LMFDB - Embedded newform 29.9.c.a.12.1

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			12.1
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.1

$q$-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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

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

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 $

$2$	−21.4922	−	21.4922i	−1.34326	−	1.34326i	−0.892789	−	0.450475i	$-0.851255\pi$
$2$	−21.4922	−	21.4922i	−1.34326	−	1.34326i	−0.450475	−	0.892789i	$-0.648745\pi$
$3$	−26.9761	−	26.9761i	−0.333038	−	0.333038i	0.520701	−	0.853739i	$-0.325671\pi$
$3$	−26.9761	−	26.9761i	−0.333038	−	0.333038i	−0.853739	+	0.520701i	$0.825671\pi$
$4$			667.831i			2.60872i
$5$		−	209.913i		−	0.335860i	−0.985799	−	0.167930i	$-0.946292\pi$
$5$		−	209.913i		−	0.335860i	0.985799	−	0.167930i	$-0.0537083\pi$
$6$			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	0.991434	+	0.130607i	$0.0416928\pi$
$11$	16427.8	+	16427.8i	1.12204	+	1.12204i	0.130607	+	0.991434i	$0.458307\pi$
$12$	18015.5	−	18015.5i	0.868801	−	0.868801i
$13$			722.752i			0.0253056i	0.999920	+	0.0126528i	$0.00402761\pi$
$13$			722.752i			0.0253056i	−0.999920	+	0.0126528i	$0.995972\pi$
$14$	−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	0.915743	−	0.401765i	$-0.131603\pi$
$17$	42927.9	+	42927.9i	0.513977	+	0.513977i	−0.401765	+	0.915743i	$0.631603\pi$
$18$	−109730.	+	109730.i	−1.04529	+	1.04529i
$19$	−102986.	−	102986.i	−0.790251	−	0.790251i	0.191284	−	0.981535i	$-0.438735\pi$
$19$	−102986.	−	102986.i	−0.790251	−	0.790251i	−0.981535	+	0.191284i	$0.938735\pi$
$20$	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	−0.991777	−	0.127980i	$-0.959151\pi$
$31$	−1.03412e6	−	1.03412e6i	−1.11976	−	1.11976i	−0.127980	−	0.991777i	$-0.540849\pi$
$32$	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	−0.480852	−	0.876802i	$-0.659672\pi$
$37$	742075.	−	742075.i	0.395950	−	0.395950i	0.876802	+	0.480852i	$0.159672\pi$
$38$			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	−0.240165	−	0.970732i	$-0.577202\pi$
$41$	2.06441e6	−	2.06441e6i	0.730567	−	0.730567i	0.970732	+	0.240165i	$0.0772016\pi$
$42$			2.74834e6i			0.883228i
$43$	−2.46092e6	−	2.46092e6i	−0.719820	−	0.719820i	0.248748	−	0.968568i	$-0.419981\pi$
$43$	−2.46092e6	−	2.46092e6i	−0.719820	−	0.719820i	−0.968568	+	0.248748i	$0.919981\pi$
$44$	−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	−0.520723	−	0.853726i	$-0.674338\pi$
$47$	1.62495e6	−	1.62495e6i	0.333003	−	0.333003i	0.853726	+	0.520723i	$0.174338\pi$
$48$	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	0.134040	−	0.990976i	$-0.457205\pi$
$61$	−1.18650e7	−	1.18650e7i	−0.856936	−	0.856936i	−0.990976	+	0.134040i	$0.957205\pi$
$62$			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	$0.361043\pi$
$67$			3.65226e7i			1.81243i	−0.422813	+	0.906217i	$0.638957\pi$
$68$	−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	$-0.871915\pi$
$71$		−	1.99035e7i		−	0.783240i	0.920127	−	0.391620i	$-0.128085\pi$
$72$	−4.51904e7	−	4.51904e7i	−1.68157	−	1.68157i
$73$	9.33351e6	−	9.33351e6i	0.328665	−	0.328665i	−0.523414	−	0.852079i	$-0.675342\pi$
$73$	9.33351e6	−	9.33351e6i	0.328665	−	0.328665i	0.852079	+	0.523414i	$0.175342\pi$
$74$	−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	0.923085	+	0.384595i	$0.125659\pi$
$79$	5.09343e7	+	5.09343e7i	1.30768	+	1.30768i	0.384595	+	0.923085i	$0.374341\pi$
$80$			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	0.564698	−	0.825298i	$-0.308993\pi$
$89$	−1.63507e7	−	1.63507e7i	−0.260600	−	0.260600i	−0.825298	+	0.564698i	$0.808993\pi$
$90$	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	−0.437515	−	0.899211i	$-0.644141\pi$
$97$	4.08736e7	−	4.08736e7i	0.461696	−	0.461696i	0.899211	+	0.437515i	$0.144141\pi$
$98$	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	−0.994144	−	0.108065i	$-0.965535\pi$
$101$	−1.14696e8	−	1.14696e8i	−1.10221	−	1.10221i	−0.108065	−	0.994144i	$-0.534465\pi$
$102$	−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	$-0.657691\pi$
$109$		−	2.48376e8i		−	1.75956i	0.475384	−	0.879778i	$-0.342309\pi$
$110$	−1.48228e8			−1.01242
$111$	−4.00365e7			−0.263733
$112$	−4.96546e8			−3.15564
$113$	−5.02743e7	+	5.02743e7i	−0.308342	+	0.308342i	−0.844266	−	0.535924i	$-0.819963\pi$
$113$	−5.02743e7	+	5.02743e7i	−0.308342	+	0.308342i	0.535924	+	0.844266i	$0.319963\pi$
$114$	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	0.227489	−	0.973781i	$-0.426948\pi$
$127$	−1.94144e8	−	1.94144e8i	−0.746292	−	0.746292i	−0.973781	+	0.227489i	$0.926948\pi$
$128$	−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	0.311363	−	0.950291i	$-0.399215\pi$
$131$	3.71557e8	−	3.71557e8i	1.26165	−	1.26165i	0.950291	−	0.311363i	$-0.100785\pi$
$132$	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	0.733956	−	0.679197i	$-0.237672\pi$
$137$	1.92903e7	+	1.92903e7i	0.0547593	+	0.0547593i	−0.679197	+	0.733956i	$0.737672\pi$
$138$			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	$0.245511\pi$
$149$			6.87144e8i			1.39413i	−0.717009	+	0.697064i	$0.754489\pi$
$150$			4.01856e8i			0.793790i
$151$			7.79086e8i			1.49857i	0.662246	+	0.749286i	$0.269603\pi$
$151$			7.79086e8i			1.49857i	−0.662246	+	0.749286i	$0.730397\pi$
$152$	−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	−0.0993759	+	0.995050i	$0.531685\pi$
$157$	−6.64944e8	+	6.64944e8i	−1.09443	+	1.09443i	−0.995050	+	0.0993759i	$0.968315\pi$
$158$		−	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	−0.731312	−	0.682043i	$-0.761092\pi$
$163$	−3.47793e7	+	3.47793e7i	−0.0492686	+	0.0492686i	0.682043	+	0.731312i	$0.261092\pi$
$164$	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	$-0.946494\pi$
$167$		−	2.60258e8i		−	0.334610i	0.985905	−	0.167305i	$-0.0535064\pi$
$168$	−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	$0.0762531\pi$
$173$			4.25070e8i			0.474543i	−0.971443	+	0.237272i	$0.923747\pi$
$174$	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	$0.142656\pi$
$179$			8.89701e8i			0.866626i	−0.901243	+	0.433313i	$0.857344\pi$
$180$		−	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	0.688787	−	0.724963i	$-0.258143\pi$
$191$	−4.81455e7	−	4.81455e7i	−0.0361761	−	0.0361761i	−0.724963	+	0.688787i	$0.758143\pi$
$192$	−1.14677e9	+	1.14677e9i	−0.843864	+	0.843864i
$193$	−7.23566e8	−	7.23566e8i	−0.521493	−	0.521493i	0.396529	−	0.918022i	$-0.370215\pi$
$193$	−7.23566e8	−	7.23566e8i	−0.521493	−	0.521493i	−0.918022	+	0.396529i	$0.870215\pi$
$194$	−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	−0.596109	−	0.802904i	$-0.703287\pi$
$211$	4.09891e8	−	4.09891e8i	0.206794	−	0.206794i	0.802904	+	0.596109i	$0.203287\pi$
$212$			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	−0.924234	−	0.381828i	$-0.875295\pi$
$229$	−1.49165e9	+	1.49165e9i	−0.542406	+	0.542406i	0.381828	+	0.924234i	$0.375295\pi$
$230$	−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	$0.0273444\pi$
$241$			5.78872e8i			0.171599i	−0.996312	+	0.0857994i	$0.972656\pi$
$242$	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	0.229345	−	0.973345i	$-0.426342\pi$
$251$	−2.95303e9	−	2.95303e9i	−0.744000	−	0.744000i	−0.973345	+	0.229345i	$0.926342\pi$
$252$	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	0.483489	−	0.875350i	$-0.339369\pi$
$263$	−1.87480e9	−	1.87480e9i	−0.391862	−	0.391862i	−0.875350	+	0.483489i	$0.839369\pi$
$264$	−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	−0.876707	−	0.481026i	$-0.840264\pi$
$269$	−2.07183e9	+	2.07183e9i	−0.395681	+	0.395681i	0.481026	+	0.876707i	$0.340264\pi$
$270$		−	2.83970e9i		−	0.534339i
$271$	1.19437e9	−	1.19437e9i	0.221444	−	0.221444i	−0.587662	−	0.809106i	$-0.699952\pi$
$271$	1.19437e9	−	1.19437e9i	0.221444	−	0.221444i	0.809106	+	0.587662i	$0.199952\pi$
$272$	−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	$0.178575\pi$
$283$			6.82528e9i			1.06408i	−0.846719	+	0.532041i	$0.821425\pi$
$284$	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	0.983221	−	0.182416i	$-0.0583918\pi$
$293$	5.90198e9	+	5.90198e9i	0.800805	+	0.800805i	−0.182416	+	0.983221i	$0.558392\pi$
$294$		−	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	0.840218	+	0.542248i	$0.182427\pi$
$307$	1.22803e10	+	1.22803e10i	1.38247	+	1.38247i	0.542248	+	0.840218i	$0.317573\pi$
$308$	−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	0.982112	−	0.188299i	$-0.0602973\pi$
$311$	7.42608e9	+	7.42608e9i	0.793813	+	0.793813i	−0.188299	+	0.982112i	$0.560297\pi$
$312$		−	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	−0.975520	−	0.219909i	$-0.929424\pi$
$317$	−7.63020e9	+	7.63020e9i	−0.755612	+	0.755612i	0.219909	+	0.975520i	$0.429424\pi$
$318$			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	−0.575325	−	0.817925i	$-0.695125\pi$
$331$	2.91207e9	−	2.91207e9i	0.242599	−	0.242599i	0.817925	+	0.575325i	$0.195125\pi$
$332$		−	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	−0.937836	−	0.347079i	$-0.887174\pi$
$337$	−7.61954e9	+	7.61954e9i	−0.590757	+	0.590757i	0.347079	+	0.937836i	$0.387174\pi$
$338$	−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	$0.295122\pi$
$347$			2.31949e10i			1.59983i	−0.600113	+	0.799915i	$0.704878\pi$
$348$	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	$0.0404260\pi$
$353$			3.93343e9i			0.253322i	−0.991946	+	0.126661i	$0.959574\pi$
$354$			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	0.651053	−	0.759032i	$-0.274328\pi$
$359$	−1.79357e9	−	1.79357e9i	−0.107980	−	0.107980i	−0.759032	+	0.651053i	$0.774328\pi$
$360$	−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	0.911659	−	0.410948i	$-0.134802\pi$
$367$	9.08346e9	+	9.08346e9i	0.500711	+	0.500711i	−0.410948	+	0.911659i	$0.634802\pi$
$368$	−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	0.463442	−	0.886127i	$-0.346614\pi$
$379$	−8.72115e9	−	8.72115e9i	−0.422685	−	0.422685i	−0.886127	+	0.463442i	$0.846614\pi$
$380$	−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	$-0.864571\pi$
$383$		−	1.77624e10i		−	0.825482i	0.910848	−	0.412741i	$-0.135429\pi$
$384$	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	−0.561130	−	0.827728i	$-0.689633\pi$
$389$	6.10458e9	−	6.10458e9i	0.266598	−	0.266598i	0.827728	+	0.561130i	$0.189633\pi$
$390$			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	0.506686	−	0.862131i	$-0.330870\pi$
$409$	−9.94638e9	−	9.94638e9i	−0.355444	−	0.355444i	−0.862131	+	0.506686i	$0.830870\pi$
$410$			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	$-0.998185\pi$
$419$		−	3.51412e8i		−	0.0114015i	0.999984	−	0.00570073i	$-0.00181461\pi$
$420$	−8.96321e9	−	8.96321e9i	−0.288049	−	0.288049i
$421$	−2.06616e10	+	2.06616e10i	−0.657712	+	0.657712i	−0.954838	−	0.297126i	$-0.903972\pi$
$421$	−2.06616e10	+	2.06616e10i	−0.657712	+	0.657712i	0.297126	+	0.954838i	$0.403972\pi$
$422$	−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	−0.178570	−	0.983927i	$-0.557147\pi$
$433$	2.83100e10	−	2.83100e10i	0.805357	−	0.805357i	0.983927	+	0.178570i	$0.0571471\pi$
$434$			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	$0.000307928\pi$
$439$			7.18599e7i			0.00193477i	−1.00000		0.000967383i	$0.999692\pi$
$440$		−	6.10448e10i		−	1.62869i
$441$			7.50983e8i			0.0198553i
$442$	1.33365e9			0.0349423
$443$	−2.70241e10	+	2.70241e10i	−0.701676	+	0.701676i	−0.964770	−	0.263094i	$-0.915257\pi$
$443$	−2.70241e10	+	2.70241e10i	−0.701676	+	0.701676i	0.263094	+	0.964770i	$0.415257\pi$
$444$		−	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	0.732723	−	0.680527i	$-0.238249\pi$
$449$	2.12136e9	+	2.12136e9i	0.0521951	+	0.0521951i	−0.680527	+	0.732723i	$0.738249\pi$
$450$	−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	$0.0250707\pi$
$457$			6.86377e9i			0.157361i	−0.996900	+	0.0786806i	$0.974929\pi$
$458$	6.41177e10			1.45719
$459$	−2.70204e10			−0.608753
$460$	6.35141e9			0.141853
$461$	−4.34253e10	+	4.34253e10i	−0.961478	+	0.961478i	−0.999285	−	0.0378070i	$-0.987963\pi$
$461$	−4.34253e10	+	4.34253e10i	−0.961478	+	0.961478i	0.0378070	+	0.999285i	$0.487963\pi$
$462$	−4.51491e10	+	4.51491e10i	−0.991018	+	0.991018i
$463$			2.12906e10i			0.463302i	0.972799	+	0.231651i	$0.0744127\pi$
$463$			2.12906e10i			0.463302i	−0.972799	+	0.231651i	$0.925587\pi$
$464$	−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	0.972350	−	0.233529i	$-0.0750273\pi$
$467$	3.51404e10	+	3.51404e10i	0.738821	+	0.738821i	−0.233529	+	0.972350i	$0.575027\pi$
$468$			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	−0.711536	−	0.702650i	$-0.752000\pi$
$479$	−4.67787e8	+	4.67787e8i	−0.00888599	+	0.00888599i	0.702650	+	0.711536i	$0.252000\pi$
$480$	−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	−0.885572	−	0.464501i	$-0.846234\pi$
$491$	−2.44727e10	+	2.44727e10i	−0.421071	+	0.421071i	0.464501	+	0.885572i	$0.346234\pi$
$492$		−	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	$0.0344342\pi$
$499$			1.33883e10i			0.215935i	−0.994154	+	0.107967i	$0.965566\pi$
$500$	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	−0.964393	−	0.264474i	$-0.914802\pi$
$503$	−4.48043e10	+	4.48043e10i	−0.699919	+	0.699919i	0.264474	+	0.964393i	$0.414802\pi$
$504$	−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	$-0.832186\pi$
$521$		−	7.41399e10i		−	1.00624i	0.864217	−	0.503120i	$-0.167814\pi$
$522$	−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	−0.995170	−	0.0981691i	$-0.968701\pi$
$541$	−9.36578e10	−	9.36578e10i	−1.09334	−	1.09334i	−0.0981691	−	0.995170i	$-0.531299\pi$
$542$	−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	$0.198062\pi$
$557$			1.12204e11i			1.16570i	−0.812580	+	0.582849i	$0.801938\pi$
$558$	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	−0.829812	−	0.558043i	$-0.811552\pi$
$563$	−2.73044e10	+	2.73044e10i	−0.271769	+	0.271769i	0.558043	+	0.829812i	$0.311552\pi$
$564$		−	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	−0.732763	−	0.680483i	$-0.761770\pi$
$569$	−5.48006e9	+	5.48006e9i	−0.0522801	+	0.0522801i	0.680483	+	0.732763i	$0.261770\pi$
$570$	−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	−0.403323	−	0.915058i	$-0.632145\pi$
$577$	5.67215e10	−	5.67215e10i	0.511734	−	0.511734i	0.915058	+	0.403323i	$0.132145\pi$
$578$	−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	$0.124083\pi$
$593$			9.39842e10i			0.760040i	−0.924978	+	0.380020i	$0.875917\pi$
$594$	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	0.780954	−	0.624588i	$-0.214733\pi$
$599$	2.01303e10	+	2.01303e10i	0.156366	+	0.156366i	−0.624588	+	0.780954i	$0.714733\pi$
$600$	−1.65497e11			−1.27698
$601$	4.58385e10	+	4.58385e10i	0.351344	+	0.351344i	0.860610	−	0.509265i	$-0.170083\pi$
$601$	4.58385e10	+	4.58385e10i	0.351344	+	0.351344i	−0.509265	+	0.860610i	$0.670083\pi$
$602$			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	−0.823970	−	0.566634i	$-0.808245\pi$
$607$	−3.49346e10	+	3.49346e10i	−0.257336	+	0.257336i	0.566634	+	0.823970i	$0.308245\pi$
$608$		−	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	$0.0521897\pi$
$613$			4.60955e10i			0.326450i	−0.986589	+	0.163225i	$0.947810\pi$
$614$		−	5.27861e11i		−	3.71403i
$615$			2.33799e10i			0.163434i
$616$	6.89271e11			4.78704
$617$	−9.45765e10	+	9.45765e10i	−0.652593	+	0.652593i	−0.953617	−	0.301023i	$-0.902672\pi$
$617$	−9.45765e10	+	9.45765e10i	−0.652593	+	0.652593i	0.301023	+	0.953617i	$0.402672\pi$
$618$			1.90006e11i			1.30260i
$619$	5.90151e10	−	5.90151e10i	0.401977	−	0.401977i	−0.476952	−	0.878929i	$-0.658259\pi$
$619$	5.90151e10	−	5.90151e10i	0.401977	−	0.401977i	0.878929	+	0.476952i	$0.158259\pi$
$620$	−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	$0.0269402\pi$
$631$			2.68027e10i			0.169068i	−0.996421	+	0.0845340i	$0.973060\pi$
$632$	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	0.604344	−	0.796724i	$-0.293435\pi$
$641$	−3.24782e10	−	3.24782e10i	−0.192380	−	0.192380i	−0.796724	+	0.604344i	$0.793435\pi$
$642$		−	2.89212e10i		−	0.170246i
$643$			1.65188e11i			0.966352i	0.875523	+	0.483176i	$0.160517\pi$
$643$			1.65188e11i			0.966352i	−0.875523	+	0.483176i	$0.839483\pi$
$644$			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	$-0.953248\pi$
$647$		−	5.12902e10i		−	0.292697i	0.989233	−	0.146348i	$-0.0467520\pi$
$648$	−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	−0.896926	−	0.442181i	$-0.854205\pi$
$653$	−8.26839e10	+	8.26839e10i	−0.454745	+	0.454745i	0.442181	+	0.896926i	$0.354205\pi$
$654$	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	0.495065	−	0.868856i	$-0.335144\pi$
$659$	−7.04970e10	−	7.04970e10i	−0.373791	−	0.373791i	−0.868856	+	0.495065i	$0.835144\pi$
$660$		−	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	$0.00559251\pi$
$673$			7.20817e9i			0.0351370i	−0.999846	+	0.0175685i	$0.994407\pi$
$674$	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	0.123794	−	0.992308i	$-0.460494\pi$
$677$	2.34455e11	−	2.34455e11i	1.11610	−	1.11610i	0.992308	−	0.123794i	$-0.0395063\pi$
$678$	−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	$0.00218861\pi$
$701$			3.32060e9i			0.0137513i	−0.999976	+	0.00687566i	$0.997811\pi$
$702$			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	$-0.873680\pi$
$709$		−	1.95333e11i		−	0.773020i	0.922285	−	0.386510i	$-0.126320\pi$
$710$	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	0.948211	−	0.317642i	$-0.102891\pi$
$727$	1.76145e11	+	1.76145e11i	0.630569	+	0.630569i	−0.317642	+	0.948211i	$0.602891\pi$
$728$	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	−0.546112	−	0.837712i	$-0.683893\pi$
$733$	8.41791e10	−	8.41791e10i	0.291601	−	0.291601i	0.837712	+	0.546112i	$0.183893\pi$
$734$		−	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	0.992000	−	0.126236i	$-0.0402895\pi$
$739$	2.58213e11	+	2.58213e11i	0.865765	+	0.865765i	−0.126236	+	0.992000i	$0.540290\pi$
$740$	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	−0.273591	−	0.961846i	$-0.588212\pi$
$743$	2.09751e11	−	2.09751e11i	0.688255	−	0.688255i	0.961846	+	0.273591i	$0.0882116\pi$
$744$	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	−0.270679	−	0.962670i	$-0.587248\pi$
$751$	2.20120e11	−	2.20120e11i	0.691991	−	0.691991i	0.962670	+	0.270679i	$0.0872480\pi$
$752$	−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	0.359055	−	0.933316i	$-0.383099\pi$
$757$	−1.88579e11	−	1.88579e11i	−0.574261	−	0.574261i	−0.933316	+	0.359055i	$0.883099\pi$
$758$			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	0.0517089	−	0.998662i	$-0.483533\pi$
$769$	3.67323e11	−	3.67323e11i	1.05037	−	1.05037i	0.998662	−	0.0517089i	$-0.0164668\pi$
$770$	−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	0.382259	−	0.924055i	$-0.375146\pi$
$773$	−1.93444e11	−	1.93444e11i	−0.541797	−	0.541797i	−0.924055	+	0.382259i	$0.875146\pi$
$774$	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	$0.336203\pi$
$787$			6.67878e11i			1.74100i	−0.492171	+	0.870498i	$0.663797\pi$
$788$			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	0.999951	+	0.00989991i	$0.00315129\pi$
$797$	4.07465e11	+	4.07465e11i	1.00985	+	1.00985i	0.00989991	+	0.999951i	$0.496849\pi$
$798$	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	−0.255295	+	0.966863i	$0.582173\pi$
$809$	−5.23506e11	+	5.23506e11i	−1.22216	+	1.22216i	−0.966863	+	0.255295i	$0.917827\pi$
$810$	7.45207e10	−	7.45207e10i	0.173116	−	0.173116i
$811$			5.87394e11i			1.35783i	0.734216	+	0.678916i	$0.237550\pi$
$811$			5.87394e11i			1.35783i	−0.734216	+	0.678916i	$0.762450\pi$
$812$	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	$-0.872478\pi$
$821$		−	3.54372e11i		−	0.779985i	0.920818	−	0.389993i	$-0.127522\pi$
$822$	−2.23681e10	+	2.23681e10i	−0.0489940	+	0.0489940i
$823$	−1.45838e11	−	1.45838e11i	−0.317885	−	0.317885i	0.530069	−	0.847954i	$-0.322166\pi$
$823$	−1.45838e11	−	1.45838e11i	−0.317885	−	0.317885i	−0.847954	+	0.530069i	$0.822166\pi$
$824$	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	−0.960832	−	0.277133i	$-0.910616\pi$
$827$	−3.19806e11	+	3.19806e11i	−0.683699	+	0.683699i	0.277133	+	0.960832i	$0.410616\pi$
$828$	1.54482e11			0.328667
$829$	1.02979e11	+	1.02979e11i	0.218037	+	0.218037i	0.807671	−	0.589634i	$-0.200728\pi$
$829$	1.02979e11	+	1.02979e11i	0.218037	+	0.218037i	−0.589634	+	0.807671i	$0.700728\pi$
$830$	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	−0.964193	−	0.265202i	$-0.914561\pi$
$839$	−3.46353e11	+	3.46353e11i	−0.698991	+	0.698991i	0.265202	+	0.964193i	$0.414561\pi$
$840$			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	−0.948996	−	0.315288i	$-0.897899\pi$
$853$	−3.35494e11	+	3.35494e11i	−0.633708	+	0.633708i	0.315288	+	0.948996i	$0.397899\pi$
$854$			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	−0.521630	−	0.853172i	$-0.674676\pi$
$859$	1.80514e11	−	1.80514e11i	0.331541	−	0.331541i	0.853172	+	0.521630i	$0.174676\pi$
$860$	−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	$-0.829294\pi$
$863$		−	5.66826e11i		−	1.02190i	0.859611	−	0.510948i	$-0.170706\pi$
$864$	−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	0.0748988	−	0.997191i	$-0.476137\pi$
$881$	−5.55613e11	−	5.55613e11i	−0.922292	−	0.922292i	−0.997191	+	0.0748988i	$0.976137\pi$
$882$	1.61403e10	−	1.61403e10i	0.0266709	−	0.0266709i
$883$			1.08883e12i			1.79109i	0.444966	+	0.895547i	$0.353216\pi$
$883$			1.08883e12i			1.79109i	−0.444966	+	0.895547i	$0.646784\pi$
$884$	−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	0.999134	+	0.0416170i	$0.0132509\pi$
$887$	6.44230e11	+	6.44230e11i	1.04075	+	1.04075i	0.0416170	+	0.999134i	$0.486749\pi$
$888$	−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	−0.483332	+	0.875437i	$0.660574\pi$
$907$	−9.19549e11	+	9.19549e11i	−1.35877	+	1.35877i	−0.875437	+	0.483332i	$0.839426\pi$
$908$			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	−0.268943	−	0.963156i	$-0.586674\pi$
$911$	4.78152e11	−	4.78152e11i	0.694213	−	0.694213i	0.963156	+	0.268943i	$0.0866743\pi$
$912$		−	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	$-0.993942\pi$
$937$		−	2.93398e10i		−	0.0380626i	0.999819	−	0.0190313i	$-0.00605822\pi$
$938$	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	$-0.750908\pi$
$941$		−	1.10568e12i		−	1.41017i	0.709122	−	0.705086i	$-0.249092\pi$
$942$	−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	0.948023	−	0.318201i	$-0.103079\pi$
$947$	5.06545e11	+	5.06545e11i	0.629822	+	0.629822i	−0.318201	+	0.948023i	$0.603079\pi$
$948$	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	−0.0452579	−	0.998975i	$-0.514411\pi$
$967$	8.33922e11	−	8.33922e11i	0.953717	−	0.953717i	0.998975	+	0.0452579i	$0.0144110\pi$
$968$	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	0.899632	−	0.436648i	$-0.143834\pi$
$971$	4.11570e11	+	4.11570e11i	0.462985	+	0.462985i	−0.436648	+	0.899632i	$0.643834\pi$
$972$	−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	−0.0286897	−	0.999588i	$-0.509133\pi$
$983$	9.06542e11	−	9.06542e11i	0.970899	−	0.970899i	0.999588	+	0.0286897i	$0.00913347\pi$
$984$	−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	$-0.933950\pi$
$991$		−	3.97401e11i		−	0.412035i	0.978548	−	0.206017i	$-0.0660504\pi$
$992$		−	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	0.283476	−	0.958979i	$-0.408512\pi$
$997$	−6.67434e11	−	6.67434e11i	−0.675504	−	0.675504i	−0.958979	+	0.283476i	$0.908512\pi$
$998$	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.12.1	✓	38
29.17	odd	4	inner	29.9.c.a.17.1	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.1	✓	38	1.1	even	1	trivial
29.9.c.a.17.1	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)

\(f(q)\)	\(=\)	\(q+(-21.4922 - 21.4922i) q^{2} +(-26.9761 - 26.9761i) q^{3} +667.831i q^{4} -209.913i q^{5} +1159.55i q^{6} +2370.17 q^{7} +(8851.17 - 8851.17i) q^{8} -5105.58i q^{9} +O(q^{10})\)	\(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