LMFDB - Embedded newform 8.7.d.b.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,7,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$1.84043266896$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.3803625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 6x^{2} - 16x + 256 $ x^4 - x^3 + 6x^2 - 16x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$2.81174 + 2.84502i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.7.d.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.62348 + 5.69004i) q^{2} +8.49390 q^{3} +(-0.753049 + 63.9956i) q^{4} -59.7107i q^{5} +(47.7652 + 48.3306i) q^{6} -483.584i q^{7} +(-368.372 + 355.593i) q^{8} -656.854 q^{9} +O(q^{10})$	\(q+(5.62348 + 5.69004i) q^{2} +8.49390 q^{3} +(-0.753049 + 63.9956i) q^{4} -59.7107i q^{5} +(47.7652 + 48.3306i) q^{6} -483.584i q^{7} +(-368.372 + 355.593i) q^{8} -656.854 q^{9} +(339.756 - 335.782i) q^{10} +1412.15 q^{11} +(-6.39633 + 543.572i) q^{12} +3450.70i q^{13} +(2751.61 - 2719.42i) q^{14} -507.177i q^{15} +(-4094.87 - 96.3836i) q^{16} -3056.78 q^{17} +(-3693.80 - 3737.52i) q^{18} +968.104 q^{19} +(3821.22 + 44.9651i) q^{20} -4107.51i q^{21} +(7941.20 + 8035.20i) q^{22} -3314.31i q^{23} +(-3128.91 + 3020.37i) q^{24} +12059.6 q^{25} +(-19634.6 + 19404.9i) q^{26} -11771.3 q^{27} +(30947.2 + 364.162i) q^{28} -26351.6i q^{29} +(2885.85 - 2852.10i) q^{30} +27104.3i q^{31} +(-22479.0 - 23842.0i) q^{32} +11994.7 q^{33} +(-17189.7 - 17393.2i) q^{34} -28875.1 q^{35} +(494.643 - 42035.7i) q^{36} +36097.0i q^{37} +(5444.11 + 5508.55i) q^{38} +29309.9i q^{39} +(21232.7 + 21995.7i) q^{40} -6860.73 q^{41} +(23371.9 - 23098.5i) q^{42} +92831.6 q^{43} +(-1063.42 + 90371.5i) q^{44} +39221.2i q^{45} +(18858.5 - 18637.9i) q^{46} -159323. i q^{47} +(-34781.4 - 818.673i) q^{48} -116204. q^{49} +(67817.1 + 68619.8i) q^{50} -25964.0 q^{51} +(-220829. - 2598.54i) q^{52} -86612.3i q^{53} +(-66195.6 - 66979.2i) q^{54} -84320.6i q^{55} +(171959. + 178139. i) q^{56} +8222.98 q^{57} +(149942. - 148188. i) q^{58} +128806. q^{59} +(32457.1 + 381.929i) q^{60} +189486. i q^{61} +(-154224. + 152420. i) q^{62} +317644. i q^{63} +(9251.76 - 261981. i) q^{64} +206043. q^{65} +(67451.8 + 68250.2i) q^{66} -319835. q^{67} +(2301.91 - 195620. i) q^{68} -28151.4i q^{69} +(-162379. - 164301. i) q^{70} +196890. i q^{71} +(241966. - 233572. i) q^{72} -63957.9 q^{73} +(-205393. + 202991. i) q^{74} +102433. q^{75} +(-729.030 + 61954.3i) q^{76} -682894. i q^{77} +(-166774. + 164823. i) q^{78} -164678. i q^{79} +(-5755.13 + 244507. i) q^{80} +378862. q^{81} +(-38581.2 - 39037.8i) q^{82} -802946. q^{83} +(262863. + 3093.16i) q^{84} +182522. i q^{85} +(522036. + 528215. i) q^{86} -223828. i q^{87} +(-520197. + 502151. i) q^{88} -54145.3 q^{89} +(-223170. + 220559. i) q^{90} +1.66870e6 q^{91} +(212101. + 2495.84i) q^{92} +230221. i q^{93} +(906555. - 895950. i) q^{94} -57806.1i q^{95} +(-190934. - 202511. i) q^{96} -1.10670e6 q^{97} +(-653472. - 661207. i) q^{98} -927577. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 48 q^{3} - 44 q^{4} + 396 q^{6} + 248 q^{8} - 660 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 48 * q^3 - 44 * q^4 + 396 * q^6 + 248 * q^8 - 660 * q^9	\( 4 q + 2 q^{2} - 48 q^{3} - 44 q^{4} + 396 q^{6} + 248 q^{8} - 660 q^{9} - 1920 q^{10} + 976 q^{11} + 1368 q^{12} + 5760 q^{14} - 14576 q^{16} + 4168 q^{17} - 10410 q^{18} - 1456 q^{19} + 31680 q^{20} + 24428 q^{22} - 38256 q^{24} - 23900 q^{25} - 59520 q^{26} + 2592 q^{27} + 59520 q^{28} + 90240 q^{30} - 48928 q^{32} + 84048 q^{33} - 81916 q^{34} - 49920 q^{35} - 12900 q^{36} + 26572 q^{38} - 13440 q^{40} - 117944 q^{41} + 38400 q^{42} + 197456 q^{43} + 37144 q^{44} - 213120 q^{46} + 137952 q^{48} + 2116 q^{49} + 357650 q^{50} - 386016 q^{51} - 254400 q^{52} - 253224 q^{54} + 349440 q^{56} + 126672 q^{57} + 516480 q^{58} + 542032 q^{59} - 716160 q^{60} - 407040 q^{62} + 463936 q^{64} - 205440 q^{65} - 142776 q^{66} - 790192 q^{67} - 213848 q^{68} - 360960 q^{70} + 805800 q^{72} + 443912 q^{73} - 32640 q^{74} + 1765200 q^{75} + 70616 q^{76} + 324480 q^{78} - 1032960 q^{80} - 568044 q^{81} + 404708 q^{82} - 3465008 q^{83} + 602880 q^{84} + 989548 q^{86} - 1950448 q^{88} + 761224 q^{89} - 1296000 q^{90} + 3398400 q^{91} + 2743680 q^{92} + 971520 q^{94} - 252864 q^{96} - 926776 q^{97} - 2391262 q^{98} - 2459280 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 48 * q^3 - 44 * q^4 + 396 * q^6 + 248 * q^8 - 660 * q^9 - 1920 * q^10 + 976 * q^11 + 1368 * q^12 + 5760 * q^14 - 14576 * q^16 + 4168 * q^17 - 10410 * q^18 - 1456 * q^19 + 31680 * q^20 + 24428 * q^22 - 38256 * q^24 - 23900 * q^25 - 59520 * q^26 + 2592 * q^27 + 59520 * q^28 + 90240 * q^30 - 48928 * q^32 + 84048 * q^33 - 81916 * q^34 - 49920 * q^35 - 12900 * q^36 + 26572 * q^38 - 13440 * q^40 - 117944 * q^41 + 38400 * q^42 + 197456 * q^43 + 37144 * q^44 - 213120 * q^46 + 137952 * q^48 + 2116 * q^49 + 357650 * q^50 - 386016 * q^51 - 254400 * q^52 - 253224 * q^54 + 349440 * q^56 + 126672 * q^57 + 516480 * q^58 + 542032 * q^59 - 716160 * q^60 - 407040 * q^62 + 463936 * q^64 - 205440 * q^65 - 142776 * q^66 - 790192 * q^67 - 213848 * q^68 - 360960 * q^70 + 805800 * q^72 + 443912 * q^73 - 32640 * q^74 + 1765200 * q^75 + 70616 * q^76 + 324480 * q^78 - 1032960 * q^80 - 568044 * q^81 + 404708 * q^82 - 3465008 * q^83 + 602880 * q^84 + 989548 * q^86 - 1950448 * q^88 + 761224 * q^89 - 1296000 * q^90 + 3398400 * q^91 + 2743680 * q^92 + 971520 * q^94 - 252864 * q^96 - 926776 * q^97 - 2391262 * q^98 - 2459280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	5.62348	+	5.69004i	0.702934	+	0.711255i
$2$	5.62348	+	5.69004i	0.702934	+	0.711255i
$3$	8.49390			0.314589			0.157294	−	0.987552i	$-0.449723\pi$
$3$	8.49390			0.314589			0.157294	+	0.987552i	$0.449723\pi$
$4$	−0.753049	+	63.9956i	−0.0117664	+	0.999931i
$5$		−	59.7107i		−	0.477686i	−0.971058	−	0.238843i	$-0.923232\pi$
$5$		−	59.7107i		−	0.477686i	0.971058	−	0.238843i	$-0.0767681\pi$
$6$	47.7652	+	48.3306i	0.221135	+	0.223753i
$7$		−	483.584i		−	1.40987i	−0.709274	−	0.704933i	$-0.750977\pi$
$7$		−	483.584i		−	1.40987i	0.709274	−	0.704933i	$-0.249023\pi$
$8$	−368.372	+	355.593i	−0.719476	+	0.694517i
$9$	−656.854			−0.901034
$10$	339.756	−	335.782i	0.339756	−	0.335782i
$11$	1412.15			1.06097			0.530485	−	0.847694i	$-0.322010\pi$
$11$	1412.15			1.06097			0.530485	+	0.847694i	$0.322010\pi$
$12$	−6.39633	+	543.572i	−0.00370158	+	0.314567i
$13$			3450.70i			1.57064i	0.619090	+	0.785320i	$0.287501\pi$
$13$			3450.70i			1.57064i	−0.619090	+	0.785320i	$0.712499\pi$
$14$	2751.61	−	2719.42i	1.00277	−	0.991043i
$15$		−	507.177i		−	0.150275i
$16$	−4094.87	−	96.3836i	−0.999723	−	0.0235312i
$17$	−3056.78			−0.622182			−0.311091	−	0.950380i	$-0.600694\pi$
$17$	−3056.78			−0.622182			−0.311091	+	0.950380i	$0.600694\pi$
$18$	−3693.80	−	3737.52i	−0.633368	−	0.640864i
$19$	968.104			0.141144			0.0705718	−	0.997507i	$-0.477518\pi$
$19$	968.104			0.141144			0.0705718	+	0.997507i	$0.477518\pi$
$20$	3821.22	+	44.9651i	0.477652	+	0.00562064i
$21$		−	4107.51i		−	0.443528i
$22$	7941.20	+	8035.20i	0.745793	+	0.754621i
$23$		−	3314.31i		−	0.272401i	−0.990681	−	0.136201i	$-0.956511\pi$
$23$		−	3314.31i		−	0.272401i	0.990681	−	0.136201i	$-0.0434892\pi$
$24$	−3128.91	+	3020.37i	−0.226339	+	0.218487i
$25$	12059.6			0.771817
$26$	−19634.6	+	19404.9i	−1.11712	+	1.10406i
$27$	−11771.3			−0.598044
$28$	30947.2	+	364.162i	1.40977	+	0.0165890i
$29$		−	26351.6i		−	1.08047i	−0.841513	−	0.540236i	$-0.818335\pi$
$29$		−	26351.6i		−	1.08047i	0.841513	−	0.540236i	$-0.181665\pi$
$30$	2885.85	−	2852.10i	0.106884	−	0.105633i
$31$			27104.3i			0.909815i	0.890539	+	0.454907i	$0.150328\pi$
$31$			27104.3i			0.909815i	−0.890539	+	0.454907i	$0.849672\pi$
$32$	−22479.0	−	23842.0i	−0.686003	−	0.727599i
$33$	11994.7			0.333770
$34$	−17189.7	−	17393.2i	−0.437353	−	0.442530i
$35$	−28875.1			−0.673472
$36$	494.643	−	42035.7i	0.0106019	−	0.900971i
$37$			36097.0i			0.712633i	0.934365	+	0.356317i	$0.115968\pi$
$37$			36097.0i			0.712633i	−0.934365	+	0.356317i	$0.884032\pi$
$38$	5444.11	+	5508.55i	0.0992147	+	0.100389i
$39$			29309.9i			0.494106i
$40$	21232.7	+	21995.7i	0.331761	+	0.343683i
$41$	−6860.73			−0.0995449			−0.0497724	−	0.998761i	$-0.515850\pi$
$41$	−6860.73			−0.0995449			−0.0497724	+	0.998761i	$0.515850\pi$
$42$	23371.9	−	23098.5i	0.315461	−	0.311771i
$43$	92831.6			1.16759			0.583795	−	0.811901i	$-0.301567\pi$
$43$	92831.6			1.16759			0.583795	+	0.811901i	$0.301567\pi$
$44$	−1063.42	+	90371.5i	−0.0124838	+	1.06090i
$45$			39221.2i			0.430411i
$46$	18858.5	−	18637.9i	0.193747	−	0.191480i
$47$		−	159323.i		−	1.53456i	−0.641309	−	0.767282i	$-0.721608\pi$
$47$		−	159323.i		−	1.53456i	0.641309	−	0.767282i	$-0.278392\pi$
$48$	−34781.4	−	818.673i	−0.314502	−	0.00740264i
$49$	−116204.			−0.987720
$50$	67817.1	+	68619.8i	0.542536	+	0.548958i
$51$	−25964.0			−0.195732
$52$	−220829.	−	2598.54i	−1.57053	−	0.0184808i
$53$		−	86612.3i		−	0.581771i	−0.956758	−	0.290885i	$-0.906050\pi$
$53$		−	86612.3i		−	0.581771i	0.956758	−	0.290885i	$-0.0939498\pi$
$54$	−66195.6	−	66979.2i	−0.420386	−	0.425362i
$55$		−	84320.6i		−	0.506810i
$56$	171959.	+	178139.i	0.979175	+	1.01436i
$57$	8222.98			0.0444022
$58$	149942.	−	148188.i	0.768491	−	0.759501i
$59$	128806.			0.627165			0.313582	−	0.949561i	$-0.398471\pi$
$59$	128806.			0.627165			0.313582	+	0.949561i	$0.398471\pi$
$60$	32457.1	+	381.929i	0.150264	+	0.00176819i
$61$			189486.i			0.834810i	0.908721	+	0.417405i	$0.137060\pi$
$61$			189486.i			0.834810i	−0.908721	+	0.417405i	$0.862940\pi$
$62$	−154224.	+	152420.i	−0.647110	+	0.639540i
$63$			317644.i			1.27034i
$64$	9251.76	−	261981.i	0.0352927	−	0.999377i
$65$	206043.			0.750272
$66$	67451.8	+	68250.2i	0.234618	+	0.237395i
$67$	−319835.			−1.06341			−0.531706	−	0.846929i	$-0.678449\pi$
$67$	−319835.			−1.06341			−0.531706	+	0.846929i	$0.678449\pi$
$68$	2301.91	−	195620.i	0.00732084	−	0.622139i
$69$		−	28151.4i		−	0.0856945i
$70$	−162379.	−	164301.i	−0.473407	−	0.479010i
$71$			196890.i			0.550108i	0.961429	+	0.275054i	$0.0886957\pi$
$71$			196890.i			0.550108i	−0.961429	+	0.275054i	$0.911304\pi$
$72$	241966.	−	233572.i	0.648273	−	0.625783i
$73$	−63957.9			−0.164409			−0.0822046	−	0.996615i	$-0.526196\pi$
$73$	−63957.9			−0.164409			−0.0822046	+	0.996615i	$0.526196\pi$
$74$	−205393.	+	202991.i	−0.506864	+	0.500934i
$75$	102433.			0.242805
$76$	−729.030	+	61954.3i	−0.00166075	+	0.141134i
$77$		−	682894.i		−	1.49583i
$78$	−166774.	+	164823.i	−0.351435	+	0.347324i
$79$		−	164678.i		−	0.334006i	−0.985956	−	0.167003i	$-0.946591\pi$
$79$		−	164678.i		−	0.334006i	0.985956	−	0.167003i	$-0.0534090\pi$
$80$	−5755.13	+	244507.i	−0.0112405	+	0.477553i
$81$	378862.			0.712896
$82$	−38581.2	−	39037.8i	−0.0699735	−	0.0708018i
$83$	−802946.			−1.40428			−0.702138	−	0.712041i	$-0.747771\pi$
$83$	−802946.			−1.40428			−0.702138	+	0.712041i	$0.747771\pi$
$84$	262863.	+	3093.16i	0.443497	+	0.00521873i
$85$			182522.i			0.297207i
$86$	522036.	+	528215.i	0.820739	+	0.830454i
$87$		−	223828.i		−	0.339905i
$88$	−520197.	+	502151.i	−0.763344	+	0.736862i
$89$	−54145.3			−0.0768052			−0.0384026	−	0.999262i	$-0.512227\pi$
$89$	−54145.3			−0.0768052			−0.0384026	+	0.999262i	$0.512227\pi$
$90$	−223170.	+	220559.i	−0.306132	+	0.302551i
$91$	1.66870e6			2.21439
$92$	212101.	+	2495.84i	0.272383	+	0.00320518i
$93$			230221.i			0.286218i
$94$	906555.	−	895950.i	1.09147	−	1.07870i
$95$		−	57806.1i		−	0.0674222i
$96$	−190934.	−	202511.i	−0.215809	−	0.228894i
$97$	−1.10670e6			−1.21259			−0.606297	−	0.795238i	$-0.707346\pi$
$97$	−1.10670e6			−1.21259			−0.606297	+	0.795238i	$0.707346\pi$
$98$	−653472.	−	661207.i	−0.694302	−	0.702520i
$99$	−927577.			−0.955971
$100$	−9081.50	+	771763.i	−0.00908150	+	0.771763i
$101$			809583.i			0.785773i	0.919587	+	0.392887i	$0.128524\pi$
$101$			809583.i			0.785773i	−0.919587	+	0.392887i	$0.871476\pi$
$102$	−146008.	−	147736.i	−0.137586	−	0.139215i
$103$		−	619448.i		−	0.566883i	−0.958990	−	0.283442i	$-0.908524\pi$
$103$		−	619448.i		−	0.566883i	0.958990	−	0.283442i	$-0.0914762\pi$
$104$	−1.22704e6	−	1.27114e6i	−1.09084	−	1.13004i
$105$	−245262.			−0.211867
$106$	492827.	−	487062.i	0.413787	−	0.408947i
$107$	1.08619e6			0.886657			0.443328	−	0.896359i	$-0.353798\pi$
$107$	1.08619e6			0.886657			0.443328	+	0.896359i	$0.353798\pi$
$108$	8864.37	−	753311.i	0.00703682	−	0.598003i
$109$			1.71692e6i			1.32578i	0.748717	+	0.662890i	$0.230670\pi$
$109$			1.71692e6i			1.32578i	−0.748717	+	0.662890i	$0.769330\pi$
$110$	479787.	−	474175.i	0.360471	−	0.356255i
$111$			306604.i			0.224187i
$112$	−46609.6	+	1.98021e6i	−0.0331758	+	1.40947i
$113$	645423.			0.447311			0.223655	−	0.974668i	$-0.428201\pi$
$113$	645423.			0.447311			0.223655	+	0.974668i	$0.428201\pi$
$114$	46241.7	+	46789.0i	0.0312118	+	0.0315813i
$115$	−197900.			−0.130122
$116$	1.68639e6	+	19844.1i	1.08040	+	0.0127133i
$117$		−	2.26660e6i		−	1.41520i
$118$	724340.	+	732914.i	0.440856	+	0.446074i
$119$			1.47821e6i			0.877193i
$120$	180348.	+	186830.i	0.104368	+	0.108119i
$121$	222613.			0.125659
$122$	−1.07818e6	+	1.06557e6i	−0.593762	+	0.586816i
$123$	−58274.4			−0.0313157
$124$	−1.73455e6	−	20410.9i	−0.909752	−	0.0107052i
$125$		−	1.65307e6i		−	0.846371i
$126$	−1.80740e6	+	1.78626e6i	−0.903533	+	0.892963i
$127$		−	2.51504e6i		−	1.22781i	−0.789378	−	0.613907i	$-0.789597\pi$
$127$		−	2.51504e6i		−	1.22781i	0.789378	−	0.613907i	$-0.210403\pi$
$128$	1.54271e6	−	1.42060e6i	0.735620	−	0.677394i
$129$	788502.			0.367311
$130$	1.15868e6	+	1.17239e6i	0.527392	+	0.533634i
$131$	−3.77470e6			−1.67907			−0.839536	−	0.543305i	$-0.817173\pi$
$131$	−3.77470e6			−1.67907			−0.839536	+	0.543305i	$0.817173\pi$
$132$	−9032.59	+	767607.i	−0.00392727	+	0.333747i
$133$		−	468159.i		−	0.198993i
$134$	−1.79858e6	−	1.81987e6i	−0.747509	−	0.756357i
$135$			702873.i			0.285677i
$136$	1.12603e6	−	1.08697e6i	0.447645	−	0.432116i
$137$	1.40637e6			0.546939			0.273470	−	0.961881i	$-0.411829\pi$
$137$	1.40637e6			0.546939			0.273470	+	0.961881i	$0.411829\pi$
$138$	160183.	−	158309.i	0.0609506	−	0.0602376i
$139$	2.31561e6			0.862227			0.431114	−	0.902298i	$-0.358121\pi$
$139$	2.31561e6			0.862227			0.431114	+	0.902298i	$0.358121\pi$
$140$	21744.4	−	1.84788e6i	0.00792434	−	0.673426i
$141$		−	1.35327e6i		−	0.482757i
$142$	−1.12031e6	+	1.10720e6i	−0.391267	+	0.386690i
$143$			4.87291e6i			1.66640i
$144$	2.68973e6	+	63309.9i	0.900784	+	0.0212024i
$145$	−1.57347e6			−0.516126
$146$	−359666.	−	363923.i	−0.115569	−	0.116937i
$147$	−987028.			−0.310726
$148$	−2.31005e6	−	27182.8i	−0.712584	−	0.00838512i
$149$			4.74866e6i			1.43553i	0.696285	+	0.717765i	$0.254835\pi$
$149$			4.74866e6i			1.43553i	−0.696285	+	0.717765i	$0.745165\pi$
$150$	576031.	+	582850.i	0.170676	+	0.172696i
$151$		−	1.11787e6i		−	0.324684i	−0.986735	−	0.162342i	$-0.948095\pi$
$151$		−	1.11787e6i		−	0.324684i	0.986735	−	0.162342i	$-0.0519047\pi$
$152$	−356622.	+	344251.i	−0.101549	+	0.0980266i
$153$	2.00786e6			0.560607
$154$	3.88569e6	−	3.84024e6i	1.06391	−	1.05147i
$155$	1.61842e6			0.434605
$156$	−1.87570e6	−	22071.8i	−0.494072	−	0.00581384i
$157$			1.00407e6i			0.259458i	0.991550	+	0.129729i	$0.0414107\pi$
$157$			1.00407e6i			0.259458i	−0.991550	+	0.129729i	$0.958589\pi$
$158$	937025.	−	926064.i	0.237564	−	0.234785i
$159$		−	735676.i		−	0.183019i
$160$	−1.42362e6	+	1.34223e6i	−0.347563	+	0.327694i
$161$	−1.60275e6			−0.384049
$162$	2.13052e6	+	2.15574e6i	0.501119	+	0.507050i
$163$	1.47315e6			0.340161			0.170080	−	0.985430i	$-0.445597\pi$
$163$	1.47315e6			0.340161			0.170080	+	0.985430i	$0.445597\pi$
$164$	5166.47	−	439056.i	0.00117128	−	0.0995380i
$165$		−	716211.i		−	0.159437i
$166$	−4.51535e6	−	4.56879e6i	−0.987113	−	0.998797i
$167$		−	5.16350e6i		−	1.10865i	−0.832300	−	0.554326i	$-0.812976\pi$
$167$		−	5.16350e6i		−	1.10865i	0.832300	−	0.554326i	$-0.187024\pi$
$168$	1.46060e6	+	1.51309e6i	0.308038	+	0.319108i
$169$	−7.08049e6			−1.46691
$170$	−1.03856e6	+	1.02641e6i	−0.211390	+	0.208917i
$171$	−635902.			−0.127175
$172$	−69906.7	+	5.94081e6i	−0.0137383	+	1.16751i
$173$		−	600245.i		−	0.115928i	−0.998319	−	0.0579642i	$-0.981539\pi$
$173$		−	600245.i		−	0.115928i	0.998319	−	0.0579642i	$-0.0184609\pi$
$174$	1.27359e6	−	1.25869e6i	0.241759	−	0.238931i
$175$		−	5.83184e6i		−	1.08816i
$176$	−5.78257e6	−	136108.i	−1.06068	−	0.0249659i
$177$	1.09407e6			0.197299
$178$	−304485.	−	308089.i	−0.0539890	−	0.0546280i
$179$	6.34654e6			1.10657			0.553284	−	0.832993i	$-0.313375\pi$
$179$	6.34654e6			1.10657			0.553284	+	0.832993i	$0.313375\pi$
$180$	−2.50998e6	−	29535.5i	−0.430381	−	0.00506438i
$181$		−	1.35031e6i		−	0.227719i	−0.993497	−	0.113859i	$-0.963679\pi$
$181$		−	1.35031e6i		−	0.227719i	0.993497	−	0.113859i	$-0.0363213\pi$
$182$	9.38389e6	+	9.49497e6i	1.55657	+	1.57500i
$183$			1.60947e6i			0.262622i
$184$	1.17854e6	+	1.22090e6i	0.189187	+	0.195986i
$185$	2.15538e6			0.340415
$186$	−1.30997e6	+	1.29464e6i	−0.203574	+	0.201192i
$187$	−4.31664e6			−0.660117
$188$	1.01960e7	+	119978.i	1.53446	+	0.0180563i
$189$			5.69241e6i			0.843162i
$190$	328919.	−	325071.i	0.0479544	−	0.0473934i
$191$			3.32043e6i			0.476534i	0.971200	+	0.238267i	$0.0765794\pi$
$191$			3.32043e6i			0.476534i	−0.971200	+	0.238267i	$0.923421\pi$
$192$	78583.5	−	2.22524e6i	0.0111027	−	0.314393i
$193$	5.59202e6			0.777852			0.388926	−	0.921269i	$-0.372846\pi$
$193$	5.59202e6			0.777852			0.388926	+	0.921269i	$0.372846\pi$
$194$	−6.22351e6	−	6.29717e6i	−0.852374	−	0.862463i
$195$	1.75011e6			0.236027
$196$	87507.5	−	7.43656e6i	0.0116219	−	0.987652i
$197$		−	7.19799e6i		−	0.941483i	−0.882271	−	0.470742i	$-0.843986\pi$
$197$		−	7.19799e6i		−	0.941483i	0.882271	−	0.470742i	$-0.156014\pi$
$198$	−5.21621e6	−	5.27795e6i	−0.671985	−	0.679939i
$199$			1.15838e7i			1.46991i	0.678116	+	0.734955i	$0.262797\pi$
$199$			1.15838e7i			1.46991i	−0.678116	+	0.734955i	$0.737203\pi$
$200$	−4.44243e6	+	4.28832e6i	−0.555304	+	0.536040i
$201$	−2.71665e6			−0.334538
$202$	−4.60656e6	+	4.55267e6i	−0.558885	+	0.552347i
$203$	−1.27432e7			−1.52332
$204$	19552.2	−	1.66158e6i	0.00230306	−	0.195718i
$205$			409659.i			0.0475511i
$206$	3.52468e6	−	3.48345e6i	0.403198	−	0.398482i
$207$			2.17701e6i			0.245443i
$208$	332591.	−	1.41301e7i	0.0369590	−	1.57020i
$209$	1.36711e6			0.149749
$210$	−1.37923e6	−	1.39555e6i	−0.148929	−	0.150691i
$211$	−639344.			−0.0680592			−0.0340296	−	0.999421i	$-0.510834\pi$
$211$	−639344.			−0.0680592			−0.0340296	+	0.999421i	$0.510834\pi$
$212$	5.54280e6	+	65223.3i	0.581730	+	0.00684534i
$213$			1.67236e6i			0.173058i
$214$	6.10818e6	+	6.18048e6i	0.623262	+	0.630639i
$215$		−	5.54304e6i		−	0.557741i
$216$	4.33622e6	−	4.18579e6i	0.430279	−	0.415352i
$217$	1.31072e7			1.28272
$218$	−9.76936e6	+	9.65508e6i	−0.942968	+	0.931937i
$219$	−543252.			−0.0517213
$220$	5.39614e6	+	63497.6i	0.506775	+	0.00596333i
$221$		−	1.05480e7i		−	0.977224i
$222$	−1.74459e6	+	1.72418e6i	−0.159454	+	0.157588i
$223$			9.51144e6i			0.857693i	0.903377	+	0.428846i	$0.141080\pi$
$223$			9.51144e6i			0.857693i	−0.903377	+	0.428846i	$0.858920\pi$
$224$	−1.15296e7	+	1.08705e7i	−1.02582	+	0.967172i
$225$	−7.92141e6			−0.695433
$226$	3.62952e6	+	3.67248e6i	0.314430	+	0.318152i
$227$	1.27875e7			1.09322			0.546610	−	0.837387i	$-0.315918\pi$
$227$	1.27875e7			1.09322			0.546610	+	0.837387i	$0.315918\pi$
$228$	−6192.31	+	526234.i	−0.000522454	+	0.0443991i
$229$			4.61930e6i			0.384653i	0.981331	+	0.192327i	$0.0616033\pi$
$229$			4.61930e6i			0.384653i	−0.981331	+	0.192327i	$0.938397\pi$
$230$	−1.11288e6	−	1.12606e6i	−0.0914674	−	0.0925500i
$231$		−	5.80043e6i		−	0.470570i
$232$	9.37045e6	+	9.70720e6i	0.750406	+	0.777374i
$233$	−9.41375e6			−0.744209			−0.372105	−	0.928191i	$-0.621364\pi$
$233$	−9.41375e6			−0.744209			−0.372105	+	0.928191i	$0.621364\pi$
$234$	1.28970e7	−	1.27462e7i	1.00657	−	0.994792i
$235$	−9.51329e6			−0.733039
$236$	−96997.6	+	8.24304e6i	−0.00737947	+	0.627121i
$237$		−	1.39876e6i		−	0.105075i
$238$	−8.41107e6	+	8.31267e6i	−0.623907	+	0.616609i
$239$		−	2.57043e7i		−	1.88283i	−0.337247	−	0.941416i	$-0.609496\pi$
$239$		−	2.57043e7i		−	1.88283i	0.337247	−	0.941416i	$-0.390504\pi$
$240$	−48883.5	+	2.07682e6i	−0.00353614	+	0.150233i
$241$	8.16838e6			0.583559			0.291779	−	0.956486i	$-0.405753\pi$
$241$	8.16838e6			0.583559			0.291779	+	0.956486i	$0.405753\pi$
$242$	1.25186e6	+	1.26668e6i	0.0883303	+	0.0893759i
$243$	1.17993e7			0.822313
$244$	−1.21263e7	−	142692.i	−0.834752	−	0.00982270i
$245$			6.93864e6i			0.471820i
$246$	−327705.	−	331583.i	−0.0220129	−	0.0222735i
$247$			3.34063e6i			0.221686i
$248$	−9.63808e6	−	9.98446e6i	−0.631882	−	0.654590i
$249$	−6.82015e6			−0.441769
$250$	9.40602e6	−	9.29599e6i	0.601985	−	0.594943i
$251$	−8.44540e6			−0.534071			−0.267035	−	0.963687i	$-0.586044\pi$
$251$	−8.44540e6			−0.534071			−0.267035	+	0.963687i	$0.586044\pi$
$252$	−2.03278e7	−	239201.i	−1.27025	−	0.0149473i
$253$		−	4.68031e6i		−	0.289010i
$254$	1.43106e7	−	1.41432e7i	0.873289	−	0.863073i
$255$			1.55033e6i			0.0934981i
$256$	1.67586e7	+	789356.i	0.998893	+	0.0470493i
$257$	−1.84481e7			−1.08681			−0.543403	−	0.839472i	$-0.682864\pi$
$257$	−1.84481e7			−1.08681			−0.543403	+	0.839472i	$0.682864\pi$
$258$	4.43412e6	+	4.48661e6i	0.258195	+	0.261252i
$259$	1.74559e7			1.00472
$260$	−155161.	+	1.31859e7i	−0.00882799	+	0.750220i
$261$			1.73092e7i			0.973542i
$262$	−2.12270e7	−	2.14782e7i	−1.18028	−	1.19425i
$263$			3.84095e6i			0.211140i	0.994412	+	0.105570i	$0.0336668\pi$
$263$			3.84095e6i			0.211140i	−0.994412	+	0.105570i	$0.966333\pi$
$264$	−4.41850e6	+	4.26522e6i	−0.240139	+	0.231809i
$265$	−5.17168e6			−0.277903
$266$	2.66384e6	−	2.63268e6i	0.141535	−	0.139879i
$267$	−459904.			−0.0241621
$268$	240852.	−	2.04680e7i	0.0125125	−	1.06334i
$269$			3.10430e7i			1.59480i	0.603451	+	0.797400i	$0.293792\pi$
$269$			3.10430e7i			1.59480i	−0.603451	+	0.797400i	$0.706208\pi$
$270$	−3.99937e6	+	3.95259e6i	−0.203189	+	0.200812i
$271$			2.35560e7i			1.18357i	0.806097	+	0.591784i	$0.201576\pi$
$271$			2.35560e7i			1.18357i	−0.806097	+	0.591784i	$0.798424\pi$
$272$	1.25171e7	+	294624.i	0.622010	+	0.0146407i
$273$	1.41738e7			0.696623
$274$	7.90871e6	+	8.00232e6i	0.384462	+	0.389013i
$275$	1.70300e7			0.818875
$276$	1.80156e6	+	21199.4i	0.0856885	+	0.00100831i
$277$		−	2.32189e7i		−	1.09245i	−0.837638	−	0.546225i	$-0.816064\pi$
$277$		−	2.32189e7i		−	1.09245i	0.837638	−	0.546225i	$-0.183936\pi$
$278$	1.30218e7	+	1.31759e7i	0.606089	+	0.613263i
$279$		−	1.78035e7i		−	0.819774i
$280$	1.06368e7	−	1.02678e7i	0.484547	−	0.467738i
$281$	2.99519e7			1.34991			0.674955	−	0.737859i	$-0.264163\pi$
$281$	2.99519e7			1.34991			0.674955	+	0.737859i	$0.264163\pi$
$282$	7.70018e6	−	7.61011e6i	0.343363	−	0.339347i
$283$	−3.68036e7			−1.62380			−0.811898	−	0.583800i	$-0.801565\pi$
$283$	−3.68036e7			−1.62380			−0.811898	+	0.583800i	$0.801565\pi$
$284$	−1.26001e7	−	148268.i	−0.550070	−	0.00647279i
$285$		−	491000.i		−	0.0212103i
$286$	−2.77270e7	+	2.74027e7i	−1.18524	+	1.17137i
$287$			3.31774e6i			0.140345i
$288$	1.47654e7	+	1.56607e7i	0.618112	+	0.655591i
$289$	−1.47937e7			−0.612890
$290$	−8.84840e6	−	8.95313e6i	−0.362803	−	0.367097i
$291$	−9.40021e6			−0.381469
$292$	48163.5	−	4.09303e6i	0.00193450	−	0.164398i
$293$		−	3.36919e7i		−	1.33944i	−0.742615	−	0.669718i	$-0.766415\pi$
$293$		−	3.36919e7i		−	1.33944i	0.742615	−	0.669718i	$-0.233585\pi$
$294$	−5.55053e6	−	5.61622e6i	−0.218420	−	0.221005i
$295$		−	7.69112e6i		−	0.299588i
$296$	−1.28358e7	−	1.32971e7i	−0.494936	−	0.512723i
$297$	−1.66229e7			−0.634508
$298$	−2.70201e7	+	2.67040e7i	−1.02103	+	1.00908i
$299$	1.14367e7			0.427844
$300$	−77137.3	+	6.55528e6i	−0.00285694	+	0.242788i
$301$		−	4.48918e7i		−	1.64614i
$302$	6.36072e6	−	6.28631e6i	0.230933	−	0.228231i
$303$			6.87652e6i			0.247196i
$304$	−3.96425e6	−	93309.3i	−0.141104	−	0.00332127i
$305$	1.13143e7			0.398776
$306$	1.12911e7	+	1.14248e7i	0.394070	+	0.398734i
$307$	−3.69782e7			−1.27800			−0.639000	−	0.769207i	$-0.720651\pi$
$307$	−3.69782e7			−1.27800			−0.639000	+	0.769207i	$0.720651\pi$
$308$	4.37022e7	+	514253.i	1.49572	+	0.0176005i
$309$		−	5.26153e6i		−	0.178335i
$310$	9.10112e6	+	9.20884e6i	0.305499	+	0.309115i
$311$			3.65356e7i			1.21461i	0.794470	+	0.607303i	$0.207749\pi$
$311$			3.65356e7i			1.21461i	−0.794470	+	0.607303i	$0.792251\pi$
$312$	−1.04224e7	−	1.07969e7i	−0.343165	−	0.355498i
$313$	5.50169e7			1.79417			0.897083	−	0.441861i	$-0.145682\pi$
$313$	5.50169e7			1.79417			0.897083	+	0.441861i	$0.145682\pi$
$314$	−5.71322e6	+	5.64638e6i	−0.184541	+	0.182382i
$315$	1.89667e7			0.606821
$316$	1.05387e7	+	124011.i	0.333983	+	0.00393005i
$317$			4.12495e7i			1.29491i	0.762102	+	0.647457i	$0.224168\pi$
$317$			4.12495e7i			1.29491i	−0.762102	+	0.647457i	$0.775832\pi$
$318$	4.18602e6	−	4.13706e6i	0.130173	−	0.128650i
$319$		−	3.72125e7i		−	1.14635i
$320$	−1.56430e7	−	552429.i	−0.477388	−	0.0168588i
$321$	9.22601e6			0.278932
$322$	−9.01300e6	−	9.11968e6i	−0.269961	−	0.273157i
$323$	−2.95928e6			−0.0878170
$324$	−285302.	+	2.42455e7i	−0.00838821	+	0.712846i
$325$			4.16141e7i			1.21225i
$326$	8.28422e6	+	8.38228e6i	0.239111	+	0.241941i
$327$			1.45834e7i			0.417076i
$328$	2.52730e6	−	2.43963e6i	0.0716202	−	0.0691356i
$329$	−7.70461e7			−2.16353
$330$	4.07527e6	−	4.02759e6i	0.113400	−	0.112074i
$331$	2.72892e7			0.752502			0.376251	−	0.926518i	$-0.377213\pi$
$331$	2.72892e7			0.752502			0.376251	+	0.926518i	$0.377213\pi$
$332$	604658.	−	5.13850e7i	0.0165233	−	1.40418i
$333$		−	2.37104e7i		−	0.642107i
$334$	2.93805e7	−	2.90368e7i	0.788534	−	0.779310i
$335$			1.90976e7i			0.507977i
$336$	−395897.	+	1.68197e7i	−0.0104367	+	0.443405i
$337$	−1.36843e6			−0.0357547			−0.0178774	−	0.999840i	$-0.505691\pi$
$337$	−1.36843e6			−0.0357547			−0.0178774	+	0.999840i	$0.505691\pi$
$338$	−3.98170e7	−	4.02882e7i	−1.03114	−	1.04335i
$339$	5.48216e6			0.140719
$340$	−1.16806e7	−	137448.i	−0.297187	−	0.00349706i
$341$			3.82754e7i			0.965287i
$342$	−3.57598e6	−	3.61831e6i	−0.0893958	−	0.0904539i
$343$		−	698651.i		−	0.0173132i
$344$	−3.41965e7	+	3.30102e7i	−0.840053	+	0.810911i
$345$	−1.68094e6			−0.0409350
$346$	3.41542e6	−	3.37546e6i	0.0824547	−	0.0814901i
$347$	1.07803e7			0.258013			0.129006	−	0.991644i	$-0.458821\pi$
$347$	1.07803e7			0.258013			0.129006	+	0.991644i	$0.458821\pi$
$348$	1.43240e7	+	168554.i	0.339881	+	0.00399945i
$349$		−	1.33186e6i		−	0.0313316i	−0.999877	−	0.0156658i	$-0.995013\pi$
$349$		−	1.33186e6i		−	0.0313316i	0.999877	−	0.0156658i	$-0.00498678\pi$
$350$	3.31834e7	−	3.27952e7i	0.773957	−	0.764903i
$351$		−	4.06192e7i		−	0.939312i
$352$	−3.17437e7	−	3.36685e7i	−0.727829	−	0.771961i
$353$	798852.			0.0181611			0.00908055	−	0.999959i	$-0.497110\pi$
$353$	798852.			0.0181611			0.00908055	+	0.999959i	$0.497110\pi$
$354$	6.15247e6	+	6.22530e6i	0.138688	+	0.140330i
$355$	1.17564e7			0.262779
$356$	40774.0	−	3.46506e6i	0.000903720	−	0.0767998i
$357$			1.25558e7i			0.275955i
$358$	3.56896e7	+	3.61121e7i	0.777844	+	0.787051i
$359$		−	5.67611e7i		−	1.22678i	−0.789779	−	0.613392i	$-0.789805\pi$
$359$		−	5.67611e7i		−	1.22678i	0.789779	−	0.613392i	$-0.210195\pi$
$360$	−1.39468e7	−	1.44480e7i	−0.298928	−	0.309670i
$361$	−4.61087e7			−0.980078
$362$	7.68333e6	−	7.59345e6i	0.161966	−	0.160071i
$363$	1.89086e6			0.0395311
$364$	−1.25661e6	+	1.06789e8i	−0.0260554	+	2.21424i
$365$			3.81897e6i			0.0785359i
$366$	−9.15797e6	+	9.05084e6i	−0.186791	+	0.184606i
$367$			1.80379e7i			0.364911i	0.983214	+	0.182456i	$0.0584046\pi$
$367$			1.80379e7i			0.364911i	−0.983214	+	0.182456i	$0.941595\pi$
$368$	−319445.	+	1.35716e7i	−0.00640992	+	0.272326i
$369$	4.50650e6			0.0896933
$370$	1.21207e7	+	1.22642e7i	0.239289	+	0.242121i
$371$	−4.18843e7			−0.820218
$372$	−1.47331e7	−	173368.i	−0.286198	−	0.00336775i
$373$		−	3.58446e7i		−	0.690712i	−0.938472	−	0.345356i	$-0.887758\pi$
$373$		−	3.58446e7i		−	0.690712i	0.938472	−	0.345356i	$-0.112242\pi$
$374$	−2.42745e7	−	2.45618e7i	−0.464019	−	0.469511i
$375$		−	1.40410e7i		−	0.266259i
$376$	5.66541e7	+	5.86902e7i	1.06578	+	1.10408i
$377$	9.09315e7			1.69703
$378$	−3.23900e7	+	3.20111e7i	−0.599703	+	0.592687i
$379$	9.70544e7			1.78278			0.891390	−	0.453238i	$-0.149731\pi$
$379$	9.70544e7			1.78278			0.891390	+	0.453238i	$0.149731\pi$
$380$	3.69934e6	+	43530.9i	0.0674176	+	0.000793317i
$381$		−	2.13625e7i		−	0.386257i
$382$	−1.88934e7	+	1.86723e7i	−0.338937	+	0.334972i
$383$			3.16741e7i			0.563779i	0.959447	+	0.281889i	$0.0909611\pi$
$383$			3.16741e7i			0.563779i	−0.959447	+	0.281889i	$0.909039\pi$
$384$	1.31036e7	−	1.20664e7i	0.231418	−	0.213101i
$385$	−4.07761e7			−0.714534
$386$	3.14466e7	+	3.18188e7i	0.546779	+	0.553251i
$387$	−6.09768e7			−1.05204
$388$	833401.	−	7.08240e7i	0.0142679	−	1.21251i
$389$		−	5.50526e7i		−	0.935252i	−0.883926	−	0.467626i	$-0.845109\pi$
$389$		−	5.50526e7i		−	0.935252i	0.883926	−	0.467626i	$-0.154891\pi$
$390$	9.84171e6	+	9.95820e6i	0.165912	+	0.167875i
$391$			1.01311e7i			0.169483i
$392$	4.28064e7	−	4.13214e7i	0.710641	−	0.685988i
$393$	−3.20620e7			−0.528217
$394$	4.09568e7	−	4.04777e7i	0.669634	−	0.661801i
$395$	−9.83305e6			−0.159550
$396$	698511.	−	5.93608e7i	0.0112483	−	0.955905i
$397$			8.33093e7i			1.33144i	0.746201	+	0.665721i	$0.231876\pi$
$397$			8.33093e7i			1.33144i	−0.746201	+	0.665721i	$0.768124\pi$
$398$	−6.59121e7	+	6.51410e7i	−1.04548	+	1.03325i
$399$		−	3.97650e6i		−	0.0626011i
$400$	−4.93826e7	−	1.16235e6i	−0.771603	−	0.0181617i
$401$	4.24726e7			0.658682			0.329341	−	0.944211i	$-0.393174\pi$
$401$	4.24726e7			0.658682			0.329341	+	0.944211i	$0.393174\pi$
$402$	−1.52770e7	−	1.54578e7i	−0.235158	−	0.237942i
$403$	−9.35286e7			−1.42899
$404$	−5.18097e7	−	609656.i	−0.785719	−	0.00924572i
$405$		−	2.26221e7i		−	0.340540i
$406$	−7.16612e7	−	7.25094e7i	−1.07079	−	1.08347i
$407$			5.09745e7i			0.756083i
$408$	9.56441e6	−	9.23260e6i	0.140824	−	0.135939i
$409$	4.61036e7			0.673853			0.336926	−	0.941531i	$-0.390613\pi$
$409$	4.61036e7			0.673853			0.336926	+	0.941531i	$0.390613\pi$
$410$	−2.33098e6	+	2.30371e6i	−0.0338210	+	0.0334253i
$411$	1.19456e7			0.172061
$412$	3.96420e7	+	466475.i	0.566844	+	0.00667017i
$413$		−	6.22887e7i		−	0.884218i
$414$	−1.23873e7	+	1.22424e7i	−0.174572	+	0.172530i
$415$			4.79445e7i			0.670802i
$416$	8.22713e7	−	7.75680e7i	1.14280	−	1.07746i
$417$	1.96686e7			0.271247
$418$	7.68791e6	+	7.77891e6i	0.105264	+	0.106510i
$419$	−3.86614e7			−0.525575			−0.262788	−	0.964854i	$-0.584642\pi$
$419$	−3.86614e7			−0.525575			−0.262788	+	0.964854i	$0.584642\pi$
$420$	184695.	−	1.56957e7i	0.00249291	−	0.211852i
$421$			2.58211e7i			0.346042i	0.984918	+	0.173021i	$0.0553528\pi$
$421$			2.58211e7i			0.346042i	−0.984918	+	0.173021i	$0.944647\pi$
$422$	−3.59533e6	−	3.63789e6i	−0.0478412	−	0.0484074i
$423$			1.04652e8i			1.38269i
$424$	3.07987e7	+	3.19055e7i	0.404049	+	0.418570i
$425$	−3.68636e7			−0.480210
$426$	−9.51580e6	+	9.40448e6i	−0.123088	+	0.121648i
$427$	9.16323e7			1.17697
$428$	−817957.	+	6.95115e7i	−0.0104328	+	0.886595i
$429$			4.13900e7i			0.524232i
$430$	3.15401e7	−	3.11711e7i	0.396696	−	0.392055i
$431$		−	3.09589e7i		−	0.386681i	−0.981132	−	0.193341i	$-0.938068\pi$
$431$		−	3.09589e7i		−	0.386681i	0.981132	−	0.193341i	$-0.0619322\pi$
$432$	4.82019e7	+	1.13456e6i	0.597879	+	0.0140727i
$433$	4.64302e7			0.571921			0.285961	−	0.958241i	$-0.407687\pi$
$433$	4.64302e7			0.571921			0.285961	+	0.958241i	$0.407687\pi$
$434$	7.37080e7	+	7.45804e7i	0.901665	+	0.912338i
$435$	−1.33649e7			−0.162368
$436$	−1.09876e8	−	1.29293e6i	−1.32569	−	0.0155997i
$437$		−	3.20859e6i		−	0.0384477i
$438$	−3.05497e6	−	3.09113e6i	−0.0363567	−	0.0367870i
$439$		−	1.33692e8i		−	1.58020i	−0.612979	−	0.790099i	$-0.710029\pi$
$439$		−	1.33692e8i		−	1.58020i	0.612979	−	0.790099i	$-0.289971\pi$
$440$	2.99838e7	+	3.10613e7i	0.351988	+	0.364638i
$441$	7.63292e7			0.889969
$442$	6.00186e7	−	5.93165e7i	0.695055	−	0.686924i
$443$	−5.29536e6			−0.0609094			−0.0304547	−	0.999536i	$-0.509696\pi$
$443$	−5.29536e6			−0.0609094			−0.0304547	+	0.999536i	$0.509696\pi$
$444$	−1.96213e7	−	230888.i	−0.224171	−	0.00263787i
$445$			3.23305e6i			0.0366887i
$446$	−5.41205e7	+	5.34874e7i	−0.610038	+	0.602902i
$447$			4.03347e7i			0.451602i
$448$	−1.26690e8	−	4.47400e6i	−1.40899	−	0.0497579i
$449$	−1.20011e8			−1.32582			−0.662908	−	0.748701i	$-0.730678\pi$
$449$	−1.20011e8			−1.32582			−0.662908	+	0.748701i	$0.730678\pi$
$450$	−4.45459e7	−	4.50731e7i	−0.488844	−	0.494630i
$451$	−9.68840e6			−0.105614
$452$	−486036.	+	4.13042e7i	−0.00526324	+	0.447280i
$453$		−	9.49508e6i		−	0.102142i
$454$	7.19101e7	+	7.27613e7i	0.768462	+	0.777558i
$455$		−	9.96392e7i		−	1.05778i
$456$	−3.02911e6	+	2.92403e6i	−0.0319463	+	0.0308381i
$457$	−1.84689e8			−1.93505			−0.967527	−	0.252767i	$-0.918660\pi$
$457$	−1.84689e8			−1.93505			−0.967527	+	0.252767i	$0.918660\pi$
$458$	−2.62840e7	+	2.59765e7i	−0.273586	+	0.270386i
$459$	3.59823e7			0.372092
$460$	149028.	−	1.26647e7i	0.00153107	−	0.130113i
$461$		−	1.46730e8i		−	1.49767i	−0.662755	−	0.748836i	$-0.730613\pi$
$461$		−	1.46730e8i		−	1.49767i	0.662755	−	0.748836i	$-0.269387\pi$
$462$	3.30047e7	−	3.26186e7i	0.334695	−	0.330780i
$463$		−	1.55124e8i		−	1.56292i	−0.623956	−	0.781459i	$-0.714476\pi$
$463$		−	1.55124e8i		−	1.56292i	0.623956	−	0.781459i	$-0.285524\pi$
$464$	−2.53987e6	+	1.07906e8i	−0.0254248	+	1.08017i
$465$	1.37467e7			0.136722
$466$	−5.29380e7	−	5.35646e7i	−0.523130	−	0.529322i
$467$	1.07539e8			1.05589			0.527943	−	0.849280i	$-0.322963\pi$
$467$	1.07539e8			1.05589			0.527943	+	0.849280i	$0.322963\pi$
$468$	1.45052e8	+	1.70686e6i	1.41510	+	0.0166518i
$469$			1.54667e8i			1.49927i
$470$	−5.34978e7	−	5.41310e7i	−0.515279	−	0.521378i
$471$			8.52850e6i			0.0816225i
$472$	−4.74487e7	+	4.58026e7i	−0.451230	+	0.435577i
$473$	1.31092e8			1.23878
$474$	7.95900e6	−	7.86589e6i	0.0747349	−	0.0738606i
$475$	1.16750e7			0.108937
$476$	−9.45988e7	−	1.11316e6i	−0.877132	−	0.0103214i
$477$			5.68916e7i			0.524195i
$478$	1.46258e8	−	1.44547e8i	1.33917	−	1.32351i
$479$			1.48881e7i			0.135467i	0.997703	+	0.0677333i	$0.0215767\pi$
$479$			1.48881e7i			0.135467i	−0.997703	+	0.0677333i	$0.978423\pi$
$480$	−1.20921e7	+	1.14008e7i	−0.109340	+	0.103089i
$481$	−1.24560e8			−1.11929
$482$	4.59347e7	+	4.64784e7i	0.410204	+	0.415059i
$483$	−1.36136e7			−0.120818
$484$	−167639.	+	1.42463e7i	−0.00147856	+	0.125651i
$485$			6.60819e7i			0.579239i
$486$	6.63531e7	+	6.71384e7i	0.578032	+	0.584874i
$487$			9.69346e7i			0.839251i	0.907697	+	0.419625i	$0.137839\pi$
$487$			9.69346e7i			0.839251i	−0.907697	+	0.419625i	$0.862161\pi$
$488$	−6.73798e7	−	6.98013e7i	−0.579789	−	0.600626i
$489$	1.25128e7			0.107011
$490$	−3.94811e7	+	3.90193e7i	−0.335584	+	0.331658i
$491$	−6.45564e7			−0.545374			−0.272687	−	0.962103i	$-0.587912\pi$
$491$	−6.45564e7			−0.545374			−0.272687	+	0.962103i	$0.587912\pi$
$492$	43883.5	−	3.72930e6i	0.000368473	−	0.0313136i
$493$			8.05512e7i			0.672250i
$494$	−1.90083e7	+	1.87860e7i	−0.157675	+	0.155830i
$495$			5.53863e7i			0.456653i
$496$	2.61241e6	−	1.10988e8i	0.0214090	−	0.909563i
$497$	9.52126e7			0.775578
$498$	−3.83529e7	−	3.88069e7i	−0.310535	−	0.314211i
$499$	8.09040e7			0.651131			0.325565	−	0.945520i	$-0.394445\pi$
$499$	8.09040e7			0.651131			0.325565	+	0.945520i	$0.394445\pi$
$500$	1.05789e8	+	1.24484e6i	0.846313	+	0.00995874i
$501$		−	4.38583e7i		−	0.348770i
$502$	−4.74925e7	−	4.80546e7i	−0.375417	−	0.379860i
$503$			1.32342e8i			1.03990i	0.854196	+	0.519951i	$0.174050\pi$
$503$			1.32342e8i			1.03990i	−0.854196	+	0.519951i	$0.825950\pi$
$504$	−1.12952e8	−	1.17011e8i	−0.882270	−	0.913977i
$505$	4.83408e7			0.375352
$506$	2.66311e7	−	2.63196e7i	0.205560	−	0.203155i
$507$	−6.01410e7			−0.461473
$508$	1.60951e8	+	1.89395e6i	1.22773	+	0.0144470i
$509$			1.39233e7i			0.105582i	0.998606	+	0.0527909i	$0.0168117\pi$
$509$			1.39233e7i			0.105582i	−0.998606	+	0.0527909i	$0.983188\pi$
$510$	−8.82142e6	+	8.71823e6i	−0.0665010	+	0.0657231i
$511$			3.09290e7i			0.231795i
$512$	8.97503e7	+	9.97962e7i	0.668692	+	0.743540i
$513$	−1.13958e7			−0.0844101
$514$	−1.03742e8	−	1.04970e8i	−0.763953	−	0.772995i
$515$	−3.69877e7			−0.270792
$516$	−593781.	+	5.04606e7i	−0.00432192	+	0.367285i
$517$		−	2.24989e8i		−	1.62813i
$518$	9.81630e7	+	9.93249e7i	0.706250	+	0.714609i
$519$		−	5.09842e6i		−	0.0364698i
$520$	−7.59006e7	+	7.32675e7i	−0.539803	+	0.521076i
$521$	−9.25151e7			−0.654183			−0.327092	−	0.944993i	$-0.606069\pi$
$521$	−9.25151e7			−0.654183			−0.327092	+	0.944993i	$0.606069\pi$
$522$	−9.84898e7	+	9.73377e7i	−0.692436	+	0.684336i
$523$	−5.17905e7			−0.362030			−0.181015	−	0.983480i	$-0.557938\pi$
$523$	−5.17905e7			−0.362030			−0.181015	+	0.983480i	$0.557938\pi$
$524$	2.84254e6	−	2.41564e8i	0.0197566	−	1.67895i
$525$		−	4.95351e7i		−	0.342322i
$526$	−2.18551e7	+	2.15995e7i	−0.150175	+	0.148418i
$527$		−	8.28518e7i		−	0.566070i
$528$	−4.91166e7	−	1.15609e6i	−0.333677	−	0.00785399i
$529$	1.37051e8			0.925797
$530$	−2.90828e7	−	2.94270e7i	−0.195348	−	0.197660i
$531$	−8.46070e7			−0.565097
$532$	2.99601e7	+	352547.i	0.198980	+	0.00234143i
$533$		−	2.36743e7i		−	0.156349i
$534$	−2.58626e6	−	2.61687e6i	−0.0169843	−	0.0171854i
$535$		−	6.48573e7i		−	0.423543i
$536$	1.17818e8	−	1.13731e8i	0.765100	−	0.738558i
$537$	5.39069e7			0.348114
$538$	−1.76636e8	+	1.74569e8i	−1.13431	+	1.12104i
$539$	−1.64098e8			−1.04794
$540$	−4.49807e7	−	529298.i	−0.285657	−	0.00336139i
$541$			2.48317e7i			0.156825i	0.996921	+	0.0784125i	$0.0249851\pi$
$541$			2.48317e7i			0.156825i	−0.996921	+	0.0784125i	$0.975015\pi$
$542$	−1.34034e8	+	1.32466e8i	−0.841818	+	0.831970i
$543$		−	1.14694e7i		−	0.0716378i
$544$	6.87132e7	+	7.28796e7i	0.426819	+	0.452699i
$545$	1.02519e8			0.633306
$546$	7.97059e7	+	8.06493e7i	0.489680	+	0.495476i
$547$	8.23167e7			0.502951			0.251476	−	0.967864i	$-0.419084\pi$
$547$	8.23167e7			0.502951			0.251476	+	0.967864i	$0.419084\pi$
$548$	−1.05907e6	+	9.00017e7i	−0.00643550	+	0.546901i
$549$		−	1.24465e8i		−	0.752192i
$550$	9.57680e7	+	9.69016e7i	0.575615	+	0.582429i
$551$		−	2.55111e7i		−	0.152502i
$552$	1.00104e7	+	1.03702e7i	0.0595162	+	0.0616551i
$553$	−7.96357e7			−0.470904
$554$	1.32116e8	−	1.30571e8i	0.777010	−	0.767921i
$555$	1.83076e7			0.107091
$556$	−1.74377e6	+	1.48189e8i	−0.0101453	+	0.862168i
$557$		−	1.99169e7i		−	0.115254i	−0.998338	−	0.0576271i	$-0.981647\pi$
$557$		−	1.99169e7i		−	0.115254i	0.998338	−	0.0576271i	$-0.0183534\pi$
$558$	1.01303e8	−	1.00118e8i	0.583068	−	0.576247i
$559$			3.20333e8i			1.83386i
$560$	1.18240e8	+	2.78309e6i	0.673286	+	0.0158476i
$561$	−3.66651e7			−0.207666
$562$	1.68434e8	+	1.70427e8i	0.948898	+	0.960130i
$563$	3.05819e8			1.71372			0.856859	−	0.515550i	$-0.172412\pi$
$563$	3.05819e8			1.71372			0.856859	+	0.515550i	$0.172412\pi$
$564$	8.66036e7	+	1.01908e6i	0.482724	+	0.00568031i
$565$		−	3.85387e7i		−	0.213674i
$566$	−2.06964e8	−	2.09414e8i	−1.14142	−	1.15493i
$567$		−	1.83212e8i		−	1.00509i
$568$	−7.00125e7	−	7.25286e7i	−0.382059	−	0.395790i
$569$	−2.25936e6			−0.0122644			−0.00613222	−	0.999981i	$-0.501952\pi$
$569$	−2.25936e6			−0.0122644			−0.00613222	+	0.999981i	$0.501952\pi$
$570$	2.79381e6	−	2.76112e6i	0.0150859	−	0.0149094i
$571$	−6.55464e7			−0.352079			−0.176040	−	0.984383i	$-0.556329\pi$
$571$	−6.55464e7			−0.352079			−0.176040	+	0.984383i	$0.556329\pi$
$572$	−3.11844e8	−	3.66954e6i	−1.66629	−	0.0196076i
$573$			2.82034e7i			0.149912i
$574$	−1.88781e7	+	1.86572e7i	−0.0998209	+	0.0986532i
$575$		−	3.99693e7i		−	0.210244i
$576$	−6.07705e6	+	1.72083e8i	−0.0317999	+	0.900472i
$577$	5.43876e7			0.283121			0.141561	−	0.989930i	$-0.454788\pi$
$577$	5.43876e7			0.283121			0.141561	+	0.989930i	$0.454788\pi$
$578$	−8.31918e7	−	8.41765e7i	−0.430821	−	0.435921i
$579$	4.74981e7			0.244703
$580$	1.18490e6	−	1.00695e8i	0.00607294	−	0.516090i
$581$			3.88292e8i			1.97984i
$582$	−5.28619e7	−	5.34876e7i	−0.268147	−	0.271321i
$583$		−	1.22310e8i		−	0.617242i
$584$	2.35603e7	−	2.27430e7i	0.118288	−	0.114185i
$585$	−1.35340e8			−0.676020
$586$	1.91708e8	−	1.89465e8i	0.952681	−	0.941536i
$587$	−3.85369e8			−1.90529			−0.952647	−	0.304078i	$-0.901652\pi$
$587$	−3.85369e8			−1.90529			−0.952647	+	0.304078i	$0.901652\pi$
$588$	743280.	−	6.31654e7i	0.00365612	−	0.310704i
$589$			2.62398e7i			0.128414i
$590$	4.37628e7	−	4.32509e7i	0.213083	−	0.210590i
$591$		−	6.11390e7i		−	0.296180i
$592$	3.47916e6	−	1.47812e8i	0.0167691	−	0.712436i
$593$	−3.00090e8			−1.43909			−0.719545	−	0.694446i	$-0.755650\pi$
$593$	−3.00090e8			−1.43909			−0.719545	+	0.694446i	$0.755650\pi$
$594$	−9.34783e7	−	9.45848e7i	−0.446017	−	0.451296i
$595$	8.82649e7			0.419022
$596$	−3.03893e8	−	3.57598e6i	−1.43543	−	0.0168910i
$597$			9.83914e7i			0.462417i
$598$	6.43138e7	+	6.50751e7i	0.300747	+	0.304306i
$599$			3.11371e8i			1.44876i	0.689400	+	0.724381i	$0.257874\pi$
$599$			3.11371e8i			1.44876i	−0.689400	+	0.724381i	$0.742126\pi$
$600$	−3.77336e7	+	3.64245e7i	−0.174692	+	0.168632i
$601$	2.10925e8			0.971637			0.485818	−	0.874060i	$-0.338522\pi$
$601$	2.10925e8			0.971637			0.485818	+	0.874060i	$0.338522\pi$
$602$	2.55436e8	−	2.52448e8i	1.17083	−	1.15713i
$603$	2.10085e8			0.958171
$604$	7.15387e7	+	841811.i	0.324661	+	0.00382036i
$605$		−	1.32924e7i		−	0.0600257i
$606$	−3.91276e7	+	3.86699e7i	−0.175819	+	0.173762i
$607$		−	3.28208e8i		−	1.46752i	−0.679410	−	0.733759i	$-0.737764\pi$
$607$		−	3.28208e8i		−	1.46752i	0.679410	−	0.733759i	$-0.262236\pi$
$608$	−2.17620e7	−	2.30815e7i	−0.0968249	−	0.102696i
$609$	−1.08240e8			−0.479220
$610$	6.36259e7	+	6.43790e7i	0.280314	+	0.283632i
$611$	5.49776e8			2.41025
$612$	−1.51202e6	+	1.28494e8i	−0.00659632	+	0.560568i
$613$			1.43677e8i			0.623743i	0.950124	+	0.311872i	$0.100956\pi$
$613$			1.43677e8i			0.623743i	−0.950124	+	0.311872i	$0.899044\pi$
$614$	−2.07946e8	−	2.10407e8i	−0.898350	−	0.908983i
$615$			3.47960e6i			0.0149591i
$616$	2.42832e8	+	2.51559e8i	1.03888	+	1.07621i
$617$	−1.50375e8			−0.640206			−0.320103	−	0.947383i	$-0.603717\pi$
$617$	−1.50375e8			−0.640206			−0.320103	+	0.947383i	$0.603717\pi$
$618$	2.99383e7	−	2.95881e7i	0.126842	−	0.125358i
$619$	−2.07480e8			−0.874793			−0.437396	−	0.899269i	$-0.644099\pi$
$619$	−2.07480e8			−0.874793			−0.437396	+	0.899269i	$0.644099\pi$
$620$	−1.21875e6	+	1.03571e8i	−0.00511374	+	0.434575i
$621$			3.90137e7i			0.162908i
$622$	−2.07889e8	+	2.05457e8i	−0.863894	+	0.853788i
$623$			2.61838e7i			0.108285i
$624$	2.82499e6	−	1.20020e8i	0.0116269	−	0.493969i
$625$	8.97259e7			0.367517
$626$	3.09386e8	+	3.13048e8i	1.26118	+	1.27611i
$627$	1.16121e7			0.0471094
$628$	−6.42563e7	−	756117.i	−0.259440	−	0.00305288i
$629$		−	1.10341e8i		−	0.443388i
$630$	1.06659e8	+	1.07921e8i	0.426556	+	0.431604i
$631$			9.08069e7i			0.361436i	0.983535	+	0.180718i	$0.0578421\pi$
$631$			9.08069e7i			0.361436i	−0.983535	+	0.180718i	$0.942158\pi$
$632$	5.85583e7	+	6.06628e7i	0.231973	+	0.240310i
$633$	−5.43052e6			−0.0214107
$634$	−2.34711e8	+	2.31966e8i	−0.921014	+	0.910240i
$635$	−1.50174e8			−0.586509
$636$	4.70800e7	+	554000.i	0.183006	+	0.00215347i
$637$		−	4.00986e8i		−	1.55135i
$638$	2.11741e8	−	2.09264e8i	0.815347	−	0.805809i
$639$		−	1.29328e8i		−	0.495666i
$640$	−8.48250e7	−	9.21161e7i	−0.323582	−	0.351395i
$641$	1.95456e8			0.742121			0.371061	−	0.928609i	$-0.378994\pi$
$641$	1.95456e8			0.742121			0.371061	+	0.928609i	$0.378994\pi$
$642$	5.18823e7	+	5.24964e7i	0.196071	+	0.198392i
$643$	−3.72026e8			−1.39939			−0.699697	−	0.714440i	$-0.746682\pi$
$643$	−3.72026e8			−1.39939			−0.699697	+	0.714440i	$0.746682\pi$
$644$	1.20695e6	−	1.02569e8i	0.00451887	−	0.384023i
$645$		−	4.70820e7i		−	0.175459i
$646$	−1.66414e7	−	1.68384e7i	−0.0617296	−	0.0624602i
$647$		−	2.47447e8i		−	0.913627i	−0.889563	−	0.456813i	$-0.848991\pi$
$647$		−	2.47447e8i		−	0.913627i	0.889563	−	0.456813i	$-0.151009\pi$
$648$	−1.39562e8	+	1.34721e8i	−0.512912	+	0.495118i
$649$	1.81894e8			0.665404
$650$	−2.36786e8	+	2.34016e8i	−0.862215	+	0.852129i
$651$	1.11331e8			0.403528
$652$	−1.10935e6	+	9.42750e7i	−0.00400246	+	0.340137i
$653$			1.98187e8i			0.711764i	0.934531	+	0.355882i	$0.115820\pi$
$653$			1.98187e8i			0.711764i	−0.934531	+	0.355882i	$0.884180\pi$
$654$	−8.29800e7	+	8.20093e7i	−0.296647	+	0.293177i
$655$			2.25390e8i			0.802068i
$656$	2.80938e7	+	661262.i	0.0995173	+	0.00234241i
$657$	4.20110e7			0.148138
$658$	−4.33267e8	−	4.38395e8i	−1.52082	−	1.53882i
$659$	−5.71625e7			−0.199735			−0.0998677	−	0.995001i	$-0.531842\pi$
$659$	−5.71625e7			−0.199735			−0.0998677	+	0.995001i	$0.531842\pi$
$660$	4.58343e7	+	539342.i	0.159426	+	0.00187600i
$661$		−	5.04948e8i		−	1.74841i	−0.485561	−	0.874203i	$-0.661385\pi$
$661$		−	5.04948e8i		−	1.74841i	0.485561	−	0.874203i	$-0.338615\pi$
$662$	1.53460e8	+	1.55277e8i	0.528959	+	0.535220i
$663$		−	8.95938e7i		−	0.307424i
$664$	2.95783e8	−	2.85522e8i	1.01034	−	0.975293i
$665$	−2.79541e7			−0.0950563
$666$	1.34913e8	−	1.33335e8i	0.456701	−	0.451359i
$667$	−8.73374e7			−0.294322
$668$	3.30441e8	+	3.88837e6i	1.10858	+	0.0130448i
$669$			8.07893e7i			0.269821i
$670$	−1.08666e8	+	1.07395e8i	−0.361301	+	0.357074i
$671$			2.67583e8i			0.885709i
$672$	−9.79311e7	+	9.23326e7i	−0.322710	+	0.304262i
$673$	−1.59423e8			−0.523004			−0.261502	−	0.965203i	$-0.584218\pi$
$673$	−1.59423e8			−0.523004			−0.261502	+	0.965203i	$0.584218\pi$
$674$	−7.69534e6	−	7.78643e6i	−0.0251332	−	0.0254307i
$675$	−1.41958e8			−0.461580
$676$	5.33196e6	−	4.53120e8i	0.0172602	−	1.46681i
$677$		−	1.89358e8i		−	0.610265i	−0.952310	−	0.305132i	$-0.901299\pi$
$677$		−	1.89358e8i		−	0.610265i	0.952310	−	0.305132i	$-0.0987007\pi$
$678$	3.08288e7	+	3.11937e7i	0.0989163	+	0.100087i
$679$			5.35183e8i			1.70959i
$680$	−6.49036e7	−	6.72362e7i	−0.206416	−	0.213834i
$681$	1.08616e8			0.343915
$682$	−2.17788e8	+	2.15241e8i	−0.686565	+	0.678533i
$683$	6.31662e7			0.198254			0.0991272	−	0.995075i	$-0.468395\pi$
$683$	6.31662e7			0.198254			0.0991272	+	0.995075i	$0.468395\pi$
$684$	478866.	−	4.06949e7i	0.00149639	−	0.127166i
$685$		−	8.39755e7i		−	0.261265i
$686$	3.97535e6	−	3.92885e6i	0.0123141	−	0.0121701i
$687$			3.92358e7i			0.121008i
$688$	−3.80133e8	−	8.94744e6i	−1.16727	−	0.0274747i
$689$	2.98872e8			0.913752
$690$	−9.45272e6	−	9.56461e6i	−0.0287746	−	0.0291152i
$691$	−1.37266e8			−0.416033			−0.208016	−	0.978125i	$-0.566701\pi$
$691$	−1.37266e8			−0.416033			−0.208016	+	0.978125i	$0.566701\pi$
$692$	3.84130e7	+	452014.i	0.115920	+	0.00136406i
$693$			4.48561e8i			1.34779i
$694$	6.06226e7	+	6.13401e7i	0.181366	+	0.183513i
$695$		−	1.38267e8i		−	0.411873i
$696$	7.95917e7	+	8.24520e7i	0.236069	+	0.244553i
$697$	2.09718e7			0.0619350
$698$	7.57834e6	−	7.48969e6i	0.0222847	−	0.0220241i
$699$	−7.99595e7			−0.234120
$700$	3.73212e8	+	4.39166e6i	1.08808	+	0.0128037i
$701$			6.02955e8i			1.75037i	0.483784	+	0.875187i	$0.339262\pi$
$701$			6.02955e8i			1.75037i	−0.483784	+	0.875187i	$0.660738\pi$
$702$	2.31125e8	−	2.28421e8i	0.668090	−	0.660275i
$703$			3.49456e7i			0.100584i
$704$	1.30649e7	−	3.69957e8i	0.0374445	−	1.06031i
$705$	−8.08050e7			−0.230606
$706$	4.49232e6	+	4.54550e6i	0.0127661	+	0.0129172i
$707$	3.91501e8			1.10783
$708$	−823888.	+	7.00156e7i	−0.00232150	+	0.197285i
$709$			4.41370e7i			0.123841i	0.998081	+	0.0619205i	$0.0197225\pi$
$709$			4.41370e7i			0.123841i	−0.998081	+	0.0619205i	$0.980277\pi$
$710$	6.61119e7	+	6.68945e7i	0.184716	+	0.186902i
$711$			1.08169e8i			0.300951i
$712$	1.99456e7	−	1.92537e7i	0.0552595	−	0.0533425i
$713$	8.98319e7			0.247835
$714$	−7.14428e7	+	7.06070e7i	−0.196274	+	0.193978i
$715$	2.90965e8			0.796017
$716$	−4.77926e6	+	4.06150e8i	−0.0130203	+	1.10649i
$717$		−	2.18330e8i		−	0.592318i
$718$	3.22973e8	−	3.19195e8i	0.872555	−	0.862348i
$719$		−	3.59817e8i		−	0.968045i	−0.875056	−	0.484022i	$-0.839175\pi$
$719$		−	3.59817e8i		−	0.968045i	0.875056	−	0.484022i	$-0.160825\pi$
$720$	3.78028e6	−	1.60605e8i	0.0101281	−	0.430292i
$721$	−2.99555e8			−0.799229
$722$	−2.59291e8	−	2.62360e8i	−0.688931	−	0.697085i
$723$	6.93814e7			0.183581
$724$	8.64140e7	+	1.01685e6i	0.227703	+	0.00267943i
$725$		−	3.17791e8i		−	0.833926i
$726$	1.06332e7	+	1.07590e7i	0.0277878	+	0.0281167i
$727$		−	1.23355e7i		−	0.0321035i	−0.999871	−	0.0160518i	$-0.994890\pi$
$727$		−	1.23355e7i		−	0.0321035i	0.999871	−	0.0160518i	$-0.00510965\pi$
$728$	−6.14702e8	+	5.93378e8i	−1.59320	+	1.53793i
$729$	−1.75968e8			−0.454205
$730$	−2.17301e7	+	2.14759e7i	−0.0558590	+	0.0552056i
$731$	−2.83766e8			−0.726453
$732$	−1.02999e8	−	1.21201e6i	−0.262604	−	0.00309011i
$733$			3.54832e7i			0.0900972i	0.998985	+	0.0450486i	$0.0143443\pi$
$733$			3.54832e7i			0.0900972i	−0.998985	+	0.0450486i	$0.985656\pi$
$734$	−1.02636e8	+	1.01436e8i	−0.259545	+	0.256509i
$735$			5.89361e7i			0.148429i
$736$	−7.90196e7	+	7.45022e7i	−0.198199	+	0.186868i
$737$	−4.51656e8			−1.12825
$738$	2.53422e7	+	2.56421e7i	0.0630485	+	0.0637948i
$739$	−4.32139e8			−1.07076			−0.535378	−	0.844612i	$-0.679831\pi$
$739$	−4.32139e8			−1.07076			−0.535378	+	0.844612i	$0.679831\pi$
$740$	−1.62311e6	+	1.37935e8i	−0.00400545	+	0.340391i
$741$			2.83750e7i			0.0697399i
$742$	−2.35535e8	−	2.38323e8i	−0.576559	−	0.583384i
$743$		−	7.42345e8i		−	1.80984i	−0.425586	−	0.904918i	$-0.639932\pi$
$743$		−	7.42345e8i		−	1.80984i	0.425586	−	0.904918i	$-0.360068\pi$
$744$	−8.18649e7	−	8.48070e7i	−0.198783	−	0.205927i
$745$	2.83546e8			0.685732
$746$	2.03957e8	−	2.01571e8i	0.491272	−	0.485525i
$747$	5.27418e8			1.26530
$748$	3.25064e6	−	2.76246e8i	0.00776720	−	0.660071i
$749$		−	5.25265e8i		−	1.25007i
$750$	7.98938e7	−	7.89592e7i	0.189378	−	0.187163i
$751$		−	6.22745e8i		−	1.47025i	−0.677933	−	0.735124i	$-0.737124\pi$
$751$		−	6.22745e8i		−	1.47025i	0.677933	−	0.735124i	$-0.262876\pi$
$752$	−1.53561e7	+	6.52407e8i	−0.0361101	+	1.53414i
$753$	−7.17344e7			−0.168013
$754$	5.11351e8	+	5.17403e8i	1.19290	+	1.20702i
$755$	−6.67488e7			−0.155097
$756$	−3.64289e8	−	4.28667e6i	−0.843103	−	0.00992097i
$757$			8.38267e8i			1.93239i	0.257815	+	0.966194i	$0.416998\pi$
$757$			8.38267e8i			1.93239i	−0.257815	+	0.966194i	$0.583002\pi$
$758$	5.45783e8	+	5.52243e8i	1.25318	+	1.26801i
$759$		−	3.97541e7i		−	0.0909193i
$760$	2.05554e7	+	2.12942e7i	0.0468259	+	0.0485087i
$761$	−6.44538e8			−1.46250			−0.731248	−	0.682112i	$-0.761062\pi$
$761$	−6.44538e8			−1.46250			−0.731248	+	0.682112i	$0.761062\pi$
$762$	1.21553e8	−	1.20131e8i	0.274727	−	0.271513i
$763$	8.30277e8			1.86917
$764$	−2.12493e8	−	2.50045e6i	−0.476501	−	0.00560709i
$765$		−	1.19891e8i		−	0.267794i
$766$	−1.80227e8	+	1.78119e8i	−0.400990	+	0.396299i
$767$			4.44472e8i			0.985050i
$768$	1.42346e8	+	6.70471e6i	0.314241	+	0.0148012i
$769$	7.83458e8			1.72281			0.861404	−	0.507921i	$-0.169586\pi$
$769$	7.83458e8			1.72281			0.861404	+	0.507921i	$0.169586\pi$
$770$	−2.29303e8	−	2.32017e8i	−0.502271	−	0.508216i
$771$	−1.56696e8			−0.341897
$772$	−4.21107e6	+	3.57864e8i	−0.00915251	+	0.777798i
$773$		−	7.79311e7i		−	0.168722i	−0.996435	−	0.0843611i	$-0.973115\pi$
$773$		−	7.79311e7i		−	0.168722i	0.996435	−	0.0843611i	$-0.0268849\pi$
$774$	−3.42901e8	−	3.46960e8i	−0.739514	−	0.748267i
$775$			3.26868e8i			0.702210i
$776$	4.07678e8	−	3.93535e8i	0.872433	−	0.842167i
$777$	1.48269e8			0.316073
$778$	3.13251e8	−	3.09587e8i	0.665203	−	0.657421i
$779$	−6.64190e6			−0.0140501
$780$	−1.31792e6	+	1.11999e8i	−0.00277719	+	0.236011i
$781$			2.78038e8i			0.583649i
$782$	−5.76464e7	+	5.69720e7i	−0.120546	+	0.119136i
$783$			3.10193e8i			0.646170i
$784$	4.75841e8	+	1.12002e7i	0.987446	+	0.0232422i
$785$	5.99539e7			0.123939
$786$	−1.80300e8	−	1.82434e8i	−0.371302	−	0.375697i
$787$	−4.76683e8			−0.977924			−0.488962	−	0.872305i	$-0.662624\pi$
$787$	−4.76683e8			−0.977924			−0.488962	+	0.872305i	$0.662624\pi$
$788$	4.60639e8	+	5.42044e6i	0.941418	+	0.0110779i
$789$			3.26246e7i			0.0664224i
$790$	−5.52959e7	−	5.59504e7i	−0.112153	−	0.113481i
$791$		−	3.12116e8i		−	0.630648i
$792$	3.41693e8	−	3.29840e8i	0.687798	−	0.663938i
$793$	−6.53858e8			−1.31118
$794$	−4.74033e8	+	4.68488e8i	−0.946994	+	0.935916i
$795$	−4.39277e7			−0.0874253
$796$	−7.41310e8	−	8.72315e6i	−1.46981	−	0.0172955i
$797$		−	2.49479e7i		−	0.0492788i	−0.999696	−	0.0246394i	$-0.992156\pi$
$797$		−	2.49479e7i		−	0.0492788i	0.999696	−	0.0246394i	$-0.00784375\pi$
$798$	2.26264e7	−	2.23617e7i	0.0445253	−	0.0440045i
$799$			4.87016e8i			0.954779i
$800$	−2.71088e8	−	2.87525e8i	−0.529469	−	0.561573i
$801$	3.55655e7			0.0692040
$802$	2.38844e8	+	2.41671e8i	0.463010	+	0.468490i
$803$	−9.03184e7			−0.174433
$804$	2.04577e6	−	1.73853e8i	0.00393630	−	0.334515i
$805$			9.57010e7i			0.183455i
$806$	−5.25956e8	−	5.32181e8i	−1.00449	−	1.01638i
$807$			2.63676e8i			0.501707i
$808$	−2.87882e8	−	2.98228e8i	−0.545733	−	0.565345i
$809$	6.82458e8			1.28893			0.644467	−	0.764632i	$-0.277079\pi$
$809$	6.82458e8			1.28893			0.644467	+	0.764632i	$0.277079\pi$
$810$	1.28721e8	−	1.27215e8i	0.242211	−	0.239377i
$811$	3.51060e8			0.658140			0.329070	−	0.944306i	$-0.393265\pi$
$811$	3.51060e8			0.658140			0.329070	+	0.944306i	$0.393265\pi$
$812$	9.59628e6	−	8.15510e8i	0.0179240	−	1.52321i
$813$			2.00082e8i			0.372337i
$814$	−2.90047e8	+	2.86654e8i	−0.537768	+	0.531477i
$815$		−	8.79628e7i		−	0.162490i
$816$	1.06319e8	+	2.50250e6i	0.195677	+	0.00460579i
$817$	8.98706e7			0.164798
$818$	2.59263e8	+	2.62331e8i	0.473674	+	0.479281i
$819$	−1.09609e9			−1.99524
$820$	−2.62164e7	−	308493.i	−0.0475479	−	0.000559506i
$821$		−	6.38664e8i		−	1.15410i	−0.816709	−	0.577049i	$-0.804204\pi$
$821$		−	6.38664e8i		−	1.15410i	0.816709	−	0.577049i	$-0.195796\pi$
$822$	6.71758e7	+	6.79709e7i	0.120948	+	0.122379i
$823$			1.77607e8i			0.318611i	0.987229	+	0.159305i	$0.0509254\pi$
$823$			1.77607e8i			0.318611i	−0.987229	+	0.159305i	$0.949075\pi$
$824$	2.20271e8	+	2.28187e8i	0.393710	+	0.407859i
$825$	1.44651e8			0.257609
$826$	3.54425e8	−	3.50279e8i	0.628904	−	0.621547i
$827$	2.12047e7			0.0374900			0.0187450	−	0.999824i	$-0.494033\pi$
$827$	2.12047e7			0.0374900			0.0187450	+	0.999824i	$0.494033\pi$
$828$	−1.39319e8	−	1.63940e6i	−0.245426	−	0.00288798i
$829$		−	6.30661e8i		−	1.10696i	−0.832862	−	0.553480i	$-0.813299\pi$
$829$		−	6.30661e8i		−	1.10696i	0.832862	−	0.553480i	$-0.186701\pi$
$830$	−2.72806e8	+	2.69615e8i	−0.477111	+	0.471530i
$831$		−	1.97219e8i		−	0.343673i
$832$	9.04016e8	+	3.19250e7i	1.56966	+	0.0554321i
$833$	3.55211e8			0.614542
$834$	1.10606e8	+	1.11915e8i	0.190669	+	0.192926i
$835$	−3.08316e8			−0.529587
$836$	−1.02950e6	+	8.74890e7i	−0.00176201	+	0.149739i
$837$		−	3.19053e8i		−	0.544109i
$838$	−2.17411e8	−	2.19985e8i	−0.369445	−	0.373818i
$839$			9.45472e8i			1.60089i	0.599403	+	0.800447i	$0.295405\pi$
$839$			9.45472e8i			1.60089i	−0.599403	+	0.800447i	$0.704595\pi$
$840$	9.03478e7	−	8.72135e7i	0.152433	−	0.147145i
$841$	−9.95855e7			−0.167420
$842$	−1.46923e8	+	1.45204e8i	−0.246124	+	0.243245i
$843$	2.54408e8			0.424667
$844$	481457.	−	4.09152e7i	0.000800811	−	0.0680545i
$845$			4.22781e8i			0.700721i
$846$	−5.95474e8	+	5.88508e8i	−0.983448	+	0.971944i
$847$		−	1.07652e8i		−	0.177163i
$848$	−8.34800e6	+	3.54666e8i	−0.0136897	+	0.581609i
$849$	−3.12606e8			−0.510828
$850$	−2.07302e8	−	2.09756e8i	−0.337556	−	0.341552i
$851$	1.19637e8			0.194122
$852$	−1.07024e8	−	1.25937e6i	−0.173046	−	0.00203627i
$853$		−	3.08597e8i		−	0.497216i	−0.968604	−	0.248608i	$-0.920027\pi$
$853$		−	3.08597e8i		−	0.497216i	0.968604	−	0.248608i	$-0.0799731\pi$
$854$	5.15292e8	+	5.21391e8i	0.827332	+	0.837125i
$855$			3.79702e7i			0.0607497i
$856$	−4.00123e8	+	3.86242e8i	−0.637929	+	0.615798i
$857$	2.45043e8			0.389314			0.194657	−	0.980871i	$-0.437641\pi$
$857$	2.45043e8			0.389314			0.194657	+	0.980871i	$0.437641\pi$
$858$	−2.35511e8	+	2.32756e8i	−0.372862	+	0.368501i
$859$	6.90100e8			1.08876			0.544380	−	0.838839i	$-0.316765\pi$
$859$	6.90100e8			1.08876			0.544380	+	0.838839i	$0.316765\pi$
$860$	3.54730e8	+	4.17418e6i	0.557702	+	0.00656260i
$861$			2.81805e7i			0.0441509i
$862$	1.76157e8	−	1.74096e8i	0.275029	−	0.271812i
$863$		−	6.89145e8i		−	1.07221i	−0.844153	−	0.536103i	$-0.819896\pi$
$863$		−	6.89145e8i		−	1.07221i	0.844153	−	0.536103i	$-0.180104\pi$
$864$	2.64607e8	+	2.80651e8i	0.410260	+	0.435136i
$865$	−3.58410e7			−0.0553773
$866$	2.61099e8	+	2.64189e8i	0.402023	+	0.406782i
$867$	−1.25656e8			−0.192808
$868$	−9.87036e6	+	8.38802e8i	−0.0150929	+	1.28263i
$869$		−	2.32551e8i		−	0.354371i
$870$	−7.51574e7	−	7.60470e7i	−0.114134	−	0.115485i
$871$		−	1.10365e9i		−	1.67024i
$872$	−6.10526e8	−	6.32467e8i	−0.920777	−	0.953868i
$873$	7.26941e8			1.09259
$874$	1.82570e7	−	1.80434e7i	0.0273461	−	0.0270262i
$875$	−7.99397e8			−1.19327
$876$	409096.	−	3.47658e7i	0.000608573	−	0.0517177i
$877$			8.03085e8i			1.19059i	0.803507	+	0.595296i	$0.202965\pi$
$877$			8.03085e8i			1.19059i	−0.803507	+	0.595296i	$0.797035\pi$
$878$	7.60712e8	−	7.51813e8i	1.12392	−	1.11078i
$879$		−	2.86175e8i		−	0.421372i
$880$	−8.12712e6	+	3.45282e8i	−0.0119258	+	0.506670i
$881$	−4.58820e8			−0.670988			−0.335494	−	0.942042i	$-0.608903\pi$
$881$	−4.58820e8			−0.670988			−0.335494	+	0.942042i	$0.608903\pi$
$882$	4.29235e8	+	4.34316e8i	0.625590	+	0.632995i
$883$	1.80291e8			0.261874			0.130937	−	0.991391i	$-0.458201\pi$
$883$	1.80291e8			0.261874			0.130937	+	0.991391i	$0.458201\pi$
$884$	6.75026e8	+	7.94318e6i	0.977156	+	0.0114984i
$885$		−	6.53277e7i		−	0.0942469i
$886$	−2.97783e7	−	3.01308e7i	−0.0428153	−	0.0433221i
$887$			6.63542e8i			0.950818i	0.879765	+	0.475409i	$0.157700\pi$
$887$			6.63542e8i			0.950818i	−0.879765	+	0.475409i	$0.842300\pi$
$888$	−1.09026e8	−	1.12944e8i	−0.155701	−	0.161297i
$889$	−1.21623e9			−1.73105
$890$	−1.83962e7	+	1.81810e7i	−0.0260950	+	0.0257898i
$891$	5.35011e8			0.756362
$892$	−6.08690e8	−	7.16259e6i	−0.857634	−	0.0100920i
$893$		−	1.54241e8i		−	0.216594i
$894$	−2.29506e8	+	2.26821e8i	−0.321204	+	0.317447i
$895$		−	3.78956e8i		−	0.528591i
$896$	−6.86979e8	−	7.46028e8i	−0.955035	−	1.03713i
$897$	9.71419e7			0.134595
$898$	−6.74880e8	−	6.82869e8i	−0.931961	−	0.942992i
$899$	7.14242e8			0.983029
$900$	5.96521e6	−	5.06935e8i	0.00818274	−	0.695385i
$901$			2.64755e8i			0.361967i
$902$	−5.44825e7	−	5.51274e7i	−0.0742399	−	0.0751186i
$903$		−	3.81307e8i		−	0.517859i
$904$	−2.37756e8	+	2.29508e8i	−0.321830	+	0.310665i
$905$	−8.06281e7			−0.108778
$906$	5.40273e7	−	5.33953e7i	0.0726489	−	0.0717991i
$907$	2.51825e8			0.337503			0.168751	−	0.985659i	$-0.446027\pi$
$907$	2.51825e8			0.337503			0.168751	+	0.985659i	$0.446027\pi$
$908$	−9.62961e6	+	8.18343e8i	−0.0128633	+	1.09314i
$909$		−	5.31777e8i		−	0.708008i
$910$	5.66951e8	−	5.60319e8i	0.752353	−	0.743551i
$911$			1.33414e9i			1.76459i	0.470694	+	0.882297i	$0.344004\pi$
$911$			1.33414e9i			1.76459i	−0.470694	+	0.882297i	$0.655996\pi$
$912$	−3.36720e7	−	792560.i	−0.0443899	−	0.00104484i
$913$	−1.13388e9			−1.48990
$914$	−1.03860e9	−	1.05089e9i	−1.36022	−	1.37632i
$915$	9.61028e7			0.125451
$916$	−2.95614e8	−	3.47856e6i	−0.384627	−	0.00452598i
$917$			1.82539e9i			2.36726i
$918$	2.02346e8	+	2.04741e8i	0.261557	+	0.264652i
$919$		−	9.68344e8i		−	1.24762i	−0.781575	−	0.623811i	$-0.785583\pi$
$919$		−	9.68344e8i		−	1.24762i	0.781575	−	0.623811i	$-0.214417\pi$
$920$	7.29007e7	−	7.03716e7i	0.0936199	−	0.0903721i
$921$	−3.14089e8			−0.402044
$922$	8.34901e8	−	8.25134e8i	1.06523	−	1.05277i
$923$	−6.79406e8			−0.864021
$924$	3.71202e8	+	4.36801e6i	0.470538	+	0.00553692i
$925$			4.35317e8i			0.550022i
$926$	8.82662e8	−	8.72337e8i	1.11163	−	1.09863i
$927$			4.06887e8i			0.510781i
$928$	−6.28274e8	+	5.92357e8i	−0.786150	+	0.741207i
$929$	9.60464e8			1.19794			0.598968	−	0.800773i	$-0.295577\pi$
$929$	9.60464e8			1.19794			0.598968	+	0.800773i	$0.295577\pi$
$930$	7.73040e7	+	7.82190e7i	0.0961066	+	0.0972442i
$931$	−1.12498e8			−0.139410
$932$	7.08902e6	−	6.02438e8i	0.00875666	−	0.744158i
$933$			3.10330e8i			0.382102i
$934$	6.04745e8	+	6.11903e8i	0.742219	+	0.751004i
$935$			2.57750e8i			0.315328i
$936$	8.05987e8	+	8.34952e8i	0.982880	+	1.01820i
$937$	9.88309e8			1.20136			0.600681	−	0.799489i	$-0.294896\pi$
$937$	9.88309e8			1.20136			0.600681	+	0.799489i	$0.294896\pi$
$938$	−8.80061e8	+	8.69766e8i	−1.06636	+	1.05389i
$939$	4.67308e8			0.564425
$940$	7.16398e6	−	6.08809e8i	0.00862523	−	0.732989i
$941$		−	1.34529e8i		−	0.161454i	−0.996736	−	0.0807269i	$-0.974276\pi$
$941$		−	1.34529e8i		−	0.161454i	0.996736	−	0.0807269i	$-0.0257242\pi$
$942$	−4.85275e7	+	4.79598e7i	−0.0580544	+	0.0573753i
$943$			2.27386e7i			0.0271162i
$944$	−5.27445e8	−	1.24148e7i	−0.626991	−	0.0147579i
$945$	3.39898e8			0.402766
$946$	7.37194e8	+	7.45920e8i	0.870780	+	0.881087i
$947$	4.96808e8			0.584976			0.292488	−	0.956269i	$-0.405517\pi$
$947$	4.96808e8			0.584976			0.292488	+	0.956269i	$0.405517\pi$
$948$	8.95144e7	+	1.05334e6i	0.105067	+	0.00123635i
$949$		−	2.20699e8i		−	0.258227i
$950$	6.56539e7	+	6.64310e7i	0.0765755	+	0.0774819i
$951$			3.50369e8i			0.407366i
$952$	−5.25640e8	−	5.44531e8i	−0.609225	−	0.631120i
$953$	−4.73453e8			−0.547014			−0.273507	−	0.961870i	$-0.588184\pi$
$953$	−4.73453e8			−0.547014			−0.273507	+	0.961870i	$0.588184\pi$
$954$	−3.23715e8	+	3.19928e8i	−0.372836	+	0.368475i
$955$	1.98265e8			0.227633
$956$	1.64496e9	+	1.93566e7i	1.88270	+	0.0221542i
$957$		−	3.16080e8i		−	0.360629i
$958$	−8.47138e7	+	8.37228e7i	−0.0963513	+	0.0952242i
$959$		−	6.80099e8i		−	0.771110i
$960$	−1.32871e8	−	4.69228e6i	−0.150181	−	0.00530359i
$961$	1.52861e8			0.172238
$962$	−7.00459e8	−	7.08750e8i	−0.786787	−	0.796100i
$963$	−7.13470e8			−0.798908
$964$	−6.15119e6	+	5.22740e8i	−0.00686638	+	0.583518i
$965$		−	3.33903e8i		−	0.371568i
$966$	−7.65555e7	−	7.74617e7i	−0.0849269	−	0.0859321i
$967$		−	3.26806e8i		−	0.361418i	−0.983537	−	0.180709i	$-0.942161\pi$
$967$		−	3.26806e8i		−	0.361418i	0.983537	−	0.180709i	$-0.0578393\pi$
$968$	−8.20045e7	+	7.91597e7i	−0.0904090	+	0.0872726i
$969$	−2.51358e7			−0.0276263
$970$	−3.76009e8	+	3.71610e8i	−0.411986	+	0.407167i
$971$	−7.38503e8			−0.806667			−0.403333	−	0.915053i	$-0.632149\pi$
$971$	−7.38503e8			−0.806667			−0.403333	+	0.915053i	$0.632149\pi$
$972$	−8.88545e6	+	7.55103e8i	−0.00967566	+	0.822256i
$973$		−	1.11979e9i		−	1.21562i
$974$	−5.51561e8	+	5.45109e8i	−0.596921	+	0.589938i
$975$			3.53466e8i			0.381359i
$976$	1.82633e7	−	7.75919e8i	0.0196440	−	0.834578i
$977$	−8.98069e8			−0.962999			−0.481500	−	0.876446i	$-0.659908\pi$
$977$	−8.98069e8			−0.962999			−0.481500	+	0.876446i	$0.659908\pi$
$978$	7.03654e7	+	7.11982e7i	0.0752216	+	0.0761119i
$979$	−7.64614e7			−0.0814880
$980$	−4.44042e8	−	5.22514e6i	−0.471787	−	0.00555161i
$981$		−	1.12777e9i		−	1.19457i
$982$	−3.63031e8	−	3.67328e8i	−0.383362	−	0.387900i
$983$			5.63791e8i			0.593551i	0.954947	+	0.296775i	$0.0959112\pi$
$983$			5.63791e8i			0.593551i	−0.954947	+	0.296775i	$0.904089\pi$
$984$	2.14666e7	−	2.07219e7i	0.0225309	−	0.0217493i
$985$	−4.29797e8			−0.449733
$986$	−4.58339e8	+	4.52978e8i	−0.478141	+	0.472548i
$987$	−6.54422e8			−0.680622
$988$	−2.13786e8	−	2.51566e6i	−0.221670	−	0.00260844i
$989$		−	3.07672e8i		−	0.318053i
$990$	−3.15150e8	+	3.11463e8i	−0.324797	+	0.320997i
$991$		−	4.94832e8i		−	0.508437i	−0.967147	−	0.254218i	$-0.918182\pi$
$991$		−	4.94832e8i		−	0.508437i	0.967147	−	0.254218i	$-0.0818182\pi$
$992$	6.46219e8	−	6.09276e8i	0.661980	−	0.624136i
$993$	2.31792e8			0.236729
$994$	5.35426e8	+	5.41764e8i	0.545180	+	0.551633i
$995$	6.91675e8			0.702155
$996$	5.13591e6	−	4.36459e8i	0.00519803	−	0.441739i
$997$		−	2.35279e8i		−	0.237409i	−0.992930	−	0.118705i	$-0.962126\pi$
$997$		−	2.35279e8i		−	0.237409i	0.992930	−	0.118705i	$-0.0378742\pi$
$998$	4.54961e8	+	4.60347e8i	0.457702	+	0.463120i
$999$		−	4.24909e8i		−	0.426186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.7.d.b.3.4	yes	4
3.2	odd	2		72.7.b.b.19.1		4
4.3	odd	2		32.7.d.b.15.1		4
8.3	odd	2	inner	8.7.d.b.3.3	✓	4
8.5	even	2		32.7.d.b.15.2		4
12.11	even	2		288.7.b.b.271.3		4
16.3	odd	4		256.7.c.l.255.3		8
16.5	even	4		256.7.c.l.255.4		8
16.11	odd	4		256.7.c.l.255.6		8
16.13	even	4		256.7.c.l.255.5		8
24.5	odd	2		288.7.b.b.271.2		4
24.11	even	2		72.7.b.b.19.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.7.d.b.3.3	✓	4	8.3	odd	2	inner
8.7.d.b.3.4	yes	4	1.1	even	1	trivial
32.7.d.b.15.1		4	4.3	odd	2
32.7.d.b.15.2		4	8.5	even	2
72.7.b.b.19.1		4	3.2	odd	2
72.7.b.b.19.2		4	24.11	even	2
256.7.c.l.255.3		8	16.3	odd	4
256.7.c.l.255.4		8	16.5	even	4
256.7.c.l.255.5		8	16.13	even	4
256.7.c.l.255.6		8	16.11	odd	4
288.7.b.b.271.2		4	24.5	odd	2
288.7.b.b.271.3		4	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.62348 + 5.69004i) q^{2} +8.49390 q^{3} +(-0.753049 + 63.9956i) q^{4} -59.7107i q^{5} +(47.7652 + 48.3306i) q^{6} -483.584i q^{7} +(-368.372 + 355.593i) q^{8} -656.854 q^{9} +O(q^{10})\)	\(q+(5.62348 + 5.69004i) q^{2} +8.49390 q^{3} +(-0.753049 + 63.9956i) q^{4} -59.7107i q^{5} +(47.7652 + 48.3306i) q^{6} -483.584i q^{7} +(-368.372 + 355.593i) q^{8} -656.854 q^{9} +(339.756 - 335.782i) q^{10} +1412.15 q^{11} +(-6.39633 + 543.572i) q^{12} +3450.70i q^{13} +(2751.61 - 2719.42i) q^{14} -507.177i q^{15} +(-4094.87 - 96.3836i) q^{16} -3056.78 q^{17} +(-3693.80 - 3737.52i) q^{18} +968.104 q^{19} +(3821.22 + 44.9651i) q^{20} -4107.51i q^{21} +(7941.20 + 8035.20i) q^{22} -3314.31i q^{23} +(-3128.91 + 3020.37i) q^{24} +12059.6 q^{25} +(-19634.6 + 19404.9i) q^{26} -11771.3 q^{27} +(30947.2 + 364.162i) q^{28} -26351.6i q^{29} +(2885.85 - 2852.10i) q^{30} +27104.3i q^{31} +(-22479.0 - 23842.0i) q^{32} +11994.7 q^{33} +(-17189.7 - 17393.2i) q^{34} -28875.1 q^{35} +(494.643 - 42035.7i) q^{36} +36097.0i q^{37} +(5444.11 + 5508.55i) q^{38} +29309.9i q^{39} +(21232.7 + 21995.7i) q^{40} -6860.73 q^{41} +(23371.9 - 23098.5i) q^{42} +92831.6 q^{43} +(-1063.42 + 90371.5i) q^{44} +39221.2i q^{45} +(18858.5 - 18637.9i) q^{46} -159323. i q^{47} +(-34781.4 - 818.673i) q^{48} -116204. q^{49} +(67817.1 + 68619.8i) q^{50} -25964.0 q^{51} +(-220829. - 2598.54i) q^{52} -86612.3i q^{53} +(-66195.6 - 66979.2i) q^{54} -84320.6i q^{55} +(171959. + 178139. i) q^{56} +8222.98 q^{57} +(149942. - 148188. i) q^{58} +128806. q^{59} +(32457.1 + 381.929i) q^{60} +189486. i q^{61} +(-154224. + 152420. i) q^{62} +317644. i q^{63} +(9251.76 - 261981. i) q^{64} +206043. q^{65} +(67451.8 + 68250.2i) q^{66} -319835. q^{67} +(2301.91 - 195620. i) q^{68} -28151.4i q^{69} +(-162379. - 164301. i) q^{70} +196890. i q^{71} +(241966. - 233572. i) q^{72} -63957.9 q^{73} +(-205393. + 202991. i) q^{74} +102433. q^{75} +(-729.030 + 61954.3i) q^{76} -682894. i q^{77} +(-166774. + 164823. i) q^{78} -164678. i q^{79} +(-5755.13 + 244507. i) q^{80} +378862. q^{81} +(-38581.2 - 39037.8i) q^{82} -802946. q^{83} +(262863. + 3093.16i) q^{84} +182522. i q^{85} +(522036. + 528215. i) q^{86} -223828. i q^{87} +(-520197. + 502151. i) q^{88} -54145.3 q^{89} +(-223170. + 220559. i) q^{90} +1.66870e6 q^{91} +(212101. + 2495.84i) q^{92} +230221. i q^{93} +(906555. - 895950. i) q^{94} -57806.1i q^{95} +(-190934. - 202511. i) q^{96} -1.10670e6 q^{97} +(-653472. - 661207. i) q^{98} -927577. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 48 q^{3} - 44 q^{4} + 396 q^{6} + 248 q^{8} - 660 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 48 * q^3 - 44 * q^4 + 396 * q^6 + 248 * q^8 - 660 * q^9	\( 4 q + 2 q^{2} - 48 q^{3} - 44 q^{4} + 396 q^{6} + 248 q^{8} - 660 q^{9} - 1920 q^{10} + 976 q^{11} + 1368 q^{12} + 5760 q^{14} - 14576 q^{16} + 4168 q^{17} - 10410 q^{18} - 1456 q^{19} + 31680 q^{20} + 24428 q^{22} - 38256 q^{24} - 23900 q^{25} - 59520 q^{26} + 2592 q^{27} + 59520 q^{28} + 90240 q^{30} - 48928 q^{32} + 84048 q^{33} - 81916 q^{34} - 49920 q^{35} - 12900 q^{36} + 26572 q^{38} - 13440 q^{40} - 117944 q^{41} + 38400 q^{42} + 197456 q^{43} + 37144 q^{44} - 213120 q^{46} + 137952 q^{48} + 2116 q^{49} + 357650 q^{50} - 386016 q^{51} - 254400 q^{52} - 253224 q^{54} + 349440 q^{56} + 126672 q^{57} + 516480 q^{58} + 542032 q^{59} - 716160 q^{60} - 407040 q^{62} + 463936 q^{64} - 205440 q^{65} - 142776 q^{66} - 790192 q^{67} - 213848 q^{68} - 360960 q^{70} + 805800 q^{72} + 443912 q^{73} - 32640 q^{74} + 1765200 q^{75} + 70616 q^{76} + 324480 q^{78} - 1032960 q^{80} - 568044 q^{81} + 404708 q^{82} - 3465008 q^{83} + 602880 q^{84} + 989548 q^{86} - 1950448 q^{88} + 761224 q^{89} - 1296000 q^{90} + 3398400 q^{91} + 2743680 q^{92} + 971520 q^{94} - 252864 q^{96} - 926776 q^{97} - 2391262 q^{98} - 2459280 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 48 * q^3 - 44 * q^4 + 396 * q^6 + 248 * q^8 - 660 * q^9 - 1920 * q^10 + 976 * q^11 + 1368 * q^12 + 5760 * q^14 - 14576 * q^16 + 4168 * q^17 - 10410 * q^18 - 1456 * q^19 + 31680 * q^20 + 24428 * q^22 - 38256 * q^24 - 23900 * q^25 - 59520 * q^26 + 2592 * q^27 + 59520 * q^28 + 90240 * q^30 - 48928 * q^32 + 84048 * q^33 - 81916 * q^34 - 49920 * q^35 - 12900 * q^36 + 26572 * q^38 - 13440 * q^40 - 117944 * q^41 + 38400 * q^42 + 197456 * q^43 + 37144 * q^44 - 213120 * q^46 + 137952 * q^48 + 2116 * q^49 + 357650 * q^50 - 386016 * q^51 - 254400 * q^52 - 253224 * q^54 + 349440 * q^56 + 126672 * q^57 + 516480 * q^58 + 542032 * q^59 - 716160 * q^60 - 407040 * q^62 + 463936 * q^64 - 205440 * q^65 - 142776 * q^66 - 790192 * q^67 - 213848 * q^68 - 360960 * q^70 + 805800 * q^72 + 443912 * q^73 - 32640 * q^74 + 1765200 * q^75 + 70616 * q^76 + 324480 * q^78 - 1032960 * q^80 - 568044 * q^81 + 404708 * q^82 - 3465008 * q^83 + 602880 * q^84 + 989548 * q^86 - 1950448 * q^88 + 761224 * q^89 - 1296000 * q^90 + 3398400 * q^91 + 2743680 * q^92 + 971520 * q^94 - 252864 * q^96 - 926776 * q^97 - 2391262 * q^98 - 2459280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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