LMFDB - Embedded newform 29.9.c.a.17.1

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			17.1
Character	$\chi$	$=$	29.17
Dual form			29.9.c.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.4922 + 21.4922i) q^{2} +(-26.9761 + 26.9761i) q^{3} -667.831i q^{4} +209.913i q^{5} -1159.55i q^{6} +2370.17 q^{7} +(8851.17 + 8851.17i) q^{8} +5105.58i q^{9} +O(q^{10})$	\(q+(-21.4922 + 21.4922i) q^{2} +(-26.9761 + 26.9761i) q^{3} -667.831i q^{4} +209.913i q^{5} -1159.55i q^{6} +2370.17 q^{7} +(8851.17 + 8851.17i) q^{8} +5105.58i q^{9} +(-4511.49 - 4511.49i) q^{10} +(16427.8 - 16427.8i) q^{11} +(18015.5 + 18015.5i) q^{12} -722.752i q^{13} +(-50940.2 + 50940.2i) q^{14} +(-5662.62 - 5662.62i) q^{15} -209498. q^{16} +(42927.9 - 42927.9i) q^{17} +(-109730. - 109730. i) q^{18} +(-102986. + 102986. i) q^{19} +140186. q^{20} +(-63937.9 + 63937.9i) q^{21} +706140. i q^{22} +45306.9 q^{23} -477540. q^{24} +346562. q^{25} +(15533.5 + 15533.5i) q^{26} +(-314719. - 314719. i) q^{27} -1.58287e6i q^{28} +(609827. + 358270. i) q^{29} +243404. q^{30} +(-1.03412e6 + 1.03412e6i) q^{31} +(2.23667e6 - 2.23667e6i) q^{32} +886316. i q^{33} +1.84523e6i q^{34} +497529. i q^{35} +3.40967e6 q^{36} +(742075. + 742075. i) q^{37} -4.42681e6i q^{38} +(19497.0 + 19497.0i) q^{39} +(-1.85797e6 + 1.85797e6i) q^{40} +(2.06441e6 + 2.06441e6i) q^{41} -2.74834e6i q^{42} +(-2.46092e6 + 2.46092e6i) q^{43} +(-1.09710e7 - 1.09710e7i) q^{44} -1.07173e6 q^{45} +(-973747. + 973747. i) q^{46} +(1.62495e6 + 1.62495e6i) q^{47} +(5.65143e6 - 5.65143e6i) q^{48} -147091. q^{49} +(-7.44838e6 + 7.44838e6i) q^{50} +2.31605e6i q^{51} -482676. q^{52} +535025. q^{53} +1.35280e7 q^{54} +(3.44840e6 + 3.44840e6i) q^{55} +(2.09788e7 + 2.09788e7i) q^{56} -5.55633e6i q^{57} +(-2.08066e7 + 5.40650e6i) q^{58} +1.94347e7 q^{59} +(-3.78167e6 + 3.78167e6i) q^{60} +(-1.18650e7 + 1.18650e7i) q^{61} -4.44510e7i q^{62} +1.21011e7i q^{63} +4.25107e7i q^{64} +151715. q^{65} +(-1.90489e7 - 1.90489e7i) q^{66} -3.65226e7i q^{67} +(-2.86686e7 - 2.86686e7i) q^{68} +(-1.22220e6 + 1.22220e6i) q^{69} +(-1.06930e7 - 1.06930e7i) q^{70} +1.99035e7i q^{71} +(-4.51904e7 + 4.51904e7i) q^{72} +(9.33351e6 + 9.33351e6i) q^{73} -3.18977e7 q^{74} +(-9.34888e6 + 9.34888e6i) q^{75} +(6.87775e7 + 6.87775e7i) q^{76} +(3.89367e7 - 3.89367e7i) q^{77} -838068. q^{78} +(5.09343e7 - 5.09343e7i) q^{79} -4.39762e7i q^{80} -1.65180e7 q^{81} -8.87374e7 q^{82} -2.13278e7 q^{83} +(4.26997e7 + 4.26997e7i) q^{84} +(9.01110e6 + 9.01110e6i) q^{85} -1.05781e8i q^{86} +(-2.61155e7 + 6.78600e6i) q^{87} +2.90811e8 q^{88} +(-1.63507e7 + 1.63507e7i) q^{89} +(2.30338e7 - 2.30338e7i) q^{90} -1.71305e6i q^{91} -3.02574e7i q^{92} -5.57929e7i q^{93} -6.98475e7 q^{94} +(-2.16181e7 - 2.16181e7i) q^{95} +1.20673e8i q^{96} +(4.08736e7 + 4.08736e7i) q^{97} +(3.16130e6 - 3.16130e6i) q^{98} +(8.38736e7 + 8.38736e7i) 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

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

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 $

$2$	−21.4922	+	21.4922i	−1.34326	+	1.34326i	−0.450475	+	0.892789i	$0.648745\pi$
$2$	−21.4922	+	21.4922i	−1.34326	+	1.34326i	−0.892789	+	0.450475i	$0.851255\pi$
$3$	−26.9761	+	26.9761i	−0.333038	+	0.333038i	−0.853739	−	0.520701i	$-0.825671\pi$
$3$	−26.9761	+	26.9761i	−0.333038	+	0.333038i	0.520701	+	0.853739i	$0.325671\pi$
$4$		−	667.831i		−	2.60872i
$5$			209.913i			0.335860i	0.985799	+	0.167930i	$0.0537083\pi$
$5$			209.913i			0.335860i	−0.985799	+	0.167930i	$0.946292\pi$
$6$		−	1159.55i		−	0.894716i
$7$	2370.17			0.987160			0.493580	−	0.869700i	$-0.335688\pi$
$7$	2370.17			0.987160			0.493580	+	0.869700i	$0.335688\pi$
$8$	8851.17	+	8851.17i	2.16093	+	2.16093i
$9$			5105.58i			0.778171i
$10$	−4511.49	−	4511.49i	−0.451149	−	0.451149i
$11$	16427.8	−	16427.8i	1.12204	−	1.12204i	0.130607	−	0.991434i	$-0.458307\pi$
$11$	16427.8	−	16427.8i	1.12204	−	1.12204i	0.991434	−	0.130607i	$-0.0416928\pi$
$12$	18015.5	+	18015.5i	0.868801	+	0.868801i
$13$		−	722.752i		−	0.0253056i	−0.999920	−	0.0126528i	$-0.995972\pi$
$13$		−	722.752i		−	0.0253056i	0.999920	−	0.0126528i	$-0.00402761\pi$
$14$	−50940.2	+	50940.2i	−1.32602	+	1.32602i
$15$	−5662.62	−	5662.62i	−0.111854	−	0.111854i
$16$	−209498.			−3.19668
$17$	42927.9	−	42927.9i	0.513977	−	0.513977i	−0.401765	−	0.915743i	$-0.631603\pi$
$17$	42927.9	−	42927.9i	0.513977	−	0.513977i	0.915743	+	0.401765i	$0.131603\pi$
$18$	−109730.	−	109730.i	−1.04529	−	1.04529i
$19$	−102986.	+	102986.i	−0.790251	+	0.790251i	−0.981535	−	0.191284i	$-0.938735\pi$
$19$	−102986.	+	102986.i	−0.790251	+	0.790251i	0.191284	+	0.981535i	$0.438735\pi$
$20$	140186.			0.876163
$21$	−63937.9	+	63937.9i	−0.328762	+	0.328762i
$22$			706140.i			3.01440i
$23$	45306.9			0.161902			0.0809512	−	0.996718i	$-0.474204\pi$
$23$	45306.9			0.161902			0.0809512	+	0.996718i	$0.474204\pi$
$24$	−477540.			−1.43934
$25$	346562.			0.887198
$26$	15533.5	+	15533.5i	0.0339920	+	0.0339920i
$27$	−314719.	−	314719.i	−0.592199	−	0.592199i
$28$		−	1.58287e6i		−	2.57522i
$29$	609827.	+	358270.i	0.862213	+	0.506546i
$29$	609827.	+	358270.i	0.862213	+	0.506546i
$30$	243404.			0.300499
$31$	−1.03412e6	+	1.03412e6i	−1.11976	+	1.11976i	−0.127980	+	0.991777i	$0.540849\pi$
$31$	−1.03412e6	+	1.03412e6i	−1.11976	+	1.11976i	−0.991777	+	0.127980i	$0.959151\pi$
$32$	2.23667e6	−	2.23667e6i	2.13306	−	2.13306i
$33$			886316.i			0.747365i
$34$			1.84523e6i			1.38081i
$35$			497529.i			0.331548i
$36$	3.40967e6			2.03003
$37$	742075.	+	742075.i	0.395950	+	0.395950i	0.876802	−	0.480852i	$-0.159672\pi$
$37$	742075.	+	742075.i	0.395950	+	0.395950i	−0.480852	+	0.876802i	$0.659672\pi$
$38$		−	4.42681e6i		−	2.12303i
$39$	19497.0	+	19497.0i	0.00842771	+	0.00842771i
$40$	−1.85797e6	+	1.85797e6i	−0.725770	+	0.725770i
$41$	2.06441e6	+	2.06441e6i	0.730567	+	0.730567i	0.970732	−	0.240165i	$-0.0772016\pi$
$41$	2.06441e6	+	2.06441e6i	0.730567	+	0.730567i	−0.240165	+	0.970732i	$0.577202\pi$
$42$		−	2.74834e6i		−	0.883228i
$43$	−2.46092e6	+	2.46092e6i	−0.719820	+	0.719820i	−0.968568	−	0.248748i	$-0.919981\pi$
$43$	−2.46092e6	+	2.46092e6i	−0.719820	+	0.719820i	0.248748	+	0.968568i	$0.419981\pi$
$44$	−1.09710e7	−	1.09710e7i	−2.92709	−	2.92709i
$45$	−1.07173e6			−0.261357
$46$	−973747.	+	973747.i	−0.217478	+	0.217478i
$47$	1.62495e6	+	1.62495e6i	0.333003	+	0.333003i	0.853726	−	0.520723i	$-0.174338\pi$
$47$	1.62495e6	+	1.62495e6i	0.333003	+	0.333003i	−0.520723	+	0.853726i	$0.674338\pi$
$48$	5.65143e6	−	5.65143e6i	1.06462	−	1.06462i
$49$	−147091.			−0.0255153
$50$	−7.44838e6	+	7.44838e6i	−1.19174	+	1.19174i
$51$			2.31605e6i			0.342348i
$52$	−482676.			−0.0660150
$53$	535025.			0.0678064			0.0339032	−	0.999425i	$-0.489206\pi$
$53$	535025.			0.0678064			0.0339032	+	0.999425i	$0.489206\pi$
$54$	1.35280e7			1.59096
$55$	3.44840e6	+	3.44840e6i	0.376849	+	0.376849i
$56$	2.09788e7	+	2.09788e7i	2.13318	+	2.13318i
$57$		−	5.55633e6i		−	0.526367i
$58$	−2.08066e7	+	5.40650e6i	−1.83860	+	0.477754i
$59$	1.94347e7			1.60387			0.801936	−	0.597410i	$-0.203803\pi$
$59$	1.94347e7			1.60387			0.801936	+	0.597410i	$0.203803\pi$
$60$	−3.78167e6	+	3.78167e6i	−0.291796	+	0.291796i
$61$	−1.18650e7	+	1.18650e7i	−0.856936	+	0.856936i	−0.990976	−	0.134040i	$-0.957205\pi$
$61$	−1.18650e7	+	1.18650e7i	−0.856936	+	0.856936i	0.134040	+	0.990976i	$0.457205\pi$
$62$		−	4.44510e7i		−	3.00826i
$63$			1.21011e7i			0.768180i
$64$			4.25107e7i			2.53384i
$65$	151715.			0.00849913
$66$	−1.90489e7	−	1.90489e7i	−1.00391	−	1.00391i
$67$		−	3.65226e7i		−	1.81243i	−0.422813	−	0.906217i	$-0.638957\pi$
$67$		−	3.65226e7i		−	1.81243i	0.422813	−	0.906217i	$-0.361043\pi$
$68$	−2.86686e7	−	2.86686e7i	−1.34082	−	1.34082i
$69$	−1.22220e6	+	1.22220e6i	−0.0539197	+	0.0539197i
$70$	−1.06930e7	−	1.06930e7i	−0.445356	−	0.445356i
$71$			1.99035e7i			0.783240i	0.920127	+	0.391620i	$0.128085\pi$
$71$			1.99035e7i			0.783240i	−0.920127	+	0.391620i	$0.871915\pi$
$72$	−4.51904e7	+	4.51904e7i	−1.68157	+	1.68157i
$73$	9.33351e6	+	9.33351e6i	0.328665	+	0.328665i	0.852079	−	0.523414i	$-0.175342\pi$
$73$	9.33351e6	+	9.33351e6i	0.328665	+	0.328665i	−0.523414	+	0.852079i	$0.675342\pi$
$74$	−3.18977e7			−1.06373
$75$	−9.34888e6	+	9.34888e6i	−0.295471	+	0.295471i
$76$	6.87775e7	+	6.87775e7i	2.06154	+	2.06154i
$77$	3.89367e7	−	3.89367e7i	1.10763	−	1.10763i
$78$	−838068.			−0.0226413
$79$	5.09343e7	−	5.09343e7i	1.30768	−	1.30768i	0.384595	−	0.923085i	$-0.374341\pi$
$79$	5.09343e7	−	5.09343e7i	1.30768	−	1.30768i	0.923085	−	0.384595i	$-0.125659\pi$
$80$		−	4.39762e7i		−	1.07364i
$81$	−1.65180e7			−0.383722
$82$	−8.87374e7			−1.96269
$83$	−2.13278e7			−0.449401			−0.224701	−	0.974428i	$-0.572140\pi$
$83$	−2.13278e7			−0.449401			−0.224701	+	0.974428i	$0.572140\pi$
$84$	4.26997e7	+	4.26997e7i	0.857646	+	0.857646i
$85$	9.01110e6	+	9.01110e6i	0.172624	+	0.172624i
$86$		−	1.05781e8i		−	1.93382i
$87$	−2.61155e7	+	6.78600e6i	−0.455849	+	0.118450i
$88$	2.90811e8			4.84931
$89$	−1.63507e7	+	1.63507e7i	−0.260600	+	0.260600i	−0.825298	−	0.564698i	$-0.808993\pi$
$89$	−1.63507e7	+	1.63507e7i	−0.260600	+	0.260600i	0.564698	+	0.825298i	$0.308993\pi$
$90$	2.30338e7	−	2.30338e7i	0.351071	−	0.351071i
$91$		−	1.71305e6i		−	0.0249806i
$92$		−	3.02574e7i		−	0.422357i
$93$		−	5.57929e7i		−	0.745843i
$94$	−6.98475e7			−0.894621
$95$	−2.16181e7	−	2.16181e7i	−0.265414	−	0.265414i
$96$			1.20673e8i			1.42078i
$97$	4.08736e7	+	4.08736e7i	0.461696	+	0.461696i	0.899211	−	0.437515i	$-0.144141\pi$
$97$	4.08736e7	+	4.08736e7i	0.461696	+	0.461696i	−0.437515	+	0.899211i	$0.644141\pi$
$98$	3.16130e6	−	3.16130e6i	0.0342738	−	0.0342738i
$99$	8.38736e7	+	8.38736e7i	0.873141	+	0.873141i
$100$		−	2.31445e8i		−	2.31445i
$101$	−1.14696e8	+	1.14696e8i	−1.10221	+	1.10221i	−0.108065	+	0.994144i	$0.534465\pi$
$101$	−1.14696e8	+	1.14696e8i	−1.10221	+	1.10221i	−0.994144	+	0.108065i	$0.965535\pi$
$102$	−4.97771e7	−	4.97771e7i	−0.459864	−	0.459864i
$103$	1.63861e8			1.45589			0.727943	−	0.685637i	$-0.240476\pi$
$103$	1.63861e8			1.45589			0.727943	+	0.685637i	$0.240476\pi$
$104$	6.39720e6	−	6.39720e6i	0.0546835	−	0.0546835i
$105$	−1.34214e7	−	1.34214e7i	−0.110418	−	0.110418i
$106$	−1.14989e7	+	1.14989e7i	−0.0910819	+	0.0910819i
$107$	−2.49417e7			−0.190279			−0.0951395	−	0.995464i	$-0.530330\pi$
$107$	−2.49417e7			−0.190279			−0.0951395	+	0.995464i	$0.530330\pi$
$108$	−2.10179e8	+	2.10179e8i	−1.54488	+	1.54488i
$109$			2.48376e8i			1.75956i	0.475384	+	0.879778i	$0.342309\pi$
$109$			2.48376e8i			1.75956i	−0.475384	+	0.879778i	$0.657691\pi$
$110$	−1.48228e8			−1.01242
$111$	−4.00365e7			−0.263733
$112$	−4.96546e8			−3.15564
$113$	−5.02743e7	−	5.02743e7i	−0.308342	−	0.308342i	0.535924	−	0.844266i	$-0.319963\pi$
$113$	−5.02743e7	−	5.02743e7i	−0.308342	−	0.308342i	−0.844266	+	0.535924i	$0.819963\pi$
$114$	1.19418e8	+	1.19418e8i	0.707050	+	0.707050i
$115$			9.51049e6i			0.0543766i
$116$	2.39264e8	−	4.07261e8i	1.32143	−	2.24927i
$117$	3.69007e6			0.0196921
$118$	−4.17695e8	+	4.17695e8i	−2.15442	+	2.15442i
$119$	1.01746e8	−	1.01746e8i	0.507378	−	0.507378i
$120$		−	1.00242e8i		−	0.483418i
$121$		−	3.25387e8i		−	1.51795i
$122$		−	5.10010e8i		−	2.30218i
$123$	−1.11379e8			−0.486613
$124$	6.90617e8	+	6.90617e8i	2.92113	+	2.92113i
$125$			1.54745e8i			0.633834i
$126$	−2.60080e8	−	2.60080e8i	−1.03187	−	1.03187i
$127$	−1.94144e8	+	1.94144e8i	−0.746292	+	0.746292i	−0.973781	−	0.227489i	$-0.926948\pi$
$127$	−1.94144e8	+	1.94144e8i	−0.746292	+	0.746292i	0.227489	+	0.973781i	$0.426948\pi$
$128$	−3.41062e8	−	3.41062e8i	−1.27055	−	1.27055i
$129$		−	1.32772e8i		−	0.479455i
$130$	−3.26069e6	+	3.26069e6i	−0.0114166	+	0.0114166i
$131$	3.71557e8	+	3.71557e8i	1.26165	+	1.26165i	0.950291	+	0.311363i	$0.100785\pi$
$131$	3.71557e8	+	3.71557e8i	1.26165	+	1.26165i	0.311363	+	0.950291i	$0.399215\pi$
$132$	5.91909e8			1.94966
$133$	−2.44095e8	+	2.44095e8i	−0.780104	+	0.780104i
$134$	7.84951e8	+	7.84951e8i	2.43458	+	2.43458i
$135$	6.60634e7	−	6.60634e7i	0.198896	−	0.198896i
$136$	7.59924e8			2.22134
$137$	1.92903e7	−	1.92903e7i	0.0547593	−	0.0547593i	−0.679197	−	0.733956i	$-0.737672\pi$
$137$	1.92903e7	−	1.92903e7i	0.0547593	−	0.0547593i	0.733956	+	0.679197i	$0.237672\pi$
$138$		−	5.25357e7i		−	0.144857i
$139$	−2.61982e8			−0.701797			−0.350899	−	0.936413i	$-0.614124\pi$
$139$	−2.61982e8			−0.701797			−0.350899	+	0.936413i	$0.614124\pi$
$140$	3.32265e8			0.864913
$141$	−8.76694e7			−0.221805
$142$	−4.27769e8	−	4.27769e8i	−1.05210	−	1.05210i
$143$	−1.18732e7	−	1.18732e7i	−0.0283939	−	0.0283939i
$144$		−	1.06961e9i		−	2.48757i
$145$	−7.52055e7	+	1.28010e8i	−0.170129	+	0.289583i
$146$	−4.01196e8			−0.882968
$147$	3.96792e6	−	3.96792e6i	0.00849756	−	0.00849756i
$148$	4.95581e8	−	4.95581e8i	1.03292	−	1.03292i
$149$		−	6.87144e8i		−	1.39413i	−0.717009	−	0.697064i	$-0.754489\pi$
$149$		−	6.87144e8i		−	1.39413i	0.717009	−	0.697064i	$-0.245511\pi$
$150$		−	4.01856e8i		−	0.793790i
$151$		−	7.79086e8i		−	1.49857i	−0.662246	−	0.749286i	$-0.730397\pi$
$151$		−	7.79086e8i		−	1.49857i	0.662246	−	0.749286i	$-0.269603\pi$
$152$	−1.82310e9			−3.41535
$153$	2.19172e8	+	2.19172e8i	0.399962	+	0.399962i
$154$			1.67367e9i			2.97569i
$155$	−2.17074e8	−	2.17074e8i	−0.376081	−	0.376081i
$156$	1.30207e7	−	1.30207e7i	0.0219855	−	0.0219855i
$157$	−6.64944e8	−	6.64944e8i	−1.09443	−	1.09443i	−0.995050	−	0.0993759i	$-0.968315\pi$
$157$	−6.64944e8	−	6.64944e8i	−1.09443	−	1.09443i	−0.0993759	−	0.995050i	$-0.531685\pi$
$158$			2.18938e9i			3.51312i
$159$	−1.44329e7	+	1.44329e7i	−0.0225821	+	0.0225821i
$160$	4.69506e8	+	4.69506e8i	0.716409	+	0.716409i
$161$	1.07385e8			0.159824
$162$	3.55008e8	−	3.55008e8i	0.515440	−	0.515440i
$163$	−3.47793e7	−	3.47793e7i	−0.0492686	−	0.0492686i	0.682043	−	0.731312i	$-0.261092\pi$
$163$	−3.47793e7	−	3.47793e7i	−0.0492686	−	0.0492686i	−0.731312	+	0.682043i	$0.761092\pi$
$164$	1.37868e9	−	1.37868e9i	1.90584	−	1.90584i
$165$	−1.86049e8			−0.251010
$166$	4.58383e8	−	4.58383e8i	0.603665	−	0.603665i
$167$			2.60258e8i			0.334610i	0.985905	+	0.167305i	$0.0535064\pi$
$167$			2.60258e8i			0.334610i	−0.985905	+	0.167305i	$0.946494\pi$
$168$	−1.13185e9			−1.42086
$169$	8.15208e8			0.999360
$170$	−3.87337e8			−0.463760
$171$	−5.25805e8	−	5.25805e8i	−0.614951	−	0.614951i
$172$	1.64348e9	+	1.64348e9i	1.87781	+	1.87781i
$173$		−	4.25070e8i		−	0.474543i	−0.971443	−	0.237272i	$-0.923747\pi$
$173$		−	4.25070e8i		−	0.474543i	0.971443	−	0.237272i	$-0.0762531\pi$
$174$	4.15433e8	−	7.07126e8i	0.453215	−	0.771435i
$175$	8.21411e8			0.875806
$176$	−3.44159e9	+	3.44159e9i	−3.58681	+	3.58681i
$177$	−5.24272e8	+	5.24272e8i	−0.534150	+	0.534150i
$178$		−	7.02824e8i		−	0.700110i
$179$		−	8.89701e8i		−	0.866626i	−0.901243	−	0.433313i	$-0.857344\pi$
$179$		−	8.89701e8i		−	0.866626i	0.901243	−	0.433313i	$-0.142656\pi$
$180$			7.15732e8i			0.681805i
$181$	1.66710e8			0.155327			0.0776635	−	0.996980i	$-0.475254\pi$
$181$	1.66710e8			0.155327			0.0776635	+	0.996980i	$0.475254\pi$
$182$	3.68172e7	+	3.68172e7i	0.0335556	+	0.0335556i
$183$		−	6.40142e8i		−	0.570784i
$184$	4.01019e8	+	4.01019e8i	0.349860	+	0.349860i
$185$	−1.55771e8	+	1.55771e8i	−0.132984	+	0.132984i
$186$	1.19911e9	+	1.19911e9i	1.00186	+	1.00186i
$187$		−	1.41042e9i		−	1.15341i
$188$	1.08519e9	−	1.08519e9i	0.868710	−	0.868710i
$189$	−7.45937e8	−	7.45937e8i	−0.584595	−	0.584595i
$190$	9.29243e8			0.713041
$191$	−4.81455e7	+	4.81455e7i	−0.0361761	+	0.0361761i	−0.724963	−	0.688787i	$-0.758143\pi$
$191$	−4.81455e7	+	4.81455e7i	−0.0361761	+	0.0361761i	0.688787	+	0.724963i	$0.258143\pi$
$192$	−1.14677e9	−	1.14677e9i	−0.843864	−	0.843864i
$193$	−7.23566e8	+	7.23566e8i	−0.521493	+	0.521493i	−0.918022	−	0.396529i	$-0.870215\pi$
$193$	−7.23566e8	+	7.23566e8i	−0.521493	+	0.521493i	0.396529	+	0.918022i	$0.370215\pi$
$194$	−1.75693e9			−1.24036
$195$	−4.09267e6	+	4.09267e6i	−0.00283053	+	0.00283053i
$196$			9.82316e7i			0.0665621i
$197$	1.63923e9			1.08837			0.544183	−	0.838967i	$-0.316840\pi$
$197$	1.63923e9			1.08837			0.544183	+	0.838967i	$0.316840\pi$
$198$	−3.60526e9			−2.34572
$199$	−6.73400e8			−0.429399			−0.214699	−	0.976680i	$-0.568877\pi$
$199$	−6.73400e8			−0.429399			−0.214699	+	0.976680i	$0.568877\pi$
$200$	3.06748e9	+	3.06748e9i	1.91717	+	1.91717i
$201$	9.85236e8	+	9.85236e8i	0.603609	+	0.603609i
$202$		−	4.93016e9i		−	2.96111i
$203$	1.44539e9	+	8.49162e8i	0.851142	+	0.500042i
$204$	1.54673e9			0.893088
$205$	−4.33345e8	+	4.33345e8i	−0.245368	+	0.245368i
$206$	−3.52174e9	+	3.52174e9i	−1.95564	+	1.95564i
$207$			2.31318e8i			0.125988i
$208$			1.51415e8i			0.0808938i
$209$			3.38368e9i			1.77339i
$210$	5.76910e8			0.296641
$211$	4.09891e8	+	4.09891e8i	0.206794	+	0.206794i	0.802904	−	0.596109i	$-0.203287\pi$
$211$	4.09891e8	+	4.09891e8i	0.206794	+	0.206794i	−0.596109	+	0.802904i	$0.703287\pi$
$212$		−	3.57306e8i		−	0.176888i
$213$	−5.36917e8	−	5.36917e8i	−0.260849	−	0.260849i
$214$	5.36053e8	−	5.36053e8i	0.255595	−	0.255595i
$215$	−5.16578e8	−	5.16578e8i	−0.241759	−	0.241759i
$216$		−	5.57125e9i		−	2.55940i
$217$	−2.45104e9	+	2.45104e9i	−1.10538	+	1.10538i
$218$	−5.33815e9	−	5.33815e9i	−2.36355	−	2.36355i
$219$	−5.03563e8			−0.218916
$220$	2.30295e9	−	2.30295e9i	0.983092	−	0.983092i
$221$	−3.10262e7	−	3.10262e7i	−0.0130065	−	0.0130065i
$222$	8.60474e8	−	8.60474e8i	0.354263	−	0.354263i
$223$	3.52972e8			0.142732			0.0713660	−	0.997450i	$-0.477264\pi$
$223$	3.52972e8			0.142732			0.0713660	+	0.997450i	$0.477264\pi$
$224$	5.30130e9	−	5.30130e9i	2.10567	−	2.10567i
$225$			1.76940e9i			0.690392i
$226$	2.16101e9			0.828369
$227$	4.06724e9			1.53178			0.765890	−	0.642971i	$-0.222298\pi$
$227$	4.06724e9			1.53178			0.765890	+	0.642971i	$0.222298\pi$
$228$	−3.71069e9			−1.37314
$229$	−1.49165e9	−	1.49165e9i	−0.542406	−	0.542406i	0.381828	−	0.924234i	$-0.375295\pi$
$229$	−1.49165e9	−	1.49165e9i	−0.542406	−	0.542406i	−0.924234	+	0.381828i	$0.875295\pi$
$230$	−2.04402e8	−	2.04402e8i	−0.0730421	−	0.0730421i
$231$			2.10072e9i			0.737769i
$232$	2.22657e9	+	8.56879e9i	0.768571	+	2.95779i
$233$	2.83212e8			0.0960923			0.0480462	−	0.998845i	$-0.484701\pi$
$233$	2.83212e8			0.0960923			0.0480462	+	0.998845i	$0.484701\pi$
$234$	−7.93078e7	+	7.93078e7i	−0.0264516	+	0.0264516i
$235$	−3.41097e8	+	3.41097e8i	−0.111842	+	0.111842i
$236$		−	1.29791e10i		−	4.18405i
$237$			2.74801e9i			0.871014i
$238$			4.37351e9i			1.36308i
$239$	2.32626e9			0.712963			0.356481	−	0.934302i	$-0.383976\pi$
$239$	2.32626e9			0.712963			0.356481	+	0.934302i	$0.383976\pi$
$240$	1.18631e9	+	1.18631e9i	0.357562	+	0.357562i
$241$		−	5.78872e8i		−	0.171599i	−0.996312	−	0.0857994i	$-0.972656\pi$
$241$		−	5.78872e8i		−	0.171599i	0.996312	−	0.0857994i	$-0.0273444\pi$
$242$	6.99329e9	+	6.99329e9i	2.03901	+	2.03901i
$243$	2.51046e9	−	2.51046e9i	0.719993	−	0.719993i
$244$	7.92382e9	+	7.92382e9i	2.23550	+	2.23550i
$245$		−	3.08761e7i		−	0.00856956i
$246$	2.39379e9	−	2.39379e9i	0.653650	−	0.653650i
$247$	7.44336e7	+	7.44336e7i	0.0199977	+	0.0199977i
$248$	−1.83063e10			−4.83943
$249$	5.75341e8	−	5.75341e8i	0.149668	−	0.149668i
$250$	−3.32581e9	−	3.32581e9i	−0.851407	−	0.851407i
$251$	−2.95303e9	+	2.95303e9i	−0.744000	+	0.744000i	−0.973345	−	0.229345i	$-0.926342\pi$
$251$	−2.95303e9	+	2.95303e9i	−0.744000	+	0.744000i	0.229345	+	0.973345i	$0.426342\pi$
$252$	8.08150e9			2.00396
$253$	7.44294e8	−	7.44294e8i	0.181661	−	0.181661i
$254$		−	8.34516e9i		−	2.00493i
$255$	−4.86168e8			−0.114981
$256$	3.77760e9			0.879541
$257$	2.57050e9			0.589231			0.294615	−	0.955616i	$-0.404808\pi$
$257$	2.57050e9			0.589231			0.294615	+	0.955616i	$0.404808\pi$
$258$	2.85357e9	+	2.85357e9i	0.644034	+	0.644034i
$259$	1.75884e9	+	1.75884e9i	0.390866	+	0.390866i
$260$		−	1.01320e8i		−	0.0221718i
$261$	−1.82918e9	+	3.11352e9i	−0.394180	+	0.670949i
$262$	−1.59712e10			−3.38947
$263$	−1.87480e9	+	1.87480e9i	−0.391862	+	0.391862i	−0.875350	−	0.483489i	$-0.839369\pi$
$263$	−1.87480e9	+	1.87480e9i	−0.391862	+	0.391862i	0.483489	+	0.875350i	$0.339369\pi$
$264$	−7.84493e9	+	7.84493e9i	−1.61500	+	1.61500i
$265$			1.12308e8i			0.0227735i
$266$		−	1.04923e10i		−	2.09577i
$267$		−	8.82153e8i		−	0.173580i
$268$	−2.43909e10			−4.72813
$269$	−2.07183e9	−	2.07183e9i	−0.395681	−	0.395681i	0.481026	−	0.876707i	$-0.340264\pi$
$269$	−2.07183e9	−	2.07183e9i	−0.395681	−	0.395681i	−0.876707	+	0.481026i	$0.840264\pi$
$270$			2.83970e9i			0.534339i
$271$	1.19437e9	+	1.19437e9i	0.221444	+	0.221444i	0.809106	−	0.587662i	$-0.199952\pi$
$271$	1.19437e9	+	1.19437e9i	0.221444	+	0.221444i	−0.587662	+	0.809106i	$0.699952\pi$
$272$	−8.99330e9	+	8.99330e9i	−1.64302	+	1.64302i
$273$	4.62113e7	+	4.62113e7i	0.00831950	+	0.00831950i
$274$			8.29185e8i			0.147112i
$275$	5.69325e9	−	5.69325e9i	0.995473	−	0.995473i
$276$	8.16226e8	+	8.16226e8i	0.140661	+	0.140661i
$277$	7.79288e8			0.132367			0.0661834	−	0.997807i	$-0.478918\pi$
$277$	7.79288e8			0.132367			0.0661834	+	0.997807i	$0.478918\pi$
$278$	5.63057e9	−	5.63057e9i	0.942699	−	0.942699i
$279$	−5.27978e9	−	5.27978e9i	−0.871363	−	0.871363i
$280$	−4.40371e9	+	4.40371e9i	−0.716451	+	0.716451i
$281$	1.54167e9			0.247266			0.123633	−	0.992328i	$-0.460545\pi$
$281$	1.54167e9			0.247266			0.123633	+	0.992328i	$0.460545\pi$
$282$	1.88421e9	−	1.88421e9i	0.297943	−	0.297943i
$283$		−	6.82528e9i		−	1.06408i	−0.846719	−	0.532041i	$-0.821425\pi$
$283$		−	6.82528e9i		−	1.06408i	0.846719	−	0.532041i	$-0.178575\pi$
$284$	1.32921e10			2.04325
$285$	1.16634e9			0.176786
$286$	5.10364e8			0.0762810
$287$	4.89300e9	+	4.89300e9i	0.721186	+	0.721186i
$288$	1.14195e10	+	1.14195e10i	1.65988	+	1.65988i
$289$			3.29015e9i			0.471655i
$290$	−1.13489e9	−	4.36756e9i	−0.160459	−	0.617514i
$291$	−2.20522e9			−0.307524
$292$	6.23321e9	−	6.23321e9i	0.857394	−	0.857394i
$293$	5.90198e9	−	5.90198e9i	0.800805	−	0.800805i	−0.182416	−	0.983221i	$-0.558392\pi$
$293$	5.90198e9	−	5.90198e9i	0.800805	−	0.800805i	0.983221	+	0.182416i	$0.0583918\pi$
$294$			1.70559e8i			0.0228289i
$295$			4.07959e9i			0.538677i
$296$			1.31365e10i			1.71124i
$297$	−1.03403e10			−1.32894
$298$	1.47682e10	+	1.47682e10i	1.87268	+	1.87268i
$299$		−	3.27457e7i		−	0.00409703i
$300$	6.24347e9	+	6.24347e9i	0.770799	+	0.770799i
$301$	−5.83281e9	+	5.83281e9i	−0.710578	+	0.710578i
$302$	1.67443e10	+	1.67443e10i	2.01298	+	2.01298i
$303$		−	6.18811e9i		−	0.734155i
$304$	2.15754e10	−	2.15754e10i	2.52618	−	2.52618i
$305$	−2.49061e9	−	2.49061e9i	−0.287811	−	0.287811i
$306$	−9.42098e9			−1.07451
$307$	1.22803e10	−	1.22803e10i	1.38247	−	1.38247i	0.542248	−	0.840218i	$-0.317573\pi$
$307$	1.22803e10	−	1.22803e10i	1.38247	−	1.38247i	0.840218	−	0.542248i	$-0.182427\pi$
$308$	−2.60032e10	−	2.60032e10i	−2.88950	−	2.88950i
$309$	−4.42033e9	+	4.42033e9i	−0.484865	+	0.484865i
$310$	9.33083e9			1.01035
$311$	7.42608e9	−	7.42608e9i	0.793813	−	0.793813i	−0.188299	−	0.982112i	$-0.560297\pi$
$311$	7.42608e9	−	7.42608e9i	0.793813	−	0.793813i	0.982112	+	0.188299i	$0.0602973\pi$
$312$			3.45143e8i			0.0364234i
$313$	−1.83063e10			−1.90732			−0.953661	−	0.300882i	$-0.902719\pi$
$313$	−1.83063e10			−1.90732			−0.953661	+	0.300882i	$0.902719\pi$
$314$	2.85822e10			2.94021
$315$	−2.54017e9			−0.258001
$316$	−3.40155e10	−	3.40155e10i	−3.41137	−	3.41137i
$317$	−7.63020e9	−	7.63020e9i	−0.755612	−	0.755612i	0.219909	−	0.975520i	$-0.429424\pi$
$317$	−7.63020e9	−	7.63020e9i	−0.755612	−	0.755612i	−0.975520	+	0.219909i	$0.929424\pi$
$318$		−	6.20389e8i		−	0.0606675i
$319$	1.59037e10	−	4.13252e9i	1.53580	−	0.399073i
$320$	−8.92353e9			−0.851015
$321$	6.72829e8	−	6.72829e8i	0.0633702	−	0.0633702i
$322$	−2.30795e9	+	2.30795e9i	−0.214685	+	0.214685i
$323$			8.84197e9i			0.812342i
$324$			1.10312e10i			1.00102i
$325$		−	2.50478e8i		−	0.0224510i
$326$	1.49497e9			0.132361
$327$	−6.70020e9	−	6.70020e9i	−0.585999	−	0.585999i
$328$			3.65448e10i			3.15741i
$329$	3.85140e9	+	3.85140e9i	0.328727	+	0.328727i
$330$	3.99860e9	−	3.99860e9i	0.337173	−	0.337173i
$331$	2.91207e9	+	2.91207e9i	0.242599	+	0.242599i	0.817925	−	0.575325i	$-0.195125\pi$
$331$	2.91207e9	+	2.91207e9i	0.242599	+	0.242599i	−0.575325	+	0.817925i	$0.695125\pi$
$332$			1.42434e10i			1.17236i
$333$	−3.78872e9	+	3.78872e9i	−0.308117	+	0.308117i
$334$	−5.59353e9	−	5.59353e9i	−0.449469	−	0.449469i
$335$	7.66655e9			0.608724
$336$	1.33948e10	−	1.33948e10i	1.05095	−	1.05095i
$337$	−7.61954e9	−	7.61954e9i	−0.590757	−	0.590757i	0.347079	−	0.937836i	$-0.387174\pi$
$337$	−7.61954e9	−	7.61954e9i	−0.590757	−	0.590757i	−0.937836	+	0.347079i	$0.887174\pi$
$338$	−1.75206e10	+	1.75206e10i	−1.34240	+	1.34240i
$339$	2.71241e9			0.205379
$340$	6.01790e9	−	6.01790e9i	0.450328	−	0.450328i
$341$			3.39766e10i			2.51283i
$342$	2.26014e10			1.65208
$343$	−1.40122e10			−1.01235
$344$	−4.35641e10			−3.11096
$345$	−2.56556e8	−	2.56556e8i	−0.0181095	−	0.0181095i
$346$	9.13569e9	+	9.13569e9i	0.637437	+	0.637437i
$347$		−	2.31949e10i		−	1.59983i	−0.600113	−	0.799915i	$-0.704878\pi$
$347$		−	2.31949e10i		−	1.59983i	0.600113	−	0.799915i	$-0.295122\pi$
$348$	4.53190e9	+	1.74407e10i	0.309004	+	1.18918i
$349$	−7.40204e9			−0.498942			−0.249471	−	0.968382i	$-0.580257\pi$
$349$	−7.40204e9			−0.498942			−0.249471	+	0.968382i	$0.580257\pi$
$350$	−1.76539e10	+	1.76539e10i	−1.17644	+	1.17644i
$351$	−2.27464e8	+	2.27464e8i	−0.0149859	+	0.0149859i
$352$		−	7.34873e10i		−	4.78676i
$353$		−	3.93343e9i		−	0.253322i	−0.991946	−	0.126661i	$-0.959574\pi$
$353$		−	3.93343e9i		−	0.253322i	0.991946	−	0.126661i	$-0.0404260\pi$
$354$		−	2.25355e10i		−	1.43501i
$355$	−4.17798e9			−0.263059
$356$	1.09195e10	+	1.09195e10i	0.679832	+	0.679832i
$357$			5.48944e9i			0.337952i
$358$	1.91216e10	+	1.91216e10i	1.16411	+	1.16411i
$359$	−1.79357e9	+	1.79357e9i	−0.107980	+	0.107980i	−0.759032	−	0.651053i	$-0.774328\pi$
$359$	−1.79357e9	+	1.79357e9i	−0.107980	+	0.107980i	0.651053	+	0.759032i	$0.274328\pi$
$360$	−9.48602e9	−	9.48602e9i	−0.564773	−	0.564773i
$361$		−	4.22879e9i		−	0.248993i
$362$	−3.58296e9	+	3.58296e9i	−0.208645	+	0.208645i
$363$	8.77767e9	+	8.77767e9i	0.505537	+	0.505537i
$364$	−1.14403e9			−0.0651674
$365$	−1.95922e9	+	1.95922e9i	−0.110385	+	0.110385i
$366$	1.37581e10	+	1.37581e10i	0.766714	+	0.766714i
$367$	9.08346e9	−	9.08346e9i	0.500711	−	0.500711i	−0.410948	−	0.911659i	$-0.634802\pi$
$367$	9.08346e9	−	9.08346e9i	0.500711	−	0.500711i	0.911659	+	0.410948i	$0.134802\pi$
$368$	−9.49170e9			−0.517551
$369$	−1.05400e10	+	1.05400e10i	−0.568506	+	0.568506i
$370$		−	6.69572e9i		−	0.357265i
$371$	1.26810e9			0.0669358
$372$	−3.72603e10			−1.94569
$373$	1.97512e10			1.02037			0.510186	−	0.860064i	$-0.329577\pi$
$373$	1.97512e10			1.02037			0.510186	+	0.860064i	$0.329577\pi$
$374$	3.03131e10	+	3.03131e10i	1.54933	+	1.54933i
$375$	−4.17441e9	−	4.17441e9i	−0.211091	−	0.211091i
$376$			2.87654e10i			1.43919i
$377$	2.58941e8	−	4.40754e8i	0.0128184	−	0.0218188i
$378$	3.20637e10			1.57053
$379$	−8.72115e9	+	8.72115e9i	−0.422685	+	0.422685i	−0.886127	−	0.463442i	$-0.846614\pi$
$379$	−8.72115e9	+	8.72115e9i	−0.422685	+	0.422685i	0.463442	+	0.886127i	$0.346614\pi$
$380$	−1.44373e10	+	1.44373e10i	−0.692389	+	0.692389i
$381$		−	1.04745e10i		−	0.497087i
$382$		−	2.06951e9i		−	0.0971882i
$383$			1.77624e10i			0.825482i	0.910848	+	0.412741i	$0.135429\pi$
$383$			1.77624e10i			0.825482i	−0.910848	+	0.412741i	$0.864571\pi$
$384$	1.84010e10			0.846285
$385$	8.17331e9	+	8.17331e9i	0.372010	+	0.372010i
$386$		−	3.11021e10i		−	1.40101i
$387$	−1.25644e10	−	1.25644e10i	−0.560143	−	0.560143i
$388$	2.72966e10	−	2.72966e10i	1.20443	−	1.20443i
$389$	6.10458e9	+	6.10458e9i	0.266598	+	0.266598i	0.827728	−	0.561130i	$-0.189633\pi$
$389$	6.10458e9	+	6.10458e9i	0.266598	+	0.266598i	−0.561130	+	0.827728i	$0.689633\pi$
$390$		−	1.75921e8i		−	0.00760430i
$391$	1.94493e9	−	1.94493e9i	0.0832142	−	0.0832142i
$392$	−1.30192e9	−	1.30192e9i	−0.0551367	−	0.0551367i
$393$	−2.00463e10			−0.840357
$394$	−3.52307e10	+	3.52307e10i	−1.46196	+	1.46196i
$395$	1.06917e10	+	1.06917e10i	0.439198	+	0.439198i
$396$	5.60134e10	−	5.60134e10i	2.27778	−	2.27778i
$397$	−2.30104e10			−0.926321			−0.463160	−	0.886274i	$-0.653285\pi$
$397$	−2.30104e10			−0.926321			−0.463160	+	0.886274i	$0.653285\pi$
$398$	1.44729e10	−	1.44729e10i	0.576796	−	0.576796i
$399$		−	1.31695e10i		−	0.519609i
$400$	−7.26039e10			−2.83609
$401$	−5.69117e8			−0.0220102			−0.0110051	−	0.999939i	$-0.503503\pi$
$401$	−5.69117e8			−0.0220102			−0.0110051	+	0.999939i	$0.503503\pi$
$402$	−4.23498e10			−1.62161
$403$	7.47411e8	+	7.47411e8i	0.0283361	+	0.0283361i
$404$	7.65978e10	+	7.65978e10i	2.87535	+	2.87535i
$405$		−	3.46733e9i		−	0.128877i
$406$	−4.93151e10	+	1.28143e10i	−1.81500	+	0.471620i
$407$	2.43813e10			0.888545
$408$	−2.04998e10	+	2.04998e10i	−0.739790	+	0.739790i
$409$	−9.94638e9	+	9.94638e9i	−0.355444	+	0.355444i	−0.862131	−	0.506686i	$-0.830870\pi$
$409$	−9.94638e9	+	9.94638e9i	−0.355444	+	0.355444i	0.506686	+	0.862131i	$0.330870\pi$
$410$		−	1.86271e10i		−	0.659188i
$411$			1.04076e9i			0.0364738i
$412$		−	1.09432e11i		−	3.79799i
$413$	4.60636e10			1.58328
$414$	−4.97155e9	−	4.97155e9i	−0.169235	−	0.169235i
$415$		−	4.47698e9i		−	0.150936i
$416$	−1.61656e9	−	1.61656e9i	−0.0539782	−	0.0539782i
$417$	7.06724e9	−	7.06724e9i	0.233725	−	0.233725i
$418$	−7.27228e10	−	7.27228e10i	−2.38213	−	2.38213i
$419$			3.51412e8i			0.0114015i	0.999984	+	0.00570073i	$0.00181461\pi$
$419$			3.51412e8i			0.0114015i	−0.999984	+	0.00570073i	$0.998185\pi$
$420$	−8.96321e9	+	8.96321e9i	−0.288049	+	0.288049i
$421$	−2.06616e10	−	2.06616e10i	−0.657712	−	0.657712i	0.297126	−	0.954838i	$-0.403972\pi$
$421$	−2.06616e10	−	2.06616e10i	−0.657712	−	0.657712i	−0.954838	+	0.297126i	$0.903972\pi$
$422$	−1.76190e10			−0.555559
$423$	−8.29630e9	+	8.29630e9i	−0.259133	+	0.259133i
$424$	4.73560e9	+	4.73560e9i	0.146525	+	0.146525i
$425$	1.48772e10	−	1.48772e10i	0.456000	−	0.456000i
$426$	2.30791e10			0.700777
$427$	−2.81221e10	+	2.81221e10i	−0.845933	+	0.845933i
$428$			1.66568e10i			0.496384i
$429$	6.40587e8			0.0189125
$430$	2.22048e10			0.649492
$431$	−1.05622e10			−0.306087			−0.153044	−	0.988219i	$-0.548908\pi$
$431$	−1.05622e10			−0.306087			−0.153044	+	0.988219i	$0.548908\pi$
$432$	6.59328e10	+	6.59328e10i	1.89307	+	1.89307i
$433$	2.83100e10	+	2.83100e10i	0.805357	+	0.805357i	0.983927	−	0.178570i	$-0.0571471\pi$
$433$	2.83100e10	+	2.83100e10i	0.805357	+	0.805357i	−0.178570	+	0.983927i	$0.557147\pi$
$434$		−	1.05357e11i		−	2.96963i
$435$	−1.42447e9	−	5.48196e9i	−0.0397828	−	0.153101i
$436$	1.65873e11			4.59018
$437$	−4.66599e9	+	4.66599e9i	−0.127944	+	0.127944i
$438$	1.08227e10	−	1.08227e10i	0.294062	−	0.294062i
$439$		−	7.18599e7i		−	0.00193477i	−1.00000		0.000967383i	$-0.999692\pi$
$439$		−	7.18599e7i		−	0.00193477i	1.00000		0.000967383i	$-0.000307928\pi$
$440$			6.10448e10i			1.62869i
$441$		−	7.50983e8i		−	0.0198553i
$442$	1.33365e9			0.0349423
$443$	−2.70241e10	−	2.70241e10i	−0.701676	−	0.701676i	0.263094	−	0.964770i	$-0.415257\pi$
$443$	−2.70241e10	−	2.70241e10i	−0.701676	−	0.701676i	−0.964770	+	0.263094i	$0.915257\pi$
$444$			2.67376e10i			0.688004i
$445$	−3.43221e9	−	3.43221e9i	−0.0875252	−	0.0875252i
$446$	−7.58616e9	+	7.58616e9i	−0.191727	+	0.191727i
$447$	1.85364e10	+	1.85364e10i	0.464297	+	0.464297i
$448$			1.00758e11i			2.50130i
$449$	2.12136e9	−	2.12136e9i	0.0521951	−	0.0521951i	−0.680527	−	0.732723i	$-0.738249\pi$
$449$	2.12136e9	−	2.12136e9i	0.0521951	−	0.0521951i	0.732723	+	0.680527i	$0.238249\pi$
$450$	−3.80283e10	−	3.80283e10i	−0.927379	−	0.927379i
$451$	6.78274e10			1.63945
$452$	−3.35747e10	+	3.35747e10i	−0.804376	+	0.804376i
$453$	2.10167e10	+	2.10167e10i	0.499081	+	0.499081i
$454$	−8.74141e10	+	8.74141e10i	−2.05759	+	2.05759i
$455$	3.59590e8			0.00839000
$456$	4.91800e10	−	4.91800e10i	1.13744	−	1.13744i
$457$		−	6.86377e9i		−	0.157361i	−0.996900	−	0.0786806i	$-0.974929\pi$
$457$		−	6.86377e9i		−	0.157361i	0.996900	−	0.0786806i	$-0.0250707\pi$
$458$	6.41177e10			1.45719
$459$	−2.70204e10			−0.608753
$460$	6.35141e9			0.141853
$461$	−4.34253e10	−	4.34253e10i	−0.961478	−	0.961478i	0.0378070	−	0.999285i	$-0.487963\pi$
$461$	−4.34253e10	−	4.34253e10i	−0.961478	−	0.961478i	−0.999285	+	0.0378070i	$0.987963\pi$
$462$	−4.51491e10	−	4.51491e10i	−0.991018	−	0.991018i
$463$		−	2.12906e10i		−	0.463302i	−0.972799	−	0.231651i	$-0.925587\pi$
$463$		−	2.12906e10i		−	0.463302i	0.972799	−	0.231651i	$-0.0744127\pi$
$464$	−1.27757e11	−	7.50569e10i	−2.75622	−	1.61927i
$465$	1.17116e10			0.250499
$466$	−6.08687e9	+	6.08687e9i	−0.129077	+	0.129077i
$467$	3.51404e10	−	3.51404e10i	0.738821	−	0.738821i	−0.233529	−	0.972350i	$-0.575027\pi$
$467$	3.51404e10	−	3.51404e10i	0.738821	−	0.738821i	0.972350	+	0.233529i	$0.0750273\pi$
$468$		−	2.46434e9i		−	0.0513710i
$469$		−	8.65648e10i		−	1.78916i
$470$		−	1.46619e10i		−	0.300468i
$471$	3.58751e10			0.728971
$472$	1.72020e11	+	1.72020e11i	3.46586	+	3.46586i
$473$			8.08551e10i			1.61534i
$474$	−5.90609e10	−	5.90609e10i	−1.17000	−	1.17000i
$475$	−3.56911e10	+	3.56911e10i	−0.701109	+	0.701109i
$476$	−6.79495e10	−	6.79495e10i	−1.32360	−	1.32360i
$477$			2.73162e9i			0.0527650i
$478$	−4.99965e10	+	4.99965e10i	−0.957697	+	0.957697i
$479$	−4.67787e8	−	4.67787e8i	−0.00888599	−	0.00888599i	0.702650	−	0.711536i	$-0.252000\pi$
$479$	−4.67787e8	−	4.67787e8i	−0.00888599	−	0.00888599i	−0.711536	+	0.702650i	$0.752000\pi$
$480$	−2.53308e10			−0.477183
$481$	5.36336e8	−	5.36336e8i	0.0100197	−	0.0100197i
$482$	1.24412e10	+	1.24412e10i	0.230502	+	0.230502i
$483$	−2.89683e9	+	2.89683e9i	−0.0532273	+	0.0532273i
$484$	−2.17304e11			−3.95991
$485$	−8.57987e9	+	8.57987e9i	−0.155065	+	0.155065i
$486$			1.07911e11i			1.93428i
$487$	6.15616e10			1.09445			0.547223	−	0.836987i	$-0.315685\pi$
$487$	6.15616e10			1.09445			0.547223	+	0.836987i	$0.315685\pi$
$488$	−2.10038e11			−3.70356
$489$	1.87642e9			0.0328166
$490$	6.63597e8	+	6.63597e8i	0.0115112	+	0.0115112i
$491$	−2.44727e10	−	2.44727e10i	−0.421071	−	0.421071i	0.464501	−	0.885572i	$-0.346234\pi$
$491$	−2.44727e10	−	2.44727e10i	−0.421071	−	0.421071i	−0.885572	+	0.464501i	$0.846234\pi$
$492$			7.43825e10i			1.26943i
$493$	4.15584e10	−	1.07988e10i	0.703511	−	0.182805i
$494$	−3.19949e9			−0.0537245
$495$	−1.76061e10	+	1.76061e10i	−0.293253	+	0.293253i
$496$	2.16646e11	−	2.16646e11i	3.57951	−	3.57951i
$497$			4.71746e10i			0.773183i
$498$			2.47307e10i			0.402086i
$499$		−	1.33883e10i		−	0.215935i	−0.994154	−	0.107967i	$-0.965566\pi$
$499$		−	1.33883e10i		−	0.215935i	0.994154	−	0.107967i	$-0.0344342\pi$
$500$	1.03343e11			1.65349
$501$	−7.02074e9	−	7.02074e9i	−0.111438	−	0.111438i
$502$		−	1.26934e11i		−	1.99878i
$503$	−4.48043e10	−	4.48043e10i	−0.699919	−	0.699919i	0.264474	−	0.964393i	$-0.414802\pi$
$503$	−4.48043e10	−	4.48043e10i	−0.699919	−	0.699919i	−0.964393	+	0.264474i	$0.914802\pi$
$504$	−1.07109e11	+	1.07109e11i	−1.65998	+	1.65998i
$505$	−2.40762e10	−	2.40762e10i	−0.370188	−	0.370188i
$506$			3.19931e10i			0.488038i
$507$	−2.19911e10	+	2.19911e10i	−0.332825	+	0.332825i
$508$	1.29655e11	+	1.29655e11i	1.94686	+	1.94686i
$509$	9.04091e10			1.34692			0.673459	−	0.739225i	$-0.264808\pi$
$509$	9.04091e10			1.34692			0.673459	+	0.739225i	$0.264808\pi$
$510$	1.04488e10	−	1.04488e10i	0.154450	−	0.154450i
$511$	2.21220e10	+	2.21220e10i	0.324445	+	0.324445i
$512$	6.12275e9	−	6.12275e9i	0.0890977	−	0.0890977i
$513$	6.48234e10			0.935971
$514$	−5.52458e10	+	5.52458e10i	−0.791492	+	0.791492i
$515$			3.43965e10i			0.488974i
$516$	−8.86693e10			−1.25076
$517$	5.33887e10			0.747286
$518$	−7.56029e10			−1.05007
$519$	1.14667e10	+	1.14667e10i	0.158041	+	0.158041i
$520$	1.34285e9	+	1.34285e9i	0.0183660	+	0.0183660i
$521$			7.41399e10i			1.00624i	0.864217	+	0.503120i	$0.167814\pi$
$521$			7.41399e10i			1.00624i	−0.864217	+	0.503120i	$0.832186\pi$
$522$	−2.76034e10	−	1.06230e11i	−0.371775	−	1.43075i
$523$	−1.26338e11			−1.68860			−0.844298	−	0.535874i	$-0.819982\pi$
$523$	−1.26338e11			−1.68860			−0.844298	+	0.535874i	$0.819982\pi$
$524$	2.48137e11	−	2.48137e11i	3.29130	−	3.29130i
$525$	−2.21584e10	+	2.21584e10i	−0.291677	+	0.291677i
$526$		−	8.05874e10i		−	1.05275i
$527$			8.87851e10i			1.15106i
$528$		−	1.85681e11i		−	2.38909i
$529$	−7.62583e10			−0.973788
$530$	−2.41376e9	−	2.41376e9i	−0.0305908	−	0.0305908i
$531$			9.92255e10i			1.24809i
$532$	1.63014e11	+	1.63014e11i	2.03507	+	2.03507i
$533$	1.49205e9	−	1.49205e9i	0.0184874	−	0.0184874i
$534$	1.89594e10	+	1.89594e10i	0.233163	+	0.233163i
$535$		−	5.23558e9i		−	0.0639071i
$536$	3.23268e11	−	3.23268e11i	3.91654	−	3.91654i
$537$	2.40006e10	+	2.40006e10i	0.288619	+	0.288619i
$538$	8.90565e10			1.06301
$539$	−2.41638e9	+	2.41638e9i	−0.0286292	+	0.0286292i
$540$	−4.41192e10	−	4.41192e10i	−0.518863	−	0.518863i
$541$	−9.36578e10	+	9.36578e10i	−1.09334	+	1.09334i	−0.0981691	+	0.995170i	$0.531299\pi$
$541$	−9.36578e10	+	9.36578e10i	−1.09334	+	1.09334i	−0.995170	+	0.0981691i	$0.968701\pi$
$542$	−5.13395e10			−0.594915
$543$	−4.49718e9	+	4.49718e9i	−0.0517298	+	0.0517298i
$544$		−	1.92031e11i		−	2.19269i
$545$	−5.21372e10			−0.590965
$546$	−1.98637e9			−0.0223506
$547$	6.04649e10			0.675389			0.337694	−	0.941256i	$-0.390353\pi$
$547$	6.04649e10			0.675389			0.337694	+	0.941256i	$0.390353\pi$
$548$	−1.28827e10	−	1.28827e10i	−0.142851	−	0.142851i
$549$	−6.05777e10	−	6.05777e10i	−0.666843	−	0.666843i
$550$			2.44721e11i			2.67437i
$551$	−9.97008e10	+	2.59068e10i	−1.08166	+	0.281066i
$552$	−2.16359e10			−0.233033
$553$	1.20723e11	−	1.20723e11i	1.29089	−	1.29089i
$554$	−1.67486e10	+	1.67486e10i	−0.177803	+	0.177803i
$555$		−	8.40417e9i		−	0.0885773i
$556$			1.74960e11i			1.83079i
$557$		−	1.12204e11i		−	1.16570i	−0.812580	−	0.582849i	$-0.801938\pi$
$557$		−	1.12204e11i		−	1.16570i	0.812580	−	0.582849i	$-0.198062\pi$
$558$	2.26948e11			2.34094
$559$	1.77864e9	+	1.77864e9i	0.0182154	+	0.0182154i
$560$		−	1.04231e11i		−	1.05985i
$561$	3.80477e10	+	3.80477e10i	0.384129	+	0.384129i
$562$	−3.31338e10	+	3.31338e10i	−0.332144	+	0.332144i
$563$	−2.73044e10	−	2.73044e10i	−0.271769	−	0.271769i	0.558043	−	0.829812i	$-0.311552\pi$
$563$	−2.73044e10	−	2.73044e10i	−0.271769	−	0.271769i	−0.829812	+	0.558043i	$0.811552\pi$
$564$			5.85484e10i			0.578627i
$565$	1.05532e10	−	1.05532e10i	0.103560	−	0.103560i
$566$	1.46690e11	+	1.46690e11i	1.42934	+	1.42934i
$567$	−3.91504e10			−0.378795
$568$	−1.76169e11	+	1.76169e11i	−1.69253	+	1.69253i
$569$	−5.48006e9	−	5.48006e9i	−0.0522801	−	0.0522801i	0.680483	−	0.732763i	$-0.261770\pi$
$569$	−5.48006e9	−	5.48006e9i	−0.0522801	−	0.0522801i	−0.732763	+	0.680483i	$0.761770\pi$
$570$	−2.50673e10	+	2.50673e10i	−0.237470	+	0.237470i
$571$	3.32854e10			0.313119			0.156559	−	0.987669i	$-0.449960\pi$
$571$	3.32854e10			0.313119			0.156559	+	0.987669i	$0.449960\pi$
$572$	−7.92932e9	+	7.92932e9i	−0.0740716	+	0.0740716i
$573$		−	2.59755e9i		−	0.0240960i
$574$	−2.10323e11			−1.93749
$575$	1.57017e10			0.143640
$576$	−2.17042e11			−1.97176
$577$	5.67215e10	+	5.67215e10i	0.511734	+	0.511734i	0.915058	−	0.403323i	$-0.132145\pi$
$577$	5.67215e10	+	5.67215e10i	0.511734	+	0.511734i	−0.403323	+	0.915058i	$0.632145\pi$
$578$	−7.07126e10	−	7.07126e10i	−0.633557	−	0.633557i
$579$		−	3.90379e10i		−	0.347354i
$580$	8.54893e10	+	5.02246e10i	0.755439	+	0.443817i
$581$	−5.05506e10			−0.443631
$582$	4.73950e10	−	4.73950e10i	0.413086	−	0.413086i
$583$	8.78929e9	−	8.78929e9i	0.0760816	−	0.0760816i
$584$			1.65225e11i			1.42044i
$585$			7.74592e8i			0.00661378i
$586$			2.53693e11i			2.15139i
$587$	−1.92954e11			−1.62518			−0.812591	−	0.582835i	$-0.801944\pi$
$587$	−1.92954e11			−1.62518			−0.812591	+	0.582835i	$0.801944\pi$
$588$	−2.64990e9	−	2.64990e9i	−0.0221677	−	0.0221677i
$589$		−	2.13000e11i		−	1.76978i
$590$	−8.76794e10	−	8.76794e10i	−0.723585	−	0.723585i
$591$	−4.42200e10	+	4.42200e10i	−0.362467	+	0.362467i
$592$	−1.55463e11	−	1.55463e11i	−1.26573	−	1.26573i
$593$		−	9.39842e10i		−	0.760040i	−0.924978	−	0.380020i	$-0.875917\pi$
$593$		−	9.39842e10i		−	0.760040i	0.924978	−	0.380020i	$-0.124083\pi$
$594$	2.22236e11	−	2.22236e11i	1.78512	−	1.78512i
$595$	2.13579e10	+	2.13579e10i	0.170408	+	0.170408i
$596$	−4.58896e11			−3.63688
$597$	1.81657e10	−	1.81657e10i	0.143006	−	0.143006i
$598$	7.03778e8	+	7.03778e8i	0.00550340	+	0.00550340i
$599$	2.01303e10	−	2.01303e10i	0.156366	−	0.156366i	−0.624588	−	0.780954i	$-0.714733\pi$
$599$	2.01303e10	−	2.01303e10i	0.156366	−	0.156366i	0.780954	+	0.624588i	$0.214733\pi$
$600$	−1.65497e11			−1.27698
$601$	4.58385e10	−	4.58385e10i	0.351344	−	0.351344i	−0.509265	−	0.860610i	$-0.670083\pi$
$601$	4.58385e10	−	4.58385e10i	0.351344	−	0.351344i	0.860610	+	0.509265i	$0.170083\pi$
$602$		−	2.50720e11i		−	1.90899i
$603$	1.86469e11			1.41038
$604$	−5.20298e11			−3.90935
$605$	6.83028e10			0.509820
$606$	1.32996e11	+	1.32996e11i	0.986164	+	0.986164i
$607$	−3.49346e10	−	3.49346e10i	−0.257336	−	0.257336i	0.566634	−	0.823970i	$-0.308245\pi$
$607$	−3.49346e10	−	3.49346e10i	−0.257336	−	0.257336i	−0.823970	+	0.566634i	$0.808245\pi$
$608$			4.60693e11i			3.37130i
$609$	−6.18981e10	+	1.60840e10i	−0.449996	+	0.116930i
$610$	1.07058e11			0.773211
$611$	1.17443e9	−	1.17443e9i	0.00842682	−	0.00842682i
$612$	1.46370e11	−	1.46370e11i	1.04339	−	1.04339i
$613$		−	4.60955e10i		−	0.326450i	−0.986589	−	0.163225i	$-0.947810\pi$
$613$		−	4.60955e10i		−	0.326450i	0.986589	−	0.163225i	$-0.0521897\pi$
$614$			5.27861e11i			3.71403i
$615$		−	2.33799e10i		−	0.163434i
$616$	6.89271e11			4.78704
$617$	−9.45765e10	−	9.45765e10i	−0.652593	−	0.652593i	0.301023	−	0.953617i	$-0.402672\pi$
$617$	−9.45765e10	−	9.45765e10i	−0.652593	−	0.652593i	−0.953617	+	0.301023i	$0.902672\pi$
$618$		−	1.90006e11i		−	1.30260i
$619$	5.90151e10	+	5.90151e10i	0.401977	+	0.401977i	0.878929	−	0.476952i	$-0.158259\pi$
$619$	5.90151e10	+	5.90151e10i	0.401977	+	0.401977i	−0.476952	+	0.878929i	$0.658259\pi$
$620$	−1.44969e11	+	1.44969e11i	−0.981090	+	0.981090i
$621$	−1.42589e10	−	1.42589e10i	−0.0958784	−	0.0958784i
$622$			3.19206e11i			2.13260i
$623$	−3.87538e10	+	3.87538e10i	−0.257254	+	0.257254i
$624$	−4.08458e9	−	4.08458e9i	−0.0269407	−	0.0269407i
$625$	1.02893e11			0.674318
$626$	3.93444e11	−	3.93444e11i	2.56204	−	2.56204i
$627$	−9.12784e10	−	9.12784e10i	−0.590606	−	0.590606i
$628$	−4.44070e11	+	4.44070e11i	−2.85505	+	2.85505i
$629$	6.37114e10			0.407019
$630$	5.45940e10	−	5.45940e10i	0.346563	−	0.346563i
$631$		−	2.68027e10i		−	0.169068i	−0.996421	−	0.0845340i	$-0.973060\pi$
$631$		−	2.68027e10i		−	0.169068i	0.996421	−	0.0845340i	$-0.0269402\pi$
$632$	9.01655e11			5.65161
$633$	−2.21145e10			−0.137741
$634$	3.27980e11			2.02997
$635$	−4.07532e10	−	4.07532e10i	−0.250650	−	0.250650i
$636$	9.63873e9	+	9.63873e9i	0.0589103	+	0.0589103i
$637$			1.06310e8i			0.000645678i
$638$	−2.52989e11	+	4.30623e11i	−1.52693	+	2.59905i
$639$	−1.01619e11			−0.609495
$640$	7.15931e10	−	7.15931e10i	0.426728	−	0.426728i
$641$	−3.24782e10	+	3.24782e10i	−0.192380	+	0.192380i	−0.796724	−	0.604344i	$-0.793435\pi$
$641$	−3.24782e10	+	3.24782e10i	−0.192380	+	0.192380i	0.604344	+	0.796724i	$0.293435\pi$
$642$			2.89212e10i			0.170246i
$643$		−	1.65188e11i		−	0.966352i	−0.875523	−	0.483176i	$-0.839483\pi$
$643$		−	1.65188e11i		−	0.966352i	0.875523	−	0.483176i	$-0.160517\pi$
$644$		−	7.17152e10i		−	0.416934i
$645$	2.78705e10			0.161030
$646$	−1.90034e11	−	1.90034e11i	−1.09119	−	1.09119i
$647$			5.12902e10i			0.292697i	0.989233	+	0.146348i	$0.0467520\pi$
$647$			5.12902e10i			0.292697i	−0.989233	+	0.146348i	$0.953248\pi$
$648$	−1.46203e11	−	1.46203e11i	−0.829197	−	0.829197i
$649$	3.19270e11	−	3.19270e11i	1.79961	−	1.79961i
$650$	5.38333e9	+	5.38333e9i	0.0301577	+	0.0301577i
$651$		−	1.32239e11i		−	0.736266i
$652$	−2.32267e10	+	2.32267e10i	−0.128528	+	0.128528i
$653$	−8.26839e10	−	8.26839e10i	−0.454745	−	0.454745i	0.442181	−	0.896926i	$-0.354205\pi$
$653$	−8.26839e10	−	8.26839e10i	−0.454745	−	0.454745i	−0.896926	+	0.442181i	$0.854205\pi$
$654$	2.88005e11			1.57430
$655$	−7.79945e10	+	7.79945e10i	−0.423739	+	0.423739i
$656$	−4.32489e11	−	4.32489e11i	−2.33539	−	2.33539i
$657$	−4.76530e10	+	4.76530e10i	−0.255758	+	0.255758i
$658$	−1.65550e11			−0.883134
$659$	−7.04970e10	+	7.04970e10i	−0.373791	+	0.373791i	−0.868856	−	0.495065i	$-0.835144\pi$
$659$	−7.04970e10	+	7.04970e10i	−0.373791	+	0.373791i	0.495065	+	0.868856i	$0.335144\pi$
$660$			1.24249e11i			0.654814i
$661$	−1.55677e11			−0.815491			−0.407746	−	0.913096i	$-0.633685\pi$
$661$	−1.55677e11			−0.815491			−0.407746	+	0.913096i	$0.633685\pi$
$662$	−1.25174e11			−0.651750
$663$	1.67393e9			0.00866330
$664$	−1.88776e11	−	1.88776e11i	−0.971125	−	0.971125i
$665$	−5.12386e10	−	5.12386e10i	−0.262006	−	0.262006i
$666$		−	1.62856e11i		−	0.827765i
$667$	2.76294e10	+	1.62321e10i	0.139594	+	0.0820111i
$668$	1.73809e11			0.872902
$669$	−9.52181e9	+	9.52181e9i	−0.0475352	+	0.0475352i
$670$	−1.64771e11	+	1.64771e11i	−0.817677	+	0.817677i
$671$			3.89832e11i			1.92304i
$672$			2.86016e11i			1.40254i
$673$		−	7.20817e9i		−	0.0351370i	−0.999846	−	0.0175685i	$-0.994407\pi$
$673$		−	7.20817e9i		−	0.0351370i	0.999846	−	0.0175685i	$-0.00559251\pi$
$674$	3.27522e11			1.58709
$675$	−1.09069e11	−	1.09069e11i	−0.525397	−	0.525397i
$676$		−	5.44422e11i		−	2.60705i
$677$	2.34455e11	+	2.34455e11i	1.11610	+	1.11610i	0.992308	+	0.123794i	$0.0395063\pi$
$677$	2.34455e11	+	2.34455e11i	1.11610	+	1.11610i	0.123794	+	0.992308i	$0.460494\pi$
$678$	−5.82956e10	+	5.82956e10i	−0.275878	+	0.275878i
$679$	9.68774e10	+	9.68774e10i	0.455767	+	0.455767i
$680$			1.59518e11i			0.746058i
$681$	−1.09718e11	+	1.09718e11i	−0.510141	+	0.510141i
$682$	−7.30233e11	−	7.30233e11i	−3.37539	−	3.37539i
$683$	−1.43840e11			−0.660995			−0.330498	−	0.943807i	$-0.607217\pi$
$683$	−1.43840e11			−0.660995			−0.330498	+	0.943807i	$0.607217\pi$
$684$	−3.51149e11	+	3.51149e11i	−1.60423	+	1.60423i
$685$	4.04928e9	+	4.04928e9i	0.0183915	+	0.0183915i
$686$	3.01153e11	−	3.01153e11i	1.35985	−	1.35985i
$687$	8.04776e10			0.361284
$688$	5.15558e11	−	5.15558e11i	2.30104	−	2.30104i
$689$		−	3.86691e8i		−	0.00171588i
$690$	1.10279e10			0.0486516
$691$	−1.90222e10			−0.0834350			−0.0417175	−	0.999129i	$-0.513283\pi$
$691$	−1.90222e10			−0.0834350			−0.0417175	+	0.999129i	$0.513283\pi$
$692$	−2.83875e11			−1.23795
$693$	1.98795e11	+	1.98795e11i	0.861930	+	0.861930i
$694$	4.98509e11	+	4.98509e11i	2.14899	+	2.14899i
$695$		−	5.49932e10i		−	0.235706i
$696$	−2.91216e11	−	1.71088e11i	−1.24102	−	0.729094i
$697$	1.77241e11			0.750989
$698$	1.59086e11	−	1.59086e11i	0.670210	−	0.670210i
$699$	−7.63996e9	+	7.63996e9i	−0.0320024	+	0.0320024i
$700$		−	5.48564e11i		−	2.28473i
$701$		−	3.32060e9i		−	0.0137513i	−0.999976	−	0.00687566i	$-0.997811\pi$
$701$		−	3.32060e9i		−	0.0137513i	0.999976	−	0.00687566i	$-0.00218861\pi$
$702$		−	9.77739e9i		−	0.0402601i
$703$	−1.52847e11			−0.625800
$704$	6.98358e11	+	6.98358e11i	2.84307	+	2.84307i
$705$		−	1.84029e10i		−	0.0744955i
$706$	8.45382e10	+	8.45382e10i	0.340278	+	0.340278i
$707$	−2.71850e11	+	2.71850e11i	−1.08806	+	1.08806i
$708$	3.50125e11	+	3.50125e11i	1.39345	+	1.39345i
$709$			1.95333e11i			0.773020i	0.922285	+	0.386510i	$0.126320\pi$
$709$			1.95333e11i			0.773020i	−0.922285	+	0.386510i	$0.873680\pi$
$710$	8.97941e10	−	8.97941e10i	0.353358	−	0.353358i
$711$	2.60049e11	+	2.60049e11i	1.01760	+	1.01760i
$712$	−2.89445e11			−1.12628
$713$	−4.68528e10	+	4.68528e10i	−0.181291	+	0.181291i
$714$	−1.17980e11	−	1.17980e11i	−0.453959	−	0.453959i
$715$	2.49234e9	−	2.49234e9i	0.00953637	−	0.00953637i
$716$	−5.94170e11			−2.26078
$717$	−6.27534e10	+	6.27534e10i	−0.237444	+	0.237444i
$718$		−	7.70958e10i		−	0.290090i
$719$	8.05264e10			0.301316			0.150658	−	0.988586i	$-0.451861\pi$
$719$	8.05264e10			0.301316			0.150658	+	0.988586i	$0.451861\pi$
$720$	2.24524e11			0.835474
$721$	3.88379e11			1.43719
$722$	9.08861e10	+	9.08861e10i	0.334464	+	0.334464i
$723$	1.56157e10	+	1.56157e10i	0.0571489	+	0.0571489i
$724$		−	1.11334e11i		−	0.405204i
$725$	2.11343e11	+	1.24163e11i	0.764954	+	0.449407i
$726$	−3.77303e11			−1.35814
$727$	1.76145e11	−	1.76145e11i	0.630569	−	0.630569i	−0.317642	−	0.948211i	$-0.602891\pi$
$727$	1.76145e11	−	1.76145e11i	0.630569	−	0.630569i	0.948211	+	0.317642i	$0.102891\pi$
$728$	1.51625e10	−	1.51625e10i	0.0539814	−	0.0539814i
$729$			2.70702e10i			0.0958475i
$730$		−	8.42160e10i		−	0.296554i
$731$			2.11284e11i			0.739942i
$732$	−4.27507e11			−1.48901
$733$	8.41791e10	+	8.41791e10i	0.291601	+	0.291601i	0.837712	−	0.546112i	$-0.183893\pi$
$733$	8.41791e10	+	8.41791e10i	0.291601	+	0.291601i	−0.546112	+	0.837712i	$0.683893\pi$
$734$			3.90448e11i			1.34517i
$735$	8.32917e8	+	8.32917e8i	0.00285399	+	0.00285399i
$736$	1.01337e11	−	1.01337e11i	0.345347	−	0.345347i
$737$	−5.99986e11	−	5.99986e11i	−2.03363	−	2.03363i
$738$		−	4.53056e11i		−	1.52731i
$739$	2.58213e11	−	2.58213e11i	0.865765	−	0.865765i	−0.126236	−	0.992000i	$-0.540290\pi$
$739$	2.58213e11	−	2.58213e11i	0.865765	−	0.865765i	0.992000	+	0.126236i	$0.0402895\pi$
$740$	1.04029e11	+	1.04029e11i	0.346917	+	0.346917i
$741$	−4.01585e9			−0.0133200
$742$	−2.72543e10	+	2.72543e10i	−0.0899124	+	0.0899124i
$743$	2.09751e11	+	2.09751e11i	0.688255	+	0.688255i	0.961846	−	0.273591i	$-0.0882116\pi$
$743$	2.09751e11	+	2.09751e11i	0.688255	+	0.688255i	−0.273591	+	0.961846i	$0.588212\pi$
$744$	4.93833e11	−	4.93833e11i	1.61171	−	1.61171i
$745$	1.44240e11			0.468232
$746$	−4.24497e11	+	4.24497e11i	−1.37063	+	1.37063i
$747$		−	1.08891e11i		−	0.349711i
$748$	−9.41924e11			−3.00891
$749$	−5.91161e10			−0.187836
$750$	1.79434e11			0.567102
$751$	2.20120e11	+	2.20120e11i	0.691991	+	0.691991i	0.962670	−	0.270679i	$-0.0872480\pi$
$751$	2.20120e11	+	2.20120e11i	0.691991	+	0.691991i	−0.270679	+	0.962670i	$0.587248\pi$
$752$	−3.40423e11	−	3.40423e11i	−1.06450	−	1.06450i
$753$		−	1.59322e11i		−	0.495561i
$754$	3.90756e9	+	1.50380e10i	0.0120898	+	0.0465269i
$755$	1.63540e11			0.503310
$756$	−4.98160e11	+	4.98160e11i	−1.52504	+	1.52504i
$757$	−1.88579e11	+	1.88579e11i	−0.574261	+	0.574261i	−0.933316	−	0.359055i	$-0.883099\pi$
$757$	−1.88579e11	+	1.88579e11i	−0.574261	+	0.574261i	0.359055	+	0.933316i	$0.383099\pi$
$758$		−	3.74874e11i		−	1.13555i
$759$			4.01563e10i			0.121000i
$760$		−	3.82691e11i		−	1.14708i
$761$	−4.56938e11			−1.36244			−0.681222	−	0.732076i	$-0.738551\pi$
$761$	−4.56938e11			−1.36244			−0.681222	+	0.732076i	$0.738551\pi$
$762$	2.25120e11	+	2.25120e11i	0.667719	+	0.667719i
$763$			5.88693e11i			1.73696i
$764$	3.21531e10	+	3.21531e10i	0.0943732	+	0.0943732i
$765$	−4.60069e10	+	4.60069e10i	−0.134331	+	0.134331i
$766$	−3.81754e11	−	3.81754e11i	−1.10884	−	1.10884i
$767$		−	1.40465e10i		−	0.0405869i
$768$	−1.01905e11	+	1.01905e11i	−0.292921	+	0.292921i
$769$	3.67323e11	+	3.67323e11i	1.05037	+	1.05037i	0.998662	+	0.0517089i	$0.0164668\pi$
$769$	3.67323e11	+	3.67323e11i	1.05037	+	1.05037i	0.0517089	+	0.998662i	$0.483533\pi$
$770$	−3.51325e11			−0.999416
$771$	−6.93421e10	+	6.93421e10i	−0.196236	+	0.196236i
$772$	4.83220e11	+	4.83220e11i	1.36043	+	1.36043i
$773$	−1.93444e11	+	1.93444e11i	−0.541797	+	0.541797i	−0.924055	−	0.382259i	$-0.875146\pi$
$773$	−1.93444e11	+	1.93444e11i	−0.541797	+	0.541797i	0.382259	+	0.924055i	$0.375146\pi$
$774$	5.40075e11			1.50484
$775$	−3.58386e11	+	3.58386e11i	−0.993446	+	0.993446i
$776$			7.23558e11i			1.99538i
$777$	−9.48934e10			−0.260347
$778$	−2.62402e11			−0.716224
$779$	−4.25211e11			−1.15466
$780$	2.73321e9	+	2.73321e9i	0.00738405	+	0.00738405i
$781$	3.26970e11	+	3.26970e11i	0.878828	+	0.878828i
$782$			8.36018e10i			0.223557i
$783$	−7.91694e10	−	3.04678e11i	−0.210625	−	0.810577i
$784$	3.08151e10			0.0815642
$785$	1.39580e11	−	1.39580e11i	0.367574	−	0.367574i
$786$	4.30839e11	−	4.30839e11i	1.12882	−	1.12882i
$787$		−	6.67878e11i		−	1.74100i	−0.492171	−	0.870498i	$-0.663797\pi$
$787$		−	6.67878e11i		−	1.74100i	0.492171	−	0.870498i	$-0.336203\pi$
$788$		−	1.09473e12i		−	2.83924i
$789$		−	1.01150e11i		−	0.261010i
$790$	−4.59578e11			−1.17992
$791$	−1.19159e11	−	1.19159e11i	−0.304383	−	0.304383i
$792$			1.48476e12i			3.77359i
$793$	8.57545e9	+	8.57545e9i	0.0216852	+	0.0216852i
$794$	4.94544e11	−	4.94544e11i	1.24429	−	1.24429i
$795$	−3.02964e9	−	3.02964e9i	−0.00758443	−	0.00758443i
$796$			4.49717e11i			1.12018i
$797$	4.07465e11	−	4.07465e11i	1.00985	−	1.00985i	0.00989991	−	0.999951i	$-0.496849\pi$
$797$	4.07465e11	−	4.07465e11i	1.00985	−	1.00985i	0.999951	−	0.00989991i	$-0.00315129\pi$
$798$	2.83041e11	+	2.83041e11i	0.697971	+	0.697971i
$799$	1.39511e11			0.342312
$800$	7.75145e11	−	7.75145e11i	1.89244	−	1.89244i
$801$	−8.34796e10	−	8.34796e10i	−0.202792	−	0.202792i
$802$	1.22316e10	−	1.22316e10i	0.0295655	−	0.0295655i
$803$	3.06658e11			0.737552
$804$	6.57971e11	−	6.57971e11i	1.57465	−	1.57465i
$805$			2.25415e10i			0.0536784i
$806$	−3.21271e10			−0.0761256
$807$	1.11780e11			0.263553
$808$	−2.03039e12			−4.76359
$809$	−5.23506e11	−	5.23506e11i	−1.22216	−	1.22216i	−0.966863	−	0.255295i	$-0.917827\pi$
$809$	−5.23506e11	−	5.23506e11i	−1.22216	−	1.22216i	−0.255295	−	0.966863i	$-0.582173\pi$
$810$	7.45207e10	+	7.45207e10i	0.173116	+	0.173116i
$811$		−	5.87394e11i		−	1.35783i	−0.734216	−	0.678916i	$-0.762450\pi$
$811$		−	5.87394e11i		−	1.35783i	0.734216	−	0.678916i	$-0.237550\pi$
$812$	5.67097e11	−	9.65279e11i	1.30447	−	2.22039i
$813$	−6.44391e10			−0.147498
$814$	−5.24009e11	+	5.24009e11i	−1.19355	+	1.19355i
$815$	7.30061e9	−	7.30061e9i	0.0165474	−	0.0165474i
$816$		−	4.85208e11i		−	1.09438i
$817$		−	5.06882e11i		−	1.13768i
$818$		−	4.27540e11i		−	0.954911i
$819$	8.74610e9			0.0194392
$820$	2.89401e11	+	2.89401e11i	0.640096	+	0.640096i
$821$			3.54372e11i			0.779985i	0.920818	+	0.389993i	$0.127522\pi$
$821$			3.54372e11i			0.779985i	−0.920818	+	0.389993i	$0.872478\pi$
$822$	−2.23681e10	−	2.23681e10i	−0.0489940	−	0.0489940i
$823$	−1.45838e11	+	1.45838e11i	−0.317885	+	0.317885i	−0.847954	−	0.530069i	$-0.822166\pi$
$823$	−1.45838e11	+	1.45838e11i	−0.317885	+	0.317885i	0.530069	+	0.847954i	$0.322166\pi$
$824$	1.45036e12	+	1.45036e12i	3.14607	+	3.14607i
$825$			3.07163e11i			0.663061i
$826$	−9.90008e11	+	9.90008e11i	−2.12676	+	2.12676i
$827$	−3.19806e11	−	3.19806e11i	−0.683699	−	0.683699i	0.277133	−	0.960832i	$-0.410616\pi$
$827$	−3.19806e11	−	3.19806e11i	−0.683699	−	0.683699i	−0.960832	+	0.277133i	$0.910616\pi$
$828$	1.54482e11			0.328667
$829$	1.02979e11	−	1.02979e11i	0.218037	−	0.218037i	−0.589634	−	0.807671i	$-0.700728\pi$
$829$	1.02979e11	−	1.02979e11i	0.218037	−	0.218037i	0.807671	+	0.589634i	$0.200728\pi$
$830$	9.62202e10	+	9.62202e10i	0.202747	+	0.202747i
$831$	−2.10221e10	+	2.10221e10i	−0.0440831	+	0.0440831i
$832$	3.07247e10			0.0641202
$833$	−6.31429e9	+	6.31429e9i	−0.0131143	+	0.0131143i
$834$			3.03781e11i			0.627909i
$835$	−5.46314e10			−0.112382
$836$	2.25973e12			4.62627
$837$	6.50913e11			1.32624
$838$	−7.55262e9	−	7.55262e9i	−0.0153152	−	0.0153152i
$839$	−3.46353e11	−	3.46353e11i	−0.698991	−	0.698991i	0.265202	−	0.964193i	$-0.414561\pi$
$839$	−3.46353e11	−	3.46353e11i	−0.698991	−	0.698991i	−0.964193	+	0.265202i	$0.914561\pi$
$840$		−	2.37590e11i		−	0.477211i
$841$	2.43531e11	+	4.36966e11i	0.486822	+	0.873501i
$842$	8.88128e11			1.76696
$843$	−4.15881e10	+	4.15881e10i	−0.0823491	+	0.0823491i
$844$	2.73738e11	−	2.73738e11i	0.539468	−	0.539468i
$845$			1.71122e11i			0.335645i
$846$		−	3.56612e11i		−	0.696169i
$847$		−	7.71223e11i		−	1.49846i
$848$	−1.12087e11			−0.216756
$849$	1.84119e11	+	1.84119e11i	0.354379	+	0.354379i
$850$			6.39487e11i			1.22506i
$851$	3.36211e10	+	3.36211e10i	0.0641053	+	0.0641053i
$852$	−3.58570e11	+	3.58570e11i	−0.680480	+	0.680480i
$853$	−3.35494e11	−	3.35494e11i	−0.633708	−	0.633708i	0.315288	−	0.948996i	$-0.397899\pi$
$853$	−3.35494e11	−	3.35494e11i	−0.633708	−	0.633708i	−0.948996	+	0.315288i	$0.897899\pi$
$854$		−	1.20881e12i		−	2.27262i
$855$	1.10373e11	−	1.10373e11i	0.206537	−	0.206537i
$856$	−2.20763e11	−	2.20763e11i	−0.411180	−	0.411180i
$857$	1.01005e12			1.87249			0.936246	−	0.351346i	$-0.114276\pi$
$857$	1.01005e12			1.87249			0.936246	+	0.351346i	$0.114276\pi$
$858$	−1.37676e10	+	1.37676e10i	−0.0254045	+	0.0254045i
$859$	1.80514e11	+	1.80514e11i	0.331541	+	0.331541i	0.853172	−	0.521630i	$-0.174676\pi$
$859$	1.80514e11	+	1.80514e11i	0.331541	+	0.331541i	−0.521630	+	0.853172i	$0.674676\pi$
$860$	−3.44987e11	+	3.44987e11i	−0.630680	+	0.630680i
$861$	−2.63988e11			−0.480365
$862$	2.27005e11	−	2.27005e11i	0.411156	−	0.411156i
$863$			5.66826e11i			1.02190i	0.859611	+	0.510948i	$0.170706\pi$
$863$			5.66826e11i			1.02190i	−0.859611	+	0.510948i	$0.829294\pi$
$864$	−1.40785e12			−2.52639
$865$	8.92275e10			0.159380
$866$	−1.21689e12			−2.16361
$867$	−8.87553e10	−	8.87553e10i	−0.157079	−	0.157079i
$868$	1.63688e12	+	1.63688e12i	2.88362	+	2.88362i
$869$		−	1.67348e12i		−	2.93454i
$870$	1.48435e11	+	8.72046e10i	0.259094	+	0.152217i
$871$	−2.63968e10			−0.0458647
$872$	−2.19842e12	+	2.19842e12i	−3.80228	+	3.80228i
$873$	−2.08683e11	+	2.08683e11i	−0.359278	+	0.359278i
$874$		−	2.00565e11i		−	0.343724i
$875$			3.66771e11i			0.625696i
$876$			3.36295e11i			0.571089i
$877$	−7.97814e11			−1.34866			−0.674331	−	0.738429i	$-0.735568\pi$
$877$	−7.97814e11			−1.34866			−0.674331	+	0.738429i	$0.735568\pi$
$878$	1.54443e9	+	1.54443e9i	0.00259890	+	0.00259890i
$879$			3.18424e11i			0.533397i
$880$	−7.22433e11	−	7.22433e11i	−1.20467	−	1.20467i
$881$	−5.55613e11	+	5.55613e11i	−0.922292	+	0.922292i	−0.997191	−	0.0748988i	$-0.976137\pi$
$881$	−5.55613e11	+	5.55613e11i	−0.922292	+	0.922292i	0.0748988	+	0.997191i	$0.476137\pi$
$882$	1.61403e10	+	1.61403e10i	0.0266709	+	0.0266709i
$883$		−	1.08883e12i		−	1.79109i	−0.444966	−	0.895547i	$-0.646784\pi$
$883$		−	1.08883e12i		−	1.79109i	0.444966	−	0.895547i	$-0.353216\pi$
$884$	−2.07203e10	+	2.07203e10i	−0.0339302	+	0.0339302i
$885$	−1.10051e11	−	1.10051e11i	−0.179400	−	0.179400i
$886$	1.16162e12			1.88507
$887$	6.44230e11	−	6.44230e11i	1.04075	−	1.04075i	0.0416170	−	0.999134i	$-0.486749\pi$
$887$	6.44230e11	−	6.44230e11i	1.04075	−	1.04075i	0.999134	−	0.0416170i	$-0.0132509\pi$
$888$	−3.54370e11	−	3.54370e11i	−0.569908	−	0.569908i
$889$	−4.60154e11	+	4.60154e11i	−0.736709	+	0.736709i
$890$	1.47531e11			0.235139
$891$	−2.71354e11	+	2.71354e11i	−0.430552	+	0.430552i
$892$		−	2.35726e11i		−	0.372347i
$893$	−3.34695e11			−0.526312
$894$	−7.96779e11			−1.24735
$895$	1.86759e11			0.291065
$896$	−8.08375e11	−	8.08375e11i	−1.25424	−	1.25424i
$897$	8.83350e8	+	8.83350e8i	0.00136447	+	0.00136447i
$898$			9.11855e10i			0.140223i
$899$	−1.00113e12	+	2.60139e11i	−1.53268	+	0.398260i
$900$	1.18166e12			1.80104
$901$	2.29675e10	−	2.29675e10i	0.0348509	−	0.0348509i
$902$	−1.45776e12	+	1.45776e12i	−2.20222	+	2.20222i
$903$		−	3.14692e11i		−	0.473299i
$904$		−	8.89973e11i		−	1.33261i
$905$			3.49945e10i			0.0521681i
$906$	−9.03390e11			−1.34080
$907$	−9.19549e11	−	9.19549e11i	−1.35877	−	1.35877i	−0.875437	−	0.483332i	$-0.839426\pi$
$907$	−9.19549e11	−	9.19549e11i	−1.35877	−	1.35877i	−0.483332	−	0.875437i	$-0.660574\pi$
$908$		−	2.71623e12i		−	3.99598i
$909$	−5.85591e11	−	5.85591e11i	−0.857707	−	0.857707i
$910$	−7.72838e9	+	7.72838e9i	−0.0112700	+	0.0112700i
$911$	4.78152e11	+	4.78152e11i	0.694213	+	0.694213i	0.963156	−	0.268943i	$-0.0866743\pi$
$911$	4.78152e11	+	4.78152e11i	0.694213	+	0.694213i	−0.268943	+	0.963156i	$0.586674\pi$
$912$			1.16404e12i			1.68263i
$913$	−3.50370e11	+	3.50370e11i	−0.504247	+	0.504247i
$914$	1.47518e11	+	1.47518e11i	0.211378	+	0.211378i
$915$	1.34374e11			0.191704
$916$	−9.96169e11	+	9.96169e11i	−1.41498	+	1.41498i
$917$	8.80654e11	+	8.80654e11i	1.24545	+	1.24545i
$918$	5.80729e11	−	5.80729e11i	0.817716	−	0.817716i
$919$	1.14150e12			1.60035			0.800176	−	0.599765i	$-0.204739\pi$
$919$	1.14150e12			1.60035			0.800176	+	0.599765i	$0.204739\pi$
$920$	−8.41790e10	+	8.41790e10i	−0.117504	+	0.117504i
$921$			6.62547e11i			0.920828i
$922$	1.86661e12			2.58304
$923$	1.43853e10			0.0198203
$924$	1.40293e12			1.92463
$925$	2.57175e11	+	2.57175e11i	0.351286	+	0.351286i
$926$	4.57583e11	+	4.57583e11i	0.622337	+	0.622337i
$927$			8.36607e11i			1.13293i
$928$	2.16532e12	−	5.62649e11i	2.91964	−	0.758658i
$929$	−8.78153e11			−1.17898			−0.589491	−	0.807775i	$-0.700672\pi$
$929$	−8.78153e11			−1.17898			−0.589491	+	0.807775i	$0.700672\pi$
$930$	−2.51709e11	+	2.51709e11i	−0.336486	+	0.336486i
$931$	1.51483e10	−	1.51483e10i	0.0201635	−	0.0201635i
$932$		−	1.89138e11i		−	0.250678i
$933$			4.00653e11i			0.528740i
$934$			1.51049e12i			1.98486i
$935$	2.96065e11			0.387384
$936$	3.26614e10	+	3.26614e10i	0.0425532	+	0.0425532i
$937$			2.93398e10i			0.0380626i	0.999819	+	0.0190313i	$0.00605822\pi$
$937$			2.93398e10i			0.0380626i	−0.999819	+	0.0190313i	$0.993942\pi$
$938$	1.86047e12	+	1.86047e12i	2.40332	+	2.40332i
$939$	4.93833e11	−	4.93833e11i	0.635211	−	0.635211i
$940$	2.27795e11	+	2.27795e11i	0.291765	+	0.291765i
$941$			1.10568e12i			1.41017i	0.709122	+	0.705086i	$0.249092\pi$
$941$			1.10568e12i			1.41017i	−0.709122	+	0.705086i	$0.750908\pi$
$942$	−7.71037e11	+	7.71037e11i	−0.979200	+	0.979200i
$943$	9.35320e10	+	9.35320e10i	0.118281	+	0.118281i
$944$	−4.07153e12			−5.12707
$945$	1.56581e11	−	1.56581e11i	0.196342	−	0.196342i
$946$	−1.73776e12	−	1.73776e12i	−2.16982	−	2.16982i
$947$	5.06545e11	−	5.06545e11i	0.629822	−	0.629822i	−0.318201	−	0.948023i	$-0.603079\pi$
$947$	5.06545e11	−	5.06545e11i	0.629822	−	0.629822i	0.948023	+	0.318201i	$0.103079\pi$
$948$	1.83521e12			2.27223
$949$	6.74582e9	−	6.74582e9i	0.00831706	−	0.00831706i
$950$		−	1.53416e12i		−	1.88355i
$951$	4.11666e11			0.503295
$952$	1.80115e12			2.19282
$953$	−2.36153e11			−0.286300			−0.143150	−	0.989701i	$-0.545723\pi$
$953$	−2.36153e11			−0.286300			−0.143150	+	0.989701i	$0.545723\pi$
$954$	−5.87085e10	−	5.87085e10i	−0.0708773	−	0.0708773i
$955$	−1.01063e10	−	1.01063e10i	−0.0121501	−	0.0121501i
$956$		−	1.55355e12i		−	1.85992i
$957$	−3.17541e11	+	5.40499e11i	−0.378575	+	0.644388i
$958$	2.01076e10			0.0238725
$959$	4.57214e10	−	4.57214e10i	0.0540562	−	0.0540562i
$960$	2.40722e11	−	2.40722e11i	0.283420	−	0.283420i
$961$		−	1.28591e12i		−	1.50771i
$962$			2.30541e10i			0.0269183i
$963$		−	1.27342e11i		−	0.148070i
$964$	−3.86589e11			−0.447652
$965$	−1.51886e11	−	1.51886e11i	−0.175149	−	0.175149i
$966$		−	1.24519e11i		−	0.142997i
$967$	8.33922e11	+	8.33922e11i	0.953717	+	0.953717i	0.998975	−	0.0452579i	$-0.0144110\pi$
$967$	8.33922e11	+	8.33922e11i	0.953717	+	0.953717i	−0.0452579	+	0.998975i	$0.514411\pi$
$968$	2.88006e12	−	2.88006e12i	3.28019	−	3.28019i
$969$	−2.38522e11	−	2.38522e11i	−0.270541	−	0.270541i
$970$		−	3.68801e11i		−	0.416587i
$971$	4.11570e11	−	4.11570e11i	0.462985	−	0.462985i	−0.436648	−	0.899632i	$-0.643834\pi$
$971$	4.11570e11	−	4.11570e11i	0.462985	−	0.462985i	0.899632	+	0.436648i	$0.143834\pi$
$972$	−1.67656e12	−	1.67656e12i	−1.87826	−	1.87826i
$973$	−6.20941e11			−0.692786
$974$	−1.32310e12	+	1.32310e12i	−1.47013	+	1.47013i
$975$	6.75692e9	+	6.75692e9i	0.00747705	+	0.00747705i
$976$	2.48569e12	−	2.48569e12i	2.73935	−	2.73935i
$977$	−9.52144e11			−1.04502			−0.522510	−	0.852633i	$-0.675004\pi$
$977$	−9.52144e11			−1.04502			−0.522510	+	0.852633i	$0.675004\pi$
$978$	−4.03284e10	+	4.03284e10i	−0.0440814	+	0.0440814i
$979$			5.37211e11i			0.584809i
$980$	−2.06201e10			−0.0223556
$981$	−1.26810e12			−1.36924
$982$	1.05194e12			1.13122
$983$	9.06542e11	+	9.06542e11i	0.970899	+	0.970899i	0.999588	−	0.0286897i	$-0.00913347\pi$
$983$	9.06542e11	+	9.06542e11i	0.970899	+	0.970899i	−0.0286897	+	0.999588i	$0.509133\pi$
$984$	−9.85836e11	−	9.85836e11i	−1.05154	−	1.05154i
$985$			3.44095e11i			0.365538i
$986$	−6.61092e11	+	1.12527e12i	−0.699446	+	1.19056i
$987$	−2.07792e11			−0.218957
$988$	4.97091e10	−	4.97091e10i	0.0521684	−	0.0521684i
$989$	−1.11497e11	+	1.11497e11i	−0.116541	+	0.116541i
$990$		−	7.56789e11i		−	0.787833i
$991$			3.97401e11i			0.412035i	0.978548	+	0.206017i	$0.0660504\pi$
$991$			3.97401e11i			0.412035i	−0.978548	+	0.206017i	$0.933950\pi$
$992$			4.62597e12i			4.77701i
$993$	−1.57112e11			−0.161590
$994$	−1.01389e12	−	1.01389e12i	−1.03859	−	1.03859i
$995$		−	1.41355e11i		−	0.144218i
$996$	−3.84231e11	−	3.84231e11i	−0.390441	−	0.390441i
$997$	−6.67434e11	+	6.67434e11i	−0.675504	+	0.675504i	−0.958979	−	0.283476i	$-0.908512\pi$
$997$	−6.67434e11	+	6.67434e11i	−0.675504	+	0.675504i	0.283476	+	0.958979i	$0.408512\pi$
$998$	2.87744e11	+	2.87744e11i	0.290057	+	0.290057i
$999$		−	4.67089e11i		−	0.468962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.17.1	yes	38
29.12	odd	4	inner	29.9.c.a.12.1	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.1	✓	38	29.12	odd	4	inner
29.9.c.a.17.1	yes	38	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.4922 + 21.4922i) q^{2} +(-26.9761 + 26.9761i) q^{3} -667.831i q^{4} +209.913i q^{5} -1159.55i q^{6} +2370.17 q^{7} +(8851.17 + 8851.17i) q^{8} +5105.58i q^{9} +O(q^{10})\)	\(q+(-21.4922 + 21.4922i) q^{2} +(-26.9761 + 26.9761i) q^{3} -667.831i q^{4} +209.913i q^{5} -1159.55i q^{6} +2370.17 q^{7} +(8851.17 + 8851.17i) q^{8} +5105.58i q^{9} +(-4511.49 - 4511.49i) q^{10} +(16427.8 - 16427.8i) q^{11} +(18015.5 + 18015.5i) q^{12} -722.752i q^{13} +(-50940.2 + 50940.2i) q^{14} +(-5662.62 - 5662.62i) q^{15} -209498. q^{16} +(42927.9 - 42927.9i) q^{17} +(-109730. - 109730. i) q^{18} +(-102986. + 102986. i) q^{19} +140186. q^{20} +(-63937.9 + 63937.9i) q^{21} +706140. i q^{22} +45306.9 q^{23} -477540. q^{24} +346562. q^{25} +(15533.5 + 15533.5i) q^{26} +(-314719. - 314719. i) q^{27} -1.58287e6i q^{28} +(609827. + 358270. i) q^{29} +243404. q^{30} +(-1.03412e6 + 1.03412e6i) q^{31} +(2.23667e6 - 2.23667e6i) q^{32} +886316. i q^{33} +1.84523e6i q^{34} +497529. i q^{35} +3.40967e6 q^{36} +(742075. + 742075. i) q^{37} -4.42681e6i q^{38} +(19497.0 + 19497.0i) q^{39} +(-1.85797e6 + 1.85797e6i) q^{40} +(2.06441e6 + 2.06441e6i) q^{41} -2.74834e6i q^{42} +(-2.46092e6 + 2.46092e6i) q^{43} +(-1.09710e7 - 1.09710e7i) q^{44} -1.07173e6 q^{45} +(-973747. + 973747. i) q^{46} +(1.62495e6 + 1.62495e6i) q^{47} +(5.65143e6 - 5.65143e6i) q^{48} -147091. q^{49} +(-7.44838e6 + 7.44838e6i) q^{50} +2.31605e6i q^{51} -482676. q^{52} +535025. q^{53} +1.35280e7 q^{54} +(3.44840e6 + 3.44840e6i) q^{55} +(2.09788e7 + 2.09788e7i) q^{56} -5.55633e6i q^{57} +(-2.08066e7 + 5.40650e6i) q^{58} +1.94347e7 q^{59} +(-3.78167e6 + 3.78167e6i) q^{60} +(-1.18650e7 + 1.18650e7i) q^{61} -4.44510e7i q^{62} +1.21011e7i q^{63} +4.25107e7i q^{64} +151715. q^{65} +(-1.90489e7 - 1.90489e7i) q^{66} -3.65226e7i q^{67} +(-2.86686e7 - 2.86686e7i) q^{68} +(-1.22220e6 + 1.22220e6i) q^{69} +(-1.06930e7 - 1.06930e7i) q^{70} +1.99035e7i q^{71} +(-4.51904e7 + 4.51904e7i) q^{72} +(9.33351e6 + 9.33351e6i) q^{73} -3.18977e7 q^{74} +(-9.34888e6 + 9.34888e6i) q^{75} +(6.87775e7 + 6.87775e7i) q^{76} +(3.89367e7 - 3.89367e7i) q^{77} -838068. q^{78} +(5.09343e7 - 5.09343e7i) q^{79} -4.39762e7i q^{80} -1.65180e7 q^{81} -8.87374e7 q^{82} -2.13278e7 q^{83} +(4.26997e7 + 4.26997e7i) q^{84} +(9.01110e6 + 9.01110e6i) q^{85} -1.05781e8i q^{86} +(-2.61155e7 + 6.78600e6i) q^{87} +2.90811e8 q^{88} +(-1.63507e7 + 1.63507e7i) q^{89} +(2.30338e7 - 2.30338e7i) q^{90} -1.71305e6i q^{91} -3.02574e7i q^{92} -5.57929e7i q^{93} -6.98475e7 q^{94} +(-2.16181e7 - 2.16181e7i) q^{95} +1.20673e8i q^{96} +(4.08736e7 + 4.08736e7i) q^{97} +(3.16130e6 - 3.16130e6i) q^{98} +(8.38736e7 + 8.38736e7i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more