LMFDB - Embedded newform 24.8.d.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.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:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 $ x^14 - 6x^13 - 52x^12 + 300x^11 - 1005x^10 - 23250x^9 + 349930x^8 + 2867784x^7 - 20463993x^6 - 78987210x^5 + 94608296x^4 - 6477861300x^3 - 21982316987x^2 + 613270661346*x + 3813237677250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.7
Root			$-5.80663 - 4.20354i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.8.d.a.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60309 - 11.0102i) q^{2} -27.0000i q^{3} +(-114.448 + 57.3210i) q^{4} +468.400i q^{5} +(-297.275 + 70.2836i) q^{6} +81.2421 q^{7} +(929.033 + 1110.88i) q^{8} -729.000 q^{9} +O(q^{10})$	\(q+(-2.60309 - 11.0102i) q^{2} -27.0000i q^{3} +(-114.448 + 57.3210i) q^{4} +468.400i q^{5} +(-297.275 + 70.2836i) q^{6} +81.2421 q^{7} +(929.033 + 1110.88i) q^{8} -729.000 q^{9} +(5157.17 - 1219.29i) q^{10} -3394.58i q^{11} +(1547.67 + 3090.09i) q^{12} +14492.5i q^{13} +(-211.481 - 894.489i) q^{14} +12646.8 q^{15} +(9812.60 - 13120.5i) q^{16} +5178.19 q^{17} +(1897.66 + 8026.42i) q^{18} +46067.9i q^{19} +(-26849.2 - 53607.4i) q^{20} -2193.54i q^{21} +(-37374.9 + 8836.41i) q^{22} -67535.4 q^{23} +(29993.7 - 25083.9i) q^{24} -141274. q^{25} +(159565. - 37725.4i) q^{26} +19683.0i q^{27} +(-9297.97 + 4656.88i) q^{28} +25387.3i q^{29} +(-32920.8 - 139244. i) q^{30} +123808. q^{31} +(-170002. - 73884.4i) q^{32} -91653.7 q^{33} +(-13479.3 - 57012.8i) q^{34} +38053.8i q^{35} +(83432.4 - 41787.0i) q^{36} +104623. i q^{37} +(507216. - 119919. i) q^{38} +391298. q^{39} +(-520336. + 435159. i) q^{40} -160655. q^{41} +(-24151.2 + 5709.98i) q^{42} +378823. i q^{43} +(194581. + 388502. i) q^{44} -341464. i q^{45} +(175801. + 743577. i) q^{46} +683674. q^{47} +(-354254. - 264940. i) q^{48} -816943. q^{49} +(367749. + 1.55545e6i) q^{50} -139811. i q^{51} +(-830726. - 1.65864e6i) q^{52} -1.74261e6i q^{53} +(216713. - 51236.7i) q^{54} +1.59002e6 q^{55} +(75476.6 + 90250.0i) q^{56} +1.24383e6 q^{57} +(279518. - 66085.5i) q^{58} -1.48196e6i q^{59} +(-1.44740e6 + 724928. i) q^{60} +444587. i q^{61} +(-322284. - 1.36315e6i) q^{62} -59225.5 q^{63} +(-370947. + 2.06408e6i) q^{64} -6.78830e6 q^{65} +(238583. + 1.00912e6i) q^{66} -2.48180e6i q^{67} +(-592632. + 296819. i) q^{68} +1.82346e6i q^{69} +(418979. - 99057.7i) q^{70} -510618. q^{71} +(-677265. - 809830. i) q^{72} +4.80319e6 q^{73} +(1.15191e6 - 272342. i) q^{74} +3.81440e6i q^{75} +(-2.64066e6 - 5.27237e6i) q^{76} -275783. i q^{77} +(-1.01859e6 - 4.30826e6i) q^{78} +1.57434e6 q^{79} +(6.14566e6 + 4.59622e6i) q^{80} +531441. q^{81} +(418201. + 1.76884e6i) q^{82} +7.91066e6i q^{83} +(125736. + 251045. i) q^{84} +2.42547e6i q^{85} +(4.17091e6 - 986113. i) q^{86} +685456. q^{87} +(3.77096e6 - 3.15368e6i) q^{88} +6.35526e6 q^{89} +(-3.75958e6 + 888863. i) q^{90} +1.17740e6i q^{91} +(7.72928e6 - 3.87120e6i) q^{92} -3.34282e6i q^{93} +(-1.77967e6 - 7.52737e6i) q^{94} -2.15782e7 q^{95} +(-1.99488e6 + 4.59007e6i) q^{96} -3.68231e6 q^{97} +(2.12658e6 + 8.99468e6i) q^{98} +2.47465e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−2.60309	−	11.0102i	−0.230083	−	0.973171i
$2$	−2.60309	−	11.0102i	−0.230083	−	0.973171i
$3$		−	27.0000i		−	0.577350i
$3$		−	27.0000i		−	0.577350i
$4$	−114.448	+	57.3210i	−0.894123	+	0.447821i
$5$			468.400i			1.67580i	0.545824	+	0.837900i	$0.316217\pi$
$5$			468.400i			1.67580i	−0.545824	+	0.837900i	$0.683783\pi$
$6$	−297.275	+	70.2836i	−0.561861	+	0.132839i
$7$	81.2421			0.0895237			0.0447618	−	0.998998i	$-0.485747\pi$
$7$	81.2421			0.0895237			0.0447618	+	0.998998i	$0.485747\pi$
$8$	929.033	+	1110.88i	0.641529	+	0.767099i
$9$	−729.000			−0.333333
$10$	5157.17	−	1219.29i	1.63084	−	0.385574i
$11$		−	3394.58i		−	0.768974i	−0.923130	−	0.384487i	$-0.874378\pi$
$11$		−	3394.58i		−	0.768974i	0.923130	−	0.384487i	$-0.125622\pi$
$12$	1547.67	+	3090.09i	0.258549	+	0.516222i
$13$			14492.5i			1.82954i	0.403975	+	0.914770i	$0.367628\pi$
$13$			14492.5i			1.82954i	−0.403975	+	0.914770i	$0.632372\pi$
$14$	−211.481	−	894.489i	−0.0205979	−	0.0871218i
$15$	12646.8			0.967524
$16$	9812.60	−	13120.5i	0.598913	−	0.800814i
$17$	5178.19			0.255627			0.127814	−	0.991798i	$-0.459204\pi$
$17$	5178.19			0.255627			0.127814	+	0.991798i	$0.459204\pi$
$18$	1897.66	+	8026.42i	0.0766944	+	0.324390i
$19$			46067.9i			1.54085i	0.637529	+	0.770426i	$0.279956\pi$
$19$			46067.9i			1.54085i	−0.637529	+	0.770426i	$0.720044\pi$
$20$	−26849.2	−	53607.4i	−0.750458	−	1.49837i
$21$		−	2193.54i		−	0.0516865i
$22$	−37374.9	+	8836.41i	−0.748343	+	0.176928i
$23$	−67535.4			−1.15740			−0.578701	−	0.815540i	$-0.696440\pi$
$23$	−67535.4			−1.15740			−0.578701	+	0.815540i	$0.696440\pi$
$24$	29993.7	−	25083.9i	0.442885	−	0.370387i
$25$	−141274.			−1.80831
$26$	159565.	−	37725.4i	1.78046	−	0.420947i
$27$			19683.0i			0.192450i
$28$	−9297.97	+	4656.88i	−0.0800452	+	0.0400905i
$29$			25387.3i			0.193296i	0.995319	+	0.0966480i	$0.0308121\pi$
$29$			25387.3i			0.193296i	−0.995319	+	0.0966480i	$0.969188\pi$
$30$	−32920.8	−	139244.i	−0.222611	−	0.941566i
$31$	123808.			0.746419			0.373210	−	0.927747i	$-0.378257\pi$
$31$	123808.			0.746419			0.373210	+	0.927747i	$0.378257\pi$
$32$	−170002.	−	73884.4i	−0.917129	−	0.398591i
$33$	−91653.7			−0.443967
$34$	−13479.3	−	57012.8i	−0.0588155	−	0.248769i
$35$			38053.8i			0.150024i
$36$	83432.4	−	41787.0i	0.298041	−	0.149274i
$37$			104623.i			0.339562i	0.985482	+	0.169781i	$0.0543061\pi$
$37$			104623.i			0.339562i	−0.985482	+	0.169781i	$0.945694\pi$
$38$	507216.	−	119919.i	1.49951	−	0.354524i
$39$	391298.			1.05629
$40$	−520336.	+	435159.i	−1.28550	+	1.07507i
$41$	−160655.			−0.364042			−0.182021	−	0.983295i	$-0.558264\pi$
$41$	−160655.			−0.364042			−0.182021	+	0.983295i	$0.558264\pi$
$42$	−24151.2	+	5709.98i	−0.0502998	+	0.0118922i
$43$			378823.i			0.726603i	0.931672	+	0.363301i	$0.118350\pi$
$43$			378823.i			0.726603i	−0.931672	+	0.363301i	$0.881650\pi$
$44$	194581.	+	388502.i	0.344362	+	0.687558i
$45$		−	341464.i		−	0.558600i
$46$	175801.	+	743577.i	0.266299	+	1.12635i
$47$	683674.			0.960520			0.480260	−	0.877126i	$-0.340542\pi$
$47$	683674.			0.960520			0.480260	+	0.877126i	$0.340542\pi$
$48$	−354254.	−	264940.i	−0.462350	−	0.345783i
$49$	−816943.			−0.991986
$50$	367749.	+	1.55545e6i	0.416061	+	1.75979i
$51$		−	139811.i		−	0.147586i
$52$	−830726.	−	1.65864e6i	−0.819306	−	1.63583i
$53$		−	1.74261e6i		−	1.60781i	−0.594757	−	0.803906i	$-0.702752\pi$
$53$		−	1.74261e6i		−	1.60781i	0.594757	−	0.803906i	$-0.297248\pi$
$54$	216713.	−	51236.7i	0.187287	−	0.0442795i
$55$	1.59002e6			1.28865
$56$	75476.6	+	90250.0i	0.0574320	+	0.0686735i
$57$	1.24383e6			0.889611
$58$	279518.	−	66085.5i	0.188110	−	0.0444742i
$59$		−	1.48196e6i		−	0.939406i	−0.882824	−	0.469703i	$-0.844361\pi$
$59$		−	1.48196e6i		−	0.939406i	0.882824	−	0.469703i	$-0.155639\pi$
$60$	−1.44740e6	+	724928.i	−0.865086	+	0.433277i
$61$			444587.i			0.250785i	0.992107	+	0.125393i	$0.0400191\pi$
$61$			444587.i			0.250785i	−0.992107	+	0.125393i	$0.959981\pi$
$62$	−322284.	−	1.36315e6i	−0.171739	−	0.726393i
$63$	−59225.5			−0.0298412
$64$	−370947.	+	2.06408e6i	−0.176881	+	0.984232i
$65$	−6.78830e6			−3.06594
$66$	238583.	+	1.00912e6i	0.102149	+	0.432056i
$67$		−	2.48180e6i		−	1.00810i	−0.863674	−	0.504051i	$-0.831842\pi$
$67$		−	2.48180e6i		−	1.00810i	0.863674	−	0.504051i	$-0.168158\pi$
$68$	−592632.	+	296819.i	−0.228562	+	0.114475i
$69$			1.82346e6i			0.668226i
$70$	418979.	−	99057.7i	0.145999	−	0.0345180i
$71$	−510618.			−0.169313			−0.0846567	−	0.996410i	$-0.526979\pi$
$71$	−510618.			−0.169313			−0.0846567	+	0.996410i	$0.526979\pi$
$72$	−677265.	−	809830.i	−0.213843	−	0.255700i
$73$	4.80319e6			1.44511			0.722553	−	0.691315i	$-0.242968\pi$
$73$	4.80319e6			1.44511			0.722553	+	0.691315i	$0.242968\pi$
$74$	1.15191e6	−	272342.i	0.330452	−	0.0781276i
$75$			3.81440e6i			1.04403i
$76$	−2.64066e6	−	5.27237e6i	−0.690025	−	1.37771i
$77$		−	275783.i		−	0.0688414i
$78$	−1.01859e6	−	4.30826e6i	−0.243034	−	1.02795i
$79$	1.57434e6			0.359255			0.179627	−	0.983735i	$-0.442511\pi$
$79$	1.57434e6			0.359255			0.179627	+	0.983735i	$0.442511\pi$
$80$	6.14566e6	+	4.59622e6i	1.34200	+	1.00366i
$81$	531441.			0.111111
$82$	418201.	+	1.76884e6i	0.0837600	+	0.354275i
$83$			7.91066e6i			1.51859i	0.650749	+	0.759293i	$0.274455\pi$
$83$			7.91066e6i			1.51859i	−0.650749	+	0.759293i	$0.725545\pi$
$84$	125736.	+	251045.i	0.0231463	+	0.0462141i
$85$			2.42547e6i			0.428380i
$86$	4.17091e6	−	986113.i	0.707109	−	0.167179i
$87$	685456.			0.111600
$88$	3.77096e6	−	3.15368e6i	0.589879	−	0.493319i
$89$	6.35526e6			0.955583			0.477791	−	0.878473i	$-0.341437\pi$
$89$	6.35526e6			0.955583			0.477791	+	0.878473i	$0.341437\pi$
$90$	−3.75958e6	+	888863.i	−0.543613	+	0.128525i
$91$			1.17740e6i			0.163787i
$92$	7.72928e6	−	3.87120e6i	1.03486	−	0.518308i
$93$		−	3.34282e6i		−	0.430945i
$94$	−1.77967e6	−	7.52737e6i	−0.221000	−	0.934750i
$95$	−2.15782e7			−2.58216
$96$	−1.99488e6	+	4.59007e6i	−0.230127	+	0.529505i
$97$	−3.68231e6			−0.409656			−0.204828	−	0.978798i	$-0.565664\pi$
$97$	−3.68231e6			−0.409656			−0.204828	+	0.978798i	$0.565664\pi$
$98$	2.12658e6	+	8.99468e6i	0.228239	+	0.965371i
$99$			2.47465e6i			0.256325i
$100$	1.61685e7	−	8.09797e6i	1.61685	−	0.809797i
$101$			1.61014e6i			0.155503i	0.996973	+	0.0777514i	$0.0247740\pi$
$101$			1.61014e6i			0.155503i	−0.996973	+	0.0777514i	$0.975226\pi$
$102$	−1.53934e6	+	363942.i	−0.143627	+	0.0339571i
$103$	392152.			0.0353609			0.0176805	−	0.999844i	$-0.494372\pi$
$103$	392152.			0.0353609			0.0176805	+	0.999844i	$0.494372\pi$
$104$	−1.60994e7	+	1.34640e7i	−1.40344	+	1.17370i
$105$	1.02745e6			0.0866163
$106$	−1.91865e7	+	4.53618e6i	−1.56468	+	0.369930i
$107$		−	1.62922e7i		−	1.28569i	−0.765998	−	0.642843i	$-0.777755\pi$
$107$		−	1.62922e7i		−	1.28569i	0.765998	−	0.642843i	$-0.222245\pi$
$108$	−1.12825e6	−	2.25268e6i	−0.0861831	−	0.172074i
$109$			2.39639e7i			1.77241i	0.463294	+	0.886205i	$0.346667\pi$
$109$			2.39639e7i			1.77241i	−0.463294	+	0.886205i	$0.653333\pi$
$110$	−4.13898e6	−	1.75064e7i	−0.296496	−	1.25407i
$111$	2.82481e6			0.196046
$112$	797195.	−	1.06594e6i	0.0536169	−	0.0716918i
$113$	1.91168e7			1.24635			0.623176	−	0.782081i	$-0.285842\pi$
$113$	1.91168e7			1.24635			0.623176	+	0.782081i	$0.285842\pi$
$114$	−3.23782e6	−	1.36948e7i	−0.204685	−	0.865744i
$115$		−	3.16336e7i		−	1.93957i
$116$	−1.45522e6	−	2.90552e6i	−0.0865620	−	0.172831i
$117$		−	1.05650e7i		−	0.609847i
$118$	−1.63166e7	+	3.85767e6i	−0.914203	+	0.216142i
$119$	420687.			0.0228847
$120$	1.17493e7	+	1.40491e7i	0.620694	+	0.742186i
$121$	7.96400e6			0.408679
$122$	4.89498e6	−	1.15730e6i	0.244057	−	0.0577015i
$123$			4.33770e6i			0.210180i
$124$	−1.41696e7	+	7.09680e6i	−0.667391	+	0.334262i
$125$		−	2.95790e7i		−	1.35456i
$126$	154169.	+	652083.i	0.00686596	+	0.0290406i
$127$	−1.67337e7			−0.724901			−0.362451	−	0.932003i	$-0.618060\pi$
$127$	−1.67337e7			−0.724901			−0.362451	+	0.932003i	$0.618060\pi$
$128$	2.36915e7	−	1.28881e6i	0.998524	−	0.0543195i
$129$	1.02282e7			0.419504
$130$	1.76706e7	+	7.47403e7i	0.705422	+	2.98369i
$131$			2.21897e7i			0.862386i	0.902260	+	0.431193i	$0.141907\pi$
$131$			2.21897e7i			0.862386i	−0.902260	+	0.431193i	$0.858093\pi$
$132$	1.04896e7	−	5.25368e6i	0.396962	−	0.198818i
$133$			3.74265e6i			0.137943i
$134$	−2.73250e7	+	6.46035e6i	−0.981056	+	0.231947i
$135$	−9.21953e6			−0.322508
$136$	4.81071e6	+	5.75234e6i	0.163992	+	0.196091i
$137$	−582593.			−0.0193572			−0.00967862	−	0.999953i	$-0.503081\pi$
$137$	−582593.			−0.0193572			−0.00967862	+	0.999953i	$0.503081\pi$
$138$	2.00766e7	−	4.74663e6i	0.650298	−	0.153748i
$139$		−	3.81869e6i		−	0.120604i	−0.998180	−	0.0603021i	$-0.980794\pi$
$139$		−	3.81869e6i		−	0.120604i	0.998180	−	0.0603021i	$-0.0192064\pi$
$140$	−2.18128e6	−	4.35518e6i	−0.0671837	−	0.134140i
$141$		−	1.84592e7i		−	0.554557i
$142$	1.32919e6	+	5.62199e6i	0.0389562	+	0.164771i
$143$	4.91960e7			1.40687
$144$	−7.15338e6	+	9.56487e6i	−0.199638	+	0.266938i
$145$	−1.18914e7			−0.323926
$146$	−1.25032e7	−	5.28840e7i	−0.332495	−	1.40634i
$147$			2.20575e7i			0.572723i
$148$	−5.99707e6	−	1.19738e7i	−0.152063	−	0.303611i
$149$		−	8.12196e6i		−	0.201145i	−0.994930	−	0.100572i	$-0.967933\pi$
$149$		−	8.12196e6i		−	0.201145i	0.994930	−	0.100572i	$-0.0320674\pi$
$150$	4.19972e7	−	9.92924e6i	1.01602	−	0.240213i
$151$	2.00853e7			0.474744			0.237372	−	0.971419i	$-0.423714\pi$
$151$	2.00853e7			0.474744			0.237372	+	0.971419i	$0.423714\pi$
$152$	−5.11758e7	+	4.27986e7i	−1.18199	+	0.988501i
$153$	−3.77490e6			−0.0852090
$154$	−3.03641e6	+	717888.i	−0.0669944	+	0.0158392i
$155$			5.79917e7i			1.25085i
$156$	−4.47832e7	+	2.24296e7i	−0.944450	+	0.473026i
$157$			7.13959e7i			1.47239i	0.676767	+	0.736197i	$0.263380\pi$
$157$			7.13959e7i			1.47239i	−0.676767	+	0.736197i	$0.736620\pi$
$158$	−4.09815e6	−	1.73337e7i	−0.0826585	−	0.349616i
$159$	−4.70505e7			−0.928270
$160$	3.46075e7	−	7.96292e7i	0.667959	−	1.53692i
$161$	−5.48672e6			−0.103615
$162$	−1.38339e6	−	5.85126e6i	−0.0255648	−	0.108130i
$163$		−	7.14988e7i		−	1.29313i	−0.762859	−	0.646565i	$-0.776205\pi$
$163$		−	7.14988e7i		−	1.29313i	0.762859	−	0.646565i	$-0.223795\pi$
$164$	1.83867e7	−	9.20893e6i	0.325499	−	0.163026i
$165$		−	4.29306e7i		−	0.744001i
$166$	8.70978e7	−	2.05922e7i	1.47784	−	0.349401i
$167$	7.80714e7			1.29713			0.648566	−	0.761158i	$-0.275369\pi$
$167$	7.80714e7			1.29713			0.648566	+	0.761158i	$0.275369\pi$
$168$	2.43675e6	−	2.03787e6i	0.0396487	−	0.0331584i
$169$	−1.47284e8			−2.34722
$170$	2.67048e7	−	6.31372e6i	0.416887	−	0.0985630i
$171$		−	3.35835e7i		−	0.513617i
$172$	−2.17145e7	−	4.33555e7i	−0.325388	−	0.649673i
$173$			4.84863e7i			0.711963i	0.934493	+	0.355981i	$0.115853\pi$
$173$			4.84863e7i			0.711963i	−0.934493	+	0.355981i	$0.884147\pi$
$174$	−1.78431e6	−	7.54699e6i	−0.0256772	−	0.108605i
$175$	−1.14774e7			−0.161886
$176$	−4.45387e7	−	3.33096e7i	−0.615805	−	0.460549i
$177$	−4.00128e7			−0.542366
$178$	−1.65433e7	−	6.99725e7i	−0.219864	−	0.929946i
$179$			7.56733e7i			0.986182i	0.869978	+	0.493091i	$0.164133\pi$
$179$			7.56733e7i			0.986182i	−0.869978	+	0.493091i	$0.835867\pi$
$180$	1.95731e7	+	3.90798e7i	0.250153	+	0.499457i
$181$			2.01200e7i			0.252204i	0.992017	+	0.126102i	$0.0402467\pi$
$181$			2.01200e7i			0.252204i	−0.992017	+	0.126102i	$0.959753\pi$
$182$	1.29634e7	−	3.06489e6i	0.159393	−	0.0376847i
$183$	1.20038e7			0.144791
$184$	−6.27426e7	−	7.50236e7i	−0.742507	−	0.887842i
$185$	−4.90053e7			−0.569038
$186$	−3.68050e7	+	8.70167e6i	−0.419383	+	0.0991533i
$187$		−	1.75778e7i		−	0.196571i
$188$	−7.82450e7	+	3.91889e7i	−0.858824	+	0.430141i
$189$			1.59909e6i			0.0172288i
$190$	5.61702e7	+	2.37580e8i	0.594112	+	2.51288i
$191$	−3.28127e7			−0.340741			−0.170371	−	0.985380i	$-0.554496\pi$
$191$	−3.28127e7			−0.340741			−0.170371	+	0.985380i	$0.554496\pi$
$192$	5.57303e7	+	1.00156e7i	0.568247	+	0.102123i
$193$	9.98286e7			0.999550			0.499775	−	0.866155i	$-0.333416\pi$
$193$	9.98286e7			0.999550			0.499775	+	0.866155i	$0.333416\pi$
$194$	9.58541e6	+	4.05429e7i	0.0942551	+	0.398666i
$195$			1.83284e8i			1.77012i
$196$	9.34973e7	−	4.68280e7i	0.886957	−	0.444232i
$197$		−	8.59728e7i		−	0.801179i	−0.916258	−	0.400589i	$-0.868805\pi$
$197$		−	8.59728e7i		−	0.801179i	0.916258	−	0.400589i	$-0.131195\pi$
$198$	2.72463e7	−	6.44175e6i	0.249448	−	0.0589760i
$199$	1.62250e8			1.45948			0.729741	−	0.683724i	$-0.239641\pi$
$199$	1.62250e8			1.45948			0.729741	+	0.683724i	$0.239641\pi$
$200$	−1.31248e8	−	1.56938e8i	−1.16008	−	1.38715i
$201$	−6.70085e7			−0.582028
$202$	1.77279e7	−	4.19134e6i	0.151331	−	0.0357786i
$203$			2.06251e6i			0.0173046i
$204$	8.01412e6	+	1.60011e7i	0.0660922	+	0.131960i
$205$		−	7.52511e7i		−	0.610062i
$206$	−1.02081e6	−	4.31766e6i	−0.00813596	−	0.0344122i
$207$	4.92333e7			0.385801
$208$	1.90150e8	+	1.42209e8i	1.46512	+	1.09574i
$209$	1.56381e8			1.18488
$210$	−2.67456e6	−	1.13124e7i	−0.0199289	−	0.0842924i
$211$		−	2.14780e8i		−	1.57400i	−0.616953	−	0.787000i	$-0.711633\pi$
$211$		−	2.14780e8i		−	1.57400i	0.616953	−	0.787000i	$-0.288367\pi$
$212$	9.98883e7	+	1.99438e8i	0.720011	+	1.43758i
$213$			1.37867e7i			0.0977532i
$214$	−1.79379e8	+	4.24100e7i	−1.25119	+	0.295815i
$215$	−1.77441e8			−1.21764
$216$	−2.18654e7	+	1.82862e7i	−0.147628	+	0.123462i
$217$	1.00584e7			0.0668222
$218$	2.63846e8	−	6.23802e7i	1.72486	−	0.407802i
$219$		−	1.29686e8i		−	0.834333i
$220$	−1.81975e8	+	9.11418e7i	−1.15221	+	0.577083i
$221$			7.50450e7i			0.467680i
$222$	−7.35325e6	−	3.11016e7i	−0.0451070	−	0.190787i
$223$	1.26786e8			0.765603			0.382802	−	0.923831i	$-0.374959\pi$
$223$	1.26786e8			0.765603			0.382802	+	0.923831i	$0.374959\pi$
$224$	−1.38114e7	−	6.00252e6i	−0.0821047	−	0.0356833i
$225$	1.02989e8			0.602769
$226$	−4.97629e7	−	2.10479e8i	−0.286765	−	1.21291i
$227$		−	1.99430e8i		−	1.13162i	−0.824536	−	0.565810i	$-0.808564\pi$
$227$		−	1.99430e8i		−	1.13162i	0.824536	−	0.565810i	$-0.191436\pi$
$228$	−1.42354e8	+	7.12978e7i	−0.795422	+	0.398386i
$229$			3.66567e7i			0.201711i	0.994901	+	0.100856i	$0.0321580\pi$
$229$			3.66567e7i			0.201711i	−0.994901	+	0.100856i	$0.967842\pi$
$230$	−3.48292e8	+	8.23453e7i	−1.88754	+	0.446264i
$231$	−7.44613e6			−0.0397456
$232$	−2.82022e7	+	2.35856e7i	−0.148277	+	0.124005i
$233$	9.86007e7			0.510663			0.255331	−	0.966854i	$-0.417815\pi$
$233$	9.86007e7			0.510663			0.255331	+	0.966854i	$0.417815\pi$
$234$	−1.16323e8	+	2.75018e7i	−0.593485	+	0.140316i
$235$			3.20233e8i			1.60964i
$236$	8.49473e7	+	1.69607e8i	0.420685	+	0.839945i
$237$		−	4.25071e7i		−	0.207416i
$238$	−1.09509e6	−	4.63183e6i	−0.00526538	−	0.0222707i
$239$	−1.07872e8			−0.511110			−0.255555	−	0.966795i	$-0.582258\pi$
$239$	−1.07872e8			−0.511110			−0.255555	+	0.966795i	$0.582258\pi$
$240$	1.24098e8	−	1.65933e8i	0.579463	−	0.774806i
$241$	−9.47834e7			−0.436187			−0.218093	−	0.975928i	$-0.569984\pi$
$241$	−9.47834e7			−0.436187			−0.218093	+	0.975928i	$0.569984\pi$
$242$	−2.07310e7	−	8.76850e7i	−0.0940302	−	0.397715i
$243$		−	1.43489e7i		−	0.0641500i
$244$	−2.54842e7	−	5.08820e7i	−0.112307	−	0.224233i
$245$		−	3.82656e8i		−	1.66237i
$246$	4.77588e7	−	1.12914e7i	0.204541	−	0.0483589i
$247$	−6.67640e8			−2.81905
$248$	1.15022e8	+	1.37536e8i	0.478849	+	0.572577i
$249$	2.13588e8			0.876756
$250$	−3.25670e8	+	7.69969e7i	−1.31822	+	0.311662i
$251$		−	1.76729e8i		−	0.705422i	−0.935732	−	0.352711i	$-0.885260\pi$
$251$		−	1.76729e8i		−	0.705422i	0.935732	−	0.352711i	$-0.114740\pi$
$252$	6.77822e6	−	3.39487e6i	0.0266817	−	0.0133635i
$253$			2.29254e8i			0.890012i
$254$	4.35594e7	+	1.84241e8i	0.166788	+	0.705453i
$255$	6.54876e7			0.247325
$256$	−7.58614e7	−	2.57493e8i	−0.282606	−	0.959236i
$257$	−4.65413e8			−1.71030			−0.855151	−	0.518380i	$-0.826535\pi$
$257$	−4.65413e8			−1.71030			−0.855151	+	0.518380i	$0.826535\pi$
$258$	−2.66250e7	−	1.12615e8i	−0.0965209	−	0.408249i
$259$			8.49975e6i			0.0303988i
$260$	7.76906e8	−	3.89112e8i	2.74133	−	1.37299i
$261$		−	1.85073e7i		−	0.0644320i
$262$	2.44312e8	−	5.77619e7i	0.839249	−	0.198421i
$263$	1.23925e8			0.420061			0.210031	−	0.977695i	$-0.432644\pi$
$263$	1.23925e8			0.420061			0.210031	+	0.977695i	$0.432644\pi$
$264$	−8.51493e7	−	1.01816e8i	−0.284818	−	0.340567i
$265$	8.16240e8			2.69437
$266$	4.12072e7	−	9.74248e6i	0.134242	−	0.0317383i
$267$		−	1.71592e8i		−	0.551706i
$268$	1.42259e8	+	2.84036e8i	0.451449	+	0.901368i
$269$			4.78420e8i			1.49857i	0.662250	+	0.749283i	$0.269602\pi$
$269$			4.78420e8i			1.49857i	−0.662250	+	0.749283i	$0.730398\pi$
$270$	2.39993e7	+	1.01509e8i	0.0742037	+	0.313855i
$271$	−1.18688e8			−0.362255			−0.181128	−	0.983460i	$-0.557975\pi$
$271$	−1.18688e8			−0.362255			−0.181128	+	0.983460i	$0.557975\pi$
$272$	5.08115e7	−	6.79406e7i	0.153098	−	0.204710i
$273$	3.17898e7			0.0945625
$274$	1.51655e6	+	6.41445e6i	0.00445378	+	0.0188379i
$275$			4.79566e8i			1.39054i
$276$	−1.04522e8	−	2.08691e8i	−0.299245	−	0.597477i
$277$		−	1.89410e8i		−	0.535455i	−0.963495	−	0.267728i	$-0.913727\pi$
$277$		−	1.89410e8i		−	0.535455i	0.963495	−	0.267728i	$-0.0862727\pi$
$278$	−4.20444e7	+	9.94041e6i	−0.117369	+	0.0277490i
$279$	−9.02560e7			−0.248806
$280$	−4.22731e7	+	3.53533e7i	−0.115083	+	0.0962446i
$281$	9.40783e6			0.0252940			0.0126470	−	0.999920i	$-0.495974\pi$
$281$	9.40783e6			0.0252940			0.0126470	+	0.999920i	$0.495974\pi$
$282$	−2.03239e8	+	4.80510e7i	−0.539678	+	0.127594i
$283$			5.76835e8i			1.51286i	0.654075	+	0.756430i	$0.273058\pi$
$283$			5.76835e8i			1.51286i	−0.654075	+	0.756430i	$0.726942\pi$
$284$	5.84391e7	−	2.92691e7i	0.151387	−	0.0758221i
$285$			5.82612e8i			1.49081i
$286$	−1.28062e8	−	5.41656e8i	−0.323697	−	1.36912i
$287$	−1.30520e7			−0.0325904
$288$	1.23932e8	+	5.38617e7i	0.305710	+	0.132864i
$289$	−3.83525e8			−0.934655
$290$	3.09545e7	+	1.30926e8i	0.0745299	+	0.315235i
$291$			9.94225e7i			0.236515i
$292$	−5.49715e8	+	2.75324e8i	−1.29210	+	0.647149i
$293$			2.91338e8i			0.676643i	0.941031	+	0.338322i	$0.109859\pi$
$293$			2.91338e8i			0.676643i	−0.941031	+	0.338322i	$0.890141\pi$
$294$	2.42856e8	−	5.74176e7i	0.557357	−	0.131774i
$295$	6.94149e8			1.57426
$296$	−1.16223e8	+	9.71978e7i	−0.260478	+	0.217839i
$297$	6.68155e7			0.147989
$298$	−8.94241e7	+	2.11422e7i	−0.195748	+	0.0462800i
$299$		−	9.78758e8i		−	2.11751i
$300$	−2.18645e8	−	4.36549e8i	−0.467537	−	0.933488i
$301$			3.07764e7i			0.0650481i
$302$	−5.22840e7	−	2.21143e8i	−0.109231	−	0.462007i
$303$	4.34737e7			0.0897796
$304$	6.04436e8	+	4.52046e8i	1.23394	+	0.922837i
$305$	−2.08245e8			−0.420266
$306$	9.82642e6	+	4.15623e7i	0.0196052	+	0.0829229i
$307$		−	2.68815e8i		−	0.530236i	−0.964216	−	0.265118i	$-0.914589\pi$
$307$		−	2.68815e8i		−	0.530236i	0.964216	−	0.265118i	$-0.0854108\pi$
$308$	1.58082e7	+	3.15627e7i	0.0308286	+	0.0615527i
$309$		−	1.05881e7i		−	0.0204156i
$310$	6.38499e8	−	1.50958e8i	1.21729	−	0.287800i
$311$	−8.66482e8			−1.63342			−0.816711	−	0.577047i	$-0.804205\pi$
$311$	−8.66482e8			−1.63342			−0.816711	+	0.577047i	$0.804205\pi$
$312$	3.63529e8	+	4.34684e8i	0.677638	+	0.810275i
$313$	−4.30400e8			−0.793353			−0.396677	−	0.917958i	$-0.629837\pi$
$313$	−4.30400e8			−0.793353			−0.396677	+	0.917958i	$0.629837\pi$
$314$	7.86081e8	−	1.85850e8i	1.43289	−	0.338773i
$315$		−	2.77412e7i		−	0.0500079i
$316$	−1.80179e8	+	9.02426e7i	−0.321218	+	0.160882i
$317$		−	3.18718e8i		−	0.561953i	−0.959715	−	0.280976i	$-0.909342\pi$
$317$		−	3.18718e8i		−	0.561953i	0.959715	−	0.280976i	$-0.0906583\pi$
$318$	1.22477e8	+	5.18034e8i	0.213579	+	0.903366i
$319$	8.61791e7			0.148640
$320$	−9.66818e8	−	1.73752e8i	−1.64938	−	0.296418i
$321$	−4.39888e8			−0.742292
$322$	1.42824e7	+	6.04097e7i	0.0238400	+	0.100835i
$323$			2.38548e8i			0.393883i
$324$	−6.08223e7	+	3.04628e7i	−0.0993470	+	0.0497579i
$325$		−	2.04741e9i		−	3.30837i
$326$	−7.87214e8	+	1.86118e8i	−1.25844	+	0.297527i
$327$	6.47024e8			1.02330
$328$	−1.49254e8	−	1.78469e8i	−0.233544	−	0.279256i
$329$	5.55431e7			0.0859893
$330$	−4.72673e8	+	1.11752e8i	−0.724040	+	0.171182i
$331$			1.06114e9i			1.60832i	0.594411	+	0.804161i	$0.297385\pi$
$331$			1.06114e9i			1.60832i	−0.594411	+	0.804161i	$0.702615\pi$
$332$	−4.53447e8	−	9.05358e8i	−0.680054	−	1.35780i
$333$		−	7.62699e7i		−	0.113187i
$334$	−2.03227e8	−	8.59579e8i	−0.298448	−	1.26233i
$335$	1.16247e9			1.68938
$336$	−2.87804e7	−	2.15243e7i	−0.0413913	−	0.0309557i
$337$	6.46738e8			0.920499			0.460250	−	0.887790i	$-0.347760\pi$
$337$	6.46738e8			0.920499			0.460250	+	0.887790i	$0.347760\pi$
$338$	3.83395e8	+	1.62163e9i	0.540055	+	2.28424i
$339$		−	5.16154e8i		−	0.719582i
$340$	−1.39030e8	−	2.77589e8i	−0.191837	−	0.383024i
$341$		−	4.20276e8i		−	0.573977i
$342$	−3.69760e8	+	8.74210e7i	−0.499837	+	0.118175i
$343$	−1.33276e8			−0.178330
$344$	−4.20826e8	+	3.51939e8i	−0.557376	+	0.466137i
$345$	−8.54108e8			−1.11981
$346$	5.33842e8	−	1.26214e8i	0.692862	−	0.163811i
$347$			5.65479e7i			0.0726546i	0.999340	+	0.0363273i	$0.0115659\pi$
$347$			5.65479e7i			0.0726546i	−0.999340	+	0.0363273i	$0.988434\pi$
$348$	−7.84490e7	+	3.92911e7i	−0.0997838	+	0.0499766i
$349$			2.17863e8i			0.274343i	0.990547	+	0.137172i	$0.0438012\pi$
$349$			2.17863e8i			0.274343i	−0.990547	+	0.137172i	$0.956199\pi$
$350$	2.98767e7	+	1.26368e8i	0.0372473	+	0.157543i
$351$	−2.85256e8			−0.352095
$352$	−2.50806e8	+	5.77087e8i	−0.306506	+	0.705248i
$353$	7.33462e8			0.887496			0.443748	−	0.896152i	$-0.353649\pi$
$353$	7.33462e8			0.887496			0.443748	+	0.896152i	$0.353649\pi$
$354$	1.04157e8	+	4.40548e8i	0.124789	+	0.527815i
$355$		−	2.39173e8i		−	0.283736i
$356$	−7.27346e8	+	3.64290e8i	−0.854409	+	0.427930i
$357$		−	1.13585e7i		−	0.0132125i
$358$	8.33176e8	−	1.96985e8i	0.959724	−	0.226904i
$359$	1.21920e9			1.39073			0.695366	−	0.718656i	$-0.255242\pi$
$359$	1.21920e9			1.39073			0.695366	+	0.718656i	$0.255242\pi$
$360$	3.79325e8	−	3.17231e8i	0.428502	−	0.358358i
$361$	−1.22838e9			−1.37422
$362$	2.21524e8	−	5.23742e7i	0.245438	−	0.0580279i
$363$		−	2.15028e8i		−	0.235951i
$364$	−6.74899e7	−	1.34751e8i	−0.0733473	−	0.146446i
$365$			2.24982e9i			2.42171i
$366$	−3.12472e7	−	1.32164e8i	−0.0333140	−	0.140906i
$367$	6.80496e8			0.718612			0.359306	−	0.933220i	$-0.383013\pi$
$367$	6.80496e8			0.718612			0.359306	+	0.933220i	$0.383013\pi$
$368$	−6.62698e8	+	8.86101e8i	−0.693183	+	0.926863i
$369$	1.17118e8			0.121347
$370$	1.27565e8	+	5.39556e8i	0.130926	+	0.553772i
$371$		−	1.41573e8i		−	0.143937i
$372$	1.91614e8	+	3.82578e8i	0.192986	+	0.385318i
$373$		−	7.23854e8i		−	0.722221i	−0.932523	−	0.361110i	$-0.882398\pi$
$373$		−	7.23854e8i		−	0.722221i	0.932523	−	0.361110i	$-0.117602\pi$
$374$	−1.93534e8	+	4.57566e7i	−0.191297	+	0.0452276i
$375$	−7.98633e8			−0.782056
$376$	6.35156e8	+	7.59478e8i	0.616201	+	0.736814i
$377$	−3.67925e8			−0.353643
$378$	1.76062e7	−	4.16258e6i	0.0167666	−	0.00396407i
$379$		−	8.60978e8i		−	0.812372i	−0.913790	−	0.406186i	$-0.866859\pi$
$379$		−	8.60978e8i		−	0.812372i	0.913790	−	0.406186i	$-0.133141\pi$
$380$	2.46958e9	−	1.23689e9i	2.30877	−	1.15634i
$381$			4.51810e8i			0.418522i
$382$	8.54145e7	+	3.61273e8i	0.0783988	+	0.331599i
$383$	1.03603e8			0.0942269			0.0471135	−	0.998890i	$-0.484998\pi$
$383$	1.03603e8			0.0942269			0.0471135	+	0.998890i	$0.484998\pi$
$384$	−3.47980e7	−	6.39671e8i	−0.0313614	−	0.576498i
$385$	1.29177e8			0.115364
$386$	−2.59863e8	−	1.09913e9i	−0.229980	−	0.972733i
$387$		−	2.76162e8i		−	0.242201i
$388$	4.21433e8	−	2.11074e8i	0.366283	−	0.183453i
$389$		−	2.23948e8i		−	0.192896i	−0.995338	−	0.0964481i	$-0.969252\pi$
$389$		−	2.23948e8i		−	0.192896i	0.995338	−	0.0964481i	$-0.0307482\pi$
$390$	2.01799e9	−	4.77106e8i	1.72263	−	0.407276i
$391$	−3.49711e8			−0.295863
$392$	−7.58967e8	−	9.07524e8i	−0.636387	−	0.760951i
$393$	5.99122e8			0.497899
$394$	−9.46576e8	+	2.23795e8i	−0.779684	+	0.184338i
$395$			7.37420e8i			0.602039i
$396$	−1.41849e8	−	2.83218e8i	−0.114787	−	0.229186i
$397$			1.14346e9i			0.917179i	0.888648	+	0.458589i	$0.151645\pi$
$397$			1.14346e9i			0.917179i	−0.888648	+	0.458589i	$0.848355\pi$
$398$	−4.22352e8	−	1.78640e9i	−0.335802	−	1.42033i
$399$	1.01052e8			0.0796412
$400$	−1.38626e9	+	1.85359e9i	−1.08302	+	1.44812i
$401$	3.48918e8			0.270220			0.135110	−	0.990831i	$-0.456861\pi$
$401$	3.48918e8			0.270220			0.135110	+	0.990831i	$0.456861\pi$
$402$	1.74430e8	+	7.37775e8i	0.133915	+	0.566413i
$403$			1.79429e9i			1.36560i
$404$	−9.22947e7	−	1.84277e8i	−0.0696373	−	0.139039i
$405$			2.48927e8i			0.186200i
$406$	2.27086e7	−	5.36892e6i	0.0168403	−	0.00398149i
$407$	3.55150e8			0.261115
$408$	1.55313e8	−	1.29889e8i	0.113213	−	0.0946809i
$409$	1.29700e8			0.0937368			0.0468684	−	0.998901i	$-0.485076\pi$
$409$	1.29700e8			0.0937368			0.0468684	+	0.998901i	$0.485076\pi$
$410$	−8.28527e8	+	1.95886e8i	−0.593695	+	0.140365i
$411$			1.57300e7i			0.0111759i
$412$	−4.48809e7	+	2.24785e7i	−0.0316170	+	0.0158354i
$413$		−	1.20397e8i		−	0.0840991i
$414$	−1.28159e8	−	5.42067e8i	−0.0887662	−	0.375450i
$415$	−3.70536e9			−2.54485
$416$	1.07077e9	−	2.46376e9i	0.729239	−	1.67792i
$417$	−1.03105e8			−0.0696309
$418$	−4.07075e8	−	1.72178e9i	−0.272620	−	1.15309i
$419$		−	1.23819e8i		−	0.0822312i	−0.999154	−	0.0411156i	$-0.986909\pi$
$419$		−	1.23819e8i		−	0.0822312i	0.999154	−	0.0411156i	$-0.0130912\pi$
$420$	−1.17590e8	+	5.88947e7i	−0.0774456	+	0.0387886i
$421$			2.72698e7i			0.0178112i	0.999960	+	0.00890562i	$0.00283478\pi$
$421$			2.72698e7i			0.0178112i	−0.999960	+	0.00890562i	$0.997165\pi$
$422$	−2.36476e9	+	5.59092e8i	−1.53177	+	0.362151i
$423$	−4.98398e8			−0.320173
$424$	1.93583e9	−	1.61894e9i	1.23335	−	1.03146i
$425$	−7.31543e8			−0.462252
$426$	1.51794e8	−	3.58880e7i	0.0951306	−	0.0224914i
$427$			3.61192e7i			0.0224512i
$428$	9.33883e8	+	1.86460e9i	0.575757	+	1.14956i
$429$		−	1.32829e9i		−	0.812256i
$430$	4.61896e8	+	1.95366e9i	0.280159	+	1.18497i
$431$	−1.06503e9			−0.640754			−0.320377	−	0.947290i	$-0.603810\pi$
$431$	−1.06503e9			−0.640754			−0.320377	+	0.947290i	$0.603810\pi$
$432$	2.58251e8	+	1.93141e8i	0.154117	+	0.115261i
$433$	7.41521e8			0.438951			0.219475	−	0.975618i	$-0.429565\pi$
$433$	7.41521e8			0.438951			0.219475	+	0.975618i	$0.429565\pi$
$434$	−2.61830e7	−	1.10745e8i	−0.0153747	−	0.0650294i
$435$			3.21068e8i			0.187019i
$436$	−1.37363e9	−	2.74261e9i	−0.793721	−	1.58475i
$437$		−	3.11122e9i		−	1.78338i
$438$	−1.42787e9	+	3.37585e8i	−0.811949	+	0.191966i
$439$	−1.10708e9			−0.624531			−0.312265	−	0.949995i	$-0.601088\pi$
$439$	−1.10708e9			−0.624531			−0.312265	+	0.949995i	$0.601088\pi$
$440$	1.47718e9	+	1.76632e9i	0.826704	+	0.988520i
$441$	5.95551e8			0.330662
$442$	8.26258e8	−	1.95349e8i	0.455133	−	0.107605i
$443$			1.11670e9i			0.610272i	0.952309	+	0.305136i	$0.0987019\pi$
$443$			1.11670e9i			0.610272i	−0.952309	+	0.305136i	$0.901298\pi$
$444$	−3.23293e8	+	1.61921e8i	−0.175290	+	0.0877936i
$445$			2.97681e9i			1.60137i
$446$	−3.30036e8	−	1.39593e9i	−0.176153	−	0.745063i
$447$	−2.19293e8			−0.116131
$448$	−3.01365e7	+	1.67690e8i	−0.0158351	+	0.0881121i
$449$	1.94185e9			1.01240			0.506201	−	0.862416i	$-0.331050\pi$
$449$	1.94185e9			1.01240			0.506201	+	0.862416i	$0.331050\pi$
$450$	−2.68089e8	−	1.13392e9i	−0.138687	−	0.586597i
$451$			5.45358e8i			0.279939i
$452$	−2.18788e9	+	1.09580e9i	−1.11439	+	0.558142i
$453$		−	5.42304e8i		−	0.274094i
$454$	−2.19576e9	+	5.19136e8i	−1.10126	+	0.260367i
$455$	−5.51495e8			−0.274475
$456$	1.15556e9	+	1.38175e9i	0.570711	+	0.682420i
$457$	1.89332e9			0.927936			0.463968	−	0.885852i	$-0.346425\pi$
$457$	1.89332e9			0.927936			0.463968	+	0.885852i	$0.346425\pi$
$458$	4.03597e8	−	9.54210e7i	0.196299	−	0.0464103i
$459$			1.01922e8i			0.0491954i
$460$	1.81327e9	+	3.62040e9i	0.868581	+	1.73422i
$461$			2.70468e9i			1.28577i	0.765964	+	0.642883i	$0.222262\pi$
$461$			2.70468e9i			1.28577i	−0.765964	+	0.642883i	$0.777738\pi$
$462$	1.93830e7	+	8.19832e7i	0.00914479	+	0.0386792i
$463$	3.19942e9			1.49809			0.749046	−	0.662518i	$-0.230512\pi$
$463$	3.19942e9			1.49809			0.749046	+	0.662518i	$0.230512\pi$
$464$	3.33095e8	+	2.49115e8i	0.154794	+	0.115768i
$465$	1.56578e9			0.722178
$466$	−2.56667e8	−	1.08561e9i	−0.117495	−	0.496962i
$467$		−	4.00868e9i		−	1.82134i	−0.413130	−	0.910672i	$-0.635565\pi$
$467$		−	4.00868e9i		−	1.82134i	0.413130	−	0.910672i	$-0.364435\pi$
$468$	6.05599e8	+	1.20915e9i	0.273102	+	0.545278i
$469$		−	2.01626e8i		−	0.0902490i
$470$	3.52582e9	−	8.33597e8i	1.56645	−	0.370351i
$471$	1.92769e9			0.850087
$472$	1.64627e9	−	1.37679e9i	0.720617	−	0.602656i
$473$	1.28595e9			0.558739
$474$	−4.68010e8	+	1.10650e8i	−0.201851	+	0.0477229i
$475$		−	6.50820e9i		−	2.78633i
$476$	−4.81467e7	+	2.41142e7i	−0.0204617	+	0.0102482i
$477$			1.27036e9i			0.535937i
$478$	2.80800e8	+	1.18768e9i	0.117598	+	0.497398i
$479$	−2.36136e9			−0.981721			−0.490860	−	0.871238i	$-0.663317\pi$
$479$	−2.36136e9			−0.981721			−0.490860	+	0.871238i	$0.663317\pi$
$480$	−2.14999e9	−	9.34402e8i	−0.887344	−	0.385646i
$481$	−1.51624e9			−0.621243
$482$	2.46730e8	+	1.04358e9i	0.100359	+	0.424484i
$483$			1.48141e8i			0.0598220i
$484$	−9.11462e8	+	4.56505e8i	−0.365409	+	0.183015i
$485$		−	1.72480e9i		−	0.686502i
$486$	−1.57984e8	+	3.73516e7i	−0.0624289	+	0.0147598i
$487$	2.82968e9			1.11016			0.555080	−	0.831797i	$-0.312688\pi$
$487$	2.82968e9			1.11016			0.555080	+	0.831797i	$0.312688\pi$
$488$	−4.93882e8	+	4.13036e8i	−0.192377	+	0.160886i
$489$	−1.93047e9			−0.746588
$490$	−4.21311e9	+	9.96091e8i	−1.61777	+	0.382483i
$491$			3.04210e9i			1.15981i	0.814682	+	0.579907i	$0.196911\pi$
$491$			3.04210e9i			1.15981i	−0.814682	+	0.579907i	$0.803089\pi$
$492$	−2.48641e8	−	4.96440e8i	−0.0941229	−	0.187927i
$493$			1.31460e8i			0.0494117i
$494$	1.73793e9	+	7.35083e9i	0.648616	+	2.74342i
$495$	−1.15913e9			−0.429549
$496$	1.21488e9	−	1.62443e9i	0.447040	−	0.597743i
$497$	−4.14836e7			−0.0151576
$498$	−5.55990e8	−	2.35164e9i	−0.201727	−	0.853234i
$499$			6.92433e8i			0.249474i	0.992190	+	0.124737i	$0.0398088\pi$
$499$			6.92433e8i			0.249474i	−0.992190	+	0.124737i	$0.960191\pi$
$500$	1.69550e9	+	3.38525e9i	0.606600	+	1.21114i
$501$		−	2.10793e9i		−	0.748900i
$502$	−1.94581e9	+	4.60042e8i	−0.686496	+	0.162306i
$503$	−3.40321e9			−1.19234			−0.596171	−	0.802858i	$-0.703312\pi$
$503$	−3.40321e9			−1.19234			−0.596171	+	0.802858i	$0.703312\pi$
$504$	−5.50224e7	−	6.57923e7i	−0.0191440	−	0.0228912i
$505$	−7.54189e8			−0.260592
$506$	2.52413e9	−	5.96771e8i	0.866134	−	0.204777i
$507$			3.97668e9i			1.35517i
$508$	1.91514e9	−	9.59193e8i	0.648151	−	0.324626i
$509$		−	2.36640e8i		−	0.0795383i	−0.999209	−	0.0397691i	$-0.987338\pi$
$509$		−	2.36640e8i		−	0.0795383i	0.999209	−	0.0397691i	$-0.0126623\pi$
$510$	−1.70470e8	−	7.21030e8i	−0.0569054	−	0.240690i
$511$	3.90221e8			0.129371
$512$	−2.63757e9	+	1.50553e9i	−0.868478	+	0.495728i
$513$	−9.06755e8			−0.296537
$514$	1.21151e9	+	5.12428e9i	0.393512	+	1.66442i
$515$			1.83684e8i			0.0592579i
$516$	−1.17060e9	+	5.86293e8i	−0.375089	+	0.187863i
$517$		−	2.32079e9i		−	0.738615i
$518$	9.35837e7	−	2.21257e7i	0.0295833	−	0.00699427i
$519$	1.30913e9			0.411052
$520$	−6.30655e9	−	7.54097e9i	−1.96689	−	2.35188i
$521$	−2.10503e8			−0.0652119			−0.0326059	−	0.999468i	$-0.510381\pi$
$521$	−2.10503e8			−0.0652119			−0.0326059	+	0.999468i	$0.510381\pi$
$522$	−2.03769e8	+	4.81763e7i	−0.0627034	+	0.0148247i
$523$		−	4.88451e9i		−	1.49302i	−0.665376	−	0.746509i	$-0.731729\pi$
$523$		−	4.88451e9i		−	1.49302i	0.665376	−	0.746509i	$-0.268271\pi$
$524$	−1.27194e9	−	2.53956e9i	−0.386194	−	0.771080i
$525$			3.09889e8i			0.0934650i
$526$	−3.22588e8	−	1.36443e9i	−0.0966491	−	0.408792i
$527$	6.41101e8			0.190805
$528$	−8.99360e8	+	1.20254e9i	−0.265898	+	0.355535i
$529$	1.15621e9			0.339579
$530$	−2.12475e9	−	8.98694e9i	−0.619930	−	2.62208i
$531$			1.08035e9i			0.313135i
$532$	−2.14533e8	−	4.28338e8i	−0.0617736	−	0.123338i
$533$		−	2.32830e9i		−	0.666030i
$534$	−1.88926e9	+	4.46670e8i	−0.536904	+	0.126938i
$535$	7.63125e9			2.15455
$536$	2.75697e9	−	2.30567e9i	0.773314	−	0.646727i
$537$	2.04318e9			0.569373
$538$	5.26748e9	−	1.24537e9i	1.45836	−	0.344795i
$539$			2.77318e9i			0.762811i
$540$	1.05515e9	−	5.28473e8i	0.288362	−	0.144426i
$541$			3.13607e9i			0.851521i	0.904836	+	0.425760i	$0.139993\pi$
$541$			3.13607e9i			0.851521i	−0.904836	+	0.425760i	$0.860007\pi$
$542$	3.08957e8	+	1.30678e9i	0.0833489	+	0.352536i
$543$	5.43239e8			0.145610
$544$	−8.80305e8	−	3.82587e8i	−0.234443	−	0.101891i
$545$	−1.12247e10			−2.97020
$546$	−8.27520e7	−	3.50012e8i	−0.0217573	−	0.0920255i
$547$			2.24354e9i			0.586110i	0.956096	+	0.293055i	$0.0946719\pi$
$547$			2.24354e9i			0.586110i	−0.956096	+	0.293055i	$0.905328\pi$
$548$	6.66765e7	−	3.33949e7i	0.0173078	−	0.00866858i
$549$		−	3.24104e8i		−	0.0835951i
$550$	5.28010e9	−	1.24836e9i	1.35323	−	0.319940i
$551$	−1.16954e9			−0.297841
$552$	−2.02564e9	+	1.69405e9i	−0.512596	+	0.428686i
$553$	1.27902e8			0.0321618
$554$	−2.08543e9	+	4.93051e8i	−0.521089	+	0.123199i
$555$			1.32314e9i			0.328535i
$556$	2.18891e8	+	4.37041e8i	0.0540091	+	0.107835i
$557$		−	4.59390e9i		−	1.12639i	−0.826324	−	0.563195i	$-0.809572\pi$
$557$		−	4.59390e9i		−	1.12639i	0.826324	−	0.563195i	$-0.190428\pi$
$558$	2.34945e8	+	9.93735e8i	0.0572462	+	0.242131i
$559$	−5.49010e9			−1.32935
$560$	4.99286e8	+	3.73407e8i	0.120141	+	0.0898512i
$561$	−4.74600e8			−0.113490
$562$	−2.44895e7	−	1.03582e8i	−0.00581973	−	0.0246154i
$563$			9.25935e7i			0.0218676i	0.999940	+	0.0109338i	$0.00348040\pi$
$563$			9.25935e7i			0.0218676i	−0.999940	+	0.0109338i	$0.996520\pi$
$564$	1.05810e9	+	2.11261e9i	0.248342	+	0.495842i
$565$			8.95432e9i			2.08864i
$566$	6.35105e9	−	1.50156e9i	1.47227	−	0.348084i
$567$	4.31754e7			0.00994707
$568$	−4.74381e8	−	5.67234e8i	−0.108619	−	0.129880i
$569$	−1.80174e9			−0.410013			−0.205007	−	0.978761i	$-0.565722\pi$
$569$	−1.80174e9			−0.410013			−0.205007	+	0.978761i	$0.565722\pi$
$570$	6.41466e9	−	1.51659e9i	1.45081	−	0.343011i
$571$			4.05799e9i			0.912188i	0.889932	+	0.456094i	$0.150752\pi$
$571$			4.05799e9i			0.912188i	−0.889932	+	0.456094i	$0.849248\pi$
$572$	−5.63037e9	+	2.81997e9i	−1.25791	+	0.630025i
$573$			8.85942e8i			0.196727i
$574$	3.39755e7	+	1.43704e8i	0.00749850	+	0.0317160i
$575$	9.54099e9			2.09294
$576$	2.70421e8	−	1.50472e9i	0.0589605	−	0.328077i
$577$	−7.82764e9			−1.69635			−0.848175	−	0.529716i	$-0.822298\pi$
$577$	−7.82764e9			−1.69635			−0.848175	+	0.529716i	$0.822298\pi$
$578$	9.98352e8	+	4.22268e9i	0.215048	+	0.909579i
$579$		−	2.69537e9i		−	0.577090i
$580$	1.36095e9	−	6.81628e8i	0.289629	−	0.145061i
$581$			6.42679e8i			0.135949i
$582$	1.09466e9	−	2.58806e8i	0.230170	−	0.0544182i
$583$	−5.91543e9			−1.23637
$584$	4.46232e9	+	5.33576e9i	0.927078	+	1.10854i
$585$	4.94867e9			1.02198
$586$	3.20768e9	−	7.58379e8i	0.658490	−	0.155684i
$587$		−	1.45350e9i		−	0.296607i	−0.988942	−	0.148304i	$-0.952619\pi$
$587$		−	1.45350e9i		−	0.296607i	0.988942	−	0.148304i	$-0.0473813\pi$
$588$	−1.26436e9	−	2.52443e9i	−0.256477	−	0.512085i
$589$			5.70358e9i			1.15012i
$590$	−1.80694e9	−	7.64270e9i	−0.362210	−	1.53202i
$591$	−2.32127e9			−0.462561
$592$	1.37270e9	+	1.02662e9i	0.271926	+	0.203368i
$593$	8.26005e8			0.162664			0.0813320	−	0.996687i	$-0.474083\pi$
$593$	8.26005e8			0.162664			0.0813320	+	0.996687i	$0.474083\pi$
$594$	−1.73927e8	−	7.35650e8i	−0.0340498	−	0.144019i
$595$			1.97050e8i			0.0383501i
$596$	4.65559e8	+	9.29540e8i	0.0900768	+	0.179848i
$597$		−	4.38075e9i		−	0.842632i
$598$	−1.07763e10	+	2.54780e9i	−2.06070	+	0.487204i
$599$	3.81768e9			0.725780			0.362890	−	0.931832i	$-0.381790\pi$
$599$	3.81768e9			0.725780			0.362890	+	0.931832i	$0.381790\pi$
$600$	−4.23733e9	+	3.54370e9i	−0.800871	+	0.669773i
$601$	1.48375e9			0.278805			0.139402	−	0.990236i	$-0.455482\pi$
$601$	1.48375e9			0.278805			0.139402	+	0.990236i	$0.455482\pi$
$602$	3.38853e8	−	8.01138e7i	0.0633030	−	0.0149665i
$603$			1.80923e9i			0.336034i
$604$	−2.29872e9	+	1.15131e9i	−0.424480	+	0.212600i
$605$			3.73034e9i			0.684864i
$606$	−1.13166e8	−	4.78653e8i	−0.0206568	−	0.0873709i
$607$	1.01217e10			1.83693			0.918463	−	0.395506i	$-0.129431\pi$
$607$	1.01217e10			1.83693			0.918463	+	0.395506i	$0.129431\pi$
$608$	3.40370e9	−	7.83166e9i	0.614170	−	1.41316i
$609$	5.56879e7			0.00999080
$610$	5.42081e8	+	2.29281e9i	0.0966962	+	0.408991i
$611$			9.90815e9i			1.75731i
$612$	4.32029e8	−	2.16381e8i	0.0761874	−	0.0381584i
$613$		−	8.24178e9i		−	1.44514i	−0.691299	−	0.722569i	$-0.742961\pi$
$613$		−	8.24178e9i		−	1.44514i	0.691299	−	0.722569i	$-0.257039\pi$
$614$	−2.95970e9	+	6.99750e8i	−0.516010	+	0.121998i
$615$	−2.03178e9			−0.352220
$616$	3.06361e8	−	2.56211e8i	0.0528081	−	0.0441637i
$617$	8.98164e9			1.53942			0.769710	−	0.638393i	$-0.220401\pi$
$617$	8.98164e9			1.53942			0.769710	+	0.638393i	$0.220401\pi$
$618$	−1.16577e8	+	2.75618e7i	−0.0198679	+	0.00469730i
$619$		−	3.83653e9i		−	0.650162i	−0.945686	−	0.325081i	$-0.894608\pi$
$619$		−	3.83653e9i		−	0.650162i	0.945686	−	0.325081i	$-0.105392\pi$
$620$	−3.32415e9	−	6.63702e9i	−0.560156	−	1.11841i
$621$		−	1.32930e9i		−	0.222742i
$622$	2.25554e9	+	9.54012e9i	0.375823	+	1.58960i
$623$	5.16315e8			0.0855473
$624$	3.83965e9	−	5.13404e9i	0.632623	−	0.845888i
$625$	2.81779e9			0.461666
$626$	1.12037e9	+	4.73877e9i	0.182537	+	0.772068i
$627$		−	4.22229e9i		−	0.684088i
$628$	−4.09248e9	−	8.17110e9i	−0.659369	−	1.31650i
$629$			5.41756e8i			0.0868013i
$630$	−3.05436e8	+	7.22131e7i	−0.0486663	+	0.0115060i
$631$	−5.55269e9			−0.879834			−0.439917	−	0.898039i	$-0.644992\pi$
$631$	−5.55269e9			−0.879834			−0.439917	+	0.898039i	$0.644992\pi$
$632$	1.46261e9	+	1.74890e9i	0.230472	+	0.275584i
$633$	−5.79906e9			−0.908750
$634$	−3.50914e9	+	8.29654e8i	−0.546876	+	0.129296i
$635$		−	7.83807e9i		−	1.21479i
$636$	5.38483e9	−	2.69698e9i	0.829988	−	0.415699i
$637$		−	1.18396e10i		−	1.81488i
$638$	−2.24332e8	−	9.48847e8i	−0.0341995	−	0.144652i
$639$	3.72240e8			0.0564378
$640$	6.03681e8	+	1.10971e10i	0.0910286	+	1.67333i
$641$	7.35378e9			1.10283			0.551413	−	0.834232i	$-0.314089\pi$
$641$	7.35378e9			1.10283			0.551413	+	0.834232i	$0.314089\pi$
$642$	1.14507e9	+	4.84324e9i	0.170789	+	0.722377i
$643$		−	4.34387e9i		−	0.644375i	−0.946676	−	0.322187i	$-0.895582\pi$
$643$		−	4.34387e9i		−	0.644375i	0.946676	−	0.322187i	$-0.104418\pi$
$644$	6.27943e8	−	3.14504e8i	0.0926444	−	0.0464009i
$645$			4.79091e9i			0.703005i
$646$	2.62646e9	−	6.20964e8i	0.383316	−	0.0906260i
$647$	−9.96133e9			−1.44595			−0.722973	−	0.690876i	$-0.757225\pi$
$647$	−9.96133e9			−1.44595			−0.722973	+	0.690876i	$0.757225\pi$
$648$	4.93726e8	+	5.90366e8i	0.0712810	+	0.0852332i
$649$	−5.03062e9			−0.722379
$650$	−2.25424e10	+	5.32961e9i	−3.21961	+	0.761200i
$651$		−	2.71577e8i		−	0.0385798i
$652$	4.09838e9	+	8.18288e9i	0.579090	+	1.15622i
$653$		−	2.99451e9i		−	0.420852i	−0.977610	−	0.210426i	$-0.932515\pi$
$653$		−	2.99451e9i		−	0.420852i	0.977610	−	0.210426i	$-0.0674850\pi$
$654$	−1.68427e9	−	7.12385e9i	−0.235444	−	0.995847i
$655$	−1.03937e10			−1.44519
$656$	−1.57645e9	+	2.10788e9i	−0.218030	+	0.291530i
$657$	−3.50153e9			−0.481702
$658$	−1.44584e8	−	6.11539e8i	−0.0197847	−	0.0836823i
$659$		−	7.84192e9i		−	1.06739i	−0.845677	−	0.533695i	$-0.820803\pi$
$659$		−	7.84192e9i		−	1.06739i	0.845677	−	0.533695i	$-0.179197\pi$
$660$	2.46083e9	+	4.91331e9i	0.333179	+	0.665228i
$661$			5.55066e9i			0.747549i	0.927520	+	0.373775i	$0.121937\pi$
$661$			5.55066e9i			0.747549i	−0.927520	+	0.373775i	$0.878063\pi$
$662$	1.16833e10	−	2.76224e9i	1.56517	−	0.370048i
$663$	2.02621e9			0.270015
$664$	−8.78778e9	+	7.34927e9i	−1.16491	+	0.974217i
$665$	−1.75306e9			−0.231164
$666$	−8.39744e8	+	1.98538e8i	−0.110151	+	0.0260425i
$667$		−	1.71454e9i		−	0.223721i
$668$	−8.93510e9	+	4.47513e9i	−1.15980	+	0.580883i
$669$		−	3.42322e9i		−	0.442021i
$670$	−3.02603e9	−	1.27990e10i	−0.388697	−	1.64405i
$671$	1.50919e9			0.192847
$672$	−1.62068e8	+	3.72906e8i	−0.0206018	+	0.0474032i
$673$	9.93043e9			1.25578			0.627892	−	0.778300i	$-0.283918\pi$
$673$	9.93043e9			1.25578			0.627892	+	0.778300i	$0.283918\pi$
$674$	−1.68352e9	−	7.12069e9i	−0.211791	−	0.895803i
$675$		−	2.78070e9i		−	0.348009i
$676$	1.68564e10	−	8.44250e9i	2.09870	−	1.05113i
$677$			8.68747e9i			1.07605i	0.842929	+	0.538026i	$0.180830\pi$
$677$			8.68747e9i			1.07605i	−0.842929	+	0.538026i	$0.819170\pi$
$678$	−5.68294e9	+	1.34360e9i	−0.700276	+	0.165564i
$679$	−2.99159e8			−0.0366739
$680$	−2.69440e9	+	2.25334e9i	−0.328610	+	0.274818i
$681$	−5.38461e9			−0.653341
$682$	−4.62731e9	+	1.09402e9i	−0.558578	+	0.132062i
$683$			9.19143e8i			0.110385i	0.998476	+	0.0551925i	$0.0175773\pi$
$683$			9.19143e8i			0.110385i	−0.998476	+	0.0551925i	$0.982423\pi$
$684$	1.92504e9	+	3.84356e9i	0.230008	+	0.459237i
$685$		−	2.72887e8i		−	0.0324389i
$686$	3.46931e8	+	1.46740e9i	0.0410307	+	0.173545i
$687$	9.89732e8			0.116458
$688$	4.97036e9	+	3.71724e9i	0.581874	+	0.435172i
$689$	2.52548e10			2.94156
$690$	2.22332e9	+	9.40387e9i	0.257650	+	1.08977i
$691$			2.66387e9i			0.307142i	0.988138	+	0.153571i	$0.0490774\pi$
$691$			2.66387e9i			0.307142i	−0.988138	+	0.153571i	$0.950923\pi$
$692$	−2.77928e9	−	5.54915e9i	−0.318832	−	0.636583i
$693$			2.01046e8i			0.0229471i
$694$	6.22602e8	−	1.47199e8i	0.0707054	−	0.0167166i
$695$	1.78868e9			0.202109
$696$	6.36812e8	+	7.61458e8i	0.0715943	+	0.0856079i
$697$	−8.31904e8			−0.0930590
$698$	2.39871e9	−	5.67118e8i	0.266983	−	0.0631218i
$699$		−	2.66222e9i		−	0.294831i
$700$	1.31356e9	−	6.57896e8i	0.144746	−	0.0724960i
$701$			9.10026e9i			0.997794i	0.866661	+	0.498897i	$0.166261\pi$
$701$			9.10026e9i			0.997794i	−0.866661	+	0.498897i	$0.833739\pi$
$702$	7.42549e8	+	3.14072e9i	0.0810112	+	0.342649i
$703$	−4.81974e9			−0.523215
$704$	7.00670e9	+	1.25921e9i	0.756849	+	0.136017i
$705$	8.64630e9			0.929326
$706$	−1.90927e9	−	8.07555e9i	−0.204198	−	0.863685i
$707$			1.30811e8i			0.0139212i
$708$	4.57938e9	−	2.29358e9i	0.484942	−	0.242883i
$709$		−	4.42773e9i		−	0.466573i	−0.972408	−	0.233286i	$-0.925052\pi$
$709$		−	4.42773e9i		−	0.466573i	0.972408	−	0.233286i	$-0.0749480\pi$
$710$	−2.63334e9	+	6.22591e8i	−0.276123	+	0.0652828i
$711$	−1.14769e9			−0.119752
$712$	5.90425e9	+	7.05992e9i	0.613034	+	0.733027i
$713$	−8.36142e9			−0.863907
$714$	−1.25060e8	+	2.95674e7i	−0.0128580	+	0.00303997i
$715$			2.30434e10i			2.35763i
$716$	−4.33767e9	−	8.66065e9i	−0.441633	−	0.881769i
$717$			2.91253e9i			0.295090i
$718$	−3.17369e9	−	1.34236e10i	−0.319984	−	1.35342i
$719$	−2.91984e9			−0.292960			−0.146480	−	0.989214i	$-0.546794\pi$
$719$	−2.91984e9			−0.292960			−0.146480	+	0.989214i	$0.546794\pi$
$720$	−4.48019e9	−	3.35065e9i	−0.447335	−	0.334553i
$721$	3.18592e7			0.00316564
$722$	3.19759e9	+	1.35247e10i	0.316186	+	1.33736i
$723$			2.55915e9i			0.251833i
$724$	−1.15330e9	−	2.30269e9i	−0.112942	−	0.225502i
$725$		−	3.58656e9i		−	0.349539i
$726$	−2.36749e9	+	5.59738e8i	−0.229621	+	0.0542884i
$727$	1.29199e10			1.24706			0.623530	−	0.781799i	$-0.285698\pi$
$727$	1.29199e10			1.24706			0.623530	+	0.781799i	$0.285698\pi$
$728$	−1.30795e9	+	1.09385e9i	−0.125641	+	0.105074i
$729$	−3.87420e8			−0.0370370
$730$	2.47709e10	−	5.85649e9i	2.35674	−	0.557195i
$731$			1.96162e9i			0.185739i
$732$	−1.37381e9	+	6.88073e8i	−0.129461	+	0.0648404i
$733$		−	1.48967e10i		−	1.39710i	−0.715563	−	0.698548i	$-0.753830\pi$
$733$		−	1.48967e10i		−	1.39710i	0.715563	−	0.698548i	$-0.246170\pi$
$734$	−1.77140e9	−	7.49238e9i	−0.165341	−	0.699333i
$735$	−1.03317e10			−0.959770
$736$	1.14812e10	+	4.98981e9i	1.06149	+	0.461330i
$737$	−8.42466e9			−0.775204
$738$	−3.04869e8	−	1.28949e9i	−0.0279200	−	0.118092i
$739$			3.02167e9i			0.275418i	0.990473	+	0.137709i	$0.0439738\pi$
$739$			3.02167e9i			0.275418i	−0.990473	+	0.137709i	$0.956026\pi$
$740$	5.60854e9	−	2.80903e9i	0.508791	−	0.254827i
$741$			1.80263e10i			1.62758i
$742$	−1.55875e9	+	3.68529e8i	−0.140075	+	0.0331175i
$743$	−1.52499e10			−1.36397			−0.681985	−	0.731366i	$-0.738883\pi$
$743$	−1.52499e10			−1.36397			−0.681985	+	0.731366i	$0.738883\pi$
$744$	3.71346e9	−	3.10559e9i	0.330578	−	0.276464i
$745$	3.80433e9			0.337078
$746$	−7.96976e9	+	1.88426e9i	−0.702844	+	0.166171i
$747$		−	5.76687e9i		−	0.506196i
$748$	1.00758e9	+	2.01174e9i	0.0880284	+	0.175758i
$749$		−	1.32361e9i		−	0.115099i
$750$	2.07892e9	+	8.79309e9i	0.179938	+	0.761074i
$751$	−1.30306e9			−0.112260			−0.0561298	−	0.998423i	$-0.517876\pi$
$751$	−1.30306e9			−0.112260			−0.0561298	+	0.998423i	$0.517876\pi$
$752$	6.70862e9	−	8.97017e9i	0.575268	−	0.769198i
$753$	−4.77168e9			−0.407276
$754$	9.57745e8	+	4.05092e9i	0.0813673	+	0.344155i
$755$			9.40797e9i			0.795576i
$756$	−9.16614e7	−	1.83012e8i	−0.00771543	−	0.0154047i
$757$		−	3.51770e9i		−	0.294729i	−0.989082	−	0.147364i	$-0.952921\pi$
$757$		−	3.51770e9i		−	0.294729i	0.989082	−	0.147364i	$-0.0470790\pi$
$758$	−9.47952e9	+	2.24121e9i	−0.790576	+	0.186913i
$759$	6.18987e9			0.513849
$760$	−2.00469e10	−	2.39708e10i	−1.65653	−	1.98077i
$761$	−1.23448e10			−1.01541			−0.507703	−	0.861532i	$-0.669505\pi$
$761$	−1.23448e10			−1.01541			−0.507703	+	0.861532i	$0.669505\pi$
$762$	4.97451e9	−	1.17610e9i	0.407294	−	0.0962949i
$763$			1.94687e9i			0.158673i
$764$	3.75534e9	−	1.88086e9i	0.304665	−	0.152591i
$765$		−	1.76817e9i		−	0.142793i
$766$	−2.69687e8	−	1.14068e9i	−0.0216800	−	0.0916989i
$767$	2.14773e10			1.71868
$768$	−6.95231e9	+	2.04826e9i	−0.553815	+	0.163162i
$769$	1.18155e10			0.936940			0.468470	−	0.883479i	$-0.344805\pi$
$769$	1.18155e10			0.936940			0.468470	+	0.883479i	$0.344805\pi$
$770$	−3.36259e8	−	1.42226e9i	−0.0265434	−	0.112269i
$771$			1.25662e10i			0.987443i
$772$	−1.14252e10	+	5.72228e9i	−0.893721	+	0.447619i
$773$			1.62582e10i			1.26603i	0.774138	+	0.633017i	$0.218184\pi$
$773$			1.62582e10i			1.26603i	−0.774138	+	0.633017i	$0.781816\pi$
$774$	−3.04059e9	+	7.18876e8i	−0.235703	+	0.0557264i
$775$	−1.74908e10			−1.34975
$776$	−3.42099e9	−	4.09060e9i	−0.262806	−	0.314247i
$777$	2.29493e8			0.0175508
$778$	−2.46571e9	+	5.82958e8i	−0.187721	+	0.0443822i
$779$		−	7.40106e9i		−	0.560935i
$780$	−1.05060e10	−	2.09765e10i	−0.792698	−	1.58271i
$781$			1.73333e9i			0.130198i
$782$	9.10331e8	+	3.85038e9i	0.0680732	+	0.287925i
$783$	−4.99698e8			−0.0371998
$784$	−8.01633e9	+	1.07187e10i	−0.594113	+	0.794396i
$785$	−3.34418e10			−2.46744
$786$	−1.55957e9	−	6.59644e9i	−0.114558	−	0.484541i
$787$		−	1.80876e10i		−	1.32273i	−0.750066	−	0.661363i	$-0.769978\pi$
$787$		−	1.80876e10i		−	1.32273i	0.750066	−	0.661363i	$-0.230022\pi$
$788$	4.92805e9	+	9.83940e9i	0.358784	+	0.716353i
$789$		−	3.34597e9i		−	0.242523i
$790$	8.11912e9	−	1.91957e9i	0.585887	−	0.138519i
$791$	1.55309e9			0.111578
$792$	−2.74903e9	+	2.29903e9i	−0.196626	+	0.164440i
$793$	−6.44318e9			−0.458822
$794$	1.25897e10	−	2.97653e9i	0.892572	−	0.211027i
$795$		−	2.20385e10i		−	1.55560i
$796$	−1.85691e10	+	9.30033e9i	−1.30496	+	0.653586i
$797$		−	8.07805e9i		−	0.565201i	−0.959238	−	0.282600i	$-0.908803\pi$
$797$		−	8.07805e9i		−	0.565201i	0.959238	−	0.282600i	$-0.0911970\pi$
$798$	−2.63047e8	−	1.11260e9i	−0.0183241	−	0.0775046i
$799$	3.54019e9			0.245535
$800$	2.40169e10	+	1.04379e10i	1.65845	+	0.720775i
$801$	−4.63299e9			−0.318528
$802$	−9.08267e8	−	3.84165e9i	−0.0621732	−	0.262971i
$803$		−	1.63048e10i		−	1.11125i
$804$	7.66898e9	−	3.84100e9i	0.520405	−	0.260644i
$805$		−	2.56998e9i		−	0.173638i
$806$	1.97554e10	−	4.67070e9i	1.32897	−	0.314203i
$807$	1.29173e10			0.865198
$808$	−1.78867e9	+	1.49587e9i	−0.119286	+	0.0997595i
$809$	6.18309e9			0.410568			0.205284	−	0.978702i	$-0.434188\pi$
$809$	6.18309e9			0.410568			0.205284	+	0.978702i	$0.434188\pi$
$810$	2.74073e9	−	6.47981e8i	0.181204	−	0.0428415i
$811$			3.48351e9i			0.229321i	0.993405	+	0.114660i	$0.0365780\pi$
$811$			3.48351e9i			0.229321i	−0.993405	+	0.114660i	$0.963422\pi$
$812$	−1.18225e8	−	2.36050e8i	−0.00774934	−	0.0154724i
$813$			3.20458e9i			0.209148i
$814$	−9.24488e8	−	3.91026e9i	−0.0600781	−	0.254109i
$815$	3.34901e10			2.16703
$816$	−1.83440e9	−	1.37191e9i	−0.118189	−	0.0883914i
$817$	−1.74516e10			−1.11959
$818$	−3.37623e8	−	1.42802e9i	−0.0215673	−	0.0912219i
$819$		−	8.58326e8i		−	0.0545957i
$820$	4.31347e9	+	8.61232e9i	0.273198	+	0.545471i
$821$			2.22317e10i			1.40208i	0.713123	+	0.701039i	$0.247280\pi$
$821$			2.22317e10i			1.40208i	−0.713123	+	0.701039i	$0.752720\pi$
$822$	1.73190e8	−	4.09467e7i	0.0108761	−	0.00257139i
$823$	2.30533e10			1.44156			0.720781	−	0.693163i	$-0.243783\pi$
$823$	2.30533e10			1.44156			0.720781	+	0.693163i	$0.243783\pi$
$824$	3.64322e8	+	4.35632e8i	0.0226851	+	0.0271253i
$825$	1.29483e10			0.802829
$826$	−1.32559e9	+	3.13405e8i	−0.0818428	+	0.0193498i
$827$		−	3.93422e9i		−	0.241874i	−0.992660	−	0.120937i	$-0.961410\pi$
$827$		−	3.93422e9i		−	0.241874i	0.992660	−	0.120937i	$-0.0385899\pi$
$828$	−5.63464e9	+	2.82211e9i	−0.344953	+	0.172769i
$829$		−	2.39962e10i		−	1.46286i	−0.681917	−	0.731430i	$-0.738853\pi$
$829$		−	2.39962e10i		−	1.46286i	0.681917	−	0.731430i	$-0.261147\pi$
$830$	9.64540e9	+	4.07966e10i	0.585527	+	2.47657i
$831$	−5.11406e9			−0.309145
$832$	−2.99138e10	−	5.37596e9i	−1.80069	−	0.323612i
$833$	−4.23028e9			−0.253578
$834$	2.68391e8	+	1.13520e9i	0.0160209	+	0.0677628i
$835$			3.65687e10i			2.17373i
$836$	−1.78975e10	+	8.96393e9i	−1.05942	+	0.530612i
$837$			2.43691e9i			0.143648i
$838$	−1.36326e9	+	3.22311e8i	−0.0800250	+	0.0189200i
$839$	−2.16432e10			−1.26518			−0.632592	−	0.774485i	$-0.718009\pi$
$839$	−2.16432e10			−1.26518			−0.632592	+	0.774485i	$0.718009\pi$
$840$	9.54538e8	+	1.14137e9i	0.0555668	+	0.0664432i
$841$	1.66054e10			0.962637
$842$	3.00245e8	−	7.09858e7i	0.0173334	−	0.00409807i
$843$		−	2.54012e8i		−	0.0146035i
$844$	1.23114e10	+	2.45811e10i	0.704870	+	1.40735i
$845$		−	6.89881e10i		−	3.93347i
$846$	1.29738e9	+	5.48745e9i	0.0736665	+	0.311583i
$847$	6.47012e8			0.0365864
$848$	−2.28640e10	−	1.70995e10i	−1.28756	−	0.962940i
$849$	1.55745e10			0.873450
$850$	1.90428e9	+	8.05442e9i	0.106356	+	0.449850i
$851$		−	7.06573e9i		−	0.393010i
$852$	−7.90267e8	−	1.57785e9i	−0.0437759	−	0.0874034i
$853$			2.96549e10i			1.63597i	0.575239	+	0.817985i	$0.304909\pi$
$853$			2.96549e10i			1.63597i	−0.575239	+	0.817985i	$0.695091\pi$
$854$	3.97678e8	−	9.40216e7i	0.0218489	−	0.00516565i
$855$	1.57305e10			0.860720
$856$	1.80986e10	−	1.51359e10i	0.986249	−	0.824805i
$857$	1.12112e10			0.608442			0.304221	−	0.952602i	$-0.401604\pi$
$857$	1.12112e10			0.608442			0.304221	+	0.952602i	$0.401604\pi$
$858$	−1.46247e10	+	3.45767e9i	−0.790464	+	0.186887i
$859$			3.49012e10i			1.87873i	0.342917	+	0.939366i	$0.388585\pi$
$859$			3.49012e10i			1.87873i	−0.342917	+	0.939366i	$0.611415\pi$
$860$	2.03077e10	−	1.01711e10i	1.08872	−	0.545285i
$861$			3.52403e8i			0.0188161i
$862$	2.77237e9	+	1.17262e10i	0.147427	+	0.623563i
$863$	−1.84338e10			−0.976286			−0.488143	−	0.872764i	$-0.662326\pi$
$863$	−1.84338e10			−0.976286			−0.488143	+	0.872764i	$0.662326\pi$
$864$	1.45427e9	−	3.34616e9i	0.0767089	−	0.176502i
$865$	−2.27110e10			−1.19311
$866$	−1.93025e9	−	8.16427e9i	−0.100995	−	0.427174i
$867$			1.03552e10i			0.539623i
$868$	−1.15116e9	+	5.76559e8i	−0.0597473	+	0.0299243i
$869$		−	5.34421e9i		−	0.276258i
$870$	3.53501e9	−	8.35770e8i	0.182001	−	0.0430298i
$871$	3.59675e10			1.84436
$872$	−2.66209e10	+	2.22632e10i	−1.35961	+	1.13705i
$873$	2.68441e9			0.136552
$874$	−3.42550e10	+	8.09879e9i	−1.73554	+	0.410327i
$875$		−	2.40306e9i		−	0.121265i
$876$	7.43375e9	+	1.48423e10i	0.373631	+	0.745997i
$877$			5.90107e9i			0.295415i	0.989031	+	0.147707i	$0.0471894\pi$
$877$			5.90107e9i			0.295415i	−0.989031	+	0.147707i	$0.952811\pi$
$878$	2.88184e9	+	1.21892e10i	0.143694	+	0.607775i
$879$	7.86611e9			0.390660
$880$	1.56022e10	−	2.08619e10i	0.771788	−	1.03197i
$881$	4.16251e9			0.205088			0.102544	−	0.994728i	$-0.467302\pi$
$881$	4.16251e9			0.205088			0.102544	+	0.994728i	$0.467302\pi$
$882$	−1.55028e9	−	6.55712e9i	−0.0760797	−	0.321790i
$883$		−	3.49741e10i		−	1.70956i	−0.518990	−	0.854780i	$-0.673692\pi$
$883$		−	3.49741e10i		−	1.70956i	0.518990	−	0.854780i	$-0.326308\pi$
$884$	−4.30166e9	−	8.58873e9i	−0.209437	−	0.418164i
$885$		−	1.87420e10i		−	0.908898i
$886$	1.22951e10	−	2.90687e9i	0.593899	−	0.140413i
$887$	−9.16854e9			−0.441131			−0.220566	−	0.975372i	$-0.570790\pi$
$887$	−9.16854e9			−0.441131			−0.220566	+	0.975372i	$0.570790\pi$
$888$	2.62434e9	+	3.13802e9i	0.125769	+	0.150387i
$889$	−1.35948e9			−0.0648958
$890$	3.27752e10	−	7.74891e9i	1.55840	−	0.368448i
$891$		−	1.80402e9i		−	0.0854416i
$892$	−1.45104e10	+	7.26750e9i	−0.684544	+	0.342853i
$893$			3.14954e10i			1.48002i
$894$	5.70840e8	+	2.41445e9i	0.0267198	+	0.113015i
$895$	−3.54454e10			−1.65264
$896$	1.92475e9	−	1.04706e8i	0.0893915	−	0.00486288i
$897$	−2.64265e10			−1.22255
$898$	−5.05481e9	−	2.13801e10i	−0.232937	−	0.985239i
$899$			3.14315e9i			0.144280i
$900$	−1.17868e10	+	5.90342e9i	−0.538950	+	0.269932i
$901$		−	9.02358e9i		−	0.411000i
$902$	6.00448e9	−	1.41962e9i	0.272429	−	0.0644093i
$903$	8.30962e8			0.0375556
$904$	1.77601e10	+	2.12364e10i	0.799571	+	0.956075i
$905$	−9.42420e9			−0.422644
$906$	−5.97086e9	+	1.41167e9i	−0.266740	+	0.0630643i
$907$		−	6.50089e9i		−	0.289299i	−0.989483	−	0.144650i	$-0.953794\pi$
$907$		−	6.50089e9i		−	0.289299i	0.989483	−	0.144650i	$-0.0462055\pi$
$908$	1.14315e10	+	2.28243e10i	0.506763	+	1.01181i
$909$		−	1.17379e9i		−	0.0518342i
$910$	1.43559e9	+	6.07206e9i	0.0631520	+	0.267111i
$911$	−2.88490e10			−1.26420			−0.632100	−	0.774887i	$-0.717807\pi$
$911$	−2.88490e10			−1.26420			−0.632100	+	0.774887i	$0.717807\pi$
$912$	1.22052e10	−	1.63198e10i	0.532800	−	0.712413i
$913$	2.68534e10			1.16775
$914$	−4.92850e9	−	2.08458e10i	−0.213503	−	0.903041i
$915$			5.62261e9i			0.242641i
$916$	−2.10120e9	−	4.19528e9i	−0.0903304	−	0.180355i
$917$			1.80274e9i			0.0772040i
$918$	1.12218e9	−	2.65313e8i	0.0478756	−	0.0113190i
$919$	−2.06389e10			−0.877167			−0.438584	−	0.898690i	$-0.644520\pi$
$919$	−2.06389e10			−0.877167			−0.438584	+	0.898690i	$0.644520\pi$
$920$	3.51411e10	−	2.93887e10i	1.48785	−	1.24429i
$921$	−7.25800e9			−0.306132
$922$	2.97790e10	−	7.04053e9i	1.25127	−	0.295833i
$923$		−	7.40013e9i		−	0.309766i
$924$	8.52193e8	−	4.26820e8i	0.0355375	−	0.0177989i
$925$		−	1.47804e10i		−	0.614033i
$926$	−8.32841e9	−	3.52262e10i	−0.344686	−	1.45790i
$927$	−2.85878e8			−0.0117870
$928$	1.87572e9	−	4.31590e9i	0.0770461	−	0.177277i
$929$	2.08036e10			0.851301			0.425651	−	0.904888i	$-0.360045\pi$
$929$	2.08036e10			0.851301			0.425651	+	0.904888i	$0.360045\pi$
$930$	−4.07586e9	−	1.72395e10i	−0.166161	−	0.702803i
$931$		−	3.76348e10i		−	1.52850i
$932$	−1.12846e10	+	5.65190e9i	−0.456596	+	0.228685i
$933$			2.33950e10i			0.943057i
$934$	−4.41362e10	+	1.04350e10i	−1.77248	+	0.419061i
$935$	8.23344e9			0.329413
$936$	1.17365e10	−	9.81527e9i	0.467813	−	0.391234i
$937$	−1.01845e10			−0.404437			−0.202219	−	0.979340i	$-0.564815\pi$
$937$	−1.01845e10			−0.404437			−0.202219	+	0.979340i	$0.564815\pi$
$938$	−2.21994e9	+	5.24852e8i	−0.0878277	+	0.0207648i
$939$			1.16208e10i			0.458043i
$940$	−1.83561e10	−	3.66500e10i	−0.720830	−	1.43922i
$941$			1.22264e10i			0.478340i	0.970978	+	0.239170i	$0.0768753\pi$
$941$			1.22264e10i			0.478340i	−0.970978	+	0.239170i	$0.923125\pi$
$942$	−5.01795e9	−	2.12242e10i	−0.195591	−	0.827280i
$943$	1.08499e10			0.421343
$944$	−1.94441e10	−	1.45418e10i	−0.752289	−	0.562623i
$945$	−7.49013e8			−0.0288721
$946$	−3.34744e9	−	1.41585e10i	−0.128556	−	0.543748i
$947$			1.46789e10i			0.561654i	0.959758	+	0.280827i	$0.0906087\pi$
$947$			1.46789e10i			0.561654i	−0.959758	+	0.280827i	$0.909391\pi$
$948$	2.43655e9	+	4.86484e9i	0.0928851	+	0.185455i
$949$			6.96103e10i			2.64388i
$950$	−7.16564e10	+	1.69415e10i	−2.71158	+	0.641088i
$951$	−8.60540e9			−0.324444
$952$	3.90832e8	+	4.67332e8i	0.0146812	+	0.0175548i
$953$	3.02381e10			1.13170			0.565848	−	0.824510i	$-0.308549\pi$
$953$	3.02381e10			1.13170			0.565848	+	0.824510i	$0.308549\pi$
$954$	1.39869e10	−	3.30688e9i	0.521558	−	0.123310i
$955$		−	1.53695e10i		−	0.571014i
$956$	1.23457e10	−	6.18331e9i	0.456996	−	0.228886i
$957$		−	2.32684e9i		−	0.0858171i
$958$	6.14684e9	+	2.59990e10i	0.225877	+	0.955382i
$959$	−4.73311e7			−0.00173293
$960$	−4.69130e9	+	2.61041e10i	−0.171137	+	0.952268i
$961$	−1.21842e10			−0.442858
$962$	3.94693e9	+	1.66941e10i	0.142938	+	0.604575i
$963$			1.18770e10i			0.428562i
$964$	1.08477e10	−	5.43308e9i	0.390005	−	0.195333i
$965$			4.67598e10i			1.67505i
$966$	1.63106e9	−	3.85626e8i	0.0582171	−	0.0137641i
$967$	5.85290e9			0.208151			0.104075	−	0.994569i	$-0.466812\pi$
$967$	5.85290e9			0.208151			0.104075	+	0.994569i	$0.466812\pi$
$968$	7.39882e9	+	8.84703e9i	0.262179	+	0.313497i
$969$	6.44081e9			0.227409
$970$	−1.89903e10	+	4.48981e9i	−0.668084	+	0.157953i
$971$			3.40526e10i			1.19367i	0.802366	+	0.596833i	$0.203574\pi$
$971$			3.40526e10i			1.19367i	−0.802366	+	0.596833i	$0.796426\pi$
$972$	8.22494e8	+	1.64220e9i	0.0287277	+	0.0573580i
$973$		−	3.10238e8i		−	0.0107969i
$974$	−7.36592e9	−	3.11552e10i	−0.255429	−	1.08038i
$975$	−5.52802e10			−1.91009
$976$	5.83322e9	+	4.36255e9i	0.200832	+	0.150199i
$977$	−1.22080e10			−0.418807			−0.209404	−	0.977829i	$-0.567152\pi$
$977$	−1.22080e10			−0.418807			−0.209404	+	0.977829i	$0.567152\pi$
$978$	5.02519e9	+	2.12548e10i	0.171777	+	0.726558i
$979$		−	2.15734e10i		−	0.734818i
$980$	2.19343e10	+	4.37942e10i	0.744443	+	1.48636i
$981$		−	1.74697e10i		−	0.590803i
$982$	3.34941e10	−	7.91888e9i	1.12870	−	0.266854i
$983$	−2.99405e10			−1.00536			−0.502680	−	0.864473i	$-0.667652\pi$
$983$	−2.99405e10			−1.00536			−0.502680	+	0.864473i	$0.667652\pi$
$984$	−4.81865e9	+	4.02986e9i	−0.161229	+	0.134836i
$985$	4.02697e10			1.34262
$986$	1.44740e9	−	3.42203e8i	0.0480860	−	0.0113688i
$987$		−	1.49966e9i		−	0.0496459i
$988$	7.64099e10	−	3.82698e10i	2.52058	−	1.26243i
$989$		−	2.55840e10i		−	0.840971i
$990$	3.01732e9	+	1.27622e10i	0.0988320	+	0.418025i
$991$	−2.04298e10			−0.666815			−0.333408	−	0.942783i	$-0.608199\pi$
$991$	−2.04298e10			−0.666815			−0.333408	+	0.942783i	$0.608199\pi$
$992$	−2.10477e10	−	9.14748e9i	−0.684562	−	0.297516i
$993$	2.86507e10			0.928565
$994$	1.07986e8	+	4.56742e8i	0.00348750	+	0.0147509i
$995$			7.59979e10i			2.44580i
$996$	−2.44447e10	+	1.22431e10i	−0.783928	+	0.392630i
$997$		−	2.36775e10i		−	0.756664i	−0.925670	−	0.378332i	$-0.876498\pi$
$997$		−	2.36775e10i		−	0.756664i	0.925670	−	0.378332i	$-0.123502\pi$
$998$	7.62381e9	−	1.80247e9i	0.242781	−	0.0573999i
$999$	−2.05929e9			−0.0653488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.d.a.13.7	✓	14
3.2	odd	2		72.8.d.d.37.8		14
4.3	odd	2		96.8.d.a.49.14		14
8.3	odd	2		96.8.d.a.49.1		14
8.5	even	2	inner	24.8.d.a.13.8	yes	14
12.11	even	2		288.8.d.d.145.1		14
24.5	odd	2		72.8.d.d.37.7		14
24.11	even	2		288.8.d.d.145.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.d.a.13.7	✓	14	1.1	even	1	trivial
24.8.d.a.13.8	yes	14	8.5	even	2	inner
72.8.d.d.37.7		14	24.5	odd	2
72.8.d.d.37.8		14	3.2	odd	2
96.8.d.a.49.1		14	8.3	odd	2
96.8.d.a.49.14		14	4.3	odd	2
288.8.d.d.145.1		14	12.11	even	2
288.8.d.d.145.14		14	24.11	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60309 - 11.0102i) q^{2} -27.0000i q^{3} +(-114.448 + 57.3210i) q^{4} +468.400i q^{5} +(-297.275 + 70.2836i) q^{6} +81.2421 q^{7} +(929.033 + 1110.88i) q^{8} -729.000 q^{9} +O(q^{10})\)	\(q+(-2.60309 - 11.0102i) q^{2} -27.0000i q^{3} +(-114.448 + 57.3210i) q^{4} +468.400i q^{5} +(-297.275 + 70.2836i) q^{6} +81.2421 q^{7} +(929.033 + 1110.88i) q^{8} -729.000 q^{9} +(5157.17 - 1219.29i) q^{10} -3394.58i q^{11} +(1547.67 + 3090.09i) q^{12} +14492.5i q^{13} +(-211.481 - 894.489i) q^{14} +12646.8 q^{15} +(9812.60 - 13120.5i) q^{16} +5178.19 q^{17} +(1897.66 + 8026.42i) q^{18} +46067.9i q^{19} +(-26849.2 - 53607.4i) q^{20} -2193.54i q^{21} +(-37374.9 + 8836.41i) q^{22} -67535.4 q^{23} +(29993.7 - 25083.9i) q^{24} -141274. q^{25} +(159565. - 37725.4i) q^{26} +19683.0i q^{27} +(-9297.97 + 4656.88i) q^{28} +25387.3i q^{29} +(-32920.8 - 139244. i) q^{30} +123808. q^{31} +(-170002. - 73884.4i) q^{32} -91653.7 q^{33} +(-13479.3 - 57012.8i) q^{34} +38053.8i q^{35} +(83432.4 - 41787.0i) q^{36} +104623. i q^{37} +(507216. - 119919. i) q^{38} +391298. q^{39} +(-520336. + 435159. i) q^{40} -160655. q^{41} +(-24151.2 + 5709.98i) q^{42} +378823. i q^{43} +(194581. + 388502. i) q^{44} -341464. i q^{45} +(175801. + 743577. i) q^{46} +683674. q^{47} +(-354254. - 264940. i) q^{48} -816943. q^{49} +(367749. + 1.55545e6i) q^{50} -139811. i q^{51} +(-830726. - 1.65864e6i) q^{52} -1.74261e6i q^{53} +(216713. - 51236.7i) q^{54} +1.59002e6 q^{55} +(75476.6 + 90250.0i) q^{56} +1.24383e6 q^{57} +(279518. - 66085.5i) q^{58} -1.48196e6i q^{59} +(-1.44740e6 + 724928. i) q^{60} +444587. i q^{61} +(-322284. - 1.36315e6i) q^{62} -59225.5 q^{63} +(-370947. + 2.06408e6i) q^{64} -6.78830e6 q^{65} +(238583. + 1.00912e6i) q^{66} -2.48180e6i q^{67} +(-592632. + 296819. i) q^{68} +1.82346e6i q^{69} +(418979. - 99057.7i) q^{70} -510618. q^{71} +(-677265. - 809830. i) q^{72} +4.80319e6 q^{73} +(1.15191e6 - 272342. i) q^{74} +3.81440e6i q^{75} +(-2.64066e6 - 5.27237e6i) q^{76} -275783. i q^{77} +(-1.01859e6 - 4.30826e6i) q^{78} +1.57434e6 q^{79} +(6.14566e6 + 4.59622e6i) q^{80} +531441. q^{81} +(418201. + 1.76884e6i) q^{82} +7.91066e6i q^{83} +(125736. + 251045. i) q^{84} +2.42547e6i q^{85} +(4.17091e6 - 986113. i) q^{86} +685456. q^{87} +(3.77096e6 - 3.15368e6i) q^{88} +6.35526e6 q^{89} +(-3.75958e6 + 888863. i) q^{90} +1.17740e6i q^{91} +(7.72928e6 - 3.87120e6i) q^{92} -3.34282e6i q^{93} +(-1.77967e6 - 7.52737e6i) q^{94} -2.15782e7 q^{95} +(-1.99488e6 + 4.59007e6i) q^{96} -3.68231e6 q^{97} +(2.12658e6 + 8.99468e6i) q^{98} +2.47465e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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