LMFDB - Embedded newform 60.7.c.a.31.12

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			31.12
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +(-18.5589 - 446.828i) q^{10} -1284.63i q^{11} +(-82.7325 - 994.225i) q^{12} -2513.57 q^{13} +(-4412.22 + 183.260i) q^{14} -871.421i q^{15} +(4039.67 - 676.993i) q^{16} +4597.01 q^{17} +(-80.6740 - 1942.33i) q^{18} -9800.21i q^{19} +(3565.39 - 296.687i) q^{20} -8604.88 q^{21} +(10268.2 - 426.487i) q^{22} +15217.2i q^{23} +(7919.48 - 991.364i) q^{24} +3125.00 q^{25} +(-834.485 - 20091.2i) q^{26} -3788.00i q^{27} +(-2929.64 - 35206.5i) q^{28} -14380.1 q^{29} +(6965.36 - 289.305i) q^{30} -34497.8i q^{31} +(6752.42 + 32064.7i) q^{32} +20025.4 q^{33} +(1526.17 + 36744.4i) q^{34} -30857.9i q^{35} +(15498.4 - 1289.67i) q^{36} -71409.5 q^{37} +(78334.2 - 3253.59i) q^{38} -39182.7i q^{39} +(3555.13 + 28400.0i) q^{40} -37657.2 q^{41} +(-2856.75 - 68779.7i) q^{42} -1535.15i q^{43} +(6817.91 + 81933.1i) q^{44} +13584.1 q^{45} +(-121633. + 5052.00i) q^{46} +131297. i q^{47} +(10553.3 + 62972.2i) q^{48} -187058. q^{49} +(1037.47 + 24978.5i) q^{50} +71660.4i q^{51} +(160314. - 13340.3i) q^{52} -228206. q^{53} +(30277.9 - 1257.58i) q^{54} +71813.0i q^{55} +(280437. - 35105.2i) q^{56} +152770. q^{57} +(-4774.07 - 114942. i) q^{58} +271199. i q^{59} +(4624.89 + 55578.9i) q^{60} -252456. q^{61} +(275745. - 11453.0i) q^{62} -134137. i q^{63} +(-254055. + 64618.0i) q^{64} +140513. q^{65} +(6648.27 + 160065. i) q^{66} -71786.4i q^{67} +(-293196. + 24397.7i) q^{68} -237213. q^{69} +(246651. - 10244.6i) q^{70} -193845. i q^{71} +(15453.8 + 123453. i) q^{72} +125558. q^{73} +(-23707.4 - 570784. i) q^{74} +48713.9i q^{75} +(52012.6 + 625053. i) q^{76} +709120. q^{77} +(313192. - 13008.3i) q^{78} +609914. i q^{79} +(-225824. + 37845.1i) q^{80} +59049.0 q^{81} +(-12501.9 - 300998. i) q^{82} -592195. i q^{83} +(548815. - 45668.6i) q^{84} -256981. q^{85} +(12270.6 - 509.657i) q^{86} -224163. i q^{87} +(-652637. + 81697.4i) q^{88} -154289. q^{89} +(4509.81 + 108579. i) q^{90} -1.38750e6i q^{91} +(-80762.4 - 970549. i) q^{92} +537768. q^{93} +(-1.04947e6 + 43589.6i) q^{94} +547849. i q^{95} +(-499840. + 105260. i) q^{96} -1.46175e6 q^{97} +(-62101.9 - 1.49518e6i) q^{98} +312165. 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 $

$2$	0.331992	+	7.99311i	0.0414990	+	0.999139i
$2$	0.331992	+	7.99311i	0.0414990	+	0.999139i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−63.7796	+	5.30729i	−0.996556	+	0.0829264i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	−124.600	+	5.17524i	−0.576853	+	0.0239594i
$7$			552.003i			1.60934i	0.593723	+	0.804669i	$0.297657\pi$
$7$			552.003i			1.60934i	−0.593723	+	0.804669i	$0.702343\pi$
$8$	−63.5960	−	508.035i	−0.124211	−	0.992256i
$9$	−243.000			−0.333333
$10$	−18.5589	−	446.828i	−0.0185589	−	0.446828i
$11$		−	1284.63i		−	0.965162i	−0.875851	−	0.482581i	$-0.839699\pi$
$11$		−	1284.63i		−	0.965162i	0.875851	−	0.482581i	$-0.160301\pi$
$12$	−82.7325	−	994.225i	−0.0478776	−	0.575362i
$13$	−2513.57			−1.14409			−0.572046	−	0.820221i	$-0.693850\pi$
$13$	−2513.57			−1.14409			−0.572046	+	0.820221i	$0.693850\pi$
$14$	−4412.22	+	183.260i	−1.60795	+	0.0667859i
$15$		−	871.421i		−	0.258199i
$16$	4039.67	−	676.993i	0.986246	−	0.165282i
$17$	4597.01			0.935684			0.467842	−	0.883812i	$-0.345032\pi$
$17$	4597.01			0.935684			0.467842	+	0.883812i	$0.345032\pi$
$18$	−80.6740	−	1942.33i	−0.0138330	−	0.333046i
$19$		−	9800.21i		−	1.42881i	−0.699732	−	0.714405i	$-0.746697\pi$
$19$		−	9800.21i		−	1.42881i	0.699732	−	0.714405i	$-0.253303\pi$
$20$	3565.39	−	296.687i	0.445673	−	0.0370858i
$21$	−8604.88			−0.929152
$22$	10268.2	−	426.487i	0.964330	−	0.0400532i
$23$			15217.2i			1.25070i	0.780345	+	0.625349i	$0.215043\pi$
$23$			15217.2i			1.25070i	−0.780345	+	0.625349i	$0.784957\pi$
$24$	7919.48	−	991.364i	0.572879	−	0.0717133i
$25$	3125.00			0.200000
$26$	−834.485	−	20091.2i	−0.0474787	−	1.14311i
$27$		−	3788.00i		−	0.192450i
$28$	−2929.64	−	35206.5i	−0.133457	−	1.60380i
$29$	−14380.1			−0.589614			−0.294807	−	0.955557i	$-0.595255\pi$
$29$	−14380.1			−0.589614			−0.294807	+	0.955557i	$0.595255\pi$
$30$	6965.36	−	289.305i	0.257976	−	0.0107150i
$31$		−	34497.8i		−	1.15800i	−0.815329	−	0.578998i	$-0.803444\pi$
$31$		−	34497.8i		−	1.15800i	0.815329	−	0.578998i	$-0.196556\pi$
$32$	6752.42	+	32064.7i	0.206067	+	0.978538i
$33$	20025.4			0.557236
$34$	1526.17	+	36744.4i	0.0388299	+	0.934878i
$35$		−	30857.9i		−	0.719718i
$36$	15498.4	−	1289.67i	0.332185	−	0.0276421i
$37$	−71409.5			−1.40978			−0.704889	−	0.709318i	$-0.749003\pi$
$37$	−71409.5			−1.40978			−0.704889	+	0.709318i	$0.749003\pi$
$38$	78334.2	−	3253.59i	1.42758	−	0.0592942i
$39$		−	39182.7i		−	0.660542i
$40$	3555.13	+	28400.0i	0.0555489	+	0.443750i
$41$	−37657.2			−0.546383			−0.273191	−	0.961960i	$-0.588079\pi$
$41$	−37657.2			−0.546383			−0.273191	+	0.961960i	$0.588079\pi$
$42$	−2856.75	−	68779.7i	−0.0385588	−	0.928352i
$43$		−	1535.15i		−	0.0193083i	−0.999953	−	0.00965417i	$-0.996927\pi$
$43$		−	1535.15i		−	0.0193083i	0.999953	−	0.00965417i	$-0.00307307\pi$
$44$	6817.91	+	81933.1i	0.0800374	+	0.961837i
$45$	13584.1			0.149071
$46$	−121633.	+	5052.00i	−1.24962	+	0.0519027i
$47$			131297.i			1.26463i	0.774713	+	0.632313i	$0.217894\pi$
$47$			131297.i			1.26463i	−0.774713	+	0.632313i	$0.782106\pi$
$48$	10553.3	+	62972.2i	0.0954254	+	0.569410i
$49$	−187058.			−1.58997
$50$	1037.47	+	24978.5i	0.00829979	+	0.199828i
$51$			71660.4i			0.540217i
$52$	160314.	−	13340.3i	1.14015	−	0.0948755i
$53$	−228206.			−1.53285			−0.766424	−	0.642336i	$-0.777966\pi$
$53$	−228206.			−1.53285			−0.766424	+	0.642336i	$0.777966\pi$
$54$	30277.9	−	1257.58i	0.192284	−	0.00798648i
$55$			71813.0i			0.431633i
$56$	280437.	−	35105.2i	1.59688	−	0.199898i
$57$	152770.			0.824924
$58$	−4774.07	−	114942.i	−0.0244684	−	0.589106i
$59$			271199.i			1.32048i	0.751053	+	0.660241i	$0.229546\pi$
$59$			271199.i			1.32048i	−0.751053	+	0.660241i	$0.770454\pi$
$60$	4624.89	+	55578.9i	0.0214115	+	0.257310i
$61$	−252456.			−1.11223			−0.556116	−	0.831105i	$-0.687709\pi$
$61$	−252456.			−1.11223			−0.556116	+	0.831105i	$0.687709\pi$
$62$	275745.	−	11453.0i	1.15700	−	0.0480556i
$63$		−	134137.i		−	0.536446i
$64$	−254055.	+	64618.0i	−0.969143	+	0.246498i
$65$	140513.			0.511654
$66$	6648.27	+	160065.i	0.0231247	+	0.556756i
$67$		−	71786.4i		−	0.238681i	−0.992853	−	0.119340i	$-0.961922\pi$
$67$		−	71786.4i		−	0.238681i	0.992853	−	0.119340i	$-0.0380780\pi$
$68$	−293196.	+	24397.7i	−0.932461	+	0.0775929i
$69$	−237213.			−0.722091
$70$	246651.	−	10244.6i	0.719098	−	0.0298676i
$71$		−	193845.i		−	0.541601i	−0.962635	−	0.270801i	$-0.912712\pi$
$71$		−	193845.i		−	0.541601i	0.962635	−	0.270801i	$-0.0872884\pi$
$72$	15453.8	+	123453.i	0.0414037	+	0.330752i
$73$	125558.			0.322758			0.161379	−	0.986893i	$-0.448406\pi$
$73$	125558.			0.322758			0.161379	+	0.986893i	$0.448406\pi$
$74$	−23707.4	−	570784.i	−0.0585043	−	1.40856i
$75$			48713.9i			0.115470i
$76$	52012.6	+	625053.i	0.118486	+	1.42389i
$77$	709120.			1.55327
$78$	313192.	−	13008.3i	0.659973	−	0.0274118i
$79$			609914.i			1.23705i	0.785765	+	0.618525i	$0.212270\pi$
$79$			609914.i			1.23705i	−0.785765	+	0.618525i	$0.787730\pi$
$80$	−225824.	+	37845.1i	−0.441063	+	0.0739162i
$81$	59049.0			0.111111
$82$	−12501.9	−	300998.i	−0.0226743	−	0.545912i
$83$		−	592195.i		−	1.03569i	−0.855474	−	0.517846i	$-0.826734\pi$
$83$		−	592195.i		−	1.03569i	0.855474	−	0.517846i	$-0.173266\pi$
$84$	548815.	−	45668.6i	0.925952	−	0.0770513i
$85$	−256981.			−0.418451
$86$	12270.6	−	509.657i	0.0192917	−	0.000801276i
$87$		−	224163.i		−	0.340414i
$88$	−652637.	+	81697.4i	−0.957687	+	0.119884i
$89$	−154289.			−0.218859			−0.109429	−	0.993995i	$-0.534902\pi$
$89$	−154289.			−0.218859			−0.109429	+	0.993995i	$0.534902\pi$
$90$	4509.81	+	108579.i	0.00618630	+	0.148943i
$91$		−	1.38750e6i		−	1.84123i
$92$	−80762.4	−	970549.i	−0.103716	−	1.24639i
$93$	537768.			0.668569
$94$	−1.04947e6	+	43589.6i	−1.26354	+	0.0524807i
$95$			547849.i			0.638984i
$96$	−499840.	+	105260.i	−0.564959	+	0.118973i
$97$	−1.46175e6			−1.60162			−0.800810	−	0.598919i	$-0.795597\pi$
$97$	−1.46175e6			−1.60162			−0.800810	+	0.598919i	$0.795597\pi$
$98$	−62101.9	−	1.49518e6i	−0.0659821	−	1.58860i
$99$			312165.i			0.321721i
$100$	−199311.	+	16585.3i	−0.199311	+	0.0165853i
$101$	963761.			0.935417			0.467708	−	0.883883i	$-0.345080\pi$
$101$	963761.			0.935417			0.467708	+	0.883883i	$0.345080\pi$
$102$	−572789.	+	23790.6i	−0.539752	+	0.0224185i
$103$		−	1.01542e6i		−	0.929250i	−0.885508	−	0.464625i	$-0.846189\pi$
$103$		−	1.01542e6i		−	0.929250i	0.885508	−	0.464625i	$-0.153811\pi$
$104$	159853.	+	1.27698e6i	0.142109	+	1.13523i
$105$	481027.			0.415529
$106$	−75762.4	−	1.82407e6i	−0.0636116	−	1.53153i
$107$			509249.i			0.415699i	0.978161	+	0.207849i	$0.0666463\pi$
$107$			509249.i			0.415699i	−0.978161	+	0.207849i	$0.933354\pi$
$108$	20104.0	+	241597.i	0.0159592	+	0.191787i
$109$	2.13481e6			1.64846			0.824231	−	0.566254i	$-0.191608\pi$
$109$	2.13481e6			1.64846			0.824231	+	0.566254i	$0.191608\pi$
$110$	−574009.	+	23841.3i	−0.431262	+	0.0179123i
$111$		−	1.11316e6i		−	0.813936i
$112$	373703.	+	2.22991e6i	0.265994	+	1.58720i
$113$	178688.			0.123840			0.0619200	−	0.998081i	$-0.480278\pi$
$113$	178688.			0.123840			0.0619200	+	0.998081i	$0.480278\pi$
$114$	50718.4	+	1.22111e6i	0.0342335	+	0.824214i
$115$		−	850670.i		−	0.559329i
$116$	917156.	−	76319.3i	0.587583	−	0.0488946i
$117$	610798.			0.381364
$118$	−2.16773e6	+	90036.0i	−1.31935	+	0.0547987i
$119$			2.53757e6i			1.50583i
$120$	−442712.	+	55418.9i	−0.256199	+	0.0320711i
$121$	121287.			0.0684633
$122$	−83813.2	−	2.01790e6i	−0.0461565	−	1.11127i
$123$		−	587018.i		−	0.315454i
$124$	183090.	+	2.20026e6i	0.0960284	+	1.15401i
$125$	−174693.			−0.0894427
$126$	1.07217e6	−	44532.3i	0.535984	−	0.0222620i
$127$			1.94450e6i			0.949286i	0.880178	+	0.474643i	$0.157423\pi$
$127$			1.94450e6i			0.949286i	−0.880178	+	0.474643i	$0.842577\pi$
$128$	−600843.	−	2.00924e6i	−0.286504	−	0.958079i
$129$	23930.6			0.0111477
$130$	46649.1	+	1.12313e6i	0.0212331	+	0.511213i
$131$			3.66180e6i			1.62885i	0.580270	+	0.814424i	$0.302947\pi$
$131$			3.66180e6i			1.62885i	−0.580270	+	0.814424i	$0.697053\pi$
$132$	−1.27721e6	+	106281.i	−0.555317	+	0.0462096i
$133$	5.40975e6			2.29944
$134$	573796.	−	23832.5i	0.238475	−	0.00990501i
$135$			211755.i			0.0860663i
$136$	−292352.	−	2.33544e6i	−0.116222	−	0.928438i
$137$	477013.			0.185510			0.0927552	−	0.995689i	$-0.470433\pi$
$137$	477013.			0.185510			0.0927552	+	0.995689i	$0.470433\pi$
$138$	−78752.9	−	1.89607e6i	−0.0299660	−	0.721469i
$139$			874957.i			0.325793i	0.986643	+	0.162897i	$0.0520837\pi$
$139$			874957.i			0.325793i	−0.986643	+	0.162897i	$0.947916\pi$
$140$	163772.	+	1.96810e6i	0.0596837	+	0.717239i
$141$	−2.04672e6			−0.730132
$142$	1.54942e6	−	64354.9i	0.541135	−	0.0224759i
$143$			3.22901e6i			1.10423i
$144$	−981639.	+	164509.i	−0.328749	+	0.0550939i
$145$	803871.			0.263683
$146$	41684.3	+	1.00360e6i	0.0133941	+	0.322480i
$147$		−	2.91595e6i		−	0.917970i
$148$	4.55447e6	−	378991.i	1.40492	−	0.116908i
$149$	−2.52851e6			−0.764375			−0.382187	−	0.924085i	$-0.624829\pi$
$149$	−2.52851e6			−0.764375			−0.382187	+	0.924085i	$0.624829\pi$
$150$	−389376.	+	16172.6i	−0.115371	+	0.00479189i
$151$		−	3.24281e6i		−	0.941869i	−0.882168	−	0.470934i	$-0.843917\pi$
$151$		−	3.24281e6i		−	0.941869i	0.882168	−	0.470934i	$-0.156083\pi$
$152$	−4.97885e6	+	623255.i	−1.41775	+	0.177474i
$153$	−1.11707e6			−0.311895
$154$	235422.	+	5.66807e6i	0.0644592	+	1.55193i
$155$			1.92849e6i			0.517871i
$156$	207954.	+	2.49906e6i	0.0547764	+	0.658267i
$157$	−5.96596e6			−1.54164			−0.770818	−	0.637056i	$-0.780152\pi$
$157$	−5.96596e6			−1.54164			−0.770818	+	0.637056i	$0.780152\pi$
$158$	−4.87511e6	+	202487.i	−1.23599	+	0.0513363i
$159$		−	3.55737e6i		−	0.884990i
$160$	−377472.	−	1.79247e6i	−0.0921562	−	0.437615i
$161$	−8.39997e6			−2.01280
$162$	19603.8	+	471985.i	0.00461100	+	0.111015i
$163$		−	4.08504e6i		−	0.943265i	−0.881795	−	0.471632i	$-0.843665\pi$
$163$		−	4.08504e6i		−	0.943265i	0.881795	−	0.471632i	$-0.156335\pi$
$164$	2.40176e6	−	199858.i	0.544501	−	0.0453096i
$165$	−1.11945e6			−0.249204
$166$	4.73348e6	−	196604.i	1.03480	−	0.0429801i
$167$		−	2.47808e6i		−	0.532067i	−0.963964	−	0.266034i	$-0.914287\pi$
$167$		−	2.47808e6i		−	0.532067i	0.963964	−	0.266034i	$-0.0857132\pi$
$168$	547236.	+	4.37158e6i	0.115411	+	0.921957i
$169$	1.49123e6			0.308948
$170$	−85315.5	−	2.05408e6i	−0.0173653	−	0.418090i
$171$			2.38145e6i			0.476270i
$172$	8147.48	+	97911.1i	0.00160117	+	0.0192418i
$173$	8.20504e6			1.58468			0.792341	−	0.610078i	$-0.208862\pi$
$173$	8.20504e6			1.58468			0.792341	+	0.610078i	$0.208862\pi$
$174$	1.79176e6	−	74420.4i	0.340120	−	0.0141268i
$175$			1.72501e6i			0.321868i
$176$	−869686.	−	5.18948e6i	−0.159523	−	0.951887i
$177$	−4.22758e6			−0.762381
$178$	−51222.6	−	1.23325e6i	−0.00908241	−	0.218670i
$179$			3.09966e6i			0.540450i	0.962797	+	0.270225i	$0.0870981\pi$
$179$			3.09966e6i			0.540450i	−0.962797	+	0.270225i	$0.912902\pi$
$180$	−866389.	+	72094.8i	−0.148558	+	0.0123619i
$181$	−2.47886e6			−0.418038			−0.209019	−	0.977912i	$-0.567027\pi$
$181$	−2.47886e6			−0.418038			−0.209019	+	0.977912i	$0.567027\pi$
$182$	1.10904e7	−	460638.i	1.83965	−	0.0764092i
$183$		−	3.93539e6i		−	0.642148i
$184$	7.73089e6	−	967757.i	1.24101	−	0.155351i
$185$	3.99191e6			0.630472
$186$	178535.	+	4.29844e6i	0.0277449	+	0.667993i
$187$		−	5.90546e6i		−	0.903086i
$188$	−696833.	−	8.37408e6i	−0.104871	−	1.26027i
$189$	2.09099e6			0.309717
$190$	−4.37901e6	+	181881.i	−0.638433	+	0.0265172i
$191$			1.42970e6i			0.205185i	0.994723	+	0.102592i	$0.0327137\pi$
$191$			1.42970e6i			0.205185i	−0.994723	+	0.102592i	$0.967286\pi$
$192$	−1.00730e6	−	3.96033e6i	−0.142316	−	0.559535i
$193$	−1.81356e6			−0.252266			−0.126133	−	0.992013i	$-0.540257\pi$
$193$	−1.81356e6			−0.252266			−0.126133	+	0.992013i	$0.540257\pi$
$194$	−485291.	−	1.16840e7i	−0.0664656	−	1.60024i
$195$			2.19038e6i			0.295403i
$196$	1.19305e7	−	992774.i	1.58449	−	0.131851i
$197$	−8.69647e6			−1.13748			−0.568740	−	0.822517i	$-0.692569\pi$
$197$	−8.69647e6			−1.13748			−0.568740	+	0.822517i	$0.692569\pi$
$198$	−2.49517e6	+	103636.i	−0.321443	+	0.0133511i
$199$			5.01570e6i			0.636462i	0.948013	+	0.318231i	$0.103089\pi$
$199$			5.01570e6i			0.636462i	−0.948013	+	0.318231i	$0.896911\pi$
$200$	−198738.	−	1.58761e6i	−0.0248422	−	0.198451i
$201$	1.11904e6			0.137802
$202$	319961.	+	7.70344e6i	0.0388188	+	0.934611i
$203$		−	7.93785e6i		−	0.948888i
$204$	−380322.	−	4.57047e6i	−0.0447983	−	0.538357i
$205$	2.10510e6			0.244350
$206$	8.11634e6	−	337110.i	0.928450	−	0.0385629i
$207$		−	3.69779e6i		−	0.416899i
$208$	−1.01540e7	+	1.70167e6i	−1.12836	+	0.189097i
$209$	−1.25896e7			−1.37903
$210$	159697.	+	3.84490e6i	0.0172440	+	0.415171i
$211$		−	6.77795e6i		−	0.721525i	−0.932658	−	0.360762i	$-0.882517\pi$
$211$		−	6.77795e6i		−	0.721525i	0.932658	−	0.360762i	$-0.117483\pi$
$212$	1.45549e7	−	1.21115e6i	1.52757	−	0.127114i
$213$	3.02175e6			0.312694
$214$	−4.07048e6	+	169066.i	−0.415340	+	0.0172511i
$215$			85817.4i			0.00863495i
$216$	−1.92443e6	+	240902.i	−0.190960	+	0.0239044i
$217$	1.90429e7			1.86361
$218$	708738.	+	1.70637e7i	0.0684095	+	1.64704i
$219$			1.95726e6i			0.186344i
$220$	−381133.	−	4.58020e6i	−0.0357938	−	0.430147i
$221$	−1.15549e7			−1.07051
$222$	8.89764e6	−	369561.i	0.813235	−	0.0337775i
$223$			1.21767e7i			1.09803i	0.835812	+	0.549016i	$0.184997\pi$
$223$			1.21767e7i			1.09803i	−0.835812	+	0.549016i	$0.815003\pi$
$224$	−1.76998e7	+	3.72736e6i	−1.57480	+	0.331632i
$225$	−759375.			−0.0666667
$226$	59323.1	+	1.42828e6i	0.00513923	+	0.123733i
$227$			8.92756e6i			0.763230i	0.924321	+	0.381615i	$0.124632\pi$
$227$			8.92756e6i			0.763230i	−0.924321	+	0.381615i	$0.875368\pi$
$228$	−9.74362e6	+	810796.i	−0.822083	+	0.0684080i
$229$	−1.61284e7			−1.34302			−0.671512	−	0.740994i	$-0.734355\pi$
$229$	−1.61284e7			−1.34302			−0.671512	+	0.740994i	$0.734355\pi$
$230$	6.79950e6	−	282415.i	0.558847	−	0.0232116i
$231$			1.10541e7i			0.896782i
$232$	914517.	+	7.30559e6i	0.0732365	+	0.585048i
$233$	5.66976e6			0.448226			0.224113	−	0.974563i	$-0.428052\pi$
$233$	5.66976e6			0.448226			0.224113	+	0.974563i	$0.428052\pi$
$234$	202780.	+	4.88217e6i	0.0158262	+	0.381036i
$235$		−	7.33974e6i		−	0.565558i
$236$	−1.43933e6	−	1.72970e7i	−0.109503	−	1.31593i
$237$	−9.50762e6			−0.714212
$238$	−2.02830e7	+	842451.i	−1.50453	+	0.0624905i
$239$		−	1.01650e7i		−	0.744583i	−0.928116	−	0.372291i	$-0.878572\pi$
$239$		−	1.01650e7i		−	0.744583i	0.928116	−	0.372291i	$-0.121428\pi$
$240$	−589947.	−	3.52025e6i	−0.0426755	−	0.254648i
$241$	−1.87229e7			−1.33759			−0.668795	−	0.743447i	$-0.733189\pi$
$241$	−1.87229e7			−1.33759			−0.668795	+	0.743447i	$0.733189\pi$
$242$	40266.2	+	969459.i	0.00284115	+	0.0684043i
$243$			920483.i			0.0641500i
$244$	1.61015e7	−	1.33986e6i	1.10840	−	0.0922335i
$245$	1.04569e7			0.711057
$246$	4.69210e6	−	194885.i	0.315182	−	0.0130910i
$247$			2.46335e7i			1.63469i
$248$	−1.75261e7	+	2.19393e6i	−1.14903	+	0.143836i
$249$	9.23140e6			0.597957
$250$	−57996.6	−	1.39634e6i	−0.00371178	−	0.0893657i
$251$			3.39034e6i			0.214398i	0.994238	+	0.107199i	$0.0341883\pi$
$251$			3.39034e6i			0.214398i	−0.994238	+	0.107199i	$0.965812\pi$
$252$	711903.	+	8.55518e6i	0.0444856	+	0.534599i
$253$	1.95485e7			1.20713
$254$	−1.55426e7	+	645559.i	−0.948468	+	0.0393944i
$255$		−	4.00594e6i		−	0.241593i
$256$	1.58606e7	−	5.46965e6i	0.945364	−	0.326017i
$257$	2.79800e7			1.64835			0.824173	−	0.566338i	$-0.191640\pi$
$257$	2.79800e7			1.64835			0.824173	+	0.566338i	$0.191640\pi$
$258$	7944.76	+	191280.i	0.000462617	+	0.0111381i
$259$		−	3.94183e7i		−	2.26881i
$260$	−8.96185e6	+	745743.i	−0.509891	+	0.0424296i
$261$	3.49436e6			0.196538
$262$	−2.92692e7	+	1.21569e6i	−1.62745	+	0.0675955i
$263$			2.67037e7i			1.46793i	0.679189	+	0.733963i	$0.262331\pi$
$263$			2.67037e7i			1.46793i	−0.679189	+	0.733963i	$0.737669\pi$
$264$	−1.27354e6	−	1.01736e7i	−0.0692149	−	0.552921i
$265$	1.27571e7			0.685510
$266$	1.79599e6	+	4.32407e7i	0.0954244	+	2.29746i
$267$		−	2.40512e6i		−	0.126358i
$268$	380991.	+	4.57850e6i	0.0197929	+	0.237859i
$269$	2.74962e7			1.41259			0.706295	−	0.707917i	$-0.250365\pi$
$269$	2.74962e7			1.41259			0.706295	+	0.707917i	$0.250365\pi$
$270$	−1.69258e6	+	70301.0i	−0.0859922	+	0.00357166i
$271$			7.82244e6i			0.393038i	0.980500	+	0.196519i	$0.0629637\pi$
$271$			7.82244e6i			0.393038i	−0.980500	+	0.196519i	$0.937036\pi$
$272$	1.85704e7	−	3.11215e6i	0.922815	−	0.154651i
$273$	2.16290e7			1.06304
$274$	158364.	+	3.81281e6i	0.00769849	+	0.185351i
$275$		−	4.01447e6i		−	0.193032i
$276$	1.51294e7	−	1.25896e6i	0.719604	−	0.0598804i
$277$	−3.48863e7			−1.64140			−0.820702	−	0.571356i	$-0.806418\pi$
$277$	−3.48863e7			−1.64140			−0.820702	+	0.571356i	$0.806418\pi$
$278$	−6.99362e6	+	290478.i	−0.325513	+	0.0135201i
$279$			8.38297e6i			0.385998i
$280$	−1.56769e7	+	1.96244e6i	−0.714144	+	0.0893969i
$281$	−2.43392e6			−0.109695			−0.0548476	−	0.998495i	$-0.517467\pi$
$281$	−2.43392e6			−0.109695			−0.0548476	+	0.998495i	$0.517467\pi$
$282$	−679495.	−	1.63597e7i	−0.0302997	−	0.729503i
$283$			3.82558e7i			1.68787i	0.536447	+	0.843934i	$0.319766\pi$
$283$			3.82558e7i			1.68787i	−0.536447	+	0.843934i	$0.680234\pi$
$284$	1.02879e6	+	1.23634e7i	0.0449131	+	0.539736i
$285$	−8.54011e6			−0.368917
$286$	−2.58098e7	+	1.07200e6i	−1.10328	+	0.0458246i
$287$		−	2.07869e7i		−	0.879315i
$288$	−1.64084e6	−	7.79173e6i	−0.0686891	−	0.326179i
$289$	−3.00503e6			−0.124496
$290$	266879.	+	6.42543e6i	0.0109426	+	0.263456i
$291$		−	2.27865e7i		−	0.924695i
$292$	−8.00805e6	+	666374.i	−0.321646	+	0.0267651i
$293$	2.04358e7			0.812436			0.406218	−	0.913776i	$-0.366847\pi$
$293$	2.04358e7			0.812436			0.406218	+	0.913776i	$0.366847\pi$
$294$	2.33075e7	−	968072.i	0.917179	−	0.0380948i
$295$		−	1.51605e7i		−	0.590538i
$296$	4.54136e6	+	3.62785e7i	0.175110	+	1.39886i
$297$	−4.86617e6			−0.185745
$298$	−839445.	−	2.02107e7i	−0.0317208	−	0.763716i
$299$		−	3.82496e7i		−	1.43091i
$300$	−258539.	−	3.10695e6i	−0.00957552	−	0.115072i
$301$	847407.			0.0310737
$302$	2.59201e7	−	1.07659e6i	0.941058	−	0.0390866i
$303$			1.50235e7i			0.540063i
$304$	−6.63468e6	−	3.95896e7i	−0.236156	−	1.40916i
$305$	1.41127e7			0.497405
$306$	−370859.	−	8.92890e6i	−0.0129433	−	0.311626i
$307$		−	9.54158e6i		−	0.329765i	−0.986313	−	0.164883i	$-0.947275\pi$
$307$		−	9.54158e6i		−	0.329765i	0.986313	−	0.164883i	$-0.0527246\pi$
$308$	−4.52273e7	+	3.76351e6i	−1.54792	+	0.128807i
$309$	1.58288e7			0.536503
$310$	−1.54146e7	+	640242.i	−0.517425	+	0.0214911i
$311$			2.91657e6i			0.0969595i	0.998824	+	0.0484798i	$0.0154376\pi$
$311$			2.91657e6i			0.0969595i	−0.998824	+	0.0484798i	$0.984562\pi$
$312$	−1.99062e7	+	2.49186e6i	−0.655427	+	0.0820466i
$313$	1.93741e7			0.631814			0.315907	−	0.948790i	$-0.397691\pi$
$313$	1.93741e7			0.631814			0.315907	+	0.948790i	$0.397691\pi$
$314$	−1.98065e6	−	4.76866e7i	−0.0639763	−	1.54031i
$315$			7.49847e6i			0.239906i
$316$	−3.23699e6	−	3.89001e7i	−0.102584	−	1.23279i
$317$	6.50536e6			0.204218			0.102109	−	0.994773i	$-0.467441\pi$
$317$	6.50536e6			0.204218			0.102109	+	0.994773i	$0.467441\pi$
$318$	2.84345e7	−	1.18102e6i	0.884227	−	0.0367262i
$319$			1.84731e7i			0.569072i
$320$	1.42021e7	−	3.61226e6i	0.433414	−	0.110237i
$321$	−7.93840e6			−0.240004
$322$	−2.78872e6	−	6.71419e7i	−0.0835290	−	2.01106i
$323$		−	4.50517e7i		−	1.33692i
$324$	−3.76612e6	+	313390.i	−0.110728	+	0.00921405i
$325$	−7.85491e6			−0.228818
$326$	3.26522e7	−	1.35620e6i	0.942452	−	0.0391445i
$327$			3.32783e7i			0.951740i
$328$	2.39485e6	+	1.91312e7i	0.0678668	+	0.542151i
$329$	−7.24765e7			−2.03521
$330$	−371649.	−	8.94792e6i	−0.0103417	−	0.248989i
$331$			2.30862e7i			0.636603i	0.947990	+	0.318301i	$0.103112\pi$
$331$			2.30862e7i			0.636603i	−0.947990	+	0.318301i	$0.896888\pi$
$332$	3.14295e6	+	3.77699e7i	0.0858862	+	1.03212i
$333$	1.73525e7			0.469926
$334$	1.98076e7	−	822703.i	0.531609	−	0.0220802i
$335$			4.01298e6i			0.106741i
$336$	−3.47608e7	+	5.82545e6i	−0.916373	+	0.153572i
$337$	−4.43828e7			−1.15965			−0.579823	−	0.814743i	$-0.696878\pi$
$337$	−4.43828e7			−1.15965			−0.579823	+	0.814743i	$0.696878\pi$
$338$	495076.	+	1.19196e7i	0.0128210	+	0.308681i
$339$			2.78548e6i			0.0714991i
$340$	1.63901e7	−	1.36387e6i	0.417009	−	0.0347006i
$341$	−4.43170e7			−1.11765
$342$	−1.90352e7	+	790622.i	−0.475860	+	0.0197647i
$343$		−	3.83142e7i		−	0.949463i
$344$	−779909.	+	97629.4i	−0.0191588	+	0.00239831i
$345$	1.32606e7			0.322929
$346$	2.72400e6	+	6.55838e7i	0.0657627	+	1.58332i
$347$		−	2.62548e7i		−	0.628376i	−0.949361	−	0.314188i	$-0.898268\pi$
$347$		−	2.62548e7i		−	0.628376i	0.949361	−	0.314188i	$-0.101732\pi$
$348$	1.18970e6	+	1.42970e7i	0.0282293	+	0.339241i
$349$	7.54811e7			1.77567			0.887834	−	0.460164i	$-0.152209\pi$
$349$	7.54811e7			1.77567			0.887834	+	0.460164i	$0.152209\pi$
$350$	−1.37882e7	+	572689.i	−0.321590	+	0.0133572i
$351$			9.52140e6i			0.220181i
$352$	4.11913e7	−	8.67436e6i	0.944447	−	0.198888i
$353$	−7.31900e6			−0.166390			−0.0831951	−	0.996533i	$-0.526512\pi$
$353$	−7.31900e6			−0.166390			−0.0831951	+	0.996533i	$0.526512\pi$
$354$	−1.40352e6	−	3.37915e7i	−0.0316380	−	0.761724i
$355$			1.08363e7i			0.242211i
$356$	9.84046e6	−	818855.i	0.218105	−	0.0181492i
$357$	−3.95567e7			−0.869393
$358$	−2.47759e7	+	1.02906e6i	−0.539984	+	0.0224281i
$359$			4.02979e7i			0.870961i	0.900198	+	0.435480i	$0.143421\pi$
$359$			4.02979e7i			0.870961i	−0.900198	+	0.435480i	$0.856579\pi$
$360$	−863896.	−	6.90120e6i	−0.0185163	−	0.147917i
$361$	−4.89983e7			−1.04150
$362$	−822960.	−	1.98138e7i	−0.0173482	−	0.417678i
$363$			1.89067e6i			0.0395273i
$364$	7.36386e6	+	8.84941e7i	0.152687	+	1.83489i
$365$	−7.01892e6			−0.144342
$366$	3.14560e7	−	1.30652e6i	0.641594	−	0.0266485i
$367$			2.15750e7i			0.436469i	0.975896	+	0.218234i	$0.0700297\pi$
$367$			2.15750e7i			0.436469i	−0.975896	+	0.218234i	$0.929970\pi$
$368$	1.03020e7	+	6.14726e7i	0.206717	+	1.23350i
$369$	9.15071e6			0.182128
$370$	1.32528e6	+	3.19078e7i	0.0261639	+	0.629929i
$371$		−	1.25970e8i		−	2.46687i
$372$	−3.42986e7	+	2.85409e6i	−0.666266	+	0.0554420i
$373$	5.20071e7			1.00216			0.501079	−	0.865401i	$-0.332937\pi$
$373$	5.20071e7			1.00216			0.501079	+	0.865401i	$0.332937\pi$
$374$	4.72030e7	−	1.96056e6i	0.902308	−	0.0374771i
$375$		−	2.72319e6i		−	0.0516398i
$376$	6.67036e7	−	8.34999e6i	1.25483	−	0.157081i
$377$	3.61454e7			0.674573
$378$	694190.	+	1.67135e7i	0.0128529	+	0.309451i
$379$			9.39645e6i			0.172602i	0.996269	+	0.0863010i	$0.0275047\pi$
$379$			9.39645e6i			0.172602i	−0.996269	+	0.0863010i	$0.972495\pi$
$380$	−2.90759e6	−	3.49415e7i	−0.0529886	−	0.636783i
$381$	−3.03118e7			−0.548071
$382$	−1.14277e7	+	474649.i	−0.205008	+	0.00851495i
$383$		−	1.54516e7i		−	0.275028i	−0.990500	−	0.137514i	$-0.956089\pi$
$383$		−	1.54516e7i		−	0.275028i	0.990500	−	0.137514i	$-0.0439112\pi$
$384$	3.13209e7	−	9.36622e6i	0.553147	−	0.165413i
$385$	−3.96410e7			−0.694644
$386$	−602086.	−	1.44960e7i	−0.0104688	−	0.252049i
$387$			373041.i			0.00643612i
$388$	9.32301e7	−	7.75796e6i	1.59610	−	0.132817i
$389$	−5.51480e7			−0.936873			−0.468437	−	0.883497i	$-0.655183\pi$
$389$	−5.51480e7			−0.936873			−0.468437	+	0.883497i	$0.655183\pi$
$390$	−1.75079e7	+	727188.i	−0.295149	+	0.0122589i
$391$			6.99539e7i			1.17026i
$392$	1.18962e7	+	9.50322e7i	0.197492	+	1.57766i
$393$	−5.70818e7			−0.940416
$394$	−2.88715e6	−	6.95118e7i	−0.0472043	−	1.13650i
$395$		−	3.40952e7i		−	0.553226i
$396$	−1.65675e6	−	1.99098e7i	−0.0266791	−	0.320612i
$397$	−9.29579e7			−1.48564			−0.742822	−	0.669489i	$-0.766513\pi$
$397$	−9.29579e7			−1.48564			−0.742822	+	0.669489i	$0.766513\pi$
$398$	−4.00910e7	+	1.66517e6i	−0.635914	+	0.0264125i
$399$			8.43296e7i			1.32758i
$400$	1.26240e7	−	2.11560e6i	0.197249	−	0.0330563i
$401$	1.17915e8			1.82867			0.914334	−	0.404960i	$-0.132715\pi$
$401$	1.17915e8			1.82867			0.914334	+	0.404960i	$0.132715\pi$
$402$	371512.	+	8.94460e6i	0.00571866	+	0.137684i
$403$			8.67128e7i			1.32485i
$404$	−6.14682e7	+	5.11496e6i	−0.932195	+	0.0775708i
$405$	−3.30094e6			−0.0496904
$406$	6.34481e7	−	2.63530e6i	0.948071	−	0.0393779i
$407$			9.17348e7i			1.36066i
$408$	3.64060e7	−	4.55732e6i	0.536034	−	0.0671009i
$409$	6.08808e7			0.889836			0.444918	−	0.895571i	$-0.353233\pi$
$409$	6.08808e7			0.889836			0.444918	+	0.895571i	$0.353233\pi$
$410$	698877.	+	1.68263e7i	0.0101403	+	0.244139i
$411$			7.43589e6i			0.107104i
$412$	5.38911e6	+	6.47628e7i	0.0770594	+	0.926050i
$413$	−1.49703e8			−2.12510
$414$	2.95568e7	−	1.22764e6i	0.416540	−	0.0173009i
$415$			3.31047e7i			0.463175i
$416$	−1.69727e7	−	8.05970e7i	−0.235760	−	1.11954i
$417$	−1.36392e7			−0.188097
$418$	−4.17966e6	−	1.00630e8i	−0.0572285	−	1.37785i
$419$			3.24991e7i			0.441803i	0.975296	+	0.220902i	$0.0709000\pi$
$419$			3.24991e7i			0.441803i	−0.975296	+	0.220902i	$0.929100\pi$
$420$	−3.06797e7	+	2.55295e6i	−0.414098	+	0.0344584i
$421$	4.14006e7			0.554830			0.277415	−	0.960750i	$-0.410522\pi$
$421$	4.14006e7			0.554830			0.277415	+	0.960750i	$0.410522\pi$
$422$	5.41769e7	−	2.25022e6i	0.720903	−	0.0299425i
$423$		−	3.19052e7i		−	0.421542i
$424$	1.45130e7	+	1.15936e8i	0.190397	+	1.52098i
$425$	1.43657e7			0.187137
$426$	1.00319e6	+	2.41531e7i	0.0129765	+	0.312424i
$427$		−	1.39356e8i		−	1.78996i
$428$	−2.70273e6	−	3.24797e7i	−0.0344724	−	0.414267i
$429$	−5.03353e7			−0.637530
$430$	−685948.	+	28490.7i	−0.00862752	+	0.000358342i
$431$			2.64521e7i			0.330391i	0.986261	+	0.165196i	$0.0528255\pi$
$431$			2.64521e7i			0.330391i	−0.986261	+	0.165196i	$0.947174\pi$
$432$	−2.56445e6	−	1.53022e7i	−0.0318085	−	0.189803i
$433$	−2.52090e7			−0.310521			−0.155261	−	0.987874i	$-0.549622\pi$
$433$	−2.52090e7			−0.310521			−0.155261	+	0.987874i	$0.549622\pi$
$434$	6.32209e6	+	1.52212e8i	0.0773377	+	1.86200i
$435$			1.25311e7i			0.152238i
$436$	−1.36157e8	+	1.13300e7i	−1.64278	+	0.136701i
$437$	1.49132e8			1.78701
$438$	−1.56446e7	+	649794.i	−0.186184	+	0.00773309i
$439$		−	1.58533e8i		−	1.87381i	−0.349589	−	0.936903i	$-0.613679\pi$
$439$		−	1.58533e8i		−	1.87381i	0.349589	−	0.936903i	$-0.386321\pi$
$440$	3.64835e7	−	4.56702e6i	0.428291	−	0.0536136i
$441$	4.54552e7			0.529990
$442$	−3.83614e6	−	9.23598e7i	−0.0444250	−	1.06959i
$443$		−	1.05332e8i		−	1.21157i	−0.795627	−	0.605787i	$-0.792858\pi$
$443$		−	1.05332e8i		−	1.21157i	0.795627	−	0.605787i	$-0.207142\pi$
$444$	5.90789e6	+	7.09971e7i	0.0674968	+	0.811132i
$445$	8.62500e6			0.0978766
$446$	−9.73297e7	+	4.04256e6i	−1.09709	+	0.0455672i
$447$		−	3.94156e7i		−	0.441312i
$448$	−3.56694e7	−	1.40239e8i	−0.396699	−	1.55968i
$449$	−1.45273e8			−1.60490			−0.802448	−	0.596722i	$-0.796470\pi$
$449$	−1.45273e8			−1.60490			−0.802448	+	0.596722i	$0.796470\pi$
$450$	−252106.	−	6.06977e6i	−0.00276660	−	0.0666092i
$451$			4.83756e7i			0.527348i
$452$	−1.13967e7	+	948351.i	−0.123413	+	0.0102696i
$453$	5.05504e7			0.543788
$454$	−7.13590e7	+	2.96388e6i	−0.762572	+	0.0316732i
$455$			7.75636e7i			0.823424i
$456$	−9.71558e6	−	7.76126e7i	−0.102465	−	0.818536i
$457$	1.00926e8			1.05744			0.528718	−	0.848797i	$-0.322673\pi$
$457$	1.00926e8			1.05744			0.528718	+	0.848797i	$0.322673\pi$
$458$	−5.35448e6	−	1.28916e8i	−0.0557341	−	1.34187i
$459$		−	1.74135e7i		−	0.180072i
$460$	4.51475e6	+	5.42554e7i	0.0463832	+	0.557403i
$461$	−1.04798e8			−1.06968			−0.534838	−	0.844955i	$-0.679627\pi$
$461$	−1.04798e8			−1.06968			−0.534838	+	0.844955i	$0.679627\pi$
$462$	−8.83565e7	+	3.66986e6i	−0.896009	+	0.0372155i
$463$			8.32165e7i			0.838430i	0.907887	+	0.419215i	$0.137695\pi$
$463$			8.32165e7i			0.838430i	−0.907887	+	0.419215i	$0.862305\pi$
$464$	−5.80907e7	+	9.73523e6i	−0.581504	+	0.0974523i
$465$	−3.00621e7			−0.298993
$466$	1.88231e6	+	4.53190e7i	0.0186009	+	0.447840i
$467$			7.13276e6i			0.0700337i	0.999387	+	0.0350168i	$0.0111485\pi$
$467$			7.13276e6i			0.0700337i	−0.999387	+	0.0350168i	$0.988852\pi$
$468$	−3.89564e7	+	3.24168e6i	−0.380051	+	0.0316252i
$469$	3.96263e7			0.384118
$470$	5.86673e7	−	2.43673e6i	0.565071	−	0.0234701i
$471$		−	9.30002e7i		−	0.890064i
$472$	1.37779e8	−	1.72472e7i	1.31026	−	0.164019i
$473$	−1.97210e6			−0.0186357
$474$	−3.15645e6	−	7.59955e7i	−0.0296390	−	0.713596i
$475$		−	3.06257e7i		−	0.285762i
$476$	−1.34676e7	−	1.61845e8i	−0.124873	−	1.50065i
$477$	5.54540e7			0.510949
$478$	8.12498e7	−	3.37469e6i	0.743941	−	0.0308994i
$479$			1.02247e8i			0.930346i	0.885220	+	0.465173i	$0.154008\pi$
$479$			1.02247e8i			0.930346i	−0.885220	+	0.465173i	$0.845992\pi$
$480$	2.79419e7	−	5.88420e6i	0.252657	−	0.0532064i
$481$	1.79493e8			1.61292
$482$	−6.21586e6	−	1.49654e8i	−0.0555086	−	1.33644i
$483$		−	1.30943e8i		−	1.16209i
$484$	−7.73562e6	+	643705.i	−0.0682274	+	0.00567741i
$485$	8.17146e7			0.716266
$486$	−7.35752e6	+	305593.i	−0.0640948	+	0.00266216i
$487$		−	7.59619e6i		−	0.0657671i	−0.999459	−	0.0328836i	$-0.989531\pi$
$487$		−	7.59619e6i		−	0.0657671i	0.999459	−	0.0328836i	$-0.0104691\pi$
$488$	1.60552e7	+	1.28256e8i	0.138152	+	1.10362i
$489$	6.36795e7			0.544594
$490$	3.47160e6	+	8.35830e7i	0.0295081	+	0.710444i
$491$			4.78138e7i			0.403932i	0.979393	+	0.201966i	$0.0647331\pi$
$491$			4.78138e7i			0.403932i	−0.979393	+	0.201966i	$0.935267\pi$
$492$	3.11548e6	+	3.74398e7i	0.0261595	+	0.314368i
$493$	−6.61055e7			−0.551692
$494$	−1.96899e8	+	8.17813e6i	−1.63328	+	0.0678380i
$495$		−	1.74506e7i		−	0.143878i
$496$	−2.33548e7	−	1.39360e8i	−0.191395	−	1.14207i
$497$	1.07003e8			0.871620
$498$	3.06475e6	+	7.37876e7i	0.0248146	+	0.597441i
$499$		−	7.03458e7i		−	0.566157i	−0.959097	−	0.283078i	$-0.908644\pi$
$499$		−	7.03458e7i		−	0.566157i	0.959097	−	0.283078i	$-0.0913556\pi$
$500$	1.11418e7	−	927146.i	0.0891346	−	0.00741717i
$501$	3.86295e7			0.307189
$502$	−2.70993e7	+	1.12556e6i	−0.214214	+	0.00889731i
$503$		−	1.29972e7i		−	0.102128i	−0.998695	−	0.0510639i	$-0.983739\pi$
$503$		−	1.29972e7i		−	0.102128i	0.998695	−	0.0510639i	$-0.0162612\pi$
$504$	−6.81462e7	+	8.53057e6i	−0.532292	+	0.0666325i
$505$	−5.38759e7			−0.418331
$506$	6.48995e6	+	1.56254e8i	0.0500945	+	1.20609i
$507$			2.32460e7i			0.178371i
$508$	−1.03200e7	−	1.24019e8i	−0.0787209	−	0.946017i
$509$	1.39419e8			1.05723			0.528616	−	0.848861i	$-0.322711\pi$
$509$	1.39419e8			1.05723			0.528616	+	0.848861i	$0.322711\pi$
$510$	3.20199e7	−	1.32994e6i	0.241384	−	0.0100258i
$511$			6.93085e7i			0.519426i
$512$	4.89851e7	+	1.24959e8i	0.364968	+	0.931020i
$513$	−3.71232e7			−0.274975
$514$	9.28913e6	+	2.23647e8i	0.0684047	+	1.64693i
$515$			5.67635e7i			0.415573i
$516$	−1.52628e6	+	127007.i	−0.0111093	+	0.000924437i
$517$	1.68668e8			1.22057
$518$	3.15074e8	−	1.30865e7i	2.26686	−	0.0941533i
$519$			1.27904e8i			0.914917i
$520$	−8.93606e6	−	7.13855e7i	−0.0635530	−	0.507691i
$521$	−1.76371e6			−0.0124714			−0.00623570	−	0.999981i	$-0.501985\pi$
$521$	−1.76371e6			−0.0124714			−0.00623570	+	0.999981i	$0.501985\pi$
$522$	1.16010e6	+	2.79308e7i	0.00815612	+	0.196369i
$523$		−	2.26098e8i		−	1.58049i	−0.612792	−	0.790244i	$-0.709954\pi$
$523$		−	2.26098e8i		−	1.58049i	0.612792	−	0.790244i	$-0.290046\pi$
$524$	−1.94342e7	−	2.33548e8i	−0.135075	−	1.62324i
$525$	−2.68902e7			−0.185830
$526$	−2.13446e8	+	8.86541e6i	−1.46666	+	0.0609174i
$527$		−	1.58587e8i		−	1.08352i
$528$	8.08959e7	−	1.35571e7i	0.549572	−	0.0921009i
$529$	−8.35287e7			−0.564246
$530$	4.23525e6	+	1.01969e8i	0.0284480	+	0.684920i
$531$		−	6.59015e7i		−	0.440161i
$532$	−3.45031e8	+	2.87111e7i	−2.29152	+	0.190684i
$533$	9.46542e7			0.625112
$534$	1.92244e7	−	798481.i	0.126249	−	0.00524373i
$535$		−	2.84679e7i		−	0.185906i
$536$	−3.64700e7	+	4.56533e6i	−0.236832	+	0.0296468i
$537$	−4.83190e7			−0.312029
$538$	9.12852e6	+	2.19780e8i	0.0586210	+	1.41137i
$539$			2.40301e8i			1.53458i
$540$	−1.12385e6	−	1.35057e7i	−0.00713717	−	0.0857699i
$541$	1.06341e8			0.671596			0.335798	−	0.941934i	$-0.390994\pi$
$541$	1.06341e8			0.671596			0.335798	+	0.941934i	$0.390994\pi$
$542$	−6.25256e7	+	2.59699e6i	−0.392699	+	0.0163107i
$543$		−	3.86416e7i		−	0.241354i
$544$	3.10410e7	+	1.47402e8i	0.192814	+	0.915602i
$545$	−1.19339e8			−0.737215
$546$	7.18064e6	+	1.72883e8i	0.0441149	+	1.06212i
$547$			1.70542e7i			0.104200i	0.998642	+	0.0521002i	$0.0165915\pi$
$547$			1.70542e7i			0.104200i	−0.998642	+	0.0521002i	$0.983408\pi$
$548$	−3.04237e7	+	2.53165e6i	−0.184871	+	0.0153837i
$549$	6.13467e7			0.370744
$550$	3.20881e7	−	1.33277e6i	0.192866	−	0.00801064i
$551$			1.40928e8i			0.842446i
$552$	1.50858e7	+	1.20513e8i	0.0896917	+	0.716499i
$553$	−3.36675e8			−1.99083
$554$	−1.15820e7	−	2.78850e8i	−0.0681166	−	1.63999i
$555$			6.22278e7i			0.364003i
$556$	−4.64365e6	−	5.58043e7i	−0.0270169	−	0.324671i
$557$	−1.31701e8			−0.762118			−0.381059	−	0.924551i	$-0.624441\pi$
$557$	−1.31701e8			−0.762118			−0.381059	+	0.924551i	$0.624441\pi$
$558$	−6.70060e7	+	2.78308e6i	−0.385666	+	0.0160185i
$559$			3.85871e6i			0.0220905i
$560$	−2.08906e7	−	1.24656e8i	−0.118956	−	0.709819i
$561$	9.20571e7			0.521397
$562$	−808042.	−	1.94546e7i	−0.00455224	−	0.109601i
$563$			9.70061e7i			0.543593i	0.962355	+	0.271797i	$0.0876178\pi$
$563$			9.70061e7i			0.543593i	−0.962355	+	0.271797i	$0.912382\pi$
$564$	1.30539e8	−	1.08626e7i	0.727617	−	0.0605473i
$565$	−9.98898e6			−0.0553829
$566$	−3.05783e8	+	1.27006e7i	−1.68641	+	0.0700448i
$567$			3.25952e7i			0.178815i
$568$	−9.84801e7	+	1.23278e7i	−0.537407	+	0.0672728i
$569$	2.37401e8			1.28868			0.644341	−	0.764738i	$-0.277132\pi$
$569$	2.37401e8			1.28868			0.644341	+	0.764738i	$0.277132\pi$
$570$	−2.83525e6	−	6.82621e7i	−0.0153097	−	0.368600i
$571$		−	8.85844e7i		−	0.475827i	−0.971286	−	0.237913i	$-0.923537\pi$
$571$		−	8.85844e7i		−	0.475827i	0.971286	−	0.237913i	$-0.0764635\pi$
$572$	−1.71373e7	−	2.05945e8i	−0.0915702	−	1.10043i
$573$	−2.22868e7			−0.118463
$574$	1.66152e8	−	6.90108e6i	0.878557	−	0.0364907i
$575$			4.75539e7i			0.250140i
$576$	6.17354e7	−	1.57022e7i	0.323048	−	0.0821661i
$577$	−2.33160e8			−1.21374			−0.606871	−	0.794800i	$-0.707576\pi$
$577$	−2.33160e8			−1.21374			−0.606871	+	0.794800i	$0.707576\pi$
$578$	−997644.	−	2.40195e7i	−0.00516645	−	0.124389i
$579$		−	2.82706e7i		−	0.145646i
$580$	−5.12706e7	+	4.26638e6i	−0.262775	+	0.0218663i
$581$	3.26893e8			1.66678
$582$	1.82135e8	−	7.56493e6i	0.923899	−	0.0383739i
$583$			2.93160e8i			1.47945i
$584$	−7.98500e6	−	6.37880e7i	−0.0400901	−	0.320258i
$585$	−3.41446e7			−0.170551
$586$	6.78452e6	+	1.63346e8i	0.0337152	+	0.811736i
$587$			3.20487e8i			1.58451i	0.610187	+	0.792257i	$0.291094\pi$
$587$			3.20487e8i			1.58451i	−0.610187	+	0.792257i	$0.708906\pi$
$588$	1.54758e7	+	1.85978e8i	0.0761240	+	0.914808i
$589$	−3.38086e8			−1.65456
$590$	1.21180e8	−	5.03316e6i	0.590029	−	0.0245067i
$591$		−	1.35564e8i		−	0.656725i
$592$	−2.88470e8	+	4.83438e7i	−1.39039	+	0.233010i
$593$	−2.06932e8			−0.992345			−0.496173	−	0.868224i	$-0.665262\pi$
$593$	−2.06932e8			−0.992345			−0.496173	+	0.868224i	$0.665262\pi$
$594$	−1.61553e6	−	3.88958e7i	−0.00770824	−	0.185585i
$595$		−	1.41854e8i		−	0.673429i
$596$	1.61267e8	−	1.34196e7i	0.761742	−	0.0633869i
$597$	−7.81871e7			−0.367462
$598$	3.05733e8	−	1.26986e7i	1.42968	−	0.0593815i
$599$			1.70428e8i			0.792976i	0.918040	+	0.396488i	$0.129771\pi$
$599$			1.70428e8i			0.792976i	−0.918040	+	0.396488i	$0.870229\pi$
$600$	2.47484e7	−	3.09801e6i	0.114576	−	0.0143427i
$601$	−2.51778e8			−1.15983			−0.579914	−	0.814678i	$-0.696914\pi$
$601$	−2.51778e8			−1.15983			−0.579914	+	0.814678i	$0.696914\pi$
$602$	281332.	+	6.77342e6i	0.00128953	+	0.0310469i
$603$			1.74441e7i			0.0795603i
$604$	1.72105e7	+	2.06825e8i	0.0781058	+	0.938625i
$605$	−6.78014e6			−0.0306177
$606$	−1.20085e8	+	4.98769e6i	−0.539598	+	0.0224121i
$607$			3.60842e8i			1.61343i	0.590940	+	0.806716i	$0.298757\pi$
$607$			3.60842e8i			1.61343i	−0.590940	+	0.806716i	$0.701243\pi$
$608$	3.14241e8	−	6.61751e7i	1.39815	−	0.294431i
$609$	1.23739e8			0.547841
$610$	4.68530e6	+	1.12804e8i	0.0206418	+	0.496977i
$611$		−	3.30025e8i		−	1.44685i
$612$	7.12465e7	−	5.92864e6i	0.310820	−	0.0258643i
$613$	2.76049e6			0.0119841			0.00599203	−	0.999982i	$-0.498093\pi$
$613$	2.76049e6			0.0119841			0.00599203	+	0.999982i	$0.498093\pi$
$614$	7.62669e7	−	3.16773e6i	0.329481	−	0.0136849i
$615$			3.28153e7i			0.141075i
$616$	−4.50972e7	−	3.60258e8i	−0.192933	−	1.54124i
$617$	−5.86892e7			−0.249863			−0.124932	−	0.992165i	$-0.539871\pi$
$617$	−5.86892e7			−0.249863			−0.124932	+	0.992165i	$0.539871\pi$
$618$	5.25502e6	+	1.26521e8i	0.0222643	+	0.536041i
$619$		−	2.86112e8i		−	1.20632i	−0.797619	−	0.603161i	$-0.793907\pi$
$619$		−	2.86112e8i		−	1.20632i	0.797619	−	0.603161i	$-0.206093\pi$
$620$	−1.02350e7	−	1.22998e8i	−0.0429452	−	0.516087i
$621$	5.76429e7			0.240697
$622$	−2.33124e7	+	968275.i	−0.0968760	+	0.00402372i
$623$		−	8.51678e7i		−	0.352218i
$624$	−2.65264e7	−	1.58285e8i	−0.109175	−	0.651457i
$625$	9.76562e6			0.0400000
$626$	6.43205e6	+	1.54859e8i	0.0262196	+	0.631269i
$627$		−	1.96253e8i		−	0.796185i
$628$	3.80507e8	−	3.16631e7i	1.53633	−	0.127842i
$629$	−3.28270e8			−1.31911
$630$	−5.99361e7	+	2.48943e6i	−0.239699	+	0.00995585i
$631$		−	2.43261e8i		−	0.968244i	−0.875001	−	0.484122i	$-0.839139\pi$
$631$		−	2.43261e8i		−	0.968244i	0.875001	−	0.484122i	$-0.160861\pi$
$632$	3.09858e8	−	3.87881e7i	1.22747	−	0.153655i
$633$	1.05658e8			0.416572
$634$	2.15972e6	+	5.19980e7i	0.00847482	+	0.204042i
$635$		−	1.08701e8i		−	0.424534i
$636$	1.88800e7	+	2.26888e8i	0.0733890	+	0.881941i
$637$	4.70185e8			1.81907
$638$	−1.47657e8	+	6.13291e6i	−0.568582	+	0.0236159i
$639$			4.71043e7i			0.180534i
$640$	3.35882e7	+	1.12320e8i	0.128129	+	0.428466i
$641$	1.54539e8			0.586766			0.293383	−	0.955995i	$-0.405219\pi$
$641$	1.54539e8			0.586766			0.293383	+	0.955995i	$0.405219\pi$
$642$	−2.63548e6	−	6.34525e7i	−0.00995990	−	0.239797i
$643$			1.73101e8i			0.651130i	0.945520	+	0.325565i	$0.105555\pi$
$643$			1.73101e8i			0.651130i	−0.945520	+	0.325565i	$0.894445\pi$
$644$	5.35746e8	−	4.45811e7i	2.00586	−	0.166914i
$645$	−1.33776e6			−0.00498539
$646$	3.60103e8	−	1.49568e7i	1.33576	−	0.0554806i
$647$		−	2.97783e8i		−	1.09948i	−0.835336	−	0.549740i	$-0.814727\pi$
$647$		−	2.97783e8i		−	1.09948i	0.835336	−	0.549740i	$-0.185273\pi$
$648$	−3.75528e6	−	2.99990e7i	−0.0138012	−	0.110251i
$649$	3.48391e8			1.27448
$650$	−2.60777e6	−	6.27851e7i	−0.00949573	−	0.228621i
$651$			2.96850e8i			1.07595i
$652$	2.16805e7	+	2.60542e8i	0.0782216	+	0.940016i
$653$	−4.67892e8			−1.68038			−0.840188	−	0.542296i	$-0.817555\pi$
$653$	−4.67892e8			−1.68038			−0.840188	+	0.542296i	$0.817555\pi$
$654$	−2.65997e8	+	1.10481e7i	−0.950920	+	0.0394962i
$655$		−	2.04701e8i		−	0.728443i
$656$	−1.52123e8	+	2.54937e7i	−0.538868	+	0.0903070i
$657$	−3.05106e7			−0.107586
$658$	−2.40616e7	−	5.79313e8i	−0.0844592	−	2.03346i
$659$		−	3.65042e8i		−	1.27552i	−0.770236	−	0.637759i	$-0.779862\pi$
$659$		−	3.65042e8i		−	1.27552i	0.770236	−	0.637759i	$-0.220138\pi$
$660$	7.13983e7	−	5.94127e6i	0.248345	−	0.0206656i
$661$	2.50270e7			0.0866573			0.0433287	−	0.999061i	$-0.486204\pi$
$661$	2.50270e7			0.0866573			0.0433287	+	0.999061i	$0.486204\pi$
$662$	−1.84530e8	+	7.66443e6i	−0.636054	+	0.0264183i
$663$		−	1.80123e8i		−	0.618059i
$664$	−3.00856e8	+	3.76612e7i	−1.02767	+	0.128644i
$665$	−3.02414e8			−1.02834
$666$	5.76089e6	+	1.38700e8i	0.0195014	+	0.469521i
$667$		−	2.18825e8i		−	0.737429i
$668$	1.31519e7	+	1.58051e8i	0.0441224	+	0.530234i
$669$	−1.89816e8			−0.633949
$670$	−3.20762e7	+	1.33228e6i	−0.106649	+	0.00442965i
$671$			3.24312e8i			1.07348i
$672$	−5.81037e7	−	2.75913e8i	−0.191468	−	0.909210i
$673$	−4.07582e8			−1.33712			−0.668559	−	0.743659i	$-0.733088\pi$
$673$	−4.07582e8			−1.33712			−0.668559	+	0.743659i	$0.733088\pi$
$674$	−1.47347e7	−	3.54757e8i	−0.0481241	−	1.15865i
$675$		−	1.18375e7i		−	0.0384900i
$676$	−9.51101e7	+	7.91440e6i	−0.307883	+	0.0256199i
$677$	−3.08100e8			−0.992946			−0.496473	−	0.868052i	$-0.665372\pi$
$677$	−3.08100e8			−0.992946			−0.496473	+	0.868052i	$0.665372\pi$
$678$	−2.22646e7	+	924755.i	−0.0714375	+	0.00296714i
$679$		−	8.06893e8i		−	2.57755i
$680$	1.63430e7	+	1.30555e8i	0.0519762	+	0.415210i
$681$	−1.39167e8			−0.440651
$682$	−1.47129e7	−	3.54230e8i	−0.0463814	−	1.11669i
$683$			2.86032e8i			0.897744i	0.893596	+	0.448872i	$0.148174\pi$
$683$			2.86032e8i			0.897744i	−0.893596	+	0.448872i	$0.851826\pi$
$684$	−1.26391e7	−	1.51888e8i	−0.0394954	−	0.474630i
$685$	−2.66658e7			−0.0829628
$686$	3.06250e8	−	1.27200e7i	0.948645	−	0.0394017i
$687$		−	2.51416e8i		−	0.775395i
$688$	−1.03929e6	−	6.20149e6i	−0.00319131	−	0.0190428i
$689$	5.73611e8			1.75372
$690$	4.40242e6	+	1.05994e8i	0.0134012	+	0.322651i
$691$			6.17632e8i			1.87196i	0.352059	+	0.935978i	$0.385482\pi$
$691$			6.17632e8i			1.87196i	−0.352059	+	0.935978i	$0.614518\pi$
$692$	−5.23314e8	+	4.35465e7i	−1.57922	+	0.131412i
$693$	−1.72316e8			−0.517757
$694$	2.09857e8	−	8.71636e6i	0.627835	−	0.0260770i
$695$		−	4.89116e7i		−	0.145699i
$696$	−1.13883e8	+	1.42559e7i	−0.337777	+	0.0422831i
$697$	−1.73111e8			−0.511241
$698$	2.50591e7	+	6.03328e8i	0.0736884	+	1.77414i
$699$			8.83828e7i			0.258783i
$700$	−9.15513e6	−	1.10020e8i	−0.0266913	−	0.320759i
$701$	−2.90668e8			−0.843808			−0.421904	−	0.906641i	$-0.638638\pi$
$701$	−2.90668e8			−0.843808			−0.421904	+	0.906641i	$0.638638\pi$
$702$	−7.61055e7	+	3.16102e6i	−0.219991	+	0.00913727i
$703$			6.99828e8i			2.01431i
$704$	8.30103e7	+	3.26367e8i	0.237911	+	0.935380i
$705$	1.14415e8			0.326525
$706$	−2.42985e6	−	5.85016e7i	−0.00690502	−	0.166247i
$707$			5.31999e8i			1.50540i
$708$	2.69633e8	−	2.24370e7i	0.759755	−	0.0632216i
$709$	5.33660e7			0.149736			0.0748679	−	0.997193i	$-0.476146\pi$
$709$	5.33660e7			0.149736			0.0748679	+	0.997193i	$0.476146\pi$
$710$	−8.66155e7	+	3.59755e6i	−0.242003	+	0.0100515i
$711$		−	1.48209e8i		−	0.412350i
$712$	9.81215e6	+	7.83840e7i	0.0271847	+	0.217164i
$713$	5.24962e8			1.44830
$714$	−1.31325e7	−	3.16181e8i	−0.0360789	−	0.868644i
$715$		−	1.80507e8i		−	0.493828i
$716$	−1.64508e7	−	1.97695e8i	−0.0448176	−	0.538588i
$717$	1.58456e8			0.429885
$718$	−3.22105e8	+	1.33786e7i	−0.870210	+	0.0361440i
$719$			8.54538e7i			0.229903i	0.993371	+	0.114951i	$0.0366713\pi$
$719$			8.54538e7i			0.229903i	−0.993371	+	0.114951i	$0.963329\pi$
$720$	5.48753e7	−	9.19636e6i	0.147021	−	0.0246387i
$721$	5.60513e8			1.49548
$722$	−1.62670e7	−	3.91649e8i	−0.0432212	−	1.04060i
$723$		−	2.91862e8i		−	0.772258i
$724$	1.58100e8	−	1.31560e7i	0.416598	−	0.0346664i
$725$	−4.49378e7			−0.117923
$726$	−1.51124e7	+	627688.i	−0.0394932	+	0.00164034i
$727$			4.69711e8i			1.22244i	0.791461	+	0.611220i	$0.209321\pi$
$727$			4.69711e8i			1.22244i	−0.791461	+	0.611220i	$0.790679\pi$
$728$	−7.04898e8	+	8.82395e7i	−1.82697	+	0.228701i
$729$	−1.43489e7			−0.0370370
$730$	−2.33022e6	−	5.61030e7i	−0.00599003	−	0.144217i
$731$		−	7.05710e6i		−	0.0180665i
$732$	2.08863e7	+	2.50998e8i	0.0532510	+	0.639936i
$733$	3.65700e8			0.928567			0.464283	−	0.885687i	$-0.346312\pi$
$733$	3.65700e8			0.928567			0.464283	+	0.885687i	$0.346312\pi$
$734$	−1.72452e8	+	7.16273e6i	−0.436093	+	0.0181130i
$735$			1.63007e8i			0.410529i
$736$	−4.87937e8	+	1.02753e8i	−1.22386	+	0.257728i
$737$	−9.22189e7			−0.230366
$738$	3.03796e6	+	7.31426e7i	0.00755811	+	0.181971i
$739$		−	4.87643e8i		−	1.20828i	−0.796877	−	0.604142i	$-0.793516\pi$
$739$		−	4.87643e8i		−	1.20828i	0.796877	−	0.604142i	$-0.206484\pi$
$740$	−2.54602e8	+	2.11862e7i	−0.628300	+	0.0522828i
$741$	−3.83999e8			−0.943790
$742$	1.00689e9	−	4.18211e7i	2.46474	−	0.102373i
$743$		−	7.13753e8i		−	1.74013i	−0.492939	−	0.870064i	$-0.664077\pi$
$743$		−	7.13753e8i		−	1.74013i	0.492939	−	0.870064i	$-0.335923\pi$
$744$	−3.41999e7	−	2.73205e8i	−0.0830436	−	0.663391i
$745$	1.41348e8			0.341839
$746$	1.72659e7	+	4.15699e8i	0.0415885	+	1.00129i
$747$			1.43903e8i			0.345230i
$748$	3.13420e7	+	3.76648e8i	0.0748897	+	0.899975i
$749$	−2.81107e8			−0.669000
$750$	2.17668e7	−	904077.i	0.0515953	−	0.00214300i
$751$		−	3.91873e8i		−	0.925180i	−0.886572	−	0.462590i	$-0.846920\pi$
$751$		−	3.91873e8i		−	0.925180i	0.886572	−	0.462590i	$-0.153080\pi$
$752$	8.88874e7	+	5.30397e8i	0.209019	+	1.24723i
$753$	−5.28501e7			−0.123783
$754$	1.20000e7	+	2.88914e8i	0.0279941	+	0.673991i
$755$			1.81279e8i			0.421217i
$756$	−1.33362e8	+	1.10975e7i	−0.308651	+	0.0256838i
$757$	2.04521e7			0.0471466			0.0235733	−	0.999722i	$-0.492496\pi$
$757$	2.04521e7			0.0471466			0.0235733	+	0.999722i	$0.492496\pi$
$758$	−7.51068e7	+	3.11954e6i	−0.172453	+	0.00716281i
$759$			3.04731e8i			0.696934i
$760$	2.78326e8	−	3.48410e7i	0.634035	−	0.0793688i
$761$	5.17521e8			1.17429			0.587143	−	0.809483i	$-0.300252\pi$
$761$	5.17521e8			1.17429			0.587143	+	0.809483i	$0.300252\pi$
$762$	−1.00633e7	−	2.42285e8i	−0.0227444	−	0.547599i
$763$			1.17842e9i			2.65293i
$764$	−7.58784e6	−	9.11857e7i	−0.0170152	−	0.204478i
$765$	6.24464e7			0.139484
$766$	1.23506e8	−	5.12980e6i	0.274791	−	0.0114134i
$767$		−	6.81679e8i		−	1.51075i
$768$	8.52635e7	+	2.47242e8i	0.188226	+	0.545806i
$769$	−2.63067e8			−0.578478			−0.289239	−	0.957257i	$-0.593402\pi$
$769$	−2.63067e8			−0.578478			−0.289239	+	0.957257i	$0.593402\pi$
$770$	−1.31605e7	−	3.16855e8i	−0.0288270	−	0.694046i
$771$			4.36165e8i			0.951673i
$772$	1.15668e8	−	9.62508e6i	0.251397	−	0.0209196i
$773$	5.41479e8			1.17231			0.586155	−	0.810199i	$-0.300641\pi$
$773$	5.41479e8			1.17231			0.586155	+	0.810199i	$0.300641\pi$
$774$	−2.98176e6	+	123847.i	−0.00643057	+	0.000267092i
$775$		−	1.07806e8i		−	0.231599i
$776$	9.29618e7	+	7.42623e8i	0.198939	+	1.58922i
$777$	6.14470e8			1.30990
$778$	−1.83087e7	−	4.40804e8i	−0.0388793	−	0.936066i
$779$			3.69049e8i			0.780678i
$780$	−1.16250e7	−	1.39701e8i	−0.0244968	−	0.294386i
$781$	−2.49019e8			−0.522733
$782$	−5.59149e8	+	2.32241e7i	−1.16925	+	0.0485645i
$783$			5.44717e7i			0.113471i
$784$	−7.55654e8	+	1.26637e8i	−1.56810	+	0.262793i
$785$	3.33508e8			0.689440
$786$	−1.89507e7	−	4.56261e8i	−0.0390263	−	0.939606i
$787$		−	2.07996e7i		−	0.0426709i	−0.999772	−	0.0213354i	$-0.993208\pi$
$787$		−	2.07996e7i		−	0.0426709i	0.999772	−	0.0213354i	$-0.00679179\pi$
$788$	5.54657e8	−	4.61547e7i	1.13356	−	0.0943272i
$789$	−4.16269e8			−0.847507
$790$	2.72527e8	−	1.13193e7i	0.552749	−	0.0229583i
$791$			9.86365e7i			0.199300i
$792$	1.58591e8	−	1.98525e7i	0.319229	−	0.0399612i
$793$	6.34565e8			1.27250
$794$	−3.08613e7	−	7.43023e8i	−0.0616527	−	1.48436i
$795$			1.98863e8i			0.395779i
$796$	−2.66198e7	−	3.19899e8i	−0.0527795	−	0.634270i
$797$	6.81937e8			1.34701			0.673503	−	0.739185i	$-0.264789\pi$
$797$	6.81937e8			1.34701			0.673503	+	0.739185i	$0.264789\pi$
$798$	−6.74056e8	+	2.79967e7i	−1.32644	+	0.0550933i
$799$			6.03575e8i			1.18329i
$800$	2.11013e7	+	1.00202e8i	0.0412135	+	0.195708i
$801$	3.74921e7			0.0729529
$802$	3.91467e7	+	9.42505e8i	0.0758879	+	1.82709i
$803$		−	1.61296e8i		−	0.311513i
$804$	−7.13718e7	+	5.93906e6i	−0.137328	+	0.0114275i
$805$	4.69572e8			0.900150
$806$	−6.93105e8	+	2.87879e7i	−1.32371	+	0.0549801i
$807$			4.28624e8i			0.815559i
$808$	−6.12914e7	−	4.89624e8i	−0.116189	−	0.928173i
$809$	−7.38152e7			−0.139412			−0.0697060	−	0.997568i	$-0.522206\pi$
$809$	−7.38152e7			−0.139412			−0.0697060	+	0.997568i	$0.522206\pi$
$810$	−1.09588e6	−	2.63848e7i	−0.00206210	−	0.0496476i
$811$			1.60157e8i			0.300250i	0.988667	+	0.150125i	$0.0479675\pi$
$811$			1.60157e8i			0.300250i	−0.988667	+	0.150125i	$0.952032\pi$
$812$	4.21285e7	+	5.06273e8i	0.0786879	+	0.945620i
$813$	−1.21940e8			−0.226920
$814$	−7.33246e8	+	3.04552e7i	−1.35949	+	0.0564661i
$815$			2.28361e8i			0.421841i
$816$	4.85136e7	+	2.89484e8i	0.0892880	+	0.532787i
$817$	−1.50448e7			−0.0275880
$818$	2.02119e7	+	4.86626e8i	0.0369273	+	0.889070i
$819$			3.37162e8i			0.613744i
$820$	−1.34263e8	+	1.11724e7i	−0.243508	+	0.0202631i
$821$	−7.70613e8			−1.39254			−0.696269	−	0.717781i	$-0.745158\pi$
$821$	−7.70613e8			−1.39254			−0.696269	+	0.717781i	$0.745158\pi$
$822$	−5.94359e7	+	2.46865e6i	−0.107012	+	0.00444472i
$823$		−	8.88839e8i		−	1.59450i	−0.603652	−	0.797248i	$-0.706288\pi$
$823$		−	8.88839e8i		−	1.59450i	0.603652	−	0.797248i	$-0.293712\pi$
$824$	−5.15867e8	+	6.45765e7i	−0.922054	+	0.115423i
$825$	6.25794e7			0.111447
$826$	−4.97001e7	−	1.19659e9i	−0.0881896	−	2.12327i
$827$		−	7.22792e8i		−	1.27790i	−0.769248	−	0.638950i	$-0.779369\pi$
$827$		−	7.22792e8i		−	1.27790i	0.769248	−	0.638950i	$-0.220631\pi$
$828$	1.96253e7	+	2.35843e8i	0.0345720	+	0.415464i
$829$	7.80531e8			1.37002			0.685009	−	0.728534i	$-0.259798\pi$
$829$	7.80531e8			1.37002			0.685009	+	0.728534i	$0.259798\pi$
$830$	−2.64609e8	+	1.09905e7i	−0.462776	+	0.0192213i
$831$		−	5.43824e8i		−	0.947666i
$832$	6.38586e8	−	1.62422e8i	1.10879	−	0.282017i
$833$	−8.59910e8			−1.48771
$834$	−4.52811e6	−	1.09020e8i	−0.00780582	−	0.187935i
$835$			1.38529e8i			0.237948i
$836$	8.02962e8	−	6.68169e7i	1.37428	−	0.114358i
$837$	−1.30678e8			−0.222856
$838$	−2.59769e8	+	1.07894e7i	−0.441423	+	0.0183344i
$839$		−	3.58594e8i		−	0.607180i	−0.952803	−	0.303590i	$-0.901815\pi$
$839$		−	3.58594e8i		−	0.607180i	0.952803	−	0.303590i	$-0.0981853\pi$
$840$	−3.05914e7	−	2.44379e8i	−0.0516133	−	0.412312i
$841$	−3.88036e8			−0.652356
$842$	1.37446e7	+	3.30919e8i	0.0230249	+	0.554352i
$843$		−	3.79411e7i		−	0.0633326i
$844$	3.59726e7	+	4.32295e8i	0.0598335	+	0.719039i
$845$	−8.33623e7			−0.138166
$846$	2.55022e8	−	1.05923e7i	0.421179	−	0.0174936i
$847$			6.69507e7i			0.110181i
$848$	−9.21875e8	+	1.54494e8i	−1.51176	+	0.253351i
$849$	−5.96349e8			−0.974491
$850$	4.76928e6	+	1.14826e8i	0.00776598	+	0.186976i
$851$		−	1.08666e9i		−	1.76321i
$852$	−1.92726e8	+	1.60373e7i	−0.311617	+	0.0259306i
$853$	7.64679e8			1.23206			0.616031	−	0.787722i	$-0.288740\pi$
$853$	7.64679e8			1.23206			0.616031	+	0.787722i	$0.288740\pi$
$854$	1.11389e9	−	4.62651e7i	1.78842	−	0.0742814i
$855$		−	1.33127e8i		−	0.212995i
$856$	2.58716e8	−	3.23862e7i	0.412479	−	0.0516343i
$857$	−7.39540e8			−1.17495			−0.587474	−	0.809243i	$-0.699878\pi$
$857$	−7.39540e8			−1.17495			−0.587474	+	0.809243i	$0.699878\pi$
$858$	−1.67109e7	−	4.02335e8i	−0.0264568	−	0.636981i
$859$		−	2.38366e8i		−	0.376067i	−0.982163	−	0.188034i	$-0.939789\pi$
$859$		−	2.38366e8i		−	0.376067i	0.982163	−	0.188034i	$-0.0602114\pi$
$860$	−455458.	−	5.47340e6i	−0.000716066	−	0.00860521i
$861$	3.24036e8			0.507673
$862$	−2.11435e8	+	8.78188e6i	−0.330107	+	0.0137109i
$863$		−	1.16251e9i		−	1.80870i	−0.426794	−	0.904349i	$-0.640357\pi$
$863$		−	1.16251e9i		−	1.80870i	0.426794	−	0.904349i	$-0.359643\pi$
$864$	1.21461e8	−	2.55781e7i	0.188320	−	0.0396577i
$865$	−4.58676e8			−0.708692
$866$	−8.36917e6	−	2.01498e8i	−0.0128863	−	0.310254i
$867$		−	4.68437e7i		−	0.0718777i
$868$	−1.21455e9	+	1.01066e8i	−1.85719	+	0.154542i
$869$	7.83514e8			1.19395
$870$	−1.00163e8	+	4.16023e6i	−0.152106	+	0.00631770i
$871$			1.80440e8i			0.273073i
$872$	−1.35765e8	−	1.08456e9i	−0.204757	−	1.63570i
$873$	3.55206e8			0.533873
$874$	4.95107e7	+	1.19203e9i	0.0741591	+	1.78547i
$875$		−	9.64310e7i		−	0.143944i
$876$	−1.03877e7	−	1.24833e8i	−0.0154529	−	0.185702i
$877$	1.18584e8			0.175803			0.0879016	−	0.996129i	$-0.471984\pi$
$877$	1.18584e8			0.175803			0.0879016	+	0.996129i	$0.471984\pi$
$878$	1.26717e9	−	5.26315e7i	1.87219	−	0.0777610i
$879$			3.18563e8i			0.469060i
$880$	4.86169e7	+	2.90100e8i	0.0713411	+	0.425697i
$881$	−5.84028e8			−0.854095			−0.427047	−	0.904229i	$-0.640446\pi$
$881$	−5.84028e8			−0.854095			−0.427047	+	0.904229i	$0.640446\pi$
$882$	1.50908e7	+	3.63328e8i	0.0219940	+	0.529534i
$883$			3.76901e8i			0.547451i	0.961808	+	0.273725i	$0.0882560\pi$
$883$			3.76901e8i			0.547451i	−0.961808	+	0.273725i	$0.911744\pi$
$884$	7.36968e8	−	6.13253e7i	1.06682	−	0.0887735i
$885$	2.36329e8			0.340947
$886$	8.41932e8	−	3.49694e7i	1.21053	−	0.0502791i
$887$		−	9.41273e8i		−	1.34879i	−0.738370	−	0.674395i	$-0.764404\pi$
$887$		−	9.41273e8i		−	1.34879i	0.738370	−	0.674395i	$-0.235596\pi$
$888$	−5.65526e8	+	7.07928e7i	−0.807633	+	0.101100i
$889$	−1.07337e9			−1.52772
$890$	2.86343e6	+	6.89405e7i	0.00406178	+	0.0977923i
$891$		−	7.58561e7i		−	0.107240i
$892$	−6.46253e7	−	7.76625e8i	−0.0910559	−	1.09425i
$893$	1.28674e9			1.80691
$894$	3.15053e8	−	1.30857e7i	0.440932	−	0.0183140i
$895$		−	1.73276e8i		−	0.241697i
$896$	1.10911e9	−	3.31667e8i	1.54187	−	0.461082i
$897$	5.96253e8			0.826139
$898$	−4.82295e7	−	1.16119e9i	−0.0666015	−	1.60351i
$899$			4.96082e8i			0.682770i
$900$	4.84326e7	−	4.03022e6i	0.0664370	−	0.00552843i
$901$	−1.04906e9			−1.43426
$902$	−3.86672e8	+	1.60603e7i	−0.526893	+	0.0218844i
$903$			1.32098e7i			0.0179404i
$904$	−1.13639e7	−	9.07799e7i	−0.0153823	−	0.122881i
$905$	1.38572e8			0.186952
$906$	1.67823e7	+	4.04055e8i	0.0225667	+	0.543320i
$907$			1.10117e9i			1.47582i	0.674902	+	0.737908i	$0.264186\pi$
$907$			1.10117e9i			1.47582i	−0.674902	+	0.737908i	$0.735814\pi$
$908$	−4.73812e7	−	5.69396e8i	−0.0632919	−	0.760601i
$909$	−2.34194e8			−0.311806
$910$	−6.19974e8	+	2.57505e7i	−0.822715	+	0.0341712i
$911$			5.43788e8i			0.719241i	0.933099	+	0.359621i	$0.117094\pi$
$911$			5.43788e8i			0.719241i	−0.933099	+	0.359621i	$0.882906\pi$
$912$	6.17141e8	−	1.03424e8i	0.813579	−	0.136345i
$913$	−7.60751e8			−0.999609
$914$	3.35066e7	+	8.06712e8i	0.0438825	+	1.05653i
$915$			2.19995e8i			0.287177i
$916$	1.02866e9	−	8.55979e7i	1.33840	−	0.111372i
$917$	−2.02132e9			−2.62137
$918$	1.39188e8	−	5.78113e6i	0.179917	−	0.00747282i
$919$		−	1.23288e9i		−	1.58845i	−0.607626	−	0.794224i	$-0.707878\pi$
$919$		−	1.23288e9i		−	1.58845i	0.607626	−	0.794224i	$-0.292122\pi$
$920$	−4.32170e8	+	5.40992e7i	−0.554998	+	0.0694749i
$921$	1.48738e8			0.190390
$922$	−3.47922e7	−	8.37665e8i	−0.0443904	−	1.06875i
$923$			4.87243e8i			0.619642i
$924$	−5.86672e7	−	7.05025e8i	−0.0743669	−	0.893693i
$925$	−2.23155e8			−0.281956
$926$	−6.65159e8	+	2.76272e7i	−0.837707	+	0.0347940i
$927$			2.46746e8i			0.309750i
$928$	−9.71004e7	−	4.61094e8i	−0.121500	−	0.576959i
$929$	5.78905e8			0.722038			0.361019	−	0.932558i	$-0.382429\pi$
$929$	5.78905e8			0.722038			0.361019	+	0.932558i	$0.382429\pi$
$930$	−9.98038e6	−	2.40290e8i	−0.0124079	−	0.298736i
$931$			1.83321e9i			2.27177i
$932$	−3.61615e8	+	3.00911e7i	−0.446682	+	0.0371698i
$933$	−4.54648e7			−0.0559796
$934$	−5.70129e7	+	2.36802e6i	−0.0699733	+	0.00290633i
$935$			3.30125e8i			0.403872i
$936$	−3.88443e7	−	3.10307e8i	−0.0473696	−	0.378411i
$937$	−7.59361e8			−0.923059			−0.461529	−	0.887125i	$-0.652699\pi$
$937$	−7.59361e8			−0.923059			−0.461529	+	0.887125i	$0.652699\pi$
$938$	1.31556e7	+	3.16737e8i	0.0159405	+	0.383787i
$939$			3.02013e8i			0.364778i
$940$	3.89541e7	+	4.68125e8i	0.0468997	+	0.563610i
$941$	5.09200e8			0.611110			0.305555	−	0.952174i	$-0.401158\pi$
$941$	5.09200e8			0.611110			0.305555	+	0.952174i	$0.401158\pi$
$942$	7.43360e8	−	3.08753e7i	0.889297	−	0.0369367i
$943$		−	5.73040e8i		−	0.683360i
$944$	1.83600e8	+	1.09556e9i	0.218252	+	1.30232i
$945$	−1.16890e8			−0.138510
$946$	−654720.	−	1.57632e7i	−0.000773361	−	0.0186196i
$947$			5.18817e8i			0.610892i	0.952209	+	0.305446i	$0.0988055\pi$
$947$			5.18817e8i			0.610892i	−0.952209	+	0.305446i	$0.901194\pi$
$948$	6.06392e8	−	5.04597e7i	0.711752	−	0.0592270i
$949$	−3.15599e8			−0.369265
$950$	2.44794e8	−	1.01675e7i	0.285516	−	0.0118588i
$951$			1.01408e8i			0.117905i
$952$	1.28917e9	−	1.61379e8i	1.49417	−	0.187041i
$953$	1.67690e9			1.93745			0.968723	−	0.248146i	$-0.0798213\pi$
$953$	1.67690e9			1.93745			0.968723	+	0.248146i	$0.0798213\pi$
$954$	1.84103e7	+	4.43250e8i	0.0212039	+	0.510509i
$955$		−	7.99227e7i		−	0.0917614i
$956$	5.39485e7	+	6.48318e8i	0.0617456	+	0.742018i
$957$	−2.87967e8			−0.328554
$958$	−8.17272e8	+	3.39452e7i	−0.929544	+	0.0386084i
$959$			2.63312e8i			0.298549i
$960$	5.63095e7	+	2.21389e8i	0.0636456	+	0.250232i
$961$	−3.02597e8			−0.340953
$962$	5.95901e7	+	1.43471e9i	0.0669344	+	1.61153i
$963$		−	1.23747e8i		−	0.138566i
$964$	1.19414e9	−	9.93681e7i	1.33298	−	0.110922i
$965$	1.01381e8			0.112817
$966$	1.04664e9	−	4.34718e7i	1.16109	−	0.0482255i
$967$		−	1.67789e9i		−	1.85560i	−0.373082	−	0.927798i	$-0.621699\pi$
$967$		−	1.67789e9i		−	1.85560i	0.373082	−	0.927798i	$-0.378301\pi$
$968$	−7.71336e6	−	6.16180e7i	−0.00850389	−	0.0679331i
$969$	7.02287e8			0.771868
$970$	2.71286e7	+	6.53154e8i	0.0297243	+	0.715649i
$971$		−	5.10919e8i		−	0.558078i	−0.960280	−	0.279039i	$-0.909984\pi$
$971$		−	5.10919e8i		−	0.558078i	0.960280	−	0.279039i	$-0.0900158\pi$
$972$	−4.88527e6	−	5.87080e7i	−0.00531973	−	0.0639291i
$973$	−4.82979e8			−0.524312
$974$	6.07172e7	−	2.52187e6i	0.0657105	−	0.00272927i
$975$		−	1.22446e8i		−	0.132108i
$976$	−1.01984e9	+	1.70911e8i	−1.09694	+	0.183832i
$977$	3.24832e7			0.0348318			0.0174159	−	0.999848i	$-0.494456\pi$
$977$	3.24832e7			0.0348318			0.0174159	+	0.999848i	$0.494456\pi$
$978$	2.11411e7	+	5.08997e8i	0.0226001	+	0.544125i
$979$			1.98204e8i			0.211234i
$980$	−6.66936e8	+	5.54977e7i	−0.708607	+	0.0589654i
$981$	−5.18758e8			−0.549487
$982$	−3.82181e8	+	1.58738e7i	−0.403584	+	0.0167628i
$983$			7.49859e8i			0.789439i	0.918802	+	0.394720i	$0.129158\pi$
$983$			7.49859e8i			0.789439i	−0.918802	+	0.394720i	$0.870842\pi$
$984$	−2.98226e8	+	3.73320e7i	−0.313011	+	0.0391829i
$985$	4.86147e8			0.508697
$986$	−2.19465e7	−	5.28388e8i	−0.0228946	−	0.551217i
$987$		−	1.12980e9i		−	1.17503i
$988$	−1.30737e8	−	1.57112e9i	−0.135559	−	1.62906i
$989$	2.33607e7			0.0241489
$990$	1.39484e8	−	5.79344e6i	0.143754	−	0.00597078i
$991$		−	6.65908e8i		−	0.684216i	−0.939661	−	0.342108i	$-0.888859\pi$
$991$		−	6.65908e8i		−	0.684216i	0.939661	−	0.342108i	$-0.111141\pi$
$992$	1.10616e9	−	2.32944e8i	1.13314	−	0.238625i
$993$	−3.59878e8			−0.367543
$994$	3.55241e7	+	8.55287e8i	0.0361713	+	0.870869i
$995$		−	2.80386e8i		−	0.284634i
$996$	−5.88775e8	+	4.89937e7i	−0.595897	+	0.0495864i
$997$	−6.37105e8			−0.642873			−0.321437	−	0.946931i	$-0.604166\pi$
$997$	−6.37105e8			−0.642873			−0.321437	+	0.946931i	$0.604166\pi$
$998$	5.62282e8	−	2.33542e7i	0.565669	−	0.0234949i
$999$			2.70499e8i			0.271312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.12	yes	24
3.2	odd	2		180.7.c.b.91.13		24
4.3	odd	2	inner	60.7.c.a.31.11	✓	24
12.11	even	2		180.7.c.b.91.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.11	✓	24	4.3	odd	2	inner
60.7.c.a.31.12	yes	24	1.1	even	1	trivial
180.7.c.b.91.13		24	3.2	odd	2
180.7.c.b.91.14		24	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +(-18.5589 - 446.828i) q^{10} -1284.63i q^{11} +(-82.7325 - 994.225i) q^{12} -2513.57 q^{13} +(-4412.22 + 183.260i) q^{14} -871.421i q^{15} +(4039.67 - 676.993i) q^{16} +4597.01 q^{17} +(-80.6740 - 1942.33i) q^{18} -9800.21i q^{19} +(3565.39 - 296.687i) q^{20} -8604.88 q^{21} +(10268.2 - 426.487i) q^{22} +15217.2i q^{23} +(7919.48 - 991.364i) q^{24} +3125.00 q^{25} +(-834.485 - 20091.2i) q^{26} -3788.00i q^{27} +(-2929.64 - 35206.5i) q^{28} -14380.1 q^{29} +(6965.36 - 289.305i) q^{30} -34497.8i q^{31} +(6752.42 + 32064.7i) q^{32} +20025.4 q^{33} +(1526.17 + 36744.4i) q^{34} -30857.9i q^{35} +(15498.4 - 1289.67i) q^{36} -71409.5 q^{37} +(78334.2 - 3253.59i) q^{38} -39182.7i q^{39} +(3555.13 + 28400.0i) q^{40} -37657.2 q^{41} +(-2856.75 - 68779.7i) q^{42} -1535.15i q^{43} +(6817.91 + 81933.1i) q^{44} +13584.1 q^{45} +(-121633. + 5052.00i) q^{46} +131297. i q^{47} +(10553.3 + 62972.2i) q^{48} -187058. q^{49} +(1037.47 + 24978.5i) q^{50} +71660.4i q^{51} +(160314. - 13340.3i) q^{52} -228206. q^{53} +(30277.9 - 1257.58i) q^{54} +71813.0i q^{55} +(280437. - 35105.2i) q^{56} +152770. q^{57} +(-4774.07 - 114942. i) q^{58} +271199. i q^{59} +(4624.89 + 55578.9i) q^{60} -252456. q^{61} +(275745. - 11453.0i) q^{62} -134137. i q^{63} +(-254055. + 64618.0i) q^{64} +140513. q^{65} +(6648.27 + 160065. i) q^{66} -71786.4i q^{67} +(-293196. + 24397.7i) q^{68} -237213. q^{69} +(246651. - 10244.6i) q^{70} -193845. i q^{71} +(15453.8 + 123453. i) q^{72} +125558. q^{73} +(-23707.4 - 570784. i) q^{74} +48713.9i q^{75} +(52012.6 + 625053. i) q^{76} +709120. q^{77} +(313192. - 13008.3i) q^{78} +609914. i q^{79} +(-225824. + 37845.1i) q^{80} +59049.0 q^{81} +(-12501.9 - 300998. i) q^{82} -592195. i q^{83} +(548815. - 45668.6i) q^{84} -256981. q^{85} +(12270.6 - 509.657i) q^{86} -224163. i q^{87} +(-652637. + 81697.4i) q^{88} -154289. q^{89} +(4509.81 + 108579. i) q^{90} -1.38750e6i q^{91} +(-80762.4 - 970549. i) q^{92} +537768. q^{93} +(-1.04947e6 + 43589.6i) q^{94} +547849. i q^{95} +(-499840. + 105260. i) q^{96} -1.46175e6 q^{97} +(-62101.9 - 1.49518e6i) q^{98} +312165. 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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