LMFDB - Embedded newform 16.9.f.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	16.11
Dual form			16.9.f.a.3.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.2357 - 11.3912i) q^{2} +(23.8972 + 23.8972i) q^{3} +(-3.51862 - 255.976i) q^{4} +(-695.590 - 695.590i) q^{5} +(540.720 - 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 - 2835.98i) q^{8} -5418.84i q^{9} +O(q^{10})$	\(q+(11.2357 - 11.3912i) q^{2} +(23.8972 + 23.8972i) q^{3} +(-3.51862 - 255.976i) q^{4} +(-695.590 - 695.590i) q^{5} +(540.720 - 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 - 2835.98i) q^{8} -5418.84i q^{9} +(-15739.0 + 108.169i) q^{10} +(-295.121 + 295.121i) q^{11} +(6033.03 - 6201.20i) q^{12} +(-20441.3 + 20441.3i) q^{13} +(35592.3 - 36084.9i) q^{14} -33245.4i q^{15} +(-65511.2 + 1801.36i) q^{16} +143214. q^{17} +(-61727.1 - 60884.4i) q^{18} +(128582. + 128582. i) q^{19} +(-175607. + 180502. i) q^{20} +(75701.5 + 75701.5i) q^{21} +(45.8931 + 6677.66i) q^{22} -61807.0 q^{23} +(-2853.84 - 138398. i) q^{24} +577067. i q^{25} +(3178.75 + 462522. i) q^{26} +(286285. - 286285. i) q^{27} +(-11146.3 - 810878. i) q^{28} +(233312. - 233312. i) q^{29} +(-378705. - 373535. i) q^{30} -374476. i q^{31} +(-715544. + 766491. i) q^{32} -14105.1 q^{33} +(1.60911e6 - 1.63138e6i) q^{34} +(-2.20348e6 - 2.20348e6i) q^{35} +(-1.38709e6 + 19066.9i) q^{36} +(516796. + 516796. i) q^{37} +(2.90942e6 - 19995.4i) q^{38} -976980. q^{39} +(83068.3 + 4.02843e6i) q^{40} +1.82949e6i q^{41} +(1.71289e6 - 11772.1i) q^{42} +(-834182. + 834182. i) q^{43} +(76582.2 + 74505.3i) q^{44} +(-3.76929e6 + 3.76929e6i) q^{45} +(-694444. + 704055. i) q^{46} -8.50247e6i q^{47} +(-1.60859e6 - 1.52249e6i) q^{48} +4.27010e6 q^{49} +(6.57348e6 + 6.48374e6i) q^{50} +(3.42242e6 + 3.42242e6i) q^{51} +(5.30440e6 + 5.16055e6i) q^{52} +(-3.16752e6 - 3.16752e6i) q^{53} +(-44519.2 - 6.47774e6i) q^{54} +410566. q^{55} +(-9.36210e6 - 8.98380e6i) q^{56} +6.14553e6i q^{57} +(-36281.5 - 5.27912e6i) q^{58} +(-9.18487e6 + 9.18487e6i) q^{59} +(-8.51001e6 + 116978. i) q^{60} +(-132625. + 132625. i) q^{61} +(-4.26573e6 - 4.20750e6i) q^{62} -1.71658e7i q^{63} +(691615. + 1.67630e7i) q^{64} +2.84375e7 q^{65} +(-158481. + 160674. i) q^{66} +(164015. + 164015. i) q^{67} +(-503916. - 3.66593e7i) q^{68} +(-1.47702e6 - 1.47702e6i) q^{69} +(-4.98580e7 + 342656. i) q^{70} +3.54013e7 q^{71} +(-1.53677e7 + 1.60149e7i) q^{72} -9.75074e6i q^{73} +(1.16935e7 - 80365.0i) q^{74} +(-1.37903e7 + 1.37903e7i) q^{75} +(3.24615e7 - 3.33664e7i) q^{76} +(-934880. + 934880. i) q^{77} +(-1.09770e7 + 1.11290e7i) q^{78} +4.97804e7i q^{79} +(4.68220e7 + 4.43160e7i) q^{80} -2.18702e7 q^{81} +(2.08401e7 + 2.05556e7i) q^{82} +(5.00207e7 + 5.00207e7i) q^{83} +(1.91114e7 - 1.96441e7i) q^{84} +(-9.96182e7 - 9.96182e7i) q^{85} +(129721. + 1.88749e7i) q^{86} +1.11510e7 q^{87} +(1.70916e6 - 35243.7i) q^{88} +3.66516e7i q^{89} +(586149. + 8.52874e7i) q^{90} +(-6.47537e7 + 6.47537e7i) q^{91} +(217475. + 1.58211e7i) q^{92} +(8.94895e6 - 8.94895e6i) q^{93} +(-9.68533e7 - 9.55311e7i) q^{94} -1.78881e8i q^{95} +(-3.54166e7 + 1.21749e6i) q^{96} +1.20777e8 q^{97} +(4.79775e7 - 4.86415e7i) q^{98} +(1.59921e6 + 1.59921e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	11.2357	−	11.3912i	0.702231	−	0.711950i
$2$	11.2357	−	11.3912i	0.702231	−	0.711950i
$3$	23.8972	+	23.8972i	0.295028	+	0.295028i	0.839063	−	0.544035i	$-0.183104\pi$
$3$	23.8972	+	23.8972i	0.295028	+	0.295028i	−0.544035	+	0.839063i	$0.683104\pi$
$4$	−3.51862	−	255.976i	−0.0137446	−	0.999906i
$5$	−695.590	−	695.590i	−1.11294	−	1.11294i	−0.992750	−	0.120194i	$-0.961648\pi$
$5$	−695.590	−	695.590i	−1.11294	−	1.11294i	−0.120194	−	0.992750i	$-0.538352\pi$
$6$	540.720	−	3.71617i	0.417222	−	0.00286742i
$7$	3167.79			1.31936			0.659681	−	0.751545i	$-0.270691\pi$
$7$	3167.79			1.31936			0.659681	+	0.751545i	$0.270691\pi$
$8$	−2955.40	−	2835.98i	−0.721534	−	0.692379i
$9$		−	5418.84i		−	0.825917i
$10$	−15739.0	+	108.169i	−1.57390	+	0.0108169i
$11$	−295.121	+	295.121i	−0.0201571	+	0.0201571i	−0.717114	−	0.696956i	$-0.754537\pi$
$11$	−295.121	+	295.121i	−0.0201571	+	0.0201571i	0.696956	+	0.717114i	$0.254537\pi$
$12$	6033.03	−	6201.20i	0.290945	−	0.299055i
$13$	−20441.3	+	20441.3i	−0.715706	+	0.715706i	−0.967723	−	0.252017i	$-0.918906\pi$
$13$	−20441.3	+	20441.3i	−0.715706	+	0.715706i	0.252017	+	0.967723i	$0.418906\pi$
$14$	35592.3	−	36084.9i	0.926497	−	0.939320i
$15$		−	33245.4i		−	0.656699i
$16$	−65511.2	+	1801.36i	−0.999622	+	0.0274866i
$17$	143214.			1.71470			0.857352	−	0.514730i	$-0.172108\pi$
$17$	143214.			1.71470			0.857352	+	0.514730i	$0.172108\pi$
$18$	−61727.1	−	60884.4i	−0.588012	−	0.579984i
$19$	128582.	+	128582.i	0.986659	+	0.986659i	0.999912	−	0.0132534i	$-0.00421882\pi$
$19$	128582.	+	128582.i	0.986659	+	0.986659i	−0.0132534	+	0.999912i	$0.504219\pi$
$20$	−175607.	+	180502.i	−1.09754	+	1.12814i
$21$	75701.5	+	75701.5i	0.389249	+	0.389249i
$22$	45.8931	+	6677.66i	0.000195910	+	0.0285058i
$23$	−61807.0			−0.220865			−0.110432	−	0.993884i	$-0.535224\pi$
$23$	−61807.0			−0.220865			−0.110432	+	0.993884i	$0.535224\pi$
$24$	−2853.84	−	138398.i	−0.00860171	−	0.417144i
$25$			577067.i			1.47729i
$26$	3178.75	+	462522.i	0.00695605	+	1.01214i
$27$	286285.	−	286285.i	0.538696	−	0.538696i
$28$	−11146.3	−	810878.i	−0.0181341	−	1.31924i
$29$	233312.	−	233312.i	0.329872	−	0.329872i	−0.522666	−	0.852538i	$-0.675062\pi$
$29$	233312.	−	233312.i	0.329872	−	0.329872i	0.852538	+	0.522666i	$0.175062\pi$
$30$	−378705.	−	373535.i	−0.467537	−	0.461154i
$31$		−	374476.i		−	0.405487i	−0.979232	−	0.202744i	$-0.935014\pi$
$31$		−	374476.i		−	0.405487i	0.979232	−	0.202744i	$-0.0649858\pi$
$32$	−715544.	+	766491.i	−0.682396	+	0.730983i
$33$	−14105.1			−0.0118938
$34$	1.60911e6	−	1.63138e6i	1.20412	−	1.22078i
$35$	−2.20348e6	−	2.20348e6i	−1.46838	−	1.46838i
$36$	−1.38709e6	+	19066.9i	−0.825839	+	0.0113519i
$37$	516796.	+	516796.i	0.275748	+	0.275748i	0.831409	−	0.555661i	$-0.187535\pi$
$37$	516796.	+	516796.i	0.275748	+	0.275748i	−0.555661	+	0.831409i	$0.687535\pi$
$38$	2.90942e6	−	19995.4i	1.39531	−	0.00958948i
$39$	−976980.			−0.422306
$40$	83068.3	+	4.02843e6i	0.0324486	+	1.57361i
$41$			1.82949e6i			0.647434i	0.946154	+	0.323717i	$0.104933\pi$
$41$			1.82949e6i			0.647434i	−0.946154	+	0.323717i	$0.895067\pi$
$42$	1.71289e6	−	11772.1i	0.550468	−	0.00378316i
$43$	−834182.	+	834182.i	−0.243998	+	0.243998i	−0.818502	−	0.574504i	$-0.805195\pi$
$43$	−834182.	+	834182.i	−0.243998	+	0.243998i	0.574504	+	0.818502i	$0.305195\pi$
$44$	76582.2	+	74505.3i	0.0204323	+	0.0198782i
$45$	−3.76929e6	+	3.76929e6i	−0.919200	+	0.919200i
$46$	−694444.	+	704055.i	−0.155098	+	0.157244i
$47$		−	8.50247e6i		−	1.74242i	−0.490907	−	0.871212i	$-0.663335\pi$
$47$		−	8.50247e6i		−	1.74242i	0.490907	−	0.871212i	$-0.336665\pi$
$48$	−1.60859e6	−	1.52249e6i	−0.303026	−	0.286807i
$49$	4.27010e6			0.740719
$50$	6.57348e6	+	6.48374e6i	1.05176	+	1.03740i
$51$	3.42242e6	+	3.42242e6i	0.505885	+	0.505885i
$52$	5.30440e6	+	5.16055e6i	0.725475	+	0.705801i
$53$	−3.16752e6	−	3.16752e6i	−0.401436	−	0.401436i	0.477303	−	0.878739i	$-0.341614\pi$
$53$	−3.16752e6	−	3.16752e6i	−0.401436	−	0.401436i	−0.878739	+	0.477303i	$0.841614\pi$
$54$	−44519.2	−	6.47774e6i	−0.00523567	−	0.761814i
$55$	410566.			0.0448675
$56$	−9.36210e6	−	8.98380e6i	−0.951966	−	0.913499i
$57$			6.14553e6i			0.582183i
$58$	−36281.5	−	5.27912e6i	−0.00320607	−	0.466498i
$59$	−9.18487e6	+	9.18487e6i	−0.757992	+	0.757992i	−0.975957	−	0.217964i	$-0.930058\pi$
$59$	−9.18487e6	+	9.18487e6i	−0.757992	+	0.757992i	0.217964	+	0.975957i	$0.430058\pi$
$60$	−8.51001e6	+	116978.i	−0.656637	+	0.00902608i
$61$	−132625.	+	132625.i	−0.00957866	+	0.00957866i	−0.711880	−	0.702301i	$-0.752156\pi$
$61$	−132625.	+	132625.i	−0.00957866	+	0.00957866i	0.702301	+	0.711880i	$0.252156\pi$
$62$	−4.26573e6	−	4.20750e6i	−0.288687	−	0.284746i
$63$		−	1.71658e7i		−	1.08968i
$64$	691615.	+	1.67630e7i	0.0412235	+	0.999150i
$65$	2.84375e7			1.59308
$66$	−158481.	+	160674.i	−0.00835221	+	0.00846781i
$67$	164015.	+	164015.i	0.00813926	+	0.00813926i	0.711165	−	0.703025i	$-0.248168\pi$
$67$	164015.	+	164015.i	0.00813926	+	0.00813926i	−0.703025	+	0.711165i	$0.748168\pi$
$68$	−503916.	−	3.66593e7i	−0.0235680	−	1.71454i
$69$	−1.47702e6	−	1.47702e6i	−0.0651612	−	0.0651612i
$70$	−4.98580e7	+	342656.i	−2.07655	+	0.0142714i
$71$	3.54013e7			1.39311			0.696555	−	0.717504i	$-0.254715\pi$
$71$	3.54013e7			1.39311			0.696555	+	0.717504i	$0.254715\pi$
$72$	−1.53677e7	+	1.60149e7i	−0.571848	+	0.595928i
$73$		−	9.75074e6i		−	0.343357i	−0.985153	−	0.171679i	$-0.945081\pi$
$73$		−	9.75074e6i		−	0.343357i	0.985153	−	0.171679i	$-0.0549191\pi$
$74$	1.16935e7	−	80365.0i	0.389957	−	0.00268003i
$75$	−1.37903e7	+	1.37903e7i	−0.435842	+	0.435842i
$76$	3.24615e7	−	3.33664e7i	0.973004	−	1.00013i
$77$	−934880.	+	934880.i	−0.0265946	+	0.0265946i
$78$	−1.09770e7	+	1.11290e7i	−0.296556	+	0.300661i
$79$			4.97804e7i			1.27806i	0.769183	+	0.639028i	$0.220663\pi$
$79$			4.97804e7i			1.27806i	−0.769183	+	0.639028i	$0.779337\pi$
$80$	4.68220e7	+	4.43160e7i	1.14312	+	1.08193i
$81$	−2.18702e7			−0.508057
$82$	2.08401e7	+	2.05556e7i	0.460941	+	0.454648i
$83$	5.00207e7	+	5.00207e7i	1.05399	+	1.05399i	0.998457	+	0.0555358i	$0.0176867\pi$
$83$	5.00207e7	+	5.00207e7i	1.05399	+	1.05399i	0.0555358	+	0.998457i	$0.482313\pi$
$84$	1.91114e7	−	1.96441e7i	0.383862	−	0.394562i
$85$	−9.96182e7	−	9.96182e7i	−1.90837	−	1.90837i
$86$	129721.	+	1.88749e7i	0.00237146	+	0.345058i
$87$	1.11510e7			0.194643
$88$	1.70916e6	−	35243.7i	0.0285004	−	0.000587693i
$89$			3.66516e7i			0.584161i	0.956394	+	0.292080i	$0.0943475\pi$
$89$			3.66516e7i			0.584161i	−0.956394	+	0.292080i	$0.905653\pi$
$90$	586149.	+	8.52874e7i	0.00893384	+	1.29991i
$91$	−6.47537e7	+	6.47537e7i	−0.944276	+	0.944276i
$92$	217475.	+	1.58211e7i	0.00303570	+	0.220844i
$93$	8.94895e6	−	8.94895e6i	0.119630	−	0.119630i
$94$	−9.68533e7	−	9.55311e7i	−1.24052	−	1.22358i
$95$		−	1.78881e8i		−	2.19619i
$96$	−3.54166e7	+	1.21749e6i	−0.416986	+	0.0143344i
$97$	1.20777e8			1.36426			0.682128	−	0.731233i	$-0.261055\pi$
$97$	1.20777e8			1.36426			0.682128	+	0.731233i	$0.261055\pi$
$98$	4.79775e7	−	4.86415e7i	0.520155	−	0.527354i
$99$	1.59921e6	+	1.59921e6i	0.0166481	+	0.0166481i
$100$	1.47715e8	−	2.03048e6i	1.47715	−	0.0203048i
$101$	−6.69104e7	−	6.69104e7i	−0.642996	−	0.642996i	0.308295	−	0.951291i	$-0.400242\pi$
$101$	−6.69104e7	−	6.69104e7i	−0.642996	−	0.642996i	−0.951291	+	0.308295i	$0.900242\pi$
$102$	7.74386e7	−	532207.i	0.715413	−	0.00491677i
$103$	−1.42395e8			−1.26516			−0.632582	−	0.774493i	$-0.718005\pi$
$103$	−1.42395e8			−1.26516			−0.632582	+	0.774493i	$0.718005\pi$
$104$	1.18383e8	−	2.44112e6i	1.01195	−	0.0208668i
$105$		−	1.05314e8i		−	0.866424i
$106$	−7.16711e7	+	492569.i	−0.567702	+	0.00390161i
$107$	−2.13988e7	+	2.13988e7i	−0.163251	+	0.163251i	−0.784005	−	0.620754i	$-0.786826\pi$
$107$	−2.13988e7	+	2.13988e7i	−0.163251	+	0.163251i	0.620754	+	0.784005i	$0.286826\pi$
$108$	−7.42894e7	−	7.22748e7i	−0.546050	−	0.531241i
$109$	−1.34195e8	+	1.34195e8i	−0.950669	+	0.950669i	−0.998839	−	0.0481704i	$-0.984661\pi$
$109$	−1.34195e8	+	1.34195e8i	−0.950669	+	0.950669i	0.0481704	+	0.998839i	$0.484661\pi$
$110$	4.61299e6	−	4.67684e6i	0.0315074	−	0.0319434i
$111$			2.47000e7i			0.162706i
$112$	−2.07526e8	+	5.70635e6i	−1.31886	+	0.0362649i
$113$	4.73205e7			0.290226			0.145113	−	0.989415i	$-0.453645\pi$
$113$	4.73205e7			0.290226			0.145113	+	0.989415i	$0.453645\pi$
$114$	7.00049e7	+	6.90492e7i	0.414485	+	0.408827i
$115$	4.29923e7	+	4.29923e7i	0.245810	+	0.245810i
$116$	−6.05432e7	−	5.89013e7i	−0.334374	−	0.325307i
$117$	1.10768e8	+	1.10768e8i	0.591114	+	0.591114i
$118$	1.42830e6	+	2.07825e8i	0.00736704	+	1.07194i
$119$	4.53671e8			2.26232
$120$	−9.42834e7	+	9.82536e7i	−0.454684	+	0.473831i
$121$			2.14185e8i			0.999187i
$122$	20624.0	+	3.00088e6i	9.30964e−5	+	0.0135460i
$123$	−4.37199e7	+	4.37199e7i	−0.191011	+	0.191011i
$124$	−9.58568e7	+	1.31764e6i	−0.405449	+	0.00557327i
$125$	1.29687e8	−	1.29687e8i	0.531198	−	0.531198i
$126$	−1.95539e8	−	1.92869e8i	−0.775801	−	0.765210i
$127$			3.31500e7i			0.127429i	0.997968	+	0.0637145i	$0.0202947\pi$
$127$			3.31500e7i			0.127429i	−0.997968	+	0.0637145i	$0.979705\pi$
$128$	1.98721e8	+	1.80465e8i	0.740293	+	0.672285i
$129$	−3.98693e7			−0.143973
$130$	3.19515e8	−	3.23937e8i	1.11871	−	1.13419i
$131$	−3.21149e8	−	3.21149e8i	−1.09049	−	1.09049i	−0.995476	−	0.0950128i	$-0.969711\pi$
$131$	−3.21149e8	−	3.21149e8i	−1.09049	−	1.09049i	−0.0950128	−	0.995476i	$-0.530289\pi$
$132$	49630.7	+	3.61057e6i	0.000163476	+	0.0118927i
$133$	4.07322e8	+	4.07322e8i	1.30176	+	1.30176i
$134$	3.71115e6	−	25505.4i	0.0115104	−	7.91066e-5i
$135$	−3.98275e8			−1.19908
$136$	−4.23255e8	−	4.06152e8i	−1.23722	−	1.18722i
$137$			3.35313e8i			0.951849i	0.879486	+	0.475924i	$0.157886\pi$
$137$			3.35313e8i			0.951849i	−0.879486	+	0.475924i	$0.842114\pi$
$138$	−3.34203e7	+	229685.i	−0.0921497	+	0.000633311i
$139$	4.80067e8	−	4.80067e8i	1.28600	−	1.28600i	0.348812	−	0.937193i	$-0.386585\pi$
$139$	4.80067e8	−	4.80067e8i	1.28600	−	1.28600i	0.937193	−	0.348812i	$-0.113415\pi$
$140$	−5.56285e8	+	5.71792e8i	−1.44806	+	1.48842i
$141$	2.03186e8	−	2.03186e8i	0.514063	−	0.514063i
$142$	3.97758e8	−	4.03263e8i	0.978284	−	0.991824i
$143$		−	1.20653e7i		−	0.0288532i
$144$	9.76131e6	+	3.54995e8i	0.0227017	+	0.825605i
$145$	−3.24579e8			−0.734258
$146$	−1.11073e8	−	1.09556e8i	−0.244453	−	0.241116i
$147$	1.02044e8	+	1.02044e8i	0.218533	+	0.218533i
$148$	1.30469e8	−	1.34106e8i	0.271932	−	0.279512i
$149$	−1.55412e8	−	1.55412e8i	−0.315312	−	0.315312i	0.531651	−	0.846963i	$-0.321572\pi$
$149$	−1.55412e8	−	1.55412e8i	−0.315312	−	0.315312i	−0.846963	+	0.531651i	$0.821572\pi$
$150$	2.14448e6	+	3.12032e8i	0.00423601	+	0.616359i
$151$	−3.58922e8			−0.690387			−0.345193	−	0.938532i	$-0.612187\pi$
$151$	−3.58922e8			−0.690387			−0.345193	+	0.938532i	$0.612187\pi$
$152$	−1.53555e7	−	7.44670e8i	−0.0287666	−	1.39505i
$153$		−	7.76053e8i		−	1.41620i
$154$	145380.	+	2.11534e7i	0.000258477	+	0.0376095i
$155$	−2.60482e8	+	2.60482e8i	−0.451285	+	0.451285i
$156$	3.43763e6	+	2.50083e8i	0.00580444	+	0.422266i
$157$	−5.90001e8	+	5.90001e8i	−0.971077	+	0.971077i	−0.999593	−	0.0285160i	$-0.990922\pi$
$157$	−5.90001e8	+	5.90001e8i	−0.971077	+	0.971077i	0.0285160	+	0.999593i	$0.490922\pi$
$158$	5.67058e8	+	5.59317e8i	0.909912	+	0.897491i
$159$		−	1.51390e8i		−	0.236869i
$160$	1.03089e9	−	3.54380e7i	1.57301	−	0.0540741i
$161$	−1.95792e8			−0.291401
$162$	−2.45726e8	+	2.49127e8i	−0.356773	+	0.361711i
$163$	−1.82545e8	−	1.82545e8i	−0.258595	−	0.258595i	0.565887	−	0.824483i	$-0.308534\pi$
$163$	−1.82545e8	−	1.82545e8i	−0.258595	−	0.258595i	−0.824483	+	0.565887i	$0.808534\pi$
$164$	4.68306e8	−	6.43730e6i	0.647373	−	0.00889874i
$165$	9.81140e6	+	9.81140e6i	0.0132372	+	0.0132372i
$166$	1.13181e9	−	7.77854e6i	1.49054	−	0.0102439i
$167$	−2.64912e8			−0.340593			−0.170296	−	0.985393i	$-0.554473\pi$
$167$	−2.64912e8			−0.340593			−0.170296	+	0.985393i	$0.554473\pi$
$168$	−9.04037e6	−	4.38417e8i	−0.0113488	−	0.550364i
$169$		−	1.99605e7i		−	0.0244695i
$170$	−2.25405e9	+	1.54913e7i	−2.69878	+	0.0185477i
$171$	6.96768e8	−	6.96768e8i	0.814899	−	0.814899i
$172$	2.16466e8	+	2.10595e8i	0.247329	+	0.240622i
$173$	4.96669e8	−	4.96669e8i	0.554476	−	0.554476i	−0.373253	−	0.927729i	$-0.621758\pi$
$173$	4.96669e8	−	4.96669e8i	0.554476	−	0.554476i	0.927729	+	0.373253i	$0.121758\pi$
$174$	1.25289e8	−	1.27024e8i	0.136684	−	0.138576i
$175$			1.82803e9i			1.94908i
$176$	1.88021e7	−	1.98653e7i	0.0195955	−	0.0207036i
$177$	−4.38986e8			−0.447258
$178$	4.17505e8	+	4.11805e8i	0.415893	+	0.410215i
$179$	−3.33878e6	−	3.33878e6i	−0.00325219	−	0.00325219i	0.705479	−	0.708731i	$-0.250732\pi$
$179$	−3.33878e6	−	3.33878e6i	−0.00325219	−	0.00325219i	−0.708731	+	0.705479i	$0.750732\pi$
$180$	9.78111e8	+	9.51586e8i	0.931747	+	0.906479i
$181$	6.56966e8	+	6.56966e8i	0.612108	+	0.612108i	0.943495	−	0.331387i	$-0.107516\pi$
$181$	6.56966e8	+	6.56966e8i	0.612108	+	0.612108i	−0.331387	+	0.943495i	$0.607516\pi$
$182$	1.00696e7	+	1.46517e9i	0.00917755	+	1.33538i
$183$	−6.33873e6			−0.00565194
$184$	1.82665e8	+	1.75284e8i	0.159361	+	0.152922i
$185$		−	7.18956e8i		−	0.613784i
$186$	−1.39162e6	−	2.02487e8i	−0.00116270	−	0.169178i
$187$	−4.22654e7	+	4.22654e7i	−0.0345635	+	0.0345635i
$188$	−2.17643e9	+	2.99170e7i	−1.74226	+	0.0239490i
$189$	9.06892e8	−	9.06892e8i	0.710736	−	0.710736i
$190$	−2.03767e9	−	2.00985e9i	−1.56358	−	1.54223i
$191$			1.21820e9i			0.915343i	0.889121	+	0.457671i	$0.151316\pi$
$191$			1.21820e9i			0.915343i	−0.889121	+	0.457671i	$0.848684\pi$
$192$	−3.84061e8	+	4.17116e8i	−0.282615	+	0.306939i
$193$	−1.88102e9			−1.35570			−0.677852	−	0.735199i	$-0.737089\pi$
$193$	−1.88102e9			−1.35570			−0.677852	+	0.735199i	$0.737089\pi$
$194$	1.35701e9	−	1.37579e9i	0.958022	−	0.971282i
$195$	6.79578e8	+	6.79578e8i	0.470003	+	0.470003i
$196$	−1.50249e7	−	1.09304e9i	−0.0101809	−	0.740649i
$197$	−7.15815e8	−	7.15815e8i	−0.475265	−	0.475265i	0.428349	−	0.903614i	$-0.359096\pi$
$197$	−7.15815e8	−	7.15815e8i	−0.475265	−	0.475265i	−0.903614	+	0.428349i	$0.859096\pi$
$198$	3.61852e7	−	248688.i	0.0235434	−	0.000161806i
$199$	7.60687e8			0.485058			0.242529	−	0.970144i	$-0.422023\pi$
$199$	7.60687e8			0.485058			0.242529	+	0.970144i	$0.422023\pi$
$200$	1.63655e9	−	1.70547e9i	1.02284	−	1.06592i
$201$			7.83903e6i			0.00480262i
$202$	−1.51397e9	+	1.04050e7i	−0.909313	+	0.00624937i
$203$	7.39083e8	−	7.39083e8i	0.435220	−	0.435220i
$204$	8.64014e8	−	8.88098e8i	0.498884	−	0.512791i
$205$	1.27258e9	−	1.27258e9i	0.720559	−	0.720559i
$206$	−1.59991e9	+	1.62205e9i	−0.888437	+	0.900733i
$207$			3.34922e8i			0.182416i
$208$	1.30231e9	−	1.37596e9i	0.695763	−	0.735108i
$209$	−7.58946e7			−0.0397764
$210$	−1.19966e9	−	1.18328e9i	−0.616850	−	0.608430i
$211$	2.66751e8	+	2.66751e8i	0.134579	+	0.134579i	0.771187	−	0.636609i	$-0.219663\pi$
$211$	2.66751e8	+	2.66751e8i	0.134579	+	0.134579i	−0.636609	+	0.771187i	$0.719663\pi$
$212$	−7.99663e8	+	8.21954e8i	−0.395880	+	0.406915i
$213$	8.45993e8	+	8.45993e8i	0.411006	+	0.411006i
$214$	3.32765e6	+	4.84188e8i	0.00158666	+	0.230866i
$215$	1.16050e9			0.543113
$216$	−1.65799e9	+	3.41886e7i	−0.761670	+	0.0157060i
$217$		−	1.18626e9i		−	0.534985i
$218$	2.08681e7	+	3.03641e9i	0.00923969	+	1.34442i
$219$	2.33016e8	−	2.33016e8i	0.101300	−	0.101300i
$220$	−1.44463e6	−	1.05095e8i	−0.000616687	−	0.0448633i
$221$	−2.92747e9	+	2.92747e9i	−1.22722	+	1.22722i
$222$	2.81362e8	+	2.77521e8i	0.115839	+	0.114257i
$223$		−	8.47191e8i		−	0.342580i	−0.985221	−	0.171290i	$-0.945206\pi$
$223$		−	8.47191e8i		−	0.342580i	0.985221	−	0.171290i	$-0.0547935\pi$
$224$	−2.26669e9	+	2.42808e9i	−0.900328	+	0.964431i
$225$	3.12703e9			1.22012
$226$	5.31679e8	−	5.39037e8i	0.203805	−	0.206626i
$227$	−2.77203e8	−	2.77203e8i	−0.104399	−	0.104399i	0.652978	−	0.757377i	$-0.273519\pi$
$227$	−2.77203e8	−	2.77203e8i	−0.104399	−	0.104399i	−0.757377	+	0.652978i	$0.773519\pi$
$228$	1.57311e9	−	2.16238e7i	0.582128	−	0.00800189i
$229$	6.77332e8	+	6.77332e8i	0.246297	+	0.246297i	0.819449	−	0.573152i	$-0.194279\pi$
$229$	6.77332e8	+	6.77332e8i	0.246297	+	0.246297i	−0.573152	+	0.819449i	$0.694279\pi$
$230$	9.72782e8	−	6.68558e6i	0.347620	−	0.00238906i
$231$	−4.46821e7			−0.0156923
$232$	−1.35120e9	+	2.78624e7i	−0.466410	+	0.00961760i
$233$			1.65304e9i			0.560867i	0.959873	+	0.280433i	$0.0904782\pi$
$233$			1.65304e9i			0.560867i	−0.959873	+	0.280433i	$0.909522\pi$
$234$	2.50634e9	−	1.72251e7i	0.835941	−	0.00574512i
$235$	−5.91424e9	+	5.91424e9i	−1.93922	+	1.93922i
$236$	2.38342e9	+	2.31879e9i	0.768339	+	0.747503i
$237$	−1.18962e9	+	1.18962e9i	−0.377062	+	0.377062i
$238$	5.09731e9	−	5.16786e9i	1.58867	−	1.61066i
$239$		−	5.89940e9i		−	1.80807i	−0.427455	−	0.904037i	$-0.640590\pi$
$239$		−	5.89940e9i		−	1.80807i	0.427455	−	0.904037i	$-0.359410\pi$
$240$	5.98871e7	+	2.17795e9i	0.0180505	+	0.656451i
$241$	3.20243e9			0.949318			0.474659	−	0.880170i	$-0.342571\pi$
$241$	3.20243e9			0.949318			0.474659	+	0.880170i	$0.342571\pi$
$242$	2.43982e9	+	2.40651e9i	0.711371	+	0.701660i
$243$	−2.40095e9	−	2.40095e9i	−0.688587	−	0.688587i
$244$	3.44153e7	+	3.34820e7i	0.00970941	+	0.00944610i
$245$	−2.97024e9	−	2.97024e9i	−0.824379	−	0.824379i
$246$	6.79872e6	+	9.89245e8i	0.00185646	+	0.270124i
$247$	−5.25677e9			−1.41231
$248$	−1.06201e9	+	1.10673e9i	−0.280751	+	0.292573i
$249$			2.39071e9i			0.621914i
$250$	−2.01672e7	−	2.93441e9i	−0.00516279	−	0.751210i
$251$	4.48339e9	−	4.48339e9i	1.12957	−	1.12957i	0.139318	−	0.990248i	$-0.455509\pi$
$251$	4.48339e9	−	4.48339e9i	1.12957	−	1.12957i	0.990248	−	0.139318i	$-0.0444911\pi$
$252$	−4.39402e9	+	6.03998e7i	−1.08958	+	0.0149773i
$253$	1.82405e7	−	1.82405e7i	0.00445200	−	0.00445200i
$254$	3.77618e8	+	3.72463e8i	0.0907230	+	0.0894845i
$255$		−	4.76120e9i		−	1.12604i
$256$	4.28848e9	−	2.36019e8i	0.998489	−	0.0549525i
$257$	−3.66793e8			−0.0840792			−0.0420396	−	0.999116i	$-0.513386\pi$
$257$	−3.66793e8			−0.0840792			−0.0420396	+	0.999116i	$0.513386\pi$
$258$	−4.47959e8	+	4.54159e8i	−0.101102	+	0.102501i
$259$	1.63710e9	+	1.63710e9i	0.363811	+	0.363811i
$260$	−1.00061e8	−	7.27931e9i	−0.0218963	−	1.59293i
$261$	−1.26428e9	−	1.26428e9i	−0.272447	−	0.272447i
$262$	−7.26660e9	+	4.99407e7i	−1.54215	+	0.0105986i
$263$	4.42614e9			0.925129			0.462564	−	0.886586i	$-0.346929\pi$
$263$	4.42614e9			0.925129			0.462564	+	0.886586i	$0.346929\pi$
$264$	4.16864e7	+	4.00019e7i	0.00858180	+	0.00823503i
$265$			4.40659e9i			0.893551i
$266$	9.21643e9	−	6.33411e7i	1.84092	−	0.0126520i
$267$	−8.75871e8	+	8.75871e8i	−0.172344	+	0.172344i
$268$	4.14068e7	−	4.25610e7i	0.00802662	−	0.00825036i
$269$	−7.49923e8	+	7.49923e8i	−0.143221	+	0.143221i	−0.775082	−	0.631861i	$-0.782291\pi$
$269$	−7.49923e8	+	7.49923e8i	−0.143221	+	0.143221i	0.631861	+	0.775082i	$0.282291\pi$
$270$	−4.47489e9	+	4.53682e9i	−0.842029	+	0.853683i
$271$		−	6.15923e8i		−	0.114196i	−0.998369	−	0.0570978i	$-0.981815\pi$
$271$		−	6.15923e8i		−	0.114196i	0.998369	−	0.0570978i	$-0.0181847\pi$
$272$	−9.38212e9	+	2.57980e8i	−1.71406	+	0.0471315i
$273$	−3.09487e9			−0.557175
$274$	3.81961e9	+	3.76747e9i	0.677668	+	0.668417i
$275$	−1.70304e8	−	1.70304e8i	−0.0297779	−	0.0297779i
$276$	−3.72883e8	+	3.83278e8i	−0.0642594	+	0.0660506i
$277$	−3.61003e9	−	3.61003e9i	−0.613186	−	0.613186i	0.330589	−	0.943775i	$-0.392753\pi$
$277$	−3.61003e9	−	3.61003e9i	−0.613186	−	0.613186i	−0.943775	+	0.330589i	$0.892753\pi$
$278$	−7.46534e7	−	1.08624e10i	−0.0124989	−	1.81864i
$279$	−2.02923e9			−0.334899
$280$	2.63143e8	+	1.27612e10i	0.0428114	+	2.07616i
$281$			1.95702e9i			0.313885i	0.987608	+	0.156942i	$0.0501637\pi$
$281$			1.95702e9i			0.313885i	−0.987608	+	0.156942i	$0.949836\pi$
$282$	−3.15967e7	−	4.59746e9i	−0.00499626	−	0.726978i
$283$	−3.38369e9	+	3.38369e9i	−0.527527	+	0.527527i	−0.919834	−	0.392307i	$-0.871677\pi$
$283$	−3.38369e9	+	3.38369e9i	−0.527527	+	0.527527i	0.392307	+	0.919834i	$0.371677\pi$
$284$	−1.24564e8	−	9.06187e9i	−0.0191478	−	1.39298i
$285$	4.27477e9	−	4.27477e9i	0.647938	−	0.647938i
$286$	−1.37438e8	−	1.35562e8i	−0.0205420	−	0.0202616i
$287$			5.79546e9i			0.854201i
$288$	4.15349e9	+	3.87742e9i	0.603731	+	0.563603i
$289$	1.35344e10			1.94021
$290$	−3.64687e9	+	3.69734e9i	−0.515618	+	0.522754i
$291$	2.88623e9	+	2.88623e9i	0.402493	+	0.402493i
$292$	−2.49595e9	+	3.43092e7i	−0.343325	+	0.00471931i
$293$	7.39270e9	+	7.39270e9i	1.00307	+	1.00307i	0.999995	+	0.00307783i	$0.000979704\pi$
$293$	7.39270e9	+	7.39270e9i	1.00307	+	1.00307i	0.00307783	+	0.999995i	$0.499020\pi$
$294$	2.30893e9	−	1.58684e7i	0.309044	−	0.00212395i
$295$	1.27778e10			1.68721
$296$	−6.17164e7	−	2.99296e9i	−0.00803959	−	0.389883i
$297$			1.68977e8i			0.0217171i
$298$	−3.51650e9	+	2.41676e7i	−0.445908	+	0.00306456i
$299$	1.26341e9	−	1.26341e9i	0.158074	−	0.158074i
$300$	3.57851e9	+	3.48146e9i	0.441791	+	0.429810i
$301$	−2.64251e9	+	2.64251e9i	−0.321922	+	0.321922i
$302$	−4.03274e9	+	4.08855e9i	−0.484811	+	0.491521i
$303$		−	3.19795e9i		−	0.379403i
$304$	−8.65521e9	−	8.19197e9i	−1.01341	−	0.959166i
$305$	1.84505e8			0.0213210
$306$	−8.84017e9	−	8.71949e9i	−1.00827	−	0.994502i
$307$	−5.14116e9	−	5.14116e9i	−0.578773	−	0.578773i	0.355792	−	0.934565i	$-0.384211\pi$
$307$	−5.14116e9	−	5.14116e9i	−0.578773	−	0.578773i	−0.934565	+	0.355792i	$0.884211\pi$
$308$	2.42596e8	+	2.36017e8i	0.0269576	+	0.0262265i
$309$	−3.40286e9	−	3.40286e9i	−0.373258	−	0.373258i
$310$	4.05066e7	+	5.89389e9i	0.00438610	+	0.638198i
$311$	−2.71733e9			−0.290469			−0.145235	−	0.989397i	$-0.546394\pi$
$311$	−2.71733e9			−0.290469			−0.145235	+	0.989397i	$0.546394\pi$
$312$	2.88737e9	+	2.77070e9i	0.304708	+	0.292396i
$313$		−	2.51178e9i		−	0.261700i	−0.991402	−	0.130850i	$-0.958229\pi$
$313$		−	2.51178e9i		−	0.261700i	0.991402	−	0.130850i	$-0.0417706\pi$
$314$	9.17488e7	+	1.33499e10i	0.00943804	+	1.37328i
$315$	−1.19403e10	+	1.19403e10i	−1.21276	+	1.21276i
$316$	1.27426e10	−	1.75159e8i	1.27794	−	0.0175664i
$317$	−6.58549e9	+	6.58549e9i	−0.652156	+	0.652156i	−0.953512	−	0.301356i	$-0.902561\pi$
$317$	−6.58549e9	+	6.58549e9i	−0.652156	+	0.652156i	0.301356	+	0.953512i	$0.402561\pi$
$318$	−1.72451e9	−	1.70097e9i	−0.168639	−	0.166337i
$319$			1.37710e8i			0.0132985i
$320$	1.11791e10	−	1.21412e10i	1.06612	−	1.15788i
$321$	−1.02275e9			−0.0963269
$322$	−2.19985e9	+	2.23030e9i	−0.204630	+	0.207463i
$323$	1.84148e10	+	1.84148e10i	1.69183	+	1.69183i
$324$	7.69529e7	+	5.59823e9i	0.00698305	+	0.508009i
$325$	−1.17960e10	−	1.17960e10i	−1.05731	−	1.05731i
$326$	−4.13043e9	+	2.83870e7i	−0.365700	+	0.00251332i
$327$	−6.41377e9			−0.560947
$328$	5.18842e9	−	5.40690e9i	0.448270	−	0.467146i
$329$		−	2.69341e10i		−	2.29889i
$330$	2.22001e8	−	1.52573e6i	0.0187197	−	0.000128654i
$331$	9.88763e9	−	9.88763e9i	0.823721	−	0.823721i	−0.162918	−	0.986640i	$-0.552091\pi$
$331$	9.88763e9	−	9.88763e9i	0.823721	−	0.823721i	0.986640	+	0.162918i	$0.0520907\pi$
$332$	1.26281e10	−	1.29801e10i	1.03941	−	1.06838i
$333$	2.80043e9	−	2.80043e9i	0.227745	−	0.227745i
$334$	−2.97647e9	+	3.01766e9i	−0.239175	+	0.242485i
$335$		−	2.28175e8i		−	0.0181171i
$336$	−5.09566e9	−	4.82293e9i	−0.399801	−	0.378402i
$337$	−1.42761e10			−1.10685			−0.553426	−	0.832898i	$-0.686680\pi$
$337$	−1.42761e10			−1.10685			−0.553426	+	0.832898i	$0.686680\pi$
$338$	−2.27374e8	−	2.24270e8i	−0.0174211	−	0.0171832i
$339$	1.13083e9	+	1.13083e9i	0.0856246	+	0.0856246i
$340$	−2.51493e10	+	2.58504e10i	−1.88196	+	1.93442i
$341$	1.10516e8	+	1.10516e8i	0.00817346	+	0.00817346i
$342$	−1.08352e8	−	1.57657e10i	−0.00792012	−	1.15241i
$343$	−4.73491e9			−0.342086
$344$	4.83107e9	−	9.96191e7i	0.344993	−	0.00711392i
$345$			2.05480e9i			0.145042i
$346$	−7.72352e7	−	1.12381e10i	−0.00538903	−	0.784129i
$347$	6.45408e9	−	6.45408e9i	0.445161	−	0.445161i	−0.448581	−	0.893742i	$-0.648071\pi$
$347$	6.45408e9	−	6.45408e9i	0.445161	−	0.445161i	0.893742	+	0.448581i	$0.148071\pi$
$348$	−3.92363e7	−	2.85439e9i	−0.00267529	−	0.194624i
$349$	1.58170e10	−	1.58170e10i	1.06616	−	1.06616i	0.0685130	−	0.997650i	$-0.478175\pi$
$349$	1.58170e10	−	1.58170e10i	1.06616	−	1.06616i	0.997650	−	0.0685130i	$-0.0218255\pi$
$350$	2.08234e10	+	2.05391e10i	1.38765	+	1.36871i
$351$			1.17041e10i			0.771096i
$352$	−1.50354e7	−	4.37379e8i	−0.000979365	−	0.0284897i
$353$	−2.81679e10			−1.81408			−0.907039	−	0.421046i	$-0.861663\pi$
$353$	−2.81679e10			−1.81408			−0.907039	+	0.421046i	$0.861663\pi$
$354$	−4.93231e9	+	5.00058e9i	−0.314078	+	0.318425i
$355$	−2.46248e10	−	2.46248e10i	−1.55045	−	1.55045i
$356$	9.38191e9	−	1.28963e8i	0.584106	−	0.00802907i
$357$	1.08415e10	+	1.08415e10i	0.667446	+	0.667446i
$358$	−7.55462e7	+	519202.i	−0.00459918	+	3.16085e-5i
$359$	−2.15720e9			−0.129871			−0.0649357	−	0.997889i	$-0.520684\pi$
$359$	−2.15720e9			−0.129871			−0.0649357	+	0.997889i	$0.520684\pi$
$360$	2.18294e10	−	4.50134e8i	1.29967	−	0.0267998i
$361$			1.60833e10i			0.946991i
$362$	1.48651e10	−	1.02162e8i	0.865632	−	0.00594917i
$363$	−5.11842e9	+	5.11842e9i	−0.294788	+	0.294788i
$364$	1.68032e10	+	1.63475e10i	0.957165	+	0.931208i
$365$	−6.78252e9	+	6.78252e9i	−0.382138	+	0.382138i
$366$	−7.12199e7	+	7.22057e7i	−0.00396897	+	0.00402390i
$367$			2.90608e10i			1.60193i	0.598710	+	0.800966i	$0.295680\pi$
$367$			2.90608e10i			1.60193i	−0.598710	+	0.800966i	$0.704320\pi$
$368$	4.04905e9	−	1.11337e8i	0.220781	−	0.00607083i
$369$	9.91375e9			0.534727
$370$	−8.18977e9	−	8.07797e9i	−0.436983	−	0.431018i
$371$	−1.00340e10	−	1.00340e10i	−0.529639	−	0.529639i
$372$	−2.32220e9	−	2.25923e9i	−0.121263	−	0.117974i
$373$	2.00021e10	+	2.00021e10i	1.03333	+	1.03333i	0.999425	+	0.0339059i	$0.0107947\pi$
$373$	2.00021e10	+	2.00021e10i	1.03333	+	1.03333i	0.0339059	+	0.999425i	$0.489205\pi$
$374$	6.57253e6	+	9.56333e8i	0.000335928	+	0.0488791i
$375$	6.19833e9			0.313436
$376$	−2.41129e10	+	2.51282e10i	−1.20642	+	1.25722i
$377$			9.53839e9i			0.472182i
$378$	−1.41027e8	−	2.05201e10i	−0.00690774	−	1.00511i
$379$	1.32718e10	−	1.32718e10i	0.643241	−	0.643241i	−0.308110	−	0.951351i	$-0.599696\pi$
$379$	1.32718e10	−	1.32718e10i	0.643241	−	0.643241i	0.951351	+	0.308110i	$0.0996964\pi$
$380$	−4.57893e10	+	6.29416e8i	−2.19599	+	0.0301858i
$381$	−7.92193e8	+	7.92193e8i	−0.0375951	+	0.0375951i
$382$	1.38767e10	+	1.36873e10i	0.651678	+	0.642782i
$383$		−	5.09072e9i		−	0.236583i	−0.992979	−	0.118292i	$-0.962258\pi$
$383$		−	5.09072e9i		−	0.236583i	0.992979	−	0.118292i	$-0.0377418\pi$
$384$	4.36264e8	+	9.06150e9i	0.0200643	+	0.416750i
$385$	1.30059e9			0.0591966
$386$	−2.11346e10	+	2.14271e10i	−0.952016	+	0.965193i
$387$	4.52030e9	+	4.52030e9i	0.201522	+	0.201522i
$388$	−4.24967e8	−	3.09159e10i	−0.0187512	−	1.36413i
$389$	7.86395e9	+	7.86395e9i	0.343433	+	0.343433i	0.857656	−	0.514223i	$-0.171920\pi$
$389$	7.86395e9	+	7.86395e9i	0.343433	+	0.343433i	−0.514223	+	0.857656i	$0.671920\pi$
$390$	1.53767e10	−	1.05679e8i	0.664669	−	0.00456803i
$391$	−8.85161e9			−0.378718
$392$	−1.26199e10	−	1.21099e10i	−0.534454	−	0.512858i
$393$		−	1.53491e10i		−	0.643449i
$394$	−1.61967e10	+	1.11314e8i	−0.672110	+	0.00461917i
$395$	3.46268e10	−	3.46268e10i	1.42241	−	1.42241i
$396$	4.03733e8	−	4.14987e8i	0.0164177	−	0.0168754i
$397$	1.90783e10	−	1.90783e10i	0.768029	−	0.768029i	−0.209730	−	0.977759i	$-0.567258\pi$
$397$	1.90783e10	−	1.90783e10i	0.768029	−	0.768029i	0.977759	+	0.209730i	$0.0672585\pi$
$398$	8.54684e9	−	8.66513e9i	0.340622	−	0.345337i
$399$			1.94677e10i			0.768111i
$400$	−1.03951e9	−	3.78044e10i	−0.0406058	−	1.47673i
$401$	−1.34169e10			−0.518891			−0.259446	−	0.965758i	$-0.583540\pi$
$401$	−1.34169e10			−0.518891			−0.259446	+	0.965758i	$0.583540\pi$
$402$	8.92959e7	+	8.80768e7i	0.00341922	+	0.00337254i
$403$	7.65477e9	+	7.65477e9i	0.290210	+	0.290210i
$404$	−1.68920e10	+	1.73629e10i	−0.634098	+	0.651773i
$405$	1.52127e10	+	1.52127e10i	0.565439	+	0.565439i
$406$	−1.14932e8	−	1.67232e10i	−0.00422997	−	0.615480i
$407$	−3.05034e8			−0.0111166
$408$	−4.08709e8	−	1.98205e10i	−0.0147494	−	0.715278i
$409$		−	1.71881e10i		−	0.614236i	−0.951671	−	0.307118i	$-0.900635\pi$
$409$		−	1.71881e10i		−	0.614236i	0.951671	−	0.307118i	$-0.0993646\pi$
$410$	−1.97894e8	−	2.87945e10i	−0.00700321	−	1.01900i
$411$	−8.01306e9	+	8.01306e9i	−0.280822	+	0.280822i
$412$	5.01035e8	+	3.64498e10i	0.0173892	+	1.26504i
$413$	−2.90957e10	+	2.90957e10i	−1.00007	+	1.00007i
$414$	3.81516e9	+	3.76308e9i	0.129871	+	0.128098i
$415$		−	6.95879e10i		−	2.34607i
$416$	−1.04141e9	−	3.02947e10i	−0.0347737	−	1.01156i
$417$	2.29446e10			0.758814
$418$	−8.52728e8	+	8.64530e8i	−0.0279322	+	0.0283188i
$419$	−1.16702e9	−	1.16702e9i	−0.0378638	−	0.0378638i	0.687921	−	0.725785i	$-0.258523\pi$
$419$	−1.16702e9	−	1.16702e9i	−0.0378638	−	0.0378638i	−0.725785	+	0.687921i	$0.758523\pi$
$420$	−2.69579e10	+	3.70562e8i	−0.866342	+	0.0119087i
$421$	−3.29147e9	−	3.29147e9i	−0.104776	−	0.104776i	0.652776	−	0.757551i	$-0.273604\pi$
$421$	−3.29147e9	−	3.29147e9i	−0.104776	−	0.104776i	−0.757551	+	0.652776i	$0.773604\pi$
$422$	6.03574e9	−	4.14814e7i	0.190318	−	0.00130799i
$423$	−4.60736e10			−1.43910
$424$	3.78270e8	+	1.83443e10i	0.0117041	+	0.567595i
$425$			8.26439e10i			2.53312i
$426$	1.91422e10	−	1.31557e8i	0.581237	−	0.00399463i
$427$	−4.20127e8	+	4.20127e8i	−0.0126377	+	0.0126377i
$428$	5.55287e9	+	5.40228e9i	0.165479	+	0.160991i
$429$	2.88327e8	−	2.88327e8i	0.00851248	−	0.00851248i
$430$	1.30390e10	−	1.32195e10i	0.381391	−	0.386669i
$431$			1.20233e10i			0.348429i	0.984708	+	0.174214i	$0.0557386\pi$
$431$			1.20233e10i			0.348429i	−0.984708	+	0.174214i	$0.944261\pi$
$432$	−1.82392e10	+	1.92706e10i	−0.523686	+	0.553300i
$433$	4.36305e10			1.24119			0.620595	−	0.784131i	$-0.286891\pi$
$433$	4.36305e10			1.24119			0.620595	+	0.784131i	$0.286891\pi$
$434$	−1.35129e10	−	1.33285e10i	−0.380882	−	0.375683i
$435$	−7.75655e9	−	7.75655e9i	−0.216626	−	0.216626i
$436$	3.48228e10	+	3.38784e10i	0.963645	+	0.937512i
$437$	−7.94729e9	−	7.94729e9i	−0.217918	−	0.217918i
$438$	−3.62354e7	−	5.27242e9i	−0.000984548	−	0.143256i
$439$	−6.61882e8			−0.0178206			−0.00891030	−	0.999960i	$-0.502836\pi$
$439$	−6.61882e8			−0.0178206			−0.00891030	+	0.999960i	$0.502836\pi$
$440$	−1.21339e9	−	1.16436e9i	−0.0323735	−	0.0310653i
$441$		−	2.31390e10i		−	0.611772i
$442$	4.55241e8	+	6.62396e10i	0.0119276	+	1.73552i
$443$	−4.04686e10	+	4.04686e10i	−1.05076	+	1.05076i	−0.0521171	+	0.998641i	$0.516597\pi$
$443$	−4.04686e10	+	4.04686e10i	−1.05076	+	1.05076i	−0.998641	+	0.0521171i	$0.983403\pi$
$444$	6.32260e9	−	8.69099e7i	0.162691	−	0.00223634i
$445$	2.54945e10	−	2.54945e10i	0.650138	−	0.650138i
$446$	−9.65052e9	−	9.51878e9i	−0.243900	−	0.240570i
$447$		−	7.42786e9i		−	0.186052i
$448$	2.19089e9	+	5.31015e10i	0.0543887	+	1.31824i
$449$	−7.08087e10			−1.74221			−0.871107	−	0.491093i	$-0.836597\pi$
$449$	−7.08087e10			−1.74221			−0.871107	+	0.491093i	$0.836597\pi$
$450$	3.51344e10	−	3.56207e10i	0.856806	−	0.868664i
$451$	−5.39922e8	−	5.39922e8i	−0.0130504	−	0.0130504i
$452$	−1.66503e8	−	1.21129e10i	−0.00398904	−	0.290198i
$453$	−8.57725e9	−	8.57725e9i	−0.203683	−	0.203683i
$454$	−6.27224e9	+	4.31068e7i	−0.147638	+	0.00101467i
$455$	9.00840e10			2.10185
$456$	1.74286e10	−	1.81625e10i	0.403091	−	0.420065i
$457$		−	7.55905e10i		−	1.73301i	−0.499164	−	0.866507i	$-0.666360\pi$
$457$		−	7.55905e10i		−	1.73301i	0.499164	−	0.866507i	$-0.333640\pi$
$458$	1.53259e10	−	1.05329e8i	0.348309	−	0.00239380i
$459$	4.10000e10	−	4.10000e10i	0.923705	−	0.923705i
$460$	1.08537e10	−	1.11563e10i	0.242408	−	0.249165i
$461$	−3.00010e10	+	3.00010e10i	−0.664250	+	0.664250i	−0.956379	−	0.292129i	$-0.905636\pi$
$461$	−3.00010e10	+	3.00010e10i	−0.664250	+	0.664250i	0.292129	+	0.956379i	$0.405636\pi$
$462$	−5.02034e8	+	5.08983e8i	−0.0110196	+	0.0111721i
$463$			8.11242e10i			1.76533i	0.470000	+	0.882666i	$0.344254\pi$
$463$			8.11242e10i			1.76533i	−0.470000	+	0.882666i	$0.655746\pi$
$464$	−1.48643e10	+	1.57048e10i	−0.320680	+	0.338814i
$465$	−1.24496e10			−0.266283
$466$	1.88301e10	+	1.85730e10i	0.399309	+	0.393858i
$467$	2.37442e9	+	2.37442e9i	0.0499217	+	0.0499217i	0.731627	−	0.681705i	$-0.238761\pi$
$467$	2.37442e9	+	2.37442e9i	0.0499217	+	0.0499217i	−0.681705	+	0.731627i	$0.738761\pi$
$468$	2.79642e10	−	2.87437e10i	0.582933	−	0.599183i
$469$	5.19566e8	+	5.19566e8i	0.0107386	+	0.0107386i
$470$	9.19701e8	+	1.33821e11i	0.0188476	+	2.74241i
$471$	−2.81988e10			−0.572989
$472$	5.31931e10	−	1.09687e9i	1.07174	−	0.0220997i
$473$		−	4.92369e8i		−	0.00983662i
$474$	1.84993e8	+	2.69173e10i	0.00366472	+	0.533234i
$475$	−7.42006e10	+	7.42006e10i	−1.45758	+	1.45758i
$476$	−1.59630e9	−	1.16129e11i	−0.0310947	−	2.26210i
$477$	−1.71643e10	+	1.71643e10i	−0.331553	+	0.331553i
$478$	−6.72012e10	−	6.62838e10i	−1.28726	−	1.26968i
$479$		−	6.65324e10i		−	1.26384i	−0.775035	−	0.631918i	$-0.782268\pi$
$479$		−	6.65324e10i		−	1.26384i	0.775035	−	0.631918i	$-0.217732\pi$
$480$	2.54823e10	+	2.37885e10i	0.480036	+	0.448129i
$481$	−2.11279e10			−0.394708
$482$	3.59815e10	−	3.64795e10i	0.666640	−	0.675867i
$483$	−4.67888e9	−	4.67888e9i	−0.0859713	−	0.0859713i
$484$	5.48261e10	−	7.53635e8i	0.999093	−	0.0137335i
$485$	−8.40111e10	−	8.40111e10i	−1.51834	−	1.51834i
$486$	−5.43261e10	+	3.73364e8i	−0.973786	+	0.00669248i
$487$	5.24988e10			0.933327			0.466663	−	0.884435i	$-0.345456\pi$
$487$	5.24988e10			0.933327			0.466663	+	0.884435i	$0.345456\pi$
$488$	7.68080e8	−	1.58382e7i	0.0135434	−	0.000279272i
$489$		−	8.72467e9i		−	0.152586i
$490$	−6.72072e10	+	4.61891e8i	−1.16582	+	0.00801226i
$491$	−1.00556e10	+	1.00556e10i	−0.173015	+	0.173015i	−0.788303	−	0.615288i	$-0.789040\pi$
$491$	−1.00556e10	+	1.00556e10i	−0.173015	+	0.173015i	0.615288	+	0.788303i	$0.289040\pi$
$492$	1.13451e10	+	1.10374e10i	0.193618	+	0.188368i
$493$	3.34135e10	−	3.34135e10i	0.565632	−	0.565632i
$494$	−5.90635e10	+	5.98809e10i	−0.991770	+	1.00550i
$495$		−	2.22479e9i		−	0.0370569i
$496$	6.74568e8	+	2.45324e10i	0.0111455	+	0.405334i
$497$	1.12144e11			1.83802
$498$	2.72331e10	+	2.68613e10i	0.442771	+	0.436727i
$499$	−1.39400e9	−	1.39400e9i	−0.0224834	−	0.0224834i	0.695776	−	0.718259i	$-0.255061\pi$
$499$	−1.39400e9	−	1.39400e9i	−0.0224834	−	0.0224834i	−0.718259	+	0.695776i	$0.755061\pi$
$500$	−3.36531e10	−	3.27404e10i	−0.538449	−	0.523847i
$501$	−6.33066e9	−	6.33066e9i	−0.100484	−	0.100484i
$502$	−6.97195e8	−	1.01445e11i	−0.0109784	−	1.59741i
$503$	−5.63295e10			−0.879962			−0.439981	−	0.898007i	$-0.645015\pi$
$503$	−5.63295e10			−0.879962			−0.439981	+	0.898007i	$0.645015\pi$
$504$	−4.86818e10	+	5.07318e10i	−0.754474	+	0.786245i
$505$			9.30845e10i			1.43124i
$506$	−2.83651e6	−	4.12726e8i	−4.32696e−5	−	0.00629593i
$507$	4.77002e8	−	4.77002e8i	0.00721918	−	0.00721918i
$508$	8.48559e9	−	1.16642e8i	0.127417	−	0.00175146i
$509$	3.78176e10	−	3.78176e10i	0.563408	−	0.563408i	−0.366866	−	0.930274i	$-0.619569\pi$
$509$	3.78176e10	−	3.78176e10i	0.563408	−	0.563408i	0.930274	+	0.366866i	$0.119569\pi$
$510$	−5.42358e10	−	5.34954e10i	−0.801687	−	0.790743i
$511$		−	3.08883e10i		−	0.453013i
$512$	4.54955e10	−	5.15027e10i	0.662046	−	0.749463i
$513$	7.36225e10			1.06302
$514$	−4.12117e9	+	4.17821e9i	−0.0590430	+	0.0598601i
$515$	9.90488e10	+	9.90488e10i	1.40806	+	1.40806i
$516$	1.40285e8	+	1.02056e10i	0.00197885	+	0.143959i
$517$	2.50925e9	+	2.50925e9i	0.0351223	+	0.0351223i
$518$	3.70425e10	−	2.54579e8i	0.514495	−	0.00353593i
$519$	2.37380e10			0.327172
$520$	−8.40443e10	−	8.06483e10i	−1.14946	−	1.10302i
$521$		−	5.45288e10i		−	0.740074i	−0.929017	−	0.370037i	$-0.879345\pi$
$521$		−	5.45288e10i		−	0.740074i	0.929017	−	0.370037i	$-0.120655\pi$
$522$	−2.86067e10	+	1.96604e8i	−0.385289	+	0.00264795i
$523$	−3.17681e10	+	3.17681e10i	−0.424604	+	0.424604i	−0.886786	−	0.462181i	$-0.847067\pi$
$523$	−3.17681e10	+	3.17681e10i	−0.424604	+	0.424604i	0.462181	+	0.886786i	$0.347067\pi$
$524$	−8.10763e10	+	8.33363e10i	−1.07540	+	1.10537i
$525$	−4.36848e10	+	4.36848e10i	−0.575034	+	0.575034i
$526$	4.97307e10	−	5.04190e10i	0.649654	−	0.658645i
$527$		−	5.36301e10i		−	0.695291i
$528$	9.24045e8	−	2.54085e7i	0.0118893	−	0.000326921i
$529$	−7.44909e10			−0.951219
$530$	5.01964e10	+	4.95111e10i	0.636164	+	0.627479i
$531$	4.97714e10	+	4.97714e10i	0.626039	+	0.626039i
$532$	1.02831e11	−	1.05698e11i	1.28375	−	1.31953i
$533$	−3.73972e10	−	3.73972e10i	−0.463373	−	0.463373i
$534$	1.36203e8	+	1.98182e10i	0.00167503	+	0.243725i
$535$	2.97696e10			0.363378
$536$	−1.95869e7	−	9.49876e8i	−0.000237305	−	0.0115082i
$537$		−	1.59575e8i		−	0.00191897i
$538$	1.16618e8	+	1.69684e10i	0.00139199	+	0.202541i
$539$	−1.26019e9	+	1.26019e9i	−0.0149308	+	0.0149308i
$540$	1.40138e9	+	1.01949e11i	0.0164809	+	1.19896i
$541$	−2.81164e10	+	2.81164e10i	−0.328224	+	0.328224i	−0.851911	−	0.523687i	$-0.824556\pi$
$541$	−2.81164e10	+	2.81164e10i	−0.328224	+	0.328224i	0.523687	+	0.851911i	$0.324556\pi$
$542$	−7.01610e9	−	6.92032e9i	−0.0813015	−	0.0801916i
$543$			3.13993e10i			0.361178i
$544$	−1.02476e11	+	1.09772e11i	−1.17011	+	1.25342i
$545$	1.86689e11			2.11608
$546$	−3.47730e10	+	3.52543e10i	−0.391265	+	0.396681i
$547$	4.72086e10	+	4.72086e10i	0.527317	+	0.527317i	0.919771	−	0.392454i	$-0.128374\pi$
$547$	4.72086e10	+	4.72086e10i	0.527317	+	0.527317i	−0.392454	+	0.919771i	$0.628374\pi$
$548$	8.58320e10	−	1.17984e9i	0.951759	−	0.0130828i
$549$	7.18672e8	+	7.18672e8i	0.00791118	+	0.00791118i
$550$	−3.85346e9	+	2.64834e7i	−0.0421114	+	0.000289416i
$551$	5.99996e10			0.650941
$552$	1.76387e8	+	8.55397e9i	0.00189981	+	0.0921322i
$553$			1.57694e11i			1.68622i
$554$	−8.16838e10	+	5.61383e8i	−0.867155	+	0.00595964i
$555$	1.71811e10	−	1.71811e10i	0.181083	−	0.181083i
$556$	−1.24575e11	−	1.21196e11i	−1.30356	−	1.26821i
$557$	−4.42829e10	+	4.42829e10i	−0.460061	+	0.460061i	−0.898675	−	0.438614i	$-0.855469\pi$
$557$	−4.42829e10	+	4.42829e10i	−0.460061	+	0.460061i	0.438614	+	0.898675i	$0.355469\pi$
$558$	−2.27998e10	+	2.31153e10i	−0.235176	+	0.238431i
$559$		−	3.41035e10i		−	0.349262i
$560$	1.48322e11	+	1.40384e11i	1.50818	+	1.42746i
$561$	−2.02005e9			−0.0203944
$562$	2.22928e10	+	2.19885e10i	0.223470	+	0.220419i
$563$	−1.27892e11	−	1.27892e11i	−1.27294	−	1.27294i	−0.944537	−	0.328406i	$-0.893489\pi$
$563$	−1.27892e11	−	1.27892e11i	−1.27294	−	1.27294i	−0.328406	−	0.944537i	$-0.606511\pi$
$564$	−5.27256e10	−	5.12957e10i	−0.521080	−	0.506949i
$565$	−3.29157e10	−	3.29157e10i	−0.323005	−	0.323005i
$566$	5.26185e8	+	7.65623e10i	0.00512711	+	0.746018i
$567$	−6.92801e10			−0.670311
$568$	−1.04625e11	−	1.00397e11i	−1.00518	−	0.964559i
$569$		−	6.51664e10i		−	0.621691i	−0.950460	−	0.310846i	$-0.899388\pi$
$569$		−	6.51664e10i		−	0.621691i	0.950460	−	0.310846i	$-0.100612\pi$
$570$	−6.64754e8	−	9.67247e10i	−0.00629740	−	0.916301i
$571$	−1.63001e10	+	1.63001e10i	−0.153337	+	0.153337i	−0.779607	−	0.626270i	$-0.784581\pi$
$571$	−1.63001e10	+	1.63001e10i	−0.153337	+	0.153337i	0.626270	+	0.779607i	$0.284581\pi$
$572$	−3.08842e9	+	4.24532e7i	−0.0288504	+	0.000396576i
$573$	−2.91115e10	+	2.91115e10i	−0.270051	+	0.270051i
$574$	6.60172e10	+	6.51159e10i	0.608148	+	0.599846i
$575$		−	3.56667e10i		−	0.326281i
$576$	9.08358e10	−	3.74775e9i	0.825215	−	0.0340472i
$577$	−1.52954e11			−1.37993			−0.689965	−	0.723843i	$-0.742374\pi$
$577$	−1.52954e11			−1.37993			−0.689965	+	0.723843i	$0.742374\pi$
$578$	1.52069e11	−	1.54174e11i	1.36248	−	1.38133i
$579$	−4.49513e10	−	4.49513e10i	−0.399970	−	0.399970i
$580$	1.14207e9	+	8.30844e10i	0.0100921	+	0.734188i
$581$	1.58455e11	+	1.58455e11i	1.39060	+	1.39060i
$582$	6.53064e10	−	4.48827e8i	0.569198	−	0.00391189i
$583$	1.86960e9			0.0161836
$584$	−2.76529e10	+	2.88174e10i	−0.237733	+	0.247744i
$585$		−	1.54098e11i		−	1.31575i
$586$	1.67274e11	−	1.14961e9i	1.41853	−	0.00974901i
$587$	7.45208e10	−	7.45208e10i	0.627661	−	0.627661i	−0.319818	−	0.947479i	$-0.603622\pi$
$587$	7.45208e10	−	7.45208e10i	0.627661	−	0.627661i	0.947479	+	0.319818i	$0.103622\pi$
$588$	2.57616e10	−	2.64797e10i	0.215508	−	0.221516i
$589$	4.81510e10	−	4.81510e10i	0.400078	−	0.400078i
$590$	1.43568e11	−	1.45555e11i	1.18481	−	1.20121i
$591$		−	3.42120e10i		−	0.280433i
$592$	−3.47869e10	−	3.29250e10i	−0.283223	−	0.268064i
$593$	−1.69443e11			−1.37027			−0.685133	−	0.728418i	$-0.740256\pi$
$593$	−1.69443e11			−1.37027			−0.685133	+	0.728418i	$0.740256\pi$
$594$	1.92485e9	+	1.89858e9i	0.0154615	+	0.0152504i
$595$	−3.15569e11	−	3.15569e11i	−2.51783	−	2.51783i
$596$	−3.92350e10	+	4.03287e10i	−0.310948	+	0.319616i
$597$	1.81783e10	+	1.81783e10i	0.143106	+	0.143106i
$598$	−1.96469e8	−	2.85871e10i	−0.00153634	−	0.223545i
$599$	−2.07574e11			−1.61237			−0.806185	−	0.591663i	$-0.798472\pi$
$599$	−2.07574e11			−1.61237			−0.806185	+	0.591663i	$0.798472\pi$
$600$	7.98650e10	−	1.64686e9i	0.616242	−	0.0127072i
$601$			1.88953e11i			1.44829i	0.689647	+	0.724146i	$0.257766\pi$
$601$			1.88953e11i			1.44829i	−0.689647	+	0.724146i	$0.742234\pi$
$602$	4.10928e8	+	5.97918e10i	0.00312881	+	0.455256i
$603$	8.88773e8	−	8.88773e8i	0.00672236	−	0.00672236i
$604$	1.26291e9	+	9.18754e10i	0.00948910	+	0.690322i
$605$	1.48985e11	−	1.48985e11i	1.11204	−	1.11204i
$606$	−3.64285e10	−	3.59312e10i	−0.270116	−	0.266429i
$607$			7.61960e10i			0.561277i	0.959813	+	0.280639i	$0.0905463\pi$
$607$			7.61960e10i			0.561277i	−0.959813	+	0.280639i	$0.909454\pi$
$608$	−1.90564e11	+	6.55084e9i	−1.39452	+	0.0479383i
$609$	3.53241e10			0.256804
$610$	2.07304e9	−	2.10173e9i	0.0149723	−	0.0151795i
$611$	1.73801e11	+	1.73801e11i	1.24706	+	1.24706i
$612$	−1.98651e11	+	2.73064e9i	−1.41607	+	0.0194652i
$613$	2.80322e10	+	2.80322e10i	0.198525	+	0.198525i	0.799368	−	0.600842i	$-0.205168\pi$
$613$	2.80322e10	+	2.80322e10i	0.198525	+	0.198525i	−0.600842	+	0.799368i	$0.705168\pi$
$614$	−1.16329e11	+	7.99483e8i	−0.818489	+	0.00562517i
$615$	6.08223e10			0.425170
$616$	5.41425e9	−	1.11645e8i	0.0376024	−	0.000775381i
$617$			1.36999e10i			0.0945315i	0.998882	+	0.0472658i	$0.0150508\pi$
$617$			1.36999e10i			0.0945315i	−0.998882	+	0.0472658i	$0.984949\pi$
$618$	−7.69960e10	+	5.29166e8i	−0.527855	+	0.00362775i
$619$	6.45196e10	−	6.45196e10i	0.439470	−	0.439470i	−0.452364	−	0.891833i	$-0.649419\pi$
$619$	6.45196e10	−	6.45196e10i	0.439470	−	0.439470i	0.891833	+	0.452364i	$0.149419\pi$
$620$	6.75936e10	+	6.57605e10i	0.457445	+	0.445039i
$621$	−1.76944e10	+	1.76944e10i	−0.118979	+	0.118979i
$622$	−3.05310e10	+	3.09536e10i	−0.203976	+	0.206799i
$623$			1.16104e11i			0.770720i
$624$	6.40032e10	−	1.75990e9i	0.422147	−	0.0116078i
$625$	4.49985e10			0.294902
$626$	−2.86121e10	−	2.82215e10i	−0.186317	−	0.183774i
$627$	−1.81367e9	−	1.81367e9i	−0.0117351	−	0.0117351i
$628$	1.53102e11	+	1.48950e11i	0.984333	+	0.957639i
$629$	7.40123e10	+	7.40123e10i	0.472826	+	0.472826i
$630$	1.85680e9	+	2.70173e11i	0.0117870	+	1.71506i
$631$	−1.59056e10			−0.100331			−0.0501653	−	0.998741i	$-0.515975\pi$
$631$	−1.59056e10			−0.100331			−0.0501653	+	0.998741i	$0.515975\pi$
$632$	1.41176e11	−	1.47121e11i	0.884899	−	0.922162i
$633$			1.27492e10i			0.0794088i
$634$	1.02409e9	+	1.49009e11i	0.00633839	+	0.922265i
$635$	2.30588e10	−	2.30588e10i	0.141821	−	0.141821i
$636$	−3.87522e10	+	5.32684e8i	−0.236847	+	0.00325568i
$637$	−8.72862e10	+	8.72862e10i	−0.530137	+	0.530137i
$638$	1.56869e9	+	1.54727e9i	0.00946789	+	0.00933864i
$639$		−	1.91834e11i		−	1.15059i
$640$	−1.26986e10	−	2.63758e11i	−0.0756895	−	1.57212i
$641$	−1.62329e11			−0.961531			−0.480765	−	0.876849i	$-0.659641\pi$
$641$	−1.62329e11			−0.961531			−0.480765	+	0.876849i	$0.659641\pi$
$642$	−1.14912e10	+	1.16503e10i	−0.0676437	+	0.0685799i
$643$	1.41233e11	+	1.41233e11i	0.826215	+	0.826215i	0.986991	−	0.160776i	$-0.0513996\pi$
$643$	1.41233e11	+	1.41233e11i	0.826215	+	0.826215i	−0.160776	+	0.986991i	$0.551400\pi$
$644$	6.88917e8	+	5.01179e10i	0.00400519	+	0.291373i
$645$	2.77327e10	+	2.77327e10i	0.160234	+	0.160234i
$646$	4.16669e11	−	2.86361e9i	2.39255	−	0.0164431i
$647$	1.50305e11			0.857739			0.428870	−	0.903366i	$-0.358912\pi$
$647$	1.50305e11			0.857739			0.428870	+	0.903366i	$0.358912\pi$
$648$	6.46352e10	+	6.20234e10i	0.366580	+	0.351768i
$649$		−	5.42129e9i		−	0.0305579i
$650$	−2.66906e11	+	1.83435e9i	−1.49522	+	0.0102761i
$651$	2.83484e10	−	2.83484e10i	0.157835	−	0.157835i
$652$	−4.60849e10	+	4.73695e10i	−0.255017	+	0.262125i
$653$	−8.21695e10	+	8.21695e10i	−0.451916	+	0.451916i	−0.895990	−	0.444074i	$-0.853533\pi$
$653$	−8.21695e10	+	8.21695e10i	−0.451916	+	0.451916i	0.444074	+	0.895990i	$0.353533\pi$
$654$	−7.20631e10	+	7.30604e10i	−0.393914	+	0.399366i
$655$			4.46776e11i			2.42731i
$656$	−3.29559e9	−	1.19852e11i	−0.0177958	−	0.647190i
$657$	−5.28377e10			−0.283585
$658$	−3.06811e11	−	3.02623e11i	−1.63669	−	1.61435i
$659$	3.54829e10	+	3.54829e10i	0.188139	+	0.188139i	0.794891	−	0.606752i	$-0.207528\pi$
$659$	3.54829e10	+	3.54829e10i	0.188139	+	0.188139i	−0.606752	+	0.794891i	$0.707528\pi$
$660$	2.47696e9	−	2.54600e9i	0.0130540	−	0.0134179i
$661$	−2.89050e10	−	2.89050e10i	−0.151414	−	0.151414i	0.627335	−	0.778749i	$-0.284146\pi$
$661$	−2.89050e10	−	2.89050e10i	−0.151414	−	0.151414i	−0.778749	+	0.627335i	$0.784146\pi$
$662$	−1.53759e9	−	2.23726e11i	−0.00800586	−	1.16489i
$663$	−1.39917e11			−0.724130
$664$	−5.97354e9	−	2.89689e11i	−0.0307298	−	1.49025i
$665$		−	5.66658e11i		−	2.89758i
$666$	−4.35485e8	−	6.33651e10i	−0.00221348	−	0.322072i
$667$	−1.44203e10	+	1.44203e10i	−0.0728570	+	0.0728570i
$668$	9.32125e8	+	6.78110e10i	0.00468132	+	0.340561i
$669$	2.02455e10	−	2.02455e10i	0.101071	−	0.101071i
$670$	−2.59918e9	−	2.56370e9i	−0.0128985	−	0.0127224i
$671$		−	7.82805e7i		−	0.000386157i
$672$	−1.12192e11	+	3.85674e9i	−0.550156	+	0.0189122i
$673$	1.55445e11			0.757736			0.378868	−	0.925451i	$-0.376313\pi$
$673$	1.55445e11			0.757736			0.378868	+	0.925451i	$0.376313\pi$
$674$	−1.60402e11	+	1.62622e11i	−0.777266	+	0.788023i
$675$	1.65206e11	+	1.65206e11i	0.795811	+	0.795811i
$676$	−5.10941e9	+	7.02336e7i	−0.0244672	+	0.000336324i
$677$	8.73806e10	+	8.73806e10i	0.415969	+	0.415969i	0.883812	−	0.467843i	$-0.154969\pi$
$677$	8.73806e10	+	8.73806e10i	0.415969	+	0.415969i	−0.467843	+	0.883812i	$0.654969\pi$
$678$	2.55872e10	−	1.75851e8i	0.121089	−	0.000832198i
$679$	3.82595e11			1.79995
$680$	1.18965e10	+	5.76927e11i	0.0556397	+	2.69827i
$681$		−	1.32488e10i		−	0.0616010i
$682$	2.50062e9	−	1.71859e7i	0.0115587	−	7.94390e-5i
$683$	1.49587e11	−	1.49587e11i	0.687400	−	0.687400i	−0.274256	−	0.961657i	$-0.588432\pi$
$683$	1.49587e11	−	1.49587e11i	0.687400	−	0.687400i	0.961657	+	0.274256i	$0.0884316\pi$
$684$	−1.80807e11	−	1.75904e11i	−0.826022	−	0.803621i
$685$	2.33240e11	−	2.33240e11i	1.05935	−	1.05935i
$686$	−5.32000e10	+	5.39363e10i	−0.240223	+	0.243548i
$687$			3.23727e10i			0.145329i
$688$	5.31456e10	−	5.61510e10i	0.237200	−	0.250613i
$689$	1.29496e11			0.574620
$690$	2.34066e10	+	2.30871e10i	0.103262	+	0.101853i
$691$	−1.35304e11	−	1.35304e11i	−0.593469	−	0.593469i	0.345098	−	0.938567i	$-0.387846\pi$
$691$	−1.35304e11	−	1.35304e11i	−0.593469	−	0.593469i	−0.938567	+	0.345098i	$0.887846\pi$
$692$	−1.28883e11	−	1.25388e11i	−0.562045	−	0.546802i
$693$	5.06597e9	+	5.06597e9i	0.0219649	+	0.0219649i
$694$	−1.00365e9	−	1.46036e11i	−0.00432658	−	0.629537i
$695$	−6.67860e11			−2.86250
$696$	−3.29558e10	−	3.16241e10i	−0.140441	−	0.134766i
$697$			2.62009e11i			1.11016i
$698$	−2.45965e9	−	3.57890e11i	−0.0103622	−	1.50775i
$699$	−3.95031e10	+	3.95031e10i	−0.165471	+	0.165471i
$700$	4.67931e11	−	6.43214e9i	1.94890	−	0.0267894i
$701$	−6.13294e10	+	6.13294e10i	−0.253978	+	0.253978i	−0.822600	−	0.568621i	$-0.807477\pi$
$701$	−6.13294e10	+	6.13294e10i	−0.253978	+	0.253978i	0.568621	+	0.822600i	$0.307477\pi$
$702$	1.33323e11	+	1.31503e11i	0.548982	+	0.541487i
$703$			1.32902e11i			0.544138i
$704$	−5.15120e9	−	4.74298e9i	−0.0209709	−	0.0193091i
$705$	−2.82668e11			−1.14425
$706$	−3.16486e11	+	3.20866e11i	−1.27390	+	1.29153i
$707$	−2.11958e11	−	2.11958e11i	−0.848345	−	0.848345i
$708$	1.54463e9	+	1.12370e11i	0.00614739	+	0.447215i
$709$	−2.97366e11	−	2.97366e11i	−1.17681	−	1.17681i	−0.980553	−	0.196255i	$-0.937122\pi$
$709$	−2.97366e11	−	2.97366e11i	−1.17681	−	1.17681i	−0.196255	−	0.980553i	$-0.562878\pi$
$710$	−5.57182e11	+	3.82931e9i	−2.19262	+	0.0150691i
$711$	2.69752e11			1.05557
$712$	1.03943e11	−	1.08320e11i	0.404460	−	0.421492i
$713$			2.31452e10i			0.0895578i
$714$	2.45309e11	−	1.68592e9i	0.943890	−	0.00648701i
$715$	−8.39249e9	+	8.39249e9i	−0.0321120	+	0.0321120i
$716$	−8.42900e8	+	8.66395e8i	−0.00320718	+	0.00329658i
$717$	1.40979e11	−	1.40979e11i	0.533432	−	0.533432i
$718$	−2.42377e10	+	2.45731e10i	−0.0911996	+	0.0924619i
$719$			2.39540e11i			0.896317i	0.893954	+	0.448158i	$0.147920\pi$
$719$			2.39540e11i			0.896317i	−0.893954	+	0.448158i	$0.852080\pi$
$720$	2.40141e11	−	2.53721e11i	0.893587	−	0.944119i
$721$	−4.51079e11			−1.66921
$722$	1.83208e11	+	1.80707e11i	0.674210	+	0.665006i
$723$	7.65293e10	+	7.65293e10i	0.280075	+	0.280075i
$724$	1.65856e11	−	1.70479e11i	0.603637	−	0.620464i
$725$	1.34637e11	+	1.34637e11i	0.487316	+	0.487316i
$726$	7.95947e8	+	1.15814e11i	0.00286509	+	0.416883i
$727$	3.85457e11			1.37987			0.689935	−	0.723871i	$-0.257639\pi$
$727$	3.85457e11			1.37987			0.689935	+	0.723871i	$0.257639\pi$
$728$	3.75014e11	−	7.73297e9i	1.33512	−	0.0275309i
$729$			2.87378e10i			0.101752i
$730$	1.05472e9	+	1.53467e11i	0.00371405	+	0.540411i
$731$	−1.19466e11	+	1.19466e11i	−0.418385	+	0.418385i
$732$	2.23036e7	+	1.62256e9i	7.76838e−5	+	0.00565141i
$733$	1.71097e11	−	1.71097e11i	0.592688	−	0.592688i	−0.345669	−	0.938357i	$-0.612348\pi$
$733$	1.71097e11	−	1.71097e11i	0.592688	−	0.592688i	0.938357	+	0.345669i	$0.112348\pi$
$734$	3.31038e11	+	3.26519e11i	1.14049	+	1.12493i
$735$		−	1.41961e11i		−	0.486429i
$736$	4.42256e10	−	4.73745e10i	0.150717	−	0.161448i
$737$	−9.68085e7			−0.000328128
$738$	1.11388e11	−	1.12929e11i	0.375502	−	0.380699i
$739$	−1.02838e9	−	1.02838e9i	−0.00344807	−	0.00344807i	0.705381	−	0.708829i	$-0.250776\pi$
$739$	−1.02838e9	−	1.02838e9i	−0.00344807	−	0.00344807i	−0.708829	+	0.705381i	$0.750776\pi$
$740$	−1.84035e11	+	2.52974e9i	−0.613726	+	0.00843623i
$741$	−1.25622e11	−	1.25622e11i	−0.416672	−	0.416672i
$742$	−2.27039e11	+	1.56036e9i	−0.749006	+	0.00514764i
$743$	−5.54577e11			−1.81973			−0.909864	−	0.414907i	$-0.863814\pi$
$743$	−5.54577e11			−1.81973			−0.909864	+	0.414907i	$0.863814\pi$
$744$	−5.18268e10	+	1.06869e9i	−0.169146	+	0.00348788i
$745$			2.16207e11i			0.701850i
$746$	4.52584e11	−	3.11045e9i	1.46132	−	0.0100431i
$747$	2.71054e11	−	2.71054e11i	0.870511	−	0.870511i
$748$	1.09676e10	+	1.06702e10i	0.0350353	+	0.0340852i
$749$	−6.77870e10	+	6.77870e10i	−0.215387	+	0.215387i
$750$	6.96425e10	−	7.06064e10i	0.220105	−	0.223151i
$751$		−	1.50943e11i		−	0.474519i	−0.971446	−	0.237259i	$-0.923751\pi$
$751$		−	1.50943e11i		−	0.474519i	0.971446	−	0.237259i	$-0.0762491\pi$
$752$	1.53161e10	+	5.57008e11i	0.0478934	+	1.74177i
$753$	2.14281e11			0.666506
$754$	1.08654e11	+	1.07170e11i	0.336170	+	0.331581i
$755$	2.49663e11	+	2.49663e11i	0.768362	+	0.768362i
$756$	−2.35333e11	−	2.28951e11i	−0.720438	−	0.700900i
$757$	−1.83096e11	−	1.83096e11i	−0.557564	−	0.557564i	0.371049	−	0.928613i	$-0.378998\pi$
$757$	−1.83096e11	−	1.83096e11i	−0.557564	−	0.557564i	−0.928613	+	0.371049i	$0.878998\pi$
$758$	−2.06385e9	−	3.00300e11i	−0.00625175	−	0.909659i
$759$	8.71796e8			0.00262693
$760$	−5.07304e11	+	5.28667e11i	−1.52060	+	1.58463i
$761$		−	2.59965e11i		−	0.775133i	−0.921842	−	0.387566i	$-0.873316\pi$
$761$		−	2.59965e11i		−	0.775133i	0.921842	−	0.387566i	$-0.126684\pi$
$762$	1.23191e8	+	1.79249e10i	0.000365392	+	0.0531662i
$763$	−4.25101e11	+	4.25101e11i	−1.25428	+	1.25428i
$764$	3.11829e11	−	4.28637e9i	0.915256	−	0.0125810i
$765$	−5.39815e11	+	5.39815e11i	−1.57616	+	1.57616i
$766$	−5.79894e10	−	5.71977e10i	−0.168435	−	0.166136i
$767$		−	3.75501e11i		−	1.08500i
$768$	1.08123e11	+	9.68426e10i	0.310794	+	0.278369i
$769$	2.77968e11			0.794857			0.397429	−	0.917633i	$-0.369903\pi$
$769$	2.77968e11			0.794857			0.397429	+	0.917633i	$0.369903\pi$
$770$	1.46130e10	−	1.48152e10i	0.0415696	−	0.0421450i
$771$	−8.76534e9	−	8.76534e9i	−0.0248057	−	0.0248057i
$772$	6.61861e9	+	4.81496e11i	0.0186336	+	1.35558i
$773$	1.64912e11	+	1.64912e11i	0.461884	+	0.461884i	0.899273	−	0.437388i	$-0.144096\pi$
$773$	1.64912e11	+	1.64912e11i	0.461884	+	0.461884i	−0.437388	+	0.899273i	$0.644096\pi$
$774$	1.02280e11	−	7.02935e8i	0.284989	−	0.00195863i
$775$	2.16098e11			0.599023
$776$	−3.56944e11	−	3.42521e11i	−0.984358	−	0.944582i
$777$			7.82444e10i			0.214669i
$778$	1.77937e11	−	1.22289e9i	0.485677	−	0.00333788i
$779$	−2.35241e11	+	2.35241e11i	−0.638797	+	0.638797i
$780$	1.71564e11	−	1.76347e11i	0.463499	−	0.476419i
$781$	−1.04476e10	+	1.04476e10i	−0.0280811	+	0.0280811i
$782$	−9.94540e10	+	1.00830e11i	−0.265947	+	0.269628i
$783$		−	1.33588e11i		−	0.355401i
$784$	−2.79739e11	+	7.69200e9i	−0.740439	+	0.0203599i
$785$	8.20797e11			2.16151
$786$	−1.74845e11	−	1.72458e11i	−0.458103	−	0.451849i
$787$	−4.59612e11	−	4.59612e11i	−1.19810	−	1.19810i	−0.974735	−	0.223363i	$-0.928296\pi$
$787$	−4.59612e11	−	4.59612e11i	−1.19810	−	1.19810i	−0.223363	−	0.974735i	$-0.571704\pi$
$788$	−1.80713e11	+	1.85750e11i	−0.468688	+	0.481752i
$789$	1.05773e11	+	1.05773e11i	0.272939	+	0.272939i
$790$	−5.38468e9	−	7.83496e11i	−0.0138246	−	2.01154i
$791$	1.49902e11			0.382913
$792$	−1.90980e8	−	9.26166e9i	−0.000485386	−	0.0235390i
$793$		−	5.42203e9i		−	0.0137110i
$794$	−2.96680e9	−	4.31683e11i	−0.00746459	−	1.08613i
$795$	−1.05305e11	+	1.05305e11i	−0.263622	+	0.263622i
$796$	−2.67657e9	−	1.94717e11i	−0.00666694	−	0.485012i
$797$	−3.31197e11	+	3.31197e11i	−0.820829	+	0.820829i	−0.986227	−	0.165398i	$-0.947109\pi$
$797$	−3.31197e11	+	3.31197e11i	−0.820829	+	0.820829i	0.165398	+	0.986227i	$0.447109\pi$
$798$	2.21761e11	+	2.18734e11i	0.546857	+	0.539391i
$799$		−	1.21767e12i		−	2.98774i
$800$	−4.42316e11	−	4.12917e11i	−1.07987	−	1.00810i
$801$	1.98609e11			0.482468
$802$	−1.50749e11	+	1.52835e11i	−0.364381	+	0.369424i
$803$	2.87764e9	+	2.87764e9i	0.00692110	+	0.00692110i
$804$	2.00660e9	−	2.75826e7i	0.00480216	−	6.60101e-5i
$805$	1.36191e11	+	1.36191e11i	0.324313	+	0.324313i
$806$	1.73203e11	−	1.19036e9i	0.410409	−	0.00282059i
$807$	−3.58422e10			−0.0845085
$808$	7.99053e9	+	3.87504e11i	0.0187469	+	0.909141i
$809$			4.11196e11i			0.959964i	0.877278	+	0.479982i	$0.159357\pi$
$809$			4.11196e11i			0.959964i	−0.877278	+	0.479982i	$0.840643\pi$
$810$	3.44216e11	−	2.36567e9i	0.799632	−	0.00549558i
$811$	4.48542e11	−	4.48542e11i	1.03686	−	1.03686i	0.0375659	−	0.999294i	$-0.488040\pi$
$811$	4.48542e11	−	4.48542e11i	1.03686	−	1.03686i	0.999294	−	0.0375659i	$-0.0119604\pi$
$812$	−1.91788e11	−	1.86587e11i	−0.441161	−	0.429197i
$813$	1.47189e10	−	1.47189e10i	0.0336908	−	0.0336908i
$814$	−3.42727e9	+	3.47470e9i	−0.00780639	+	0.00791444i
$815$			2.53954e11i			0.575604i
$816$	−2.30372e11	−	2.18042e11i	−0.519599	−	0.491789i
$817$	−2.14522e11			−0.481486
$818$	−1.95793e11	−	1.93120e11i	−0.437305	−	0.431335i
$819$	3.50890e11	+	3.50890e11i	0.779894	+	0.779894i
$820$	−3.30227e11	−	3.21272e11i	−0.730394	−	0.710587i
$821$	−3.88002e11	−	3.88002e11i	−0.854006	−	0.854006i	0.136618	−	0.990624i	$-0.456377\pi$
$821$	−3.88002e11	−	3.88002e11i	−0.854006	−	0.854006i	−0.990624	+	0.136618i	$0.956377\pi$
$822$	1.24608e9	+	1.81310e11i	0.00272935	+	0.397133i
$823$	6.43194e11			1.40198			0.700991	−	0.713170i	$-0.252741\pi$
$823$	6.43194e11			1.40198			0.700991	+	0.713170i	$0.252741\pi$
$824$	4.20836e11	+	4.03831e11i	0.912859	+	0.875973i
$825$		−	8.13961e9i		−	0.0175706i
$826$	4.52457e9	+	6.58346e11i	0.00971980	+	1.41428i
$827$	−5.21402e11	+	5.21402e11i	−1.11468	+	1.11468i	−0.122173	+	0.992509i	$0.538986\pi$
$827$	−5.21402e11	+	5.21402e11i	−1.11468	+	1.11468i	−0.992509	+	0.122173i	$0.961014\pi$
$828$	8.57320e10	−	1.17847e9i	0.182399	−	0.00250724i
$829$	4.52099e11	−	4.52099e11i	0.957227	−	0.957227i	−0.0418949	−	0.999122i	$-0.513339\pi$
$829$	4.52099e11	−	4.52099e11i	0.957227	−	0.957227i	0.999122	+	0.0418949i	$0.0133395\pi$
$830$	−7.92689e11	−	7.81867e11i	−1.67028	−	1.64748i
$831$		−	1.72540e11i		−	0.361814i
$832$	−3.56794e11	−	3.28519e11i	−0.744601	−	0.685594i
$833$	6.11537e11			1.27011
$834$	2.57798e11	−	2.61366e11i	0.532862	−	0.540238i
$835$	1.84270e11	+	1.84270e11i	0.379061	+	0.379061i
$836$	2.67044e8	+	1.94272e10i	0.000546712	+	0.0397727i
$837$	−1.07207e11	−	1.07207e11i	−0.218434	−	0.218434i
$838$	−2.64061e10	+	1.81480e8i	−0.0535462	+	0.000368003i
$839$	2.15602e11			0.435117			0.217558	−	0.976047i	$-0.430191\pi$
$839$	2.15602e11			0.435117			0.217558	+	0.976047i	$0.430191\pi$
$840$	−2.98670e11	+	3.11247e11i	−0.599894	+	0.625155i
$841$			3.91377e11i			0.782369i
$842$	−7.44757e10	+	5.11844e8i	−0.148172	+	0.00101833i
$843$	−4.67674e10	+	4.67674e10i	−0.0926047	+	0.0926047i
$844$	6.73432e10	−	6.92204e10i	0.132716	−	0.136416i
$845$	−1.38843e10	+	1.38843e10i	−0.0272332	+	0.0272332i
$846$	−5.17668e11	+	5.24833e11i	−1.01058	+	1.02457i
$847$			6.78492e11i			1.31829i
$848$	2.13214e11	+	2.01802e11i	0.412318	+	0.390250i
$849$	−1.61722e11			−0.311270
$850$	9.41413e11	+	9.28562e11i	1.80345	+	1.77883i
$851$	−3.19416e10	−	3.19416e10i	−0.0609029	−	0.0609029i
$852$	2.13577e11	−	2.19530e11i	0.405318	−	0.416616i
$853$	1.70081e11	+	1.70081e11i	0.321262	+	0.321262i	0.849251	−	0.527989i	$-0.177054\pi$
$853$	1.70081e11	+	1.70081e11i	0.321262	+	0.321262i	−0.527989	+	0.849251i	$0.677054\pi$
$854$	6.53324e7	+	9.50616e9i	0.000122828	+	0.0178720i
$855$	−9.69330e11			−1.81387
$856$	1.23929e11	−	2.55547e9i	0.230822	−	0.00475967i
$857$			7.04199e11i			1.30548i	0.757580	+	0.652742i	$0.226382\pi$
$857$			7.04199e11i			1.30548i	−0.757580	+	0.652742i	$0.773618\pi$
$858$	−4.48367e7	−	6.52394e9i	−8.27340e−5	−	0.0120382i
$859$	5.07217e10	−	5.07217e10i	0.0931583	−	0.0931583i	−0.658992	−	0.752150i	$-0.729017\pi$
$859$	5.07217e10	−	5.07217e10i	0.0931583	−	0.0931583i	0.752150	+	0.658992i	$0.229017\pi$
$860$	−4.08335e9	−	2.97059e11i	−0.00746489	−	0.543062i
$861$	−1.38495e11	+	1.38495e11i	−0.252013	+	0.252013i
$862$	1.36960e11	+	1.35090e11i	0.248064	+	0.244677i
$863$		−	1.98911e11i		−	0.358605i	−0.983794	−	0.179303i	$-0.942616\pi$
$863$		−	1.98911e11i		−	0.358605i	0.983794	−	0.179303i	$-0.0573841\pi$
$864$	1.45853e10	+	4.24285e11i	0.0261734	+	0.761382i
$865$	−6.90956e11			−1.23420
$866$	4.90219e11	−	4.97003e11i	0.871602	−	0.883665i
$867$	3.23436e11	+	3.23436e11i	0.572416	+	0.572416i
$868$	−3.03654e11	+	4.17401e9i	−0.534934	+	0.00735316i
$869$	−1.46912e10	−	1.46912e10i	−0.0257620	−	0.0257620i
$870$	−1.75506e11	+	1.20619e9i	−0.306349	+	0.00210542i
$871$	−6.70536e9			−0.0116506
$872$	7.77173e11	−	1.60257e10i	1.34416	−	0.0277173i
$873$		−	6.54470e11i		−	1.12676i
$874$	−1.79822e11	+	1.23585e9i	−0.308175	+	0.00211798i
$875$	4.10821e11	−	4.10821e11i	0.700843	−	0.700843i
$876$	−6.04663e10	−	5.88265e10i	−0.102683	−	0.0998980i
$877$	−2.40245e11	+	2.40245e11i	−0.406122	+	0.406122i	−0.880384	−	0.474262i	$-0.842715\pi$
$877$	−2.40245e11	+	2.40245e11i	−0.406122	+	0.406122i	0.474262	+	0.880384i	$0.342715\pi$
$878$	−7.43670e9	+	7.53962e9i	−0.0125142	+	0.0126874i
$879$			3.53330e11i			0.591869i
$880$	−2.68967e10	+	7.39579e8i	−0.0448506	+	0.00123326i
$881$	9.94503e10			0.165083			0.0825415	−	0.996588i	$-0.473696\pi$
$881$	9.94503e10			0.165083			0.0825415	+	0.996588i	$0.473696\pi$
$882$	−2.63581e11	−	2.59982e11i	−0.435551	−	0.429605i
$883$	−7.99563e11	−	7.99563e11i	−1.31525	−	1.31525i	−0.917486	−	0.397769i	$-0.869785\pi$
$883$	−7.99563e11	−	7.99563e11i	−1.31525	−	1.31525i	−0.397769	−	0.917486i	$-0.630215\pi$
$884$	7.59663e11	+	7.39062e11i	1.24398	+	1.21024i
$885$	3.05355e11	+	3.05355e11i	0.497773	+	0.497773i
$886$	6.29311e9	+	9.15677e11i	0.0102125	+	1.48596i
$887$	2.85580e10			0.0461352			0.0230676	−	0.999734i	$-0.492657\pi$
$887$	2.85580e10			0.0461352			0.0230676	+	0.999734i	$0.492657\pi$
$888$	7.00487e10	−	7.29984e10i	0.112654	−	0.117398i
$889$			1.05012e11i			0.168125i
$890$	−3.96455e9	−	5.76860e11i	−0.00631879	−	0.919413i
$891$	6.45434e9	−	6.45434e9i	0.0102410	−	0.0102410i
$892$	−2.16861e11	+	2.98095e9i	−0.342548	+	0.00470863i
$893$	1.09327e12	−	1.09327e12i	1.71918	−	1.71918i
$894$	−8.46122e10	−	8.34571e10i	−0.132459	−	0.130651i
$895$			4.64485e9i			0.00723901i
$896$	6.29506e11	+	5.71675e11i	0.976715	+	0.886987i
$897$	6.03842e10			0.0932725
$898$	−7.95585e11	+	8.06596e11i	−1.22344	+	1.24037i
$899$	−8.73697e10	−	8.73697e10i	−0.133759	−	0.133759i
$900$	−1.10029e10	−	8.00445e11i	−0.0167701	−	1.22000i
$901$	−4.53633e11	−	4.53633e11i	−0.688344	−	0.688344i
$902$	−1.22167e10	+	8.39612e7i	−0.0184556	+	0.000126839i
$903$	−1.26298e11			−0.189952
$904$	−1.39851e11	−	1.34200e11i	−0.209408	−	0.200946i
$905$		−	9.13958e11i		−	1.36249i
$906$	−1.94076e11	+	1.33382e9i	−0.288045	+	0.00197963i
$907$	−6.40471e10	+	6.40471e10i	−0.0946390	+	0.0946390i	−0.752841	−	0.658202i	$-0.771317\pi$
$907$	−6.40471e10	+	6.40471e10i	−0.0946390	+	0.0946390i	0.658202	+	0.752841i	$0.271317\pi$
$908$	−6.99820e10	+	7.19327e10i	−0.102954	+	0.105824i
$909$	−3.62577e11	+	3.62577e11i	−0.531062	+	0.531062i
$910$	1.01216e12	−	1.02616e12i	1.47599	−	1.49641i
$911$		−	7.81198e9i		−	0.0113419i	−0.999984	−	0.00567097i	$-0.998195\pi$
$911$		−	7.81198e9i		−	0.0113419i	0.999984	−	0.00567097i	$-0.00180514\pi$
$912$	−1.10703e10	−	4.02601e11i	−0.0160023	−	0.581963i
$913$	−2.95243e10			−0.0424909
$914$	−8.61066e11	−	8.49311e11i	−1.23382	−	1.21698i
$915$	4.40916e9	+	4.40916e9i	0.00629030	+	0.00629030i
$916$	1.70997e11	−	1.75764e11i	0.242889	−	0.249659i
$917$	−1.01733e12	−	1.01733e12i	−1.43875	−	1.43875i
$918$	−6.37576e9	−	9.27703e11i	−0.00897762	−	1.30629i
$919$	4.51092e11			0.632417			0.316209	−	0.948690i	$-0.397590\pi$
$919$	4.51092e11			0.632417			0.316209	+	0.948690i	$0.397590\pi$
$920$	−5.13420e9	−	2.48985e11i	−0.00716674	−	0.347554i
$921$		−	2.45719e11i		−	0.341508i
$922$	4.66534e9	+	6.78828e11i	0.00645594	+	0.939369i
$923$	−7.23647e11	+	7.23647e11i	−0.997057	+	0.997057i
$924$	1.57220e8	+	1.14375e10i	0.000215684	+	0.0156908i
$925$	−2.98226e11	+	2.98226e11i	−0.407360	+	0.407360i
$926$	9.24102e11	+	9.11486e11i	1.25683	+	1.23967i
$927$			7.71618e11i			1.04492i
$928$	1.18865e10	+	3.45776e11i	0.0160273	+	0.466234i
$929$	−7.44358e11			−0.999353			−0.499676	−	0.866212i	$-0.666548\pi$
$929$	−7.44358e11			−0.999353			−0.499676	+	0.866212i	$0.666548\pi$
$930$	−1.39880e11	+	1.41816e11i	−0.186992	+	0.189580i
$931$	5.49059e11	+	5.49059e11i	0.730837	+	0.730837i
$932$	4.23138e11	−	5.81643e9i	0.560814	−	0.00770890i
$933$	−6.49366e10	−	6.49366e10i	−0.0856965	−	0.0856965i
$934$	5.37257e10	−	3.69237e8i	0.0705983	−	0.000485197i
$935$	5.87987e10			0.0769346
$936$	−1.32281e10	−	6.41501e11i	−0.0172343	−	0.835783i
$937$		−	1.06265e12i		−	1.37859i	−0.724483	−	0.689293i	$-0.757921\pi$
$937$		−	1.06265e12i		−	1.37859i	0.724483	−	0.689293i	$-0.242079\pi$
$938$	1.17562e10	−	8.07958e7i	0.0151864	−	0.000104370i
$939$	6.00245e10	−	6.00245e10i	0.0772087	−	0.0772087i
$940$	1.53471e12	+	1.49309e12i	1.96569	+	1.91238i
$941$	−7.14601e11	+	7.14601e11i	−0.911392	+	0.911392i	−0.996382	−	0.0849900i	$-0.972914\pi$
$941$	−7.14601e11	+	7.14601e11i	−0.911392	+	0.911392i	0.0849900	+	0.996382i	$0.472914\pi$
$942$	−3.16833e11	+	3.21218e11i	−0.402371	+	0.407940i
$943$		−	1.13076e11i		−	0.142995i
$944$	5.85167e11	−	6.18257e11i	0.736871	−	0.778541i
$945$	−1.26165e12			−1.58202
$946$	−5.60867e9	−	5.53210e9i	−0.00700318	−	0.00690757i
$947$	5.62085e11	+	5.62085e11i	0.698879	+	0.698879i	0.964169	−	0.265290i	$-0.0854676\pi$
$947$	5.62085e11	+	5.62085e11i	0.698879	+	0.698879i	−0.265290	+	0.964169i	$0.585468\pi$
$948$	3.08698e11	+	3.00327e11i	0.382209	+	0.371844i
$949$	1.99318e11	+	1.99318e11i	0.245743	+	0.245743i
$950$	1.15387e10	+	1.67893e12i	0.0141664	+	2.06128i
$951$	−3.14750e11			−0.384808
$952$	−1.34078e12	−	1.28660e12i	−1.63234	−	1.56638i
$953$		−	5.74014e11i		−	0.695906i	−0.937512	−	0.347953i	$-0.886877\pi$
$953$		−	5.74014e11i		−	0.695906i	0.937512	−	0.347953i	$-0.113123\pi$
$954$	2.66916e9	+	3.88375e11i	0.00322241	+	0.468875i
$955$	8.47365e11	−	8.47365e11i	1.01873	−	1.01873i
$956$	−1.51010e12	+	2.07578e10i	−1.80790	+	0.0248513i
$957$	−3.29090e9	+	3.29090e9i	−0.00392344	+	0.00392344i
$958$	−7.57883e11	−	7.47537e11i	−0.899788	−	0.887505i
$959$			1.06220e12i			1.25583i
$960$	5.57291e11	−	2.29930e10i	0.656141	−	0.0270714i
$961$	7.12659e11			0.835580
$962$	−2.37387e11	+	2.40672e11i	−0.277176	+	0.281013i
$963$	1.15957e11	+	1.15957e11i	0.134831	+	0.134831i
$964$	−1.12682e10	−	8.19745e11i	−0.0130480	−	0.949228i
$965$	1.30842e12	+	1.30842e12i	1.50882	+	1.50882i
$966$	−1.05868e11	+	7.27595e8i	−0.121579	+	0.000835567i
$967$	7.84920e10			0.0897676			0.0448838	−	0.998992i	$-0.485708\pi$
$967$	7.84920e10			0.0897676			0.0448838	+	0.998992i	$0.485708\pi$
$968$	6.07424e11	−	6.33002e11i	0.691816	−	0.720948i
$969$			8.80125e11i			0.998273i
$970$	−1.90091e12	+	1.30642e10i	−2.14721	+	0.0147570i
$971$	6.36692e11	−	6.36692e11i	0.716230	−	0.716230i	−0.251601	−	0.967831i	$-0.580957\pi$
$971$	6.36692e11	−	6.36692e11i	0.716230	−	0.716230i	0.967831	+	0.251601i	$0.0809571\pi$
$972$	−6.06138e11	+	6.23034e11i	−0.679058	+	0.697986i
$973$	1.52075e12	−	1.52075e12i	1.69671	−	1.69671i
$974$	5.89860e11	−	5.98024e11i	0.655411	−	0.664482i
$975$		−	5.63783e11i		−	0.623869i
$976$	8.44950e9	−	8.92731e9i	0.00931176	−	0.00983833i
$977$	6.26449e11			0.687555			0.343778	−	0.939051i	$-0.388293\pi$
$977$	6.26449e11			0.687555			0.343778	+	0.939051i	$0.388293\pi$
$978$	−9.93844e10	−	9.80276e10i	−0.108633	−	0.107150i
$979$	−1.08166e10	−	1.08166e10i	−0.0117750	−	0.0117750i
$980$	−7.49858e11	+	7.70760e11i	−0.812970	+	0.835632i
$981$	7.27180e11	+	7.27180e11i	0.785174	+	0.785174i
$982$	1.56371e9	+	2.27528e11i	0.00168156	+	0.244674i
$983$	−5.92199e11			−0.634240			−0.317120	−	0.948385i	$-0.602716\pi$
$983$	−5.92199e11			−0.634240			−0.317120	+	0.948385i	$0.602716\pi$
$984$	2.53199e11	−	5.22109e9i	0.270073	−	0.00556904i
$985$			9.95828e11i			1.05789i
$986$	−5.19601e9	−	7.56043e11i	−0.00549746	−	0.799906i
$987$	6.43650e11	−	6.43650e11i	0.678236	−	0.678236i
$988$	1.84966e10	+	1.34561e12i	0.0194117	+	1.41218i
$989$	5.15583e10	−	5.15583e10i	0.0538906	−	0.0538906i
$990$	−2.53431e10	−	2.49971e10i	−0.0263826	−	0.0260225i
$991$			9.90287e11i			1.02675i	0.858163	+	0.513377i	$0.171606\pi$
$991$			9.90287e11i			1.02675i	−0.858163	+	0.513377i	$0.828394\pi$
$992$	2.87032e11	+	2.67954e11i	0.296404	+	0.276703i
$993$	4.72574e11			0.486041
$994$	1.26001e12	−	1.27745e12i	1.29071	−	1.30858i
$995$	−5.29126e11	−	5.29126e11i	−0.539842	−	0.539842i
$996$	6.11965e11	−	8.41202e9i	0.621855	−	0.00854797i
$997$	3.70968e11	+	3.70968e11i	0.375454	+	0.375454i	0.869459	−	0.494005i	$-0.164468\pi$
$997$	3.70968e11	+	3.70968e11i	0.375454	+	0.375454i	−0.494005	+	0.869459i	$0.664468\pi$
$998$	−3.15420e10	+	2.16776e8i	−0.0317956	+	0.000218519i
$999$	2.95902e11			0.297089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.11.12	yes	30
4.3	odd	2		64.9.f.a.15.6		30
8.3	odd	2		128.9.f.a.31.10		30
8.5	even	2		128.9.f.b.31.6		30
16.3	odd	4	inner	16.9.f.a.3.12	✓	30
16.5	even	4		128.9.f.a.95.10		30
16.11	odd	4		128.9.f.b.95.6		30
16.13	even	4		64.9.f.a.47.6		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.12	✓	30	16.3	odd	4	inner
16.9.f.a.11.12	yes	30	1.1	even	1	trivial
64.9.f.a.15.6		30	4.3	odd	2
64.9.f.a.47.6		30	16.13	even	4
128.9.f.a.31.10		30	8.3	odd	2
128.9.f.a.95.10		30	16.5	even	4
128.9.f.b.31.6		30	8.5	even	2
128.9.f.b.95.6		30	16.11	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.2357 - 11.3912i) q^{2} +(23.8972 + 23.8972i) q^{3} +(-3.51862 - 255.976i) q^{4} +(-695.590 - 695.590i) q^{5} +(540.720 - 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 - 2835.98i) q^{8} -5418.84i q^{9} +O(q^{10})\)	\(q+(11.2357 - 11.3912i) q^{2} +(23.8972 + 23.8972i) q^{3} +(-3.51862 - 255.976i) q^{4} +(-695.590 - 695.590i) q^{5} +(540.720 - 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 - 2835.98i) q^{8} -5418.84i q^{9} +(-15739.0 + 108.169i) q^{10} +(-295.121 + 295.121i) q^{11} +(6033.03 - 6201.20i) q^{12} +(-20441.3 + 20441.3i) q^{13} +(35592.3 - 36084.9i) q^{14} -33245.4i q^{15} +(-65511.2 + 1801.36i) q^{16} +143214. q^{17} +(-61727.1 - 60884.4i) q^{18} +(128582. + 128582. i) q^{19} +(-175607. + 180502. i) q^{20} +(75701.5 + 75701.5i) q^{21} +(45.8931 + 6677.66i) q^{22} -61807.0 q^{23} +(-2853.84 - 138398. i) q^{24} +577067. i q^{25} +(3178.75 + 462522. i) q^{26} +(286285. - 286285. i) q^{27} +(-11146.3 - 810878. i) q^{28} +(233312. - 233312. i) q^{29} +(-378705. - 373535. i) q^{30} -374476. i q^{31} +(-715544. + 766491. i) q^{32} -14105.1 q^{33} +(1.60911e6 - 1.63138e6i) q^{34} +(-2.20348e6 - 2.20348e6i) q^{35} +(-1.38709e6 + 19066.9i) q^{36} +(516796. + 516796. i) q^{37} +(2.90942e6 - 19995.4i) q^{38} -976980. q^{39} +(83068.3 + 4.02843e6i) q^{40} +1.82949e6i q^{41} +(1.71289e6 - 11772.1i) q^{42} +(-834182. + 834182. i) q^{43} +(76582.2 + 74505.3i) q^{44} +(-3.76929e6 + 3.76929e6i) q^{45} +(-694444. + 704055. i) q^{46} -8.50247e6i q^{47} +(-1.60859e6 - 1.52249e6i) q^{48} +4.27010e6 q^{49} +(6.57348e6 + 6.48374e6i) q^{50} +(3.42242e6 + 3.42242e6i) q^{51} +(5.30440e6 + 5.16055e6i) q^{52} +(-3.16752e6 - 3.16752e6i) q^{53} +(-44519.2 - 6.47774e6i) q^{54} +410566. q^{55} +(-9.36210e6 - 8.98380e6i) q^{56} +6.14553e6i q^{57} +(-36281.5 - 5.27912e6i) q^{58} +(-9.18487e6 + 9.18487e6i) q^{59} +(-8.51001e6 + 116978. i) q^{60} +(-132625. + 132625. i) q^{61} +(-4.26573e6 - 4.20750e6i) q^{62} -1.71658e7i q^{63} +(691615. + 1.67630e7i) q^{64} +2.84375e7 q^{65} +(-158481. + 160674. i) q^{66} +(164015. + 164015. i) q^{67} +(-503916. - 3.66593e7i) q^{68} +(-1.47702e6 - 1.47702e6i) q^{69} +(-4.98580e7 + 342656. i) q^{70} +3.54013e7 q^{71} +(-1.53677e7 + 1.60149e7i) q^{72} -9.75074e6i q^{73} +(1.16935e7 - 80365.0i) q^{74} +(-1.37903e7 + 1.37903e7i) q^{75} +(3.24615e7 - 3.33664e7i) q^{76} +(-934880. + 934880. i) q^{77} +(-1.09770e7 + 1.11290e7i) q^{78} +4.97804e7i q^{79} +(4.68220e7 + 4.43160e7i) q^{80} -2.18702e7 q^{81} +(2.08401e7 + 2.05556e7i) q^{82} +(5.00207e7 + 5.00207e7i) q^{83} +(1.91114e7 - 1.96441e7i) q^{84} +(-9.96182e7 - 9.96182e7i) q^{85} +(129721. + 1.88749e7i) q^{86} +1.11510e7 q^{87} +(1.70916e6 - 35243.7i) q^{88} +3.66516e7i q^{89} +(586149. + 8.52874e7i) q^{90} +(-6.47537e7 + 6.47537e7i) q^{91} +(217475. + 1.58211e7i) q^{92} +(8.94895e6 - 8.94895e6i) q^{93} +(-9.68533e7 - 9.55311e7i) q^{94} -1.78881e8i q^{95} +(-3.54166e7 + 1.21749e6i) q^{96} +1.20777e8 q^{97} +(4.79775e7 - 4.86415e7i) q^{98} +(1.59921e6 + 1.59921e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

L-functions

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Database

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