LMFDB - Embedded newform 29.9.c.a.12.5

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			12.5
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.2859 - 15.2859i) q^{2} +(93.1254 + 93.1254i) q^{3} +211.315i q^{4} -424.754i q^{5} -2847.00i q^{6} +996.548 q^{7} +(-683.041 + 683.041i) q^{8} +10783.7i q^{9} +O(q^{10})$	\(q+(-15.2859 - 15.2859i) q^{2} +(93.1254 + 93.1254i) q^{3} +211.315i q^{4} -424.754i q^{5} -2847.00i q^{6} +996.548 q^{7} +(-683.041 + 683.041i) q^{8} +10783.7i q^{9} +(-6492.74 + 6492.74i) q^{10} +(12173.4 + 12173.4i) q^{11} +(-19678.8 + 19678.8i) q^{12} -12505.9i q^{13} +(-15233.1 - 15233.1i) q^{14} +(39555.4 - 39555.4i) q^{15} +74978.5 q^{16} +(-902.401 - 902.401i) q^{17} +(164838. - 164838. i) q^{18} +(84405.1 + 84405.1i) q^{19} +89757.1 q^{20} +(92803.9 + 92803.9i) q^{21} -372161. i q^{22} +363267. q^{23} -127217. q^{24} +210209. q^{25} +(-191164. + 191164. i) q^{26} +(-393238. + 393238. i) q^{27} +210586. i q^{28} +(-682982. - 183800. i) q^{29} -1.20928e6 q^{30} +(1.12833e6 + 1.12833e6i) q^{31} +(-971253. - 971253. i) q^{32} +2.26730e6i q^{33} +27588.0i q^{34} -423288. i q^{35} -2.27876e6 q^{36} +(1.28207e6 - 1.28207e6i) q^{37} -2.58041e6i q^{38} +(1.16462e6 - 1.16462e6i) q^{39} +(290125. + 290125. i) q^{40} +(-433964. + 433964. i) q^{41} -2.83718e6i q^{42} +(649594. + 649594. i) q^{43} +(-2.57242e6 + 2.57242e6i) q^{44} +4.58041e6 q^{45} +(-5.55285e6 - 5.55285e6i) q^{46} +(-3.20802e6 + 3.20802e6i) q^{47} +(6.98240e6 + 6.98240e6i) q^{48} -4.77169e6 q^{49} +(-3.21323e6 - 3.21323e6i) q^{50} -168073. i q^{51} +2.64269e6 q^{52} -9.37513e6 q^{53} +1.20220e7 q^{54} +(5.17069e6 - 5.17069e6i) q^{55} +(-680684. + 680684. i) q^{56} +1.57205e7i q^{57} +(7.63043e6 + 1.32495e7i) q^{58} -3.37856e6 q^{59} +(8.35867e6 + 8.35867e6i) q^{60} +(-2.81831e6 - 2.81831e6i) q^{61} -3.44950e7i q^{62} +1.07464e7i q^{63} +1.04984e7i q^{64} -5.31194e6 q^{65} +(3.46577e7 - 3.46577e7i) q^{66} -3.39890e7i q^{67} +(190691. - 190691. i) q^{68} +(3.38294e7 + 3.38294e7i) q^{69} +(-6.47033e6 + 6.47033e6i) q^{70} -3.53222e7i q^{71} +(-7.36569e6 - 7.36569e6i) q^{72} +(-3.20554e7 + 3.20554e7i) q^{73} -3.91951e7 q^{74} +(1.95758e7 + 1.95758e7i) q^{75} +(-1.78361e7 + 1.78361e7i) q^{76} +(1.21314e7 + 1.21314e7i) q^{77} -3.56044e7 q^{78} +(3.31673e7 + 3.31673e7i) q^{79} -3.18474e7i q^{80} -2.48917e6 q^{81} +1.32670e7 q^{82} +1.04934e7 q^{83} +(-1.96109e7 + 1.96109e7i) q^{84} +(-383299. + 383299. i) q^{85} -1.98592e7i q^{86} +(-4.64865e7 - 8.07193e7i) q^{87} -1.66298e7 q^{88} +(-6.19962e7 - 6.19962e7i) q^{89} +(-7.00155e7 - 7.00155e7i) q^{90} -1.24627e7i q^{91} +7.67640e7i q^{92} +2.10152e8i q^{93} +9.80747e7 q^{94} +(3.58514e7 - 3.58514e7i) q^{95} -1.80897e8i q^{96} +(-1.03873e8 + 1.03873e8i) q^{97} +(7.29395e7 + 7.29395e7i) q^{98} +(-1.31274e8 + 1.31274e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−15.2859	−	15.2859i	−0.955367	−	0.955367i	0.0436789	−	0.999046i	$-0.486092\pi$
$2$	−15.2859	−	15.2859i	−0.955367	−	0.955367i	−0.999046	+	0.0436789i	$0.986092\pi$
$3$	93.1254	+	93.1254i	1.14970	+	1.14970i	0.986612	+	0.163084i	$0.0521441\pi$
$3$	93.1254	+	93.1254i	1.14970	+	1.14970i	0.163084	+	0.986612i	$0.447856\pi$
$4$			211.315i			0.825451i
$5$		−	424.754i		−	0.679607i	−0.940497	−	0.339803i	$-0.889639\pi$
$5$		−	424.754i		−	0.679607i	0.940497	−	0.339803i	$-0.110361\pi$
$6$		−	2847.00i		−	2.19676i
$7$	996.548			0.415056			0.207528	−	0.978229i	$-0.433458\pi$
$7$	996.548			0.415056			0.207528	+	0.978229i	$0.433458\pi$
$8$	−683.041	+	683.041i	−0.166758	+	0.166758i
$9$			10783.7i			1.64360i
$10$	−6492.74	+	6492.74i	−0.649274	+	0.649274i
$11$	12173.4	+	12173.4i	0.831458	+	0.831458i	0.987716	−	0.156258i	$-0.0499432\pi$
$11$	12173.4	+	12173.4i	0.831458	+	0.831458i	−0.156258	+	0.987716i	$0.549943\pi$
$12$	−19678.8	+	19678.8i	−0.949018	+	0.949018i
$13$		−	12505.9i		−	0.437867i	−0.975740	−	0.218933i	$-0.929742\pi$
$13$		−	12505.9i		−	0.437867i	0.975740	−	0.218933i	$-0.0702577\pi$
$14$	−15233.1	−	15233.1i	−0.396530	−	0.396530i
$15$	39555.4	−	39555.4i	0.781341	−	0.781341i
$16$	74978.5			1.14408
$17$	−902.401	−	902.401i	−0.0108045	−	0.0108045i	0.701684	−	0.712488i	$-0.252432\pi$
$17$	−902.401	−	902.401i	−0.0108045	−	0.0108045i	−0.712488	+	0.701684i	$0.752432\pi$
$18$	164838.	−	164838.i	1.57024	−	1.57024i
$19$	84405.1	+	84405.1i	0.647671	+	0.647671i	0.952430	−	0.304759i	$-0.0985759\pi$
$19$	84405.1	+	84405.1i	0.647671	+	0.647671i	−0.304759	+	0.952430i	$0.598576\pi$
$20$	89757.1			0.560982
$21$	92803.9	+	92803.9i	0.477188	+	0.477188i
$22$		−	372161.i		−	1.58869i
$23$	363267.			1.29812			0.649060	−	0.760737i	$-0.275162\pi$
$23$	363267.			1.29812			0.649060	+	0.760737i	$0.275162\pi$
$24$	−127217.			−0.383442
$25$	210209.			0.538135
$26$	−191164.	+	191164.i	−0.418323	+	0.418323i
$27$	−393238.	+	393238.i	−0.739946	+	0.739946i
$28$			210586.i			0.342608i
$29$	−682982.	−	183800.i	−0.965644	−	0.259868i
$29$	−682982.	−	183800.i	−0.965644	−	0.259868i
$30$	−1.20928e6			−1.49293
$31$	1.12833e6	+	1.12833e6i	1.22177	+	1.22177i	0.967003	+	0.254766i	$0.0819985\pi$
$31$	1.12833e6	+	1.12833e6i	1.22177	+	1.22177i	0.254766	+	0.967003i	$0.418001\pi$
$32$	−971253.	−	971253.i	−0.926259	−	0.926259i
$33$			2.26730e6i			1.91185i
$34$			27588.0i			0.0206445i
$35$		−	423288.i		−	0.282075i
$36$	−2.27876e6			−1.35671
$37$	1.28207e6	−	1.28207e6i	0.684077	−	0.684077i	−0.276839	−	0.960916i	$-0.589287\pi$
$37$	1.28207e6	−	1.28207e6i	0.684077	−	0.684077i	0.960916	+	0.276839i	$0.0892869\pi$
$38$		−	2.58041e6i		−	1.23753i
$39$	1.16462e6	−	1.16462e6i	0.503413	−	0.503413i
$40$	290125.	+	290125.i	0.113330	+	0.113330i
$41$	−433964.	+	433964.i	−0.153574	+	0.153574i	−0.779712	−	0.626138i	$-0.784635\pi$
$41$	−433964.	+	433964.i	−0.153574	+	0.153574i	0.626138	+	0.779712i	$0.284635\pi$
$42$		−	2.83718e6i		−	0.911778i
$43$	649594.	+	649594.i	0.190006	+	0.190006i	0.795699	−	0.605692i	$-0.207104\pi$
$43$	649594.	+	649594.i	0.190006	+	0.190006i	−0.605692	+	0.795699i	$0.707104\pi$
$44$	−2.57242e6	+	2.57242e6i	−0.686328	+	0.686328i
$45$	4.58041e6			1.11700
$46$	−5.55285e6	−	5.55285e6i	−1.24018	−	1.24018i
$47$	−3.20802e6	+	3.20802e6i	−0.657424	+	0.657424i	−0.954770	−	0.297346i	$-0.903899\pi$
$47$	−3.20802e6	+	3.20802e6i	−0.657424	+	0.657424i	0.297346	+	0.954770i	$0.403899\pi$
$48$	6.98240e6	+	6.98240e6i	1.31535	+	1.31535i
$49$	−4.77169e6			−0.827729
$50$	−3.21323e6	−	3.21323e6i	−0.514116	−	0.514116i
$51$		−	168073.i		−	0.0248437i
$52$	2.64269e6			0.361437
$53$	−9.37513e6			−1.18816			−0.594078	−	0.804407i	$-0.702483\pi$
$53$	−9.37513e6			−1.18816			−0.594078	+	0.804407i	$0.702483\pi$
$54$	1.20220e7			1.41384
$55$	5.17069e6	−	5.17069e6i	0.565064	−	0.565064i
$56$	−680684.	+	680684.i	−0.0692139	+	0.0692139i
$57$			1.57205e7i			1.48925i
$58$	7.63043e6	+	1.32495e7i	0.674275	+	1.17081i
$59$	−3.37856e6			−0.278820			−0.139410	−	0.990235i	$-0.544521\pi$
$59$	−3.37856e6			−0.278820			−0.139410	+	0.990235i	$0.544521\pi$
$60$	8.35867e6	+	8.35867e6i	0.644959	+	0.644959i
$61$	−2.81831e6	−	2.81831e6i	−0.203549	−	0.203549i	0.597970	−	0.801519i	$-0.295974\pi$
$61$	−2.81831e6	−	2.81831e6i	−0.203549	−	0.203549i	−0.801519	+	0.597970i	$0.795974\pi$
$62$		−	3.44950e7i		−	2.33447i
$63$			1.07464e7i			0.682186i
$64$			1.04984e7i			0.625753i
$65$	−5.31194e6			−0.297577
$66$	3.46577e7	−	3.46577e7i	1.82652	−	1.82652i
$67$		−	3.39890e7i		−	1.68671i	−0.537359	−	0.843354i	$-0.680578\pi$
$67$		−	3.39890e7i		−	1.68671i	0.537359	−	0.843354i	$-0.319422\pi$
$68$	190691.	−	190691.i	0.00891857	−	0.00891857i
$69$	3.38294e7	+	3.38294e7i	1.49244	+	1.49244i
$70$	−6.47033e6	+	6.47033e6i	−0.269485	+	0.269485i
$71$		−	3.53222e7i		−	1.39000i	−0.719010	−	0.695000i	$-0.755405\pi$
$71$		−	3.53222e7i		−	1.39000i	0.719010	−	0.695000i	$-0.244595\pi$
$72$	−7.36569e6	−	7.36569e6i	−0.274084	−	0.274084i
$73$	−3.20554e7	+	3.20554e7i	−1.12878	+	1.12878i	−0.138406	+	0.990376i	$0.544198\pi$
$73$	−3.20554e7	+	3.20554e7i	−1.12878	+	1.12878i	−0.990376	+	0.138406i	$0.955802\pi$
$74$	−3.91951e7			−1.30709
$75$	1.95758e7	+	1.95758e7i	0.618691	+	0.618691i
$76$	−1.78361e7	+	1.78361e7i	−0.534620	+	0.534620i
$77$	1.21314e7	+	1.21314e7i	0.345101	+	0.345101i
$78$	−3.56044e7			−0.961889
$79$	3.31673e7	+	3.31673e7i	0.851533	+	0.851533i	0.990322	−	0.138789i	$-0.0443210\pi$
$79$	3.31673e7	+	3.31673e7i	0.851533	+	0.851533i	−0.138789	+	0.990322i	$0.544321\pi$
$80$		−	3.18474e7i		−	0.777525i
$81$	−2.48917e6			−0.0578248
$82$	1.32670e7			0.293440
$83$	1.04934e7			0.221109			0.110554	−	0.993870i	$-0.464737\pi$
$83$	1.04934e7			0.221109			0.110554	+	0.993870i	$0.464737\pi$
$84$	−1.96109e7	+	1.96109e7i	−0.393895	+	0.393895i
$85$	−383299.	+	383299.i	−0.00734280	+	0.00734280i
$86$		−	1.98592e7i		−	0.363052i
$87$	−4.64865e7	−	8.07193e7i	−0.811428	−	1.40897i
$88$	−1.66298e7			−0.277305
$89$	−6.19962e7	−	6.19962e7i	−0.988109	−	0.988109i	0.0118215	−	0.999930i	$-0.496237\pi$
$89$	−6.19962e7	−	6.19962e7i	−0.988109	−	0.988109i	−0.999930	+	0.0118215i	$0.996237\pi$
$90$	−7.00155e7	−	7.00155e7i	−1.06715	−	1.06715i
$91$		−	1.24627e7i		−	0.181739i
$92$			7.67640e7i			1.07153i
$93$			2.10152e8i			2.80933i
$94$	9.80747e7			1.25616
$95$	3.58514e7	−	3.58514e7i	0.440161	−	0.440161i
$96$		−	1.80897e8i		−	2.12983i
$97$	−1.03873e8	+	1.03873e8i	−1.17332	+	1.17332i	−0.191903	+	0.981414i	$0.561466\pi$
$97$	−1.03873e8	+	1.03873e8i	−1.17332	+	1.17332i	−0.981414	+	0.191903i	$0.938534\pi$
$98$	7.29395e7	+	7.29395e7i	0.790785	+	0.790785i
$99$	−1.31274e8	+	1.31274e8i	−1.36659	+	1.36659i
$100$			4.44204e7i			0.444204i
$101$	−6.52446e7	−	6.52446e7i	−0.626987	−	0.626987i	0.320322	−	0.947309i	$-0.396209\pi$
$101$	−6.52446e7	−	6.52446e7i	−0.626987	−	0.626987i	−0.947309	+	0.320322i	$0.896209\pi$
$102$	−2.56914e6	+	2.56914e6i	−0.0237349	+	0.0237349i
$103$	1.45571e8			1.29338			0.646690	−	0.762753i	$-0.276153\pi$
$103$	1.45571e8			1.29338			0.646690	+	0.762753i	$0.276153\pi$
$104$	8.54205e6	+	8.54205e6i	0.0730178	+	0.0730178i
$105$	3.94189e7	−	3.94189e7i	0.324300	−	0.324300i
$106$	1.43307e8	+	1.43307e8i	1.13513	+	1.13513i
$107$	−6.19745e7			−0.472800			−0.236400	−	0.971656i	$-0.575968\pi$
$107$	−6.19745e7			−0.472800			−0.236400	+	0.971656i	$0.575968\pi$
$108$	−8.30972e7	−	8.30972e7i	−0.610789	−	0.610789i
$109$		−	9.39632e7i		−	0.665659i	−0.942987	−	0.332829i	$-0.891997\pi$
$109$		−	9.39632e7i		−	0.665659i	0.942987	−	0.332829i	$-0.108003\pi$
$110$	−1.58077e8			−1.07969
$111$	2.38787e8			1.57296
$112$	7.47197e7			0.474857
$113$	1.20763e8	−	1.20763e8i	0.740661	−	0.740661i	−0.232044	−	0.972705i	$-0.574541\pi$
$113$	1.20763e8	−	1.20763e8i	0.740661	−	0.740661i	0.972705	+	0.232044i	$0.0745413\pi$
$114$	2.40302e8	−	2.40302e8i	1.42278	−	1.42278i
$115$		−	1.54299e8i		−	0.882211i
$116$	3.88397e7	−	1.44325e8i	0.214508	−	0.797092i
$117$	1.34860e8			0.719678
$118$	5.16442e7	+	5.16442e7i	0.266375	+	0.266375i
$119$	−899286.	−	899286.i	−0.00448446	−	0.00448446i
$120$			5.40359e7i			0.260590i
$121$			8.20233e7i			0.382645i
$122$			8.61605e7i			0.388928i
$123$	−8.08262e7			−0.353128
$124$	−2.38433e8	+	2.38433e8i	−1.00851	+	1.00851i
$125$		−	2.55207e8i		−	1.04533i
$126$	1.64269e8	−	1.64269e8i	0.651738	−	0.651738i
$127$	3.27469e8	+	3.27469e8i	1.25880	+	1.25880i	0.951668	+	0.307128i	$0.0993680\pi$
$127$	3.27469e8	+	3.27469e8i	1.25880	+	1.25880i	0.307128	+	0.951668i	$0.400632\pi$
$128$	−8.81638e7	+	8.81638e7i	−0.328436	+	0.328436i
$129$			1.20987e8i			0.436899i
$130$	8.11975e7	+	8.11975e7i	0.284295	+	0.284295i
$131$	2.58928e7	−	2.58928e7i	0.0879211	−	0.0879211i	−0.661778	−	0.749700i	$-0.730198\pi$
$131$	2.58928e7	−	2.58928e7i	0.0879211	−	0.0879211i	0.749700	+	0.661778i	$0.230198\pi$
$132$	−4.79116e8			−1.57814
$133$	8.41137e7	+	8.41137e7i	0.268819	+	0.268819i
$134$	−5.19552e8	+	5.19552e8i	−1.61142	+	1.61142i
$135$	1.67029e8	+	1.67029e8i	0.502872	+	0.502872i
$136$	1.23275e6			0.00360347
$137$	−2.17612e8	−	2.17612e8i	−0.617734	−	0.617734i	0.327216	−	0.944950i	$-0.393890\pi$
$137$	−2.17612e8	−	2.17612e8i	−0.617734	−	0.617734i	−0.944950	+	0.327216i	$0.893890\pi$
$138$		−	1.03422e9i		−	2.85166i
$139$	−5.37450e8			−1.43972			−0.719862	−	0.694117i	$-0.755795\pi$
$139$	−5.37450e8			−1.43972			−0.719862	+	0.694117i	$0.755795\pi$
$140$	8.94473e7			0.232839
$141$	−5.97496e8			−1.51167
$142$	−5.39931e8	+	5.39931e8i	−1.32796	+	1.32796i
$143$	1.52239e8	−	1.52239e8i	0.364068	−	0.364068i
$144$			8.08544e8i			1.88041i
$145$	−7.80696e7	+	2.90099e8i	−0.176608	+	0.656258i
$146$	9.79989e8			2.15680
$147$	−4.44366e8	−	4.44366e8i	−0.951637	−	0.951637i
$148$	2.70921e8	+	2.70921e8i	0.564672	+	0.564672i
$149$			8.52261e8i			1.72913i	0.502521	+	0.864565i	$0.332406\pi$
$149$			8.52261e8i			1.72913i	−0.502521	+	0.864565i	$0.667594\pi$
$150$		−	5.98466e8i		−	1.18215i
$151$		−	3.52776e8i		−	0.678564i	−0.940685	−	0.339282i	$-0.889816\pi$
$151$		−	3.52776e8i		−	0.678564i	0.940685	−	0.339282i	$-0.110184\pi$
$152$	−1.15304e8			−0.216009
$153$	9.73120e6	−	9.73120e6i	0.0177583	−	0.0177583i
$154$		−	3.70877e8i		−	0.659396i
$155$	4.79263e8	−	4.79263e8i	0.830322	−	0.830322i
$156$	2.46102e8	+	2.46102e8i	0.415543	+	0.415543i
$157$	5.44556e8	−	5.44556e8i	0.896281	−	0.896281i	−0.0988238	−	0.995105i	$-0.531508\pi$
$157$	5.44556e8	−	5.44556e8i	0.896281	−	0.896281i	0.995105	+	0.0988238i	$0.0315080\pi$
$158$		−	1.01398e9i		−	1.62705i
$159$	−8.73062e8	−	8.73062e8i	−1.36602	−	1.36602i
$160$	−4.12544e8	+	4.12544e8i	−0.629492	+	0.629492i
$161$	3.62013e8			0.538792
$162$	3.80491e7	+	3.80491e7i	0.0552439	+	0.0552439i
$163$	2.92713e8	−	2.92713e8i	0.414659	−	0.414659i	−0.468699	−	0.883358i	$-0.655277\pi$
$163$	2.92713e8	−	2.92713e8i	0.414659	−	0.414659i	0.883358	+	0.468699i	$0.155277\pi$
$164$	−9.17034e7	−	9.17034e7i	−0.126768	−	0.126768i
$165$	9.63045e8			1.29930
$166$	−1.60401e8	−	1.60401e8i	−0.211240	−	0.211240i
$167$			2.15786e8i			0.277433i	0.990332	+	0.138716i	$0.0442977\pi$
$167$			2.15786e8i			0.277433i	−0.990332	+	0.138716i	$0.955702\pi$
$168$	−1.26778e8			−0.159150
$169$	6.59333e8			0.808273
$170$	1.17181e7			0.0140301
$171$	−9.10197e8	+	9.10197e8i	−1.06451	+	1.06451i
$172$	−1.37269e8	+	1.37269e8i	−0.156841	+	0.156841i
$173$		−	9.42203e8i		−	1.05186i	−0.850526	−	0.525932i	$-0.823716\pi$
$173$		−	9.42203e8i		−	1.05186i	0.850526	−	0.525932i	$-0.176284\pi$
$174$	−5.23278e8	+	1.94445e9i	−0.570868	+	2.12129i
$175$	2.09483e8			0.223356
$176$	9.12742e8	+	9.12742e8i	0.951256	+	0.951256i
$177$	−3.14630e8	−	3.14630e8i	−0.320558	−	0.320558i
$178$			1.89533e9i			1.88801i
$179$			1.23083e9i			1.19891i	0.800410	+	0.599453i	$0.204615\pi$
$179$			1.23083e9i			1.19891i	−0.800410	+	0.599453i	$0.795385\pi$
$180$			9.67911e8i			0.922031i
$181$	−5.77694e8			−0.538250			−0.269125	−	0.963105i	$-0.586734\pi$
$181$	−5.77694e8			−0.538250			−0.269125	+	0.963105i	$0.586734\pi$
$182$	−1.90504e8	+	1.90504e8i	−0.173627	+	0.173627i
$183$		−	5.24911e8i		−	0.468039i
$184$	−2.48127e8	+	2.48127e8i	−0.216472	+	0.216472i
$185$	−5.44565e8	−	5.44565e8i	−0.464903	−	0.464903i
$186$	3.21236e9	−	3.21236e9i	2.68394	−	2.68394i
$187$		−	2.19705e7i		−	0.0179669i
$188$	−6.77904e8	−	6.77904e8i	−0.542671	−	0.542671i
$189$	−3.91880e8	+	3.91880e8i	−0.307119	+	0.307119i
$190$	−1.09604e9			−0.841031
$191$	−2.63046e8	−	2.63046e8i	−0.197651	−	0.197651i	0.601341	−	0.798992i	$-0.294633\pi$
$191$	−2.63046e8	−	2.63046e8i	−0.197651	−	0.197651i	−0.798992	+	0.601341i	$0.794633\pi$
$192$	−9.77667e8	+	9.77667e8i	−0.719426	+	0.719426i
$193$	−1.01159e9	−	1.01159e9i	−0.729080	−	0.729080i	0.241357	−	0.970436i	$-0.422408\pi$
$193$	−1.01159e9	−	1.01159e9i	−0.729080	−	0.729080i	−0.970436	+	0.241357i	$0.922408\pi$
$194$	3.17558e9			2.24190
$195$	−4.94676e8	−	4.94676e8i	−0.342123	−	0.342123i
$196$		−	1.00833e9i		−	0.683250i
$197$	8.34636e8			0.554156			0.277078	−	0.960847i	$-0.410634\pi$
$197$	8.34636e8			0.554156			0.277078	+	0.960847i	$0.410634\pi$
$198$	4.01326e9			2.61118
$199$	−1.82005e9			−1.16057			−0.580284	−	0.814414i	$-0.697058\pi$
$199$	−1.82005e9			−1.16057			−0.580284	+	0.814414i	$0.697058\pi$
$200$	−1.43581e8	+	1.43581e8i	−0.0897384	+	0.0897384i
$201$	3.16524e9	−	3.16524e9i	1.93920	−	1.93920i
$202$			1.99464e9i			1.19801i
$203$	−6.80624e8	−	1.83165e8i	−0.400796	−	0.107860i
$204$	3.55164e7			0.0205073
$205$	1.84328e8	+	1.84328e8i	0.104370	+	0.104370i
$206$	−2.22518e9	−	2.22518e9i	−1.23565	−	1.23565i
$207$			3.91735e9i			2.13359i
$208$		−	9.37674e8i		−	0.500955i
$209$			2.05499e9i			1.07702i
$210$	−1.20510e9			−0.619651
$211$	−1.90442e9	+	1.90442e9i	−0.960798	+	0.960798i	−0.999260	−	0.0384617i	$-0.987754\pi$
$211$	−1.90442e9	+	1.90442e9i	−0.960798	+	0.960798i	0.0384617	+	0.999260i	$0.487754\pi$
$212$		−	1.98111e9i		−	0.980765i
$213$	3.28939e9	−	3.28939e9i	1.59808	−	1.59808i
$214$	9.47333e8	+	9.47333e8i	0.451698	+	0.451698i
$215$	2.75918e8	−	2.75918e8i	0.129130	−	0.129130i
$216$		−	5.37195e8i		−	0.246784i
$217$	1.12443e9	+	1.12443e9i	0.507102	+	0.507102i
$218$	−1.43631e9	+	1.43631e9i	−0.635948	+	0.635948i
$219$	−5.97034e9			−2.59551
$220$	1.09265e9	+	1.09265e9i	0.466433	+	0.466433i
$221$	−1.12853e7	+	1.12853e7i	−0.00473092	+	0.00473092i
$222$	−3.65006e9	−	3.65006e9i	−1.50276	−	1.50276i
$223$	1.83633e9			0.742561			0.371280	−	0.928521i	$-0.378919\pi$
$223$	1.83633e9			0.742561			0.371280	+	0.928521i	$0.378919\pi$
$224$	−9.67901e8	−	9.67901e8i	−0.384449	−	0.384449i
$225$			2.26682e9i			0.884479i
$226$	−3.69193e9			−1.41521
$227$	7.27923e8			0.274146			0.137073	−	0.990561i	$-0.456231\pi$
$227$	7.27923e8			0.274146			0.137073	+	0.990561i	$0.456231\pi$
$228$	−3.32199e9			−1.22930
$229$	1.20220e9	−	1.20220e9i	0.437155	−	0.437155i	−0.453898	−	0.891054i	$-0.649967\pi$
$229$	1.20220e9	−	1.20220e9i	0.437155	−	0.437155i	0.891054	+	0.453898i	$0.149967\pi$
$230$	−2.35860e9	+	2.35860e9i	−0.842835	+	0.842835i
$231$			2.25947e9i			0.793523i
$232$	5.92048e8	−	3.40962e8i	0.204364	−	0.117694i
$233$	1.51077e9			0.512596			0.256298	−	0.966598i	$-0.417497\pi$
$233$	1.51077e9			0.512596			0.256298	+	0.966598i	$0.417497\pi$
$234$	−2.06145e9	−	2.06145e9i	−0.687557	−	0.687557i
$235$	1.36262e9	+	1.36262e9i	0.446790	+	0.446790i
$236$		−	7.13942e8i		−	0.230152i
$237$			6.17743e9i			1.95801i
$238$			2.74927e7i			0.00856861i
$239$	−4.27284e9			−1.30956			−0.654779	−	0.755821i	$-0.727238\pi$
$239$	−4.27284e9			−1.30956			−0.654779	+	0.755821i	$0.727238\pi$
$240$	2.96581e9	−	2.96581e9i	0.893918	−	0.893918i
$241$		−	2.55642e9i		−	0.757816i	−0.925434	−	0.378908i	$-0.876300\pi$
$241$		−	2.55642e9i		−	0.757816i	0.925434	−	0.378908i	$-0.123700\pi$
$242$	1.25380e9	−	1.25380e9i	0.365566	−	0.365566i
$243$	2.34823e9	+	2.34823e9i	0.673465	+	0.673465i
$244$	5.95552e8	−	5.95552e8i	0.168020	−	0.168020i
$245$			2.02680e9i			0.562530i
$246$	1.23550e9	+	1.23550e9i	0.337366	+	0.337366i
$247$	1.05556e9	−	1.05556e9i	0.283593	−	0.283593i
$248$	−1.54139e9			−0.407480
$249$	9.77206e8	+	9.77206e8i	0.254208	+	0.254208i
$250$	−3.90106e9	+	3.90106e9i	−0.998670	+	0.998670i
$251$	3.18466e9	+	3.18466e9i	0.802359	+	0.802359i	0.983464	−	0.181105i	$-0.0579673\pi$
$251$	3.18466e9	+	3.18466e9i	0.802359	+	0.802359i	−0.181105	+	0.983464i	$0.557967\pi$
$252$	−2.27089e9			−0.563111
$253$	4.42219e9	+	4.42219e9i	1.07933	+	1.07933i
$254$		−	1.00113e10i		−	2.40522i
$255$	−7.13897e7			−0.0168840
$256$	5.38291e9			1.25331
$257$	2.58300e9			0.592096			0.296048	−	0.955173i	$-0.404331\pi$
$257$	2.58300e9			0.592096			0.296048	+	0.955173i	$0.404331\pi$
$258$	1.84940e9	−	1.84940e9i	0.417399	−	0.417399i
$259$	1.27765e9	−	1.27765e9i	0.283930	−	0.283930i
$260$		−	1.12249e9i		−	0.245635i
$261$	1.98203e9	−	7.36505e9i	0.427119	−	1.58713i
$262$	−7.91587e8			−0.167994
$263$	−1.88537e9	−	1.88537e9i	−0.394071	−	0.394071i	0.482065	−	0.876136i	$-0.339887\pi$
$263$	−1.88537e9	−	1.88537e9i	−0.394071	−	0.394071i	−0.876136	+	0.482065i	$0.839887\pi$
$264$	−1.54866e9	−	1.54866e9i	−0.318816	−	0.318816i
$265$			3.98212e9i			0.807479i
$266$		−	2.57150e9i		−	0.513642i
$267$		−	1.15468e10i		−	2.27205i
$268$	7.18241e9			1.39229
$269$	−2.88197e9	+	2.88197e9i	−0.550402	+	0.550402i	−0.926557	−	0.376155i	$-0.877246\pi$
$269$	−2.88197e9	+	2.88197e9i	−0.550402	+	0.550402i	0.376155	+	0.926557i	$0.377246\pi$
$270$		−	5.10638e9i		−	0.960855i
$271$	3.69140e9	−	3.69140e9i	0.684406	−	0.684406i	−0.276584	−	0.960990i	$-0.589202\pi$
$271$	3.69140e9	−	3.69140e9i	0.684406	−	0.684406i	0.960990	+	0.276584i	$0.0892024\pi$
$272$	−6.76607e7	−	6.76607e7i	−0.0123612	−	0.0123612i
$273$	1.16060e9	−	1.16060e9i	0.208944	−	0.208944i
$274$			6.65279e9i			1.18032i
$275$	2.55895e9	+	2.55895e9i	0.447436	+	0.447436i
$276$	−7.14867e9	+	7.14867e9i	−1.23194	+	1.23194i
$277$	2.44530e9			0.415348			0.207674	−	0.978198i	$-0.433411\pi$
$277$	2.44530e9			0.415348			0.207674	+	0.978198i	$0.433411\pi$
$278$	8.21540e9	+	8.21540e9i	1.37546	+	1.37546i
$279$	−1.21675e10	+	1.21675e10i	−2.00810	+	2.00810i
$280$	2.89123e8	+	2.89123e8i	0.0470382	+	0.0470382i
$281$	−9.42536e9			−1.51172			−0.755862	−	0.654730i	$-0.772782\pi$
$281$	−9.42536e9			−1.51172			−0.755862	+	0.654730i	$0.772782\pi$
$282$	9.13324e9	+	9.13324e9i	1.44420	+	1.44420i
$283$			1.39614e9i			0.217662i	0.994060	+	0.108831i	$0.0347107\pi$
$283$			1.39614e9i			0.217662i	−0.994060	+	0.108831i	$0.965289\pi$
$284$	7.46413e9			1.14738
$285$	6.67735e9			1.01210
$286$	−4.65421e9			−0.695636
$287$	−4.32467e8	+	4.32467e8i	−0.0637419	+	0.0637419i
$288$	1.04737e10	−	1.04737e10i	1.52240	−	1.52240i
$289$		−	6.97413e9i		−	0.999767i
$290$	5.62778e9	−	3.24106e9i	0.795693	−	0.458242i
$291$	−1.93464e10			−2.69792
$292$	−6.77380e9	−	6.77380e9i	−0.931754	−	0.931754i
$293$	−8.56039e9	−	8.56039e9i	−1.16151	−	1.16151i	−0.984145	−	0.177366i	$-0.943242\pi$
$293$	−8.56039e9	−	8.56039e9i	−1.16151	−	1.16151i	−0.177366	−	0.984145i	$-0.556758\pi$
$294$			1.35850e10i			1.81832i
$295$			1.43506e9i			0.189488i
$296$			1.75141e9i			0.228151i
$297$	−9.57406e9			−1.23047
$298$	1.30276e10	−	1.30276e10i	1.65195	−	1.65195i
$299$		−	4.54298e9i		−	0.568403i
$300$	−4.13667e9	+	4.13667e9i	−0.510699	+	0.510699i
$301$	6.47352e8	+	6.47352e8i	0.0788632	+	0.0788632i
$302$	−5.39249e9	+	5.39249e9i	−0.648278	+	0.648278i
$303$		−	1.21518e10i		−	1.44169i
$304$	6.32857e9	+	6.32857e9i	0.740988	+	0.740988i
$305$	−1.19709e9	+	1.19709e9i	−0.138333	+	0.138333i
$306$	−2.97500e8			−0.0339313
$307$	−3.59557e9	−	3.59557e9i	−0.404775	−	0.404775i	0.475137	−	0.879912i	$-0.342399\pi$
$307$	−3.59557e9	−	3.59557e9i	−0.404775	−	0.404775i	−0.879912	+	0.475137i	$0.842399\pi$
$308$	−2.56354e9	+	2.56354e9i	−0.284864	+	0.284864i
$309$	1.35564e10	+	1.35564e10i	1.48699	+	1.48699i
$310$	−1.46519e10			−1.58652
$311$	6.16760e9	+	6.16760e9i	0.659288	+	0.659288i	0.955212	−	0.295924i	$-0.0956275\pi$
$311$	6.16760e9	+	6.16760e9i	0.659288	+	0.659288i	−0.295924	+	0.955212i	$0.595627\pi$
$312$			1.59096e9i			0.167897i
$313$	−7.29709e9			−0.760277			−0.380139	−	0.924929i	$-0.624124\pi$
$313$	−7.29709e9			−0.760277			−0.380139	+	0.924929i	$0.624124\pi$
$314$	−1.66480e10			−1.71255
$315$	4.56460e9			0.463618
$316$	−7.00876e9	+	7.00876e9i	−0.702899	+	0.702899i
$317$	1.00339e10	−	1.00339e10i	0.993645	−	0.993645i	−0.00633527	−	0.999980i	$-0.502017\pi$
$317$	1.00339e10	−	1.00339e10i	0.993645	−	0.993645i	0.999980	+	0.00633527i	$0.00201659\pi$
$318$			2.66910e10i			2.61010i
$319$	−6.07673e9	−	1.05517e10i	−0.586823	−	1.01896i
$320$	4.45924e9			0.425266
$321$	−5.77139e9	−	5.77139e9i	−0.543576	−	0.543576i
$322$	−5.53369e9	−	5.53369e9i	−0.514744	−	0.514744i
$323$		−	1.52334e8i		−	0.0139955i
$324$		−	5.26000e8i		−	0.0477315i
$325$		−	2.62885e9i		−	0.235631i
$326$	−8.94874e9			−0.792303
$327$	8.75035e9	−	8.75035e9i	0.765305	−	0.765305i
$328$		−	5.92831e8i		−	0.0512196i
$329$	−3.19695e9	+	3.19695e9i	−0.272867	+	0.272867i
$330$	−1.47210e10	−	1.47210e10i	−1.24131	−	1.24131i
$331$	1.25087e8	−	1.25087e8i	0.0104208	−	0.0104208i	−0.701877	−	0.712298i	$-0.747654\pi$
$331$	1.25087e8	−	1.25087e8i	0.0104208	−	0.0104208i	0.712298	+	0.701877i	$0.247654\pi$
$332$			2.21743e9i			0.182514i
$333$	1.38254e10	+	1.38254e10i	1.12435	+	1.12435i
$334$	3.29848e9	−	3.29848e9i	0.265050	−	0.265050i
$335$	−1.44370e10			−1.14630
$336$	6.95830e9	+	6.95830e9i	0.545942	+	0.545942i
$337$	1.45723e10	−	1.45723e10i	1.12982	−	1.12982i	0.139613	−	0.990206i	$-0.455414\pi$
$337$	1.45723e10	−	1.45723e10i	1.12982	−	1.12982i	0.990206	−	0.139613i	$-0.0445859\pi$
$338$	−1.00785e10	−	1.00785e10i	−0.772197	−	0.772197i
$339$	2.24922e10			1.70307
$340$	−8.09969e7	−	8.09969e7i	−0.00606112	−	0.00606112i
$341$			2.74712e10i			2.03170i
$342$	2.78263e10			2.03400
$343$	−1.05001e10			−0.758609
$344$	−8.87400e8			−0.0633702
$345$	1.43692e10	−	1.43692e10i	1.01427	−	1.01427i
$346$	−1.44024e10	+	1.44024e10i	−1.00492	+	1.00492i
$347$			6.69871e9i			0.462034i	0.972950	+	0.231017i	$0.0742052\pi$
$347$			6.69871e9i			0.462034i	−0.972950	+	0.231017i	$0.925795\pi$
$348$	1.70572e10	−	9.82332e9i	1.16303	−	0.669794i
$349$	−3.85706e9			−0.259989			−0.129994	−	0.991515i	$-0.541496\pi$
$349$	−3.85706e9			−0.259989			−0.129994	+	0.991515i	$0.541496\pi$
$350$	−3.20213e9	−	3.20213e9i	−0.213387	−	0.213387i
$351$	4.91779e9	+	4.91779e9i	0.323998	+	0.323998i
$352$		−	2.36469e10i		−	1.54029i
$353$		−	1.29283e10i		−	0.832614i	−0.909224	−	0.416307i	$-0.863324\pi$
$353$		−	1.29283e10i		−	0.832614i	0.909224	−	0.416307i	$-0.136676\pi$
$354$			9.61878e9i			0.612501i
$355$	−1.50033e10			−0.944653
$356$	1.31007e10	−	1.31007e10i	0.815635	−	0.815635i
$357$		−	1.67493e8i		−	0.0103115i
$358$	1.88143e10	−	1.88143e10i	1.14540	−	1.14540i
$359$	4.14763e9	+	4.14763e9i	0.249702	+	0.249702i	0.820848	−	0.571146i	$-0.193501\pi$
$359$	4.14763e9	+	4.14763e9i	0.249702	+	0.249702i	−0.571146	+	0.820848i	$0.693501\pi$
$360$	−3.12861e9	+	3.12861e9i	−0.186269	+	0.186269i
$361$		−	2.73513e9i		−	0.161046i
$362$	8.83056e9	+	8.83056e9i	0.514226	+	0.514226i
$363$	−7.63845e9	+	7.63845e9i	−0.439925	+	0.439925i
$364$	2.63357e9			0.150017
$365$	1.36157e10	+	1.36157e10i	0.767127	+	0.767127i
$366$	−8.02373e9	+	8.02373e9i	−0.447149	+	0.447149i
$367$	−4.94529e9	−	4.94529e9i	−0.272601	−	0.272601i	0.557545	−	0.830146i	$-0.311743\pi$
$367$	−4.94529e9	−	4.94529e9i	−0.272601	−	0.272601i	−0.830146	+	0.557545i	$0.811743\pi$
$368$	2.72372e10			1.48515
$369$	−4.67973e9	−	4.67973e9i	−0.252415	−	0.252415i
$370$			1.66483e10i			0.888307i
$371$	−9.34277e9			−0.493151
$372$	−4.44084e10			−2.31896
$373$	−4.05866e9			−0.209675			−0.104838	−	0.994489i	$-0.533432\pi$
$373$	−4.05866e9			−0.209675			−0.104838	+	0.994489i	$0.533432\pi$
$374$	−3.35839e8	+	3.35839e8i	−0.0171650	+	0.0171650i
$375$	2.37662e10	−	2.37662e10i	1.20181	−	1.20181i
$376$		−	4.38242e9i		−	0.219262i
$377$	−2.29858e9	+	8.54131e9i	−0.113787	+	0.422823i
$378$	1.19805e10			0.586822
$379$	−1.81678e10	−	1.81678e10i	−0.880531	−	0.880531i	0.113057	−	0.993588i	$-0.463936\pi$
$379$	−1.81678e10	−	1.81678e10i	−0.880531	−	0.880531i	−0.993588	+	0.113057i	$0.963936\pi$
$380$	7.57596e9	+	7.57596e9i	0.363332	+	0.363332i
$381$			6.09914e10i			2.89447i
$382$			8.04178e9i			0.377658i
$383$			9.59197e9i			0.445772i	0.974845	+	0.222886i	$0.0715477\pi$
$383$			9.59197e9i			0.445772i	−0.974845	+	0.222886i	$0.928452\pi$
$384$	−1.64206e10			−0.755202
$385$	5.15284e9	−	5.15284e9i	0.234533	−	0.234533i
$386$			3.09260e10i			1.39308i
$387$	−7.00501e9	+	7.00501e9i	−0.312295	+	0.312295i
$388$	−2.19500e10	−	2.19500e10i	−0.968516	−	0.968516i
$389$	7.39188e9	−	7.39188e9i	0.322817	−	0.322817i	−0.527030	−	0.849847i	$-0.676694\pi$
$389$	7.39188e9	−	7.39188e9i	0.322817	−	0.322817i	0.849847	+	0.527030i	$0.176694\pi$
$390$			1.51231e10i			0.653706i
$391$	−3.27813e8	−	3.27813e8i	−0.0140255	−	0.0140255i
$392$	3.25926e9	−	3.25926e9i	0.138031	−	0.138031i
$393$	4.82255e9			0.202165
$394$	−1.27581e10	−	1.27581e10i	−0.529422	−	0.529422i
$395$	1.40879e10	−	1.40879e10i	0.578707	−	0.578707i
$396$	−2.77402e10	−	2.77402e10i	−1.12805	−	1.12805i
$397$	3.63683e10			1.46407			0.732033	−	0.681269i	$-0.238572\pi$
$397$	3.63683e10			1.46407			0.732033	+	0.681269i	$0.238572\pi$
$398$	2.78210e10	+	2.78210e10i	1.10877	+	1.10877i
$399$			1.56662e10i			0.618121i
$400$	1.57612e10			0.615670
$401$	−2.87379e10			−1.11142			−0.555709	−	0.831377i	$-0.687553\pi$
$401$	−2.87379e10			−1.11142			−0.555709	+	0.831377i	$0.687553\pi$
$402$	−9.67670e10			−3.70530
$403$	1.41108e10	−	1.41108e10i	0.534972	−	0.534972i
$404$	1.37872e10	−	1.37872e10i	0.517547	−	0.517547i
$405$			1.05728e9i			0.0392981i
$406$	7.60410e9	+	1.32038e10i	0.279862	+	0.485953i
$407$	3.12143e10			1.13756
$408$	1.14801e8	+	1.14801e8i	0.00414290	+	0.00414290i
$409$	−1.19347e10	−	1.19347e10i	−0.426499	−	0.426499i	0.460935	−	0.887434i	$-0.347514\pi$
$409$	−1.19347e10	−	1.19347e10i	−0.426499	−	0.426499i	−0.887434	+	0.460935i	$0.847514\pi$
$410$		−	5.63523e9i		−	0.199424i
$411$		−	4.05305e10i		−	1.42041i
$412$			3.07614e10i			1.06762i
$413$	−3.36690e9			−0.115726
$414$	5.98801e10	−	5.98801e10i	2.03836	−	2.03836i
$415$		−	4.45714e9i		−	0.150267i
$416$	−1.21464e10	+	1.21464e10i	−0.405578	+	0.405578i
$417$	−5.00503e10	−	5.00503e10i	−1.65524	−	1.65524i
$418$	3.14123e10	−	3.14123e10i	1.02895	−	1.02895i
$419$			3.60356e10i			1.16917i	0.811334	+	0.584583i	$0.198742\pi$
$419$			3.60356e10i			1.16917i	−0.811334	+	0.584583i	$0.801258\pi$
$420$	8.32982e9	+	8.32982e9i	0.267694	+	0.267694i
$421$	2.35035e10	−	2.35035e10i	0.748177	−	0.748177i	−0.225960	−	0.974137i	$-0.572552\pi$
$421$	2.35035e10	−	2.35035e10i	0.748177	−	0.748177i	0.974137	+	0.225960i	$0.0725519\pi$
$422$	5.82213e10			1.83583
$423$	−3.45942e10	−	3.45942e10i	−1.08054	−	1.08054i
$424$	6.40360e9	−	6.40360e9i	0.198135	−	0.198135i
$425$	−1.89693e8	−	1.89693e8i	−0.00581427	−	0.00581427i
$426$	−1.00562e11			−3.05350
$427$	−2.80858e9	−	2.80858e9i	−0.0844841	−	0.0844841i
$428$		−	1.30962e10i		−	0.390273i
$429$	2.83546e10			0.837134
$430$	−8.43529e9			−0.246732
$431$	−3.90623e10			−1.13200			−0.566002	−	0.824404i	$-0.691511\pi$
$431$	−3.90623e10			−1.13200			−0.566002	+	0.824404i	$0.691511\pi$
$432$	−2.94844e10	+	2.94844e10i	−0.846559	+	0.846559i
$433$	−2.73122e10	+	2.73122e10i	−0.776973	+	0.776973i	−0.979315	−	0.202342i	$-0.935145\pi$
$433$	−2.73122e10	+	2.73122e10i	−0.776973	+	0.776973i	0.202342	+	0.979315i	$0.435145\pi$
$434$		−	3.43759e10i		−	0.968937i
$435$	−3.42859e10	+	1.97453e10i	−0.957543	+	0.551452i
$436$	1.98559e10			0.549469
$437$	3.06616e10	+	3.06616e10i	0.840754	+	0.840754i
$438$	9.12619e10	+	9.12619e10i	2.47966	+	2.47966i
$439$			6.47050e10i			1.74213i	0.491172	+	0.871063i	$0.336569\pi$
$439$			6.47050e10i			1.74213i	−0.491172	+	0.871063i	$0.663431\pi$
$440$			7.06359e9i			0.188458i
$441$		−	5.14564e10i		−	1.36046i
$442$	3.45013e8			0.00903953
$443$	−3.86326e10	+	3.86326e10i	−1.00309	+	1.00309i	−0.00309265	+	0.999995i	$0.500984\pi$
$443$	−3.86326e10	+	3.86326e10i	−1.00309	+	1.00309i	−0.999995	+	0.00309265i	$0.999016\pi$
$444$			5.04593e10i			1.29840i
$445$	−2.63331e10	+	2.63331e10i	−0.671525	+	0.671525i
$446$	−2.80699e10	−	2.80699e10i	−0.709418	−	0.709418i
$447$	−7.93671e10	+	7.93671e10i	−1.98797	+	1.98797i
$448$			1.04622e10i			0.259722i
$449$	−1.66065e10	−	1.66065e10i	−0.408594	−	0.408594i	0.472654	−	0.881248i	$-0.343296\pi$
$449$	−1.66065e10	−	1.66065e10i	−0.408594	−	0.408594i	−0.881248	+	0.472654i	$0.843296\pi$
$450$	3.46504e10	−	3.46504e10i	0.845002	−	0.845002i
$451$	−1.05656e10			−0.255381
$452$	2.55191e10	+	2.55191e10i	0.611380	+	0.611380i
$453$	3.28524e10	−	3.28524e10i	0.780143	−	0.780143i
$454$	−1.11269e10	−	1.11269e10i	−0.261910	−	0.261910i
$455$	−5.29360e9			−0.123511
$456$	−1.07378e10	−	1.07378e10i	−0.248344	−	0.248344i
$457$			1.96106e10i			0.449599i	0.974405	+	0.224800i	$0.0721727\pi$
$457$			1.96106e10i			0.449599i	−0.974405	+	0.224800i	$0.927827\pi$
$458$	−3.67534e10			−0.835287
$459$	7.09716e8			0.0159895
$460$	3.26058e10			0.728222
$461$	7.49353e9	−	7.49353e9i	0.165914	−	0.165914i	−0.619267	−	0.785181i	$-0.712570\pi$
$461$	7.49353e9	−	7.49353e9i	0.165914	−	0.165914i	0.785181	+	0.619267i	$0.212570\pi$
$462$	3.45380e10	−	3.45380e10i	0.758105	−	0.758105i
$463$			2.31769e10i			0.504350i	0.967682	+	0.252175i	$0.0811458\pi$
$463$			2.31769e10i			0.504350i	−0.967682	+	0.252175i	$0.918854\pi$
$464$	−5.12090e10	−	1.37810e10i	−1.10478	−	0.297310i
$465$	8.92630e10			1.90924
$466$	−2.30934e10	−	2.30934e10i	−0.489717	−	0.489717i
$467$	−2.48492e10	−	2.48492e10i	−0.522451	−	0.522451i	0.395860	−	0.918311i	$-0.370447\pi$
$467$	−2.48492e10	−	2.48492e10i	−0.522451	−	0.522451i	−0.918311	+	0.395860i	$0.870447\pi$
$468$			2.84979e10i			0.594059i
$469$		−	3.38717e10i		−	0.700077i
$470$		−	4.16576e10i		−	0.853696i
$471$	1.01424e11			2.06090
$472$	2.30770e9	−	2.30770e9i	0.0464955	−	0.0464955i
$473$			1.58155e10i			0.315965i
$474$	9.44274e10	−	9.44274e10i	1.87062	−	1.87062i
$475$	1.77427e10	+	1.77427e10i	0.348534	+	0.348534i
$476$	1.90033e8	−	1.90033e8i	0.00370170	−	0.00370170i
$477$		−	1.01098e11i		−	1.95286i
$478$	6.53140e10	+	6.53140e10i	1.25111	+	1.25111i
$479$	4.55455e10	−	4.55455e10i	0.865174	−	0.865174i	−0.126760	−	0.991933i	$-0.540458\pi$
$479$	4.55455e10	−	4.55455e10i	0.865174	−	0.865174i	0.991933	+	0.126760i	$0.0404577\pi$
$480$	−7.68366e10			−1.44745
$481$	−1.60335e10	−	1.60335e10i	−0.299534	−	0.299534i
$482$	−3.90771e10	+	3.90771e10i	−0.723992	+	0.723992i
$483$	3.37126e10	+	3.37126e10i	0.619447	+	0.619447i
$484$	−1.73328e10			−0.315855
$485$	4.41205e10	+	4.41205e10i	0.797394	+	0.797394i
$486$		−	7.17894e10i		−	1.28681i
$487$	−4.30485e10			−0.765318			−0.382659	−	0.923890i	$-0.624992\pi$
$487$	−4.30485e10			−0.765318			−0.382659	+	0.923890i	$0.624992\pi$
$488$	3.85004e9			0.0678869
$489$	5.45180e10			0.953464
$490$	3.09813e10	−	3.09813e10i	0.537423	−	0.537423i
$491$	2.04704e10	−	2.04704e10i	0.352208	−	0.352208i	−0.508722	−	0.860931i	$-0.669882\pi$
$491$	2.04704e10	−	2.04704e10i	0.352208	−	0.352208i	0.860931	+	0.508722i	$0.169882\pi$
$492$		−	1.70798e10i		−	0.291490i
$493$	4.50463e8	+	7.82185e8i	0.00762555	+	0.0132410i
$494$	−3.22704e10			−0.541871
$495$	5.57590e10	+	5.57590e10i	0.928741	+	0.928741i
$496$	8.46005e10	+	8.46005e10i	1.39780	+	1.39780i
$497$		−	3.52003e10i		−	0.576927i
$498$		−	2.98749e10i		−	0.485723i
$499$			1.10457e11i			1.78153i	0.454469	+	0.890763i	$0.349829\pi$
$499$			1.10457e11i			1.78153i	−0.454469	+	0.890763i	$0.650171\pi$
$500$	5.39291e10			0.862866
$501$	−2.00952e10	+	2.00952e10i	−0.318963	+	0.318963i
$502$		−	9.73607e10i		−	1.53309i
$503$	−3.48785e10	+	3.48785e10i	−0.544861	+	0.544861i	−0.924950	−	0.380089i	$-0.875893\pi$
$503$	−3.48785e10	+	3.48785e10i	−0.544861	+	0.544861i	0.380089	+	0.924950i	$0.375893\pi$
$504$	−7.34027e9	−	7.34027e9i	−0.113760	−	0.113760i
$505$	−2.77129e10	+	2.77129e10i	−0.426105	+	0.426105i
$506$		−	1.35194e11i		−	2.06232i
$507$	6.14006e10	+	6.14006e10i	0.929268	+	0.929268i
$508$	−6.91993e10	+	6.91993e10i	−1.03907	+	1.03907i
$509$	−3.97798e10			−0.592640			−0.296320	−	0.955089i	$-0.595760\pi$
$509$	−3.97798e10			−0.592640			−0.296320	+	0.955089i	$0.595760\pi$
$510$	1.09125e9	+	1.09125e9i	0.0161304	+	0.0161304i
$511$	−3.19448e10	+	3.19448e10i	−0.468507	+	0.468507i
$512$	−5.97125e10	−	5.97125e10i	−0.868931	−	0.868931i
$513$	−6.63825e10			−0.958483
$514$	−3.94834e10	−	3.94834e10i	−0.565669	−	0.565669i
$515$		−	6.18319e10i		−	0.878989i
$516$	−2.55665e10			−0.360639
$517$	−7.81048e10			−1.09324
$518$	−3.90598e10			−0.542515
$519$	8.77430e10	−	8.77430e10i	1.20932	−	1.20932i
$520$	3.62827e9	−	3.62827e9i	0.0496234	−	0.0496234i
$521$			2.88564e10i			0.391644i	0.980640	+	0.195822i	$0.0627374\pi$
$521$			2.88564e10i			0.391644i	−0.980640	+	0.195822i	$0.937263\pi$
$522$	−1.42878e11	+	8.22841e10i	−1.92435	+	1.10824i
$523$	−5.35499e9			−0.0715735			−0.0357868	−	0.999359i	$-0.511394\pi$
$523$	−5.35499e9			−0.0715735			−0.0357868	+	0.999359i	$0.511394\pi$
$524$	5.47154e9	+	5.47154e9i	0.0725746	+	0.0725746i
$525$	1.95082e10	+	1.95082e10i	0.256791	+	0.256791i
$526$			5.76392e10i			0.752965i
$527$		−	2.03641e9i		−	0.0264012i
$528$			1.69999e11i			2.18731i
$529$	5.36520e10			0.685115
$530$	6.08702e10	−	6.08702e10i	0.771439	−	0.771439i
$531$		−	3.64333e10i		−	0.458269i
$532$	−1.77745e10	+	1.77745e10i	−0.221897	+	0.221897i
$533$	5.42712e9	+	5.42712e9i	0.0672451	+	0.0672451i
$534$	−1.76503e11	+	1.76503e11i	−2.17064	+	2.17064i
$535$			2.63239e10i			0.321318i
$536$	2.32159e10	+	2.32159e10i	0.281272	+	0.281272i
$537$	−1.14621e11	+	1.14621e11i	−1.37838	+	1.37838i
$538$	8.81068e10			1.05167
$539$	−5.80876e10	−	5.80876e10i	−0.688222	−	0.688222i
$540$	−3.52959e10	+	3.52959e10i	−0.415097	+	0.415097i
$541$	−1.86628e10	−	1.86628e10i	−0.217865	−	0.217865i	0.589733	−	0.807598i	$-0.299233\pi$
$541$	−1.86628e10	−	1.86628e10i	−0.217865	−	0.217865i	−0.807598	+	0.589733i	$0.799233\pi$
$542$	−1.12852e11			−1.30772
$543$	−5.37980e10	−	5.37980e10i	−0.618823	−	0.618823i
$544$			1.75292e9i			0.0200155i
$545$	−3.99112e10			−0.452386
$546$	−3.54815e10			−0.399237
$547$	1.15466e11			1.28975			0.644874	−	0.764289i	$-0.276910\pi$
$547$	1.15466e11			1.28975			0.644874	+	0.764289i	$0.276910\pi$
$548$	4.59849e10	−	4.59849e10i	0.509909	−	0.509909i
$549$	3.03917e10	−	3.03917e10i	0.334553	−	0.334553i
$550$		−	7.82316e10i		−	0.854932i
$551$	−4.21335e10	−	7.31608e10i	−0.457111	−	0.793728i
$552$	−4.62137e10			−0.497754
$553$	3.30528e10	+	3.30528e10i	0.353433	+	0.353433i
$554$	−3.73785e10	−	3.73785e10i	−0.396810	−	0.396810i
$555$		−	1.01426e11i		−	1.06900i
$556$		−	1.13572e11i		−	1.18842i
$557$			1.21639e11i			1.26372i	0.775082	+	0.631860i	$0.217708\pi$
$557$			1.21639e11i			1.26372i	−0.775082	+	0.631860i	$0.782292\pi$
$558$	3.71983e11			3.83695
$559$	8.12376e9	−	8.12376e9i	0.0831975	−	0.0831975i
$560$		−	3.17375e10i		−	0.322716i
$561$	2.04601e9	−	2.04601e9i	0.0206565	−	0.0206565i
$562$	1.44075e11	+	1.44075e11i	1.44425	+	1.44425i
$563$	8.87312e10	−	8.87312e10i	0.883167	−	0.883167i	−0.110688	−	0.993855i	$-0.535305\pi$
$563$	8.87312e10	−	8.87312e10i	0.883167	−	0.883167i	0.993855	+	0.110688i	$0.0353055\pi$
$564$		−	1.26260e11i		−	1.24781i
$565$	−5.12945e10	−	5.12945e10i	−0.503358	−	0.503358i
$566$	2.13411e10	−	2.13411e10i	0.207947	−	0.207947i
$567$	−2.48058e9			−0.0240005
$568$	2.41265e10	+	2.41265e10i	0.231794	+	0.231794i
$569$	−6.38061e10	+	6.38061e10i	−0.608714	+	0.608714i	−0.942610	−	0.333896i	$-0.891637\pi$
$569$	−6.38061e10	+	6.38061e10i	−0.608714	+	0.608714i	0.333896	+	0.942610i	$0.391637\pi$
$570$	−1.02069e11	−	1.02069e11i	−0.966930	−	0.966930i
$571$	−1.08647e11			−1.02205			−0.511024	−	0.859566i	$-0.670734\pi$
$571$	−1.08647e11			−1.02205			−0.511024	+	0.859566i	$0.670734\pi$
$572$	3.21705e10	+	3.21705e10i	0.300520	+	0.300520i
$573$		−	4.89925e10i		−	0.454476i
$574$	1.32213e10			0.121794
$575$	7.63620e10			0.698563
$576$	−1.13211e11			−1.02849
$577$	−1.89913e10	+	1.89913e10i	−0.171337	+	0.171337i	−0.787567	−	0.616229i	$-0.788659\pi$
$577$	−1.89913e10	+	1.89913e10i	−0.171337	+	0.171337i	0.616229	+	0.787567i	$0.288659\pi$
$578$	−1.06606e11	+	1.06606e11i	−0.955144	+	0.955144i
$579$		−	1.88409e11i		−	1.67644i
$580$	−6.13025e10	−	1.64973e10i	−0.541709	−	0.145781i
$581$	1.04572e10			0.0917724
$582$	2.95727e11	+	2.95727e11i	2.57750	+	2.57750i
$583$	−1.14127e11	−	1.14127e11i	−0.987902	−	0.987902i
$584$		−	4.37903e10i		−	0.376467i
$585$		−	5.72822e10i		−	0.489098i
$586$			2.61706e11i			2.21934i
$587$	1.48583e11			1.25146			0.625730	−	0.780040i	$-0.284801\pi$
$587$	1.48583e11			1.25146			0.625730	+	0.780040i	$0.284801\pi$
$588$	9.39013e10	−	9.39013e10i	0.785530	−	0.785530i
$589$			1.90473e11i			1.58261i
$590$	2.19361e10	−	2.19361e10i	0.181030	−	0.181030i
$591$	7.77257e10	+	7.77257e10i	0.637111	+	0.637111i
$592$	9.61278e10	−	9.61278e10i	0.782640	−	0.782640i
$593$		−	1.75655e11i		−	1.42050i	−0.703950	−	0.710250i	$-0.748582\pi$
$593$		−	1.75655e11i		−	1.42050i	0.703950	−	0.710250i	$-0.251418\pi$
$594$	1.46348e11	+	1.46348e11i	1.17555	+	1.17555i
$595$	−3.81976e8	+	3.81976e8i	−0.00304767	+	0.00304767i
$596$	−1.80096e11			−1.42731
$597$	−1.69493e11	−	1.69493e11i	−1.33430	−	1.33430i
$598$	−6.94435e10	+	6.94435e10i	−0.543033	+	0.543033i
$599$	8.96808e8	+	8.96808e8i	0.00696614	+	0.00696614i	0.710581	−	0.703615i	$-0.248432\pi$
$599$	8.96808e8	+	8.96808e8i	0.00696614	+	0.00696614i	−0.703615	+	0.710581i	$0.748432\pi$
$600$	−2.67421e10			−0.206344
$601$	3.52662e10	+	3.52662e10i	0.270309	+	0.270309i	0.829225	−	0.558916i	$-0.188782\pi$
$601$	3.52662e10	+	3.52662e10i	0.270309	+	0.270309i	−0.558916	+	0.829225i	$0.688782\pi$
$602$		−	1.97907e10i		−	0.150687i
$603$	3.66527e11			2.77228
$604$	7.45470e10			0.560122
$605$	3.48397e10			0.260048
$606$	−1.85752e11	+	1.85752e11i	−1.37734	+	1.37734i
$607$	−1.09385e11	+	1.09385e11i	−0.805758	+	0.805758i	−0.983989	−	0.178231i	$-0.942963\pi$
$607$	−1.09385e11	+	1.09385e11i	−0.805758	+	0.805758i	0.178231	+	0.983989i	$0.442963\pi$
$608$		−	1.63957e11i		−	1.19982i
$609$	−4.63261e10	−	8.04407e10i	−0.336788	−	0.584799i
$610$	3.65970e10			0.264318
$611$	4.01192e10	+	4.01192e10i	0.287864	+	0.287864i
$612$	2.05635e9	+	2.05635e9i	0.0146586	+	0.0146586i
$613$			8.90683e10i			0.630785i	0.948961	+	0.315393i	$0.102136\pi$
$613$			8.90683e10i			0.630785i	−0.948961	+	0.315393i	$0.897864\pi$
$614$			1.09923e11i			0.773418i
$615$			3.43313e10i			0.239988i
$616$	−1.65724e10			−0.115097
$617$	−4.02526e10	+	4.02526e10i	−0.277750	+	0.277750i	−0.832210	−	0.554460i	$-0.812925\pi$
$617$	−4.02526e10	+	4.02526e10i	−0.277750	+	0.277750i	0.554460	+	0.832210i	$0.312925\pi$
$618$		−	4.14441e11i		−	2.84125i
$619$	1.63845e11	−	1.63845e11i	1.11602	−	1.11602i	0.123698	−	0.992320i	$-0.460525\pi$
$619$	1.63845e11	−	1.63845e11i	1.11602	−	1.11602i	0.992320	−	0.123698i	$-0.0394754\pi$
$620$	1.01276e11	+	1.01276e11i	0.685391	+	0.685391i
$621$	−1.42850e11	+	1.42850e11i	−0.960539	+	0.960539i
$622$		−	1.88554e11i		−	1.25972i
$623$	−6.17822e10	−	6.17822e10i	−0.410120	−	0.410120i
$624$	8.73213e10	−	8.73213e10i	0.575946	−	0.575946i
$625$	−2.62873e10			−0.172276
$626$	1.11542e11	+	1.11542e11i	0.726344	+	0.726344i
$627$	−1.91372e11	+	1.91372e11i	−1.23825	+	1.23825i
$628$	1.15073e11	+	1.15073e11i	0.739836	+	0.739836i
$629$	−2.31388e9			−0.0147822
$630$	−6.97739e10	−	6.97739e10i	−0.442925	−	0.442925i
$631$		−	1.56676e11i		−	0.988291i	−0.869379	−	0.494146i	$-0.835481\pi$
$631$		−	1.56676e11i		−	0.988291i	0.869379	−	0.494146i	$-0.164519\pi$
$632$	−4.53092e10			−0.284000
$633$	−3.54699e11			−2.20925
$634$	−3.06753e11			−1.89859
$635$	1.39094e11	−	1.39094e11i	0.855486	−	0.855486i
$636$	1.84492e11	−	1.84492e11i	1.12758	−	1.12758i
$637$			5.96743e10i			0.362435i
$638$	−6.84031e10	+	2.54179e11i	−0.412851	+	1.53411i
$639$	3.80903e11			2.28460
$640$	3.74479e10	+	3.74479e10i	0.223207	+	0.223207i
$641$	1.45444e11	+	1.45444e11i	0.861519	+	0.861519i	0.991515	−	0.129996i	$-0.0414963\pi$
$641$	1.45444e11	+	1.45444e11i	0.861519	+	0.861519i	−0.129996	+	0.991515i	$0.541496\pi$
$642$			1.76442e11i			1.03863i
$643$		−	2.03036e11i		−	1.18776i	−0.804553	−	0.593880i	$-0.797595\pi$
$643$		−	2.03036e11i		−	1.18776i	0.804553	−	0.593880i	$-0.202405\pi$
$644$			7.64990e10i			0.444746i
$645$	5.13899e10			0.296920
$646$	−2.32856e9	+	2.32856e9i	−0.0133708	+	0.0133708i
$647$			1.41490e11i			0.807439i	0.914883	+	0.403719i	$0.132283\pi$
$647$			1.41490e11i			0.807439i	−0.914883	+	0.403719i	$0.867717\pi$
$648$	1.70020e9	−	1.70020e9i	0.00964275	−	0.00964275i
$649$	−4.11285e10	−	4.11285e10i	−0.231827	−	0.231827i
$650$	−4.01843e10	+	4.01843e10i	−0.225114	+	0.225114i
$651$			2.09427e11i			1.16603i
$652$	6.18548e10	+	6.18548e10i	0.342281	+	0.342281i
$653$	−6.28364e10	+	6.28364e10i	−0.345588	+	0.345588i	−0.858463	−	0.512875i	$-0.828580\pi$
$653$	−6.28364e10	+	6.28364e10i	−0.345588	+	0.345588i	0.512875	+	0.858463i	$0.328580\pi$
$654$	−2.67513e11			−1.46229
$655$	−1.09981e10	−	1.09981e10i	−0.0597518	−	0.0597518i
$656$	−3.25380e10	+	3.25380e10i	−0.175702	+	0.175702i
$657$	−3.45675e11	−	3.45675e11i	−1.85527	−	1.85527i
$658$	9.77362e10			0.521377
$659$	6.60098e10	+	6.60098e10i	0.349999	+	0.349999i	0.860109	−	0.510110i	$-0.170395\pi$
$659$	6.60098e10	+	6.60098e10i	0.349999	+	0.349999i	−0.510110	+	0.860109i	$0.670395\pi$
$660$			2.03506e11i			1.07251i
$661$	−2.09873e11			−1.09939			−0.549695	−	0.835366i	$-0.685256\pi$
$661$	−2.09873e11			−1.09939			−0.549695	+	0.835366i	$0.685256\pi$
$662$	−3.82412e9			−0.0199113
$663$	−2.10190e9			−0.0108782
$664$	−7.16746e9	+	7.16746e9i	−0.0368717	+	0.0368717i
$665$	3.57277e10	−	3.57277e10i	0.182691	−	0.182691i
$666$		−	4.22667e11i		−	2.14833i
$667$	−2.48105e11	−	6.67683e10i	−1.25352	−	0.337340i
$668$	−4.55990e10			−0.229007
$669$	1.71009e11	+	1.71009e11i	0.853719	+	0.853719i
$670$	2.20682e11	+	2.20682e11i	1.09513	+	1.09513i
$671$		−	6.86166e10i		−	0.338485i
$672$		−	1.80272e11i		−	0.883999i
$673$		−	2.34655e11i		−	1.14385i	−0.820306	−	0.571925i	$-0.806197\pi$
$673$		−	2.34655e11i		−	1.14385i	0.820306	−	0.571925i	$-0.193803\pi$
$674$	−4.45501e11			−2.15878
$675$	−8.26621e10	+	8.26621e10i	−0.398191	+	0.398191i
$676$			1.39327e11i			0.667190i
$677$	2.68509e11	−	2.68509e11i	1.27821	−	1.27821i	0.336547	−	0.941667i	$-0.390741\pi$
$677$	2.68509e11	−	2.68509e11i	1.27821	−	1.27821i	0.941667	−	0.336547i	$-0.109259\pi$
$678$	−3.43812e11	−	3.43812e11i	−1.62706	−	1.62706i
$679$	−1.03514e11	+	1.03514e11i	−0.486992	+	0.486992i
$680$		−	5.23618e8i		−	0.00244894i
$681$	6.77881e10	+	6.77881e10i	0.315185	+	0.315185i
$682$	4.19920e11	−	4.19920e11i	1.94102	−	1.94102i
$683$	1.48776e11			0.683676			0.341838	−	0.939759i	$-0.388951\pi$
$683$	1.48776e11			0.683676			0.341838	+	0.939759i	$0.388951\pi$
$684$	−1.92339e11	−	1.92339e11i	−0.878703	−	0.878703i
$685$	−9.24318e10	+	9.24318e10i	−0.419816	+	0.419816i
$686$	1.60504e11	+	1.60504e11i	0.724750	+	0.724750i
$687$	2.23911e11			1.00519
$688$	4.87056e10	+	4.87056e10i	0.217383	+	0.217383i
$689$			1.17244e11i			0.520254i
$690$	−4.39291e11			−1.93801
$691$	−1.77099e11			−0.776789			−0.388394	−	0.921493i	$-0.626970\pi$
$691$	−1.77099e11			−0.776789			−0.388394	+	0.921493i	$0.626970\pi$
$692$	1.99102e11			0.868263
$693$	−1.30821e11	+	1.30821e11i	−0.567209	+	0.567209i
$694$	1.02396e11	−	1.02396e11i	0.441411	−	0.441411i
$695$			2.28284e11i			0.978446i
$696$	8.68869e10	+	2.33824e10i	0.370269	+	0.0996443i
$697$	7.83220e8			0.00331858
$698$	5.89585e10	+	5.89585e10i	0.248385	+	0.248385i
$699$	1.40691e11	+	1.40691e11i	0.589329	+	0.589329i
$700$			4.42671e10i			0.184369i
$701$		−	4.22110e11i		−	1.74805i	−0.485883	−	0.874024i	$-0.661502\pi$
$701$		−	4.22110e11i		−	1.74805i	0.485883	−	0.874024i	$-0.338498\pi$
$702$		−	1.50346e11i		−	0.619073i
$703$	2.16427e11			0.886113
$704$	−1.27801e11	+	1.27801e11i	−0.520287	+	0.520287i
$705$			2.53789e11i			1.02734i
$706$	−1.97621e11	+	1.97621e11i	−0.795451	+	0.795451i
$707$	−6.50193e10	−	6.50193e10i	−0.260235	−	0.260235i
$708$	6.64862e10	−	6.64862e10i	0.264605	−	0.264605i
$709$			2.20079e11i			0.870952i	0.900200	+	0.435476i	$0.143420\pi$
$709$			2.20079e11i			0.870952i	−0.900200	+	0.435476i	$0.856580\pi$
$710$	2.29338e11	+	2.29338e11i	0.902490	+	0.902490i
$711$	−3.57665e11	+	3.57665e11i	−1.39958	+	1.39958i
$712$	8.46919e10			0.329550
$713$	4.09885e11	+	4.09885e11i	1.58600	+	1.58600i
$714$	−2.56027e9	+	2.56027e9i	−0.00985129	+	0.00985129i
$715$	−6.46642e10	−	6.46642e10i	−0.247423	−	0.247423i
$716$	−2.60093e11			−0.989639
$717$	−3.97909e11	−	3.97909e11i	−1.50559	−	1.50559i
$718$		−	1.26800e11i		−	0.477115i
$719$	5.01062e11			1.87489			0.937445	−	0.348134i	$-0.113185\pi$
$719$	5.01062e11			1.87489			0.937445	+	0.348134i	$0.113185\pi$
$720$	3.43432e11			1.27794
$721$	1.45069e11			0.536824
$722$	−4.18088e10	+	4.18088e10i	−0.153858	+	0.153858i
$723$	2.38067e11	−	2.38067e11i	0.871258	−	0.871258i
$724$		−	1.22076e11i		−	0.444299i
$725$	−1.43569e11	−	3.86363e10i	−0.519647	−	0.139844i
$726$	2.33521e11			0.840580
$727$	−2.65104e11	−	2.65104e11i	−0.949027	−	0.949027i	0.0497354	−	0.998762i	$-0.484162\pi$
$727$	−2.65104e11	−	2.65104e11i	−0.949027	−	0.949027i	−0.998762	+	0.0497354i	$0.984162\pi$
$728$	8.51257e9	+	8.51257e9i	0.0303064	+	0.0303064i
$729$			4.53691e11i			1.60639i
$730$		−	4.16255e11i		−	1.46578i
$731$		−	1.17239e9i		−	0.00410584i
$732$	1.10922e11			0.386343
$733$	−1.80221e11	+	1.80221e11i	−0.624295	+	0.624295i	−0.946627	−	0.322332i	$-0.895533\pi$
$733$	−1.80221e11	+	1.80221e11i	−0.624295	+	0.624295i	0.322332	+	0.946627i	$0.395533\pi$
$734$			1.51186e11i			0.520868i
$735$	−1.88746e11	+	1.88746e11i	−0.646739	+	0.646739i
$736$	−3.52824e11	−	3.52824e11i	−1.20240	−	1.20240i
$737$	4.13761e11	−	4.13761e11i	1.40243	−	1.40243i
$738$			1.43067e11i			0.482298i
$739$	−3.58152e11	−	3.58152e11i	−1.20085	−	1.20085i	−0.973907	−	0.226946i	$-0.927126\pi$
$739$	−3.58152e11	−	3.58152e11i	−1.20085	−	1.20085i	−0.226946	−	0.973907i	$-0.572874\pi$
$740$	1.15075e11	−	1.15075e11i	0.383755	−	0.383755i
$741$	1.96599e11			0.652092
$742$	1.42812e11	+	1.42812e11i	0.471140	+	0.471140i
$743$	2.40901e11	−	2.40901e11i	0.790467	−	0.790467i	−0.191103	−	0.981570i	$-0.561206\pi$
$743$	2.40901e11	−	2.40901e11i	0.790467	−	0.790467i	0.981570	+	0.191103i	$0.0612064\pi$
$744$	−1.43543e11	−	1.43543e11i	−0.468478	−	0.468478i
$745$	3.62002e11			1.17513
$746$	6.20402e10	+	6.20402e10i	0.200317	+	0.200317i
$747$			1.13158e11i			0.363415i
$748$	4.64272e9			0.0148308
$749$	−6.17605e10			−0.196238
$750$	−7.26575e11			−2.29633
$751$	−9.52608e10	+	9.52608e10i	−0.299471	+	0.299471i	−0.840807	−	0.541336i	$-0.817919\pi$
$751$	−9.52608e10	+	9.52608e10i	−0.299471	+	0.299471i	0.541336	+	0.840807i	$0.317919\pi$
$752$	−2.40532e11	+	2.40532e11i	−0.752146	+	0.752146i
$753$			5.93146e11i			1.84494i
$754$	1.65697e11	−	9.54255e10i	0.512660	−	0.295243i
$755$	−1.49843e11			−0.461157
$756$	−8.28104e10	−	8.28104e10i	−0.253512	−	0.253512i
$757$	6.68238e10	+	6.68238e10i	0.203492	+	0.203492i	0.801494	−	0.598002i	$-0.204039\pi$
$757$	6.68238e10	+	6.68238e10i	0.203492	+	0.203492i	−0.598002	+	0.801494i	$0.704039\pi$
$758$			5.55420e11i			1.68246i
$759$			8.23636e11i			2.48181i
$760$			4.89760e10i			0.146801i
$761$	−1.65489e11			−0.493436			−0.246718	−	0.969087i	$-0.579352\pi$
$761$	−1.65489e11			−0.493436			−0.246718	+	0.969087i	$0.579352\pi$
$762$	9.32306e11	−	9.32306e11i	2.76528	−	2.76528i
$763$		−	9.36388e10i		−	0.276285i
$764$	5.55857e10	−	5.55857e10i	0.163151	−	0.163151i
$765$	−4.13337e9	−	4.13337e9i	−0.0120686	−	0.0120686i
$766$	1.46622e11	−	1.46622e11i	0.425876	−	0.425876i
$767$			4.22520e10i			0.122086i
$768$	5.01285e11	+	5.01285e11i	1.44092	+	1.44092i
$769$	−2.43284e11	+	2.43284e11i	−0.695677	+	0.695677i	−0.963475	−	0.267798i	$-0.913704\pi$
$769$	−2.43284e11	+	2.43284e11i	−0.695677	+	0.695677i	0.267798	+	0.963475i	$0.413704\pi$
$770$	−1.57531e11			−0.448130
$771$	2.40543e11	+	2.40543e11i	0.680731	+	0.680731i
$772$	2.13764e11	−	2.13764e11i	0.601820	−	0.601820i
$773$	−2.41551e11	−	2.41551e11i	−0.676535	−	0.676535i	0.282679	−	0.959214i	$-0.408777\pi$
$773$	−2.41551e11	−	2.41551e11i	−0.676535	−	0.676535i	−0.959214	+	0.282679i	$0.908777\pi$
$774$	2.14155e11			0.596712
$775$	2.37185e11	+	2.37185e11i	0.657476	+	0.657476i
$776$		−	1.41899e11i		−	0.391320i
$777$	2.37962e11			0.652866
$778$	−2.25983e11			−0.616817
$779$	−7.32576e10			−0.198931
$780$	1.04533e11	−	1.04533e11i	0.282406	−	0.282406i
$781$	4.29991e11	−	4.29991e11i	1.15573	−	1.15573i
$782$			1.00218e10i			0.0267990i
$783$	3.40851e11	−	1.96297e11i	0.906813	−	0.522237i
$784$	−3.57774e11			−0.946989
$785$	−2.31303e11	−	2.31303e11i	−0.609119	−	0.609119i
$786$	−7.37168e10	−	7.37168e10i	−0.193142	−	0.193142i
$787$		−	4.43795e10i		−	0.115687i	−0.998326	−	0.0578434i	$-0.981578\pi$
$787$		−	4.43795e10i		−	0.115687i	0.998326	−	0.0578434i	$-0.0184224\pi$
$788$			1.76371e11i			0.457429i
$789$		−	3.51152e11i		−	0.906124i
$790$	−4.30693e11			−1.10576
$791$	1.20346e11	−	1.20346e11i	0.307416	−	0.307416i
$792$		−	1.79331e11i		−	0.455779i
$793$	−3.52455e10	+	3.52455e10i	−0.0891272	+	0.0891272i
$794$	−5.55921e11	−	5.55921e11i	−1.39872	−	1.39872i
$795$	−3.70837e11	+	3.70837e11i	−0.928356	+	0.928356i
$796$		−	3.84604e11i		−	0.957992i
$797$	−2.57295e11	−	2.57295e11i	−0.637673	−	0.637673i	0.312308	−	0.949981i	$-0.398898\pi$
$797$	−2.57295e11	−	2.57295e11i	−0.637673	−	0.637673i	−0.949981	+	0.312308i	$0.898898\pi$
$798$	2.39472e11	−	2.39472e11i	0.590532	−	0.590532i
$799$	5.78984e9			0.0142062
$800$	−2.04166e11	−	2.04166e11i	−0.498452	−	0.498452i
$801$	6.68546e11	−	6.68546e11i	1.62406	−	1.62406i
$802$	4.39284e11	+	4.39284e11i	1.06181	+	1.06181i
$803$	−7.80445e11			−1.87707
$804$	6.68865e11	+	6.68865e11i	1.60072	+	1.60072i
$805$		−	1.53767e11i		−	0.366167i
$806$	−4.31391e11			−1.02219
$807$	−5.36769e11			−1.26559
$808$	8.91295e10			0.209111
$809$	1.16232e11	−	1.16232e11i	0.271351	−	0.271351i	−0.558293	−	0.829644i	$-0.688543\pi$
$809$	1.16232e11	−	1.16232e11i	0.271351	−	0.271351i	0.829644	+	0.558293i	$0.188543\pi$
$810$	1.61615e10	−	1.61615e10i	0.0375441	−	0.0375441i
$811$			4.76210e11i			1.10082i	0.834895	+	0.550409i	$0.185528\pi$
$811$			4.76210e11i			1.10082i	−0.834895	+	0.550409i	$0.814472\pi$
$812$	3.87056e10	−	1.43826e11i	0.0890328	−	0.330837i
$813$	6.87525e11			1.57372
$814$	−4.77137e11	−	4.77137e11i	−1.08679	−	1.08679i
$815$	−1.24331e11	−	1.24331e11i	−0.281805	−	0.281805i
$816$		−	1.26019e10i		−	0.0284233i
$817$			1.09658e11i			0.246123i
$818$			3.64864e11i			0.814926i
$819$	1.34394e11			0.298706
$820$	−3.89514e10	+	3.89514e10i	−0.0861525	+	0.0861525i
$821$			1.87399e11i			0.412472i	0.978502	+	0.206236i	$0.0661215\pi$
$821$			1.87399e11i			0.412472i	−0.978502	+	0.206236i	$0.933878\pi$
$822$	−6.19543e11	+	6.19543e11i	−1.35701	+	1.35701i
$823$	1.75449e11	+	1.75449e11i	0.382429	+	0.382429i	0.871977	−	0.489547i	$-0.162838\pi$
$823$	1.75449e11	+	1.75449e11i	0.382429	+	0.382429i	−0.489547	+	0.871977i	$0.662838\pi$
$824$	−9.94310e10	+	9.94310e10i	−0.215682	+	0.215682i
$825$			4.76607e11i			1.02883i
$826$	5.14660e10	+	5.14660e10i	0.110561	+	0.110561i
$827$	−2.93156e11	+	2.93156e11i	−0.626724	+	0.626724i	−0.947242	−	0.320518i	$-0.896143\pi$
$827$	−2.93156e11	+	2.93156e11i	−0.626724	+	0.626724i	0.320518	+	0.947242i	$0.396143\pi$
$828$	−8.27797e11			−1.76118
$829$	−3.48336e11	−	3.48336e11i	−0.737531	−	0.737531i	0.234569	−	0.972100i	$-0.424632\pi$
$829$	−3.48336e11	−	3.48336e11i	−0.737531	−	0.737531i	−0.972100	+	0.234569i	$0.924632\pi$
$830$	−6.81312e10	+	6.81312e10i	−0.143560	+	0.143560i
$831$	2.27719e11	+	2.27719e11i	0.477524	+	0.477524i
$832$	1.31292e11			0.273996
$833$	4.30598e9	+	4.30598e9i	0.00894318	+	0.00894318i
$834$			1.53012e12i			3.16273i
$835$	9.16561e10			0.188545
$836$	−4.34251e11			−0.889029
$837$	−8.87403e11			−1.80809
$838$	5.50836e11	−	5.50836e11i	1.11698	−	1.11698i
$839$	−2.91675e11	+	2.91675e11i	−0.588643	+	0.588643i	−0.937264	−	0.348621i	$-0.886650\pi$
$839$	−2.91675e11	+	2.91675e11i	−0.588643	+	0.588643i	0.348621	+	0.937264i	$0.386650\pi$
$840$			5.38494e10i			0.108159i
$841$	4.32682e11	+	2.51064e11i	0.864937	+	0.501880i
$842$	−7.18543e11			−1.42957
$843$	−8.77740e11	−	8.77740e11i	−1.73802	−	1.73802i
$844$	−4.02433e11	−	4.02433e11i	−0.793092	−	0.793092i
$845$		−	2.80054e11i		−	0.549308i
$846$			1.05761e12i			2.06463i
$847$			8.17402e10i			0.158819i
$848$	−7.02933e11			−1.35935
$849$	−1.30016e11	+	1.30016e11i	−0.250245	+	0.250245i
$850$			5.79924e9i			0.0111095i
$851$	4.65734e11	−	4.65734e11i	0.888014	−	0.888014i
$852$	6.95100e11	+	6.95100e11i	1.31913	+	1.31913i
$853$	4.47893e11	−	4.47893e11i	0.846016	−	0.846016i	−0.143617	−	0.989633i	$-0.545873\pi$
$853$	4.47893e11	−	4.47893e11i	0.846016	−	0.846016i	0.989633	+	0.143617i	$0.0458734\pi$
$854$			8.58631e10i			0.161427i
$855$	3.86610e11	+	3.86610e11i	0.723450	+	0.723450i
$856$	4.23311e10	−	4.23311e10i	0.0788433	−	0.0788433i
$857$	1.00582e12			1.86465			0.932327	−	0.361617i	$-0.117775\pi$
$857$	1.00582e12			1.86465			0.932327	+	0.361617i	$0.117775\pi$
$858$	−4.33425e11	−	4.33425e11i	−0.799770	−	0.799770i
$859$	−5.65722e11	+	5.65722e11i	−1.03904	+	1.03904i	−0.0398286	+	0.999207i	$0.512681\pi$
$859$	−5.65722e11	+	5.65722e11i	−1.03904	+	1.03904i	−0.999207	+	0.0398286i	$0.987319\pi$
$860$	5.83057e10	+	5.83057e10i	0.106590	+	0.106590i
$861$	−8.05472e10			−0.146568
$862$	5.97100e11	+	5.97100e11i	1.08148	+	1.08148i
$863$		−	2.49119e11i		−	0.449122i	−0.974460	−	0.224561i	$-0.927905\pi$
$863$		−	2.49119e11i		−	0.449122i	0.974460	−	0.224561i	$-0.0720948\pi$
$864$	7.63867e11			1.37076
$865$	−4.00205e11			−0.714854
$866$	8.34983e11			1.48459
$867$	6.49468e11	−	6.49468e11i	1.14943	−	1.14943i
$868$	−2.37610e11	+	2.37610e11i	−0.418588	+	0.418588i
$869$			8.07515e11i			1.41603i
$870$	8.25914e11	+	2.22265e11i	1.44164	+	0.387966i
$871$	−4.25064e11			−0.738553
$872$	6.41807e10	+	6.41807e10i	0.111004	+	0.111004i
$873$	−1.12013e12	−	1.12013e12i	−1.92847	−	1.92847i
$874$		−	9.37378e11i		−	1.60646i
$875$		−	2.54326e11i		−	0.433869i
$876$		−	1.26163e12i		−	2.14247i
$877$	−6.31136e11			−1.06690			−0.533451	−	0.845831i	$-0.679105\pi$
$877$	−6.31136e11			−1.06690			−0.533451	+	0.845831i	$0.679105\pi$
$878$	9.89071e11	−	9.89071e11i	1.66437	−	1.66437i
$879$		−	1.59438e12i		−	2.67077i
$880$	3.87691e11	−	3.87691e11i	0.646480	−	0.646480i
$881$	4.34870e11	+	4.34870e11i	0.721865	+	0.721865i	0.968985	−	0.247120i	$-0.0794843\pi$
$881$	4.34870e11	+	4.34870e11i	0.721865	+	0.721865i	−0.247120	+	0.968985i	$0.579484\pi$
$882$	−7.86555e11	+	7.86555e11i	−1.29973	+	1.29973i
$883$		−	6.93380e11i		−	1.14059i	−0.821441	−	0.570294i	$-0.806829\pi$
$883$		−	6.93380e11i		−	1.14059i	0.821441	−	0.570294i	$-0.193171\pi$
$884$	−2.38477e9	−	2.38477e9i	−0.00390514	−	0.00390514i
$885$	−1.33640e11	+	1.33640e11i	−0.217853	+	0.217853i
$886$	1.18107e12			1.91663
$887$	2.79111e11	+	2.79111e11i	0.450902	+	0.450902i	0.895654	−	0.444752i	$-0.146708\pi$
$887$	2.79111e11	+	2.79111e11i	0.450902	+	0.450902i	−0.444752	+	0.895654i	$0.646708\pi$
$888$	−1.63101e11	+	1.63101e11i	−0.262304	+	0.262304i
$889$	3.26339e11	+	3.26339e11i	0.522470	+	0.522470i
$890$	8.05049e11			1.28311
$891$	−3.03016e10	−	3.03016e10i	−0.0480789	−	0.0480789i
$892$			3.88046e11i			0.612947i
$893$	−5.41546e11			−0.851588
$894$	2.42639e12			3.79849
$895$	5.22799e11			0.814785
$896$	−8.78595e10	+	8.78595e10i	−0.136319	+	0.136319i
$897$	4.23067e11	−	4.23067e11i	0.653491	−	0.653491i
$898$			5.07689e11i			0.780714i
$899$	−5.63242e11	−	9.78015e11i	−0.862296	−	1.49729i
$900$	−4.79015e11			−0.730094
$901$	8.46013e9	+	8.46013e9i	0.0128374	+	0.0128374i
$902$	1.61505e11	+	1.61505e11i	0.243983	+	0.243983i
$903$			1.20570e11i			0.181337i
$904$			1.64972e11i			0.247023i
$905$			2.45378e11i			0.365798i
$906$	−1.00435e12			−1.49064
$907$	1.09682e11	−	1.09682e11i	0.162072	−	0.162072i	−0.621412	−	0.783484i	$-0.713441\pi$
$907$	1.09682e11	−	1.09682e11i	0.162072	−	0.162072i	0.783484	+	0.621412i	$0.213441\pi$
$908$			1.53821e11i			0.226294i
$909$	7.03576e11	−	7.03576e11i	1.03052	−	1.03052i
$910$	8.09173e10	+	8.09173e10i	0.117998	+	0.117998i
$911$	−1.65920e11	+	1.65920e11i	−0.240893	+	0.240893i	−0.817220	−	0.576326i	$-0.804486\pi$
$911$	−1.65920e11	+	1.65920e11i	−0.240893	+	0.240893i	0.576326	+	0.817220i	$0.304486\pi$
$912$			1.17870e12i			1.70382i
$913$	1.27741e11	+	1.27741e11i	0.183843	+	0.183843i
$914$	2.99765e11	−	2.99765e11i	0.429532	−	0.429532i
$915$	−2.22958e11			−0.318082
$916$	2.54044e11	+	2.54044e11i	0.360850	+	0.360850i
$917$	2.58034e10	−	2.58034e10i	0.0364922	−	0.0364922i
$918$	−1.08486e10	−	1.08486e10i	−0.0152758	−	0.0152758i
$919$	−5.90991e11			−0.828550			−0.414275	−	0.910152i	$-0.635965\pi$
$919$	−5.90991e11			−0.828550			−0.414275	+	0.910152i	$0.635965\pi$
$920$	1.05393e11	+	1.05393e11i	0.147116	+	0.147116i
$921$		−	6.69677e11i		−	0.930737i
$922$	−2.29090e11			−0.317017
$923$	−4.41736e11			−0.608634
$924$	−4.77462e11			−0.655014
$925$	2.69503e11	−	2.69503e11i	0.368126	−	0.368126i
$926$	3.54279e11	−	3.54279e11i	0.481839	−	0.481839i
$927$			1.56979e12i			2.12580i
$928$	4.84832e11	+	8.41864e11i	0.653732	+	1.13514i
$929$	3.77141e11			0.506339			0.253169	−	0.967422i	$-0.418527\pi$
$929$	3.77141e11			0.506339			0.253169	+	0.967422i	$0.418527\pi$
$930$	−1.36446e12	−	1.36446e12i	−1.82402	−	1.82402i
$931$	−4.02755e11	−	4.02755e11i	−0.536096	−	0.536096i
$932$			3.19249e11i			0.423123i
$933$			1.14872e12i			1.51596i
$934$			7.59684e11i			0.998264i
$935$	−9.33208e9			−0.0122105
$936$	−9.21147e10	+	9.21147e10i	−0.120012	+	0.120012i
$937$			8.21066e11i			1.06517i	0.846376	+	0.532586i	$0.178780\pi$
$937$			8.21066e11i			1.06517i	−0.846376	+	0.532586i	$0.821220\pi$
$938$	−5.17759e11	+	5.17759e11i	−0.668831	+	0.668831i
$939$	−6.79544e11	−	6.79544e11i	−0.874088	−	0.874088i
$940$	−2.87943e11	+	2.87943e11i	−0.368803	+	0.368803i
$941$			7.07516e11i			0.902356i	0.892434	+	0.451178i	$0.148996\pi$
$941$			7.07516e11i			0.902356i	−0.892434	+	0.451178i	$0.851004\pi$
$942$	−1.55035e12	−	1.55035e12i	−1.96892	−	1.96892i
$943$	−1.57645e11	+	1.57645e11i	−0.199358	+	0.199358i
$944$	−2.53320e11			−0.318993
$945$	1.66453e11	+	1.66453e11i	0.208720	+	0.208720i
$946$	2.41754e11	−	2.41754e11i	0.301862	−	0.301862i
$947$	9.46957e11	+	9.46957e11i	1.17742	+	1.17742i	0.980400	+	0.197017i	$0.0631255\pi$
$947$	9.46957e11	+	9.46957e11i	1.17742	+	1.17742i	0.197017	+	0.980400i	$0.436875\pi$
$948$	−1.30539e12			−1.61624
$949$	4.00882e11	+	4.00882e11i	0.494256	+	0.494256i
$950$		−	5.42425e11i		−	0.665956i
$951$	1.86881e12			2.28478
$952$	1.22850e9			0.00149564
$953$	2.17385e11			0.263547			0.131774	−	0.991280i	$-0.457933\pi$
$953$	2.17385e11			0.263547			0.131774	+	0.991280i	$0.457933\pi$
$954$	−1.54538e12	+	1.54538e12i	−1.86569	+	1.86569i
$955$	−1.11730e11	+	1.11730e11i	−0.134325	+	0.134325i
$956$		−	9.02916e11i		−	1.08098i
$957$	4.16729e11	−	1.54852e12i	0.496828	−	1.84616i
$958$	−1.39240e12			−1.65312
$959$	−2.16861e11	−	2.16861e11i	−0.256394	−	0.256394i
$960$	4.15268e11	+	4.15268e11i	0.488927	+	0.488927i
$961$			1.69336e12i			1.98544i
$962$			4.90171e11i			0.572331i
$963$		−	6.68312e11i		−	0.777095i
$964$	5.40211e11			0.625540
$965$	−4.29677e11	+	4.29677e11i	−0.495487	+	0.495487i
$966$		−	1.03065e12i		−	1.18360i
$967$	−7.75823e11	+	7.75823e11i	−0.887272	+	0.887272i	−0.994260	−	0.106988i	$-0.965879\pi$
$967$	−7.75823e11	+	7.75823e11i	−0.887272	+	0.887272i	0.106988	+	0.994260i	$0.465879\pi$
$968$	−5.60253e10	−	5.60253e10i	−0.0638091	−	0.0638091i
$969$	1.41862e10	−	1.41862e10i	0.0160906	−	0.0160906i
$970$		−	1.34884e12i		−	1.52361i
$971$	6.46904e11	+	6.46904e11i	0.727718	+	0.727718i	0.970165	−	0.242447i	$-0.0779500\pi$
$971$	6.46904e11	+	6.46904e11i	0.727718	+	0.727718i	−0.242447	+	0.970165i	$0.577950\pi$
$972$	−4.96217e11	+	4.96217e11i	−0.555913	+	0.555913i
$973$	−5.35595e11			−0.597565
$974$	6.58033e11	+	6.58033e11i	0.731159	+	0.731159i
$975$	2.44813e11	−	2.44813e11i	0.270904	−	0.270904i
$976$	−2.11312e11	−	2.11312e11i	−0.232876	−	0.232876i
$977$	1.56375e12			1.71628			0.858142	−	0.513412i	$-0.171619\pi$
$977$	1.56375e12			1.71628			0.858142	+	0.513412i	$0.171619\pi$
$978$	−8.33355e11	−	8.33355e11i	−0.910908	−	0.910908i
$979$		−	1.50940e12i		−	1.64314i
$980$	−4.28293e11			−0.464341
$981$	1.01327e12			1.09408
$982$	−6.25814e11			−0.672976
$983$	−4.04201e11	+	4.04201e11i	−0.432896	+	0.432896i	−0.889612	−	0.456716i	$-0.849025\pi$
$983$	−4.04201e11	+	4.04201e11i	−0.432896	+	0.432896i	0.456716	+	0.889612i	$0.349025\pi$
$984$	5.52076e10	−	5.52076e10i	0.0588869	−	0.0588869i
$985$		−	3.54515e11i		−	0.376608i
$986$	5.07066e9	−	1.88421e10i	0.00536484	−	0.0199352i
$987$	−5.95433e11			−0.627429
$988$	2.23057e11	+	2.23057e11i	0.234092	+	0.234092i
$989$	2.35976e11	+	2.35976e11i	0.246651	+	0.246651i
$990$		−	1.70465e12i		−	1.77458i
$991$		−	1.20738e12i		−	1.25184i	−0.779887	−	0.625921i	$-0.784723\pi$
$991$		−	1.20738e12i		−	1.25184i	0.779887	−	0.625921i	$-0.215277\pi$
$992$		−	2.19179e12i		−	2.26335i
$993$	2.32975e10			0.0239614
$994$	−5.38067e11	+	5.38067e11i	−0.551177	+	0.551177i
$995$			7.73073e11i			0.788730i
$996$	−2.06499e11	+	2.06499e11i	−0.209836	+	0.209836i
$997$	−3.90913e11	−	3.90913e11i	−0.395639	−	0.395639i	0.481053	−	0.876692i	$-0.340255\pi$
$997$	−3.90913e11	−	3.90913e11i	−0.395639	−	0.395639i	−0.876692	+	0.481053i	$0.840255\pi$
$998$	1.68843e12	−	1.68843e12i	1.70201	−	1.70201i
$999$			1.00832e12i			1.01236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.5	✓	38
29.17	odd	4	inner	29.9.c.a.17.5	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.5	✓	38	1.1	even	1	trivial
29.9.c.a.17.5	yes	38	29.17	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.2859 - 15.2859i) q^{2} +(93.1254 + 93.1254i) q^{3} +211.315i q^{4} -424.754i q^{5} -2847.00i q^{6} +996.548 q^{7} +(-683.041 + 683.041i) q^{8} +10783.7i q^{9} +O(q^{10})\)	\(q+(-15.2859 - 15.2859i) q^{2} +(93.1254 + 93.1254i) q^{3} +211.315i q^{4} -424.754i q^{5} -2847.00i q^{6} +996.548 q^{7} +(-683.041 + 683.041i) q^{8} +10783.7i q^{9} +(-6492.74 + 6492.74i) q^{10} +(12173.4 + 12173.4i) q^{11} +(-19678.8 + 19678.8i) q^{12} -12505.9i q^{13} +(-15233.1 - 15233.1i) q^{14} +(39555.4 - 39555.4i) q^{15} +74978.5 q^{16} +(-902.401 - 902.401i) q^{17} +(164838. - 164838. i) q^{18} +(84405.1 + 84405.1i) q^{19} +89757.1 q^{20} +(92803.9 + 92803.9i) q^{21} -372161. i q^{22} +363267. q^{23} -127217. q^{24} +210209. q^{25} +(-191164. + 191164. i) q^{26} +(-393238. + 393238. i) q^{27} +210586. i q^{28} +(-682982. - 183800. i) q^{29} -1.20928e6 q^{30} +(1.12833e6 + 1.12833e6i) q^{31} +(-971253. - 971253. i) q^{32} +2.26730e6i q^{33} +27588.0i q^{34} -423288. i q^{35} -2.27876e6 q^{36} +(1.28207e6 - 1.28207e6i) q^{37} -2.58041e6i q^{38} +(1.16462e6 - 1.16462e6i) q^{39} +(290125. + 290125. i) q^{40} +(-433964. + 433964. i) q^{41} -2.83718e6i q^{42} +(649594. + 649594. i) q^{43} +(-2.57242e6 + 2.57242e6i) q^{44} +4.58041e6 q^{45} +(-5.55285e6 - 5.55285e6i) q^{46} +(-3.20802e6 + 3.20802e6i) q^{47} +(6.98240e6 + 6.98240e6i) q^{48} -4.77169e6 q^{49} +(-3.21323e6 - 3.21323e6i) q^{50} -168073. i q^{51} +2.64269e6 q^{52} -9.37513e6 q^{53} +1.20220e7 q^{54} +(5.17069e6 - 5.17069e6i) q^{55} +(-680684. + 680684. i) q^{56} +1.57205e7i q^{57} +(7.63043e6 + 1.32495e7i) q^{58} -3.37856e6 q^{59} +(8.35867e6 + 8.35867e6i) q^{60} +(-2.81831e6 - 2.81831e6i) q^{61} -3.44950e7i q^{62} +1.07464e7i q^{63} +1.04984e7i q^{64} -5.31194e6 q^{65} +(3.46577e7 - 3.46577e7i) q^{66} -3.39890e7i q^{67} +(190691. - 190691. i) q^{68} +(3.38294e7 + 3.38294e7i) q^{69} +(-6.47033e6 + 6.47033e6i) q^{70} -3.53222e7i q^{71} +(-7.36569e6 - 7.36569e6i) q^{72} +(-3.20554e7 + 3.20554e7i) q^{73} -3.91951e7 q^{74} +(1.95758e7 + 1.95758e7i) q^{75} +(-1.78361e7 + 1.78361e7i) q^{76} +(1.21314e7 + 1.21314e7i) q^{77} -3.56044e7 q^{78} +(3.31673e7 + 3.31673e7i) q^{79} -3.18474e7i q^{80} -2.48917e6 q^{81} +1.32670e7 q^{82} +1.04934e7 q^{83} +(-1.96109e7 + 1.96109e7i) q^{84} +(-383299. + 383299. i) q^{85} -1.98592e7i q^{86} +(-4.64865e7 - 8.07193e7i) q^{87} -1.66298e7 q^{88} +(-6.19962e7 - 6.19962e7i) q^{89} +(-7.00155e7 - 7.00155e7i) q^{90} -1.24627e7i q^{91} +7.67640e7i q^{92} +2.10152e8i q^{93} +9.80747e7 q^{94} +(3.58514e7 - 3.58514e7i) q^{95} -1.80897e8i q^{96} +(-1.03873e8 + 1.03873e8i) q^{97} +(7.29395e7 + 7.29395e7i) q^{98} +(-1.31274e8 + 1.31274e8i) 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

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