LMFDB - Embedded newform 60.7.f.a.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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, 1]))

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.294917 - 7.99456i) q^{2} +15.5885 q^{3} +(-63.8260 + 4.71546i) q^{4} +(71.1255 - 102.792i) q^{5} +(-4.59730 - 124.623i) q^{6} +496.078 q^{7} +(56.5214 + 508.871i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(-0.294917 - 7.99456i) q^{2} +15.5885 q^{3} +(-63.8260 + 4.71546i) q^{4} +(71.1255 - 102.792i) q^{5} +(-4.59730 - 124.623i) q^{6} +496.078 q^{7} +(56.5214 + 508.871i) q^{8} +243.000 q^{9} +(-842.752 - 538.302i) q^{10} -561.571i q^{11} +(-994.950 + 73.5067i) q^{12} -1584.68i q^{13} +(-146.302 - 3965.93i) q^{14} +(1108.74 - 1602.37i) q^{15} +(4051.53 - 601.938i) q^{16} +4503.06i q^{17} +(-71.6647 - 1942.68i) q^{18} -10102.8i q^{19} +(-4054.95 + 6896.19i) q^{20} +7733.09 q^{21} +(-4489.52 + 165.617i) q^{22} -16192.2 q^{23} +(881.081 + 7932.51i) q^{24} +(-5507.32 - 14622.2i) q^{25} +(-12668.8 + 467.349i) q^{26} +3788.00 q^{27} +(-31662.7 + 2339.24i) q^{28} +2001.00 q^{29} +(-13137.2 - 8391.30i) q^{30} -7380.01i q^{31} +(-6007.10 - 32212.7i) q^{32} -8754.03i q^{33} +(36000.0 - 1328.03i) q^{34} +(35283.8 - 50992.8i) q^{35} +(-15509.7 + 1145.86i) q^{36} +66699.3i q^{37} +(-80767.5 + 2979.48i) q^{38} -24702.8i q^{39} +(56327.9 + 30383.7i) q^{40} -97191.8 q^{41} +(-2280.62 - 61822.7i) q^{42} +112822. q^{43} +(2648.07 + 35842.9i) q^{44} +(17283.5 - 24978.4i) q^{45} +(4775.36 + 129450. i) q^{46} +196416. q^{47} +(63157.1 - 9383.29i) q^{48} +128445. q^{49} +(-115274. + 48341.0i) q^{50} +70195.8i q^{51} +(7472.50 + 101144. i) q^{52} +72076.9i q^{53} +(-1117.14 - 30283.4i) q^{54} +(-57724.9 - 39942.0i) q^{55} +(28039.0 + 252440. i) q^{56} -157487. i q^{57} +(-590.128 - 15997.1i) q^{58} -141896. i q^{59} +(-63210.4 + 107501. i) q^{60} +201436. q^{61} +(-59000.0 + 2176.49i) q^{62} +120547. q^{63} +(-255755. + 57524.2i) q^{64} +(-162892. - 112711. i) q^{65} +(-69984.6 + 2581.71i) q^{66} +216637. q^{67} +(-21234.0 - 287413. i) q^{68} -252412. q^{69} +(-418071. - 267040. i) q^{70} +358449. i q^{71} +(13734.7 + 123656. i) q^{72} +411536. i q^{73} +(533231. - 19670.7i) q^{74} +(-85850.7 - 227938. i) q^{75} +(47639.3 + 644822. i) q^{76} -278583. i q^{77} +(-197488. + 7285.25i) q^{78} +272036. i q^{79} +(226293. - 459277. i) q^{80} +59049.0 q^{81} +(28663.5 + 777005. i) q^{82} -252398. q^{83} +(-493573. + 36465.1i) q^{84} +(462878. + 320283. i) q^{85} +(-33273.2 - 901965. i) q^{86} +31192.5 q^{87} +(285767. - 31740.8i) q^{88} -87241.6 q^{89} +(-204789. - 130807. i) q^{90} -786126. i q^{91} +(1.03349e6 - 76353.9i) q^{92} -115043. i q^{93} +(-57926.2 - 1.57026e6i) q^{94} +(-1.03849e6 - 718567. i) q^{95} +(-93641.4 - 502146. i) q^{96} -130653. i q^{97} +(-37880.4 - 1.02686e6i) q^{98} -136462. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

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 $

$2$	−0.294917	−	7.99456i	−0.0368646	−	0.999320i
$2$	−0.294917	−	7.99456i	−0.0368646	−	0.999320i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−63.8260	+	4.71546i	−0.997282	+	0.0736790i
$5$	71.1255	−	102.792i	0.569004	−	0.822335i
$5$	71.1255	−	102.792i	0.569004	−	0.822335i
$6$	−4.59730	−	124.623i	−0.0212838	−	0.576958i
$7$	496.078			1.44629			0.723146	−	0.690695i	$-0.242695\pi$
$7$	496.078			1.44629			0.723146	+	0.690695i	$0.242695\pi$
$8$	56.5214	+	508.871i	0.110393	+	0.993888i
$9$	243.000			0.333333
$10$	−842.752	−	538.302i	−0.842752	−	0.538302i
$11$		−	561.571i		−	0.421917i	−0.977495	−	0.210958i	$-0.932342\pi$
$11$		−	561.571i		−	0.421917i	0.977495	−	0.210958i	$-0.0676585\pi$
$12$	−994.950	+	73.5067i	−0.575781	+	0.0425386i
$13$		−	1584.68i		−	0.721294i	−0.932702	−	0.360647i	$-0.882556\pi$
$13$		−	1584.68i		−	0.721294i	0.932702	−	0.360647i	$-0.117444\pi$
$14$	−146.302	−	3965.93i	−0.0533169	−	1.44531i
$15$	1108.74	−	1602.37i	0.328515	−	0.474775i
$16$	4051.53	−	601.938i	0.989143	−	0.146958i
$17$			4503.06i			0.916561i	0.888808	+	0.458281i	$0.151535\pi$
$17$			4503.06i			0.916561i	−0.888808	+	0.458281i	$0.848465\pi$
$18$	−71.6647	−	1942.68i	−0.0122882	−	0.333107i
$19$		−	10102.8i		−	1.47293i	−0.676478	−	0.736463i	$-0.736495\pi$
$19$		−	10102.8i		−	1.47293i	0.676478	−	0.736463i	$-0.263505\pi$
$20$	−4054.95	+	6896.19i	−0.506869	+	0.862023i
$21$	7733.09			0.835017
$22$	−4489.52	+	165.617i	−0.421630	+	0.0155538i
$23$	−16192.2			−1.33083			−0.665417	−	0.746472i	$-0.731746\pi$
$23$	−16192.2			−1.33083			−0.665417	+	0.746472i	$0.731746\pi$
$24$	881.081	+	7932.51i	0.0637356	+	0.573821i
$25$	−5507.32	−	14622.2i	−0.352469	−	0.935824i
$26$	−12668.8	+	467.349i	−0.720803	+	0.0265902i
$27$	3788.00			0.192450
$28$	−31662.7	+	2339.24i	−1.44236	+	0.106561i
$29$	2001.00			0.0820451			0.0410225	−	0.999158i	$-0.486938\pi$
$29$	2001.00			0.0820451			0.0410225	+	0.999158i	$0.486938\pi$
$30$	−13137.2	−	8391.30i	−0.486563	−	0.310789i
$31$		−	7380.01i		−	0.247726i	−0.992299	−	0.123863i	$-0.960472\pi$
$31$		−	7380.01i		−	0.247726i	0.992299	−	0.123863i	$-0.0395284\pi$
$32$	−6007.10	−	32212.7i	−0.183322	−	0.983053i
$33$		−	8754.03i		−	0.243594i
$34$	36000.0	−	1328.03i	0.915938	−	0.0337886i
$35$	35283.8	−	50992.8i	0.822946	−	1.18934i
$36$	−15509.7	+	1145.86i	−0.332427	+	0.0245597i
$37$			66699.3i			1.31679i	0.752674	+	0.658394i	$0.228764\pi$
$37$			66699.3i			1.31679i	−0.752674	+	0.658394i	$0.771236\pi$
$38$	−80767.5	+	2979.48i	−1.47192	+	0.0542988i
$39$		−	24702.8i		−	0.416439i
$40$	56327.9	+	30383.7i	0.880123	+	0.474746i
$41$	−97191.8			−1.41019			−0.705095	−	0.709113i	$-0.749096\pi$
$41$	−97191.8			−1.41019			−0.705095	+	0.709113i	$0.749096\pi$
$42$	−2280.62	−	61822.7i	−0.0307826	−	0.834449i
$43$	112822.			1.41902			0.709512	−	0.704693i	$-0.248915\pi$
$43$	112822.			1.41902			0.709512	+	0.704693i	$0.248915\pi$
$44$	2648.07	+	35842.9i	0.0310864	+	0.420770i
$45$	17283.5	−	24978.4i	0.189668	−	0.274112i
$46$	4775.36	+	129450.i	0.0490606	+	1.32993i
$47$	196416.			1.89183			0.945916	−	0.324412i	$-0.105167\pi$
$47$	196416.			1.89183			0.945916	+	0.324412i	$0.105167\pi$
$48$	63157.1	−	9383.29i	0.571082	−	0.0848460i
$49$	128445.			1.09176
$50$	−115274.	+	48341.0i	−0.922194	+	0.386728i
$51$			70195.8i			0.529177i
$52$	7472.50	+	101144.i	0.0531442	+	0.719333i
$53$			72076.9i			0.484137i	0.970259	+	0.242069i	$0.0778260\pi$
$53$			72076.9i			0.484137i	−0.970259	+	0.242069i	$0.922174\pi$
$54$	−1117.14	−	30283.4i	−0.00709459	−	0.192319i
$55$	−57724.9	−	39942.0i	−0.346957	−	0.240072i
$56$	28039.0	+	252440.i	0.159661	+	1.43745i
$57$		−	157487.i		−	0.850394i
$58$	−590.128	−	15997.1i	−0.00302456	−	0.0819893i
$59$		−	141896.i		−	0.690898i	−0.938438	−	0.345449i	$-0.887727\pi$
$59$		−	141896.i		−	0.690898i	0.938438	−	0.345449i	$-0.112273\pi$
$60$	−63210.4	+	107501.i	−0.292641	+	0.497689i
$61$	201436.			0.887457			0.443728	−	0.896161i	$-0.353656\pi$
$61$	201436.			0.887457			0.443728	+	0.896161i	$0.353656\pi$
$62$	−59000.0	+	2176.49i	−0.247558	+	0.00913233i
$63$	120547.			0.482097
$64$	−255755.	+	57524.2i	−0.975627	+	0.219437i
$65$	−162892.	−	112711.i	−0.593145	−	0.410419i
$66$	−69984.6	+	2581.71i	−0.243428	+	0.00897998i
$67$	216637.			0.720293			0.360146	−	0.932896i	$-0.382727\pi$
$67$	216637.			0.720293			0.360146	+	0.932896i	$0.382727\pi$
$68$	−21234.0	−	287413.i	−0.0675313	−	0.914070i
$69$	−252412.			−0.768357
$70$	−418071.	−	267040.i	−1.21887	−	0.778542i
$71$			358449.i			1.00150i	0.865591	+	0.500751i	$0.166943\pi$
$71$			358449.i			1.00150i	−0.865591	+	0.500751i	$0.833057\pi$
$72$	13734.7	+	123656.i	0.0367978	+	0.331296i
$73$			411536.i			1.05789i	0.848657	+	0.528944i	$0.177412\pi$
$73$			411536.i			1.05789i	−0.848657	+	0.528944i	$0.822588\pi$
$74$	533231.	−	19670.7i	1.31589	−	0.0485428i
$75$	−85850.7	−	227938.i	−0.203498	−	0.540298i
$76$	47639.3	+	644822.i	0.108524	+	1.46892i
$77$		−	278583.i		−	0.610215i
$78$	−197488.	+	7285.25i	−0.416156	+	0.0153519i
$79$			272036.i			0.551754i	0.961193	+	0.275877i	$0.0889683\pi$
$79$			272036.i			0.551754i	−0.961193	+	0.275877i	$0.911032\pi$
$80$	226293.	−	459277.i	0.441978	−	0.897026i
$81$	59049.0			0.111111
$82$	28663.5	+	777005.i	0.0519861	+	1.40923i
$83$	−252398.			−0.441419			−0.220709	−	0.975340i	$-0.570837\pi$
$83$	−252398.			−0.441419			−0.220709	+	0.975340i	$0.570837\pi$
$84$	−493573.	+	36465.1i	−0.832748	+	0.0615233i
$85$	462878.	+	320283.i	0.753720	+	0.521527i
$86$	−33273.2	−	901965.i	−0.0523117	−	1.41806i
$87$	31192.5			0.0473688
$88$	285767.	−	31740.8i	0.419338	−	0.0465768i
$89$	−87241.6			−0.123752			−0.0618762	−	0.998084i	$-0.519708\pi$
$89$	−87241.6			−0.123752			−0.0618762	+	0.998084i	$0.519708\pi$
$90$	−204789.	−	130807.i	−0.280917	−	0.179434i
$91$		−	786126.i		−	1.04320i
$92$	1.03349e6	−	76353.9i	1.32722	−	0.0980545i
$93$		−	115043.i		−	0.143025i
$94$	−57926.2	−	1.57026e6i	−0.0697416	−	1.89055i
$95$	−1.03849e6	−	718567.i	−1.21124	−	0.838101i
$96$	−93641.4	−	502146.i	−0.105841	−	0.567566i
$97$		−	130653.i		−	0.143154i	−0.997435	−	0.0715771i	$-0.977197\pi$
$97$		−	130653.i		−	0.143154i	0.997435	−	0.0715771i	$-0.0228032\pi$
$98$	−37880.4	−	1.02686e6i	−0.0402473	−	1.09102i
$99$		−	136462.i		−	0.140639i
$100$	420461.	+	907310.i	0.420461	+	0.907310i
$101$	−1.08656e6			−1.05460			−0.527300	−	0.849679i	$-0.676796\pi$
$101$	−1.08656e6			−1.05460			−0.527300	+	0.849679i	$0.676796\pi$
$102$	561185.	−	20701.9i	0.528817	−	0.0195079i
$103$	−1.78249e6			−1.63123			−0.815616	−	0.578594i	$-0.803602\pi$
$103$	−1.78249e6			−1.63123			−0.815616	+	0.578594i	$0.803602\pi$
$104$	806398.	−	89568.5i	0.716885	−	0.0796260i
$105$	550020.	−	794899.i	0.475128	−	0.686664i
$106$	576224.	−	21256.7i	0.483808	−	0.0178475i
$107$	558410.			0.455829			0.227915	−	0.973681i	$-0.426809\pi$
$107$	558410.			0.455829			0.227915	+	0.973681i	$0.426809\pi$
$108$	−241773.	+	17862.1i	−0.191927	+	0.0141795i
$109$	−453156.			−0.349920			−0.174960	−	0.984576i	$-0.555980\pi$
$109$	−453156.			−0.349920			−0.174960	+	0.984576i	$0.555980\pi$
$110$	−302295.	+	473265.i	−0.227119	+	0.355571i
$111$			1.03974e6i			0.760248i
$112$	2.00987e6	−	298608.i	1.43059	−	0.212544i
$113$			1.83286e6i			1.27026i	0.772403	+	0.635132i	$0.219054\pi$
$113$			1.83286e6i			1.27026i	−0.772403	+	0.635132i	$0.780946\pi$
$114$	−1.25904e6	+	46445.6i	−0.849816	+	0.0313494i
$115$	−1.15168e6	+	1.66443e6i	−0.757250	+	1.09439i
$116$	−127716.	+	9435.62i	−0.0818221	+	0.00604500i
$117$		−	385078.i		−	0.240431i
$118$	−1.13440e6	+	41847.4i	−0.690428	+	0.0254696i
$119$			2.23387e6i			1.32562i
$120$	878064.	+	473636.i	0.508139	+	0.274095i
$121$	1.45620e6			0.821986
$122$	−59406.8	−	1.61039e6i	−0.0327157	−	0.886853i
$123$	−1.51507e6			−0.814174
$124$	34800.2	+	471037.i	0.0182522	+	0.247053i
$125$	−1.89476e6	−	473907.i	−0.970116	−	0.242640i
$126$	−35551.3	−	963720.i	−0.0177723	−	0.481770i
$127$	1.99686e6			0.974847			0.487423	−	0.873166i	$-0.337937\pi$
$127$	1.99686e6			0.974847			0.487423	+	0.873166i	$0.337937\pi$
$128$	535307.	+	2.02768e6i	0.255254	+	0.966874i
$129$	1.75873e6			0.819274
$130$	−853038.	+	1.33549e6i	−0.388274	+	0.607872i
$131$		−	596204.i		−	0.265205i	−0.991169	−	0.132602i	$-0.957667\pi$
$131$		−	596204.i		−	0.265205i	0.991169	−	0.132602i	$-0.0423333\pi$
$132$	41279.3	+	558735.i	0.0179478	+	0.242932i
$133$		−	5.01178e6i		−	2.13028i
$134$	−63890.0	−	1.73192e6i	−0.0265533	−	0.719803i
$135$	269423.	−	389375.i	0.109505	−	0.158258i
$136$	−2.29148e6	+	254519.i	−0.910959	+	0.101182i
$137$			4.42870e6i			1.72232i	0.508332	+	0.861161i	$0.330262\pi$
$137$			4.42870e6i			1.72232i	−0.508332	+	0.861161i	$0.669738\pi$
$138$	74440.6	+	2.01792e6i	0.0283252	+	0.767835i
$139$			5.04455e6i			1.87836i	0.343431	+	0.939178i	$0.388411\pi$
$139$			5.04455e6i			1.87836i	−0.343431	+	0.939178i	$0.611589\pi$
$140$	−2.01157e6	+	3.42105e6i	−0.733080	+	1.24674i
$141$	3.06182e6			1.09225
$142$	2.86564e6	−	105713.i	1.00082	−	0.0369200i
$143$	−889912.			−0.304326
$144$	984522.	−	146271.i	0.329714	−	0.0489859i
$145$	142322.	−	205686.i	0.0466840	−	0.0674685i
$146$	3.29005e6	−	121369.i	1.05717	−	0.0389986i
$147$	2.00225e6			0.630328
$148$	−314518.	−	4.25715e6i	−0.0970197	−	1.31321i
$149$	−2.31618e6			−0.700185			−0.350093	−	0.936715i	$-0.613850\pi$
$149$	−2.31618e6			−0.700185			−0.350093	+	0.936715i	$0.613850\pi$
$150$	−1.79695e6	+	753561.i	−0.532429	+	0.223277i
$151$		−	5.72844e6i		−	1.66382i	−0.554912	−	0.831909i	$-0.687248\pi$
$151$		−	5.72844e6i		−	1.66382i	0.554912	−	0.831909i	$-0.312752\pi$
$152$	5.14102e6	−	571024.i	1.46392	−	0.162601i
$153$			1.09424e6i			0.305520i
$154$	−2.22715e6	+	82158.8i	−0.609800	+	0.0224953i
$155$	−758605.	−	524907.i	−0.203714	−	0.140957i
$156$	116485.	+	1.57668e6i	0.0306828	+	0.415307i
$157$		−	214345.i		−	0.0553879i	−0.999616	−	0.0276940i	$-0.991184\pi$
$157$		−	214345.i		−	0.0553879i	0.999616	−	0.0276940i	$-0.00881639\pi$
$158$	2.17481e6	−	80228.0i	0.551379	−	0.0203402i
$159$			1.12357e6i			0.279517i
$160$	−3.73846e6	−	1.67366e6i	−0.912710	−	0.408609i
$161$	−8.03262e6			−1.92477
$162$	−17414.5	−	472071.i	−0.00409606	−	0.111036i
$163$	5.13155e6			1.18491			0.592456	−	0.805603i	$-0.298158\pi$
$163$	5.13155e6			1.18491			0.592456	+	0.805603i	$0.298158\pi$
$164$	6.20337e6	−	458304.i	1.40636	−	0.103902i
$165$	−899843.	−	622635.i	−0.200316	−	0.138606i
$166$	74436.2	+	2.01781e6i	0.0162727	+	0.441119i
$167$	3.05651e6			0.656260			0.328130	−	0.944633i	$-0.393582\pi$
$167$	3.05651e6			0.656260			0.328130	+	0.944633i	$0.393582\pi$
$168$	437085.	+	3.93514e6i	0.0921803	+	0.829913i
$169$	2.31559e6			0.479735
$170$	2.42401e6	−	3.79497e6i	0.493387	−	0.772434i
$171$		−	2.45498e6i		−	0.490975i
$172$	−7.20100e6	+	532009.i	−1.41517	+	0.104552i
$173$			5.15201e6i			0.995034i	0.867454	+	0.497517i	$0.165755\pi$
$173$			5.15201e6i			0.995034i	−0.867454	+	0.497517i	$0.834245\pi$
$174$	−9199.18	−	249370.i	−0.00174623	−	0.0473366i
$175$	−2.73206e6	−	7.25378e6i	−0.509773	−	1.35347i
$176$	−338031.	−	2.27522e6i	−0.0620039	−	0.417336i
$177$		−	2.21194e6i		−	0.398890i
$178$	25729.0	+	697459.i	0.00456208	+	0.123668i
$179$			1.97052e6i			0.343576i	0.985134	+	0.171788i	$0.0549543\pi$
$179$			1.97052e6i			0.343576i	−0.985134	+	0.171788i	$0.945046\pi$
$180$	−985353.	+	1.67577e6i	−0.168956	+	0.287341i
$181$	2.34636e6			0.395694			0.197847	−	0.980233i	$-0.436605\pi$
$181$	2.34636e6			0.395694			0.197847	+	0.980233i	$0.436605\pi$
$182$	−6.28474e6	+	231842.i	−1.04249	+	0.0384572i
$183$	3.14007e6			0.512373
$184$	−915208.	−	8.23976e6i	−0.146915	−	1.32270i
$185$	6.85614e6	+	4.74402e6i	1.08284	+	0.749258i
$186$	−919719.	+	33928.1i	−0.142928	+	0.00527255i
$187$	2.52879e6			0.386713
$188$	−1.25364e7	+	926190.i	−1.88669	+	0.139388i
$189$	1.87914e6			0.278339
$190$	−5.43836e6	+	8.51415e6i	−0.792879	+	1.24131i
$191$		−	9.12751e6i		−	1.30994i	−0.755654	−	0.654971i	$-0.772681\pi$
$191$		−	9.12751e6i		−	1.30994i	0.755654	−	0.654971i	$-0.227319\pi$
$192$	−3.98682e6	+	896713.i	−0.563278	+	0.126692i
$193$		−	1.21768e7i		−	1.69379i	−0.531758	−	0.846896i	$-0.678468\pi$
$193$		−	1.21768e7i		−	1.69379i	0.531758	−	0.846896i	$-0.321532\pi$
$194$	−1.04451e6	+	38531.7i	−0.143057	+	0.00527732i
$195$	−2.53924e6	−	1.75700e6i	−0.342452	−	0.236956i
$196$	−8.19811e6	+	605675.i	−1.08879	+	0.0804399i
$197$		−	5.33007e6i		−	0.697162i	−0.937279	−	0.348581i	$-0.886664\pi$
$197$		−	5.33007e6i		−	0.697162i	0.937279	−	0.348581i	$-0.113336\pi$
$198$	−1.09095e6	+	40244.9i	−0.140543	+	0.00518459i
$199$		−	1.70499e6i		−	0.216353i	−0.994132	−	0.108177i	$-0.965499\pi$
$199$		−	1.70499e6i		−	0.216353i	0.994132	−	0.108177i	$-0.0345012\pi$
$200$	7.12955e6	−	3.62899e6i	0.891194	−	0.453623i
$201$	3.37704e6			0.415861
$202$	320444.	+	8.68654e6i	0.0388774	+	1.05388i
$203$	992651.			0.118661
$204$	−331006.	−	4.48032e6i	−0.0389892	−	0.527739i
$205$	−6.91281e6	+	9.99052e6i	−0.802404	+	1.15965i
$206$	525686.	+	1.42502e7i	0.0601347	+	1.63012i
$207$	−3.93472e6			−0.443611
$208$	−953881.	−	6.42039e6i	−0.106000	−	0.713463i
$209$	−5.67344e6			−0.621452
$210$	−6.51708e6	−	4.16274e6i	−0.703712	−	0.449492i
$211$			1.25661e7i			1.33768i	0.743407	+	0.668840i	$0.233209\pi$
$211$			1.25661e7i			1.33768i	−0.743407	+	0.668840i	$0.766791\pi$
$212$	−339876.	−	4.60039e6i	−0.0356708	−	0.482822i
$213$			5.58766e6i			0.578218i
$214$	−164685.	−	4.46425e6i	−0.0168040	−	0.455519i
$215$	8.02455e6	−	1.15972e7i	0.807430	−	1.16691i
$216$	214103.	+	1.92760e6i	0.0212452	+	0.191274i
$217$		−	3.66106e6i		−	0.358285i
$218$	133643.	+	3.62279e6i	0.0128997	+	0.349682i
$219$			6.41521e6i			0.610771i
$220$	3.87270e6	+	2.27714e6i	0.363702	+	0.213856i
$221$	7.13593e6			0.661110
$222$	8.31225e6	−	306636.i	0.759731	−	0.0280262i
$223$	−4.78645e6			−0.431617			−0.215809	−	0.976436i	$-0.569239\pi$
$223$	−4.78645e6			−0.431617			−0.215809	+	0.976436i	$0.569239\pi$
$224$	−2.97999e6	−	1.59800e7i	−0.265137	−	1.42178i
$225$	−1.33828e6	−	3.55321e6i	−0.117490	−	0.311941i
$226$	1.46529e7	−	540541.i	1.26940	−	0.0468278i
$227$	−178099.			−0.0152259			−0.00761296	−	0.999971i	$-0.502423\pi$
$227$	−178099.			−0.0152259			−0.00761296	+	0.999971i	$0.502423\pi$
$228$	742624.	+	1.00518e7i	0.0626562	+	0.848083i
$229$	−1.01777e6			−0.0847505			−0.0423753	−	0.999102i	$-0.513493\pi$
$229$	−1.01777e6			−0.0847505			−0.0423753	+	0.999102i	$0.513493\pi$
$230$	1.36460e7	+	8.71632e6i	1.12156	+	0.716391i
$231$		−	4.34268e6i		−	0.352308i
$232$	113099.	+	1.01825e6i	0.00905723	+	0.0815436i
$233$		−	2.23582e6i		−	0.176754i	−0.996087	−	0.0883769i	$-0.971832\pi$
$233$		−	2.23582e6i		−	0.176754i	0.996087	−	0.0883769i	$-0.0281680\pi$
$234$	−3.07853e6	+	113566.i	−0.240268	+	0.00886340i
$235$	1.39702e7	−	2.01899e7i	1.07646	−	1.55572i
$236$	669104.	+	9.05665e6i	0.0509047	+	0.689020i
$237$			4.24063e6i			0.318555i
$238$	1.78588e7	−	658806.i	1.32471	−	0.0488682i
$239$			2.49242e7i			1.82569i	0.408305	+	0.912846i	$0.366120\pi$
$239$			2.49242e7i			1.82569i	−0.408305	+	0.912846i	$0.633880\pi$
$240$	3.52755e6	−	7.15942e6i	0.255176	−	0.517898i
$241$	−5.64081e6			−0.402986			−0.201493	−	0.979490i	$-0.564579\pi$
$241$	−5.64081e6			−0.402986			−0.201493	+	0.979490i	$0.564579\pi$
$242$	−429457.	−	1.16417e7i	−0.0303022	−	0.821428i
$243$	920483.			0.0641500
$244$	−1.28569e7	+	949862.i	−0.885045	+	0.0653870i
$245$	9.13568e6	−	1.32031e7i	0.621216	−	0.897793i
$246$	446819.	+	1.21123e7i	0.0300142	+	0.813621i
$247$	−1.60097e7			−1.06241
$248$	3.75547e6	−	417129.i	0.246212	−	0.0273473i
$249$	−3.93449e6			−0.254853
$250$	−3.22988e6	+	1.52875e7i	−0.206712	+	0.978402i
$251$			8.24054e6i			0.521116i	0.965458	+	0.260558i	$0.0839066\pi$
$251$			8.24054e6i			0.521116i	−0.965458	+	0.260558i	$0.916093\pi$
$252$	−7.69404e6	+	568434.i	−0.480787	+	0.0355205i
$253$			9.09310e6i			0.561501i
$254$	−588907.	−	1.59640e7i	−0.0359373	−	0.974184i
$255$	7.21556e6	+	4.99271e6i	0.435160	+	0.301104i
$256$	1.60526e7	−	4.87754e6i	0.956807	−	0.290724i
$257$			1.29601e7i			0.763501i	0.924265	+	0.381750i	$0.124679\pi$
$257$			1.29601e7i			0.763501i	−0.924265	+	0.381750i	$0.875321\pi$
$258$	−518678.	−	1.40602e7i	−0.0302022	−	0.818717i
$259$			3.30880e7i			1.90446i
$260$	1.09283e7	+	6.42581e6i	0.621772	+	0.365601i
$261$	486242.			0.0273484
$262$	−4.76639e6	+	175830.i	−0.265024	+	0.00977665i
$263$	−6.15939e6			−0.338587			−0.169294	−	0.985566i	$-0.554149\pi$
$263$	−6.15939e6			−0.338587			−0.169294	+	0.985566i	$0.554149\pi$
$264$	4.45467e6	−	494790.i	0.242105	−	0.0268911i
$265$	7.40892e6	+	5.12651e6i	0.398123	+	0.275476i
$266$	−4.00670e7	+	1.47806e6i	−2.12883	+	0.0785319i
$267$	−1.35996e6			−0.0714485
$268$	−1.38271e7	+	1.02154e6i	−0.718335	+	0.0530705i
$269$	2.56743e6			0.131899			0.0659494	−	0.997823i	$-0.478992\pi$
$269$	2.56743e6			0.131899			0.0659494	+	0.997823i	$0.478992\pi$
$270$	−3.19234e6	−	2.03909e6i	−0.162188	−	0.103596i
$271$			9.66745e6i			0.485740i	0.970059	+	0.242870i	$0.0780888\pi$
$271$			9.66745e6i			0.485740i	−0.970059	+	0.242870i	$0.921911\pi$
$272$	2.71057e6	+	1.82443e7i	0.134696	+	0.906610i
$273$		−	1.22545e7i		−	0.602293i
$274$	3.54055e7	−	1.30610e6i	1.72115	−	0.0634927i
$275$	−8.21143e6	+	3.09275e6i	−0.394840	+	0.148712i
$276$	1.61105e7	−	1.19024e6i	0.766269	−	0.0566118i
$277$			1.59611e7i			0.750972i	0.926828	+	0.375486i	$0.122524\pi$
$277$			1.59611e7i			0.750972i	−0.926828	+	0.375486i	$0.877476\pi$
$278$	4.03290e7	−	1.48772e6i	1.87708	−	0.0692448i
$279$		−	1.79334e6i		−	0.0825754i
$280$	2.79430e7	+	1.50727e7i	1.27291	+	0.686621i
$281$	−4.28821e7			−1.93267			−0.966334	−	0.257290i	$-0.917170\pi$
$281$	−4.28821e7			−1.93267			−0.966334	+	0.257290i	$0.917170\pi$
$282$	−902981.	−	2.44779e7i	−0.0402653	−	1.09151i
$283$	6.36296e6			0.280737			0.140369	−	0.990099i	$-0.455171\pi$
$283$	6.36296e6			0.280737			0.140369	+	0.990099i	$0.455171\pi$
$284$	−1.69025e6	−	2.28784e7i	−0.0737898	−	0.998781i
$285$	−1.61884e7	−	1.12013e7i	−0.699309	−	0.483878i
$286$	262450.	+	7.11446e6i	0.0112188	+	0.304119i
$287$	−4.82147e7			−2.03955
$288$	−1.45972e6	−	7.82768e6i	−0.0611073	−	0.327684i
$289$	3.85998e6			0.159916
$290$	−1.68634e6	−	1.07714e6i	−0.0691437	−	0.0441651i
$291$		−	2.03668e6i		−	0.0826501i
$292$	−1.94058e6	−	2.62667e7i	−0.0779441	−	1.05501i
$293$		−	1.17997e7i		−	0.469102i	−0.972104	−	0.234551i	$-0.924638\pi$
$293$		−	1.17997e7i		−	0.469102i	0.972104	−	0.234551i	$-0.0753620\pi$
$294$	−590497.	−	1.60071e7i	−0.0232368	−	0.629900i
$295$	−1.45857e7	−	1.00924e7i	−0.568149	−	0.393124i
$296$	−3.39413e7	+	3.76993e6i	−1.30874	+	0.145365i
$297$		−	2.12723e6i		−	0.0811979i
$298$	683079.	+	1.85168e7i	0.0258120	+	0.699709i
$299$			2.56596e7i			0.959922i
$300$	6.55434e6	+	1.41436e7i	0.242753	+	0.523836i
$301$	5.59687e7			2.05232
$302$	−4.57964e7	+	1.68941e6i	−1.66269	+	0.0613359i
$303$	−1.69377e7			−0.608874
$304$	−6.08126e6	−	4.09318e7i	−0.216458	−	1.45693i
$305$	1.43272e7	−	2.07060e7i	0.504966	−	0.729786i
$306$	8.74801e6	−	322711.i	0.305313	−	0.0112629i
$307$	−3.47430e7			−1.20075			−0.600374	−	0.799719i	$-0.704982\pi$
$307$	−3.47430e7			−1.20075			−0.600374	+	0.799719i	$0.704982\pi$
$308$	1.31365e6	+	1.77809e7i	0.0449600	+	0.608556i
$309$	−2.77863e7			−0.941792
$310$	−3.97268e6	+	6.21952e6i	−0.133352	+	0.208772i
$311$		−	5.00149e7i		−	1.66272i	−0.555737	−	0.831358i	$-0.687564\pi$
$311$		−	5.00149e7i		−	1.66272i	0.555737	−	0.831358i	$-0.312436\pi$
$312$	1.25705e7	−	1.39623e6i	0.413894	−	0.0459721i
$313$			5.15834e7i			1.68220i	0.540882	+	0.841099i	$0.318091\pi$
$313$			5.15834e7i			1.68220i	−0.540882	+	0.841099i	$0.681909\pi$
$314$	−1.71360e6	+	63214.0i	−0.0553503	+	0.00204185i
$315$	8.57397e6	−	1.23912e7i	0.274315	−	0.396445i
$316$	−1.28278e6	−	1.73630e7i	−0.0406527	−	0.550254i
$317$		−	4.05089e7i		−	1.27166i	−0.771827	−	0.635832i	$-0.780657\pi$
$317$		−	4.05089e7i		−	1.27166i	0.771827	−	0.635832i	$-0.219343\pi$
$318$	8.98244e6	−	331359.i	0.279327	−	0.0103043i
$319$		−	1.12370e6i		−	0.0346162i
$320$	−1.22777e7	+	3.03809e7i	−0.374685	+	0.927152i
$321$	8.70476e6			0.263173
$322$	2.36895e6	+	6.42173e7i	0.0709560	+	1.92347i
$323$	4.54936e7			1.35003
$324$	−3.76886e6	+	278443.i	−0.110809	+	0.00818656i
$325$	−2.31716e7	+	8.72736e6i	−0.675004	+	0.254234i
$326$	−1.51338e6	−	4.10245e7i	−0.0436813	−	1.18411i
$327$	−7.06401e6			−0.202026
$328$	−5.49341e6	−	4.94580e7i	−0.155676	−	1.40157i
$329$	9.74375e7			2.73614
$330$	−4.71231e6	+	7.37747e6i	−0.131127	+	0.205289i
$331$		−	4.67744e7i		−	1.28981i	−0.764264	−	0.644903i	$-0.776898\pi$
$331$		−	4.67744e7i		−	1.28981i	0.764264	−	0.644903i	$-0.223102\pi$
$332$	1.61095e7	−	1.19017e6i	0.440219	−	0.0325233i
$333$			1.62079e7i			0.438929i
$334$	−901415.	−	2.44354e7i	−0.0241928	−	0.655814i
$335$	1.54084e7	−	2.22686e7i	0.409850	−	0.592322i
$336$	3.13309e7	−	4.65484e6i	0.825951	−	0.122712i
$337$		−	4.77282e7i		−	1.24705i	−0.781802	−	0.623527i	$-0.785699\pi$
$337$		−	4.77282e7i		−	1.24705i	0.781802	−	0.623527i	$-0.214301\pi$
$338$	−682906.	−	1.85121e7i	−0.0176852	−	0.479409i
$339$			2.85715e7i			0.733388i
$340$	−3.10540e7	−	1.82597e7i	−0.790097	−	0.464576i
$341$	−4.14440e6			−0.104520
$342$	−1.96265e7	+	724015.i	−0.490642	+	0.0180996i
$343$	5.35543e6			0.132713
$344$	6.37688e6	+	5.74120e7i	0.156651	+	1.41035i
$345$	−1.79529e7	+	2.59459e7i	−0.437198	+	0.631847i
$346$	4.11880e7	−	1.51941e6i	0.994358	−	0.0366815i
$347$	3.93322e7			0.941368			0.470684	−	0.882302i	$-0.344007\pi$
$347$	3.93322e7			0.941368			0.470684	+	0.882302i	$0.344007\pi$
$348$	−1.99089e6	+	147087.i	−0.0472400	+	0.00349008i
$349$	−7.65808e7			−1.80154			−0.900769	−	0.434299i	$-0.856996\pi$
$349$	−7.65808e7			−1.80154			−0.900769	+	0.434299i	$0.856996\pi$
$350$	−5.71850e7	+	2.39809e7i	−1.33376	+	0.559321i
$351$		−	6.00277e6i		−	0.138813i
$352$	−1.80897e7	+	3.37341e6i	−0.414767	+	0.0773466i
$353$		−	1.22834e7i		−	0.279250i	−0.990204	−	0.139625i	$-0.955410\pi$
$353$		−	1.22834e7i		−	0.279250i	0.990204	−	0.139625i	$-0.0445897\pi$
$354$	−1.76835e7	+	652337.i	−0.398619	+	0.0147049i
$355$	3.68456e7	+	2.54949e7i	0.823570	+	0.569859i
$356$	5.56829e6	−	411384.i	0.123416	−	0.00911796i
$357$			3.48226e7i			0.765344i
$358$	1.57535e7	−	581140.i	0.343342	−	0.0126658i
$359$		−	1.10395e7i		−	0.238598i	−0.992858	−	0.119299i	$-0.961935\pi$
$359$		−	1.10395e7i		−	0.238598i	0.992858	−	0.119299i	$-0.0380647\pi$
$360$	1.36877e7	+	7.38325e6i	0.293374	+	0.158249i
$361$	−5.50207e7			−1.16951
$362$	−691982.	−	1.87582e7i	−0.0145871	−	0.395425i
$363$	2.26999e7			0.474574
$364$	3.70695e6	+	5.01753e7i	0.0768621	+	1.04037i
$365$	4.23025e7	+	2.92707e7i	0.869937	+	0.601942i
$366$	−926060.	−	2.51035e7i	−0.0188884	−	0.512025i
$367$	5.87412e7			1.18835			0.594175	−	0.804336i	$-0.297479\pi$
$367$	5.87412e7			1.18835			0.594175	+	0.804336i	$0.297479\pi$
$368$	−6.56034e7	+	9.74673e6i	−1.31638	+	0.195576i
$369$	−2.36176e7			−0.470064
$370$	3.59044e7	−	5.62109e7i	0.708830	−	1.10973i
$371$			3.57558e7i			0.700204i
$372$	542481.	+	7.34274e6i	0.0105379	+	0.142636i
$373$			1.24158e7i			0.239247i	0.992819	+	0.119624i	$0.0381688\pi$
$373$			1.24158e7i			0.239247i	−0.992819	+	0.119624i	$0.961831\pi$
$374$	−745783.	−	2.02166e7i	−0.0142560	−	0.386450i
$375$	−2.95364e7	−	7.38747e6i	−0.560097	−	0.140088i
$376$	1.11017e7	+	9.99501e7i	0.208846	+	1.88027i
$377$		−	3.17095e6i		−	0.0591786i
$378$	−554190.	−	1.50229e7i	−0.0102609	−	0.278150i
$379$			4.18480e7i			0.768701i	0.923187	+	0.384350i	$0.125575\pi$
$379$			4.18480e7i			0.768701i	−0.923187	+	0.384350i	$0.874425\pi$
$380$	6.96708e7	+	4.09663e7i	1.26970	+	0.746580i
$381$	3.11280e7			0.562828
$382$	−7.29704e7	+	2.69185e6i	−1.30905	+	0.0482905i
$383$	−5.12412e7			−0.912058			−0.456029	−	0.889965i	$-0.650729\pi$
$383$	−5.12412e7			−0.912058			−0.456029	+	0.889965i	$0.650729\pi$
$384$	8.34461e6	+	3.16084e7i	0.147371	+	0.558225i
$385$	−2.86361e7	−	1.98144e7i	−0.501801	−	0.347215i
$386$	−9.73480e7	+	3.59113e6i	−1.69264	+	0.0624410i
$387$	2.74158e7			0.473008
$388$	616089.	+	8.33906e6i	0.0105475	+	0.142765i
$389$	4.98250e7			0.846444			0.423222	−	0.906026i	$-0.360899\pi$
$389$	4.98250e7			0.846444			0.423222	+	0.906026i	$0.360899\pi$
$390$	−1.32975e7	+	2.08183e7i	−0.224170	+	0.350955i
$391$		−	7.29147e7i		−	1.21979i
$392$	7.25986e6	+	6.53617e7i	0.120523	+	1.08509i
$393$		−	9.29390e6i		−	0.153116i
$394$	−4.26115e7	+	1.57193e6i	−0.696688	+	0.0257006i
$395$	2.79631e7	+	1.93487e7i	0.453727	+	0.313950i
$396$	643480.	+	8.70982e6i	0.0103621	+	0.140257i
$397$		−	3.92214e7i		−	0.626832i	−0.949616	−	0.313416i	$-0.898527\pi$
$397$		−	3.92214e7i		−	0.626832i	0.949616	−	0.313416i	$-0.101473\pi$
$398$	−1.36307e7	+	502831.i	−0.216206	+	0.00797578i
$399$		−	7.81259e7i		−	1.22992i
$400$	−3.11148e7	−	5.59274e7i	−0.486168	−	0.873865i
$401$	−5.63354e6			−0.0873671			−0.0436836	−	0.999045i	$-0.513909\pi$
$401$	−5.63354e6			−0.0873671			−0.0436836	+	0.999045i	$0.513909\pi$
$402$	−995946.	−	2.69980e7i	−0.0153306	−	0.415579i
$403$	−1.16950e7			−0.178683
$404$	6.93506e7	−	5.12361e6i	1.05173	−	0.0777020i
$405$	4.19989e6	−	6.06976e6i	0.0632227	−	0.0913705i
$406$	−292749.	−	7.93581e6i	−0.00437439	−	0.118581i
$407$	3.74564e7			0.555575
$408$	−3.57206e7	+	3.96757e6i	−0.525942	+	0.0584176i
$409$	−2.95973e7			−0.432596			−0.216298	−	0.976327i	$-0.569398\pi$
$409$	−2.95973e7			−0.432596			−0.216298	+	0.976327i	$0.569398\pi$
$410$	8.19085e7	+	5.23185e7i	1.18844	+	0.759109i
$411$			6.90366e7i			0.994384i
$412$	1.13769e8	−	8.40526e6i	1.62680	−	0.120188i
$413$		−	7.03914e7i		−	0.999240i
$414$	1.16041e6	+	3.14563e7i	0.0163535	+	0.443310i
$415$	−1.79519e7	+	2.59444e7i	−0.251169	+	0.362994i
$416$	−5.10469e7	+	9.51934e6i	−0.709070	+	0.132229i
$417$			7.86367e7i			1.08447i
$418$	1.67319e6	+	4.53567e7i	0.0229096	+	0.621030i
$419$			1.15258e7i			0.156686i	0.996926	+	0.0783428i	$0.0249629\pi$
$419$			1.15258e7i			0.156686i	−0.996926	+	0.0783428i	$0.975037\pi$
$420$	−3.13573e7	+	5.33289e7i	−0.423244	+	0.719804i
$421$	3.57459e7			0.479049			0.239525	−	0.970890i	$-0.423008\pi$
$421$	3.57459e7			0.479049			0.239525	+	0.970890i	$0.423008\pi$
$422$	1.00460e8	−	3.70594e6i	1.33677	−	0.0493130i
$423$	4.77290e7			0.630611
$424$	−3.66778e7	+	4.07389e6i	−0.481178	+	0.0534456i
$425$	6.58449e7	−	2.47998e7i	0.857740	−	0.323059i
$426$	4.46709e7	−	1.64790e6i	0.577825	−	0.0213158i
$427$	9.99279e7			1.28352
$428$	−3.56411e7	+	2.63316e6i	−0.454590	+	0.0335851i
$429$	−1.38724e7			−0.175703
$430$	−9.50812e7	−	6.07325e7i	−1.19588	−	0.763864i
$431$			8.20839e6i			0.102524i	0.998685	+	0.0512621i	$0.0163244\pi$
$431$			8.20839e6i			0.102524i	−0.998685	+	0.0512621i	$0.983676\pi$
$432$	1.53472e7	−	2.28014e6i	0.190361	−	0.0282820i
$433$			4.37930e7i			0.539437i	0.962939	+	0.269719i	$0.0869307\pi$
$433$			4.37930e7i			0.539437i	−0.962939	+	0.269719i	$0.913069\pi$
$434$	−2.92686e7	+	1.07971e6i	−0.358041	+	0.0132080i
$435$	2.21858e6	−	3.20633e6i	0.0269530	−	0.0389530i
$436$	2.89232e7	−	2.13684e6i	0.348969	−	0.0257818i
$437$			1.63587e8i			1.96022i
$438$	5.12868e7	−	1.89195e6i	0.610356	−	0.0225158i
$439$		−	9.07805e7i		−	1.07300i	−0.843901	−	0.536499i	$-0.819746\pi$
$439$		−	9.07805e7i		−	1.07300i	0.843901	−	0.536499i	$-0.180254\pi$
$440$	1.70626e7	−	3.16321e7i	0.200303	−	0.371339i
$441$	3.12120e7			0.363920
$442$	−2.10450e6	−	5.70486e7i	−0.0243715	−	0.660660i
$443$	4.40997e6			0.0507253			0.0253626	−	0.999678i	$-0.491926\pi$
$443$	4.40997e6			0.0507253			0.0253626	+	0.999678i	$0.491926\pi$
$444$	−4.90284e6	−	6.63624e7i	−0.0560143	−	0.758181i
$445$	−6.20511e6	+	8.96773e6i	−0.0704156	+	0.101766i
$446$	1.41160e6	+	3.82655e7i	0.0159114	+	0.431324i
$447$	−3.61056e7			−0.404252
$448$	−1.26874e8	+	2.85365e7i	−1.41104	+	0.317370i
$449$	−7.74897e7			−0.856062			−0.428031	−	0.903764i	$-0.640793\pi$
$449$	−7.74897e7			−0.856062			−0.428031	+	0.903764i	$0.640793\pi$
$450$	−2.80116e7	+	1.17469e7i	−0.307398	+	0.128909i
$451$			5.45801e7i			0.594983i
$452$	−8.64278e6	−	1.16984e8i	−0.0935919	−	1.26681i
$453$		−	8.92976e7i		−	0.960606i
$454$	52524.3	+	1.42382e6i	0.000561297	+	0.0152156i
$455$	−8.08074e7	−	5.59136e7i	−0.857861	−	0.593586i
$456$	8.01405e7	−	8.90139e6i	0.845197	−	0.0938779i
$457$		−	1.64079e8i		−	1.71911i	−0.511045	−	0.859554i	$-0.670741\pi$
$457$		−	1.64079e8i		−	1.71911i	0.511045	−	0.859554i	$-0.329259\pi$
$458$	300157.	+	8.13661e6i	0.00312429	+	0.0846929i
$459$			1.70576e7i			0.176392i
$460$	6.56588e7	−	1.11665e8i	0.674558	−	1.14721i
$461$	−1.26212e8			−1.28824			−0.644121	−	0.764924i	$-0.722777\pi$
$461$	−1.26212e8			−1.28824			−0.644121	+	0.764924i	$0.722777\pi$
$462$	−3.47178e7	+	1.28073e6i	−0.352068	+	0.0129877i
$463$	−3.21664e7			−0.324085			−0.162043	−	0.986784i	$-0.551808\pi$
$463$	−3.21664e7			−0.324085			−0.162043	+	0.986784i	$0.551808\pi$
$464$	8.10710e6	−	1.20448e6i	0.0811543	−	0.0120571i
$465$	−1.18255e7	−	8.18249e6i	−0.117614	−	0.0813817i
$466$	−1.78744e7	+	659380.i	−0.176634	+	0.00651596i
$467$	1.95660e7			0.192110			0.0960551	−	0.995376i	$-0.469377\pi$
$467$	1.95660e7			0.192110			0.0960551	+	0.995376i	$0.469377\pi$
$468$	1.81582e6	+	2.45780e7i	0.0177147	+	0.239778i
$469$	1.07469e8			1.04175
$470$	−1.65530e8	−	1.05731e8i	−1.59434	−	1.01838i
$471$		−	3.34131e6i		−	0.0319782i
$472$	7.22066e7	−	8.02015e6i	0.686675	−	0.0762705i
$473$		−	6.33578e7i		−	0.598710i
$474$	3.39020e7	−	1.25063e6i	0.318339	−	0.0117434i
$475$	−1.47726e8	+	5.56394e7i	−1.37840	+	0.519160i
$476$	−1.05337e7	−	1.42579e8i	−0.0976700	−	1.32201i
$477$			1.75147e7i			0.161379i
$478$	1.99258e8	−	7.35056e6i	1.82445	−	0.0673033i
$479$		−	1.93927e8i		−	1.76454i	−0.470743	−	0.882270i	$-0.656014\pi$
$479$		−	1.93927e8i		−	1.76454i	0.470743	−	0.882270i	$-0.343986\pi$
$480$	−5.82768e7	−	2.60898e7i	−0.526953	−	0.235911i
$481$	1.05697e8			0.949791
$482$	1.66357e6	+	4.50958e7i	0.0148559	+	0.402712i
$483$	−1.25216e8			−1.11127
$484$	−9.29434e7	+	6.86665e6i	−0.819752	+	0.0605632i
$485$	−1.34301e7	−	9.29276e6i	−0.117721	−	0.0814553i
$486$	−271466.	−	7.35886e6i	−0.00236486	−	0.0641064i
$487$	−1.62572e8			−1.40754			−0.703768	−	0.710430i	$-0.748500\pi$
$487$	−1.62572e8			−1.40754			−0.703768	+	0.710430i	$0.748500\pi$
$488$	1.13854e7	+	1.02505e8i	0.0979693	+	0.882033i
$489$	7.99930e7			0.684109
$490$	−1.08247e8	−	6.91420e7i	−0.920083	−	0.587697i
$491$			1.55899e8i			1.31704i	0.752564	+	0.658519i	$0.228817\pi$
$491$			1.55899e8i			1.31704i	−0.752564	+	0.658519i	$0.771183\pi$
$492$	9.67009e7	−	7.14425e6i	0.811961	−	0.0599876i
$493$			9.01062e6i			0.0751993i
$494$	4.72154e6	+	1.27991e8i	0.0391654	+	1.06169i
$495$	−1.40272e7	−	9.70592e6i	−0.115652	−	0.0800241i
$496$	−4.44231e6	−	2.99003e7i	−0.0364053	−	0.245037i
$497$			1.77819e8i			1.44847i
$498$	1.16035e6	+	3.14545e7i	0.00939506	+	0.254680i
$499$		−	5.34345e7i		−	0.430051i	−0.976608	−	0.215026i	$-0.931017\pi$
$499$		−	5.34345e7i		−	0.430051i	0.976608	−	0.215026i	$-0.0689835\pi$
$500$	1.23170e8	+	2.13129e7i	0.985357	+	0.170503i
$501$	4.76462e7			0.378892
$502$	6.58795e7	−	2.43027e6i	0.520762	−	0.0192107i
$503$	−1.13337e8			−0.890565			−0.445283	−	0.895390i	$-0.646897\pi$
$503$	−1.13337e8			−0.890565			−0.445283	+	0.895390i	$0.646897\pi$
$504$	6.81348e6	+	6.13428e7i	0.0532203	+	0.479151i
$505$	−7.72819e7	+	1.11689e8i	−0.600072	+	0.867235i
$506$	7.26954e7	−	2.68171e6i	0.561119	−	0.0206995i
$507$	3.60965e7			0.276975
$508$	−1.27452e8	+	9.41611e6i	−0.972197	+	0.0718258i
$509$	−1.55905e8			−1.18224			−0.591120	−	0.806584i	$-0.701314\pi$
$509$	−1.55905e8			−1.18224			−0.591120	+	0.806584i	$0.701314\pi$
$510$	3.77866e7	−	5.91577e7i	0.284857	−	0.445965i
$511$			2.04154e8i			1.53001i
$512$	−4.37280e7	−	1.26895e8i	−0.325799	−	0.945439i
$513$		−	3.82694e7i		−	0.283465i
$514$	1.03610e8	−	3.82215e6i	0.762982	−	0.0281461i
$515$	−1.26781e8	+	1.83226e8i	−0.928178	+	1.34142i
$516$	−1.12253e8	+	8.29320e6i	−0.817047	+	0.0603633i
$517$		−	1.10301e8i		−	0.798195i
$518$	2.64524e8	−	9.75821e6i	1.90317	−	0.0702071i
$519$			8.03118e7i			0.574483i
$520$	4.81486e7	−	8.92618e7i	0.342431	−	0.634827i
$521$	−1.28940e8			−0.911750			−0.455875	−	0.890044i	$-0.650674\pi$
$521$	−1.28940e8			−0.911750			−0.455875	+	0.890044i	$0.650674\pi$
$522$	−143401.	−	3.88730e6i	−0.00100819	−	0.0273298i
$523$	−5.74458e7			−0.401562			−0.200781	−	0.979636i	$-0.564348\pi$
$523$	−5.74458e7			−0.401562			−0.200781	+	0.979636i	$0.564348\pi$
$524$	2.81137e6	+	3.80533e7i	0.0195400	+	0.264484i
$525$	−4.25886e7	−	1.13075e8i	−0.294317	−	0.781429i
$526$	1.81651e6	+	4.92416e7i	0.0124819	+	0.338357i
$527$	3.32327e7			0.227056
$528$	−5.26938e6	−	3.54672e7i	−0.0357979	−	0.240949i
$529$	1.14153e8			0.771117
$530$	3.87992e7	−	6.07430e7i	0.260612	−	0.408008i
$531$		−	3.44807e7i		−	0.230299i
$532$	2.36328e7	+	3.19882e8i	0.156957	+	2.12449i
$533$			1.54018e8i			1.01716i
$534$	401076.	+	1.08723e7i	0.00263392	+	0.0713999i
$535$	3.97172e7	−	5.74000e7i	0.259369	−	0.374844i
$536$	1.22446e7	+	1.10240e8i	0.0795155	+	0.715890i
$537$			3.07174e7i			0.198363i
$538$	−757177.	−	2.05254e7i	−0.00486240	−	0.131809i
$539$		−	7.21308e7i		−	0.460632i
$540$	−1.53601e7	+	2.61227e7i	−0.0975469	+	0.165896i
$541$	−8.81969e7			−0.557008			−0.278504	−	0.960435i	$-0.589839\pi$
$541$	−8.81969e7			−0.557008			−0.278504	+	0.960435i	$0.589839\pi$
$542$	7.72870e7	−	2.85109e6i	0.485410	−	0.0179066i
$543$	3.65762e7			0.228454
$544$	1.45056e8	−	2.70503e7i	0.901028	−	0.168026i
$545$	−3.22310e7	+	4.65808e7i	−0.199106	+	0.287751i
$546$	−9.79693e7	+	3.61406e6i	−0.601883	+	0.0222033i
$547$	2.52994e8			1.54578			0.772892	−	0.634538i	$-0.218810\pi$
$547$	2.52994e8			1.54578			0.772892	+	0.634538i	$0.218810\pi$
$548$	−2.08834e7	−	2.82666e8i	−0.126899	−	1.71764i
$549$	4.89489e7			0.295819
$550$	2.71469e7	+	6.47347e7i	0.163167	+	0.389089i
$551$		−	2.02157e7i		−	0.120846i
$552$	−1.42667e7	−	1.28445e8i	−0.0848215	−	0.763661i
$553$			1.34951e8i			0.797998i
$554$	1.27602e8	−	4.70720e6i	0.750462	−	0.0276843i
$555$	1.06877e8	+	7.39519e7i	0.625178	+	0.432584i
$556$	−2.37874e7	−	3.21974e8i	−0.138395	−	1.87325i
$557$		−	2.32228e8i		−	1.34384i	−0.740622	−	0.671922i	$-0.765469\pi$
$557$		−	2.32228e8i		−	1.34384i	0.740622	−	0.671922i	$-0.234531\pi$
$558$	−1.43370e7	+	528887.i	−0.0825193	+	0.00304411i
$559$		−	1.78788e8i		−	1.02353i
$560$	1.12259e8	−	2.27837e8i	0.639229	−	1.29736i
$561$	3.94200e7			0.223269
$562$	1.26467e7	+	3.42824e8i	0.0712470	+	1.93135i
$563$	2.04220e8			1.14439			0.572193	−	0.820119i	$-0.306093\pi$
$563$	2.04220e8			1.14439			0.572193	+	0.820119i	$0.306093\pi$
$564$	−1.95424e8	+	1.44379e7i	−1.08928	+	0.0804759i
$565$	1.88403e8	+	1.30363e8i	1.04458	+	0.722786i
$566$	−1.87654e6	−	5.08691e7i	−0.0103493	−	0.280547i
$567$	2.92929e7			0.160699
$568$	−1.82404e8	+	2.02600e7i	−0.995382	+	0.110559i
$569$	1.10819e8			0.601558			0.300779	−	0.953694i	$-0.402753\pi$
$569$	1.10819e8			0.601558			0.300779	+	0.953694i	$0.402753\pi$
$570$	−8.47756e7	+	1.32723e8i	−0.457769	+	0.716671i
$571$			1.80433e8i			0.969186i	0.874740	+	0.484593i	$0.161032\pi$
$571$			1.80433e8i			0.969186i	−0.874740	+	0.484593i	$0.838968\pi$
$572$	5.67996e7	−	4.19634e6i	0.303499	−	0.0224224i
$573$		−	1.42284e8i		−	0.756295i
$574$	1.42193e7	+	3.85455e8i	0.0751871	+	2.03816i
$575$	8.91760e7	+	2.36767e8i	0.469077	+	1.24543i
$576$	−6.21484e7	+	1.39784e7i	−0.325209	+	0.0731457i
$577$		−	1.16278e8i		−	0.605297i	−0.953102	−	0.302648i	$-0.902129\pi$
$577$		−	1.16278e8i		−	0.605297i	0.953102	−	0.302648i	$-0.0978708\pi$
$578$	−1.13837e6	−	3.08588e7i	−0.00589523	−	0.159807i
$579$		−	1.89817e8i		−	0.977912i
$580$	−8.11395e6	+	1.37993e7i	−0.0415861	+	0.0707248i
$581$	−1.25209e8			−0.638421
$582$	−1.62824e7	+	600650.i	−0.0825939	+	0.00304686i
$583$	4.04763e7			0.204266
$584$	−2.09419e8	+	2.32606e7i	−1.05142	+	0.116784i
$585$	−3.95829e7	−	2.73889e7i	−0.197715	−	0.136806i
$586$	−9.43332e7	+	3.47992e6i	−0.468783	+	0.0172932i
$587$	−8.67855e7			−0.429075			−0.214537	−	0.976716i	$-0.568824\pi$
$587$	−8.67855e7			−0.429075			−0.214537	+	0.976716i	$0.568824\pi$
$588$	−1.27796e8	+	9.44154e6i	−0.628615	+	0.0464420i
$589$	−7.45588e7			−0.364882
$590$	−7.63829e7	+	1.19583e8i	−0.371912	+	0.582255i
$591$		−	8.30875e7i		−	0.402507i
$592$	4.01488e7	+	2.70234e8i	0.193512	+	1.30249i
$593$		−	1.04689e8i		−	0.502038i	−0.967982	−	0.251019i	$-0.919234\pi$
$593$		−	1.04689e8i		−	0.502038i	0.967982	−	0.251019i	$-0.0807657\pi$
$594$	−1.70063e7	+	627355.i	−0.0811427	+	0.00299333i
$595$	2.29624e8	+	1.58885e8i	1.09010	+	0.754280i
$596$	1.47832e8	−	1.09218e7i	0.698282	−	0.0515890i
$597$		−	2.65782e7i		−	0.124912i
$598$	2.05137e8	−	7.56743e6i	0.959269	−	0.0353871i
$599$			6.77750e7i			0.315347i	0.987491	+	0.157674i	$0.0503994\pi$
$599$			6.77750e7i			0.315347i	−0.987491	+	0.157674i	$0.949601\pi$
$600$	1.11139e8	−	5.65703e7i	0.514531	−	0.261899i
$601$	2.94031e8			1.35447			0.677236	−	0.735766i	$-0.263177\pi$
$601$	2.94031e8			1.35447			0.677236	+	0.735766i	$0.263177\pi$
$602$	−1.65061e7	−	4.47445e8i	−0.0756580	−	2.05093i
$603$	5.26429e7			0.240098
$604$	2.70122e7	+	3.65624e8i	0.122588	+	1.65930i
$605$	1.03573e8	−	1.49685e8i	0.467714	−	0.675948i
$606$	4.99522e6	+	1.35410e8i	0.0224459	+	0.608460i
$607$	−1.77492e8			−0.793618			−0.396809	−	0.917901i	$-0.629882\pi$
$607$	−1.77492e8			−0.793618			−0.396809	+	0.917901i	$0.629882\pi$
$608$	−3.25438e8	+	6.06885e7i	−1.44796	+	0.270020i
$609$	1.54739e7			0.0685091
$610$	−1.69760e8	−	1.08433e8i	−0.747906	−	0.477720i
$611$		−	3.11256e8i		−	1.36457i
$612$	−5.15987e6	−	6.98413e7i	−0.0225104	−	0.304690i
$613$			1.82426e8i			0.791962i	0.918259	+	0.395981i	$0.129595\pi$
$613$			1.82426e8i			0.791962i	−0.918259	+	0.395981i	$0.870405\pi$
$614$	1.02463e7	+	2.77755e8i	0.0442651	+	1.19993i
$615$	−1.07760e8	+	1.55737e8i	−0.463268	+	0.669524i
$616$	1.41763e8	−	1.57459e7i	0.606485	−	0.0673637i
$617$			2.51870e8i			1.07231i	0.844119	+	0.536156i	$0.180124\pi$
$617$			2.51870e8i			1.07231i	−0.844119	+	0.536156i	$0.819876\pi$
$618$	8.19464e6	+	2.22139e8i	0.0347188	+	0.941152i
$619$		−	2.50301e8i		−	1.05534i	−0.849450	−	0.527669i	$-0.823066\pi$
$619$		−	2.50301e8i		−	1.05534i	0.849450	−	0.527669i	$-0.176934\pi$
$620$	5.08939e7	+	2.99256e7i	0.213546	+	0.125565i
$621$	−6.13362e7			−0.256119
$622$	−3.99847e8	+	1.47502e7i	−1.66159	+	0.0612953i
$623$	−4.32787e7			−0.178982
$624$	−1.48695e7	−	1.00084e8i	−0.0611989	−	0.411918i
$625$	−1.83479e8	+	1.61059e8i	−0.751532	+	0.659697i
$626$	4.12387e8	−	1.52128e7i	1.68105	−	0.0620135i
$627$	−8.84402e7			−0.358796
$628$	1.01074e6	+	1.36808e7i	0.00408093	+	0.0552374i
$629$	−3.00351e8			−1.20692
$630$	−1.01591e8	−	6.48907e7i	−0.406288	−	0.259514i
$631$		−	2.44022e8i		−	0.971272i	−0.874161	−	0.485636i	$-0.838588\pi$
$631$		−	2.44022e8i		−	0.971272i	0.874161	−	0.485636i	$-0.161412\pi$
$632$	−1.38431e8	+	1.53759e7i	−0.548382	+	0.0609100i
$633$			1.95886e8i			0.772309i
$634$	−3.23851e8	+	1.19467e7i	−1.27080	+	0.0468794i
$635$	1.42028e8	−	2.05261e8i	0.554692	−	0.801650i
$636$	−5.29814e6	−	7.17129e7i	−0.0205945	−	0.278757i
$637$		−	2.03544e8i		−	0.787480i
$638$	−8.98351e6	+	331399.i	−0.0345927	+	0.00127611i
$639$			8.71031e7i			0.333834i
$640$	2.46503e8	+	8.91947e7i	0.940335	+	0.340251i
$641$	2.17104e8			0.824317			0.412159	−	0.911112i	$-0.364775\pi$
$641$	2.17104e8			0.824317			0.412159	+	0.911112i	$0.364775\pi$
$642$	−2.56718e6	−	6.95907e7i	−0.00970177	−	0.262994i
$643$	−7.06668e7			−0.265817			−0.132908	−	0.991128i	$-0.542432\pi$
$643$	−7.06668e7			−0.265817			−0.132908	+	0.991128i	$0.542432\pi$
$644$	5.12690e8	−	3.78775e7i	1.91954	−	0.141815i
$645$	1.25090e8	−	1.80783e8i	0.466170	−	0.673717i
$646$	−1.34168e7	−	3.63701e8i	−0.0497682	−	1.34911i
$647$	1.10253e8			0.407077			0.203539	−	0.979067i	$-0.434756\pi$
$647$	1.10253e8			0.407077			0.203539	+	0.979067i	$0.434756\pi$
$648$	3.33753e6	+	3.00483e7i	0.0122659	+	0.110432i
$649$	−7.96846e7			−0.291501
$650$	7.66051e7	+	1.82673e8i	0.278944	+	0.665173i
$651$		−	5.70703e7i		−	0.206856i
$652$	−3.27527e8	+	2.41976e7i	−1.18169	+	0.0873032i
$653$			2.64139e8i			0.948622i	0.880357	+	0.474311i	$0.157303\pi$
$653$			2.64139e8i			0.948622i	−0.880357	+	0.474311i	$0.842697\pi$
$654$	2.08329e6	+	5.64737e7i	0.00744762	+	0.201889i
$655$	−6.12849e7	−	4.24053e7i	−0.218087	−	0.150902i
$656$	−3.93775e8	+	5.85034e7i	−1.39488	+	0.207238i
$657$			1.00003e8i			0.352629i
$658$	−2.87359e7	−	7.78970e8i	−0.100867	−	2.73428i
$659$		−	3.71991e8i		−	1.29980i	−0.760020	−	0.649900i	$-0.774811\pi$
$659$		−	3.71991e8i		−	1.29980i	0.760020	−	0.649900i	$-0.225189\pi$
$660$	6.03694e7	+	3.54971e7i	0.209983	+	0.123470i
$661$	8.07649e6			0.0279652			0.0139826	−	0.999902i	$-0.495549\pi$
$661$	8.07649e6			0.0279652			0.0139826	+	0.999902i	$0.495549\pi$
$662$	−3.73941e8	+	1.37946e7i	−1.28893	+	0.0475482i
$663$	1.11238e8			0.381692
$664$	−1.42659e7	−	1.28438e8i	−0.0487297	−	0.438721i
$665$	−5.15170e8	−	3.56465e8i	−1.75180	−	1.21214i
$666$	1.29575e8	−	4.77999e6i	0.438631	−	0.0161809i
$667$	−3.24007e7			−0.109188
$668$	−1.95085e8	+	1.44128e7i	−0.654476	+	0.0483526i
$669$	−7.46133e7			−0.249194
$670$	−1.82572e8	−	1.16616e8i	−0.607028	−	0.387735i
$671$		−	1.13121e8i		−	0.374433i
$672$	−4.64534e7	−	2.49104e8i	−0.153077	−	0.820866i
$673$		−	4.68686e8i		−	1.53758i	−0.639504	−	0.768788i	$-0.720860\pi$
$673$		−	4.68686e8i		−	1.53758i	0.639504	−	0.768788i	$-0.279140\pi$
$674$	−3.81566e8	+	1.40758e7i	−1.24621	+	0.0459721i
$675$	−2.08617e7	−	5.53890e7i	−0.0678326	−	0.180099i
$676$	−1.47795e8	+	1.09191e7i	−0.478431	+	0.0353464i
$677$			4.87718e8i			1.57182i	0.618340	+	0.785911i	$0.287805\pi$
$677$			4.87718e8i			1.57182i	−0.618340	+	0.785911i	$0.712195\pi$
$678$	2.28416e8	−	8.42620e6i	0.732889	−	0.0270360i
$679$		−	6.48141e7i		−	0.207043i
$680$	−1.36820e8	+	2.53648e8i	−0.435134	+	0.806686i
$681$	−2.77629e6			−0.00879069
$682$	1.22225e6	+	3.31327e7i	0.00385308	+	0.104449i
$683$	1.37472e8			0.431473			0.215736	−	0.976452i	$-0.430785\pi$
$683$	1.37472e8			0.431473			0.215736	+	0.976452i	$0.430785\pi$
$684$	1.15764e7	+	1.56692e8i	0.0361746	+	0.489641i
$685$	4.55234e8	+	3.14994e8i	1.41633	+	0.980009i
$686$	−1.57941e6	−	4.28143e7i	−0.00489239	−	0.132622i
$687$	−1.58654e7			−0.0489307
$688$	4.57103e8	−	6.79121e7i	1.40362	−	0.208536i
$689$	1.14219e8			0.349205
$690$	2.12721e8	+	1.35874e8i	0.647534	+	0.413608i
$691$			3.91195e7i			0.118566i	0.998241	+	0.0592829i	$0.0188814\pi$
$691$			3.91195e7i			0.118566i	−0.998241	+	0.0592829i	$0.981119\pi$
$692$	−2.42941e7	−	3.28832e8i	−0.0733132	−	0.992330i
$693$		−	6.76957e7i		−	0.203405i
$694$	−1.15997e7	−	3.14443e8i	−0.0347031	−	0.940728i
$695$	5.18538e8	+	3.58796e8i	1.54464	+	1.06879i
$696$	1.76304e6	+	1.58729e7i	0.00522920	+	0.0470792i
$697$		−	4.37661e8i		−	1.29253i
$698$	2.25849e7	+	6.12230e8i	0.0664129	+	1.80031i
$699$		−	3.48530e7i		−	0.102049i
$700$	2.08582e8	+	4.50097e8i	0.608110	+	1.31224i
$701$	7.90495e7			0.229480			0.114740	−	0.993396i	$-0.463396\pi$
$701$	7.90495e7			0.229480			0.114740	+	0.993396i	$0.463396\pi$
$702$	−4.79895e7	+	1.77032e6i	−0.138719	+	0.00511728i
$703$	6.73849e8			1.93953
$704$	3.23039e7	+	1.43624e8i	0.0925843	+	0.411633i
$705$	2.17773e8	−	3.14730e8i	0.621494	−	0.898195i
$706$	−9.82002e7	+	3.62257e6i	−0.279060	+	0.0102944i
$707$	−5.39017e8			−1.52526
$708$	1.04303e7	+	1.41179e8i	0.0293898	+	0.397806i
$709$	3.79297e8			1.06424			0.532121	−	0.846668i	$-0.321395\pi$
$709$	3.79297e8			1.06424			0.532121	+	0.846668i	$0.321395\pi$
$710$	1.92954e8	−	3.02083e8i	0.539111	−	0.844018i
$711$			6.61048e7i			0.183918i
$712$	−4.93102e6	−	4.43947e7i	−0.0136614	−	0.122996i
$713$			1.19499e8i			0.329682i
$714$	2.78392e8	−	1.02698e7i	0.764824	−	0.0282141i
$715$	−6.32954e7	+	9.14757e7i	−0.173163	+	0.250258i
$716$	−9.29192e6	−	1.25771e8i	−0.0253143	−	0.342642i
$717$			3.88530e8i			1.05406i
$718$	−8.82560e7	+	3.25573e6i	−0.238436	+	0.00879581i
$719$		−	9.42836e7i		−	0.253659i	−0.991925	−	0.126829i	$-0.959520\pi$
$719$		−	9.42836e7i		−	0.253659i	0.991925	−	0.126829i	$-0.0404801\pi$
$720$	5.49891e7	−	1.11604e8i	0.147326	−	0.299009i
$721$	−8.84255e8			−2.35924
$722$	1.62265e7	+	4.39866e8i	0.0431135	+	1.16872i
$723$	−8.79315e7			−0.232664
$724$	−1.49759e8	+	1.10642e7i	−0.394619	+	0.0291544i
$725$	−1.10201e7	−	2.92591e7i	−0.0289183	−	0.0767797i
$726$	−6.69458e6	−	1.81476e8i	−0.0174950	−	0.474251i
$727$	−3.70399e8			−0.963977			−0.481988	−	0.876178i	$-0.660085\pi$
$727$	−3.70399e8			−0.963977			−0.481988	+	0.876178i	$0.660085\pi$
$728$	4.00037e8	−	4.44330e7i	1.03683	−	0.115162i
$729$	1.43489e7			0.0370370
$730$	2.21531e8	−	3.46823e8i	0.569463	−	0.891536i
$731$			5.08046e8i			1.30062i
$732$	−2.00418e8	+	1.48069e7i	−0.510981	+	0.0377512i
$733$			2.70421e8i			0.686639i	0.939219	+	0.343320i	$0.111551\pi$
$733$			2.70421e8i			0.686639i	−0.939219	+	0.343320i	$0.888449\pi$
$734$	−1.73238e7	−	4.69610e8i	−0.0438080	−	1.18754i
$735$	1.42411e8	−	2.05815e8i	0.358659	−	0.518341i
$736$	9.72684e7	+	5.21596e8i	0.243971	+	1.30828i
$737$		−	1.21657e8i		−	0.303904i
$738$	6.96522e6	+	1.88812e8i	0.0173287	+	0.469744i
$739$			1.34877e8i			0.334199i	0.985940	+	0.167099i	$0.0534400\pi$
$739$			1.34877e8i			0.334199i	−0.985940	+	0.167099i	$0.946560\pi$
$740$	−4.59970e8	−	2.70462e8i	−1.13510	−	0.667439i
$741$	−2.49567e8			−0.613384
$742$	2.85852e8	−	1.05450e7i	0.699728	−	0.0258127i
$743$	−3.91308e8			−0.954008			−0.477004	−	0.878901i	$-0.658277\pi$
$743$	−3.91308e8			−0.954008			−0.477004	+	0.878901i	$0.658277\pi$
$744$	5.85420e7	−	6.50239e6i	0.142151	−	0.0157890i
$745$	−1.64739e8	+	2.38084e8i	−0.398408	+	0.575787i
$746$	9.92586e7	−	3.66161e6i	0.239085	−	0.00881975i
$747$	−6.13326e7			−0.147140
$748$	−1.61403e8	+	1.19244e7i	−0.385661	+	0.0284926i
$749$	2.77015e8			0.659262
$750$	−5.03488e7	+	2.38309e8i	−0.119345	+	0.564881i
$751$			2.95353e8i			0.697303i	0.937253	+	0.348651i	$0.113360\pi$
$751$			2.95353e8i			0.697303i	−0.937253	+	0.348651i	$0.886640\pi$
$752$	7.95784e8	−	1.18230e8i	1.87129	−	0.278019i
$753$			1.28457e8i			0.300867i
$754$	−2.53503e7	+	935165.i	−0.0591384	+	0.00218159i
$755$	−5.88837e8	−	4.07438e8i	−1.36821	−	0.946719i
$756$	−1.19938e8	+	8.86102e6i	−0.277583	+	0.0205078i
$757$		−	4.40767e8i		−	1.01607i	−0.861338	−	0.508033i	$-0.830373\pi$
$757$		−	4.40767e8i		−	1.01607i	0.861338	−	0.508033i	$-0.169627\pi$
$758$	3.34557e8	−	1.23417e7i	0.768178	−	0.0283378i
$759$			1.41747e8i			0.324183i
$760$	3.06961e8	−	5.69069e8i	0.699266	−	1.29636i
$761$	8.11422e8			1.84117			0.920583	−	0.390548i	$-0.127714\pi$
$761$	8.11422e8			1.84117			0.920583	+	0.390548i	$0.127714\pi$
$762$	−9.18015e6	−	2.48854e8i	−0.0207484	−	0.562445i
$763$	−2.24801e8			−0.506086
$764$	4.30404e7	+	5.82573e8i	0.0965153	+	1.30638i
$765$	1.12479e8	+	7.78287e7i	0.251240	+	0.173842i
$766$	1.51119e7	+	4.09651e8i	0.0336226	+	0.911438i
$767$	−2.24860e8			−0.498340
$768$	2.50235e8	−	7.60333e7i	0.552413	−	0.167850i
$769$	−4.57333e8			−1.00567			−0.502833	−	0.864383i	$-0.667709\pi$
$769$	−4.57333e8			−1.00567			−0.502833	+	0.864383i	$0.667709\pi$
$770$	−1.49962e8	+	2.34777e8i	−0.328480	+	0.514260i
$771$			2.02028e8i			0.440807i
$772$	5.74191e7	+	7.77195e8i	0.124797	+	1.68919i
$773$		−	7.52735e8i		−	1.62969i	−0.579682	−	0.814843i	$-0.696823\pi$
$773$		−	7.52735e8i		−	1.62969i	0.579682	−	0.814843i	$-0.303177\pi$
$774$	−8.08538e6	−	2.19178e8i	−0.0174372	−	0.472686i
$775$	−1.07912e8	+	4.06441e7i	−0.231828	+	0.0873158i
$776$	6.64855e7	−	7.38469e6i	0.142279	−	0.0158033i
$777$			5.15792e8i			1.09954i
$778$	−1.46942e7	−	3.98329e8i	−0.0312038	−	0.845869i
$779$			9.81909e8i			2.07711i
$780$	1.70355e8	+	1.00168e8i	0.358980	+	0.211080i
$781$	2.01295e8			0.422551
$782$	−5.82921e8	+	2.15038e7i	−1.21896	+	0.0449670i
$783$	7.57977e6			0.0157896
$784$	5.20397e8	−	7.73157e7i	1.07991	−	0.160442i
$785$	−2.20330e7	−	1.52454e7i	−0.0455474	−	0.0315160i
$786$	−7.43007e7	+	2.74093e6i	−0.153012	+	0.00564455i
$787$	−2.11025e8			−0.432921			−0.216461	−	0.976291i	$-0.569451\pi$
$787$	−2.11025e8			−0.432921			−0.216461	+	0.976291i	$0.569451\pi$
$788$	2.51337e7	+	3.40197e8i	0.0513663	+	0.695267i
$789$	−9.60154e7			−0.195483
$790$	1.46438e8	−	2.29259e8i	0.297011	−	0.464992i
$791$			9.09242e8i			1.83717i
$792$	6.94414e7	−	7.71301e6i	0.139779	−	0.0155256i
$793$		−	3.19212e8i		−	0.640117i
$794$	−3.13558e8	+	1.15670e7i	−0.626406	+	0.0231079i
$795$	1.15494e8	+	7.99144e7i	0.229856	+	0.159046i
$796$	8.03983e6	+	1.08823e8i	0.0159407	+	0.215765i
$797$		−	2.07292e8i		−	0.409456i	−0.978819	−	0.204728i	$-0.934369\pi$
$797$		−	2.07292e8i		−	0.409456i	0.978819	−	0.204728i	$-0.0656310\pi$
$798$	−6.24582e8	+	2.30406e7i	−1.22908	+	0.0453404i
$799$			8.84472e8i			1.73398i
$800$	−4.37939e8	+	2.65243e8i	−0.855349	+	0.518052i
$801$	−2.11997e7			−0.0412508
$802$	1.66142e6	+	4.50377e7i	0.00322075	+	0.0873078i
$803$	2.31107e8			0.446340
$804$	−2.15543e8	+	1.59243e7i	−0.414731	+	0.0306403i
$805$	−5.71324e8	+	8.25688e8i	−1.09520	+	1.58281i
$806$	3.44904e6	+	9.34962e7i	0.00658709	+	0.178562i
$807$	4.00222e7			0.0761518
$808$	−6.14137e7	−	5.52917e8i	−0.116421	−	1.04816i
$809$	4.26907e8			0.806283			0.403142	−	0.915138i	$-0.367918\pi$
$809$	4.26907e8			0.806283			0.403142	+	0.915138i	$0.367918\pi$
$810$	−4.97637e7	−	3.17862e7i	−0.0936391	−	0.0598114i
$811$		−	6.62743e8i		−	1.24246i	−0.783628	−	0.621230i	$-0.786633\pi$
$811$		−	6.62743e8i		−	1.24246i	0.783628	−	0.621230i	$-0.213367\pi$
$812$	−6.33570e7	+	4.68081e6i	−0.118339	+	0.00874284i
$813$			1.50701e8i			0.280442i
$814$	−1.10465e7	−	2.99447e8i	−0.0204810	−	0.555197i
$815$	3.64984e8	−	5.27482e8i	0.674220	−	0.974394i
$816$	4.22536e7	+	2.84400e8i	0.0777665	+	0.523431i
$817$		−	1.13982e9i		−	2.09012i
$818$	8.72874e6	+	2.36617e8i	0.0159475	+	0.432302i
$819$		−	1.91029e8i		−	0.347734i
$820$	3.94108e8	−	6.70252e8i	0.714781	−	1.21562i
$821$	5.73913e8			1.03709			0.518545	−	0.855050i	$-0.326474\pi$
$821$	5.73913e8			1.03709			0.518545	+	0.855050i	$0.326474\pi$
$822$	5.51917e8	−	2.03600e7i	0.993708	−	0.0366575i
$823$	−5.19180e8			−0.931362			−0.465681	−	0.884953i	$-0.654191\pi$
$823$	−5.19180e8			−0.931362			−0.465681	+	0.884953i	$0.654191\pi$
$824$	−1.00749e8	−	9.07058e8i	−0.180077	−	1.62126i
$825$	−1.28004e8	+	4.82113e7i	−0.227961	+	0.0858592i
$826$	−5.62749e8	+	2.07596e7i	−0.998560	+	0.0368366i
$827$	4.62996e8			0.818580			0.409290	−	0.912404i	$-0.365776\pi$
$827$	4.62996e8			0.818580			0.409290	+	0.912404i	$0.365776\pi$
$828$	2.51137e8	−	1.85540e7i	0.442405	−	0.0326848i
$829$	−7.20209e8			−1.26414			−0.632069	−	0.774912i	$-0.717794\pi$
$829$	−7.20209e8			−1.26414			−0.632069	+	0.774912i	$0.717794\pi$
$830$	2.12709e8	+	1.35866e8i	0.372007	+	0.237617i
$831$			2.48809e8i			0.433574i
$832$	9.11575e7	+	4.05290e8i	0.158279	+	0.703713i
$833$			5.78394e8i			1.00067i
$834$	6.28666e8	−	2.31913e7i	1.08373	−	0.0399785i
$835$	2.17396e8	−	3.14184e8i	0.373415	−	0.539665i
$836$	3.62113e8	−	2.67529e7i	0.619763	−	0.0457880i
$837$		−	2.79555e7i		−	0.0476749i
$838$	9.21438e7	−	3.39915e6i	0.156579	−	0.00577615i
$839$		−	3.84875e8i		−	0.651680i	−0.945425	−	0.325840i	$-0.894353\pi$
$839$		−	3.84875e8i		−	0.651680i	0.945425	−	0.325840i	$-0.105647\pi$
$840$	4.35589e8	+	2.34960e8i	0.734918	+	0.396421i
$841$	−5.90819e8			−0.993269
$842$	−1.05421e7	−	2.85773e8i	−0.0176599	−	0.478723i
$843$	−6.68466e8			−1.11583
$844$	−5.92548e7	−	8.02042e8i	−0.0985589	−	1.33404i
$845$	1.64698e8	−	2.38024e8i	0.272971	−	0.394503i
$846$	−1.40761e7	−	3.81572e8i	−0.0232472	−	0.630182i
$847$	7.22388e8			1.18883
$848$	4.33859e7	+	2.92022e8i	0.0711477	+	0.478881i
$849$	9.91888e7			0.162084
$850$	−2.17683e8	−	5.19087e8i	−0.354460	−	0.845247i
$851$		−	1.08001e9i		−	1.75243i
$852$	−2.63484e7	−	3.56639e8i	−0.0426025	−	0.576646i
$853$			5.38061e8i			0.866931i	0.901170	+	0.433466i	$0.142709\pi$
$853$			5.38061e8i			0.866931i	−0.901170	+	0.433466i	$0.857291\pi$
$854$	−2.94704e7	−	7.98880e8i	−0.0473165	−	1.28265i
$855$	−2.52352e8	−	1.74612e8i	−0.403746	−	0.279367i
$856$	3.15621e7	+	2.84159e8i	0.0503205	+	0.453043i
$857$			3.71687e8i			0.590521i	0.955417	+	0.295261i	$0.0954065\pi$
$857$			3.71687e8i			0.590521i	−0.955417	+	0.295261i	$0.904594\pi$
$858$	4.09119e6	+	1.10903e8i	0.00647721	+	0.175583i
$859$			3.70545e7i			0.0584603i	0.999573	+	0.0292302i	$0.00930557\pi$
$859$			3.70545e7i			0.0584603i	−0.999573	+	0.0292302i	$0.990694\pi$
$860$	−4.57489e8	+	7.78044e8i	−0.719259	+	1.22323i
$861$	−7.51593e8			−1.17753
$862$	6.56225e7	−	2.42079e6i	0.102454	−	0.00377951i
$863$	2.37470e7			0.0369468			0.0184734	−	0.999829i	$-0.494119\pi$
$863$	2.37470e7			0.0369468			0.0184734	+	0.999829i	$0.494119\pi$
$864$	−2.27548e7	−	1.22021e8i	−0.0352803	−	0.189189i
$865$	5.29584e8	+	3.66439e8i	0.818251	+	0.566178i
$866$	3.50106e8	−	1.29153e7i	0.539071	−	0.0198861i
$867$	6.01711e7			0.0923274
$868$	1.72636e7	+	2.33671e8i	0.0263981	+	0.357311i
$869$	1.52768e8			0.232794
$870$	−2.62875e7	−	1.67910e7i	−0.0399201	−	0.0254987i
$871$		−	3.43302e8i		−	0.519543i
$872$	−2.56130e7	−	2.30598e8i	−0.0386288	−	0.347781i
$873$		−	3.17487e7i		−	0.0477181i
$874$	1.30781e9	−	4.82445e7i	1.95889	−	0.0722626i
$875$	−9.39948e8	−	2.35095e8i	−1.40307	−	0.350929i
$876$	−3.02507e7	−	4.09458e8i	−0.0450011	−	0.609111i
$877$			9.70223e8i			1.43838i	0.694815	+	0.719189i	$0.255486\pi$
$877$			9.70223e8i			1.43838i	−0.694815	+	0.719189i	$0.744514\pi$
$878$	−7.25751e8	+	2.67727e7i	−1.07227	+	0.0395556i
$879$		−	1.83939e8i		−	0.270836i
$880$	−2.57917e8	−	1.27079e8i	−0.378470	−	0.186478i
$881$	3.34234e8			0.488791			0.244396	−	0.969676i	$-0.421410\pi$
$881$	3.34234e8			0.488791			0.244396	+	0.969676i	$0.421410\pi$
$882$	−9.20494e6	−	2.49526e8i	−0.0134158	−	0.363673i
$883$	−1.04292e9			−1.51485			−0.757426	−	0.652921i	$-0.773543\pi$
$883$	−1.04292e9			−1.51485			−0.757426	+	0.652921i	$0.773543\pi$
$884$	−4.55458e8	+	3.36492e7i	−0.659313	+	0.0487099i
$885$	−2.27369e8	−	1.57325e8i	−0.328021	−	0.226970i
$886$	−1.30057e6	−	3.52558e7i	−0.00186997	−	0.0506908i
$887$	2.82542e8			0.404867			0.202434	−	0.979296i	$-0.435115\pi$
$887$	2.82542e8			0.404867			0.202434	+	0.979296i	$0.435115\pi$
$888$	−5.29092e8	+	5.87675e7i	−0.755601	+	0.0839263i
$889$	9.90598e8			1.40991
$890$	7.35230e7	+	4.69624e7i	0.104293	+	0.0666162i
$891$		−	3.31602e7i		−	0.0468796i
$892$	3.05500e8	−	2.25703e7i	0.430444	−	0.0318011i
$893$		−	1.98435e9i		−	2.78653i
$894$	1.06481e7	+	2.88649e8i	0.0149026	+	0.403977i
$895$	2.02554e8	+	1.40154e8i	0.282534	+	0.195496i
$896$	2.65554e8	+	1.00589e9i	0.369172	+	1.39838i
$897$			3.99993e8i			0.554211i
$898$	2.28530e7	+	6.19497e8i	0.0315584	+	0.855480i
$899$		−	1.47674e7i		−	0.0203247i
$900$	1.02172e8	+	2.20476e8i	0.140154	+	0.302437i
$901$	−3.24567e8			−0.443742
$902$	4.36344e8	−	1.60966e7i	0.594579	−	0.0219338i
$903$	8.72466e8			1.18491
$904$	−9.32689e8	+	1.03596e8i	−1.26250	+	0.140229i
$905$	1.66886e8	−	2.41187e8i	0.225152	−	0.325393i
$906$	−7.13895e8	+	2.63353e7i	−0.959953	+	0.0354123i
$907$	6.77657e7			0.0908214			0.0454107	−	0.998968i	$-0.485540\pi$
$907$	6.77657e7			0.0908214			0.0454107	+	0.998968i	$0.485540\pi$
$908$	1.13673e7	−	839818.i	0.0151845	−	0.00112183i
$909$	−2.64033e8			−0.351534
$910$	−4.23174e8	+	6.62509e8i	−0.561558	+	0.879160i
$911$		−	9.61421e7i		−	0.127162i	−0.997977	−	0.0635812i	$-0.979748\pi$
$911$		−	9.61421e7i		−	0.127162i	0.997977	−	0.0635812i	$-0.0202522\pi$
$912$	−9.47975e7	−	6.38063e8i	−0.124972	−	0.841161i
$913$			1.41739e8i			0.186242i
$914$	−1.31174e9	+	4.83895e7i	−1.71794	+	0.0633742i
$915$	2.23339e8	−	3.22774e8i	0.291543	−	0.421342i
$916$	6.49601e7	−	4.79924e6i	0.0845202	−	0.00624434i
$917$		−	2.95764e8i		−	0.383563i
$918$	1.36368e8	−	5.03057e6i	0.176272	−	0.00650263i
$919$			5.40889e8i			0.696885i	0.937330	+	0.348443i	$0.113289\pi$
$919$			5.40889e8i			0.696885i	−0.937330	+	0.348443i	$0.886711\pi$
$920$	−9.12075e8	−	4.91981e8i	−1.17130	−	0.631808i
$921$	−5.41590e8			−0.693253
$922$	3.72220e7	+	1.00901e9i	0.0474905	+	1.28737i
$923$	5.68028e8			0.722378
$924$	2.04777e7	+	2.77176e8i	0.0259577	+	0.351350i
$925$	9.75293e8	−	3.67334e8i	1.23228	−	0.464127i
$926$	9.48641e6	+	2.57156e8i	0.0119473	+	0.323865i
$927$	−4.33145e8			−0.543744
$928$	−1.20202e7	−	6.44575e7i	−0.0150407	−	0.0806547i
$929$	−1.21327e9			−1.51325			−0.756626	−	0.653848i	$-0.773154\pi$
$929$	−1.21327e9			−1.51325			−0.756626	+	0.653848i	$0.773154\pi$
$930$	−6.19279e7	+	9.69527e7i	−0.0769906	+	0.120534i
$931$		−	1.29765e9i		−	1.60808i
$932$	1.05429e7	+	1.42703e8i	0.0130231	+	0.176273i
$933$		−	7.79655e8i		−	0.959970i
$934$	−5.77033e6	−	1.56421e8i	−0.00708207	−	0.191980i
$935$	1.79862e8	−	2.59939e8i	0.220041	−	0.318007i
$936$	1.95955e8	−	2.17651e7i	0.238962	−	0.0265420i
$937$			4.32441e8i			0.525663i	0.964842	+	0.262832i	$0.0846564\pi$
$937$			4.32441e8i			0.525663i	−0.964842	+	0.262832i	$0.915344\pi$
$938$	−3.16944e7	−	8.59168e8i	−0.0384038	−	1.04105i
$939$			8.04106e8i			0.971217i
$940$	−7.96455e8	+	1.35452e9i	−0.958910	+	1.63080i
$941$	1.21123e9			1.45364			0.726821	−	0.686827i	$-0.240997\pi$
$941$	1.21123e9			1.45364			0.726821	+	0.686827i	$0.240997\pi$
$942$	−2.67123e7	+	985409.i	−0.0319565	+	0.00117886i
$943$	1.57375e9			1.87673
$944$	−8.54125e7	−	5.74895e8i	−0.101533	−	0.683396i
$945$	1.33655e8	−	1.93160e8i	0.158376	−	0.228888i
$946$	−5.06518e8	+	1.86853e7i	−0.598303	+	0.0220712i
$947$	6.93040e8			0.816034			0.408017	−	0.912974i	$-0.366220\pi$
$947$	6.93040e8			0.816034			0.408017	+	0.912974i	$0.366220\pi$
$948$	−1.99965e7	−	2.70662e8i	−0.0234709	−	0.317690i
$949$	6.52154e8			0.763047
$950$	4.88379e8	+	1.16459e9i	0.569622	+	1.35832i
$951$		−	6.31471e8i		−	0.734196i
$952$	−1.13675e9	+	1.26262e8i	−1.31751	+	0.146339i
$953$			3.68416e8i			0.425657i	0.977090	+	0.212828i	$0.0682675\pi$
$953$			3.68416e8i			0.425657i	−0.977090	+	0.212828i	$0.931732\pi$
$954$	1.40022e8	−	5.16538e6i	0.161269	−	0.00594918i
$955$	−9.38233e8	−	6.49198e8i	−1.07721	−	0.745362i
$956$	−1.17529e8	−	1.59081e9i	−0.134515	−	1.82073i
$957$		−	1.75168e7i		−	0.0199857i
$958$	−1.55036e9	+	5.71923e7i	−1.76334	+	0.0650490i
$959$			2.19698e9i			2.49098i
$960$	−1.91390e8	+	4.73592e8i	−0.216324	+	0.535292i
$961$	8.33039e8			0.938632
$962$	−3.11718e7	−	8.45002e8i	−0.0350136	−	0.949145i
$963$	1.35694e8			0.151943
$964$	3.60031e8	−	2.65990e7i	0.401891	−	0.0296916i
$965$	−1.25167e9	−	8.66079e8i	−1.39286	−	0.963775i
$966$	3.69283e7	+	1.00105e9i	0.0409664	+	1.11051i
$967$	1.15287e9			1.27497			0.637485	−	0.770463i	$-0.279975\pi$
$967$	1.15287e9			1.27497			0.637485	+	0.770463i	$0.279975\pi$
$968$	8.23064e7	+	7.41017e8i	0.0907418	+	0.816962i
$969$	7.09174e8			0.779438
$970$	−7.03308e7	+	1.10108e8i	−0.0770602	+	0.120643i
$971$		−	4.34130e8i		−	0.474201i	−0.971485	−	0.237100i	$-0.923803\pi$
$971$		−	4.34130e8i		−	0.474201i	0.971485	−	0.237100i	$-0.0761971\pi$
$972$	−5.87508e7	+	4.34050e6i	−0.0639757	+	0.00472651i
$973$			2.50249e9i			2.71665i
$974$	4.79452e7	+	1.29969e9i	0.0518882	+	1.40658i
$975$	−3.61210e8	+	1.36046e8i	−0.389714	+	0.146782i
$976$	8.16123e8	−	1.21252e8i	0.877821	−	0.130418i
$977$			1.16648e9i			1.25082i	0.780297	+	0.625410i	$0.215068\pi$
$977$			1.16648e9i			1.25082i	−0.780297	+	0.625410i	$0.784932\pi$
$978$	−2.35913e7	−	6.39509e8i	−0.0252194	−	0.683644i
$979$			4.89924e7i			0.0522132i
$980$	−5.20836e8	+	8.85777e8i	−0.553379	+	0.941123i
$981$	−1.10117e8			−0.116640
$982$	1.24634e9	−	4.59771e7i	1.31614	−	0.0485520i
$983$	−4.61997e8			−0.486384			−0.243192	−	0.969978i	$-0.578194\pi$
$983$	−4.61997e8			−0.486384			−0.243192	+	0.969978i	$0.578194\pi$
$984$	−8.56338e7	−	7.70974e8i	−0.0898794	−	0.809198i
$985$	−5.47887e8	−	3.79104e8i	−0.573301	−	0.396688i
$986$	7.20360e7	−	2.65738e6i	0.0751482	−	0.00277219i
$987$	1.51890e9			1.57971
$988$	1.02184e9	−	7.54932e7i	1.05952	−	0.0782775i
$989$	−1.82685e9			−1.88848
$990$	−7.34577e7	+	1.15003e8i	−0.0757063	+	0.118524i
$991$			1.16310e9i			1.19508i	0.801841	+	0.597538i	$0.203854\pi$
$991$			1.16310e9i			1.19508i	−0.801841	+	0.597538i	$0.796146\pi$
$992$	−2.37730e8	+	4.43324e7i	−0.243528	+	0.0454137i
$993$		−	7.29141e8i		−	0.744670i
$994$	1.42158e9	−	5.24417e7i	1.44748	−	0.0533971i
$995$	−1.75259e8	−	1.21269e8i	−0.177915	−	0.123106i
$996$	2.51123e8	−	1.85529e7i	0.254161	−	0.0187773i
$997$		−	1.47436e9i		−	1.48771i	−0.668343	−	0.743853i	$-0.732996\pi$
$997$		−	1.47436e9i		−	1.48771i	0.668343	−	0.743853i	$-0.267004\pi$
$998$	−4.27185e8	+	1.57587e7i	−0.429759	+	0.0158537i
$999$			2.52656e8i			0.253416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.17	✓	36
3.2	odd	2		180.7.f.g.19.20		36
4.3	odd	2	inner	60.7.f.a.19.19	yes	36
5.4	even	2	inner	60.7.f.a.19.20	yes	36
12.11	even	2		180.7.f.g.19.18		36
15.14	odd	2		180.7.f.g.19.17		36
20.19	odd	2	inner	60.7.f.a.19.18	yes	36
60.59	even	2		180.7.f.g.19.19		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.17	✓	36	1.1	even	1	trivial
60.7.f.a.19.18	yes	36	20.19	odd	2	inner
60.7.f.a.19.19	yes	36	4.3	odd	2	inner
60.7.f.a.19.20	yes	36	5.4	even	2	inner
180.7.f.g.19.17		36	15.14	odd	2
180.7.f.g.19.18		36	12.11	even	2
180.7.f.g.19.19		36	60.59	even	2
180.7.f.g.19.20		36	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.294917 - 7.99456i) q^{2} +15.5885 q^{3} +(-63.8260 + 4.71546i) q^{4} +(71.1255 - 102.792i) q^{5} +(-4.59730 - 124.623i) q^{6} +496.078 q^{7} +(56.5214 + 508.871i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(-0.294917 - 7.99456i) q^{2} +15.5885 q^{3} +(-63.8260 + 4.71546i) q^{4} +(71.1255 - 102.792i) q^{5} +(-4.59730 - 124.623i) q^{6} +496.078 q^{7} +(56.5214 + 508.871i) q^{8} +243.000 q^{9} +(-842.752 - 538.302i) q^{10} -561.571i q^{11} +(-994.950 + 73.5067i) q^{12} -1584.68i q^{13} +(-146.302 - 3965.93i) q^{14} +(1108.74 - 1602.37i) q^{15} +(4051.53 - 601.938i) q^{16} +4503.06i q^{17} +(-71.6647 - 1942.68i) q^{18} -10102.8i q^{19} +(-4054.95 + 6896.19i) q^{20} +7733.09 q^{21} +(-4489.52 + 165.617i) q^{22} -16192.2 q^{23} +(881.081 + 7932.51i) q^{24} +(-5507.32 - 14622.2i) q^{25} +(-12668.8 + 467.349i) q^{26} +3788.00 q^{27} +(-31662.7 + 2339.24i) q^{28} +2001.00 q^{29} +(-13137.2 - 8391.30i) q^{30} -7380.01i q^{31} +(-6007.10 - 32212.7i) q^{32} -8754.03i q^{33} +(36000.0 - 1328.03i) q^{34} +(35283.8 - 50992.8i) q^{35} +(-15509.7 + 1145.86i) q^{36} +66699.3i q^{37} +(-80767.5 + 2979.48i) q^{38} -24702.8i q^{39} +(56327.9 + 30383.7i) q^{40} -97191.8 q^{41} +(-2280.62 - 61822.7i) q^{42} +112822. q^{43} +(2648.07 + 35842.9i) q^{44} +(17283.5 - 24978.4i) q^{45} +(4775.36 + 129450. i) q^{46} +196416. q^{47} +(63157.1 - 9383.29i) q^{48} +128445. q^{49} +(-115274. + 48341.0i) q^{50} +70195.8i q^{51} +(7472.50 + 101144. i) q^{52} +72076.9i q^{53} +(-1117.14 - 30283.4i) q^{54} +(-57724.9 - 39942.0i) q^{55} +(28039.0 + 252440. i) q^{56} -157487. i q^{57} +(-590.128 - 15997.1i) q^{58} -141896. i q^{59} +(-63210.4 + 107501. i) q^{60} +201436. q^{61} +(-59000.0 + 2176.49i) q^{62} +120547. q^{63} +(-255755. + 57524.2i) q^{64} +(-162892. - 112711. i) q^{65} +(-69984.6 + 2581.71i) q^{66} +216637. q^{67} +(-21234.0 - 287413. i) q^{68} -252412. q^{69} +(-418071. - 267040. i) q^{70} +358449. i q^{71} +(13734.7 + 123656. i) q^{72} +411536. i q^{73} +(533231. - 19670.7i) q^{74} +(-85850.7 - 227938. i) q^{75} +(47639.3 + 644822. i) q^{76} -278583. i q^{77} +(-197488. + 7285.25i) q^{78} +272036. i q^{79} +(226293. - 459277. i) q^{80} +59049.0 q^{81} +(28663.5 + 777005. i) q^{82} -252398. q^{83} +(-493573. + 36465.1i) q^{84} +(462878. + 320283. i) q^{85} +(-33273.2 - 901965. i) q^{86} +31192.5 q^{87} +(285767. - 31740.8i) q^{88} -87241.6 q^{89} +(-204789. - 130807. i) q^{90} -786126. i q^{91} +(1.03349e6 - 76353.9i) q^{92} -115043. i q^{93} +(-57926.2 - 1.57026e6i) q^{94} +(-1.03849e6 - 718567. i) q^{95} +(-93641.4 - 502146. i) q^{96} -130653. i q^{97} +(-37880.4 - 1.02686e6i) q^{98} -136462. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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