LMFDB - Embedded newform 43.8.c.a.6.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, 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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.8
Character	$\chi$	$=$	43.6
Dual form			43.8.c.a.36.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.69651 q^{2} +(-18.8428 + 32.6367i) q^{3} -33.9777 q^{4} +(119.656 - 207.250i) q^{5} +(182.709 - 316.462i) q^{6} +(493.624 + 854.982i) q^{7} +1570.62 q^{8} +(383.397 + 664.064i) q^{9} +O(q^{10})$	\(q-9.69651 q^{2} +(-18.8428 + 32.6367i) q^{3} -33.9777 q^{4} +(119.656 - 207.250i) q^{5} +(182.709 - 316.462i) q^{6} +(493.624 + 854.982i) q^{7} +1570.62 q^{8} +(383.397 + 664.064i) q^{9} +(-1160.25 + 2009.60i) q^{10} +71.3912 q^{11} +(640.235 - 1108.92i) q^{12} +(-1635.79 - 2833.27i) q^{13} +(-4786.43 - 8290.34i) q^{14} +(4509.31 + 7810.35i) q^{15} -10880.4 q^{16} +(-11569.7 - 20039.4i) q^{17} +(-3717.62 - 6439.10i) q^{18} +(-24489.5 + 42417.1i) q^{19} +(-4065.64 + 7041.89i) q^{20} -37205.0 q^{21} -692.246 q^{22} +(-11335.0 + 19632.8i) q^{23} +(-29594.9 + 51259.8i) q^{24} +(10427.4 + 18060.8i) q^{25} +(15861.4 + 27472.8i) q^{26} -111316. q^{27} +(-16772.2 - 29050.3i) q^{28} +(-46185.3 - 79995.3i) q^{29} +(-43724.6 - 75733.2i) q^{30} +(-48322.4 + 83696.9i) q^{31} -95537.5 q^{32} +(-1345.21 + 2329.97i) q^{33} +(112186. + 194312. i) q^{34} +236260. q^{35} +(-13027.0 - 22563.4i) q^{36} +(-35430.6 + 61367.6i) q^{37} +(237463. - 411298. i) q^{38} +123291. q^{39} +(187934. - 325511. i) q^{40} +183851. q^{41} +360759. q^{42} +(-468175. + 229414. i) q^{43} -2425.71 q^{44} +183503. q^{45} +(109910. - 190370. i) q^{46} +311915. q^{47} +(205017. - 355099. i) q^{48} +(-75557.8 + 130870. i) q^{49} +(-101109. - 175126. i) q^{50} +872026. q^{51} +(55580.3 + 96267.9i) q^{52} +(-790638. + 1.36943e6i) q^{53} +1.07937e6 q^{54} +(8542.39 - 14795.8i) q^{55} +(775295. + 1.34285e6i) q^{56} +(-922903. - 1.59852e6i) q^{57} +(447836. + 775675. i) q^{58} -1.46477e6 q^{59} +(-153216. - 265378. i) q^{60} +(-1.66048e6 - 2.87603e6i) q^{61} +(468559. - 811567. i) q^{62} +(-378508. + 655596. i) q^{63} +2.31907e6 q^{64} -782928. q^{65} +(13043.9 - 22592.6i) q^{66} +(-1.51656e6 + 2.62676e6i) q^{67} +(393113. + 680892. i) q^{68} +(-427168. - 739876. i) q^{69} -2.29090e6 q^{70} +(157114. + 272129. i) q^{71} +(602171. + 1.04299e6i) q^{72} +(-973486. - 1.68613e6i) q^{73} +(343553. - 595051. i) q^{74} -785925. q^{75} +(832098. - 1.44124e6i) q^{76} +(35240.4 + 61038.2i) q^{77} -1.19550e6 q^{78} +(1.65479e6 + 2.86618e6i) q^{79} +(-1.30190e6 + 2.25496e6i) q^{80} +(1.25901e6 - 2.18066e6i) q^{81} -1.78271e6 q^{82} +(-1.82188e6 + 3.15559e6i) q^{83} +1.26414e6 q^{84} -5.53756e6 q^{85} +(4.53966e6 - 2.22452e6i) q^{86} +3.48104e6 q^{87} +112128. q^{88} +(-3.32655e6 + 5.76175e6i) q^{89} -1.77934e6 q^{90} +(1.61493e6 - 2.79714e6i) q^{91} +(385138. - 667079. i) q^{92} +(-1.82106e6 - 3.15417e6i) q^{93} -3.02449e6 q^{94} +(5.86064e6 + 1.01509e7i) q^{95} +(1.80019e6 - 3.11803e6i) q^{96} -6.68568e6 q^{97} +(732647. - 1.26898e6i) q^{98} +(27371.2 + 47408.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9}+O(q^{10}) $ 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99}+O(q^{100}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9 + 1667 * q^10 - 4594 * q^11 - 8448 * q^12 + 2972 * q^13 - 15928 * q^14 - 2485 * q^15 + 185846 * q^16 + 25298 * q^17 + 13249 * q^18 + 3269 * q^19 + 2705 * q^20 - 85260 * q^21 + 150968 * q^22 - 19120 * q^23 - 55070 * q^24 - 296876 * q^25 - 139545 * q^26 - 274154 * q^27 - 118970 * q^28 - 231057 * q^29 + 240447 * q^30 - 177637 * q^31 + 1254274 * q^32 - 344986 * q^33 + 104923 * q^34 - 518850 * q^35 + 816168 * q^36 + 885140 * q^37 + 200956 * q^38 - 59884 * q^39 + 160425 * q^40 + 2202852 * q^41 - 349786 * q^42 + 1009342 * q^43 - 1012518 * q^44 + 775768 * q^45 - 1277532 * q^46 - 2784982 * q^47 - 2238049 * q^48 - 1241240 * q^49 - 5126146 * q^50 - 2477574 * q^51 - 268404 * q^52 - 398258 * q^53 + 6491644 * q^54 - 2551752 * q^55 - 4471819 * q^56 + 2094777 * q^57 - 2294852 * q^58 + 5664766 * q^59 + 1374965 * q^60 + 2652290 * q^61 - 5621243 * q^62 - 3210173 * q^63 + 5395148 * q^64 + 22093214 * q^65 - 284525 * q^66 + 5696184 * q^67 + 2422800 * q^68 + 4199245 * q^69 - 8874170 * q^70 - 16652990 * q^71 + 5916954 * q^72 + 108058 * q^73 + 8260200 * q^74 - 3594466 * q^75 - 7386456 * q^76 - 8874183 * q^77 - 27627308 * q^78 - 7378370 * q^79 + 7523523 * q^80 - 14862361 * q^81 + 7898428 * q^82 + 18099816 * q^83 + 47917640 * q^84 + 5843026 * q^85 + 14578342 * q^86 - 24244628 * q^87 + 23110740 * q^88 - 20405960 * q^89 + 32640076 * q^90 + 10283016 * q^91 - 27186571 * q^92 - 19267997 * q^93 - 52636002 * q^94 + 1708621 * q^95 + 8113092 * q^96 + 53505940 * q^97 - 3752059 * q^98 + 10929650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−9.69651			−0.857058			−0.428529	−	0.903528i	$-0.640968\pi$
$2$	−9.69651			−0.857058			−0.428529	+	0.903528i	$0.640968\pi$
$3$	−18.8428	+	32.6367i	−0.402922	+	0.697882i	−0.994077	−	0.108676i	$-0.965339\pi$
$3$	−18.8428	+	32.6367i	−0.402922	+	0.697882i	0.591155	+	0.806558i	$0.298672\pi$
$4$	−33.9777			−0.265451
$5$	119.656	−	207.250i	0.428094	−	0.741481i	−0.568610	−	0.822608i	$-0.692518\pi$
$5$	119.656	−	207.250i	0.428094	−	0.741481i	0.996704	+	0.0811265i	$0.0258518\pi$
$6$	182.709	−	316.462i	0.345328	−	0.598125i
$7$	493.624	+	854.982i	0.543943	+	0.942136i	0.998673	+	0.0515070i	$0.0164024\pi$
$7$	493.624	+	854.982i	0.543943	+	0.942136i	−0.454730	+	0.890629i	$0.650264\pi$
$8$	1570.62			1.08457
$9$	383.397	+	664.064i	0.175307	+	0.303641i
$10$	−1160.25	+	2009.60i	−0.366902	+	0.635493i
$11$	71.3912			0.0161722			0.00808612	−	0.999967i	$-0.497426\pi$
$11$	71.3912			0.0161722			0.00808612	+	0.999967i	$0.497426\pi$
$12$	640.235	−	1108.92i	0.106956	−	0.185253i
$13$	−1635.79	−	2833.27i	−0.206503	−	0.357673i	0.744108	−	0.668059i	$-0.232875\pi$
$13$	−1635.79	−	2833.27i	−0.206503	−	0.357673i	−0.950610	+	0.310387i	$0.899541\pi$
$14$	−4786.43	−	8290.34i	−0.466191	−	0.807466i
$15$	4509.31	+	7810.35i	0.344977	+	0.597518i
$16$	−10880.4			−0.664085
$17$	−11569.7	−	20039.4i	−0.571153	−	0.989266i	−0.996448	−	0.0842114i	$-0.973163\pi$
$17$	−11569.7	−	20039.4i	−0.571153	−	0.989266i	0.425295	−	0.905055i	$-0.360170\pi$
$18$	−3717.62	−	6439.10i	−0.150249	−	0.260238i
$19$	−24489.5	+	42417.1i	−0.819112	+	1.41874i	0.0872258	+	0.996189i	$0.472200\pi$
$19$	−24489.5	+	42417.1i	−0.819112	+	1.41874i	−0.906338	+	0.422554i	$0.861134\pi$
$20$	−4065.64	+	7041.89i	−0.113638	+	0.196827i
$21$	−37205.0			−0.876666
$22$	−692.246			−0.0138606
$23$	−11335.0	+	19632.8i	−0.194256	+	0.336462i	−0.946656	−	0.322244i	$-0.895563\pi$
$23$	−11335.0	+	19632.8i	−0.194256	+	0.336462i	0.752400	+	0.658706i	$0.228896\pi$
$24$	−29594.9	+	51259.8i	−0.436995	+	0.756898i
$25$	10427.4	+	18060.8i	0.133471	+	0.231178i
$26$	15861.4	+	27472.8i	0.176985	+	0.306547i
$27$	−111316.			−1.08839
$28$	−16772.2	−	29050.3i	−0.144390	−	0.250091i
$29$	−46185.3	−	79995.3i	−0.351650	−	0.609076i	0.634889	−	0.772604i	$-0.281046\pi$
$29$	−46185.3	−	79995.3i	−0.351650	−	0.609076i	−0.986539	+	0.163528i	$0.947713\pi$
$30$	−43724.6	−	75733.2i	−0.295666	−	0.512108i
$31$	−48322.4	+	83696.9i	−0.291328	+	0.504595i	−0.974124	−	0.226014i	$-0.927431\pi$
$31$	−48322.4	+	83696.9i	−0.291328	+	0.504595i	0.682796	+	0.730609i	$0.260764\pi$
$32$	−95537.5			−0.515405
$33$	−1345.21	+	2329.97i	−0.00651616	+	0.0112863i
$34$	112186.	+	194312.i	0.489512	+	0.847859i
$35$	236260.			0.931435
$36$	−13027.0	−	22563.4i	−0.0465355	−	0.0806018i
$37$	−35430.6	+	61367.6i	−0.114993	+	0.199174i	−0.917777	−	0.397096i	$-0.870018\pi$
$37$	−35430.6	+	61367.6i	−0.114993	+	0.199174i	0.802784	+	0.596270i	$0.203351\pi$
$38$	237463.	−	411298.i	0.702027	−	1.21595i
$39$	123291.			0.332818
$40$	187934.	−	325511.i	0.464296	−	0.804185i
$41$	183851.			0.416603			0.208301	−	0.978065i	$-0.433207\pi$
$41$	183851.			0.416603			0.208301	+	0.978065i	$0.433207\pi$
$42$	360759.			0.751354
$43$	−468175.	+	229414.i	−0.897984	+	0.440029i
$43$	−468175.	+	229414.i	−0.897984	+	0.440029i
$44$	−2425.71			−0.00429294
$45$	183503.			0.300193
$46$	109910.	−	190370.i	0.166489	−	0.288368i
$47$	311915.			0.438222			0.219111	−	0.975700i	$-0.429684\pi$
$47$	311915.			0.438222			0.219111	+	0.975700i	$0.429684\pi$
$48$	205017.	−	355099.i	0.267575	−	0.463453i
$49$	−75557.8	+	130870.i	−0.0917473	+	0.158911i
$50$	−101109.	−	175126.i	−0.114392	−	0.198133i
$51$	872026.			0.920521
$52$	55580.3	+	96267.9i	0.0548163	+	0.0949445i
$53$	−790638.	+	1.36943e6i	−0.729478	+	1.26349i	0.227626	+	0.973749i	$0.426904\pi$
$53$	−790638.	+	1.36943e6i	−0.729478	+	1.26349i	−0.957104	+	0.289744i	$0.906430\pi$
$54$	1.07937e6			0.932810
$55$	8542.39	−	14795.8i	0.00692325	−	0.0119914i
$56$	775295.	+	1.34285e6i	0.589941	+	1.02181i
$57$	−922903.	−	1.59852e6i	−0.660076	−	1.14329i
$58$	447836.	+	775675.i	0.301385	+	0.522014i
$59$	−1.46477e6			−0.928510			−0.464255	−	0.885702i	$-0.653678\pi$
$59$	−1.46477e6			−0.928510			−0.464255	+	0.885702i	$0.653678\pi$
$60$	−153216.	−	265378.i	−0.0915745	−	0.158612i
$61$	−1.66048e6	−	2.87603e6i	−0.936652	−	1.62233i	−0.771661	−	0.636034i	$-0.780574\pi$
$61$	−1.66048e6	−	2.87603e6i	−0.936652	−	1.62233i	−0.164991	−	0.986295i	$-0.552760\pi$
$62$	468559.	−	811567.i	0.249685	−	0.432468i
$63$	−378508.	+	655596.i	−0.190714	+	0.330327i
$64$	2.31907e6			1.10582
$65$	−782928.			−0.353610
$66$	13043.9	−	22592.6i	0.00558473	−	0.00967303i
$67$	−1.51656e6	+	2.62676e6i	−0.616025	+	1.06699i	0.374179	+	0.927356i	$0.377925\pi$
$67$	−1.51656e6	+	2.62676e6i	−0.616025	+	1.06699i	−0.990204	+	0.139630i	$0.955409\pi$
$68$	393113.	+	680892.i	0.151613	+	0.262601i
$69$	−427168.	−	739876.i	−0.156540	−	0.271136i
$70$	−2.29090e6			−0.798294
$71$	157114.	+	272129.i	0.0520968	+	0.0902342i	0.890898	−	0.454204i	$-0.150076\pi$
$71$	157114.	+	272129.i	0.0520968	+	0.0902342i	−0.838801	+	0.544438i	$0.816743\pi$
$72$	602171.	+	1.04299e6i	0.190132	+	0.329319i
$73$	−973486.	−	1.68613e6i	−0.292887	−	0.507295i	0.681604	−	0.731721i	$-0.261283\pi$
$73$	−973486.	−	1.68613e6i	−0.292887	−	0.507295i	−0.974491	+	0.224426i	$0.927949\pi$
$74$	343553.	−	595051.i	0.0985559	−	0.170704i
$75$	−785925.			−0.215113
$76$	832098.	−	1.44124e6i	0.217434	−	0.376606i
$77$	35240.4	+	61038.2i	0.00879678	+	0.0152365i
$78$	−1.19550e6			−0.285244
$79$	1.65479e6	+	2.86618e6i	0.377615	+	0.654048i	0.990715	−	0.135958i	$-0.0434111\pi$
$79$	1.65479e6	+	2.86618e6i	0.377615	+	0.654048i	−0.613100	+	0.790005i	$0.710078\pi$
$80$	−1.30190e6	+	2.25496e6i	−0.284291	+	0.492407i
$81$	1.25901e6	−	2.18066e6i	0.263227	−	0.455923i
$82$	−1.78271e6			−0.357053
$83$	−1.82188e6	+	3.15559e6i	−0.349741	+	0.605769i	−0.986203	−	0.165539i	$-0.947064\pi$
$83$	−1.82188e6	+	3.15559e6i	−0.349741	+	0.605769i	0.636463	+	0.771308i	$0.280397\pi$
$84$	1.26414e6			0.232712
$85$	−5.53756e6			−0.978030
$86$	4.53966e6	−	2.22452e6i	0.769624	−	0.377131i
$87$	3.48104e6			0.566750
$88$	112128.			0.0175399
$89$	−3.32655e6	+	5.76175e6i	−0.500183	+	0.866342i	0.499817	+	0.866131i	$0.333401\pi$
$89$	−3.32655e6	+	5.76175e6i	−0.500183	+	0.866342i	−1.00000		0.000211262i	$0.999933\pi$
$90$	−1.77934e6			−0.257283
$91$	1.61493e6	−	2.79714e6i	0.224651	−	0.389107i
$92$	385138.	−	667079.i	0.0515655	−	0.0893141i
$93$	−1.82106e6	−	3.15417e6i	−0.234765	−	0.406625i
$94$	−3.02449e6			−0.375582
$95$	5.86064e6	+	1.01509e7i	0.701314	+	1.21471i
$96$	1.80019e6	−	3.11803e6i	0.207668	−	0.359692i
$97$	−6.68568e6			−0.743780			−0.371890	−	0.928277i	$-0.621290\pi$
$97$	−6.68568e6			−0.743780			−0.371890	+	0.928277i	$0.621290\pi$
$98$	732647.	−	1.26898e6i	0.0786328	−	0.136196i
$99$	27371.2	+	47408.3i	0.00283512	+	0.00491057i
$100$	−354299.	−	613663.i	−0.0354299	−	0.0613663i
$101$	2.68774e6	+	4.65530e6i	0.259575	+	0.449596i	0.966128	−	0.258063i	$-0.0830843\pi$
$101$	2.68774e6	+	4.65530e6i	0.259575	+	0.449596i	−0.706553	+	0.707660i	$0.749751\pi$
$102$	−8.45561e6			−0.788940
$103$	−7.62326e6	−	1.32039e7i	−0.687402	−	1.19061i	−0.972676	−	0.232169i	$-0.925418\pi$
$103$	−7.62326e6	−	1.32039e7i	−0.687402	−	1.19061i	0.285274	−	0.958446i	$-0.407915\pi$
$104$	−2.56920e6	−	4.44998e6i	−0.223965	−	0.387920i
$105$	−4.45181e6	+	7.71075e6i	−0.375296	+	0.650031i
$106$	7.66643e6	−	1.32786e7i	0.625205	−	1.08289i
$107$	5.48275e6			0.432669			0.216334	−	0.976319i	$-0.430590\pi$
$107$	5.48275e6			0.432669			0.216334	+	0.976319i	$0.430590\pi$
$108$	3.78225e6			0.288913
$109$	930807.	−	1.61221e6i	0.0688441	−	0.119242i	−0.829549	−	0.558434i	$-0.811402\pi$
$109$	930807.	−	1.61221e6i	0.0688441	−	0.119242i	0.898393	+	0.439193i	$0.144736\pi$
$110$	−82831.3	+	143468.i	−0.00593363	+	0.0102773i
$111$	−1.33522e6	−	2.31267e6i	−0.0926667	−	0.160503i
$112$	−5.37081e6	−	9.30252e6i	−0.361224	−	0.625659i
$113$	2.71638e7			1.77099			0.885496	−	0.464647i	$-0.153819\pi$
$113$	2.71638e7			1.77099			0.885496	+	0.464647i	$0.153819\pi$
$114$	8.94894e6	+	1.55000e7i	0.565724	+	0.979863i
$115$	2.71261e6	+	4.69838e6i	0.166320	+	0.288075i
$116$	1.56927e6	+	2.71805e6i	0.0933458	+	0.161680i
$117$	1.25431e6	−	2.17254e6i	0.0724029	−	0.125405i
$118$	1.42031e7			0.795787
$119$	1.14222e7	−	1.97838e7i	0.621349	−	1.07621i
$120$	7.08240e6	+	1.22671e7i	0.374150	+	0.648048i
$121$	−1.94821e7			−0.999738
$122$	1.61008e7	+	2.78875e7i	0.802766	+	1.39043i
$123$	−3.46426e6	+	6.00028e6i	−0.167858	+	0.290739i
$124$	1.64188e6	−	2.84383e6i	0.0773333	−	0.133945i
$125$	2.36870e7			1.08474
$126$	3.67021e6	−	6.35699e6i	0.163453	−	0.283110i
$127$	2.96273e7			1.28345			0.641726	−	0.766934i	$-0.278219\pi$
$127$	2.96273e7			1.28345			0.641726	+	0.766934i	$0.278219\pi$
$128$	−1.02581e7			−0.432345
$129$	1.33440e6	−	1.96025e7i	0.0547294	−	0.803984i
$130$	7.59166e6			0.303065
$131$	131814.			0.00512284			0.00256142	−	0.999997i	$-0.499185\pi$
$131$	131814.			0.00512284			0.00256142	+	0.999997i	$0.499185\pi$
$132$	45707.2	−	79167.1i	0.00172972	−	0.00299596i
$133$	−4.83545e7			−1.78220
$134$	1.47054e7	−	2.54704e7i	0.527969	−	0.914470i
$135$	−1.33196e7	+	2.30702e7i	−0.465932	+	0.807017i
$136$	−1.81717e7	−	3.14742e7i	−0.619453	−	1.07292i
$137$	−3.98414e7			−1.32377			−0.661885	−	0.749605i	$-0.730243\pi$
$137$	−3.98414e7			−1.32377			−0.661885	+	0.749605i	$0.730243\pi$
$138$	4.14203e6	+	7.17421e6i	0.134164	+	0.232379i
$139$	378301.	−	655237.i	0.0119477	−	0.0206941i	−0.859990	−	0.510311i	$-0.829530\pi$
$139$	378301.	−	655237.i	0.0119477	−	0.0206941i	0.871937	+	0.489617i	$0.162863\pi$
$140$	−8.02758e6			−0.247250
$141$	−5.87736e6	+	1.01799e7i	−0.176569	+	0.305827i
$142$	−1.52346e6	−	2.63871e6i	−0.0446500	−	0.0773360i
$143$	−116781.	−	202271.i	−0.00333961	−	0.00578437i
$144$	−4.17151e6	−	7.22526e6i	−0.116419	−	0.201644i
$145$	−2.21054e7			−0.602158
$146$	9.43942e6	+	1.63496e7i	0.251021	+	0.434781i
$147$	−2.84744e6	−	4.93191e6i	−0.0739340	−	0.128057i
$148$	1.20385e6	−	2.08513e6i	0.0305250	−	0.0528709i
$149$	−8.60747e6	+	1.49086e7i	−0.213169	+	0.369219i	−0.952705	−	0.303898i	$-0.901712\pi$
$149$	−8.60747e6	+	1.49086e7i	−0.213169	+	0.369219i	0.739536	+	0.673117i	$0.235045\pi$
$150$	7.62073e6			0.184364
$151$	−7.52235e7			−1.77801			−0.889005	−	0.457897i	$-0.848603\pi$
$151$	−7.52235e7			−1.77801			−0.889005	+	0.457897i	$0.848603\pi$
$152$	−3.84637e7	+	6.66211e7i	−0.888380	+	1.53872i
$153$	8.87162e6	−	1.53661e7i	0.200255	−	0.346852i
$154$	−341709.	−	591858.i	−0.00753935	−	0.0130585i
$155$	1.15641e7	+	2.00297e7i	0.249432	+	0.432029i
$156$	−4.18916e6			−0.0883467
$157$	2.85633e7	+	4.94731e7i	0.589060	+	1.02028i	0.994356	+	0.106096i	$0.0338351\pi$
$157$	2.85633e7	+	4.94731e7i	0.589060	+	1.02028i	−0.405296	+	0.914185i	$0.632832\pi$
$158$	−1.60457e7	−	2.77920e7i	−0.323638	−	0.560557i
$159$	−2.97957e7	−	5.16076e7i	−0.587846	−	1.01818i
$160$	−1.14316e7	+	1.98002e7i	−0.220642	+	0.382163i
$161$	−2.23810e7			−0.422657
$162$	−1.22080e7	+	2.11448e7i	−0.225601	+	0.390752i
$163$	2.63095e7	+	4.55694e7i	0.475834	+	0.824169i	0.999617	−	0.0276830i	$-0.00881289\pi$
$163$	2.63095e7	+	4.55694e7i	0.475834	+	0.824169i	−0.523783	+	0.851852i	$0.675480\pi$
$164$	−6.24683e6			−0.110587
$165$	321925.	+	557591.i	0.00557906	+	0.00966322i
$166$	1.76659e7	−	3.05982e7i	0.299748	−	0.519179i
$167$	2.54181e7	−	4.40255e7i	0.422314	−	0.731470i	−0.573851	−	0.818960i	$-0.694551\pi$
$167$	2.54181e7	−	4.40255e7i	0.422314	−	0.731470i	0.996165	+	0.0874897i	$0.0278845\pi$
$168$	−5.84349e7			−0.950802
$169$	2.60227e7	−	4.50726e7i	0.414713	−	0.718305i
$170$	5.36950e7			0.838229
$171$	−3.75569e7			−0.574386
$172$	1.59075e7	−	7.79498e6i	0.238370	−	0.116806i
$173$	4.97271e7			0.730183			0.365091	−	0.930972i	$-0.381038\pi$
$173$	4.97271e7			0.730183			0.365091	+	0.930972i	$0.381038\pi$
$174$	−3.37540e7			−0.485738
$175$	−1.02944e7	+	1.78304e7i	−0.145201	+	0.251495i
$176$	−776763.			−0.0107398
$177$	2.76003e7	−	4.78052e7i	0.374117	−	0.647990i
$178$	3.22559e7	−	5.58689e7i	0.428686	−	0.742506i
$179$	5.15144e7	+	8.92256e7i	0.671341	+	1.16280i	0.977524	+	0.210824i	$0.0676146\pi$
$179$	5.15144e7	+	8.92256e7i	0.671341	+	1.16280i	−0.306183	+	0.951973i	$0.599052\pi$
$180$	−6.23502e6			−0.0796863
$181$	2.51431e7	+	4.35492e7i	0.315169	+	0.545890i	0.979474	−	0.201573i	$-0.0646053\pi$
$181$	2.51431e7	+	4.35492e7i	0.315169	+	0.545890i	−0.664304	+	0.747462i	$0.731272\pi$
$182$	−1.56592e7	+	2.71225e7i	−0.192539	+	0.333488i
$183$	1.25152e8			1.50959
$184$	−1.78030e7	+	3.08357e7i	−0.210684	+	0.364915i
$185$	8.47896e6	+	1.46860e7i	0.0984559	+	0.170531i
$186$	1.76579e7	+	3.05844e7i	0.201208	+	0.348502i
$187$	−825978.	−	1.43064e6i	−0.00923683	−	0.0159987i
$188$	−1.05982e7			−0.116326
$189$	−5.49480e7	−	9.51728e7i	−0.592019	−	1.02541i
$190$	−5.68278e7	−	9.84286e7i	−0.601067	−	1.04108i
$191$	5.21122e7	−	9.02609e7i	0.541156	−	0.937309i	−0.457682	−	0.889116i	$-0.651320\pi$
$191$	5.21122e7	−	9.02609e7i	0.541156	−	0.937309i	0.998838	−	0.0481934i	$-0.0153464\pi$
$192$	−4.36977e7	+	7.56867e7i	−0.445558	+	0.771730i
$193$	9.85926e7			0.987174			0.493587	−	0.869696i	$-0.335685\pi$
$193$	9.85926e7			0.987174			0.493587	+	0.869696i	$0.335685\pi$
$194$	6.48277e7			0.637463
$195$	1.47526e7	−	2.55522e7i	0.142477	−	0.246778i
$196$	2.56728e6	−	4.44666e6i	0.0243544	−	0.0421830i
$197$	3.67793e7	+	6.37036e7i	0.342745	+	0.593652i	0.984941	−	0.172888i	$-0.0553099\pi$
$197$	3.67793e7	+	6.37036e7i	0.342745	+	0.593652i	−0.642196	+	0.766540i	$0.721977\pi$
$198$	−265405.	−	459695.i	−0.00242986	−	0.00420864i
$199$	2.29490e7			0.206432			0.103216	−	0.994659i	$-0.467087\pi$
$199$	2.29490e7			0.206432			0.103216	+	0.994659i	$0.467087\pi$
$200$	1.63774e7	+	2.83666e7i	0.144758	+	0.250727i
$201$	−5.71525e7	−	9.89911e7i	−0.496420	−	0.859825i
$202$	−2.60617e7	−	4.51402e7i	−0.222471	−	0.385330i
$203$	4.55963e7	−	7.89752e7i	0.382555	−	0.662605i
$204$	−2.96294e7			−0.244353
$205$	2.19988e7	−	3.81031e7i	0.178345	−	0.308903i
$206$	7.39190e7	+	1.28032e8i	0.589143	+	1.02043i
$207$	−1.73833e7			−0.136218
$208$	1.77980e7	+	3.08270e7i	0.137135	+	0.237525i
$209$	−1.74834e6	+	3.02821e6i	−0.0132469	+	0.0229443i
$210$	4.31670e7	−	7.47674e7i	0.321650	−	0.557115i
$211$	−9.90749e6			−0.0726064			−0.0363032	−	0.999341i	$-0.511558\pi$
$211$	−9.90749e6			−0.0726064			−0.0363032	+	0.999341i	$0.511558\pi$
$212$	2.68641e7	−	4.65299e7i	0.193640	−	0.335395i
$213$	−1.18419e7			−0.0839637
$214$	−5.31636e7			−0.370822
$215$	−8.47371e6	+	1.24480e8i	−0.0581485	+	0.854212i
$216$	−1.74834e8			−1.18043
$217$	−9.54124e7			−0.633863
$218$	−9.02558e6	+	1.56328e7i	−0.0590035	+	0.102197i
$219$	7.33729e7			0.472042
$220$	−290251.	+	502729.i	−0.00183778	+	0.00318313i
$221$	−3.78513e7	+	6.55604e7i	−0.235889	+	0.408572i
$222$	1.29470e7	+	2.24249e7i	0.0794207	+	0.137561i
$223$	2.30010e8			1.38893			0.694465	−	0.719527i	$-0.255641\pi$
$223$	2.30010e8			1.38893			0.694465	+	0.719527i	$0.255641\pi$
$224$	−4.71596e7	−	8.16828e7i	−0.280351	−	0.485582i
$225$	−7.99567e6	+	1.38489e7i	−0.0467968	+	0.0810544i
$226$	−2.63394e8			−1.51784
$227$	−6.93089e7	+	1.20046e8i	−0.393277	+	0.681175i	−0.992880	−	0.119122i	$-0.961992\pi$
$227$	−6.93089e7	+	1.20046e8i	−0.393277	+	0.681175i	0.599603	+	0.800298i	$0.295325\pi$
$228$	3.13581e7	+	5.43139e7i	0.175218	+	0.303486i
$229$	1.13060e8	+	1.95826e8i	0.622136	+	1.07757i	0.989087	+	0.147330i	$0.0470681\pi$
$229$	1.13060e8	+	1.95826e8i	0.622136	+	1.07757i	−0.366952	+	0.930240i	$0.619599\pi$
$230$	−2.63028e7	−	4.55579e7i	−0.142546	−	0.246897i
$231$	−2.65611e6			−0.0141777
$232$	−7.25395e7	−	1.25642e8i	−0.381387	−	0.660582i
$233$	1.23439e8	+	2.13803e8i	0.639303	+	1.10731i	0.985586	+	0.169176i	$0.0541105\pi$
$233$	1.23439e8	+	2.13803e8i	0.639303	+	1.10731i	−0.346283	+	0.938130i	$0.612556\pi$
$234$	−1.21625e7	+	2.10660e7i	−0.0620535	+	0.107480i
$235$	3.73225e7	−	6.46445e7i	0.187600	−	0.324933i
$236$	4.97694e7			0.246474
$237$	−1.24724e8			−0.608597
$238$	−1.10756e8	+	1.91834e8i	−0.532533	+	0.922374i
$239$	1.06505e8	−	1.84473e8i	0.504637	−	0.874057i	−0.495348	−	0.868694i	$-0.664960\pi$
$239$	1.06505e8	−	1.84473e8i	0.504637	−	0.874057i	0.999986	−	0.00536294i	$-0.00170708\pi$
$240$	−4.90630e7	−	8.49795e7i	−0.229094	−	0.396803i
$241$	−1.12585e8	−	1.95003e8i	−0.518110	−	0.897393i	−0.999779	−	0.0210395i	$-0.993302\pi$
$241$	−1.12585e8	−	1.95003e8i	−0.518110	−	0.897393i	0.481669	−	0.876353i	$-0.340031\pi$
$242$	1.88908e8			0.856834
$243$	−7.42771e7	−	1.28652e8i	−0.332073	−	0.575167i
$244$	5.64192e7	+	9.77209e7i	0.248635	+	0.430648i
$245$	1.80819e7	+	3.13188e7i	0.0785530	+	0.136058i
$246$	3.35913e7	−	5.81818e7i	0.143864	−	0.249181i
$247$	1.60239e8			0.676595
$248$	−7.58961e7	+	1.31456e8i	−0.315965	+	0.547267i
$249$	−6.86586e7	−	1.18920e8i	−0.281836	−	0.488155i
$250$	−2.29682e8			−0.929686
$251$	−5.06151e7	−	8.76679e7i	−0.202033	−	0.349931i	0.747150	−	0.664655i	$-0.231421\pi$
$251$	−5.06151e7	−	8.76679e7i	−0.202033	−	0.349931i	−0.949183	+	0.314724i	$0.898088\pi$
$252$	1.28608e7	−	2.22756e7i	0.0506253	−	0.0876856i
$253$	−809222.	+	1.40161e6i	−0.00314156	+	0.00544135i
$254$	−2.87282e8			−1.09999
$255$	1.04343e8	−	1.80728e8i	0.394070	−	0.682549i
$256$	−1.97373e8			−0.735273
$257$	−5.13212e8			−1.88595			−0.942976	−	0.332861i	$-0.891986\pi$
$257$	−5.13212e8			−1.88595			−0.942976	+	0.332861i	$0.891986\pi$
$258$	−1.29390e7	+	1.90076e8i	−0.0469063	+	0.689061i
$259$	−6.99576e7			−0.250199
$260$	2.66021e7			0.0938661
$261$	3.54146e7	−	6.13400e7i	0.123294	−	0.213551i
$262$	−1.27813e6			−0.00439058
$263$	−1.21191e8	+	2.09909e8i	−0.410795	+	0.711518i	−0.994977	−	0.100105i	$-0.968082\pi$
$263$	−1.21191e8	+	2.09909e8i	−0.410795	+	0.711518i	0.584182	+	0.811623i	$0.301416\pi$
$264$	−2.11281e6	+	3.65950e6i	−0.00706720	+	0.0122407i
$265$	1.89209e8	+	3.27720e8i	0.624571	+	1.08179i
$266$	4.68870e8			1.52745
$267$	−1.25363e8	−	2.17135e8i	−0.403070	−	0.698137i
$268$	5.15293e7	−	8.92513e7i	0.163524	−	0.283232i
$269$	1.18359e8			0.370739			0.185369	−	0.982669i	$-0.440652\pi$
$269$	1.18359e8			0.370739			0.185369	+	0.982669i	$0.440652\pi$
$270$	1.29153e8	−	2.23700e8i	0.399331	−	0.691661i
$271$	−8.83130e7	−	1.52963e8i	−0.269545	−	0.466866i	0.699199	−	0.714927i	$-0.253540\pi$
$271$	−8.83130e7	−	1.52963e8i	−0.269545	−	0.466866i	−0.968745	+	0.248061i	$0.920207\pi$
$272$	1.25883e8	+	2.18036e8i	0.379294	+	0.656957i
$273$	6.08596e7	+	1.05412e8i	0.181034	+	0.313560i
$274$	3.86323e8			1.13455
$275$	744424.	+	1.28938e6i	0.00215852	+	0.00373866i
$276$	1.45142e7	+	2.51393e7i	0.0415538	+	0.0719732i
$277$	−1.10790e8	+	1.91895e8i	−0.313201	+	0.542480i	−0.979053	−	0.203604i	$-0.934735\pi$
$277$	−1.10790e8	+	1.91895e8i	−0.313201	+	0.542480i	0.665853	+	0.746083i	$0.268068\pi$
$278$	−3.66820e6	+	6.35351e6i	−0.0102399	+	0.0177361i
$279$	−7.41067e7			−0.204288
$280$	3.71075e8			1.01020
$281$	−3.72618e7	+	6.45394e7i	−0.100183	+	0.173521i	−0.911760	−	0.410724i	$-0.865276\pi$
$281$	−3.72618e7	+	6.45394e7i	−0.100183	+	0.173521i	0.811577	+	0.584245i	$0.198609\pi$
$282$	5.69899e7	−	9.87094e7i	0.151330	−	0.262112i
$283$	3.36933e7	+	5.83585e7i	0.0883672	+	0.153056i	0.906821	−	0.421516i	$-0.138502\pi$
$283$	3.36933e7	+	5.83585e7i	0.0883672	+	0.153056i	−0.818454	+	0.574572i	$0.805168\pi$
$284$	−5.33837e6	−	9.24633e6i	−0.0138291	−	0.0239527i
$285$	−4.41724e8			−1.13030
$286$	1.13237e6	+	1.96132e6i	0.00286224	+	0.00495755i
$287$	9.07531e7	+	1.57189e8i	0.226608	+	0.392496i
$288$	−3.66288e7	−	6.34430e7i	−0.0903544	−	0.156498i
$289$	−6.25487e7	+	1.08338e8i	−0.152432	+	0.264020i
$290$	2.14345e8			0.516084
$291$	1.25977e8	−	2.18198e8i	0.299685	−	0.519070i
$292$	3.30768e7	+	5.72907e7i	0.0777470	+	0.134662i
$293$	−3.61214e8			−0.838935			−0.419468	−	0.907770i	$-0.637783\pi$
$293$	−3.61214e8			−0.838935			−0.419468	+	0.907770i	$0.637783\pi$
$294$	2.76102e7	+	4.78224e7i	0.0633658	+	0.109753i
$295$	−1.75268e8	+	3.03573e8i	−0.397490	+	0.688473i
$296$	−5.56479e7	+	9.63850e7i	−0.124718	+	0.216017i
$297$	−7.94695e6			−0.0176016
$298$	8.34624e7	−	1.44561e8i	0.182698	−	0.316442i
$299$	7.41668e7			0.160458
$300$	2.67039e7			0.0571019
$301$	−4.27248e8	−	2.87036e8i	−0.903019	−	0.606672i
$302$	7.29406e8			1.52386
$303$	−2.02578e8			−0.418353
$304$	2.66455e8	−	4.61514e8i	0.543960	−	0.942166i
$305$	−7.94744e8			−1.60390
$306$	−8.60238e7	+	1.48998e8i	−0.171630	+	0.297272i
$307$	−5.03803e7	+	8.72613e7i	−0.0993749	+	0.172122i	−0.911426	−	0.411464i	$-0.865018\pi$
$307$	−5.03803e7	+	8.72613e7i	−0.0993749	+	0.172122i	0.812051	+	0.583586i	$0.198351\pi$
$308$	−1.19739e6	−	2.07394e6i	−0.00233511	−	0.00404453i
$309$	5.74575e8			1.10788
$310$	−1.12132e8	−	1.94218e8i	−0.213778	−	0.370274i
$311$	4.58907e8	−	7.94851e8i	0.865095	−	1.49839i	−0.00185873	−	0.999998i	$-0.500592\pi$
$311$	4.58907e8	−	7.94851e8i	0.865095	−	1.49839i	0.866953	−	0.498389i	$-0.166075\pi$
$312$	1.93644e8			0.360963
$313$	−2.57821e8	+	4.46560e8i	−0.475241	+	0.823141i	−0.999598	−	0.0283573i	$-0.990972\pi$
$313$	−2.57821e8	+	4.46560e8i	−0.475241	+	0.823141i	0.524357	+	0.851498i	$0.324306\pi$
$314$	−2.76964e8	−	4.79716e8i	−0.504859	−	0.874441i
$315$	9.05816e7	+	1.56892e8i	0.163288	+	0.282822i
$316$	−5.62260e7	−	9.73864e7i	−0.100238	−	0.173617i
$317$	5.75463e8			1.01463			0.507317	−	0.861759i	$-0.330637\pi$
$317$	5.75463e8			1.01463			0.507317	+	0.861759i	$0.330637\pi$
$318$	2.88914e8	+	5.00414e8i	0.503818	+	0.872639i
$319$	−3.29722e6	−	5.71096e6i	−0.00568697	−	0.00985012i
$320$	2.77490e8	−	4.80627e8i	0.473394	−	0.819943i
$321$	−1.03310e8	+	1.78939e8i	−0.174332	+	0.301952i
$322$	2.17017e8			0.362242
$323$	1.13335e9			1.87135
$324$	−4.27782e7	+	7.40939e7i	−0.0698738	+	0.121025i
$325$	3.41140e7	−	5.90872e7i	0.0551240	−	0.0954776i
$326$	−2.55110e8	−	4.41864e8i	−0.407818	−	0.706361i
$327$	3.50780e7	+	6.07569e7i	0.0554777	+	0.0960901i
$328$	2.88759e8			0.451833
$329$	1.53969e8	+	2.66682e8i	0.238368	+	0.412865i
$330$	−3.12155e6	−	5.40668e6i	−0.00478158	−	0.00828194i
$331$	−5.30582e8	−	9.18995e8i	−0.804183	−	1.39289i	−0.916841	−	0.399252i	$-0.869270\pi$
$331$	−5.30582e8	−	9.18995e8i	−0.804183	−	1.39289i	0.112659	−	0.993634i	$-0.464063\pi$
$332$	6.19032e7	−	1.07220e8i	0.0928389	−	0.160802i
$333$	−5.43360e7			−0.0806367
$334$	−2.46467e8	+	4.26894e8i	−0.361948	+	0.626913i
$335$	3.62931e8	+	6.28615e8i	0.527433	+	0.913541i
$336$	4.04805e8			0.582181
$337$	−4.27752e8	−	7.40889e8i	−0.608818	−	1.05450i	−0.991436	−	0.130597i	$-0.958311\pi$
$337$	−4.27752e8	−	7.40889e8i	−0.608818	−	1.05450i	0.382617	−	0.923907i	$-0.375023\pi$
$338$	−2.52329e8	+	4.37046e8i	−0.355434	+	0.615629i
$339$	−5.11843e8	+	8.86538e8i	−0.713572	+	1.23594i
$340$	1.88153e8			0.259619
$341$	−3.44980e6	+	5.97522e6i	−0.00471143	+	0.00816044i
$342$	3.64171e8			0.492282
$343$	6.63853e8			0.888264
$344$	−7.35324e8	+	3.60323e8i	−0.973922	+	0.477240i
$345$	−2.04453e8			−0.268056
$346$	−4.82179e8			−0.625809
$347$	−4.24334e8	+	7.34967e8i	−0.545198	+	0.944311i	0.453396	+	0.891309i	$0.350212\pi$
$347$	−4.24334e8	+	7.34967e8i	−0.545198	+	0.944311i	−0.998594	+	0.0530016i	$0.983121\pi$
$348$	−1.18278e8			−0.150444
$349$	−1.19381e8	+	2.06775e8i	−0.150331	+	0.260380i	−0.931349	−	0.364128i	$-0.881367\pi$
$349$	−1.19381e8	+	2.06775e8i	−0.150331	+	0.260380i	0.781018	+	0.624508i	$0.214700\pi$
$350$	9.98199e7	−	1.72893e8i	0.124445	−	0.215546i
$351$	1.82089e8	+	3.15387e8i	0.224754	+	0.389286i
$352$	−6.82054e6			−0.00833527
$353$	−9.87854e7	−	1.71101e8i	−0.119531	−	0.207034i	0.800051	−	0.599932i	$-0.204806\pi$
$353$	−9.87854e7	−	1.71101e8i	−0.119531	−	0.207034i	−0.919582	+	0.392898i	$0.871472\pi$
$354$	−2.67627e8	+	4.63543e8i	−0.320640	+	0.555365i
$355$	7.51985e7			0.0892093
$356$	1.13028e8	−	1.95771e8i	0.132774	−	0.229971i
$357$	4.30453e8	+	7.45566e8i	0.500711	+	0.867256i
$358$	−4.99510e8	−	8.65177e8i	−0.575378	−	0.996585i
$359$	−1.15696e8	−	2.00392e8i	−0.131974	−	0.228586i	0.792463	−	0.609920i	$-0.208798\pi$
$359$	−1.15696e8	−	2.00392e8i	−0.131974	−	0.228586i	−0.924437	+	0.381334i	$0.875465\pi$
$360$	2.88214e8			0.325578
$361$	−7.52540e8	−	1.30344e9i	−0.841888	−	1.45819i
$362$	−2.43801e8	−	4.22275e8i	−0.270119	−	0.467859i
$363$	3.67097e8	−	6.35831e8i	0.402817	−	0.697699i
$364$	−5.48716e7	+	9.50403e7i	−0.0596338	+	0.103289i
$365$	−4.65934e8			−0.501533
$366$	−1.21354e9			−1.29381
$367$	1.01162e8	−	1.75219e8i	0.106829	−	0.185033i	−0.807655	−	0.589655i	$-0.799264\pi$
$367$	1.01162e8	−	1.75219e8i	0.106829	−	0.185033i	0.914484	+	0.404622i	$0.132597\pi$
$368$	1.23329e8	−	2.13613e8i	0.129003	−	0.223439i
$369$	7.04879e7	+	1.22089e8i	0.0730335	+	0.126498i
$370$	−8.22164e7	−	1.42403e8i	−0.0843825	−	0.146155i
$371$	−1.56111e9			−1.58718
$372$	6.18754e7	+	1.07171e8i	0.0623186	+	0.107939i
$373$	6.15456e8	+	1.06600e9i	0.614068	+	1.06360i	0.990547	+	0.137172i	$0.0438013\pi$
$373$	6.15456e8	+	1.06600e9i	0.614068	+	1.06360i	−0.376479	+	0.926425i	$0.622865\pi$
$374$	8.00911e6	+	1.38722e7i	0.00791651	+	0.0137118i
$375$	−4.46330e8	+	7.73067e8i	−0.437066	+	0.757020i
$376$	4.89900e8			0.475280
$377$	−1.51099e8	+	2.61711e8i	−0.145233	+	0.251551i
$378$	5.32804e8	+	9.22844e8i	0.507395	+	0.878834i
$379$	−1.02381e8			−0.0966010			−0.0483005	−	0.998833i	$-0.515381\pi$
$379$	−1.02381e8			−0.0966010			−0.0483005	+	0.998833i	$0.515381\pi$
$380$	−1.99131e8	−	3.44905e8i	−0.186164	−	0.322446i
$381$	−5.58262e8	+	9.66938e8i	−0.517131	+	0.895697i
$382$	−5.05306e8	+	8.75216e8i	−0.463802	+	0.803329i
$383$	3.65727e8			0.332630			0.166315	−	0.986073i	$-0.446813\pi$
$383$	3.65727e8			0.332630			0.166315	+	0.986073i	$0.446813\pi$
$384$	1.93291e8	−	3.34789e8i	0.174201	−	0.301726i
$385$	1.68669e7			0.0150634
$386$	−9.56004e8			−0.846066
$387$	−3.31843e8	−	2.22941e8i	−0.291034	−	0.195525i
$388$	2.27164e8			0.197437
$389$	−1.95028e9			−1.67986			−0.839930	−	0.542695i	$-0.817404\pi$
$389$	−1.95028e9			−1.67986			−0.839930	+	0.542695i	$0.817404\pi$
$390$	−1.43048e8	+	2.47767e8i	−0.122111	+	0.211503i
$391$	5.24574e8			0.443801
$392$	−1.18672e8	+	2.05547e8i	−0.0995059	+	0.172349i
$393$	−2.48374e6	+	4.30196e6i	−0.00206411	+	0.00357514i
$394$	−3.56631e8	−	6.17702e8i	−0.293753	−	0.508795i
$395$	7.92023e8			0.646619
$396$	−930011.	−	1.61083e6i	−0.000752584	−	0.00130351i
$397$	4.73213e8	−	8.19628e8i	0.379568	−	0.657431i	−0.611431	−	0.791297i	$-0.709406\pi$
$397$	4.73213e8	−	8.19628e8i	0.379568	−	0.657431i	0.990999	+	0.133866i	$0.0427393\pi$
$398$	−2.22525e8			−0.176925
$399$	9.11135e8	−	1.57813e9i	0.718088	−	1.24376i
$400$	−1.13454e8	−	1.96508e8i	−0.0886358	−	0.153522i
$401$	−6.92530e8	−	1.19950e9i	−0.536331	−	0.928953i	−0.999098	−	0.0424726i	$-0.986476\pi$
$401$	−6.92530e8	−	1.19950e9i	−0.536331	−	0.928953i	0.462767	−	0.886480i	$-0.346857\pi$
$402$	5.54180e8	+	9.59868e8i	0.425461	+	0.736920i
$403$	3.16181e8			0.240640
$404$	−9.13231e7	−	1.58176e8i	−0.0689043	−	0.119346i
$405$	−3.01296e8	−	5.21859e8i	−0.225372	−	0.390356i
$406$	−4.42125e8	+	7.65784e8i	−0.327872	+	0.567891i
$407$	−2.52943e6	+	4.38111e6i	−0.00185970	+	0.00322109i
$408$	1.36962e9			0.998365
$409$	1.62032e9			1.17103			0.585517	−	0.810660i	$-0.300892\pi$
$409$	1.62032e9			1.17103			0.585517	+	0.810660i	$0.300892\pi$
$410$	−2.13312e8	+	3.69467e8i	−0.152852	+	0.264748i
$411$	7.50724e8	−	1.30029e9i	0.533376	−	0.923835i
$412$	2.59021e8	+	4.48637e8i	0.182471	+	0.316050i
$413$	−7.23044e8	−	1.25235e9i	−0.505056	−	0.874783i
$414$	1.68557e8			0.116747
$415$	4.35997e8	+	7.55170e8i	0.299444	+	0.518652i
$416$	1.56279e8	+	2.70683e8i	0.106433	+	0.184347i
$417$	1.42565e7	+	2.46930e7i	0.00962802	+	0.0166762i
$418$	1.69528e7	−	2.93631e7i	0.0113533	−	0.0196646i
$419$	2.48162e9			1.64811			0.824054	−	0.566512i	$-0.191708\pi$
$419$	2.48162e9			1.64811			0.824054	+	0.566512i	$0.191708\pi$
$420$	1.51262e8	−	2.61994e8i	0.0996226	−	0.172551i
$421$	4.92664e8	+	8.53320e8i	0.321783	+	0.557345i	0.980856	−	0.194734i	$-0.0623844\pi$
$421$	4.92664e8	+	8.53320e8i	0.321783	+	0.557345i	−0.659073	+	0.752079i	$0.729051\pi$
$422$	9.60681e7			0.0622280
$423$	1.19588e8	+	2.07132e8i	0.0768236	+	0.133062i
$424$	−1.24179e9	+	2.15084e9i	−0.791167	+	1.37034i
$425$	2.41284e8	−	4.17917e8i	0.152464	−	0.264076i
$426$	1.14825e8			0.0719618
$427$	1.63930e9	−	2.83935e9i	1.01897	−	1.76491i
$428$	−1.86291e8			−0.114852
$429$	8.80192e6			0.00538241
$430$	8.21654e7	−	1.20702e9i	0.0498367	−	0.732109i
$431$	2.40873e9			1.44917			0.724583	−	0.689187i	$-0.242032\pi$
$431$	2.40873e9			1.44917			0.724583	+	0.689187i	$0.242032\pi$
$432$	1.21115e9			0.722781
$433$	−1.55328e9	+	2.69037e9i	−0.919482	+	1.59259i	−0.119280	+	0.992861i	$0.538058\pi$
$433$	−1.55328e9	+	2.69037e9i	−0.919482	+	1.59259i	−0.800203	+	0.599730i	$0.795275\pi$
$434$	9.25167e8			0.543258
$435$	4.16528e8	−	7.21447e8i	0.242623	−	0.420235i
$436$	−3.16267e7	+	5.47790e7i	−0.0182747	+	0.0316528i
$437$	−5.55180e8	−	9.61599e8i	−0.318235	−	0.551200i
$438$	−7.11461e8			−0.404568
$439$	1.55286e9	+	2.68963e9i	0.876003	+	1.51728i	0.855690	+	0.517489i	$0.173133\pi$
$439$	1.55286e9	+	2.68963e9i	0.876003	+	1.51728i	0.0203134	+	0.999794i	$0.493534\pi$
$440$	1.34168e7	−	2.32386e7i	0.00750871	−	0.0130055i
$441$	−1.15875e8			−0.0643359
$442$	3.67026e8	−	6.35707e8i	0.202171	−	0.350170i
$443$	2.62487e8	+	4.54640e8i	0.143448	+	0.248459i	0.928793	−	0.370599i	$-0.120848\pi$
$443$	2.62487e8	+	4.54640e8i	0.143448	+	0.248459i	−0.785345	+	0.619058i	$0.787514\pi$
$444$	4.53678e7	+	7.85794e7i	0.0245984	+	0.0426057i
$445$	7.96083e8	+	1.37886e9i	0.428251	+	0.741752i
$446$	−2.23030e9			−1.19039
$447$	−3.24378e8	−	5.61839e8i	−0.171781	−	0.297533i
$448$	1.14475e9	+	1.98276e9i	0.601501	+	1.04183i
$449$	6.33177e8	−	1.09670e9i	0.330113	−	0.571773i	−0.652420	−	0.757857i	$-0.726246\pi$
$449$	6.33177e8	−	1.09670e9i	0.330113	−	0.571773i	0.982534	+	0.186084i	$0.0595797\pi$
$450$	7.75300e7	−	1.34286e8i	0.0401076	−	0.0694683i
$451$	1.31253e7			0.00673740
$452$	−9.22965e8			−0.470111
$453$	1.41742e9	−	2.45505e9i	0.716400	−	1.24084i
$454$	6.72054e8	−	1.16403e9i	0.337061	−	0.583807i
$455$	−3.86472e8	−	6.69389e8i	−0.192344	−	0.333149i
$456$	−1.44953e9	−	2.51066e9i	−0.715896	−	1.23997i
$457$	1.20204e9			0.589131			0.294566	−	0.955631i	$-0.404825\pi$
$457$	1.20204e9			0.589131			0.294566	+	0.955631i	$0.404825\pi$
$458$	−1.09629e9	−	1.89883e9i	−0.533207	−	0.923541i
$459$	1.28789e9	+	2.23070e9i	0.621635	+	1.07670i
$460$	−9.21682e7	−	1.59640e8i	−0.0441498	−	0.0764697i
$461$	−9.20737e8	+	1.59476e9i	−0.437706	+	0.758129i	−0.997512	−	0.0704946i	$-0.977542\pi$
$461$	−9.20737e8	+	1.59476e9i	−0.437706	+	0.758129i	0.559806	+	0.828624i	$0.310876\pi$
$462$	2.57550e7			0.0121511
$463$	−4.62021e8	+	8.00244e8i	−0.216336	+	0.374705i	−0.953685	−	0.300807i	$-0.902744\pi$
$463$	−4.62021e8	+	8.00244e8i	−0.216336	+	0.374705i	0.737349	+	0.675512i	$0.236077\pi$
$464$	5.02513e8	+	8.70378e8i	0.233526	+	0.404478i
$465$	−8.71603e8			−0.402007
$466$	−1.19693e9	−	2.07314e9i	−0.547920	−	0.949026i
$467$	1.63573e9	−	2.83316e9i	0.743193	−	1.28725i	−0.207841	−	0.978163i	$-0.566644\pi$
$467$	1.63573e9	−	2.83316e9i	0.743193	−	1.28725i	0.951034	−	0.309086i	$-0.100023\pi$
$468$	−4.26187e7	+	7.38178e7i	−0.0192194	+	0.0332890i
$469$	−2.99444e9			−1.34033
$470$	−3.61898e8	+	6.26826e8i	−0.160784	+	0.278487i
$471$	−2.15285e9			−0.949381
$472$	−2.30059e9			−1.00703
$473$	−3.34236e7	+	1.63782e7i	−0.0145224	+	0.00711626i
$474$	1.20938e9			0.521603
$475$	−1.02145e9			−0.437309
$476$	−3.88100e8	+	6.72210e8i	−0.164938	+	0.285680i
$477$	−1.21251e9			−0.511532
$478$	−1.03273e9	+	1.78874e9i	−0.432504	+	0.749118i
$479$	−1.18051e9	+	2.04470e9i	−0.490789	+	0.850072i	−0.999944	−	0.0106030i	$-0.996625\pi$
$479$	−1.18051e9	+	2.04470e9i	−0.490789	+	0.850072i	0.509154	+	0.860675i	$0.329958\pi$
$480$	−4.30808e8	−	7.46182e8i	−0.177803	−	0.307964i
$481$	2.31828e8			0.0949856
$482$	1.09168e9	+	1.89085e9i	0.444051	+	0.769118i
$483$	4.21720e8	−	7.30441e8i	0.170298	−	0.294965i
$484$	6.61956e8			0.265381
$485$	−7.99981e8	+	1.38561e9i	−0.318408	+	0.551499i
$486$	7.20229e8	+	1.24747e9i	0.284606	+	0.492951i
$487$	2.45406e9	+	4.25056e9i	0.962795	+	1.66761i	0.715426	+	0.698688i	$0.246233\pi$
$487$	2.45406e9	+	4.25056e9i	0.962795	+	1.66761i	0.247369	+	0.968921i	$0.420434\pi$
$488$	−2.60797e9	−	4.51714e9i	−1.01586	−	1.75952i
$489$	−1.98298e9			−0.766897
$490$	−1.75331e8	−	3.03683e8i	−0.0673245	−	0.116609i
$491$	−2.27531e9	−	3.94095e9i	−0.867471	−	1.50250i	−0.864573	−	0.502507i	$-0.832411\pi$
$491$	−2.27531e9	−	3.94095e9i	−0.867471	−	1.50250i	−0.00289764	−	0.999996i	$-0.500922\pi$
$492$	1.17708e8	−	2.03876e8i	0.0445581	−	0.0771770i
$493$	−1.06870e9	+	1.85105e9i	−0.401692	+	0.695751i
$494$	−1.55376e9			−0.579881
$495$	1.31005e7			0.00485479
$496$	5.25766e8	−	9.10653e8i	0.193467	−	0.335094i
$497$	−1.55110e8	+	2.68659e8i	−0.0566753	+	0.0981645i
$498$	6.65749e8	+	1.15311e9i	0.241550	+	0.418377i
$499$	5.94328e7	+	1.02941e8i	0.0214128	+	0.0370881i	0.876533	−	0.481341i	$-0.159850\pi$
$499$	5.94328e7	+	1.02941e8i	0.0214128	+	0.0370881i	−0.855120	+	0.518429i	$0.826517\pi$
$500$	−8.04831e8			−0.287945
$501$	9.57898e8	+	1.65913e9i	0.340320	+	0.589451i
$502$	4.90790e8	+	8.50073e8i	0.173154	+	0.299912i
$503$	1.25290e9	+	2.17008e9i	0.438963	+	0.760306i	0.997610	−	0.0690995i	$-0.0220126\pi$
$503$	1.25290e9	+	2.17008e9i	0.438963	+	0.760306i	−0.558647	+	0.829406i	$0.688679\pi$
$504$	−5.94492e8	+	1.02969e9i	−0.206842	+	0.358261i
$505$	1.28642e9			0.444490
$506$	7.84663e6	−	1.35908e7i	0.00269250	−	0.00466355i
$507$	9.80679e8	+	1.69859e9i	0.334194	+	0.578842i
$508$	−1.00667e9			−0.340693
$509$	−5.43848e8	−	9.41973e8i	−0.182795	−	0.316611i	0.760036	−	0.649881i	$-0.225181\pi$
$509$	−5.43848e8	−	9.41973e8i	−0.182795	−	0.316611i	−0.942831	+	0.333270i	$0.891848\pi$
$510$	−1.01176e9	+	1.75243e9i	−0.337741	+	0.584984i
$511$	9.61072e8	−	1.66463e9i	0.318627	−	0.551879i
$512$	3.22686e9			1.06252
$513$	2.72607e9	−	4.72169e9i	0.891509	−	1.54414i
$514$	4.97636e9			1.61637
$515$	−3.64868e9			−1.17709
$516$	−4.53397e7	+	6.66047e8i	−0.0145280	+	0.213418i
$517$	2.22680e7			0.00708704
$518$	6.78344e8			0.214435
$519$	−9.36997e8	+	1.62293e9i	−0.294207	+	0.509581i
$520$	−1.22968e9			−0.383513
$521$	−9.47007e8	+	1.64026e9i	−0.293374	+	0.508138i	−0.974605	−	0.223930i	$-0.928111\pi$
$521$	−9.47007e8	+	1.64026e9i	−0.293374	+	0.508138i	0.681232	+	0.732068i	$0.261445\pi$
$522$	−3.43398e8	+	5.94784e8i	−0.105670	+	0.183026i
$523$	−2.07009e9	−	3.58550e9i	−0.632752	−	1.09596i	−0.986987	−	0.160802i	$-0.948592\pi$
$523$	−2.07009e9	−	3.58550e9i	−0.632752	−	1.09596i	0.354235	−	0.935157i	$-0.384741\pi$
$524$	−4.47873e6			−0.00135986
$525$	−3.87951e8	−	6.71951e8i	−0.117009	−	0.202666i
$526$	1.17513e9	−	2.03539e9i	0.352076	−	0.609813i
$527$	2.23631e9			0.665572
$528$	1.46364e7	−	2.53510e7i	0.00432728	−	0.00749507i
$529$	1.44545e9	+	2.50359e9i	0.424529	+	0.735306i
$530$	−1.83467e9	−	3.17774e9i	−0.535294	−	0.927156i
$531$	−5.61588e8	−	9.72699e8i	−0.162775	−	0.281934i
$532$	1.64297e9			0.473086
$533$	−3.00741e8	−	5.20899e8i	−0.0860295	−	0.149007i
$534$	1.21558e9	+	2.10545e9i	0.345454	+	0.598344i
$535$	6.56044e8	−	1.13630e9i	0.185223	−	0.320816i
$536$	−2.38194e9	+	4.12564e9i	−0.668119	+	1.15722i
$537$	−3.88270e9			−1.08199
$538$	−1.14767e9			−0.317745
$539$	−5.39416e6	+	9.34297e6i	−0.00148376	+	0.00256995i
$540$	4.52568e8	−	7.83872e8i	0.123682	−	0.214223i
$541$	−1.53592e9	−	2.66029e9i	−0.417040	−	0.722335i	0.578600	−	0.815611i	$-0.303599\pi$
$541$	−1.53592e9	−	2.66029e9i	−0.417040	−	0.722335i	−0.995640	+	0.0932765i	$0.970266\pi$
$542$	8.56328e8	+	1.48320e9i	0.231016	+	0.400132i
$543$	−1.89507e9			−0.507955
$544$	1.10534e9	+	1.91451e9i	0.294375	+	0.509873i
$545$	−2.22753e8	−	3.85820e8i	−0.0589436	−	0.102093i
$546$	−5.90125e8	−	1.02213e9i	−0.155157	−	0.268739i
$547$	−8.07253e7	+	1.39820e8i	−0.0210889	+	0.0365271i	−0.876377	−	0.481625i	$-0.840047\pi$
$547$	−8.07253e7	+	1.39820e8i	−0.0210889	+	0.0365271i	0.855288	+	0.518152i	$0.173380\pi$
$548$	1.35372e9			0.351396
$549$	1.27324e9	−	2.20532e9i	0.328404	−	0.568813i
$550$	−7.21831e6	−	1.25025e7i	−0.00184998	−	0.00320425i
$551$	4.52423e9			1.15216
$552$	−6.70917e8	−	1.16206e9i	−0.169778	−	0.294065i
$553$	−1.63369e9	+	2.82964e9i	−0.410801	+	0.711529i
$554$	1.07428e9	−	1.86071e9i	0.268431	−	0.464937i
$555$	−6.39070e8			−0.158680
$556$	−1.28538e7	+	2.22634e7i	−0.00317154	+	0.00549326i
$557$	2.42440e8			0.0594445			0.0297223	−	0.999558i	$-0.490538\pi$
$557$	2.42440e8			0.0594445			0.0297223	+	0.999558i	$0.490538\pi$
$558$	7.18577e8			0.175087
$559$	1.41583e9	+	9.51191e8i	0.342822	+	0.230317i
$560$	−2.57060e9			−0.618552
$561$	6.22550e7			0.0148869
$562$	3.61310e8	−	6.25807e8i	0.0858623	−	0.148718i
$563$	−7.27048e9			−1.71705			−0.858526	−	0.512770i	$-0.828619\pi$
$563$	−7.27048e9			−1.71705			−0.858526	+	0.512770i	$0.828619\pi$
$564$	1.99699e8	−	3.45889e8i	0.0468705	−	0.0811820i
$565$	3.25032e9	−	5.62971e9i	0.758152	−	1.31316i
$566$	−3.26707e8	−	5.65874e8i	−0.0757359	−	0.131178i
$567$	2.48590e9			0.572722
$568$	2.46766e8	+	4.27411e8i	0.0565023	+	0.0978649i
$569$	2.29788e9	−	3.98004e9i	0.522918	−	0.905721i	−0.476726	−	0.879052i	$-0.658177\pi$
$569$	2.29788e9	−	3.98004e9i	0.522918	−	0.905721i	0.999644	−	0.0266693i	$-0.00849011\pi$
$570$	4.28318e9			0.968733
$571$	−3.98858e8	+	6.90842e8i	−0.0896585	+	0.155293i	−0.907367	−	0.420340i	$-0.861911\pi$
$571$	−3.98858e8	+	6.90842e8i	−0.0896585	+	0.155293i	0.817708	+	0.575633i	$0.195244\pi$
$572$	3.96795e6	+	6.87269e6i	0.000886502	+	0.00153547i
$573$	1.96388e9	+	3.40154e9i	0.436087	+	0.755325i
$574$	−8.79989e8	−	1.52419e9i	−0.194216	−	0.336392i
$575$	−4.72779e8			−0.103710
$576$	8.89125e8	+	1.54001e9i	0.193858	+	0.335772i
$577$	3.23087e9	+	5.59603e9i	0.700171	+	1.21273i	0.968406	+	0.249379i	$0.0802264\pi$
$577$	3.23087e9	+	5.59603e9i	0.700171	+	1.21273i	−0.268235	+	0.963354i	$0.586440\pi$
$578$	6.06504e8	−	1.05050e9i	0.130643	−	0.226280i
$579$	−1.85776e9	+	3.21774e9i	−0.397754	+	0.688931i
$580$	7.51090e8			0.159843
$581$	−3.59729e9			−0.760955
$582$	−1.22154e9	+	2.11576e9i	−0.256848	+	0.444873i
$583$	−5.64446e7	+	9.77650e7i	−0.0117973	+	0.0204335i
$584$	−1.52898e9	−	2.64826e9i	−0.317655	−	0.550194i
$585$	−3.00172e8	−	5.19914e8i	−0.0619905	−	0.107371i
$586$	3.50252e9			0.719017
$587$	4.20763e9	+	7.28783e9i	0.858626	+	1.48718i	0.873240	+	0.487291i	$0.162015\pi$
$587$	4.20763e9	+	7.28783e9i	0.858626	+	1.48718i	−0.0146136	+	0.999893i	$0.504652\pi$
$588$	9.67495e7	+	1.67575e8i	0.0196258	+	0.0339929i
$589$	−2.36679e9	−	4.09940e9i	−0.477261	−	0.826640i
$590$	1.69949e9	−	2.94360e9i	0.340672	−	0.590061i
$591$	−2.77210e9			−0.552399
$592$	3.85498e8	−	6.67702e8i	0.0763653	−	0.132269i
$593$	2.69456e8	+	4.66712e8i	0.0530636	+	0.0919089i	0.891337	−	0.453341i	$-0.149768\pi$
$593$	2.69456e8	+	4.66712e8i	0.0530636	+	0.0919089i	−0.838273	+	0.545250i	$0.816435\pi$
$594$	7.70577e7			0.0150856
$595$	−2.73347e9	−	4.73451e9i	−0.531992	−	0.921437i
$596$	2.92462e8	−	5.06559e8i	0.0565858	−	0.0980095i
$597$	−4.32423e8	+	7.48979e8i	−0.0831761	+	0.144065i
$598$	−7.19160e8			−0.137522
$599$	2.79212e9	−	4.83609e9i	0.530811	−	0.919391i	−0.468543	−	0.883441i	$-0.655221\pi$
$599$	2.79212e9	−	4.83609e9i	0.530811	−	0.919391i	0.999354	−	0.0359506i	$-0.0114459\pi$
$600$	−1.23439e9			−0.233304
$601$	4.92623e9			0.925665			0.462833	−	0.886446i	$-0.346833\pi$
$601$	4.92623e9			0.925665			0.462833	+	0.886446i	$0.346833\pi$
$602$	4.14281e9	+	2.78325e9i	0.773940	+	0.519954i
$603$	−2.32578e9			−0.431975
$604$	2.55592e9			0.471974
$605$	−2.33115e9	+	4.03767e9i	−0.427982	+	0.741287i
$606$	1.96430e9			0.358553
$607$	−2.41398e9	+	4.18113e9i	−0.438100	+	0.758811i	−0.997543	−	0.0700578i	$-0.977682\pi$
$607$	−2.41398e9	+	4.18113e9i	−0.438100	+	0.758811i	0.559443	+	0.828869i	$0.311015\pi$
$608$	2.33967e9	−	4.05243e9i	0.422175	−	0.731228i
$609$	1.71833e9	+	2.97623e9i	0.308280	+	0.533956i
$610$	7.70624e9			1.37464
$611$	−5.10227e8	−	8.83740e8i	−0.0904940	−	0.156740i
$612$	−3.01437e8	+	5.22105e8i	−0.0531578	+	0.0920720i
$613$	3.12945e9			0.548726			0.274363	−	0.961626i	$-0.411533\pi$
$613$	3.12945e9			0.548726			0.274363	+	0.961626i	$0.411533\pi$
$614$	4.88513e8	−	8.46130e8i	0.0851701	−	0.147519i
$615$	8.29040e8	+	1.43594e9i	0.143718	+	0.248928i
$616$	5.53493e7	+	9.58677e7i	0.00954068	+	0.0165249i
$617$	4.03275e9	+	6.98492e9i	0.691199	+	1.19719i	0.971445	+	0.237263i	$0.0762504\pi$
$617$	4.03275e9	+	6.98492e9i	0.691199	+	1.19719i	−0.280247	+	0.959928i	$0.590416\pi$
$618$	−5.57137e9			−0.949516
$619$	−1.13639e9	−	1.96828e9i	−0.192579	−	0.333557i	0.753525	−	0.657419i	$-0.228352\pi$
$619$	−1.13639e9	−	1.96828e9i	−0.192579	−	0.333557i	−0.946104	+	0.323862i	$0.895019\pi$
$620$	−3.92923e8	−	6.80562e8i	−0.0662119	−	0.114682i
$621$	1.26177e9	−	2.18544e9i	0.211426	−	0.366200i
$622$	−4.44980e9	+	7.70728e9i	−0.741437	+	1.28421i
$623$	−6.56826e9			−1.08828
$624$	−1.34146e9			−0.221019
$625$	2.01966e9	−	3.49815e9i	0.330901	−	0.573137i
$626$	2.49997e9	−	4.33007e9i	0.407309	−	0.705480i
$627$	−6.58872e7	−	1.14120e8i	−0.0106749	−	0.0184895i
$628$	−9.70515e8	−	1.68098e9i	−0.156366	−	0.270834i
$629$	1.63969e9			0.262715
$630$	−8.78325e8	−	1.52130e9i	−0.139947	−	0.242395i
$631$	−5.38915e9	−	9.33428e9i	−0.853920	−	1.47903i	−0.877643	−	0.479315i	$-0.840885\pi$
$631$	−5.38915e9	−	9.33428e9i	−0.853920	−	1.47903i	0.0237228	−	0.999719i	$-0.492448\pi$
$632$	2.59905e9	+	4.50168e9i	0.409548	+	0.709357i
$633$	1.86685e8	−	3.23348e8i	0.0292547	−	0.0506707i
$634$	−5.57998e9			−0.869601
$635$	3.54509e9	−	6.14027e9i	0.549438	−	0.951655i
$636$	1.01239e9	+	1.75351e9i	0.156044	+	0.270276i
$637$	4.94386e8			0.0757842
$638$	3.19716e7	+	5.53764e7i	0.00487407	+	0.00844213i
$639$	−1.20474e8	+	2.08667e8i	−0.0182659	+	0.0316375i
$640$	−1.22744e9	+	2.12599e9i	−0.185084	+	0.320576i
$641$	5.06219e9			0.759164			0.379582	−	0.925158i	$-0.376068\pi$
$641$	5.06219e9			0.759164			0.379582	+	0.925158i	$0.376068\pi$
$642$	1.00175e9	−	1.73508e9i	0.149413	−	0.258790i
$643$	−1.05103e10			−1.55911			−0.779553	−	0.626337i	$-0.784553\pi$
$643$	−1.05103e10			−1.55911			−0.779553	+	0.626337i	$0.784553\pi$
$644$	7.60454e8			0.112195
$645$	−3.90295e9	−	2.62211e9i	−0.572709	−	0.384762i
$646$	−1.09896e10			−1.60386
$647$	−3.53856e9			−0.513643			−0.256821	−	0.966459i	$-0.582675\pi$
$647$	−3.53856e9			−0.513643			−0.256821	+	0.966459i	$0.582675\pi$
$648$	1.97742e9	−	3.42499e9i	0.285487	−	0.494478i
$649$	−1.04572e8			−0.0150161
$650$	−3.30787e8	+	5.72939e8i	−0.0472445	+	0.0818299i
$651$	1.79784e9	−	3.11395e9i	0.255398	−	0.442362i
$652$	−8.93936e8	−	1.54834e9i	−0.126311	−	0.218776i
$653$	1.22309e10			1.71895			0.859476	−	0.511176i	$-0.170790\pi$
$653$	1.22309e10			1.71895			0.859476	+	0.511176i	$0.170790\pi$
$654$	−3.40135e8	−	5.89130e8i	−0.0475476	−	0.0823549i
$655$	1.57723e7	−	2.73184e7i	0.00219306	−	0.00379849i
$656$	−2.00036e9			−0.276660
$657$	7.46464e8	−	1.29291e9i	0.102691	−	0.177865i
$658$	−1.49296e9	−	2.58588e9i	−0.204295	−	0.353849i
$659$	5.94769e9	+	1.03017e10i	0.809560	+	1.40220i	0.913169	+	0.407582i	$0.133628\pi$
$659$	5.94769e9	+	1.03017e10i	0.809560	+	1.40220i	−0.103608	+	0.994618i	$0.533039\pi$
$660$	−1.09383e7	−	1.89456e7i	−0.00148097	−	0.00256511i
$661$	−1.36517e10			−1.83857			−0.919286	−	0.393591i	$-0.871233\pi$
$661$	−1.36517e10			−1.83857			−0.919286	+	0.393591i	$0.871233\pi$
$662$	5.14480e9	+	8.91105e9i	0.689232	+	1.19378i
$663$	−1.42645e9	−	2.47068e9i	−0.190090	−	0.329245i
$664$	−2.86148e9	+	4.95622e9i	−0.379317	+	0.656996i
$665$	−5.78591e9	+	1.00215e10i	−0.762949	+	1.32147i
$666$	5.26869e8			0.0691104
$667$	2.09405e9			0.273241
$668$	−8.63649e8	+	1.49588e9i	−0.112104	+	0.194169i
$669$	−4.33404e9	+	7.50677e9i	−0.559630	+	0.969308i
$670$	−3.51917e9	−	6.09538e9i	−0.452041	−	0.782958i
$671$	−1.18543e8	−	2.05323e8i	−0.0151478	−	0.0262367i
$672$	3.55448e9			0.451839
$673$	9.54662e8	+	1.65352e9i	0.120725	+	0.209102i	0.920054	−	0.391792i	$-0.128145\pi$
$673$	9.54662e8	+	1.65352e9i	0.120725	+	0.209102i	−0.799329	+	0.600894i	$0.794811\pi$
$674$	4.14770e9	+	7.18403e9i	0.521793	+	0.903772i
$675$	−1.16073e9	−	2.01044e9i	−0.145267	−	0.251610i
$676$	−8.84190e8	+	1.53146e9i	−0.110086	+	0.190675i
$677$	1.47595e10			1.82815			0.914074	−	0.405547i	$-0.132919\pi$
$677$	1.47595e10			1.82815			0.914074	+	0.405547i	$0.132919\pi$
$678$	4.96309e9	−	8.59632e9i	0.611573	−	1.05928i
$679$	−3.30021e9	−	5.71613e9i	−0.404573	−	0.700742i
$680$	−8.69739e9			−1.06074
$681$	−2.61195e9	−	4.52402e9i	−0.316920	−	0.548921i
$682$	3.34510e7	−	5.79388e7i	0.00403797	−	0.00699398i
$683$	−4.72498e9	+	8.18390e9i	−0.567450	+	0.982852i	0.429367	+	0.903130i	$0.358737\pi$
$683$	−4.72498e9	+	8.18390e9i	−0.567450	+	0.982852i	−0.996817	+	0.0797219i	$0.974597\pi$
$684$	1.27610e9			0.152471
$685$	−4.76726e9	+	8.25714e9i	−0.566699	+	0.981551i
$686$	−6.43705e9			−0.761295
$687$	−8.52148e9			−1.00269
$688$	5.09392e9	−	2.49611e9i	0.596338	−	0.292217i
$689$	5.17327e9			0.602556
$690$	1.98248e9			0.229740
$691$	−2.89286e9	+	5.01058e9i	−0.333545	+	0.577717i	−0.983204	−	0.182509i	$-0.941578\pi$
$691$	−2.89286e9	+	5.01058e9i	−0.333545	+	0.577717i	0.649659	+	0.760226i	$0.274912\pi$
$692$	−1.68961e9			−0.193828
$693$	−2.70222e7	+	4.68038e7i	−0.00308428	+	0.00534213i
$694$	4.11455e9	−	7.12662e9i	0.467267	−	0.809329i
$695$	−9.05320e7	−	1.56806e8i	−0.0102295	−	0.0177181i
$696$	5.46739e9			0.614678
$697$	−2.12711e9	−	3.68426e9i	−0.237944	−	0.412131i
$698$	1.15758e9	−	2.00499e9i	0.128842	−	0.223161i
$699$	−9.30376e9			−1.03036
$700$	3.49781e8	−	6.05838e8i	0.0385436	−	0.0667595i
$701$	−2.77965e9	−	4.81450e9i	−0.304774	−	0.527883i	0.672437	−	0.740154i	$-0.265247\pi$
$701$	−2.77965e9	−	4.81450e9i	−0.304774	−	0.527883i	−0.977211	+	0.212271i	$0.931914\pi$
$702$	−1.76562e9	−	3.05815e9i	−0.192628	−	0.333641i
$703$	−1.73536e9	−	3.00573e9i	−0.188385	−	0.326292i
$704$	1.65561e8			0.0178836
$705$	1.40652e9	+	2.43617e9i	0.151177	+	0.261846i
$706$	9.57874e8	+	1.65909e9i	0.102445	+	0.177440i
$707$	−2.65346e9	+	4.59593e9i	−0.282387	+	0.489109i
$708$	−9.37795e8	+	1.62431e9i	−0.0993097	+	0.172009i
$709$	−8.99372e9			−0.947714			−0.473857	−	0.880602i	$-0.657139\pi$
$709$	−8.99372e9			−0.947714			−0.473857	+	0.880602i	$0.657139\pi$
$710$	−7.29163e8			−0.0764576
$711$	−1.26889e9	+	2.19778e9i	−0.132397	+	0.229319i
$712$	−5.22474e9	+	9.04951e9i	−0.542481	+	0.939605i
$713$	−1.09547e9	−	1.89741e9i	−0.113185	−	0.196042i
$714$	−4.17389e9	−	7.22939e9i	−0.429138	−	0.743289i
$715$	−5.58942e7			−0.00571867
$716$	−1.75034e9	−	3.03168e9i	−0.178208	−	0.308665i
$717$	4.01372e9	+	6.95197e9i	0.406659	+	0.704354i
$718$	1.12185e9	+	1.94310e9i	0.113110	+	0.195912i
$719$	3.39758e9	−	5.88478e9i	0.340893	−	0.590444i	−0.643706	−	0.765273i	$-0.722604\pi$
$719$	3.39758e9	−	5.88478e9i	0.340893	−	0.590444i	0.984599	+	0.174829i	$0.0559372\pi$
$720$	−1.99658e9			−0.199353
$721$	7.52605e9	−	1.30355e10i	0.747814	−	1.29525i
$722$	7.29701e9	+	1.26388e10i	0.721547	+	1.24976i
$723$	8.48569e9			0.835032
$724$	−8.54305e8	−	1.47970e9i	−0.0836620	−	0.144907i
$725$	9.63184e8	−	1.66828e9i	0.0938698	−	0.162587i
$726$	−3.55956e9	+	6.16534e9i	−0.345238	+	0.597969i
$727$	3.46971e9			0.334906			0.167453	−	0.985880i	$-0.446446\pi$
$727$	3.46971e9			0.334906			0.167453	+	0.985880i	$0.446446\pi$
$728$	2.53644e9	−	4.39324e9i	0.243649	−	0.422012i
$729$	1.11053e10			1.06165
$730$	4.51793e9			0.429843
$731$	1.00140e10	+	6.72767e9i	0.948192	+	0.637021i
$732$	−4.25238e9			−0.400722
$733$	−2.56478e9			−0.240540			−0.120270	−	0.992741i	$-0.538376\pi$
$733$	−2.56478e9			−0.240540			−0.120270	+	0.992741i	$0.538376\pi$
$734$	−9.80923e8	+	1.69901e9i	−0.0915585	+	0.158584i
$735$	−1.36285e9			−0.126603
$736$	1.08292e9	−	1.87567e9i	0.100121	−	0.173414i
$737$	−1.08269e8	+	1.87528e8i	−0.00996251	+	0.0172556i
$738$	−6.83487e8	−	1.18383e9i	−0.0625940	−	0.108416i
$739$	1.33179e10			1.21389			0.606944	−	0.794744i	$-0.292395\pi$
$739$	1.33179e10			1.21389			0.606944	+	0.794744i	$0.292395\pi$
$740$	−2.88096e8	−	4.98996e8i	−0.0261352	−	0.0452675i
$741$	−3.01935e9	+	5.22967e9i	−0.272615	+	0.472183i
$742$	1.51373e10			1.36030
$743$	6.76368e9	−	1.17150e10i	0.604954	−	1.04781i	−0.387105	−	0.922036i	$-0.626525\pi$
$743$	6.76368e9	−	1.17150e10i	0.604954	−	1.04781i	0.992059	−	0.125775i	$-0.0401418\pi$
$744$	−2.86019e9	−	4.95399e9i	−0.254618	−	0.441012i
$745$	2.05987e9	+	3.56780e9i	0.182513	+	0.316121i
$746$	−5.96778e9	−	1.03365e10i	−0.526292	−	0.911565i
$747$	−2.79401e9			−0.245249
$748$	2.80648e7	+	4.86097e7i	0.00245192	+	0.00424686i
$749$	2.70642e9	+	4.68765e9i	0.235347	+	0.407633i
$750$	4.32785e9	−	7.49605e9i	0.374591	−	0.648811i
$751$	−6.43186e8	+	1.11403e9i	−0.0554111	+	0.0959748i	−0.892400	−	0.451244i	$-0.850980\pi$
$751$	−6.43186e8	+	1.11403e9i	−0.0554111	+	0.0959748i	0.836989	+	0.547219i	$0.184314\pi$
$752$	−3.39375e9			−0.291017
$753$	3.81492e9			0.325614
$754$	1.46513e9	−	2.53768e9i	0.124473	−	0.215594i
$755$	−9.00095e9	+	1.55901e10i	−0.761156	+	1.31836i
$756$	1.86701e9	+	3.23375e9i	0.157152	+	0.272195i
$757$	−1.09264e10	−	1.89250e10i	−0.915462	−	1.58563i	−0.806224	−	0.591611i	$-0.798492\pi$
$757$	−1.09264e10	−	1.89250e10i	−0.915462	−	1.58563i	−0.109238	−	0.994016i	$-0.534841\pi$
$758$	9.92737e8			0.0827927
$759$	−3.04960e7	−	5.28206e7i	−0.00253161	−	0.00438488i
$760$	9.20483e9	+	1.59432e10i	0.760621	+	1.31743i
$761$	−1.15523e9	−	2.00092e9i	−0.0950219	−	0.164583i	0.814596	−	0.580029i	$-0.196959\pi$
$761$	−1.15523e9	−	2.00092e9i	−0.0950219	−	0.164583i	−0.909618	+	0.415446i	$0.863625\pi$
$762$	5.41319e9	−	9.37592e9i	0.443211	−	0.767665i
$763$	1.83788e9			0.149789
$764$	−1.77065e9	+	3.06686e9i	−0.143650	+	0.248809i
$765$	−2.12309e9	−	3.67729e9i	−0.171456	−	0.296970i
$766$	−3.54628e9			−0.285083
$767$	2.39605e9	+	4.15008e9i	0.191740	+	0.332103i
$768$	3.71907e9	−	6.44161e9i	0.296258	−	0.513133i
$769$	9.78893e9	−	1.69549e10i	0.776235	−	1.34448i	−0.157863	−	0.987461i	$-0.550460\pi$
$769$	9.78893e9	−	1.69549e10i	0.776235	−	1.34448i	0.934098	−	0.357017i	$-0.116206\pi$
$770$	−1.63550e8			−0.0129102
$771$	9.67035e9	−	1.67495e10i	0.759892	−	1.31617i
$772$	−3.34995e9			−0.262046
$773$	1.59380e10			1.24110			0.620549	−	0.784167i	$-0.286910\pi$
$773$	1.59380e10			1.24110			0.620549	+	0.784167i	$0.286910\pi$
$774$	3.21772e9	+	2.16175e9i	0.249433	+	0.167576i
$775$	−2.01551e9			−0.155535
$776$	−1.05006e10			−0.806678
$777$	1.31820e9	−	2.28318e9i	0.100811	−	0.174609i
$778$	1.89109e10			1.43974
$779$	−4.50242e9	+	7.79842e9i	−0.341244	+	0.591052i
$780$	−5.01258e8	+	8.68204e8i	−0.0378207	+	0.0655074i
$781$	1.12166e7	+	1.94277e7i	0.000842522	+	0.00145929i
$782$	−5.08653e9			−0.380363
$783$	5.14114e9	+	8.90472e9i	0.382731	+	0.662909i
$784$	8.22097e8	−	1.42391e9i	0.0609280	−	0.105530i
$785$	1.36711e10			1.00869
$786$	2.40836e7	−	4.17140e7i	0.00176906	−	0.00306410i
$787$	−1.03761e10	−	1.79720e10i	−0.758794	−	1.31427i	−0.943466	−	0.331470i	$-0.892455\pi$
$787$	−1.03761e10	−	1.79720e10i	−0.758794	−	1.31427i	0.184671	−	0.982800i	$-0.440878\pi$
$788$	−1.24968e9	−	2.16450e9i	−0.0909820	−	0.157585i
$789$	−4.56716e9	−	7.91055e9i	−0.331037	−	0.573373i
$790$	−7.67986e9			−0.554190
$791$	1.34087e10	+	2.32246e10i	0.963318	+	1.66852i
$792$	4.29897e7	+	7.44604e7i	0.00307487	+	0.00532583i
$793$	−5.43238e9	+	9.40915e9i	−0.386842	+	0.670030i
$794$	−4.58851e9	+	7.94753e9i	−0.325312	+	0.563457i
$795$	−1.42609e10			−1.00661
$796$	−7.79753e8			−0.0547976
$797$	8.04710e9	−	1.39380e10i	0.563035	−	0.975205i	−0.434195	−	0.900819i	$-0.642967\pi$
$797$	8.04710e9	−	1.39380e10i	0.563035	−	0.975205i	0.997230	−	0.0743859i	$-0.0236996\pi$
$798$	−8.83483e9	+	1.53024e10i	−0.615443	+	1.06598i
$799$	−3.60878e9	−	6.25059e9i	−0.250292	−	0.433518i
$800$	−9.96207e8	−	1.72548e9i	−0.0687914	−	0.119150i
$801$	−5.10156e9			−0.350743
$802$	6.71512e9	+	1.16309e10i	0.459667	+	0.796167i
$803$	−6.94984e7	−	1.20375e8i	−0.00473664	−	0.00820410i
$804$	1.94191e9	+	3.36349e9i	0.131775	+	0.228241i
$805$	−2.67802e9	+	4.63846e9i	−0.180937	+	0.313392i
$806$	−3.06585e9			−0.206243
$807$	−2.23021e9	+	3.86284e9i	−0.149379	+	0.258732i
$808$	4.22141e9	+	7.31170e9i	0.281526	+	0.487617i
$809$	1.77444e10			1.17826			0.589131	−	0.808038i	$-0.299470\pi$
$809$	1.77444e10			1.17826			0.589131	+	0.808038i	$0.299470\pi$
$810$	2.92151e9	+	5.06021e9i	0.193157	+	0.334558i
$811$	−8.02017e9	+	1.38913e10i	−0.527972	+	0.914474i	0.471497	+	0.881868i	$0.343714\pi$
$811$	−8.02017e9	+	1.38913e10i	−0.527972	+	0.914474i	−0.999468	+	0.0326058i	$0.989619\pi$
$812$	−1.54926e9	+	2.68339e9i	−0.101549	+	0.175889i
$813$	6.65626e9			0.434423
$814$	2.45267e7	−	4.24814e7i	0.00159387	−	0.00276067i
$815$	1.25923e10			0.814808
$816$	−9.48797e9			−0.611304
$817$	1.73428e9	−	2.54769e10i	0.111261	−	1.63444i
$818$	−1.57115e10			−1.00364
$819$	2.47664e9			0.157532
$820$	−7.47470e8	+	1.29466e9i	−0.0473419	+	0.0819985i
$821$	−2.93832e9			−0.185310			−0.0926549	−	0.995698i	$-0.529535\pi$
$821$	−2.93832e9			−0.185310			−0.0926549	+	0.995698i	$0.529535\pi$
$822$	−7.27940e9	+	1.26083e10i	−0.457135	+	0.791781i
$823$	−1.12747e10	+	1.95284e10i	−0.705028	+	1.22114i	0.261654	+	0.965162i	$0.415732\pi$
$823$	−1.12747e10	+	1.95284e10i	−0.705028	+	1.22114i	−0.966682	+	0.255982i	$0.917601\pi$
$824$	−1.19732e10	−	2.07383e10i	−0.745532	−	1.29130i
$825$	−5.61081e7			−0.00347886
$826$	7.01101e9	+	1.21434e10i	0.432863	+	0.749740i
$827$	−6.53406e9	+	1.13173e10i	−0.401711	+	0.695784i	−0.993933	−	0.109991i	$-0.964918\pi$
$827$	−6.53406e9	+	1.13173e10i	−0.401711	+	0.695784i	0.592222	+	0.805775i	$0.298251\pi$
$828$	5.90644e8			0.0361593
$829$	−1.46219e10	+	2.53259e10i	−0.891380	+	1.54392i	−0.0531576	+	0.998586i	$0.516929\pi$
$829$	−1.46219e10	+	2.53259e10i	−0.891380	+	1.54392i	−0.838222	+	0.545329i	$0.816405\pi$
$830$	−4.22765e9	−	7.32251e9i	−0.256641	−	0.444515i
$831$	−4.17520e9	−	7.23166e9i	−0.252391	−	0.437154i
$832$	−3.79350e9	−	6.57054e9i	−0.228354	−	0.395521i
$833$	3.49674e9			0.209607
$834$	−1.38238e8	−	2.39436e8i	−0.00825178	−	0.0142925i
$835$	−6.08286e9	−	1.05358e10i	−0.361581	−	0.626276i
$836$	5.94045e7	−	1.02892e8i	0.00351639	−	0.00609057i
$837$	5.37904e9	−	9.31676e9i	0.317077	−	0.549194i
$838$	−2.40630e10			−1.41252
$839$	−1.44408e10			−0.844160			−0.422080	−	0.906559i	$-0.638700\pi$
$839$	−1.44408e10			−0.844160			−0.422080	+	0.906559i	$0.638700\pi$
$840$	−6.99209e9	+	1.21107e10i	−0.407033	+	0.705002i
$841$	4.35878e9	−	7.54962e9i	0.252684	−	0.437662i
$842$	−4.77712e9	−	8.27422e9i	−0.275787	−	0.477678i
$843$	−1.40424e9	−	2.43221e9i	−0.0807316	−	0.139831i
$844$	3.36634e8			0.0192734
$845$	−6.22753e9	−	1.07864e10i	−0.355073	−	0.615004i
$846$	−1.15958e9	−	2.00845e9i	−0.0658423	−	0.114042i
$847$	−9.61682e9	−	1.66568e10i	−0.543800	−	0.941890i
$848$	8.60244e9	−	1.48999e10i	0.484436	−	0.839067i
$849$	−2.53951e9			−0.142420
$850$	−2.33962e9	+	4.05233e9i	−0.130671	+	0.226328i
$851$	−8.03214e8	−	1.39121e9i	−0.0446763	−	0.0773817i
$852$	4.02360e8			0.0222882
$853$	−1.04901e10	−	1.81694e10i	−0.578708	−	1.00235i	−0.995628	−	0.0934080i	$-0.970224\pi$
$853$	−1.04901e10	−	1.81694e10i	−0.578708	−	1.00235i	0.416920	−	0.908943i	$-0.363109\pi$
$854$	−1.58955e10	+	2.75318e10i	−0.873317	+	1.51263i
$855$	−4.49391e9	+	7.78368e9i	−0.245891	+	0.425896i
$856$	8.61131e9			0.469258
$857$	1.74710e9	−	3.02606e9i	0.0948166	−	0.164227i	−0.814715	−	0.579861i	$-0.803107\pi$
$857$	1.74710e9	−	3.02606e9i	0.0948166	−	0.164227i	0.909532	+	0.415634i	$0.136440\pi$
$858$	−8.53479e7			−0.00461304
$859$	2.16065e10			1.16308			0.581538	−	0.813519i	$-0.302451\pi$
$859$	2.16065e10			1.16308			0.581538	+	0.813519i	$0.302451\pi$
$860$	2.87917e8	−	4.22955e9i	0.0154356	−	0.226751i
$861$	−6.84018e9			−0.365221
$862$	−2.33563e10			−1.24202
$863$	−1.57468e10	+	2.72743e10i	−0.833980	+	1.44450i	0.0608784	+	0.998145i	$0.480610\pi$
$863$	−1.57468e10	+	2.72743e10i	−0.833980	+	1.44450i	−0.894858	+	0.446350i	$0.852724\pi$
$864$	1.06348e10			0.560960
$865$	5.95014e9	−	1.03059e10i	0.312587	−	0.541417i
$866$	1.50614e10	−	2.60872e10i	0.788050	−	1.36494i
$867$	−2.35719e9	−	4.08277e9i	−0.122836	−	0.212759i
$868$	3.24189e9			0.168260
$869$	1.18138e8	+	2.04620e8i	0.00610688	+	0.0105774i
$870$	−4.03886e9	+	6.99552e9i	−0.207942	+	0.360166i
$871$	9.92309e9			0.508843
$872$	1.46194e9	−	2.53216e9i	0.0746660	−	0.129325i
$873$	−2.56327e9	−	4.43972e9i	−0.130390	−	0.225842i
$874$	5.38330e9	+	9.32416e9i	0.272746	+	0.472410i
$875$	1.16925e10	+	2.02520e10i	0.590037	+	1.02197i
$876$	−2.49304e9			−0.125304
$877$	1.52464e10	+	2.64075e10i	0.763253	+	1.32199i	0.941165	+	0.337947i	$0.109732\pi$
$877$	1.52464e10	+	2.64075e10i	0.763253	+	1.32199i	−0.177912	+	0.984046i	$0.556934\pi$
$878$	−1.50573e10	−	2.60800e10i	−0.750786	−	1.30040i
$879$	6.80629e9	−	1.17888e10i	0.338026	−	0.585478i
$880$	−9.29444e7	+	1.60984e8i	−0.00459763	+	0.00796332i
$881$	−1.84061e10			−0.906871			−0.453435	−	0.891289i	$-0.649802\pi$
$881$	−1.84061e10			−0.906871			−0.453435	+	0.891289i	$0.649802\pi$
$882$	1.12358e9			0.0551396
$883$	−1.49232e10	+	2.58478e10i	−0.729457	+	1.26346i	0.227655	+	0.973742i	$0.426894\pi$
$883$	−1.49232e10	+	2.58478e10i	−0.729457	+	1.26346i	−0.957113	+	0.289716i	$0.906439\pi$
$884$	1.28610e9	−	2.22759e9i	0.0626170	−	0.108456i
$885$	−6.60509e9	−	1.14403e10i	−0.320315	−	0.554802i
$886$	−2.54520e9	−	4.40842e9i	−0.122943	−	0.212944i
$887$	3.72756e10			1.79346			0.896731	−	0.442575i	$-0.145935\pi$
$887$	3.72756e10			1.79346			0.896731	+	0.442575i	$0.145935\pi$
$888$	−2.09713e9	−	3.63233e9i	−0.100503	−	0.174076i
$889$	1.46248e10	+	2.53308e10i	0.698124	+	1.20919i
$890$	−7.71923e9	−	1.33701e10i	−0.367036	−	0.635725i
$891$	8.98821e7	−	1.55680e8i	0.00425697	−	0.00737330i
$892$	−7.81522e9			−0.368692
$893$	−7.63866e9	+	1.32306e10i	−0.358953	+	0.621724i
$894$	3.14533e9	+	5.44787e9i	0.147226	+	0.255003i
$895$	2.46560e10			1.14959
$896$	−5.06363e9	−	8.77046e9i	−0.235171	−	0.407328i
$897$	−1.39751e9	+	2.42056e9i	−0.0646520	+	0.111981i
$898$	−6.13961e9	+	1.06341e10i	−0.282926	+	0.490043i
$899$	8.92714e9			0.409782
$900$	2.71674e8	−	4.70554e8i	0.0124222	−	0.0215159i
$901$	3.65899e10			1.66657
$902$	−1.27270e8			−0.00577435
$903$	1.74185e10	−	8.53538e9i	0.787232	−	0.385758i
$904$	4.26640e10			1.92076
$905$	1.20341e10			0.539689
$906$	−1.37440e10	+	2.38054e10i	−0.613997	+	1.06347i
$907$	2.96534e10			1.31962			0.659809	−	0.751433i	$-0.270637\pi$
$907$	2.96534e10			1.31962			0.659809	+	0.751433i	$0.270637\pi$
$908$	2.35496e9	−	4.07890e9i	0.104396	−	0.180819i
$909$	−2.06094e9	+	3.56966e9i	−0.0910107	+	0.157635i
$910$	3.74743e9	+	6.49074e9i	0.164850	+	0.285528i
$911$	−2.48470e10			−1.08883			−0.544415	−	0.838816i	$-0.683248\pi$
$911$	−2.48470e10			−1.08883			−0.544415	+	0.838816i	$0.683248\pi$
$912$	1.00415e10	+	1.73924e10i	0.438347	+	0.759239i
$913$	−1.30066e8	+	2.25281e8i	−0.00565609	+	0.00979664i
$914$	−1.16556e10			−0.504920
$915$	1.49752e10	−	2.59378e10i	0.646248	−	1.11933i
$916$	−3.84152e9	−	6.65371e9i	−0.165146	−	0.286042i
$917$	6.50664e7	+	1.12698e8i	0.00278653	+	0.00482642i
$918$	−1.24881e10	−	2.16300e10i	−0.532777	−	0.922797i
$919$	−3.39442e10			−1.44265			−0.721326	−	0.692596i	$-0.756467\pi$
$919$	−3.39442e10			−1.44265			−0.721326	+	0.692596i	$0.756467\pi$
$920$	4.26047e9	+	7.37936e9i	0.180385	+	0.312436i
$921$	−1.89861e9	−	3.28850e9i	−0.0800807	−	0.138704i
$922$	8.92794e9	−	1.54636e10i	0.375140	−	0.649761i
$923$	5.14010e8	−	8.90292e8i	0.0215162	−	0.0372672i
$924$	9.02486e7			0.00376347
$925$	−1.47779e9			−0.0613928
$926$	4.47999e9	−	7.75957e9i	0.185412	−	0.321144i
$927$	5.84548e9	−	1.01247e10i	0.241013	−	0.417447i
$928$	4.41243e9	+	7.64255e9i	0.181242	+	0.313921i
$929$	−1.61941e10	−	2.80490e10i	−0.662677	−	1.14779i	−0.979909	−	0.199443i	$-0.936087\pi$
$929$	−1.61941e10	−	2.80490e10i	−0.662677	−	1.14779i	0.317232	−	0.948348i	$-0.397247\pi$
$930$	8.45150e9			0.344543
$931$	−3.70075e9	−	6.40989e9i	−0.150302	−	0.260332i
$932$	−4.19418e9	−	7.26453e9i	−0.169704	−	0.293935i
$933$	1.72942e10	+	2.99544e10i	0.697132	+	1.20747i
$934$	−1.58608e10	+	2.74718e10i	−0.636960	+	1.10325i
$935$	−3.95333e8			−0.0158169
$936$	1.97005e9	−	3.41222e9i	0.0785256	−	0.136010i
$937$	6.30555e7	+	1.09215e8i	0.00250400	+	0.00433706i	0.867275	−	0.497830i	$-0.165870\pi$
$937$	6.30555e7	+	1.09215e8i	0.00250400	+	0.00433706i	−0.864771	+	0.502167i	$0.832536\pi$
$938$	2.90357e10			1.14874
$939$	−9.71615e9	−	1.68289e10i	−0.382970	−	0.663324i
$940$	−1.26813e9	+	2.19647e9i	−0.0497987	+	0.0862538i
$941$	1.44716e10	−	2.50655e10i	0.566176	−	0.980646i	−0.430763	−	0.902465i	$-0.641755\pi$
$941$	1.44716e10	−	2.50655e10i	0.566176	−	0.980646i	0.996939	−	0.0781811i	$-0.0249112\pi$
$942$	2.08751e10			0.813675
$943$	−2.08395e9	+	3.60951e9i	−0.0809277	+	0.140171i
$944$	1.59372e10			0.616610
$945$	−2.62994e10			−1.01376
$946$	3.24092e8	−	1.58811e8i	0.0124466	−	0.00609905i
$947$	−4.20167e10			−1.60767			−0.803834	−	0.594853i	$-0.797210\pi$
$947$	−4.20167e10			−1.60767			−0.803834	+	0.594853i	$0.797210\pi$
$948$	4.23782e9			0.161553
$949$	−3.18484e9	+	5.51630e9i	−0.120964	+	0.209515i
$950$	9.90448e9			0.374799
$951$	−1.08433e10	+	1.87812e10i	−0.408819	+	0.708095i
$952$	1.79399e10	−	3.10729e10i	0.673894	−	1.16722i
$953$	1.69158e10	+	2.92990e10i	0.633092	+	1.09655i	0.986916	+	0.161235i	$0.0515477\pi$
$953$	1.69158e10	+	2.92990e10i	0.633092	+	1.09655i	−0.353825	+	0.935312i	$0.615119\pi$
$954$	1.17572e10			0.438413
$955$	−1.24711e10	−	2.16005e10i	−0.463331	−	0.802514i
$956$	−3.61881e9	+	6.26796e9i	−0.133956	+	0.232019i
$957$	2.48516e8			0.00916563
$958$	1.14468e10	−	1.98265e10i	0.420635	−	0.728562i
$959$	−1.96667e10	−	3.40637e10i	−0.720055	−	1.24717i
$960$	1.04574e10	+	1.81127e10i	0.381482	+	0.660746i
$961$	9.08620e9	+	1.57378e10i	0.330256	+	0.572020i
$962$	−2.24792e9			−0.0814082
$963$	2.10207e9	+	3.64090e9i	0.0758501	+	0.131376i
$964$	3.82539e9	+	6.62577e9i	0.137533	+	0.238214i
$965$	1.17972e10	−	2.04333e10i	0.422604	−	0.731971i
$966$	−4.08922e9	+	7.08273e9i	−0.145955	+	0.252802i
$967$	−3.36031e10			−1.19505			−0.597527	−	0.801849i	$-0.703850\pi$
$967$	−3.36031e10			−1.19505			−0.597527	+	0.801849i	$0.703850\pi$
$968$	−3.05989e10			−1.08428
$969$	−2.13555e10	+	3.69888e10i	−0.754010	+	1.30598i
$970$	7.75703e9	−	1.34356e10i	0.272894	−	0.472666i
$971$	−1.07510e10	−	1.86212e10i	−0.376860	−	0.652740i	0.613744	−	0.789505i	$-0.289663\pi$
$971$	−1.07510e10	−	1.86212e10i	−0.376860	−	0.652740i	−0.990604	+	0.136765i	$0.956329\pi$
$972$	2.52377e9	+	4.37129e9i	0.0881489	+	0.152678i
$973$	7.46954e8			0.0259955
$974$	−2.37958e10	−	4.12156e10i	−0.825172	−	1.42924i
$975$	1.28561e9	+	2.22674e9i	0.0444214	+	0.0769401i
$976$	1.80666e10	+	3.12923e10i	0.622017	+	1.07736i
$977$	2.96821e7	−	5.14108e7i	0.00101827	−	0.00176370i	−0.865516	−	0.500882i	$-0.833009\pi$
$977$	2.96821e7	−	5.14108e7i	0.00101827	−	0.00176370i	0.866534	+	0.499118i	$0.166343\pi$
$978$	1.92280e10			0.657275
$979$	−2.37486e8	+	4.11338e8i	−0.00808908	+	0.0140107i
$980$	−6.14381e8	−	1.06414e9i	−0.0208519	−	0.0361166i
$981$	1.42748e9			0.0482756
$982$	2.20625e10	+	3.82134e10i	0.743473	+	1.28773i
$983$	−2.51495e10	+	4.35603e10i	−0.844487	+	1.46269i	0.0415793	+	0.999135i	$0.486761\pi$
$983$	−2.51495e10	+	4.35603e10i	−0.844487	+	1.46269i	−0.886066	+	0.463559i	$0.846572\pi$
$984$	−5.44104e9	+	9.42415e9i	−0.182053	+	0.315326i
$985$	1.76034e10			0.586909
$986$	1.03627e10	−	1.79487e10i	0.344274	−	0.596299i
$987$	−1.16048e10			−0.384174
$988$	−5.44455e9			−0.179603
$989$	8.02716e8	−	1.17920e10i	0.0263861	−	0.387616i
$990$	−1.27029e8			−0.00416084
$991$	−2.47796e9			−0.0808790			−0.0404395	−	0.999182i	$-0.512876\pi$
$991$	−2.47796e9			−0.0808790			−0.0404395	+	0.999182i	$0.512876\pi$
$992$	4.61660e9	−	7.99619e9i	0.150152	−	0.260071i
$993$	3.99906e10			1.29609
$994$	1.50403e9	−	2.60506e9i	0.0485740	−	0.0841327i
$995$	2.74598e9	−	4.75618e9i	0.0883725	−	0.153066i
$996$	2.33286e9	+	4.04063e9i	0.0748137	+	0.129581i
$997$	−1.88133e10			−0.601218			−0.300609	−	0.953747i	$-0.597190\pi$
$997$	−1.88133e10			−0.601218			−0.300609	+	0.953747i	$0.597190\pi$
$998$	−5.76291e8	−	9.98164e8i	−0.0183521	−	0.0317867i
$999$	3.94398e9	−	6.83117e9i	0.125157	−	0.216778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.c.a.6.8	✓	50
43.36	even	3	inner	43.8.c.a.36.8	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.c.a.6.8	✓	50	1.1	even	1	trivial
43.8.c.a.36.8	yes	50	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-9.69651 q^{2} +(-18.8428 + 32.6367i) q^{3} -33.9777 q^{4} +(119.656 - 207.250i) q^{5} +(182.709 - 316.462i) q^{6} +(493.624 + 854.982i) q^{7} +1570.62 q^{8} +(383.397 + 664.064i) q^{9} +O(q^{10})\)	\(q-9.69651 q^{2} +(-18.8428 + 32.6367i) q^{3} -33.9777 q^{4} +(119.656 - 207.250i) q^{5} +(182.709 - 316.462i) q^{6} +(493.624 + 854.982i) q^{7} +1570.62 q^{8} +(383.397 + 664.064i) q^{9} +(-1160.25 + 2009.60i) q^{10} +71.3912 q^{11} +(640.235 - 1108.92i) q^{12} +(-1635.79 - 2833.27i) q^{13} +(-4786.43 - 8290.34i) q^{14} +(4509.31 + 7810.35i) q^{15} -10880.4 q^{16} +(-11569.7 - 20039.4i) q^{17} +(-3717.62 - 6439.10i) q^{18} +(-24489.5 + 42417.1i) q^{19} +(-4065.64 + 7041.89i) q^{20} -37205.0 q^{21} -692.246 q^{22} +(-11335.0 + 19632.8i) q^{23} +(-29594.9 + 51259.8i) q^{24} +(10427.4 + 18060.8i) q^{25} +(15861.4 + 27472.8i) q^{26} -111316. q^{27} +(-16772.2 - 29050.3i) q^{28} +(-46185.3 - 79995.3i) q^{29} +(-43724.6 - 75733.2i) q^{30} +(-48322.4 + 83696.9i) q^{31} -95537.5 q^{32} +(-1345.21 + 2329.97i) q^{33} +(112186. + 194312. i) q^{34} +236260. q^{35} +(-13027.0 - 22563.4i) q^{36} +(-35430.6 + 61367.6i) q^{37} +(237463. - 411298. i) q^{38} +123291. q^{39} +(187934. - 325511. i) q^{40} +183851. q^{41} +360759. q^{42} +(-468175. + 229414. i) q^{43} -2425.71 q^{44} +183503. q^{45} +(109910. - 190370. i) q^{46} +311915. q^{47} +(205017. - 355099. i) q^{48} +(-75557.8 + 130870. i) q^{49} +(-101109. - 175126. i) q^{50} +872026. q^{51} +(55580.3 + 96267.9i) q^{52} +(-790638. + 1.36943e6i) q^{53} +1.07937e6 q^{54} +(8542.39 - 14795.8i) q^{55} +(775295. + 1.34285e6i) q^{56} +(-922903. - 1.59852e6i) q^{57} +(447836. + 775675. i) q^{58} -1.46477e6 q^{59} +(-153216. - 265378. i) q^{60} +(-1.66048e6 - 2.87603e6i) q^{61} +(468559. - 811567. i) q^{62} +(-378508. + 655596. i) q^{63} +2.31907e6 q^{64} -782928. q^{65} +(13043.9 - 22592.6i) q^{66} +(-1.51656e6 + 2.62676e6i) q^{67} +(393113. + 680892. i) q^{68} +(-427168. - 739876. i) q^{69} -2.29090e6 q^{70} +(157114. + 272129. i) q^{71} +(602171. + 1.04299e6i) q^{72} +(-973486. - 1.68613e6i) q^{73} +(343553. - 595051. i) q^{74} -785925. q^{75} +(832098. - 1.44124e6i) q^{76} +(35240.4 + 61038.2i) q^{77} -1.19550e6 q^{78} +(1.65479e6 + 2.86618e6i) q^{79} +(-1.30190e6 + 2.25496e6i) q^{80} +(1.25901e6 - 2.18066e6i) q^{81} -1.78271e6 q^{82} +(-1.82188e6 + 3.15559e6i) q^{83} +1.26414e6 q^{84} -5.53756e6 q^{85} +(4.53966e6 - 2.22452e6i) q^{86} +3.48104e6 q^{87} +112128. q^{88} +(-3.32655e6 + 5.76175e6i) q^{89} -1.77934e6 q^{90} +(1.61493e6 - 2.79714e6i) q^{91} +(385138. - 667079. i) q^{92} +(-1.82106e6 - 3.15417e6i) q^{93} -3.02449e6 q^{94} +(5.86064e6 + 1.01509e7i) q^{95} +(1.80019e6 - 3.11803e6i) q^{96} -6.68568e6 q^{97} +(732647. - 1.26898e6i) q^{98} +(27371.2 + 47408.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9}+O(q^{10}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99}+O(q^{100}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9 + 1667 * q^10 - 4594 * q^11 - 8448 * q^12 + 2972 * q^13 - 15928 * q^14 - 2485 * q^15 + 185846 * q^16 + 25298 * q^17 + 13249 * q^18 + 3269 * q^19 + 2705 * q^20 - 85260 * q^21 + 150968 * q^22 - 19120 * q^23 - 55070 * q^24 - 296876 * q^25 - 139545 * q^26 - 274154 * q^27 - 118970 * q^28 - 231057 * q^29 + 240447 * q^30 - 177637 * q^31 + 1254274 * q^32 - 344986 * q^33 + 104923 * q^34 - 518850 * q^35 + 816168 * q^36 + 885140 * q^37 + 200956 * q^38 - 59884 * q^39 + 160425 * q^40 + 2202852 * q^41 - 349786 * q^42 + 1009342 * q^43 - 1012518 * q^44 + 775768 * q^45 - 1277532 * q^46 - 2784982 * q^47 - 2238049 * q^48 - 1241240 * q^49 - 5126146 * q^50 - 2477574 * q^51 - 268404 * q^52 - 398258 * q^53 + 6491644 * q^54 - 2551752 * q^55 - 4471819 * q^56 + 2094777 * q^57 - 2294852 * q^58 + 5664766 * q^59 + 1374965 * q^60 + 2652290 * q^61 - 5621243 * q^62 - 3210173 * q^63 + 5395148 * q^64 + 22093214 * q^65 - 284525 * q^66 + 5696184 * q^67 + 2422800 * q^68 + 4199245 * q^69 - 8874170 * q^70 - 16652990 * q^71 + 5916954 * q^72 + 108058 * q^73 + 8260200 * q^74 - 3594466 * q^75 - 7386456 * q^76 - 8874183 * q^77 - 27627308 * q^78 - 7378370 * q^79 + 7523523 * q^80 - 14862361 * q^81 + 7898428 * q^82 + 18099816 * q^83 + 47917640 * q^84 + 5843026 * q^85 + 14578342 * q^86 - 24244628 * q^87 + 23110740 * q^88 - 20405960 * q^89 + 32640076 * q^90 + 10283016 * q^91 - 27186571 * q^92 - 19267997 * q^93 - 52636002 * q^94 + 1708621 * q^95 + 8113092 * q^96 + 53505940 * q^97 - 3752059 * q^98 + 10929650 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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