e9i	0.0448907	−	0.0448907i
$589$		−	8.75630e10i		−	0.727544i
$590$	−3.20425e10	+	3.20425e10i	−0.264435	+	0.264435i
$591$	−1.29193e10	−	1.29193e10i	−0.105898	−	0.105898i
$592$	−1.30984e11	+	1.30984e11i	−1.06643	+	1.06643i
$593$			8.39238e10i			0.678682i	0.940663	+	0.339341i	$0.110204\pi$
$593$			8.39238e10i			0.678682i	−0.940663	+	0.339341i	$0.889796\pi$
$594$	3.25454e10	+	3.25454e10i	0.261423	+	0.261423i
$595$	−3.80291e10	+	3.80291e10i	−0.303423	+	0.303423i
$596$	−8.08264e10			−0.640572
$597$	−2.66625e9	−	2.66625e9i	−0.0209896	−	0.0209896i
$598$	−2.74905e11	+	2.74905e11i	−2.14970	+	2.14970i
$599$	−1.14075e11	−	1.14075e11i	−0.886104	−	0.886104i	0.108042	−	0.994146i	$-0.465542\pi$
$599$	−1.14075e11	−	1.14075e11i	−0.886104	−	0.886104i	−0.994146	+	0.108042i	$0.965542\pi$
$600$	2.72404e6			2.10188e−5
$601$	−9.26577e10	−	9.26577e10i	−0.710205	−	0.710205i	0.256373	−	0.966578i	$-0.417472\pi$
$601$	−9.26577e10	−	9.26577e10i	−0.710205	−	0.710205i	−0.966578	+	0.256373i	$0.917472\pi$
$602$			4.76574e10i			0.362864i
$603$	−1.13355e10			−0.0857379
$604$	−1.29797e11			−0.975254
$605$	1.79064e11			1.33656
$606$	−5.34316e9	+	5.34316e9i	−0.0396194	+	0.0396194i
$607$	1.68230e11	−	1.68230e11i	1.23922	−	1.23922i	0.278896	−	0.960321i	$-0.410032\pi$
$607$	1.68230e11	−	1.68230e11i	1.23922	−	1.23922i	0.960321	−	0.278896i	$-0.0899684\pi$
$608$		−	2.04641e11i		−	1.49754i
$609$	4.38615e9	−	2.36701e9i	0.0318871	−	0.0172080i
$610$	1.25793e11			0.908523
$611$	2.47243e11	+	2.47243e11i	1.77402	+	1.77402i
$612$	8.85386e10	+	8.85386e10i	0.631142	+	0.631142i
$613$		−	1.18219e11i		−	0.837234i	−0.908163	−	0.418617i	$-0.862515\pi$
$613$		−	1.18219e11i		−	0.837234i	0.908163	−	0.418617i	$-0.137485\pi$
$614$		−	6.68631e10i		−	0.470450i
$615$		−	4.64030e8i		−	0.00324374i
$616$	−1.80100e10			−0.125081
$617$	−1.82717e10	+	1.82717e10i	−0.126077	+	0.126077i	−0.767330	−	0.641253i	$-0.778415\pi$
$617$	−1.82717e10	+	1.82717e10i	−0.126077	+	0.126077i	0.641253	+	0.767330i	$0.278415\pi$
$618$			1.19438e10i			0.0818821i
$619$	1.12831e11	−	1.12831e11i	0.768542	−	0.768542i	−0.209308	−	0.977850i	$-0.567121\pi$
$619$	1.12831e11	−	1.12831e11i	0.768542	−	0.768542i	0.977850	+	0.209308i	$0.0671212\pi$
$620$	−5.75894e10	−	5.75894e10i	−0.389741	−	0.389741i
$621$	−3.22317e10	+	3.22317e10i	−0.216729	+	0.216729i
$622$			6.98550e10i			0.466698i
$623$	3.75140e10	+	3.75140e10i	0.249024	+	0.249024i
$624$	−1.39590e10	+	1.39590e10i	−0.0920698	+	0.0920698i
$625$	−1.52766e11			−1.00117
$626$	−1.24834e11	−	1.24834e11i	−0.812896	−	0.812896i
$627$	1.67692e10	−	1.67692e10i	0.108503	−	0.108503i
$628$	1.55076e11	+	1.55076e11i	0.997028	+	0.997028i
$629$	−2.21398e11			−1.41440
$630$	−6.10962e10	−	6.10962e10i	−0.387839	−	0.387839i
$631$			1.62098e11i			1.02249i	0.859434	+	0.511246i	$0.170816\pi$
$631$			1.62098e11i			1.02249i	−0.859434	+	0.511246i	$0.829184\pi$
$632$	3.73787e10			0.234291
$633$	5.00571e9			0.0311782
$634$	−2.83912e11			−1.75722
$635$	−5.46512e10	+	5.46512e10i	−0.336128	+	0.336128i
$636$	1.16270e10	−	1.16270e10i	0.0710621	−	0.0710621i
$637$		−	1.78155e11i		−	1.08203i
$638$	−3.30151e11	−	9.87125e10i	−1.99265	−	0.595785i
$639$	−2.63590e10			−0.158098
$640$	4.73256e10	+	4.73256e10i	0.282082	+	0.282082i
$641$	−1.49792e11	−	1.49792e11i	−0.887272	−	0.887272i	0.106988	−	0.994260i	$-0.465879\pi$
$641$	−1.49792e11	−	1.49792e11i	−0.887272	−	0.887272i	−0.994260	+	0.106988i	$0.965879\pi$
$642$		−	3.07555e10i		−	0.181043i
$643$		−	1.72562e11i		−	1.00949i	−0.863268	−	0.504745i	$-0.831586\pi$
$643$		−	1.72562e11i		−	1.00949i	0.863268	−	0.504745i	$-0.168414\pi$
$644$			1.02589e11i			0.596427i
$645$	1.01482e10			0.0586341
$646$	1.99140e11	−	1.99140e11i	1.14348	−	1.14348i
$647$			2.86075e11i			1.63253i	0.577674	+	0.816267i	$0.303960\pi$
$647$			2.86075e11i			1.63253i	−0.577674	+	0.816267i	$0.696040\pi$
$648$	2.45307e10	−	2.45307e10i	0.139126	−	0.139126i
$649$	−5.26565e10	−	5.26565e10i	−0.296806	−	0.296806i
$650$	−2.60080e8	+	2.60080e8i	−0.00145698	+	0.00145698i
$651$			4.20818e9i			0.0234299i
$652$	1.22173e11	+	1.22173e11i	0.676060	+	0.676060i
$653$	1.53601e11	−	1.53601e11i	0.844773	−	0.844773i	−0.144702	−	0.989475i	$-0.546222\pi$
$653$	1.53601e11	−	1.53601e11i	0.844773	−	0.844773i	0.989475	+	0.144702i	$0.0462224\pi$
$654$	9.00787e9			0.0492392
$655$	−5.27671e10	−	5.27671e10i	−0.286680	−	0.286680i
$656$	5.35748e9	−	5.35748e9i	0.0289298	−	0.0289298i
$657$	6.32572e10	+	6.32572e10i	0.339507	+	0.339507i
$658$	2.00574e11			1.06997
$659$	1.75647e10	+	1.75647e10i	0.0931319	+	0.0931319i	0.752138	−	0.659006i	$-0.229023\pi$
$659$	1.75647e10	+	1.75647e10i	0.0931319	+	0.0931319i	−0.659006	+	0.752138i	$0.729023\pi$
$660$		−	2.20580e10i		−	0.116249i
$661$	2.74091e11			1.43578			0.717892	−	0.696155i	$-0.245107\pi$
$661$	2.74091e11			1.43578			0.717892	+	0.696155i	$0.245107\pi$
$662$	−1.02044e11			−0.531317
$663$	−2.35946e10			−0.122112
$664$	3.62369e9	−	3.62369e9i	0.0186414	−	0.0186414i
$665$	−6.32132e10	+	6.32132e10i	−0.323237	+	0.323237i
$666$		−	3.55691e11i		−	1.80791i
$667$	9.77611e10	−	3.26969e11i	0.493927	−	1.65198i
$668$	9.75298e10			0.489814
$669$	3.94745e9	+	3.94745e9i	0.0197066	+	0.0197066i
$670$	1.67683e10	+	1.67683e10i	0.0832130	+	0.0832130i
$671$			2.06719e11i			1.01974i
$672$			9.83484e9i			0.0482270i
$673$			2.79451e11i			1.36221i	0.732184	+	0.681107i	$0.238501\pi$
$673$			2.79451e11i			1.36221i	−0.732184	+	0.681107i	$0.761499\pi$
$674$	1.32333e11			0.641250
$675$	−3.04936e7	+	3.04936e7i	−0.000146890	+	0.000146890i
$676$		−	1.20742e11i		−	0.578190i
$677$	−1.48704e11	+	1.48704e11i	−0.707895	+	0.707895i	−0.966092	−	0.258197i	$-0.916872\pi$
$677$	−1.48704e11	+	1.48704e11i	−0.707895	+	0.707895i	0.258197	+	0.966092i	$0.416872\pi$
$678$	2.58806e10	+	2.58806e10i	0.122477	+	0.122477i
$679$	2.11898e10	−	2.11898e10i	0.0996890	−	0.0996890i
$680$			4.55426e10i			0.213001i
$681$	8.92134e9	+	8.92134e9i	0.0414803	+	0.0414803i
$682$	2.05731e11	−	2.05731e11i	0.950961	−	0.950961i
$683$	4.35058e10			0.199924			0.0999618	−	0.994991i	$-0.468128\pi$
$683$	4.35058e10			0.199924			0.0999618	+	0.994991i	$0.468128\pi$
$684$	1.47172e11	+	1.47172e11i	0.672357	+	0.672357i
$685$	−1.11403e10	+	1.11403e10i	−0.0505980	+	0.0505980i
$686$	−1.58793e11	−	1.58793e11i	−0.717028	−	0.717028i
$687$	−1.15607e10			−0.0518988
$688$	1.17166e11	+	1.17166e11i	0.522937	+	0.522937i
$689$		−	3.86010e11i		−	1.71286i
$690$	4.74889e10			0.209506
$691$	−1.41552e11			−0.620875			−0.310438	−	0.950594i	$-0.600476\pi$
$691$	−1.41552e11			−0.620875			−0.310438	+	0.950594i	$0.600476\pi$
$692$	−3.83953e11			−1.67438
$693$	1.00401e11	−	1.00401e11i	0.435318	−	0.435318i
$694$	−1.47745e11	+	1.47745e11i	−0.636904	+	0.636904i
$695$			3.78035e11i			1.62029i
$696$	1.20903e9	−	4.04370e9i	0.00515230	−	0.0172323i
$697$	9.05559e9			0.0383694
$698$	6.61521e10	+	6.61521e10i	0.278690	+	0.278690i
$699$	−1.85951e10	−	1.85951e10i	−0.0778913	−	0.0778913i
$700$			9.70568e7i			0.000404235i
$701$			2.09807e11i			0.868857i	0.900706	+	0.434428i	$0.143050\pi$
$701$			2.09807e11i			0.868857i	−0.900706	+	0.434428i	$0.856950\pi$
$702$		−	7.61167e10i		−	0.313423i
$703$	−3.68016e11			−1.50676
$704$	1.81860e11	−	1.81860e11i	0.740367	−	0.740367i
$705$		−	4.27104e10i		−	0.172893i
$706$	1.98069e11	−	1.98069e11i	0.797255	−	0.797255i
$707$	3.30993e10	+	3.30993e10i	0.132477	+	0.132477i
$708$	−3.70946e9	+	3.70946e9i	−0.0147631	+	0.0147631i
$709$		−	4.30105e11i		−	1.70212i	−0.525070	−	0.851059i	$-0.675961\pi$
$709$		−	4.30105e11i		−	1.70212i	0.525070	−	0.851059i	$-0.324039\pi$
$710$	3.89922e10	+	3.89922e10i	0.153442	+	0.153442i
$711$	−2.08377e11	+	2.08377e11i	−0.815403	+	0.815403i
$712$	4.49257e10			0.174814
$713$	2.03749e11	+	2.03749e11i	0.788382	+	0.788382i
$714$	−9.57045e9	+	9.57045e9i	−0.0368247	+	0.0368247i
$715$	−3.66157e11	−	3.66157e11i	−1.40102	−	1.40102i
$716$	4.56609e10			0.173737
$717$	−2.88714e10	−	2.88714e10i	−0.109242	−	0.109242i
$718$			4.95034e11i			1.86268i
$719$	−4.61926e11			−1.72845			−0.864225	−	0.503105i	$-0.832191\pi$
$719$	−4.61926e11			−1.72845			−0.864225	+	0.503105i	$0.832191\pi$
$720$	−3.00412e11			−1.11786
$721$	7.39882e10			0.273792
$722$	6.95357e10	−	6.95357e10i	0.255893	−	0.255893i
$723$	−1.08788e10	+	1.08788e10i	−0.0398131	+	0.0398131i
$724$		−	2.06508e11i		−	0.751592i
$725$	9.24893e7	−	3.09337e8i	0.000334764	−	0.00111964i
$726$	4.50636e10			0.162211
$727$	4.89137e10	+	4.89137e10i	0.175103	+	0.175103i	0.789217	−	0.614114i	$-0.210487\pi$
$727$	4.89137e10	+	4.89137e10i	0.175103	+	0.175103i	−0.614114	+	0.789217i	$0.710487\pi$
$728$	2.10608e10	+	2.10608e10i	0.0749806	+	0.0749806i
$729$			2.69025e11i			0.952539i
$730$		−	1.87149e11i		−	0.659017i
$731$			1.98043e11i			0.693570i
$732$	1.45626e10			0.0507219
$733$	−4.55945e10	+	4.55945e10i	−0.157941	+	0.157941i	−0.781654	−	0.623712i	$-0.785624\pi$
$733$	−4.55945e10	+	4.55945e10i	−0.157941	+	0.157941i	0.623712	+	0.781654i	$0.285624\pi$
$734$		−	2.62807e11i		−	0.905425i
$735$	−1.53878e10	+	1.53878e10i	−0.0527264	+	0.0527264i
$736$	4.76176e11	+	4.76176e11i	1.62277	+	1.62277i
$737$	−2.75560e10	+	2.75560e10i	−0.0933998	+	0.0933998i
$738$			1.45484e10i			0.0490444i
$739$	−4.47578e10	−	4.47578e10i	−0.150069	−	0.150069i	0.628080	−	0.778149i	$-0.283841\pi$
$739$	−4.47578e10	−	4.47578e10i	−0.150069	−	0.150069i	−0.778149	+	0.628080i	$0.783841\pi$
$740$	−2.42041e11	+	2.42041e11i	−0.807164	+	0.807164i
$741$	−3.92197e10			−0.130086
$742$	−1.56574e11	−	1.56574e11i	−0.516539	−	0.516539i
$743$	3.61072e10	−	3.61072e10i	0.118478	−	0.118478i	−0.645382	−	0.763860i	$-0.723302\pi$
$743$	3.61072e10	−	3.61072e10i	0.118478	−	0.118478i	0.763860	+	0.645382i	$0.223302\pi$
$744$	2.51980e9	+	2.51980e9i	0.00822384	+	0.00822384i
$745$	2.31774e11			0.752383
$746$	1.10581e11	+	1.10581e11i	0.357048	+	0.357048i
$747$			4.04023e10i			0.129755i
$748$	4.30463e11			1.37509
$749$	−1.90521e11			−0.605362
$750$	−3.84004e10			−0.121364
$751$	−2.18652e11	+	2.18652e11i	−0.687374	+	0.687374i	−0.961651	−	0.274277i	$-0.911562\pi$
$751$	−2.18652e11	+	2.18652e11i	−0.687374	+	0.687374i	0.274277	+	0.961651i	$0.411562\pi$
$752$	4.93115e11	−	4.93115e11i	1.54197	−	1.54197i
$753$		−	5.17463e10i		−	0.160953i
$754$	2.70643e11	+	5.01510e11i	0.837358	+	1.55165i
$755$	3.72200e11			1.14548
$756$	−1.42026e10	−	1.42026e10i	−0.0434791	−	0.0434791i
$757$	−5.29732e10	−	5.29732e10i	−0.161314	−	0.161314i	0.621834	−	0.783149i	$-0.286388\pi$
$757$	−5.29732e10	−	5.29732e10i	−0.161314	−	0.161314i	−0.783149	+	0.621834i	$0.786388\pi$
$758$			1.05928e11i			0.320873i
$759$			7.80400e10i			0.235153i
$760$			7.57024e10i			0.226911i
$761$	−1.65420e11			−0.493231			−0.246616	−	0.969113i	$-0.579318\pi$
$761$	−1.65420e11			−0.493231			−0.246616	+	0.969113i	$0.579318\pi$
$762$	−1.37536e10	+	1.37536e10i	−0.0407940	+	0.0407940i
$763$		−	5.58010e10i		−	0.164643i
$764$	−2.21382e11	+	2.21382e11i	−0.649785	+	0.649785i
$765$	−2.53889e11	−	2.53889e11i	−0.741307	−	0.741307i
$766$	3.15645e11	−	3.15645e11i	0.916819	−	0.916819i
$767$			1.23152e11i			0.355845i
$768$	2.69489e10	+	2.69489e10i	0.0774632	+	0.0774632i
$769$	−2.60151e11	+	2.60151e11i	−0.743909	+	0.743909i	−0.973328	−	0.229419i	$-0.926318\pi$
$769$	−2.60151e11	+	2.60151e11i	−0.743909	+	0.743909i	0.229419	+	0.973328i	$0.426318\pi$
$770$	−2.97042e11			−0.844996
$771$	8.55240e9	+	8.55240e9i	0.0242031	+	0.0242031i
$772$	−5.57303e10	+	5.57303e10i	−0.156900	+	0.156900i
$773$	2.78540e11	+	2.78540e11i	0.780135	+	0.780135i	0.979853	−	0.199718i	$-0.0640027\pi$
$773$	2.78540e11	+	2.78540e11i	0.780135	+	0.780135i	−0.199718	+	0.979853i	$0.564003\pi$
$774$	−3.18169e11			−0.886531
$775$	1.92761e8	+	1.92761e8i	0.000534334	+	0.000534334i
$776$		−	2.53763e10i		−	0.0699812i
$777$	1.76864e10			0.0485240
$778$	3.12766e11			0.853691
$779$	1.50525e10			0.0408751
$780$	−2.57944e10	+	2.57944e10i	−0.0696864	+	0.0696864i
$781$	−6.40772e10	+	6.40772e10i	−0.172226	+	0.172226i
$782$			9.26750e11i			2.47819i
$783$	3.17320e10	+	5.88005e10i	0.0844210	+	0.156435i
$784$	−3.55321e11			−0.940496
$785$	−4.44690e11	−	4.44690e11i	−1.17106	−	1.17106i
$786$	−1.32794e10	−	1.32794e10i	−0.0347928	−	0.0347928i
$787$			1.11553e11i			0.290792i	0.989374	+	0.145396i	$0.0464456\pi$
$787$			1.11553e11i			0.290792i	−0.989374	+	0.145396i	$0.953554\pi$
$788$		−	5.51257e11i		−	1.42971i
$789$		−	1.47575e10i		−	0.0380806i
$790$	6.16494e11			1.58278
$791$	1.60322e11	−	1.60322e11i	0.409532	−	0.409532i
$792$		−	1.20238e11i		−	0.305591i
$793$	2.41736e11	−	2.41736e11i	0.611292	−	0.611292i
$794$	−4.69181e11	−	4.69181e11i	−1.18048	−	1.18048i
$795$	−3.33409e10	+	3.33409e10i	−0.0834659	+	0.0834659i
$796$		−	1.13767e11i		−	0.283376i
$797$	3.16261e11	+	3.16261e11i	0.783812	+	0.783812i	0.980472	−	0.196660i	$-0.0630095\pi$
$797$	3.16261e11	+	3.16261e11i	0.783812	+	0.783812i	−0.196660	+	0.980472i	$0.563010\pi$
$798$	−1.59083e10	+	1.59083e10i	−0.0392295	+	0.0392295i
$799$	8.33498e11			2.04511
$800$	4.50497e8	+	4.50497e8i	0.00109985	+	0.00109985i
$801$	−2.50450e11	+	2.50450e11i	−0.608402	+	0.608402i
$802$	3.16186e11	+	3.16186e11i	0.764266	+	0.764266i
$803$	3.07548e11			0.739692
$804$	1.94122e9	+	1.94122e9i	0.00464569	+	0.00464569i
$805$		−	2.94179e11i		−	0.700533i
$806$	−4.81162e11			−1.14012
$807$	3.27697e10			0.0772642
$808$	3.96388e10			0.0929982
$809$	3.32250e11	−	3.32250e11i	0.775658	−	0.775658i	−0.203431	−	0.979089i	$-0.565209\pi$
$809$	3.32250e11	−	3.32250e11i	0.775658	−	0.775658i	0.979089	+	0.203431i	$0.0652093\pi$
$810$	4.04588e11	−	4.04588e11i	0.939882	−	0.939882i
$811$			5.96713e11i			1.37938i	0.724107	+	0.689688i	$0.242252\pi$
$811$			5.96713e11i			1.37938i	−0.724107	+	0.689688i	$0.757748\pi$
$812$	1.44076e11	+	4.30775e10i	0.331412	+	0.0990893i
$813$	6.53867e10			0.149667
$814$	−8.64662e11	−	8.64662e11i	−1.96947	−	1.96947i
$815$	−3.50338e11	−	3.50338e11i	−0.794066	−	0.794066i
$816$			4.70582e10i			0.106139i
$817$			3.29194e11i			0.738863i
$818$		−	7.93024e11i		−	1.77122i
$819$	−2.34817e11			−0.521909
$820$	9.89990e9	−	9.89990e9i	0.0218965	−	0.0218965i
$821$		−	9.55681e10i		−	0.210349i	−0.994454	−	0.105174i	$-0.966460\pi$
$821$		−	9.55681e10i		−	0.210349i	0.994454	−	0.105174i	$-0.0335401\pi$
$822$	−2.80358e9	+	2.80358e9i	−0.00614080	+	0.00614080i
$823$	−4.37108e11	−	4.37108e11i	−0.952772	−	0.952772i	0.0461617	−	0.998934i	$-0.485301\pi$
$823$	−4.37108e11	−	4.37108e11i	−0.952772	−	0.952772i	−0.998934	+	0.0461617i	$0.985301\pi$
$824$	4.43031e10	−	4.43031e10i	0.0961005	−	0.0961005i
$825$			7.38316e7i			0.000159377i
$826$	4.99532e10	+	4.99532e10i	0.107311	+	0.107311i
$827$	5.73747e11	−	5.73747e11i	1.22659	−	1.22659i	0.261340	−	0.965247i	$-0.415836\pi$
$827$	5.73747e11	−	5.73747e11i	1.22659	−	1.22659i	0.965247	−	0.261340i	$-0.0841643\pi$
$828$	−6.84902e11			−1.45716
$829$	1.62544e11	+	1.62544e11i	0.344155	+	0.344155i	0.857927	−	0.513772i	$-0.171752\pi$
$829$	1.62544e11	+	1.62544e11i	0.344155	+	0.344155i	−0.513772	+	0.857927i	$0.671752\pi$
$830$	5.97660e10	−	5.97660e10i	0.125934	−	0.125934i
$831$	−3.97061e10	−	3.97061e10i	−0.0832632	−	0.0832632i
$832$	−4.25332e11			−0.887637
$833$	−3.00295e11	−	3.00295e11i	−0.623688	−	0.623688i
$834$			9.51369e10i			0.196646i
$835$	−2.79672e11			−0.575311
$836$	7.15531e11			1.46488
$837$	−5.64147e10			−0.114945
$838$	−3.31224e11	+	3.31224e11i	−0.671654	+	0.671654i
$839$	6.24136e10	−	6.24136e10i	0.125960	−	0.125960i	−0.641317	−	0.767276i	$-0.721612\pi$
$839$	6.24136e10	−	6.24136e10i	0.125960	−	0.125960i	0.767276	+	0.641317i	$0.221612\pi$
$840$		−	3.63818e9i		−	0.00730746i
$841$	−4.18146e11	−	2.74592e11i	−0.835880	−	0.548913i
$842$	−5.86613e11			−1.16709
$843$	3.34509e10	+	3.34509e10i	0.0662365	+	0.0662365i
$844$	1.06795e11	+	1.06795e11i	0.210465	+	0.210465i
$845$			3.46233e11i			0.679113i
$846$			1.33907e12i			2.61409i
$847$		−	2.79155e11i		−	0.542390i
$848$	−7.69878e11			−1.48881
$849$	−4.08976e9	+	4.08976e9i	−0.00787168	+	0.00787168i
$850$			8.76774e8i			0.00167962i
$851$	8.56329e11	−	8.56329e11i	1.63276	−	1.63276i
$852$	4.51401e9	+	4.51401e9i	0.00856651	+	0.00856651i
$853$	−1.72432e11	+	1.72432e11i	−0.325703	+	0.325703i	−0.850950	−	0.525247i	$-0.823973\pi$
$853$	−1.72432e11	+	1.72432e11i	−0.325703	+	0.325703i	0.525247	+	0.850950i	$0.323973\pi$
$854$		−	1.96106e11i		−	0.368689i
$855$	−4.22023e11	−	4.22023e11i	−0.789717	−	0.789717i
$856$	−1.14081e11	+	1.14081e11i	−0.212481	+	0.212481i
$857$	−6.02583e11			−1.11710			−0.558552	−	0.829470i	$-0.688643\pi$
$857$	−6.02583e11			−1.11710			−0.558552	+	0.829470i	$0.688643\pi$
$858$	−9.21475e10	−	9.21475e10i	−0.170034	−	0.170034i
$859$	6.92154e11	−	6.92154e11i	1.27125	−	1.27125i	0.325813	−	0.945434i	$-0.394362\pi$
$859$	6.92154e11	−	6.92154e11i	1.27125	−	1.27125i	0.945434	−	0.325813i	$-0.105638\pi$
$860$	2.16508e11	+	2.16508e11i	0.395804	+	0.395804i
$861$	−7.23407e8			−0.00131635
$862$	6.70566e11	+	6.70566e11i	1.21454	+	1.21454i
$863$		−	8.84258e11i		−	1.59417i	−0.603865	−	0.797087i	$-0.706373\pi$
$863$		−	8.84258e11i		−	1.59417i	0.603865	−	0.797087i	$-0.293627\pi$
$864$	−1.31845e11			−0.236597
$865$	1.10100e12			1.96664
$866$	−2.91279e11			−0.517890
$867$	−4.11732e9	+	4.11732e9i	−0.00728682	+	0.00728682i
$868$	−8.97799e10	+	8.97799e10i	−0.158161	+	0.158161i
$869$			1.01310e12i			1.77654i
$870$	1.99408e10	−	6.66934e10i	0.0348069	−	0.116414i
$871$	6.44475e10			0.111978
$872$	−3.34129e10	−	3.34129e10i	−0.0577894	−	0.0577894i
$873$	1.41467e11	+	1.41467e11i	0.243555	+	0.243555i
$874$			1.54047e12i			2.64003i
$875$			2.37879e11i			0.405811i
$876$		−	2.16657e10i		−	0.0367922i
$877$	−5.18258e11			−0.876088			−0.438044	−	0.898954i	$-0.644329\pi$
$877$	−5.18258e11			−0.876088			−0.438044	+	0.898954i	$0.644329\pi$
$878$	1.80220e11	−	1.80220e11i	0.303268	−	0.303268i
$879$		−	6.41153e10i		−	0.107401i
$880$	−7.30282e11	+	7.30282e11i	−1.21776	+	1.21776i
$881$	7.88434e11	+	7.88434e11i	1.30877	+	1.30877i	0.922307	+	0.386459i	$0.126302\pi$
$881$	7.88434e11	+	7.88434e11i	1.30877	+	1.30877i	0.386459	+	0.922307i	$0.373698\pi$
$882$	4.82443e11	−	4.82443e11i	0.797208	−	0.797208i
$883$			7.29701e11i			1.20033i	0.799875	+	0.600167i	$0.204899\pi$
$883$			7.29701e11i			1.20033i	−0.799875	+	0.600167i	$0.795101\pi$
$884$	−5.03381e11	−	5.03381e11i	−0.824304	−	0.824304i
$885$	1.06371e10	−	1.06371e10i	0.0173400	−	0.0173400i
$886$	5.69115e11			0.923560
$887$	1.35218e11	+	1.35218e11i	0.218444	+	0.218444i	0.807843	−	0.589398i	$-0.200635\pi$
$887$	1.35218e11	+	1.35218e11i	0.218444	+	0.218444i	−0.589398	+	0.807843i	$0.700635\pi$
$888$	1.05904e10	−	1.05904e10i	0.0170318	−	0.0170318i
$889$	8.51994e10	+	8.51994e10i	0.136405	+	0.136405i
$890$	7.40967e11			1.18097
$891$	6.64873e11	+	6.64873e11i	1.05494	+	1.05494i
$892$			1.68435e11i			0.266056i
$893$	1.38547e12			2.17867
$894$	5.83285e10			0.0913126
$895$	−1.30935e11			−0.204063
$896$	7.37789e10	−	7.37789e10i	0.114472	−	0.114472i
$897$	9.12595e10	−	9.12595e10i	0.140964	−	0.140964i
$898$		−	1.00301e12i		−	1.54241i
$899$	3.71700e11	−	2.00590e11i	0.569054	−	0.307093i
$900$	−6.47968e8			−0.000987606
$901$	−6.50651e11	−	6.50651e11i	−0.987300	−	0.987300i
$902$	3.53662e10	+	3.53662e10i	0.0534272	+	0.0534272i
$903$		−	1.58207e10i		−	0.0237944i
$904$		−	1.91998e11i		−	0.287489i
$905$			5.92171e11i			0.882781i
$906$	9.36685e10			0.139021
$907$	−5.40196e11	+	5.40196e11i	−0.798219	+	0.798219i	−0.982815	−	0.184595i	$-0.940903\pi$
$907$	−5.40196e11	+	5.40196e11i	−0.798219	+	0.798219i	0.184595	+	0.982815i	$0.440903\pi$
$908$			3.80667e11i			0.560017i
$909$	−2.20976e11	+	2.20976e11i	−0.323661	+	0.323661i
$910$	3.47359e11	+	3.47359e11i	0.506539	+	0.506539i
$911$	−7.22295e11	+	7.22295e11i	−1.04868	+	1.04868i	−0.0499220	+	0.998753i	$0.515897\pi$
$911$	−7.22295e11	+	7.22295e11i	−1.04868	+	1.04868i	−0.998753	+	0.0499220i	$0.984103\pi$
$912$			7.82218e10i			0.113070i
$913$	9.82155e10	+	9.82155e10i	0.141350	+	0.141350i
$914$	−6.59227e11	+	6.59227e11i	−0.944605	+	0.944605i
$915$	−4.17591e10			−0.0595754
$916$	−2.46643e11	−	2.46643e11i	−0.350338	−	0.350338i
$917$	−8.22620e10	+	8.22620e10i	−0.116338	+	0.116338i
$918$	−1.28301e11	−	1.28301e11i	−0.180659	−	0.180659i
$919$	3.94693e11			0.553347			0.276673	−	0.960964i	$-0.410768\pi$
$919$	3.94693e11			0.553347			0.276673	+	0.960964i	$0.410768\pi$
$920$	−1.76150e11	−	1.76150e11i	−0.245885	−	0.245885i
$921$			2.21964e10i			0.0308492i
$922$	−1.51727e12			−2.09961
$923$	1.49863e11			0.206484
$924$	−3.43876e10			−0.0471752
$925$	8.10151e8	−	8.10151e8i	0.00110662	−	0.00110662i
$926$	−4.56225e11	+	4.56225e11i	−0.620490	+	0.620490i
$927$			4.93958e11i			0.668916i
$928$	8.68689e11	−	4.68793e11i	1.17131	−	0.632105i
$929$	2.57946e11			0.346310			0.173155	−	0.984895i	$-0.444604\pi$
$929$	2.57946e11			0.346310			0.173155	+	0.984895i	$0.444604\pi$
$930$	4.15595e10	+	4.15595e10i	0.0555570	+	0.0555570i
$931$	−4.99160e11	−	4.99160e11i	−0.664417	−	0.664417i
$932$		−	7.93437e11i		−	1.05160i
$933$		−	2.31896e10i		−	0.0306032i
$934$		−	8.03739e11i		−	1.05615i
$935$	−1.23437e12			−1.61510
$936$	−1.40605e11	+	1.40605e11i	−0.183189	+	0.183189i
$937$		−	1.33694e12i		−	1.73442i	−0.497940	−	0.867211i	$-0.665910\pi$
$937$		−	1.33694e12i		−	1.73442i	0.497940	−	0.867211i	$-0.334090\pi$
$938$	2.61413e10	−	2.61413e10i	0.0337688	−	0.0337688i
$939$	4.14408e10	+	4.14408e10i	0.0533047	+	0.0533047i
$940$	9.11210e11	−	9.11210e11i	1.16710	−	1.16710i
$941$			1.46089e12i			1.86320i	0.363483	+	0.931601i	$0.381587\pi$
$941$			1.46089e12i			1.86320i	−0.363483	+	0.931601i	$0.618413\pi$
$942$	−1.11911e11	−	1.11911e11i	−0.142125	−	0.142125i
$943$	−3.50254e10	+	3.50254e10i	−0.0442931	+	0.0442931i
$944$	2.45621e11			0.309299
$945$	4.07267e10	+	4.07267e10i	0.0510684	+	0.0510684i
$946$	−7.73449e11	+	7.73449e11i	−0.965755	+	0.965755i
$947$	−5.87086e11	−	5.87086e11i	−0.729964	−	0.729964i	0.240648	−	0.970612i	$-0.422640\pi$
$947$	−5.87086e11	−	5.87086e11i	−0.729964	−	0.729964i	−0.970612	+	0.240648i	$0.922640\pi$
$948$	7.13696e10			0.0883649
$949$	−3.59645e11	−	3.59645e11i	−0.443414	−	0.443414i
$950$			1.45740e9i			0.00178931i
$951$	9.42497e10			0.115228
$952$	7.09993e10			0.0864383
$953$	−6.92282e11			−0.839288			−0.419644	−	0.907689i	$-0.637845\pi$
$953$	−6.92282e11			−0.839288			−0.419644	+	0.907689i	$0.637845\pi$
$954$	1.04531e12	−	1.04531e12i	1.26198	−	1.26198i
$955$	6.34825e11	−	6.34825e11i	0.763204	−	0.763204i
$956$		−	1.23192e12i		−	1.47486i
$957$	1.09599e11	+	3.27693e10i	0.130665	+	0.0390679i
$958$	1.10817e10			0.0131566
$959$	1.73673e10	+	1.73673e10i	0.0205333	+	0.0205333i
$960$	3.67374e10	+	3.67374e10i	0.0432537	+	0.0432537i
$961$		−	4.96273e11i		−	0.581872i
$962$			2.02226e12i			2.36122i
$963$		−	1.27195e12i		−	1.47899i
$964$	−4.64188e11			−0.537509
$965$	1.59810e11	−	1.59810e11i	0.184286	−	0.184286i
$966$		−	7.40335e10i		−	0.0850198i
$967$	2.21435e11	−	2.21435e11i	0.253245	−	0.253245i	−0.569055	−	0.822300i	$-0.692691\pi$
$967$	2.21435e11	−	2.21435e11i	0.253245	−	0.253245i	0.822300	+	0.569055i	$0.192691\pi$
$968$	−1.67154e11	−	1.67154e11i	−0.190378	−	0.190378i
$969$	−6.61080e10	+	6.61080e10i	−0.0749823	+	0.0749823i
$970$		−	4.18535e11i		−	0.472765i
$971$	−5.64626e10	−	5.64626e10i	−0.0635162	−	0.0635162i	0.674635	−	0.738151i	$-0.264301\pi$
$971$	−5.64626e10	−	5.64626e10i	−0.0635162	−	0.0635162i	−0.738151	+	0.674635i	$0.764301\pi$
$972$	1.42418e11	−	1.42418e11i	0.159551	−	0.159551i
$973$	5.89344e11			0.657533
$974$	7.10969e11	+	7.10969e11i	0.789978	+	0.789978i
$975$	8.63382e7	−	8.63382e7i	9.55399e−5	−	9.55399e-5i
$976$	−4.82131e11	−	4.82131e11i	−0.531332	−	0.531332i
$977$	−1.32057e11			−0.144938			−0.0724690	−	0.997371i	$-0.523088\pi$
$977$	−1.32057e11			−0.144938			−0.0724690	+	0.997371i	$0.523088\pi$
$978$	−8.81665e10	−	8.81665e10i	−0.0963714	−	0.0963714i
$979$			1.21766e12i			1.32554i
$980$	−6.56586e11			−0.711848
$981$	3.72537e11			0.402248
$982$	5.05850e11			0.543971
$983$	−3.78656e10	+	3.78656e10i	−0.0405537	+	0.0405537i	−0.727093	−	0.686539i	$-0.759129\pi$
$983$	−3.78656e10	+	3.78656e10i	−0.0405537	+	0.0405537i	0.686539	+	0.727093i	$0.259129\pi$
$984$	−4.33166e8	+	4.33166e8i	−0.000462034	+	0.000462034i
$985$			1.58076e12i			1.67927i
$986$	1.30153e12	+	3.89146e11i	1.37704	+	0.411723i
$987$	−6.65841e10			−0.0701620
$988$	−8.36737e11	−	8.36737e11i	−0.878134	−	0.878134i
$989$	−7.65995e11	−	7.65995e11i	−0.800646	−	0.800646i
$990$		−	1.98310e12i		−	2.06445i
$991$		−	3.34309e11i		−	0.346620i	−0.984867	−	0.173310i	$-0.944554\pi$
$991$		−	3.34309e11i		−	0.346620i	0.984867	−	0.173310i	$-0.0554463\pi$
$992$			8.33442e11i			0.860655i
$993$	3.38751e10			0.0348405
$994$	6.07875e10	−	6.07875e10i	0.0622685	−	0.0622685i
$995$			3.26232e11i			0.332839i
$996$	6.91893e9	−	6.91893e9i	0.00703075	−	0.00703075i
$997$	4.68876e11	+	4.68876e11i	0.474545	+	0.474545i	0.903382	−	0.428837i	$-0.141077\pi$
$997$	4.68876e11	+	4.68876e11i	0.474545	+	0.474545i	−0.428837	+	0.903382i	$0.641077\pi$
$998$	1.00009e12	−	1.00009e12i	1.00813	−	1.00813i
$999$			2.37103e11i			0.238054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.4	✓	38
29.17	odd	4	inner	29.9.c.a.17.4	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.4	✓	38	1.1	even	1	trivial
29.9.c.a.17.4	yes	38	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.3962 - 15.3962i) q^{2} +(5.11102 + 5.11102i) q^{3} +218.083i q^{4} -625.365i q^{5} -157.380i q^{6} -974.923 q^{7} +(-583.770 + 583.770i) q^{8} -6508.75i q^{9} +O(q^{10})\)	\(q+(-15.3962 - 15.3962i) q^{2} +(5.11102 + 5.11102i) q^{3} +218.083i q^{4} -625.365i q^{5} -157.380i q^{6} -974.923 q^{7} +(-583.770 + 583.770i) q^{8} -6508.75i q^{9} +(-9628.22 + 9628.22i) q^{10} +(-15822.4 - 15822.4i) q^{11} +(-1114.63 + 1114.63i) q^{12} +37005.1i q^{13} +(15010.1 + 15010.1i) q^{14} +(3196.26 - 3196.26i) q^{15} +73805.0 q^{16} +(62375.2 + 62375.2i) q^{17} +(-100210. + 100210. i) q^{18} +(103682. + 103682. i) q^{19} +136382. q^{20} +(-4982.85 - 4982.85i) q^{21} +487207. i q^{22} -482512. q^{23} -5967.33 q^{24} -456.492 q^{25} +(569737. - 569737. i) q^{26} +(66799.8 - 66799.8i) q^{27} -212614. i q^{28} +(-202609. + 677640. i) q^{29} -98420.1 q^{30} +(-422266. - 422266. i) q^{31} +(-986868. - 986868. i) q^{32} -161737. i q^{33} -1.92068e6i q^{34} +609683. i q^{35} +1.41945e6 q^{36} +(-1.77473e6 + 1.77473e6i) q^{37} -3.19261e6i q^{38} +(-189134. + 189134. i) q^{39} +(365070. + 365070. i) q^{40} +(72589.6 - 72589.6i) q^{41} +153434. i q^{42} +(1.58751e6 + 1.58751e6i) q^{43} +(3.45060e6 - 3.45060e6i) q^{44} -4.07035e6 q^{45} +(7.42883e6 + 7.42883e6i) q^{46} +(6.68132e6 - 6.68132e6i) q^{47} +(377219. + 377219. i) q^{48} -4.81433e6 q^{49} +(7028.22 + 7028.22i) q^{50} +637602. i q^{51} -8.07021e6 q^{52} -1.04312e7 q^{53} -2.05692e6 q^{54} +(-9.89476e6 + 9.89476e6i) q^{55} +(569131. - 569131. i) q^{56} +1.05984e6i q^{57} +(1.35525e7 - 7.31366e6i) q^{58} +3.32798e6 q^{59} +(697050. + 697050. i) q^{60} +(-6.53250e6 - 6.53250e6i) q^{61} +1.30026e7i q^{62} +6.34553e6i q^{63} +1.14939e7i q^{64} +2.31417e7 q^{65} +(-2.49013e6 + 2.49013e6i) q^{66} -1.74158e6i q^{67} +(-1.36030e7 + 1.36030e7i) q^{68} +(-2.46613e6 - 2.46613e6i) q^{69} +(9.38677e6 - 9.38677e6i) q^{70} -4.04978e6i q^{71} +(3.79962e6 + 3.79962e6i) q^{72} +(-9.71878e6 + 9.71878e6i) q^{73} +5.46481e7 q^{74} +(-2333.14 - 2333.14i) q^{75} +(-2.26114e7 + 2.26114e7i) q^{76} +(1.54256e7 + 1.54256e7i) q^{77} +5.82388e6 q^{78} +(-3.20149e7 - 3.20149e7i) q^{79} -4.61551e7i q^{80} -4.20211e7 q^{81} -2.23520e6 q^{82} -6.20738e6 q^{83} +(1.08668e6 - 1.08668e6i) q^{84} +(3.90073e7 - 3.90073e7i) q^{85} -4.88832e7i q^{86} +(-4.49897e6 + 2.42790e6i) q^{87} +1.84733e7 q^{88} +(-3.84789e7 - 3.84789e7i) q^{89} +(6.26677e7 + 6.26677e7i) q^{90} -3.60771e7i q^{91} -1.05228e8i q^{92} -4.31643e6i q^{93} -2.05733e8 q^{94} +(6.48392e7 - 6.48392e7i) q^{95} -1.00878e7i q^{96} +(-2.17348e7 + 2.17348e7i) q^{97} +(7.41221e7 + 7.41221e7i) q^{98} +(-1.02984e8 + 1.02984e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

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