LMFDB - Embedded newform 165.6.f.a.131.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(131,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.131");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.42
Character	$\chi$	$=$	165.131
Dual form			165.6.f.a.131.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.11974 q^{2} +(11.9738 + 9.98135i) q^{3} -30.7462 q^{4} -25.0000i q^{5} +(13.4076 + 11.1765i) q^{6} -234.320i q^{7} -70.2596 q^{8} +(43.7452 + 239.030i) q^{9} +O(q^{10})$	\(q+1.11974 q^{2} +(11.9738 + 9.98135i) q^{3} -30.7462 q^{4} -25.0000i q^{5} +(13.4076 + 11.1765i) q^{6} -234.320i q^{7} -70.2596 q^{8} +(43.7452 + 239.030i) q^{9} -27.9936i q^{10} +(-251.688 + 312.577i) q^{11} +(-368.149 - 306.888i) q^{12} +844.172i q^{13} -262.378i q^{14} +(249.534 - 299.346i) q^{15} +905.205 q^{16} +1237.52 q^{17} +(48.9834 + 267.652i) q^{18} +1295.98i q^{19} +768.654i q^{20} +(2338.83 - 2805.70i) q^{21} +(-281.826 + 350.005i) q^{22} +3747.48i q^{23} +(-841.276 - 701.286i) q^{24} -625.000 q^{25} +945.255i q^{26} +(-1862.04 + 3298.74i) q^{27} +7204.43i q^{28} +1669.28 q^{29} +(279.414 - 335.190i) q^{30} -8616.52 q^{31} +3261.90 q^{32} +(-6133.61 + 1230.55i) q^{33} +1385.71 q^{34} -5857.99 q^{35} +(-1345.00 - 7349.26i) q^{36} +180.772 q^{37} +1451.16i q^{38} +(-8425.98 + 10108.0i) q^{39} +1756.49i q^{40} +10447.4 q^{41} +(2618.88 - 3141.67i) q^{42} +5263.72i q^{43} +(7738.44 - 9610.54i) q^{44} +(5975.75 - 1093.63i) q^{45} +4196.21i q^{46} +7288.78i q^{47} +(10838.8 + 9035.17i) q^{48} -38098.7 q^{49} -699.839 q^{50} +(14817.9 + 12352.1i) q^{51} -25955.1i q^{52} +5281.46i q^{53} +(-2085.01 + 3693.74i) q^{54} +(7814.42 + 6292.20i) q^{55} +16463.2i q^{56} +(-12935.6 + 15517.8i) q^{57} +1869.16 q^{58} -27778.1i q^{59} +(-7672.21 + 9203.74i) q^{60} -6016.73i q^{61} -9648.29 q^{62} +(56009.4 - 10250.4i) q^{63} -25314.1 q^{64} +21104.3 q^{65} +(-6868.06 + 1377.90i) q^{66} +15751.5 q^{67} -38049.1 q^{68} +(-37404.9 + 44871.6i) q^{69} -6559.44 q^{70} +50634.9i q^{71} +(-3073.52 - 16794.1i) q^{72} +3192.49i q^{73} +202.418 q^{74} +(-7483.64 - 6238.34i) q^{75} -39846.4i q^{76} +(73242.9 + 58975.4i) q^{77} +(-9434.93 + 11318.3i) q^{78} +106364. i q^{79} -22630.1i q^{80} +(-55221.7 + 20912.8i) q^{81} +11698.4 q^{82} +79935.2 q^{83} +(-71910.0 + 86264.7i) q^{84} -30938.1i q^{85} +5894.01i q^{86} +(19987.6 + 16661.6i) q^{87} +(17683.5 - 21961.5i) q^{88} -9012.82i q^{89} +(6691.30 - 1224.59i) q^{90} +197806. q^{91} -115221. i q^{92} +(-103173. - 86004.5i) q^{93} +8161.55i q^{94} +32399.5 q^{95} +(39057.5 + 32558.2i) q^{96} +120699. q^{97} -42660.8 q^{98} +(-85725.4 - 46487.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.11974			0.197944			0.0989722	−	0.995090i	$-0.468445\pi$
$2$	1.11974			0.197944			0.0989722	+	0.995090i	$0.468445\pi$
$3$	11.9738	+	9.98135i	0.768122	+	0.640304i
$3$	11.9738	+	9.98135i	0.768122	+	0.640304i
$4$	−30.7462			−0.960818
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	13.4076	+	11.1765i	0.152045	+	0.126745i
$7$		−	234.320i		−	1.80744i	−0.428125	−	0.903720i	$-0.640826\pi$
$7$		−	234.320i		−	1.80744i	0.428125	−	0.903720i	$-0.359174\pi$
$8$	−70.2596			−0.388133
$9$	43.7452	+	239.030i	0.180022	+	0.983663i
$10$		−	27.9936i		−	0.0885234i
$11$	−251.688	+	312.577i	−0.627163	+	0.778888i
$11$	−251.688	+	312.577i	−0.627163	+	0.778888i
$12$	−368.149	−	306.888i	−0.738025	−	0.615216i
$13$			844.172i			1.38539i	0.721230	+	0.692696i	$0.243577\pi$
$13$			844.172i			1.38539i	−0.721230	+	0.692696i	$0.756423\pi$
$14$		−	262.378i		−	0.357773i
$15$	249.534	−	299.346i	0.286353	−	0.343514i
$16$	905.205			0.883989
$17$	1237.52			1.03856			0.519279	−	0.854605i	$-0.326201\pi$
$17$	1237.52			1.03856			0.519279	+	0.854605i	$0.326201\pi$
$18$	48.9834	+	267.652i	0.0356343	+	0.194711i
$19$			1295.98i			0.823595i	0.911275	+	0.411798i	$0.135099\pi$
$19$			1295.98i			0.823595i	−0.911275	+	0.411798i	$0.864901\pi$
$20$			768.654i			0.429691i
$21$	2338.83	−	2805.70i	1.15731	−	1.38833i
$22$	−281.826	+	350.005i	−0.124144	+	0.154176i
$23$			3747.48i			1.47713i	0.674181	+	0.738566i	$0.264497\pi$
$23$			3747.48i			1.47713i	−0.674181	+	0.738566i	$0.735503\pi$
$24$	−841.276	−	701.286i	−0.298133	−	0.248523i
$25$	−625.000			−0.200000
$26$			945.255i			0.274231i
$27$	−1862.04	+	3298.74i	−0.491565	+	0.870841i
$28$			7204.43i			1.73662i
$29$	1669.28			0.368581			0.184291	−	0.982872i	$-0.441001\pi$
$29$	1669.28			0.368581			0.184291	+	0.982872i	$0.441001\pi$
$30$	279.414	−	335.190i	0.0566819	−	0.0679968i
$31$	−8616.52			−1.61038			−0.805189	−	0.593018i	$-0.797936\pi$
$31$	−8616.52			−1.61038			−0.805189	+	0.593018i	$0.797936\pi$
$32$	3261.90			0.563114
$33$	−6133.61	+	1230.55i	−0.980463	+	0.196705i
$34$	1385.71			0.205577
$35$	−5857.99			−0.808311
$36$	−1345.00	−	7349.26i	−0.172968	−	0.945121i
$37$	180.772			0.0217084			0.0108542	−	0.999941i	$-0.496545\pi$
$37$	180.772			0.0217084			0.0108542	+	0.999941i	$0.496545\pi$
$38$			1451.16i			0.163026i
$39$	−8425.98	+	10108.0i	−0.887072	+	1.06415i
$40$			1756.49i			0.173578i
$41$	10447.4			0.970621			0.485310	−	0.874342i	$-0.338707\pi$
$41$	10447.4			0.970621			0.485310	+	0.874342i	$0.338707\pi$
$42$	2618.88	−	3141.67i	0.229083	−	0.274813i
$43$			5263.72i			0.434132i	0.976157	+	0.217066i	$0.0696487\pi$
$43$			5263.72i			0.434132i	−0.976157	+	0.217066i	$0.930351\pi$
$44$	7738.44	−	9610.54i	0.602590	−	0.748369i
$45$	5975.75	−	1093.63i	0.439907	−	0.0805081i
$46$			4196.21i			0.292390i
$47$			7288.78i			0.481293i	0.970613	+	0.240647i	$0.0773595\pi$
$47$			7288.78i			0.481293i	−0.970613	+	0.240647i	$0.922640\pi$
$48$	10838.8	+	9035.17i	0.679011	+	0.566022i
$49$	−38098.7			−2.26684
$50$	−699.839			−0.0395889
$51$	14817.9	+	12352.1i	0.797739	+	0.664993i
$52$		−	25955.1i		−	1.33111i
$53$			5281.46i			0.258264i	0.991627	+	0.129132i	$0.0412191\pi$
$53$			5281.46i			0.258264i	−0.991627	+	0.129132i	$0.958781\pi$
$54$	−2085.01	+	3693.74i	−0.0973025	+	0.172378i
$55$	7814.42	+	6292.20i	0.348329	+	0.280476i
$56$			16463.2i			0.701527i
$57$	−12935.6	+	15517.8i	−0.527351	+	0.632621i
$58$	1869.16			0.0729586
$59$		−	27778.1i		−	1.03890i	−0.854501	−	0.519449i	$-0.826137\pi$
$59$		−	27778.1i		−	1.03890i	0.854501	−	0.519449i	$-0.173863\pi$
$60$	−7672.21	+	9203.74i	−0.275133	+	0.330055i
$61$		−	6016.73i		−	0.207031i	−0.994628	−	0.103516i	$-0.966991\pi$
$61$		−	6016.73i		−	0.207031i	0.994628	−	0.103516i	$-0.0330092\pi$
$62$	−9648.29			−0.318765
$63$	56009.4	−	10250.4i	1.77791	−	0.325378i
$64$	−25314.1			−0.772524
$65$	21104.3			0.619566
$66$	−6868.06	+	1377.90i	−0.194077	+	0.0389367i
$67$	15751.5			0.428680			0.214340	−	0.976759i	$-0.431240\pi$
$67$	15751.5			0.428680			0.214340	+	0.976759i	$0.431240\pi$
$68$	−38049.1			−0.997865
$69$	−37404.9	+	44871.6i	−0.945814	+	1.13462i
$70$	−6559.44			−0.160001
$71$			50634.9i			1.19208i	0.802956	+	0.596038i	$0.203259\pi$
$71$			50634.9i			1.19208i	−0.802956	+	0.596038i	$0.796741\pi$
$72$	−3073.52	−	16794.1i	−0.0698723	−	0.381792i
$73$			3192.49i			0.0701169i	0.999385	+	0.0350584i	$0.0111617\pi$
$73$			3192.49i			0.0701169i	−0.999385	+	0.0350584i	$0.988838\pi$
$74$	202.418			0.00429705
$75$	−7483.64	−	6238.34i	−0.153624	−	0.128061i
$76$		−	39846.4i		−	0.791325i
$77$	73242.9	+	58975.4i	1.40779	+	1.13356i
$78$	−9434.93	+	11318.3i	−0.175591	+	0.210642i
$79$			106364.i			1.91747i	0.284309	+	0.958733i	$0.408236\pi$
$79$			106364.i			1.91747i	−0.284309	+	0.958733i	$0.591764\pi$
$80$		−	22630.1i		−	0.395332i
$81$	−55221.7	+	20912.8i	−0.935185	+	0.354161i
$82$	11698.4			0.192129
$83$	79935.2			1.27363			0.636814	−	0.771017i	$-0.280252\pi$
$83$	79935.2			1.27363			0.636814	+	0.771017i	$0.280252\pi$
$84$	−71910.0	+	86264.7i	−1.11196	+	1.33394i
$85$		−	30938.1i		−	0.464457i
$86$			5894.01i			0.0859340i
$87$	19987.6	+	16661.6i	0.283115	+	0.236004i
$88$	17683.5	−	21961.5i	0.243423	−	0.302312i
$89$		−	9012.82i		−	0.120611i	−0.998180	−	0.0603053i	$-0.980793\pi$
$89$		−	9012.82i		−	0.120611i	0.998180	−	0.0603053i	$-0.0192074\pi$
$90$	6691.30	−	1224.59i	0.0870772	−	0.0159361i
$91$	197806.			2.50401
$92$		−	115221.i		−	1.41925i
$93$	−103173.	−	86004.5i	−1.23697	−	1.03113i
$94$			8161.55i			0.0952694i
$95$	32399.5			0.368323
$96$	39057.5	+	32558.2i	0.432540	+	0.360564i
$97$	120699.			1.30249			0.651247	−	0.758866i	$-0.274246\pi$
$97$	120699.			1.30249			0.651247	+	0.758866i	$0.274246\pi$
$98$	−42660.8			−0.448708
$99$	−85725.4	−	46487.2i	−0.879066	−	0.476701i
$100$	19216.4			0.192164
$101$	−183456.			−1.78949			−0.894745	−	0.446577i	$-0.852643\pi$
$101$	−183456.			−1.78949			−0.894745	+	0.446577i	$0.852643\pi$
$102$	16592.2	+	13831.2i	0.157908	+	0.131632i
$103$	−79046.7			−0.734160			−0.367080	−	0.930189i	$-0.619643\pi$
$103$	−79046.7			−0.734160			−0.367080	+	0.930189i	$0.619643\pi$
$104$		−	59311.2i		−	0.537716i
$105$	−70142.6	−	58470.7i	−0.620881	−	0.517565i
$106$			5913.88i			0.0511220i
$107$	−121050.			−1.02213			−0.511064	−	0.859543i	$-0.670748\pi$
$107$	−121050.			−1.02213			−0.511064	+	0.859543i	$0.670748\pi$
$108$	57250.8	−	101424.i	0.472304	−	0.836720i
$109$		−	181918.i		−	1.46659i	−0.679911	−	0.733294i	$-0.737982\pi$
$109$		−	181918.i		−	1.46659i	0.679911	−	0.733294i	$-0.262018\pi$
$110$	8750.14	+	7045.65i	0.0689498	+	0.0555187i
$111$	2164.54	+	1804.35i	0.0166747	+	0.0139000i
$112$		−	212107.i		−	1.59776i
$113$			67055.9i			0.494016i	0.969013	+	0.247008i	$0.0794473\pi$
$113$			67055.9i			0.494016i	−0.969013	+	0.247008i	$0.920553\pi$
$114$	−14484.6	+	17376.0i	−0.104386	+	0.125224i
$115$	93686.9			0.660593
$116$	−51323.9			−0.354140
$117$	−201782.	+	36928.5i	−1.36276	+	0.249400i
$118$		−	31104.4i		−	0.205644i
$119$		−	289976.i		−	1.87713i
$120$	−17532.1	+	21031.9i	−0.111143	+	0.133329i
$121$	−34357.3	−	157344.i	−0.213332	−	0.976980i
$122$		−	6737.19i		−	0.0409807i
$123$	125096.	+	104279.i	0.745555	+	0.621492i
$124$	264925.			1.54728
$125$			15625.0i			0.0894427i
$126$	62716.2	−	11477.8i	0.351927	−	0.0644067i
$127$			49070.3i			0.269966i	0.990848	+	0.134983i	$0.0430980\pi$
$127$			49070.3i			0.269966i	−0.990848	+	0.134983i	$0.956902\pi$
$128$	−132726.			−0.716031
$129$	−52539.0	+	63026.9i	−0.277976	+	0.333466i
$130$	23631.4			0.122640
$131$	162331.			0.826464			0.413232	−	0.910626i	$-0.364400\pi$
$131$	162331.			0.826464			0.413232	+	0.910626i	$0.364400\pi$
$132$	188585.	−	37834.8i	0.942046	−	0.188998i
$133$	303673.			1.48860
$134$	17637.6			0.0848549
$135$	82468.5	+	46551.1i	0.389452	+	0.219834i
$136$	−86947.8			−0.403099
$137$			223091.i			1.01550i	0.861504	+	0.507750i	$0.169523\pi$
$137$			223091.i			1.01550i	−0.861504	+	0.507750i	$0.830477\pi$
$138$	−41883.8	+	50244.7i	−0.187219	+	0.224591i
$139$		−	137620.i		−	0.604150i	−0.953284	−	0.302075i	$-0.902321\pi$
$139$		−	137620.i		−	0.604150i	0.953284	−	0.302075i	$-0.0976793\pi$
$140$	180111.			0.776640
$141$	−72751.8	+	87274.6i	−0.308174	+	0.369692i
$142$			56698.0i			0.235965i
$143$	−263868.	−	212468.i	−1.07906	−	0.868867i
$144$	39598.4	+	216371.i	0.159137	+	0.869547i
$145$		−	41731.9i		−	0.164835i
$146$			3574.77i			0.0138792i
$147$	−456187.	−	380277.i	−1.74121	−	1.45146i
$148$	−5558.06			−0.0208578
$149$	232740.			0.858828			0.429414	−	0.903108i	$-0.358720\pi$
$149$	232740.			0.858828			0.429414	+	0.903108i	$0.358720\pi$
$150$	−8379.76	−	6985.34i	−0.0304091	−	0.0253489i
$151$		−	92762.1i		−	0.331076i	−0.986203	−	0.165538i	$-0.947064\pi$
$151$		−	92762.1i		−	0.331076i	0.986203	−	0.165538i	$-0.0529361\pi$
$152$		−	91054.9i		−	0.319665i
$153$	54135.7	+	295805.i	0.186963	+	1.02159i
$154$	82013.2	+	66037.3i	0.278665	+	0.224382i
$155$			215413.i			0.720183i
$156$	259067.	−	310781.i	0.852315	−	1.02245i
$157$	−273708.			−0.886214			−0.443107	−	0.896469i	$-0.646124\pi$
$157$	−273708.			−0.886214			−0.443107	+	0.896469i	$0.646124\pi$
$158$			119100.i			0.379552i
$159$	−52716.1	+	63239.3i	−0.165368	+	0.198378i
$160$		−	81547.6i		−	0.251832i
$161$	878107.			2.66983
$162$	−61834.1	+	23417.0i	−0.185115	+	0.0701042i
$163$	36024.5			0.106201			0.0531006	−	0.998589i	$-0.483090\pi$
$163$	36024.5			0.106201			0.0531006	+	0.998589i	$0.483090\pi$
$164$	−321218.			−0.932590
$165$	30763.8	+	153340.i	0.0879692	+	0.438476i
$166$	89506.9			0.252108
$167$	−422601.			−1.17257			−0.586286	−	0.810104i	$-0.699411\pi$
$167$	−422601.			−1.17257			−0.586286	+	0.810104i	$0.699411\pi$
$168$	−164325.	+	197128.i	−0.449190	+	0.538858i
$169$	−341333.			−0.919310
$170$		−	34642.7i		−	0.0919367i
$171$	−309778.	+	56692.9i	−0.810140	+	0.148265i
$172$		−	161839.i		−	0.417122i
$173$	−323980.			−0.823006			−0.411503	−	0.911408i	$-0.634996\pi$
$173$	−323980.			−0.823006			−0.411503	+	0.911408i	$0.634996\pi$
$174$	22381.0	+	18656.7i	0.0560411	+	0.0467157i
$175$			146450.i			0.361488i
$176$	−227829.	+	282946.i	−0.554406	+	0.688528i
$177$	277263.	−	332611.i	0.665211	−	0.798000i
$178$		−	10092.0i		−	0.0238742i
$179$			466728.i			1.08876i	0.838839	+	0.544379i	$0.183235\pi$
$179$			466728.i			1.08876i	−0.838839	+	0.544379i	$0.816765\pi$
$180$	−183731.	+	33625.0i	−0.422671	+	0.0773536i
$181$	−49956.5			−0.113343			−0.0566716	−	0.998393i	$-0.518049\pi$
$181$	−49956.5			−0.113343			−0.0566716	+	0.998393i	$0.518049\pi$
$182$	221492.			0.495655
$183$	60055.1	−	72043.3i	0.132563	−	0.159025i
$184$		−	263296.i		−	0.573324i
$185$		−	4519.31i		−	0.00970829i
$186$	−115527.	−	96303.0i	−0.244851	−	0.204107i
$187$	−311470.	+	386821.i	−0.651346	+	0.808920i
$188$		−	224102.i		−	0.462435i
$189$	772960.	+	436314.i	1.57399	+	0.888473i
$190$	36279.1			0.0729075
$191$		−	229359.i		−	0.454917i	−0.973788	−	0.227459i	$-0.926958\pi$
$191$		−	229359.i		−	0.454917i	0.973788	−	0.227459i	$-0.0730416\pi$
$192$	−303106.	−	252669.i	−0.593392	−	0.494650i
$193$		−	427368.i		−	0.825865i	−0.910762	−	0.412933i	$-0.864505\pi$
$193$		−	427368.i		−	0.825865i	0.910762	−	0.412933i	$-0.135495\pi$
$194$	135152.			0.257821
$195$	252699.	+	210649.i	0.475902	+	0.396711i
$196$	1.17139e6			2.17802
$197$	126977.			0.233109			0.116555	−	0.993184i	$-0.462815\pi$
$197$	126977.			0.233109			0.116555	+	0.993184i	$0.462815\pi$
$198$	−95990.4	−	52053.8i	−0.174006	−	0.0943603i
$199$	699943.			1.25294			0.626469	−	0.779446i	$-0.284499\pi$
$199$	699943.			1.25294			0.626469	+	0.779446i	$0.284499\pi$
$200$	43912.2			0.0776266
$201$	188605.	+	157221.i	0.329279	+	0.274486i
$202$	−205424.			−0.354220
$203$		−	391144.i		−	0.666188i
$204$	−455593.	−	379781.i	−0.766482	−	0.638937i
$205$		−	261186.i		−	0.434075i
$206$	−88512.0			−0.145323
$207$	−895759.	+	163934.i	−1.45300	+	0.265916i
$208$			764149.i			1.22467i
$209$	−405093.	−	326182.i	−0.641488	−	0.516529i
$210$	−78541.7	−	65472.1i	−0.122900	−	0.102449i
$211$		−	313959.i		−	0.485475i	−0.970092	−	0.242738i	$-0.921955\pi$
$211$		−	313959.i		−	0.485475i	0.970092	−	0.242738i	$-0.0780454\pi$
$212$		−	162385.i		−	0.248145i
$213$	−505405.	+	606293.i	−0.763291	+	0.915659i
$214$	−135545.			−0.202324
$215$	131593.			0.194150
$216$	130826.	−	231768.i	0.190793	−	0.338002i
$217$			2.01902e6i			2.91066i
$218$		−	203701.i		−	0.290303i
$219$	−31865.4	+	38226.3i	−0.0448961	+	0.0538583i
$220$	−240263.	−	193461.i	−0.334681	−	0.269486i
$221$			1.04468e6i			1.43881i
$222$	2423.72	+	2020.41i	0.00330066	+	0.00275142i
$223$	694761.			0.935564			0.467782	−	0.883844i	$-0.345053\pi$
$223$	694761.			0.935564			0.467782	+	0.883844i	$0.345053\pi$
$224$		−	764328.i		−	1.01779i
$225$	−27340.8	−	149394.i	−0.0360043	−	0.196733i
$226$			75085.3i			0.0977876i
$227$	−88327.8			−0.113771			−0.0568857	−	0.998381i	$-0.518117\pi$
$227$	−88327.8			−0.113771			−0.0568857	+	0.998381i	$0.518117\pi$
$228$	397721.	−	477114.i	0.506689	−	0.607834i
$229$	−825068.			−1.03968			−0.519841	−	0.854263i	$-0.674009\pi$
$229$	−825068.			−1.03968			−0.519841	+	0.854263i	$0.674009\pi$
$230$	104905.			0.130761
$231$	288343.	+	1.43722e6i	0.355533	+	1.77213i
$232$	−117283.			−0.143059
$233$	861282.			1.03934			0.519668	−	0.854369i	$-0.326056\pi$
$233$	861282.			1.03934			0.519668	+	0.854369i	$0.326056\pi$
$234$	−225944.	+	41350.4i	−0.269750	+	0.0493674i
$235$	182219.			0.215241
$236$			854071.i			0.998192i
$237$	−1.06166e6	+	1.27359e6i	−1.22776	+	1.47285i
$238$		−	324698.i		−	0.371568i
$239$	−1.18028e6			−1.33656			−0.668280	−	0.743910i	$-0.732969\pi$
$239$	−1.18028e6			−1.33656			−0.668280	+	0.743910i	$0.732969\pi$
$240$	225879.	−	270969.i	0.253133	−	0.303663i
$241$		−	1.61924e6i		−	1.79584i	−0.440154	−	0.897922i	$-0.645076\pi$
$241$		−	1.61924e6i		−	1.79584i	0.440154	−	0.897922i	$-0.354924\pi$
$242$	−38471.4	−	176184.i	−0.0422279	−	0.193388i
$243$	−869954.	−	300780.i	−0.945106	−	0.326764i
$244$			184991.i			0.198919i
$245$			952468.i			1.01376i
$246$	140075.	+	116766.i	0.147578	+	0.123021i
$247$	−1.09403e6			−1.14100
$248$	605393.			0.625041
$249$	957131.	+	797861.i	0.978302	+	0.815510i
$250$			17496.0i			0.0177047i
$251$			1.50782e6i			1.51065i	0.655350	+	0.755325i	$0.272521\pi$
$251$			1.50782e6i			1.51065i	−0.655350	+	0.755325i	$0.727479\pi$
$252$	−1.72208e6	+	315160.i	−1.70825	+	0.312629i
$253$	−1.17137e6	−	943195.i	−1.15052	−	0.926403i
$254$			54946.1i			0.0534383i
$255$	308804.	−	370447.i	0.297394	−	0.356760i
$256$	661431.			0.630790
$257$			360186.i			0.340168i	0.985430	+	0.170084i	$0.0544039\pi$
$257$			360186.i			0.340168i	−0.985430	+	0.170084i	$0.945596\pi$
$258$	−58830.2	+	70573.9i	−0.0550239	+	0.0660078i
$259$		−	42358.5i		−	0.0392366i
$260$	−648876.			−0.595290
$261$	73022.9	+	399007.i	0.0663526	+	0.362560i
$262$	181769.			0.163594
$263$	1.58347e6			1.41163			0.705814	−	0.708398i	$-0.250582\pi$
$263$	1.58347e6			1.41163			0.705814	+	0.708398i	$0.250582\pi$
$264$	430945.	−	86458.2i	0.380550	−	0.0763478i
$265$	132037.			0.115499
$266$	340036.			0.294660
$267$	89960.1	−	107918.i	0.0772275	−	0.0926436i
$268$	−484297.			−0.411884
$269$			1.10995e6i			0.935243i	0.883929	+	0.467622i	$0.154889\pi$
$269$			1.10995e6i			0.935243i	−0.883929	+	0.467622i	$0.845111\pi$
$270$	92343.6	+	52125.3i	0.0770898	+	0.0435150i
$271$			1.69786e6i			1.40436i	0.712000	+	0.702180i	$0.247790\pi$
$271$			1.69786e6i			1.40436i	−0.712000	+	0.702180i	$0.752210\pi$
$272$	1.12021e6			0.918074
$273$	2.36850e6	+	1.97437e6i	1.92338	+	1.60333i
$274$			249804.i			0.201013i
$275$	157305.	−	195360.i	0.125433	−	0.155778i
$276$	1.15006e6	−	1.37963e6i	0.908755	−	1.09016i
$277$		−	1.65370e6i		−	1.29496i	−0.762081	−	0.647482i	$-0.775822\pi$
$277$		−	1.65370e6i		−	1.29496i	0.762081	−	0.647482i	$-0.224178\pi$
$278$		−	154099.i		−	0.119588i
$279$	−376932.	−	2.05961e6i	−0.289903	−	1.58407i
$280$	411580.			0.313732
$281$	2.42502e6			1.83210			0.916051	−	0.401062i	$-0.131359\pi$
$281$	2.42502e6			1.83210			0.916051	+	0.401062i	$0.131359\pi$
$282$	−81463.3	+	97725.1i	−0.0610013	+	0.0731784i
$283$			360325.i			0.267442i	0.991019	+	0.133721i	$0.0426925\pi$
$283$			360325.i			0.267442i	−0.991019	+	0.133721i	$0.957307\pi$
$284$		−	1.55683e6i		−	1.14537i
$285$	387946.	+	323391.i	0.282917	+	0.235839i
$286$	−295465.	−	237909.i	−0.213595	−	0.171987i
$287$		−	2.44804e6i		−	1.75434i
$288$	142693.	+	779693.i	0.101373	+	0.553914i
$289$	111605.			0.0786030
$290$		−	46729.0i		−	0.0326281i
$291$	1.44523e6	+	1.20474e6i	1.00047	+	0.833992i
$292$		−	98156.9i		−	0.0673696i
$293$	−1.69556e6			−1.15384			−0.576918	−	0.816802i	$-0.695745\pi$
$293$	−1.69556e6			−1.15384			−0.576918	+	0.816802i	$0.695745\pi$
$294$	−510813.	−	425812.i	−0.344662	−	0.287309i
$295$	−694453.			−0.464609
$296$	−12701.0			−0.00842574
$297$	−562455.	−	1.41229e6i	−0.369996	−	0.929033i
$298$	260609.			0.170000
$299$	−3.16351e6			−2.04641
$300$	230093.	+	191805.i	0.147605	+	0.123043i
$301$	1.23339e6			0.784667
$302$		−	103870.i		−	0.0655347i
$303$	−2.19668e6	−	1.83114e6i	−1.37455	−	1.14582i
$304$			1.17313e6i			0.728049i
$305$	−150418.			−0.0925872
$306$	60618.1	+	331226.i	0.0370082	+	0.202218i
$307$		−	953530.i		−	0.577415i	−0.957417	−	0.288708i	$-0.906774\pi$
$307$		−	953530.i		−	0.577415i	0.957417	−	0.288708i	$-0.0932255\pi$
$308$	−2.25194e6	−	1.81327e6i	−1.35263	−	1.08914i
$309$	−946492.	−	788993.i	−0.563924	−	0.470086i
$310$			241207.i			0.142556i
$311$		−	377212.i		−	0.221149i	−0.993868	−	0.110574i	$-0.964731\pi$
$311$		−	377212.i		−	0.221149i	0.993868	−	0.110574i	$-0.0352690\pi$
$312$	592006.	−	710182.i	0.344302	−	0.413031i
$313$	1.69453e6			0.977661			0.488831	−	0.872379i	$-0.337424\pi$
$313$	1.69453e6			0.977661			0.488831	+	0.872379i	$0.337424\pi$
$314$	−306483.			−0.175421
$315$	−256259.	−	1.40024e6i	−0.145513	−	0.795106i
$316$		−	3.27029e6i		−	1.84234i
$317$		−	275111.i		−	0.153766i	−0.997040	−	0.0768830i	$-0.975503\pi$
$317$		−	275111.i		−	0.153766i	0.997040	−	0.0768830i	$-0.0244968\pi$
$318$	−59028.5	+	70811.8i	−0.0327336	+	0.0392679i
$319$	−420137.	+	521777.i	−0.231161	+	0.287083i
$320$			632852.i			0.345483i
$321$	−1.44943e6	−	1.20824e6i	−0.785118	−	0.654472i
$322$	983254.			0.528477
$323$			1.60380e6i			0.855352i
$324$	1.69786e6	−	642990.i	0.898542	−	0.340284i
$325$		−	527607.i		−	0.277078i
$326$	40338.2			0.0210219
$327$	1.81578e6	−	2.17825e6i	0.939063	−	1.12652i
$328$	−734032.			−0.376730
$329$	1.70790e6			0.869908
$330$	34447.6	+	171702.i	0.0174130	+	0.0867939i
$331$	−385308.			−0.193303			−0.0966515	−	0.995318i	$-0.530813\pi$
$331$	−385308.			−0.193303			−0.0966515	+	0.995318i	$0.530813\pi$
$332$	−2.45770e6			−1.22373
$333$	7907.92	+	43210.0i	0.00390798	+	0.0213537i
$334$	−473205.			−0.232104
$335$		−	393786.i		−	0.191712i
$336$	2.11712e6	−	2.53974e6i	1.02305	−	1.22727i
$337$			2.23866e6i			1.07378i	0.843654	+	0.536888i	$0.180400\pi$
$337$			2.23866e6i			1.07378i	−0.843654	+	0.536888i	$0.819600\pi$
$338$	−382205.			−0.181972
$339$	−669308.	+	802916.i	−0.316320	+	0.379464i
$340$			951227.i			0.446259i
$341$	2.16867e6	−	2.69332e6i	1.00997	−	1.25430i
$342$	−346872.	+	63481.5i	−0.160363	+	0.0293482i
$343$			4.98907e6i			2.28973i
$344$		−	369827.i		−	0.168501i
$345$	1.12179e6	+	935122.i	0.507416	+	0.422981i
$346$	−362774.			−0.162909
$347$	−2.10979e6			−0.940624			−0.470312	−	0.882500i	$-0.655859\pi$
$347$	−2.10979e6			−0.940624			−0.470312	+	0.882500i	$0.655859\pi$
$348$	−614543.	−	512282.i	−0.272022	−	0.226757i
$349$			547910.i			0.240794i	0.992726	+	0.120397i	$0.0384168\pi$
$349$			547910.i			0.240794i	−0.992726	+	0.120397i	$0.961583\pi$
$350$			163986.i			0.0715545i
$351$	−2.78470e6	−	1.57189e6i	−1.20646	−	0.681010i
$352$	−820982.	+	1.01959e6i	−0.353164	+	0.438602i
$353$		−	3.81149e6i		−	1.62801i	−0.580856	−	0.814007i	$-0.697282\pi$
$353$		−	3.81149e6i		−	1.62801i	0.580856	−	0.814007i	$-0.302718\pi$
$354$	310464.	−	372438.i	0.131675	−	0.157960i
$355$	1.26587e6			0.533113
$356$			277110.i			0.115885i
$357$	2.89435e6	−	3.47212e6i	1.20193	−	1.44186i
$358$			522616.i			0.215514i
$359$	343143.			0.140520			0.0702601	−	0.997529i	$-0.477617\pi$
$359$	343143.			0.140520			0.0702601	+	0.997529i	$0.477617\pi$
$360$	−419854.	+	76838.0i	−0.170743	+	0.0312478i
$361$	796538.			0.321691
$362$	−55938.4			−0.0224357
$363$	1.15911e6	−	2.22694e6i	0.461699	−	0.887037i
$364$	−6.08178e6			−2.40590
$365$	79812.3			0.0313572
$366$	67246.3	−	80670.0i	0.0262401	−	0.0314781i
$367$	1.19589e6			0.463475			0.231738	−	0.972778i	$-0.425559\pi$
$367$	1.19589e6			0.463475			0.231738	+	0.972778i	$0.425559\pi$
$368$			3.39223e6i			1.30577i
$369$	457025.	+	2.49725e6i	0.174733	+	0.954764i
$370$		−	5060.46i		−	0.00192170i
$371$	1.23755e6			0.466797
$372$	3.17217e6	+	2.64431e6i	1.18850	+	0.990730i
$373$			1.45487e6i			0.541441i	0.962658	+	0.270721i	$0.0872620\pi$
$373$			1.45487e6i			0.541441i	−0.962658	+	0.270721i	$0.912738\pi$
$374$	−348766.	+	433140.i	−0.128930	+	0.160121i
$375$	−155959.	+	187091.i	−0.0572705	+	0.0687029i
$376$		−	512106.i		−	0.186806i
$377$			1.40916e6i			0.510629i
$378$	865516.	+	488559.i	0.311563	+	0.175868i
$379$	782886.			0.279963			0.139981	−	0.990154i	$-0.455296\pi$
$379$	782886.			0.279963			0.139981	+	0.990154i	$0.455296\pi$
$380$	−996160.			−0.353891
$381$	−489788.	+	587559.i	−0.172860	+	0.207367i
$382$		−	256823.i		−	0.0900483i
$383$		−	2.00675e6i		−	0.699032i	−0.936930	−	0.349516i	$-0.886346\pi$
$383$		−	2.00675e6i		−	0.699032i	0.936930	−	0.349516i	$-0.113654\pi$
$384$	−1.58924e6	−	1.32479e6i	−0.549999	−	0.458477i
$385$	1.47439e6	−	1.83107e6i	0.506943	−	0.629584i
$386$		−	478543.i		−	0.163475i
$387$	−1.25819e6	+	230263.i	−0.427039	+	0.0781531i
$388$	−3.71104e6			−1.25146
$389$		−	997047.i		−	0.334073i	−0.985951	−	0.167037i	$-0.946580\pi$
$389$		−	997047.i		−	0.334073i	0.985951	−	0.167037i	$-0.0534198\pi$
$390$	282958.	+	235873.i	0.0942021	+	0.0785266i
$391$			4.63759e6i			1.53409i
$392$	2.67680e6			0.879834
$393$	1.94373e6	+	1.62029e6i	0.634825	+	0.529188i
$394$	142182.			0.0461427
$395$	2.65910e6			0.857517
$396$	2.63573e6	+	1.42931e6i	0.844622	+	0.458023i
$397$	−5.07653e6			−1.61656			−0.808278	−	0.588801i	$-0.799600\pi$
$397$	−5.07653e6			−1.61656			−0.808278	+	0.588801i	$0.799600\pi$
$398$	783756.			0.248012
$399$	3.63613e6	+	3.03107e6i	1.14342	+	0.953156i
$400$	−565753.			−0.176798
$401$			4.56530e6i			1.41778i	0.705320	+	0.708889i	$0.250803\pi$
$401$			4.56530e6i			1.41778i	−0.705320	+	0.708889i	$0.749197\pi$
$402$	211189.	+	176047.i	0.0651789	+	0.0543329i
$403$		−	7.27383e6i		−	2.23100i
$404$	5.64058e6			1.71937
$405$	522821.	+	1.38054e6i	0.158386	+	0.418227i
$406$		−	437981.i		−	0.131868i
$407$	−45498.2	+	56505.2i	−0.0136147	+	0.0169084i
$408$	−1.04110e6	−	867857.i	−0.309629	−	0.258106i
$409$		−	614997.i		−	0.181788i	−0.995861	−	0.0908939i	$-0.971028\pi$
$409$		−	614997.i		−	0.181788i	0.995861	−	0.0908939i	$-0.0289724\pi$
$410$		−	292461.i		−	0.0859227i
$411$	−2.22675e6	+	2.67125e6i	−0.650229	+	0.780028i
$412$	2.43038e6			0.705394
$413$	−6.50896e6			−1.87774
$414$	−1.00302e6	+	183564.i	−0.287613	+	0.0526365i
$415$		−	1.99838e6i		−	0.569584i
$416$			2.75361e6i			0.780133i
$417$	1.37363e6	−	1.64784e6i	0.386839	−	0.464060i
$418$	−453600.	−	365240.i	−0.126979	−	0.102244i
$419$			4.21998e6i			1.17429i	0.809482	+	0.587144i	$0.199748\pi$
$419$			4.21998e6i			1.17429i	−0.809482	+	0.587144i	$0.800252\pi$
$420$	2.15662e6	+	1.79775e6i	0.596554	+	0.497286i
$421$	−98362.5			−0.0270473			−0.0135237	−	0.999909i	$-0.504305\pi$
$421$	−98362.5			−0.0270473			−0.0135237	+	0.999909i	$0.504305\pi$
$422$		−	351553.i		−	0.0960971i
$423$	−1.74224e6	+	318849.i	−0.473430	+	0.0866432i
$424$		−	371073.i		−	0.100241i
$425$	−773452.			−0.207712
$426$	−565923.	+	678893.i	−0.151089	+	0.181250i
$427$	−1.40984e6			−0.374196
$428$	3.72182e6			0.982079
$429$	−1.03880e6	−	5.17782e6i	−0.272514	−	1.35832i
$430$	147350.			0.0384309
$431$	−534145.			−0.138505			−0.0692526	−	0.997599i	$-0.522061\pi$
$431$	−534145.			−0.138505			−0.0692526	+	0.997599i	$0.522061\pi$
$432$	−1.68553e6	+	2.98604e6i	−0.434538	+	0.769814i
$433$	−1.23870e6			−0.317502			−0.158751	−	0.987319i	$-0.550747\pi$
$433$	−1.23870e6			−0.317502			−0.158751	+	0.987319i	$0.550747\pi$
$434$			2.26078e6i			0.576149i
$435$	416541.	−	499691.i	0.105544	−	0.126613i
$436$			5.59327e6i			1.40912i
$437$	−4.85665e6			−1.21656
$438$	−35681.0	+	42803.7i	−0.00888694	+	0.0106609i
$439$		−	1.47738e6i		−	0.365874i	−0.983125	−	0.182937i	$-0.941439\pi$
$439$		−	1.47738e6i		−	0.365874i	0.983125	−	0.182937i	$-0.0585605\pi$
$440$	−549038.	−	442087.i	−0.135198	−	0.108862i
$441$	−1.66664e6	−	9.10674e6i	−0.408079	−	2.22980i
$442$			1.16977e6i			0.284804i
$443$		−	2.05767e6i		−	0.498158i	−0.968483	−	0.249079i	$-0.919872\pi$
$443$		−	2.05767e6i		−	0.498158i	0.968483	−	0.249079i	$-0.0801278\pi$
$444$	−66551.2	−	55476.9i	−0.0160213	−	0.0133553i
$445$	−225320.			−0.0539387
$446$	777954.			0.185190
$447$	2.78679e6	+	2.32306e6i	0.659684	+	0.549911i
$448$			5.93158e6i			1.39629i
$449$		−	2.78549e6i		−	0.652058i	−0.945360	−	0.326029i	$-0.894289\pi$
$449$		−	2.78549e6i		−	0.652058i	0.945360	−	0.326029i	$-0.105711\pi$
$450$	−30614.6	−	167283.i	−0.00712685	−	0.0389421i
$451$	−2.62949e6	+	3.26562e6i	−0.608738	+	0.756005i
$452$		−	2.06171e6i		−	0.474659i
$453$	925891.	−	1.11072e6i	0.211990	−	0.254307i
$454$	−98904.5			−0.0225204
$455$		−	4.94515e6i		−	1.11983i
$456$	908851.	−	1.09028e6i	0.204682	−	0.245541i
$457$		−	2.92752e6i		−	0.655707i	−0.944729	−	0.327854i	$-0.893675\pi$
$457$		−	2.92752e6i		−	0.655707i	0.944729	−	0.327854i	$-0.106325\pi$
$458$	−923863.			−0.205799
$459$	−2.30432e6	+	4.08227e6i	−0.510519	+	0.904419i
$460$	−2.88051e6			−0.634710
$461$	−7.30999e6			−1.60201			−0.801004	−	0.598659i	$-0.795700\pi$
$461$	−7.30999e6			−1.60201			−0.801004	+	0.598659i	$0.795700\pi$
$462$	322870.	+	1.60932e6i	0.0703757	+	0.350783i
$463$	−2.05913e6			−0.446406			−0.223203	−	0.974772i	$-0.571651\pi$
$463$	−2.05913e6			−0.446406			−0.223203	+	0.974772i	$0.571651\pi$
$464$	1.51104e6			0.325822
$465$	−2.15011e6	+	2.57932e6i	−0.461136	+	0.553188i
$466$	964415.			0.205731
$467$			5.56483e6i			1.18076i	0.807127	+	0.590378i	$0.201021\pi$
$467$			5.56483e6i			1.18076i	−0.807127	+	0.590378i	$0.798979\pi$
$468$	6.20404e6	−	1.13541e6i	1.30936	−	0.239628i
$469$		−	3.69088e6i		−	0.774814i
$470$	204039.			0.0426057
$471$	−3.27733e6	−	2.73198e6i	−0.680720	−	0.567446i
$472$			1.95168e6i			0.403231i
$473$	−1.64532e6	−	1.32482e6i	−0.338140	−	0.272272i
$474$	−1.18878e6	+	1.42609e6i	−0.243028	+	0.291542i
$475$		−	809987.i		−	0.164719i
$476$			8.91565e6i			1.80358i
$477$	−1.26243e6	+	231039.i	−0.254045	+	0.0464931i
$478$	−1.32160e6			−0.264565
$479$	7.74294e6			1.54194			0.770969	−	0.636872i	$-0.219772\pi$
$479$	7.74294e6			1.54194			0.770969	+	0.636872i	$0.219772\pi$
$480$	813955.	−	976437.i	0.161249	−	0.193438i
$481$			152603.i			0.0300746i
$482$		−	1.81313e6i		−	0.355477i
$483$	1.05143e7	+	8.76470e6i	2.05075	+	1.70950i
$484$	1.05636e6	+	4.83771e6i	0.204973	+	0.938700i
$485$		−	3.01748e6i		−	0.582493i
$486$	−974125.	−	336797.i	−0.187078	−	0.0646811i
$487$	5.59877e6			1.06972			0.534860	−	0.844940i	$-0.320364\pi$
$487$	5.59877e6			1.06972			0.534860	+	0.844940i	$0.320364\pi$
$488$			422733.i			0.0803557i
$489$	431352.	+	359573.i	0.0815754	+	0.0680010i
$490$			1.06652e6i			0.200668i
$491$	6.70479e6			1.25511			0.627555	−	0.778573i	$-0.284056\pi$
$491$	6.70479e6			1.25511			0.627555	+	0.778573i	$0.284056\pi$
$492$	−3.84621e6	−	3.20619e6i	−0.716342	−	0.597141i
$493$	2.06577e6			0.382793
$494$	−1.22503e6			−0.225855
$495$	−1.16218e6	+	2.14313e6i	−0.213187	+	0.393130i
$496$	−7.79972e6			−1.42356
$497$	1.18647e7			2.15460
$498$	1.07174e6	+	893400.i	0.193649	+	0.161426i
$499$	1.02366e7			1.84036			0.920181	−	0.391494i	$-0.128042\pi$
$499$	1.02366e7			1.84036			0.920181	+	0.391494i	$0.128042\pi$
$500$		−	480409.i		−	0.0859382i
$501$	−5.06016e6	−	4.21813e6i	−0.900678	−	0.750803i
$502$			1.68837e6i			0.299025i
$503$	−6.20531e6			−1.09356			−0.546781	−	0.837276i	$-0.684147\pi$
$503$	−6.20531e6			−1.09356			−0.546781	+	0.837276i	$0.684147\pi$
$504$	−3.93520e6	+	720187.i	−0.690066	+	0.126290i
$505$			4.58641e6i			0.800284i
$506$	−1.31164e6	−	1.05614e6i	−0.227739	−	0.183376i
$507$	−4.08707e6	−	3.40697e6i	−0.706142	−	0.588638i
$508$		−	1.50872e6i		−	0.259388i
$509$			9.84568e6i			1.68442i	0.539148	+	0.842211i	$0.318747\pi$
$509$			9.84568e6i			1.68442i	−0.539148	+	0.842211i	$0.681253\pi$
$510$	345781.	−	414806.i	0.0588675	−	0.0706186i
$511$	748063.			0.126732
$512$	4.98787e6			0.840892
$513$	−4.27510e6	−	2.41317e6i	−0.717221	−	0.404850i
$514$			403315.i			0.0673344i
$515$			1.97617e6i			0.328326i
$516$	1.61537e6	−	1.93784e6i	0.267085	−	0.320400i
$517$	−2.27830e6	−	1.83450e6i	−0.374873	−	0.301850i
$518$		−	47430.6i		−	0.00776666i
$519$	−3.87928e6	−	3.23376e6i	−0.632169	−	0.526974i
$520$	−1.48278e6			−0.240474
$521$		−	2.35088e6i		−	0.379434i	−0.981839	−	0.189717i	$-0.939243\pi$
$521$		−	2.35088e6i		−	0.379434i	0.981839	−	0.189717i	$-0.0607570\pi$
$522$	81766.8	+	446785.i	0.0131341	+	0.0717667i
$523$		−	2.26028e6i		−	0.361334i	−0.983544	−	0.180667i	$-0.942174\pi$
$523$		−	2.26028e6i		−	0.361334i	0.983544	−	0.180667i	$-0.0578256\pi$
$524$	−4.99107e6			−0.794082
$525$	−1.46177e6	+	1.75357e6i	−0.231462	+	0.277667i
$526$	1.77308e6			0.279424
$527$	−1.06631e7			−1.67247
$528$	−5.55217e6	+	1.11390e6i	−0.866718	+	0.173885i
$529$	−7.60723e6			−1.18192
$530$	147847.			0.0228624
$531$	6.63981e6	−	1.21516e6i	1.02193	−	0.187024i
$532$	−9.33679e6			−1.43027
$533$			8.81942e6i			1.34469i
$534$	100732.	−	120840.i	0.0152867	−	0.0183383i
$535$			3.02625e6i			0.457109i
$536$	−1.10669e6			−0.166385
$537$	−4.65858e6	+	5.58853e6i	−0.697136	+	0.836299i
$538$			1.24286e6i			0.185126i
$539$	9.58899e6	−	1.19088e7i	1.42168	−	1.76561i
$540$	−2.53559e6	−	1.43127e6i	−0.374192	−	0.211221i
$541$		−	1.28358e7i		−	1.88551i	−0.333488	−	0.942754i	$-0.608226\pi$
$541$		−	1.28358e7i		−	1.88551i	0.333488	−	0.942754i	$-0.391774\pi$
$542$			1.90117e6i			0.277985i
$543$	−598171.	−	498633.i	−0.0870614	−	0.0725741i
$544$	4.03668e6			0.584826
$545$	−4.54794e6			−0.655878
$546$	2.65211e6	+	2.21079e6i	0.380723	+	0.317370i
$547$		−	1.69453e6i		−	0.242147i	−0.992644	−	0.121074i	$-0.961366\pi$
$547$		−	1.69453e6i		−	0.242147i	0.992644	−	0.121074i	$-0.0386337\pi$
$548$		−	6.85919e6i		−	0.975712i
$549$	1.43818e6	−	263203.i	0.203649	−	0.0372701i
$550$	176141.	−	218753.i	0.0248287	−	0.0308353i
$551$			2.16335e6i			0.303562i
$552$	2.62805e6	−	3.15266e6i	0.367101	−	0.440382i
$553$	2.49232e7			3.46570
$554$		−	1.85172e6i		−	0.256331i
$555$	45108.8	−	54113.4i	0.00621625	−	0.00745714i
$556$			4.23129e6i			0.580478i
$557$	−1.93379e6			−0.264102			−0.132051	−	0.991243i	$-0.542156\pi$
$557$	−1.93379e6			−0.264102			−0.132051	+	0.991243i	$0.542156\pi$
$558$	−422067.	−	2.30623e6i	−0.0573846	−	0.313558i
$559$	−4.44349e6			−0.601443
$560$	−5.30268e6			−0.714538
$561$	−7.59048e6	+	1.52284e6i	−1.01827	+	0.204290i
$562$	2.71540e6			0.362654
$563$	9.03918e6			1.20187			0.600936	−	0.799298i	$-0.294795\pi$
$563$	9.03918e6			1.20187			0.600936	+	0.799298i	$0.294795\pi$
$564$	2.23684e6	−	2.68336e6i	0.296099	−	0.355207i
$565$	1.67640e6			0.220930
$566$			403472.i			0.0529386i
$567$	4.90029e6	+	1.29395e7i	0.640124	+	1.69029i
$568$		−	3.55759e6i		−	0.462684i
$569$	1.77052e6			0.229256			0.114628	−	0.993408i	$-0.463432\pi$
$569$	1.77052e6			0.229256			0.114628	+	0.993408i	$0.463432\pi$
$570$	434399.	+	362114.i	0.0560018	+	0.0466830i
$571$		−	234510.i		−	0.0301003i	−0.999887	−	0.0150502i	$-0.995209\pi$
$571$		−	234510.i		−	0.0301003i	0.999887	−	0.0150502i	$-0.00479080\pi$
$572$	8.11295e6	+	6.53258e6i	1.03678	+	0.834823i
$573$	2.28931e6	−	2.74631e6i	0.291285	−	0.349432i
$574$		−	2.74117e6i		−	0.347261i
$575$		−	2.34217e6i		−	0.295426i
$576$	−1.10737e6	−	6.05082e6i	−0.139071	−	0.759903i
$577$	1.44098e7			1.80185			0.900927	−	0.433971i	$-0.142888\pi$
$577$	1.44098e7			1.80185			0.900927	+	0.433971i	$0.142888\pi$
$578$	124969.			0.0155590
$579$	4.26571e6	−	5.11724e6i	0.528805	−	0.634365i
$580$			1.28310e6i			0.158376i
$581$		−	1.87304e7i		−	2.30201i
$582$	1.61829e6	+	1.34900e6i	0.198038	+	0.165084i
$583$	−1.65086e6	−	1.32928e6i	−0.201159	−	0.161974i
$584$		−	224303.i		−	0.0272147i
$585$	923212.	+	5.04456e6i	0.111535	+	0.609444i
$586$	−1.89859e6			−0.228395
$587$		−	1.55870e6i		−	0.186710i	−0.995633	−	0.0933550i	$-0.970241\pi$
$587$		−	1.55870e6i		−	0.186710i	0.995633	−	0.0933550i	$-0.0297592\pi$
$588$	1.40260e7	+	1.16921e7i	1.67298	+	1.39459i
$589$		−	1.11668e7i		−	1.32630i
$590$	−777609.			−0.0919668
$591$	1.52040e6	+	1.26740e6i	0.179056	+	0.149261i
$592$	163636.			0.0191900
$593$	−1.34282e7			−1.56812			−0.784061	−	0.620684i	$-0.786855\pi$
$593$	−1.34282e7			−1.56812			−0.784061	+	0.620684i	$0.786855\pi$
$594$	−629805.	−	1.58140e6i	−0.0732386	−	0.183897i
$595$	−7.24940e6			−0.839478
$596$	−7.15588e6			−0.825177
$597$	8.38100e6	+	6.98638e6i	0.962409	+	0.802262i
$598$	−3.54232e6			−0.405075
$599$			1.15496e7i			1.31523i	0.753356	+	0.657613i	$0.228434\pi$
$599$			1.15496e7i			1.31523i	−0.753356	+	0.657613i	$0.771566\pi$
$600$	525798.	+	438304.i	0.0596267	+	0.0497046i
$601$		−	1.62504e6i		−	0.183517i	−0.995781	−	0.0917586i	$-0.970751\pi$
$601$		−	1.62504e6i		−	0.183517i	0.995781	−	0.0917586i	$-0.0292488\pi$
$602$	1.38108e6			0.155320
$603$	689051.	+	3.76507e6i	0.0771717	+	0.421677i
$604$			2.85208e6i			0.318104i
$605$	−3.93359e6	+	858933.i	−0.436919	+	0.0954050i
$606$	−2.45971e6	−	2.05041e6i	−0.272084	−	0.226808i
$607$			8.72795e6i			0.961480i	0.876863	+	0.480740i	$0.159632\pi$
$607$			8.72795e6i			0.961480i	−0.876863	+	0.480740i	$0.840368\pi$
$608$			4.22736e6i			0.463778i
$609$	3.90415e6	−	4.68350e6i	0.426563	−	0.511714i
$610$	−168430.			−0.0183271
$611$	−6.15298e6			−0.666780
$612$	−1.66447e6	−	9.09487e6i	−0.179637	−	0.981563i
$613$		−	313111.i		−	0.0336549i	−0.999858	−	0.0168274i	$-0.994643\pi$
$613$		−	313111.i		−	0.0336549i	0.999858	−	0.0168274i	$-0.00535659\pi$
$614$		−	1.06771e6i		−	0.114296i
$615$	2.60699e6	−	3.12739e6i	0.277940	−	0.333422i
$616$	−5.14601e6	−	4.14359e6i	−0.546411	−	0.439972i
$617$		−	8.80113e6i		−	0.930734i	−0.885118	−	0.465367i	$-0.845922\pi$
$617$		−	8.80113e6i		−	0.930734i	0.885118	−	0.465367i	$-0.154078\pi$
$618$	−1.05983e6	−	883470.i	−0.111626	−	0.0930509i
$619$	1.63079e7			1.71069			0.855345	−	0.518059i	$-0.173345\pi$
$619$	1.63079e7			1.71069			0.855345	+	0.518059i	$0.173345\pi$
$620$		−	6.62313e6i		−	0.691965i
$621$	−1.23620e7	−	6.97797e6i	−1.28635	−	0.726106i
$622$		−	422380.i		−	0.0437751i
$623$	−2.11188e6			−0.217996
$624$	−7.62724e6	+	9.14979e6i	−0.784162	+	0.940696i
$625$	390625.			0.0400000
$626$	1.89744e6			0.193523
$627$	−1.59477e6	−	7.94902e6i	−0.162005	−	0.807505i
$628$	8.41548e6			0.851490
$629$	223710.			0.0225454
$630$	−286944.	−	1.56790e6i	−0.0288036	−	0.157387i
$631$	−7.82635e6			−0.782502			−0.391251	−	0.920284i	$-0.627958\pi$
$631$	−7.82635e6			−0.782502			−0.391251	+	0.920284i	$0.627958\pi$
$632$		−	7.47310e6i		−	0.744232i
$633$	3.13374e6	−	3.75929e6i	0.310852	−	0.372904i
$634$		−	308054.i		−	0.0304371i
$635$	1.22676e6			0.120732
$636$	1.62082e6	−	1.94437e6i	0.158888	−	0.190606i
$637$		−	3.21619e7i		−	3.14046i
$638$	−470445.	+	584256.i	−0.0457570	+	0.0568266i
$639$	−1.21033e7	+	2.21503e6i	−1.17260	+	0.214599i
$640$			3.31815e6i			0.320219i
$641$			7.45408e6i			0.716554i	0.933615	+	0.358277i	$0.116636\pi$
$641$			7.45408e6i			0.716554i	−0.933615	+	0.358277i	$0.883364\pi$
$642$	−1.62299e6	−	1.35292e6i	−0.155410	−	0.129549i
$643$	−1.11841e7			−1.06678			−0.533391	−	0.845869i	$-0.679082\pi$
$643$	−1.11841e7			−1.06678			−0.533391	+	0.845869i	$0.679082\pi$
$644$	−2.69984e7			−2.56522
$645$	1.57567e6	+	1.31348e6i	0.149131	+	0.124315i
$646$			1.79585e6i			0.169312i
$647$			1.95797e7i			1.83885i	0.393266	+	0.919425i	$0.371345\pi$
$647$			1.95797e7i			1.83885i	−0.393266	+	0.919425i	$0.628655\pi$
$648$	3.87985e6	−	1.46933e6i	0.362976	−	0.137462i
$649$	8.68279e6	+	6.99142e6i	0.809185	+	0.651559i
$650$		−	590785.i		−	0.0548461i
$651$	−2.01526e7	+	2.41754e7i	−1.86371	+	2.23574i
$652$	−1.10762e6			−0.102040
$653$		−	2.00673e7i		−	1.84165i	−0.389980	−	0.920823i	$-0.627518\pi$
$653$		−	2.00673e7i		−	1.84165i	0.389980	−	0.920823i	$-0.372482\pi$
$654$	2.03321e6	−	2.43908e6i	0.185882	−	0.222988i
$655$		−	4.05828e6i		−	0.369606i
$656$	9.45706e6			0.858018
$657$	−763101.	+	139656.i	−0.0689714	+	0.0126225i
$658$	1.91241e6			0.172194
$659$	3.50415e6			0.314318			0.157159	−	0.987573i	$-0.449767\pi$
$659$	3.50415e6			0.314318			0.157159	+	0.987573i	$0.449767\pi$
$660$	−945870.	−	4.71462e6i	−0.0845224	−	0.421296i
$661$	1.37842e7			1.22710			0.613549	−	0.789657i	$-0.289741\pi$
$661$	1.37842e7			1.22710			0.613549	+	0.789657i	$0.289741\pi$
$662$	−431446.			−0.0382633
$663$	−1.04273e7	+	1.25088e7i	−0.921276	+	1.10518i
$664$	−5.61621e6			−0.494337
$665$		−	7.59183e6i		−	0.665721i
$666$	8854.84	+	48384.1i	0.000773562	+	0.00422685i
$667$			6.25557e6i			0.544443i
$668$	1.29934e7			1.12663
$669$	8.31895e6	+	6.93466e6i	0.718627	+	0.599045i
$670$		−	440939.i		−	0.0379483i
$671$	1.88069e6	+	1.51434e6i	0.161254	+	0.129842i
$672$	7.62903e6	−	9.15194e6i	0.651697	−	0.781789i
$673$		−	5.55465e6i		−	0.472736i	−0.971664	−	0.236368i	$-0.924043\pi$
$673$		−	5.55465e6i		−	0.472736i	0.971664	−	0.236368i	$-0.0759571\pi$
$674$			2.50672e6i			0.212548i
$675$	1.16378e6	−	2.06171e6i	0.0983130	−	0.174168i
$676$	1.04947e7			0.883289
$677$	6.79721e6			0.569979			0.284990	−	0.958531i	$-0.408010\pi$
$677$	6.79721e6			0.569979			0.284990	+	0.958531i	$0.408010\pi$
$678$	−749453.	+	899059.i	−0.0626138	+	0.0751128i
$679$		−	2.82822e7i		−	2.35418i
$680$			2.17370e6i			0.180271i
$681$	−1.05762e6	−	881631.i	−0.0873902	−	0.0728483i
$682$	2.42836e6	−	3.01583e6i	0.199918	−	0.248282i
$683$		−	1.92071e7i		−	1.57547i	−0.616017	−	0.787733i	$-0.711255\pi$
$683$		−	1.92071e7i		−	1.57547i	0.616017	−	0.787733i	$-0.288745\pi$
$684$	9.52448e6	−	1.74309e6i	0.778397	−	0.142456i
$685$	5.57727e6			0.454146
$686$			5.58647e6i			0.453239i
$687$	−9.87922e6	−	8.23529e6i	−0.798603	−	0.665713i
$688$			4.76475e6i			0.383768i
$689$	−4.45846e6			−0.357797
$690$	1.25612e6	+	1.04710e6i	0.100440	+	0.0837267i
$691$	−6.15718e6			−0.490554			−0.245277	−	0.969453i	$-0.578879\pi$
$691$	−6.15718e6			−0.490554			−0.245277	+	0.969453i	$0.578879\pi$
$692$	9.96115e6			0.790759
$693$	−1.08929e7	+	2.00871e7i	−0.861608	+	1.58886i
$694$	−2.36243e6			−0.186191
$695$	−3.44050e6			−0.270184
$696$	−1.40432e6	−	1.17064e6i	−0.109886	−	0.0916010i
$697$	1.29289e7			1.00805
$698$			613518.i			0.0476638i
$699$	1.03128e7	+	8.59676e6i	0.798336	+	0.665491i
$700$		−	4.50277e6i		−	0.347324i
$701$	6.48251e6			0.498251			0.249126	−	0.968471i	$-0.419857\pi$
$701$	6.48251e6			0.498251			0.249126	+	0.968471i	$0.419857\pi$
$702$	−3.11815e6	−	1.76011e6i	−0.238811	−	0.134802i
$703$			234277.i			0.0178789i
$704$	6.37125e6	−	7.91259e6i	0.484499	−	0.601709i
$705$	2.18186e6	+	1.81880e6i	0.165331	+	0.137820i
$706$		−	4.26789e6i		−	0.322256i
$707$			4.29874e7i			3.23439i
$708$	−8.52478e6	+	1.02265e7i	−0.639146	+	0.766733i
$709$	1.16281e7			0.868743			0.434371	−	0.900734i	$-0.356971\pi$
$709$	1.16281e7			0.868743			0.434371	+	0.900734i	$0.356971\pi$
$710$	1.41745e6			0.105527
$711$	−2.54242e7	+	4.65292e6i	−1.88614	+	0.345185i
$712$			633237.i			0.0468130i
$713$		−	3.22902e7i		−	2.37874i
$714$	3.24093e6	−	3.88788e6i	0.237916	−	0.285409i
$715$	−5.31170e6	+	6.59671e6i	−0.388569	+	0.482572i
$716$		−	1.43501e7i		−	1.04610i
$717$	−1.41324e7	−	1.17807e7i	−1.02664	−	0.855805i
$718$	384232.			0.0278152
$719$			3.29440e6i			0.237659i	0.992915	+	0.118830i	$0.0379142\pi$
$719$			3.29440e6i			0.237659i	−0.992915	+	0.118830i	$0.962086\pi$
$720$	5.40928e6	−	989960.i	0.388873	−	0.0711683i
$721$			1.85222e7i			1.32695i
$722$	891918.			0.0636769
$723$	1.61622e7	−	1.93885e7i	1.14989	−	1.37943i
$724$	1.53597e6			0.108902
$725$	−1.04330e6			−0.0737163
$726$	1.29791e6	−	2.49360e6i	0.0913908	−	0.175584i
$727$	1.20758e7			0.847384			0.423692	−	0.905806i	$-0.360734\pi$
$727$	1.20758e7			0.847384			0.423692	+	0.905806i	$0.360734\pi$
$728$	−1.38978e7			−0.971889
$729$	−7.41448e6	−	1.22848e7i	−0.516728	−	0.856150i
$730$	89369.2			0.00620699
$731$			6.51397e6i			0.450871i
$732$	−1.84646e6	+	2.21506e6i	−0.127369	+	0.152794i
$733$			1.20720e7i			0.829885i	0.909848	+	0.414943i	$0.136198\pi$
$733$			1.20720e7i			0.829885i	−0.909848	+	0.414943i	$0.863802\pi$
$734$	1.33909e6			0.0917424
$735$	−9.50692e6	+	1.14047e7i	−0.649114	+	0.778691i
$736$			1.22239e7i			0.831793i
$737$	−3.96445e6	+	4.92354e6i	−0.268853	+	0.333894i
$738$	511750.	+	2.79628e6i	0.0345874	+	0.188990i
$739$			1.38349e7i			0.931894i	0.884813	+	0.465947i	$0.154286\pi$
$739$			1.38349e7i			0.931894i	−0.884813	+	0.465947i	$0.845714\pi$
$740$			138951.i			0.00932790i
$741$	−1.30997e7	−	1.09199e7i	−0.876428	−	0.730588i
$742$	1.38574e6			0.0923999
$743$	1.72397e6			0.114567			0.0572833	−	0.998358i	$-0.481756\pi$
$743$	1.72397e6			0.114567			0.0572833	+	0.998358i	$0.481756\pi$
$744$	7.24888e6	+	6.04264e6i	0.480107	+	0.400216i
$745$		−	5.81851e6i		−	0.384079i
$746$			1.62908e6i			0.107175i
$747$	3.49678e6	+	1.91069e7i	0.229281	+	1.25282i
$748$	9.57650e6	−	1.18933e7i	0.625825	−	0.777225i
$749$			2.83644e7i			1.84743i
$750$	−174634.	+	209494.i	−0.0113364	+	0.0135994i
$751$	8.29378e6			0.536603			0.268301	−	0.963335i	$-0.413538\pi$
$751$	8.29378e6			0.536603			0.268301	+	0.963335i	$0.413538\pi$
$752$			6.59784e6i			0.425458i
$753$	−1.50500e7	+	1.80543e7i	−0.967276	+	1.16036i
$754$			1.57789e6i			0.101076i
$755$	−2.31905e6			−0.148062
$756$	−2.37656e7	−	1.34150e7i	−1.51232	−	0.853661i
$757$	2.35537e7			1.49389			0.746946	−	0.664884i	$-0.231519\pi$
$757$	2.35537e7			1.49389			0.746946	+	0.664884i	$0.231519\pi$
$758$	876631.			0.0554171
$759$	−4.61147e6	−	2.29855e7i	−0.290559	−	1.44827i
$760$	−2.27637e6			−0.142958
$761$	2.67767e7			1.67608			0.838042	−	0.545605i	$-0.183700\pi$
$761$	2.67767e7			1.67608			0.838042	+	0.545605i	$0.183700\pi$
$762$	−548436.	+	657915.i	−0.0342167	+	0.0410471i
$763$	−4.26269e7			−2.65077
$764$			7.05191e6i			0.437093i
$765$	7.39513e6	−	1.35339e6i	0.456869	−	0.0836123i
$766$		−	2.24705e6i		−	0.138369i
$767$	2.34495e7			1.43928
$768$	7.91986e6	+	6.60198e6i	0.484523	+	0.403897i
$769$			9.86685e6i			0.601676i	0.953675	+	0.300838i	$0.0972663\pi$
$769$			9.86685e6i			0.601676i	−0.953675	+	0.300838i	$0.902734\pi$
$770$	1.65093e6	−	2.05033e6i	0.100347	−	0.124623i
$771$	−3.59514e6	+	4.31280e6i	−0.217811	+	0.261291i
$772$			1.31399e7i			0.793506i
$773$			5.57255e6i			0.335433i	0.985835	+	0.167716i	$0.0536393\pi$
$773$			5.57255e6i			0.335433i	−0.985835	+	0.167716i	$0.946361\pi$
$774$	−1.40885e6	+	257835.i	−0.0845301	+	0.0154700i
$775$	5.38533e6			0.322076
$776$	−8.48028e6			−0.505541
$777$	422795.	−	507194.i	0.0251233	−	0.0301385i
$778$		−	1.11644e6i		−	0.0661280i
$779$			1.35396e7i			0.799399i
$780$	−7.76954e6	−	6.47666e6i	−0.457255	−	0.381167i
$781$	−1.58273e7	−	1.27442e7i	−0.928493	−	0.747626i
$782$			5.19290e6i			0.303664i
$783$	−3.10827e6	+	5.50651e6i	−0.181182	+	0.320976i
$784$	−3.44871e7			−2.00386
$785$			6.84270e6i			0.396327i
$786$	2.17647e6	+	1.81430e6i	0.125660	+	0.104750i
$787$		−	2.45700e7i		−	1.41406i	−0.707184	−	0.707029i	$-0.750035\pi$
$787$		−	2.45700e7i		−	1.41406i	0.707184	−	0.707029i	$-0.249965\pi$
$788$	−3.90406e6			−0.223976
$789$	1.89602e7	+	1.58052e7i	1.08430	+	0.903871i
$790$	2.97751e6			0.169741
$791$	1.57125e7			0.892903
$792$	6.02303e6	+	3.26617e6i	0.341194	+	0.185023i
$793$	5.07915e6			0.286819
$794$	−5.68441e6			−0.319988
$795$	1.58098e6	+	1.31790e6i	0.0887175	+	0.0739547i
$796$	−2.15206e7			−1.20385
$797$		−	2.36087e7i		−	1.31651i	−0.752793	−	0.658257i	$-0.771294\pi$
$797$		−	2.36087e7i		−	1.31651i	0.752793	−	0.658257i	$-0.228706\pi$
$798$	4.07153e6	+	3.39402e6i	0.226335	+	0.188672i
$799$			9.02002e6i			0.499851i
$800$	−2.03869e6			−0.112623
$801$	2.15433e6	−	394268.i	0.118640	−	0.0217125i
$802$			5.11196e6i			0.280641i
$803$	−997898.	−	803512.i	−0.0546132	−	0.0439747i
$804$	−5.79889e6	−	4.83394e6i	−0.316377	−	0.263731i
$805$		−	2.19527e7i		−	1.19398i
$806$		−	8.14481e6i		−	0.441615i
$807$	−1.10788e7	+	1.32904e7i	−0.598840	+	0.718380i
$808$	1.28896e7			0.694560
$809$	2.32655e7			1.24980			0.624901	−	0.780704i	$-0.285139\pi$
$809$	2.32655e7			1.24980			0.624901	+	0.780704i	$0.285139\pi$
$810$	585425.	+	1.54585e6i	0.0313515	+	0.0827858i
$811$			2.18935e7i			1.16886i	0.811445	+	0.584429i	$0.198682\pi$
$811$			2.18935e7i			1.16886i	−0.811445	+	0.584429i	$0.801318\pi$
$812$			1.20262e7i			0.640086i
$813$	−1.69469e7	+	2.03299e7i	−0.899217	+	1.07872i
$814$	−50946.3	+	63271.3i	−0.00269496	+	0.00334692i
$815$		−	900613.i		−	0.0474946i
$816$	1.34132e7	+	1.11812e7i	0.705193	+	0.587847i
$817$	−6.82167e6			−0.357549
$818$		−	688638.i		−	0.0359839i
$819$	8.65307e6	+	4.72816e7i	0.450776	+	2.46310i
$820$			8.03046e6i			0.417067i
$821$	−2.96969e7			−1.53764			−0.768819	−	0.639467i	$-0.779155\pi$
$821$	−2.96969e7			−1.53764			−0.768819	+	0.639467i	$0.779155\pi$
$822$	−2.49339e6	+	2.99112e6i	−0.128709	+	0.154402i
$823$	8.07668e6			0.415655			0.207828	−	0.978165i	$-0.433361\pi$
$823$	8.07668e6			0.415655			0.207828	+	0.978165i	$0.433361\pi$
$824$	5.55379e6			0.284952
$825$	3.83350e6	−	769096.i	0.196093	−	0.0393410i
$826$	−7.28836e6			−0.371689
$827$	−3.59285e6			−0.182674			−0.0913368	−	0.995820i	$-0.529114\pi$
$827$	−3.59285e6			−0.182674			−0.0913368	+	0.995820i	$0.529114\pi$
$828$	2.75412e7	−	5.04035e6i	1.39607	−	0.255496i
$829$	6.73661e6			0.340451			0.170226	−	0.985405i	$-0.445550\pi$
$829$	6.73661e6			0.340451			0.170226	+	0.985405i	$0.445550\pi$
$830$		−	2.23767e6i		−	0.112746i
$831$	1.65062e7	−	1.98011e7i	0.829171	−	0.994690i
$832$		−	2.13694e7i		−	1.07025i
$833$	−4.71480e7			−2.35424
$834$	1.53812e6	−	1.84516e6i	0.0765727	−	0.0918582i
$835$			1.05650e7i			0.524390i
$836$	1.24551e7	+	1.00289e7i	0.616353	+	0.496290i
$837$	1.60444e7	−	2.84237e7i	0.791605	−	1.40238i
$838$			4.72529e6i			0.232444i
$839$		−	6.92962e6i		−	0.339863i	−0.985456	−	0.169932i	$-0.945645\pi$
$839$		−	6.92962e6i		−	0.339863i	0.985456	−	0.169932i	$-0.0543547\pi$
$840$	4.92819e6	+	4.10813e6i	0.240985	+	0.200884i
$841$	−1.77247e7			−0.864148
$842$	−110141.			−0.00535387
$843$	2.90368e7	+	2.42050e7i	1.40728	+	1.17310i
$844$			9.65304e6i			0.466453i
$845$			8.53333e6i			0.411128i
$846$	−1.95086e6	+	357029.i	−0.0937129	+	0.0171505i
$847$	−3.68687e7	+	8.05060e6i	−1.76583	+	0.385585i
$848$			4.78081e6i			0.228303i
$849$	−3.59653e6	+	4.31448e6i	−0.171244	+	0.205428i
$850$	−866067.			−0.0411154
$851$			677440.i			0.0320662i
$852$	1.55393e7	−	1.86412e7i	0.733384	−	0.879782i
$853$			2.62654e7i			1.23598i	0.786186	+	0.617990i	$0.212053\pi$
$853$			2.62654e7i			1.23598i	−0.786186	+	0.617990i	$0.787947\pi$
$854$	−1.57866e6			−0.0740701
$855$	1.41732e6	+	7.74445e6i	0.0663061	+	0.362306i
$856$	8.50492e6			0.396721
$857$	3.81241e7			1.77316			0.886580	−	0.462575i	$-0.153074\pi$
$857$	3.81241e7			1.77316			0.886580	+	0.462575i	$0.153074\pi$
$858$	−1.16319e6	−	5.79783e6i	−0.0539426	−	0.268873i
$859$	−6.39571e6			−0.295737			−0.147869	−	0.989007i	$-0.547241\pi$
$859$	−6.39571e6			−0.295737			−0.147869	+	0.989007i	$0.547241\pi$
$860$	−4.04598e6			−0.186543
$861$	2.44347e7	−	2.93124e7i	1.12331	−	1.34754i
$862$	−598105.			−0.0274163
$863$		−	1.61537e7i		−	0.738322i	−0.929365	−	0.369161i	$-0.879645\pi$
$863$		−	1.61537e7i		−	0.738322i	0.929365	−	0.369161i	$-0.120355\pi$
$864$	−6.07381e6	+	1.07602e7i	−0.276807	+	0.490383i
$865$			8.09950e6i			0.368060i
$866$	−1.38703e6			−0.0628478
$867$	1.33634e6	+	1.11397e6i	0.0603767	+	0.0503298i
$868$		−	6.20772e7i		−	2.79661i
$869$	−3.32469e7	−	2.67706e7i	−1.49349	−	1.20256i
$870$	466419.	−	559525.i	0.0208919	−	0.0250623i
$871$			1.32969e7i			0.593890i
$872$			1.27814e7i			0.569231i
$873$	5.28002e6	+	2.88508e7i	0.234477	+	1.28121i
$874$	−5.43820e6			−0.240811
$875$	3.66124e6			0.161662
$876$	979739.	−	1.17531e6i	0.0431370	−	0.0517480i
$877$			1.10339e7i			0.484427i	0.970223	+	0.242214i	$0.0778735\pi$
$877$			1.10339e7i			0.484427i	−0.970223	+	0.242214i	$0.922126\pi$
$878$		−	1.65429e6i		−	0.0724228i
$879$	−2.03024e7	−	1.69240e7i	−0.886287	−	0.738806i
$880$	7.07365e6	+	5.69573e6i	0.307919	+	0.247938i
$881$		−	322597.i		−	0.0140030i	−0.999975	−	0.00700149i	$-0.997771\pi$
$881$		−	322597.i		−	0.0140030i	0.999975	−	0.00700149i	$-0.00222866\pi$
$882$	−1.86620e6	−	1.01972e7i	−0.0807770	−	0.441377i
$883$	−1.88473e7			−0.813482			−0.406741	−	0.913543i	$-0.633335\pi$
$883$	−1.88473e7			−0.813482			−0.406741	+	0.913543i	$0.633335\pi$
$884$		−	3.21200e7i		−	1.38243i
$885$	−8.31526e6	−	6.93158e6i	−0.356876	−	0.297491i
$886$		−	2.30406e6i		−	0.0986075i
$887$	8.28004e6			0.353365			0.176683	−	0.984268i	$-0.443463\pi$
$887$	8.28004e6			0.353365			0.176683	+	0.984268i	$0.443463\pi$
$888$	−152079.	−	126773.i	−0.00647199	−	0.00539504i
$889$	1.14981e7			0.487947
$890$	−252301.			−0.0106769
$891$	7.36177e6	−	2.25245e7i	0.310662	−	0.950520i
$892$	−2.13612e7			−0.898906
$893$	−9.44610e6			−0.396391
$894$	3.12049e6	+	2.60123e6i	0.130581	+	0.108852i
$895$	1.16682e7			0.486908
$896$			3.11003e7i			1.29418i
$897$	−3.78794e7	−	3.15761e7i	−1.57189	−	1.31032i
$898$		−	3.11904e6i		−	0.129071i
$899$	−1.43834e7			−0.593555
$900$	840624.	+	4.59329e6i	0.0345936	+	0.189024i
$901$			6.53593e6i			0.268223i
$902$	−2.94435e6	+	3.65666e6i	−0.120496	+	0.149647i
$903$	1.47684e7	+	1.23109e7i	0.602720	+	0.502425i
$904$		−	4.71132e6i		−	0.191744i
$905$			1.24891e6i			0.0506886i
$906$	1.03676e6	−	1.24372e6i	0.0419622	−	0.0503386i
$907$	2.25383e6			0.0909711			0.0454855	−	0.998965i	$-0.485517\pi$
$907$	2.25383e6			0.0909711			0.0454855	+	0.998965i	$0.485517\pi$
$908$	2.71574e6			0.109314
$909$	−8.02534e6	−	4.38516e7i	−0.322147	−	1.76025i
$910$		−	5.53730e6i		−	0.221664i
$911$			2.96357e7i			1.18309i	0.806271	+	0.591547i	$0.201483\pi$
$911$			2.96357e7i			1.18309i	−0.806271	+	0.591547i	$0.798517\pi$
$912$	−1.17094e7	+	1.40468e7i	−0.466173	+	0.559230i
$913$	−2.01187e7	+	2.49859e7i	−0.798773	+	0.992014i
$914$		−	3.27807e6i		−	0.129794i
$915$	−1.80108e6	−	1.50138e6i	−0.0711182	−	0.0592840i
$916$	2.53677e7			0.998946
$917$		−	3.80374e7i		−	1.49378i
$918$	−2.58025e6	+	4.57109e6i	−0.101054	+	0.179025i
$919$		−	4.75315e6i		−	0.185649i	−0.995682	−	0.0928245i	$-0.970410\pi$
$919$		−	4.75315e6i		−	0.185649i	0.995682	−	0.0928245i	$-0.0295895\pi$
$920$	−6.58240e6			−0.256398
$921$	9.51751e6	−	1.14174e7i	0.369721	−	0.443525i
$922$	−8.18531e6			−0.317108
$923$	−4.27445e7			−1.65149
$924$	−8.86544e6	−	4.41892e7i	−0.341602	−	1.70269i
$925$	−112983.			−0.00434168
$926$	−2.30569e6			−0.0883637
$927$	−3.45792e6	−	1.88945e7i	−0.132165	−	0.722166i
$928$	5.44502e6			0.207553
$929$		−	1.77405e6i		−	0.0674415i	−0.999431	−	0.0337207i	$-0.989264\pi$
$929$		−	1.77405e6i		−	0.0674415i	0.999431	−	0.0337207i	$-0.0107357\pi$
$930$	−2.40757e6	+	2.88817e6i	−0.0912793	+	0.109500i
$931$		−	4.93751e7i		−	1.86696i
$932$	−2.64811e7			−0.998612
$933$	3.76508e6	−	4.51667e6i	0.141602	−	0.169869i
$934$			6.23118e6i			0.233724i
$935$	9.67052e6	+	7.78674e6i	0.361760	+	0.291291i
$936$	1.41771e7	−	2.59458e6i	0.528931	−	0.0968005i
$937$		−	112720.i		−	0.00419423i	−0.999998	−	0.00209712i	$-0.999332\pi$
$937$		−	112720.i		−	0.00419423i	0.999998	−	0.00209712i	$-0.000667534\pi$
$938$		−	4.13283e6i		−	0.153370i
$939$	2.02900e7	+	1.69137e7i	0.750963	+	0.626000i
$940$	−5.60255e6			−0.206807
$941$	2.06036e7			0.758522			0.379261	−	0.925290i	$-0.376178\pi$
$941$	2.06036e7			0.758522			0.379261	+	0.925290i	$0.376178\pi$
$942$	−3.66977e6	−	3.05911e6i	−0.134745	−	0.112323i
$943$			3.91515e7i			1.43374i
$944$		−	2.51449e7i		−	0.918375i
$945$	1.09078e7	−	1.93240e7i	0.397337	−	0.703911i
$946$	−1.84233e6	−	1.48345e6i	−0.0669329	−	0.0538947i
$947$		−	2.99712e7i		−	1.08600i	−0.839733	−	0.542999i	$-0.817289\pi$
$947$		−	2.99712e7i		−	1.08600i	0.839733	−	0.542999i	$-0.182711\pi$
$948$	3.26419e7	−	3.91579e7i	1.17965	−	1.41514i
$949$	−2.69501e6			−0.0971393
$950$		−	906977.i		−	0.0326052i
$951$	2.74598e6	−	3.29413e6i	0.0984569	−	0.118111i
$952$			2.03736e7i			0.728576i
$953$	2.28973e7			0.816679			0.408339	−	0.912830i	$-0.366108\pi$
$953$	2.28973e7			0.816679			0.408339	+	0.912830i	$0.366108\pi$
$954$	−1.41359e6	+	258704.i	−0.0502868	+	0.00920306i
$955$	−5.73398e6			−0.203445
$956$	3.62889e7			1.28419
$957$	−1.02387e7	+	2.05413e6i	−0.361380	+	0.0725018i
$958$	8.67010e6			0.305218
$959$	5.22746e7			1.83546
$960$	−6.31672e6	+	7.57766e6i	−0.221214	+	0.265373i
$961$	4.56153e7			1.59332
$962$			170876.i			0.00595310i
$963$	−5.29536e6	−	2.89346e7i	−0.184005	−	1.00543i
$964$			4.97854e7i			1.72548i
$965$	−1.06842e7			−0.369338
$966$	1.17733e7	+	9.81421e6i	0.405935	+	0.338386i
$967$			5.04187e7i			1.73391i	0.498390	+	0.866953i	$0.333925\pi$
$967$			5.04187e7i			1.73391i	−0.498390	+	0.866953i	$0.666075\pi$
$968$	2.41393e6	+	1.10549e7i	0.0828012	+	0.379198i
$969$	−1.60081e7	+	1.92037e7i	−0.547685	+	0.657014i
$970$		−	3.37881e6i		−	0.115301i
$971$			2.05230e7i			0.698543i	0.937022	+	0.349272i	$0.113571\pi$
$971$			2.05230e7i			0.698543i	−0.937022	+	0.349272i	$0.886429\pi$
$972$	2.67478e7	+	9.24785e6i	0.908075	+	0.313961i
$973$	−3.22471e7			−1.09196
$974$	6.26919e6			0.211745
$975$	5.26624e6	−	6.31748e6i	0.177414	−	0.212830i
$976$		−	5.44637e6i		−	0.183013i
$977$			3.88123e7i			1.30087i	0.759563	+	0.650434i	$0.225413\pi$
$977$			3.88123e7i			1.30087i	−0.759563	+	0.650434i	$0.774587\pi$
$978$	483003.	+	402630.i	0.0161474	+	0.0134604i
$979$	2.81720e6	+	2.26842e6i	0.0939421	+	0.0756426i
$980$		−	2.92847e7i		−	0.974039i
$981$	4.34837e7	−	7.95802e6i	1.44263	−	0.264017i
$982$	7.50764e6			0.248442
$983$			1.09680e7i			0.362031i	0.983480	+	0.181015i	$0.0579384\pi$
$983$			1.09680e7i			0.362031i	−0.983480	+	0.181015i	$0.942062\pi$
$984$	−8.78917e6	−	7.32663e6i	−0.289374	−	0.241222i
$985$		−	3.17443e6i		−	0.104250i
$986$	2.31313e6			0.0757718
$987$	2.04501e7	+	1.70472e7i	0.668195	+	0.557006i
$988$	3.36372e7			1.09630
$989$	−1.97257e7			−0.641270
$990$	−1.30134e6	+	2.39976e6i	−0.0421992	+	0.0778179i
$991$	1.70066e7			0.550090			0.275045	−	0.961431i	$-0.411307\pi$
$991$	1.70066e7			0.550090			0.275045	+	0.961431i	$0.411307\pi$
$992$	−2.81063e7			−0.906826
$993$	−4.61362e6	−	3.84590e6i	−0.148480	−	0.123773i
$994$	1.32855e7			0.426492
$995$		−	1.74986e7i		−	0.560331i
$996$	−2.94281e7	−	2.45312e7i	−0.939970	−	0.783556i
$997$		−	8.21167e6i		−	0.261634i	−0.991407	−	0.130817i	$-0.958240\pi$
$997$		−	8.21167e6i		−	0.261634i	0.991407	−	0.130817i	$-0.0417600\pi$
$998$	1.14623e7			0.364289
$999$	−336606.	+	596321.i	−0.0106711	+	0.0189046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.f.a.131.42	yes	80
3.2	odd	2	inner	165.6.f.a.131.40	yes	80
11.10	odd	2	inner	165.6.f.a.131.39	✓	80
33.32	even	2	inner	165.6.f.a.131.41	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.f.a.131.39	✓	80	11.10	odd	2	inner
165.6.f.a.131.40	yes	80	3.2	odd	2	inner
165.6.f.a.131.41	yes	80	33.32	even	2	inner
165.6.f.a.131.42	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.11974 q^{2} +(11.9738 + 9.98135i) q^{3} -30.7462 q^{4} -25.0000i q^{5} +(13.4076 + 11.1765i) q^{6} -234.320i q^{7} -70.2596 q^{8} +(43.7452 + 239.030i) q^{9} +O(q^{10})\)	\(q+1.11974 q^{2} +(11.9738 + 9.98135i) q^{3} -30.7462 q^{4} -25.0000i q^{5} +(13.4076 + 11.1765i) q^{6} -234.320i q^{7} -70.2596 q^{8} +(43.7452 + 239.030i) q^{9} -27.9936i q^{10} +(-251.688 + 312.577i) q^{11} +(-368.149 - 306.888i) q^{12} +844.172i q^{13} -262.378i q^{14} +(249.534 - 299.346i) q^{15} +905.205 q^{16} +1237.52 q^{17} +(48.9834 + 267.652i) q^{18} +1295.98i q^{19} +768.654i q^{20} +(2338.83 - 2805.70i) q^{21} +(-281.826 + 350.005i) q^{22} +3747.48i q^{23} +(-841.276 - 701.286i) q^{24} -625.000 q^{25} +945.255i q^{26} +(-1862.04 + 3298.74i) q^{27} +7204.43i q^{28} +1669.28 q^{29} +(279.414 - 335.190i) q^{30} -8616.52 q^{31} +3261.90 q^{32} +(-6133.61 + 1230.55i) q^{33} +1385.71 q^{34} -5857.99 q^{35} +(-1345.00 - 7349.26i) q^{36} +180.772 q^{37} +1451.16i q^{38} +(-8425.98 + 10108.0i) q^{39} +1756.49i q^{40} +10447.4 q^{41} +(2618.88 - 3141.67i) q^{42} +5263.72i q^{43} +(7738.44 - 9610.54i) q^{44} +(5975.75 - 1093.63i) q^{45} +4196.21i q^{46} +7288.78i q^{47} +(10838.8 + 9035.17i) q^{48} -38098.7 q^{49} -699.839 q^{50} +(14817.9 + 12352.1i) q^{51} -25955.1i q^{52} +5281.46i q^{53} +(-2085.01 + 3693.74i) q^{54} +(7814.42 + 6292.20i) q^{55} +16463.2i q^{56} +(-12935.6 + 15517.8i) q^{57} +1869.16 q^{58} -27778.1i q^{59} +(-7672.21 + 9203.74i) q^{60} -6016.73i q^{61} -9648.29 q^{62} +(56009.4 - 10250.4i) q^{63} -25314.1 q^{64} +21104.3 q^{65} +(-6868.06 + 1377.90i) q^{66} +15751.5 q^{67} -38049.1 q^{68} +(-37404.9 + 44871.6i) q^{69} -6559.44 q^{70} +50634.9i q^{71} +(-3073.52 - 16794.1i) q^{72} +3192.49i q^{73} +202.418 q^{74} +(-7483.64 - 6238.34i) q^{75} -39846.4i q^{76} +(73242.9 + 58975.4i) q^{77} +(-9434.93 + 11318.3i) q^{78} +106364. i q^{79} -22630.1i q^{80} +(-55221.7 + 20912.8i) q^{81} +11698.4 q^{82} +79935.2 q^{83} +(-71910.0 + 86264.7i) q^{84} -30938.1i q^{85} +5894.01i q^{86} +(19987.6 + 16661.6i) q^{87} +(17683.5 - 21961.5i) q^{88} -9012.82i q^{89} +(6691.30 - 1224.59i) q^{90} +197806. q^{91} -115221. i q^{92} +(-103173. - 86004.5i) q^{93} +8161.55i q^{94} +32399.5 q^{95} +(39057.5 + 32558.2i) q^{96} +120699. q^{97} -42660.8 q^{98} +(-85725.4 - 46487.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

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