LMFDB - Embedded newform 200.6.f.d.149.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.29
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.87282 - 4.12326i) q^{2} -18.2848 q^{3} +(-2.00256 - 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} -2.25573i q^{7} +(-139.441 - 115.430i) q^{8} +91.3327 q^{9} +O(q^{10})$	\(q+(3.87282 - 4.12326i) q^{2} -18.2848 q^{3} +(-2.00256 - 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} -2.25573i q^{7} +(-139.441 - 115.430i) q^{8} +91.3327 q^{9} +419.261i q^{11} +(36.6163 + 583.966i) q^{12} -106.889 q^{13} +(-9.30095 - 8.73602i) q^{14} +(-1015.98 + 127.912i) q^{16} +849.098i q^{17} +(353.715 - 376.589i) q^{18} +335.414i q^{19} +41.2454i q^{21} +(1728.72 + 1623.72i) q^{22} -3541.78i q^{23} +(2549.65 + 2110.61i) q^{24} +(-413.961 + 440.731i) q^{26} +2773.20 q^{27} +(-72.0418 + 4.51722i) q^{28} +5208.57i q^{29} +5637.83 q^{31} +(-3407.29 + 4684.53i) q^{32} -7666.09i q^{33} +(3501.05 + 3288.40i) q^{34} +(-182.899 - 2916.92i) q^{36} +61.9860 q^{37} +(1383.00 + 1299.00i) q^{38} +1954.44 q^{39} +16286.1 q^{41} +(170.066 + 159.736i) q^{42} -2417.19 q^{43} +(13390.1 - 839.594i) q^{44} +(-14603.7 - 13716.7i) q^{46} -22781.9i q^{47} +(18576.9 - 2338.85i) q^{48} +16801.9 q^{49} -15525.6i q^{51} +(214.051 + 3413.74i) q^{52} +13667.5 q^{53} +(10740.1 - 11434.6i) q^{54} +(-260.379 + 314.541i) q^{56} -6132.98i q^{57} +(21476.3 + 20171.9i) q^{58} +23407.1i q^{59} +33444.7i q^{61} +(21834.3 - 23246.3i) q^{62} -206.022i q^{63} +(6119.73 + 32191.5i) q^{64} +(-31609.3 - 29689.4i) q^{66} +66162.9 q^{67} +(27117.9 - 1700.37i) q^{68} +64760.7i q^{69} -51421.4 q^{71} +(-12735.5 - 10542.6i) q^{72} -21271.6i q^{73} +(240.060 - 255.584i) q^{74} +(10712.2 - 671.686i) q^{76} +945.738 q^{77} +(7569.18 - 8058.66i) q^{78} -38418.7 q^{79} -72901.2 q^{81} +(63073.0 - 67151.7i) q^{82} -93166.7 q^{83} +(1317.27 - 82.5963i) q^{84} +(-9361.33 + 9966.69i) q^{86} -95237.5i q^{87} +(48395.4 - 58462.3i) q^{88} +60678.0 q^{89} +241.112i q^{91} +(-113115. + 7092.62i) q^{92} -103086. q^{93} +(-93935.8 - 88230.2i) q^{94} +(62301.5 - 85655.5i) q^{96} +157428. i q^{97} +(65070.8 - 69278.7i) q^{98} +38292.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	3.87282	−	4.12326i	0.684624	−	0.728896i
$2$	3.87282	−	4.12326i	0.684624	−	0.728896i
$3$	−18.2848			−1.17297			−0.586484	−	0.809961i	$-0.699488\pi$
$3$	−18.2848			−1.17297			−0.586484	+	0.809961i	$0.699488\pi$
$4$	−2.00256	−	31.9373i	−0.0625799	−	0.998040i
$5$		0			0
$5$		0			0
$6$	−70.8136	+	75.3929i	−0.803042	+	0.854972i
$7$		−	2.25573i		−	0.0173997i	−0.999962	−	0.00869984i	$-0.997231\pi$
$7$		−	2.25573i		−	0.0173997i	0.999962	−	0.00869984i	$-0.00276928\pi$
$8$	−139.441	−	115.430i	−0.770311	−	0.637668i
$9$	91.3327			0.375855
$10$		0			0
$11$			419.261i			1.04473i	0.852723	+	0.522363i	$0.174950\pi$
$11$			419.261i			1.04473i	−0.852723	+	0.522363i	$0.825050\pi$
$12$	36.6163	+	583.966i	0.0734042	+	1.17067i
$13$	−106.889			−0.175418			−0.0877090	−	0.996146i	$-0.527955\pi$
$13$	−106.889			−0.175418			−0.0877090	+	0.996146i	$0.527955\pi$
$14$	−9.30095	−	8.73602i	−0.0126826	−	0.0119122i
$15$		0			0
$16$	−1015.98	+	127.912i	−0.992168	+	0.124914i
$17$			849.098i			0.712584i	0.934375	+	0.356292i	$0.115959\pi$
$17$			849.098i			0.712584i	−0.934375	+	0.356292i	$0.884041\pi$
$18$	353.715	−	376.589i	0.257319	−	0.273959i
$19$			335.414i			0.213156i	0.994304	+	0.106578i	$0.0339894\pi$
$19$			335.414i			0.213156i	−0.994304	+	0.106578i	$0.966011\pi$
$20$		0			0
$21$			41.2454i			0.0204093i
$22$	1728.72	+	1623.72i	0.761497	+	0.715245i
$23$		−	3541.78i		−	1.39605i	−0.716071	−	0.698027i	$-0.754062\pi$
$23$		−	3541.78i		−	1.39605i	0.716071	−	0.698027i	$-0.245938\pi$
$24$	2549.65	+	2110.61i	0.903551	+	0.747964i
$25$		0			0
$26$	−413.961	+	440.731i	−0.120095	+	0.127862i
$27$	2773.20			0.732103
$28$	−72.0418	+	4.51722i	−0.0173656	+	0.00108887i
$29$			5208.57i			1.15007i	0.818129	+	0.575034i	$0.195011\pi$
$29$			5208.57i			1.15007i	−0.818129	+	0.575034i	$0.804989\pi$
$30$		0			0
$31$	5637.83			1.05368			0.526839	−	0.849965i	$-0.323377\pi$
$31$	5637.83			1.05368			0.526839	+	0.849965i	$0.323377\pi$
$32$	−3407.29	+	4684.53i	−0.588212	+	0.808707i
$33$		−	7666.09i		−	1.22543i
$34$	3501.05	+	3288.40i	0.519400	+	0.487852i
$35$		0			0
$36$	−182.899	−	2916.92i	−0.0235209	−	0.375118i
$37$	61.9860			0.00744370			0.00372185	−	0.999993i	$-0.498815\pi$
$37$	61.9860			0.00744370			0.00372185	+	0.999993i	$0.498815\pi$
$38$	1383.00	+	1299.00i	0.155369	+	0.145932i
$39$	1954.44			0.205760
$40$		0			0
$41$	16286.1			1.51306			0.756531	−	0.653958i	$-0.226893\pi$
$41$	16286.1			1.51306			0.756531	+	0.653958i	$0.226893\pi$
$42$	170.066	+	159.736i	0.0148762	+	0.0139727i
$43$	−2417.19			−0.199361			−0.0996803	−	0.995020i	$-0.531782\pi$
$43$	−2417.19			−0.199361			−0.0996803	+	0.995020i	$0.531782\pi$
$44$	13390.1	−	839.594i	1.04268	−	0.0653789i
$45$		0			0
$46$	−14603.7	−	13716.7i	−1.01758	−	0.955772i
$47$		−	22781.9i		−	1.50434i	−0.658970	−	0.752170i	$-0.729007\pi$
$47$		−	22781.9i		−	1.50434i	0.658970	−	0.752170i	$-0.270993\pi$
$48$	18576.9	−	2338.85i	1.16378	−	0.146521i
$49$	16801.9			0.999697
$50$		0			0
$51$		−	15525.6i		−	0.835838i
$52$	214.051	+	3413.74i	0.0109776	+	0.175074i
$53$	13667.5			0.668344			0.334172	−	0.942512i	$-0.391543\pi$
$53$	13667.5			0.668344			0.334172	+	0.942512i	$0.391543\pi$
$54$	10740.1	−	11434.6i	0.501215	−	0.533627i
$55$		0			0
$56$	−260.379	+	314.541i	−0.0110952	+	0.0134032i
$57$		−	6132.98i		−	0.250025i
$58$	21476.3	+	20171.9i	0.838281	+	0.787365i
$59$			23407.1i			0.875423i	0.899116	+	0.437711i	$0.144211\pi$
$59$			23407.1i			0.875423i	−0.899116	+	0.437711i	$0.855789\pi$
$60$		0			0
$61$			33444.7i			1.15081i	0.817869	+	0.575405i	$0.195155\pi$
$61$			33444.7i			1.15081i	−0.817869	+	0.575405i	$0.804845\pi$
$62$	21834.3	−	23246.3i	0.721373	−	0.768022i
$63$		−	206.022i		−	0.00653975i
$64$	6119.73	+	32191.5i	0.186759	+	0.982406i
$65$		0			0
$66$	−31609.3	−	29689.4i	−0.893212	−	0.838960i
$67$	66162.9			1.80064			0.900321	−	0.435226i	$-0.143332\pi$
$67$	66162.9			1.80064			0.900321	+	0.435226i	$0.143332\pi$
$68$	27117.9	−	1700.37i	0.711187	−	0.0445934i
$69$			64760.7i			1.63753i
$70$		0			0
$71$	−51421.4			−1.21059			−0.605296	−	0.796001i	$-0.706945\pi$
$71$	−51421.4			−1.21059			−0.605296	+	0.796001i	$0.706945\pi$
$72$	−12735.5	−	10542.6i	−0.289525	−	0.239670i
$73$		−	21271.6i		−	0.467189i	−0.972334	−	0.233595i	$-0.924951\pi$
$73$		−	21271.6i		−	0.467189i	0.972334	−	0.233595i	$-0.0750489\pi$
$74$	240.060	−	255.584i	0.00509614	−	0.00542569i
$75$		0			0
$76$	10712.2	−	671.686i	0.212738	−	0.0133393i
$77$	945.738			0.0181779
$78$	7569.18	−	8058.66i	0.140868	−	0.149978i
$79$	−38418.7			−0.692589			−0.346294	−	0.938126i	$-0.612560\pi$
$79$	−38418.7			−0.692589			−0.346294	+	0.938126i	$0.612560\pi$
$80$		0			0
$81$	−72901.2			−1.23459
$82$	63073.0	−	67151.7i	1.03588	−	1.10286i
$83$	−93166.7			−1.48445			−0.742225	−	0.670151i	$-0.766229\pi$
$83$	−93166.7			−1.48445			−0.742225	+	0.670151i	$0.766229\pi$
$84$	1317.27	−	82.5963i	0.0203693	−	0.00127721i
$85$		0			0
$86$	−9361.33	+	9966.69i	−0.136487	+	0.145313i
$87$		−	95237.5i		−	1.34899i
$88$	48395.4	−	58462.3i	0.666189	−	0.804765i
$89$	60678.0			0.812000			0.406000	−	0.913873i	$-0.366923\pi$
$89$	60678.0			0.812000			0.406000	+	0.913873i	$0.366923\pi$
$90$		0			0
$91$			241.112i			0.00305222i
$92$	−113115.	+	7092.62i	−1.39332	+	0.0873649i
$93$	−103086.			−1.23593
$94$	−93935.8	−	88230.2i	−1.09651	−	1.02991i
$95$		0			0
$96$	62301.5	−	85655.5i	0.689954	−	0.948587i
$97$			157428.i			1.69884i	0.527721	+	0.849418i	$0.323047\pi$
$97$			157428.i			1.69884i	−0.527721	+	0.849418i	$0.676953\pi$
$98$	65070.8	−	69278.7i	0.684417	−	0.728676i
$99$			38292.2i			0.392665i
$100$		0			0
$101$			124508.i			1.21449i	0.794516	+	0.607243i	$0.207725\pi$
$101$			124508.i			1.21449i	−0.794516	+	0.607243i	$0.792275\pi$
$102$	−64016.0	−	60127.7i	−0.609239	−	0.572235i
$103$			10346.4i			0.0960938i	0.998845	+	0.0480469i	$0.0152997\pi$
$103$			10346.4i			0.0960938i	−0.998845	+	0.0480469i	$0.984700\pi$
$104$	14904.7	+	12338.2i	0.135126	+	0.111858i
$105$		0			0
$106$	52931.8	−	56354.7i	0.457564	−	0.487153i
$107$	70765.9			0.597537			0.298769	−	0.954326i	$-0.403424\pi$
$107$	70765.9			0.597537			0.298769	+	0.954326i	$0.403424\pi$
$108$	−5553.49	−	88568.5i	−0.0458149	−	0.730668i
$109$			128453.i			1.03557i	0.855511	+	0.517784i	$0.173243\pi$
$109$			128453.i			1.03557i	−0.855511	+	0.517784i	$0.826757\pi$
$110$		0			0
$111$	−1133.40			−0.00873123
$112$	288.535	+	2291.77i	0.00217347	+	0.0172634i
$113$			115196.i			0.848672i	0.905505	+	0.424336i	$0.139492\pi$
$113$			115196.i			0.848672i	−0.905505	+	0.424336i	$0.860508\pi$
$114$	−25287.9	−	23751.9i	−0.182243	−	0.171173i
$115$		0			0
$116$	166348.	−	10430.5i	1.14781	−	0.0719712i
$117$	−9762.45			−0.0659317
$118$	96513.6	+	90651.5i	0.638093	+	0.599335i
$119$	1915.33			0.0123987
$120$		0			0
$121$	−14728.7			−0.0914537
$122$	137901.	+	129525.i	0.838821	+	0.787872i
$123$	−297787.			−1.77477
$124$	−11290.1	−	180057.i	−0.0659391	−	1.05161i
$125$		0			0
$126$	−849.481	−	797.884i	−0.00476680	−	0.00447727i
$127$			146026.i			0.803378i	0.915776	+	0.401689i	$0.131577\pi$
$127$			146026.i			0.803378i	−0.915776	+	0.401689i	$0.868423\pi$
$128$	156434.	+	99438.5i	0.843932	+	0.536450i
$129$	44197.7			0.233844
$130$		0			0
$131$			12998.0i			0.0661757i	0.999452	+	0.0330878i	$0.0105341\pi$
$131$			12998.0i			0.0661757i	−0.999452	+	0.0330878i	$0.989466\pi$
$132$	−244834.	+	15351.8i	−1.22303	+	0.0766873i
$133$	756.603			0.00370885
$134$	256237.	−	272807.i	1.23276	−	1.31248i
$135$		0			0
$136$	98011.6	−	118399.i	0.454392	−	0.548911i
$137$			189204.i			0.861249i	0.902531	+	0.430624i	$0.141707\pi$
$137$			189204.i			0.861249i	−0.902531	+	0.430624i	$0.858293\pi$
$138$	267025.	+	250806.i	1.19359	+	1.12109i
$139$			44334.4i			0.194627i	0.995254	+	0.0973136i	$0.0310250\pi$
$139$			44334.4i			0.194627i	−0.995254	+	0.0973136i	$0.968975\pi$
$140$		0			0
$141$			416562.i			1.76454i
$142$	−199146.	+	212024.i	−0.828800	+	0.882396i
$143$		−	44814.3i		−	0.183264i
$144$	−92792.2	+	11682.6i	−0.372911	+	0.0469497i
$145$		0			0
$146$	−87708.3	−	82381.0i	−0.340533	−	0.319849i
$147$	−307219.			−1.17261
$148$	−124.130	−	1979.66i	−0.000465826	−	0.00742911i
$149$		−	352240.i		−	1.29979i	−0.760024	−	0.649895i	$-0.774813\pi$
$149$		−	352240.i		−	1.29979i	0.760024	−	0.649895i	$-0.225187\pi$
$150$		0			0
$151$	446273.			1.59279			0.796395	−	0.604776i	$-0.206738\pi$
$151$	446273.			1.59279			0.796395	+	0.604776i	$0.206738\pi$
$152$	38717.0	−	46770.6i	0.135923	−	0.164197i
$153$			77550.5i			0.267828i
$154$	3662.67	−	3899.52i	0.0124450	−	0.0132498i
$155$		0			0
$156$	−3913.87	−	62419.4i	−0.0128764	−	0.205356i
$157$	383316.			1.24110			0.620552	−	0.784165i	$-0.286909\pi$
$157$	383316.			1.24110			0.620552	+	0.784165i	$0.286909\pi$
$158$	−148789.	+	158410.i	−0.474163	+	0.504825i
$159$	−249907.			−0.783946
$160$		0			0
$161$	−7989.29			−0.0242909
$162$	−282333.	+	300591.i	−0.845229	+	0.899887i
$163$	−405200.			−1.19454			−0.597270	−	0.802040i	$-0.703748\pi$
$163$	−405200.			−1.19454			−0.597270	+	0.802040i	$0.703748\pi$
$164$	−32613.8	−	520133.i	−0.0946872	−	1.51010i
$165$		0			0
$166$	−360818.	+	384150.i	−1.01629	+	1.08201i
$167$		−	193042.i		−	0.535625i	−0.963471	−	0.267812i	$-0.913699\pi$
$167$		−	193042.i		−	0.535625i	0.963471	−	0.267812i	$-0.0863008\pi$
$168$	4760.97	−	5751.31i	0.0130143	−	0.0157215i
$169$	−359868.			−0.969229
$170$		0			0
$171$			30634.3i			0.0801157i
$172$	4840.55	+	77198.4i	0.0124760	+	0.198970i
$173$	−599397.			−1.52265			−0.761323	−	0.648372i	$-0.775450\pi$
$173$	−599397.			−1.52265			−0.761323	+	0.648372i	$0.775450\pi$
$174$	−392689.	−	368838.i	−0.983277	−	0.923554i
$175$		0			0
$176$	−53628.7	−	425960.i	−0.130501	−	1.03654i
$177$		−	427994.i		−	1.02684i
$178$	234995.	−	250191.i	0.555915	−	0.591864i
$179$			421278.i			0.982736i	0.870952	+	0.491368i	$0.163503\pi$
$179$			421278.i			0.982736i	−0.870952	+	0.491368i	$0.836497\pi$
$180$		0			0
$181$			183362.i			0.416018i	0.978127	+	0.208009i	$0.0666983\pi$
$181$			183362.i			0.416018i	−0.978127	+	0.208009i	$0.933302\pi$
$182$	994.168	+	933.783i	0.00222475	+	0.00208962i
$183$		−	611529.i		−	1.34986i
$184$	−408829.	+	493871.i	−0.890219	+	1.07540i
$185$		0			0
$186$	−399235.	+	425052.i	−0.846148	+	0.900866i
$187$	−355994.			−0.744455
$188$	−727593.	+	45622.1i	−1.50139	+	0.0941414i
$189$		−	6255.58i		−	0.0127384i
$190$		0			0
$191$	982533.			1.94878			0.974392	−	0.224856i	$-0.0721912\pi$
$191$	982533.			1.94878			0.974392	+	0.224856i	$0.0721912\pi$
$192$	−111898.	−	588614.i	−0.219063	−	1.15233i
$193$			164978.i			0.318810i	0.987213	+	0.159405i	$0.0509576\pi$
$193$			164978.i			0.318810i	−0.987213	+	0.159405i	$0.949042\pi$
$194$	649115.	+	609688.i	1.23827	+	1.16306i
$195$		0			0
$196$	−33646.8	−	536607.i	−0.0625609	−	0.997738i
$197$	506605.			0.930044			0.465022	−	0.885299i	$-0.346046\pi$
$197$	506605.			0.930044			0.465022	+	0.885299i	$0.346046\pi$
$198$	157889.	+	148299.i	0.286212	+	0.268828i
$199$	−475645.			−0.851433			−0.425716	−	0.904857i	$-0.639978\pi$
$199$	−475645.			−0.851433			−0.425716	+	0.904857i	$0.639978\pi$
$200$		0			0
$201$	−1.20977e6			−2.11210
$202$	513378.	+	482196.i	0.885235	+	0.831467i
$203$	11749.1			0.0200108
$204$	−495844.	+	31090.8i	−0.834200	+	0.0523066i
$205$		0			0
$206$	42660.8	+	40069.7i	0.0700425	+	0.0657882i
$207$		−	323481.i		−	0.524714i
$208$	108597.	−	13672.4i	0.174044	−	0.0219122i
$209$	−140626.			−0.222690
$210$		0			0
$211$		−	260466.i		−	0.402759i	−0.979513	−	0.201379i	$-0.935458\pi$
$211$		−	260466.i		−	0.402759i	0.979513	−	0.201379i	$-0.0645424\pi$
$212$	−27370.0	−	436503.i	−0.0418249	−	0.667034i
$213$	940228.			1.41999
$214$	274064.	−	291786.i	0.409088	−	0.435543i
$215$		0			0
$216$	−386699.	−	320111.i	−0.563947	−	0.466838i
$217$		−	12717.4i		−	0.0183337i
$218$	529646.	+	497476.i	0.754822	+	0.708975i
$219$			388946.i			0.547998i
$220$		0			0
$221$		−	90759.2i		−	0.125000i
$222$	−4389.45	+	4673.30i	−0.00597761	+	0.00636416i
$223$		−	624180.i		−	0.840519i	−0.907404	−	0.420260i	$-0.861939\pi$
$223$		−	624180.i		−	0.840519i	0.907404	−	0.420260i	$-0.138061\pi$
$224$	10567.0	+	7685.91i	0.0140712	+	0.0102347i
$225$		0			0
$226$	474982.	+	446132.i	0.618594	+	0.581021i
$227$	−656014.			−0.844984			−0.422492	−	0.906367i	$-0.638845\pi$
$227$	−656014.			−0.844984			−0.422492	+	0.906367i	$0.638845\pi$
$228$	−195871.	+	12281.6i	−0.249535	+	0.0156466i
$229$		−	807777.i		−	1.01790i	−0.860798	−	0.508948i	$-0.830035\pi$
$229$		−	807777.i		−	1.01790i	0.860798	−	0.508948i	$-0.169965\pi$
$230$		0			0
$231$	−17292.6			−0.0213221
$232$	601227.	−	726290.i	0.733362	−	0.885911i
$233$			1.30452e6i			1.57421i	0.616822	+	0.787103i	$0.288420\pi$
$233$			1.30452e6i			1.57421i	−0.616822	+	0.787103i	$0.711580\pi$
$234$	−37808.2	+	40253.1i	−0.0451384	+	0.0480574i
$235$		0			0
$236$	747560.	−	46874.1i	0.873707	−	0.0547839i
$237$	702478.			0.812385
$238$	7417.74	−	7897.42i	0.00848847	−	0.00903739i
$239$	1.21861e6			1.37997			0.689985	−	0.723824i	$-0.257617\pi$
$239$	1.21861e6			1.37997			0.689985	+	0.723824i	$0.257617\pi$
$240$		0			0
$241$	−983578.			−1.09085			−0.545426	−	0.838159i	$-0.683632\pi$
$241$	−983578.			−1.09085			−0.545426	+	0.838159i	$0.683632\pi$
$242$	−57041.6	+	60730.3i	−0.0626114	+	0.0666603i
$243$	659093.			0.716030
$244$	1.06813e6	−	66975.0i	1.14855	−	0.0720175i
$245$		0			0
$246$	−1.15327e6	+	1.22785e6i	−1.21505	+	1.29363i
$247$		−	35852.1i		−	0.0373914i
$248$	−786147.	−	650776.i	−0.811660	−	0.671897i
$249$	1.70353e6			1.74121
$250$		0			0
$251$		−	1.60324e6i		−	1.60625i	−0.595809	−	0.803126i	$-0.703168\pi$
$251$		−	1.60324e6i		−	1.60625i	0.595809	−	0.803126i	$-0.296832\pi$
$252$	−6579.77	+	412.570i	−0.00652693	+	0.000409257i
$253$	1.48493e6			1.45849
$254$	602102.	+	565531.i	0.585579	+	0.550012i
$255$		0			0
$256$	1.01585e6	−	259913.i	0.968793	−	0.247872i
$257$			1.07709e6i			1.01723i	0.860993	+	0.508617i	$0.169843\pi$
$257$			1.07709e6i			1.01723i	−0.860993	+	0.508617i	$0.830157\pi$
$258$	171170.	−	182239.i	0.160095	−	0.170448i
$259$		−	139.823i		−	0.000129518i
$260$		0			0
$261$			475713.i			0.432259i
$262$	53594.2	+	50338.9i	0.0482352	+	0.0453055i
$263$			812889.i			0.724673i	0.932047	+	0.362336i	$0.118021\pi$
$263$			812889.i			0.724673i	−0.932047	+	0.362336i	$0.881979\pi$
$264$	−884898.	+	1.06897e6i	−0.781418	+	0.943964i
$265$		0			0
$266$	2930.19	−	3119.67i	0.00253917	−	0.00270337i
$267$	−1.10948e6			−0.952451
$268$	−132495.	−	2.11306e6i	−0.112684	−	1.79711i
$269$			113957.i			0.0960201i	0.998847	+	0.0480101i	$0.0152880\pi$
$269$			113957.i			0.0960201i	−0.998847	+	0.0480101i	$0.984712\pi$
$270$		0			0
$271$	372728.			0.308297			0.154148	−	0.988048i	$-0.450737\pi$
$271$	372728.			0.308297			0.154148	+	0.988048i	$0.450737\pi$
$272$	−108610.	−	862667.i	−0.0890120	−	0.707002i
$273$		−	4408.68i		−	0.00358015i
$274$	780137.	+	732752.i	0.627761	+	0.589632i
$275$		0			0
$276$	2.06828e6	−	129687.i	1.63432	−	0.102476i
$277$	914263.			0.715932			0.357966	−	0.933735i	$-0.383470\pi$
$277$	914263.			0.715932			0.357966	+	0.933735i	$0.383470\pi$
$278$	182802.	+	171699.i	0.141863	+	0.133247i
$279$	514918.			0.396030
$280$		0			0
$281$	−511184.			−0.386199			−0.193100	−	0.981179i	$-0.561854\pi$
$281$	−511184.			−0.386199			−0.193100	+	0.981179i	$0.561854\pi$
$282$	1.71759e6	+	1.61327e6i	1.28617	+	1.20805i
$283$	533078.			0.395662			0.197831	−	0.980236i	$-0.436610\pi$
$283$	533078.			0.395662			0.197831	+	0.980236i	$0.436610\pi$
$284$	102974.	+	1.64226e6i	0.0757587	+	1.20822i
$285$		0			0
$286$	−184781.	−	173558.i	−0.133580	−	0.125467i
$287$		−	36736.9i		−	0.0263268i
$288$	−311197.	+	427851.i	−0.221082	+	0.303956i
$289$	698889.			0.492225
$290$		0			0
$291$		−	2.87853e6i		−	1.99268i
$292$	−679357.	+	42597.6i	−0.466273	+	0.0292366i
$293$	2.54648e6			1.73289			0.866445	−	0.499273i	$-0.166400\pi$
$293$	2.54648e6			1.73289			0.866445	+	0.499273i	$0.166400\pi$
$294$	−1.18980e6	+	1.26674e6i	−0.802799	+	0.854714i
$295$		0			0
$296$	−8643.40	−	7155.05i	−0.00573397	−	0.00474661i
$297$			1.16269e6i			0.764847i
$298$	−1.45238e6	−	1.36416e6i	−0.947412	−	0.889868i
$299$			378577.i			0.244893i
$300$		0			0
$301$			5452.51i			0.00346881i
$302$	1.72834e6	−	1.84010e6i	1.09046	−	1.16098i
$303$		−	2.27659e6i		−	1.42455i
$304$	−42903.7	−	340774.i	−0.0266263	−	0.211487i
$305$		0			0
$306$	319761.	+	300339.i	0.195219	+	0.183361i
$307$	740673.			0.448518			0.224259	−	0.974530i	$-0.428004\pi$
$307$	740673.			0.448518			0.224259	+	0.974530i	$0.428004\pi$
$308$	−1893.89	−	30204.3i	−0.00113757	−	0.0181423i
$309$		−	189181.i		−	0.112715i
$310$		0			0
$311$	1.08876e6			0.638310			0.319155	−	0.947702i	$-0.396601\pi$
$311$	1.08876e6			0.638310			0.319155	+	0.947702i	$0.396601\pi$
$312$	−272529.	−	225601.i	−0.158499	−	0.131206i
$313$		−	1.08277e6i		−	0.624705i	−0.949966	−	0.312353i	$-0.898883\pi$
$313$		−	1.08277e6i		−	0.624705i	0.949966	−	0.312353i	$-0.101117\pi$
$314$	1.48451e6	−	1.58051e6i	0.849690	−	0.904636i
$315$		0			0
$316$	76935.7	+	1.22699e6i	0.0433421	+	0.691231i
$317$	−2.93243e6			−1.63900			−0.819501	−	0.573078i	$-0.805749\pi$
$317$	−2.93243e6			−1.63900			−0.819501	+	0.573078i	$0.805749\pi$
$318$	−967845.	+	1.03043e6i	−0.536708	+	0.571415i
$319$	−2.18375e6			−1.20151
$320$		0			0
$321$	−1.29394e6			−0.700892
$322$	−30941.1	+	32941.9i	−0.0166301	+	0.0177055i
$323$	−284800.			−0.151892
$324$	145989.	+	2.32827e6i	0.0772604	+	1.23217i
$325$		0			0
$326$	−1.56927e6	+	1.67075e6i	−0.817811	+	0.870696i
$327$		−	2.34874e6i		−	1.21469i
$328$	−2.27095e6	−	1.87990e6i	−1.16553	−	0.964831i
$329$	−51389.8			−0.0261750
$330$		0			0
$331$		−	357214.i		−	0.179209i	−0.995977	−	0.0896043i	$-0.971440\pi$
$331$		−	357214.i		−	0.179209i	0.995977	−	0.0896043i	$-0.0285602\pi$
$332$	186572.	+	2.97549e6i	0.0928967	+	1.48154i
$333$	5661.34			0.00279775
$334$	−795963.	−	747617.i	−0.390415	−	0.366702i
$335$		0			0
$336$	−5275.80	−	41904.5i	−0.00254941	−	0.0202494i
$337$			1.45195e6i			0.696429i	0.937415	+	0.348215i	$0.113212\pi$
$337$			1.45195e6i			0.696429i	−0.937415	+	0.348215i	$0.886788\pi$
$338$	−1.39370e6	+	1.48383e6i	−0.663557	+	0.706467i
$339$		−	2.10633e6i		−	0.995465i
$340$		0			0
$341$			2.36372e6i			1.10081i
$342$	126313.	+	118641.i	0.0583961	+	0.0548492i
$343$		−	75812.5i		−	0.0347941i
$344$	337056.	+	279016.i	0.153570	+	0.127126i
$345$		0			0
$346$	−2.32135e6	+	2.47147e6i	−1.04244	+	1.10985i
$347$	393735.			0.175541			0.0877707	−	0.996141i	$-0.472026\pi$
$347$	393735.			0.175541			0.0877707	+	0.996141i	$0.472026\pi$
$348$	−3.04163e6	+	190719.i	−1.34635	+	0.0844199i
$349$		−	1.73875e6i		−	0.764140i	−0.924133	−	0.382070i	$-0.875211\pi$
$349$		−	1.73875e6i		−	0.764140i	0.924133	−	0.382070i	$-0.124789\pi$
$350$		0			0
$351$	−296424.			−0.128424
$352$	−1.96404e6	−	1.42854e6i	−0.844877	−	0.614521i
$353$			2.05124e6i			0.876154i	0.898937	+	0.438077i	$0.144340\pi$
$353$			2.05124e6i			0.876154i	−0.898937	+	0.438077i	$0.855660\pi$
$354$	−1.76473e6	−	1.65754e6i	−0.748462	−	0.703002i
$355$		0			0
$356$	−121511.	−	1.93789e6i	−0.0508149	−	0.810409i
$357$	−35021.4			−0.0145433
$358$	1.73704e6	+	1.63153e6i	0.716312	+	0.672804i
$359$	−3.56728e6			−1.46084			−0.730418	−	0.683000i	$-0.760675\pi$
$359$	−3.56728e6			−1.46084			−0.730418	+	0.683000i	$0.760675\pi$
$360$		0			0
$361$	2.36360e6			0.954564
$362$	756048.	+	710126.i	0.303234	+	0.284816i
$363$	269311.			0.107272
$364$	7700.46	−	482.840i	0.00304623	−	0.000191007i
$365$		0			0
$366$	−2.52149e6	−	2.36834e6i	−0.983910	−	0.924148i
$367$		−	3.72721e6i		−	1.44450i	−0.691631	−	0.722251i	$-0.743107\pi$
$367$		−	3.72721e6i		−	1.44450i	0.691631	−	0.722251i	$-0.256893\pi$
$368$	453038.	+	3.59838e6i	0.174387	+	1.38512i
$369$	1.48745e6			0.568691
$370$		0			0
$371$		−	30830.2i		−	0.0116290i
$372$	206436.	+	3.29230e6i	0.0773444	+	1.23351i
$373$	1.71134e6			0.636891			0.318446	−	0.947941i	$-0.396839\pi$
$373$	1.71134e6			0.636891			0.318446	+	0.947941i	$0.396839\pi$
$374$	−1.37870e6	+	1.46786e6i	−0.509672	+	0.542631i
$375$		0			0
$376$	−2.62972e6	+	3.17674e6i	−0.959269	+	1.15881i
$377$		−	556738.i		−	0.201743i
$378$	−25793.4	−	24226.7i	−0.00928494	−	0.00872098i
$379$		−	3.60174e6i		−	1.28799i	−0.765028	−	0.643997i	$-0.777275\pi$
$379$		−	3.60174e6i		−	1.28799i	0.765028	−	0.643997i	$-0.222725\pi$
$380$		0			0
$381$		−	2.67005e6i		−	0.942337i
$382$	3.80517e6	−	4.05124e6i	1.33418	−	1.42046i
$383$			3.80875e6i			1.32674i	0.748293	+	0.663369i	$0.230874\pi$
$383$			3.80875e6i			1.32674i	−0.748293	+	0.663369i	$0.769126\pi$
$384$	−2.86037e6	−	1.81821e6i	−0.989905	−	0.629239i
$385$		0			0
$386$	680246.	+	638929.i	0.232379	+	0.218265i
$387$	−220768.			−0.0749306
$388$	5.02781e6	−	315257.i	1.69551	−	0.106313i
$389$		−	431800.i		−	0.144680i	−0.997380	−	0.0723401i	$-0.976953\pi$
$389$		−	431800.i		−	0.144680i	0.997380	−	0.0723401i	$-0.0230467\pi$
$390$		0			0
$391$	3.00732e6			0.994805
$392$	−2.34288e6	−	1.93945e6i	−0.770078	−	0.637475i
$393$		−	237665.i		−	0.0776220i
$394$	1.96199e6	−	2.08886e6i	0.636731	−	0.677906i
$395$		0			0
$396$	1.22295e6	−	76682.3i	0.391896	−	0.0245730i
$397$	−2.28465e6			−0.727518			−0.363759	−	0.931493i	$-0.618507\pi$
$397$	−2.28465e6			−0.727518			−0.363759	+	0.931493i	$0.618507\pi$
$398$	−1.84209e6	+	1.96121e6i	−0.582911	+	0.620606i
$399$	−13834.3			−0.00435036
$400$		0			0
$401$	1.63473e6			0.507674			0.253837	−	0.967247i	$-0.418307\pi$
$401$	1.63473e6			0.507674			0.253837	+	0.967247i	$0.418307\pi$
$402$	−4.68523e6	+	4.98821e6i	−1.44599	+	1.53950i
$403$	−602621.			−0.184834
$404$	3.97644e6	−	249334.i	1.21211	−	0.0760024i
$405$		0			0
$406$	45502.2	−	48444.7i	0.0136999	−	0.0145858i
$407$			25988.3i			0.00777663i
$408$	−1.79212e6	+	2.16490e6i	−0.532987	+	0.643855i
$409$	−5.21834e6			−1.54250			−0.771248	−	0.636534i	$-0.780367\pi$
$409$	−5.21834e6			−1.54250			−0.771248	+	0.636534i	$0.780367\pi$
$410$		0			0
$411$		−	3.45955e6i		−	1.01022i
$412$	330435.	−	20719.2i	0.0959055	−	0.00601354i
$413$	52800.0			0.0152321
$414$	−1.33379e6	−	1.25278e6i	−0.382462	−	0.359231i
$415$		0			0
$416$	364201.	−	500724.i	0.103183	−	0.141862i
$417$		−	810644.i		−	0.228292i
$418$	−544620.	+	579838.i	−0.152459	+	0.162318i
$419$			666477.i			0.185460i	0.995691	+	0.0927299i	$0.0295593\pi$
$419$			666477.i			0.185460i	−0.995691	+	0.0927299i	$0.970441\pi$
$420$		0			0
$421$			6.82007e6i			1.87536i	0.347504	+	0.937678i	$0.387029\pi$
$421$			6.82007e6i			1.87536i	−0.347504	+	0.937678i	$0.612971\pi$
$422$	−1.07397e6	−	1.00874e6i	−0.293569	−	0.275738i
$423$		−	2.08073e6i		−	0.565413i
$424$	−1.90581e6	−	1.57764e6i	−0.514833	−	0.426181i
$425$		0			0
$426$	3.64133e6	−	3.87680e6i	0.972156	−	1.03502i
$427$	75442.2			0.0200237
$428$	−141713.	−	2.26007e6i	−0.0373938	−	0.596366i
$429$			819419.i			0.214963i
$430$		0			0
$431$	−1.38707e6			−0.359671			−0.179836	−	0.983697i	$-0.557557\pi$
$431$	−1.38707e6			−0.359671			−0.179836	+	0.983697i	$0.557557\pi$
$432$	−2.81752e6	+	354727.i	−0.726368	+	0.0914502i
$433$		−	1.33169e6i		−	0.341336i	−0.985329	−	0.170668i	$-0.945407\pi$
$433$		−	1.33169e6i		−	0.341336i	0.985329	−	0.170668i	$-0.0545926\pi$
$434$	−52437.2	−	49252.2i	−0.0133633	−	0.0125517i
$435$		0			0
$436$	4.10245e6	−	257235.i	1.03354	−	0.0648058i
$437$	1.18797e6			0.297577
$438$	1.60373e6	+	1.50632e6i	0.399434	+	0.375173i
$439$	2.78241e6			0.689064			0.344532	−	0.938775i	$-0.388038\pi$
$439$	2.78241e6			0.689064			0.344532	+	0.938775i	$0.388038\pi$
$440$		0			0
$441$	1.53456e6			0.375741
$442$	−374224.	−	351494.i	−0.0911120	−	0.0855780i
$443$	−4.63595e6			−1.12235			−0.561177	−	0.827696i	$-0.689651\pi$
$443$	−4.63595e6			−1.12235			−0.561177	+	0.827696i	$0.689651\pi$
$444$	2269.69	+	36197.7i	0.000546399	+	0.00871411i
$445$		0			0
$446$	−2.57366e6	−	2.41734e6i	−0.612651	−	0.575440i
$447$			6.44063e6i			1.52461i
$448$	72615.1	−	13804.4i	0.0170935	−	0.00324955i
$449$	−1.18197e6			−0.276688			−0.138344	−	0.990384i	$-0.544178\pi$
$449$	−1.18197e6			−0.276688			−0.138344	+	0.990384i	$0.544178\pi$
$450$		0			0
$451$			6.82811e6i			1.58074i
$452$	3.67903e6	−	230686.i	0.847009	−	0.0531098i
$453$	−8.16001e6			−1.86829
$454$	−2.54062e6	+	2.70492e6i	−0.578496	+	0.615906i
$455$		0			0
$456$	−707931.	+	855190.i	−0.159433	+	0.192597i
$457$			1.55240e6i			0.347708i	0.984771	+	0.173854i	$0.0556220\pi$
$457$			1.55240e6i			0.347708i	−0.984771	+	0.173854i	$0.944378\pi$
$458$	−3.33068e6	−	3.12838e6i	−0.741940	−	0.696875i
$459$			2.35472e6i			0.521684i
$460$		0			0
$461$		−	7.43437e6i		−	1.62926i	−0.579978	−	0.814632i	$-0.696939\pi$
$461$		−	7.43437e6i		−	1.62926i	0.579978	−	0.814632i	$-0.303061\pi$
$462$	−66971.1	+	71301.9i	−0.0145976	+	0.0155416i
$463$		−	20179.5i		−	0.00437480i	−0.999998	−	0.00218740i	$-0.999304\pi$
$463$		−	20179.5i		−	0.00437480i	0.999998	−	0.00218740i	$-0.000696271\pi$
$464$	−666241.	−	5.29180e6i	−0.143660	−	1.14106i
$465$		0			0
$466$	5.37888e6	+	5.05218e6i	1.14743	+	1.07774i
$467$	−3.58698e6			−0.761092			−0.380546	−	0.924762i	$-0.624264\pi$
$467$	−3.58698e6			−0.761092			−0.380546	+	0.924762i	$0.624264\pi$
$468$	19549.8	+	311786.i	0.00412600	+	0.0658024i
$469$		−	149245.i		−	0.0313306i
$470$		0			0
$471$	−7.00885e6			−1.45578
$472$	2.70189e6	−	3.26392e6i	0.558229	−	0.674348i
$473$		−	1.01343e6i		−	0.208277i
$474$	2.72057e6	−	2.89650e6i	0.556178	−	0.592144i
$475$		0			0
$476$	−3835.56	−	61170.5i	−0.000775911	−	0.0123744i
$477$	1.24829e6			0.251200
$478$	4.71945e6	−	5.02464e6i	0.944760	−	1.00585i
$479$	−183482.			−0.0365388			−0.0182694	−	0.999833i	$-0.505816\pi$
$479$	−183482.			−0.0365388			−0.0182694	+	0.999833i	$0.505816\pi$
$480$		0			0
$481$	−6625.61			−0.00130576
$482$	−3.80922e6	+	4.05555e6i	−0.746824	+	0.795119i
$483$	146082.			0.0284925
$484$	29495.1	+	470395.i	0.00572316	+	0.0912744i
$485$		0			0
$486$	2.55255e6	−	2.71761e6i	0.490211	−	0.521912i
$487$			6.68968e6i			1.27815i	0.769143	+	0.639077i	$0.220683\pi$
$487$			6.68968e6i			1.27815i	−0.769143	+	0.639077i	$0.779317\pi$
$488$	3.86053e6	−	4.66358e6i	0.733834	−	0.886481i
$489$	7.40899e6			1.40116
$490$		0			0
$491$			9.90038e6i			1.85331i	0.375913	+	0.926655i	$0.377329\pi$
$491$			9.90038e6i			1.85331i	−0.375913	+	0.926655i	$0.622671\pi$
$492$	596335.	+	9.51050e6i	0.111065	+	1.77129i
$493$	−4.42259e6			−0.819520
$494$	−147827.	−	138849.i	−0.0272545	−	0.0255991i
$495$		0			0
$496$	−5.72792e6	+	721149.i	−1.04543	+	0.131620i
$497$			115993.i			0.0210639i
$498$	6.59747e6	−	7.02410e6i	1.19208	−	1.26916i
$499$			5.95907e6i			1.07134i	0.844428	+	0.535670i	$0.179941\pi$
$499$			5.95907e6i			1.07134i	−0.844428	+	0.535670i	$0.820059\pi$
$500$		0			0
$501$			3.52973e6i			0.628271i
$502$	−6.61057e6	−	6.20905e6i	−1.17079	−	1.09968i
$503$			3.69353e6i			0.650910i	0.945557	+	0.325455i	$0.105518\pi$
$503$			3.69353e6i			0.650910i	−0.945557	+	0.325455i	$0.894482\pi$
$504$	−23781.1	+	28727.9i	−0.00417019	+	0.00503765i
$505$		0			0
$506$	5.75087e6	−	6.12276e6i	0.998521	−	1.06309i
$507$	6.58010e6			1.13687
$508$	4.66366e6	−	292425.i	0.801803	−	0.0502753i
$509$			7.94222e6i			1.35877i	0.733780	+	0.679387i	$0.237754\pi$
$509$			7.94222e6i			1.35877i	−0.733780	+	0.679387i	$0.762246\pi$
$510$		0			0
$511$	−47982.9			−0.00812894
$512$	2.86253e6	−	5.19522e6i	0.482586	−	0.875849i
$513$			930172.i			0.156052i
$514$	4.44114e6	+	4.17139e6i	0.741458	+	0.696423i
$515$		0			0
$516$	−88508.4	−	1.41155e6i	−0.0146339	−	0.233385i
$517$	9.55157e6			1.57162
$518$	−576.528	−	541.510i	−9.44052e−5	−	8.86712e-5i
$519$	1.09598e7			1.78602
$520$		0			0
$521$	−1.06312e7			−1.71588			−0.857940	−	0.513749i	$-0.828256\pi$
$521$	−1.06312e7			−1.71588			−0.857940	+	0.513749i	$0.828256\pi$
$522$	1.96149e6	+	1.84235e6i	0.315072	+	0.295935i
$523$	3.13913e6			0.501828			0.250914	−	0.968009i	$-0.419269\pi$
$523$	3.13913e6			0.501828			0.250914	+	0.968009i	$0.419269\pi$
$524$	415121.	−	26029.2i	0.0660460	−	0.00414127i
$525$		0			0
$526$	3.35175e6	+	3.14817e6i	0.528211	+	0.496128i
$527$			4.78708e6i			0.750834i
$528$	980588.	+	7.78859e6i	0.153074	+	1.21583i
$529$	−6.10788e6			−0.948967
$530$		0			0
$531$			2.13783e6i			0.329032i
$532$	−1515.14	−	24163.8i	−0.000232099	−	0.00370158i
$533$	−1.74080e6			−0.265418
$534$	−4.29683e6	+	4.57469e6i	−0.652071	+	0.694238i
$535$		0			0
$536$	−9.22584e6	−	7.63720e6i	−1.38706	−	1.14821i
$537$		−	7.70298e6i		−	1.15272i
$538$	469876.	+	441337.i	0.0699887	+	0.0657377i
$539$			7.04438e6i			1.04441i
$540$		0			0
$541$		−	1.20044e7i		−	1.76339i	−0.471821	−	0.881694i	$-0.656403\pi$
$541$		−	1.20044e7i		−	1.76339i	0.471821	−	0.881694i	$-0.343597\pi$
$542$	1.44351e6	−	1.53686e6i	0.211067	−	0.224716i
$543$		−	3.35273e6i		−	0.487976i
$544$	−3.97763e6	−	2.89312e6i	−0.576271	−	0.419150i
$545$		0			0
$546$	−18178.1	−	17074.0i	−0.00260956	−	0.00245106i
$547$	9.93035e6			1.41905			0.709523	−	0.704682i	$-0.248910\pi$
$547$	9.93035e6			1.41905			0.709523	+	0.704682i	$0.248910\pi$
$548$	6.04266e6	−	378891.i	0.859561	−	0.0538969i
$549$			3.05460e6i			0.432537i
$550$		0			0
$551$	−1.74703e6			−0.245144
$552$	7.47534e6	−	9.03031e6i	1.04420	−	1.26141i
$553$			86662.2i			0.0120508i
$554$	3.54077e6	−	3.76974e6i	0.490144	−	0.521840i
$555$		0			0
$556$	1.41592e6	−	88782.1i	0.194246	−	0.0121798i
$557$	−8.72764e6			−1.19195			−0.595976	−	0.803002i	$-0.703235\pi$
$557$	−8.72764e6			−1.19195			−0.595976	+	0.803002i	$0.703235\pi$
$558$	1.99419e6	−	2.12314e6i	0.271132	−	0.288665i
$559$	258370.			0.0349714
$560$		0			0
$561$	6.50926e6			0.873222
$562$	−1.97972e6	+	2.10774e6i	−0.264401	+	0.281499i
$563$	2.13884e6			0.284386			0.142193	−	0.989839i	$-0.454585\pi$
$563$	2.13884e6			0.284386			0.142193	+	0.989839i	$0.454585\pi$
$564$	1.33039e7	−	834189.i	1.76108	−	0.110425i
$565$		0			0
$566$	2.06451e6	−	2.19802e6i	0.270880	−	0.288397i
$567$			164445.i			0.0214814i
$568$	7.17026e6	+	5.93558e6i	0.932533	+	0.771956i
$569$	−2.98366e6			−0.386339			−0.193169	−	0.981165i	$-0.561877\pi$
$569$	−2.98366e6			−0.386339			−0.193169	+	0.981165i	$0.561877\pi$
$570$		0			0
$571$			8.50264e6i			1.09135i	0.837997	+	0.545674i	$0.183726\pi$
$571$			8.50264e6i			1.09135i	−0.837997	+	0.545674i	$0.816274\pi$
$572$	−1.43125e6	+	89743.2i	−0.182905	+	0.0114686i
$573$	−1.79654e7			−2.28586
$574$	−151476.	−	142275.i	−0.0191895	−	0.0180239i
$575$		0			0
$576$	558931.	+	2.94013e6i	0.0701944	+	0.369242i
$577$		−	1.55926e7i		−	1.94975i	−0.222756	−	0.974874i	$-0.571505\pi$
$577$		−	1.55926e7i		−	1.94975i	0.222756	−	0.974874i	$-0.428495\pi$
$578$	2.70667e6	−	2.88170e6i	0.336989	−	0.358781i
$579$		−	3.01658e6i		−	0.373954i
$580$		0			0
$581$			210159.i			0.0258289i
$582$	−1.18689e7	−	1.11480e7i	−1.45246	−	1.36424i
$583$			5.73025e6i			0.698236i
$584$	−2.45538e6	+	2.96614e6i	−0.297912	+	0.359881i
$585$		0			0
$586$	9.86205e6	−	1.04998e7i	1.18638	−	1.26310i
$587$	−1.01432e7			−1.21501			−0.607507	−	0.794314i	$-0.707830\pi$
$587$	−1.01432e7			−1.21501			−0.607507	+	0.794314i	$0.707830\pi$
$588$	615223.	+	9.81174e6i	0.0733820	+	1.17031i
$589$			1.89101e6i			0.224598i
$590$		0			0
$591$	−9.26315e6			−1.09091
$592$	−62976.5	+	7928.77i	−0.00738540	+	0.000929826i
$593$		−	1.44098e7i		−	1.68276i	−0.540442	−	0.841381i	$-0.681743\pi$
$593$		−	1.44098e7i		−	1.68276i	0.540442	−	0.841381i	$-0.318257\pi$
$594$	4.79409e6	+	4.50291e6i	0.557494	+	0.523633i
$595$		0			0
$596$	−1.12496e7	+	705381.i	−1.29724	+	0.0813407i
$597$	8.69706e6			0.998704
$598$	1.56097e6	+	1.46616e6i	0.178502	+	0.167660i
$599$	3.13415e6			0.356905			0.178452	−	0.983949i	$-0.442891\pi$
$599$	3.13415e6			0.356905			0.178452	+	0.983949i	$0.442891\pi$
$600$		0			0
$601$	1.57244e7			1.77578			0.887889	−	0.460058i	$-0.152171\pi$
$601$	1.57244e7			1.77578			0.887889	+	0.460058i	$0.152171\pi$
$602$	22482.1	+	21116.6i	0.00252840	+	0.00237483i
$603$	6.04283e6			0.676780
$604$	−893688.	−	1.42528e7i	−0.0996766	−	1.58967i
$605$		0			0
$606$	−9.38699e6	−	8.81683e6i	−1.03835	−	0.975284i
$607$		−	1.03887e7i		−	1.14443i	−0.820102	−	0.572217i	$-0.806083\pi$
$607$		−	1.03887e7i		−	1.14443i	0.820102	−	0.572217i	$-0.193917\pi$
$608$	−1.57126e6	−	1.14285e6i	−0.172381	−	0.125381i
$609$	−214830.			−0.0234721
$610$		0			0
$611$			2.43513e6i			0.263888i
$612$	2.47675e6	−	155299.i	0.267303	−	0.0167606i
$613$	1.46355e7			1.57310			0.786551	−	0.617525i	$-0.211865\pi$
$613$	1.46355e7			1.57310			0.786551	+	0.617525i	$0.211865\pi$
$614$	2.86849e6	−	3.05399e6i	0.307067	−	0.326923i
$615$		0			0
$616$	−131875.	−	109167.i	−0.0140027	−	0.0115915i
$617$		−	6.06227e6i		−	0.641095i	−0.947233	−	0.320547i	$-0.896133\pi$
$617$		−	6.06227e6i		−	0.641095i	0.947233	−	0.320547i	$-0.103867\pi$
$618$	−780044.	−	732665.i	−0.0821576	−	0.0771674i
$619$			888836.i			0.0932384i	0.998913	+	0.0466192i	$0.0148447\pi$
$619$			888836.i			0.0932384i	−0.998913	+	0.0466192i	$0.985155\pi$
$620$		0			0
$621$		−	9.82207e6i		−	1.02205i
$622$	4.21658e6	−	4.48925e6i	0.437003	−	0.465262i
$623$		−	136873.i		−	0.0141285i
$624$	−1.98567e6	+	249997.i	−0.204148	+	0.0257024i
$625$		0			0
$626$	−4.46454e6	−	4.19337e6i	−0.455346	−	0.427688i
$627$	2.57132e6			0.261208
$628$	−767613.	−	1.22421e7i	−0.0776682	−	1.23867i
$629$			52632.2i			0.00530426i
$630$		0			0
$631$	5.86047e6			0.585948			0.292974	−	0.956120i	$-0.405355\pi$
$631$	5.86047e6			0.585948			0.292974	+	0.956120i	$0.405355\pi$
$632$	5.35716e6	+	4.43468e6i	0.533509	+	0.441642i
$633$			4.76256e6i			0.472423i
$634$	−1.13568e7	+	1.20912e7i	−1.12210	+	1.19466i
$635$		0			0
$636$	500453.	+	7.98136e6i	0.0490592	+	0.782409i
$637$	−1.79594e6			−0.175365
$638$	−8.45727e6	+	9.00418e6i	−0.822581	+	0.875774i
$639$	−4.69645e6			−0.455007
$640$		0			0
$641$	6.88679e6			0.662021			0.331011	−	0.943627i	$-0.392610\pi$
$641$	6.88679e6			0.662021			0.331011	+	0.943627i	$0.392610\pi$
$642$	−5.01119e6	+	5.33525e6i	−0.479848	+	0.510878i
$643$	−7.66403e6			−0.731021			−0.365510	−	0.930807i	$-0.619106\pi$
$643$	−7.66403e6			−0.731021			−0.365510	+	0.930807i	$0.619106\pi$
$644$	15999.0	+	255156.i	0.00152012	+	0.0242433i
$645$		0			0
$646$	−1.10298e6	+	1.17430e6i	−0.103989	+	0.110713i
$647$			3.93185e6i			0.369263i	0.982808	+	0.184631i	$0.0591092\pi$
$647$			3.93185e6i			0.369263i	−0.982808	+	0.184631i	$0.940891\pi$
$648$	1.01654e7	+	8.41500e6i	0.951017	+	0.787257i
$649$	−9.81369e6			−0.914577
$650$		0			0
$651$			232535.i			0.0215048i
$652$	811436.	+	1.29410e7i	0.0747542	+	1.19220i
$653$	−5.55582e6			−0.509876			−0.254938	−	0.966957i	$-0.582055\pi$
$653$	−5.55582e6			−0.509876			−0.254938	+	0.966957i	$0.582055\pi$
$654$	−9.68446e6	−	9.09623e6i	−0.885382	−	0.831605i
$655$		0			0
$656$	−1.65463e7	+	2.08319e6i	−1.50121	+	0.189003i
$657$		−	1.94279e6i		−	0.175595i
$658$	−199023.	+	211893.i	−0.0179200	+	0.0190789i
$659$			2.17299e6i			0.194914i	0.995240	+	0.0974572i	$0.0310709\pi$
$659$			2.17299e6i			0.194914i	−0.995240	+	0.0974572i	$0.968929\pi$
$660$		0			0
$661$			6.93458e6i			0.617329i	0.951171	+	0.308665i	$0.0998821\pi$
$661$			6.93458e6i			0.617329i	−0.951171	+	0.308665i	$0.900118\pi$
$662$	−1.47289e6	−	1.38343e6i	−0.130625	−	0.122691i
$663$			1.65951e6i			0.146621i
$664$	1.29913e7	+	1.07542e7i	1.14349	+	0.946586i
$665$		0			0
$666$	21925.4	−	23343.2i	0.00191541	−	0.00203927i
$667$	1.84476e7			1.60556
$668$	−6.16524e6	+	386578.i	−0.534575	+	0.0335193i
$669$			1.14130e7i			0.985902i
$670$		0			0
$671$	−1.40221e7			−1.20228
$672$	−193215.	−	140535.i	−0.0165051	−	0.0120050i
$673$		−	7.72402e6i		−	0.657364i	−0.944441	−	0.328682i	$-0.893396\pi$
$673$		−	7.72402e6i		−	0.657364i	0.944441	−	0.328682i	$-0.106604\pi$
$674$	5.98677e6	+	5.62314e6i	0.507625	+	0.476792i
$675$		0			0
$676$	720655.	+	1.14932e7i	0.0606542	+	0.967329i
$677$	−1.38586e7			−1.16211			−0.581054	−	0.813865i	$-0.697360\pi$
$677$	−1.38586e7			−1.16211			−0.581054	+	0.813865i	$0.697360\pi$
$678$	−8.68493e6	−	8.15742e6i	−0.725591	−	0.681520i
$679$	355113.			0.0295592
$680$		0			0
$681$	1.19951e7			0.991139
$682$	9.74625e6	+	9.15427e6i	0.802373	+	0.753638i
$683$	778871.			0.0638872			0.0319436	−	0.999490i	$-0.489830\pi$
$683$	778871.			0.0638872			0.0319436	+	0.999490i	$0.489830\pi$
$684$	978377.	−	61346.9i	0.0799587	−	0.00501363i
$685$		0			0
$686$	−312595.	−	293608.i	−0.0253613	−	0.0238209i
$687$			1.47700e7i			1.19396i
$688$	2.45581e6	−	309188.i	0.197799	−	0.0249030i
$689$	−1.46090e6			−0.117239
$690$		0			0
$691$			6.98899e6i			0.556826i	0.960461	+	0.278413i	$0.0898084\pi$
$691$			6.98899e6i			0.556826i	−0.960461	+	0.278413i	$0.910192\pi$
$692$	1.20033e6	+	1.91431e7i	0.0952871	+	1.51966i
$693$	86376.8			0.00683225
$694$	1.52486e6	−	1.62347e6i	0.120180	−	0.127952i
$695$		0			0
$696$	−1.09933e7	+	1.32800e7i	−0.860210	+	1.03915i
$697$			1.38285e7i			1.07818i
$698$	−7.16931e6	−	6.73386e6i	−0.556979	−	0.523149i
$699$		−	2.38529e7i		−	1.84649i
$700$		0			0
$701$		−	4.14587e6i		−	0.318655i	−0.987226	−	0.159328i	$-0.949067\pi$
$701$		−	4.14587e6i		−	0.318655i	0.987226	−	0.159328i	$-0.0509326\pi$
$702$	−1.14800e6	+	1.22223e6i	−0.0879221	+	0.0936077i
$703$			20791.0i			0.00158667i
$704$	−1.34966e7	+	2.56576e6i	−1.02635	+	0.195112i
$705$		0			0
$706$	8.45781e6	+	7.94410e6i	0.638626	+	0.599836i
$707$	280855.			0.0211317
$708$	−1.36690e7	+	857081.i	−1.02483	+	0.0642597i
$709$		−	1.52511e7i		−	1.13943i	−0.821843	−	0.569714i	$-0.807054\pi$
$709$		−	1.52511e7i		−	1.13943i	0.821843	−	0.569714i	$-0.192946\pi$
$710$		0			0
$711$	−3.50889e6			−0.260313
$712$	−8.46102e6	−	7.00407e6i	−0.625493	−	0.517787i
$713$		−	1.99680e7i		−	1.47099i
$714$	−135632.	+	144402.i	−0.00995670	+	0.0106006i
$715$		0			0
$716$	1.34545e7	−	843634.i	0.980809	−	0.0614995i
$717$	−2.22820e7			−1.61866
$718$	−1.38154e7	+	1.47088e7i	−1.00012	+	1.06480i
$719$	1.60151e6			0.115534			0.0577668	−	0.998330i	$-0.481602\pi$
$719$	1.60151e6			0.115534			0.0577668	+	0.998330i	$0.481602\pi$
$720$		0			0
$721$	23338.6			0.00167200
$722$	9.15378e6	−	9.74572e6i	0.653518	−	0.695779i
$723$	1.79845e7			1.27954
$724$	5.85607e6	−	367192.i	0.415203	−	0.0260344i
$725$		0			0
$726$	1.04299e6	−	1.11044e6i	0.0734412	−	0.0781904i
$727$		−	6.15453e6i		−	0.431876i	−0.976407	−	0.215938i	$-0.930719\pi$
$727$		−	6.15453e6i		−	0.431876i	0.976407	−	0.215938i	$-0.0692809\pi$
$728$	27831.6	−	33621.0i	0.00194630	−	0.00235116i
$729$	5.66362e6			0.394708
$730$		0			0
$731$		−	2.05243e6i		−	0.142061i
$732$	−1.95306e7	+	1.22462e6i	−1.34722	+	0.0844742i
$733$	−7.15476e6			−0.491853			−0.245926	−	0.969289i	$-0.579092\pi$
$733$	−7.15476e6			−0.491853			−0.245926	+	0.969289i	$0.579092\pi$
$734$	−1.53682e7	−	1.44348e7i	−1.05289	−	0.988941i
$735$		0			0
$736$	1.65916e7	+	1.20679e7i	1.12900	+	0.821176i
$737$			2.77395e7i			1.88118i
$738$	5.76062e6	−	6.13314e6i	0.389340	−	0.414517i
$739$		−	2.74026e7i		−	1.84578i	−0.385063	−	0.922890i	$-0.625820\pi$
$739$		−	2.74026e7i		−	1.84578i	0.385063	−	0.922890i	$-0.374180\pi$
$740$		0			0
$741$			655547.i			0.0438589i
$742$	−127121.	−	119400.i	−0.00847631	−	0.00796147i
$743$			1.20016e7i			0.797569i	0.917045	+	0.398785i	$0.130568\pi$
$743$			1.20016e7i			0.797569i	−0.917045	+	0.398785i	$0.869432\pi$
$744$	1.43745e7	+	1.18993e7i	0.952052	+	0.788114i
$745$		0			0
$746$	6.62773e6	−	7.05632e6i	0.436031	−	0.464228i
$747$	−8.50916e6			−0.557937
$748$	712898.	+	1.13695e7i	0.0465879	+	0.742996i
$749$		−	159629.i		−	0.0103970i
$750$		0			0
$751$	3.38961e6			0.219305			0.109653	−	0.993970i	$-0.465026\pi$
$751$	3.38961e6			0.219305			0.109653	+	0.993970i	$0.465026\pi$
$752$	2.91409e6	+	2.31460e7i	0.187914	+	1.49256i
$753$			2.93148e7i			1.88408i
$754$	−2.29558e6	−	2.15615e6i	−0.147050	−	0.138118i
$755$		0			0
$756$	−199786.	+	12527.2i	−0.0127134	+	0.000797165i
$757$	−3.47336e6			−0.220298			−0.110149	−	0.993915i	$-0.535133\pi$
$757$	−3.47336e6			−0.220298			−0.110149	+	0.993915i	$0.535133\pi$
$758$	−1.48509e7	−	1.39489e7i	−0.938814	−	0.881792i
$759$	−2.71516e7			−1.71077
$760$		0			0
$761$	−1.16257e6			−0.0727710			−0.0363855	−	0.999338i	$-0.511584\pi$
$761$	−1.16257e6			−0.0727710			−0.0363855	+	0.999338i	$0.511584\pi$
$762$	−1.10093e7	−	1.03406e7i	−0.686866	−	0.645147i
$763$	289755.			0.0180186
$764$	−1.96758e6	−	3.13794e7i	−0.121955	−	1.94496i
$765$		0			0
$766$	1.57045e7	+	1.47506e7i	0.967054	+	0.908317i
$767$		−	2.50196e6i		−	0.153565i
$768$	−1.85746e7	+	4.75244e6i	−1.13636	+	0.290746i
$769$	1.71387e7			1.04511			0.522556	−	0.852605i	$-0.324979\pi$
$769$	1.71387e7			1.04511			0.522556	+	0.852605i	$0.324979\pi$
$770$		0			0
$771$		−	1.96944e7i		−	1.19318i
$772$	5.26894e6	−	330377.i	0.318185	−	0.0199511i
$773$	3.17392e7			1.91050			0.955250	−	0.295800i	$-0.0955860\pi$
$773$	3.17392e7			1.91050			0.955250	+	0.295800i	$0.0955860\pi$
$774$	−854995.	+	910285.i	−0.0512993	+	0.0546166i
$775$		0			0
$776$	1.81719e7	−	2.19519e7i	1.08329	−	1.30863i
$777$			2556.64i			0.000151921i
$778$	−1.78043e6	−	1.67228e6i	−0.105457	−	0.0990515i
$779$			5.46258e6i			0.322518i
$780$		0			0
$781$		−	2.15590e7i		−	1.26474i
$782$	1.16468e7	−	1.24000e7i	0.681068	−	0.725110i
$783$			1.44444e7i			0.841968i
$784$	−1.70704e7	+	2.14917e6i	−0.991867	+	0.124877i
$785$		0			0
$786$	−979957.	−	920435.i	−0.0565784	−	0.0531419i
$787$	−2.67032e6			−0.153683			−0.0768416	−	0.997043i	$-0.524484\pi$
$787$	−2.67032e6			−0.153683			−0.0768416	+	0.997043i	$0.524484\pi$
$788$	−1.01450e6	−	1.61796e7i	−0.0582021	−	0.928221i
$789$		−	1.48635e7i		−	0.850018i
$790$		0			0
$791$	259850.			0.0147666
$792$	4.42008e6	−	5.33952e6i	0.250390	−	0.302475i
$793$		−	3.57487e6i		−	0.201873i
$794$	−8.84804e6	+	9.42021e6i	−0.498076	+	0.530285i
$795$		0			0
$796$	952506.	+	1.51908e7i	0.0532826	+	0.849764i
$797$	−3.37393e7			−1.88144			−0.940719	−	0.339188i	$-0.889848\pi$
$797$	−3.37393e7			−1.88144			−0.940719	+	0.339188i	$0.889848\pi$
$798$	−53577.8	+	57042.5i	−0.00297836	+	0.00317096i
$799$	1.93441e7			1.07197
$800$		0			0
$801$	5.54189e6			0.305194
$802$	6.33102e6	−	6.74042e6i	0.347566	−	0.370042i
$803$	8.91835e6			0.488085
$804$	2.42264e6	+	3.86369e7i	0.132175	+	2.10796i
$805$		0			0
$806$	−2.33384e6	+	2.48477e6i	−0.126542	+	0.134725i
$807$		−	2.08369e6i		−	0.112629i
$808$	1.43719e7	−	1.73615e7i	0.774439	−	0.935533i
$809$	−1.25443e6			−0.0673870			−0.0336935	−	0.999432i	$-0.510727\pi$
$809$	−1.25443e6			−0.0673870			−0.0336935	+	0.999432i	$0.510727\pi$
$810$		0			0
$811$		−	1.12827e7i		−	0.602365i	−0.953567	−	0.301182i	$-0.902619\pi$
$811$		−	1.12827e7i		−	0.602365i	0.953567	−	0.301182i	$-0.0973813\pi$
$812$	−23528.3	−	375235.i	−0.00125228	−	0.0199716i
$813$	−6.81525e6			−0.361622
$814$	107156.	+	100648.i	0.00566836	+	0.00532407i
$815$		0			0
$816$	1.98591e6	+	1.57737e7i	0.104408	+	0.829291i
$817$		−	810760.i		−	0.0424949i
$818$	−2.02097e7	+	2.15166e7i	−1.05603	+	1.12432i
$819$			22021.4i			0.00114719i
$820$		0			0
$821$			1.21845e7i			0.630886i	0.948945	+	0.315443i	$0.102153\pi$
$821$			1.21845e7i			0.630886i	−0.948945	+	0.315443i	$0.897847\pi$
$822$	−1.42646e7	−	1.33982e7i	−0.736344	−	0.691619i
$823$			2.12650e7i			1.09437i	0.837010	+	0.547187i	$0.184302\pi$
$823$			2.12650e7i			1.09437i	−0.837010	+	0.547187i	$0.815698\pi$
$824$	1.19429e6	−	1.44271e6i	0.0612760	−	0.0740222i
$825$		0			0
$826$	204485.	−	217708.i	0.0104282	−	0.0111026i
$827$	6.06316e6			0.308273			0.154136	−	0.988050i	$-0.450740\pi$
$827$	6.06316e6			0.308273			0.154136	+	0.988050i	$0.450740\pi$
$828$	−1.03311e7	+	647788.i	−0.523685	+	0.0328365i
$829$			727353.i			0.0367586i	0.999831	+	0.0183793i	$0.00585064\pi$
$829$			727353.i			0.0367586i	−0.999831	+	0.0183793i	$0.994149\pi$
$830$		0			0
$831$	−1.67171e7			−0.839765
$832$	−654131.	−	3.44091e6i	−0.0327609	−	0.172332i
$833$			1.42665e7i			0.712368i
$834$	−3.34250e6	−	3.13948e6i	−0.166401	−	0.156294i
$835$		0			0
$836$	281612.	+	4.49122e6i	0.0139359	+	0.222253i
$837$	1.56348e7			0.771401
$838$	2.74806e6	+	2.58114e6i	0.135181	+	0.126970i
$839$	1.36723e7			0.670560			0.335280	−	0.942118i	$-0.391169\pi$
$839$	1.36723e7			0.670560			0.335280	+	0.942118i	$0.391169\pi$
$840$		0			0
$841$	−6.61809e6			−0.322658
$842$	2.81209e7	+	2.64129e7i	1.36694	+	1.28391i
$843$	9.34688e6			0.452999
$844$	−8.31858e6	+	521598.i	−0.401969	+	0.0252046i
$845$		0			0
$846$	−8.57941e6	−	8.05831e6i	−0.412127	−	0.387095i
$847$			33223.9i			0.00159126i
$848$	−1.38859e7	+	1.74824e6i	−0.663109	+	0.0834858i
$849$	−9.74720e6			−0.464099
$850$		0			0
$851$		−	219541.i		−	0.0103918i
$852$	−1.88286e6	−	3.00283e7i	−0.0888626	−	1.41720i
$853$	3.66971e7			1.72687			0.863434	−	0.504462i	$-0.168309\pi$
$853$	3.66971e7			1.72687			0.863434	+	0.504462i	$0.168309\pi$
$854$	292174.	−	311068.i	0.0137087	−	0.0145952i
$855$		0			0
$856$	−9.86769e6	−	8.16853e6i	−0.460290	−	0.381030i
$857$		−	1.73498e7i		−	0.806941i	−0.914993	−	0.403470i	$-0.867804\pi$
$857$		−	1.73498e7i		−	0.806941i	0.914993	−	0.403470i	$-0.132196\pi$
$858$	3.37868e6	+	3.17346e6i	0.156685	+	0.147169i
$859$		−	1.90085e7i		−	0.878954i	−0.898254	−	0.439477i	$-0.855164\pi$
$859$		−	1.90085e7i		−	0.878954i	0.898254	−	0.439477i	$-0.144836\pi$
$860$		0			0
$861$			671726.i			0.0308805i
$862$	−5.37187e6	+	5.71925e6i	−0.246239	+	0.262163i
$863$		−	3.46920e7i		−	1.58563i	−0.609460	−	0.792816i	$-0.708614\pi$
$863$		−	3.46920e7i		−	1.58563i	0.609460	−	0.792816i	$-0.291386\pi$
$864$	−9.44910e6	+	1.29911e7i	−0.430632	+	0.592056i
$865$		0			0
$866$	−5.49089e6	−	5.15738e6i	−0.248799	−	0.233687i
$867$	−1.27790e7			−0.577364
$868$	−406159.	+	25467.3i	−0.0182977	+	0.00114732i
$869$		−	1.61075e7i		−	0.723566i
$870$		0			0
$871$	−7.07207e6			−0.315865
$872$	1.48274e7	−	1.79117e7i	0.660349	−	0.797710i
$873$			1.43783e7i			0.638515i
$874$	4.60077e6	−	4.89829e6i	0.203729	−	0.216903i
$875$		0			0
$876$	1.24219e7	−	778886.i	0.546924	−	0.0342937i
$877$	3.99003e7			1.75177			0.875885	−	0.482520i	$-0.160279\pi$
$877$	3.99003e7			1.75177			0.875885	+	0.482520i	$0.160279\pi$
$878$	1.07758e7	−	1.14726e7i	0.471750	−	0.502256i
$879$	−4.65618e7			−2.03262
$880$		0			0
$881$	−3.50875e7			−1.52304			−0.761522	−	0.648139i	$-0.775548\pi$
$881$	−3.50875e7			−1.52304			−0.761522	+	0.648139i	$0.775548\pi$
$882$	5.94309e6	−	6.32741e6i	0.257241	−	0.273876i
$883$	−1.47881e7			−0.638279			−0.319139	−	0.947708i	$-0.603394\pi$
$883$	−1.47881e7			−0.638279			−0.319139	+	0.947708i	$0.603394\pi$
$884$	−2.89860e6	+	181750.i	−0.124755	+	0.00782248i
$885$		0			0
$886$	−1.79542e7	+	1.91152e7i	−0.768390	+	0.818079i
$887$		−	1.17291e7i		−	0.500560i	−0.968173	−	0.250280i	$-0.919477\pi$
$887$		−	1.17291e7i		−	0.500560i	0.968173	−	0.250280i	$-0.0805228\pi$
$888$	158043.	+	130828.i	0.00672576	+	0.00556762i
$889$	329394.			0.0139785
$890$		0			0
$891$		−	3.05646e7i		−	1.28981i
$892$	−1.99346e7	+	1.24996e6i	−0.838872	+	0.0525996i
$893$	7.64139e6			0.320659
$894$	2.65564e7	+	2.49434e7i	1.11128	+	1.04379i
$895$		0			0
$896$	224306.	−	352873.i	0.00933406	−	0.0146841i
$897$		−	6.92219e6i		−	0.287252i
$898$	−4.57755e6	+	4.87356e6i	−0.189427	+	0.201677i
$899$			2.93651e7i			1.21180i
$900$		0			0
$901$			1.16051e7i			0.476251i
$902$	2.81541e7	+	2.64440e7i	1.15219	+	1.08221i
$903$		−	99697.9i		−	0.00406880i
$904$	1.32971e7	−	1.60630e7i	0.541171	−	0.653742i
$905$		0			0
$906$	−3.16022e7	+	3.36458e7i	−1.27908	+	1.36179i
$907$	−1.36136e7			−0.549483			−0.274742	−	0.961518i	$-0.588592\pi$
$907$	−1.36136e7			−0.549483			−0.274742	+	0.961518i	$0.588592\pi$
$908$	1.31370e6	+	2.09513e7i	0.0528790	+	0.843328i
$909$			1.13716e7i			0.456470i
$910$		0			0
$911$	1.26888e7			0.506551			0.253276	−	0.967394i	$-0.418492\pi$
$911$	1.26888e7			0.506551			0.253276	+	0.967394i	$0.418492\pi$
$912$	784484.	+	6.23098e6i	0.0312318	+	0.248067i
$913$		−	3.90611e7i		−	1.55084i
$914$	6.40097e6	+	6.01218e6i	0.253443	+	0.238049i
$915$		0			0
$916$	−2.57982e7	+	1.61762e6i	−1.01590	+	0.0636998i
$917$	29319.9			0.00115144
$918$	9.70913e6	+	9.11941e6i	0.380254	+	0.357158i
$919$	4.25253e7			1.66096			0.830479	−	0.557050i	$-0.188067\pi$
$919$	4.25253e7			1.66096			0.830479	+	0.557050i	$0.188067\pi$
$920$		0			0
$921$	−1.35430e7			−0.526098
$922$	−3.06538e7	−	2.87919e7i	−1.18757	−	1.11543i
$923$	5.49637e6			0.212360
$924$	34629.4	+	552278.i	0.00133434	+	0.0212803i
$925$		0			0
$926$	−83205.3	−	78151.5i	−0.00318877	−	0.00299509i
$927$			944963.i			0.0361173i
$928$	−2.43997e7	−	1.77471e7i	−0.930068	−	0.676484i
$929$	−4.25450e6			−0.161737			−0.0808686	−	0.996725i	$-0.525769\pi$
$929$	−4.25450e6			−0.161737			−0.0808686	+	0.996725i	$0.525769\pi$
$930$		0			0
$931$			5.63560e6i			0.213092i
$932$	4.16629e7	−	2.61238e6i	1.57112	−	0.0985136i
$933$	−1.99078e7			−0.748718
$934$	−1.38917e7	+	1.47901e7i	−0.521062	+	0.554757i
$935$		0			0
$936$	1.36129e6	+	1.12688e6i	0.0507879	+	0.0420425i
$937$			1.07844e7i			0.401279i	0.979665	+	0.200640i	$0.0643020\pi$
$937$			1.07844e7i			0.401279i	−0.979665	+	0.200640i	$0.935698\pi$
$938$	−615377.	−	578000.i	−0.0228368	−	0.0214497i
$939$			1.97982e7i			0.732760i
$940$		0			0
$941$		−	112960.i		−	0.00415862i	−0.999998	−	0.00207931i	$-0.999338\pi$
$941$		−	112960.i		−	0.00415862i	0.999998	−	0.00207931i	$-0.000661865\pi$
$942$	−2.71440e7	+	2.88993e7i	−0.996659	+	1.06111i
$943$		−	5.76817e7i		−	2.11232i
$944$	−2.99406e6	−	2.37811e7i	−0.109353	−	0.868566i
$945$		0			0
$946$	−4.17864e6	−	3.92484e6i	−0.151813	−	0.142592i
$947$	−1.62952e7			−0.590454			−0.295227	−	0.955427i	$-0.595395\pi$
$947$	−1.62952e7			−0.590454			−0.295227	+	0.955427i	$0.595395\pi$
$948$	−1.40675e6	−	2.24352e7i	−0.0508389	−	0.810792i
$949$			2.27370e6i			0.0819534i
$950$		0			0
$951$	5.36188e7			1.92250
$952$	−267077.	−	221087.i	−0.00955088	−	0.00790627i
$953$			1.07203e7i			0.382363i	0.981555	+	0.191181i	$0.0612318\pi$
$953$			1.07203e7i			0.382363i	−0.981555	+	0.191181i	$0.938768\pi$
$954$	4.83440e6	−	5.14703e6i	0.171978	−	0.183099i
$955$		0			0
$956$	−2.44033e6	−	3.89190e7i	−0.0863583	−	1.37726i
$957$	3.99294e7			1.40933
$958$	−710592.	+	756544.i	−0.0250154	+	0.0266330i
$959$	426792.			0.0149855
$960$		0			0
$961$	3.15601e6			0.110238
$962$	−25659.8	+	27319.1i	−0.000893954	+	0.000951763i
$963$	6.46324e6			0.224587
$964$	1.96967e6	+	3.14128e7i	0.0682654	+	1.08871i
$965$		0			0
$966$	565750.	−	602335.i	0.0195066	−	0.0207680i
$967$		−	3.92793e7i		−	1.35082i	−0.737442	−	0.675411i	$-0.763966\pi$
$967$		−	3.92793e7i		−	1.35082i	0.737442	−	0.675411i	$-0.236034\pi$
$968$	2.05379e6	+	1.70014e6i	0.0704478	+	0.0583171i
$969$	5.20750e6			0.178164
$970$		0			0
$971$			2.76288e7i			0.940405i	0.882559	+	0.470202i	$0.155819\pi$
$971$			2.76288e7i			0.940405i	−0.882559	+	0.470202i	$0.844181\pi$
$972$	−1.31987e6	−	2.10496e7i	−0.0448091	−	0.714626i
$973$	100006.			0.00338645
$974$	2.75833e7	+	2.59079e7i	0.931642	+	0.875055i
$975$		0			0
$976$	−4.27800e6	−	3.39792e7i	−0.143753	−	1.14180i
$977$		−	2.56548e7i		−	0.859868i	−0.902860	−	0.429934i	$-0.858537\pi$
$977$		−	2.56548e7i		−	0.859868i	0.902860	−	0.429934i	$-0.141463\pi$
$978$	2.86937e7	−	3.05492e7i	0.959266	−	1.02130i
$979$			2.54399e7i			0.848318i
$980$		0			0
$981$			1.17320e7i			0.389223i
$982$	4.08218e7	+	3.83424e7i	1.35087	+	1.26882i
$983$			5.21860e6i			0.172254i	0.996284	+	0.0861271i	$0.0274491\pi$
$983$			5.21860e6i			0.172254i	−0.996284	+	0.0861271i	$0.972551\pi$
$984$	4.15238e7	+	3.43736e7i	1.36713	+	1.13172i
$985$		0			0
$986$	−1.71279e7	+	1.82355e7i	−0.561063	+	0.597345i
$987$	939650.			0.0307025
$988$	−1.14502e6	+	71795.8i	−0.0373181	+	0.00233995i
$989$			8.56115e6i			0.278318i
$990$		0			0
$991$	4.76772e7			1.54215			0.771075	−	0.636744i	$-0.219719\pi$
$991$	4.76772e7			1.54215			0.771075	+	0.636744i	$0.219719\pi$
$992$	−1.92097e7	+	2.64106e7i	−0.619786	+	0.852117i
$993$			6.53158e6i			0.210206i
$994$	478267.	+	449218.i	0.0153534	+	0.0144209i
$995$		0			0
$996$	−3.41142e6	−	5.44061e7i	−0.108965	−	1.73780i
$997$	2.96368e7			0.944263			0.472132	−	0.881528i	$-0.343485\pi$
$997$	2.96368e7			0.944263			0.472132	+	0.881528i	$0.343485\pi$
$998$	2.45708e7	+	2.30784e7i	0.780896	+	0.733465i
$999$	171900.			0.00544955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.29		40
4.3	odd	2		800.6.f.d.49.32		40
5.2	odd	4		200.6.d.d.101.16	yes	20
5.3	odd	4		200.6.d.c.101.5	✓	20
5.4	even	2	inner	200.6.f.d.149.12		40
8.3	odd	2		800.6.f.d.49.10		40
8.5	even	2	inner	200.6.f.d.149.11		40
20.3	even	4		800.6.d.d.401.16		20
20.7	even	4		800.6.d.b.401.5		20
20.19	odd	2		800.6.f.d.49.9		40
40.3	even	4		800.6.d.d.401.5		20
40.13	odd	4		200.6.d.c.101.6	yes	20
40.19	odd	2		800.6.f.d.49.31		40
40.27	even	4		800.6.d.b.401.16		20
40.29	even	2	inner	200.6.f.d.149.30		40
40.37	odd	4		200.6.d.d.101.15	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.5	✓	20	5.3	odd	4
200.6.d.c.101.6	yes	20	40.13	odd	4
200.6.d.d.101.15	yes	20	40.37	odd	4
200.6.d.d.101.16	yes	20	5.2	odd	4
200.6.f.d.149.11		40	8.5	even	2	inner
200.6.f.d.149.12		40	5.4	even	2	inner
200.6.f.d.149.29		40	1.1	even	1	trivial
200.6.f.d.149.30		40	40.29	even	2	inner
800.6.d.b.401.5		20	20.7	even	4
800.6.d.b.401.16		20	40.27	even	4
800.6.d.d.401.5		20	40.3	even	4
800.6.d.d.401.16		20	20.3	even	4
800.6.f.d.49.9		40	20.19	odd	2
800.6.f.d.49.10		40	8.3	odd	2
800.6.f.d.49.31		40	40.19	odd	2
800.6.f.d.49.32		40	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.87282 - 4.12326i) q^{2} -18.2848 q^{3} +(-2.00256 - 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} -2.25573i q^{7} +(-139.441 - 115.430i) q^{8} +91.3327 q^{9} +O(q^{10})\)	\(q+(3.87282 - 4.12326i) q^{2} -18.2848 q^{3} +(-2.00256 - 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} -2.25573i q^{7} +(-139.441 - 115.430i) q^{8} +91.3327 q^{9} +419.261i q^{11} +(36.6163 + 583.966i) q^{12} -106.889 q^{13} +(-9.30095 - 8.73602i) q^{14} +(-1015.98 + 127.912i) q^{16} +849.098i q^{17} +(353.715 - 376.589i) q^{18} +335.414i q^{19} +41.2454i q^{21} +(1728.72 + 1623.72i) q^{22} -3541.78i q^{23} +(2549.65 + 2110.61i) q^{24} +(-413.961 + 440.731i) q^{26} +2773.20 q^{27} +(-72.0418 + 4.51722i) q^{28} +5208.57i q^{29} +5637.83 q^{31} +(-3407.29 + 4684.53i) q^{32} -7666.09i q^{33} +(3501.05 + 3288.40i) q^{34} +(-182.899 - 2916.92i) q^{36} +61.9860 q^{37} +(1383.00 + 1299.00i) q^{38} +1954.44 q^{39} +16286.1 q^{41} +(170.066 + 159.736i) q^{42} -2417.19 q^{43} +(13390.1 - 839.594i) q^{44} +(-14603.7 - 13716.7i) q^{46} -22781.9i q^{47} +(18576.9 - 2338.85i) q^{48} +16801.9 q^{49} -15525.6i q^{51} +(214.051 + 3413.74i) q^{52} +13667.5 q^{53} +(10740.1 - 11434.6i) q^{54} +(-260.379 + 314.541i) q^{56} -6132.98i q^{57} +(21476.3 + 20171.9i) q^{58} +23407.1i q^{59} +33444.7i q^{61} +(21834.3 - 23246.3i) q^{62} -206.022i q^{63} +(6119.73 + 32191.5i) q^{64} +(-31609.3 - 29689.4i) q^{66} +66162.9 q^{67} +(27117.9 - 1700.37i) q^{68} +64760.7i q^{69} -51421.4 q^{71} +(-12735.5 - 10542.6i) q^{72} -21271.6i q^{73} +(240.060 - 255.584i) q^{74} +(10712.2 - 671.686i) q^{76} +945.738 q^{77} +(7569.18 - 8058.66i) q^{78} -38418.7 q^{79} -72901.2 q^{81} +(63073.0 - 67151.7i) q^{82} -93166.7 q^{83} +(1317.27 - 82.5963i) q^{84} +(-9361.33 + 9966.69i) q^{86} -95237.5i q^{87} +(48395.4 - 58462.3i) q^{88} +60678.0 q^{89} +241.112i q^{91} +(-113115. + 7092.62i) q^{92} -103086. q^{93} +(-93935.8 - 88230.2i) q^{94} +(62301.5 - 85655.5i) q^{96} +157428. i q^{97} +(65070.8 - 69278.7i) q^{98} +38292.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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