LMFDB - Embedded newform 80.6.l.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65572 + 0.113075i) q^{2} +(-18.3942 + 18.3942i) q^{3} +(31.9744 - 1.27904i) q^{4} +(17.6777 + 17.6777i) q^{5} +(101.953 - 106.113i) q^{6} -47.3499i q^{7} +(-180.694 + 10.8494i) q^{8} -433.697i q^{9} +O(q^{10})$	\(q+(-5.65572 + 0.113075i) q^{2} +(-18.3942 + 18.3942i) q^{3} +(31.9744 - 1.27904i) q^{4} +(17.6777 + 17.6777i) q^{5} +(101.953 - 106.113i) q^{6} -47.3499i q^{7} +(-180.694 + 10.8494i) q^{8} -433.697i q^{9} +(-101.979 - 97.9811i) q^{10} +(-285.234 - 285.234i) q^{11} +(-564.618 + 611.673i) q^{12} +(301.631 - 301.631i) q^{13} +(5.35409 + 267.798i) q^{14} -650.335 q^{15} +(1020.73 - 81.7933i) q^{16} +387.084 q^{17} +(49.0403 + 2452.87i) q^{18} +(1151.39 - 1151.39i) q^{19} +(587.844 + 542.623i) q^{20} +(870.965 + 870.965i) q^{21} +(1645.45 + 1580.95i) q^{22} +4570.65i q^{23} +(3124.16 - 3523.30i) q^{24} +625.000i q^{25} +(-1671.83 + 1740.05i) q^{26} +(3507.72 + 3507.72i) q^{27} +(-60.5625 - 1513.99i) q^{28} +(5716.62 - 5716.62i) q^{29} +(3678.11 - 73.5366i) q^{30} -5216.43 q^{31} +(-5763.71 + 578.019i) q^{32} +10493.3 q^{33} +(-2189.24 + 43.7696i) q^{34} +(837.036 - 837.036i) q^{35} +(-554.716 - 13867.2i) q^{36} +(6376.99 + 6376.99i) q^{37} +(-6381.75 + 6642.13i) q^{38} +11096.5i q^{39} +(-3386.04 - 3002.45i) q^{40} +6877.46i q^{41} +(-5024.42 - 4827.46i) q^{42} +(2857.60 + 2857.60i) q^{43} +(-9485.01 - 8755.35i) q^{44} +(7666.75 - 7666.75i) q^{45} +(-516.827 - 25850.3i) q^{46} -10988.9 q^{47} +(-17271.0 + 20280.1i) q^{48} +14565.0 q^{49} +(-70.6719 - 3534.83i) q^{50} +(-7120.12 + 7120.12i) q^{51} +(9258.67 - 10030.3i) q^{52} +(-12360.5 - 12360.5i) q^{53} +(-20235.3 - 19442.1i) q^{54} -10084.5i q^{55} +(513.719 + 8555.84i) q^{56} +42357.9i q^{57} +(-31685.2 + 32978.0i) q^{58} +(21041.9 + 21041.9i) q^{59} +(-20794.1 + 831.806i) q^{60} +(13843.3 - 13843.3i) q^{61} +(29502.7 - 589.848i) q^{62} -20535.5 q^{63} +(32532.6 - 3920.85i) q^{64} +10664.3 q^{65} +(-59347.3 + 1186.53i) q^{66} +(17308.5 - 17308.5i) q^{67} +(12376.8 - 495.097i) q^{68} +(-84073.7 - 84073.7i) q^{69} +(-4639.39 + 4828.69i) q^{70} +11324.5i q^{71} +(4705.36 + 78366.3i) q^{72} -81459.8i q^{73} +(-36787.6 - 35345.4i) q^{74} +(-11496.4 - 11496.4i) q^{75} +(35342.3 - 38287.7i) q^{76} +(-13505.8 + 13505.8i) q^{77} +(-1254.74 - 62758.9i) q^{78} +36891.5 q^{79} +(19490.0 + 16598.2i) q^{80} -23655.5 q^{81} +(-777.669 - 38897.0i) q^{82} +(82684.9 - 82684.9i) q^{83} +(28962.6 + 26734.6i) q^{84} +(6842.75 + 6842.75i) q^{85} +(-16484.9 - 15838.7i) q^{86} +210306. i q^{87} +(54634.6 + 48445.3i) q^{88} +126381. i q^{89} +(-42494.1 + 44227.9i) q^{90} +(-14282.2 - 14282.2i) q^{91} +(5846.06 + 146144. i) q^{92} +(95952.3 - 95952.3i) q^{93} +(62150.3 - 1242.57i) q^{94} +40707.8 q^{95} +(95386.8 - 116651. i) q^{96} -4401.13 q^{97} +(-82375.6 + 1646.94i) q^{98} +(-123705. + 123705. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−5.65572	+	0.113075i	−0.999800	+	0.0199890i
$2$	−5.65572	+	0.113075i	−0.999800	+	0.0199890i
$3$	−18.3942	+	18.3942i	−1.17999	+	1.17999i	−0.200246	+	0.979746i	$0.564174\pi$
$3$	−18.3942	+	18.3942i	−1.17999	+	1.17999i	−0.979746	+	0.200246i	$0.935826\pi$
$4$	31.9744	−	1.27904i	0.999201	−	0.0399701i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$	101.953	−	106.113i	1.15617	−	1.20334i
$7$		−	47.3499i		−	0.365236i	−0.983184	−	0.182618i	$-0.941543\pi$
$7$		−	47.3499i		−	0.365236i	0.983184	−	0.182618i	$-0.0584572\pi$
$8$	−180.694	+	10.8494i	−0.998202	+	0.0599351i
$9$		−	433.697i		−	1.78476i
$10$	−101.979	−	97.9811i	−0.322486	−	0.309843i
$11$	−285.234	−	285.234i	−0.710753	−	0.710753i	0.255940	−	0.966693i	$-0.417615\pi$
$11$	−285.234	−	285.234i	−0.710753	−	0.710753i	−0.966693	+	0.255940i	$0.917615\pi$
$12$	−564.618	+	611.673i	−1.13188	+	1.22621i
$13$	301.631	−	301.631i	0.495013	−	0.495013i	−0.414868	−	0.909882i	$-0.636172\pi$
$13$	301.631	−	301.631i	0.495013	−	0.495013i	0.909882	+	0.414868i	$0.136172\pi$
$14$	5.35409	+	267.798i	0.00730072	+	0.365163i
$15$	−650.335			−0.746292
$16$	1020.73	−	81.7933i	0.996805	−	0.0798763i
$17$	387.084			0.324850			0.162425	−	0.986721i	$-0.448068\pi$
$17$	387.084			0.324850			0.162425	+	0.986721i	$0.448068\pi$
$18$	49.0403	+	2452.87i	0.0356756	+	1.78440i
$19$	1151.39	−	1151.39i	0.731709	−	0.731709i	−0.239250	−	0.970958i	$-0.576901\pi$
$19$	1151.39	−	1151.39i	0.731709	−	0.731709i	0.970958	+	0.239250i	$0.0769014\pi$
$20$	587.844	+	542.623i	0.328615	+	0.303335i
$21$	870.965	+	870.965i	0.430976	+	0.430976i
$22$	1645.45	+	1580.95i	0.724819	+	0.696404i
$23$			4570.65i			1.80160i	0.434234	+	0.900800i	$0.357019\pi$
$23$			4570.65i			1.80160i	−0.434234	+	0.900800i	$0.642981\pi$
$24$	3124.16	−	3523.30i	1.10715	−	1.24859i
$25$			625.000i			0.200000i
$26$	−1671.83	+	1740.05i	−0.485020	+	0.504809i
$27$	3507.72	+	3507.72i	0.926010	+	0.926010i
$28$	−60.5625	−	1513.99i	−0.0145985	−	0.364944i
$29$	5716.62	−	5716.62i	1.26225	−	1.26225i	0.312246	−	0.950001i	$-0.398919\pi$
$29$	5716.62	−	5716.62i	1.26225	−	1.26225i	0.950001	−	0.312246i	$-0.101081\pi$
$30$	3678.11	−	73.5366i	0.746143	−	0.0149177i
$31$	−5216.43			−0.974920			−0.487460	−	0.873145i	$-0.662077\pi$
$31$	−5216.43			−0.974920			−0.487460	+	0.873145i	$0.662077\pi$
$32$	−5763.71	+	578.019i	−0.995009	+	0.0997855i
$33$	10493.3			1.67737
$34$	−2189.24	+	43.7696i	−0.324785	+	0.00649344i
$35$	837.036	−	837.036i	0.115498	−	0.115498i
$36$	−554.716	−	13867.2i	−0.0713370	−	1.78333i
$37$	6376.99	+	6376.99i	0.765793	+	0.765793i	0.977363	−	0.211569i	$-0.0678575\pi$
$37$	6376.99	+	6376.99i	0.765793	+	0.765793i	−0.211569	+	0.977363i	$0.567857\pi$
$38$	−6381.75	+	6642.13i	−0.716936	+	0.746189i
$39$			11096.5i			1.16822i
$40$	−3386.04	−	3002.45i	−0.334612	−	0.296706i
$41$			6877.46i			0.638952i	0.947594	+	0.319476i	$0.103507\pi$
$41$			6877.46i			0.638952i	−0.947594	+	0.319476i	$0.896493\pi$
$42$	−5024.42	−	4827.46i	−0.439504	−	0.422275i
$43$	2857.60	+	2857.60i	0.235684	+	0.235684i	0.815060	−	0.579376i	$-0.196704\pi$
$43$	2857.60	+	2857.60i	0.235684	+	0.235684i	−0.579376	+	0.815060i	$0.696704\pi$
$44$	−9485.01	−	8755.35i	−0.738594	−	0.681776i
$45$	7666.75	−	7666.75i	0.564391	−	0.564391i
$46$	−516.827	−	25850.3i	−0.0360122	−	1.80124i
$47$	−10988.9			−0.725622			−0.362811	−	0.931863i	$-0.618183\pi$
$47$	−10988.9			−0.725622			−0.362811	+	0.931863i	$0.618183\pi$
$48$	−17271.0	+	20280.1i	−1.08197	+	1.27047i
$49$	14565.0			0.866603
$50$	−70.6719	−	3534.83i	−0.00399781	−	0.199960i
$51$	−7120.12	+	7120.12i	−0.383321	+	0.383321i
$52$	9258.67	−	10030.3i	0.474832	−	0.514404i
$53$	−12360.5	−	12360.5i	−0.604432	−	0.604432i	0.337054	−	0.941485i	$-0.390570\pi$
$53$	−12360.5	−	12360.5i	−0.604432	−	0.604432i	−0.941485	+	0.337054i	$0.890570\pi$
$54$	−20235.3	−	19442.1i	−0.944335	−	0.907315i
$55$		−	10084.5i		−	0.449520i
$56$	513.719	+	8555.84i	0.0218905	+	0.364580i
$57$			42357.9i			1.72682i
$58$	−31685.2	+	32978.0i	−1.23676	+	1.28723i
$59$	21041.9	+	21041.9i	0.786964	+	0.786964i	0.980995	−	0.194032i	$-0.0621565\pi$
$59$	21041.9	+	21041.9i	0.786964	+	0.786964i	−0.194032	+	0.980995i	$0.562156\pi$
$60$	−20794.1	+	831.806i	−0.745696	+	0.0298294i
$61$	13843.3	−	13843.3i	0.476337	−	0.476337i	−0.427621	−	0.903958i	$-0.640648\pi$
$61$	13843.3	−	13843.3i	0.476337	−	0.476337i	0.903958	+	0.427621i	$0.140648\pi$
$62$	29502.7	−	589.848i	0.974725	−	0.0194877i
$63$	−20535.5			−0.651859
$64$	32532.6	−	3920.85i	0.992816	−	0.119655i
$65$	10664.3			0.313074
$66$	−59347.3	+	1186.53i	−1.67703	+	0.0335289i
$67$	17308.5	−	17308.5i	0.471055	−	0.471055i	−0.431201	−	0.902256i	$-0.641910\pi$
$67$	17308.5	−	17308.5i	0.471055	−	0.471055i	0.902256	+	0.431201i	$0.141910\pi$
$68$	12376.8	−	495.097i	0.324591	−	0.0129843i
$69$	−84073.7	−	84073.7i	−2.12587	−	2.12587i
$70$	−4639.39	+	4828.69i	−0.113166	+	0.117783i
$71$			11324.5i			0.266608i	0.991075	+	0.133304i	$0.0425587\pi$
$71$			11324.5i			0.266608i	−0.991075	+	0.133304i	$0.957441\pi$
$72$	4705.36	+	78366.3i	0.106970	+	1.78155i
$73$		−	81459.8i		−	1.78911i	−0.446962	−	0.894553i	$-0.647494\pi$
$73$		−	81459.8i		−	1.78911i	0.446962	−	0.894553i	$-0.352506\pi$
$74$	−36787.6	−	35345.4i	−0.780948	−	0.750333i
$75$	−11496.4	−	11496.4i	−0.235998	−	0.235998i
$76$	35342.3	−	38287.7i	0.701877	−	0.760370i
$77$	−13505.8	+	13505.8i	−0.259593	+	0.259593i
$78$	−1254.74	−	62758.9i	−0.0233517	−	1.16799i
$79$	36891.5			0.665057			0.332529	−	0.943093i	$-0.392098\pi$
$79$	36891.5			0.665057			0.332529	+	0.943093i	$0.392098\pi$
$80$	19490.0	+	16598.2i	0.340476	+	0.289958i
$81$	−23655.5			−0.400608
$82$	−777.669	−	38897.0i	−0.0127720	−	0.638825i
$83$	82684.9	−	82684.9i	1.31744	−	1.31744i	0.401646	−	0.915795i	$-0.368438\pi$
$83$	82684.9	−	82684.9i	1.31744	−	1.31744i	0.915795	−	0.401646i	$-0.131562\pi$
$84$	28962.6	+	26734.6i	0.447857	+	0.413405i
$85$	6842.75	+	6842.75i	0.102727	+	0.102727i
$86$	−16484.9	−	15838.7i	−0.240348	−	0.230926i
$87$			210306.i			2.97888i
$88$	54634.6	+	48445.3i	0.752075	+	0.666876i
$89$			126381.i			1.69125i	0.533780	+	0.845623i	$0.320771\pi$
$89$			126381.i			1.69125i	−0.533780	+	0.845623i	$0.679229\pi$
$90$	−42494.1	+	44227.9i	−0.552996	+	0.575559i
$91$	−14282.2	−	14282.2i	−0.180797	−	0.180797i
$92$	5846.06	+	146144.i	0.0720101	+	1.80016i
$93$	95952.3	−	95952.3i	1.15040	−	1.15040i
$94$	62150.3	−	1242.57i	0.725477	−	0.0145045i
$95$	40707.8			0.462773
$96$	95386.8	−	116651.i	1.05636	−	1.29185i
$97$	−4401.13			−0.0474936			−0.0237468	−	0.999718i	$-0.507560\pi$
$97$	−4401.13			−0.0474936			−0.0237468	+	0.999718i	$0.507560\pi$
$98$	−82375.6	+	1646.94i	−0.866429	+	0.0173225i
$99$	−123705.	+	123705.i	−1.26852	+	1.26852i
$100$	799.401	+	19984.0i	0.00799401	+	0.199840i
$101$	70949.2	+	70949.2i	0.692061	+	0.692061i	0.962685	−	0.270624i	$-0.0872301\pi$
$101$	70949.2	+	70949.2i	0.692061	+	0.692061i	−0.270624	+	0.962685i	$0.587230\pi$
$102$	39464.3	−	41074.6i	0.375582	−	0.390906i
$103$		−	65793.1i		−	0.611065i	−0.952182	−	0.305532i	$-0.901166\pi$
$103$		−	65793.1i		−	0.611065i	0.952182	−	0.305532i	$-0.0988344\pi$
$104$	−51230.3	+	57775.3i	−0.464455	+	0.523792i
$105$			30793.3i			0.272573i
$106$	71305.4	+	68510.0i	0.616393	+	0.592229i
$107$	44614.9	+	44614.9i	0.376721	+	0.376721i	0.869918	−	0.493197i	$-0.164172\pi$
$107$	44614.9	+	44614.9i	0.376721	+	0.376721i	−0.493197	+	0.869918i	$0.664172\pi$
$108$	116644.	+	107671.i	0.962283	+	0.888257i
$109$	117486.	−	117486.i	0.947149	−	0.947149i	−0.0515228	−	0.998672i	$-0.516407\pi$
$109$	117486.	−	117486.i	0.947149	−	0.947149i	0.998672	+	0.0515228i	$0.0164075\pi$
$110$	1140.31	+	57035.3i	0.00898547	+	0.449430i
$111$	−234600.			−1.80726
$112$	−3872.90	−	48331.4i	−0.0291737	−	0.364069i
$113$	−48951.7			−0.360638			−0.180319	−	0.983608i	$-0.557713\pi$
$113$	−48951.7			−0.360638			−0.180319	+	0.983608i	$0.557713\pi$
$114$	−4789.62	−	239564.i	−0.0345175	−	1.72647i
$115$	−80798.5	+	80798.5i	−0.569716	+	0.569716i
$116$	175474.	−	190098.i	1.21079	−	1.31169i
$117$	−130816.	−	130816.i	−0.883480	−	0.883480i
$118$	−121386.	−	116628.i	−0.802537	−	0.771076i
$119$		−	18328.4i		−	0.118647i
$120$	117512.	−	7055.76i	0.744951	−	0.0447291i
$121$			1665.34i			0.0103405i
$122$	−76728.5	+	79859.2i	−0.466721	+	0.485764i
$123$	−126506.	−	126506.i	−0.753958	−	0.753958i
$124$	−166792.	+	6672.03i	−0.974141	+	0.0389676i
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$	116143.	−	2322.05i	0.651729	−	0.0130300i
$127$	350103.			1.92613			0.963067	−	0.269262i	$-0.0867796\pi$
$127$	350103.			1.92613			0.963067	+	0.269262i	$0.0867796\pi$
$128$	−183552.	+	25853.9i	−0.990225	+	0.139476i
$129$	−105127.			−0.556211
$130$	−60314.1	+	1205.86i	−0.313011	+	0.00625805i
$131$	−208219.	+	208219.i	−1.06009	+	1.06009i	−0.0620143	+	0.998075i	$0.519752\pi$
$131$	−208219.	+	208219.i	−1.06009	+	1.06009i	−0.998075	+	0.0620143i	$0.980248\pi$
$132$	335518.	−	13421.4i	1.67603	−	0.0670444i
$133$	−54518.1	−	54518.1i	−0.267246	−	0.267246i
$134$	−95934.8	+	99849.2i	−0.461545	+	0.480377i
$135$			124017.i			0.585660i
$136$	−69943.8	+	4199.64i	−0.324266	+	0.0194699i
$137$		−	342023.i		−	1.55688i	−0.627721	−	0.778438i	$-0.716012\pi$
$137$		−	342023.i		−	1.55688i	0.627721	−	0.778438i	$-0.283988\pi$
$138$	485004.	+	465991.i	2.16794	+	2.08295i
$139$	−190884.	−	190884.i	−0.837979	−	0.837979i	0.150614	−	0.988593i	$-0.451875\pi$
$139$	−190884.	−	190884.i	−0.837979	−	0.837979i	−0.988593	+	0.150614i	$0.951875\pi$
$140$	25693.1	−	27834.3i	0.110789	−	0.120022i
$141$	202133.	−	202133.i	0.856228	−	0.856228i
$142$	−1280.52	−	64048.3i	−0.00532924	−	0.266555i
$143$	−172070.			−0.703665
$144$	−35473.5	−	442686.i	−0.142560	−	1.77906i
$145$	202113.			0.798315
$146$	9211.07	+	460714.i	0.0357625	+	1.78875i
$147$	−267912.	+	267912.i	−1.02258	+	1.02258i
$148$	212057.	+	195744.i	0.795790	+	0.734573i
$149$	−55329.1	−	55329.1i	−0.204168	−	0.204168i	0.597615	−	0.801783i	$-0.296115\pi$
$149$	−55329.1	−	55329.1i	−0.204168	−	0.204168i	−0.801783	+	0.597615i	$0.796115\pi$
$150$	66320.4	+	63720.5i	0.240669	+	0.231234i
$151$		−	295727.i		−	1.05548i	−0.849407	−	0.527739i	$-0.823040\pi$
$151$		−	295727.i		−	1.05548i	0.849407	−	0.527739i	$-0.176960\pi$
$152$	−195557.	+	220541.i	−0.686538	+	0.774248i
$153$		−	167877.i		−	0.579780i
$154$	74857.8	−	77912.1i	0.254352	−	0.264730i
$155$	−92214.3	−	92214.3i	−0.308297	−	0.308297i
$156$	14192.9	+	354805.i	0.0466940	+	1.16729i
$157$	−76397.2	+	76397.2i	−0.247359	+	0.247359i	−0.819886	−	0.572527i	$-0.805963\pi$
$157$	−76397.2	+	76397.2i	−0.247359	+	0.247359i	0.572527	+	0.819886i	$0.305963\pi$
$158$	−208648.	+	4171.51i	−0.664924	+	0.0132938i
$159$	454725.			1.42645
$160$	−112107.	−	91670.9i	−0.346204	−	0.283095i
$161$	216420.			0.658010
$162$	133789.	−	2674.84i	0.400528	−	0.00800776i
$163$	−171462.	+	171462.i	−0.505474	+	0.505474i	−0.913134	−	0.407660i	$-0.866345\pi$
$163$	−171462.	+	171462.i	−0.505474	+	0.505474i	0.407660	+	0.913134i	$0.366345\pi$
$164$	8796.56	+	219903.i	0.0255390	+	0.638442i
$165$	185497.	+	185497.i	0.530430	+	0.530430i
$166$	−458294.	+	476993.i	−1.29084	+	1.34351i
$167$			58773.9i			0.163077i	0.996670	+	0.0815387i	$0.0259834\pi$
$167$			58773.9i			0.163077i	−0.996670	+	0.0815387i	$0.974017\pi$
$168$	−166828.	−	147929.i	−0.456031	−	0.404370i
$169$			189331.i			0.509923i
$170$	−39474.4	−	37927.0i	−0.104760	−	0.100653i
$171$	−499354.	−	499354.i	−1.30592	−	1.30592i
$172$	95025.3	+	87715.3i	0.244916	+	0.226076i
$173$	18792.0	−	18792.0i	0.0477373	−	0.0477373i	−0.682835	−	0.730572i	$-0.739253\pi$
$173$	18792.0	−	18792.0i	0.0477373	−	0.0477373i	0.730572	+	0.682835i	$0.239253\pi$
$174$	−23780.3	−	1.18943e6i	−0.0595450	−	2.97829i
$175$	29593.7			0.0730472
$176$	−314476.	−	267816.i	−0.765255	−	0.651710i
$177$	−774099.			−1.85722
$178$	−14290.5	−	714776.i	−0.0338064	−	1.69091i
$179$	233429.	−	233429.i	0.544530	−	0.544530i	−0.380324	−	0.924854i	$-0.624187\pi$
$179$	233429.	−	233429.i	0.544530	−	0.544530i	0.924854	+	0.380324i	$0.124187\pi$
$180$	235334.	−	254946.i	0.541381	−	0.586498i
$181$	384731.	+	384731.i	0.872892	+	0.872892i	0.992787	−	0.119894i	$-0.0382556\pi$
$181$	384731.	+	384731.i	0.872892	+	0.872892i	−0.119894	+	0.992787i	$0.538256\pi$
$182$	82391.0	+	79161.1i	0.184375	+	0.177147i
$183$			509274.i			1.12415i
$184$	−49588.9	−	825889.i	−0.107979	−	1.79836i
$185$			225461.i			0.484330i
$186$	−531830.	+	553529.i	−1.12717	+	1.17316i
$187$	−110409.	−	110409.i	−0.230888	−	0.230888i
$188$	−351365.	+	14055.3i	−0.725042	+	0.0290032i
$189$	166090.	−	166090.i	0.338212	−	0.338212i
$190$	−230232.	+	4603.03i	−0.462681	+	0.00925039i
$191$	570105.			1.13076			0.565382	−	0.824829i	$-0.308729\pi$
$191$	570105.			1.13076			0.565382	+	0.824829i	$0.308729\pi$
$192$	−526291.	+	670533.i	−1.03032	+	1.31271i
$193$	−404843.			−0.782335			−0.391168	−	0.920319i	$-0.627929\pi$
$193$	−404843.			−0.782335			−0.391168	+	0.920319i	$0.627929\pi$
$194$	24891.6	−	497.658i	0.0474841	−	0.000949352i
$195$	−196161.	+	196161.i	−0.369425	+	0.369425i
$196$	465707.	−	18629.2i	0.865910	−	0.0346382i
$197$	165404.	+	165404.i	0.303655	+	0.303655i	0.842442	−	0.538787i	$-0.181117\pi$
$197$	165404.	+	165404.i	0.303655	+	0.303655i	−0.538787	+	0.842442i	$0.681117\pi$
$198$	685652.	−	713628.i	1.24291	−	1.29363i
$199$			160343.i			0.287023i	0.989649	+	0.143512i	$0.0458395\pi$
$199$			160343.i			0.287023i	−0.989649	+	0.143512i	$0.954161\pi$
$200$	−6780.89	−	112934.i	−0.0119870	−	0.199640i
$201$			636753.i			1.11168i
$202$	−409292.	−	393247.i	−0.705756	−	0.678089i
$203$	−270681.	−	270681.i	−0.461018	−	0.461018i
$204$	−218555.	+	236769.i	−0.367693	+	0.398336i
$205$	−121577.	+	121577.i	−0.202054	+	0.202054i
$206$	7439.56	+	372108.i	0.0122146	+	0.610943i
$207$	1.98228e6			3.21542
$208$	283211.	−	332554.i	0.453892	−	0.532972i
$209$	−656830.			−1.04013
$210$	−3481.95	−	174158.i	−0.00544847	−	0.272518i
$211$	811200.	−	811200.i	1.25436	−	1.25436i	0.300613	−	0.953746i	$-0.402809\pi$
$211$	811200.	−	811200.i	1.25436	−	1.25436i	0.953746	−	0.300613i	$-0.0971914\pi$
$212$	−411030.	−	379411.i	−0.628108	−	0.579789i
$213$	−208306.	−	208306.i	−0.314595	−	0.314595i
$214$	−257374.	−	247285.i	−0.384176	−	0.369116i
$215$			101032.i			0.149060i
$216$	−671881.	−	595767.i	−0.979846	−	0.868845i
$217$			246997.i			0.356076i
$218$	−651181.	+	677751.i	−0.928027	+	0.965892i
$219$	1.49839e6	+	1.49839e6i	2.11113	+	2.11113i
$220$	−12898.5	−	322447.i	−0.0179673	−	0.449161i
$221$	116756.	−	116756.i	0.160805	−	0.160805i
$222$	1.32683e6	−	26527.4i	1.80690	−	0.0361254i
$223$	566028.			0.762212			0.381106	−	0.924531i	$-0.375543\pi$
$223$	566028.			0.762212			0.381106	+	0.924531i	$0.375543\pi$
$224$	27369.1	+	272911.i	0.0364453	+	0.363413i
$225$	271060.			0.356952
$226$	276857.	−	5535.21i	0.360566	−	0.00720881i
$227$	632132.	−	632132.i	0.814222	−	0.814222i	−0.171042	−	0.985264i	$-0.554713\pi$
$227$	632132.	−	632132.i	0.814222	−	0.814222i	0.985264	+	0.171042i	$0.0547133\pi$
$228$	54177.5	+	1.35437e6i	0.0690211	+	1.72544i
$229$	370947.	+	370947.i	0.467437	+	0.467437i	0.901083	−	0.433646i	$-0.142773\pi$
$229$	370947.	+	370947.i	0.467437	+	0.467437i	−0.433646	+	0.901083i	$0.642773\pi$
$230$	447838.	−	466110.i	0.558214	−	0.580990i
$231$		−	496857.i		−	0.612635i
$232$	−970937.	+	1.09498e6i	−1.18433	+	1.33563i
$233$			1.20923e6i			1.45922i	0.683864	+	0.729609i	$0.260298\pi$
$233$			1.20923e6i			1.45922i	−0.683864	+	0.729609i	$0.739702\pi$
$234$	754652.	+	725068.i	0.900963	+	0.865644i
$235$	−194259.	−	194259.i	−0.229462	−	0.229462i
$236$	699716.	+	645889.i	0.817790	+	0.754880i
$237$	−678592.	+	678592.i	−0.784762	+	0.784762i
$238$	2072.48	+	103660.i	0.00237164	+	0.118623i
$239$	−794920.			−0.900179			−0.450089	−	0.892983i	$-0.648608\pi$
$239$	−794920.			−0.900179			−0.450089	+	0.892983i	$0.648608\pi$
$240$	−663815.	+	53193.0i	−0.743908	+	0.0596110i
$241$	109688.			0.121651			0.0608256	−	0.998148i	$-0.480627\pi$
$241$	109688.			0.121651			0.0608256	+	0.998148i	$0.480627\pi$
$242$	−188.309	−	9418.72i	−0.000206696	−	0.0103384i
$243$	−417251.	+	417251.i	−0.453296	+	0.453296i
$244$	424925.	−	460337.i	0.456918	−	0.494996i
$245$	257475.	+	257475.i	0.274044	+	0.274044i
$246$	729786.	+	701177.i	0.768879	+	0.738737i
$247$		−	694588.i		−	0.724411i
$248$	942577.	−	56595.2i	0.973167	−	0.0584320i
$249$			3.04185e6i			3.10914i
$250$	61238.2	−	63736.8i	0.0619687	−	0.0644971i
$251$	−577816.	−	577816.i	−0.578902	−	0.578902i	0.355699	−	0.934601i	$-0.384243\pi$
$251$	−577816.	−	577816.i	−0.578902	−	0.578902i	−0.934601	+	0.355699i	$0.884243\pi$
$252$	−656610.	+	26265.8i	−0.651338	+	0.0260548i
$253$	1.30370e6	−	1.30370e6i	1.28049	−	1.28049i
$254$	−1.98009e6	+	39587.9i	−1.92575	+	0.0385016i
$255$	−251734.			−0.242433
$256$	1.03520e6	−	166977.i	0.987240	−	0.159242i
$257$	1.40471e6			1.32664			0.663322	−	0.748334i	$-0.269146\pi$
$257$	1.40471e6			1.32664			0.663322	+	0.748334i	$0.269146\pi$
$258$	594569.	−	11887.2i	0.556100	−	0.0111181i
$259$	301950.	−	301950.i	0.279695	−	0.279695i
$260$	340983.	−	13640.0i	0.312824	−	0.0125136i
$261$	−2.47928e6	−	2.47928e6i	−2.25281	−	2.25281i
$262$	1.15409e6	−	1.20117e6i	1.03869	−	1.08107i
$263$		−	1.85749e6i		−	1.65591i	−0.560793	−	0.827956i	$-0.689504\pi$
$263$		−	1.85749e6i		−	1.65591i	0.560793	−	0.827956i	$-0.310496\pi$
$264$	−1.89608e6	+	113846.i	−1.67435	+	0.100533i
$265$		−	437010.i		−	0.382276i
$266$	314504.	+	302175.i	0.272535	+	0.261851i
$267$	−2.32468e6	−	2.32468e6i	−1.99566	−	1.99566i
$268$	531291.	−	575567.i	0.451851	−	0.489507i
$269$	734413.	−	734413.i	0.618813	−	0.618813i	−0.326414	−	0.945227i	$-0.605840\pi$
$269$	734413.	−	734413.i	0.618813	−	0.618813i	0.945227	+	0.326414i	$0.105840\pi$
$270$	−14023.2	−	701404.i	−0.0117068	−	0.585543i
$271$	−449174.			−0.371528			−0.185764	−	0.982594i	$-0.559476\pi$
$271$	−449174.			−0.371528			−0.185764	+	0.982594i	$0.559476\pi$
$272$	395108.	−	31660.9i	0.323812	−	0.0259478i
$273$	525420.			0.426677
$274$	38674.3	+	1.93439e6i	0.0311204	+	1.55657i
$275$	178271.	−	178271.i	0.142151	−	0.142151i
$276$	−2.79574e6	−	2.58067e6i	−2.20915	−	2.03920i
$277$	−303653.	−	303653.i	−0.237782	−	0.237782i	0.578149	−	0.815931i	$-0.303775\pi$
$277$	−303653.	−	303653.i	−0.237782	−	0.237782i	−0.815931	+	0.578149i	$0.803775\pi$
$278$	1.10117e6	+	1.05800e6i	0.854562	+	0.821061i
$279$			2.26235e6i			1.74000i
$280$	−142166.	+	160329.i	−0.108368	+	0.122213i
$281$			741380.i			0.560112i	0.959984	+	0.280056i	$0.0903531\pi$
$281$			741380.i			0.560112i	−0.959984	+	0.280056i	$0.909647\pi$
$282$	−1.12035e6	+	1.16606e6i	−0.838942	+	0.873172i
$283$	−425683.	−	425683.i	−0.315951	−	0.315951i	0.531259	−	0.847210i	$-0.321719\pi$
$283$	−425683.	−	425683.i	−0.315951	−	0.315951i	−0.847210	+	0.531259i	$0.821719\pi$
$284$	14484.5	+	362095.i	0.0106563	+	0.266395i
$285$	−748788.	+	748788.i	−0.546068	+	0.546068i
$286$	973182.	−	19456.9i	0.703524	−	0.0140656i
$287$	325647.			0.233369
$288$	250685.	+	2.49970e6i	0.178093	+	1.77585i
$289$	−1.27002e6			−0.894472
$290$	−1.14310e6	+	22853.9i	−0.798156	+	0.0159575i
$291$	80955.6	−	80955.6i	0.0560421	−	0.0560421i
$292$	−104190.	−	2.60463e6i	−0.0715107	−	1.78768i
$293$	−1.68987e6	−	1.68987e6i	−1.14996	−	1.14996i	−0.986560	−	0.163402i	$-0.947753\pi$
$293$	−1.68987e6	−	1.68987e6i	−1.14996	−	1.14996i	−0.163402	−	0.986560i	$-0.552247\pi$
$294$	1.48494e6	−	1.54553e6i	1.00194	−	1.04282i
$295$			743943.i			0.497719i
$296$	−1.22147e6	−	1.08310e6i	−0.810315	−	0.718519i
$297$		−	2.00104e6i		−	1.31633i
$298$	319182.	+	306670.i	0.208208	+	0.200046i
$299$	1.37865e6	+	1.37865e6i	0.891816	+	0.891816i
$300$	−382295.	−	352887.i	−0.245243	−	0.226377i
$301$	135307.	−	135307.i	0.0860805	−	0.0860805i
$302$	33439.4	+	1.67255e6i	0.0210980	+	1.05527i
$303$	−2.61012e6			−1.63325
$304$	1.08108e6	−	1.26943e6i	0.670924	−	0.787817i
$305$	489434.			0.301262
$306$	18982.7	+	949467.i	0.0115892	+	0.579664i
$307$	−1.01461e6	+	1.01461e6i	−0.614403	+	0.614403i	−0.944090	−	0.329688i	$-0.893057\pi$
$307$	−1.01461e6	+	1.01461e6i	−0.614403	+	0.614403i	0.329688	+	0.944090i	$0.393057\pi$
$308$	−414565.	+	449114.i	−0.249009	+	0.269761i
$309$	1.21021e6	+	1.21021e6i	0.721051	+	0.721051i
$310$	531966.	+	511112.i	0.314398	+	0.302073i
$311$		−	1.13472e6i		−	0.665253i	−0.943059	−	0.332627i	$-0.892065\pi$
$311$		−	1.13472e6i		−	0.665253i	0.943059	−	0.332627i	$-0.107935\pi$
$312$	−120391.	−	2.00508e6i	−0.0700176	−	1.16612i
$313$			1.93126e6i			1.11424i	0.830432	+	0.557120i	$0.188094\pi$
$313$			1.93126e6i			1.11424i	−0.830432	+	0.557120i	$0.811906\pi$
$314$	423443.	−	440720.i	0.242365	−	0.252254i
$315$	−363020.	−	363020.i	−0.206136	−	0.206136i
$316$	1.17959e6	−	47185.8i	0.664526	−	0.0265824i
$317$	−1.01603e6	+	1.01603e6i	−0.567881	+	0.567881i	−0.931534	−	0.363653i	$-0.881529\pi$
$317$	−1.01603e6	+	1.01603e6i	−0.567881	+	0.567881i	0.363653	+	0.931534i	$0.381529\pi$
$318$	−2.57180e6	+	51418.0i	−1.42616	+	0.0285133i
$319$	−3.26114e6			−1.79429
$320$	644412.	+	505789.i	0.351794	+	0.276118i
$321$	−1.64131e6			−0.889056
$322$	−1.22401e6	+	24471.7i	−0.657878	+	0.0131530i
$323$	445685.	−	445685.i	0.237696	−	0.237696i
$324$	−756371.	+	30256.4i	−0.400288	+	0.0160123i
$325$	188519.	+	188519.i	0.0990027	+	0.0990027i
$326$	950354.	−	989130.i	0.495269	−	0.515477i
$327$			4.32212e6i			2.23526i
$328$	−74616.5	−	1.24272e6i	−0.0382957	−	0.637804i
$329$			520324.i			0.265024i
$330$	−1.07010e6	−	1.02815e6i	−0.540926	−	0.519721i
$331$	2.26166e6	+	2.26166e6i	1.13464	+	1.13464i	0.989396	+	0.145244i	$0.0463968\pi$
$331$	2.26166e6	+	2.26166e6i	1.13464	+	1.13464i	0.145244	+	0.989396i	$0.453603\pi$
$332$	2.53805e6	−	2.74956e6i	1.26373	−	1.36905i
$333$	2.76568e6	−	2.76568e6i	1.36676	−	1.36676i
$334$	−6645.87	−	332409.i	−0.00325976	−	0.163045i
$335$	611947.			0.297922
$336$	960258.	+	817780.i	0.464023	+	0.395174i
$337$	−2.88561e6			−1.38409			−0.692043	−	0.721856i	$-0.743289\pi$
$337$	−2.88561e6			−1.38409			−0.692043	+	0.721856i	$0.743289\pi$
$338$	−21408.6	−	1.07080e6i	−0.0101929	−	0.509821i
$339$	900429.	−	900429.i	0.425550	−	0.425550i
$340$	227545.	+	210041.i	0.106751	+	0.0985386i
$341$	1.48790e6	+	1.48790e6i	0.692928	+	0.692928i
$342$	2.88067e6	+	2.76774e6i	1.33177	+	1.27956i
$343$		−	1.48546e6i		−	0.681751i
$344$	−547355.	−	485348.i	−0.249387	−	0.221135i
$345$		−	2.97245e6i		−	1.34452i
$346$	−104157.	+	108407.i	−0.0467735	+	0.0486820i
$347$	−2.27827e6	−	2.27827e6i	−1.01574	−	1.01574i	−0.999874	−	0.0158647i	$-0.994950\pi$
$347$	−2.27827e6	−	2.27827e6i	−1.01574	−	1.01574i	−0.0158647	−	0.999874i	$-0.505050\pi$
$348$	268990.	+	6.72441e6i	0.119066	+	2.97650i
$349$	−408431.	+	408431.i	−0.179496	+	0.179496i	−0.791136	−	0.611640i	$-0.790510\pi$
$349$	−408431.	+	408431.i	−0.179496	+	0.179496i	0.611640	+	0.791136i	$0.290510\pi$
$350$	−167374.	+	3346.31i	−0.0730326	+	0.00146014i
$351$	2.11607e6			0.916775
$352$	1.80887e6	+	1.47913e6i	0.778129	+	0.636283i
$353$	2.60658e6			1.11336			0.556678	−	0.830728i	$-0.312076\pi$
$353$	2.60658e6			1.11336			0.556678	+	0.830728i	$0.312076\pi$
$354$	4.37809e6	−	87531.3i	1.85685	−	0.0371240i
$355$	−200191.	+	200191.i	−0.0843089	+	0.0843089i
$356$	161647.	+	4.04096e6i	0.0675992	+	1.68989i
$357$	337137.	+	337137.i	0.140003	+	0.140003i
$358$	−1.29381e6	+	1.34660e6i	−0.533537	+	0.555306i
$359$		−	2.71605e6i		−	1.11225i	−0.831100	−	0.556123i	$-0.812288\pi$
$359$		−	2.71605e6i		−	1.11225i	0.831100	−	0.556123i	$-0.187712\pi$
$360$	−1.30215e6	+	1.46851e6i	−0.529549	+	0.597203i
$361$		−	175295.i		−	0.0707948i
$362$	−2.21944e6	−	2.13243e6i	−0.890166	−	0.855270i
$363$	−30632.7	−	30632.7i	−0.0122017	−	0.0122017i
$364$	−474932.	−	438397.i	−0.187879	−	0.173426i
$365$	1.44002e6	−	1.44002e6i	0.565765	−	0.565765i
$366$	−57586.1	−	2.88031e6i	−0.0224706	−	1.12392i
$367$	1.39948e6			0.542377			0.271189	−	0.962526i	$-0.412583\pi$
$367$	1.39948e6			0.542377			0.271189	+	0.962526i	$0.412583\pi$
$368$	373849.	+	4.66539e6i	0.143905	+	1.79584i
$369$	2.98273e6			1.14038
$370$	−25494.0	−	1.27514e6i	−0.00968129	−	0.484234i
$371$	−585269.	+	585269.i	−0.220760	+	0.220760i
$372$	2.94529e6	−	3.19075e6i	1.10350	−	1.19546i
$373$	1.81071e6	+	1.81071e6i	0.673871	+	0.673871i	0.958606	−	0.284735i	$-0.0919058\pi$
$373$	1.81071e6	+	1.81071e6i	0.673871	+	0.673871i	−0.284735	+	0.958606i	$0.591906\pi$
$374$	636930.	+	611961.i	0.235458	+	0.226227i
$375$		−	406459.i		−	0.149258i
$376$	1.98563e6	−	119223.i	0.724318	−	0.0434903i
$377$		−	3.44862e6i		−	1.24966i
$378$	−920580.	+	958141.i	−0.331384	+	0.344905i
$379$	−264000.	−	264000.i	−0.0944075	−	0.0944075i	0.658326	−	0.752733i	$-0.271265\pi$
$379$	−264000.	−	264000.i	−0.0944075	−	0.0944075i	−0.752733	+	0.658326i	$0.771265\pi$
$380$	1.30161e6	−	52066.9i	0.462403	−	0.0184971i
$381$	−6.43988e6	+	6.43988e6i	−2.27282	+	2.27282i
$382$	−3.22436e6	+	64464.7i	−1.13054	+	0.0226029i
$383$	−3.94046e6			−1.37262			−0.686310	−	0.727309i	$-0.740771\pi$
$383$	−3.94046e6			−1.37262			−0.686310	+	0.727309i	$0.740771\pi$
$384$	2.90074e6	−	3.85186e6i	1.00388	−	1.33304i
$385$	−477501.			−0.164181
$386$	2.28968e6	−	45777.6i	0.782179	−	0.0156381i
$387$	1.23933e6	−	1.23933e6i	0.420640	−	0.420640i
$388$	−140724.	+	5629.24i	−0.0474557	+	0.00189832i
$389$	−1.48348e6	−	1.48348e6i	−0.497060	−	0.497060i	0.413462	−	0.910521i	$-0.364320\pi$
$389$	−1.48348e6	−	1.48348e6i	−0.497060	−	0.497060i	−0.910521	+	0.413462i	$0.864320\pi$
$390$	1.08725e6	−	1.13161e6i	0.361966	−	0.376735i
$391$			1.76923e6i			0.585250i
$392$	−2.63180e6	+	158022.i	−0.865045	+	0.0519399i
$393$		−	7.66007e6i		−	2.50179i
$394$	−954183.	−	916777.i	−0.309664	−	0.297525i
$395$	652156.	+	652156.i	0.210310	+	0.210310i
$396$	−3.79717e6	+	4.11361e6i	−1.21681	+	1.31821i
$397$	−982167.	+	982167.i	−0.312759	+	0.312759i	−0.845977	−	0.533219i	$-0.820982\pi$
$397$	−982167.	+	982167.i	−0.312759	+	0.312759i	0.533219	+	0.845977i	$0.320982\pi$
$398$	−18130.8	−	906856.i	−0.00573732	−	0.286966i
$399$	2.00564e6			0.630697
$400$	51120.8	+	637955.i	0.0159753	+	0.199361i
$401$	−5.85944e6			−1.81968			−0.909840	−	0.414958i	$-0.863796\pi$
$401$	−5.85944e6			−1.81968			−0.909840	+	0.414958i	$0.863796\pi$
$402$	−72000.9	−	3.60130e6i	−0.0222215	−	1.11146i
$403$	−1.57343e6	+	1.57343e6i	−0.482599	+	0.482599i
$404$	2.35931e6	+	2.17781e6i	0.719169	+	0.663846i
$405$	−418174.	−	418174.i	−0.126683	−	0.126683i
$406$	1.56151e6	+	1.50029e6i	0.470142	+	0.451711i
$407$		−	3.63786e6i		−	1.08858i
$408$	1.20931e6	−	1.36381e6i	0.359657	−	0.405606i
$409$			4.44740e6i			1.31461i	0.753623	+	0.657307i	$0.228304\pi$
$409$			4.44740e6i			1.31461i	−0.753623	+	0.657307i	$0.771696\pi$
$410$	673861.	−	701356.i	0.197975	−	0.206053i
$411$	6.29126e6	+	6.29126e6i	1.83710	+	1.83710i
$412$	−84152.1	−	2.10370e6i	−0.0244243	−	0.610576i
$413$	996331.	−	996331.i	0.287428	−	0.287428i
$414$	−1.12112e7	+	224146.i	−3.21478	+	0.0642732i
$415$	2.92335e6			0.833223
$416$	−1.56416e6	+	1.91286e6i	−0.443148	+	0.541938i
$417$	7.02235e6			1.97762
$418$	3.71485e6	−	74271.0i	1.03992	−	0.0207912i
$419$	−1.45666e6	+	1.45666e6i	−0.405343	+	0.405343i	−0.880111	−	0.474768i	$-0.842532\pi$
$419$	−1.45666e6	+	1.45666e6i	−0.405343	+	0.405343i	0.474768	+	0.880111i	$0.342532\pi$
$420$	39385.9	+	984597.i	0.0108948	+	0.272355i
$421$	−2.98545e6	−	2.98545e6i	−0.820927	−	0.820927i	0.165314	−	0.986241i	$-0.447136\pi$
$421$	−2.98545e6	−	2.98545e6i	−0.820927	−	0.820927i	−0.986241	+	0.165314i	$0.947136\pi$
$422$	−4.49620e6	+	4.67965e6i	−1.22904	+	1.27918i
$423$			4.76586e6i			1.29506i
$424$	2.36758e6	+	2.09937e6i	0.639572	+	0.567118i
$425$			241928.i			0.0649701i
$426$	1.20167e6	+	1.15457e6i	0.320821	+	0.308244i
$427$	−655478.	−	655478.i	−0.173976	−	0.173976i
$428$	1.48360e6	+	1.36947e6i	0.391478	+	0.361363i
$429$	3.16510e6	−	3.16510e6i	0.830319	−	0.830319i
$430$	−11424.1	−	571407.i	−0.00297956	−	0.149030i
$431$	5.51572e6			1.43024			0.715120	−	0.699002i	$-0.246372\pi$
$431$	5.51572e6			1.43024			0.715120	+	0.699002i	$0.246372\pi$
$432$	3.86734e6	+	3.29352e6i	0.997017	+	0.849085i
$433$	−882779.			−0.226273			−0.113136	−	0.993579i	$-0.536090\pi$
$433$	−882779.			−0.226273			−0.113136	+	0.993579i	$0.536090\pi$
$434$	−27929.2	−	1.39695e6i	−0.00711762	−	0.356005i
$435$	−3.71772e6	+	3.71772e6i	−0.942005	+	0.942005i
$436$	3.60627e6	−	3.90680e6i	0.908535	−	0.984250i
$437$	5.26260e6	+	5.26260e6i	1.31825	+	1.31825i
$438$	−8.64392e6	−	8.30506e6i	−2.15291	−	2.06851i
$439$		−	2.41671e6i		−	0.598499i	−0.954175	−	0.299249i	$-0.903264\pi$
$439$		−	2.41671e6i		−	0.598499i	0.954175	−	0.299249i	$-0.0967362\pi$
$440$	109411.	+	1.82221e6i	0.0269420	+	0.448712i
$441$		−	6.31679e6i		−	1.54668i
$442$	−647140.	+	673545.i	−0.157559	+	0.163987i
$443$	1.52505e6	+	1.52505e6i	0.369211	+	0.369211i	0.867190	−	0.497978i	$-0.165924\pi$
$443$	1.52505e6	+	1.52505e6i	0.369211	+	0.369211i	−0.497978	+	0.867190i	$0.665924\pi$
$444$	−7.50120e6	+	300063.i	−1.80582	+	0.0722363i
$445$	−2.23412e6	+	2.23412e6i	−0.534819	+	0.534819i
$446$	−3.20130e6	+	64003.7i	−0.762060	+	0.0152359i
$447$	2.03547e6			0.481833
$448$	−185652.	−	1.54041e6i	−0.0437023	−	0.362612i
$449$	558470.			0.130733			0.0653663	−	0.997861i	$-0.479178\pi$
$449$	558470.			0.130733			0.0653663	+	0.997861i	$0.479178\pi$
$450$	−1.53304e6	+	30650.2i	−0.356881	+	0.00713512i
$451$	1.96168e6	−	1.96168e6i	0.454138	−	0.454138i
$452$	−1.56520e6	+	62611.3i	−0.360350	+	0.0144147i
$453$	5.43968e6	+	5.43968e6i	1.24545	+	1.24545i
$454$	−3.50368e6	+	3.64664e6i	−0.797784	+	0.830335i
$455$		−	504951.i		−	0.114346i
$456$	−459558.	−	7.65381e6i	−0.103497	−	1.72372i
$457$		−	2.88592e6i		−	0.646388i	−0.946333	−	0.323194i	$-0.895243\pi$
$457$		−	2.88592e6i		−	0.646388i	0.946333	−	0.323194i	$-0.104757\pi$
$458$	−2.13992e6	−	2.05603e6i	−0.476687	−	0.458000i
$459$	1.35778e6	+	1.35778e6i	0.300815	+	0.300815i
$460$	−2.48014e6	+	2.68683e6i	−0.546489	+	0.592032i
$461$	−584765.	+	584765.i	−0.128153	+	0.128153i	−0.768274	−	0.640121i	$-0.778884\pi$
$461$	−584765.	+	584765.i	−0.128153	+	0.128153i	0.640121	+	0.768274i	$0.278884\pi$
$462$	56182.1	+	2.81009e6i	0.0122460	+	0.612512i
$463$	−4.42061e6			−0.958362			−0.479181	−	0.877716i	$-0.659066\pi$
$463$	−4.42061e6			−0.958362			−0.479181	+	0.877716i	$0.659066\pi$
$464$	5.36754e6	−	6.30270e6i	1.15739	−	1.35904i
$465$	3.39243e6			0.727575
$466$	−136734.	−	6.83909e6i	−0.0291684	−	1.45893i
$467$	−2.77168e6	+	2.77168e6i	−0.588100	+	0.588100i	−0.937117	−	0.349017i	$-0.886516\pi$
$467$	−2.77168e6	+	2.77168e6i	−0.588100	+	0.588100i	0.349017	+	0.937117i	$0.386516\pi$
$468$	−4.35009e6	−	4.01545e6i	−0.918087	−	0.847461i
$469$	−819555.	−	819555.i	−0.172046	−	0.172046i
$470$	1.12064e6	+	1.07671e6i	0.234003	+	0.224829i
$471$		−	2.81054e6i		−	0.583764i
$472$	−4.03043e6	−	3.57385e6i	−0.832716	−	0.738382i
$473$		−	1.63017e6i		−	0.335027i
$474$	3.76120e6	−	3.91466e6i	0.768918	−	0.800292i
$475$	719618.	+	719618.i	0.146342	+	0.146342i
$476$	−23442.8	−	586040.i	−0.00474233	−	0.118552i
$477$	−5.36072e6	+	5.36072e6i	−1.07877	+	1.07877i
$478$	4.49585e6	−	89885.6i	0.899999	−	0.0179937i
$479$	−6.54764e6			−1.30391			−0.651953	−	0.758259i	$-0.726050\pi$
$479$	−6.54764e6			−1.30391			−0.651953	+	0.758259i	$0.726050\pi$
$480$	3.74834e6	−	375906.i	0.742567	−	0.0744691i
$481$	3.84699e6			0.758156
$482$	−620365.	+	12403.0i	−0.121627	+	0.00243169i
$483$	−3.98088e6	+	3.98088e6i	−0.776446	+	0.776446i
$484$	2130.05	+	53248.4i	0.000413310	+	0.0103322i
$485$	−77801.8	−	77801.8i	−0.0150188	−	0.0150188i
$486$	2.31268e6	−	2.40704e6i	0.444145	−	0.462267i
$487$			4.90015e6i			0.936239i	0.883665	+	0.468119i	$0.155068\pi$
$487$			4.90015e6i			0.936239i	−0.883665	+	0.468119i	$0.844932\pi$
$488$	−2.35121e6	+	2.65159e6i	−0.446932	+	0.504030i
$489$		−	6.30783e6i		−	1.19291i
$490$	−1.48532e6	−	1.42709e6i	−0.279467	−	0.268511i
$491$	1.79890e6	+	1.79890e6i	0.336746	+	0.336746i	0.855141	−	0.518395i	$-0.173470\pi$
$491$	1.79890e6	+	1.79890e6i	0.336746	+	0.336746i	−0.518395	+	0.855141i	$0.673470\pi$
$492$	−4.20675e6	−	3.88314e6i	−0.783492	−	0.723220i
$493$	2.21281e6	−	2.21281e6i	0.410041	−	0.410041i
$494$	78540.6	+	3.92840e6i	0.0144803	+	0.724266i
$495$	−4.37363e6			−0.802285
$496$	−5.32456e6	+	426669.i	−0.971805	+	0.0778730i
$497$	536214.			0.0973749
$498$	−343958.	−	1.72039e7i	−0.0621487	−	3.10852i
$499$	−1.01225e6	+	1.01225e6i	−0.181986	+	0.181986i	−0.792221	−	0.610235i	$-0.791075\pi$
$499$	−1.01225e6	+	1.01225e6i	−0.181986	+	0.181986i	0.610235	+	0.792221i	$0.291075\pi$
$500$	−339139.	+	367402.i	−0.0606671	+	0.0657229i
$501$	−1.08110e6	−	1.08110e6i	−0.192430	−	0.192430i
$502$	3.33330e6	+	3.20263e6i	0.590358	+	0.567215i
$503$			2.25290e6i			0.397029i	0.980098	+	0.198515i	$0.0636117\pi$
$503$			2.25290e6i			0.397029i	−0.980098	+	0.198515i	$0.936388\pi$
$504$	3.71064e6	−	222798.i	0.650687	−	0.0390693i
$505$			2.50843e6i			0.437698i
$506$	−7.22597e6	+	7.52080e6i	−1.25464	+	1.30583i
$507$	−3.48260e6	−	3.48260e6i	−0.601705	−	0.601705i
$508$	1.11943e7	−	447797.i	1.92459	−	0.0769877i
$509$	5.75178e6	−	5.75178e6i	0.984028	−	0.984028i	−0.0158462	−	0.999874i	$-0.505044\pi$
$509$	5.75178e6	−	5.75178e6i	0.984028	−	0.984028i	0.999874	+	0.0158462i	$0.00504422\pi$
$510$	1.42374e6	−	28464.9i	0.242385	−	0.00484600i
$511$	−3.85711e6			−0.653446
$512$	−5.83590e6	+	1.06143e6i	−0.983859	+	0.178944i
$513$	8.07750e6			1.35514
$514$	−7.94467e6	+	158838.i	−1.32638	+	0.0265183i
$515$	1.16307e6	−	1.16307e6i	0.193236	−	0.193236i
$516$	−3.36137e6	+	134462.i	−0.555767	+	0.0222318i
$517$	3.13441e6	+	3.13441e6i	0.515738	+	0.515738i
$518$	−1.67360e6	+	1.74189e6i	−0.274049	+	0.285230i
$519$			691330.i			0.112659i
$520$	−1.92697e6	+	115701.i	−0.312511	+	0.0187641i
$521$		−	5.60222e6i		−	0.904204i	−0.891966	−	0.452102i	$-0.850674\pi$
$521$		−	5.60222e6i		−	0.904204i	0.891966	−	0.452102i	$-0.149326\pi$
$522$	1.43025e7	+	1.37418e7i	2.29739	+	2.20733i
$523$	5.10306e6	+	5.10306e6i	0.815786	+	0.815786i	0.985494	−	0.169708i	$-0.0542825\pi$
$523$	5.10306e6	+	5.10306e6i	0.815786	+	0.815786i	−0.169708	+	0.985494i	$0.554282\pi$
$524$	−6.39137e6	+	6.92401e6i	−1.01687	+	1.10161i
$525$	−544353.	+	544353.i	−0.0861951	+	0.0861951i
$526$	210036.	+	1.05055e7i	0.0331001	+	1.65558i
$527$	−2.01920e6			−0.316703
$528$	1.07108e7	−	858283.i	1.67201	−	0.133982i
$529$	−1.44545e7			−2.24576
$530$	49415.0	+	2.47161e6i	0.00764133	+	0.382200i
$531$	9.12579e6	−	9.12579e6i	1.40454	−	1.40454i
$532$	−1.81292e6	−	1.67346e6i	−0.277715	−	0.256351i
$533$	2.07445e6	+	2.07445e6i	0.316290	+	0.316290i
$534$	1.34106e7	+	1.28849e7i	2.03515	+	1.95537i
$535$			1.57737e6i			0.238259i
$536$	−2.93975e6	+	3.31532e6i	−0.441976	+	0.498441i
$537$			8.58749e6i			1.28508i
$538$	−4.07059e6	+	4.23668e6i	−0.606320	+	0.631059i
$539$	−4.15442e6	−	4.15442e6i	−0.615941	−	0.615941i
$540$	158623.	+	3.96536e6i	0.0234089	+	0.585192i
$541$	−1.10690e6	+	1.10690e6i	−0.162598	+	0.162598i	−0.783717	−	0.621119i	$-0.786679\pi$
$541$	−1.10690e6	+	1.10690e6i	−0.162598	+	0.162598i	0.621119	+	0.783717i	$0.286679\pi$
$542$	2.54041e6	−	50790.4i	0.371454	−	0.00742649i
$543$	−1.41537e7			−2.06001
$544$	−2.23104e6	+	223742.i	−0.323229	+	0.0324153i
$545$	4.15374e6			0.599030
$546$	−2.97163e6	+	59411.8i	−0.426592	+	0.00852887i
$547$	3.37869e6	−	3.37869e6i	0.482814	−	0.482814i	−0.423216	−	0.906029i	$-0.639099\pi$
$547$	3.37869e6	−	3.37869e6i	0.482814	−	0.482814i	0.906029	+	0.423216i	$0.139099\pi$
$548$	−437462.	−	1.09360e7i	−0.0622285	−	1.55563i
$549$	−6.00379e6	−	6.00379e6i	−0.850148	−	0.850148i
$550$	−988093.	+	1.02841e6i	−0.139281	+	0.144964i
$551$		−	1.31641e7i		−	1.84719i
$552$	1.61038e7	+	1.42795e7i	2.24947	+	1.99464i
$553$		−	1.74681e6i		−	0.242903i
$554$	1.75171e6	+	1.68304e6i	0.242487	+	0.232981i
$555$	−4.14718e6	−	4.14718e6i	−0.571506	−	0.571506i
$556$	−6.34757e6	−	5.85927e6i	−0.870804	−	0.803815i
$557$	4.48151e6	−	4.48151e6i	0.612050	−	0.612050i	−0.331430	−	0.943480i	$-0.607531\pi$
$557$	4.48151e6	−	4.48151e6i	0.612050	−	0.612050i	0.943480	+	0.331430i	$0.107531\pi$
$558$	−255815.	−	1.27952e7i	−0.0347809	−	1.73965i
$559$	1.72388e6			0.233334
$560$	785922.	−	922850.i	0.105903	−	0.124354i
$561$	4.06180e6			0.544893
$562$	−83831.6	−	4.19304e6i	−0.0111961	−	0.560000i
$563$	1.67275e6	−	1.67275e6i	0.222413	−	0.222413i	−0.587101	−	0.809514i	$-0.699731\pi$
$563$	1.67275e6	−	1.67275e6i	0.222413	−	0.222413i	0.809514	+	0.587101i	$0.199731\pi$
$564$	6.20455e6	−	6.72162e6i	0.821320	−	0.889767i
$565$	−865352.	−	865352.i	−0.114044	−	0.114044i
$566$	2.45568e6	+	2.35941e6i	0.322203	+	0.309572i
$567$			1.12008e6i			0.146316i
$568$	−122864.	−	2.04627e6i	−0.0159792	−	0.266129i
$569$		−	1.59258e6i		−	0.206215i	−0.994670	−	0.103107i	$-0.967121\pi$
$569$		−	1.59258e6i		−	0.206215i	0.994670	−	0.103107i	$-0.0328785\pi$
$570$	4.15027e6	−	4.31961e6i	0.535044	−	0.556875i
$571$	6.70109e6	+	6.70109e6i	0.860113	+	0.860113i	0.991351	−	0.131238i	$-0.0418952\pi$
$571$	6.70109e6	+	6.70109e6i	0.860113	+	0.860113i	−0.131238	+	0.991351i	$0.541895\pi$
$572$	−5.50185e6	+	220085.i	−0.703103	+	0.0281255i
$573$	−1.04867e7	+	1.04867e7i	−1.33429	+	1.33429i
$574$	−1.84177e6	+	36822.5i	−0.233322	+	0.00466481i
$575$	−2.85666e6			−0.360320
$576$	−1.70046e6	−	1.41093e7i	−0.213555	−	1.77194i
$577$	−1.11744e7			−1.39728			−0.698642	−	0.715472i	$-0.746212\pi$
$577$	−1.11744e7			−1.39728			−0.698642	+	0.715472i	$0.746212\pi$
$578$	7.18290e6	−	143608.i	0.894294	−	0.0178796i
$579$	7.44678e6	−	7.44678e6i	0.923149	−	0.923149i
$580$	6.46245e6	−	258511.i	0.797677	−	0.0319087i
$581$	−3.91512e6	−	3.91512e6i	−0.481177	−	0.481177i
$582$	−448708.	+	467016.i	−0.0549106	+	0.0571511i
$583$			7.05127e6i			0.859204i
$584$	883791.	+	1.47193e7i	0.107230	+	1.78589i
$585$		−	4.62505e6i		−	0.558762i
$586$	9.74850e6	+	9.36633e6i	1.17272	+	1.12674i
$587$	5.65681e6	+	5.65681e6i	0.677604	+	0.677604i	0.959457	−	0.281853i	$-0.0909492\pi$
$587$	5.65681e6	+	5.65681e6i	0.677604	+	0.677604i	−0.281853	+	0.959457i	$0.590949\pi$
$588$	−8.22366e6	+	8.90900e6i	−0.980894	+	1.06264i
$589$	−6.00614e6	+	6.00614e6i	−0.713357	+	0.713357i
$590$	−84121.4	−	4.20754e6i	−0.00994893	−	0.497620i
$591$	−6.08497e6			−0.716621
$592$	7.03077e6	+	5.98758e6i	0.824515	+	0.702178i
$593$	4.90260e6			0.572518			0.286259	−	0.958152i	$-0.407588\pi$
$593$	4.90260e6			0.572518			0.286259	+	0.958152i	$0.407588\pi$
$594$	226268.	+	1.13173e7i	0.0263121	+	1.31607i
$595$	324003.	−	324003.i	0.0375195	−	0.0375195i
$596$	−1.83988e6	−	1.69835e6i	−0.212166	−	0.195844i
$597$	−2.94939e6	−	2.94939e6i	−0.338685	−	0.338685i
$598$	−7.95314e6	−	7.64136e6i	−0.909465	−	0.873812i
$599$		−	1.22461e7i		−	1.39454i	−0.716811	−	0.697268i	$-0.754399\pi$
$599$		−	1.22461e7i		−	1.39454i	0.716811	−	0.697268i	$-0.245601\pi$
$600$	2.20206e6	+	1.95260e6i	0.249719	+	0.221429i
$601$			8.55036e6i			0.965602i	0.875730	+	0.482801i	$0.160380\pi$
$601$			8.55036e6i			0.965602i	−0.875730	+	0.482801i	$0.839620\pi$
$602$	−749960.	+	780560.i	−0.0843426	+	0.0877840i
$603$	−7.50663e6	−	7.50663e6i	−0.840721	−	0.840721i
$604$	−378248.	−	9.45571e6i	−0.0421875	−	1.05463i
$605$	−29439.4	+	29439.4i	−0.00326995	+	0.00326995i
$606$	1.47621e7	−	295139.i	1.63293	−	0.0326471i
$607$	1.28126e7			1.41145			0.705727	−	0.708483i	$-0.250620\pi$
$607$	1.28126e7			1.41145			0.705727	+	0.708483i	$0.250620\pi$
$608$	−5.97075e6	+	7.30180e6i	−0.655043	+	0.801070i
$609$	9.95796e6			1.08800
$610$	−2.76810e6	+	55342.8i	−0.301202	+	0.00602194i
$611$	−3.31460e6	+	3.31460e6i	−0.359193	+	0.359193i
$612$	−214722.	−	5.36778e6i	−0.0231738	−	0.579316i
$613$	−3.54523e6	−	3.54523e6i	−0.381060	−	0.381060i	0.490424	−	0.871484i	$-0.336842\pi$
$613$	−3.54523e6	−	3.54523e6i	−0.381060	−	0.381060i	−0.871484	+	0.490424i	$0.836842\pi$
$614$	5.62362e6	−	5.85308e6i	0.601998	−	0.626561i
$615$		−	4.47265e6i		−	0.476845i
$616$	2.29388e6	−	2.58694e6i	0.243567	−	0.274685i
$617$			1.00790e7i			1.06587i	0.846157	+	0.532934i	$0.178911\pi$
$617$			1.00790e7i			1.06587i	−0.846157	+	0.532934i	$0.821089\pi$
$618$	−6.98148e6	−	6.70779e6i	−0.735320	−	0.706494i
$619$	−1.66361e6	−	1.66361e6i	−0.174511	−	0.174511i	0.614447	−	0.788958i	$-0.289379\pi$
$619$	−1.66361e6	−	1.66361e6i	−0.174511	−	0.174511i	−0.788958	+	0.614447i	$0.789379\pi$
$620$	−3.06645e6	−	2.83055e6i	−0.320373	−	0.295728i
$621$	−1.60326e7	+	1.60326e7i	−1.66830	+	1.66830i
$622$	128308.	+	6.41765e6i	0.0132978	+	0.665120i
$623$	5.98413e6			0.617704
$624$	907622.	+	1.13265e7i	0.0933133	+	1.16449i
$625$	−390625.			−0.0400000
$626$	−218377.	−	1.09227e7i	−0.0222726	−	1.11402i
$627$	1.20819e7	−	1.20819e7i	1.22734	−	1.22734i
$628$	−2.34504e6	+	2.54047e6i	−0.237275	+	0.257049i
$629$	2.46843e6	+	2.46843e6i	0.248768	+	0.248768i
$630$	2.09419e6	+	2.01209e6i	0.210215	+	0.201974i
$631$		−	2.86871e6i		−	0.286823i	−0.989663	−	0.143411i	$-0.954193\pi$
$631$		−	2.86871e6i		−	0.286823i	0.989663	−	0.143411i	$-0.0458072\pi$
$632$	−6.66608e6	+	400252.i	−0.663862	+	0.0398603i
$633$			2.98428e7i			2.96027i
$634$	5.63148e6	−	5.86126e6i	0.556416	−	0.579119i
$635$	6.18901e6	+	6.18901e6i	0.609097	+	0.609097i
$636$	1.45396e7	−	581613.i	1.42531	−	0.0570152i
$637$	4.39325e6	−	4.39325e6i	0.428980	−	0.428980i
$638$	1.84441e7	−	368754.i	1.79393	−	0.0358662i
$639$	4.91140e6			0.475831
$640$	−3.70181e6	−	2.78773e6i	−0.357243	−	0.269030i
$641$	1.14965e7			1.10515			0.552574	−	0.833464i	$-0.313646\pi$
$641$	1.14965e7			1.10515			0.552574	+	0.833464i	$0.313646\pi$
$642$	9.28282e6	−	185592.i	0.888878	−	0.0177714i
$643$	−5.39178e6	+	5.39178e6i	−0.514286	+	0.514286i	−0.915837	−	0.401551i	$-0.868471\pi$
$643$	−5.39178e6	+	5.39178e6i	−0.514286	+	0.514286i	0.401551	+	0.915837i	$0.368471\pi$
$644$	6.91990e6	−	276810.i	0.657484	−	0.0263007i
$645$	−1.85840e6	−	1.85840e6i	−0.175889	−	0.175889i
$646$	−2.47027e6	+	2.57107e6i	−0.232897	+	0.242400i
$647$			7.41931e6i			0.696792i	0.937348	+	0.348396i	$0.113273\pi$
$647$			7.41931e6i			0.696792i	−0.937348	+	0.348396i	$0.886727\pi$
$648$	4.27440e6	−	256648.i	0.399887	−	0.0240105i
$649$		−	1.20037e7i		−	1.11867i
$650$	−1.08753e6	−	1.04490e6i	−0.100962	−	0.0970039i
$651$	−4.54333e6	−	4.54333e6i	−0.420167	−	0.420167i
$652$	−5.26309e6	+	5.70171e6i	−0.484867	+	0.525274i
$653$	9.78315e6	−	9.78315e6i	0.897834	−	0.897834i	−0.0974106	−	0.995244i	$-0.531056\pi$
$653$	9.78315e6	−	9.78315e6i	0.897834	−	0.897834i	0.995244	+	0.0974106i	$0.0310560\pi$
$654$	−488724.	−	2.44447e7i	−0.0446806	−	2.23481i
$655$	−7.36166e6			−0.670460
$656$	562530.	+	7.02002e6i	0.0510371	+	0.636911i
$657$	−3.53288e7			−3.19312
$658$	−58835.7	−	2.94281e6i	−0.00529756	−	0.264971i
$659$	1.35446e7	−	1.35446e7i	1.21493	−	1.21493i	0.245546	−	0.969385i	$-0.421033\pi$
$659$	1.35446e7	−	1.35446e7i	1.21493	−	1.21493i	0.969385	−	0.245546i	$-0.0789672\pi$
$660$	6.16843e6	+	5.69391e6i	0.551207	+	0.508804i
$661$	1.81393e6	+	1.81393e6i	0.161479	+	0.161479i	0.783222	−	0.621743i	$-0.213575\pi$
$661$	1.81393e6	+	1.81393e6i	0.161479	+	0.161479i	−0.621743	+	0.783222i	$0.713575\pi$
$662$	−1.30471e7	−	1.25356e7i	−1.15709	−	1.11173i
$663$			4.29529e6i			0.379498i
$664$	−1.40436e7	+	1.58377e7i	−1.23611	+	1.39403i
$665$		−	1.92751e6i		−	0.169021i
$666$	−1.53292e7	+	1.59547e7i	−1.33916	+	1.39380i
$667$	2.61287e7	+	2.61287e7i	2.27407	+	2.27407i
$668$	75174.4	+	1.87926e6i	0.00651821	+	0.162947i
$669$	−1.04117e7	+	1.04117e7i	−0.899404	+	0.899404i
$670$	−3.46101e6	+	69196.0i	−0.297862	+	0.00595516i
$671$	−7.89714e6			−0.677117
$672$	−5.52342e6	−	4.51656e6i	−0.471830	−	0.385819i
$673$	−4.08750e6			−0.347873			−0.173936	−	0.984757i	$-0.555649\pi$
$673$	−4.08750e6			−0.347873			−0.173936	+	0.984757i	$0.555649\pi$
$674$	1.63202e7	−	326291.i	1.38381	−	0.0276665i
$675$	−2.19233e6	+	2.19233e6i	−0.185202	+	0.185202i
$676$	242162.	+	6.05375e6i	0.0203817	+	0.509516i
$677$	−1.24789e7	−	1.24789e7i	−1.04641	−	1.04641i	−0.998869	−	0.0475455i	$-0.984860\pi$
$677$	−1.24789e7	−	1.24789e7i	−1.04641	−	1.04641i	−0.0475455	−	0.998869i	$-0.515140\pi$
$678$	−4.99076e6	+	5.19440e6i	−0.416958	+	0.433971i
$679$			208393.i			0.0173464i
$680$	−1.31068e6	−	1.16220e6i	−0.108699	−	0.0963851i
$681$			2.32552e7i			1.92155i
$682$	−8.58340e6	−	8.24691e6i	−0.706640	−	0.678938i
$683$	−4.56348e6	−	4.56348e6i	−0.374322	−	0.374322i	0.494727	−	0.869048i	$-0.335268\pi$
$683$	−4.56348e6	−	4.56348e6i	−0.374322	−	0.374322i	−0.869048	+	0.494727i	$0.835268\pi$
$684$	−1.66052e7	−	1.53279e7i	−1.35708	−	1.25268i
$685$	6.04617e6	−	6.04617e6i	0.492327	−	0.492327i
$686$	167968.	+	8.40135e6i	0.0136275	+	0.681615i
$687$	−1.36466e7			−1.10314
$688$	3.15057e6	+	2.68310e6i	0.253757	+	0.216106i
$689$	−7.45662e6			−0.598404
$690$	336110.	+	1.68114e7i	0.0268757	+	1.34425i
$691$	−1.61581e6	+	1.61581e6i	−0.128735	+	0.128735i	−0.768538	−	0.639804i	$-0.779016\pi$
$691$	−1.61581e6	+	1.61581e6i	−0.128735	+	0.128735i	0.639804	+	0.768538i	$0.279016\pi$
$692$	576828.	−	624899.i	0.0457911	−	0.0496072i
$693$	5.85741e6	+	5.85741e6i	0.463311	+	0.463311i
$694$	1.31429e7	+	1.26277e7i	1.03584	+	0.995232i
$695$		−	6.74878e6i		−	0.529985i
$696$	−2.28170e6	−	3.80010e7i	−0.178540	−	2.97353i
$697$			2.66216e6i			0.207564i
$698$	2.26379e6	−	2.35616e6i	0.175872	−	0.183048i
$699$	−2.22429e7	−	2.22429e7i	−1.72187	−	1.72187i
$700$	946241.	−	37851.6i	0.0729889	−	0.00291970i
$701$	−6.34810e6	+	6.34810e6i	−0.487920	+	0.487920i	−0.907649	−	0.419729i	$-0.862125\pi$
$701$	−6.34810e6	+	6.34810e6i	−0.487920	+	0.487920i	0.419729	+	0.907649i	$0.362125\pi$
$702$	−1.19679e7	+	239275.i	−0.916591	+	0.0183254i
$703$	1.46848e7			1.12068
$704$	−1.03977e7	−	8.16103e6i	−0.790692	−	0.620602i
$705$	7.14648e6			0.541526
$706$	−1.47421e7	+	294739.i	−1.11313	+	0.0222549i
$707$	3.35944e6	−	3.35944e6i	0.252766	−	0.252766i
$708$	−2.47514e7	+	990106.i	−1.85574	+	0.0742332i
$709$	−3.83290e6	−	3.83290e6i	−0.286360	−	0.286360i	0.549279	−	0.835639i	$-0.314902\pi$
$709$	−3.83290e6	−	3.83290e6i	−0.286360	−	0.286360i	−0.835639	+	0.549279i	$0.814902\pi$
$710$	1.10959e6	−	1.15486e6i	0.0826068	−	0.0859773i
$711$		−	1.59997e7i		−	1.18697i
$712$	−1.37116e6	−	2.28363e7i	−0.101365	−	1.68821i
$713$		−	2.38425e7i		−	1.75642i
$714$	−1.94488e6	−	1.86863e6i	−0.142773	−	0.137176i
$715$	−3.04180e6	−	3.04180e6i	−0.222518	−	0.222518i
$716$	7.16519e6	−	7.76232e6i	0.522330	−	0.565860i
$717$	1.46220e7	−	1.46220e7i	1.06220	−	1.06220i
$718$	307117.	+	1.53612e7i	0.0222327	+	1.11202i
$719$	1.87300e7			1.35119			0.675595	−	0.737273i	$-0.263887\pi$
$719$	1.87300e7			1.35119			0.675595	+	0.737273i	$0.263887\pi$
$720$	7.19857e6	−	8.45275e6i	0.517506	−	0.607669i
$721$	−3.11529e6			−0.223183
$722$	19821.5	+	991420.i	0.00141512	+	0.0707807i
$723$	−2.01763e6	+	2.01763e6i	−0.143547	+	0.143547i
$724$	1.27936e7	+	1.18095e7i	0.907084	+	0.837305i
$725$	3.57289e6	+	3.57289e6i	0.252449	+	0.252449i
$726$	176714.	+	169787.i	0.0124431	+	0.0119553i
$727$		−	7.77537e6i		−	0.545614i	−0.962069	−	0.272807i	$-0.912048\pi$
$727$		−	7.77537e6i		−	0.545614i	0.962069	−	0.272807i	$-0.0879520\pi$
$728$	2.73566e6	+	2.42575e6i	0.191308	+	0.169636i
$729$		−	2.10983e7i		−	1.47038i
$730$	−7.98152e6	+	8.30718e6i	−0.554343	+	0.576961i
$731$	1.10613e6	+	1.10613e6i	0.0765622	+	0.0765622i
$732$	651383.	+	1.62837e7i	0.0449323	+	1.12325i
$733$	6.12002e6	−	6.12002e6i	0.420719	−	0.420719i	−0.464732	−	0.885451i	$-0.653849\pi$
$733$	6.12002e6	−	6.12002e6i	0.420719	−	0.420719i	0.885451	+	0.464732i	$0.153849\pi$
$734$	−7.91507e6	+	158246.i	−0.542269	+	0.0108416i
$735$	−9.47212e6			−0.646739
$736$	−2.64192e6	−	2.63439e7i	−0.179774	−	1.79261i
$737$	−9.87392e6			−0.669608
$738$	−1.68695e7	+	337272.i	−1.14015	+	0.0227950i
$739$	−1.20529e7	+	1.20529e7i	−0.811860	+	0.811860i	−0.984913	−	0.173052i	$-0.944637\pi$
$739$	−1.20529e7	+	1.20529e7i	−0.811860	+	0.811860i	0.173052	+	0.984913i	$0.444637\pi$
$740$	288374.	+	7.20898e6i	0.0193587	+	0.483943i
$741$	1.27764e7	+	1.27764e7i	0.854799	+	0.854799i
$742$	3.24394e6	−	3.37630e6i	0.216303	−	0.225129i
$743$		−	9.16016e6i		−	0.608739i	−0.952554	−	0.304369i	$-0.901554\pi$
$743$		−	9.16016e6i		−	0.608739i	0.952554	−	0.304369i	$-0.0984457\pi$
$744$	−1.62970e7	+	1.83790e7i	−1.07938	+	1.21728i
$745$		−	1.95618e6i		−	0.129127i
$746$	−1.04456e7	−	1.00361e7i	−0.687206	−	0.660266i
$747$	−3.58602e7	−	3.58602e7i	−2.35132	−	2.35132i
$748$	−3.67150e6	−	3.38906e6i	−0.239933	−	0.221475i
$749$	2.11251e6	−	2.11251e6i	0.137592	−	0.137592i
$750$	45960.4	+	2.29882e6i	0.00298353	+	0.149229i
$751$	2.06289e7			1.33468			0.667338	−	0.744755i	$-0.267434\pi$
$751$	2.06289e7			1.33468			0.667338	+	0.744755i	$0.267434\pi$
$752$	−1.12167e7	+	898821.i	−0.723304	+	0.0579600i
$753$	2.12570e7			1.36620
$754$	389952.	+	1.95044e7i	0.0249795	+	1.24941i
$755$	5.22777e6	−	5.22777e6i	0.333771	−	0.333771i
$756$	5.09820e6	−	5.52307e6i	0.324424	−	0.351460i
$757$	4.39846e6	+	4.39846e6i	0.278972	+	0.278972i	0.832699	−	0.553726i	$-0.186795\pi$
$757$	4.39846e6	+	4.39846e6i	0.278972	+	0.278972i	−0.553726	+	0.832699i	$0.686795\pi$
$758$	1.52296e6	+	1.46326e6i	0.0962757	+	0.0925015i
$759$			4.79613e7i			3.02194i
$760$	−7.35564e6	+	441656.i	−0.461941	+	0.0277364i
$761$			9.17319e6i			0.574194i	0.957901	+	0.287097i	$0.0926903\pi$
$761$			9.17319e6i			0.574194i	−0.957901	+	0.287097i	$0.907310\pi$
$762$	3.56940e7	−	3.71504e7i	2.22694	−	2.31780i
$763$	−5.56293e6	−	5.56293e6i	−0.345933	−	0.345933i
$764$	1.82288e7	−	729189.i	1.12986	−	0.0451967i
$765$	2.96768e6	−	2.96768e6i	0.183342	−	0.183342i
$766$	2.22862e7	−	445568.i	1.37235	−	0.0274374i
$767$	1.26938e7			0.779115
$768$	−1.59702e7	+	2.21131e7i	−0.977030	+	1.35284i
$769$	−2.16378e7			−1.31946			−0.659731	−	0.751502i	$-0.729330\pi$
$769$	−2.16378e7			−1.31946			−0.659731	+	0.751502i	$0.729330\pi$
$770$	2.70062e6	−	53993.5i	0.164148	−	0.00328182i
$771$	−2.58386e7	+	2.58386e7i	−1.56543	+	1.56543i
$772$	−1.29446e7	+	517811.i	−0.781710	+	0.0312700i
$773$	7.61565e6	+	7.61565e6i	0.458415	+	0.458415i	0.898135	−	0.439720i	$-0.144922\pi$
$773$	7.61565e6	+	7.61565e6i	0.458415	+	0.458415i	−0.439720	+	0.898135i	$0.644922\pi$
$774$	−6.86919e6	+	7.14946e6i	−0.412148	+	0.428964i
$775$		−	3.26027e6i		−	0.194984i
$776$	795258.	−	47749.8i	0.0474082	−	0.00284654i
$777$			1.11083e7i			0.660077i
$778$	8.55792e6	+	8.22243e6i	0.506896	+	0.487025i
$779$	7.91863e6	+	7.91863e6i	0.467527	+	0.467527i
$780$	−6.02123e6	+	6.52303e6i	−0.354363	+	0.383895i
$781$	3.23013e6	−	3.23013e6i	0.189493	−	0.189493i
$782$	−200055.	−	1.00063e7i	−0.0116986	−	0.585133i
$783$	4.01046e7			2.33771
$784$	1.48669e7	−	1.19132e6i	0.863834	−	0.0692210i
$785$	−2.70105e6			−0.156444
$786$	866163.	+	4.33232e7i	0.0500084	+	2.50129i
$787$	−2.48752e6	+	2.48752e6i	−0.143163	+	0.143163i	−0.775056	−	0.631893i	$-0.782278\pi$
$787$	−2.48752e6	+	2.48752e6i	−0.143163	+	0.143163i	0.631893	+	0.775056i	$0.282278\pi$
$788$	5.50026e6	+	5.07714e6i	0.315550	+	0.291275i
$789$	3.41671e7	+	3.41671e7i	1.95396	+	1.95396i
$790$	−3.76216e6	−	3.61467e6i	−0.214471	−	0.206064i
$791$			2.31786e6i			0.131718i
$792$	2.10106e7	−	2.36948e7i	1.19021	−	1.34227i
$793$		−	8.35112e6i		−	0.471587i
$794$	5.44381e6	−	5.66593e6i	0.306444	−	0.318948i
$795$	8.03848e6	+	8.03848e6i	0.451083	+	0.451083i
$796$	205086.	+	5.12688e6i	0.0114723	+	0.286794i
$797$	2.03100e7	−	2.03100e7i	1.13257	−	1.13257i	0.142821	−	0.989749i	$-0.454383\pi$
$797$	2.03100e7	−	2.03100e7i	1.13257	−	1.13257i	0.989749	−	0.142821i	$-0.0456173\pi$
$798$	−1.13433e7	+	226788.i	−0.630571	+	0.0126070i
$799$	−4.25364e6			−0.235719
$800$	−361262.	−	3.60232e6i	−0.0199571	−	0.199002i
$801$	5.48110e7			3.01847
$802$	3.31394e7	−	662556.i	1.81932	−	0.0363737i
$803$	−2.32351e7	+	2.32351e7i	−1.27161	+	1.27161i
$804$	814434.	+	2.03598e7i	0.0444340	+	1.11079i
$805$	3.82580e6	+	3.82580e6i	0.208081	+	0.208081i
$806$	8.72099e6	−	9.07683e6i	0.472855	−	0.492149i
$807$			2.70179e7i			1.46039i
$808$	−1.35899e7	−	1.20503e7i	−0.732295	−	0.649338i
$809$			2.47749e7i			1.33088i	0.746450	+	0.665441i	$0.231757\pi$
$809$			2.47749e7i			1.33088i	−0.746450	+	0.665441i	$0.768243\pi$
$810$	2.41236e6	+	2.31779e6i	0.129190	+	0.124126i
$811$	9.46172e6	+	9.46172e6i	0.505147	+	0.505147i	0.913033	−	0.407886i	$-0.133734\pi$
$811$	9.46172e6	+	9.46172e6i	0.505147	+	0.505147i	−0.407886	+	0.913033i	$0.633734\pi$
$812$	−9.00109e6	−	8.30867e6i	−0.479077	−	0.442223i
$813$	8.26222e6	−	8.26222e6i	0.438400	−	0.438400i
$814$	411352.	+	2.05748e7i	0.0217597	+	1.08836i
$815$	−6.06210e6			−0.319690
$816$	−6.68533e6	+	7.85009e6i	−0.351478	+	0.412714i
$817$	6.58043e6			0.344905
$818$	−502890.	−	2.51533e7i	−0.0262778	−	1.31435i
$819$	−6.19413e6	+	6.19413e6i	−0.322679	+	0.322679i
$820$	−3.73187e6	+	4.04287e6i	−0.193817	+	0.209969i
$821$	−2.02371e6	−	2.02371e6i	−0.104783	−	0.104783i	0.652772	−	0.757555i	$-0.273606\pi$
$821$	−2.02371e6	−	2.02371e6i	−0.104783	−	0.104783i	−0.757555	+	0.652772i	$0.773606\pi$
$822$	−3.62930e7	−	3.48702e7i	−1.87346	−	1.80001i
$823$			1.29010e7i			0.663934i	0.943291	+	0.331967i	$0.107712\pi$
$823$			1.29010e7i			0.663934i	−0.943291	+	0.331967i	$0.892288\pi$
$824$	713817.	+	1.18884e7i	0.0366242	+	0.609966i
$825$			6.55832e6i			0.335473i
$826$	−5.52231e6	+	5.74763e6i	−0.281625	+	0.293116i
$827$	2.50991e6	+	2.50991e6i	0.127613	+	0.127613i	0.768029	−	0.640416i	$-0.221238\pi$
$827$	2.50991e6	+	2.50991e6i	0.127613	+	0.127613i	−0.640416	+	0.768029i	$0.721238\pi$
$828$	6.33821e7	−	2.53542e6i	3.21285	−	0.128521i
$829$	−6.30737e6	+	6.30737e6i	−0.318759	+	0.318759i	−0.848290	−	0.529532i	$-0.822368\pi$
$829$	−6.30737e6	+	6.30737e6i	−0.318759	+	0.318759i	0.529532	+	0.848290i	$0.322368\pi$
$830$	−1.65337e7	+	330558.i	−0.833056	+	0.0166553i
$831$	1.11709e7			0.561160
$832$	8.63017e6	−	1.09955e7i	0.432226	−	0.550688i
$833$	5.63788e6			0.281516
$834$	−3.97165e7	+	794052.i	−1.97722	+	0.0395306i
$835$	−1.03899e6	+	1.03899e6i	−0.0515696	+	0.0515696i
$836$	−2.10018e7	+	840113.i	−1.03930	+	0.0415740i
$837$	−1.82978e7	−	1.82978e7i	−0.902786	−	0.902786i
$838$	8.07374e6	−	8.40317e6i	0.397160	−	0.413364i
$839$			528877.i			0.0259388i	0.999916	+	0.0129694i	$0.00412840\pi$
$839$			528877.i			0.0259388i	−0.999916	+	0.0129694i	$0.995872\pi$
$840$	−334089.	−	5.56416e6i	−0.0163367	−	0.272083i
$841$		−	4.48484e7i		−	2.18654i
$842$	1.72225e7	+	1.65473e7i	0.837173	+	0.804353i
$843$	−1.36371e7	−	1.36371e7i	−0.660928	−	0.660928i
$844$	2.49001e7	−	2.69752e7i	1.20322	−	1.30349i
$845$	−3.34693e6	+	3.34693e6i	−0.161252	+	0.161252i
$846$	−538900.	−	2.69544e7i	−0.0258870	−	1.29480i
$847$	78853.8			0.00377672
$848$	−1.36277e7	−	1.16057e7i	−0.650780	−	0.554221i
$849$	1.56602e7			0.745639
$850$	−27356.0	−	1.36828e6i	−0.00129869	−	0.0649571i
$851$	−2.91470e7	+	2.91470e7i	−1.37965	+	1.37965i
$852$	−6.92689e6	−	6.39403e6i	−0.326918	−	0.301770i
$853$	−2.76340e7	−	2.76340e7i	−1.30038	−	1.30038i	−0.928131	−	0.372254i	$-0.878585\pi$
$853$	−2.76340e7	−	2.76340e7i	−1.30038	−	1.30038i	−0.372254	−	0.928131i	$-0.621415\pi$
$854$	3.78132e6	+	3.63309e6i	0.177419	+	0.170463i
$855$		−	1.76548e7i		−	0.825939i
$856$	−8.54568e6	−	7.57759e6i	−0.398623	−	0.353465i
$857$			3.21684e7i			1.49616i	0.663609	+	0.748080i	$0.269024\pi$
$857$			3.21684e7i			1.49616i	−0.663609	+	0.748080i	$0.730976\pi$
$858$	−1.75431e7	+	1.82588e7i	−0.813555	+	0.846750i
$859$	899170.	+	899170.i	0.0415775	+	0.0415775i	0.727590	−	0.686012i	$-0.240640\pi$
$859$	899170.	+	899170.i	0.0415775	+	0.0415775i	−0.686012	+	0.727590i	$0.740640\pi$
$860$	129224.	+	3.23043e6i	0.00595794	+	0.148941i
$861$	−5.99003e6	+	5.99003e6i	−0.275373	+	0.275373i
$862$	−3.11954e7	+	623690.i	−1.42995	+	0.0285891i
$863$	2.94343e6			0.134532			0.0672662	−	0.997735i	$-0.478572\pi$
$863$	2.94343e6			0.134532			0.0672662	+	0.997735i	$0.478572\pi$
$864$	−2.22450e7	−	1.81899e7i	−1.01379	−	0.828986i
$865$	664398.			0.0301917
$866$	4.99276e6	−	99820.3i	0.226228	−	0.00452297i
$867$	2.33611e7	−	2.33611e7i	1.05547	−	1.05547i
$868$	315920.	+	7.89760e6i	0.0142324	+	0.355792i
$869$	−1.05227e7	−	1.05227e7i	−0.472692	−	0.472692i
$870$	2.06060e7	−	2.14468e7i	0.922987	−	0.960647i
$871$		−	1.04415e7i		−	0.466358i
$872$	−1.99543e7	+	2.25036e7i	−0.888679	+	1.00221i
$873$			1.90876e6i			0.0847647i
$874$	−3.03589e7	−	2.91687e7i	−1.34433	−	1.29163i
$875$	523147.	+	523147.i	0.0230996	+	0.0230996i
$876$	4.98267e7	+	4.59937e7i	2.19382	+	2.02506i
$877$	1.13761e7	−	1.13761e7i	0.499452	−	0.499452i	−0.411816	−	0.911267i	$-0.635105\pi$
$877$	1.13761e7	−	1.13761e7i	0.499452	−	0.499452i	0.911267	+	0.411816i	$0.135105\pi$
$878$	273270.	+	1.36682e7i	0.0119634	+	0.598379i
$879$	6.21676e7			2.71389
$880$	−824847.	−	1.02936e7i	−0.0359060	−	0.448084i
$881$	−3.09976e7			−1.34551			−0.672757	−	0.739864i	$-0.734890\pi$
$881$	−3.09976e7			−1.34551			−0.672757	+	0.739864i	$0.734890\pi$
$882$	714271.	+	3.57260e7i	0.0309166	+	1.54637i
$883$	2.13403e7	−	2.13403e7i	0.921083	−	0.921083i	−0.0760235	−	0.997106i	$-0.524222\pi$
$883$	2.13403e7	−	2.13403e7i	0.921083	−	0.921083i	0.997106	+	0.0760235i	$0.0242224\pi$
$884$	3.58388e6	−	3.88256e6i	0.154249	−	0.167104i
$885$	−1.36843e7	−	1.36843e7i	−0.587305	−	0.587305i
$886$	−8.79771e6	−	8.45282e6i	−0.376518	−	0.361757i
$887$		−	3.98395e6i		−	0.170022i	−0.996380	−	0.0850109i	$-0.972907\pi$
$887$		−	3.98395e6i		−	0.170022i	0.996380	−	0.0850109i	$-0.0270925\pi$
$888$	4.23908e7	−	2.54527e6i	1.80401	−	0.108318i
$889$		−	1.65773e7i		−	0.703494i
$890$	1.23830e7	−	1.28882e7i	0.524022	−	0.545403i
$891$	6.74734e6	+	6.74734e6i	0.284733	+	0.284733i
$892$	1.80984e7	−	723974.i	0.761603	−	0.0304657i
$893$	−1.26525e7	+	1.26525e7i	−0.530944	+	0.530944i
$894$	−1.15121e7	+	230161.i	−0.481737	+	0.00963138i
$895$	8.25295e6			0.344391
$896$	1.22418e6	+	8.69116e6i	0.0509418	+	0.361666i
$897$	−5.07184e7			−2.10467
$898$	−3.15855e6	+	63149.0i	−0.130706	+	0.00261322i
$899$	−2.98203e7	+	2.98203e7i	−1.23059	+	1.23059i
$900$	8.66700e6	−	346698.i	0.356667	−	0.0142674i
$901$	−4.78456e6	−	4.78456e6i	−0.196350	−	0.196350i
$902$	−1.08729e7	+	1.13166e7i	−0.444969	+	0.463125i
$903$			4.97775e6i			0.203148i
$904$	8.84527e6	−	531097.i	0.359990	−	0.0216149i
$905$			1.36023e7i			0.552066i
$906$	−3.13804e7	−	3.01502e7i	−1.27010	−	1.22031i
$907$	−6.34452e6	−	6.34452e6i	−0.256083	−	0.256083i	0.567376	−	0.823459i	$-0.307959\pi$
$907$	−6.34452e6	−	6.34452e6i	−0.256083	−	0.256083i	−0.823459	+	0.567376i	$0.807959\pi$
$908$	1.94035e7	−	2.10206e7i	0.781027	−	0.846116i
$909$	3.07704e7	−	3.07704e7i	1.23516	−	1.23516i
$910$	57097.4	+	2.85586e6i	0.00228566	+	0.114323i
$911$	−4.56394e7			−1.82198			−0.910991	−	0.412426i	$-0.864682\pi$
$911$	−4.56394e7			−1.82198			−0.910991	+	0.412426i	$0.864682\pi$
$912$	3.46459e6	+	4.32359e7i	0.137932	+	1.72130i
$913$	−4.71690e7			−1.87275
$914$	326325.	+	1.63219e7i	0.0129207	+	0.646259i
$915$	−9.00277e6	+	9.00277e6i	−0.355487	+	0.355487i
$916$	1.23353e7	+	1.13864e7i	0.485747	+	0.448380i
$917$	9.85916e6	+	9.85916e6i	0.387183	+	0.387183i
$918$	−7.83278e6	−	7.52572e6i	−0.306767	−	0.294741i
$919$			2.34699e7i			0.916690i	0.888774	+	0.458345i	$0.151558\pi$
$919$			2.34699e7i			0.916690i	−0.888774	+	0.458345i	$0.848442\pi$
$920$	1.37232e7	−	1.54764e7i	0.534546	−	0.602838i
$921$		−	3.73260e7i		−	1.44998i
$922$	3.24114e6	−	3.37339e6i	0.125566	−	0.130689i
$923$	3.41582e6	+	3.41582e6i	0.131975	+	0.131975i
$924$	−635501.	−	1.58867e7i	−0.0244871	−	0.612145i
$925$	−3.98562e6	+	3.98562e6i	−0.153159	+	0.153159i
$926$	2.50017e7	−	499860.i	0.958170	−	0.0191567i
$927$	−2.85342e7			−1.09060
$928$	−2.96446e7	+	3.62533e7i	−1.12999	+	1.38190i
$929$	−1.79820e6			−0.0683593			−0.0341797	−	0.999416i	$-0.510882\pi$
$929$	−1.79820e6			−0.0683593			−0.0341797	+	0.999416i	$0.510882\pi$
$930$	−1.91866e7	+	383599.i	−0.727430	+	0.0145435i
$931$	1.67700e7	−	1.67700e7i	0.634100	−	0.634100i
$932$	1.54666e6	+	3.86645e7i	0.0583251	+	1.45805i
$933$	2.08723e7	+	2.08723e7i	0.784993	+	0.784993i
$934$	1.53625e7	−	1.59893e7i	0.576227	−	0.599738i
$935$		−	3.90356e6i		−	0.146027i
$936$	2.50570e7	+	2.22184e7i	0.934843	+	0.828940i
$937$			1.38562e7i			0.515579i	0.966201	+	0.257789i	$0.0829941\pi$
$937$			1.38562e7i			0.515579i	−0.966201	+	0.257789i	$0.917006\pi$
$938$	4.72785e6	+	4.54250e6i	0.175451	+	0.168573i
$939$	−3.55240e7	−	3.55240e7i	−1.31479	−	1.31479i
$940$	−6.45977e6	−	5.96284e6i	−0.238450	−	0.220107i
$941$	−1.37897e7	+	1.37897e7i	−0.507671	+	0.507671i	−0.913811	−	0.406140i	$-0.866875\pi$
$941$	−1.37897e7	+	1.37897e7i	−0.507671	+	0.507671i	0.406140	+	0.913811i	$0.366875\pi$
$942$	317802.	+	1.58956e7i	0.0116689	+	0.583647i
$943$	−3.14345e7			−1.15114
$944$	2.31991e7	+	1.97570e7i	0.847309	+	0.721589i
$945$	5.87217e6			0.213904
$946$	184331.	+	9.21979e6i	0.00669686	+	0.334960i
$947$	−1.90196e7	+	1.90196e7i	−0.689171	+	0.689171i	−0.962049	−	0.272877i	$-0.912025\pi$
$947$	−1.90196e7	+	1.90196e7i	−0.689171	+	0.689171i	0.272877	+	0.962049i	$0.412025\pi$
$948$	−2.08296e7	+	2.25655e7i	−0.752768	+	0.815502i
$949$	−2.45708e7	−	2.45708e7i	−0.885631	−	0.885631i
$950$	−4.15133e6	−	3.98859e6i	−0.149238	−	0.143387i
$951$		−	3.73781e7i		−	1.34019i
$952$	198852.	+	3.31183e6i	0.00711113	+	0.118434i
$953$		−	7.56812e6i		−	0.269933i	−0.990850	−	0.134966i	$-0.956907\pi$
$953$		−	7.56812e6i		−	0.269933i	0.990850	−	0.134966i	$-0.0430927\pi$
$954$	2.97126e7	−	3.09249e7i	1.05699	−	1.10011i
$955$	1.00781e7	+	1.00781e7i	0.357579	+	0.357579i
$956$	−2.54171e7	+	1.01674e6i	−0.899460	+	0.0359802i
$957$	5.99863e7	−	5.99863e7i	2.11725	−	2.11725i
$958$	3.70317e7	−	740375.i	1.30365	−	0.0260638i
$959$	−1.61948e7			−0.568628
$960$	−2.11571e7	+	2.54986e6i	−0.740930	+	0.0892974i
$961$	−1.41802e6			−0.0495308
$962$	−2.17575e7	+	434999.i	−0.758005	+	0.0151548i
$963$	1.93493e7	−	1.93493e7i	0.672357	−	0.672357i
$964$	3.50721e6	−	140296.i	0.121554	−	0.00486241i
$965$	−7.15667e6	−	7.15667e6i	−0.247396	−	0.247396i
$966$	2.20646e7	−	2.29649e7i	0.760770	−	0.791811i
$967$			2.13881e7i			0.735538i	0.929917	+	0.367769i	$0.119878\pi$
$967$			2.13881e7i			0.735538i	−0.929917	+	0.367769i	$0.880122\pi$
$968$	−18068.0	−	300917.i	−0.000619758	−	0.0103219i
$969$			1.63961e7i			0.560958i
$970$	448823.	+	431228.i	0.0153160	+	0.0147156i
$971$	−3.59844e6	−	3.59844e6i	−0.122480	−	0.122480i	0.643210	−	0.765690i	$-0.277602\pi$
$971$	−3.59844e6	−	3.59844e6i	−0.122480	−	0.122480i	−0.765690	+	0.643210i	$0.777602\pi$
$972$	−1.28077e7	+	1.38751e7i	−0.434816	+	0.471052i
$973$	−9.03835e6	+	9.03835e6i	−0.306060	+	0.306060i
$974$	−554084.	−	2.77139e7i	−0.0187145	−	0.936052i
$975$	−6.93533e6			−0.233645
$976$	1.29979e7	−	1.52625e7i	0.436767	−	0.512863i
$977$	3.48799e7			1.16907			0.584533	−	0.811370i	$-0.301278\pi$
$977$	3.48799e7			1.16907			0.584533	+	0.811370i	$0.301278\pi$
$978$	713258.	+	3.56754e7i	0.0238451	+	1.19267i
$979$	3.60481e7	−	3.60481e7i	1.20206	−	1.20206i
$980$	8.56194e6	+	7.90330e6i	0.284778	+	0.262871i
$981$	−5.09531e7	−	5.09531e7i	−1.69043	−	1.69043i
$982$	−1.03775e7	−	9.97065e6i	−0.343410	−	0.329947i
$983$			2.22783e7i			0.735358i	0.929953	+	0.367679i	$0.119847\pi$
$983$			2.22783e7i			0.735358i	−0.929953	+	0.367679i	$0.880153\pi$
$984$	2.42313e7	+	2.14863e7i	0.797792	+	0.707414i
$985$			5.84792e6i			0.192048i
$986$	−1.22649e7	+	1.27653e7i	−0.401763	+	0.418156i
$987$	−9.57098e6	−	9.57098e6i	−0.312726	−	0.312726i
$988$	−888408.	−	2.22091e7i	−0.0289548	−	0.723832i
$989$	−1.30611e7	+	1.30611e7i	−0.424609	+	0.424609i
$990$	2.47360e7	−	494548.i	0.802125	−	0.0160369i
$991$	−1.51962e6			−0.0491532			−0.0245766	−	0.999698i	$-0.507824\pi$
$991$	−1.51962e6			−0.0491532			−0.0245766	+	0.999698i	$0.507824\pi$
$992$	3.00660e7	−	3.01520e6i	0.970054	−	0.0972829i
$993$	−8.32032e7			−2.67773
$994$	−3.03268e6	+	60632.4i	−0.0973555	+	0.00194643i
$995$	−2.83449e6	+	2.83449e6i	−0.0907648	+	0.0907648i
$996$	3.89066e6	+	9.72616e7i	0.124272	+	3.10665i
$997$	543449.	+	543449.i	0.0173149	+	0.0173149i	0.715711	−	0.698396i	$-0.246103\pi$
$997$	543449.	+	543449.i	0.0173149	+	0.0173149i	−0.698396	+	0.715711i	$0.746103\pi$
$998$	5.61055e6	−	5.83948e6i	0.178312	−	0.185587i
$999$			4.47374e7i			1.41826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.1	✓	80
4.3	odd	2		320.6.l.a.241.37		80
16.3	odd	4		320.6.l.a.81.37		80
16.13	even	4	inner	80.6.l.a.61.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.1	✓	80	1.1	even	1	trivial
80.6.l.a.61.1	yes	80	16.13	even	4	inner
320.6.l.a.81.37		80	16.3	odd	4
320.6.l.a.241.37		80	4.3	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65572 + 0.113075i) q^{2} +(-18.3942 + 18.3942i) q^{3} +(31.9744 - 1.27904i) q^{4} +(17.6777 + 17.6777i) q^{5} +(101.953 - 106.113i) q^{6} -47.3499i q^{7} +(-180.694 + 10.8494i) q^{8} -433.697i q^{9} +O(q^{10})\)	\(q+(-5.65572 + 0.113075i) q^{2} +(-18.3942 + 18.3942i) q^{3} +(31.9744 - 1.27904i) q^{4} +(17.6777 + 17.6777i) q^{5} +(101.953 - 106.113i) q^{6} -47.3499i q^{7} +(-180.694 + 10.8494i) q^{8} -433.697i q^{9} +(-101.979 - 97.9811i) q^{10} +(-285.234 - 285.234i) q^{11} +(-564.618 + 611.673i) q^{12} +(301.631 - 301.631i) q^{13} +(5.35409 + 267.798i) q^{14} -650.335 q^{15} +(1020.73 - 81.7933i) q^{16} +387.084 q^{17} +(49.0403 + 2452.87i) q^{18} +(1151.39 - 1151.39i) q^{19} +(587.844 + 542.623i) q^{20} +(870.965 + 870.965i) q^{21} +(1645.45 + 1580.95i) q^{22} +4570.65i q^{23} +(3124.16 - 3523.30i) q^{24} +625.000i q^{25} +(-1671.83 + 1740.05i) q^{26} +(3507.72 + 3507.72i) q^{27} +(-60.5625 - 1513.99i) q^{28} +(5716.62 - 5716.62i) q^{29} +(3678.11 - 73.5366i) q^{30} -5216.43 q^{31} +(-5763.71 + 578.019i) q^{32} +10493.3 q^{33} +(-2189.24 + 43.7696i) q^{34} +(837.036 - 837.036i) q^{35} +(-554.716 - 13867.2i) q^{36} +(6376.99 + 6376.99i) q^{37} +(-6381.75 + 6642.13i) q^{38} +11096.5i q^{39} +(-3386.04 - 3002.45i) q^{40} +6877.46i q^{41} +(-5024.42 - 4827.46i) q^{42} +(2857.60 + 2857.60i) q^{43} +(-9485.01 - 8755.35i) q^{44} +(7666.75 - 7666.75i) q^{45} +(-516.827 - 25850.3i) q^{46} -10988.9 q^{47} +(-17271.0 + 20280.1i) q^{48} +14565.0 q^{49} +(-70.6719 - 3534.83i) q^{50} +(-7120.12 + 7120.12i) q^{51} +(9258.67 - 10030.3i) q^{52} +(-12360.5 - 12360.5i) q^{53} +(-20235.3 - 19442.1i) q^{54} -10084.5i q^{55} +(513.719 + 8555.84i) q^{56} +42357.9i q^{57} +(-31685.2 + 32978.0i) q^{58} +(21041.9 + 21041.9i) q^{59} +(-20794.1 + 831.806i) q^{60} +(13843.3 - 13843.3i) q^{61} +(29502.7 - 589.848i) q^{62} -20535.5 q^{63} +(32532.6 - 3920.85i) q^{64} +10664.3 q^{65} +(-59347.3 + 1186.53i) q^{66} +(17308.5 - 17308.5i) q^{67} +(12376.8 - 495.097i) q^{68} +(-84073.7 - 84073.7i) q^{69} +(-4639.39 + 4828.69i) q^{70} +11324.5i q^{71} +(4705.36 + 78366.3i) q^{72} -81459.8i q^{73} +(-36787.6 - 35345.4i) q^{74} +(-11496.4 - 11496.4i) q^{75} +(35342.3 - 38287.7i) q^{76} +(-13505.8 + 13505.8i) q^{77} +(-1254.74 - 62758.9i) q^{78} +36891.5 q^{79} +(19490.0 + 16598.2i) q^{80} -23655.5 q^{81} +(-777.669 - 38897.0i) q^{82} +(82684.9 - 82684.9i) q^{83} +(28962.6 + 26734.6i) q^{84} +(6842.75 + 6842.75i) q^{85} +(-16484.9 - 15838.7i) q^{86} +210306. i q^{87} +(54634.6 + 48445.3i) q^{88} +126381. i q^{89} +(-42494.1 + 44227.9i) q^{90} +(-14282.2 - 14282.2i) q^{91} +(5846.06 + 146144. i) q^{92} +(95952.3 - 95952.3i) q^{93} +(62150.3 - 1242.57i) q^{94} +40707.8 q^{95} +(95386.8 - 116651. i) q^{96} -4401.13 q^{97} +(-82375.6 + 1646.94i) q^{98} +(-123705. + 123705. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Introduction

L-functions

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