LMFDB - Embedded newform 60.7.c.a.31.21

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			31.21
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.41350 - 3.00666i) q^{2} +15.5885i q^{3} +(45.9200 - 44.5798i) q^{4} +55.9017 q^{5} +(46.8692 + 115.565i) q^{6} -453.408i q^{7} +(206.391 - 468.558i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(7.41350 - 3.00666i) q^{2} +15.5885i q^{3} +(45.9200 - 44.5798i) q^{4} +55.9017 q^{5} +(46.8692 + 115.565i) q^{6} -453.408i q^{7} +(206.391 - 468.558i) q^{8} -243.000 q^{9} +(414.427 - 168.078i) q^{10} +742.811i q^{11} +(694.930 + 715.821i) q^{12} +3331.76 q^{13} +(-1363.25 - 3361.34i) q^{14} +871.421i q^{15} +(121.284 - 4094.20i) q^{16} +3971.34 q^{17} +(-1801.48 + 730.619i) q^{18} -6358.78i q^{19} +(2567.00 - 2492.09i) q^{20} +7067.93 q^{21} +(2233.38 + 5506.83i) q^{22} +3262.96i q^{23} +(7304.10 + 3217.32i) q^{24} +3125.00 q^{25} +(24700.0 - 10017.5i) q^{26} -3788.00i q^{27} +(-20212.8 - 20820.5i) q^{28} -41595.2 q^{29} +(2620.07 + 6460.28i) q^{30} +27417.9i q^{31} +(-11410.8 - 30717.0i) q^{32} -11579.3 q^{33} +(29441.5 - 11940.5i) q^{34} -25346.3i q^{35} +(-11158.5 + 10832.9i) q^{36} -27053.6 q^{37} +(-19118.7 - 47140.8i) q^{38} +51937.0i q^{39} +(11537.6 - 26193.2i) q^{40} +99007.2 q^{41} +(52398.1 - 21250.9i) q^{42} +82076.6i q^{43} +(33114.4 + 34109.8i) q^{44} -13584.1 q^{45} +(9810.61 + 24189.9i) q^{46} +79654.0i q^{47} +(63822.3 + 1890.63i) q^{48} -87929.9 q^{49} +(23167.2 - 9395.82i) q^{50} +61907.1i q^{51} +(152994. - 148529. i) q^{52} -169163. q^{53} +(-11389.2 - 28082.3i) q^{54} +41524.4i q^{55} +(-212448. - 93579.4i) q^{56} +99123.6 q^{57} +(-308366. + 125063. i) q^{58} +152994. i q^{59} +(38847.8 + 40015.6i) q^{60} -329756. q^{61} +(82436.3 + 203262. i) q^{62} +110178. i q^{63} +(-176949. - 193412. i) q^{64} +186251. q^{65} +(-85843.0 + 34815.0i) q^{66} -20926.5i q^{67} +(182364. - 177042. i) q^{68} -50864.4 q^{69} +(-76207.7 - 187905. i) q^{70} +590336. i q^{71} +(-50153.0 + 113860. i) q^{72} -341053. q^{73} +(-200562. + 81341.2i) q^{74} +48713.9i q^{75} +(-283473. - 291995. i) q^{76} +336796. q^{77} +(156157. + 385035. i) q^{78} -756383. i q^{79} +(6779.99 - 228873. i) q^{80} +59049.0 q^{81} +(733990. - 297681. i) q^{82} +545901. i q^{83} +(324559. - 315087. i) q^{84} +222005. q^{85} +(246777. + 608475. i) q^{86} -648405. i q^{87} +(348050. + 153310. i) q^{88} +1.09085e6 q^{89} +(-100706. + 40842.9i) q^{90} -1.51065e6i q^{91} +(145462. + 149835. i) q^{92} -427402. q^{93} +(239493. + 590515. i) q^{94} -355467. i q^{95} +(478831. - 177876. i) q^{96} -977274. q^{97} +(-651868. + 264376. i) q^{98} -180503. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	7.41350	−	3.00666i	0.926687	−	0.375833i
$2$	7.41350	−	3.00666i	0.926687	−	0.375833i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	45.9200	−	44.5798i	0.717499	−	0.696559i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$	46.8692	+	115.565i	0.216987	+	0.535023i
$7$		−	453.408i		−	1.32189i	−0.750435	−	0.660945i	$-0.770156\pi$
$7$		−	453.408i		−	1.32189i	0.750435	−	0.660945i	$-0.229844\pi$
$8$	206.391	−	468.558i	0.403108	−	0.915153i
$9$	−243.000			−0.333333
$10$	414.427	−	168.078i	0.414427	−	0.168078i
$11$			742.811i			0.558085i	0.960279	+	0.279042i	$0.0900170\pi$
$11$			742.811i			0.558085i	−0.960279	+	0.279042i	$0.909983\pi$
$12$	694.930	+	715.821i	0.402159	+	0.414248i
$13$	3331.76			1.51651			0.758253	−	0.651961i	$-0.226053\pi$
$13$	3331.76			1.51651			0.758253	+	0.651961i	$0.226053\pi$
$14$	−1363.25	−	3361.34i	−0.496810	−	1.22498i
$15$			871.421i			0.258199i
$16$	121.284	−	4094.20i	0.0296104	−	0.999562i
$17$	3971.34			0.808333			0.404167	−	0.914685i	$-0.367562\pi$
$17$	3971.34			0.808333			0.404167	+	0.914685i	$0.367562\pi$
$18$	−1801.48	+	730.619i	−0.308896	+	0.125278i
$19$		−	6358.78i		−	0.927071i	−0.886078	−	0.463536i	$-0.846581\pi$
$19$		−	6358.78i		−	0.927071i	0.886078	−	0.463536i	$-0.153419\pi$
$20$	2567.00	−	2492.09i	0.320875	−	0.311511i
$21$	7067.93			0.763193
$22$	2233.38	+	5506.83i	0.209747	+	0.517170i
$23$			3262.96i			0.268181i	0.990969	+	0.134090i	$0.0428112\pi$
$23$			3262.96i			0.268181i	−0.990969	+	0.134090i	$0.957189\pi$
$24$	7304.10	+	3217.32i	0.528364	+	0.232734i
$25$	3125.00			0.200000
$26$	24700.0	−	10017.5i	1.40533	−	0.569953i
$27$		−	3788.00i		−	0.192450i
$28$	−20212.8	−	20820.5i	−0.920774	−	0.948455i
$29$	−41595.2			−1.70549			−0.852745	−	0.522327i	$-0.825064\pi$
$29$	−41595.2			−1.70549			−0.852745	+	0.522327i	$0.825064\pi$
$30$	2620.07	+	6460.28i	0.0970396	+	0.239270i
$31$			27417.9i			0.920341i	0.887831	+	0.460171i	$0.152212\pi$
$31$			27417.9i			0.920341i	−0.887831	+	0.460171i	$0.847788\pi$
$32$	−11410.8	−	30717.0i	−0.348229	−	0.937410i
$33$	−11579.3			−0.322210
$34$	29441.5	−	11940.5i	0.749073	−	0.303798i
$35$		−	25346.3i		−	0.591167i
$36$	−11158.5	+	10832.9i	−0.239166	+	0.232186i
$37$	−27053.6			−0.534098			−0.267049	−	0.963683i	$-0.586048\pi$
$37$	−27053.6			−0.534098			−0.267049	+	0.963683i	$0.586048\pi$
$38$	−19118.7	−	47140.8i	−0.348424	−	0.859105i
$39$			51937.0i			0.875555i
$40$	11537.6	−	26193.2i	0.180275	−	0.409269i
$41$	99007.2			1.43653			0.718266	−	0.695769i	$-0.244936\pi$
$41$	99007.2			1.43653			0.718266	+	0.695769i	$0.244936\pi$
$42$	52398.1	−	21250.9i	0.707242	−	0.286833i
$43$			82076.6i			1.03232i	0.856492	+	0.516160i	$0.172639\pi$
$43$			82076.6i			1.03232i	−0.856492	+	0.516160i	$0.827361\pi$
$44$	33114.4	+	34109.8i	0.388739	+	0.400425i
$45$	−13584.1			−0.149071
$46$	9810.61	+	24189.9i	0.100791	+	0.248520i
$47$			79654.0i			0.767210i	0.923497	+	0.383605i	$0.125318\pi$
$47$			79654.0i			0.767210i	−0.923497	+	0.383605i	$0.874682\pi$
$48$	63822.3	+	1890.63i	0.577097	+	0.0170956i
$49$	−87929.9			−0.747392
$50$	23167.2	−	9395.82i	0.185337	−	0.0751666i
$51$			61907.1i			0.466692i
$52$	152994.	−	148529.i	1.08809	−	1.05634i
$53$	−169163.			−1.13626			−0.568130	−	0.822939i	$-0.692333\pi$
$53$	−169163.			−1.13626			−0.568130	+	0.822939i	$0.692333\pi$
$54$	−11389.2	−	28082.3i	−0.0723291	−	0.178341i
$55$			41524.4i			0.249583i
$56$	−212448.	−	93579.4i	−1.20973	−	0.532864i
$57$	99123.6			0.535245
$58$	−308366.	+	125063.i	−1.58046	+	0.640980i
$59$			152994.i			0.744936i	0.928045	+	0.372468i	$0.121488\pi$
$59$			152994.i			0.744936i	−0.928045	+	0.372468i	$0.878512\pi$
$60$	38847.8	+	40015.6i	0.179851	+	0.185258i
$61$	−329756.			−1.45279			−0.726396	−	0.687276i	$-0.758806\pi$
$61$	−329756.			−1.45279			−0.726396	+	0.687276i	$0.758806\pi$
$62$	82436.3	+	203262.i	0.345894	+	0.852869i
$63$			110178.i			0.440630i
$64$	−176949.	−	193412.i	−0.675008	−	0.737810i
$65$	186251.			0.678202
$66$	−85843.0	+	34815.0i	−0.298588	+	0.121097i
$67$		−	20926.5i		−	0.0695779i	−0.999395	−	0.0347890i	$-0.988924\pi$
$67$		−	20926.5i		−	0.0695779i	0.999395	−	0.0347890i	$-0.0110759\pi$
$68$	182364.	−	177042.i	0.579979	−	0.563052i
$69$	−50864.4			−0.154834
$70$	−76207.7	−	187905.i	−0.222180	−	0.547827i
$71$			590336.i			1.64939i	0.565576	+	0.824696i	$0.308654\pi$
$71$			590336.i			1.64939i	−0.565576	+	0.824696i	$0.691346\pi$
$72$	−50153.0	+	113860.i	−0.134369	+	0.305051i
$73$	−341053.			−0.876706			−0.438353	−	0.898803i	$-0.644438\pi$
$73$	−341053.			−0.876706			−0.438353	+	0.898803i	$0.644438\pi$
$74$	−200562.	+	81341.2i	−0.494941	+	0.200731i
$75$			48713.9i			0.115470i
$76$	−283473.	−	291995.i	−0.645760	−	0.665173i
$77$	336796.			0.737726
$78$	156157.	+	385035.i	0.329062	+	0.811366i
$79$		−	756383.i		−	1.53412i	−0.641573	−	0.767062i	$-0.721718\pi$
$79$		−	756383.i		−	1.53412i	0.641573	−	0.767062i	$-0.278282\pi$
$80$	6779.99	−	228873.i	0.0132422	−	0.447017i
$81$	59049.0			0.111111
$82$	733990.	−	297681.i	1.33122	−	0.539896i
$83$			545901.i			0.954727i	0.878706	+	0.477364i	$0.158408\pi$
$83$			545901.i			0.954727i	−0.878706	+	0.477364i	$0.841592\pi$
$84$	324559.	−	315087.i	0.547591	−	0.531609i
$85$	222005.			0.361498
$86$	246777.	+	608475.i	0.387980	+	0.956638i
$87$		−	648405.i		−	0.984666i
$88$	348050.	+	153310.i	0.510733	+	0.224968i
$89$	1.09085e6			1.54737			0.773687	−	0.633568i	$-0.218410\pi$
$89$	1.09085e6			1.54737			0.773687	+	0.633568i	$0.218410\pi$
$90$	−100706.	+	40842.9i	−0.138142	+	0.0560259i
$91$		−	1.51065e6i		−	2.00465i
$92$	145462.	+	149835.i	0.186804	+	0.192419i
$93$	−427402.			−0.531359
$94$	239493.	+	590515.i	0.288343	+	0.710964i
$95$		−	355467.i		−	0.414599i
$96$	478831.	−	177876.i	0.541214	−	0.201050i
$97$	−977274.			−1.07078			−0.535391	−	0.844604i	$-0.679836\pi$
$97$	−977274.			−1.07078			−0.535391	+	0.844604i	$0.679836\pi$
$98$	−651868.	+	264376.i	−0.692599	+	0.280894i
$99$		−	180503.i		−	0.186028i
$100$	143500.	−	139312.i	0.143500	−	0.139312i
$101$	848296.			0.823348			0.411674	−	0.911331i	$-0.364944\pi$
$101$	848296.			0.823348			0.411674	+	0.911331i	$0.364944\pi$
$102$	186134.	+	458948.i	0.175398	+	0.432477i
$103$		−	61091.7i		−	0.0559075i	−0.999609	−	0.0279538i	$-0.991101\pi$
$103$		−	61091.7i		−	0.0559075i	0.999609	−	0.0279538i	$-0.00889912\pi$
$104$	687646.	−	1.56112e6i	0.611315	−	1.38783i
$105$	395109.			0.341310
$106$	−1.25409e6	+	508616.i	−1.05296	+	0.427044i
$107$		−	1.52764e6i		−	1.24701i	−0.781820	−	0.623504i	$-0.785709\pi$
$107$		−	1.52764e6i		−	1.24701i	0.781820	−	0.623504i	$-0.214291\pi$
$108$	−168868.	−	173945.i	−0.134053	−	0.138083i
$109$	868179.			0.670394			0.335197	−	0.942148i	$-0.391197\pi$
$109$	868179.			0.670394			0.335197	+	0.942148i	$0.391197\pi$
$110$	124850.	+	307841.i	0.0938015	+	0.231286i
$111$		−	421725.i		−	0.308361i
$112$	−1.85635e6	−	54991.2i	−1.32131	−	0.0391416i
$113$	965484.			0.669129			0.334565	−	0.942373i	$-0.391411\pi$
$113$	965484.			0.669129			0.334565	+	0.942373i	$0.391411\pi$
$114$	734853.	−	298031.i	0.496005	−	0.201163i
$115$			182405.i			0.119934i
$116$	−1.91005e6	+	1.85431e6i	−1.22369	+	1.18798i
$117$	−809618.			−0.505502
$118$	460002.	+	1.13422e6i	0.279972	+	0.690323i
$119$		−	1.80064e6i		−	1.06853i
$120$	408311.	+	179854.i	0.236291	+	0.104082i
$121$	1.21979e6			0.688541
$122$	−2.44465e6	+	991466.i	−1.34628	+	0.546007i
$123$			1.54337e6i			0.829382i
$124$	1.22228e6	+	1.25903e6i	0.641072	+	0.660344i
$125$	174693.			0.0894427
$126$	331269.	+	816806.i	0.165603	+	0.408326i
$127$			3.30531e6i			1.61362i	0.590810	+	0.806811i	$0.298808\pi$
$127$			3.30531e6i			1.61362i	−0.590810	+	0.806811i	$0.701192\pi$
$128$	−1.89334e6	−	901836.i	−0.902815	−	0.430029i
$129$	−1.27945e6			−0.596010
$130$	1.38077e6	−	559995.i	0.628481	−	0.254891i
$131$			1.38598e6i			0.616514i	0.951303	+	0.308257i	$0.0997457\pi$
$131$			1.38598e6i			0.616514i	−0.951303	+	0.308257i	$0.900254\pi$
$132$	−531720.	+	516202.i	−0.231186	+	0.224439i
$133$	−2.88312e6			−1.22549
$134$	−62918.8	−	155138.i	−0.0261497	−	0.0644770i
$135$		−	211755.i		−	0.0860663i
$136$	819650.	−	1.86080e6i	0.325845	−	0.739748i
$137$	−337054.			−0.131081			−0.0655403	−	0.997850i	$-0.520877\pi$
$137$	−337054.			−0.131081			−0.0655403	+	0.997850i	$0.520877\pi$
$138$	−377083.	+	152932.i	−0.143483	+	0.0581918i
$139$		−	3.82230e6i		−	1.42325i	−0.702560	−	0.711624i	$-0.747960\pi$
$139$		−	3.82230e6i		−	1.42325i	0.702560	−	0.711624i	$-0.252040\pi$
$140$	−1.12993e6	−	1.16390e6i	−0.411783	−	0.424162i
$141$	−1.24168e6			−0.442949
$142$	1.77494e6	+	4.37645e6i	0.619896	+	1.52847i
$143$			2.47487e6i			0.846339i
$144$	−29472.0	+	994892.i	−0.00987013	+	0.333187i
$145$	−2.32524e6			−0.762719
$146$	−2.52840e6	+	1.02543e6i	−0.812432	+	0.329495i
$147$		−	1.37069e6i		−	0.431507i
$148$	−1.24230e6	+	1.20605e6i	−0.383215	+	0.372031i
$149$	3.57763e6			1.08153			0.540763	−	0.841175i	$-0.318136\pi$
$149$	3.57763e6			1.08153			0.540763	+	0.841175i	$0.318136\pi$
$150$	146466.	+	361141.i	0.0433974	+	0.107005i
$151$		−	1.67522e6i		−	0.486566i	−0.969955	−	0.243283i	$-0.921776\pi$
$151$		−	1.67522e6i		−	0.486566i	0.969955	−	0.243283i	$-0.0782244\pi$
$152$	−2.97946e6	−	1.31240e6i	−0.848412	−	0.373710i
$153$	−965036.			−0.269444
$154$	2.49684e6	−	1.01263e6i	0.683642	−	0.277262i
$155$			1.53271e6i			0.411589i
$156$	2.31534e6	+	2.38495e6i	0.609876	+	0.628210i
$157$	2.14577e6			0.554479			0.277240	−	0.960801i	$-0.410580\pi$
$157$	2.14577e6			0.554479			0.277240	+	0.960801i	$0.410580\pi$
$158$	−2.27419e6	−	5.60745e6i	−0.576574	−	1.42165i
$159$		−	2.63699e6i		−	0.656020i
$160$	−637880.	−	1.71713e6i	−0.155733	−	0.419222i
$161$	1.47945e6			0.354505
$162$	437760.	−	177540.i	0.102965	−	0.0417592i
$163$			8.11549e6i			1.87392i	0.349433	+	0.936961i	$0.386374\pi$
$163$			8.11549e6i			1.87392i	−0.349433	+	0.936961i	$0.613626\pi$
$164$	4.54641e6	−	4.41372e6i	1.03071	−	1.00063i
$165$	−647301.			−0.144097
$166$	1.64134e6	+	4.04703e6i	0.358818	+	0.884734i
$167$		−	1.01972e6i		−	0.218942i	−0.993990	−	0.109471i	$-0.965084\pi$
$167$		−	1.01972e6i		−	0.218942i	0.993990	−	0.109471i	$-0.0349157\pi$
$168$	1.45876e6	−	3.31174e6i	0.307649	−	0.698438i
$169$	6.27383e6			1.29979
$170$	1.64583e6	−	667494.i	0.334995	−	0.135863i
$171$			1.54518e6i			0.309024i
$172$	3.65896e6	+	3.76896e6i	0.719072	+	0.740689i
$173$	−1.72089e6			−0.332364			−0.166182	−	0.986095i	$-0.553144\pi$
$173$	−1.72089e6			−0.332364			−0.166182	+	0.986095i	$0.553144\pi$
$174$	−1.94954e6	−	4.80695e6i	−0.370070	−	0.912477i
$175$		−	1.41690e6i		−	0.264378i
$176$	3.04122e6	+	90091.2i	0.557840	+	0.0165251i
$177$	−2.38495e6			−0.430089
$178$	8.08702e6	−	3.27982e6i	1.43393	−	0.581554i
$179$			5.72284e6i			0.997821i	0.866653	+	0.498911i	$0.166266\pi$
$179$			5.72284e6i			0.997821i	−0.866653	+	0.498911i	$0.833734\pi$
$180$	−623782.	+	605577.i	−0.106958	+	0.103837i
$181$	−9.73675e6			−1.64202			−0.821010	−	0.570914i	$-0.806589\pi$
$181$	−9.73675e6			−1.64202			−0.821010	+	0.570914i	$0.806589\pi$
$182$	−4.54201e6	−	1.11992e7i	−0.753414	−	1.85769i
$183$		−	5.14039e6i		−	0.838770i
$184$	1.52888e6	+	673445.i	0.245426	+	0.108106i
$185$	−1.51234e6			−0.238856
$186$	−3.16855e6	+	1.28506e6i	−0.492404	+	0.199702i
$187$			2.94996e6i			0.451119i
$188$	3.55096e6	+	3.65771e6i	0.534407	+	0.550473i
$189$	−1.71751e6			−0.254398
$190$	−1.06877e6	−	2.63525e6i	−0.155820	−	0.384204i
$191$		−	9.90591e6i		−	1.42165i	−0.703367	−	0.710827i	$-0.748321\pi$
$191$		−	9.90591e6i		−	1.42165i	0.703367	−	0.710827i	$-0.251679\pi$
$192$	3.01500e6	−	2.75837e6i	0.425975	−	0.389716i
$193$	−2.91357e6			−0.405279			−0.202640	−	0.979253i	$-0.564952\pi$
$193$	−2.91357e6			−0.405279			−0.202640	+	0.979253i	$0.564952\pi$
$194$	−7.24502e6	+	2.93833e6i	−0.992281	+	0.402435i
$195$			2.90337e6i			0.391560i
$196$	−4.03774e6	+	3.91990e6i	−0.536253	+	0.520603i
$197$	4.01339e6			0.524944			0.262472	−	0.964940i	$-0.415462\pi$
$197$	4.01339e6			0.524944			0.262472	+	0.964940i	$0.415462\pi$
$198$	−542712.	−	1.33816e6i	−0.0699155	−	0.172390i
$199$			1.13719e7i			1.44303i	0.692399	+	0.721515i	$0.256554\pi$
$199$			1.13719e7i			1.44303i	−0.692399	+	0.721515i	$0.743446\pi$
$200$	644972.	−	1.46424e6i	0.0806215	−	0.183031i
$201$	326211.			0.0401708
$202$	6.28884e6	−	2.55054e6i	0.762986	−	0.309441i
$203$			1.88596e7i			2.25447i
$204$	2.75981e6	+	2.84277e6i	0.325078	+	0.334851i
$205$	5.53467e6			0.642436
$206$	−183682.	−	452903.i	−0.0210119	−	0.0518088i
$207$		−	792898.i		−	0.0893936i
$208$	404090.	−	1.36409e7i	0.0449043	−	1.51584i
$209$	4.72337e6			0.517384
$210$	2.92914e6	−	1.18796e6i	0.316288	−	0.128276i
$211$		−	1.58351e7i		−	1.68567i	−0.538169	−	0.842837i	$-0.680884\pi$
$211$		−	1.58351e7i		−	1.68567i	0.538169	−	0.842837i	$-0.319116\pi$
$212$	−7.76795e6	+	7.54125e6i	−0.815265	+	0.791472i
$213$	−9.20242e6			−0.952277
$214$	−4.59309e6	−	1.13251e7i	−0.468666	−	1.15559i
$215$			4.58822e6i			0.461667i
$216$	−1.77490e6	−	781809.i	−0.176121	−	0.0775781i
$217$	1.24315e7			1.21659
$218$	6.43625e6	−	2.61032e6i	0.621246	−	0.251956i
$219$		−	5.31650e6i		−	0.506166i
$220$	1.85115e6	+	1.90680e6i	0.173849	+	0.179076i
$221$	1.32316e7			1.22584
$222$	−1.26798e6	−	3.12645e6i	−0.115892	−	0.285755i
$223$			5.43414e6i			0.490023i	0.969520	+	0.245011i	$0.0787917\pi$
$223$			5.43414e6i			0.490023i	−0.969520	+	0.245011i	$0.921208\pi$
$224$	−1.39274e7	+	5.17373e6i	−1.23915	+	0.460320i
$225$	−759375.			−0.0666667
$226$	7.15762e6	−	2.90289e6i	0.620074	−	0.251481i
$227$		−	1.08724e7i		−	0.929496i	−0.885443	−	0.464748i	$-0.846145\pi$
$227$		−	1.08724e7i		−	0.929496i	0.885443	−	0.464748i	$-0.153855\pi$
$228$	4.55175e6	−	4.41891e6i	0.384038	−	0.372830i
$229$	−2.12428e7			−1.76891			−0.884453	−	0.466629i	$-0.845468\pi$
$229$	−2.12428e7			−1.76891			−0.884453	+	0.466629i	$0.845468\pi$
$230$	548430.	+	1.35226e6i	0.0450752	+	0.111141i
$231$			5.25014e6i			0.425927i
$232$	−8.58488e6	+	1.94898e7i	−0.687496	+	1.56078i
$233$	−97166.1			−0.00768152			−0.00384076	−	0.999993i	$-0.501223\pi$
$233$	−97166.1			−0.00768152			−0.00384076	+	0.999993i	$0.501223\pi$
$234$	−6.00211e6	+	2.43425e6i	−0.468442	+	0.189984i
$235$			4.45280e6i			0.343107i
$236$	6.82045e6	+	7.02549e6i	0.518892	+	0.534491i
$237$	1.17908e7			0.885727
$238$	−5.41391e6	−	1.33490e7i	−0.401588	−	0.990191i
$239$		−	5.25869e6i		−	0.385198i	−0.981278	−	0.192599i	$-0.938308\pi$
$239$		−	5.25869e6i		−	0.385198i	0.981278	−	0.192599i	$-0.0616917\pi$
$240$	3.56778e6	+	105690.i	0.258086	+	0.00764537i
$241$	3.62160e6			0.258731			0.129366	−	0.991597i	$-0.458706\pi$
$241$	3.62160e6			0.258731			0.129366	+	0.991597i	$0.458706\pi$
$242$	9.04293e6	−	3.66751e6i	0.638063	−	0.258776i
$243$			920483.i			0.0641500i
$244$	−1.51424e7	+	1.47005e7i	−1.04238	+	1.01196i
$245$	−4.91543e6			−0.334244
$246$	4.64039e6	+	1.14418e7i	0.311709	+	0.768578i
$247$		−	2.11860e7i		−	1.40591i
$248$	1.28469e7	+	5.65881e6i	0.842253	+	0.370997i
$249$	−8.50975e6			−0.551212
$250$	1.29509e6	−	525242.i	0.0828854	−	0.0336155i
$251$			352728.i			0.0223058i	0.999938	+	0.0111529i	$0.00355016\pi$
$251$			352728.i			0.0223058i	−0.999938	+	0.0111529i	$0.996450\pi$
$252$	4.91172e6	+	5.05938e6i	0.306925	+	0.316152i
$253$	−2.42376e6			−0.149668
$254$	9.93797e6	+	2.45039e7i	0.606452	+	1.49532i
$255$			3.46071e6i			0.208711i
$256$	−1.67478e7	−	993124.i	−0.998246	−	0.0591948i
$257$	−2.45984e7			−1.44913			−0.724566	−	0.689206i	$-0.757960\pi$
$257$	−2.45984e7			−1.44913			−0.724566	+	0.689206i	$0.757960\pi$
$258$	−9.48519e6	+	3.84687e6i	−0.552315	+	0.224000i
$259$			1.22663e7i			0.706018i
$260$	8.55265e6	−	8.30304e6i	0.486609	−	0.472408i
$261$	1.01076e7			0.568497
$262$	4.16717e6	+	1.02750e7i	0.231706	+	0.571316i
$263$			1.04349e7i			0.573616i	0.957988	+	0.286808i	$0.0925942\pi$
$263$			1.04349e7i			0.573616i	−0.957988	+	0.286808i	$0.907406\pi$
$264$	−2.38986e6	+	5.42556e6i	−0.129885	+	0.294872i
$265$	−9.45649e6			−0.508151
$266$	−2.13740e7	+	8.66858e6i	−1.13564	+	0.460578i
$267$			1.70047e7i			0.893377i
$268$	−932898.	−	960943.i	−0.0484652	−	0.0499221i
$269$	−1.94880e7			−1.00117			−0.500587	−	0.865686i	$-0.666883\pi$
$269$	−1.94880e7			−1.00117			−0.500587	+	0.865686i	$0.666883\pi$
$270$	−636677.	−	1.56985e6i	−0.0323465	−	0.0797566i
$271$		−	3.71980e7i		−	1.86901i	−0.355947	−	0.934506i	$-0.615842\pi$
$271$		−	3.71980e7i		−	1.86901i	0.355947	−	0.934506i	$-0.384158\pi$
$272$	481661.	−	1.62595e7i	0.0239351	−	0.807979i
$273$	2.35487e7			1.15739
$274$	−2.49875e6	+	1.01341e6i	−0.121471	+	0.0492644i
$275$			2.32128e6i			0.111617i
$276$	−2.33569e6	+	2.26753e6i	−0.111093	+	0.107851i
$277$	1.38147e7			0.649982			0.324991	−	0.945717i	$-0.394639\pi$
$277$	1.38147e7			0.649982			0.324991	+	0.945717i	$0.394639\pi$
$278$	−1.14924e7	−	2.83367e7i	−0.534904	−	1.31891i
$279$		−	6.66255e6i		−	0.306780i
$280$	−1.18762e7	−	5.23125e6i	−0.541008	−	0.238304i
$281$	2.85004e6			0.128450			0.0642248	−	0.997935i	$-0.479543\pi$
$281$	2.85004e6			0.128450			0.0642248	+	0.997935i	$0.479543\pi$
$282$	−9.20522e6	+	3.73332e6i	−0.410475	+	0.166475i
$283$		−	3.31454e6i		−	0.146239i	−0.997323	−	0.0731197i	$-0.976704\pi$
$283$		−	3.31454e6i		−	0.146239i	0.997323	−	0.0731197i	$-0.0232955\pi$
$284$	2.63170e7	+	2.71082e7i	1.14890	+	1.18344i
$285$	5.54118e6			0.239369
$286$	7.44110e6	+	1.83474e7i	0.318082	+	0.784291i
$287$		−	4.48907e7i		−	1.89894i
$288$	2.77281e6	+	7.46424e6i	0.116076	+	0.312470i
$289$	−8.36601e6			−0.346597
$290$	−1.72382e7	+	6.99122e6i	−0.706802	+	0.286655i
$291$		−	1.52342e7i		−	0.618216i
$292$	−1.56612e7	+	1.52041e7i	−0.629036	+	0.610678i
$293$	2.23912e7			0.890172			0.445086	−	0.895488i	$-0.353173\pi$
$293$	2.23912e7			0.890172			0.445086	+	0.895488i	$0.353173\pi$
$294$	−4.12121e6	−	1.01616e7i	−0.162174	−	0.399872i
$295$			8.55264e6i			0.333146i
$296$	−5.58363e6	+	1.26762e7i	−0.215299	+	0.488781i
$297$	2.81376e6			0.107403
$298$	2.65228e7	−	1.07567e7i	1.00224	−	0.406473i
$299$			1.08714e7i			0.406698i
$300$	2.17166e6	+	2.23694e6i	0.0804317	+	0.0828497i
$301$	3.72142e7			1.36461
$302$	−5.03683e6	−	1.24193e7i	−0.182868	−	0.450895i
$303$			1.32236e7i			0.475360i
$304$	−2.60341e7	−	771219.i	−0.926665	−	0.0274509i
$305$	−1.84339e7			−0.649708
$306$	−7.15430e6	+	2.90154e6i	−0.249691	+	0.101266i
$307$			7.99288e6i			0.276241i	0.990415	+	0.138120i	$0.0441061\pi$
$307$			7.99288e6i			0.276241i	−0.990415	+	0.138120i	$0.955894\pi$
$308$	1.54657e7	−	1.50143e7i	0.529318	−	0.513870i
$309$	952325.			0.0322782
$310$	4.60833e6	+	1.13627e7i	0.154689	+	0.381414i
$311$		−	4.44476e7i		−	1.47763i	−0.673906	−	0.738817i	$-0.735385\pi$
$311$		−	4.44476e7i		−	1.47763i	0.673906	−	0.738817i	$-0.264615\pi$
$312$	2.43355e7	+	1.07193e7i	0.801266	+	0.352943i
$313$	−2.33025e7			−0.759924			−0.379962	−	0.925002i	$-0.624063\pi$
$313$	−2.33025e7			−0.759924			−0.379962	+	0.925002i	$0.624063\pi$
$314$	1.59077e7	−	6.45162e6i	0.513829	−	0.208391i
$315$			6.15915e6i			0.197056i
$316$	−3.37194e7	−	3.47331e7i	−1.06861	−	1.10073i
$317$	2.93661e6			0.0921866			0.0460933	−	0.998937i	$-0.485323\pi$
$317$	2.93661e6			0.0921866			0.0460933	+	0.998937i	$0.485323\pi$
$318$	−7.92854e6	−	1.95493e7i	−0.246554	−	0.607925i
$319$		−	3.08974e7i		−	0.951809i
$320$	−9.89177e6	−	1.08121e7i	−0.301873	−	0.329959i
$321$	2.38135e7			0.719960
$322$	1.09679e7	−	4.44821e6i	0.328516	−	0.133235i
$323$		−	2.52529e7i		−	0.749383i
$324$	2.71153e6	−	2.63239e6i	0.0797221	−	0.0773955i
$325$	1.04118e7			0.303301
$326$	2.44005e7	+	6.01642e7i	0.704282	+	1.73654i
$327$			1.35336e7i			0.387052i
$328$	2.04342e7	−	4.63906e7i	0.579077	−	1.31465i
$329$	3.61158e7			1.01417
$330$	−4.79877e6	+	1.94622e6i	−0.133533	+	0.0541564i
$331$			3.62314e7i			0.999083i	0.866290	+	0.499541i	$0.166498\pi$
$331$			3.62314e7i			0.999083i	−0.866290	+	0.499541i	$0.833502\pi$
$332$	2.43361e7	+	2.50677e7i	0.665024	+	0.685016i
$333$	6.57403e6			0.178033
$334$	−3.06594e6	−	7.55966e6i	−0.0822857	−	0.202891i
$335$		−	1.16983e6i		−	0.0311162i
$336$	857228.	−	2.89376e7i	0.0225984	−	0.762859i
$337$	−1.18083e7			−0.308530			−0.154265	−	0.988030i	$-0.549301\pi$
$337$	−1.18083e7			−0.308530			−0.154265	+	0.988030i	$0.549301\pi$
$338$	4.65111e7	−	1.88633e7i	1.20450	−	0.488503i
$339$			1.50504e7i			0.386322i
$340$	1.01944e7	−	9.89693e6i	0.259374	−	0.251805i
$341$	−2.03663e7			−0.513628
$342$	4.64585e6	+	1.14552e7i	0.116141	+	0.286368i
$343$		−	1.34749e7i		−	0.333920i
$344$	3.84577e7	+	1.69399e7i	0.944730	+	0.416136i
$345$	−2.84341e6			−0.0692440
$346$	−1.27578e7	+	5.17413e6i	−0.307998	+	0.124913i
$347$			9.01498e6i			0.215763i	0.994164	+	0.107881i	$0.0344067\pi$
$347$			9.01498e6i			0.215763i	−0.994164	+	0.107881i	$0.965593\pi$
$348$	−2.89058e7	−	2.97747e7i	−0.685878	−	0.706497i
$349$	6.30695e7			1.48369			0.741845	−	0.670571i	$-0.233951\pi$
$349$	6.30695e7			1.48369			0.741845	+	0.670571i	$0.233951\pi$
$350$	−4.26014e6	−	1.05042e7i	−0.0993619	−	0.244996i
$351$		−	1.26207e7i		−	0.291852i
$352$	2.28170e7	−	8.47603e6i	0.523154	−	0.194341i
$353$	−4.23757e7			−0.963370			−0.481685	−	0.876344i	$-0.659975\pi$
$353$	−4.23757e7			−0.963370			−0.481685	+	0.876344i	$0.659975\pi$
$354$	−1.76808e7	+	7.17073e6i	−0.398558	+	0.161642i
$355$			3.30008e7i			0.737631i
$356$	5.00918e7	−	4.86299e7i	1.11024	−	1.07784i
$357$	2.80692e7			0.616915
$358$	1.72067e7	+	4.24263e7i	0.375014	+	0.924669i
$359$			4.92507e7i			1.06446i	0.846600	+	0.532229i	$0.178646\pi$
$359$			4.92507e7i			1.06446i	−0.846600	+	0.532229i	$0.821354\pi$
$360$	−2.80364e6	+	6.36495e6i	−0.0600917	+	0.136423i
$361$	6.61178e6			0.140539
$362$	−7.21834e7	+	2.92751e7i	−1.52164	+	0.617125i
$363$			1.90147e7i			0.397530i
$364$	−6.73444e7	−	6.93689e7i	−1.39636	−	1.43834i
$365$	−1.90655e7			−0.392075
$366$	−1.54554e7	−	3.81083e7i	−0.315237	−	0.777278i
$367$			1.43654e7i			0.290617i	0.989386	+	0.145308i	$0.0464174\pi$
$367$			1.43654e7i			0.290617i	−0.989386	+	0.145308i	$0.953583\pi$
$368$	1.33592e7	+	395745.i	0.268063	+	0.00794093i
$369$	−2.40587e7			−0.478844
$370$	−1.12118e7	+	4.54711e6i	−0.221345	+	0.0897698i
$371$			7.66998e7i			1.50201i
$372$	−1.96263e7	+	1.90535e7i	−0.381250	+	0.370123i
$373$	−4.89814e7			−0.943854			−0.471927	−	0.881638i	$-0.656441\pi$
$373$	−4.89814e7			−0.943854			−0.471927	+	0.881638i	$0.656441\pi$
$374$	8.86953e6	+	2.18695e7i	0.169545	+	0.418046i
$375$			2.72319e6i			0.0516398i
$376$	3.73225e7	+	1.64399e7i	0.702114	+	0.309268i
$377$	−1.38585e8			−2.58639
$378$	−1.27327e7	+	5.16397e6i	−0.235747	+	0.0956110i
$379$			4.49792e6i			0.0826217i	0.999146	+	0.0413109i	$0.0131534\pi$
$379$			4.49792e6i			0.0826217i	−0.999146	+	0.0413109i	$0.986847\pi$
$380$	−1.58466e7	−	1.63230e7i	−0.288793	−	0.297474i
$381$	−5.15248e7			−0.931625
$382$	−2.97837e7	−	7.34374e7i	−0.534305	−	1.31743i
$383$			5.07825e7i			0.903894i	0.892045	+	0.451947i	$0.149270\pi$
$383$			5.07825e7i			0.903894i	−0.892045	+	0.451947i	$0.850730\pi$
$384$	1.40582e7	−	2.95143e7i	0.248277	−	0.521241i
$385$	1.88275e7			0.329921
$386$	−2.15998e7	+	8.76014e6i	−0.375567	+	0.152317i
$387$		−	1.99446e7i		−	0.344107i
$388$	−4.48764e7	+	4.35667e7i	−0.768286	+	0.745863i
$389$	−8.48144e7			−1.44086			−0.720429	−	0.693529i	$-0.756055\pi$
$389$	−8.48144e7			−1.44086			−0.720429	+	0.693529i	$0.756055\pi$
$390$	8.72945e6	+	2.15241e7i	0.147161	+	0.362854i
$391$			1.29583e7i			0.216779i
$392$	−1.81480e7	+	4.12003e7i	−0.301279	+	0.683978i
$393$	−2.16053e7			−0.355945
$394$	2.97533e7	−	1.20669e7i	0.486459	−	0.197291i
$395$		−	4.22831e7i		−	0.686081i
$396$	−8.04679e6	−	8.28869e6i	−0.129580	−	0.133475i
$397$	−2.61548e7			−0.418004			−0.209002	−	0.977915i	$-0.567022\pi$
$397$	−2.61548e7			−0.418004			−0.209002	+	0.977915i	$0.567022\pi$
$398$	3.41916e7	+	8.43058e7i	0.542338	+	1.33724i
$399$		−	4.49434e7i		−	0.707535i
$400$	379013.	−	1.27944e7i	0.00592208	−	0.199912i
$401$	2.42221e7			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$401$	2.42221e7			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$402$	2.41837e6	−	980808.i	0.0372258	−	0.0150975i
$403$			9.13499e7i			1.39570i
$404$	3.89537e7	−	3.78169e7i	0.590751	−	0.573510i
$405$	3.30094e6			0.0496904
$406$	5.67045e7	+	1.39816e8i	0.847304	+	2.08919i
$407$		−	2.00957e7i		−	0.298072i
$408$	2.90071e7	+	1.27771e7i	0.427094	+	0.188127i
$409$	5.79378e7			0.846822			0.423411	−	0.905938i	$-0.360833\pi$
$409$	5.79378e7			0.846822			0.423411	+	0.905938i	$0.360833\pi$
$410$	4.10313e7	−	1.66409e7i	0.595338	−	0.241449i
$411$		−	5.25416e6i		−	0.0756794i
$412$	−2.72345e6	−	2.80533e6i	−0.0389429	−	0.0401136i
$413$	6.93689e7			0.984724
$414$	−2.38398e6	−	5.87815e6i	−0.0335970	−	0.0828399i
$415$			3.05168e7i			0.426967i
$416$	−3.80179e7	−	1.02342e8i	−0.528091	−	1.42159i
$417$	5.95838e7			0.821713
$418$	3.50167e7	−	1.42016e7i	0.479454	−	0.194450i
$419$			6.15000e7i			0.836052i	0.908435	+	0.418026i	$0.137278\pi$
$419$			6.15000e7i			0.836052i	−0.908435	+	0.418026i	$0.862722\pi$
$420$	1.81434e7	−	1.76139e7i	0.244890	−	0.237743i
$421$	−5.99496e7			−0.803415			−0.401708	−	0.915768i	$-0.631583\pi$
$421$	−5.99496e7			−0.803415			−0.401708	+	0.915768i	$0.631583\pi$
$422$	−4.76108e7	−	1.17394e8i	−0.633532	−	1.56209i
$423$		−	1.93559e7i		−	0.255737i
$424$	−3.49137e7	+	7.92627e7i	−0.458035	+	1.03985i
$425$	1.24104e7			0.161667
$426$	−6.82221e7	+	2.76686e7i	−0.882463	+	0.357897i
$427$			1.49514e8i			1.92043i
$428$	−6.81018e7	−	7.01490e7i	−0.868615	−	0.894727i
$429$	−3.85794e7			−0.488634
$430$	1.37952e7	+	3.40148e7i	0.173510	+	0.427821i
$431$		−	9.68624e7i		−	1.20983i	−0.796291	−	0.604913i	$-0.793208\pi$
$431$		−	9.68624e7i		−	1.20983i	0.796291	−	0.604913i	$-0.206792\pi$
$432$	−1.55088e7	−	459424.i	−0.192366	−	0.00569852i
$433$	8.72663e7			1.07494			0.537468	−	0.843284i	$-0.319381\pi$
$433$	8.72663e7			1.07494			0.537468	+	0.843284i	$0.319381\pi$
$434$	9.21608e7	−	3.73773e7i	1.12740	−	0.457234i
$435$		−	3.62470e7i		−	0.440356i
$436$	3.98668e7	−	3.87033e7i	0.481007	−	0.466969i
$437$	2.07484e7			0.248623
$438$	−1.59849e7	−	3.94139e7i	−0.190234	−	0.469058i
$439$		−	1.17058e8i		−	1.38359i	−0.722096	−	0.691793i	$-0.756821\pi$
$439$		−	1.17058e8i		−	1.38359i	0.722096	−	0.691793i	$-0.243179\pi$
$440$	1.94566e7	+	8.57027e6i	0.228407	+	0.100609i
$441$	2.13670e7			0.249131
$442$	9.80922e7	−	3.97829e7i	1.13597	−	0.460712i
$443$			3.47518e7i			0.399730i	0.979823	+	0.199865i	$0.0640503\pi$
$443$			3.47518e7i			0.399730i	−0.979823	+	0.199865i	$0.935950\pi$
$444$	−1.88004e7	−	1.93656e7i	−0.214792	−	0.221249i
$445$	6.09804e7			0.692007
$446$	1.63386e7	+	4.02860e7i	0.184167	+	0.454098i
$447$			5.57697e7i			0.624419i
$448$	−8.76948e7	+	8.02303e7i	−0.975303	+	0.892287i
$449$	1.25023e8			1.38118			0.690591	−	0.723245i	$-0.257350\pi$
$449$	1.25023e8			1.38118			0.690591	+	0.723245i	$0.257350\pi$
$450$	−5.62963e6	+	2.28318e6i	−0.0617792	+	0.0250555i
$451$			7.35436e7i			0.801707i
$452$	4.43350e7	−	4.30411e7i	0.480100	−	0.466088i
$453$	2.61142e7			0.280919
$454$	−3.26896e7	−	8.06025e7i	−0.349335	−	0.861352i
$455$		−	8.44478e7i		−	0.896508i
$456$	2.04582e7	−	4.64452e7i	0.215761	−	0.489831i
$457$	1.07976e8			1.13130			0.565652	−	0.824644i	$-0.308624\pi$
$457$	1.07976e8			1.13130			0.565652	+	0.824644i	$0.308624\pi$
$458$	−1.57483e8	+	6.38699e7i	−1.63922	+	0.664813i
$459$		−	1.50434e7i		−	0.155564i
$460$	8.13157e6	+	8.37602e6i	0.0835412	+	0.0860526i
$461$	−6.83459e7			−0.697606			−0.348803	−	0.937196i	$-0.613412\pi$
$461$	−6.83459e7			−0.697606			−0.348803	+	0.937196i	$0.613412\pi$
$462$	1.57854e7	+	3.89219e7i	0.160077	+	0.394701i
$463$		−	1.86862e8i		−	1.88269i	−0.337450	−	0.941343i	$-0.609564\pi$
$463$		−	1.86862e8i		−	1.88269i	0.337450	−	0.941343i	$-0.390436\pi$
$464$	−5.04484e6	+	1.70299e8i	−0.0505002	+	1.70474i
$465$	−2.38925e7			−0.237631
$466$	−720341.	+	292146.i	−0.00711837	+	0.00288697i
$467$		−	1.04072e8i		−	1.02184i	−0.859628	−	0.510921i	$-0.829304\pi$
$467$		−	1.04072e8i		−	1.02184i	0.859628	−	0.510921i	$-0.170696\pi$
$468$	−3.71776e7	+	3.60926e7i	−0.362697	+	0.352112i
$469$	−9.48823e6			−0.0919744
$470$	1.33881e7	+	3.30108e7i	0.128951	+	0.317953i
$471$			3.34493e7i			0.320129i
$472$	7.16867e7	+	3.15767e7i	0.681730	+	0.300290i
$473$	−6.09674e7			−0.576122
$474$	8.74114e7	−	3.54511e7i	0.820792	−	0.332885i
$475$		−	1.98712e7i		−	0.185414i
$476$	−8.02721e7	−	8.26853e7i	−0.744293	−	0.766668i
$477$	4.11066e7			0.378753
$478$	−1.58111e7	−	3.89853e7i	−0.144770	−	0.356958i
$479$		−	1.37718e8i		−	1.25310i	−0.779382	−	0.626549i	$-0.784467\pi$
$479$		−	1.37718e8i		−	1.25310i	0.779382	−	0.626549i	$-0.215533\pi$
$480$	2.67675e7	−	9.94357e6i	0.242038	−	0.0899122i
$481$	−9.01363e7			−0.809962
$482$	2.68487e7	−	1.08889e7i	0.239763	−	0.0972397i
$483$			2.30623e7i			0.204674i
$484$	5.60128e7	−	5.43781e7i	0.494028	−	0.479610i
$485$	−5.46313e7			−0.478868
$486$	2.76758e6	+	6.82400e6i	0.0241097	+	0.0594470i
$487$		−	2.26516e8i		−	1.96115i	−0.196141	−	0.980576i	$-0.562841\pi$
$487$		−	2.26516e8i		−	1.96115i	0.196141	−	0.980576i	$-0.437159\pi$
$488$	−6.80588e7	+	1.54510e8i	−0.585632	+	1.32953i
$489$	−1.26508e8			−1.08191
$490$	−3.64405e7	+	1.47790e7i	−0.309740	+	0.125620i
$491$			5.01967e7i			0.424063i	0.977263	+	0.212032i	$0.0680080\pi$
$491$			5.01967e7i			0.424063i	−0.977263	+	0.212032i	$0.931992\pi$
$492$	6.88031e7	+	7.08715e7i	0.577714	+	0.595081i
$493$	−1.65189e8			−1.37861
$494$	−6.36990e7	−	1.57062e8i	−0.528387	−	1.30284i
$495$		−	1.00904e7i		−	0.0831944i
$496$	1.12254e8	+	3.32535e6i	0.919938	+	0.0272516i
$497$	2.67663e8			2.18031
$498$	−6.30870e7	+	2.55859e7i	−0.510801	+	0.207164i
$499$			4.08385e7i			0.328676i	0.986404	+	0.164338i	$0.0525488\pi$
$499$			4.08385e7i			0.328676i	−0.986404	+	0.164338i	$0.947451\pi$
$500$	8.02189e6	−	7.78777e6i	0.0641751	−	0.0623022i
$501$	1.58958e7			0.126406
$502$	1.06053e6	+	2.61495e6i	0.00838327	+	0.0206705i
$503$		−	7.02629e7i		−	0.552105i	−0.961143	−	0.276053i	$-0.910974\pi$
$503$		−	7.02629e7i		−	0.552105i	0.961143	−	0.276053i	$-0.0890264\pi$
$504$	5.16249e7	+	2.27398e7i	0.403244	+	0.177621i
$505$	4.74212e7			0.368212
$506$	−1.79685e7	+	7.28743e6i	−0.138695	+	0.0562500i
$507$			9.77994e7i			0.750434i
$508$	1.47350e8	+	1.51780e8i	1.12398	+	1.15777i
$509$	8.32274e7			0.631121			0.315561	−	0.948905i	$-0.397807\pi$
$509$	8.32274e7			0.631121			0.315561	+	0.948905i	$0.397807\pi$
$510$	1.04052e7	+	2.56560e7i	0.0784404	+	0.193410i
$511$			1.54636e8i			1.15891i
$512$	−1.27146e8	+	4.29925e7i	−0.947310	+	0.320319i
$513$	−2.40870e7			−0.178415
$514$	−1.82360e8	+	7.39591e7i	−1.34289	+	0.544631i
$515$		−	3.41513e6i		−	0.0250026i
$516$	−5.87522e7	+	5.70375e7i	−0.427637	+	0.415156i
$517$	−5.91679e7			−0.428168
$518$	3.68808e7	+	9.09365e7i	0.265345	+	0.654258i
$519$		−	2.68260e7i		−	0.191890i
$520$	3.84406e7	−	8.72695e7i	0.273388	−	0.620658i
$521$	−2.82264e7			−0.199592			−0.0997959	−	0.995008i	$-0.531819\pi$
$521$	−2.82264e7			−0.199592			−0.0997959	+	0.995008i	$0.531819\pi$
$522$	7.49330e7	−	3.03903e7i	0.526819	−	0.213660i
$523$		−	2.42494e8i		−	1.69510i	−0.530714	−	0.847551i	$-0.678076\pi$
$523$		−	2.42494e8i		−	1.69510i	0.530714	−	0.847551i	$-0.321924\pi$
$524$	6.17867e7	+	6.36441e7i	0.429439	+	0.442348i
$525$	2.20873e7			0.152639
$526$	3.13743e7	+	7.73592e7i	0.215584	+	0.531563i
$527$			1.08886e8i			0.743943i
$528$	−1.40438e6	+	4.74079e7i	−0.00954077	+	0.322069i
$529$	1.37389e8			0.928079
$530$	−7.01057e7	+	2.84325e7i	−0.470897	+	0.190980i
$531$		−	3.71776e7i		−	0.248312i
$532$	−1.32393e8	+	1.28529e8i	−0.879285	+	0.853623i
$533$	3.29868e8			2.17851
$534$	5.11274e7	+	1.26064e8i	0.335761	+	0.827881i
$535$		−	8.53975e7i		−	0.557679i
$536$	−9.80527e6	−	4.31904e6i	−0.0636744	−	0.0280474i
$537$	−8.92103e7			−0.576092
$538$	−1.44474e8	+	5.85938e7i	−0.927776	+	0.376274i
$539$		−	6.53153e7i		−	0.417108i
$540$	−9.44001e6	−	9.72380e6i	−0.0599503	−	0.0617525i
$541$	−1.52045e8			−0.960244			−0.480122	−	0.877202i	$-0.659408\pi$
$541$	−1.52045e8			−0.960244			−0.480122	+	0.877202i	$0.659408\pi$
$542$	−1.11842e8	−	2.75768e8i	−0.702436	−	1.73199i
$543$		−	1.51781e8i		−	0.948020i
$544$	−4.53160e7	−	1.21988e8i	−0.281485	−	0.757740i
$545$	4.85327e7			0.299809
$546$	1.74578e8	−	7.08029e7i	1.07254	−	0.434984i
$547$			3.04707e7i			0.186175i	0.995658	+	0.0930873i	$0.0296736\pi$
$547$			3.04707e7i			0.186175i	−0.995658	+	0.0930873i	$0.970326\pi$
$548$	−1.54775e7	+	1.50258e7i	−0.0940502	+	0.0913054i
$549$	8.01308e7			0.484264
$550$	6.97932e6	+	1.72088e7i	0.0419493	+	0.103434i
$551$			2.64495e8i			1.58111i
$552$	−1.04980e7	+	2.38329e7i	−0.0624149	+	0.141697i
$553$	−3.42950e8			−2.02794
$554$	1.02415e8	−	4.15361e7i	0.602330	−	0.244285i
$555$		−	2.35751e7i		−	0.137903i
$556$	−1.70398e8	−	1.75520e8i	−0.991377	−	1.02118i
$557$	−2.76947e8			−1.60262			−0.801311	−	0.598248i	$-0.795864\pi$
$557$	−2.76947e8			−1.60262			−0.801311	+	0.598248i	$0.795864\pi$
$558$	−2.00320e7	−	4.93928e7i	−0.115298	−	0.284290i
$559$			2.73460e8i			1.56552i
$560$	−1.03773e8	−	3.07410e6i	−0.590908	−	0.0175047i
$561$	−4.59853e7			−0.260453
$562$	2.11288e7	−	8.56913e6i	0.119033	−	0.0482756i
$563$			2.57453e8i			1.44269i	0.692576	+	0.721345i	$0.256476\pi$
$563$			2.57453e8i			1.44269i	−0.692576	+	0.721345i	$0.743524\pi$
$564$	−5.70180e7	+	5.53540e7i	−0.317815	+	0.308540i
$565$	5.39722e7			0.299244
$566$	−9.96571e6	−	2.45724e7i	−0.0549616	−	0.135518i
$567$		−	2.67733e7i		−	0.146877i
$568$	2.76607e8	+	1.21840e8i	1.50945	+	0.664883i
$569$	−6.82567e7			−0.370517			−0.185259	−	0.982690i	$-0.559312\pi$
$569$	−6.82567e7			−0.370517			−0.185259	+	0.982690i	$0.559312\pi$
$570$	4.10795e7	−	1.66605e7i	0.221820	−	0.0899627i
$571$		−	1.68017e8i		−	0.902493i	−0.892399	−	0.451246i	$-0.850980\pi$
$571$		−	1.68017e8i		−	0.902493i	0.892399	−	0.451246i	$-0.149020\pi$
$572$	1.10329e8	+	1.13646e8i	0.589525	+	0.607247i
$573$	1.54418e8			0.820793
$574$	−1.34971e8	−	3.32797e8i	−0.713683	−	1.75972i
$575$			1.01967e7i			0.0536361i
$576$	4.29987e7	+	4.69992e7i	0.225003	+	0.245937i
$577$	−1.56660e8			−0.815510			−0.407755	−	0.913091i	$-0.633688\pi$
$577$	−1.56660e8			−0.815510			−0.407755	+	0.913091i	$0.633688\pi$
$578$	−6.20214e7	+	2.51538e7i	−0.321187	+	0.130263i
$579$		−	4.54181e7i		−	0.233988i
$580$	−1.06775e8	+	1.03659e8i	−0.547250	+	0.531279i
$581$	2.47516e8			1.26204
$582$	−4.58041e7	−	1.12939e8i	−0.232346	−	0.572893i
$583$		−	1.25656e8i		−	0.634129i
$584$	−7.03904e7	+	1.59803e8i	−0.353407	+	0.802320i
$585$	−4.52590e7			−0.226067
$586$	1.65997e8	−	6.73227e7i	0.824912	−	0.334556i
$587$			1.94307e8i			0.960670i	0.877085	+	0.480335i	$0.159485\pi$
$587$			1.94307e8i			0.960670i	−0.877085	+	0.480335i	$0.840515\pi$
$588$	−6.11051e7	−	6.29421e7i	−0.300570	−	0.309606i
$589$	1.74344e8			0.853222
$590$	2.57149e7	+	6.34050e7i	0.125207	+	0.308722i
$591$			6.25626e7i			0.303077i
$592$	−3.28118e6	+	1.10763e8i	−0.0158148	+	0.533863i
$593$	1.11983e8			0.537015			0.268508	−	0.963278i	$-0.413470\pi$
$593$	1.11983e8			0.537015			0.268508	+	0.963278i	$0.413470\pi$
$594$	2.08598e7	−	8.46004e6i	0.0995295	−	0.0403658i
$595$		−	1.00659e8i		−	0.477860i
$596$	1.64285e8	−	1.59490e8i	0.775994	−	0.753347i
$597$	−1.77271e8			−0.833133
$598$	3.26866e7	+	8.05951e7i	0.152850	+	0.376882i
$599$			2.34379e8i			1.09053i	0.838263	+	0.545265i	$0.183571\pi$
$599$			2.34379e8i			1.09053i	−0.838263	+	0.545265i	$0.816429\pi$
$600$	2.28253e7	+	1.00541e7i	0.105673	+	0.0465469i
$601$	9.90791e7			0.456414			0.228207	−	0.973613i	$-0.426714\pi$
$601$	9.90791e7			0.456414			0.228207	+	0.973613i	$0.426714\pi$
$602$	2.75888e8	−	1.11891e8i	1.26457	−	0.512866i
$603$			5.08513e6i			0.0231926i
$604$	−7.46811e7	−	7.69262e7i	−0.338922	−	0.349111i
$605$	6.81885e7			0.307925
$606$	3.97590e7	+	9.80333e7i	0.178656	+	0.440510i
$607$			1.78087e8i			0.796282i	0.917324	+	0.398141i	$0.130345\pi$
$607$			1.78087e8i			0.796282i	−0.917324	+	0.398141i	$0.869655\pi$
$608$	−1.95323e8	+	7.25585e7i	−0.869046	+	0.322833i
$609$	−2.93992e8			−1.30162
$610$	−1.36660e8	+	5.54246e7i	−0.602077	+	0.244182i
$611$			2.65388e8i			1.16348i
$612$	−4.43144e7	+	4.30211e7i	−0.193326	+	0.187684i
$613$	−1.52987e8			−0.664160			−0.332080	−	0.943251i	$-0.607750\pi$
$613$	−1.52987e8			−0.664160			−0.332080	+	0.943251i	$0.607750\pi$
$614$	2.40319e7	+	5.92552e7i	0.103820	+	0.255989i
$615$			8.62770e7i			0.370911i
$616$	6.95118e7	−	1.57809e8i	0.297383	−	0.675132i
$617$	5.43254e7			0.231285			0.115642	−	0.993291i	$-0.463107\pi$
$617$	5.43254e7			0.231285			0.115642	+	0.993291i	$0.463107\pi$
$618$	7.06006e6	−	2.86332e6i	0.0299118	−	0.0121312i
$619$		−	4.57812e7i		−	0.193026i	−0.995332	−	0.0965128i	$-0.969231\pi$
$619$		−	4.57812e7i		−	0.193026i	0.995332	−	0.0965128i	$-0.0307689\pi$
$620$	6.83277e7	+	7.03818e7i	0.286696	+	0.295315i
$621$	1.23601e7			0.0516114
$622$	−1.33639e8	−	3.29512e8i	−0.555343	−	1.36930i
$623$		−	4.94601e8i		−	2.04546i
$624$	2.12641e8	+	6.29914e6i	0.875171	+	0.0259255i
$625$	9.76562e6			0.0400000
$626$	−1.72753e8	+	7.00629e7i	−0.704212	+	0.285604i
$627$			7.36301e7i			0.298712i
$628$	9.85339e7	−	9.56582e7i	0.397838	−	0.386228i
$629$	−1.07439e8			−0.431729
$630$	1.85185e7	+	4.56608e7i	0.0740600	+	0.182609i
$631$			8.56043e7i			0.340728i	0.985381	+	0.170364i	$0.0544943\pi$
$631$			8.56043e7i			0.340728i	−0.985381	+	0.170364i	$0.945506\pi$
$632$	−3.54409e8	−	1.56111e8i	−1.40396	−	0.618417i
$633$	2.46845e8			0.973224
$634$	2.17705e7	−	8.82939e6i	0.0854282	−	0.0346468i
$635$			1.84773e8i			0.721633i
$636$	−1.17556e8	−	1.21090e8i	−0.456957	−	0.470694i
$637$	−2.92962e8			−1.13342
$638$	−9.28980e7	−	2.29058e8i	−0.357721	−	0.882029i
$639$		−	1.43452e8i		−	0.549797i
$640$	−1.05841e8	−	5.04142e7i	−0.403751	−	0.192315i
$641$	1.14611e8			0.435163			0.217582	−	0.976042i	$-0.430183\pi$
$641$	1.14611e8			0.435163			0.217582	+	0.976042i	$0.430183\pi$
$642$	1.76541e8	−	7.15992e7i	0.667178	−	0.270585i
$643$		−	8.72326e7i		−	0.328130i	−0.986450	−	0.164065i	$-0.947539\pi$
$643$		−	8.72326e7i		−	0.328130i	0.986450	−	0.164065i	$-0.0524607\pi$
$644$	6.79363e7	−	6.59536e7i	0.254357	−	0.246934i
$645$	−7.15233e7			−0.266544
$646$	−7.59270e7	−	1.87212e8i	−0.281643	−	0.694444i
$647$			2.63053e8i			0.971248i	0.874168	+	0.485624i	$0.161408\pi$
$647$			2.63053e8i			0.971248i	−0.874168	+	0.485624i	$0.838592\pi$
$648$	1.21872e7	−	2.76679e7i	0.0447897	−	0.101684i
$649$	−1.13646e8			−0.415738
$650$	7.71876e7	−	3.13047e7i	0.281065	−	0.113991i
$651$			1.93788e8i			0.702398i
$652$	3.61787e8	+	3.72663e8i	1.30530	+	1.34454i
$653$	4.49574e8			1.61459			0.807293	−	0.590150i	$-0.200931\pi$
$653$	4.49574e8			1.61459			0.807293	+	0.590150i	$0.200931\pi$
$654$	4.06909e7	+	1.00331e8i	0.145467	+	0.358676i
$655$			7.74786e7i			0.275714i
$656$	1.20080e7	−	4.05356e8i	0.0425362	−	1.43590i
$657$	8.28760e7			0.292235
$658$	2.67744e8	−	1.08588e8i	0.939816	−	0.381157i
$659$		−	9.72494e7i		−	0.339806i	−0.985461	−	0.169903i	$-0.945655\pi$
$659$		−	9.72494e7i		−	0.339806i	0.985461	−	0.169903i	$-0.0543454\pi$
$660$	−2.97240e7	+	2.88566e7i	−0.103389	+	0.100372i
$661$	−3.91966e8			−1.35720			−0.678601	−	0.734507i	$-0.737413\pi$
$661$	−3.91966e8			−1.35720			−0.678601	+	0.734507i	$0.737413\pi$
$662$	1.08936e8	+	2.68602e8i	0.375488	+	0.925838i
$663$			2.06260e8i			0.707740i
$664$	2.55786e8	+	1.12669e8i	0.873721	+	0.384858i
$665$	−1.61171e8			−0.548054
$666$	4.87366e7	−	1.97659e7i	0.164980	−	0.0669105i
$667$		−	1.35723e8i		−	0.457380i
$668$	−4.54587e7	−	4.68253e7i	−0.152506	−	0.157091i
$669$	−8.47099e7			−0.282915
$670$	−3.51727e6	−	8.67250e6i	−0.0116945	−	0.0288350i
$671$		−	2.44947e8i		−	0.810781i
$672$	−8.06504e7	−	2.17106e8i	−0.265766	−	0.715425i
$673$	2.62760e8			0.862014			0.431007	−	0.902349i	$-0.358158\pi$
$673$	2.62760e8			0.862014			0.431007	+	0.902349i	$0.358158\pi$
$674$	−8.75407e7	+	3.55035e7i	−0.285911	+	0.115956i
$675$		−	1.18375e7i		−	0.0384900i
$676$	2.88094e8	−	2.79686e8i	0.932598	−	0.905380i
$677$	−3.28940e7			−0.106011			−0.0530055	−	0.998594i	$-0.516880\pi$
$677$	−3.28940e7			−0.106011			−0.0530055	+	0.998594i	$0.516880\pi$
$678$	4.52515e7	+	1.11576e8i	0.145192	+	0.358000i
$679$			4.43104e8i			1.41546i
$680$	4.58198e7	−	1.04022e8i	0.145723	−	0.330826i
$681$	1.69484e8			0.536645
$682$	−1.50986e8	+	6.12346e7i	−0.475973	+	0.193038i
$683$		−	3.66820e8i		−	1.15131i	−0.817694	−	0.575653i	$-0.804748\pi$
$683$		−	3.66820e8i		−	1.15131i	0.817694	−	0.575653i	$-0.195252\pi$
$684$	6.88840e7	+	7.09548e7i	0.215253	+	0.221724i
$685$	−1.88419e7			−0.0586210
$686$	−4.05144e7	−	9.98960e7i	−0.125498	−	0.309440i
$687$		−	3.31142e8i		−	1.02128i
$688$	3.36039e8	+	9.95459e6i	1.03187	+	0.0305674i
$689$	−5.63611e8			−1.72314
$690$	−2.10796e7	+	8.54917e6i	−0.0641675	+	0.0260242i
$691$		−	1.76538e8i		−	0.535061i	−0.963549	−	0.267530i	$-0.913792\pi$
$691$		−	1.76538e8i		−	0.535061i	0.963549	−	0.267530i	$-0.0862076\pi$
$692$	−7.90231e7	+	7.67168e7i	−0.238471	+	0.231511i
$693$	−8.18415e7			−0.245909
$694$	2.71050e7	+	6.68326e7i	0.0810907	+	0.199945i
$695$		−	2.13673e8i		−	0.636496i
$696$	−3.03816e8	−	1.33825e8i	−0.901119	−	0.396926i
$697$	3.93191e8			1.16120
$698$	4.67566e8	−	1.89629e8i	1.37492	−	0.557620i
$699$		−	1.51467e6i		−	0.00443493i
$700$	−6.31651e7	−	6.50640e7i	−0.184155	−	0.189691i
$701$	5.80710e7			0.168580			0.0842899	−	0.996441i	$-0.473138\pi$
$701$	5.80710e7			0.168580			0.0842899	+	0.996441i	$0.473138\pi$
$702$	−3.79462e7	−	9.35636e7i	−0.109687	−	0.270455i
$703$			1.72028e8i			0.495146i
$704$	1.43669e8	−	1.31440e8i	0.411761	−	0.376712i
$705$	−6.94122e7			−0.198093
$706$	−3.14153e8	+	1.27410e8i	−0.892743	+	0.362066i
$707$		−	3.84624e8i		−	1.08837i
$708$	−1.09517e8	+	1.06320e8i	−0.308589	+	0.299583i
$709$	5.63742e8			1.58176			0.790882	−	0.611969i	$-0.209622\pi$
$709$	5.63742e8			1.58176			0.790882	+	0.611969i	$0.209622\pi$
$710$	9.92222e7	+	2.44651e8i	0.277226	+	0.683553i
$711$			1.83801e8i			0.511375i
$712$	2.25142e8	−	5.11127e8i	0.623759	−	1.41608i
$713$	−8.94633e7			−0.246818
$714$	2.08091e8	−	8.43946e7i	0.571687	−	0.231857i
$715$			1.38349e8i			0.378494i
$716$	2.55123e8	+	2.62793e8i	0.695042	+	0.715936i
$717$	8.19749e7			0.222394
$718$	1.48080e8	+	3.65120e8i	0.400059	+	0.986420i
$719$		−	1.38729e8i		−	0.373234i	−0.982433	−	0.186617i	$-0.940248\pi$
$719$		−	1.38729e8i		−	0.373234i	0.982433	−	0.186617i	$-0.0597523\pi$
$720$	−1.64754e6	+	5.56161e7i	−0.00441405	+	0.149006i
$721$	−2.76995e7			−0.0739036
$722$	4.90164e7	−	1.98794e7i	0.130236	−	0.0528192i
$723$			5.64551e7i			0.149379i
$724$	−4.47111e8	+	4.34062e8i	−1.17815	+	1.14376i
$725$	−1.29985e8			−0.341098
$726$	5.71708e7	+	1.40965e8i	0.149405	+	0.368386i
$727$		−	2.59587e7i		−	0.0675584i	−0.999429	−	0.0337792i	$-0.989246\pi$
$727$		−	2.59587e7i		−	0.0675584i	0.999429	−	0.0337792i	$-0.0107543\pi$
$728$	−7.07826e8	−	3.11784e8i	−1.83456	−	0.808091i
$729$	−1.43489e7			−0.0370370
$730$	−1.41342e8	+	5.73234e7i	−0.363331	+	0.147355i
$731$			3.25954e8i			0.834459i
$732$	−2.29158e8	−	2.36047e8i	−0.584253	−	0.601817i
$733$	4.87287e8			1.23729			0.618647	−	0.785669i	$-0.287681\pi$
$733$	4.87287e8			1.23729			0.618647	+	0.785669i	$0.287681\pi$
$734$	4.31920e7	+	1.06498e8i	0.109223	+	0.269311i
$735$		−	7.66240e7i		−	0.192976i
$736$	1.00228e8	−	3.72328e7i	0.251395	−	0.0933882i
$737$	1.55444e7			0.0388304
$738$	−1.78360e8	+	7.23366e7i	−0.443739	+	0.179965i
$739$			5.91158e8i			1.46477i	0.680889	+	0.732386i	$0.261593\pi$
$739$			5.91158e8i			1.46477i	−0.680889	+	0.732386i	$0.738407\pi$
$740$	−6.94468e7	+	6.74200e7i	−0.171379	+	0.166377i
$741$	3.30256e8			0.811702
$742$	2.30611e8	+	5.68614e8i	0.564505	+	1.39189i
$743$			1.65965e8i			0.404622i	0.979321	+	0.202311i	$0.0648452\pi$
$743$			1.65965e8i			0.404622i	−0.979321	+	0.202311i	$0.935155\pi$
$744$	−8.82121e7	+	2.00263e8i	−0.214195	+	0.486275i
$745$	1.99996e8			0.483673
$746$	−3.63124e8	+	1.47271e8i	−0.874658	+	0.354731i
$747$		−	1.32654e8i		−	0.318242i
$748$	1.31508e8	+	1.35462e8i	0.314231	+	0.323677i
$749$	−6.92643e8			−1.64841
$750$	8.18772e6	+	2.01884e7i	0.0194079	+	0.0478539i
$751$		−	3.73633e8i		−	0.882115i	−0.897479	−	0.441057i	$-0.854604\pi$
$751$		−	3.73633e8i		−	0.882115i	0.897479	−	0.441057i	$-0.145396\pi$
$752$	3.26120e8	+	9.66077e6i	0.766873	+	0.0227174i
$753$	−5.49848e6			−0.0128783
$754$	−1.02740e9	+	4.16680e8i	−2.39677	+	0.972049i
$755$		−	9.36479e7i		−	0.217599i
$756$	−7.88679e7	+	7.65661e7i	−0.182530	+	0.177203i
$757$	−3.73197e7			−0.0860300			−0.0430150	−	0.999074i	$-0.513696\pi$
$757$	−3.73197e7			−0.0860300			−0.0430150	+	0.999074i	$0.513696\pi$
$758$	1.35237e7	+	3.33453e7i	0.0310520	+	0.0765645i
$759$		−	3.77827e7i		−	0.0864106i
$760$	−1.66557e8	−	7.33652e7i	−0.379421	−	0.167128i
$761$	1.26182e8			0.286314			0.143157	−	0.989700i	$-0.454275\pi$
$761$	1.26182e8			0.286314			0.143157	+	0.989700i	$0.454275\pi$
$762$	−3.81979e8	+	1.54918e8i	−0.863325	+	0.350135i
$763$		−	3.93640e8i		−	0.886187i
$764$	−4.41603e8	−	4.54879e8i	−0.990267	−	1.02004i
$765$	−5.39472e7			−0.120499
$766$	1.52686e8	+	3.76476e8i	0.339713	+	0.837627i
$767$			5.09741e8i			1.12970i
$768$	1.54813e7	−	2.61072e8i	0.0341761	−	0.576338i
$769$	6.66118e8			1.46478			0.732390	−	0.680885i	$-0.238405\pi$
$769$	6.66118e8			1.46478			0.732390	+	0.680885i	$0.238405\pi$
$770$	1.39578e8	−	5.66079e7i	0.305734	−	0.123995i
$771$		−	3.83451e8i		−	0.836656i
$772$	−1.33791e8	+	1.29887e8i	−0.290787	+	0.282301i
$773$	−7.07793e8			−1.53238			−0.766192	−	0.642612i	$-0.777851\pi$
$773$	−7.07793e8			−1.53238			−0.766192	+	0.642612i	$0.777851\pi$
$774$	−5.99668e7	−	1.47859e8i	−0.129327	−	0.318879i
$775$			8.56809e7i			0.184068i
$776$	−2.01701e8	+	4.57910e8i	−0.431641	+	0.979929i
$777$	−1.91213e8			−0.407620
$778$	−6.28772e8	+	2.55008e8i	−1.33522	+	0.541522i
$779$		−	6.29565e8i		−	1.33177i
$780$	1.29432e8	+	1.33323e8i	0.272745	+	0.280944i
$781$	−4.38508e8			−0.920501
$782$	3.89613e7	+	9.60664e7i	0.0814729	+	0.200887i
$783$			1.57562e8i			0.328222i
$784$	−1.06645e7	+	3.60003e8i	−0.0221306	+	0.747064i
$785$	1.19952e8			0.247971
$786$	−1.60171e8	+	6.49598e7i	−0.329849	+	0.133776i
$787$			5.64730e8i			1.15855i	0.815131	+	0.579277i	$0.196665\pi$
$787$			5.64730e8i			1.15855i	−0.815131	+	0.579277i	$0.803335\pi$
$788$	1.84295e8	−	1.78916e8i	0.376647	−	0.365655i
$789$	−1.62664e8			−0.331178
$790$	−1.27131e8	−	3.13466e8i	−0.257852	−	0.635783i
$791$		−	4.37758e8i		−	0.884515i
$792$	−8.45762e7	−	3.72542e7i	−0.170244	−	0.0749894i
$793$	−1.09867e9			−2.20317
$794$	−1.93899e8	+	7.86388e7i	−0.387359	+	0.157100i
$795$		−	1.47412e8i		−	0.293381i
$796$	5.06959e8	+	5.22199e8i	1.00516	+	1.03537i
$797$	8.74741e8			1.72784			0.863922	−	0.503626i	$-0.168001\pi$
$797$	8.74741e8			1.72784			0.863922	+	0.503626i	$0.168001\pi$
$798$	−1.35130e8	−	3.33188e8i	−0.265915	−	0.655663i
$799$			3.16333e8i			0.620161i
$800$	−3.56586e7	−	9.59907e7i	−0.0696457	−	0.187482i
$801$	−2.65077e8			−0.515792
$802$	1.79570e8	−	7.28277e7i	0.348106	−	0.141180i
$803$		−	2.53338e8i		−	0.489276i
$804$	1.49796e7	−	1.45424e7i	0.0288226	−	0.0279814i
$805$	8.27038e7			0.158540
$806$	2.74658e8	+	6.77222e8i	0.524551	+	1.29338i
$807$		−	3.03787e8i		−	0.578028i
$808$	1.75081e8	−	3.97476e8i	0.331898	−	0.753489i
$809$	−8.27976e8			−1.56377			−0.781883	−	0.623425i	$-0.785741\pi$
$809$	−8.27976e8			−1.56377			−0.781883	+	0.623425i	$0.785741\pi$
$810$	2.44715e7	−	9.92481e6i	0.0460475	−	0.0186753i
$811$		−	6.63138e8i		−	1.24320i	−0.783334	−	0.621601i	$-0.786483\pi$
$811$		−	6.63138e8i		−	1.24320i	0.783334	−	0.621601i	$-0.213517\pi$
$812$	8.40757e8	+	8.66032e8i	1.57037	+	1.61758i
$813$	5.79860e8			1.07907
$814$	−6.04211e7	−	1.48980e8i	−0.112025	−	0.276219i
$815$			4.53669e8i			0.838044i
$816$	2.53460e8	+	7.50835e6i	0.466487	+	0.0138189i
$817$	5.21907e8			0.957034
$818$	4.29522e8	−	1.74199e8i	0.784739	−	0.318263i
$819$			3.67088e8i			0.668218i
$820$	2.54152e8	−	2.46734e8i	0.460948	−	0.447495i
$821$	−3.59395e8			−0.649445			−0.324722	−	0.945809i	$-0.605271\pi$
$821$	−3.59395e8			−0.649445			−0.324722	+	0.945809i	$0.605271\pi$
$822$	−1.57975e7	−	3.89517e7i	−0.0284428	−	0.0701311i
$823$			2.21973e8i			0.398200i	0.979979	+	0.199100i	$0.0638018\pi$
$823$			2.21973e8i			0.398200i	−0.979979	+	0.199100i	$0.936198\pi$
$824$	−2.86250e7	−	1.26088e7i	−0.0511639	−	0.0225368i
$825$	−3.61852e7			−0.0644421
$826$	5.14266e8	−	2.08569e8i	0.912531	−	0.370092i
$827$		−	1.09633e9i		−	1.93832i	−0.246441	−	0.969158i	$-0.579261\pi$
$827$		−	1.09633e9i		−	1.93832i	0.246441	−	0.969158i	$-0.420739\pi$
$828$	−3.53472e7	−	3.64098e7i	−0.0622679	−	0.0641398i
$829$	7.26773e8			1.27566			0.637830	−	0.770177i	$-0.279832\pi$
$829$	7.26773e8			1.27566			0.637830	+	0.770177i	$0.279832\pi$
$830$	9.17536e7	+	2.26236e8i	0.160468	+	0.395665i
$831$			2.15349e8i			0.375267i
$832$	−5.89553e8	−	6.44404e8i	−1.02365	−	1.11889i
$833$	−3.49200e8			−0.604142
$834$	4.41725e8	−	1.79149e8i	0.761471	−	0.308827i
$835$		−	5.70038e7i		−	0.0979139i
$836$	2.16897e8	−	2.10567e8i	0.371223	−	0.360389i
$837$	1.03859e8			0.177120
$838$	1.84910e8	+	4.55930e8i	0.314216	+	0.774759i
$839$			1.33306e8i			0.225716i	0.993611	+	0.112858i	$0.0360006\pi$
$839$			1.33306e8i			0.225716i	−0.993611	+	0.112858i	$0.963999\pi$
$840$	8.15471e7	−	1.85132e8i	0.137585	−	0.312351i
$841$	1.13534e9			1.90870
$842$	−4.44437e8	+	1.80248e8i	−0.744515	+	0.301950i
$843$			4.44278e7i			0.0741604i
$844$	−7.05926e8	−	7.27147e8i	−1.17417	−	1.20947i
$845$	3.50718e8			0.581283
$846$	−5.81968e7	−	1.43495e8i	−0.0961142	−	0.236988i
$847$		−	5.53064e8i		−	0.910176i
$848$	−2.05168e7	+	6.92588e8i	−0.0336451	+	1.13576i
$849$	5.16686e7			0.0844313
$850$	9.20048e7	−	3.73140e7i	0.149815	−	0.0607597i
$851$		−	8.82748e7i		−	0.143235i
$852$	−4.22575e8	+	4.10242e8i	−0.683258	+	0.663317i
$853$	−4.73811e8			−0.763410			−0.381705	−	0.924284i	$-0.624663\pi$
$853$	−4.73811e8			−0.763410			−0.381705	+	0.924284i	$0.624663\pi$
$854$	4.49539e8	+	1.10842e9i	0.721761	+	1.77964i
$855$			8.63784e7i			0.138200i
$856$	−7.15787e8	−	3.15291e8i	−1.14120	−	0.502678i
$857$	2.02044e8			0.320999			0.160500	−	0.987036i	$-0.448689\pi$
$857$	2.02044e8			0.320999			0.160500	+	0.987036i	$0.448689\pi$
$858$	−2.86008e8	+	1.15995e8i	−0.452811	+	0.183645i
$859$		−	1.05577e9i		−	1.66568i	−0.553517	−	0.832838i	$-0.686715\pi$
$859$		−	1.05577e9i		−	1.66568i	0.553517	−	0.832838i	$-0.313285\pi$
$860$	2.04542e8	+	2.10691e8i	0.321579	+	0.331246i
$861$	6.99776e8			1.09635
$862$	−2.91232e8	−	7.18089e8i	−0.454693	−	1.12113i
$863$			5.91663e8i			0.920539i	0.887779	+	0.460270i	$0.152247\pi$
$863$			5.91663e8i			0.920539i	−0.887779	+	0.460270i	$0.847753\pi$
$864$	−1.16356e8	+	4.32239e7i	−0.180405	+	0.0670166i
$865$	−9.62005e7			−0.148638
$866$	6.46948e8	−	2.62380e8i	0.996130	−	0.403996i
$867$		−	1.30413e8i		−	0.200108i
$868$	5.70853e8	−	5.54193e8i	0.872902	−	0.847426i
$869$	5.61850e8			0.856171
$870$	−1.08982e8	−	2.68717e8i	−0.165500	−	0.408072i
$871$		−	6.97220e7i		−	0.105515i
$872$	1.79185e8	−	4.06793e8i	0.270241	−	0.613513i
$873$	2.37478e8			0.356927
$874$	1.53818e8	−	6.23835e7i	0.230395	−	0.0934406i
$875$		−	7.92071e7i		−	0.118233i
$876$	−2.37008e8	−	2.44133e8i	−0.352575	−	0.363174i
$877$	−1.06320e9			−1.57622			−0.788108	−	0.615537i	$-0.788939\pi$
$877$	−1.06320e9			−1.57622			−0.788108	+	0.615537i	$0.788939\pi$
$878$	−3.51953e8	−	8.67807e8i	−0.519997	−	1.28215i
$879$			3.49044e8i			0.513941i
$880$	1.70009e8	+	5.03625e6i	0.249474	+	0.00739025i
$881$	−9.56086e8			−1.39820			−0.699100	−	0.715024i	$-0.746416\pi$
$881$	−9.56086e8			−1.39820			−0.699100	+	0.715024i	$0.746416\pi$
$882$	1.58404e8	−	6.42433e7i	0.230866	−	0.0936315i
$883$			6.13116e8i			0.890555i	0.895393	+	0.445278i	$0.146895\pi$
$883$			6.13116e8i			0.890555i	−0.895393	+	0.445278i	$0.853105\pi$
$884$	6.07593e8	−	5.89861e8i	0.879541	−	0.853872i
$885$	−1.33322e8			−0.192342
$886$	1.04487e8	+	2.57633e8i	0.150232	+	0.370424i
$887$			5.76370e8i			0.825906i	0.910752	+	0.412953i	$0.135503\pi$
$887$			5.76370e8i			0.825906i	−0.910752	+	0.412953i	$0.864497\pi$
$888$	−1.97602e8	−	8.70402e7i	−0.282198	−	0.124303i
$889$	1.49866e9			2.13303
$890$	4.52078e8	−	1.83348e8i	0.641274	−	0.260079i
$891$			4.38622e7i			0.0620094i
$892$	2.42253e8	+	2.49536e8i	0.341330	+	0.351591i
$893$	5.06503e8			0.711258
$894$	1.67681e8	+	4.13449e8i	0.234677	+	0.578641i
$895$			3.19917e8i			0.446239i
$896$	−4.08900e8	+	8.58456e8i	−0.568451	+	1.19342i
$897$	−1.69468e8			−0.234807
$898$	9.26858e8	−	3.75902e8i	1.27992	−	0.519094i
$899$		−	1.14045e9i		−	1.56963i
$900$	−3.48705e7	+	3.38528e7i	−0.0478333	+	0.0464373i
$901$	−6.71804e8			−0.918477
$902$	2.21121e8	+	5.45216e8i	0.301308	+	0.742931i
$903$			5.80112e8i			0.787860i
$904$	1.99267e8	−	4.52386e8i	0.269731	−	0.612355i
$905$	−5.44301e8			−0.734333
$906$	1.93597e8	−	7.85165e7i	0.260324	−	0.105579i
$907$			3.89232e7i			0.0521659i	0.999660	+	0.0260829i	$0.00830340\pi$
$907$			3.89232e7i			0.0521659i	−0.999660	+	0.0260829i	$0.991697\pi$
$908$	−4.84689e8	−	4.99260e8i	−0.647449	−	0.666913i
$909$	−2.06136e8			−0.274449
$910$	−2.53906e8	−	6.26054e8i	−0.336937	−	0.830783i
$911$		−	5.86019e8i		−	0.775098i	−0.921849	−	0.387549i	$-0.873322\pi$
$911$		−	5.86019e8i		−	0.775098i	0.921849	−	0.387549i	$-0.126678\pi$
$912$	1.20221e7	−	4.05832e8i	0.0158488	−	0.535010i
$913$	−4.05501e8			−0.532819
$914$	8.00482e8	−	3.24648e8i	1.04837	−	0.425182i
$915$		−	2.87357e8i		−	0.375109i
$916$	−9.75467e8	+	9.46998e8i	−1.26919	+	1.23215i
$917$	6.28415e8			0.814964
$918$	−4.52305e7	−	1.11524e8i	−0.0584660	−	0.144159i
$919$		−	4.90654e7i		−	0.0632163i	−0.999500	−	0.0316081i	$-0.989937\pi$
$919$		−	4.90654e7i		−	0.0632163i	0.999500	−	0.0316081i	$-0.0100629\pi$
$920$	8.54672e7	+	3.76467e7i	0.109758	+	0.0483463i
$921$	−1.24597e8			−0.159488
$922$	−5.06683e8	+	2.05493e8i	−0.646462	+	0.262183i
$923$			1.96686e9i			2.50131i
$924$	2.34050e8	+	2.41086e8i	0.296683	+	0.305602i
$925$	−8.45426e7			−0.106820
$926$	−5.61831e8	−	1.38530e9i	−0.707576	−	1.74466i
$927$			1.48453e7i			0.0186358i
$928$	4.74633e8	+	1.27768e9i	0.593901	+	1.59874i
$929$	−4.67176e8			−0.582685			−0.291342	−	0.956619i	$-0.594102\pi$
$929$	−4.67176e8			−0.582685			−0.291342	+	0.956619i	$0.594102\pi$
$930$	−1.77127e8	+	7.18368e7i	−0.220210	+	0.0893096i
$931$			5.59127e8i			0.692885i
$932$	−4.46186e6	+	4.33165e6i	−0.00551148	+	0.00535063i
$933$	6.92869e8			0.853112
$934$	−3.12910e8	−	7.71539e8i	−0.384042	−	0.946928i
$935$			1.64908e8i			0.201746i
$936$	−1.67098e8	+	3.79353e8i	−0.203772	+	0.462611i
$937$	−7.07347e8			−0.859832			−0.429916	−	0.902869i	$-0.641457\pi$
$937$	−7.07347e8			−0.859832			−0.429916	+	0.902869i	$0.641457\pi$
$938$	−7.03410e7	+	2.85279e7i	−0.0852315	+	0.0345670i
$939$		−	3.63251e8i		−	0.438742i
$940$	1.98505e8	+	2.04472e8i	0.238994	+	0.246179i
$941$	4.13400e8			0.496137			0.248069	−	0.968742i	$-0.420204\pi$
$941$	4.13400e8			0.496137			0.248069	+	0.968742i	$0.420204\pi$
$942$	1.00571e8	+	2.47976e8i	0.120315	+	0.296659i
$943$			3.23056e8i			0.385250i
$944$	6.26390e8	+	1.85558e7i	0.744610	+	0.0220579i
$945$	−9.60116e7			−0.113770
$946$	−4.51982e8	+	1.83309e8i	−0.533885	+	0.216526i
$947$			8.08737e8i			0.952264i	0.879374	+	0.476132i	$0.157962\pi$
$947$			8.08737e8i			0.952264i	−0.879374	+	0.476132i	$0.842038\pi$
$948$	5.41435e8	−	5.25633e8i	0.635508	−	0.616961i
$949$	−1.13631e9			−1.32953
$950$	−5.97460e7	−	1.47315e8i	−0.0696848	−	0.171821i
$951$			4.57772e7i			0.0532240i
$952$	−8.43704e8	−	3.71636e8i	−0.977866	−	0.430732i
$953$	−1.68658e8			−0.194862			−0.0974311	−	0.995242i	$-0.531063\pi$
$953$	−1.68658e8			−0.194862			−0.0974311	+	0.995242i	$0.531063\pi$
$954$	3.04744e8	−	1.23594e8i	0.350986	−	0.142348i
$955$		−	5.53757e8i		−	0.635783i
$956$	−2.34431e8	−	2.41479e8i	−0.268313	−	0.276379i
$957$	4.81643e8			0.549527
$958$	−4.14072e8	−	1.02097e9i	−0.470955	−	1.16123i
$959$			1.52823e8i			0.173274i
$960$	1.68544e8	−	1.54197e8i	0.190502	−	0.174286i
$961$	1.35763e8			0.152972
$962$	−6.68226e8	+	2.71010e8i	−0.750581	+	0.304410i
$963$			3.71216e8i			0.415669i
$964$	1.66303e8	−	1.61450e8i	0.185639	−	0.180222i
$965$	−1.62874e8			−0.181246
$966$	6.93407e7	+	1.70973e8i	0.0769231	+	0.189669i
$967$		−	9.64747e7i		−	0.106693i	−0.998576	−	0.0533463i	$-0.983011\pi$
$967$		−	9.64747e7i		−	0.106693i	0.998576	−	0.0533463i	$-0.0169887\pi$
$968$	2.51754e8	−	5.71544e8i	0.277556	−	0.630120i
$969$	3.93654e8			0.432656
$970$	−4.05009e8	+	1.64258e8i	−0.443761	+	0.179975i
$971$		−	6.98532e8i		−	0.763007i	−0.924367	−	0.381504i	$-0.875406\pi$
$971$		−	6.98532e8i		−	0.763007i	0.924367	−	0.381504i	$-0.124594\pi$
$972$	4.10349e7	+	4.22685e7i	0.0446843	+	0.0460276i
$973$	−1.73306e9			−1.88138
$974$	−6.81056e8	−	1.67927e9i	−0.737065	−	1.81737i
$975$			1.62303e8i			0.175111i
$976$	−3.99942e7	+	1.35009e9i	−0.0430177	+	1.45216i
$977$	−8.97904e8			−0.962822			−0.481411	−	0.876495i	$-0.659876\pi$
$977$	−8.97904e8			−0.962822			−0.481411	+	0.876495i	$0.659876\pi$
$978$	−9.37866e8	+	3.80367e8i	−1.00259	+	0.406617i
$979$			8.10296e8i			0.863566i
$980$	−2.25716e8	+	2.19129e8i	−0.239820	+	0.232821i
$981$	−2.10968e8			−0.223465
$982$	1.50925e8	+	3.72133e8i	0.159377	+	0.392974i
$983$			1.80056e9i			1.89560i	0.318866	+	0.947800i	$0.396698\pi$
$983$			1.80056e9i			1.89560i	−0.318866	+	0.947800i	$0.603302\pi$
$984$	7.23158e8	+	3.18538e8i	0.759011	+	0.334330i
$985$	2.24355e8			0.234762
$986$	−1.22463e9	+	4.96667e8i	−1.27754	+	0.518125i
$987$			5.62989e8i			0.585529i
$988$	−9.44465e8	−	9.72858e8i	−0.979299	−	1.00874i
$989$	−2.67812e8			−0.276848
$990$	−3.03385e7	−	7.48054e7i	−0.0312672	−	0.0770952i
$991$			5.16757e8i			0.530964i	0.964116	+	0.265482i	$0.0855311\pi$
$991$			5.16757e8i			0.530964i	−0.964116	+	0.265482i	$0.914469\pi$
$992$	8.42196e8	−	3.12859e8i	0.862737	−	0.320489i
$993$	−5.64792e8			−0.576821
$994$	1.98432e9	−	8.04772e8i	2.02047	−	0.819434i
$995$			6.35710e8i			0.645342i
$996$	−3.90767e8	+	3.79363e8i	−0.395494	+	0.383952i
$997$	6.95298e8			0.701594			0.350797	−	0.936452i	$-0.385911\pi$
$997$	6.95298e8			0.701594			0.350797	+	0.936452i	$0.385911\pi$
$998$	1.22788e8	+	3.02756e8i	0.123527	+	0.304580i
$999$			1.02479e8i			0.102787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.21	✓	24
3.2	odd	2		180.7.c.b.91.4		24
4.3	odd	2	inner	60.7.c.a.31.22	yes	24
12.11	even	2		180.7.c.b.91.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.21	✓	24	1.1	even	1	trivial
60.7.c.a.31.22	yes	24	4.3	odd	2	inner
180.7.c.b.91.3		24	12.11	even	2
180.7.c.b.91.4		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(7.41350 - 3.00666i) q^{2} +15.5885i q^{3} +(45.9200 - 44.5798i) q^{4} +55.9017 q^{5} +(46.8692 + 115.565i) q^{6} -453.408i q^{7} +(206.391 - 468.558i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(7.41350 - 3.00666i) q^{2} +15.5885i q^{3} +(45.9200 - 44.5798i) q^{4} +55.9017 q^{5} +(46.8692 + 115.565i) q^{6} -453.408i q^{7} +(206.391 - 468.558i) q^{8} -243.000 q^{9} +(414.427 - 168.078i) q^{10} +742.811i q^{11} +(694.930 + 715.821i) q^{12} +3331.76 q^{13} +(-1363.25 - 3361.34i) q^{14} +871.421i q^{15} +(121.284 - 4094.20i) q^{16} +3971.34 q^{17} +(-1801.48 + 730.619i) q^{18} -6358.78i q^{19} +(2567.00 - 2492.09i) q^{20} +7067.93 q^{21} +(2233.38 + 5506.83i) q^{22} +3262.96i q^{23} +(7304.10 + 3217.32i) q^{24} +3125.00 q^{25} +(24700.0 - 10017.5i) q^{26} -3788.00i q^{27} +(-20212.8 - 20820.5i) q^{28} -41595.2 q^{29} +(2620.07 + 6460.28i) q^{30} +27417.9i q^{31} +(-11410.8 - 30717.0i) q^{32} -11579.3 q^{33} +(29441.5 - 11940.5i) q^{34} -25346.3i q^{35} +(-11158.5 + 10832.9i) q^{36} -27053.6 q^{37} +(-19118.7 - 47140.8i) q^{38} +51937.0i q^{39} +(11537.6 - 26193.2i) q^{40} +99007.2 q^{41} +(52398.1 - 21250.9i) q^{42} +82076.6i q^{43} +(33114.4 + 34109.8i) q^{44} -13584.1 q^{45} +(9810.61 + 24189.9i) q^{46} +79654.0i q^{47} +(63822.3 + 1890.63i) q^{48} -87929.9 q^{49} +(23167.2 - 9395.82i) q^{50} +61907.1i q^{51} +(152994. - 148529. i) q^{52} -169163. q^{53} +(-11389.2 - 28082.3i) q^{54} +41524.4i q^{55} +(-212448. - 93579.4i) q^{56} +99123.6 q^{57} +(-308366. + 125063. i) q^{58} +152994. i q^{59} +(38847.8 + 40015.6i) q^{60} -329756. q^{61} +(82436.3 + 203262. i) q^{62} +110178. i q^{63} +(-176949. - 193412. i) q^{64} +186251. q^{65} +(-85843.0 + 34815.0i) q^{66} -20926.5i q^{67} +(182364. - 177042. i) q^{68} -50864.4 q^{69} +(-76207.7 - 187905. i) q^{70} +590336. i q^{71} +(-50153.0 + 113860. i) q^{72} -341053. q^{73} +(-200562. + 81341.2i) q^{74} +48713.9i q^{75} +(-283473. - 291995. i) q^{76} +336796. q^{77} +(156157. + 385035. i) q^{78} -756383. i q^{79} +(6779.99 - 228873. i) q^{80} +59049.0 q^{81} +(733990. - 297681. i) q^{82} +545901. i q^{83} +(324559. - 315087. i) q^{84} +222005. q^{85} +(246777. + 608475. i) q^{86} -648405. i q^{87} +(348050. + 153310. i) q^{88} +1.09085e6 q^{89} +(-100706. + 40842.9i) q^{90} -1.51065e6i q^{91} +(145462. + 149835. i) q^{92} -427402. q^{93} +(239493. + 590515. i) q^{94} -355467. i q^{95} +(478831. - 177876. i) q^{96} -977274. q^{97} +(-651868. + 264376. i) q^{98} -180503. 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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