LMFDB - Embedded newform 60.7.c.a.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36400 - 7.88286i) q^{2} +15.5885i q^{3} +(-60.2790 + 21.5045i) q^{4} -55.9017 q^{5} +(122.882 - 21.2627i) q^{6} +86.8984i q^{7} +(251.737 + 445.839i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(-1.36400 - 7.88286i) q^{2} +15.5885i q^{3} +(-60.2790 + 21.5045i) q^{4} -55.9017 q^{5} +(122.882 - 21.2627i) q^{6} +86.8984i q^{7} +(251.737 + 445.839i) q^{8} -243.000 q^{9} +(76.2500 + 440.665i) q^{10} -1545.70i q^{11} +(-335.221 - 939.657i) q^{12} +3187.34 q^{13} +(685.008 - 118.530i) q^{14} -871.421i q^{15} +(3171.12 - 2592.54i) q^{16} +4062.12 q^{17} +(331.452 + 1915.54i) q^{18} +536.854i q^{19} +(3369.70 - 1202.14i) q^{20} -1354.61 q^{21} +(-12184.5 + 2108.34i) q^{22} -18107.3i q^{23} +(-6949.94 + 3924.20i) q^{24} +3125.00 q^{25} +(-4347.53 - 25125.3i) q^{26} -3788.00i q^{27} +(-1868.70 - 5238.15i) q^{28} +14939.5 q^{29} +(-6869.29 + 1188.62i) q^{30} -11771.9i q^{31} +(-24762.0 - 21461.2i) q^{32} +24095.1 q^{33} +(-5540.73 - 32021.1i) q^{34} -4857.77i q^{35} +(14647.8 - 5225.59i) q^{36} -34906.3 q^{37} +(4231.95 - 732.270i) q^{38} +49685.7i q^{39} +(-14072.5 - 24923.2i) q^{40} +108362. q^{41} +(1847.69 + 10678.2i) q^{42} +91972.0i q^{43} +(33239.4 + 93173.2i) q^{44} +13584.1 q^{45} +(-142737. + 24698.4i) q^{46} -17272.4i q^{47} +(40413.6 + 49432.8i) q^{48} +110098. q^{49} +(-4262.50 - 24633.9i) q^{50} +63322.2i q^{51} +(-192130. + 68542.0i) q^{52} +238792. q^{53} +(-29860.2 + 5166.83i) q^{54} +86407.2i q^{55} +(-38742.7 + 21875.6i) q^{56} -8368.73 q^{57} +(-20377.5 - 117766. i) q^{58} +95677.8i q^{59} +(18739.4 + 52528.4i) q^{60} -144057. q^{61} +(-92796.3 + 16056.9i) q^{62} -21116.3i q^{63} +(-135401. + 224469. i) q^{64} -178178. q^{65} +(-32865.7 - 189938. i) q^{66} -494031. i q^{67} +(-244860. + 87353.7i) q^{68} +282265. q^{69} +(-38293.1 + 6626.01i) q^{70} +263745. i q^{71} +(-61172.2 - 108339. i) q^{72} -225002. q^{73} +(47612.3 + 275162. i) q^{74} +48713.9i q^{75} +(-11544.8 - 32361.0i) q^{76} +134319. q^{77} +(391665. - 67771.3i) q^{78} +318736. i q^{79} +(-177271. + 144927. i) q^{80} +59049.0 q^{81} +(-147806. - 854203. i) q^{82} -880209. i q^{83} +(81654.7 - 29130.2i) q^{84} -227079. q^{85} +(725003. - 125450. i) q^{86} +232883. i q^{87} +(689133. - 389110. i) q^{88} -198618. q^{89} +(-18528.7 - 107082. i) q^{90} +276975. i q^{91} +(389388. + 1.09149e6i) q^{92} +183506. q^{93} +(-136156. + 23559.5i) q^{94} -30011.1i q^{95} +(334548. - 386001. i) q^{96} -141679. q^{97} +(-150173. - 867885. i) q^{98} +375605. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.36400	−	7.88286i	−0.170500	−	0.985358i
$2$	−1.36400	−	7.88286i	−0.170500	−	0.985358i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−60.2790	+	21.5045i	−0.941859	+	0.336007i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	122.882	−	21.2627i	0.568897	−	0.0984383i
$7$			86.8984i			0.253348i	0.991944	+	0.126674i	$0.0404302\pi$
$7$			86.8984i			0.253348i	−0.991944	+	0.126674i	$0.959570\pi$
$8$	251.737	+	445.839i	0.491675	+	0.870779i
$9$	−243.000			−0.333333
$10$	76.2500	+	440.665i	0.0762500	+	0.440665i
$11$		−	1545.70i		−	1.16131i	−0.814151	−	0.580653i	$-0.802797\pi$
$11$		−	1545.70i		−	1.16131i	0.814151	−	0.580653i	$-0.197203\pi$
$12$	−335.221	−	939.657i	−0.193994	−	0.543783i
$13$	3187.34			1.45077			0.725384	−	0.688344i	$-0.241662\pi$
$13$	3187.34			1.45077			0.725384	+	0.688344i	$0.241662\pi$
$14$	685.008	−	118.530i	0.249639	−	0.0431959i
$15$		−	871.421i		−	0.258199i
$16$	3171.12	−	2592.54i	0.774198	−	0.632943i
$17$	4062.12			0.826810			0.413405	−	0.910547i	$-0.364339\pi$
$17$	4062.12			0.826810			0.413405	+	0.910547i	$0.364339\pi$
$18$	331.452	+	1915.54i	0.0568334	+	0.328453i
$19$			536.854i			0.0782701i	0.999234	+	0.0391350i	$0.0124602\pi$
$19$			536.854i			0.0782701i	−0.999234	+	0.0391350i	$0.987540\pi$
$20$	3369.70	−	1202.14i	0.421212	−	0.150267i
$21$	−1354.61			−0.146271
$22$	−12184.5	+	2108.34i	−1.14430	+	0.198003i
$23$		−	18107.3i		−	1.48823i	−0.668052	−	0.744115i	$-0.732871\pi$
$23$		−	18107.3i		−	1.48823i	0.668052	−	0.744115i	$-0.267129\pi$
$24$	−6949.94	+	3924.20i	−0.502745	+	0.283868i
$25$	3125.00			0.200000
$26$	−4347.53	−	25125.3i	−0.247356	−	1.42953i
$27$		−	3788.00i		−	0.192450i
$28$	−1868.70	−	5238.15i	−0.0851269	−	0.238618i
$29$	14939.5			0.612549			0.306275	−	0.951943i	$-0.400917\pi$
$29$	14939.5			0.612549			0.306275	+	0.951943i	$0.400917\pi$
$30$	−6869.29	+	1188.62i	−0.254418	+	0.0440230i
$31$		−	11771.9i		−	0.395150i	−0.980288	−	0.197575i	$-0.936693\pi$
$31$		−	11771.9i		−	0.395150i	0.980288	−	0.197575i	$-0.0633066\pi$
$32$	−24762.0	−	21461.2i	−0.755676	−	0.654945i
$33$	24095.1			0.670481
$34$	−5540.73	−	32021.1i	−0.140971	−	0.814704i
$35$		−	4857.77i		−	0.113301i
$36$	14647.8	−	5225.59i	0.313953	−	0.112002i
$37$	−34906.3			−0.689127			−0.344563	−	0.938763i	$-0.611973\pi$
$37$	−34906.3			−0.689127			−0.344563	+	0.938763i	$0.611973\pi$
$38$	4231.95	−	732.270i	0.0771240	−	0.0133451i
$39$			49685.7i			0.837602i
$40$	−14072.5	−	24923.2i	−0.219884	−	0.389424i
$41$	108362.			1.57226			0.786132	−	0.618058i	$-0.212081\pi$
$41$	108362.			1.57226			0.786132	+	0.618058i	$0.212081\pi$
$42$	1847.69	+	10678.2i	0.0249392	+	0.144129i
$43$			91972.0i			1.15678i	0.815761	+	0.578389i	$0.196319\pi$
$43$			91972.0i			1.15678i	−0.815761	+	0.578389i	$0.803681\pi$
$44$	33239.4	+	93173.2i	0.390207	+	1.09379i
$45$	13584.1			0.149071
$46$	−142737.	+	24698.4i	−1.46644	+	0.253743i
$47$		−	17272.4i		−	0.166363i	−0.996534	−	0.0831817i	$-0.973492\pi$
$47$		−	17272.4i		−	0.166363i	0.996534	−	0.0831817i	$-0.0265082\pi$
$48$	40413.6	+	49432.8i	0.365430	+	0.446984i
$49$	110098.			0.935815
$50$	−4262.50	−	24633.9i	−0.0341000	−	0.197072i
$51$			63322.2i			0.477359i
$52$	−192130.	+	68542.0i	−1.36642	+	0.487469i
$53$	238792.			1.60395			0.801977	−	0.597355i	$-0.203781\pi$
$53$	238792.			1.60395			0.801977	+	0.597355i	$0.203781\pi$
$54$	−29860.2	+	5166.83i	−0.189632	+	0.0328128i
$55$			86407.2i			0.519352i
$56$	−38742.7	+	21875.6i	−0.220610	+	0.124565i
$57$	−8368.73			−0.0451892
$58$	−20377.5	−	117766.i	−0.104440	−	0.603580i
$59$			95677.8i			0.465860i	0.972494	+	0.232930i	$0.0748312\pi$
$59$			95677.8i			0.465860i	−0.972494	+	0.232930i	$0.925169\pi$
$60$	18739.4	+	52528.4i	0.0867567	+	0.243187i
$61$	−144057.			−0.634666			−0.317333	−	0.948314i	$-0.602787\pi$
$61$	−144057.			−0.634666			−0.317333	+	0.948314i	$0.602787\pi$
$62$	−92796.3	+	16056.9i	−0.389364	+	0.0673731i
$63$		−	21116.3i		−	0.0844494i
$64$	−135401.	+	224469.i	−0.516512	+	0.856280i
$65$	−178178.			−0.648803
$66$	−32865.7	−	189938.i	−0.114317	−	0.660663i
$67$		−	494031.i		−	1.64259i	−0.570501	−	0.821297i	$-0.693251\pi$
$67$		−	494031.i		−	1.64259i	0.570501	−	0.821297i	$-0.306749\pi$
$68$	−244860.	+	87353.7i	−0.778739	+	0.277814i
$69$	282265.			0.859230
$70$	−38293.1	+	6626.01i	−0.111642	+	0.0193178i
$71$			263745.i			0.736902i	0.929647	+	0.368451i	$0.120112\pi$
$71$			263745.i			0.736902i	−0.929647	+	0.368451i	$0.879888\pi$
$72$	−61172.2	−	108339.i	−0.163892	−	0.290260i
$73$	−225002.			−0.578386			−0.289193	−	0.957271i	$-0.593387\pi$
$73$	−225002.			−0.578386			−0.289193	+	0.957271i	$0.593387\pi$
$74$	47612.3	+	275162.i	0.117496	+	0.679036i
$75$			48713.9i			0.115470i
$76$	−11544.8	−	32361.0i	−0.0262993	−	0.0737194i
$77$	134319.			0.294215
$78$	391665.	−	67771.3i	0.825337	−	0.142811i
$79$			318736.i			0.646471i	0.946318	+	0.323236i	$0.104771\pi$
$79$			318736.i			0.646471i	−0.946318	+	0.323236i	$0.895229\pi$
$80$	−177271.	+	144927.i	−0.346232	+	0.283061i
$81$	59049.0			0.111111
$82$	−147806.	−	854203.i	−0.268071	−	1.54924i
$83$		−	880209.i		−	1.53940i	−0.638406	−	0.769700i	$-0.720406\pi$
$83$		−	880209.i		−	1.53940i	0.638406	−	0.769700i	$-0.279594\pi$
$84$	81654.7	−	29130.2i	0.137766	−	0.0491480i
$85$	−227079.			−0.369761
$86$	725003.	−	125450.i	1.13984	−	0.197231i
$87$			232883.i			0.353656i
$88$	689133.	−	389110.i	1.01124	−	0.570985i
$89$	−198618.			−0.281740			−0.140870	−	0.990028i	$-0.544990\pi$
$89$	−198618.			−0.281740			−0.140870	+	0.990028i	$0.544990\pi$
$90$	−18528.7	−	107082.i	−0.0254167	−	0.146888i
$91$			276975.i			0.367550i
$92$	389388.	+	1.09149e6i	0.500056	+	1.40170i
$93$	183506.			0.228140
$94$	−136156.	+	23559.5i	−0.163928	+	0.0283650i
$95$		−	30011.1i		−	0.0350034i
$96$	334548.	−	386001.i	0.378133	−	0.436290i
$97$	−141679.			−0.155235			−0.0776175	−	0.996983i	$-0.524731\pi$
$97$	−141679.			−0.155235			−0.0776175	+	0.996983i	$0.524731\pi$
$98$	−150173.	−	867885.i	−0.159557	−	0.922112i
$99$			375605.i			0.387102i
$100$	−188372.	+	67201.5i	−0.188372	+	0.0672015i
$101$	1.23128e6			1.19506			0.597532	−	0.801845i	$-0.296148\pi$
$101$	1.23128e6			1.19506			0.597532	+	0.801845i	$0.296148\pi$
$102$	499160.	−	86371.5i	0.470369	−	0.0813898i
$103$		−	1.34540e6i		−	1.23123i	−0.788047	−	0.615615i	$-0.788908\pi$
$103$		−	1.34540e6i		−	1.23123i	0.788047	−	0.615615i	$-0.211092\pi$
$104$	802372.	+	1.42104e6i	0.713306	+	1.26330i
$105$	75725.1			0.0654142
$106$	−325713.	−	1.88236e6i	−0.273475	−	1.58047i
$107$		−	1.09887e6i		−	0.897006i	−0.893781	−	0.448503i	$-0.851957\pi$
$107$		−	1.09887e6i		−	0.897006i	0.893781	−	0.448503i	$-0.148043\pi$
$108$	81458.8	+	228337.i	0.0646646	+	0.181261i
$109$	−1.90361e6			−1.46994			−0.734968	−	0.678101i	$-0.762803\pi$
$109$	−1.90361e6			−1.46994			−0.734968	+	0.678101i	$0.762803\pi$
$110$	681136.	−	117860.i	0.511747	−	0.0885496i
$111$		−	544136.i		−	0.397867i
$112$	225287.	+	275565.i	0.160355	+	0.196142i
$113$	−2.70511e6			−1.87478			−0.937389	−	0.348284i	$-0.886764\pi$
$113$	−2.70511e6			−1.87478			−0.937389	+	0.348284i	$0.886764\pi$
$114$	11415.0	+	65969.5i	0.00770477	+	0.0445276i
$115$			1.01223e6i			0.665557i
$116$	−900536.	+	321265.i	−0.576935	+	0.205821i
$117$	−774523.			−0.483589
$118$	754215.	−	130505.i	0.459038	−	0.0794291i
$119$			352992.i			0.209471i
$120$	388513.	−	219369.i	0.224834	−	0.126950i
$121$	−617624.			−0.348632
$122$	196494.	+	1.13558e6i	0.108211	+	0.625373i
$123$			1.68920e6i			0.907747i
$124$	253149.	+	709599.i	0.132773	+	0.372176i
$125$	−174693.			−0.0894427
$126$	−166457.	+	28802.7i	−0.0832129	+	0.0143986i
$127$			1.50271e6i			0.733606i	0.930299	+	0.366803i	$0.119548\pi$
$127$			1.50271e6i			0.733606i	−0.930299	+	0.366803i	$0.880452\pi$
$128$	1.95414e6	+	761169.i	0.931807	+	0.362953i
$129$	−1.43370e6			−0.667867
$130$	243035.	+	1.40455e6i	0.110621	+	0.639303i
$131$		−	4.39609e6i		−	1.95547i	−0.209832	−	0.977737i	$-0.567292\pi$
$131$		−	4.39609e6i		−	1.95547i	0.209832	−	0.977737i	$-0.432708\pi$
$132$	−1.45243e6	+	518151.i	−0.631498	+	0.225286i
$133$	−46651.8			−0.0198296
$134$	−3.89438e6	+	673860.i	−1.61854	+	0.280063i
$135$			211755.i			0.0860663i
$136$	1.02259e6	+	1.81105e6i	0.406522	+	0.719969i
$137$	2.14601e6			0.834584			0.417292	−	0.908772i	$-0.362979\pi$
$137$	2.14601e6			0.834584			0.417292	+	0.908772i	$0.362979\pi$
$138$	−385010.	−	2.22505e6i	−0.146499	−	0.846649i
$139$			3.06053e6i			1.13960i	0.821784	+	0.569800i	$0.192979\pi$
$139$			3.06053e6i			1.13960i	−0.821784	+	0.569800i	$0.807021\pi$
$140$	104464.	+	292822.i	0.0380699	+	0.106713i
$141$	269249.			0.0960500
$142$	2.07907e6	−	359749.i	0.726112	−	0.125642i
$143$		−	4.92666e6i		−	1.68479i
$144$	−770581.	+	629986.i	−0.258066	+	0.210981i
$145$	−835141.			−0.273940
$146$	306903.	+	1.77366e6i	0.0986150	+	0.569917i
$147$			1.71625e6i			0.540293i
$148$	2.10412e6	−	750642.i	0.649060	−	0.231552i
$149$	−1.56754e6			−0.473871			−0.236936	−	0.971525i	$-0.576143\pi$
$149$	−1.56754e6			−0.473871			−0.236936	+	0.971525i	$0.576143\pi$
$150$	384005.	−	66445.9i	0.113779	−	0.0196877i
$151$			5.43173e6i			1.57764i	0.614626	+	0.788819i	$0.289307\pi$
$151$			5.43173e6i			1.57764i	−0.614626	+	0.788819i	$0.710693\pi$
$152$	−239351.	+	135146.i	−0.0681559	+	0.0384834i
$153$	−987095.			−0.275603
$154$	−183211.	−	1.05882e6i	−0.0501637	−	0.289907i
$155$			658070.i			0.176716i
$156$	−1.06846e6	−	2.99500e6i	−0.281440	−	0.788903i
$157$	6.05232e6			1.56395			0.781976	−	0.623309i	$-0.214212\pi$
$157$	6.05232e6			1.56395			0.781976	+	0.623309i	$0.214212\pi$
$158$	2.51255e6	−	434756.i	0.637006	−	0.110223i
$159$			3.72240e6i			0.926044i
$160$	1.38424e6	+	1.19972e6i	0.337949	+	0.292900i
$161$	1.57350e6			0.377040
$162$	−80542.9	−	465475.i	−0.0189445	−	0.109484i
$163$		−	1.11984e6i		−	0.258578i	−0.991607	−	0.129289i	$-0.958731\pi$
$163$		−	1.11984e6i		−	0.258578i	0.991607	−	0.129289i	$-0.0412695\pi$
$164$	−6.53195e6	+	2.33027e6i	−1.48085	+	0.528292i
$165$	−1.34695e6			−0.299848
$166$	−6.93856e6	+	1.20061e6i	−1.51686	+	0.262468i
$167$			2.51799e6i			0.540636i	0.962771	+	0.270318i	$0.0871288\pi$
$167$			2.51799e6i			0.540636i	−0.962771	+	0.270318i	$0.912871\pi$
$168$	−341007.	−	603939.i	−0.0719176	−	0.127369i
$169$	5.33232e6			1.10473
$170$	309736.	+	1.79003e6i	0.0630443	+	0.364347i
$171$		−	130456.i		−	0.0260900i
$172$	−1.97781e6	−	5.54398e6i	−0.388686	−	1.08952i
$173$	4153.24			0.000802137			0.000401069	−	1.00000i	$-0.499872\pi$
$173$	4153.24			0.000802137			0.000401069		1.00000i	$0.499872\pi$
$174$	1.83579e6	−	317653.i	0.348477	−	0.0602983i
$175$			271558.i			0.0506696i
$176$	−4.00728e6	−	4.90159e6i	−0.735041	−	0.899081i
$177$	−1.49147e6			−0.268964
$178$	270916.	+	1.56568e6i	0.0480368	+	0.277615i
$179$		−	3.95787e6i		−	0.690084i	−0.938587	−	0.345042i	$-0.887865\pi$
$179$		−	3.95787e6i		−	0.690084i	0.938587	−	0.345042i	$-0.112135\pi$
$180$	−818837.	+	292119.i	−0.140404	+	0.0500890i
$181$	9.51906e6			1.60531			0.802654	−	0.596446i	$-0.203421\pi$
$181$	9.51906e6			1.60531			0.802654	+	0.596446i	$0.203421\pi$
$182$	2.18335e6	−	377794.i	0.362168	−	0.0626673i
$183$		−	2.24563e6i		−	0.366424i
$184$	8.07293e6	−	4.55828e6i	1.29592	−	0.731725i
$185$	1.95132e6			0.308187
$186$	−250302.	−	1.44655e6i	−0.0388979	−	0.224799i
$187$		−	6.27881e6i		−	0.960180i
$188$	371433.	+	1.04116e6i	0.0558993	+	0.156691i
$189$	329171.			0.0487569
$190$	−236573.	+	40935.1i	−0.0344909	+	0.00596809i
$191$		−	6.63547e6i		−	0.952295i	−0.879365	−	0.476148i	$-0.842033\pi$
$191$		−	6.63547e6i		−	0.952295i	0.879365	−	0.476148i	$-0.157967\pi$
$192$	−3.49912e6	−	2.11069e6i	−0.494373	−	0.298208i
$193$	−4.88164e6			−0.679037			−0.339519	−	0.940599i	$-0.610264\pi$
$193$	−4.88164e6			−0.679037			−0.339519	+	0.940599i	$0.610264\pi$
$194$	193250.	+	1.11683e6i	0.0264676	+	0.152962i
$195$		−	2.77751e6i		−	0.374587i
$196$	−6.63658e6	+	2.36759e6i	−0.881406	+	0.314441i
$197$	3.69499e6			0.483297			0.241649	−	0.970364i	$-0.422312\pi$
$197$	3.69499e6			0.483297			0.241649	+	0.970364i	$0.422312\pi$
$198$	2.96084e6	−	512325.i	0.381434	−	0.0660010i
$199$		−	137140.i		−	0.0174023i	−0.999962	−	0.00870113i	$-0.997230\pi$
$199$		−	137140.i		−	0.0174023i	0.999962	−	0.00870113i	$-0.00276969\pi$
$200$	786679.	+	1.39325e6i	0.0983349	+	0.174156i
$201$	7.70119e6			0.948352
$202$	−1.67946e6	−	9.70598e6i	−0.203759	−	1.17757i
$203$			1.29822e6i			0.155188i
$204$	−1.36171e6	−	3.81700e6i	−0.160396	−	0.449605i
$205$	−6.05762e6			−0.703138
$206$	−1.06056e7	+	1.83513e6i	−1.21320	+	0.209925i
$207$			4.40007e6i			0.496077i
$208$	1.01074e7	−	8.26329e6i	1.12318	−	0.918254i
$209$	829815.			0.0908955
$210$	−103289.	−	596931.i	−0.0111531	−	0.0644564i
$211$			372967.i			0.0397029i	0.999803	+	0.0198515i	$0.00631933\pi$
$211$			372967.i			0.0397029i	−0.999803	+	0.0198515i	$0.993681\pi$
$212$	−1.43941e7	+	5.13509e6i	−1.51070	+	0.538940i
$213$	−4.11138e6			−0.425451
$214$	−8.66225e6	+	1.49886e6i	−0.883872	+	0.152940i
$215$		−	5.14139e6i		−	0.517327i
$216$	1.68884e6	−	953580.i	0.167582	−	0.0946228i
$217$	1.02296e6			0.100111
$218$	2.59653e6	+	1.50059e7i	0.250625	+	1.44841i
$219$		−	3.50744e6i		−	0.333931i
$220$	−1.85814e6	−	5.20854e6i	−0.174506	−	0.489157i
$221$	1.29473e7			1.19951
$222$	−4.28935e6	+	742202.i	−0.392042	+	0.0678365i
$223$			1.01313e7i			0.913591i	0.889572	+	0.456795i	$0.151003\pi$
$223$			1.01313e7i			0.913591i	−0.889572	+	0.456795i	$0.848997\pi$
$224$	1.86495e6	−	2.15178e6i	0.165929	−	0.191449i
$225$	−759375.			−0.0666667
$226$	3.68978e6	+	2.13240e7i	0.319650	+	1.84733i
$227$			4.30252e6i			0.367829i	0.982942	+	0.183914i	$0.0588769\pi$
$227$			4.30252e6i			0.367829i	−0.982942	+	0.183914i	$0.941123\pi$
$228$	504459.	−	179965.i	0.0425619	−	0.0151839i
$229$	1.34915e7			1.12345			0.561724	−	0.827325i	$-0.310138\pi$
$229$	1.34915e7			1.12345			0.561724	+	0.827325i	$0.310138\pi$
$230$	7.97926e6	−	1.38068e6i	0.655811	−	0.113478i
$231$			2.09382e6i			0.169865i
$232$	3.76082e6	+	6.66059e6i	0.301175	+	0.533395i
$233$	−2.26239e7			−1.78855			−0.894273	−	0.447521i	$-0.852307\pi$
$233$	−2.26239e7			−1.78855			−0.894273	+	0.447521i	$0.852307\pi$
$234$	1.05645e6	+	6.10546e6i	0.0824521	+	0.476509i
$235$			965554.i			0.0744000i
$236$	−2.05750e6	−	5.76736e6i	−0.156532	−	0.438774i
$237$	−4.96860e6			−0.373240
$238$	2.78258e6	−	481481.i	0.206404	−	0.0357148i
$239$			4.98771e6i			0.365348i	0.983173	+	0.182674i	$0.0584754\pi$
$239$			4.98771e6i			0.365348i	−0.983173	+	0.182674i	$0.941525\pi$
$240$	−2.25919e6	−	2.76338e6i	−0.163425	−	0.199897i
$241$	3.64828e6			0.260637			0.130319	−	0.991472i	$-0.458400\pi$
$241$	3.64828e6			0.260637			0.130319	+	0.991472i	$0.458400\pi$
$242$	842439.	+	4.86864e6i	0.0594419	+	0.343528i
$243$			920483.i			0.0641500i
$244$	8.68361e6	−	3.09787e6i	0.597766	−	0.213252i
$245$	−6.15465e6			−0.418509
$246$	1.33157e7	−	2.30407e6i	0.894456	−	0.154771i
$247$			1.71114e6i			0.113552i
$248$	5.24838e6	−	2.96343e6i	0.344088	−	0.194285i
$249$	1.37211e7			0.888773
$250$	238281.	+	1.37708e6i	0.0152500	+	0.0881331i
$251$			9.91942e6i			0.627285i	0.949541	+	0.313643i	$0.101549\pi$
$251$			9.91942e6i			0.627285i	−0.949541	+	0.313643i	$0.898451\pi$
$252$	454095.	+	1.27287e6i	0.0283756	+	0.0795395i
$253$	−2.79884e7			−1.72829
$254$	1.18456e7	−	2.04969e6i	0.722865	−	0.125080i
$255$		−	3.53982e6i		−	0.213481i
$256$	3.33473e6	−	1.64425e7i	0.198766	−	0.980047i
$257$	1.34441e7			0.792015			0.396008	−	0.918247i	$-0.370395\pi$
$257$	1.34441e7			0.792015			0.396008	+	0.918247i	$0.370395\pi$
$258$	1.95557e6	+	1.13017e7i	0.113871	+	0.658087i
$259$		−	3.03331e6i		−	0.174589i
$260$	1.07404e7	−	3.83161e6i	0.611082	−	0.218003i
$261$	−3.63029e6			−0.204183
$262$	−3.46537e7	+	5.99627e6i	−1.92684	+	0.333409i
$263$			2.04971e7i			1.12674i	0.826204	+	0.563371i	$0.190496\pi$
$263$			2.04971e7i			1.12674i	−0.826204	+	0.563371i	$0.809504\pi$
$264$	6.06563e6	+	1.07425e7i	0.329658	+	0.583840i
$265$	−1.33489e7			−0.717310
$266$	63633.1	+	367750.i	0.00338095	+	0.0195392i
$267$		−	3.09615e6i		−	0.162663i
$268$	1.06239e7	+	2.97797e7i	0.551924	+	1.54709i
$269$	−2.45721e7			−1.26237			−0.631183	−	0.775634i	$-0.717430\pi$
$269$	−2.45721e7			−1.26237			−0.631183	+	0.775634i	$0.717430\pi$
$270$	1.66924e6	−	288835.i	0.0848061	−	0.0146743i
$271$			1.41101e7i			0.708962i	0.935063	+	0.354481i	$0.115342\pi$
$271$			1.41101e7i			0.708962i	−0.935063	+	0.354481i	$0.884658\pi$
$272$	1.28814e7	−	1.05312e7i	0.640115	−	0.523324i
$273$	−4.31761e6			−0.212205
$274$	−2.92716e6	−	1.69167e7i	−0.142297	−	0.822364i
$275$		−	4.83031e6i		−	0.232261i
$276$	−1.70146e7	+	6.06995e6i	−0.809274	+	0.288708i
$277$	−3.78003e7			−1.77851			−0.889255	−	0.457412i	$-0.848777\pi$
$277$	−3.78003e7			−1.77851			−0.889255	+	0.457412i	$0.848777\pi$
$278$	2.41257e7	−	4.17457e6i	1.12291	−	0.194302i
$279$			2.86057e6i			0.131717i
$280$	2.16578e6	−	1.22288e6i	0.0986599	−	0.0557071i
$281$	1.02523e7			0.462066			0.231033	−	0.972946i	$-0.425790\pi$
$281$	1.02523e7			0.462066			0.231033	+	0.972946i	$0.425790\pi$
$282$	−367257.	−	2.12246e6i	−0.0163765	−	0.0946436i
$283$		−	3.79250e7i		−	1.67327i	−0.547762	−	0.836635i	$-0.684520\pi$
$283$		−	3.79250e7i		−	1.67327i	0.547762	−	0.836635i	$-0.315480\pi$
$284$	−5.67170e6	−	1.58983e7i	−0.247604	−	0.694058i
$285$	467826.			0.0202092
$286$	−3.88362e7	+	6.71998e6i	−1.66012	+	0.287256i
$287$			9.41649e6i			0.398330i
$288$	6.01717e6	+	5.21508e6i	0.251892	+	0.218315i
$289$	−7.63676e6			−0.316385
$290$	1.13913e6	+	6.58330e6i	0.0467069	+	0.269929i
$291$		−	2.20855e6i		−	0.0896250i
$292$	1.35629e7	−	4.83855e6i	0.544759	−	0.194342i
$293$	−1.51174e7			−0.601000			−0.300500	−	0.953782i	$-0.597153\pi$
$293$	−1.51174e7			−0.601000			−0.300500	+	0.953782i	$0.597153\pi$
$294$	1.35290e7	−	2.34097e6i	0.532382	−	0.0921200i
$295$		−	5.34855e6i		−	0.208339i
$296$	−8.78723e6	−	1.55626e7i	−0.338826	−	0.600077i
$297$	−5.85510e6			−0.223494
$298$	2.13813e6	+	1.23567e7i	0.0807951	+	0.466932i
$299$		−	5.77141e7i		−	2.15908i
$300$	−1.04757e6	−	2.93643e6i	−0.0387988	−	0.108757i
$301$	−7.99222e6			−0.293068
$302$	4.28176e7	−	7.40889e6i	1.55454	−	0.268988i
$303$			1.91937e7i			0.689971i
$304$	1.39181e6	+	1.70243e6i	0.0495405	+	0.0605965i
$305$	8.05303e6			0.283831
$306$	1.34640e6	+	7.78113e6i	0.0469904	+	0.271568i
$307$		−	3.85776e7i		−	1.33328i	−0.745382	−	0.666638i	$-0.767733\pi$
$307$		−	3.85776e7i		−	1.33328i	0.745382	−	0.666638i	$-0.232267\pi$
$308$	−8.09660e6	+	2.88845e6i	−0.277109	+	0.0988584i
$309$	2.09727e7			0.710851
$310$	5.18747e6	−	897608.i	0.174129	−	0.0301302i
$311$			4.61860e7i			1.53543i	0.640794	+	0.767713i	$0.278605\pi$
$311$			4.61860e7i			1.53543i	−0.640794	+	0.767713i	$0.721395\pi$
$312$	−2.21518e7	+	1.25077e7i	−0.729366	+	0.411827i
$313$	−1.41773e7			−0.462339			−0.231170	−	0.972913i	$-0.574255\pi$
$313$	−1.41773e7			−0.462339			−0.231170	+	0.972913i	$0.574255\pi$
$314$	−8.25538e6	−	4.77096e7i	−0.266654	−	1.54105i
$315$			1.18044e6i			0.0377669i
$316$	−6.85424e6	−	1.92131e7i	−0.217219	−	0.608885i
$317$	6.05126e7			1.89963			0.949813	−	0.312817i	$-0.101273\pi$
$317$	6.05126e7			1.89963			0.949813	+	0.312817i	$0.101273\pi$
$318$	2.93431e7	−	5.07736e6i	0.912484	−	0.157891i
$319$		−	2.30919e7i		−	0.711357i
$320$	7.56912e6	−	1.25482e7i	0.230991	−	0.382940i
$321$	1.71297e7			0.517887
$322$	−2.14625e6	−	1.24036e7i	−0.0642854	−	0.371520i
$323$			2.18077e6i			0.0647145i
$324$	−3.55941e6	+	1.26982e6i	−0.104651	+	0.0373341i
$325$	9.96043e6			0.290154
$326$	−8.82750e6	+	1.52746e6i	−0.254792	+	0.0440876i
$327$		−	2.96744e7i		−	0.848668i
$328$	2.72788e7	+	4.83120e7i	0.773042	+	1.36909i
$329$	1.50094e6			0.0421479
$330$	1.83725e6	+	1.06179e7i	0.0511241	+	0.295458i
$331$		−	1.01477e7i		−	0.279824i	−0.990164	−	0.139912i	$-0.955318\pi$
$331$		−	1.01477e7i		−	0.279824i	0.990164	−	0.139912i	$-0.0446820\pi$
$332$	1.89284e7	+	5.30581e7i	0.517250	+	1.44990i
$333$	8.48224e6			0.229709
$334$	1.98490e7	−	3.43454e6i	0.532720	−	0.0921785i
$335$			2.76172e7i			0.734590i
$336$	−4.29563e6	+	3.51188e6i	−0.113242	+	0.0925810i
$337$	5.39701e7			1.41014			0.705072	−	0.709136i	$-0.250915\pi$
$337$	5.39701e7			1.41014			0.705072	+	0.709136i	$0.250915\pi$
$338$	−7.27329e6	−	4.20339e7i	−0.188356	−	1.08855i
$339$		−	4.21685e7i		−	1.08240i
$340$	1.36881e7	−	4.88322e6i	0.348263	−	0.124242i
$341$	−1.81958e7			−0.458890
$342$	−1.02836e6	+	177942.i	−0.0257080	+	0.00444835i
$343$			1.97908e7i			0.490435i
$344$	−4.10047e7	+	2.31528e7i	−1.00730	+	0.568759i
$345$	−1.57791e7			−0.384259
$346$	−5665.02	−	32739.4i	−0.000136765	−	0.000790392i
$347$			4.90499e7i			1.17395i	0.809605	+	0.586975i	$0.199681\pi$
$347$			4.90499e7i			1.17395i	−0.809605	+	0.586975i	$0.800319\pi$
$348$	−5.00803e6	−	1.40380e7i	−0.118831	−	0.333094i
$349$	2.30969e7			0.543346			0.271673	−	0.962390i	$-0.412423\pi$
$349$	2.30969e7			0.543346			0.271673	+	0.962390i	$0.412423\pi$
$350$	2.14065e6	−	370405.i	0.0499277	−	0.00863918i
$351$		−	1.20736e7i		−	0.279201i
$352$	−3.31726e7	+	3.82746e7i	−0.760592	+	0.877572i
$353$	−8.59041e7			−1.95294			−0.976472	−	0.215642i	$-0.930816\pi$
$353$	−8.59041e7			−1.95294			−0.976472	+	0.215642i	$0.930816\pi$
$354$	2.03437e6	+	1.17570e7i	0.0458584	+	0.265026i
$355$		−	1.47438e7i		−	0.329553i
$356$	1.19725e7	−	4.27118e6i	0.265360	−	0.0946668i
$357$	−5.50260e6			−0.120938
$358$	−3.11993e7	+	5.39854e6i	−0.679980	+	0.117660i
$359$			4.12084e7i			0.890640i	0.895371	+	0.445320i	$0.146910\pi$
$359$			4.12084e7i			0.890640i	−0.895371	+	0.445320i	$0.853090\pi$
$360$	3.41963e6	+	6.05633e6i	0.0732945	+	0.129808i
$361$	4.67577e7			0.993874
$362$	−1.29840e7	−	7.50374e7i	−0.273705	−	1.58180i
$363$		−	9.62780e6i		−	0.201283i
$364$	−5.95619e6	−	1.66958e7i	−0.123499	−	0.346180i
$365$	1.25780e7			0.258662
$366$	−1.77020e7	+	3.06304e6i	−0.361059	+	0.0624754i
$367$			5.40236e7i			1.09291i	0.837488	+	0.546456i	$0.184023\pi$
$367$			5.40236e7i			1.09291i	−0.837488	+	0.546456i	$0.815977\pi$
$368$	−4.69438e7	−	5.74203e7i	−0.941965	−	1.15218i
$369$	−2.63320e7			−0.524088
$370$	−2.66161e6	−	1.53820e7i	−0.0525459	−	0.303674i
$371$			2.07506e7i			0.406359i
$372$	−1.10616e7	+	3.94620e6i	−0.214876	+	0.0766567i
$373$	5.45778e7			1.05169			0.525847	−	0.850579i	$-0.323748\pi$
$373$	5.45778e7			1.05169			0.525847	+	0.850579i	$0.323748\pi$
$374$	−4.94950e7	+	8.56431e6i	−0.946121	+	0.163711i
$375$		−	2.72319e6i		−	0.0516398i
$376$	7.70069e6	−	4.34810e6i	0.144866	−	0.0817967i
$377$	4.76171e7			0.888667
$378$	−448990.	−	2.59481e6i	−0.00831306	−	0.0480430i
$379$			7.14006e7i			1.31155i	0.754957	+	0.655774i	$0.227658\pi$
$379$			7.14006e7i			1.31155i	−0.754957	+	0.655774i	$0.772342\pi$
$380$	645372.	+	1.80904e6i	0.0117614	+	0.0329683i
$381$	−2.34249e7			−0.423548
$382$	−5.23065e7	+	9.05079e6i	−0.938352	+	0.162367i
$383$			2.38242e7i			0.424055i	0.977264	+	0.212028i	$0.0680067\pi$
$383$			2.38242e7i			0.424055i	−0.977264	+	0.212028i	$0.931993\pi$
$384$	−1.18654e7	+	3.04621e7i	−0.209551	+	0.537979i
$385$	−7.50865e6			−0.131577
$386$	6.65856e6	+	3.84813e7i	0.115776	+	0.669095i
$387$		−	2.23492e7i		−	0.385593i
$388$	8.54026e6	−	3.04673e6i	0.146210	−	0.0521601i
$389$	−3.32214e7			−0.564377			−0.282188	−	0.959359i	$-0.591060\pi$
$389$	−3.32214e7			−0.564377			−0.282188	+	0.959359i	$0.591060\pi$
$390$	−2.18948e7	+	3.78853e6i	−0.369102	+	0.0638671i
$391$		−	7.35540e7i		−	1.23048i
$392$	2.77157e7	+	4.90858e7i	0.460116	+	0.814888i
$393$	6.85282e7			1.12899
$394$	−5.03997e6	−	2.91271e7i	−0.0824023	−	0.476221i
$395$		−	1.78179e7i		−	0.289111i
$396$	−8.07718e6	−	2.26411e7i	−0.130069	−	0.364596i
$397$	−4.02591e7			−0.643417			−0.321709	−	0.946839i	$-0.604257\pi$
$397$	−4.02591e7			−0.643417			−0.321709	+	0.946839i	$0.604257\pi$
$398$	−1.08106e6	+	187059.i	−0.0171474	+	0.00296709i
$399$		−	727230.i		−	0.0114486i
$400$	9.90974e6	−	8.10167e6i	0.154840	−	0.126589i
$401$	3.97745e7			0.616839			0.308420	−	0.951250i	$-0.400200\pi$
$401$	3.97745e7			0.616839			0.308420	+	0.951250i	$0.400200\pi$
$402$	−1.05044e7	−	6.07074e7i	−0.161694	−	0.934466i
$403$		−	3.75211e7i		−	0.573271i
$404$	−7.42201e7	+	2.64779e7i	−1.12558	+	0.401550i
$405$	−3.30094e6			−0.0496904
$406$	1.02337e7	−	1.77077e6i	0.152916	−	0.0264596i
$407$			5.39547e7i			0.800287i
$408$	−2.82315e7	+	1.59406e7i	−0.415674	+	0.234705i
$409$	−1.31428e7			−0.192097			−0.0960483	−	0.995377i	$-0.530620\pi$
$409$	−1.31428e7			−0.192097			−0.0960483	+	0.995377i	$0.530620\pi$
$410$	8.26260e6	+	4.77514e7i	0.119885	+	0.692842i
$411$			3.34530e7i			0.481847i
$412$	2.89321e7	+	8.10993e7i	0.413702	+	1.15965i
$413$	−8.31425e6			−0.118025
$414$	3.46852e7	−	6.00170e6i	0.488813	−	0.0845811i
$415$			4.92052e7i			0.688440i
$416$	−7.89249e7	−	6.84042e7i	−1.09631	−	0.950174i
$417$	−4.77089e7			−0.657948
$418$	−1.13187e6	−	6.54132e6i	−0.0154977	−	0.0895646i
$419$			7.92855e6i			0.107783i	0.998547	+	0.0538917i	$0.0171626\pi$
$419$			7.92855e6i			0.107783i	−0.998547	+	0.0538917i	$0.982837\pi$
$420$	−4.56464e6	+	1.62843e6i	−0.0616110	+	0.0219797i
$421$	9.38186e7			1.25731			0.628655	−	0.777684i	$-0.283606\pi$
$421$	9.38186e7			1.25731			0.628655	+	0.777684i	$0.283606\pi$
$422$	2.94004e6	−	508727.i	0.0391216	−	0.00676936i
$423$			4.19718e6i			0.0554545i
$424$	6.01129e7	+	1.06463e8i	0.788624	+	1.39669i
$425$	1.26941e7			0.165362
$426$	5.60793e6	+	3.24095e7i	0.0725394	+	0.419221i
$427$		−	1.25183e7i		−	0.160791i
$428$	2.36306e7	+	6.62388e7i	0.301401	+	0.844854i
$429$	7.67991e7			0.972712
$430$	−4.05289e7	+	7.01287e6i	−0.509752	+	0.0882044i
$431$			2.86716e7i			0.358114i	0.983839	+	0.179057i	$0.0573046\pi$
$431$			2.86716e7i			0.358114i	−0.983839	+	0.179057i	$0.942695\pi$
$432$	−9.82051e6	−	1.20122e7i	−0.121810	−	0.148995i
$433$	8.16883e7			1.00623			0.503114	−	0.864220i	$-0.332188\pi$
$433$	8.16883e7			1.00623			0.503114	+	0.864220i	$0.332188\pi$
$434$	−1.39532e6	−	8.06386e6i	−0.0170689	−	0.0986447i
$435$		−	1.30186e7i		−	0.158160i
$436$	1.14748e8	−	4.09361e7i	1.38447	−	0.493910i
$437$	9.72098e6			0.116484
$438$	−2.76486e7	+	4.78415e6i	−0.329042	+	0.0569354i
$439$			1.61778e8i			1.91217i	0.293085	+	0.956086i	$0.405318\pi$
$439$			1.61778e8i			1.91217i	−0.293085	+	0.956086i	$0.594682\pi$
$440$	−3.85237e7	+	2.17519e7i	−0.452241	+	0.255352i
$441$	−2.67537e7			−0.311938
$442$	−1.76602e7	−	1.02062e8i	−0.204517	−	1.18195i
$443$		−	1.00373e8i		−	1.15453i	−0.816556	−	0.577266i	$-0.804120\pi$
$443$		−	1.00373e8i		−	1.15453i	0.816556	−	0.577266i	$-0.195880\pi$
$444$	1.17014e7	+	3.28000e7i	0.133686	+	0.374735i
$445$	1.11031e7			0.125998
$446$	7.98638e7	−	1.38191e7i	0.900214	−	0.155767i
$447$		−	2.44356e7i		−	0.273590i
$448$	−1.95060e7	−	1.17661e7i	−0.216937	−	0.130857i
$449$	−4.56145e7			−0.503922			−0.251961	−	0.967737i	$-0.581075\pi$
$449$	−4.56145e7			−0.503922			−0.251961	+	0.967737i	$0.581075\pi$
$450$	1.03579e6	+	5.98605e6i	0.0113667	+	0.0656905i
$451$		−	1.67495e8i		−	1.82588i
$452$	1.63061e8	−	5.81720e7i	1.76578	−	0.629939i
$453$	−8.46723e7			−0.910850
$454$	3.39162e7	−	5.86865e6i	0.362443	−	0.0627149i
$455$		−	1.54834e7i		−	0.164373i
$456$	−2.10672e6	−	3.73111e6i	−0.0222184	−	0.0393498i
$457$	−1.29981e8			−1.36186			−0.680928	−	0.732350i	$-0.738423\pi$
$457$	−1.29981e8			−1.36186			−0.680928	+	0.732350i	$0.738423\pi$
$458$	−1.84024e7	−	1.06351e8i	−0.191548	−	1.10700i
$459$		−	1.53873e7i		−	0.159120i
$460$	−2.17674e7	−	6.10161e7i	−0.223632	−	0.626861i
$461$	−1.24776e8			−1.27358			−0.636791	−	0.771036i	$-0.719739\pi$
$461$	−1.24776e8			−1.27358			−0.636791	+	0.771036i	$0.719739\pi$
$462$	1.65053e7	−	2.85598e6i	0.167378	−	0.0289620i
$463$		−	1.12030e8i		−	1.12874i	−0.825523	−	0.564369i	$-0.809120\pi$
$463$		−	1.12030e8i		−	1.12874i	0.825523	−	0.564369i	$-0.190880\pi$
$464$	4.73748e7	−	3.87311e7i	0.474235	−	0.387709i
$465$	−1.02583e7			−0.102027
$466$	3.08591e7	+	1.78341e8i	0.304947	+	1.76236i
$467$		−	1.67693e8i		−	1.64651i	−0.567670	−	0.823256i	$-0.692155\pi$
$467$		−	1.67693e8i		−	1.64651i	0.567670	−	0.823256i	$-0.307845\pi$
$468$	4.66875e7	−	1.66557e7i	0.455473	−	0.162490i
$469$	4.29306e7			0.416148
$470$	7.61133e6	−	1.31702e6i	0.0733106	−	0.0126852i
$471$			9.43464e7i			0.902948i
$472$	−4.26569e7	+	2.40857e7i	−0.405661	+	0.229051i
$473$	1.42161e8			1.34337
$474$	6.77717e6	+	3.91668e7i	0.0636376	+	0.367775i
$475$			1.67767e6i			0.0156540i
$476$	−7.59090e6	−	2.12780e7i	−0.0703837	−	0.197292i
$477$	−5.80264e7			−0.534651
$478$	3.93174e7	−	6.80324e6i	0.359999	−	0.0622920i
$479$		−	7.64619e7i		−	0.695726i	−0.937545	−	0.347863i	$-0.886907\pi$
$479$		−	7.64619e7i		−	0.695726i	0.937545	−	0.347863i	$-0.113093\pi$
$480$	−1.87018e7	+	2.15781e7i	−0.169106	+	0.195115i
$481$	−1.11258e8			−0.999763
$482$	−4.97625e6	−	2.87588e7i	−0.0444387	−	0.256821i
$483$			2.45284e7i			0.217684i
$484$	3.72297e7	−	1.32817e7i	0.328363	−	0.117143i
$485$	7.92009e6			0.0694232
$486$	7.25604e6	−	1.25554e6i	0.0632107	−	0.0109376i
$487$			4.97455e7i			0.430692i	0.976538	+	0.215346i	$0.0690880\pi$
$487$			4.97455e7i			0.430692i	−0.976538	+	0.215346i	$0.930912\pi$
$488$	−3.62645e7	−	6.42262e7i	−0.312049	−	0.552653i
$489$	1.74565e7			0.149290
$490$	8.39495e6	+	4.85162e7i	0.0713559	+	0.412381i
$491$		−	1.85343e8i		−	1.56578i	−0.622158	−	0.782891i	$-0.713744\pi$
$491$		−	1.85343e8i		−	1.56578i	0.622158	−	0.782891i	$-0.286256\pi$
$492$	−3.63253e7	−	1.01823e8i	−0.305010	−	0.854970i
$493$	6.06859e7			0.506462
$494$	1.34886e7	−	2.33399e6i	0.111889	−	0.0193606i
$495$		−	2.09969e7i		−	0.173117i
$496$	−3.05191e7	−	3.73301e7i	−0.250107	−	0.305924i
$497$	−2.29191e7			−0.186693
$498$	−1.87156e7	−	1.08161e8i	−0.151536	−	0.875759i
$499$			1.92003e8i			1.54527i	0.634848	+	0.772637i	$0.281063\pi$
$499$			1.92003e8i			1.54527i	−0.634848	+	0.772637i	$0.718937\pi$
$500$	1.05303e7	−	3.75668e6i	0.0842425	−	0.0300534i
$501$	−3.92516e7			−0.312136
$502$	7.81934e7	−	1.35301e7i	0.618100	−	0.106952i
$503$			8.45476e7i			0.664351i	0.943218	+	0.332175i	$0.107783\pi$
$503$			8.45476e7i			0.664351i	−0.943218	+	0.332175i	$0.892217\pi$
$504$	9.41448e6	−	5.31577e6i	0.0735368	−	0.0415216i
$505$	−6.88304e7			−0.534449
$506$	3.81762e7	+	2.20629e8i	0.294674	+	1.70298i
$507$			8.31226e7i			0.637816i
$508$	−3.23149e7	−	9.05817e7i	−0.246497	−	0.690954i
$509$	−1.50345e8			−1.14008			−0.570040	−	0.821617i	$-0.693072\pi$
$509$	−1.50345e8			−1.14008			−0.570040	+	0.821617i	$0.693072\pi$
$510$	−2.79039e7	+	4.82831e6i	−0.210356	+	0.0363986i
$511$		−	1.95523e7i		−	0.146533i
$512$	−1.34162e8	−	3.85971e6i	−0.999586	−	0.0287571i
$513$	2.03360e6			0.0150631
$514$	−1.83378e7	−	1.05978e8i	−0.135039	−	0.780418i
$515$			7.52101e7i			0.550623i
$516$	8.64221e7	−	3.08310e7i	0.629036	−	0.224408i
$517$	−2.66979e7			−0.193199
$518$	−2.39111e7	+	4.13743e6i	−0.172033	+	0.0297675i
$519$			64742.6i			0.000463114i
$520$	−4.48540e7	−	7.94385e7i	−0.319000	−	0.564964i
$521$	−2.12869e8			−1.50521			−0.752607	−	0.658470i	$-0.771204\pi$
$521$	−2.12869e8			−1.50521			−0.752607	+	0.658470i	$0.771204\pi$
$522$	4.95172e6	+	2.86171e7i	0.0348133	+	0.201193i
$523$			1.22260e7i			0.0854635i	0.999087	+	0.0427317i	$0.0136061\pi$
$523$			1.22260e7i			0.0854635i	−0.999087	+	0.0427317i	$0.986394\pi$
$524$	9.45355e7	+	2.64992e8i	0.657054	+	1.84178i
$525$	−4.23316e6			−0.0292541
$526$	1.61575e8	−	2.79580e7i	1.11024	−	0.192110i
$527$		−	4.78189e7i		−	0.326714i
$528$	7.64082e7	−	6.24673e7i	0.519085	−	0.424376i
$529$	−1.79838e8			−1.21483
$530$	1.82079e7	+	1.05227e8i	0.122302	+	0.706807i
$531$		−	2.32497e7i		−	0.155287i
$532$	2.81212e6	−	1.00322e6i	0.0186767	−	0.00666288i
$533$	3.45386e8			2.28099
$534$	−2.44065e7	+	4.22316e6i	−0.160281	+	0.0277341i
$535$			6.14288e7i			0.401153i
$536$	2.20258e8	−	1.24366e8i	1.43034	−	0.807622i
$537$	6.16971e7			0.398420
$538$	3.35164e7	+	1.93699e8i	0.215234	+	1.24388i
$539$		−	1.70178e8i		−	1.08677i
$540$	−4.55369e6	−	1.27644e7i	−0.0289189	−	0.0810623i
$541$	−2.07093e8			−1.30790			−0.653949	−	0.756539i	$-0.726889\pi$
$541$	−2.07093e8			−1.30790			−0.653949	+	0.756539i	$0.726889\pi$
$542$	1.11228e8	−	1.92462e7i	0.698581	−	0.120878i
$543$			1.48387e8i			0.926824i
$544$	−1.00586e8	−	8.71781e7i	−0.624801	−	0.541515i
$545$	1.06415e8			0.657376
$546$	5.88922e6	+	3.40351e7i	0.0361810	+	0.209098i
$547$		−	1.70930e8i		−	1.04438i	−0.852831	−	0.522188i	$-0.825116\pi$
$547$		−	1.70930e8i		−	1.04438i	0.852831	−	0.522188i	$-0.174884\pi$
$548$	−1.29359e8	+	4.61488e7i	−0.786061	+	0.280426i
$549$	3.50059e7			0.211555
$550$	−3.80767e7	+	6.58855e6i	−0.228860	+	0.0396006i
$551$			8.02032e6i			0.0479443i
$552$	7.10566e7	+	1.25845e8i	0.422461	+	0.748199i
$553$	−2.76976e7			−0.163782
$554$	5.15597e7	+	2.97975e8i	0.303236	+	1.75247i
$555$			3.04181e7i			0.177932i
$556$	−6.58151e7	−	1.84486e8i	−0.382914	−	1.07334i
$557$	−1.13400e8			−0.656215			−0.328107	−	0.944640i	$-0.606411\pi$
$557$	−1.13400e8			−0.656215			−0.328107	+	0.944640i	$0.606411\pi$
$558$	2.25495e7	−	3.90183e6i	0.129788	−	0.0224577i
$559$			2.93146e8i			1.67822i
$560$	−1.25939e7	−	1.54046e7i	−0.0717130	−	0.0877172i
$561$	9.78770e7			0.554360
$562$	−1.39842e7	−	8.08177e7i	−0.0787823	−	0.455300i
$563$			1.29905e8i			0.727947i	0.931409	+	0.363973i	$0.118580\pi$
$563$			1.29905e8i			0.727947i	−0.931409	+	0.363973i	$0.881420\pi$
$564$	−1.62301e7	+	5.79007e6i	−0.0904656	+	0.0322735i
$565$	1.51220e8			0.838426
$566$	−2.98957e8	+	5.17297e7i	−1.64877	+	0.285293i
$567$			5.13127e6i			0.0281498i
$568$	−1.17588e8	+	6.63946e7i	−0.641679	+	0.362316i
$569$	1.43283e8			0.777783			0.388892	−	0.921284i	$-0.372858\pi$
$569$	1.43283e8			0.777783			0.388892	+	0.921284i	$0.372858\pi$
$570$	−638116.	−	3.68781e6i	−0.00344568	−	0.0199133i
$571$			1.43037e8i			0.768318i	0.923267	+	0.384159i	$0.125509\pi$
$571$			1.43037e8i			0.768318i	−0.923267	+	0.384159i	$0.874491\pi$
$572$	1.05945e8	+	2.96974e8i	0.566101	+	1.58683i
$573$	1.03437e8			0.549808
$574$	7.42289e7	−	1.28441e7i	0.392498	−	0.0679154i
$575$		−	5.65853e7i		−	0.297646i
$576$	3.29023e7	−	5.45459e7i	0.172171	−	0.285427i
$577$	−2.37146e8			−1.23449			−0.617245	−	0.786771i	$-0.711751\pi$
$577$	−2.37146e8			−1.23449			−0.617245	+	0.786771i	$0.711751\pi$
$578$	1.04166e7	+	6.01996e7i	0.0539437	+	0.311752i
$579$		−	7.60972e7i		−	0.392042i
$580$	5.03415e7	−	1.79593e7i	0.258013	−	0.0920460i
$581$	7.64888e7			0.390004
$582$	−1.74097e7	+	3.01247e6i	−0.0883127	+	0.0152811i
$583$		−	3.69100e8i		−	1.86268i
$584$	−5.66414e7	−	1.00315e8i	−0.284378	−	0.503647i
$585$	4.32972e7			0.216268
$586$	2.06201e7	+	1.19168e8i	0.102471	+	0.592199i
$587$			2.64831e8i			1.30935i	0.755912	+	0.654674i	$0.227194\pi$
$587$			2.64831e8i			1.30935i	−0.755912	+	0.654674i	$0.772806\pi$
$588$	−3.69071e7	−	1.03454e8i	−0.181542	−	0.508880i
$589$	6.31980e6			0.0309284
$590$	−4.21619e7	+	7.29543e6i	−0.205288	+	0.0355218i
$591$			5.75992e7i			0.279032i
$592$	−1.10692e8	+	9.04959e7i	−0.533521	+	0.436178i
$593$	−1.78125e8			−0.854200			−0.427100	−	0.904204i	$-0.640465\pi$
$593$	−1.78125e8			−0.854200			−0.427100	+	0.904204i	$0.640465\pi$
$594$	7.98636e6	+	4.61549e7i	0.0381057	+	0.220221i
$595$		−	1.97328e7i		−	0.0936782i
$596$	9.44898e7	−	3.37091e7i	0.446320	−	0.159224i
$597$	2.13780e6			0.0100472
$598$	−4.54952e8	+	7.87221e7i	−2.12746	+	0.368123i
$599$		−	1.67621e8i		−	0.779915i	−0.920833	−	0.389958i	$-0.872490\pi$
$599$		−	1.67621e8i		−	0.779915i	0.920833	−	0.389958i	$-0.127510\pi$
$600$	−2.17186e7	+	1.22631e7i	−0.100549	+	0.0567737i
$601$	2.23815e7			0.103102			0.0515508	−	0.998670i	$-0.483584\pi$
$601$	2.23815e7			0.103102			0.0515508	+	0.998670i	$0.483584\pi$
$602$	1.09014e7	+	6.30016e7i	0.0499681	+	0.288777i
$603$			1.20050e8i			0.547531i
$604$	−1.16806e8	−	3.27419e8i	−0.530098	−	1.48591i
$605$	3.45262e7			0.155913
$606$	1.51301e8	−	2.61802e7i	0.679868	−	0.117640i
$607$			2.34167e8i			1.04703i	0.852017	+	0.523515i	$0.175380\pi$
$607$			2.34167e8i			1.04703i	−0.852017	+	0.523515i	$0.824620\pi$
$608$	1.15216e7	−	1.32936e7i	0.0512626	−	0.0591468i
$609$	−2.02372e7			−0.0895980
$610$	−1.09843e7	−	6.34809e7i	−0.0483932	−	0.279675i
$611$		−	5.50528e7i		−	0.241355i
$612$	5.95011e7	−	2.12269e7i	0.259580	−	0.0926047i
$613$	3.31792e8			1.44040			0.720202	−	0.693765i	$-0.244049\pi$
$613$	3.31792e8			1.44040			0.720202	+	0.693765i	$0.244049\pi$
$614$	−3.04102e8	+	5.26199e7i	−1.31375	+	0.227324i
$615$		−	9.44290e7i		−	0.405957i
$616$	3.38131e7	+	5.98845e7i	0.144658	+	0.256196i
$617$	2.84884e8			1.21287			0.606433	−	0.795135i	$-0.292600\pi$
$617$	2.84884e8			1.21287			0.606433	+	0.795135i	$0.292600\pi$
$618$	−2.86068e7	−	1.65325e8i	−0.121200	−	0.700443i
$619$		−	2.80053e8i		−	1.18078i	−0.807119	−	0.590389i	$-0.798974\pi$
$619$		−	2.80053e8i		−	1.18078i	0.807119	−	0.590389i	$-0.201026\pi$
$620$	−1.41514e7	−	3.96678e7i	−0.0593780	−	0.166442i
$621$	−6.85903e7			−0.286410
$622$	3.64078e8	−	6.29977e7i	1.51294	−	0.261790i
$623$		−	1.72596e7i		−	0.0713784i
$624$	1.28812e8	+	1.57559e8i	0.530154	+	0.648470i
$625$	9.76562e6			0.0400000
$626$	1.93379e7	+	1.11758e8i	0.0788289	+	0.455570i
$627$			1.29355e7i			0.0524785i
$628$	−3.64828e8	+	1.30152e8i	−1.47302	+	0.525499i
$629$	−1.41794e8			−0.569777
$630$	9.30523e6	−	1.61012e6i	0.0372139	−	0.00643927i
$631$			1.42135e8i			0.565733i	0.959159	+	0.282867i	$0.0912854\pi$
$631$			1.42135e8i			0.565733i	−0.959159	+	0.282867i	$0.908715\pi$
$632$	−1.42105e8	+	8.02377e7i	−0.562934	+	0.317854i
$633$	−5.81397e6			−0.0229225
$634$	−8.25393e7	−	4.77013e8i	−0.323887	−	1.87181i
$635$		−	8.40039e7i		−	0.328079i
$636$	−8.00482e7	−	2.24382e8i	−0.311157	−	0.872203i
$637$	3.50918e8			1.35765
$638$	−1.82030e8	+	3.14974e7i	−0.700941	+	0.121287i
$639$		−	6.40901e7i		−	0.245634i
$640$	−1.09240e8	−	4.25506e7i	−0.416717	−	0.162318i
$641$	2.05020e8			0.778435			0.389217	−	0.921146i	$-0.372745\pi$
$641$	2.05020e8			0.778435			0.389217	+	0.921146i	$0.372745\pi$
$642$	−2.33649e7	−	1.35031e8i	−0.0882998	−	0.510304i
$643$			8.84803e7i			0.332823i	0.986056	+	0.166412i	$0.0532180\pi$
$643$			8.84803e7i			0.332823i	−0.986056	+	0.166412i	$0.946782\pi$
$644$	−9.48487e7	+	3.38372e7i	−0.355119	+	0.126688i
$645$	8.01464e7			0.298679
$646$	1.71907e7	−	2.97457e6i	0.0637669	−	0.0110338i
$647$		−	3.76256e8i		−	1.38922i	−0.719387	−	0.694609i	$-0.755577\pi$
$647$		−	3.76256e8i		−	1.38922i	0.719387	−	0.694609i	$-0.244423\pi$
$648$	1.48648e7	+	2.63263e7i	0.0546305	+	0.0967532i
$649$	1.47889e8			0.541006
$650$	−1.35860e7	−	7.85167e7i	−0.0494713	−	0.285905i
$651$			1.59464e7i			0.0577988i
$652$	2.40815e7	+	6.75025e7i	0.0868840	+	0.243544i
$653$	1.08922e8			0.391180			0.195590	−	0.980686i	$-0.437338\pi$
$653$	1.08922e8			0.391180			0.195590	+	0.980686i	$0.437338\pi$
$654$	−2.33919e8	+	4.04759e7i	−0.836242	+	0.144698i
$655$			2.45749e8i			0.874515i
$656$	3.43629e8	−	2.80932e8i	1.21724	−	0.995154i
$657$	5.46755e7			0.192795
$658$	−2.04729e6	−	1.18317e7i	−0.00718622	−	0.0415308i
$659$		−	2.73716e8i		−	0.956410i	−0.878248	−	0.478205i	$-0.841288\pi$
$659$		−	2.73716e8i		−	0.956410i	0.878248	−	0.478205i	$-0.158712\pi$
$660$	8.11931e7	−	2.89655e7i	0.282415	−	0.100751i
$661$	−3.25447e8			−1.12687			−0.563437	−	0.826159i	$-0.690521\pi$
$661$	−3.25447e8			−1.12687			−0.563437	+	0.826159i	$0.690521\pi$
$662$	−7.99932e7	+	1.38415e7i	−0.275727	+	0.0477101i
$663$			2.01829e8i			0.692537i
$664$	3.92431e8	−	2.21581e8i	1.34048	−	0.756884i
$665$	2.60792e6			0.00886806
$666$	−1.15698e7	−	6.68643e7i	−0.0391654	−	0.226345i
$667$		−	2.70513e8i		−	0.911614i
$668$	−5.41481e7	−	1.51782e8i	−0.181658	−	0.509203i
$669$	−1.57932e8			−0.527462
$670$	2.17703e8	−	3.76699e7i	0.723834	−	0.125248i
$671$			2.22669e8i			0.737041i
$672$	3.35429e7	+	2.90717e7i	0.110533	+	0.0957993i
$673$	−1.53428e7			−0.0503339			−0.0251669	−	0.999683i	$-0.508012\pi$
$673$	−1.53428e7			−0.0503339			−0.0251669	+	0.999683i	$0.508012\pi$
$674$	−7.36153e7	−	4.25439e8i	−0.240430	−	1.38950i
$675$		−	1.18375e7i		−	0.0384900i
$676$	−3.21427e8	+	1.14669e8i	−1.04050	+	0.371197i
$677$	−1.41403e8			−0.455715			−0.227857	−	0.973694i	$-0.573172\pi$
$677$	−1.41403e8			−0.455715			−0.227857	+	0.973694i	$0.573172\pi$
$678$	−3.32409e8	+	5.75179e7i	−1.06655	+	0.184550i
$679$		−	1.23117e7i		−	0.0393285i
$680$	−5.71643e7	−	1.01241e8i	−0.181802	−	0.321980i
$681$	−6.70697e7			−0.212366
$682$	2.48191e7	+	1.43435e8i	0.0782408	+	0.452171i
$683$			2.86757e8i			0.900020i	0.893024	+	0.450010i	$0.148580\pi$
$683$			2.86757e8i			0.900020i	−0.893024	+	0.450010i	$0.851420\pi$
$684$	2.80538e6	+	7.86373e6i	0.00876644	+	0.0245731i
$685$	−1.19966e8			−0.373237
$686$	1.56008e8	−	2.69947e7i	0.483254	−	0.0836193i
$687$			2.10311e8i			0.648623i
$688$	2.38441e8	+	2.91654e8i	0.732175	+	0.895576i
$689$	7.61111e8			2.32697
$690$	2.15227e7	+	1.24384e8i	0.0655163	+	0.378633i
$691$		−	7.86675e7i		−	0.238430i	−0.992868	−	0.119215i	$-0.961962\pi$
$691$		−	7.86675e7i		−	0.238430i	0.992868	−	0.119215i	$-0.0380378\pi$
$692$	−250353.	+	89313.2i	−0.000755500	+	0.000269524i
$693$	−3.26395e7			−0.0980716
$694$	3.86653e8	−	6.69041e7i	1.15676	−	0.200159i
$695$		−	1.71089e8i		−	0.509644i
$696$	−1.03828e8	+	5.86254e7i	−0.307956	+	0.173883i
$697$	4.40179e8			1.29996
$698$	−3.15041e7	−	1.82069e8i	−0.0926406	−	0.535390i
$699$		−	3.52672e8i		−	1.03262i
$700$	−5.83970e6	−	1.63692e7i	−0.0170254	−	0.0477237i
$701$	−3.28382e8			−0.953290			−0.476645	−	0.879096i	$-0.658147\pi$
$701$	−3.28382e8			−0.953290			−0.476645	+	0.879096i	$0.658147\pi$
$702$	−9.51747e7	+	1.64684e7i	−0.275112	+	0.0476037i
$703$		−	1.87396e7i		−	0.0539380i
$704$	3.46961e8	+	2.09289e8i	0.994403	+	0.599829i
$705$	−1.50515e7			−0.0429549
$706$	1.17173e8	+	6.77170e8i	0.332977	+	1.92435i
$707$			1.06996e8i			0.302768i
$708$	8.99043e7	−	3.20732e7i	0.253326	−	0.0903739i
$709$	−2.06210e8			−0.578591			−0.289296	−	0.957240i	$-0.593421\pi$
$709$	−2.06210e8			−0.578591			−0.289296	+	0.957240i	$0.593421\pi$
$710$	−1.16223e8	+	2.01106e7i	−0.324727	+	0.0561888i
$711$		−	7.74528e7i		−	0.215490i
$712$	−4.99996e7	−	8.85517e7i	−0.138525	−	0.245334i
$713$	−2.13157e8			−0.588074
$714$	7.50555e6	+	4.33762e7i	0.0206200	+	0.119167i
$715$			2.75409e8i			0.753459i
$716$	8.51118e7	+	2.38576e8i	0.231873	+	0.649962i
$717$	−7.77507e7			−0.210934
$718$	3.24840e8	−	5.62083e7i	0.877599	−	0.151854i
$719$		−	1.06671e8i		−	0.286986i	−0.989651	−	0.143493i	$-0.954167\pi$
$719$		−	1.06671e8i		−	0.286986i	0.989651	−	0.143493i	$-0.0458334\pi$
$720$	4.30768e7	−	3.52173e7i	0.115411	−	0.0943536i
$721$	1.16913e8			0.311930
$722$	−6.37775e7	−	3.68584e8i	−0.169456	−	0.979321i
$723$			5.68710e7i			0.150479i
$724$	−5.73799e8	+	2.04702e8i	−1.51197	+	0.539395i
$725$	4.66858e7			0.122510
$726$	−7.58946e7	+	1.31323e7i	−0.198336	+	0.0343188i
$727$		−	4.85082e8i		−	1.26244i	−0.775602	−	0.631222i	$-0.782554\pi$
$727$		−	4.85082e8i		−	1.26244i	0.775602	−	0.631222i	$-0.217446\pi$
$728$	−1.23486e8	+	6.97249e7i	−0.320054	+	0.180715i
$729$	−1.43489e7			−0.0370370
$730$	−1.71564e7	−	9.91506e7i	−0.0441020	−	0.254875i
$731$			3.73601e8i			0.956436i
$732$	4.82910e7	+	1.35364e8i	0.123121	+	0.345120i
$733$	2.57203e8			0.653077			0.326538	−	0.945184i	$-0.394118\pi$
$733$	2.57203e8			0.653077			0.326538	+	0.945184i	$0.394118\pi$
$734$	4.25860e8	−	7.36883e7i	1.07691	−	0.186342i
$735$		−	9.59414e7i		−	0.241626i
$736$	−3.88605e8	+	4.48373e8i	−0.974709	+	1.12462i
$737$	−7.63624e8			−1.90755
$738$	3.59168e7	+	2.07571e8i	0.0893571	+	0.516414i
$739$			7.60588e8i			1.88459i	0.334787	+	0.942294i	$0.391336\pi$
$739$			7.60588e8i			1.88459i	−0.334787	+	0.942294i	$0.608664\pi$
$740$	−1.17624e8	+	4.19622e7i	−0.290269	+	0.103553i
$741$	−2.66740e7			−0.0655591
$742$	1.63574e8	−	2.83039e7i	0.400409	−	0.0692843i
$743$			2.14669e8i			0.523363i	0.965154	+	0.261682i	$0.0842770\pi$
$743$			2.14669e8i			0.523363i	−0.965154	+	0.261682i	$0.915723\pi$
$744$	4.61953e7	+	8.18141e7i	0.112171	+	0.198659i
$745$	8.76282e7			0.211922
$746$	−7.44442e7	−	4.30229e8i	−0.179314	−	1.03630i
$747$			2.13891e8i			0.513133i
$748$	1.35022e8	+	3.78480e8i	0.322627	+	0.904354i
$749$	9.54902e7			0.227255
$750$	−2.14665e7	+	3.71444e6i	−0.0508837	+	0.00880459i
$751$		−	3.72415e8i		−	0.879239i	−0.898184	−	0.439620i	$-0.855113\pi$
$751$		−	3.72415e8i		−	0.879239i	0.898184	−	0.439620i	$-0.144887\pi$
$752$	−4.47792e7	−	5.47726e7i	−0.105299	−	0.128798i
$753$	−1.54628e8			−0.362163
$754$	−6.49498e7	−	3.75359e8i	−0.151518	−	0.875655i
$755$		−	3.03643e8i		−	0.705541i
$756$	−1.98421e7	+	7.07864e6i	−0.0459221	+	0.0163827i
$757$	−2.17431e8			−0.501227			−0.250613	−	0.968087i	$-0.580632\pi$
$757$	−2.17431e8			−0.501227			−0.250613	+	0.968087i	$0.580632\pi$
$758$	5.62841e8	−	9.73906e7i	1.29234	−	0.223619i
$759$		−	4.36296e8i		−	0.997829i
$760$	1.33801e7	−	7.55491e6i	0.0304803	−	0.0172103i
$761$	−3.79154e7			−0.0860322			−0.0430161	−	0.999074i	$-0.513697\pi$
$761$	−3.79154e7			−0.0860322			−0.0430161	+	0.999074i	$0.513697\pi$
$762$	3.19516e7	+	1.84655e8i	0.0722150	+	0.417346i
$763$		−	1.65421e8i		−	0.372406i
$764$	1.42692e8	+	3.99980e8i	0.319978	+	0.896928i
$765$	5.51803e7			0.123254
$766$	1.87803e8	−	3.24963e7i	0.417846	−	0.0723015i
$767$			3.04957e8i			0.675854i
$768$	2.56313e8	+	5.19834e7i	0.565830	+	0.114757i
$769$	−4.55616e8			−1.00189			−0.500945	−	0.865479i	$-0.667014\pi$
$769$	−4.55616e8			−1.00189			−0.500945	+	0.865479i	$0.667014\pi$
$770$	1.02418e7	+	5.91896e7i	0.0224339	+	0.129650i
$771$			2.09573e8i			0.457270i
$772$	2.94260e8	−	1.04977e8i	0.639558	−	0.228162i
$773$	−5.34167e8			−1.15648			−0.578241	−	0.815866i	$-0.696261\pi$
$773$	−5.34167e8			−1.15648			−0.578241	+	0.815866i	$0.696261\pi$
$774$	−1.76176e8	+	3.04843e7i	−0.379947	+	0.0657437i
$775$		−	3.67872e7i		−	0.0790300i
$776$	−3.56659e7	−	6.31659e7i	−0.0763251	−	0.135175i
$777$	4.72846e7			0.100799
$778$	4.53140e7	+	2.61880e8i	0.0962263	+	0.556113i
$779$			5.81746e7i			0.123061i
$780$	5.97290e7	+	1.67426e8i	0.125864	+	0.352808i
$781$	4.07671e8			0.855769
$782$	−5.79816e8	+	1.00328e8i	−1.21247	+	0.209798i
$783$		−	5.65906e7i		−	0.117885i
$784$	3.49132e8	−	2.85432e8i	0.724506	−	0.592318i
$785$	−3.38335e8			−0.699420
$786$	−9.34725e7	−	5.40198e8i	−0.192494	−	1.11246i
$787$			2.05724e8i			0.422048i	0.977481	+	0.211024i	$0.0676798\pi$
$787$			2.05724e8i			0.422048i	−0.977481	+	0.211024i	$0.932320\pi$
$788$	−2.22730e8	+	7.94588e7i	−0.455198	+	0.162391i
$789$	−3.19517e8			−0.650524
$790$	−1.40456e8	+	2.43036e7i	−0.284878	+	0.0492934i
$791$		−	2.35070e8i		−	0.474972i
$792$	−1.67459e8	+	9.45538e7i	−0.337080	+	0.190328i
$793$	−4.59158e8			−0.920753
$794$	5.49135e7	+	3.17357e8i	0.109703	+	0.633996i
$795$		−	2.08088e8i		−	0.414139i
$796$	2.94913e6	+	8.26667e6i	0.00584728	+	0.0163905i
$797$	−7.54211e8			−1.48977			−0.744883	−	0.667195i	$-0.767495\pi$
$797$	−7.54211e8			−1.48977			−0.744883	+	0.667195i	$0.767495\pi$
$798$	−5.73265e6	+	991942.i	−0.0112810	+	0.00195199i
$799$		−	7.01624e7i		−	0.137551i
$800$	−7.73813e7	−	6.70664e7i	−0.151135	−	0.130989i
$801$	4.82642e7			0.0939135
$802$	−5.42525e7	−	3.13537e8i	−0.105171	−	0.607807i
$803$			3.47785e8i			0.671684i
$804$	−4.64220e8	+	1.65610e8i	−0.893214	+	0.318653i
$805$	−8.79611e7			−0.168618
$806$	−2.95773e8	+	5.11788e7i	−0.564877	+	0.0977428i
$807$		−	3.83041e8i		−	0.728828i
$808$	3.09958e8	+	5.48951e8i	0.587583	+	1.04064i
$809$	−1.88932e8			−0.356828			−0.178414	−	0.983955i	$-0.557097\pi$
$809$	−1.88932e8			−0.356828			−0.178414	+	0.983955i	$0.557097\pi$
$810$	4.50249e6	+	2.60208e7i	0.00847222	+	0.0489628i
$811$			4.32976e8i			0.811711i	0.913937	+	0.405855i	$0.133026\pi$
$811$			4.32976e8i			0.811711i	−0.913937	+	0.405855i	$0.866974\pi$
$812$	−2.79174e7	−	7.82552e7i	−0.0521444	−	0.146166i
$813$	−2.19955e8			−0.409320
$814$	4.25317e8	−	7.35942e7i	0.788569	−	0.136449i
$815$			6.26007e7i			0.115640i
$816$	1.64165e8	+	2.00802e8i	0.302141	+	0.369571i
$817$	−4.93756e7			−0.0905411
$818$	1.79269e7	+	1.03603e8i	0.0327525	+	0.189284i
$819$		−	6.73049e7i		−	0.122517i
$820$	3.65147e8	−	1.30266e8i	0.662257	−	0.236259i
$821$	3.31612e8			0.599239			0.299620	−	0.954059i	$-0.403140\pi$
$821$	3.31612e8			0.599239			0.299620	+	0.954059i	$0.403140\pi$
$822$	2.63705e8	−	4.56299e7i	0.474792	−	0.0821551i
$823$		−	6.15322e8i		−	1.10383i	−0.833900	−	0.551916i	$-0.813897\pi$
$823$		−	6.15322e8i		−	1.10383i	0.833900	−	0.551916i	$-0.186103\pi$
$824$	5.99831e8	−	3.38687e8i	1.07213	−	0.605365i
$825$	7.52971e7			0.134096
$826$	1.13406e7	+	6.55401e7i	0.0201232	+	0.116297i
$827$			6.51923e8i			1.15260i	0.817237	+	0.576301i	$0.195505\pi$
$827$			6.51923e8i			1.15260i	−0.817237	+	0.576301i	$0.804495\pi$
$828$	−9.46212e7	−	2.65232e8i	−0.166685	−	0.467234i
$829$	5.30210e8			0.930645			0.465323	−	0.885141i	$-0.345938\pi$
$829$	5.30210e8			0.930645			0.465323	+	0.885141i	$0.345938\pi$
$830$	3.87877e8	−	6.71159e7i	0.678360	−	0.117379i
$831$		−	5.89249e8i		−	1.02682i
$832$	−4.31567e8	+	7.15457e8i	−0.749340	+	1.24226i
$833$	4.47230e8			0.773741
$834$	6.50751e7	+	3.76083e8i	0.112180	+	0.648314i
$835$		−	1.40760e8i		−	0.241780i
$836$	−5.00204e7	+	1.78447e7i	−0.0856108	+	0.0305416i
$837$	−4.45919e7			−0.0760466
$838$	6.24997e7	−	1.08146e7i	0.106205	−	0.0183771i
$839$			6.26328e8i			1.06051i	0.847837	+	0.530256i	$0.177904\pi$
$839$			6.26328e8i			1.06051i	−0.847837	+	0.530256i	$0.822096\pi$
$840$	1.90628e7	+	3.37612e7i	0.0321625	+	0.0569613i
$841$	−3.71636e8			−0.624783
$842$	−1.27969e8	−	7.39559e8i	−0.214372	−	1.23890i
$843$			1.59818e8i			0.266774i
$844$	−8.02045e6	−	2.24821e7i	−0.0133405	−	0.0373946i
$845$	−2.98086e8			−0.494050
$846$	3.30858e7	−	5.72496e6i	0.0546425	−	0.00945500i
$847$		−	5.36705e7i		−	0.0883254i
$848$	7.57237e8	−	6.19077e8i	1.24178	−	1.01521i
$849$	5.91192e8			0.966062
$850$	−1.73148e7	−	1.00066e8i	−0.0281943	−	0.162941i
$851$			6.32059e8i			1.02558i
$852$	2.47830e8	−	8.84131e7i	0.400715	−	0.142954i
$853$	−1.11124e8			−0.179045			−0.0895226	−	0.995985i	$-0.528534\pi$
$853$	−1.11124e8			−0.179045			−0.0895226	+	0.995985i	$0.528534\pi$
$854$	−9.86803e7	+	1.70750e7i	−0.158437	+	0.0274150i
$855$			7.29269e6i			0.0116678i
$856$	4.89919e8	−	2.76627e8i	0.781094	−	0.441035i
$857$	3.71125e7			0.0589627			0.0294814	−	0.999565i	$-0.490614\pi$
$857$	3.71125e7			0.0589627			0.0294814	+	0.999565i	$0.490614\pi$
$858$	−1.04754e8	−	6.05397e8i	−0.165848	−	0.958469i
$859$			6.43708e8i			1.01557i	0.861484	+	0.507784i	$0.169535\pi$
$859$			6.43708e8i			1.01557i	−0.861484	+	0.507784i	$0.830465\pi$
$860$	1.10563e8	+	3.09918e8i	0.173826	+	0.487249i
$861$	−1.46789e8			−0.229976
$862$	2.26015e8	−	3.91082e7i	0.352870	−	0.0610584i
$863$			4.60361e8i			0.716253i	0.933673	+	0.358126i	$0.116584\pi$
$863$			4.60361e8i			0.716253i	−0.933673	+	0.358126i	$0.883416\pi$
$864$	−8.12951e7	+	9.37984e7i	−0.126044	+	0.145430i
$865$	−232173.			−0.000358727
$866$	−1.11423e8	−	6.43938e8i	−0.171562	−	0.991494i
$867$		−	1.19045e8i		−	0.182665i
$868$	−6.16631e7	+	2.19982e7i	−0.0942900	+	0.0336379i
$869$	4.92669e8			0.750751
$870$	−1.02624e8	+	1.77573e7i	−0.155844	+	0.0269662i
$871$		−	1.57465e9i		−	2.38302i
$872$	−4.79210e8	−	8.48704e8i	−0.722731	−	1.27999i
$873$	3.44280e7			0.0517450
$874$	−1.32594e7	−	7.66291e7i	−0.0198605	−	0.114778i
$875$		−	1.51805e7i		−	0.0226602i
$876$	7.54255e7	+	2.11425e8i	0.112203	+	0.314517i
$877$	1.15420e9			1.71113			0.855563	−	0.517699i	$-0.173211\pi$
$877$	1.15420e9			1.71113			0.855563	+	0.517699i	$0.173211\pi$
$878$	1.27528e9	−	2.20666e8i	1.88417	−	0.326026i
$879$		−	2.35657e8i		−	0.346987i
$880$	2.24014e8	+	2.74007e8i	0.328720	+	0.402081i
$881$	1.14212e9			1.67026			0.835132	−	0.550049i	$-0.185391\pi$
$881$	1.14212e9			1.67026			0.835132	+	0.550049i	$0.185391\pi$
$882$	3.64921e7	+	2.10896e8i	0.0531855	+	0.307371i
$883$		−	1.26032e9i		−	1.83062i	−0.402753	−	0.915309i	$-0.631947\pi$
$883$		−	1.26032e9i		−	1.83062i	0.402753	−	0.915309i	$-0.368053\pi$
$884$	−7.80453e8	+	2.78426e8i	−1.12977	+	0.403044i
$885$	8.33757e7			0.120284
$886$	−7.91227e8	+	1.36909e8i	−1.13763	+	0.196848i
$887$		−	4.41568e8i		−	0.632742i	−0.948636	−	0.316371i	$-0.897536\pi$
$887$		−	4.41568e8i		−	0.632742i	0.948636	−	0.316371i	$-0.102464\pi$
$888$	2.42597e8	−	1.36979e8i	0.346455	−	0.195621i
$889$	−1.30583e8			−0.185858
$890$	−1.51446e7	−	8.75242e7i	−0.0214827	−	0.124153i
$891$		−	9.12720e7i		−	0.129034i
$892$	−2.17869e8	−	6.10706e8i	−0.306973	−	0.860474i
$893$	9.27274e6			0.0130213
$894$	−1.92622e8	+	3.33301e7i	−0.269584	+	0.0466471i
$895$			2.21252e8i			0.308615i
$896$	−6.61444e7	+	1.69812e8i	−0.0919536	+	0.236072i
$897$	8.99673e8			1.24654
$898$	6.22182e7	+	3.59572e8i	0.0859188	+	0.496544i
$899$		−	1.75866e8i		−	0.242049i
$900$	4.57744e7	−	1.63300e7i	0.0627906	−	0.0224005i
$901$	9.70001e8			1.32617
$902$	−1.32034e9	+	2.28463e8i	−1.79915	+	0.311313i
$903$		−	1.24586e8i		−	0.169203i
$904$	−6.80978e8	−	1.20604e9i	−0.921781	−	1.63252i
$905$	−5.32131e8			−0.717915
$906$	1.15493e8	+	6.67460e8i	0.155300	+	0.897513i
$907$			3.16399e8i			0.424046i	0.977265	+	0.212023i	$0.0680052\pi$
$907$			3.16399e8i			0.424046i	−0.977265	+	0.212023i	$0.931995\pi$
$908$	−9.25235e7	−	2.59352e8i	−0.123593	−	0.346443i
$909$	−2.99200e8			−0.398355
$910$	−1.22053e8	+	2.11193e7i	−0.161966	+	0.0280257i
$911$		−	6.09185e8i		−	0.805738i	−0.915258	−	0.402869i	$-0.868013\pi$
$911$		−	6.09185e8i		−	0.805738i	0.915258	−	0.402869i	$-0.131987\pi$
$912$	−2.65382e7	+	2.16962e7i	−0.0349854	+	0.0286022i
$913$	−1.36054e9			−1.78771
$914$	1.77294e8	+	1.02462e9i	0.232197	+	1.34192i
$915$			1.25534e8i			0.163870i
$916$	−8.13252e8	+	2.90127e8i	−1.05813	+	0.377487i
$917$	3.82013e8			0.495416
$918$	−1.21296e8	+	2.09883e7i	−0.156790	+	0.0271299i
$919$			7.84705e8i			1.01102i	0.862821	+	0.505510i	$0.168696\pi$
$919$			7.84705e8i			1.01102i	−0.862821	+	0.505510i	$0.831304\pi$
$920$	−4.51291e8	+	2.54816e8i	−0.579553	+	0.327237i
$921$	6.01365e8			0.769767
$922$	1.70194e8	+	9.83589e8i	0.217146	+	1.25493i
$923$			8.40646e8i			1.06907i
$924$	−4.50265e7	−	1.26214e8i	−0.0570759	−	0.159989i
$925$	−1.09082e8			−0.137825
$926$	−8.83120e8	+	1.52810e8i	−1.11221	+	0.192450i
$927$			3.26932e8i			0.410410i
$928$	−3.69931e8	−	3.20619e8i	−0.462889	−	0.401186i
$929$	−5.54301e8			−0.691350			−0.345675	−	0.938354i	$-0.612350\pi$
$929$	−5.54301e8			−0.691350			−0.345675	+	0.938354i	$0.612350\pi$
$930$	1.39923e7	+	8.08647e7i	0.0173957	+	0.100533i
$931$			5.91064e7i			0.0732463i
$932$	1.36375e9	−	4.86516e8i	1.68456	−	0.600965i
$933$	−7.19968e8			−0.886479
$934$	−1.32190e9	+	2.28734e8i	−1.62240	+	0.280731i
$935$			3.50996e8i			0.429405i
$936$	−1.94976e8	−	3.45313e8i	−0.237769	−	0.421100i
$937$	−2.98563e8			−0.362925			−0.181462	−	0.983398i	$-0.558083\pi$
$937$	−2.98563e8			−0.362925			−0.181462	+	0.983398i	$0.558083\pi$
$938$	−5.85573e7	−	3.38416e8i	−0.0709533	−	0.410055i
$939$		−	2.21002e8i		−	0.266932i
$940$	−2.07637e7	−	5.82026e7i	−0.0249989	−	0.0700744i
$941$	−1.17672e8			−0.141222			−0.0706111	−	0.997504i	$-0.522495\pi$
$941$	−1.17672e8			−0.141222			−0.0706111	+	0.997504i	$0.522495\pi$
$942$	7.43720e8	−	1.28689e8i	0.889727	−	0.153953i
$943$		−	1.96214e9i		−	2.33989i
$944$	2.48048e8	+	3.03405e8i	0.294863	+	0.360668i
$945$	−1.84012e7			−0.0218047
$946$	−1.93908e8	−	1.12064e9i	−0.229046	−	1.32370i
$947$		−	9.83597e8i		−	1.15816i	−0.815272	−	0.579078i	$-0.803413\pi$
$947$		−	9.83597e8i		−	1.15816i	0.815272	−	0.579078i	$-0.196587\pi$
$948$	2.99502e8	−	1.06847e8i	0.351540	−	0.125412i
$949$	−7.17158e8			−0.839105
$950$	1.32248e7	−	2.28834e6i	0.0154248	−	0.00266901i
$951$			9.43299e8i			1.09675i
$952$	−1.57377e8	+	8.88612e7i	−0.182403	+	0.102992i
$953$	3.21501e8			0.371453			0.185726	−	0.982601i	$-0.440536\pi$
$953$	3.21501e8			0.371453			0.185726	+	0.982601i	$0.440536\pi$
$954$	7.91481e7	+	4.57414e8i	0.0911582	+	0.526823i
$955$			3.70934e8i			0.425879i
$956$	−1.07258e8	−	3.00654e8i	−0.122760	−	0.344107i
$957$	3.59967e8			0.410702
$958$	−6.02738e8	+	1.04294e8i	−0.685539	+	0.118621i
$959$			1.86485e8i			0.211440i
$960$	1.95607e8	+	1.17991e8i	0.221090	+	0.133363i
$961$	7.48926e8			0.843857
$962$	1.51756e8	+	8.77034e8i	0.170460	+	0.985124i
$963$			2.67026e8i			0.299002i
$964$	−2.19914e8	+	7.84542e7i	−0.245484	+	0.0875760i
$965$	2.72892e8			0.303675
$966$	1.93354e8	−	3.34567e7i	0.214497	−	0.0371152i
$967$			5.12381e8i			0.566648i	0.959024	+	0.283324i	$0.0914372\pi$
$967$			5.12381e8i			0.566648i	−0.959024	+	0.283324i	$0.908563\pi$
$968$	−1.55479e8	−	2.75361e8i	−0.171414	−	0.303582i
$969$	−3.39948e7			−0.0373629
$970$	−1.08030e7	−	6.24330e7i	−0.0118367	−	0.0684067i
$971$			7.48118e8i			0.817170i	0.912720	+	0.408585i	$0.133978\pi$
$971$			7.48118e8i			0.817170i	−0.912720	+	0.408585i	$0.866022\pi$
$972$	−1.97945e7	−	5.54858e7i	−0.0215549	−	0.0604203i
$973$	−2.65955e8			−0.288715
$974$	3.92137e8	−	6.78530e7i	0.424386	−	0.0734331i
$975$			1.55268e8i			0.167520i
$976$	−4.56821e8	+	3.73473e8i	−0.491357	+	0.401707i
$977$	1.19213e9			1.27832			0.639160	−	0.769074i	$-0.279282\pi$
$977$	1.19213e9			1.27832			0.639160	+	0.769074i	$0.279282\pi$
$978$	−2.38107e7	−	1.37607e8i	−0.0254540	−	0.147104i
$979$			3.07004e8i			0.327187i
$980$	3.70996e8	−	1.32352e8i	0.394177	−	0.140622i
$981$	4.62577e8			0.489979
$982$	−1.46103e9	+	2.52808e8i	−1.54286	+	0.266966i
$983$		−	1.48663e9i		−	1.56510i	−0.622590	−	0.782548i	$-0.713920\pi$
$983$		−	1.48663e9i		−	1.56510i	0.622590	−	0.782548i	$-0.286080\pi$
$984$	−7.53110e8	+	4.25234e8i	−0.790447	+	0.446316i
$985$	−2.06556e8			−0.216137
$986$	−8.27756e7	−	4.78378e8i	−0.0863519	−	0.499046i
$987$			2.33974e7i			0.0243341i
$988$	−3.67971e7	−	1.03146e8i	−0.0381542	−	0.106950i
$989$	1.66536e9			1.72155
$990$	−1.65516e8	+	2.86399e7i	−0.170582	+	0.0295165i
$991$			1.07762e9i			1.10725i	0.832768	+	0.553623i	$0.186755\pi$
$991$			1.07762e9i			1.10725i	−0.832768	+	0.553623i	$0.813245\pi$
$992$	−2.52640e8	+	2.91496e8i	−0.258802	+	0.298605i
$993$	1.58188e8			0.161557
$994$	3.12616e7	+	1.80668e8i	0.0318312	+	0.183959i
$995$			7.66637e6i			0.00778252i
$996$	−8.27094e8	+	2.95065e8i	−0.837099	+	0.298634i
$997$	8.35952e8			0.843521			0.421760	−	0.906707i	$-0.361412\pi$
$997$	8.35952e8			0.843521			0.421760	+	0.906707i	$0.361412\pi$
$998$	1.51353e9	−	2.61892e8i	1.52265	−	0.263470i
$999$			1.32225e8i			0.132622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.9	✓	24
3.2	odd	2		180.7.c.b.91.16		24
4.3	odd	2	inner	60.7.c.a.31.10	yes	24
12.11	even	2		180.7.c.b.91.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.9	✓	24	1.1	even	1	trivial
60.7.c.a.31.10	yes	24	4.3	odd	2	inner
180.7.c.b.91.15		24	12.11	even	2
180.7.c.b.91.16		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.36400 - 7.88286i) q^{2} +15.5885i q^{3} +(-60.2790 + 21.5045i) q^{4} -55.9017 q^{5} +(122.882 - 21.2627i) q^{6} +86.8984i q^{7} +(251.737 + 445.839i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(-1.36400 - 7.88286i) q^{2} +15.5885i q^{3} +(-60.2790 + 21.5045i) q^{4} -55.9017 q^{5} +(122.882 - 21.2627i) q^{6} +86.8984i q^{7} +(251.737 + 445.839i) q^{8} -243.000 q^{9} +(76.2500 + 440.665i) q^{10} -1545.70i q^{11} +(-335.221 - 939.657i) q^{12} +3187.34 q^{13} +(685.008 - 118.530i) q^{14} -871.421i q^{15} +(3171.12 - 2592.54i) q^{16} +4062.12 q^{17} +(331.452 + 1915.54i) q^{18} +536.854i q^{19} +(3369.70 - 1202.14i) q^{20} -1354.61 q^{21} +(-12184.5 + 2108.34i) q^{22} -18107.3i q^{23} +(-6949.94 + 3924.20i) q^{24} +3125.00 q^{25} +(-4347.53 - 25125.3i) q^{26} -3788.00i q^{27} +(-1868.70 - 5238.15i) q^{28} +14939.5 q^{29} +(-6869.29 + 1188.62i) q^{30} -11771.9i q^{31} +(-24762.0 - 21461.2i) q^{32} +24095.1 q^{33} +(-5540.73 - 32021.1i) q^{34} -4857.77i q^{35} +(14647.8 - 5225.59i) q^{36} -34906.3 q^{37} +(4231.95 - 732.270i) q^{38} +49685.7i q^{39} +(-14072.5 - 24923.2i) q^{40} +108362. q^{41} +(1847.69 + 10678.2i) q^{42} +91972.0i q^{43} +(33239.4 + 93173.2i) q^{44} +13584.1 q^{45} +(-142737. + 24698.4i) q^{46} -17272.4i q^{47} +(40413.6 + 49432.8i) q^{48} +110098. q^{49} +(-4262.50 - 24633.9i) q^{50} +63322.2i q^{51} +(-192130. + 68542.0i) q^{52} +238792. q^{53} +(-29860.2 + 5166.83i) q^{54} +86407.2i q^{55} +(-38742.7 + 21875.6i) q^{56} -8368.73 q^{57} +(-20377.5 - 117766. i) q^{58} +95677.8i q^{59} +(18739.4 + 52528.4i) q^{60} -144057. q^{61} +(-92796.3 + 16056.9i) q^{62} -21116.3i q^{63} +(-135401. + 224469. i) q^{64} -178178. q^{65} +(-32865.7 - 189938. i) q^{66} -494031. i q^{67} +(-244860. + 87353.7i) q^{68} +282265. q^{69} +(-38293.1 + 6626.01i) q^{70} +263745. i q^{71} +(-61172.2 - 108339. i) q^{72} -225002. q^{73} +(47612.3 + 275162. i) q^{74} +48713.9i q^{75} +(-11544.8 - 32361.0i) q^{76} +134319. q^{77} +(391665. - 67771.3i) q^{78} +318736. i q^{79} +(-177271. + 144927. i) q^{80} +59049.0 q^{81} +(-147806. - 854203. i) q^{82} -880209. i q^{83} +(81654.7 - 29130.2i) q^{84} -227079. q^{85} +(725003. - 125450. i) q^{86} +232883. i q^{87} +(689133. - 389110. i) q^{88} -198618. q^{89} +(-18528.7 - 107082. i) q^{90} +276975. i q^{91} +(389388. + 1.09149e6i) q^{92} +183506. q^{93} +(-136156. + 23559.5i) q^{94} -30011.1i q^{95} +(334548. - 386001. i) q^{96} -141679. q^{97} +(-150173. - 867885. i) q^{98} +375605. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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