LMFDB - Embedded newform 60.7.c.a.31.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.23
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.99899 - 0.126876i) q^{2} -15.5885i q^{3} +(63.9678 - 2.02976i) q^{4} -55.9017 q^{5} +(-1.97780 - 124.692i) q^{6} -335.195i q^{7} +(511.421 - 24.3521i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(7.99899 - 0.126876i) q^{2} -15.5885i q^{3} +(63.9678 - 2.02976i) q^{4} -55.9017 q^{5} +(-1.97780 - 124.692i) q^{6} -335.195i q^{7} +(511.421 - 24.3521i) q^{8} -243.000 q^{9} +(-447.157 + 7.09260i) q^{10} -1644.57i q^{11} +(-31.6409 - 997.159i) q^{12} +1200.29 q^{13} +(-42.5283 - 2681.22i) q^{14} +871.421i q^{15} +(4087.76 - 259.679i) q^{16} -3941.20 q^{17} +(-1943.76 + 30.8309i) q^{18} -3733.41i q^{19} +(-3575.91 + 113.467i) q^{20} -5225.17 q^{21} +(-208.656 - 13154.9i) q^{22} -4917.71i q^{23} +(-379.611 - 7972.26i) q^{24} +3125.00 q^{25} +(9601.13 - 152.288i) q^{26} +3788.00i q^{27} +(-680.367 - 21441.7i) q^{28} +20383.8 q^{29} +(110.563 + 6970.49i) q^{30} +38457.5i q^{31} +(32665.0 - 2595.81i) q^{32} -25636.2 q^{33} +(-31525.6 + 500.045i) q^{34} +18738.0i q^{35} +(-15544.2 + 493.233i) q^{36} +17613.9 q^{37} +(-473.681 - 29863.5i) q^{38} -18710.7i q^{39} +(-28589.3 + 1361.32i) q^{40} +54135.0 q^{41} +(-41796.1 + 662.950i) q^{42} +3927.72i q^{43} +(-3338.08 - 105199. i) q^{44} +13584.1 q^{45} +(-623.940 - 39336.7i) q^{46} +145724. i q^{47} +(-4048.00 - 63721.9i) q^{48} +5293.27 q^{49} +(24996.9 - 396.488i) q^{50} +61437.2i q^{51} +(76780.0 - 2436.31i) q^{52} -223584. q^{53} +(480.607 + 30300.1i) q^{54} +91934.0i q^{55} +(-8162.69 - 171426. i) q^{56} -58198.1 q^{57} +(163050. - 2586.22i) q^{58} +349304. i q^{59} +(1768.78 + 55742.9i) q^{60} +144957. q^{61} +(4879.34 + 307621. i) q^{62} +81452.4i q^{63} +(260958. - 24908.3i) q^{64} -67098.4 q^{65} +(-205064. + 3252.63i) q^{66} +524780. i q^{67} +(-252110. + 7999.71i) q^{68} -76659.5 q^{69} +(2377.40 + 149885. i) q^{70} -202515. i q^{71} +(-124275. + 5917.55i) q^{72} +674498. q^{73} +(140893. - 2234.78i) q^{74} -48713.9i q^{75} +(-7577.94 - 238818. i) q^{76} -551250. q^{77} +(-2373.94 - 149667. i) q^{78} -311497. i q^{79} +(-228513. + 14516.5i) q^{80} +59049.0 q^{81} +(433025. - 6868.44i) q^{82} -975431. i q^{83} +(-334243. + 10605.9i) q^{84} +220320. q^{85} +(498.335 + 31417.8i) q^{86} -317753. i q^{87} +(-40048.6 - 841065. i) q^{88} -1.14871e6 q^{89} +(108659. - 1723.50i) q^{90} -402332. i q^{91} +(-9981.79 - 314575. i) q^{92} +599492. q^{93} +(18488.9 + 1.16565e6i) q^{94} +208704. i q^{95} +(-40464.7 - 509197. i) q^{96} +573799. q^{97} +(42340.8 - 671.589i) q^{98} +399630. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	7.99899	−	0.126876i	0.999874	−	0.0158595i
$2$	7.99899	−	0.126876i	0.999874	−	0.0158595i
$3$		−	15.5885i		−	0.577350i
$3$		−	15.5885i		−	0.577350i
$4$	63.9678	−	2.02976i	0.999497	−	0.0317151i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	−1.97780	−	124.692i	−0.00915650	−	0.577278i
$7$		−	335.195i		−	0.977245i	−0.872495	−	0.488623i	$-0.837500\pi$
$7$		−	335.195i		−	0.977245i	0.872495	−	0.488623i	$-0.162500\pi$
$8$	511.421	−	24.3521i	0.998868	−	0.0475626i
$9$	−243.000			−0.333333
$10$	−447.157	+	7.09260i	−0.447157	+	0.00709260i
$11$		−	1644.57i		−	1.23559i	−0.786340	−	0.617793i	$-0.788027\pi$
$11$		−	1644.57i		−	1.23559i	0.786340	−	0.617793i	$-0.211973\pi$
$12$	−31.6409	−	997.159i	−0.0183107	−	0.577060i
$13$	1200.29			0.546332			0.273166	−	0.961967i	$-0.411929\pi$
$13$	1200.29			0.546332			0.273166	+	0.961967i	$0.411929\pi$
$14$	−42.5283	−	2681.22i	−0.0154986	−	0.977122i
$15$			871.421i			0.258199i
$16$	4087.76	−	259.679i	0.997988	−	0.0633982i
$17$	−3941.20			−0.802199			−0.401099	−	0.916035i	$-0.631372\pi$
$17$	−3941.20			−0.802199			−0.401099	+	0.916035i	$0.631372\pi$
$18$	−1943.76	+	30.8309i	−0.333291	+	0.00528651i
$19$		−	3733.41i		−	0.544308i	−0.962254	−	0.272154i	$-0.912264\pi$
$19$		−	3733.41i		−	0.544308i	0.962254	−	0.272154i	$-0.0877360\pi$
$20$	−3575.91	+	113.467i	−0.446989	+	0.0141834i
$21$	−5225.17			−0.564213
$22$	−208.656	−	13154.9i	−0.0195958	−	1.23543i
$23$		−	4917.71i		−	0.404184i	−0.979367	−	0.202092i	$-0.935226\pi$
$23$		−	4917.71i		−	0.404184i	0.979367	−	0.202092i	$-0.0647740\pi$
$24$	−379.611	−	7972.26i	−0.0274603	−	0.576697i
$25$	3125.00			0.200000
$26$	9601.13	−	152.288i	0.546263	−	0.00866457i
$27$			3788.00i			0.192450i
$28$	−680.367	−	21441.7i	−0.0309934	−	0.976753i
$29$	20383.8			0.835780			0.417890	−	0.908498i	$-0.362770\pi$
$29$	20383.8			0.835780			0.417890	+	0.908498i	$0.362770\pi$
$30$	110.563	+	6970.49i	0.00409491	+	0.258166i
$31$			38457.5i			1.29091i	0.763799	+	0.645454i	$0.223332\pi$
$31$			38457.5i			1.29091i	−0.763799	+	0.645454i	$0.776668\pi$
$32$	32665.0	−	2595.81i	0.996857	−	0.0792179i
$33$	−25636.2			−0.713366
$34$	−31525.6	+	500.045i	−0.802098	+	0.0127225i
$35$			18738.0i			0.437037i
$36$	−15544.2	+	493.233i	−0.333166	+	0.0105717i
$37$	17613.9			0.347736			0.173868	−	0.984769i	$-0.444373\pi$
$37$	17613.9			0.347736			0.173868	+	0.984769i	$0.444373\pi$
$38$	−473.681	−	29863.5i	−0.00863247	−	0.544240i
$39$		−	18710.7i		−	0.315425i
$40$	−28589.3	+	1361.32i	−0.446707	+	0.0212707i
$41$	54135.0			0.785464			0.392732	−	0.919653i	$-0.371530\pi$
$41$	54135.0			0.785464			0.392732	+	0.919653i	$0.371530\pi$
$42$	−41796.1	+	662.950i	−0.564142	+	0.00894815i
$43$			3927.72i			0.0494010i	0.999695	+	0.0247005i	$0.00786321\pi$
$43$			3927.72i			0.0494010i	−0.999695	+	0.0247005i	$0.992137\pi$
$44$	−3338.08	−	105199.i	−0.0391867	−	1.23497i
$45$	13584.1			0.149071
$46$	−623.940	−	39336.7i	−0.00641017	−	0.404133i
$47$			145724.i			1.40358i	0.712382	+	0.701792i	$0.247616\pi$
$47$			145724.i			1.40358i	−0.712382	+	0.701792i	$0.752384\pi$
$48$	−4048.00	−	63721.9i	−0.0366030	−	0.576189i
$49$	5293.27			0.0449920
$50$	24996.9	−	396.488i	0.199975	−	0.00317191i
$51$			61437.2i			0.463150i
$52$	76780.0	−	2436.31i	0.546057	−	0.0173270i
$53$	−223584.			−1.50180			−0.750902	−	0.660414i	$-0.770381\pi$
$53$	−223584.			−1.50180			−0.750902	+	0.660414i	$0.770381\pi$
$54$	480.607	+	30300.1i	0.00305217	+	0.192426i
$55$			91934.0i			0.552571i
$56$	−8162.69	−	171426.i	−0.0464803	−	0.976139i
$57$	−58198.1			−0.314256
$58$	163050.	−	2586.22i	0.835675	−	0.0132551i
$59$			349304.i			1.70078i	0.526156	+	0.850388i	$0.323633\pi$
$59$			349304.i			1.70078i	−0.526156	+	0.850388i	$0.676367\pi$
$60$	1768.78	+	55742.9i	0.00818879	+	0.258069i
$61$	144957.			0.638631			0.319316	−	0.947648i	$-0.396547\pi$
$61$	144957.			0.638631			0.319316	+	0.947648i	$0.396547\pi$
$62$	4879.34	+	307621.i	0.0204732	+	1.29075i
$63$			81452.4i			0.325748i
$64$	260958.	−	24908.3i	0.995476	−	0.0950176i
$65$	−67098.4			−0.244327
$66$	−205064.	+	3252.63i	−0.713277	+	0.0113137i
$67$			524780.i			1.74483i	0.488766	+	0.872415i	$0.337447\pi$
$67$			524780.i			1.74483i	−0.488766	+	0.872415i	$0.662553\pi$
$68$	−252110.	+	7999.71i	−0.801795	+	0.0254418i
$69$	−76659.5			−0.233356
$70$	2377.40	+	149885.i	0.00693121	+	0.436982i
$71$		−	202515.i		−	0.565825i	−0.959146	−	0.282913i	$-0.908699\pi$
$71$		−	202515.i		−	0.565825i	0.959146	−	0.282913i	$-0.0913006\pi$
$72$	−124275.	+	5917.55i	−0.332956	+	0.0158542i
$73$	674498.			1.73385			0.866927	−	0.498436i	$-0.166092\pi$
$73$	674498.			1.73385			0.866927	+	0.498436i	$0.166092\pi$
$74$	140893.	−	2234.78i	0.347692	−	0.00551493i
$75$		−	48713.9i		−	0.115470i
$76$	−7577.94	−	238818.i	−0.0172628	−	0.544034i
$77$	−551250.			−1.20747
$78$	−2373.94	−	149667.i	−0.00500249	−	0.315385i
$79$		−	311497.i		−	0.631789i	−0.948794	−	0.315894i	$-0.897695\pi$
$79$		−	311497.i		−	0.631789i	0.948794	−	0.315894i	$-0.102305\pi$
$80$	−228513.	+	14516.5i	−0.446314	+	0.0283525i
$81$	59049.0			0.111111
$82$	433025.	−	6868.44i	0.785365	−	0.0124571i
$83$		−	975431.i		−	1.70593i	−0.521965	−	0.852967i	$-0.674801\pi$
$83$		−	975431.i		−	1.70593i	0.521965	−	0.852967i	$-0.325199\pi$
$84$	−334243.	+	10605.9i	−0.563929	+	0.0178940i
$85$	220320.			0.358754
$86$	498.335	+	31417.8i	0.000783476	+	0.0493948i
$87$		−	317753.i		−	0.482538i
$88$	−40048.6	−	841065.i	−0.0587678	−	1.23419i
$89$	−1.14871e6			−1.62944			−0.814722	−	0.579852i	$-0.803110\pi$
$89$	−1.14871e6			−1.62944			−0.814722	+	0.579852i	$0.803110\pi$
$90$	108659.	−	1723.50i	0.149052	−	0.00236420i
$91$		−	402332.i		−	0.533900i
$92$	−9981.79	−	314575.i	−0.0128187	−	0.403981i
$93$	599492.			0.745306
$94$	18488.9	+	1.16565e6i	0.0222602	+	1.40341i
$95$			208704.i			0.243422i
$96$	−40464.7	−	509197.i	−0.0457365	−	0.575536i
$97$	573799.			0.628702			0.314351	−	0.949307i	$-0.398213\pi$
$97$	573799.			0.628702			0.314351	+	0.949307i	$0.398213\pi$
$98$	42340.8	−	671.589i	0.0449864	−	0.000713552i
$99$			399630.i			0.411862i
$100$	199899.	−	6343.01i	0.199899	−	0.00634301i
$101$	376616.			0.365540			0.182770	−	0.983156i	$-0.441494\pi$
$101$	376616.			0.365540			0.182770	+	0.983156i	$0.441494\pi$
$102$	7794.93	+	491436.i	0.00734533	+	0.463091i
$103$		−	2.16630e6i		−	1.98247i	−0.132097	−	0.991237i	$-0.542171\pi$
$103$		−	2.16630e6i		−	1.98247i	0.132097	−	0.991237i	$-0.457829\pi$
$104$	613854.	−	29229.6i	0.545714	−	0.0259850i
$105$	292096.			0.252324
$106$	−1.78845e6	+	28367.5i	−1.50161	+	0.0238179i
$107$		−	1.67749e6i		−	1.36933i	−0.728858	−	0.684664i	$-0.759949\pi$
$107$		−	1.67749e6i		−	1.36933i	0.728858	−	0.684664i	$-0.240051\pi$
$108$	7688.74	+	242310.i	0.00610357	+	0.192353i
$109$	1.58805e6			1.22626			0.613132	−	0.789981i	$-0.289910\pi$
$109$	1.58805e6			1.22626			0.613132	+	0.789981i	$0.289910\pi$
$110$	11664.2	+	735380.i	0.00876352	+	0.552502i
$111$		−	274573.i		−	0.200765i
$112$	−87043.2	−	1.37020e6i	−0.0619556	−	0.975279i
$113$	−1.75946e6			−1.21940			−0.609699	−	0.792633i	$-0.708710\pi$
$113$	−1.75946e6			−1.21940			−0.609699	+	0.792633i	$0.708710\pi$
$114$	−465526.	+	7383.95i	−0.314217	+	0.00498396i
$115$			274908.i			0.180757i
$116$	1.30391e6	−	41374.4i	0.835360	−	0.0265068i
$117$	−291671.			−0.182111
$118$	44318.3	+	2.79408e6i	0.0269735	+	1.70056i
$119$			1.32107e6i			0.783945i
$120$	21220.9	+	445663.i	0.0122806	+	0.257907i
$121$	−933037.			−0.526675
$122$	1.15951e6	−	18391.6i	0.638551	−	0.0101284i
$123$		−	843880.i		−	0.453488i
$124$	78059.6	+	2.46004e6i	0.0409413	+	1.29026i
$125$	−174693.			−0.0894427
$126$	10334.4	+	651537.i	0.00516622	+	0.325707i
$127$		−	705905.i		−	0.344616i	−0.985043	−	0.172308i	$-0.944878\pi$
$127$		−	705905.i		−	0.344616i	0.985043	−	0.172308i	$-0.0551224\pi$
$128$	2.08424e6	−	232351.i	0.993843	−	0.110793i
$129$	61227.1			0.0285217
$130$	−536719.	+	8513.19i	−0.244296	+	0.00387491i
$131$			1.87952e6i			0.836052i	0.908435	+	0.418026i	$0.137278\pi$
$131$			1.87952e6i			0.836052i	−0.908435	+	0.418026i	$0.862722\pi$
$132$	−1.63989e6	+	52035.5i	−0.713008	+	0.0226245i
$133$	−1.25142e6			−0.531922
$134$	66582.1	+	4.19771e6i	0.0276722	+	1.74461i
$135$		−	211755.i		−	0.0860663i
$136$	−2.01561e6	+	95976.4i	−0.801291	+	0.0381547i
$137$	−2.33412e6			−0.907740			−0.453870	−	0.891068i	$-0.649957\pi$
$137$	−2.33412e6			−0.907740			−0.453870	+	0.891068i	$0.649957\pi$
$138$	−613199.	+	9726.27i	−0.233327	+	0.00370091i
$139$			4.70664e6i			1.75253i	0.481827	+	0.876267i	$0.339974\pi$
$139$			4.70664e6i			1.75253i	−0.481827	+	0.876267i	$0.660026\pi$
$140$	38033.7	+	1.19863e6i	0.0138607	+	0.436817i
$141$	2.27162e6			0.810360
$142$	−25694.3	−	1.61992e6i	−0.00897372	−	0.565754i
$143$		−	1.97396e6i		−	0.675041i
$144$	−993326.	+	63102.0i	−0.332663	+	0.0211327i
$145$	−1.13949e6			−0.373772
$146$	5.39531e6	−	85577.8i	1.73364	−	0.0274981i
$147$		−	82513.8i		−	0.0259761i
$148$	1.12672e6	−	35752.0i	0.347561	−	0.0110285i
$149$	1.58358e6			0.478718			0.239359	−	0.970931i	$-0.423063\pi$
$149$	1.58358e6			0.478718			0.239359	+	0.970931i	$0.423063\pi$
$150$	−6180.64	−	389662.i	−0.00183130	−	0.115456i
$151$			1.08810e6i			0.316036i	0.987436	+	0.158018i	$0.0505105\pi$
$151$			1.08810e6i			0.316036i	−0.987436	+	0.158018i	$0.949490\pi$
$152$	−90916.2	−	1.90934e6i	−0.0258887	−	0.543692i
$153$	957712.			0.267400
$154$	−4.40945e6	+	69940.6i	−1.20732	+	0.0191499i
$155$		−	2.14984e6i		−	0.577312i
$156$	−37978.3	−	1.19688e6i	−0.0100037	−	0.315266i
$157$	5.02586e6			1.29871			0.649354	−	0.760486i	$-0.275039\pi$
$157$	5.02586e6			1.29871			0.649354	+	0.760486i	$0.275039\pi$
$158$	−39521.5	−	2.49166e6i	−0.0100199	−	0.631709i
$159$			3.48533e6i			0.867066i
$160$	−1.82603e6	+	145110.i	−0.445808	+	0.0354273i
$161$	−1.64839e6			−0.394987
$162$	472333.	−	7491.91i	0.111097	−	0.00176217i
$163$		−	4.60727e6i		−	1.06385i	−0.846791	−	0.531926i	$-0.821468\pi$
$163$		−	4.60727e6i		−	1.06385i	0.846791	−	0.531926i	$-0.178532\pi$
$164$	3.46289e6	−	109881.i	0.785069	−	0.0249110i
$165$	1.43311e6			0.319027
$166$	−123759.	−	7.80246e6i	−0.0270553	−	1.70572i
$167$			2.82376e6i			0.606287i	0.952945	+	0.303143i	$0.0980361\pi$
$167$			2.82376e6i			0.606287i	−0.952945	+	0.303143i	$0.901964\pi$
$168$	−2.67226e6	+	127244.i	−0.563574	+	0.0268354i
$169$	−3.38611e6			−0.701521
$170$	1.76234e6	−	27953.3i	0.358709	−	0.00568967i
$171$			907218.i			0.181436i
$172$	7972.35	+	251248.i	0.00156675	+	0.0493761i
$173$	2.40352e6			0.464205			0.232102	−	0.972691i	$-0.425440\pi$
$173$	2.40352e6			0.464205			0.232102	+	0.972691i	$0.425440\pi$
$174$	−40315.3	−	2.54170e6i	−0.00765282	−	0.482477i
$175$		−	1.04748e6i		−	0.195449i
$176$	−427059.	−	6.72259e6i	−0.0783340	−	1.23310i
$177$	5.44511e6			0.981944
$178$	−9.18850e6	+	145744.i	−1.62924	+	0.0258422i
$179$			3.86839e6i			0.674484i	0.941418	+	0.337242i	$0.109494\pi$
$179$			3.86839e6i			0.674484i	−0.941418	+	0.337242i	$0.890506\pi$
$180$	868946.	−	27572.5i	0.148996	−	0.00472780i
$181$	−8.08086e6			−1.36277			−0.681384	−	0.731926i	$-0.738622\pi$
$181$	−8.08086e6			−1.36277			−0.681384	+	0.731926i	$0.738622\pi$
$182$	−51046.4	−	3.21825e6i	−0.00846741	−	0.533833i
$183$		−	2.25966e6i		−	0.368714i
$184$	−119756.	−	2.51502e6i	−0.0192241	−	0.403727i
$185$	−984645.			−0.155512
$186$	4.79534e6	−	76061.3i	0.745213	−	0.0118202i
$187$			6.48157e6i			0.991186i
$188$	295786.	+	9.32166e6i	0.0445148	+	1.40288i
$189$	1.26972e6			0.188071
$190$	26479.6	+	1.66942e6i	0.00386056	+	0.243391i
$191$			3.72445e6i			0.534518i	0.963625	+	0.267259i	$0.0861179\pi$
$191$			3.72445e6i			0.534518i	−0.963625	+	0.267259i	$0.913882\pi$
$192$	−388282.	−	4.06793e6i	−0.0548584	−	0.574738i
$193$	2.55172e6			0.354945			0.177473	−	0.984126i	$-0.443208\pi$
$193$	2.55172e6			0.354945			0.177473	+	0.984126i	$0.443208\pi$
$194$	4.58982e6	−	72801.5i	0.628623	−	0.00997092i
$195$			1.04596e6i			0.141062i
$196$	338599.	−	10744.1i	0.0449694	−	0.00142692i
$197$	−1.25901e7			−1.64675			−0.823377	−	0.567495i	$-0.807913\pi$
$197$	−1.25901e7			−1.64675			−0.823377	+	0.567495i	$0.807913\pi$
$198$	50703.5	+	3.19663e6i	0.00653194	+	0.411810i
$199$		−	2.07688e6i		−	0.263544i	−0.991280	−	0.131772i	$-0.957933\pi$
$199$		−	2.07688e6i		−	0.263544i	0.991280	−	0.131772i	$-0.0420667\pi$
$200$	1.59819e6	−	76100.2i	0.199774	−	0.00951253i
$201$	8.18051e6			1.00738
$202$	3.01255e6	−	47783.6i	0.365494	−	0.00579729i
$203$		−	6.83256e6i		−	0.816762i
$204$	124703.	+	3.93001e6i	0.0146888	+	0.462917i
$205$	−3.02624e6			−0.351270
$206$	−274852.	−	1.73282e7i	−0.0314411	−	1.98222i
$207$			1.19500e6i			0.134728i
$208$	4.90651e6	−	311691.i	0.545233	−	0.0346365i
$209$	−6.13984e6			−0.672540
$210$	2.33647e6	−	37060.1i	0.252292	−	0.00400173i
$211$			1.47283e7i			1.56786i	0.620851	+	0.783929i	$0.286787\pi$
$211$			1.47283e7i			1.56786i	−0.620851	+	0.783929i	$0.713213\pi$
$212$	−1.43022e7	+	453823.i	−1.50105	+	0.0476298i
$213$	−3.15690e6			−0.326679
$214$	−212833.	−	1.34182e7i	−0.0217169	−	1.36916i
$215$		−	219566.i		−	0.0220928i
$216$	92245.5	+	1.93726e6i	0.00915343	+	0.192232i
$217$	1.28908e7			1.26153
$218$	1.27028e7	−	201485.i	1.22611	−	0.0194480i
$219$		−	1.05144e7i		−	1.00104i
$220$	186604.	+	5.88082e6i	0.0175248	+	0.552293i
$221$	−4.73059e6			−0.438267
$222$	−34836.8	−	2.19631e6i	−0.00318405	−	0.200740i
$223$		−	7.72762e6i		−	0.696837i	−0.937339	−	0.348418i	$-0.886719\pi$
$223$		−	7.72762e6i		−	0.696837i	0.937339	−	0.348418i	$-0.113281\pi$
$224$	−870103.	−	1.09492e7i	−0.0774153	−	0.974174i
$225$	−759375.			−0.0666667
$226$	−1.40739e7	+	223234.i	−1.21924	+	0.0193391i
$227$			1.85645e7i			1.58711i	0.608500	+	0.793554i	$0.291771\pi$
$227$			1.85645e7i			1.58711i	−0.608500	+	0.793554i	$0.708229\pi$
$228$	−3.72280e6	+	118128.i	−0.314098	+	0.00996666i
$229$	1.55847e7			1.29775			0.648877	−	0.760893i	$-0.275239\pi$
$229$	1.55847e7			1.29775			0.648877	+	0.760893i	$0.275239\pi$
$230$	34879.3	+	2.19899e6i	0.00286672	+	0.180734i
$231$			8.59314e6i			0.697134i
$232$	1.04247e7	−	496389.i	0.834834	−	0.0397519i
$233$	6.64517e6			0.525338			0.262669	−	0.964886i	$-0.415397\pi$
$233$	6.64517e6			0.525338			0.262669	+	0.964886i	$0.415397\pi$
$234$	−2.33307e6	+	37006.1i	−0.182088	+	0.00288819i
$235$		−	8.14624e6i		−	0.627702i
$236$	709004.	+	2.23442e7i	0.0539402	+	1.69992i
$237$	−4.85575e6			−0.364763
$238$	167613.	+	1.05672e7i	0.0124330	+	0.783846i
$239$		−	1.66721e7i		−	1.22122i	−0.791930	−	0.610612i	$-0.790924\pi$
$239$		−	1.66721e7i		−	1.22122i	0.791930	−	0.610612i	$-0.209076\pi$
$240$	226290.	+	3.56216e6i	0.0163694	+	0.257679i
$241$	−4.37877e6			−0.312825			−0.156412	−	0.987692i	$-0.549993\pi$
$241$	−4.37877e6			−0.312825			−0.156412	+	0.987692i	$0.549993\pi$
$242$	−7.46335e6	+	118380.i	−0.526609	+	0.00835281i
$243$		−	920483.i		−	0.0641500i
$244$	9.27259e6	−	294229.i	0.638310	−	0.0202542i
$245$	−295903.			−0.0201210
$246$	−107068.	−	6.75019e6i	−0.00719210	−	0.453431i
$247$		−	4.48118e6i		−	0.297373i
$248$	936518.	+	1.96679e7i	0.0613990	+	1.28945i
$249$	−1.52055e7			−0.984921
$250$	−1.39737e6	+	22164.4i	−0.0894315	+	0.00141852i
$251$			1.83077e7i			1.15774i	0.815419	+	0.578871i	$0.196506\pi$
$251$			1.83077e7i			1.15774i	−0.815419	+	0.578871i	$0.803494\pi$
$252$	165329.	+	5.21033e6i	0.0103311	+	0.325584i
$253$	−8.08750e6			−0.499405
$254$	−89562.6	−	5.64653e6i	−0.00546545	−	0.344573i
$255$		−	3.43445e6i		−	0.207127i
$256$	1.66423e7	−	2.12301e6i	0.991961	−	0.126541i
$257$	−5.00298e6			−0.294734			−0.147367	−	0.989082i	$-0.547080\pi$
$257$	−5.00298e6			−0.294734			−0.147367	+	0.989082i	$0.547080\pi$
$258$	489755.	−	7768.27i	0.0285181	−	0.000452340i
$259$		−	5.90408e6i		−	0.339823i
$260$	−4.29213e6	+	136194.i	−0.244204	+	0.00774885i
$261$	−4.95327e6			−0.278593
$262$	238466.	+	1.50343e7i	0.0132594	+	0.835947i
$263$		−	2.92331e7i		−	1.60697i	−0.595324	−	0.803485i	$-0.702976\pi$
$263$		−	2.92331e7i		−	1.60697i	0.595324	−	0.803485i	$-0.297024\pi$
$264$	−1.31109e7	+	624296.i	−0.712559	+	0.0339296i
$265$	1.24987e7			0.671627
$266$	−1.00101e7	+	158775.i	−0.531856	+	0.00843604i
$267$			1.79066e7i			0.940760i
$268$	1.06518e6	+	3.35690e7i	0.0553374	+	1.74395i
$269$	2.26722e7			1.16476			0.582380	−	0.812917i	$-0.302121\pi$
$269$	2.26722e7			1.16476			0.582380	+	0.812917i	$0.302121\pi$
$270$	−26866.7	−	1.69383e6i	−0.00136497	−	0.0860555i
$271$			1.03314e7i			0.519102i	0.965729	+	0.259551i	$0.0835746\pi$
$271$			1.03314e7i			0.519102i	−0.965729	+	0.259551i	$0.916425\pi$
$272$	−1.61107e7	+	1.02345e6i	−0.800585	+	0.0508580i
$273$	−6.27173e6			−0.308248
$274$	−1.86706e7	+	296144.i	−0.907626	+	0.0143963i
$275$		−	5.13927e6i		−	0.247117i
$276$	−4.90374e6	+	155601.i	−0.233238	+	0.00740090i
$277$	−1.17712e6			−0.0553836			−0.0276918	−	0.999617i	$-0.508816\pi$
$277$	−1.17712e6			−0.0553836			−0.0276918	+	0.999617i	$0.508816\pi$
$278$	597160.	+	3.76484e7i	0.0277943	+	1.75231i
$279$		−	9.34516e6i		−	0.430303i
$280$	456308.	+	9.58298e6i	0.0207866	+	0.436543i
$281$	2.16145e7			0.974152			0.487076	−	0.873360i	$-0.338063\pi$
$281$	2.16145e7			0.974152			0.487076	+	0.873360i	$0.338063\pi$
$282$	1.81707e7	−	288214.i	0.810258	−	0.0128519i
$283$			4.25888e6i			0.187904i	0.995577	+	0.0939520i	$0.0299500\pi$
$283$			4.25888e6i			0.187904i	−0.995577	+	0.0939520i	$0.970050\pi$
$284$	−411058.	−	1.29544e7i	−0.0179452	−	0.565540i
$285$	3.25337e6			0.140540
$286$	−250448.	−	1.57897e7i	−0.0107058	−	0.674956i
$287$		−	1.81458e7i		−	0.767591i
$288$	−7.93760e6	+	630782.i	−0.332286	+	0.0264060i
$289$	−8.60450e6			−0.356478
$290$	−9.11478e6	+	144574.i	−0.373725	+	0.00592785i
$291$		−	8.94465e6i		−	0.362981i
$292$	4.31462e7	−	1.36907e6i	1.73298	−	0.0549893i
$293$	2.44860e7			0.973452			0.486726	−	0.873555i	$-0.338191\pi$
$293$	2.44860e7			0.973452			0.486726	+	0.873555i	$0.338191\pi$
$294$	−10469.0	−	660028.i	−0.000411969	−	0.0259729i
$295$		−	1.95267e7i		−	0.760610i
$296$	9.00810e6	−	428934.i	0.347342	−	0.0165392i
$297$	6.22961e6			0.237789
$298$	1.26670e7	−	200918.i	0.478658	−	0.00759224i
$299$		−	5.90269e6i		−	0.220819i
$300$	−98877.8	−	3.11612e6i	−0.00366214	−	0.115412i
$301$	1.31655e6			0.0482769
$302$	138054.	+	8.70369e6i	0.00501219	+	0.315997i
$303$		−	5.87086e6i		−	0.211044i
$304$	−969488.	−	1.52613e7i	−0.0345082	−	0.543213i
$305$	−8.10335e6			−0.285605
$306$	7.66073e6	−	121511.i	0.267366	−	0.00424083i
$307$			372143.i			0.0128616i	0.999979	+	0.00643079i	$0.00204700\pi$
$307$			372143.i			0.0128616i	−0.999979	+	0.00643079i	$0.997953\pi$
$308$	−3.52623e7	+	1.11891e6i	−1.20686	+	0.0382950i
$309$	−3.37693e7			−1.14458
$310$	−272763.	−	1.71965e7i	−0.00915589	−	0.577239i
$311$			4.61051e6i			0.153274i	0.997059	+	0.0766368i	$0.0244182\pi$
$311$			4.61051e6i			0.153274i	−0.997059	+	0.0766368i	$0.975582\pi$
$312$	−455644.	−	9.56904e6i	−0.0150024	−	0.315068i
$313$	−3.54207e7			−1.15511			−0.577557	−	0.816351i	$-0.695994\pi$
$313$	−3.54207e7			−1.15511			−0.577557	+	0.816351i	$0.695994\pi$
$314$	4.02018e7	−	637663.i	1.29855	−	0.0205969i
$315$		−	4.55333e6i		−	0.145679i
$316$	−632264.	−	1.99257e7i	−0.0200372	−	0.631471i
$317$	−3.61574e7			−1.13506			−0.567531	−	0.823352i	$-0.692101\pi$
$317$	−3.61574e7			−1.13506			−0.567531	+	0.823352i	$0.692101\pi$
$318$	442205.	+	2.78791e7i	0.0137513	+	0.866957i
$319$		−	3.35226e7i		−	1.03268i
$320$	−1.45880e7	+	1.39242e6i	−0.445190	+	0.0424932i
$321$	−2.61494e7			−0.790582
$322$	−1.31855e7	+	209142.i	−0.394937	+	0.00626431i
$323$			1.47141e7i			0.436643i
$324$	3.77723e6	−	119856.i	0.111055	−	0.00352390i
$325$	3.75091e6			0.109266
$326$	−584553.	−	3.68535e7i	−0.0168722	−	1.06372i
$327$		−	2.47552e7i		−	0.707983i
$328$	2.76857e7	−	1.31830e6i	0.784575	−	0.0373587i
$329$	4.88461e7			1.37165
$330$	1.14634e7	−	181828.i	0.318987	−	0.00505962i
$331$			1.43002e7i			0.394328i	0.980371	+	0.197164i	$0.0631731\pi$
$331$			1.43002e7i			0.394328i	−0.980371	+	0.197164i	$0.936827\pi$
$332$	−1.97989e6	−	6.23962e7i	−0.0541038	−	1.70508i
$333$	−4.28017e6			−0.115912
$334$	358268.	+	2.25872e7i	0.00961543	+	0.606211i
$335$		−	2.93361e7i		−	0.780312i
$336$	−2.13593e7	+	1.35687e6i	−0.563078	+	0.0357701i
$337$	5.11693e6			0.133696			0.0668482	−	0.997763i	$-0.478706\pi$
$337$	5.11693e6			0.133696			0.0668482	+	0.997763i	$0.478706\pi$
$338$	−2.70855e7	+	429617.i	−0.701433	+	0.0111258i
$339$			2.74273e7i			0.704019i
$340$	1.40934e7	−	447197.i	0.358574	−	0.0113779i
$341$	6.32458e7			1.59503
$342$	115104.	+	7.25683e6i	0.00287749	+	0.181413i
$343$		−	4.12096e7i		−	1.02121i
$344$	95648.2	+	2.00872e6i	0.00234964	+	0.0493451i
$345$	4.28540e6			0.104360
$346$	1.92257e7	−	304949.i	0.464146	−	0.00736206i
$347$			1.37663e7i			0.329480i	0.986337	+	0.164740i	$0.0526785\pi$
$347$			1.37663e7i			0.329480i	−0.986337	+	0.164740i	$0.947321\pi$
$348$	−644963.	−	2.03259e7i	−0.0153037	−	0.482295i
$349$	−3.42645e7			−0.806062			−0.403031	−	0.915186i	$-0.632043\pi$
$349$	−3.42645e7			−0.806062			−0.403031	+	0.915186i	$0.632043\pi$
$350$	−132901.	−	8.37882e6i	−0.00309973	−	0.195424i
$351$			4.54670e6i			0.105142i
$352$	−4.26898e6	−	5.37198e7i	−0.0978806	−	1.23170i
$353$	−3.92759e6			−0.0892899			−0.0446449	−	0.999003i	$-0.514216\pi$
$353$	−3.92759e6			−0.0892899			−0.0446449	+	0.999003i	$0.514216\pi$
$354$	4.35554e7	−	690855.i	0.981820	−	0.0155732i
$355$			1.13209e7i			0.253045i
$356$	−7.34803e7	+	2.33160e6i	−1.62862	+	0.0516779i
$357$	2.05935e7			0.452611
$358$	490807.	+	3.09433e7i	0.0106970	+	0.674399i
$359$			2.26847e7i			0.490287i	0.969487	+	0.245143i	$0.0788351\pi$
$359$			2.26847e7i			0.490287i	−0.969487	+	0.245143i	$0.921165\pi$
$360$	6.94719e6	−	330801.i	0.148902	−	0.00709022i
$361$	3.31075e7			0.703729
$362$	−6.46388e7	+	1.02527e6i	−1.36260	+	0.0216129i
$363$			1.45446e7i			0.304076i
$364$	−816639.	−	2.57363e7i	−0.0169327	−	0.533632i
$365$	−3.77056e7			−0.775403
$366$	−286697.	−	1.80750e7i	−0.00584763	−	0.368668i
$367$			5.14521e7i			1.04089i	0.853895	+	0.520445i	$0.174234\pi$
$367$			5.14521e7i			1.04089i	−0.853895	+	0.520445i	$0.825766\pi$
$368$	−1.27703e6	−	2.01024e7i	−0.0256246	−	0.403371i
$369$	−1.31548e7			−0.261821
$370$	−7.87617e6	+	124928.i	−0.155493	+	0.00246635i
$371$			7.49442e7i			1.46763i
$372$	3.83482e7	−	1.21683e6i	0.744931	−	0.0236374i
$373$	1.23981e7			0.238907			0.119453	−	0.992840i	$-0.461886\pi$
$373$	1.23981e7			0.238907			0.119453	+	0.992840i	$0.461886\pi$
$374$	822357.	+	5.18460e7i	0.0157197	+	0.991061i
$375$			2.72319e6i			0.0516398i
$376$	3.54869e6	+	7.45264e7i	0.0667581	+	1.40200i
$377$	2.44666e7			0.456614
$378$	1.01565e7	−	161097.i	0.188047	−	0.00298272i
$379$			1.00801e8i			1.85160i	0.378018	+	0.925798i	$0.376606\pi$
$379$			1.00801e8i			1.85160i	−0.378018	+	0.925798i	$0.623394\pi$
$380$	423620.	+	1.33503e7i	0.00772014	+	0.243300i
$381$	−1.10040e7			−0.198964
$382$	472544.	+	2.97919e7i	0.00847720	+	0.534450i
$383$			5.39003e7i			0.959389i	0.877436	+	0.479695i	$0.159253\pi$
$383$			5.39003e7i			0.959389i	−0.877436	+	0.479695i	$0.840747\pi$
$384$	−3.62199e6	−	3.24901e7i	−0.0639666	−	0.573796i
$385$	3.08158e7			0.539998
$386$	2.04112e7	−	323753.i	0.354901	−	0.00562927i
$387$		−	954437.i		−	0.0164670i
$388$	3.67047e7	−	1.16468e6i	0.628386	−	0.0199393i
$389$	−1.63608e6			−0.0277943			−0.0138971	−	0.999903i	$-0.504424\pi$
$389$	−1.63608e6			−0.0277943			−0.0138971	+	0.999903i	$0.504424\pi$
$390$	132707.	+	8.36663e6i	0.00223718	+	0.141045i
$391$			1.93817e7i			0.324236i
$392$	2.70708e6	−	128902.i	0.0449411	−	0.00213994i
$393$	2.92988e7			0.482695
$394$	−1.00708e8	+	1.59738e6i	−1.64655	+	0.0261167i
$395$			1.74132e7i			0.282545i
$396$	811154.	+	2.55634e7i	0.0130622	+	0.411655i
$397$	−5.15268e7			−0.823496			−0.411748	−	0.911298i	$-0.635082\pi$
$397$	−5.15268e7			−0.823496			−0.411748	+	0.911298i	$0.635082\pi$
$398$	−263507.	−	1.66130e7i	−0.00417968	−	0.263511i
$399$			1.95077e7i			0.307106i
$400$	1.27743e7	−	811497.i	0.199598	−	0.0126796i
$401$	−4.97131e7			−0.770970			−0.385485	−	0.922714i	$-0.625966\pi$
$401$	−4.97131e7			−0.770970			−0.385485	+	0.922714i	$0.625966\pi$
$402$	6.54359e7	−	1.03791e6i	1.00725	−	0.0159765i
$403$			4.61602e7i			0.705265i
$404$	2.40913e7	−	764441.i	0.365356	−	0.0115931i
$405$	−3.30094e6			−0.0496904
$406$	−866890.	−	5.46536e7i	−0.0129535	−	0.816659i
$407$		−	2.89672e7i		−	0.429658i
$408$	1.49612e6	+	3.14203e7i	0.0220286	+	0.462625i
$409$	−3.25227e7			−0.475354			−0.237677	−	0.971344i	$-0.576386\pi$
$409$	−3.25227e7			−0.475354			−0.237677	+	0.971344i	$0.576386\pi$
$410$	−2.42068e7	+	383957.i	−0.351226	+	0.00557098i
$411$			3.63853e7i			0.524084i
$412$	−4.39708e6	−	1.38574e8i	−0.0628743	−	1.98148i
$413$	1.17085e8			1.66208
$414$	151618.	+	9.55883e6i	0.00213672	+	0.134711i
$415$			5.45282e7i			0.762917i
$416$	3.92076e7	−	3.11573e6i	0.544615	−	0.0432793i
$417$	7.33692e7			1.01183
$418$	−4.91125e7	+	778999.i	−0.672455	+	0.0106662i
$419$			2.90909e7i			0.395471i	0.980255	+	0.197736i	$0.0633587\pi$
$419$			2.90909e7i			0.395471i	−0.980255	+	0.197736i	$0.936641\pi$
$420$	1.86847e7	−	592886.i	0.252197	−	0.00800246i
$421$	−1.08942e8			−1.45998			−0.729991	−	0.683457i	$-0.760476\pi$
$421$	−1.08942e8			−1.45998			−0.729991	+	0.683457i	$0.760476\pi$
$422$	1.86868e6	+	1.17812e8i	0.0248655	+	1.56766i
$423$		−	3.54110e7i		−	0.467861i
$424$	−1.14345e8	+	5.44473e6i	−1.50010	+	0.0714297i
$425$	−1.23163e7			−0.160440
$426$	−2.52520e7	+	400535.i	−0.326638	+	0.00518098i
$427$		−	4.85889e7i		−	0.624099i
$428$	−3.40490e6	−	1.07305e8i	−0.0434284	−	1.36864i
$429$	−3.07710e7			−0.389735
$430$	−27857.8	−	1.75631e6i	−0.000350381	−	0.0220900i
$431$		−	1.42434e8i		−	1.77902i	−0.456913	−	0.889511i	$-0.651045\pi$
$431$		−	1.42434e8i		−	1.77902i	0.456913	−	0.889511i	$-0.348955\pi$
$432$	983663.	+	1.54844e7i	0.0122010	+	0.192063i
$433$	−1.44746e8			−1.78296			−0.891481	−	0.453059i	$-0.850333\pi$
$433$	−1.44746e8			−1.78296			−0.891481	+	0.453059i	$0.850333\pi$
$434$	1.03113e8	−	1.63553e6i	1.26138	−	0.0200073i
$435$			1.77629e7i			0.215797i
$436$	1.01584e8	−	3.22336e6i	1.22565	−	0.0388910i
$437$	−1.83598e7			−0.220001
$438$	−1.33403e6	−	8.41045e7i	−0.0158760	−	1.00091i
$439$		−	1.01787e8i		−	1.20309i	−0.798837	−	0.601547i	$-0.794551\pi$
$439$		−	1.01787e8i		−	1.20309i	0.798837	−	0.601547i	$-0.205449\pi$
$440$	2.23878e6	+	4.70170e7i	0.0262817	+	0.551946i
$441$	−1.28626e6			−0.0149973
$442$	−3.78400e7	+	600200.i	−0.438212	+	0.00695071i
$443$		−	5.44035e7i		−	0.625771i	−0.949791	−	0.312885i	$-0.898704\pi$
$443$		−	5.44035e7i		−	0.625771i	0.949791	−	0.312885i	$-0.101296\pi$
$444$	−557319.	−	1.75638e7i	−0.00636729	−	0.200664i
$445$	6.42147e7			0.728709
$446$	−980451.	−	6.18132e7i	−0.0110515	−	0.696749i
$447$		−	2.46855e7i		−	0.276388i
$448$	−8.34914e6	−	8.74718e7i	−0.0928555	−	0.972824i
$449$	1.40905e8			1.55664			0.778319	−	0.627869i	$-0.216073\pi$
$449$	1.40905e8			1.55664			0.778319	+	0.627869i	$0.216073\pi$
$450$	−6.07424e6	+	96346.6i	−0.0666583	+	0.00105730i
$451$		−	8.90285e7i		−	0.970509i
$452$	−1.12549e8	+	3.57130e6i	−1.21878	+	0.0386733i
$453$	1.69618e7			0.182464
$454$	2.35540e6	+	1.48498e8i	0.0251708	+	1.58691i
$455$			2.24910e7i			0.238768i
$456$	−2.97637e7	+	1.41724e6i	−0.313901	+	0.0149469i
$457$	−6.44034e7			−0.674777			−0.337388	−	0.941366i	$-0.609544\pi$
$457$	−6.44034e7			−0.674777			−0.337388	+	0.941366i	$0.609544\pi$
$458$	1.24662e8	−	1.97733e6i	1.29759	−	0.0205818i
$459$		−	1.49293e7i		−	0.154383i
$460$	557999.	+	1.75853e7i	0.00573271	+	0.180666i
$461$	−3.82834e7			−0.390758			−0.195379	−	0.980728i	$-0.562594\pi$
$461$	−3.82834e7			−0.390758			−0.195379	+	0.980728i	$0.562594\pi$
$462$	1.09027e6	+	6.87365e7i	0.0110562	+	0.697046i
$463$		−	1.02023e8i		−	1.02791i	−0.857818	−	0.513953i	$-0.828181\pi$
$463$		−	1.02023e8i		−	1.02791i	0.857818	−	0.513953i	$-0.171819\pi$
$464$	8.33242e7	−	5.29326e6i	0.834099	−	0.0529870i
$465$	−3.35126e7			−0.333311
$466$	5.31547e7	−	843115.i	0.525272	−	0.00833161i
$467$			4.70326e7i			0.461794i	0.972978	+	0.230897i	$0.0741660\pi$
$467$			4.70326e7i			0.461794i	−0.972978	+	0.230897i	$0.925834\pi$
$468$	−1.86575e7	+	592023.i	−0.182019	+	0.00577565i
$469$	1.75904e8			1.70513
$470$	−1.03356e6	−	6.51617e7i	−0.00995505	−	0.627623i
$471$		−	7.83455e7i		−	0.749810i
$472$	8.50627e6	+	1.78641e8i	0.0808934	+	1.69885i
$473$	6.45940e6			0.0610392
$474$	−3.88411e7	+	616079.i	−0.364718	+	0.00578498i
$475$		−	1.16669e7i		−	0.108862i
$476$	2.68146e6	+	8.45060e7i	0.0248629	+	0.783550i
$477$	5.43309e7			0.500601
$478$	−2.11529e6	−	1.33360e8i	−0.0193680	−	1.22107i
$479$			3.86857e7i			0.352001i	0.984390	+	0.176001i	$0.0563161\pi$
$479$			3.86857e7i			0.352001i	−0.984390	+	0.176001i	$0.943684\pi$
$480$	2.26205e6	+	2.84650e7i	0.0204540	+	0.257387i
$481$	2.11418e7			0.189979
$482$	−3.50258e7	+	555562.i	−0.312785	+	0.00496125i
$483$			2.56959e7i			0.228046i
$484$	−5.96843e7	+	1.89384e6i	−0.526410	+	0.0167035i
$485$	−3.20764e7			−0.281164
$486$	−116787.	−	7.36294e6i	−0.00101739	−	0.0641420i
$487$			2.57826e7i			0.223224i	0.993752	+	0.111612i	$0.0356013\pi$
$487$			2.57826e7i			0.223224i	−0.993752	+	0.111612i	$0.964399\pi$
$488$	7.41341e7	−	3.53001e6i	0.637909	−	0.0303750i
$489$	−7.18203e7			−0.614215
$490$	−2.36692e6	+	37543.0i	−0.0201185	+	0.000319110i
$491$		−	1.22519e8i		−	1.03504i	−0.855671	−	0.517521i	$-0.826855\pi$
$491$		−	1.22519e8i		−	1.03504i	0.855671	−	0.517521i	$-0.173145\pi$
$492$	−1.71288e6	−	5.39812e7i	−0.0143824	−	0.453260i
$493$	−8.03368e7			−0.670462
$494$	−568555.	−	3.58449e7i	−0.00471620	−	0.297336i
$495$		−	2.23400e7i		−	0.184190i
$496$	9.98660e6	+	1.57205e8i	0.0818413	+	1.28831i
$497$	−6.78820e7			−0.552950
$498$	−1.21628e8	+	1.92921e6i	−0.984797	+	0.0156204i
$499$			3.41531e7i			0.274871i	0.990511	+	0.137436i	$0.0438860\pi$
$499$			3.41531e7i			0.274871i	−0.990511	+	0.137436i	$0.956114\pi$
$500$	−1.11747e7	+	354585.i	−0.0893977	+	0.00283668i
$501$	4.40180e7			0.350040
$502$	2.32281e6	+	1.46443e8i	0.0183612	+	1.15760i
$503$		−	7.48857e7i		−	0.588430i	−0.955739	−	0.294215i	$-0.904942\pi$
$503$		−	7.48857e7i		−	0.588430i	0.955739	−	0.294215i	$-0.0950581\pi$
$504$	1.98353e6	+	4.16564e7i	0.0154934	+	0.325380i
$505$	−2.10535e7			−0.163474
$506$	−6.46918e7	+	1.02611e6i	−0.499342	+	0.00792032i
$507$			5.27842e7i			0.405023i
$508$	−1.43282e6	−	4.51552e7i	−0.0109295	−	0.344443i
$509$	−2.15746e8			−1.63603			−0.818013	−	0.575200i	$-0.804924\pi$
$509$	−2.15746e8			−1.63603			−0.818013	+	0.575200i	$0.804924\pi$
$510$	−435750.	−	2.74721e7i	−0.00328493	−	0.207101i
$511$		−	2.26089e8i		−	1.69440i
$512$	1.32853e8	−	1.90935e7i	0.989830	−	0.142257i
$513$	1.41421e7			0.104752
$514$	−4.00188e7	+	634759.i	−0.294696	+	0.00467433i
$515$			1.21100e8i			0.886589i
$516$	3.91657e6	−	124277.i	0.0285073	−	0.000904566i
$517$	2.39653e8			1.73425
$518$	−749088.	−	4.72267e7i	−0.00538944	−	0.339781i
$519$		−	3.74672e7i		−	0.268009i
$520$	−3.43155e7	+	1.63398e6i	−0.244051	+	0.0116208i
$521$	1.33165e7			0.0941625			0.0470812	−	0.998891i	$-0.485008\pi$
$521$	1.33165e7			0.0941625			0.0470812	+	0.998891i	$0.485008\pi$
$522$	−3.96212e7	+	628453.i	−0.278558	+	0.00441836i
$523$			1.01022e8i			0.706174i	0.935590	+	0.353087i	$0.114868\pi$
$523$			1.01022e8i			0.706174i	−0.935590	+	0.353087i	$0.885132\pi$
$524$	3.81498e6	+	1.20229e8i	0.0265154	+	0.835631i
$525$	−1.63287e7			−0.112843
$526$	−3.70899e6	−	2.33836e8i	−0.0254858	−	1.60677i
$527$		−	1.51569e8i		−	1.03556i
$528$	−1.04795e8	+	6.65720e6i	−0.711931	+	0.0452262i
$529$	1.23852e8			0.836635
$530$	9.99772e7	−	1.58579e6i	0.671542	−	0.0106517i
$531$		−	8.48808e7i		−	0.566926i
$532$	−8.00506e7	+	2.54009e6i	−0.531655	+	0.0168700i
$533$	6.49777e7			0.429124
$534$	2.27192e6	+	1.43235e8i	0.0149200	+	0.940641i
$535$			9.37744e7i			0.612382i
$536$	1.27795e7	+	2.68383e8i	0.0829887	+	1.74286i
$537$	6.03023e7			0.389413
$538$	1.81355e8	−	2.87656e6i	1.16461	−	0.0184726i
$539$		−	8.70512e6i		−	0.0555915i
$540$	−429813.	−	1.35455e7i	−0.00272960	−	0.0860230i
$541$	2.05333e8			1.29678			0.648391	−	0.761307i	$-0.275442\pi$
$541$	2.05333e8			1.29678			0.648391	+	0.761307i	$0.275442\pi$
$542$	1.31081e6	+	8.26411e7i	0.00823271	+	0.519037i
$543$			1.25968e8i			0.786794i
$544$	−1.28739e8	+	1.02306e7i	−0.799677	+	0.0635485i
$545$	−8.87745e7			−0.548402
$546$	−5.01676e7	+	795734.i	−0.308209	+	0.00488866i
$547$		−	5.12695e7i		−	0.313254i	−0.987658	−	0.156627i	$-0.949938\pi$
$547$		−	5.12695e7i		−	0.313254i	0.987658	−	0.156627i	$-0.0500621\pi$
$548$	−1.49309e8	+	4.73772e6i	−0.907284	+	0.0287890i
$549$	−3.52246e7			−0.212877
$550$	−652051.	−	4.11090e7i	−0.00391916	−	0.247086i
$551$		−	7.61012e7i		−	0.454922i
$552$	−3.92052e7	+	1.86682e6i	−0.233092	+	0.0110990i
$553$	−1.04412e8			−0.617412
$554$	−9.41576e6	+	149348.i	−0.0553766	+	0.000878357i
$555$			1.53491e7i			0.0897851i
$556$	9.55336e6	+	3.01073e8i	0.0555817	+	1.75165i
$557$	−1.88880e8			−1.09300			−0.546501	−	0.837458i	$-0.684041\pi$
$557$	−1.88880e8			−1.09300			−0.546501	+	0.837458i	$0.684041\pi$
$558$	−1.18568e6	−	7.47519e7i	−0.00682440	−	0.430249i
$559$			4.71441e6i			0.0269893i
$560$	4.86586e6	+	7.65963e7i	0.0277074	+	0.436158i
$561$	1.01038e8			0.572261
$562$	1.72894e8	−	2.74237e6i	0.974030	−	0.0154496i
$563$			2.01659e8i			1.13004i	0.825078	+	0.565019i	$0.191131\pi$
$563$			2.01659e8i			1.13004i	−0.825078	+	0.565019i	$0.808869\pi$
$564$	1.45310e8	−	4.61085e6i	0.809952	−	0.0257006i
$565$	9.83571e7			0.545331
$566$	540350.	+	3.40667e7i	0.00298007	+	0.187880i
$567$		−	1.97929e7i		−	0.108583i
$568$	−4.93166e6	−	1.03570e8i	−0.0269121	−	0.565185i
$569$	−2.69336e8			−1.46204			−0.731018	−	0.682359i	$-0.760954\pi$
$569$	−2.69336e8			−1.46204			−0.731018	+	0.682359i	$0.760954\pi$
$570$	2.60237e7	−	412776.i	0.140522	−	0.00222889i
$571$			1.31483e8i			0.706256i	0.935575	+	0.353128i	$0.114882\pi$
$571$			1.31483e8i			0.706256i	−0.935575	+	0.353128i	$0.885118\pi$
$572$	−4.00667e6	−	1.26270e8i	−0.0214090	−	0.674701i
$573$	5.80584e7			0.308604
$574$	−2.30227e6	−	1.45148e8i	−0.0121736	−	0.767494i
$575$		−	1.53678e7i		−	0.0808368i
$576$	−6.34128e7	+	6.05272e6i	−0.331825	+	0.0316725i
$577$	1.62328e7			0.0845017			0.0422509	−	0.999107i	$-0.486547\pi$
$577$	1.62328e7			0.0845017			0.0422509	+	0.999107i	$0.486547\pi$
$578$	−6.88274e7	+	1.09171e6i	−0.356433	+	0.00565357i
$579$		−	3.97774e7i		−	0.204928i
$580$	−7.28908e7	+	2.31290e6i	−0.373584	+	0.0118542i
$581$	−3.26960e8			−1.66712
$582$	−1.13486e6	−	7.15482e7i	−0.00575671	−	0.362936i
$583$			3.67699e8i			1.85561i
$584$	3.44952e8	−	1.64254e7i	1.73189	−	0.0824666i
$585$	1.63049e7			0.0814424
$586$	1.95863e8	−	3.10669e6i	0.973330	−	0.0154385i
$587$		−	1.10074e8i		−	0.544216i	−0.962267	−	0.272108i	$-0.912279\pi$
$587$		−	1.10074e8i		−	0.544216i	0.962267	−	0.272108i	$-0.0877209\pi$
$588$	−167484.	−	5.27823e6i	−0.000823835	−	0.0259631i
$589$	1.43577e8			0.702652
$590$	−2.47747e6	−	1.56194e8i	−0.0120629	−	0.760515i
$591$			1.96259e8i			0.950754i
$592$	7.20013e7	−	4.57395e6i	0.347036	−	0.0220458i
$593$	3.80047e7			0.182253			0.0911263	−	0.995839i	$-0.470953\pi$
$593$	3.80047e7			0.182253			0.0911263	+	0.995839i	$0.470953\pi$
$594$	4.98306e7	−	790389.i	0.237759	−	0.00377122i
$595$		−	7.38501e7i		−	0.350591i
$596$	1.01298e8	−	3.21428e6i	0.478477	−	0.0151826i
$597$	−3.23754e7			−0.152157
$598$	−748911.	−	4.72156e7i	−0.00350208	−	0.220791i
$599$		−	1.46223e7i		−	0.0680356i	−0.999421	−	0.0340178i	$-0.989170\pi$
$599$		−	1.46223e7i		−	0.0680356i	0.999421	−	0.0340178i	$-0.0108303\pi$
$600$	−1.18628e6	−	2.49133e7i	−0.00549206	−	0.115339i
$601$	−4.14917e7			−0.191134			−0.0955671	−	0.995423i	$-0.530466\pi$
$601$	−4.14917e7			−0.191134			−0.0955671	+	0.995423i	$0.530466\pi$
$602$	1.05311e7	−	167039.i	0.0482708	−	0.000765648i
$603$		−	1.27522e8i		−	0.581610i
$604$	2.20858e6	+	6.96032e7i	0.0100231	+	0.315877i
$605$	5.21583e7			0.235536
$606$	−744873.	−	4.69610e7i	−0.00334706	−	0.211018i
$607$		−	3.48530e8i		−	1.55838i	−0.626786	−	0.779191i	$-0.715630\pi$
$607$		−	3.48530e8i		−	1.55838i	0.626786	−	0.779191i	$-0.284370\pi$
$608$	−9.69123e6	−	1.21952e8i	−0.0431189	−	0.542598i
$609$	−1.06509e8			−0.471558
$610$	−6.48187e7	+	1.02812e6i	−0.285569	+	0.00452956i
$611$			1.74912e8i			0.766823i
$612$	6.12627e7	−	1.94393e6i	0.267265	−	0.00848059i
$613$	1.70343e8			0.739509			0.369755	−	0.929129i	$-0.379442\pi$
$613$	1.70343e8			0.739509			0.369755	+	0.929129i	$0.379442\pi$
$614$	47216.1	+	2.97677e6i	0.000203979	+	0.0128600i
$615$			4.71744e7i			0.202806i
$616$	−2.81921e8	+	1.34241e7i	−1.20610	+	0.0574305i
$617$	−2.59449e8			−1.10458			−0.552289	−	0.833653i	$-0.686245\pi$
$617$	−2.59449e8			−1.10458			−0.552289	+	0.833653i	$0.686245\pi$
$618$	−2.70121e8	+	4.28452e6i	−1.14444	+	0.0181525i
$619$			2.78639e8i			1.17482i	0.809291	+	0.587408i	$0.199851\pi$
$619$			2.78639e8i			1.17482i	−0.809291	+	0.587408i	$0.800149\pi$
$620$	−4.36366e6	−	1.37520e8i	−0.0183095	−	0.577021i
$621$	1.86283e7			0.0777853
$622$	584964.	+	3.68794e7i	0.00243085	+	0.153254i
$623$			3.85041e8i			1.59237i
$624$	−4.85878e6	−	7.64848e7i	−0.0199974	−	0.314791i
$625$	9.76562e6			0.0400000
$626$	−2.83330e8	+	4.49405e6i	−1.15497	+	0.0183195i
$627$			9.57106e7i			0.388291i
$628$	3.21493e8	−	1.02013e7i	1.29806	−	0.0411886i
$629$	−6.94198e7			−0.278953
$630$	−577709.	−	3.64220e7i	−0.00231040	−	0.145661i
$631$		−	2.72427e7i		−	0.108433i	−0.998529	−	0.0542165i	$-0.982734\pi$
$631$		−	2.72427e7i		−	0.108433i	0.998529	−	0.0542165i	$-0.0172661\pi$
$632$	−7.58558e6	−	1.59306e8i	−0.0300495	−	0.631074i
$633$	2.29592e8			0.905203
$634$	−2.89223e8	+	4.58751e6i	−1.13492	+	0.0180015i
$635$			3.94613e7i			0.154117i
$636$	7.07440e6	+	2.22949e8i	0.0274991	+	0.866630i
$637$	6.35346e6			0.0245806
$638$	−4.25322e6	−	2.68147e8i	−0.0163778	−	1.03255i
$639$			4.92111e7i			0.188608i
$640$	−1.16513e8	+	1.29888e7i	−0.444460	+	0.0495483i
$641$	4.19674e8			1.59345			0.796725	−	0.604342i	$-0.206564\pi$
$641$	4.19674e8			1.59345			0.796725	+	0.604342i	$0.206564\pi$
$642$	−2.09169e8	+	3.31774e6i	−0.790483	+	0.0125383i
$643$			2.92348e8i			1.09968i	0.835269	+	0.549841i	$0.185312\pi$
$643$			2.92348e8i			1.09968i	−0.835269	+	0.549841i	$0.814688\pi$
$644$	−1.05444e8	+	3.34585e6i	−0.394788	+	0.0125270i
$645$	−3.42270e6			−0.0127553
$646$	1.86687e6	+	1.17698e8i	0.00692495	+	0.436588i
$647$			2.76931e8i			1.02249i	0.859435	+	0.511245i	$0.170815\pi$
$647$			2.76931e8i			1.02249i	−0.859435	+	0.511245i	$0.829185\pi$
$648$	3.01989e7	−	1.43797e6i	0.110985	−	0.00528474i
$649$	5.74453e8			2.10146
$650$	3.00035e7	−	475902.i	0.109253	−	0.00173291i
$651$		−	2.00947e8i		−	0.728347i
$652$	−9.35168e6	−	2.94717e8i	−0.0337401	−	1.06332i
$653$	−3.17212e8			−1.13923			−0.569613	−	0.821913i	$-0.692907\pi$
$653$	−3.17212e8			−1.13923			−0.569613	+	0.821913i	$0.692907\pi$
$654$	−3.14085e6	−	1.98017e8i	−0.0112283	−	0.707894i
$655$		−	1.05068e8i		−	0.373894i
$656$	2.21291e8	−	1.40577e7i	0.783884	−	0.0497970i
$657$	−1.63903e8			−0.577951
$658$	3.90719e8	−	6.19740e6i	1.37147	−	0.0217537i
$659$		−	2.32598e8i		−	0.812737i	−0.913709	−	0.406368i	$-0.866795\pi$
$659$		−	2.32598e8i		−	0.812737i	0.913709	−	0.406368i	$-0.133205\pi$
$660$	9.16729e7	−	2.90888e6i	0.318867	−	0.0101180i
$661$	−4.50526e8			−1.55997			−0.779983	−	0.625801i	$-0.784772\pi$
$661$	−4.50526e8			−1.55997			−0.779983	+	0.625801i	$0.784772\pi$
$662$	1.81435e6	+	1.14387e8i	0.00625385	+	0.394278i
$663$			7.37426e7i			0.253033i
$664$	−2.37537e7	−	4.98855e8i	−0.0811387	−	1.70400i
$665$	6.99565e7			0.237883
$666$	−3.42371e7	+	543052.i	−0.115897	+	0.00183831i
$667$		−	1.00242e8i		−	0.337809i
$668$	5.73157e6	+	1.80630e8i	0.0192284	+	0.605982i
$669$	−1.20462e8			−0.402319
$670$	−3.72205e6	−	2.34659e8i	−0.0123754	−	0.780213i
$671$		−	2.38392e8i		−	0.789085i
$672$	−1.70680e8	+	1.35636e7i	−0.562440	+	0.0446957i
$673$	−4.17718e8			−1.37037			−0.685185	−	0.728369i	$-0.740279\pi$
$673$	−4.17718e8			−1.37037			−0.685185	+	0.728369i	$0.740279\pi$
$674$	4.09303e7	−	649217.i	0.133680	−	0.00212036i
$675$			1.18375e7i			0.0384900i
$676$	−2.16602e8	+	6.87300e6i	−0.701168	+	0.0222488i
$677$	4.19200e8			1.35100			0.675500	−	0.737360i	$-0.263928\pi$
$677$	4.19200e8			1.35100			0.675500	+	0.737360i	$0.263928\pi$
$678$	3.47988e6	+	2.19391e8i	0.0111654	+	0.703931i
$679$		−	1.92335e8i		−	0.614396i
$680$	1.12676e8	−	5.36524e6i	0.358348	−	0.0170633i
$681$	2.89392e8			0.916317
$682$	5.05903e8	−	8.02439e6i	1.59483	−	0.0252964i
$683$			1.90249e8i			0.597119i	0.954391	+	0.298560i	$0.0965062\pi$
$683$			1.90249e8i			0.597119i	−0.954391	+	0.298560i	$0.903494\pi$
$684$	1.84144e6	+	5.80328e7i	0.00575426	+	0.181345i
$685$	1.30481e8			0.405954
$686$	−5.22852e6	−	3.29636e8i	−0.0161960	−	1.02108i
$687$		−	2.42942e8i		−	0.749259i
$688$	1.01995e6	+	1.60556e7i	0.00313193	+	0.0493016i
$689$	−2.68366e8			−0.820483
$690$	3.42789e7	−	543715.i	0.104347	−	0.00165510i
$691$		−	2.14772e8i		−	0.650945i	−0.945551	−	0.325473i	$-0.894477\pi$
$691$		−	2.14772e8i		−	0.650945i	0.945551	−	0.325473i	$-0.105523\pi$
$692$	1.53748e8	−	4.87858e6i	0.463971	−	0.0147223i
$693$	1.33954e8			0.402490
$694$	1.74662e6	+	1.10117e8i	0.00522540	+	0.329439i
$695$		−	2.63109e8i		−	0.783757i
$696$	−7.73793e6	−	1.62505e8i	−0.0229508	−	0.481992i
$697$	−2.13357e8			−0.630098
$698$	−2.74082e8	+	4.34735e6i	−0.805961	+	0.0127838i
$699$		−	1.03588e8i		−	0.303304i
$700$	−2.12615e6	−	6.70053e7i	−0.00619868	−	0.195351i
$701$	4.63107e8			1.34440			0.672199	−	0.740371i	$-0.265350\pi$
$701$	4.63107e8			1.34440			0.672199	+	0.740371i	$0.265350\pi$
$702$	576868.	+	3.63690e7i	0.00166750	+	0.105128i
$703$		−	6.57598e7i		−	0.189276i
$704$	−4.09633e7	−	4.29163e8i	−0.117402	−	1.23000i
$705$	−1.26987e8			−0.362404
$706$	−3.14168e7	+	498318.i	−0.0892786	+	0.00141610i
$707$		−	1.26240e8i		−	0.357222i
$708$	3.48312e8	−	1.10523e7i	0.981450	−	0.0311424i
$709$	3.96583e8			1.11275			0.556373	−	0.830933i	$-0.312193\pi$
$709$	3.96583e8			1.11275			0.556373	+	0.830933i	$0.312193\pi$
$710$	1.43636e6	+	9.05561e7i	0.00401317	+	0.253013i
$711$			7.56937e7i			0.210596i
$712$	−5.87472e8	+	2.79734e7i	−1.62760	+	0.0775006i
$713$	1.89123e8			0.521765
$714$	1.64727e8	−	2.61282e6i	0.452554	−	0.00717819i
$715$			1.10348e8i			0.301887i
$716$	7.85193e6	+	2.47453e8i	0.0213913	+	0.674145i
$717$	−2.59892e8			−0.705074
$718$	2.87815e6	+	1.81455e8i	0.00777572	+	0.490225i
$719$		−	3.04978e8i		−	0.820507i	−0.911971	−	0.410254i	$-0.865440\pi$
$719$		−	3.04978e8i		−	0.820507i	0.911971	−	0.410254i	$-0.134560\pi$
$720$	5.55286e7	−	3.52751e6i	0.148771	−	0.00945085i
$721$	−7.26134e8			−1.93736
$722$	2.64827e8	−	4.20056e6i	0.703640	−	0.0111608i
$723$			6.82583e7i			0.180609i
$724$	−5.16915e8	+	1.64022e7i	−1.36208	+	0.0432203i
$725$	6.36995e7			0.167156
$726$	1.84536e6	+	1.16342e8i	0.00482250	+	0.304038i
$727$			5.25666e8i			1.36807i	0.729451	+	0.684033i	$0.239775\pi$
$727$			5.25666e8i			1.36807i	−0.729451	+	0.684033i	$0.760225\pi$
$728$	−9.79761e6	−	2.05761e8i	−0.0253937	−	0.533296i
$729$	−1.43489e7			−0.0370370
$730$	−3.01607e8	+	4.78395e6i	−0.775305	+	0.0122975i
$731$		−	1.54799e7i		−	0.0396294i
$732$	−4.58658e6	−	1.44545e8i	−0.0116938	−	0.368529i
$733$	−6.44853e8			−1.63738			−0.818689	−	0.574237i	$-0.805299\pi$
$733$	−6.44853e8			−1.63738			−0.818689	+	0.574237i	$0.805299\pi$
$734$	6.52805e6	+	4.11565e8i	0.0165080	+	1.04076i
$735$			4.61266e6i			0.0116169i
$736$	−1.27654e7	−	1.60637e8i	−0.0320186	−	0.402914i
$737$	8.63036e8			2.15589
$738$	−1.05225e8	+	1.66903e6i	−0.261788	+	0.00415236i
$739$		−	3.90307e8i		−	0.967104i	−0.875316	−	0.483552i	$-0.839346\pi$
$739$		−	3.90307e8i		−	0.967104i	0.875316	−	0.483552i	$-0.160654\pi$
$740$	−6.29856e7	+	1.99860e6i	−0.155434	+	0.00493208i
$741$	−6.98547e7			−0.171688
$742$	9.50864e6	+	5.99479e8i	0.0232759	+	1.46745i
$743$			2.19194e8i			0.534395i	0.963642	+	0.267197i	$0.0860976\pi$
$743$			2.19194e8i			0.534395i	−0.963642	+	0.267197i	$0.913902\pi$
$744$	3.06593e8	−	1.45989e7i	0.744463	−	0.0354487i
$745$	−8.85245e7			−0.214089
$746$	9.91722e7	−	1.57302e6i	0.238877	−	0.00378895i
$747$			2.37030e8i			0.568644i
$748$	1.31561e7	+	4.14612e8i	0.0314355	+	0.990687i
$749$	−5.62285e8			−1.33817
$750$	345508.	+	2.17828e7i	0.000818982	+	0.0516333i
$751$			4.78886e8i			1.13061i	0.824883	+	0.565304i	$0.191241\pi$
$751$			4.78886e8i			1.13061i	−0.824883	+	0.565304i	$0.808759\pi$
$752$	3.78416e7	+	5.95686e8i	0.0889847	+	1.40076i
$753$	2.85388e8			0.668422
$754$	1.95708e8	−	3.10422e6i	0.456556	−	0.00724168i
$755$		−	6.08265e7i		−	0.141336i
$756$	8.12210e7	−	2.57723e6i	0.187976	−	0.00596468i
$757$	−4.57136e8			−1.05380			−0.526900	−	0.849927i	$-0.676646\pi$
$757$	−4.57136e8			−1.05380			−0.526900	+	0.849927i	$0.676646\pi$
$758$	1.27892e7	+	8.06305e8i	0.0293654	+	1.85136i
$759$			1.26072e8i			0.288331i
$760$	5.08237e6	+	1.06735e8i	0.0115778	+	0.243146i
$761$	5.21113e8			1.18244			0.591218	−	0.806512i	$-0.298647\pi$
$761$	5.21113e8			1.18244			0.591218	+	0.806512i	$0.298647\pi$
$762$	−8.80207e7	+	1.39614e6i	−0.198939	+	0.00315548i
$763$		−	5.32305e8i		−	1.19836i
$764$	7.55976e6	+	2.38245e8i	0.0169523	+	0.534249i
$765$	−5.35377e7			−0.119585
$766$	6.83867e6	+	4.31148e8i	0.0152155	+	0.959269i
$767$			4.19267e8i			0.929189i
$768$	−3.30945e7	−	2.59429e8i	−0.0730587	−	0.572709i
$769$	4.13541e7			0.0909367			0.0454683	−	0.998966i	$-0.485522\pi$
$769$	4.13541e7			0.0909367			0.0454683	+	0.998966i	$0.485522\pi$
$770$	2.46496e8	−	3.90980e6i	0.539930	−	0.00856411i
$771$			7.79888e7i			0.170164i
$772$	1.63228e8	−	5.17940e6i	0.354767	−	0.0112571i
$773$	4.87592e8			1.05565			0.527823	−	0.849354i	$-0.323008\pi$
$773$	4.87592e8			1.05565			0.527823	+	0.849354i	$0.323008\pi$
$774$	−121095.	−	7.63453e6i	−0.000261159	−	0.0164649i
$775$			1.20180e8i			0.258182i
$776$	2.93453e8	−	1.39732e7i	0.627991	−	0.0299027i
$777$	−9.20355e7			−0.196197
$778$	−1.30870e7	+	207580.i	−0.0277908	+	0.000440804i
$779$		−	2.02108e8i		−	0.427534i
$780$	2.12305e6	+	6.69078e7i	0.00447380	+	0.140991i
$781$	−3.33049e8			−0.699126
$782$	2.45907e6	+	1.55034e8i	0.00514223	+	0.324195i
$783$			7.72139e7i			0.160846i
$784$	2.16376e7	−	1.37455e6i	0.0449015	−	0.00285241i
$785$	−2.80954e8			−0.580800
$786$	2.34361e8	−	3.71732e6i	0.482634	−	0.00765531i
$787$			2.13319e8i			0.437628i	0.975767	+	0.218814i	$0.0702188\pi$
$787$			2.13319e8i			0.437628i	−0.975767	+	0.218814i	$0.929781\pi$
$788$	−8.05358e8	+	2.55548e7i	−1.64593	+	0.0522269i
$789$	−4.55699e8			−0.927785
$790$	2.20932e6	+	1.39288e8i	0.00448102	+	0.282509i
$791$			5.89764e8i			1.19165i
$792$	9.73180e6	+	2.04379e8i	0.0195893	+	0.411396i
$793$	1.73991e8			0.348905
$794$	−4.12162e8	+	6.53752e6i	−0.823392	+	0.0130603i
$795$		−	1.94836e8i		−	0.387764i
$796$	−4.21559e6	−	1.32854e8i	−0.00835832	−	0.263411i
$797$	1.05081e8			0.207563			0.103782	−	0.994600i	$-0.466906\pi$
$797$	1.05081e8			0.207563			0.103782	+	0.994600i	$0.466906\pi$
$798$	2.47506e6	+	1.56042e8i	0.00487055	+	0.307067i
$799$		−	5.74329e8i		−	1.12595i
$800$	1.02078e8	−	8.11191e6i	0.199371	−	0.0158436i
$801$	2.79136e8			0.543148
$802$	−3.97654e8	+	6.30740e6i	−0.770873	+	0.0122272i
$803$		−	1.10926e9i		−	2.14233i
$804$	5.23290e8	−	1.66045e7i	1.00687	−	0.0319491i
$805$	9.21479e7			0.176644
$806$	5.85663e6	+	3.69235e8i	0.0111852	+	0.705176i
$807$		−	3.53424e8i		−	0.672475i
$808$	1.92609e8	−	9.17137e6i	0.365126	−	0.0173860i
$809$	2.69036e8			0.508119			0.254059	−	0.967189i	$-0.418234\pi$
$809$	2.69036e8			0.508119			0.254059	+	0.967189i	$0.418234\pi$
$810$	−2.64042e7	+	418811.i	−0.0496841	+	0.000788066i
$811$		−	4.49639e8i		−	0.842950i	−0.906840	−	0.421475i	$-0.861513\pi$
$811$		−	4.49639e8i		−	0.842950i	0.906840	−	0.421475i	$-0.138487\pi$
$812$	−1.38685e7	−	4.37064e8i	−0.0259037	−	0.816351i
$813$	1.61051e8			0.299704
$814$	−3.67525e6	−	2.31708e8i	−0.00681417	−	0.429604i
$815$			2.57554e8i			0.475769i
$816$	1.59540e7	+	2.51141e8i	0.0293629	+	0.462218i
$817$	1.46638e7			0.0268893
$818$	−2.60149e8	+	4.12636e6i	−0.475294	+	0.00753889i
$819$			9.77667e7i			0.177967i
$820$	−1.93582e8	+	6.14255e6i	−0.351093	+	0.0111406i
$821$	−4.85361e8			−0.877073			−0.438536	−	0.898713i	$-0.644503\pi$
$821$	−4.85361e8			−0.877073			−0.438536	+	0.898713i	$0.644503\pi$
$822$	4.61644e6	+	2.91046e8i	0.00831173	+	0.524018i
$823$		−	1.54487e8i		−	0.277135i	−0.990353	−	0.138568i	$-0.955750\pi$
$823$		−	1.54487e8i		−	0.277135i	0.990353	−	0.138568i	$-0.0442498\pi$
$824$	−5.27539e7	−	1.10789e9i	−0.0942917	−	1.98023i
$825$	−8.01133e7			−0.142673
$826$	9.36562e8	−	1.48553e7i	1.66187	−	0.0263597i
$827$		−	8.90923e8i		−	1.57516i	−0.616215	−	0.787578i	$-0.711335\pi$
$827$		−	8.90923e8i		−	1.57516i	0.616215	−	0.787578i	$-0.288665\pi$
$828$	2.42558e6	+	7.64417e7i	0.00427291	+	0.134660i
$829$	1.13467e9			1.99162			0.995809	−	0.0914624i	$-0.0291541\pi$
$829$	1.13467e9			1.99162			0.995809	+	0.0914624i	$0.0291541\pi$
$830$	6.91834e6	+	4.36171e8i	0.0120995	+	0.762821i
$831$			1.83495e7i			0.0319757i
$832$	3.13226e8	−	2.98972e7i	0.543860	−	0.0519112i
$833$	−2.08618e7			−0.0360925
$834$	5.86880e8	−	9.30881e6i	1.01170	−	0.0160471i
$835$		−	1.57853e8i		−	0.271140i
$836$	−3.92752e8	+	1.24624e7i	−0.672202	+	0.0213296i
$837$	−1.45677e8			−0.248435
$838$	3.69094e6	+	2.32698e8i	0.00627198	+	0.395421i
$839$			5.96120e8i			1.00936i	0.863306	+	0.504682i	$0.168390\pi$
$839$			5.96120e8i			1.00936i	−0.863306	+	0.504682i	$0.831610\pi$
$840$	1.49384e8	−	7.11314e6i	0.252038	−	0.0120012i
$841$	−1.79322e8			−0.301472
$842$	−8.71423e8	+	1.38221e7i	−1.45980	+	0.0231546i
$843$		−	3.36937e8i		−	0.562427i
$844$	2.98951e7	+	9.42140e8i	0.0497247	+	1.56707i
$845$	1.89289e8			0.313730
$846$	−4.49281e6	−	2.83252e8i	−0.00742006	−	0.467802i
$847$			3.12749e8i			0.514690i
$848$	−9.13958e8	+	5.80601e7i	−1.49878	+	0.0952117i
$849$	6.63893e7			0.108486
$850$	−9.85176e7	+	1.56264e6i	−0.160420	+	0.00254450i
$851$		−	8.66199e7i		−	0.140549i
$852$	−2.01940e8	+	6.40776e6i	−0.326515	+	0.0103607i
$853$	−2.27412e8			−0.366409			−0.183204	−	0.983075i	$-0.558647\pi$
$853$	−2.27412e8			−0.366409			−0.183204	+	0.983075i	$0.558647\pi$
$854$	−6.16478e6	−	3.88663e8i	−0.00989792	−	0.624021i
$855$		−	5.07151e7i		−	0.0811407i
$856$	−4.08503e7	−	8.57901e8i	−0.0651289	−	1.36778i
$857$	4.29555e8			0.682459			0.341230	−	0.939980i	$-0.389157\pi$
$857$	4.29555e8			0.682459			0.341230	+	0.939980i	$0.389157\pi$
$858$	−2.46137e8	+	3.90411e6i	−0.389686	+	0.00618101i
$859$		−	1.64716e7i		−	0.0259870i	−0.999916	−	0.0129935i	$-0.995864\pi$
$859$		−	1.64716e7i		−	0.0259870i	0.999916	−	0.0129935i	$-0.00413607\pi$
$860$	−445668.	−	1.40452e7i	−0.000700674	−	0.0220817i
$861$	−2.82865e8			−0.443169
$862$	−1.80715e7	−	1.13933e9i	−0.0282145	−	1.77880i
$863$		−	6.68021e8i		−	1.03934i	−0.854367	−	0.519670i	$-0.826055\pi$
$863$		−	6.68021e8i		−	1.03934i	0.854367	−	0.519670i	$-0.173945\pi$
$864$	9.83292e6	+	1.23735e8i	0.0152455	+	0.191845i
$865$	−1.34361e8			−0.207599
$866$	−1.15782e9	+	1.83648e7i	−1.78274	+	0.0282769i
$867$			1.34131e8i			0.205812i
$868$	8.24593e8	−	2.61652e7i	1.26090	−	0.0400096i
$869$	−5.12277e8			−0.780630
$870$	2.25369e6	+	1.42085e8i	0.00342245	+	0.215770i
$871$			6.29889e8i			0.953257i
$872$	8.12160e8	−	3.86722e7i	1.22488	−	0.0583243i
$873$	−1.39433e8			−0.209567
$874$	−1.46860e8	+	2.32942e6i	−0.219973	+	0.00348911i
$875$			5.85562e7i			0.0874075i
$876$	−2.13417e7	−	6.72582e8i	−0.0317481	−	1.00054i
$877$	5.13857e8			0.761805			0.380902	−	0.924615i	$-0.375613\pi$
$877$	5.13857e8			0.761805			0.380902	+	0.924615i	$0.375613\pi$
$878$	−1.29144e7	−	8.14195e8i	−0.0190805	−	1.20294i
$879$		−	3.81699e8i		−	0.562023i
$880$	2.38734e7	+	3.75804e8i	0.0350320	+	0.551460i
$881$	−9.06780e7			−0.132609			−0.0663047	−	0.997799i	$-0.521121\pi$
$881$	−9.06780e7			−0.132609			−0.0663047	+	0.997799i	$0.521121\pi$
$882$	−1.02888e7	+	163196.i	−0.0149955	+	0.000237851i
$883$		−	6.91985e8i		−	1.00511i	−0.864545	−	0.502556i	$-0.832393\pi$
$883$		−	6.91985e8i		−	1.00511i	0.864545	−	0.502556i	$-0.167607\pi$
$884$	−3.02606e8	+	9.60199e6i	−0.438046	+	0.0138997i
$885$	−3.04391e8			−0.439139
$886$	−6.90251e6	−	4.35173e8i	−0.00992443	−	0.625692i
$887$			4.18647e8i			0.599898i	0.953955	+	0.299949i	$0.0969697\pi$
$887$			4.18647e8i			0.599898i	−0.953955	+	0.299949i	$0.903030\pi$
$888$	−6.68642e6	−	1.40422e8i	−0.00954893	−	0.200538i
$889$	−2.36616e8			−0.336774
$890$	5.13653e8	−	8.14732e6i	0.728618	−	0.0115570i
$891$		−	9.71100e7i		−	0.137287i
$892$	−1.56852e7	−	4.94319e8i	−0.0221002	−	0.696486i
$893$	5.44048e8			0.763982
$894$	−3.13200e6	−	1.97459e8i	−0.00438338	−	0.276353i
$895$		−	2.16250e8i		−	0.301638i
$896$	−7.78828e7	−	6.98627e8i	−0.108272	−	0.971229i
$897$	−9.20138e7			−0.127490
$898$	1.12710e9	−	1.78775e7i	1.55644	−	0.0246875i
$899$			7.83911e8i			1.07892i
$900$	−4.85756e7	+	1.54135e6i	−0.0666331	+	0.00211434i
$901$	8.81189e8			1.20474
$902$	−1.12956e7	−	7.12139e8i	−0.0153918	−	0.970387i
$903$		−	2.05230e7i		−	0.0278727i
$904$	−8.99826e8	+	4.28466e7i	−1.21802	+	0.0579977i
$905$	4.51734e8			0.609448
$906$	1.35677e8	−	2.15205e6i	0.182441	−	0.00289379i
$907$			2.05308e7i			0.0275159i	0.999905	+	0.0137579i	$0.00437943\pi$
$907$			2.05308e7i			0.0275159i	−0.999905	+	0.0137579i	$0.995621\pi$
$908$	3.76816e7	+	1.18753e9i	0.0503352	+	1.58631i
$909$	−9.15177e7			−0.121847
$910$	2.85358e6	+	1.79906e8i	0.00378674	+	0.238738i
$911$			4.59638e8i			0.607940i	0.952682	+	0.303970i	$0.0983123\pi$
$911$			4.59638e8i			0.607940i	−0.952682	+	0.303970i	$0.901688\pi$
$912$	−2.37900e8	+	1.51128e7i	−0.313624	+	0.0199233i
$913$	−1.60416e9			−2.10783
$914$	−5.15162e8	+	8.17126e6i	−0.674692	+	0.0107016i
$915$			1.26319e8i			0.164894i
$916$	9.96920e8	−	3.16333e7i	1.29710	−	0.0411584i
$917$	6.30006e8			0.817027
$918$	−1.89417e6	−	1.19419e8i	−0.00244844	−	0.154364i
$919$			1.30912e9i			1.68669i	0.537375	+	0.843344i	$0.319416\pi$
$919$			1.30912e9i			1.68669i	−0.537375	+	0.843344i	$0.680584\pi$
$920$	6.69459e6	+	1.40594e8i	0.00859726	+	0.180552i
$921$	5.80113e6			0.00742564
$922$	−3.06229e8	+	4.85725e6i	−0.390709	+	0.00619724i
$923$		−	2.43077e8i		−	0.309128i
$924$	1.74421e7	+	5.49685e8i	0.0221096	+	0.696783i
$925$	5.50434e7			0.0695472
$926$	−1.29442e7	−	8.16078e8i	−0.0163021	−	1.02778i
$927$			5.26412e8i			0.660825i
$928$	6.65839e8	−	5.29126e7i	0.833153	−	0.0662087i
$929$	−7.99235e8			−0.996845			−0.498422	−	0.866934i	$-0.666087\pi$
$929$	−7.99235e8			−0.996845			−0.498422	+	0.866934i	$0.666087\pi$
$930$	−2.68067e8	+	4.25196e6i	−0.333269	+	0.00528616i
$931$		−	1.97619e7i		−	0.0244895i
$932$	4.25077e8	−	1.34881e7i	0.525073	−	0.0166611i
$933$	7.18707e7			0.0884926
$934$	5.96731e6	+	3.76213e8i	0.00732383	+	0.461736i
$935$		−	3.62331e8i		−	0.443272i
$936$	−1.49166e8	+	7.10279e6i	−0.181905	+	0.00866166i
$937$	−9.78066e8			−1.18891			−0.594456	−	0.804128i	$-0.702633\pi$
$937$	−9.78066e8			−1.18891			−0.594456	+	0.804128i	$0.702633\pi$
$938$	1.40705e9	−	2.23180e7i	1.70491	−	0.0270425i
$939$			5.52155e8i			0.666905i
$940$	−1.65349e7	−	5.21097e8i	−0.0199076	−	0.627386i
$941$	−2.94969e8			−0.354004			−0.177002	−	0.984210i	$-0.556640\pi$
$941$	−2.94969e8			−0.354004			−0.177002	+	0.984210i	$0.556640\pi$
$942$	−9.94018e6	−	6.26685e8i	−0.0118916	−	0.749715i
$943$		−	2.66220e8i		−	0.317472i
$944$	9.07069e7	+	1.42787e9i	0.107826	+	1.69736i
$945$	−7.09794e7			−0.0841079
$946$	5.16687e7	−	819544.i	0.0610315	−	0.000968053i
$947$			5.93617e8i			0.698966i	0.936943	+	0.349483i	$0.113643\pi$
$947$			5.93617e8i			0.698966i	−0.936943	+	0.349483i	$0.886357\pi$
$948$	−3.10612e8	+	9.85603e6i	−0.364580	+	0.0115685i
$949$	8.09595e8			0.947260
$950$	−1.48025e6	−	9.33235e7i	−0.00172649	−	0.108848i
$951$			5.63638e8i			0.655328i
$952$	3.21708e7	+	6.75623e8i	0.0372865	+	0.783057i
$953$	9.10574e7			0.105205			0.0526025	−	0.998616i	$-0.483248\pi$
$953$	9.10574e7			0.105205			0.0526025	+	0.998616i	$0.483248\pi$
$954$	4.34593e8	−	6.89330e6i	0.500538	−	0.00793930i
$955$		−	2.08203e8i		−	0.239044i
$956$	−3.38403e7	−	1.06647e9i	−0.0387312	−	1.22061i
$957$	−5.22565e8			−0.596217
$958$	4.90830e6	+	3.09447e8i	0.00558257	+	0.351957i
$959$			7.82386e8i			0.887085i
$960$	2.17056e7	+	2.27404e8i	0.0245334	+	0.257031i
$961$	−5.91472e8			−0.666445
$962$	1.69113e8	−	2.68239e6i	0.189955	−	0.00301298i
$963$			4.07629e8i			0.456443i
$964$	−2.80100e8	+	8.88787e6i	−0.312667	+	0.00992126i
$965$	−1.42646e8			−0.158736
$966$	3.26020e6	+	2.05541e8i	0.00361670	+	0.228017i
$967$			4.80655e7i			0.0531562i	0.999647	+	0.0265781i	$0.00846107\pi$
$967$			4.80655e7i			0.0531562i	−0.999647	+	0.0265781i	$0.991539\pi$
$968$	−4.77174e8	+	2.27214e7i	−0.526079	+	0.0250500i
$969$	2.29370e8			0.252096
$970$	−2.56579e8	+	4.06973e6i	−0.281129	+	0.00445913i
$971$			2.29463e8i			0.250643i	0.992116	+	0.125321i	$0.0399962\pi$
$971$			2.29463e8i			0.250643i	−0.992116	+	0.125321i	$0.960004\pi$
$972$	−1.86836e6	−	5.88813e7i	−0.00203452	−	0.0641178i
$973$	1.57764e9			1.71265
$974$	3.27120e6	+	2.06235e8i	0.00354022	+	0.223196i
$975$		−	5.84709e7i		−	0.0630850i
$976$	5.92550e8	−	3.76424e7i	0.637347	−	0.0404881i
$977$	4.93252e8			0.528915			0.264457	−	0.964397i	$-0.414807\pi$
$977$	4.93252e8			0.528915			0.264457	+	0.964397i	$0.414807\pi$
$978$	−5.74490e8	+	9.11229e6i	−0.614138	+	0.00974116i
$979$			1.88912e9i			2.01332i
$980$	−1.89282e7	+	600612.i	−0.0201109	+	0.000638140i
$981$	−3.85895e8			−0.408754
$982$	−1.55447e7	−	9.80026e8i	−0.0164153	−	1.03491i
$983$		−	4.15036e8i		−	0.436944i	−0.975843	−	0.218472i	$-0.929893\pi$
$983$		−	4.15036e8i		−	0.436944i	0.975843	−	0.218472i	$-0.0701072\pi$
$984$	−2.05502e7	−	4.31578e8i	−0.0215691	−	0.452975i
$985$	7.03805e8			0.736451
$986$	−6.42614e8	+	1.01928e7i	−0.670377	+	0.0106332i
$987$		−	7.61435e8i		−	0.791920i
$988$	−9.09574e6	−	2.86651e8i	−0.00943121	−	0.297223i
$989$	1.93154e7			0.0199671
$990$	−2.83441e6	−	1.78697e8i	−0.00292117	−	0.184167i
$991$			1.69893e9i			1.74564i	0.488039	+	0.872822i	$0.337713\pi$
$991$			1.69893e9i			1.74564i	−0.488039	+	0.872822i	$0.662287\pi$
$992$	9.98283e7	+	1.25621e9i	0.102263	+	1.28685i
$993$	2.22918e8			0.227665
$994$	−5.42988e8	+	8.61262e6i	−0.552880	+	0.00876952i
$995$			1.16101e8i			0.117860i
$996$	−9.72660e8	+	3.08635e7i	−0.984426	+	0.0312368i
$997$	−1.43910e9			−1.45213			−0.726066	−	0.687625i	$-0.758653\pi$
$997$	−1.43910e9			−1.45213			−0.726066	+	0.687625i	$0.758653\pi$
$998$	4.33322e6	+	2.73191e8i	0.00435933	+	0.274837i
$999$			6.67213e7i			0.0669218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.23	✓	24
3.2	odd	2		180.7.c.b.91.2		24
4.3	odd	2	inner	60.7.c.a.31.24	yes	24
12.11	even	2		180.7.c.b.91.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.23	✓	24	1.1	even	1	trivial
60.7.c.a.31.24	yes	24	4.3	odd	2	inner
180.7.c.b.91.1		24	12.11	even	2
180.7.c.b.91.2		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.99899 - 0.126876i) q^{2} -15.5885i q^{3} +(63.9678 - 2.02976i) q^{4} -55.9017 q^{5} +(-1.97780 - 124.692i) q^{6} -335.195i q^{7} +(511.421 - 24.3521i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(7.99899 - 0.126876i) q^{2} -15.5885i q^{3} +(63.9678 - 2.02976i) q^{4} -55.9017 q^{5} +(-1.97780 - 124.692i) q^{6} -335.195i q^{7} +(511.421 - 24.3521i) q^{8} -243.000 q^{9} +(-447.157 + 7.09260i) q^{10} -1644.57i q^{11} +(-31.6409 - 997.159i) q^{12} +1200.29 q^{13} +(-42.5283 - 2681.22i) q^{14} +871.421i q^{15} +(4087.76 - 259.679i) q^{16} -3941.20 q^{17} +(-1943.76 + 30.8309i) q^{18} -3733.41i q^{19} +(-3575.91 + 113.467i) q^{20} -5225.17 q^{21} +(-208.656 - 13154.9i) q^{22} -4917.71i q^{23} +(-379.611 - 7972.26i) q^{24} +3125.00 q^{25} +(9601.13 - 152.288i) q^{26} +3788.00i q^{27} +(-680.367 - 21441.7i) q^{28} +20383.8 q^{29} +(110.563 + 6970.49i) q^{30} +38457.5i q^{31} +(32665.0 - 2595.81i) q^{32} -25636.2 q^{33} +(-31525.6 + 500.045i) q^{34} +18738.0i q^{35} +(-15544.2 + 493.233i) q^{36} +17613.9 q^{37} +(-473.681 - 29863.5i) q^{38} -18710.7i q^{39} +(-28589.3 + 1361.32i) q^{40} +54135.0 q^{41} +(-41796.1 + 662.950i) q^{42} +3927.72i q^{43} +(-3338.08 - 105199. i) q^{44} +13584.1 q^{45} +(-623.940 - 39336.7i) q^{46} +145724. i q^{47} +(-4048.00 - 63721.9i) q^{48} +5293.27 q^{49} +(24996.9 - 396.488i) q^{50} +61437.2i q^{51} +(76780.0 - 2436.31i) q^{52} -223584. q^{53} +(480.607 + 30300.1i) q^{54} +91934.0i q^{55} +(-8162.69 - 171426. i) q^{56} -58198.1 q^{57} +(163050. - 2586.22i) q^{58} +349304. i q^{59} +(1768.78 + 55742.9i) q^{60} +144957. q^{61} +(4879.34 + 307621. i) q^{62} +81452.4i q^{63} +(260958. - 24908.3i) q^{64} -67098.4 q^{65} +(-205064. + 3252.63i) q^{66} +524780. i q^{67} +(-252110. + 7999.71i) q^{68} -76659.5 q^{69} +(2377.40 + 149885. i) q^{70} -202515. i q^{71} +(-124275. + 5917.55i) q^{72} +674498. q^{73} +(140893. - 2234.78i) q^{74} -48713.9i q^{75} +(-7577.94 - 238818. i) q^{76} -551250. q^{77} +(-2373.94 - 149667. i) q^{78} -311497. i q^{79} +(-228513. + 14516.5i) q^{80} +59049.0 q^{81} +(433025. - 6868.44i) q^{82} -975431. i q^{83} +(-334243. + 10605.9i) q^{84} +220320. q^{85} +(498.335 + 31417.8i) q^{86} -317753. i q^{87} +(-40048.6 - 841065. i) q^{88} -1.14871e6 q^{89} +(108659. - 1723.50i) q^{90} -402332. i q^{91} +(-9981.79 - 314575. i) q^{92} +599492. q^{93} +(18488.9 + 1.16565e6i) q^{94} +208704. i q^{95} +(-40464.7 - 509197. i) q^{96} +573799. q^{97} +(42340.8 - 671.589i) q^{98} +399630. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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